diff --git "a/batch_s000003.csv" "b/batch_s000003.csv" new file mode 100644--- /dev/null +++ "b/batch_s000003.csv" @@ -0,0 +1,10428 @@ +source,target +" Our results suggest that envelope pollution by icy planetesimals has the potential to make gas giant formation with small cores possible; for example, gas giants with cores smaller than 1Mg can capture disc gas by 1Myr when Zy>0.7 for f=1 or when Z,>0.5 for f=0.01."," Our results suggest that envelope pollution by icy planetesimals has the potential to make gas giant formation with small cores possible; for example, gas giants with cores smaller than $1M_\oplus$ can capture disc gas by 1Myr when $Z_\mathrm{h} \geq 0.7$ for $f = 1$ or when $Z_\mathrm{h} \geq 0.5$ for $f = 0.01$." + We assumed that both Zi and 7i are constant with time., We assumed that both $Z_\mathrm{h}$ and $T_\mathrm{h}$ are constant with time. +" 'This may be oversimplification and questionable, especially in the phase of runaway gas accretion."," This may be oversimplification and questionable, especially in the phase of runaway gas accretion." +" When the critical core mass is attained, the accretion rate of disc gas is much higher than that of planetesimals."," When the critical core mass is attained, the accretion rate of disc gas is much higher than that of planetesimals." +" In an extreme case where the unpolluted outer envelope never exchanges material with the polluted lower envelope, the gas accretion results in increasing the mass only of the upper envelope."," In an extreme case where the unpolluted outer envelope never exchanges material with the polluted lower envelope, the gas accretion results in increasing the mass only of the upper envelope." + The lower envelope behaves like a part of the “core”., The lower envelope behaves like a part of the “core”. +" In this case, the envelope pollution does not resolve the problem of the slow formation of gas giants with small cores."," In this case, the envelope pollution does not resolve the problem of the slow formation of gas giants with small cores." +" In the other extreme case where the inner and outer envelopes exchange material instantaneously between each other via eddy diffusion, accreting fresh disc gas dilutes the polluted lower envelope, which results in decelerating the disc-gas accretion."," In the other extreme case where the inner and outer envelopes exchange material instantaneously between each other via eddy diffusion, accreting fresh disc gas dilutes the polluted lower envelope, which results in decelerating the disc-gas accretion." +" On the other hand, the dilution is inevitably accompanied by mass growth of the envelope, which accelerates the disc-gas accretion."," On the other hand, the dilution is inevitably accompanied by mass growth of the envelope, which accelerates the disc-gas accretion." +" Unfortunately, it is uncertain whether or not mixing occurs effectively, as follows."," Unfortunately, it is uncertain whether or not mixing occurs effectively, as follows." +" A characteristic time-scale of eddy diffusion, Teaay, is givenby where Πρ is the pressure scale-height and K,, is the coefficient of eddy diffusion."," A characteristic time-scale of eddy diffusion, $\tau_\mathrm{eddy}$ , is givenby where $H_p$ is the pressure scale-height and $K_\mathit{zz}$ is the coefficient of eddy diffusion." +" Estimated values ofTeaayare listed in Table 4, where we have used our numerical values of H, at the tropopause when Moore= Merit."," Estimated values of$\tau_\mathrm{eddy}$are listed in Table 4, where we have used our numerical values of $H_p$ at the tropopause when $M_\mathrm{core} = M_\mathrm{crit}$ ." + We have, We have +eo through transient outbursts. then 50 isolated. black holes per vear would be detectable as X-ray novae. so we reject this possibility since isolated X-ray novae have not been observed.,"go through transient outbursts, then 50 isolated black holes per year would be detectable as X-ray novae, so we reject this possibility since isolated X-ray novae have not been observed." + The greatest. uncertainty in our predictions is the ellicicney of black-hole accretion. with which we have parameterized our results.," The greatest uncertainty in our predictions is the efficiency of black-hole accretion, with which we have parameterized our results." + Most of the detectable black holes should reside in interstellar clouds that have higher densities: however. this leads to the problem of confusion with other X-ray sources such as the coronae of massive stars.," Most of the detectable black holes should reside in interstellar clouds that have higher densities; however, this leads to the problem of confusion with other X-ray sources such as the coronae of massive stars." + Some tests for whether an acereting object is a black hole are the following: 1) Is there high-enerey emission?, Some tests for whether an accreting object is a black hole are the following: 1) Is there high-energy emission? + Accreting black holes tend to show spectra which have power laws extending up to ~Q keV. (Grove et al., Accreting black holes tend to show spectra which have power laws extending up to $\sim 10^2$ keV (Grove et al. + 1998)., 1998). + 2) What is the nature of the variability?, 2) What is the nature of the variability? + Accreting black holes show no pulsations. show only QPOs with v«1 kllz. and show power spectra that cut olf around 500 Lz (Sunvaev Revnivisey 2000).," Accreting black holes show no pulsations, show only QPOs with $\nu < 1$ kHz, and show power spectra that cut off around 500 Hz (Sunyaev Revnivtsev 2000)." + 3) What is the mass?, 3) What is the mass? + Without a binary companion. the mass of an accreting object is cillicultἱ to measure: however. this might be achieved by carrying out astrometry of background stars to look for gravitational distortion bv the accreting object (Paczvisski 2001).," Without a binary companion, the mass of an accreting object is difficult to measure; however, this might be achieved by carrying out astrometry of background stars to look for gravitational distortion by the accreting object (Paczyńsski 2001)." + 4) What do other parts of the spectra look like?, 4) What do other parts of the spectra look like? + Accreting black holes can produce relativistic radio jets CMirabel Itodr(eguez 1999). and photoionisation of the surrounding gas might result in observable infrared lines (Maloney. €olgan Lollenbach 1997).," Accreting black holes can produce relativistic radio jets (Mirabel Rodrígguez 1999), and photoionisation of the surrounding gas might result in observable infrared lines (Maloney, Colgan Hollenbach 1997)." + There are several assumptions in our calculation that might. alleet the results., There are several assumptions in our calculation that might affect the results. + We have assumed that the accretion low is one-dimensional. and that the sonic point is at the accretion radius.," We have assumed that the accretion flow is one-dimensional, and that the sonic point is at the accretion radius." + We have also assumed that the accretion is ime steady: this may not be the case for higher accretion rates than we find for black holes accreting from the ISM. (c.g. Crindlay 1978)., We have also assumed that the accretion is time steady; this may not be the case for higher accretion rates than we find for black holes accreting from the ISM (e.g. Grindlay 1978). + Lo the black hole is moving slower than the sound speed at the accretion radius then the preheated region outside the accretion radius may have a chance to expand into the ISM. reducing the number density. and. thus reducing he accretion rate.," If the black hole is moving slower than the sound speed at the accretion radius then the preheated region outside the accretion radius may have a chance to expand into the ISM, reducing the number density, and thus reducing the accretion rate." + We have neglected mechanical feedback. which may occur if à jet or wind is developed.," We have neglected mechanical feedback, which may occur if a jet or wind is developed." + Recent work on non-radiating accretion [lows indicates that strong winds can be formed. which carry the bulk of the energy. outwards as mechanical rather than radiative energy (Blandford DBegelman 1999. leumenshehey. Abramowicz Naravan 2000. Llawley. Balbus Stone 2001).," Recent work on non-radiating accretion flows indicates that strong winds can be formed which carry the bulk of the energy outwards as mechanical rather than radiative energy (Blandford Begelman 1999, Igumenshchev, Abramowicz Narayan 2000, Hawley, Balbus Stone 2001)." + These authors argue that the acerction rate scales as Alxor., These authors argue that the accretion rate scales as $\dot M \propto r$. + H£ the outer radius is taken as iy. hen ALGO)~1O(ecyALG)~?.10TePALA).," If the outer radius is taken as $r_A$, then $\dot M (10 r_g) \sim 10 (v/c)^2 \dot M(r_A) \sim 2\times +10^{-7} v_{40}^{-2} \dot M(r_A)$." +" lU tbe outer radius is taken to be the cireularization radius. then Al(10r,)~10.CM9M.L)7707L?flkms+)U*?."," If the outer radius is taken to be the circularization radius, then $\dot M(10 r_g) \sim 10^{-3} +(M/9{\rm M}_\odot)^{-2/3} [(v^2+c_s^2)^{1/2}/40 {\rm km~s^{-1}}]^{-10/3}$." + Either of these cireunistances will make black holes loss visible. which in the formalism of this paper corresponds to a further reduction in the aceretion ellieieney.," Either of these circumstances will make black holes less visible, which in the formalism of this paper corresponds to a further reduction in the accretion efficiency." + Magnetic fields will likely av an important role as they are amplified by Hux-freezing. possibly heating the gas to virial temperatures (Leumenshchey Naravan 2001) and can transport angular momentum via the magnetorotational instability once the circularization radius is reached. mocdifving the dynamics of the accretion How.," Magnetic fields will likely play an important role as they are amplified by flux-freezing, possibly heating the gas to virial temperatures (Igumenshchev Narayan 2001) and can transport angular momentum via the magnetorotational instability once the circularization radius is reached, modifying the dynamics of the accretion flow." + We have not explored the dependence of the ellicieney on other xwameters. which may. result. for example. from changes in the gas density ancl angular momentum as a function of the accretion rate. so our extrapolation from estimated ellieiencies of black-hole X-ray binaries may be too optimistic.," We have not explored the dependence of the efficiency on other parameters, which may result, for example, from changes in the gas density and angular momentum as a function of the accretion rate, so our extrapolation from estimated efficiencies of black-hole X-ray binaries may be too optimistic." + The validity of these assumptions can be tested with 3-D radiation. SUID simulations of a black hole accreting from an inhomogeneous mecium. a daunting numerical problem.," The validity of these assumptions can be tested with 3-D radiation MHD simulations of a black hole accreting from an inhomogeneous medium, a daunting numerical problem." + Lt is possible that a population of intermediate-mass black holes (ENMBIIS) exist with larger masses around ΟΔΙΕ. the remnants of the first generation of star formation (Aladau Rees 2001).," It is possible that a population of intermediate-mass black holes (IMBHs) exist with larger masses around $250 {\rm M}_\odot$, the remnants of the first generation of star formation (Madau Rees 2001)." + The larger masses of these objects would result in vet larger aceretion rates ancl luminosities hy a factor of ~LO’. if they are distributed with same phase-space distribution as DAL. black holes.," The larger masses of these objects would result in yet larger accretion rates and luminosities by a factor of $\sim 10^3$, if they are distributed with same phase-space distribution as $9 {\rm M}_\odot$ black holes." + owe assume that ~10° ΠΛΗΡΗΣ reside in our galaxy. then we find that the number of detectable objects at high fluxes may comparable to OAL. black holes accreting at the same ellicieney. (Figure 3).," If we assume that $\sim 10^6$ IMBHs reside in our galaxy, then we find that the number of detectable objects at high fluxes may comparable to $9 {\rm M}_\odot$ black holes accreting at the same efficiency (Figure 3)." + However. if these objects reside in the halo or bulgee of the ogalaxy. the number detectable will be decreased significantInIv.," However, if these objects reside in the halo or bulge of the galaxy, the number detectable will be decreased significantly." + We acknowledge D. Bennett. L. Bildsten. O. Blaes. It. Blandford. J. Carpenter. D. Chernoll. C. Dubus. A. Esin. €. Eryer. J. Cuaincdlav. T. Ixallman. L. Ixoopmans. J. Ixrolik. Y. Lithwick. A. Melatos. S. Phinney. M. Rees. 1. Rutledge. N. Scoville. aud Ix. Sheth for useful conversations and ideas which greatly improved this work.," We acknowledge D. Bennett, L. Bildsten, O. Blaes, R. Blandford, J. Carpenter, D. Chernoff, G. Dubus, A. Esin, C. Fryer, J. Grindlay, T. Kallman, L. Koopmans, J. Krolik, Y. Lithwick, A. Melatos, S. Phinney, M. Rees, R. Rutledge, N. Scoville, and K. Sheth for useful conversations and ideas which greatly improved this work." + This work was supported in part by NSE AS'T-0096023. NASA NACG5-8506. and. Dol DI-EXGO3-92-I2140701.," This work was supported in part by NSF AST-0096023, NASA NAG5-8506, and DoE DE-FG03-92-ER40701." + Support for the work done by LA was provided by the National Acronautics and Space Administration through Chandra Postdoctoral Fellowship Award Number PEO-10013 issued by the Chandra X-ray Observatory Center. which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Acronautics Space Administration under contract NASS-39073.," Support for the work done by EA was provided by the National Aeronautics and Space Administration through Chandra Postdoctoral Fellowship Award Number PF0-10013 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-39073." +state. which are ealeulated by simulations without magnetic field irregularities.,"state, which are calculated by simulations without magnetic field irregularities." +" Ten solid lines Irom the bottom to the top are density distributions caleulated by simulations with magnetic field irregularities for time /= 2.500 to 25.000 wy” with an interval of 2.500 cw,. respectively."," Ten solid lines from the bottom to the top are density distributions calculated by simulations with magnetic field irregularities for time $t=$ 2,500 to 25,000 $\omega_p^{-1}$ with an interval of 2,500 $\omega_p^{-1}$, respectively." + Dotted vertical lines in Figures 11. and 12. show the forbidden distance. which are borders of the forbidden region calculated theoretically in Section 2.1. and shown in Figure 7..," Dotted vertical lines in Figures \ref{dhist6} and \ref{dhist18} show the forbidden distance, which are borders of the forbidden region calculated theoretically in Section \ref{sec:analy} and shown in Figure \ref{penet}." + We can see from Figure 11.. which shows the case for 6 GY cosmic ταν particles. (hat the density distribution inside and outside the forbidden region is greatly different.," We can see from Figure \ref{dhist6}, which shows the case for 6 GV cosmic ray particles, that the density distribution inside and outside the forbidden region is greatly different." + Out of (he region. there is a density bump around p=0.8 in the later time.," Out of the region, there is a density bump around $\rho=0.8$ in the later time." +" The densitv out of the forbidden region increases drastically with Gime and the bump is formed just outside the region,", The density out of the forbidden region increases drastically with time and the bump is formed just outside the region. + The bump is formed in (he following processes., The bump is formed in the following processes. + The particles penetrating [rom the outside of the flux rope edge are scattered by small-scale magnetic field irregularities between the Forbidden region aud (he [Iux rope edge. and changed their pitch angles.," The particles penetrating from the outside of the flux rope edge are scattered by small-scale magnetic field irregularities between the forbidden region and the flux rope edge, and changed their pitch angles." + These pitch angle changes can make the particles Fall into the (rap region. which is expressed as Equation (21)) and diawn in Figure 5..," These pitch angle changes can make the particles fall into the trap region, which is expressed as Equation \ref{Dregion}) ) and drawn in Figure \ref{trap}." + As a result. the particles are trapped between the forbidden region and the flux rope edge.," As a result, the particles are trapped between the forbidden region and the flux rope edge." + As the solid angle of the trap region near the forbidden region is larger (han that near the flux rope edge (see Figure 6)). cosmic rav particles tend to fall in the (trap region near the forbidden region. not near the edge.," As the solid angle of the trap region near the forbidden region is larger than that near the flux rope edge (see Figure \ref{trap_area}) ), cosmic ray particles tend to fall in the trap region near the forbidden region, not near the edge." + Accimulating these trapped particles. the bump in the density distribution is lormed.," Accumulating these trapped particles, the bump in the density distribution is formed." + Moreover. there is a small density drop just inside the flux rope edge.," Moreover, there is a small density drop just inside the flux rope edge." + The drop is formed in the following processes., The drop is formed in the following processes. + Since the solid angle of trap region is verv small just inside the flix rope edge as shown in Figure 6.. nearly particles cannot be trapped in Chis region.," Since the solid angle of trap region is very small just inside the flux rope edge as shown in Figure \ref{trap_area}, nearly particles cannot be trapped in this region." + Therefore. the cosmic ray particles in this region are distributed like (he steady state distribution without magnetic field irregularities (dashed line in Figure 11)).," Therefore, the cosmic ray particles in this region are distributed like the steady state distribution without magnetic field irregularities (dashed line in Figure \ref{dhist6}) )." + As the density bump is formed near the forbidden region. this fills in much of the densitv drop just inside the edge of the flux rope. which is why the small densitv drop is formed just inside the flux rope edge.," As the density bump is formed near the forbidden region, this fills in much of the density drop just inside the edge of the flux rope, which is why the small density drop is formed just inside the flux rope edge." + A major role of magnetic field inregularities outside of the forbidden region is to make the particles fall into the trap region by pitch angle scattering., A major role of magnetic field irregularities outside of the forbidden region is to make the particles fall into the trap region by pitch angle scattering. + Outside of the forbidden region. the effect of a finite Larmor radius is significant for density distribution.," Outside of the forbidden region, the effect of a finite Larmor radius is significant for density distribution." + Inside of (he forbidden region. the trapped particles just out of the forbidden region diffuse into the forbidden region by means of spatial diffusion due lo scattering bv magnetic field irregularities and a magnetic field line random walk. which is why the density distribution in the lorbidden region decreases monotonically toward the flux rope center.," Inside of the forbidden region, the trapped particles just out of the forbidden region diffuse into the forbidden region by means of spatial diffusion due to scattering by magnetic field irregularities and a magnetic field line random walk, which is why the density distribution in the forbidden region decreases monotonically toward the flux rope center." + Thus. a major role of magnetic field irregularities inside (he forbidden region is spatial diffusion toward the flix rope Fieure 12. shows the results for the case of 18 GV cosmic ravs particles.," Thus, a major role of magnetic field irregularities inside the forbidden region is spatial diffusion toward the flux rope Figure \ref{dhist18} shows the results for the case of 18 GV cosmic rays particles." + The bump in the density distribution appears while the peak of (he bump is located closer to the flux rope axis compared to the case of 6 GV cosmic ray. particles., The bump in the density distribution appears while the peak of the bump is located closer to the flux rope axis compared to the case of 6 GV cosmic ray particles. + This is because the effect of, This is because the effect of +the core in PA~0°.,the core in $\sim0\degr$. + Our VLBI image (Fig. 4)), Our VLBI image (Fig. \ref{fig:0749}) ) + reveals a dominant core. with an extension to the north. in roughly the direction of the previously detected VLBI jet.," reveals a dominant core, with an extension to the north, in roughly the direction of the previously detected VLBI jet." + The core shows an unusually high fractional polarization of ~9%. while no polarization was detected in the jet.," The core shows an unusually high fractional polarization of $\sim 9\%$, while no polarization was detected in the jet." + 0829--046 or O.J 049 is a οταν loud blazar (2). which shows rapid and large optical variability (?).., 0829+046 or OJ 049 is a $\gamma$ -ray loud blazar \citep{Dondi95} which shows rapid and large optical variability \citep{LillerLiller75}. + The 1.4 Gllz VLA images of ? and ο show a (wo-sided structure with an extended and curved region of emission (o (he southeast.," The 1.4 GHz VLA images of \citet{AntonucciUlv85} and \citet{Giroletti04a} + show a two-sided structure with an extended and curved region of emission to the southeast." + Previous VEDI images show a VLBI jet extending to the northeast (?).. clearly misaliened with the kpc-seale radio structure.," Previous VLBI images show a VLBI jet extending to the northeast \citep{Jorstad01}, clearly misaligned with the kpc-scale radio structure." + Our VLBI images (Fig. 5)), Our VLBI images (Fig. \ref{fig:0829}) ) + reveal the rich polarization structure of the VLBI jet. whose inferred D field geometry has remained roughly constant over about five vears.," reveal the rich polarization structure of the VLBI jet, whose inferred $B$ field geometry has remained roughly constant over about five years." + The predominant jel B field is longitudinal to the jet., The predominant jet $B$ field is longitudinal to the jet. + The polarization position angle for the knot 4 changes dramatically over the roughly five vears covered by our observations. and seems lo swing to remain perpendicular to the VLBI jet as this component propagates rom the core (making the dominant D field longitudinal essentially throughout the jet).," The polarization position angle for the knot K4 changes dramatically over the roughly five years covered by our observations, and seems to swing to remain perpendicular to the VLBI jet as this component propagates from the core (making the dominant $B$ field longitudinal essentially throughout the jet)." + Both Ix3 and Ix4 show appreciable increases in the degree of polarization accompanied by decreases in total intensity. suggesting Chis is associated with (he expansion of (hese components as thev evolve.," Both K3 and K4 show appreciable increases in the degree of polarization accompanied by decreases in total intensity, suggesting this is associated with the expansion of these components as they evolve." +These objects show significant polarization withpiv. > 1. except lor HE 1523-1155 lor which we have obtained pt = 0.349 + 0.08.,"These objects show significant polarization with$p$ ${\ge}$ 1, except for HE 1523-1155 for which we have obtained $p\%$ = 0.849 $\pm$ 0.08." + Reddening estimates £(B—V) range from 0.03 to 0.08 for these stars: the values of E(D—V) for the HE stars are taken from (2007)., Reddening estimates $E(B-V)$ range from 0.03 to 0.08 for these stars; the values of $E(B-V)$ for the HE stars are taken from \citet{beers07}. + A low carbon isotopic ratio (LC/PC < 10) for LEE 1027-2501 indicates that the star is on the first ascent of the giant braneh wherein the material (transferred. from the now unseen companion has been mixed into (he CN-burning region of the CI star or constitute a nuimor fraction of the envelop mass of the CIE star., A low carbon isotopic ratio $^{12}$ $^{13}$ C $<$ 10) for HE 1027-2501 indicates that the star is on the first ascent of the giant branch wherein the material transferred from the now unseen companion has been mixed into the CN-burning region of the CH star or constitute a minor fraction of the envelop mass of the CH star. + Such low values are believed to be due to convection which dredges up the products of internal CNO evele to the stellar atmosphere in (he ascending red giant branch (RGB)., Such low values are believed to be due to convection which dredges up the products of internal CNO cycle to the stellar atmosphere in the ascending red giant branch (RGB). + When the star reaches the AGB stage. fresh C may be supplied from the internal IHe-burning laver to the stellar surface. leading (to an increase of C/C ratio.," When the star reaches the AGB stage, fresh $^{12}$ C may be supplied from the internal He-burning layer to the stellar surface, leading to an increase of $^{12}$ $^{13}$ C ratio." + TE 13052-0001 shows enhancement of both r- ancl s-process elements including lead., HE $+$ 0007 shows enhancement of both $r$ - and $s$ -process elements including lead. + The second-peak s-process elements are more enhanced (han the first-peak s-process elements., The second-peak $s$ -process elements are more enhanced than the first-peak $s$ -process elements. + This is a low-metallicity and high-velocity object (V — 4217.8 3 L5 kms. P)its atmospheric parameters are consistent wilh a present location on the RGB (Goswamietal. (2006)))., This is a low-metallicity and high-velocity object $V_{r}$ = $+$ 217.8 $\pm$ 1.5 km $^{-1}$ ); its atmospheric parameters are consistent with a present location on the RGB \citet{goswami06}) ). + The star LP 625—44 is a carbon- ancl s-process-element-rich very metal-poor subgiant., The star LP $-$ 44 is a carbon- and $s$ -process-element-rich very metal-poor subgiant. + Abundance estimate derived using the O 7 triplet around 7770 shows excess of oxvgen by a factor of 10 (Aoki et al., Abundance estimate derived using the O $I$ triplet around 7770 shows excess of oxygen by a factor of 10 (Aoki et al. + 2002): ancl Na enhancement by about a factor of 50 in comparison to ILD 140283 (a metal-poor subgiant with normal abundance ratio) and a high Mg abundance ([Mg/Fe| = 1.12 z 0.24)., 2002); and Na enhancement by about a factor of 50 in comparison to HD 140283 (a metal-poor subgiant with normal abundance ratio) and a high Mg abundance ([Mg/Fe] = 1.12 $\pm$ 0.24). + High abundance of Na suggests. that hydrogen burning in the 7 Ne-rich laver in an AGB star must have produced (he abundance pattern of this object.," High abundance of Na suggests, that hydrogen burning in the $^{22}$ Ne-rich layer in an AGB star must have produced the abundance pattern of this object." + The Pb enhancement shown by LP 625—44 is not high enough to be placed in the group of lead stars., The Pb enhancement shown by LP $-$ 44 is not high enough to be placed in the group of lead stars. + The abundance ratio of s-process elements al (he second peak (La. Ce. and Nd) to that al the third peak (Pb) in LP 625-44 issignificantly higher (bv a factor of 5) than that in the s-process element-rich lead star TID 196944 (VanEcketal. (2001))).," The abundance ratio of $s$ -process elements at the second peak (La, Ce, and Nd) to that at the third peak (Pb) in LP 625-44 issignificantly higher (by a factor of 5) than that in the $s$ -process element-rich lead star HD 196944 \citet{van01}) )." + Unlike CID stars. the radial velocity of this object is low (e 30 km +) and the variation of the radial velocity is expected to be for about 200 davs (Aokietal. 2000)..," Unlike CH stars, the radial velocity of this object is low ${\sim}$ 30 km $^{-1}$ ) and the variation of the radial velocity is expected to be for about 200 days \citep{aoki00}. ." + Like LP 625-44. HE 1429-0551. and WE 1523-1155 are also low-velocity objects (~ —44.9 and ~ —46.03 kins +. respectively).," Like LP 625-44, HE 1429-0551, and HE 1523-1155 are also low-velocity objects ${\sim}$ $-$ 44.9 and ${\sim}$ $-$ 46.03 km $^{-1}$ , respectively)." + Both show high abundances of C. N. and Mg relative to Fe.," Both show high abundances of C, N, and Mg relative to Fe." + Estimated carbon isotopic ratio of C/C for LIE 1429-0551 is high ~30.τρ 200T).., Estimated carbon isotopic ratio of $^{12}$ $^{13}$ C for HE 1429-0551 is high $\sim ~30^{+20}_{-10}$ \citep{aoki07}. . + Such high ratios are generally noticed inC-N stars., Such high ratios are generally noticed inC-N stars. + With a marginal difference in the, With a marginal difference in the +Figure 4. presents a contour map of the outflow emission in theCO(6—5) line overlaved with the 8.6 GlIz radio continuum emission observed. toward IRAS 16562—3959 (?)..,Figure \ref{fig-outjet} presents a contour map of the outflow emission in the line overlayed with the 8.6 GHz radio continuum emission observed toward IRAS $-$ 3959 \citep{Guzman2010ApJ}. + It appears (hat the SE-NW outflow is associated with the string of radio sources. the peak position of the blue-shilted and red-shifted lobes being svimmetrically displaced Irom the bright central radio source.," It appears that the SE-NW outflow is associated with the string of radio sources, the peak position of the blue-shifted and red-shifted lobes being symmetrically displaced from the bright central radio source." +" The SE blueshifted and NW redshilted lobes extend up to 27 and ~32"" from the central radio source. respectively."," The SE blueshifted and NW redshifted lobes extend up to $\sim 27\arcsec$ and $\sim 32\arcsec$ from the central radio source, respectively." + The svmmetry axis of the SE-NW outflow is along a direction with a position angle of ~LO7*.. roughly the same as the PLA. of the svimmetry axis of the jet of 1107.," The symmetry axis of the SE-NW outflow is along a direction with a position angle of $\sim107$, roughly the same as the P.A. of the symmetry axis of the jet of $110$." +.. As noted in ?.. the radio lobes and the jet are not completely aligned. showing a small bending. which is also seen in the SE-NW outflow.," As noted in \citet{Guzman2010ApJ}, the radio lobes and the jet are not completely aligned, showing a small bending, which is also seen in the SE-NW outflow." + Possible bending mechanisms of protostellar jets are discussed in 2.. bul with the available data we can not discern between the various alternatives.," Possible bending mechanisms of protostellar jets are discussed in \citet{Fendt1998AA}, but with the available data we can not discern between the various alternatives." +" The spectroscopic signatures of the(493) andC4O(332) transitions suggest that the bulk of the molecular gas toward IRAS 16562-3959 is undergoing large-scale inward motions (e.g.ο,", The spectroscopic signatures of the and transitions suggest that the bulk of the molecular gas toward IRAS $-$ 3959 is undergoing large-scale inward motions \citep[e.g.][]{Sanhueza2010ApJ}. + Infalling motions traced by optically Chick molecular lines are expected to produce line profiles showing blue asvinimetry. whereas optically thin lines are expected to exhibit svamnietrical profiles (?)..," Infalling motions traced by optically thick molecular lines are expected to produce line profiles showing blue asymmetry, whereas optically thin lines are expected to exhibit symmetrical profiles \citep{Mardones1997ApJ}." + Figure 7 presents an image of the Two Micron. All Sky Survey (2\LASS. ?)) ἰν band emission across an 8.x8' region of the sky. centered near IRAS 16562—3959.," Figure \ref{fig-2mass} presents an image of the Two Micron All Sky Survey (2MASS, \citealt{Skrustskie2006AJ}) ) $K_s$ -band emission across an $8\arcmin\times8\arcmin$ region of the sky, centered near IRAS $-$ 3959." + Clearly seen toward (the center is diffuse emission along the SE-NW direction extending by more than 1.5 oon each side of the bright radio source., Clearly seen toward the center is diffuse emission along the SE-NW direction extending by more than $1.5$ on each side of the bright radio source. + The position angle of this diffuse A.-band emission, The position angle of this diffuse $K_s$ -band emission + 6.55+0.98 AL). 2.68+ L87+0.10 cmn? atmosphere., $6.55\pm 0.98$ $M_\oplus$ $2.68\pm 0.13$ $R_\oplus$ $1.87\pm 0.40$ $^{-3}$ atmosphere. + Another goal was to check for anv nou-periodicity iu the transit times. as a 1ieaus of discovering other plauets in the system. through the method of Tolman Murray (2005) aud Agol et al. (," Another goal was to check for any non-periodicity in the transit times, as a means of discovering other planets in the system, through the method of Holman Murray (2005) and Agol et al. (" +2005).,2005). + Supor-carths have frequently been fouud im pairs or even triples in compact arrangements (Lo Curto et al., Super-earths have frequently been found in pairs or even triples in compact arrangements (Lo Curto et al. + 2010). aud it would be interesting to know if GJ 121Lb is another such example.," 2010), and it would be interesting to know if GJ 1214b is another such example." + This paper is organized as follows., This paper is organized as follows. + Section 2. describes the observations aud data reduction., Section \ref{sec:obsred} describes the observations and data reduction. + Section 2. presents the licht. curve model. taking into account the effects of starspots.," Section \ref{sec:model} presents the light curve model, taking into account the effects of starspots." + Section [.[ discusses the method by which we estimated the model parameters aud their coufideuce intervals., Section \ref{sec:analysis} discusses the method by which we estimated the model parameters and their confidence intervals. + Section 5. discusses the results for the planet-to-star radius ratio., Section \ref{sec:radrat} discusses the results for the planet-to-star radius ratio. + Section 6.— preseuts two different iethods for determining the stellar radius (ancl hence the planetary radius). which eive discrepant results.," Section \ref{sec:radplanet} presents two different methods for determining the stellar radius (and hence the planetary radius), which give discrepant results." + Some possible resolutions of this discrepancy are discussed., Some possible resolutions of this discrepancy are discussed. + Section F presents our analysis of the measured trausit times. and constraints on the properties of a hvpothoetical second planet.," Section \ref{sec:timing} presents our analysis of the measured transit times, and constraints on the properties of a hypothetical second planet." + Finally. in Section &.. we discuss the nuplicatious of our analysis on the uuderstauding of CG 121tb and more broadly on ΑΓ dwarf trausit hosts.," Finally, in Section \ref{sec:disc}, we discuss the implications of our analysis on the understanding of GJ 1214b and more broadly on M dwarf transit hosts." + Om data were gathered during the 2009 and 2010 observing seasons., Our data were gathered during the 2009 and 2010 observing seasons. + Thirteen transits were observed witli the 1.212 telescope at the Fred WWhipple Observatory (FLWO) ou Mount IHopkius. Arizona. using Neplercam aud a Sloan z' filter.," Thirteen transits were observed with the 1.2m telescope at the Fred Whipple Observatory (FLWO) on Mount Hopkins, Arizona, using Keplercam and a Sloan $z'$ filter." + The first two of the FIAVO transits were already presented by Charbonneau et 20001 those data havebeen, The first two of the FLWO transits were already presented by Charbonneau et (2009); those data havebeen +The star ΠΟ 81032 was observed and detected by the ROSAT PSPC detector duriue the ROSAT (RASS) phase over a 2-dav period from 1990 November 10 to 12.,The star HD 81032 was observed and detected by the ROSAT PSPC detector during the ROSAT All-Sky-Survey (RASS) phase over a 2-day period from 1990 November 10 to 12. + The exposure tine was 50] s. and was accumulated im 26 separate short scans of this region of ska.," The exposure time was 501 s, and was accumulated in 26 separate short scans of this region of sky." + The PSPC had an energy range from 0.1 - 2.1 keV with a (low) spectral resolution. (AL/Ez0.12 at 1 keV).," The PSPC had an energy range from 0.1 - 2.4 keV with a (low) spectral resolution $\Delta E/E +\approx 0.42$ at 1 keV)." + A full description of the X-ray telescope aud detectors cau be found in Trimnuper (1983) aud in Pfefferiiaun ct al.(1987)., A full description of the X-ray telescope and detectors can be found in Trümmper (1983) and in Pfeffermann et al.(1987). + The ROSAT X-ray data for ΠΟ 81032 were obtained from the public archives. the relevant RASS dataset beige rs932025n00.," The ROSAT X-ray data for HD 81032 were obtained from the public archives, the relevant RASS dataset being rs932025n00." + Source spectra for IID 81032 were accunmlated from ou-source counts obtained from a circular region on the sky centered ou the N-ray peak and having a radius of 3.85 arcuun., Source spectra for HD 81032 were accumulated from on-source counts obtained from a circular region on the sky centered on the X-ray peak and having a radius of 3.85 arcmin. + The backeround was acctuuulated from several neighhborimg regions at ucarly the same offset from the source., The background was accumulated from several neighboring regions at nearly the same offset from the source. + Photometric curves corresponding to the four ruis were taken., Photometric light curves corresponding to the four observing runs were taken. + Figure 1. shows the V baxd differential lightlight. curves of he star ITD 81032 atobserving different 0ος»., Figure \ref{ligper.fig} shows the V band differential light curves of the star HD 81032 at different epochs. + We did not fiud any siguificaut variatious m the comparison star (see below)., We did not find any significant variations in the comparison star (see below). + The vearly mean of he staudard deviationte) between the ierent measures of comparison aud check stars iu he D. V alc R filters was found to be 0.011. 0.01 alc LOLOL. respectively.," The yearly mean of the standard $\sigma$ ) between the different measures of comparison and check stars in the B, V and R filters was found to be 0.011, 0.01 and 0.01, respectively." + Each lieb curve shown in Fi, Each light curve shown in Fig. +e. 1 was allaIwsed for periodicity., \ref{ligper.fig} was analysed for periodicity. + To find a period frou unequaIv spaced data. we used the CLEAN aexOxitlun (Rolxrts et al.," To find a period from unequally spaced data, we used the CLEAN algorithm (Roberts et al." + 1987) in Starlink’s PERIOD sotware., 1987) in Starlink's PERIOD software. + The obtaiied this method is shown in the mset of cach panel of Fig., The power spectrum obtained using this method is shown in the inset of each panel of Fig. + 1 wit1 the power spectudetermined.," \ref{ligper.fig} + along with the period determined." + The usingCLEAN: power spectra presented were obtained after LOO iterationsalong wih a period of 0.1., The CLEANed power spectra presented were obtained after 100 iterations with a loop gain of 0.1. + Tje period is fouxd to be constant within error for cach , The period is found to be constant within error for each epoch. +To nuprove the xeriod loopdeterminationgain of he star IID 810:32. the ¢sutire data from 2000 - 200[ wereepoch. analysed using the same algorithm.," To improve the period determination of the star HD 81032, the entire data from 2000 - 2004 were analysed using the same algorithm." + Figure 2 shows the CLEANed power spectrum from the eutire dataset., Figure \ref{power.fig} shows the CLEANed power spectrum from the entire dataset. + The highest peak in the CLEANed power spectrum corres»onds to a period of 18.502+0.07Ed., The highest peak in the CLEANed power spectrum corresponds to a period of $18.802 \pm 0.074 \rm{d}$. + The 15.502 d period is much more plausible than tje 57 d perio reported earlier (Paudey et al., The 18.802 d period is much more plausible than the 57 d period reported earlier (Pandey et al. + 2002)., 2002). + The previous determinatio was nadulv due to olbscαναολα. luitations as our carly data were too sparse and liehly uneven., The previous determination was mainly due to observational limitations as our early data were too sparse and highly uneven. + Besides a subeiaut like this ojo ds unlikely o be svuchronized im a binary of 57-days period., Besides a subgiant like this one is unlikely to be synchronized in a binary of 57-days period. +" The Julian days of the observations were couverted to the phases using the eplemeris: Phasct))=JD252307.76118""NOSE where the initial epoch corresponds to the conjunction with the first nünimuiuu observed.", The Julian days of the observations were converted to the phases using the ephemeris: $ Phase(\theta) = JD 2452307.761 + 18^{d}.802 E$ where the initial epoch corresponds to the conjunction with the first minimum observed. + Figure 3H shows the differentia D.V. Rand. V... light «irves iud. (B-V) aud (V-B) colour οrves of the star IID 81032.," Figure \ref{fold.fig} shows the differential B, V, R and $_c$, light curves and, (B-V) and (V-R) colour curves of the star HD 81032." +" Tere V, stas for the differential V baud lieht curve of the comparison aud the check stars.", Here $_c$ stands for the differential V band light curve of the comparison and the check stars. + Each point im the| light. curves is iiean of 3 - [iudeoudeut observations taken over a nieht., Each point in the light curves is mean of 3 - 4 independent observations taken over a night. + The light curve the 2001-2002 has a dense temporal coverage., The light curve during the observing years 2001-2002 has a dense temporal coverage. +" We. therefore. divided this licht curve chivingiuto wo observingdiffereut vearsepochs ο see anv variation in the 0,,5, aud the amyplitiue"," We, therefore, divided this light curve into two different epochs to see any variation in the $\theta_{min}$ and the amplitude." +" The mean epoch of the light curves. ιο observec maxiunn (AV), ,,) aud mininnuun (AV,,;,) iu fie V baud. peak to peak amplitude (AW=AlnarΔΙmin j. alc phase of nininia(0,,;,) are listed iu Table 1.."," The mean epoch of the light curves, the observed maximum $\Delta V_{max}$ ) and minimum $\Delta V_{min}$ ) in the V band, peak to peak amplitude $\Delta V = \Delta V_{max} - \Delta V_{min}$ ), and phase of $\theta_{min}$ ) are listed in Table \ref{ligper.tab}." +" The value of AV, Was constant curing each 1 indicatiug hat the ποιους of uuspot«€ photosphere was constant from epoch to eoch.", The value of $\Delta V_{max}$ was constant during each epoch indicating that the brightness of unspotted photosphere was constant from epoch to epoch. +" However. epocthe vedue of AV, παν reduced by 0.1 linag from epoch “a to epoch b. and remainect ¢constant durius he οoch ο wd aud e."," However, the value of $\Delta V_{min}$ was reduced by 0.14 mag from epoch 'a' to epoch 'b', and remained constant during the epoch 'c', 'd' and 'e'." + The RS CVu systems usually show «ne or two well defined minima. thereby iuicating that the rotational modulations caised by oue or Wo pronineif spots or o of spots.," The RS CVn systems usually show one or two well defined minima, thereby indicating that the rotational modulations caused by one or two prominent spots or groups of spots." + Ackitional may be present at other longitides. or im the circiupolar PC@IOUS but groucontribution to the overall spotsrotational modulation may not be apxeciable.," Additional spots may be present at other longitudes, or in the circumpolar regions but contribution to the overall rotational modulation may not be appreciable." + The oiase of the liebt iniwn (μμ) directly 1idicates the mean longitude of the comunaut eroups of spos., The phase of the light minimum $\theta_{min}$ ) directly indicates the mean longitude of the dominant groups of spots. + A sharp nininum was observed durius he epoch “a (see Fi, A sharp minimum was observed during the epoch 'a' (see Fig. +e. aa)., \ref{fold.fig}a a). +" At the same tiue the amplitude of the| V band light «""Uurve was fouud to be 0,288 nag. which Was mnaxinun ourybservatious."," At the same time the amplitude of the V band light curve was found to be 0.288 mag, which was maximum during our observations." + T16 of the 111ii inuuiuimdicate that 1 is the latitudinal exteut of the groups durnuegof spos that may be responsible sharpucssrather than the longitudinal exteut., The sharpness of the minimum indicate that it is the latitudinal extent of the groups of spots that may be responsible rather than the longitudinal extent. + Droad minima during the epochs b.c and d inedicate that he spots wei‘© spread over an appreciable longitudinal range (Fi," Broad minima during the epochs 'b', 'c' and 'd' indicate that the spots were spread over an appreciable longitudinal range (Fig." +e. 3 b to d)., \ref{fold.fig} b to d). + It is interesting to see the light curve «ft the star ITD 81032 during the epoch e., It is interesting to see the light curve of the star HD 81032 during the epoch 'e'. + Tere a single large spot. characterized by a broad maui ¢mine the epochs b. € aud d separated iuto two groups of spots.," Here a single large spot, characterized by a broad minimum during the epochs 'b', 'c' and 'd' separated into two groups of spots." + Tus can be easilv seeu w two well «parated λάμα (see Fi, This can be easily seen by two well separated minima (see Fig. +e. 23 ο)., \ref{fold.fig} e). + Siguificaut change iu (η (see Table 1)) is probably associated with a chaice iu the spot configuration on the surface of the star., Significant change in $\theta_{min}$ (see Table \ref{ligper.tab}) ) is probably associated with a change in the spot configuration on the surface of the star. +pile-up of mass.,pile-up of mass. + We therefore retain terms involving pressure to first order in 3., We therefore retain terms involving pressure to first order in $\beta$. + Velocity evolution is governed by a momentum equation with only these two forces., Velocity evolution is governed by a momentum equation with only these two forces. + Conservation properties become apparent when arc-length is replaced with ji. the integrated mass per unit flux: Op/Ot=pj/D;.," Conservation properties become apparent when arc-length is replaced with $\mu$, the integrated mass per unit flux: $\partial\mu/\partial\ell=\rho_i/B_i$." + The value of j(/ never changes for a given fluid element., The value of $\mu$ never changes for a given fluid element. +" The resulting momentum equation di DKt))1 = includes the parallel pressure gradient after use of pressure balance, D;=Dd4s(p.—pji)/be. valid to first order in 7."," The resulting momentum equation = ) = ), includes the parallel pressure gradient after use of pressure balance, $B_i=B_e + 4\pi(p_e-p_i)/B_e$, valid to first order in $\beta$." +" The momentum per unit flux of any section of tube, P= = changes only through forces (per unit flux) from the ends of the section, D;t/4z. directed parallel to the axis."," The momentum per unit flux of any section of tube, = =, changes only through forces (per unit flux) from the ends of the section, $B_i\that/4\pi$, directed parallel to the axis." + Momentum conservation leads to a set of shock relations for thin flux tubes., Momentum conservation leads to a set of shock relations for thin flux tubes. +" Consider two straight sections with uniform properties (designated 1 and 2), separated by an abrupt change at coordinate µῃ."," Consider two straight sections with uniform properties (designated $1$ and $2$ ), separated by an abrupt change at coordinate $\mu_0$." + The length-seale of this change is large compared to the tube radius but otherwise small enough that we hereafter call it a “discontinuity” and, The length-scale of this change is large compared to the tube radius but otherwise small enough that we hereafter call it a “discontinuity” and +"greatly reduce the required absorption column densities, is highly unlikely because of the agreement between absorption and emission, between J=13 and other direct ¢-type lines (Fig. 10)),","greatly reduce the required absorption column densities, is highly unlikely because of the agreement between absorption and emission, between $J$ =13 and other direct $\ell$ -type lines (Fig. \ref{fig:rd}) )," + and between the derived column densities and dust emission data., and between the derived column densities and dust emission data. +" Therefore, we consider LTE a good assumption for this transition."," Therefore, we consider LTE a good assumption for this transition." +" If we assume similar optical depth for the emission lines, say 0.3, and a temperaturea of 400 K, then the line intensity should be 100 K, which is just the noise level in 1 km s! channels and 0.13"" beams."," If we assume a similar optical depth for the emission lines, say 0.3, and a temperature of 400 K, then the line intensity should be 100 K, which is just the noise level in 1 km $^{-1}$ channels and $''$ beams." +" Owing to the strength of the free-free radiation, we are thus more sensitive to absorption than emission lines."," Owing to the strength of the free-free radiation, we are thus more sensitive to absorption than emission lines." + Averaging over a larger region (Fig., Averaging over a larger region (Fig. + 1 and Table 3)) lowers both noise and peak intensities., \ref{fig:spectra} and Table \ref{tab:emlines}) ) lowers both noise and peak intensities. +" The latter reach up to 300 K in G10.47+0.03, suggesting that optical depth and temperature are higher than the above mentioned assumptions."," The latter reach up to 300 K in G10.47+0.03, suggesting that optical depth and temperature are higher than the above mentioned assumptions." +" Surprising is the detection of the line toward G10.47+0.03 A, since no NH3(4,4) satellites were detected by 9"," Surprising is the detection of the line toward G10.47+0.03 A, since no $_3$ (4,4) satellites were detected by \citet{Cesaroni10}." +" In the model for SgrB2-M, we have placed the regions F3 and Fle in front of and behind the bulk of the molecular gas, respectively."," In the model for SgrB2-M, we have placed the regions F3 and F1e in front of and behind the bulk of the molecular gas, respectively." + This prevents absorption toward most of F3 and leads to stronger absorption toward Fle., This prevents absorption toward most of F3 and leads to stronger absorption toward F1e. +" The exact offsets in z are not well constrained, however."," The exact offsets in z are not well constrained, however." +" To obtain the very strong absorption toward K2 in SgrB2-N, we put a very dense core just in front of the region."," To obtain the very strong absorption toward K2 in SgrB2-N, we put a very dense core just in front of the region." + This is of course not very satisfying as it is unlikely that such a core is exactly along the line-of-, This is of course not very satisfying as it is unlikely that such a core is exactly along the line-of-sight. + It was however not possible to reproduce both emission and absorption with a more symmetric distribution., It was however not possible to reproduce both emission and absorption with a more symmetric distribution. + Heating up large masses of molecular gas requires deeply embedded massive (proto)stars with high luminosities., Heating up large masses of molecular gas requires deeply embedded massive (proto)stars with high luminosities. +" Their radiation is either originally in the infrared (?),, not producing regions, or is quickly processed to the infrared by dust absorption of the UV radiation."," Their radiation is either originally in the infrared \citep{Hosokawa09}, not producing regions, or is quickly processed to the infrared by dust absorption of the UV radiation." +" Due to high column densities in all directions, the dust is optically thick even in the infrared and this radiation cannot escape, but diffuses outwards by multiple absorption/emission events until the dust is optically thin to its own radiation."," Due to high column densities in all directions, the dust is optically thick even in the infrared and this radiation cannot escape, but diffuses outwards by multiple absorption/emission events until the dust is optically thin to its own radiation." + This diffusion (or radiative trapping) leads to, This diffusion (or radiative trapping) leads to +"Sealo. 1979... with Mj=0.1A to AL,=10 M) and with au exponent x=-1.35 (from M,=0.33AL: to AL,—10 Mj).","Scalo, \cite{miller}, with $\rm M_l=0.1~ M\odot$ to $\rm M_u = 10~ M\odot$ ) and with an exponent x=-1.35 (from $\rm M_l=0.33~ M\odot$ to $\rm M_u = 10~ M\odot$ ))." + We select all objects whose colors are consistent with the envelope of the models adopting a 20 uncertainty on cach color given bv the DAOPIIOT software.," We select all objects whose colors are consistent with the envelope of the models adopting a $\rm +2\sigma$ uncertainty on each color given by the DAOPHOT software." + We use the models of Bertelli et al. (199 D):, We use the models of Bertelli et al. \cite{bertelli}) ): + they cad to a similar selection of GC candidates., they lead to a similar selection of GC candidates. +The resulting range of acceptable colors is 0.80κV¥T<1.50.13. where d, is the so-called Iuminosity distance."," Traditional Hubble diagrams represent the relation of observed flux ${\cal F}$ to the luminosity of the source ${\cal L}$, , where $d_{L}$ is the so-called luminosity distance." + The distance modulus 4/j=m—M. where im and AM ave the apparent and absolute magnitudes respectively. is where the luminosity distance dj is in megaparsecs.," The distance modulus $\mu_p=m-M$, where $m$ and $M$ are the apparent and absolute magnitudes respectively, is where the luminosity distance $d_L$ is in megaparsecs." + The process of converting observed data into the supernova magnitudes reported actually contains an additive parameter. called (he extinction coefficient ο.," The process of converting observed data into the supernova magnitudes reported actually contains an additive parameter, called the extinction coefficient $A$ ." + Exünction max depend on lrequeney. designated by Ay. ly. ete.," Extinction may depend on frequency, designated by $A_{B}$, $A_{R}$, etc." + The units of A are magnitude., The units of $A$ are magnitude. +" In practice A shifts (he supernova magnitude mo deduced from light-curves to a reported magnitude (""extinction corrected magnitude"") mi=my—d.", In practice $A $ shifts the supernova magnitude $m_{0}$ deduced from light-curves to a reported magnitude (“extinction corrected magnitude”) $m= m_{0}-A $. + Our galaxy contributes extinction. as do (he additional extinctioneffects associated with supernova host galaxies.which are more model dependent.," Our galaxy contributes extinction, as do the additional extinctioneffects associated with supernova host galaxies,which are more model dependent." +of the individual random-phase fluxes measured of each variable. ancl converting (he average [Iuxes back into magnitudes.,"of the individual random-phase fluxes measured of each variable, and converting the average fluxes back into magnitudes." + La principle a more accurate procedure to determine (le mean magnitudes in J and Ix would be (he recipy described by Soszvuski et al. (, In principle a more accurate procedure to determine the mean magnitudes in J and K would be the recipy described by Soszynski et al. ( +2005) which uses the V and I light eurves of the variables and the known phases of the near-inlrared observations.,2005) which uses the V and I light curves of the variables and the known phases of the near-infrared observations. + Ilowever. in the present case of WLM the epoch difference between the near-intrared data reported in this paper. ancl the previous VI data reported in Paper I is so large. typically some 200 pulsation eveles. that with the limited accuracy. of (he. periods of the variables derived in Paper I the phasing of the near-IR data becomes very. uncertain.," However, in the present case of WLM the epoch difference between the near-infrared data reported in this paper, and the previous VI data reported in Paper I is so large, typically some 200 pulsation cycles, that with the limited accuracy of the periods of the variables derived in Paper I the phasing of the near-IR data becomes very uncertain." + While this is unfortunate. the simple taking of a straight average of several random-phase magnitudes in a near-IR. band of a Cepheid still does produce a rather accurate mean magnitude. given the ow light curve amplitudes of Cepheid variables at these wavelengths of (vpically 0.3 mas or stus with periods less than 10 davs (e.g. Persson et al.," While this is unfortunate, the simple taking of a straight average of several random-phase magnitudes in a near-IR band of a Cepheid still does produce a rather accurate mean magnitude, given the low light curve amplitudes of Cepheid variables at these wavelengths of typically 0.3 mag for stars with periods less than 10 days (e.g. Persson et al." + 2004)., 2004). + For the one long-period Cephleid in WLM. cepOO1 with a period of 54 days. the amplitucle of the Ix-band light curve is expected to be about 0.5 mag. but for this variable we have obtained six observations al different phases which makes us expect that their mean value is verv close to the (rue mean nagnitude of the variable. in the two bands we observed.," For the one long-period Cepheid in WLM, cep001 with a period of 54 days, the amplitude of the K-band light curve is expected to be about 0.5 mag, but for this variable we have obtained six observations at different phases which makes us expect that their mean value is very close to the true mean magnitude of the variable, in the two bands we observed." + Table 3 gives the intensity mean J and Ix magnitudes of the individual Cepheids. with their estimated. uncertainties from the number anc accuracy of the individual observations leading to the adopted mean magnitude.," Table 3 gives the intensity mean J and K magnitudes of the individual Cepheids, with their estimated uncertainties from the number and accuracy of the individual observations leading to the adopted mean magnitude." + We also provide the periods (adopted [rom Paper D., We also provide the periods (adopted from Paper I). + In Figures 4 and 5 we show the period-mean magnitude relations in the J and Ix bands as delined by the data in Table 3., In Figures 4 and 5 we show the period-mean magnitude relations in the J and K bands as defined by the data in Table 3. + There is one Cepheid. cep038. which is clearly over-Iuminous in both PL diagrams. by about 1.5 mag in J and about 2 mag in Ix. We assume that (he very bright magnitude of this variable is caused by. a nearby. bright object which is not resolved in our images.," There is one Cepheid, cep038, which is clearly over-luminous in both PL diagrams, by about 1.5 mag in J and about 2 mag in K. We assume that the very bright magnitude of this variable is caused by a nearby bright object which is not resolved in our images." + Since the V and I magnitudes of cep038 are normal for its period (see Paper 1) the blend must be a very red. object.," Since the V and I magnitudes of cep038 are normal for its period (see Paper I), the blend must be a very red object." + The ocurrence of at least one strongly blended Cepheid in WLM in a sample of about 30 stars is «uite expected [rom (he result obtained by Bresolin et al. (, The ocurrence of at least one strongly blended Cepheid in WLM in a sample of about 30 stars is quite expected from the result obtained by Bresolin et al. ( +2005) who studied the blending of Cepheids in NGC 300. al about twice the distance of WLM. from a comparison of ground-based and HST/ACS photometry. finding three strongly blended Cepheids in a sample of 16 Cepheids in this galaxy.,"2005) who studied the blending of Cepheids in NGC 300, at about twice the distance of WLM, from a comparison of ground-based and HST/ACS photometry, finding three strongly blended Cepheids in a sample of 16 Cepheids in this galaxy." + For the following distance analysis. we exclude star cepü38.," For the following distance analysis, we exclude star cep038." + For the reasons discussed in Paper L and in conformity with the approach adopted there. we adopt a period cutoff of log P. (days) = 0.5 lor the distance analvsis. retaining onlv the Cepheids with longer periods in the sample.," For the reasons discussed in Paper I, and in conformity with the approach adopted there, we adopt a period cutoff of log P (days) = 0.5 for the distance analysis, retaining only the Cepheids with longer periods in the sample." + This ensures (hat possible overtone pulsators are likely to be excluded in the sample adopted for the distance determination. ancl it eliminates (he variables with the lowest signal-to-nolse ratio in the photometry.," This ensures that possible overtone pulsators are likely to be excluded in the sample adopted for the distance determination, and it eliminates the variables with the lowest signal-to-noise ratio in the photometry." + The final sample consists of Cepheids 001-033 in Table 3 (24 stars)., The final sample consists of Cepheids 001-033 in Table 3 (24 stars). + Note that the strongly blended Cepheicl cepO38 is eliminated from the final sample also on the basis of the adopted period, Note that the strongly blended Cepheid cep038 is eliminated from the final sample also on the basis of the adopted period +of view of the included. phyvsies. our previous onc-cinensioual simulations obwviouslv could not address +ιο inpact of eenuimelv two-dimensional phenomena u the feedback phenomenon.,"of view of the included physics, our previous one-dimensional simulations obviously could not address the impact of genuinely two-dimensional phenomena on the feedback phenomenon." + We recall here the most iurportant of them. that will be discussed in this paper.," We recall here the most important of them, that will be discussed in this paper." + The first one concerus the possible instabilities (e.g. RavleighTavlor. RT) that can affect the evolution of the cold shells that appear during the evolution of ouc-dimensional models.," The first one concerns the possible instabilities (e.g., Rayleigh–Taylor, RT) that can affect the evolution of the cold shells that appear during the evolution of one-dimensional models." + The central bursts are caused by these shells. aud the shells have a two-fold origin.," The central bursts are caused by these shells, and the shells have a two-fold origin." + At the beginning of each major burst. the classical Field cooling instability (Field1965). appears around 1 kpc from the center. due to the local critical balance between heating and cooling.," At the beginning of each major burst, the classical Field cooling instability \citep{field:65} appears around 1 kpc from the center, due to the local critical balance between heating and cooling." + As the density increases. the shell starts to fall toward the ceuter and compresses the eas.," As the density increases, the shell starts to fall toward the center and compresses the gas." + Whena burst first appears. shock waves are seut from the center toward the falling shell. aud a series of 3ub-bursts and consequent reflected shock waves impact on the cold shell. increasing its deusity still further.," When a burst first appears, shock waves are sent from the center toward the falling shell, and a series of sub-bursts and consequent reflected shock waves impact on the cold shell, increasing its density still further." + As the bulk of star formation in the one-dimensional models happens in these cold shells. if is very important to understand the cold shell plivsies. not ouly from the poiut of view of central accretion. but also for the starburst which occurs Within the cold shell.," As the bulk of star formation in the one-dimensional models happens in these cold shells, it is very important to understand the cold shell physics, not only from the point of view of central accretion, but also for the starburst which occurs within the cold shell." +" From the short description above, a few obvious questions arise: for example. will the allowance of the additional deeree of freedom still lead to a formation of a cold shell near the ceuter in the case ofan aspherical galaxv?"," From the short description above, a few obvious questions arise: for example, will the allowance of the additional degree of freedom still lead to a formation of a cold shell near the center in the case of an aspherical galaxy?" + What is the effect of non-zero aueular momentum in the gas?, What is the effect of non-zero angular momentum in the gas? + Will the cold shell fall toward the center as iu the one-dineusional siuulationus or it will break up due to (RT) iustabilitv?, Will the cold shell fall toward the center as in the one-dimensional simulations or it will break up due to (RT) instability? + Even more important. what is the fate of the multiple interacting shocks?," Even more important, what is the fate of the multiple interacting shocks?" + Will the aceretion still be characterized by strong bursts separated by loueg time intervals or will the breaxup of the shells lead to cold finecrs of dense gas being acereted in a amore or less steady flow while hot gas flows outward. therefore resulting iu flows that at each radius are partially accretiug aud partially outflowiue?," Will the accretion still be characterized by strong bursts separated by long time intervals or will the breakup of the shells lead to cold fingers of dense gas being accreted in a more or less steady flow while hot gas flows outward, therefore resulting in flows that at each radius are partially accreting and partially outflowing?" + The second reason to imove το two-dimensional siuulatious is to explore the interaction (and the consequent mechanical feedback) of the conical nuclear wind with the ealaxy ISM., The second reason to move to two-dimensional simulations is to explore the interaction (and the consequent mechanical feedback) of the conical nuclear wind with the galaxy ISM. + In our previous onc-mensional sninulatious this interaction was necessarily described as a spherical average of au inhercuth non-spherical effect. even though we had taken iuto account several physical aspects of the phenomenon via a time-dependent differential equation.," In our previous one-dimensional simulations this interaction was necessarily described as a spherical average of an inherently non-spherical effect, even though we had taken into account several physical aspects of the phenomenon via a time-dependent differential equation." + Clearly. a dimensional simulation is also needed to explore IelviuUehuholtz iustabilities at the interface between the outflowiueg conical wind aud the ISM.," Clearly, a two-dimensional simulation is also needed to explore Kelvin--Helmholtz instabilities at the interface between the outflowing conical wind and the ISM." + Iu the preseut work. we focus on two-dimensional smnulatious of a galaxy wihn verv low specific angular moment iji order to niake close coutact with the existiue one-«nueusional siwulations.," In the present work, we focus on two-dimensional simulations of a galaxy with very low specific angular momentum in order to make close contact with the existing one-dimensional simulations." + We would like to isolate the effect. of increasiug the dimensionality of the simulation., We would like to isolate the effect of increasing the dimensionality of the simulation. + Tie adopted angular momentum profile is consisteut witi the slowest of he SAURON slow-rotators (Enuscllenetal.2001.., The adopted angular momentum profile is consistent with the slowest of the SAURON slow-rotators \citep{emsellem:04}. +. In fture work. we will expaud our treatiucut to include anegulay moment transport via the stateard oo prescription (Shakura&Suuvaev1973) and more recent nioccls based on exavitational torques (IHopkius&Quataert2010a)..," In future work, we will expand our treatment to include angular momentum transport via the standard $\alpha$ prescription \citep{shakura:73} and more recent models based on gravitational torques \citep{hopkins:10-analytic-preprint}." + There have OCTL Wad nuierical simulations of SMDIT accretion auk the subsequeit effects on the galaxies containing the resulting ACN., There have been many numerical simulations of SMBH accretion and the subsequent effects on the galaxies containing the resulting AGN. + Nearly all of the efforts to date can be classified into three broad categories. DiMatteoetal.(2005)... Debuhlretal.(2010.2011).," Nearly all of the efforts to date can be classified into three broad categories. \citet{dimatteo:05}, \citet{debuhr:10,debuhr:11}," +. and Johanssonetal.(2009). are examples where the siuulations cover leneth scales from z 100 pe to tens of kpe aud timescales from ai fraction of a Myr to several Cyr., and \citet{johansson:09} are examples where the simulations cover length scales from $\simeq$ 100 pc to tens of kpc and timescales from a fraction of a Myr to several Gyr. + Galactic leugth aud timescales are resolved. but the SAIBID accretion aud. feedback processes are considered to be sub-resolutiou.," Galactic length and timescales are resolved, but the SMBH accretion and feedback processes are considered to be sub-resolution." + Complementary studies by Iurosawa&Proga(2009a)) and Kurosawa&Prosa(2009b) are exaniples of iiulti-dineusional sinulatious that cover the leneth scales from a few AU to z 1 pe.," Complementary studies by \citet{kurosawa:09-2d} + and \citet{kurosawa:09-3d} are examples of multi-dimensional simulations that cover the length scales from a few AU to $\simeq$ 1 pc." + Leugth aud timescales relevant to SAIBIT accretion are resolved. aud the generation of radiativelv driven winds is computed. but these simulations do uot approach ealactic leneth or timescales. and imfall rates are taken as eiveu.," Length and timescales relevant to SMBH accretion are resolved, and the generation of radiatively driven winds is computed, but these simulations do not approach galactic length or timescales, and infall rates are taken as given." + Hopkius&Quatacrt(20100) and Levineetal.(2008) are examples of a multi-resolution studies of SMDITI aceretion involving proeressively higher spatial resolution παος run for progressvelv shorter times., \citet{hopkins:10-simulation} and \citet{levine:08} are examples of a multi-resolution studies of SMBH accretion involving progressively higher spatial resolution simulations run for progressively shorter times. + The highest spatial resolution simulations eo dowd to a fraction of à pc and are mun for about one Myr of sinulation time., The highest spatial resolution simulations go down to a fraction of a pc and are run for about one Myr of simulation time. + These simulations spatially resolve the accretion process. but do not reach galactic timescales.," These simulations spatially resolve the accretion process, but do not reach galactic timescales." + Therefore. they cannot selfconsistentlv calculate the effect of ACN feedback on the gas in the galaxy as a whole aud the subsequent SMDIT accretion.," Therefore, they cannot self-consistently calculate the effect of AGN feedback on the gas in the galaxy as a whole and the subsequent SMBH accretion." + Finally. there have been several uumerical studies of accretion by diuteriuediate-nüass black holes (IMDIIs) with the goal of understanding BIT growth in the carly universe (Alvarezctal.2000:Park&Ricotti2010).," Finally, there have been several numerical studies of accretion by intermediate-mass black holes (IMBHs) with the goal of understanding BH growth in the early universe \citep{alvarez:09, park:10-preprint}." +. Tn tenus of dimensiouless leugth scales ¢/rpondai Or relSchwarzschild: ποιο of these simulations are simular to our snmulations.," In terms of dimensionless length scales $r/r_{\rm Bondi}$ or $r/r_{\rm + Schwarzschild}$, some of these simulations are similar to our simulations." + Towever. studies of IMDIT accretion focus ou DIIS with very small masses (1001000/7.) compared to those preseuted here.," However, studies of IMBH accretion focus on BHs with very small masses (100–1000 $M_\odot$ ) compared to those presented here." + Therefore. the relevant plvsical leugth and timescales are uch sinaller and the physical sources of the infalling eas are very different from those considered iu the present work.," Therefore, the relevant physical length and timescales are much smaller and the physical sources of the infalling gas are very different from those considered in the present work." + Our goal is to resolve both the relevant accretion leugth and timescales while at the same time resolving ealactic leneth aud timescales (e£.Levineetal.2008:Al-varezetal. 2009).," Our goal is to resolve both the relevant accretion length and timescales while at the same time resolving galactic length and timescales \citep[cf.][]{levine:08, alvarez:09}." +. There have been oulv a few attempts to perform iulti-dimensional simulations that bridge the gap between galactic and SAIBID scales. although several papers have examined the interaction between an outflowineg wind‘jet with specified properties aud the surrounding intergalactic mediu (cf.Metzler&EvrardAviclictal.2010) The preseu work is an attempt to sinultaneouslv resolve the duncr leneth scales relevant to SAIBIT accretion (a ew pe). outer leugth scales relevant to ealaxies (tens of Ispe)}. iuner timescales relevant to SAIBIT accretion (a few vears). aud outer timescales relevaut to galaxies and stellar evolution (10 Cer).," There have been only a few attempts to perform multi-dimensional simulations that bridge the gap between galactic and SMBH scales, although several papers have examined the interaction between an outflowing wind/jet with specified properties and the surrounding intergalactic medium \citep[cf.][]{metzler:94,omma:04,sijacki:07,sternberg:08,reeves:09,fabian:09,arieli:10} + The present work is an attempt to simultaneously resolve the inner length scales relevant to SMBH accretion (a few pc), outer length scales relevant to galaxies (tens of kpc), inner timescales relevant to SMBH accretion (a few years), and outer timescales relevant to galaxies and stellar evolution (10 Gyr)." + However. the region inside of 1l pe including the disk and the SMIDIT itself are still treated as sub-resolutiou plysics and we compute the output from these regions as tinic- functious of the input to them. utilizing formulae from the above quoted sources.," However, the region inside of 1 pc including the disk and the SMBH itself are still treated as sub-resolution physics and we compute the output from these regions as time-dependent functions of the input to them, utilizing formulae from the above quoted sources." + We take particular care to resolve the inner scales where the rate of accretion is set (the Dondi radius) even, We take particular care to resolve the inner scales where the rate of accretion is set (the Bondi radius) even +showing different sub-samples.,showing different sub-samples. + The problem is found in individual objects., The problem is found in individual objects. + This cannot be accounted for by reddening effects., This cannot be accounted for by reddening effects. + Correcting for reddening would produce higher [NeV]/[OTI] and [NeV]/[NeIII] that would result on larger ( values., Correcting for reddening would produce higher [NeV]/[OII] and [NeV]/[NeIII] that would result on larger $U$ values. + On the other hand. [OIT/[OITII] would also become larger. implying lower (7 values.," On the other hand, [OII]/[OIII] would also become larger, implying lower $U$ values." + Therefore. the discrepancy would be worse.," Therefore, the discrepancy would be worse." + We have plotted in Fig., We have plotted in Fig. + 4 the temperature sensitive [OIII]AA3007.4959/[OTII] ratio vs. [OIITI/H-7., 4 the temperature sensitive $\lambda\lambda$ $\lambda$ 4363 ratio vs. $\beta$. + The arrows correspond to objects for A4363which [OIIT[A4363 was not detected and only upper limits could be estimated., The arrows correspond to objects for which $\lambda$ 4363 was not detected and only upper limits could be estimated. + For all objects the predicted and measured values of [OIIT[AA3007.4959/TOITI]A4363 are discrepant by at least a factor of 2 (a shift of 20.3 in 15)., For all objects the predicted and measured values of $\lambda\lambda$ $\lambda$ 4363 are discrepant by at least a factor of 2 (a shift of $>$ 0.3 in lg). + This cannot be accounted for by measurement errors (see Fig., This cannot be accounted for by measurement errors (see Fig. + +) or reddening effects. since correcting for this would result on even ower [OIIT[AA5007.4959/[OITII]44363 ratios.," 4) or reddening effects, since correcting for this would result on even lower $\lambda\lambda$ $\lambda$ 4363 ratios." + Higher densities can explain low OMTAAS007.4959/[ONTA4363 values consistent with the data. but produce strong discrepancies with other line ratios.," Higher densities can explain low $\lambda\lambda$ $\lambda$ 4363 values consistent with the data, but produce strong discrepancies with other line ratios." +" As an example. models with n=l0"" produce [OIII]AA5007.4959/TOTII]A4363)::2.. as measured for many ype 2 quasars."," As an example, models with $n$ $^5$ $^{-3}$ produce $\lambda\lambda$ $\lambda$ $\le$ 2, as measured for many type 2 quasars." + However. for such models [OITI]/[ONT]<0.02. ΟΠΗ: <0.3 (much lower than the measured values. Fig.," However, for such models $\le$ 0.02, $\beta\le$ 0.3 (much lower than the measured values, Fig." + |) and [OIII/H2 18 ¢higher than measured. Fig.," 1) and $\beta\ge$ 18 (higher than measured, Fig." + 1)., 1). + High densitiesonlv. therefore. in general do not solve the problem.," High densities, therefore, in general do not solve the problem." +" In the low density limit (Osterbrock 1989)). this discrepancy implies that the models prediet too low electron temperatures: T,x 11000 K for all models ofthe {ὁ sequence. while the measured line ratios imply 7; 15 000 K. being —20 000 in several cases. errors considered."," In the low density limit (Osterbrock \citeyear{ost89}) ), this discrepancy implies that the models predict too low electron temperatures: $T_e\le$ 11000 K for all models of the $U$ sequence, while the measured line ratios imply $T_e\ga$ 15 000 K, being $>$ 20 000 in several cases, errors considered." + The same problem has been discussed in detail for other type 2 AGNS (e.g. Binette. Wilson Storchi-Beremann 1996.. Robinson et al. 1987).," The same problem has been discussed in detail for other type 2 AGNs (e.g. Binette, Wilson Storchi-Bergmann \citeyear{bin96}, Robinson et al. \citeyear{rob87}) )." + The data present a large HeII/H.? scatter inconsistent with the standard AGN sequence (Fig., The data present a large $\beta$ scatter inconsistent with the standard AGN sequence (Fig. + | bottom panel). which is not due to errors in the measurements. neither reddening effects.," 1 bottom panel), which is not due to errors in the measurements, neither reddening effects." + There are objects with too high and objects with too low HeII/H:? ratios compared with the model predictions (see Fig., There are objects with too high and objects with too low $\beta$ ratios compared with the model predictions (see Fig. + 5)., 5). + Such large scatter has been observed also in low z radio galaxies (e.g. Robinson et al., Such large scatter has been observed also in low $z$ radio galaxies (e.g. Robinson et al. + 1987)., 1987). + The [NII/Ha vs. [OII]/JOIII]. diagram (Fig., The $\alpha$ vs. [OII]/[OIII] diagram (Fig. + |) shows a very large scatter in the [NIT]/Hea ratio inconsistent with the standard AGN (solar metallicity) predictions which again cannot be explained by errors in the measurements or reddening effects., 1) shows a very large scatter in the $\alpha$ ratio inconsistent with the standard AGN (solar metallicity) predictions which again cannot be explained by errors in the measurements or reddening effects. + For a large fraction of objects. the [NIT] emission is too strong.," For a large fraction of objects, the [NII] emission is too strong." + Given that this ratio is a direct metallicity indicator. rather than being a problem for photoionization models. the large range of values suggests that the nitrogen/hydrogen ratio varies substantially within the sample.," Given that this ratio is a direct metallicity indicator, rather than being a problem for photoionization models, the large range of values suggests that the nitrogen/hydrogen ratio varies substantially within the sample." + Nitrogen is likely to be overabundant in those objects with large [NIT]/Ha values (e.g. Robinson et al. 1987»)., Nitrogen is likely to be overabundant in those objects with large $\alpha$ values (e.g. Robinson et al. \citeyear{rob87}) ). + Possible solutions to. these problems have been extensively discussed in the literature for more than 20 years., Possible solutions to these problems have been extensively discussed in the literature for more than 20 years. + We present, We present +ln contrast with the local. universe. where only 30 of the bolometric Luminosity is released. in the HV/submum wavelength range (Soifer Neugebauer 1991). there is a erowing amount of evidence that the high.redshift universe was much more opaque.,"In contrast with the local universe, where only 30 of the bolometric luminosity is released in the IR/submm wavelength range (Soifer Neugebauer 1991), there is a growing amount of evidence that the high–redshift universe was much more opaque." + Indeed. the discovery of the Cosmic Infrared. Background. (CIRB) at a level ten times higher than the noevolution preclictions based on the local LR Iuminosity function. and twice as high as the Cosmic Optical Background obtained from optical counts. has shown that dust extinction and emission are key processes for highredshift galaxies (Puget et al.," Indeed, the discovery of the Cosmic Infrared Background (CIRB) at a level ten times higher than the no–evolution predictions based on the local IR luminosity function, and twice as high as the Cosmic Optical Background obtained from optical counts, has shown that dust extinction and emission are key processes for high--redshift galaxies (Puget et al." + 1996: Cruiderconi et al., 1996; Guiderdoni et al. + 1997: Fixsen et al., 1997; Fixsen et al. + 1998: Hauser et al., 1998; Hauser et al. + 1998: Schlegel. Finkbeiner Davis 1998).," 1998; Schlegel, Finkbeiner Davis 1998)." + Deep surveys with the180 satellite at 15 jum (Oliver et al., Deep surveys with the satellite at 15 $\mu$ m (Oliver et al. + 1997: Aussel et al., 1997; Aussel et al. + 1999: Elbaz et al., 1999; Elbaz et al. + 1999) and 175 yam (Ixawara et al., 1999) and 175 $\mu$ m (Kawara et al. + 1998: Puget et al., 1998; Puget et al. + 1999). and with the SCUBA instrument at S850 sam (Smail. Ivison Blain 1997: Barger et al.," 1999), and with the SCUBA instrument at 850 $\mu$ m (Smail, Ivison Blain 1997; Barger et al." + 1998: Hughes ct al., 1998; Hughes et al. + 1998: Eales et al., 1998; Eales et al. + 1999: Barger. Cowie Saunders 1999) have begun to resolve the CIHAD into its brightest contributors.," 1999; Barger, Cowie Saunders 1999) have begun to resolve the CIRB into its brightest contributors." + Although identification and spectroscopic Follow:up of subnim sources are not easy. such studies seem to reach the conclusion that an important fraction of these sources are the highredshift counterparts of the local luminous anc ultraluminous LR ealaxies (LIRGs and ULLIiCs) discovered. by (Smiail et al.," Although identification and spectroscopic follow–up of submm sources are not easy, such studies seem to reach the conclusion that an important fraction of these sources are the high–redshift counterparts of the local luminous and ultraluminous IR galaxies (LIRGs and ULIRGs) discovered by (Smail et al." + 1998: Lilly et al., 1998; Lilly et al. + 1999: Barger et al., 1999; Barger et al. + 1999)., 1999). + In the optical and nearLR window. careful examinations of the CanadaFrance Redshift Survey (CERS) galaxies at 2~ 1. and Lyman break galaxies at 2~3 and 4 have revealed a significant amount of extinction (Flores ct al.," In the optical and near–IR window, careful examinations of the Canada–France Redshift Survey (CFRS) galaxies at $z\sim 1$ , and Lyman break galaxies at $z \sim 3$ and 4 have revealed a significant amount of extinction (Flores et al." + 1999: Steicdel et al., 1999; Steidel et al. + 1999: Aleurer. Lleekman Calzetti 1999).," 1999; Meurer, Heckman Calzetti 1999)." + This has leac to a reassessment of previous estimates of the UV Iluxes. and consequently of the star formation rates in these objects. which are now found to be higher by a factor 2 to 5.," This has lead to a reassessment of previous estimates of the UV fluxes, and consequently of the star formation rates in these objects, which are now found to be higher by a factor 2 to 5." + In light of these observations. one can view the far infrared. background as a sink for the hidden aspects of galaxy formation.," In light of these observations, one can view the far infrared background as a sink for the hidden aspects of galaxy formation." + At optical wavelengths. cllipticals aud spheroids are old. even at ο~I1. No evidence is seen for either the luminous formation phase. orthe early evolution," At optical wavelengths, ellipticals and spheroids are old, even at $z \sim 1.$ No evidence is seen for either the luminous formation phase, orthe early evolution" +"back-evolved masses as grey circles. and the ""true"" initial cluster masses as dots. using /;—8 Gyr in the top panel and /;=| Gyr in the bottom panel.","back-evolved masses as grey circles, and the “true” initial cluster masses as dots, using $t_4 = 8$ Gyr in the top panel and $t_4 = 1$ Gyr in the bottom panel." + For us a larger /; seems to be more realistic. as the Small Magellanic Cloud has a similar value (logjo/4 =9.9. ?Y and more massive spiral galaxies with a deeper gravitational potential have smaller values.," For us a larger $t_4$ seems to be more realistic, as the Small Magellanic Cloud has a similar value \citep[$\log_{10} t_4 = 9.9, and more massive spiral galaxies with a deeper gravitational potential have smaller values." + We will. however. discuss below the implications of both values when determining the star formation history from the most massive clusters.," We will, however, discuss below the implications of both values when determining the star formation history from the most massive clusters." + Further features in the age-mass diagram besides the typical wedge-like shape were pointed out by ?:: (1) The large densities of clusters at logjo of 6.6 and 7.2: These are caused by the fitting procedure., Further features in the age-mass diagram besides the typical wedge-like shape were pointed out by \citet{degrijs+anders2006}: (1) The large densities of clusters at $\log_{10} \tau $ of 6.6 and 7.2: These are caused by the fitting procedure. + There aret no isochrones for clusters younger than 4 Myr (log;t= 6.6). and at logjot=7.2 the isochrones are discrete due to rapid evolution.," There are no isochrones for clusters younger than 4 Myr $\log_{10} \tau = 6.6$ ), and at $\log_{10} \tau = 7.2$ the isochrones are discrete due to rapid evolution." +" This does not have a large influence on the determined (2) The under-density of data points between = 3 Gyr and 13 Gyr 629.5xlogygt= 10.1). which is the ""well-known LMC cluster (3). Overdensities at 7.8xlogygt<=80. 28log;(M/M.)x3.4 and 8.2 4$ quasar to be detected at (sub)mm wavelengths (McMahon et 1994; Isaak et 1994), BR $-$ 0725 was found to contain $\sim10^9$ $_\odot$ of dust ata temperature of $\sim 50$." +. CO observations. traced more than 10! . of molecular gas (assuming locally-determined conversion factors)., CO observations traced more than $10^{11}$ $_\odot$ of molecular gas (assuming locally-determined conversion factors). + A multi-line LVG analysis by Ohta et (01998) using a range of CO transitions (COC7—-6): Omont et 11996: CO(S—4): Ohta et 11996: Omont et 11996: and CO(2—1: Ohta et 11998) suggested that the molecular gas density is 10 7., A multi-line LVG analysis by Ohta et (1998) using a range of CO transitions (CO(7–6): Omont et 1996; CO(5–4): Ohta et 1996; Omont et 1996; and CO(2--1): Ohta et 1998) suggested that the molecular gas density is $>10^4$ $^{-3}$. + This conclusion was also reached by ΟΠΗ et (2002b) using data having a much higher signal-to-noise ratio., This conclusion was also reached by Carilli et (2002b) using data having a much higher signal-to-noise ratio. + The modelling requires a number of assumptions. and it is clear that a direct measure of the dense gas is desirable in order to establish whether the host galaxies of high redshift quasars are indeed the analogues of nearby ULIRGs.," The modelling requires a number of assumptions, and it is clear that a direct measure of the dense gas is desirable in order to establish whether the host galaxies of high redshift quasars are indeed the analogues of nearby ULIRGs." + With few exceptions. studies of the molecular interstellar medium in very distant galaxies have used the CO rotational ladder.," With few exceptions, studies of the molecular interstellar medium in very distant galaxies have used the CO rotational ladder." + With a critical density of 107 >. the lowest of the HCN rotational line traces molecular gas at a much higher density than the corresponding CO transition.," With a critical density of $>10^4$ $^{-3}$, the lowest of the HCN rotational line traces molecular gas at a much higher density than the corresponding CO transition." +" In this paper we present a search for HCN(I-0) emission from BR 0725 using the Very Large Array (VLA) of the National Radio AstronomyΤοντ, with the aim of providing an independent measure of the dense gas component in its host galaxy. and to enable a direct comparison with the local ULIRGs observed by Solomon et (19923)."," In this paper we present a search for HCN(1–0) emission from BR $-$ 0725 using the Very Large Array (VLA) of the National Radio Astronomy, with the aim of providing an independent measure of the dense gas component in its host galaxy, and to enable a direct comparison with the local ULIRGs observed by Solomon et (1992a)." + The mean rest frequency of the HCN(I-0). triplet is View=88.632 GHz. which is redshifted to 15.563 GHz in BR 0725.," The mean rest frequency of the HCN(1–0) triplet is $\nu_{\rm rest} = 88.632$ GHz, which is redshifted to 15.563 GHz in BR $-$ 0725." + All quantities given here have been derived using a A-cosmology. with Hy=65 km | |.," All quantities given here have been derived using a $\Lambda$ -cosmology, with $H_0 = 65$ km $^{-1}$ $^{-1}$ ." + For comparison. the same quantities derived for a flat. Einstein-de Sitter cosmology with Hp—50 km | | are included in parentheses.," For comparison, the same quantities derived for a flat, Einstein-de Sitter cosmology with $H_0 = 50$ km $^{-1}$ $^{-1}$ are included in parentheses." +" These cosmologies give a luminosity distance Dj,=46.6(39.6) Gpe for BR 0725."," These cosmologies give a luminosity distance $D_{\rm L} += 46.6(39.6)$ Gpc for BR $-$ 0725." + The VLA observations were made on 2000 August 26. September 2—L and in 2003 January 25—29.," The VLA observations were made on 2000 August 26, September 2–4, and in 2003 January 25–29." + In 2000 the VLA was in the compact D configuration. while in 2003 it was in the DnC configuration.," In 2000 the VLA was in the compact D configuration, while in 2003 it was in the DnC configuration." + The instantaneous bandwidth of the VLA is only 50 MHz. tuneable in finite steps of 20 or 30 MHz.," The instantaneous bandwidth of the VLA is only 50 MHz, tuneable in finite steps of 20 or 30 MHz." + We therefore chose a set-up for the local oseillators that most closely centred the redshifted HCN¢!—0) line in the 50 MHz bandwidth. and covered the 50 MHz with 8 channels of 6.25 MHz (120 km s.) with both right and left circular polarizations.," We therefore chose a set-up for the local oscillators that most closely centred the redshifted HCN(1–0) line in the 50 MHz bandwidth, and covered the 50 MHz with 8 channels of 6.25 MHz (120 km $^{-1}$ ) with both right and left circular polarizations." + The narrow total bandwidth of the current 15 GHz receivers at the VLA esulted in the sensitivity achieved the frequency of the redshifted HCN line being degraded by a factor of about 2 relative to the centre of the band., The narrow total bandwidth of the current 15 GHz receivers at the VLA esulted in the sensitivity achieved the frequency of the redshifted HCN line being degraded by a factor of about 2 relative to the centre of the band. + Antenna- complex gains were monitored every |5 minutes through observations of the quasar PMN 0740., Antenna-based complex gains were monitored every 15 minutes through observations of the quasar PMN $-$ 0740. + The bandpass anc absolute flux density scale were determined through observations of 3C273 and 3C286 respectively., The bandpass and absolute flux density scale were determined through observations of 3C273 and 3C286 respectively. + The total uncertainty in the flux density calibration is estimated to be less than 5 per cent., The total uncertainty in the flux density calibration is estimated to be less than 5 per cent. + The tropospherie phase stability was relatively. poor for the observations made during 2000 late summer. and the data with particularly bad phase coherence (typically those on the longest baselines in the D configuration) have been edited.," The tropospheric phase stability was relatively poor for the observations made during 2000 late summer, and the data with particularly bad phase coherence (typically those on the longest baselines in the D configuration) have been edited." + The weather during 2003 January was excellent., The weather during 2003 January was excellent. + The data were reduced and imaged using the Astronomical Image Processing System (AIPS)., The data were reduced and imaged using the Astronomical Image Processing System (AIPS). + After combining the data from both sets of observations. the resulting naturally-weighted synthesized beam is 4.6x4.4 aresec? at position angle 660.," After combining the data from both sets of observations, the resulting naturally-weighted synthesized beam is $4.6 \times 4.4$ $^2$ at position angle $-60^\circ$." +The rms noise per channel in the final image is 60 gly ], The rms noise per channel in the final image is 60 $\mu$ Jy $^{-1}$. + No redshifted HCN(I-0). emission is detected., No redshifted HCN(1–0) emission is detected. + The central six channels are displayed in Fig. |..," The central six channels are displayed in Fig. \ref{map}," + with 2-6 contours of 120 ulJy |. and crosses denoting the positions of the two millimetre sources detected by Omont et (1996).," with $\sigma$ contours of 120 $\mu$ Jy $^{-1}$ , and crosses denoting the positions of the two millimetre sources detected by Omont et (1996)." + The CO lines reported by Omont et hhave line widths of 190 and 350 kms. |: assuming an intrinsic line width AV. for any HCN emission of 250kms | we find à 3-6 upper limit to the HCN¢1-0) emission of (3(Ανω/AVenamet}!σε rms per channel) = 31 mJy km »," The CO lines reported by Omont et have line widths of 190 and 350 km $^{-1}$; assuming an intrinsic line width $\Delta V_{\rm line}$ for any HCN emission of $\sim 250$ km $^{-1}$ we find a $\sigma$ upper limit to the HCN(1–0) emission of $3 \cdot (\Delta V_{\rm line}/\Delta V_{\rm +channel})^{1/2} \cdot$ rms per channel) = 31 mJy km $^{-1}$." + Using equations | and 3 from Solomon et ((1992b). we derive a 3-G upper limit to the line luminosity of lo Kkms | per.," Using equations 1 and 3 from Solomon et (1992b), we derive a $\sigma$ upper limit to the line luminosity of $L'_{\rm HCN} < 4.9(3.6) \times +10^{10}$ K km $^{-1}$ $^{2}$." + In order to compare the molecular properties of BR 0725 with those of local (UILIRGs we include it in plots of Luen Lig. and Ler/Leg Luen/Leo. in Fig. 2..," In order to compare the molecular properties of BR $-$ 0725 with those of local (U)LIRGs we include it in plots of $L'_{\rm HCN}$ $L_{\rm FIR}$, and $L_{\rm FIR}/L'_{\rm CO}$ $L'_{\rm HCN}/L'_{\rm +CO}$, in Fig. \ref{plots}." + The value for the far-infrared luminosity. £ya=6.3(4.6)xI0 1... has been calculated by integrating under the thermal greybody spectral energy distribution as detailed by Isaak et (2002).," The value for the far-infrared luminosity, $L_{\rm FIR} = 6.3(4.6) \times 10^{13}$ $_\odot$, has been calculated by integrating under the thermal greybody spectral energy distribution as detailed by Isaak et (2002)." + The COtl—O) luminosity comes from a recent measurement of the COtI-0) line flux. Seg=0.170:05 Jy kms.! (C. Henkel. private communication).," The CO(1–0) luminosity comes from a recent measurement of the CO(1–0) line flux, $S_{\rm CO} = 0.17 \pm +0.05$ Jy km$^{-1}$ (C. Henkel, private communication)." + The upper limit of Luc or BR 0725 is consistent with the correlations between LCN Log. and Ly/Leo L'ueN/Leo. observed in more local (UJLTRGs.," The upper limit of $L'_{\rm HCN}$ for BR $-$ 0725 is consistent with the correlations between $L'_{\rm HCN}$ $L_{\rm FIR}$, and $L_{\rm FIR}/L'_{\rm CO}$ $L'_{\rm HCN}/L'_{\rm CO}$, observed in more local (U)LIRGs." + Our measured upper limit suggests that the globally-averaged molecular properties of the host galaxy of BR 0725 are consistent with those found in more local ULIRGs., Our measured upper limit suggests that the globally-averaged molecular properties of the host galaxy of BR $-$ 0725 are consistent with those found in more local ULIRGs. + Furthermore. it is consistent with the interpretation that a large fraction of the far-infrared luminosity originates from dust heated by star formation.," Furthermore, it is consistent with the interpretation that a large fraction of the far-infrared luminosity originates from dust heated by star formation." + We note. however. that a significant fraction of ULIRGs show signs of both starburst and AGN activity (Genzel et 11998).," We note, however, that a significant fraction of ULIRGs show signs of both starburst and AGN activity (Genzel et 1998)." + This has also been found to be the case in many of the high-redshift sources identified in submillimetre surveys that have exploited the lensing effect of galaxy clusters (e.g.. Smail. Ivison Blain 1997).," This has also been found to be the case in many of the high-redshift sources identified in submillimetre surveys that have exploited the lensing effect of galaxy clusters (e.g., Smail, Ivison Blain 1997)." + Tt is therefore not surprising that a naked AGN residing in a young host galaxy might show similarities with ULIROs., It is therefore not surprising that a naked AGN residing in a young host galaxy might show similarities with ULIRGs. + A deeper limit to the HCN emission from BR 0725 will only be possible with the EVLA-.. when an improvement in sensitivity of a factor of about 6 is anticipated for spectral linework at this frequency.," A deeper limit to the HCN emission from BR $-$ 0725 will only be possible with the , when an improvement in sensitivity of a factor of about 6 is anticipated for spectral linework at this frequency." + With our current limit we do. however. exclude a low {με{μονratio.," With our current limit we do, however, exclude a low $L_{\rm FIR}/L_{\rm HCN}$ratio." + Such a ratio would be interpreted as a host galaxy with a high molecular gas density with little ongoing star formation or AGN activity. that is. gas that is to form stars," Such a ratio would be interpreted as a host galaxy with a high molecular gas density with little ongoing star formation or AGN activity, that is, gas that is to form stars" +cosmological models (Samushia&Ratra2006:YiZhang2007) and some other relevant works include Wei&Zhang(2007Ta.b);WuYu(2007a.b):Lazkoz]xurek&Szvellowski(2008):SenScherrerXuetal.ZhangZhu(2003) for examples.,"cosmological models \citep{Samushia06,Yi07} and some other relevant works include \citet{Wei07a,Wei07b,Wu07a,Wu07b,Lazkoz07,Kurek08,Sen08,Xu08,Zhang08} + for examples." + Recently. Sternοἱal.(2010) obtained the £(z) data at 11 different redshifts obtained [rom the differential ages of red-envelope galaxies: ancl other two Hubble parameter data al z=0.24 and z=0.43 were determined by Gaztanagaοἱal.(2009) [rom observations olBAO peaks.," Recently, \citet{hz2} obtained the $H(z)$ data at 11 different redshifts obtained from the differential ages of red-envelope galaxies; and other two Hubble parameter data at $z=0.24$ and $z=0.43$ were determined by \citet{hz3} from observations ofBAO peaks." + Some recent works using these newly /7(z:) data for cosmological constraint can be found in Gongetal.(2010);Liang.Wu&ZhangCao.ZhuLiane(2011):Aa&Zhang(2011);XuWang(2010):Zhaietal.(2010);Zhang.MaLan (2010).," Some recent works using these newly $H(z)$ data for cosmological constraint can be found in \citet{Gong10,Liang2010,Cao11a,Ma11,Xu10,Zhai10,ZML10}." +. In the previous works. Wei&Zhang(2007a) compared the 9 observational Lf(2) data wilh some cosmological models with/without interaction between dark energv and dust matter and found that the Z7(2) data points with fairly large errors cannot severely constrain model parameters alone.," In the previous works, \citet{Wei07a} compared the 9 observational $H(z)$ data with some cosmological models with/without interaction between dark energy and dust matter and found that the $H(z)$ data points with fairly large errors cannot severely constrain model parameters alone." + In this paper. we focus on the newly (2) data to study the interaction between the dust matter and dark energy and test ihe cosmic coincidence problem.," In this paper, we focus on the newly $H(z)$ data to study the interaction between the dust matter and dark energy and test the cosmic coincidence problem." + Ii order to break the degeneracy of model parameters. we also add the barvonic acoustic oscillation (BAO) peak detected by large-scale correlation function. of luminous red galaxies [rom Sloan Digital Skv Survey (SDSS) (Eisensteinetal.2005).. the cosmic microwave background (CAIB) detected by the 7-vear WAIAP data (Ixomatsu and the newly revised Union2 SNe Ia data set (Amanullahetal.," In order to break the degeneracy of model parameters, we also add the baryonic acoustic oscillation (BAO) peak detected by large-scale correlation function of luminous red galaxies from Sloan Digital Sky Survey (SDSS) \citep{Eisenstein05}, the cosmic microwave background (CMB) detected by the 7-year WMAP data \citep{Komatsu10} and the newly revised Union2 SNe Ia data set \citep{Amanullah}." +2010).. This paper is organized as follows: In section ??.. we introduce the observational data including the /7(:). BAO. CAIB and SNe Ia data.," This paper is organized as follows: In section \ref{sec2}, we introduce the observational data including the $H(z)$, BAO, CMB and SNe Ia data." + In section ??.. we derive two Hubble parameters and perform a Markov Chain Monte Carlo analvsis spanning the full parameter space of the model using different data sets.," In section \ref{sec3}, we derive two Hubble parameters and perform a Markov Chain Monte Carlo analysis spanning the full parameter space of the model using different data sets." + Finally. we summarize the main conclusions in Section ??..," Finally, we summarize the main conclusions in Section \ref{sec4}." + In this sectionwe will list the cosmological observations used in our ealeulations: 7 (2). BAO. CMD as well as the SNe Ia observations.," In this sectionwe will list the cosmological observations used in our calculations: $H(z)$ , BAO, CMB as well as the SNe Ia observations." + We adopt the (z) data at 11 different redshillsobtained in Ref. Sternetal. (2010)," We adopt the $H(z)$ data at 11 different redshiftsobtained in Ref. \cite{hz2}, ," +.. and two I7(2) data (7(2=0.24)τοσο 2993. and£(2=0.43) 86.4543.27) determined by Gaztanagaetal. (2009).," and two $H(z)$ data $H(z=0.24)=76.69\pm2.32$ , and$H(z=0.43)=86.45\pm3.27$ ) determined by \citet{hz3}. ." +. The corresponding V can be defined as where o5; is (he lo uncertainty in the //(2) data., The corresponding $\chi^2$ can be defined as where $\sigma_{hi}$ is the $1\sigma$ uncertainty in the $H(z)$ data. +To a very good. approximation. the equivalent. width of an absorption line in the specific intensity profile [rom any part of the stellar disc is the same as the equivalent width of the rotationallv-broadened line profile considered as a whole.,"To a very good approximation, the equivalent width of an absorption line in the specific intensity profile from any part of the stellar disc is the same as the equivalent width of the rotationally-broadened line profile considered as a whole." +" The ratio of the equivalent. width of a small starspot bump at disc centre to that of the entire line profile is therefore just the ratio of the Dux. ""missing in the spot (Piu&RoBaua d)*) to the total Dux from the remaining limb- photosphere. {ρω=wl,τςuf)Pa."," The ratio of the equivalent width of a small starspot bump at disc centre to that of the entire line profile is therefore just the ratio of the flux “missing” in the spot $F_{spot} +\simeq +\pi I_0 (R_{spot}/d)^{2}$ ) to the total flux from the remaining limb-darkened photosphere, $F_{phot} = \pi I_0 (R_{\star}/d)^2 (1-u/3)-F_{spot}$." +" Llere fy is the specific intensity of the photosphere at. disc centre. /2,,,; and £2, are the radit of the spot and the star respectively. and d is the distance to the star."," Here $I_{0}$ is the specific intensity of the photosphere at disc centre, $R_{spot}$ and $R_{\star}$ are the radii of the spot and the star respectively, and $d$ is the distance to the star." + Hence for a small. isolated. spot viewed at the centre of the stellar clise.," Hence for a small, isolated spot viewed at the centre of the stellar disc." + In reality the spots are neither isolated. nor completely dark., In reality the spots are neither isolated nor completely dark. + At the τος waveleneths observed. the continuum surface brightness of the spots is expected to be about 0.25 ο 0.3 times the photospheric value.," At the red wavelengths observed, the continuum surface brightness of the spots is expected to be about 0.25 to 0.3 times the photospheric value." + The bump amplitude or a spot of given area is thus expected to be diminished by his amount relative to the bump amplitude fora completely dark spot., The bump amplitude for a spot of given area is thus expected to be diminished by this amount relative to the bump amplitude for a completely dark spot. + However. the fractional coverage of spots on AB Dor is probably of order 30 percent. which serves to increase he loss of light from an individual spot as a fraction of the otal amount of 7clean photosphere.," However, the fractional coverage of spots on AB Dor is probably of order 30 percent, which serves to increase the loss of light from an individual spot as a fraction of the total amount of “clean” photosphere." + Overall. the ellects of inito spot surface brightness and a high spot filling factor will tend to cancel cach other out.," Overall, the effects of finite spot surface brightness and a high spot filling factor will tend to cancel each other out." + The spots listed in Table 1. have equivalent: widths ranging [rom W—0.0016 to M=0.0071 km +., The spots listed in Table \ref{tab:spotpar} have equivalent widths ranging from $W=0.0016$ to $W=0.0071$ km $^{-1}$. + Since the equivalent width of the deconvolved. stellar. profile is approximately 4.5 kms 1 (ef., Since the equivalent width of the deconvolved stellar profile is approximately 4.5 km $^{-1}$ (cf. + Fig. 1)).," Fig. \ref{fig:tellurics}) )," + the inferred fractional areas. (Rojo1)? of individual spots range [rom 0.00026, the inferred fractional areas $(R_{spot}/R_{\star})^{2}$ of individual spots range from 0.00026 +A sumnmarv of the number of stars and exposures that met each flare criterion is presented in Table 4. which also shows that the majority of flares come from the MSN sample.,"A summary of the number of stars and exposures that met each flare criterion is presented in Table 4, which also shows that the majority of flares come from the MSN sample." + This is not unexpected. since there are many more stars in (hat sample.," This is not unexpected, since there are many more stars in that sample." + Our results sugeest Chat flares in this sparsely sampled spectroscopic data set are most easily identified through emission line variability rather than the absolute strength of the emission lines., Our results suggest that flares in this sparsely sampled spectroscopic data set are most easily identified through emission line variability rather than the absolute strength of the emission lines. + We first analvzed our flare sample to verily that the properties of the Mares we identified are consistent with the characteristic time evolution seen in continuous monitoring observations., We first analyzed our flare sample to verify that the properties of the flares we identified are consistent with the characteristic time evolution seen in continuous monitoring observations. + Because our data might capture any. or all phases of a flare. we expected to see examples of flares in the rise. peak. and decay pliases as well as a few laree impulsive phase flares (hat show blue continuum flix enhancement.," Because our data might capture any or all phases of a flare, we expected to see examples of flares in the rise, peak, and decay phases as well as a few large impulsive phase flares that show blue continuum flux enhancement." + We defined decay-phase flares as those showing both Ho and IL? in at least two consecutive exposures with diminishing FLI values., We defined decay-phase flares as those showing both $\alpha$ and $\beta$ in at least two consecutive exposures with diminishing FLI values. + Rise-phase flares were delined in (he opposite sense. with (wo or more consecutive exposures having increasing FLI values for both Ila aud IL3.," Rise-phase flares were defined in the opposite sense, with two or more consecutive exposures having increasing FLI values for both $\alpha$ and $\beta$." + There were ten rise phase flares and 11 decav phase flares in the sample., There were ten rise phase flares and 11 decay phase flares in the sample. + Additionally. we saw five “peak” [lares (hat show first increasing and (hen decreasing ELI values. which we interpret as [lares that were seen through most of their evolution.," Additionally, we saw five “peak” flares that show first increasing and then decreasing FLI values, which we interpret as flares that were seen through most of their evolution." + We also identified Πάγος that occurred in only a subset of the exposures. either in the final exposure of a sequence. or in cases where some of (he exposures are separated by many hours or clavs from (he other exposures.," We also identified flares that occurred in only a subset of the exposures, either in the final exposure of a sequence, or in cases where some of the exposures are separated by many hours or days from the other exposures." + In 19 cases. at least one exposure was obtained that showed a quiescent spectrum wilh no sien of flaring.," In 19 cases, at least one exposure was obtained that showed a quiescent spectrum with no sign of flaring." + Flares with quiescent spectrum. as well as rise. decay. and peak phase flares are noted in (he final column of Table 3.," Flares with quiescent spectrum, as well as rise, decay, and peak phase flares are noted in the final column of Table 3." + The time evolution of the flares we have identified is consistent with the known characteristics of Hares., The time evolution of the flares we have identified is consistent with the known characteristics of flares. + Previous observations using time resolved spectroscopic monitoring have shown that the higher order Balmer lines show larger increases in flux during Hares than the lower order lines., Previous observations using time resolved spectroscopic monitoring have shown that the higher order Balmer lines show larger increases in flux during flares than the lower order lines. + This results in the observed. Balner clecrement (ratio of individual lines to a fiducial. often. IL? as we adopt here) becoming flatter. since H and the higher order lines," This results in the observed Balmer decrement (ratio of individual lines to a fiducial, often $\beta$ as we adopt here) becoming flatter, since $\gamma$ and the higher order lines" +broken lines indicate galaxies before they are recognized as early-type galaxies.,broken lines indicate galaxies before they are recognized as early-type galaxies. + It can easily be seen that the sample of early-type galaxies at high redshift is a small subsample of all galaxies which are classified as early-type galaxies at z=0., It can easily be seen that the sample of early-type galaxies at high redshift is a small subsample of all galaxies which are classified as early-type galaxies at $z=0$. + The two samples are therefore not directly comparable. and erroneous results are derived if morphological evolution is ignored.," The two samples are therefore not directly comparable, and erroneous results are derived if morphological evolution is ignored." + As a result. the evolution in the mean M/L ratio of the early-type galaxies is very slow (panel d).," As a result, the evolution in the mean $M/L$ ratio of the early-type galaxies is very slow (panel d)." + The slope of the M/L — z relation is comparable to the slope for a single stellar population which formed at z2x. (indicated by the dashed line). even though the mean formation redshift of the stars in all early-type galaxies at z2O 1s low at (z.;c2.," The slope of the $M/L$ – $z$ relation is comparable to the slope for a single stellar population which formed at $z=\infty$ (indicated by the dashed line), even though the mean formation redshift of the stars in all early-type galaxies at $z=0$ is low at $\langle z_* \rangle \approx 2$." + Even more remarkable ts the fact that the scatter in M/L ratios is virtually constant., Even more remarkable is the fact that the scatter in $M/L$ ratios is virtually constant. + These effects are caused by the fact that the youngest galaxies continuously drop out of the sample going to higher redshifts., These effects are caused by the fact that the youngest galaxies continuously drop out of the sample going to higher redshifts. + In the subsections below we specify a broader range of models. and explore the consequences.," In the subsections below we specify a broader range of models, and explore the consequences." + The full models are quantified by three parameters: fan. the time when star formation starts. r5. the time scale which characterizes the distribution of times when star formation stops. and 7... which describes the star formation rate between the start and end of star formation.," The full models are quantified by three parameters: $\tstart$, the time when star formation starts, $\taustop$, the time scale which characterizes the distribution of times when star formation stops, and $\fstar$, which describes the star formation rate between the start and end of star formation." + The last two parameters are defined in the following way., The last two parameters are defined in the following way. + The parameter Το determines the probability distribution Of A. the tme when star formation stops for an individual galaxy: We show later that this expression can provide a satisfactory fit to the data.," The parameter $\taustop$ determines the probability distribution of $\tstop$, the time when star formation stops for an individual galaxy: We show later that this expression can provide a satisfactory fit to the data." + If. rp»Ri. g(R)=(RyRY"" for simplicity."," Writting the Alfvènn speed associated to the random field as $v_{\rm A}^{2}=g(R) v_{\rm t}^{2}$, with the turbulent velocity dispersion $v_{\rm t}$ constant with $R$, and $dg/dR<0$ , the rotation curve changes according to the relation: Following \citet{deb02}, we define $R_{\rm in}$ as the radius of the innermost sampled point of the rotation curve, and assume that at $R>R_{\rm in}$, $g(R)=(R_{\rm in}/R)^{n}$ for simplicity." + Doing so. we are imposing that at HW. CA&ον.," Doing so, we are imposing that at $R_{\rm in}$, $v_{\rm A}\approx v_{\rm t}$." + The second term of the RIS of Eq. (12)), The second term of the RHS of Eq. \ref{eq:drift}) ) +" is of the order of the asvnuuetric dift (comparable to observational uncertainties). whereas the last term is nezRE2R""."," is of the order of the asymmetric drift (comparable to observational uncertainties), whereas the last term is $-nv_{\rm t}^{2}R_{\rm in}^{n}/2R^{n}$." + As the observed roteion curve differs from the NEW profile along a significant range of ealactocentric radius.sav at RomRinmSOO pe. then O—0zxl. implvine that ezREARx¢2/2—50 kms] ? (for ow=d0 km s +).," As the observed rotation curve differs from the NFW profile along a significant range of galactocentric radius,say at $R\gg R_{\rm in}\approx 500$ pc, then $0 1, the induced eccentricity is strongly suppressed at small radii(see 2.1)) even though the mode formally has"," For $\eta > 1$ , the induced eccentricity is strongly suppressed at small radii(see \ref{sec:wkb}) ) even though the mode formally has" +For the first four samples the mean stellar ages of ERGs at all 1«2<2.5 are spread over the range between z~5 and shortly (a few; 107 vr) before the epoch of observation.,For the first four samples the mean stellar ages of ERGs at all $15$. + These have stellar masses OO.I0ll7M... more than twice. the mass ofB any ERG4 ain our sample.," These have stellar masses $9.4\times 10^{11}M_{\odot}$, more than twice the mass of any ERG in our sample." + Llence their ages may be evidence that the very most massive spheroicals formed significantly earlier and/or Formed their stars most quickly. as in the model of Granato et al. (," Hence their ages may be evidence that the very most massive spheroidals formed significantly earlier and/or formed their stars most quickly, as in the model of Granato et al. (" +2004).,2004). + Lt is also notable that the formation redshifts appear to trace the plotted ος loci., It is also notable that the formation redshifts appear to trace the plotted $z_{msf}$ loci. + Phe ages of the oldest galaxies at each redshift. as a function of redshift. is an important tracer of the expansion of the universe and hence the cosmological mocel (e.g. Jimenez and Loeb 2002).," The ages of the oldest galaxies at each redshift, as a function of redshift, is an important tracer of the expansion of the universe and hence the cosmological model (e.g. Jimenez and Loeb 2002)." + We would expect z;r for the oldest galaxies to be constant with observed redshift. and the agreementwith the plotted loci would support a AXc0.75 cosmological constant (w= 1) model.," We would expect $z_{msf}$ for the oldest galaxies to be constant with observed redshift, and the agreementwith the plotted loci would support a $\Lambda\simeq 0.75$ cosmological constant $w=-1$ ) model." + As Pie. represents a Blux-weighted: mean stellar age. 1ο true age of a galaxy since formation must always |be ereater. to a degree dependent on the detailed form of the star-formation history.," As $T_{pas}$ represents a flux-weighted mean stellar age, the true age of a galaxy since formation must always be greater, to a degree dependent on the detailed form of the star-formation history." + One interpretation may therefore be iu most or all of the red. galaxies observed as ERCs at 2] 2 ave galaxies. or mergers of galaxies. which formed ab zz4 5. and that the spread in their stellar ages up to js maximunm. redshift can be attributed to differences in iir individual evolution. i.c. the mergers ancl starbursts jov have experienced.," One interpretation may therefore be that most or all of the red galaxies observed as ERGs at $z=1$ –2 are galaxies, or mergers of galaxies, which formed at $z\geq 4$ –5, and that the spread in their stellar ages up to this maximum redshift can be attributed to differences in their individual evolution, i.e. the mergers and starbursts they have experienced." + Caputi et al. (, Caputi et al. ( +2004. 2005) using photometric redshift estimates derived from seven-band photometry of ERGs and other A«22 galaxies in this field. found. the comoving number density of massive (2510/7M.) galaxies in a full A-selected: sample to fall only slowly from τς=1.55 to 2=3.5. where a significant traction. 2025 per cent. of today’s massive galaxies were already in place.,"2004, 2005), using photometric redshift estimates derived from seven-band photometry of ERGs and other $K<22$ galaxies in this field, found the comoving number density of massive $>5\times 10^{10}\rm +M_{\odot}$ ) galaxies in a full $K$ -selected sample to fall only slowly from $z=1.75$ to $z=3.5$, where a significant fraction, 20–25 per cent, of today's massive galaxies were already in place." + However. the comoving number density of the reddest subse of these galaxies. the ERGs. evolves much more rapicly. steadily increasing with time from z=3.5 to z=1. anc following a trend whieh extrapolates to the present-cay I5/8O population at z—0.," However, the comoving number density of the reddest subset of these galaxies, the ERGs, evolves much more rapidly, steadily increasing with time from $z=3.5$ to $z=1$, and following a trend which extrapolates to the present-day E/SO population at $z=0$." + At 2=1 1.5. the rising comoving number density of ERGs approached that of all A-selectec ealaxies at the higher recshilt of 2~3.5.," At $z=1$ –1.5, the rising comoving number density of ERGs approached that of all $K$ -selected galaxies at the higher redshift of $z\sim 3.5$." + llence. this suggests that a substantial population of massive galaxies formed at zο4 and were initially. starbursting and relatively blue. but with increasing age many became red enough to be classed as ERGs.," Hence, this suggests that a substantial population of massive galaxies formed at $z\geq 4$ and were initially starbursting and relatively blue, but with increasing age many became red enough to be classed as ERGs." + Interestinely. for the brightest. (4.<24.5) Lyman break ealaxics at 4. Allen et al. (," Interestingly, for the brightest $I<24.5$ ) Lyman break galaxies at $z\sim 4$, Allen et al. (" +"2005) measure strong clustering of ry=114c2h54, Alpe comoving. consistent with these evolving into the ERGs at z—1 2.","2005) measure strong clustering of $r_0=11.4\pm + 2 \rm h_{100}^{-1}$ Mpc comoving, consistent with these evolving into the ERGs at $z=1$ –2." + To produce the evolution in ERC number density these galaxies must have entered the ERC class over a wide redshift range κ250 per cent also show some OLI] emission.,"2005), found that $\geq 75$ per cent of ERG spectra have prominent absorption features and $4000\rm \AA$ breaks, while $>50$ per cent also show some [OII] emission." + We find the same for our slightly deeper sample., We find the same for our slightly deeper sample. + For only 3 ERGs do we find neither OL] emission nor any indication of a voung stellar population from a blue excess in the SED., For only 3 ERGs do we find neither [OII] emission nor any indication of a young stellar population from a blue excess in the SED. + This is consistent with the Doherty et al. (, This is consistent with the Doherty et al. ( +2005) estimate that 28 per cent of ERGs show no evidence of recent star-formation.,2005) estimate that 28 per cent of ERGs show no evidence of recent star-formation. + For a clear majority of ERGs. 10/13 at 2<1.5. we detect a OL]37217A emission linc.," For a clear majority of ERGs, 10/13 at $z<1.5$, we detect a $\rm [OII]3727 \AA$ emission line." + Vhis includes two galaxies where the line only just detected with an equivalent width 5X. while at the other extreme we have 3 ERGs with OL) equivalent widths zz30.," This includes two galaxies where the line only just detected with an equivalent width $\sim 5\rm \AA$ , while at the other extreme we have 3 ERGs with [OII] equivalent widths $\geq \rm 30\AA$." + For the 10 emission-line galaxies. the OLL]3727A Iluxes - uncorreeted. for dust - correspond t0 à mean SER of 1.63 Above1. intermediate between the 28 M.vr. 1amean ΟΕΠο of Yan et al. (," For the 10 emission-line galaxies, the $\rm[OII]3727 \AA$ fluxes - uncorrected for dust - correspond to a mean SFR of 1.63 $\rm M_{\odot} yr^{-1}$, intermediate between the 2.8 $\rm M_{\odot} yr^{-1}$ mean $\rm SFR_{OII}$ of Yan et al. (" +2004a) and the 1.1 Myr fof the Doherty et al. (,2004a) and the 1.1 $\rm M_{\odot} yr^{-1}$ of the Doherty et al. ( +2005) ERGs.,2005) ERGs. + Of course the true SLRs of the emission-line ELCs will be higher., Of course the true SFRs of the emission-line ERGs will be higher. + On the basis of the dust. extinction. estimated from our moclel fits. we estimate the real mean SER. will be about 1224 M.vr +t.," On the basis of the dust extinction estimated from our model fits, we estimate the real mean SFR will be about 12–24 $\rm M_{\odot} yr^{-1}$ ." + This may still be an underestimate as emission line regions of current SE may. suller more extinction than the continuum produced by SE over a longer period., This may still be an underestimate as emission line regions of current SF may suffer more extinction than the continuum produced by SF over a longer period. + Spitzer mid-I1t. observations(Yan et al., Spitzer mid-IR observations(Yan et al. + 2004b) of, 2004b) of +numbers (e.g.. plane Couette and. Couette-Tavlor flows with appropriate parameters).,"numbers (e.g., plane Couette and Couette-Taylor flows with appropriate parameters)." +" A larger minimal Ievnolds number is à sign of a greater difficulty to trigger turbulence. i.e. an increased difficulty. for turbulent. transport to dominate over the viscous one. aud therefore is a slgn of a smaller scale turbulence. due to the physical picture underlving the turbulent viscosity prescription (ie.. the (transport occurs over a smaller. ""mean [free path 7/4. and correlatively with a smaller ""random velocity ey, due to the assumption of identical shear rale between the two different. flows)."," A larger minimal Reynolds number is a sign of a greater difficulty to trigger turbulence, i.e. an increased difficulty for turbulent transport to dominate over the viscous one, and therefore is a sign of a smaller scale turbulence, due to the physical picture underlying the turbulent viscosity prescription (i.e., the transport occurs over a smaller “mean free path"" $l_M$, and correlatively with a smaller “random velocity"" $v_M$ due to the assumption of identical shear rate between the two different flows)." + From these relations. one can easily check that. at the minimum Revnolds number. the advection term. which dominates scale coupling and is (he primary cause of (he inertial turbulent spectrum. is comparable to the dissipation term. at the turbulent (ransport scale.," From these relations, one can easily check that, at the minimum Reynolds number, the advection term, which dominates scale coupling and is the primary cause of the inertial turbulent spectrum, is comparable to the dissipation term, at the turbulent transport scale." + As a consequence. the turbulence possesses litile or no inertial domain at its threshold.," As a consequence, the turbulence possesses little or no inertial domain at its threshold." + Furthermore. as long as there is no change in the turbulence generating process. increasing the Revnolds number can only result in lowering the dissipation scale with respect to 7/3. and therefore in the progressive build up of an inertial spectrum (e.g.. imagine one does this by reducing the viscosity while maintaining the large scale structure of the flow unchanged).," Furthermore, as long as there is no change in the turbulence generating process, increasing the Reynolds number can only result in lowering the dissipation scale with respect to $l_M$, and therefore in the progressive build up of an inertial spectrum (e.g., imagine one does this by reducing the viscosity while maintaining the large scale structure of the flow unchanged)." + It is important to notice that the estimates of Eqs. (17)), It is important to notice that the estimates of Eqs. \ref{lm}) ) + and (13)) remain valid. [or Revnolds numbers larger5 than the turbulence thireshold. as long5 as the turbulence 5generating process is unchanged.," and \ref{vm}) ) remain valid for Reynolds numbers larger than the turbulence threshold, as long as the turbulence generating process is unchanged." + The predictions of the scaling proposed here are well supported by the available empirical and numerical evidence. as shown in Appendix A. Eqs. (17))," The predictions of the scaling proposed here are well supported by the available empirical and numerical evidence, as shown in Appendix A. Eqs. \ref{lm}) )" + and (18)) have particularly interesting consequences for the understanding ol turbulence in Couette-Tavlor flows., and \ref{vm}) ) have particularly interesting consequences for the understanding of turbulence in Couette-Taylor flows. + For definiteness. I will first [ocus on flows where the inner evlinder is at rest.," For definiteness, I will first focus on flows where the inner cylinder is at rest." + As argued at the end of section ??.. [or r9Ar. the Navier-Stokes equation for Couette-Tavlor flows [Eq. (8))]," As argued at the end of section \ref{CTF}, for $r\gg\Delta r$, the Navier-Stokes equation for Couette-Taylor flows [Eq. \ref{NSCT}) )]" + then reduces to the Navier-Stokes equation for planar Couette flows [Eq. (1))], then reduces to the Navier-Stokes equation for planar Couette flows [Eq. \ref{NSC}) )] + and the minimal Revnolds number is constant., and the minimal Reynolds number is constant. + However. when Avr r. the geometric terms O(u?/r)e(GNO)?/r become comparable (o the advection one on scale Ar.," However, when $\Delta +r\rightarrow r$ the geometric terms $O(w^2/r)\sim +(r\Delta\Omega)^2/r$ become comparable to the advection one on scale $\Delta r$." +" Furthermore. if at some radial location r in the flow. /e,,, remained constant when Ar>>r. Eq. (17))"," Furthermore, if, at some radial location $r$ in the flow, $Re_m$ remained constant when $\Delta r\gg r$, Eq. \ref{lm}) )" +" would imply that /y, could become arbitrarily larger than r. which makes little sense."," would imply that $l_M$ could become arbitrarily larger than $r$, which makes little sense." + In fact. one expects that /3;xr once Ar/r exceecls some critical ratio A. (which for the time being is expected to be of order unitv). for two reasons: first.the geometric terms introduce a limiting scale (the radius r). which must be accounted for by," In fact, one expects that $l_M\propto r$ once $\Delta r/r$ exceeds some critical ratio $\Delta_c$ (which for the time being is expected to be of order unity), for two reasons: first,the geometric terms introduce a limiting scale (the radius $r$ ), which must be accounted for by" +In order to resolve the surface of the observed star during a microlensing event. the magnification pattern created by the lens needs to supply a large magnification gradient.,"In order to resolve the surface of the observed star during a microlensing event, the magnification pattern created by the lens needs to supply a large magnification gradient." + Two such configurations meeting this requirement have been discussed extensively in the literature: a point-caustic at the angular position of a single point-like lens (2222222222) and a line-shaped fold caustic produced by a binarylens (2222222).," Two such configurations meeting this requirement have been discussed extensively in the literature: a point-caustic at the angular position of a single point-like lens \citep{WM94,NemWick94,Gould94:extsrc,BC95,BC96,Witt95,GW96,GG:detld,Heyetal2000,Hey2003} and a line-shaped fold caustic produced by a binarylens \citep{SchneiWei:QSO,SchneiWag, GG:detld,Rhie:ld,Do:SecondLD,Do:Fold,Do:FoldLD}." + It has been pointed out by ? that fold-caustic events are more common and their observation is easier to plan. whereas close-impact events where the source transits a point caustic can provide more information.," It has been pointed out by \citet{GG:detld} that fold-caustic events are more common and their observation is easier to plan, whereas close-impact events where the source transits a point caustic can provide more information." + However. I will argue that this apparent gain of information can usually not be realized due to potential lens binarity.," However, I will argue that this apparent gain of information can usually not be realized due to potential lens binarity." + In contrast to fold caustics which form a generically stable singularity. point caustics are not stable and do not exist in reality.," In contrast to fold caustics which form a generically stable singularity, point caustics are not stable and do not exist in reality." + Instead. there is always a small diamond-shaped caustic containing four cusps.," Instead, there is always a small diamond-shaped caustic containing four cusps." + In this paper. the influence of lens binarity on the measurement of stellar. limb-darkening coefficients. and. proper motion is investigated and the arising limitations of the power of close-impact events where the source passes over a single closed caustic are discussed.," In this paper, the influence of lens binarity on the measurement of stellar limb-darkening coefficients and proper motion is investigated and the arising limitations of the power of close-impact events where the source passes over a single closed caustic are discussed." + Sect., Sect. + 2. discusses the basics of close-impact microlensing events with the effect of source size. the potential of measuring stellar proper motion and limb darkening. and the effect of lens binarity.," \ref{sec:cie} discusses the basics of close-impact microlensing events with the effect of source size, the potential of measuring stellar proper motion and limb darkening, and the effect of lens binarity." + Sect., Sect. + 3. shows the influence of lens binarity on the extraction of information from such events., \ref{sec:binvsld} shows the influence of lens binarity on the extraction of information from such events. + First. the effect of lens binarity on the light curves is demonstrated by means of two illustrative examples involving K and M Bulge giants.," First, the effect of lens binarity on the light curves is demonstrated by means of two illustrative examples involving K and M Bulge giants." + Subsequently. a simulation of data corresponding to these configurations is used to investigate the potential misestimates of parameters if lens binarity is neglected.," Subsequently, a simulation of data corresponding to these configurations is used to investigate the potential misestimates of parameters if lens binarity is neglected." + Sect., Sect. + 4. presents the final conclusions and a summary of the results., \ref{sec:conclusions} presents the final conclusions and a summary of the results. +" As pointed out by ?.. a point-like source star at a distance 2s from the observer exhibits a magnification due to the gravitational field of a lens star with mass AZ at 24, by a factor where source and lens are separated by the angle 56p and denotes the angular Einstein radius."," As pointed out by \citet{Pac86}, a point-like source star at a distance $D_\rmn{S}$ from the observer exhibits a magnification due to the gravitational field of a lens star with mass $M$ at $D_\rmn{L}$ by a factor where source and lens are separated by the angle $u\,\theta_\rmn{E}$ and denotes the angular Einstein radius." + The proper motion ;; of the source relative to the lens constitutes a microlensing event with the time-scale /p.= θε. for which the lens-source separation becomes," The proper motion $\mu$ of the source relative to the lens constitutes a microlensing event with the time-scale $t_\rmn{E} = \theta_\rmn{E}/\mu$ , for which the lens-source separation becomes" +"where /,,.= AR/o,.,.N is the number of stars, /! is the radius and σι, is the velocity dispersion.","where $t_{cross}= R/\sigma_v$ , $N$ is the number of stars, $R$ is the radius and $\sigma_v$ is the velocity dispersion." + We have used the value σι 3 km ! (?).., We have used the value $\sigma_v$ = 3 km $^{-1}$ \citep{binmer}. + The clusters were divided into regions so as to obtain a significant number of stars in each region., The clusters were divided into regions so as to obtain a significant number of stars in each region. +" For King 16, we obtained a core radius 0.59€0.24."," For King 16, we obtained a core radius $0.89 \pm 0.24$." + We divided the cluster into three regions: core (0'—0.907). halol (0.39'—3’) and halo2 (ο)—7).," We divided the cluster into three regions: core $0'-0.89'$ ), halo1 $0.89'-3'$ ) and halo2 $3'-7')$." +" In the case of NGC 1931, we divided the cluster into three regions: halol (0!— 4), halo2 (4'— *') and halo3 (s'—12’)."," In the case of NGC 1931, we divided the cluster into three regions: halo1 $0'-4'$ ), halo2 $4'-8'$ ) and halo3 $8'-12'$ )." +" Due to the central obscuring nebula, we have no stars in the core region, and hence we excluded the same."," Due to the central obscuring nebula, we have no stars in the core region, and hence we excluded the same." +" In the case of NGC 637, we divided the cluster into three regions: core (0'—0.4). halol (0.4— 3) and halo2 (3'— 6’)."," In the case of NGC 637, we divided the cluster into three regions: core $0'-0.4'$ ), halo1 $0.4-3$ ) and halo2 $3'- 6'$ )." + As there were no stars in the core of NGC 189 and the cluster is very small. we divided the cluster into only two regions: halol (0— 2.5') and halo2 (2.5'— 5’).," As there were no stars in the core of NGC 189 and the cluster is very small, we divided the cluster into only two regions: halo1 $0-2.5'$ ) and halo2 $2.5'-5'$ )." + The values of 4 for different regions of the clusters are also indicative of mass seggregation and are shown in Table 5 with the mass estimatesfor each region., The values of $\chi$ for different regions of the clusters are also indicative of mass seggregation and are shown in Table \ref{dypar} with the mass estimatesfor each region. +" The mass estimates for the clusters King 16, NGC 1931, NGC 637 and NGC 189 are 1332E44. 8,,"," The mass estimates for the clusters King 16, NGC 1931, NGC 637 and NGC 189 are $1382 \pm 44 M_{\odot}$ \ref{mfk16}," +Short Waveleught (SW) camera was used. with a projected pixel size of (71118 and a field of view of 1524152 arcsec.,"Short Wavelenght (SW) camera was used, with a projected pixel size of 148 and a field of view of $\times$ 152 arcsec." + Observations were performed through the J (A= 12h AA=0.291). H(X=1.6549: AX= 0.304) and Wy (A=2.169: AX= 0.2759) band filters.," Observations were performed through the $J$ $\lambda= 1.25 \mu$ ; $\Delta \lambda= 0.29 \mu$), $H$ $\lambda= 1.65 \mu$; $\Delta \lambda= 0.30 \mu$ ) and $K_s$ $\lambda= 2.16 \mu$; $\Delta \lambda= 0.27 \mu$ ) band filters." +" To allow for the subtraction of the variable IR sky backeround. observations 1 cach filter were split iu sequences of shorther dithered exposures with integration times of 50 sin the 7/7 aud A, baus and of 120 s in the J baud ione cach point of the dithering pattern."," To allow for the subtraction of the variable IR sky background, observations in each filter were split in sequences of shorther dithered exposures with integration times of 50 s in the $H$ and $K_s$ bands and of 120 s in the $J$ band along each point of the dithering pattern." + The journal of 6servations is reported in Table 1., The journal of observations is reported in Table 1. + The total integration times over all nights were 2154) s (J). 6250 s (If). and 1500s (I).," The total integration times over all nights were 3480 s $J$ ), 6250 s $H$ ), and 4500s $K_s$ )." + For each baud. observation were taken under photomoetric conditions with a secing often better than 1700 and aimmass below 1.5.," For each band, observation were taken under photometric conditions with a seeing often better than 0 and airmass below 1.5." + Atinospheric conditions were average with ouly the nights of February Lith. 16th. and 19th affected by a Blunidity up to1054.," Atmospheric conditions were average with only the nights of February 11th, 16th, and 19th affected by a humidity up to." +. Twilight fat fields. dark frames. as well as nuages of standard stars from the Persson e al. (," Twilight flat fields, dark frames, as well as images of standard stars from the Persson et al. (" +1998) fields. were taken daily as part of the calibration plan.,"1998) fields, were taken daily as part of the calibration plan." + We downloaded the data from the ESO publie Science Data and we reduced/calibrated them using the updated version of the ESOppipeline*., We downloaded the data from the ESO public Science Data and we reduced/calibrated them using the updated version of the ESO. +. For each exposure sequence. single frames were registered and coadded to produce a background subtracted and cosmic-ray free image.," For each exposure sequence, single frames were registered and coadded to produce a background subtracted and cosmic-ray free image." + We used the SLUW nuage as a relative reference frame to register the ppositiou ou the luuages., We used the 814W image as a relative reference frame to register the position on the images. + Photometry was performed using the v2.[. which implements the “first monent? algovitlin(7).," Photometry was performed using the v2.4, which implements the “first moment” algorithm." +". In view of the nou-optimal sky couditious. we performed a photometric calibration of cach image using a set of 25 2ALASS stars as a reference,"," In view of the non-optimal sky conditions, we performed a photometric calibration of each image using a set of 25 2MASS stars as a reference." + Our solutions turned out to be very good. with a ruis.," Our solutions turned out to be very good, with a r.m.s." + of ~0.1 mae in the J. II aud Iss bands. respectively.," of $\sim0.1$ mag in the J, H and Ks bands, respectively." + The resulting fluxes of source Z are J=21.53+0.07. W=20.63+0.11. Ks=20.53+0.18.," The resulting fluxes of source Z are $21.53\pm0.07$, $20.63\pm0.11$, $20.53\pm0.18$ ." + Such results are in broad agreemoeut with and with?., Such results are in broad agreement with and with. +. The upper limits to the ciission of aare J~23.9. II22.7 and Ks21.7.," The upper limits to the emission of are $\sim23.9$, $\sim22.7$ and $\sim21.7$." + Ou test withHST.. based ou both absolute and relative astrometry on iuultiiepoch images. firmly rules out aux physical association of Source Z with5209.," Our test with, based on both absolute and relative astrometry on multi-epoch images, firmly rules out any physical association of Source Z with." +. What is source Z?, What is source Z? + Multicolor photometry. based. on the aand ddatasets. poiuts to an unrelated background red dwarf.," Multicolor photometry, based on the and datasets, points to an unrelated background red dwarf." + Flux aud colors are consistent with (although slightlv redder than) au AIS star located at ~5 προ reddened by ECD-V)—0.1.," Flux and colors are consistent with (although slightly redder than) an M5 star located at $\sim5$ kpc, reddened by $\sim$ 0.1." + We note that the uupper lits based on our 2002 observations in the R band ive not cousisteut with the source flux as measured with im 2005., We note that the upper limits based on our 2002 observations in the R band are not consistent with the source flux as measured with in 2005. + This could be due to some intrinsic variability of the dwarf star. and/or to coufusion effects in the images. due to the PSF wines of the two much brighter stars ling a few aresec away to the South-West.," This could be due to some intrinsic variability of the dwarf star, and/or to confusion effects in the images, due to the PSF wings of the two much brighter stars lying a few arcsec away to the South-West." + Of course. in both cases the conclusion about the non-association of source Z with wwould not change.," Of course, in both cases the conclusion about the non-association of source Z with would not change." + Thus. iecluains. as vet. unidentified in the optical/IR. as all the other CCOs observed so fax(22777). with the ouly possible exception of the source in the Vela Jv. SNR(?).," Thus, remains, as yet, unidentified in the optical/IR, as all the other CCOs observed so far, with the only possible exception of the source in the Vela Jr. SNR." +. The upper limits to the optical/IR flux prescuted here are the deepest available so far for a member of the CCO class and corresponc to an (unabsorbed) optical to. X-rav flux ratio PA4qweΈναsear~55-107 s!),"," $^+$ is very irresponsive to the CR rates at high density except for very high CR rates $\zeta +> 5\cdot 10^{-14}$ $^{-1}$ )." +" In the low density case, N(CO*) does not show a very obvious trend."," In the low density case, $N({\rm + CO}^+)$ does not show a very obvious trend." +pattern of variability very simular to that of (Nicdziclski1995... 199Ga. b: Wessolowski /Niedzielskà 1996: Niedzielski 19985)).,"pattern of variability very similar to that of \cite{Niedzielski95}, 1996a, b; Wessolowski Niedzielski 1996; \cite{Niedzielski99}) )." + Stroug line-profile variability was observed. as well as apparently cvclical (according to P zx 2.667 davs) variations iu the EWs of À 1686 and À5112 (Niedzieldki 1996a)).," Strong line-profile variability was observed, as well as apparently cyclical (according to $\cal P$ $\approx$ 2.667 days) variations in the EWs of $\lambda$ 4686 and $\lambda$ 5412 \cite{Niedzielski96a}) )." + The first claim of periodic variabiltvin with Pom 7.7 days was made by Lamontagne(1983) from an analysis of the radial velocity variations of A 1686., The first claim of periodic variabilityin with $\cal P$ $\approx$ 7.7 days was made by \cite{Lamontagnep} from an analysis of the radial velocity variations of $\lambda$ 4686. + The first photometric ionitoriug of this object has shown to be variable. with au indication of a 6.1 day period (Aloffat Shara 1986).," The first photometric monitoring of this object has shown to be variable, with an indication of a 6.1 day period (Moffat Shara 1986)." + Receutly Marcheuko«al.(1998a}) discussed broadband. plotometric data which revealed that also displays relatively long-term photometric variations. with a mareial evidence for à P = 1ll.6s + 0.11 dav periodicity.," Recently, \cite{Marchenko98a} discussed broadband photometric data which revealed that also displays relatively long-term photometric variations, with a marginal evidence for a $\cal P$ = 11.68 $\pm$ 0.14 day periodicity." + As can be seen. controversy persits in the literature concerning the possible evclical nature of the variations i1.," As can be seen, controversy persits in the literature concerning the possible cyclical nature of the variations in." + We present in this paper the results of spectroscopic aud. photometric monitoring of carried out in 1995 and 1996 aiming at shedding some elt ou this issue., We present in this paper the results of spectroscopic and photometric monitoring of carried out in 1995 and 1996 aiming at shedding some light on this issue. + The photometric variability of has been investigated diving the interval 1996 September LSOctober 5 by use of the sinele chanucl photometer ou the 0.81 ii telescope of the Observatorio Astrouónmico Nacional at San Pedro Marrtir (Mexico)., The photometric variability of has been investigated during the interval 1996 September 18–October 5 by use of the single channel photometer on the 0.84 m telescope of the Observatorio Astronómmico Nacional at San Pedro Márrtir (Mexico). + Two additional objects were nonitored during this observing rum. namely. and155.," Two additional objects were monitored during this observing run, namely, and." +. The nights were generally clear., The nights were generally clear. + was observed through a narrowband ο filter centered ou 5110 ((FWIIM = 90 Aj)., was observed through a narrowband $v$ filter centered on 5140 (FWHM = 90 ). + This filter samples a continmiuu-cdominated region of the WR spectrum., This filter samples a continuum-dominated region of the WR spectrum. + We applied the following sequence of 60 s integration through a ddiaplvagim: sky. C3. CI. WR. CL. WR. CI. C2. «e.," We applied the following sequence of 60 s integration through a diaphragm: sky, C2, C1, WR, C1, WR, C1, C2, sky." + The sae nearby comparison stars as used by Moffat&Shara(19586) have heen chosen., The same nearby comparison stars as used by \cite{Moffatp} have been chosen. + These conrparison stars are simular in terms of their magnitude and colour to1: AB AVR Cl) - 0.17. ALB V|OWR Cl) = 0.17. AB (WR ο) - 0.26. ALB VP) AVR C2) = 0.9.," These comparison stars are similar in terms of their magnitude and colour to: $\Delta B$ (WR – C1) = – 0.17, $\Delta$ $B$ – $V$ ] (WR – C1) = – 0.17, $\Delta B$ (WR – C2) = – 0.26, $\Delta$ $B$ – $V$ ] (WR – C2) = – 0.19." + An extinction coefficieut hk. = 0.20 was used throughout the data reduction., An extinction coefficient $k_v$ = 0.20 was used throughout the data reduction. +" The scatter in the (C2 C1) data for the whole dataset amounts to c = L7 µας,", The scatter in the (C2 $-$ C1) data for the whole dataset amounts to $\sigma$ = 4.7 mmag. + The differential magnitudes quoted iu Table 1l are averaged over two consecutive cycles typically separated by about 20 minutes., The differential magnitudes quoted in Table 1 are averaged over two consecutive cycles typically separated by about 20 minutes. + Lone-slt spectra of have been obtained during various campaigns at the Observatoire du Mount Méeeauticao and Doiinion Astroplivsical Observatory (Canada) iu 1995 October aud 1996 September., Long-slit spectra of have been obtained during various campaigns at the Observatoire du Mont Méggantic and Dominion Astrophysical Observatory (Canada) in 1995 October and 1996 September. + Reticon spectra were also obtained at DAO iu 1996 November., Reticon spectra were also obtained at DAO in 1996 November. + The 1996 campaign at the Observatoire di Mout Móeeauticao was coordinated to support the photometric campaign described above., The 1996 campaign at the Observatoire du Mont Méggantic was coordinated to support the photometric campaign described above. + Table 2 lists the mode of observation. he dates of the spectroscopic observations. the interval of the observations du lehoceutric Julian dates. the observatory name. the mmmber of CCD spectra obtained. he selected spectral domain. the reciprocal dispersion of he spectra. and the typical signal-to-noise ratio (S/N) iu he contimmuu.," Table 2 lists the mode of observation, the dates of the spectroscopic observations, the interval of the observations in heliocentric Julian dates, the observatory name, the number of CCD spectra obtained, the selected spectral domain, the reciprocal dispersion of the spectra, and the typical signal-to-noise ratio (S/N) in the continuum." + The spectra were reduced using the data reduction packages., The spectra were reduced using the data reduction packages. + The bias and sky subtraction. flat-field clivision. removal of cosmic rav eveuts. extraction of je spectra. and waveleneth calibration were carried out in the usual wax.," The bias and sky subtraction, flat-field division, removal of cosmic ray events, extraction of the spectra, and wavelength calibration were carried out in the usual way." + Spectra of calibration laps were taken iuuediatelv before aud after the stella: exposure., Spectra of calibration lamps were taken immediately before and after the stellar exposure. + The stellar spectra were subsequently continui normalized by fitting a low-order Legeudre polvuomial to carefully selected. line-free regions., The stellar spectra were subsequently continuum normalized by fitting a low-order Legendre polynomial to carefully selected line-free regions. + Iu order to minimize the spurious velocity shifts induced by an inevitably iuperfec wavelength calibration. the spectra were coaligued iu velocity space by using the interstellar doublet AADSOU. 5896 as fiducial marks.," In order to minimize the spurious velocity shifts induced by an inevitably imperfect wavelength calibration, the spectra were coaligned in velocity space by using the interstellar doublet $\lambda$$\lambda$ 5890, 5896 as fiducial marks." + When not available. the doublet AA3931. 3968 or the diffuse interstellar baie at 1501 wwere used.," When not available, the doublet $\lambda$$\lambda$ 3934, 3968 or the diffuse interstellar band at 4501 were used." + A treud for a svstematic shift of the zero point of the wavelength scale has been correcte by redshifting most of the spectra by an average value of 35 aus i, A trend for a systematic shift of the zero point of the wavelength scale has been corrected by redshifting most of the spectra by an average value of 35 km $^{-1}$. + Echelle spectra have been obtained diving the period 1996 September 1619 with the Echelle spectrograph (Levine&Chakrabarty 1995)) on the 2.1 1m telescope of theSan Pedro Márrtir Observatory., Echelle spectra have been obtained during the period 1996 September 16–19 with the Echelle spectrograph \cite{Levine}) ) on the 2.1 m telescope of theSan Pedro Márrtir Observatory. + The UCL camera aud a 1021 « 102 coater CCD-Tek chip have been used., The UCL camera and a 1024 $\times$ 1024 coated CCD-Tek chip have been used. +" The selected erating (300 lines 1) vields a reciprocal dispersion of 0.16 and 0.23 | at Πς and Πα, respectively,"," The selected grating (300 lines $^{-1}$ ) yields a reciprocal dispersion of 0.16 and 0.23 $^{-1}$ at $\gamma$ and $\alpha$, respectively." + The spectra cover 27 orders aud span the spectral range 3720-6900Α., The spectra cover 27 orders and span the spectral range 3720-6900. +. The reduction procedure. (bias subtraction. division by a normalized flat field. removing of scattered light. extraction of the orders) was carried out using the reduction tasks iu the packageechelle.," The reduction procedure (bias subtraction, division by a normalized flat field, removing of scattered light, extraction of the orders) was carried out using the reduction tasks in the package." + Comparison spectra of ThAx lamps have been used for thewavelength calibration., Comparison spectra of Th–Ar lamps have been used for thewavelength calibration. + The typical accuracy of the waveleneth calibration can be judged by the dispersion iu the heliocentric radial velocities of the interstellar line AbBSOU: στ 2laus +., The typical accuracy of the wavelength calibration can be judged by the dispersion in the heliocentric radial velocities of the interstellar line $\lambda$5890: $\sigma$ $\approx$ 2 km $^{-1}$ . + The iustrmuental respouse has bee-, The instrumental response has been +the hyvdrodynamie calculations is concerted.,the hydrodynamic calculations is concerted. + Phe smoothing lengths in VINE are initially set to a constant value of fron.0.8 kpe at the time of the magnetic field inclusion., The smoothing lengths in $\textsc{Vine}$ are initially set to a constant value of $h_\mathrm{gas}\approx 0.3$ kpc at the time of the magnetic field inclusion. + Figs., Figs. + 7 and S show simulations starting [rom the same initial conditions as before., \ref{eulerVINE} and \ref{eulerGAD} show simulations starting from the same initial conditions as before. + However. this time the evolution of the magnetic field was Followed using the Euler potentials.," However, this time the evolution of the magnetic field was followed using the Euler potentials." + Again. we show magnetic field energies ancl gas densities.," Again, we show magnetic field energies and gas densities." + This time the amplification of the magnetic field energy. in 10 spiral arms is only three orders of magnitude for both Lgimulations with VINE and CAbGET. with both showing a remarkably similar evolution.," This time the amplification of the magnetic field energy in the spiral arms is only three orders of magnitude for both simulations with $\textsc{Vine}$ and $\textsc{Gadget}$, with both showing a remarkably similar evolution." + Phe most notable cüfference to 1e simulations with direct magnetic field treatment shown in Fig., The most notable difference to the simulations with direct magnetic field treatment shown in Fig. + 5. and 6 is at the centre of the galaxies. where in 10 direct. simulations the field amplification was strongest.," \ref{indVINE} and \ref{indGAD} is at the centre of the galaxies, where in the direct simulations the field amplification was strongest." + With Euler potentials the magnetic field grows mostly in the Esoral arms of the galaxy. (see also Fig. 13))., With Euler potentials the magnetic field grows mostly in the spiral arms of the galaxy (see also Fig. \ref{Bwithr}) ). + Since the magnetic fields in our simulations are passive. re density. profiles (Figs.," Since the magnetic fields in our simulations are passive, the density profiles (Figs." + 2 and 3)) of the disc are the same for all runs., \ref{sigma_gas} and \ref{sigma_disc}) ) of the disc are the same for all runs. + Ehus. the dillerent profiles of the magnetic field energy cannot be traced back to the density. profiles.," Thus, the different profiles of the magnetic field energy cannot be traced back to the density profiles." + In fact. it is the numerical V-B which presumably causes the high amplification of the magnetic field at the centre in simulations with the direct. magnetic field treatment.," In fact, it is the numerical $\nabla\cdot \textbf{B}$ which presumably causes the high amplification of the magnetic field at the centre in simulations with the direct magnetic field treatment." + Fig., Fig. + 10 shows the radial profile of the numerical -[VB|/|B]| at time /zz1.5 Gye for simulations using direct magnetic Ποιά treatment (blue for simulations without applying the viscosity limiter and orange where the limiter was applied) and Euler potentials (black) performed using GADGET (solid lines) and. VINE (dotted line)., \ref{divergence_radius} shows the radial profile of the numerical $h\cdot|\nabla\cdot \textbf{B}|/|\textbf{B}|$ at time $t\approx 1.5$ Gyr for simulations using direct magnetic field treatment (blue for simulations without applying the viscosity limiter and orange where the limiter was applied) and Euler potentials (black) performed using $\textsc{Gadget}$ (solid lines) and $\textsc{Vine}$ (dotted line). + Utilising the direct magnetic field description. the numerical V: is highest at small raclii. and much larger than for the EulerDB potential formalism.," Utilising the direct magnetic field description, the numerical $\nabla\cdot \textbf{B}$ is highest at small radii, and much larger than for the Euler potential formalism." + As will be discussed in the following section. high V:B corresponds to high amplification of the magnetic field.," As will be discussed in the following section, high $\nabla\cdot \textbf{B}$ corresponds to high amplification of the magnetic field." + Fig., Fig. + 11. shows the magnetic field vectors for the normal resolution VINE simulation utilising Euler potentials at the ime fz0.9 Civr., \ref{vectors} shows the magnetic field vectors for the normal resolution $\textsc{Vine}$ simulation utilising Euler potentials at the time $t\approx 0.9$ Gyr. + This time the colours correspond to the gas density on a logarithmic scale from 0.3:10.5 to 2:3107AJ. . overplotted with the field. vectors.," This time the colours correspond to the gas density on a logarithmic scale from $0.3\cdot 10^{-3}$ to $2.3\cdot 10^3 M_\odot$ $^{-3}$ , overplotted with the field vectors." +" The length. / of he vectors is normalised to the initial value ancl clisplaved ogarithmically as f=3:log(CD/Du). ic. /=0 corresponds o DzzDy or smaller. /2110 D22-Du. 1—210 De5D, and ἐξ310 D—10:By."," The length $l$ of the vectors is normalised to the initial value and displayed logarithmically as $l=3\cdot \log(B/B_0)$, i.e. $l=0$ corresponds to $ B\approx B_0$ or smaller, $l=1$ to $B\approx 2\cdot B_0$, $l=2$ to $B\approx 5\cdot B_0$ and $l=3$ to $B=10\cdot B_0$." + The magnetic field. lines follow he spiral structure of the gas., The magnetic field lines follow the spiral structure of the gas. + They. have been. amplified »v contraction in regions of higher density and restructured w dillerential rotation of the galaxy., They have been amplified by contraction in regions of higher density and restructured by differential rotation of the galaxy. + Their orientation is caused by the motion of the gas., Their orientation is caused by the motion of the gas. + These characteristics are very similar to typical observations of magnetic fields. in ealactic discs (e.g. Fig. 1))., These characteristics are very similar to typical observations of magnetic fields in galactic discs (e.g. Fig. \ref{M51}) ). + Qualitatively. this behaviour is the same for all simulations using both codes.," Qualitatively, this behaviour is the same for all simulations using both codes." + Only the central region in simulations using direct magnetic eld treatment shows chaotic orientation of the magnetic field. lines. indicating artificial amplification of the magnetic field. due to high numerical V-D.," Only the central region in simulations using direct magnetic field treatment shows chaotic orientation of the magnetic field lines, indicating artificial amplification of the magnetic field due to high numerical $\nabla\cdot \textbf{B}$." + ., Figs. +5 (6)) and 7 (8)). respectively. reveal the dilferences in the magnetic field amplification for the direct. magnetic field. treatment ancl the Euler potentials formalism: Using the direct description. the amplification of themagnetic field energy in the spiral arms is higher by at least two orders of magnitude. and at the centre even more than six orders of magnitude compared to the Euler potentials method.," \ref{indVINE} \ref{indGAD}) ) and \ref{eulerVINE} \ref{eulerGAD}) ), respectively, reveal the differences in the magnetic field amplification for the direct magnetic field treatment and the Euler potentials formalism: Using the direct description, the amplification of themagnetic field energy in the spiral arms is higher by at least two orders of magnitude, and at the centre even more than six orders of magnitude compared to the Euler potentials method." + This difference is probably caused by the numerical V:B in these simulations (Fig. 10)).," This difference is probably caused by the numerical $\nabla\cdot \textbf{B}$ in these simulations (Fig. \ref{divergence_radius}) )," + but possibly also by the fact that field winding is not traced bevond a certain evolutionary state in the Euler potentials formulation. (see section 3.1.6))., but possibly also by the fact that field winding is not traced beyond a certain evolutionary state in the Euler potentials formulation (see section \ref{EULER}) ). + Since the Euler potentials are free from physical divergence by construction (Le. the divergence is zero to measurements errors). the numerical divergence in simulations using the Euler potentials is due to the SPL derivative approximation when calculating the magnetic field. from the potentials (Eq. 18)).," Since the Euler potentials are free from physical divergence by construction (i.e. the divergence is zero to measurements errors), the numerical divergence in simulations using the Euler potentials is due to the SPH derivative approximation when calculating the magnetic field from the potentials (Eq. \ref{euler}) )." + In this sense. the numerical divergence. found in simulations using Euler potentials reflects the ability. of SPLL operators to measure the &radient of a curl to zero.," In this sense, the numerical divergence found in simulations using Euler potentials reflects the ability of SPH operators to measure the gradient of a curl to zero." + Thus. the fact that V:B is higher bv approximately one order of magnitude in the disc (i.e. within z5 to 15 kpe) and. by several orders of magnitude at the centre (Fig. 10)).," Thus, the fact that $\nabla\cdot \textbf{B}$ is higher by approximately one order of magnitude in the disc (i.e. within $\approx 5$ to 15 kpc) and by several orders of magnitude at the centre (Fig. \ref{divergence_radius}) )," + oesumably causes the dilferent magnetic field amplification in these simulations., presumably causes the different magnetic field amplification in these simulations. + This is the case at least in the disc region. where the winding of the field is not strong chough o constrain the Euler potentials formulation.," This is the case at least in the disc region, where the winding of the field is not strong enough to constrain the Euler potentials formulation." + To get a better idea of the influence of numerical VD on the amplification of the magnetic filed. we have »erformed simulations applying magnetic field smoothing. a echnique allowing for reduction of small scale Iuctuations and therefore. also the numerical divergence (2)).," To get a better idea of the influence of numerical $\nabla\cdot \textbf{B}$ on the amplification of the magnetic filed, we have performed simulations applying magnetic field smoothing, a technique allowing for reduction of small scale fluctuations and therefore also the numerical divergence \citealp{GadgetMHD}) )." + Within his method. the magnetic fieldis smoothed periodically as suggested by 7..," Within this method, the magnetic fieldis smoothed periodically as suggested by \citet{Borve2001}. ." + Fig., Fig. + 12. shows again the magnetic field energies and gas densities for a GADGET simulation starting rom the same initial conditions as before anc without, \ref{smoothGAD} shows again the magnetic field energies and gas densities for a $\textsc{Gadget}$ simulation starting from the same initial conditions as before and without +the visual extinction of the stellar light if standard gas-to-dust mass ratios are assumed.,the visual extinction of the stellar light if standard gas-to-dust mass ratios are assumed. +" This has been interpreted as being due to dust-depleted accretion streams falling from the disk to the star, thus absorbing X-rays from the underlying corona (Güdeletal.,2007b)."," This has been interpreted as being due to dust-depleted accretion streams falling from the disk to the star, thus absorbing X-rays from the underlying corona \citep{guedel07b}." +". It is possible that in these cases the soft jet component is discernible simply because the stellar component is absorbed at low X-ray energies, while in less strongly accreting (and therefore less absorbed) objects the jet component is outshone by the coronal spectrum."," It is possible that in these cases the soft jet component is discernible simply because the stellar component is absorbed at low X-ray energies, while in less strongly accreting (and therefore less absorbed) objects the jet component is outshone by the coronal spectrum." +" Four objects in our sample have been interpreted as showing soft X-ray jets: DG Tau, DP Tau, HN Tau, and also Sz 102, the latter revealing only a soft component, the hard component possibly being completely absorbed by a near-edge-on disk al., 2009b)."," Four objects in our sample have been interpreted as showing soft X-ray jets: DG Tau, DP Tau, HN Tau, and also Sz 102, the latter revealing only a soft component, the hard component possibly being completely absorbed by a near-edge-on disk \citep{guedel09b}." +. Three of these objects show very high Liwem while for DP Tau an upper limit is available.," Three of these objects show very high $L_{\rm [Ne\,II]}$, while for DP Tau an upper limit is available." +" We find no specific trend for the four objects tighter than what is shown in Figs. 2,, 3,"," We find no specific trend for the four objects tighter than what is shown in Figs. \ref{fig2}, \ref{fig3}," + or 4.., or \ref{fig4}. +" However, except for Sz 102 where only a soft component is present, we have adopted the hard component as representing the stellar radiation."," However, except for Sz 102 where only a soft component is present, we have adopted the hard component as representing the stellar radiation." +" The luminosities in the components are, 9.6x1075 erg s!, 1.5x10?? erg s, 4.0x10? erg sl, and 8.9x1025 erg s! for DG Tau, HN Tau, DP Tau, and Sz 102, respectively (see Güdeletal. 2009b,, and this paper for Sz 102)."," The luminosities in the components are, $9.6\times 10^{28}$ erg $^{-1}$, $1.5\times 10^{29}$ erg $^{-1}$, $4.0\times 10^{27}$ erg $^{-1}$, and $8.9\times 10^{28}$ erg $^{-1}$ for DG Tau, HN Tau, DP Tau, and Sz 102, respectively (see \citealt{guedel09b}, , and this paper for Sz 102)." +" The corresponding Liner values are, respectively, 6.1x103 erg s!, 5.6x1078 erg s!, <2.6x10°8 erg s, and 1.7x10? erg s!, not suggesting any correlation."," The corresponding $L_{\rm [Ne\,II]}$ values are, respectively, $6.1\times 10^{29}$ erg $^{-1}$, $5.6\times 10^{28}$ erg $^{-1}$, $<2.6\times 10^{28}$ erg $^{-1}$, and $1.7\times 10^{29}$ erg $^{-1}$, not suggesting any correlation." +" However, it may be interesting to note that MossLxsoft=(30,1.2,<0.15)x10?!Mo yr! erg s! for DG Tau, HN Tau, and DP Tau, respectively, which roughly correlates with Ίο=(24,0.6,0.06)x10?? erg s! and with Lien]=(61,5.6,<2.6)x10?5 erg s! although the statistics are too small for significant conclusions."," However, it may be interesting to note that $\dot{M}_{\rm loss}L_{\rm X, soft} = (30, 1.2, <0.15)\times 10^{21}~M_{\odot}$ $^{-1}$ erg $^{-1}$ for DG Tau, HN Tau, and DP Tau, respectively, which roughly correlates with $L_{{\rm [O\,I],}f} = (24, 0.6, 0.06)\times 10^{30}$ erg $^{-1}$ and with $L_{\rm [Ne\,II]} = (61, 5.6, <2.6)\times 10^{28}$ erg $^{-1}$ although the statistics are too small for significant conclusions." +" Although jets may produce both [Νεπ]] emission and very soft X-rays independently by shock heating, the latter may also contribute to ionization and heating of the predominantly cool jet gas locally, thus adding to π]] emission."," Although jets may produce both ] emission and very soft X-rays independently by shock heating, the latter may also contribute to ionization and heating of the predominantly cool jet gas locally, thus adding to ] emission." +" Our finding that π]] emission is enhanced in ΟΤΤΟ with jets, supported by spatially resolved π]] emission from the T Tau jet system (vanBoekeletal.,2009),, finds a parallel in observations of infrared rovibrational H» emission from similar targets."," Our finding that ] emission is enhanced in CTTS with jets, supported by spatially resolved ] emission from the T Tau jet system \citep{boekel09}, finds a parallel in observations of infrared rovibrational $_2$ emission from similar targets." +" The Hz v=1-0S(1) line at 2.12 um shares excitation conditions with ΠΠ], i.e., excitation in warm gas heated by UV, X-rays, or shocks, where emission from the disk gas is expected to be confined within 30-50 AU (Becketal.2008 and references therein)."," The $_2$ $v = 1-0~S(1)$ line at 2.12 $\mu$ m shares excitation conditions with ], i.e., excitation in warm gas heated by UV, X-rays, or shocks, where emission from the disk gas is expected to be confined within 30–50 AU \citealt{beck08} and references therein)." +" Hy rovibrational emission has been detected from many CTTS, but again, the emission source is often resolved."," $_2$ rovibrational emission has been detected from many CTTS, but again, the emission source is often resolved." +" In the Becketal.(2008) high-resolution study of six CTTS (including DG Tau, T Tau, and RW Aur from our sample), the Hz emission morphologies, its detection beyond 50 AU from the star, excitation temperatures exceeding 1800 K, kinematics measureed in the features, and the consistency with calculated shock models suggest that the bulk of the H» emission is shock-excited emission from jets and outflows rather than emission from disk gas excited by short-wavelength flux from the central star."," In the \citet{beck08} high-resolution study of six CTTS (including DG Tau, T Tau, and RW Aur from our sample), the $_2$ emission morphologies, its detection beyond 50 AU from the star, excitation temperatures exceeding 1800 K, kinematics measureed in the features, and the consistency with calculated shock models suggest that the bulk of the $_2$ emission is shock-excited emission from jets and outflows rather than emission from disk gas excited by short-wavelength flux from the central star." + A comparison of their Hy map of the T Tau system with the spatial distribution of π]] emission reported by vanBoekeletal.(2009) indeed suggests some common emission sources., A comparison of their $_2$ map of the T Tau system with the spatial distribution of ] emission reported by \citet{boekel09} indeed suggests some common emission sources. +" On the other hand, our finding of a correlation between uJ] luminosity and stellar X-ray luminosity specifically for objects with jets suggests an important role of the stellar short-wavelength radiation in exciting [Νεπ]] in the jet gas, at least relatively close to the star (see also estimates in vanBoekelal.2009 for the jet system in T Tau detected in π]] out to about 2 arcsec)."," On the other hand, our finding of a correlation between ] luminosity and stellar X-ray luminosity specifically for objects with jets suggests an important role of the stellar short-wavelength radiation in exciting ] in the jet gas, at least relatively close to the star (see also estimates in \citealt{boekel09} for the jet system in T Tau detected in ] out to about 2 arcsec)." + Explicit theoretical calculations by Shang(2010) for the X-wind model of a YSO jet irradiated by X-rays supports this conclusion further.," Explicit theoretical calculations by \citet{shang10} + for the X-wind model of a YSO jet irradiated by X-rays supports this conclusion further." +" Our correlations show systematic scatter of typically an order of magnitude in Liner, regardless of the parameter against which the latter is plotted."," Our correlations show systematic scatter of typically an order of magnitude in $L_{\rm [Ne\,II]}$, regardless of the parameter against which the latter is plotted." +" Although some stellar or disk parameters, such as Lx or Macc are themselves subject to considerable measurement error, the scatter in Liner clearly requires further systematic effects."," Although some stellar or disk parameters, such as $L_{\rm X}$ or $\dot{M}_{\rm acc}$ are themselves subject to considerable measurement error, the scatter in $L_{\rm [Ne\,II]}$ clearly requires further systematic effects." + One possibility is that several parameters considered here matter in concert., One possibility is that several parameters considered here matter in concert. + We have specifically investigated the correlations with theproduct of some parameters with Lx in an attempt to show that X- irradiation is one important factor to produce [Νοπ]] emission., We have specifically investigated the correlations with theproduct of some parameters with $L_{\rm X}$ in an attempt to show that X-ray irradiation is one important factor to produce ] emission. +" No decisive improvement of the correlations was found, however."," No decisive improvement of the correlations was found, however." +" On the other hand, we have ignored a number of parameters thatmay influence π]] emission."," On the other hand, we have ignored a number of parameters thatmay influence ] emission." +" In particular, we have not"," In particular, we have not" +that both GWB-eencrated residuals and the intrinsic timing noise are stochastic Gaussian processes. then we can represent them by the (nn) coherence matrices: with the total coherence matrix given by The timine-residuals are then distributed as a multidimensional Gaussian: where P denotes the probability. distribution of the timing-residuals.,"that both GWB-generated residuals and the intrinsic timing noise are stochastic Gaussian processes, then we can represent them by the $(n \times n)$ coherence matrices: with the total coherence matrix given by The timing-residuals are then distributed as a multidimensional Gaussian: where $P$ denotes the probability distribution of the timing-residuals." + To be able to use Eq. € 2))), To be able to use Eq. \ref{eq:gaussian}) ) + we (1) be able to evaluate the GWD-induced: coherence matrix from the theory. as a function. of variables that parametrise the CWD spectrum. and (2) introduce wellkmotivatecl parametrization of the pulsar timing noise.," we (1) be able to evaluate the GWB-induced coherence matrix from the theory, as a function of variables that parametrise the GWB spectrum, and (2) introduce well-motivated parametrization of the pulsar timing noise." + In this work. the spectral density of the stochastic GA background is taken to be a power law (222?) where ον represents the spectral density. zd is the CAV amplitude. f is the CAV frequency. ancl 5 is an exponent characterising the GWB spectrum.," In this work, the spectral density of the stochastic GW background is taken to be a power law \citep{Phinney, Jaffe, Wyithe, Maggiore} + where $S_h$ represents the spectral density, $A$ is the GW amplitude, $f$ is the GW frequency, and $\gamma$ is an exponent characterising the GWB spectrum." + I£ the GW3B is dominated by the supermassive black hole binaries. then ~=7/3 (Phinney 2001).," If the GWB is dominated by the supermassive black hole binaries, then $\gamma=7/3$ (Phinney 2001)." + This definition is equivalent to the use of the characteristic strain as defined in ?:: with=12a., This definition is equivalent to the use of the characteristic strain as defined in \citet{Jenet-2006}: with $\gamma = 1 - 2\alpha$. +" The CWD-induced coherence matrix is then given by Llere ay, is the gcometric factor given by where 6,5 is the angle between pulsar e and pulsar ο (?).. τςΌπίϊω Wü) Uis the gamma function. and. fj is the low eut-olf frequency. chosen so that ή is much greater than the duration of the PPA operation."," The GWB-induced coherence matrix is then given by Here $\alpha_{ab}$ is the geometric factor given by where $\theta_{ab}$ is the angle between pulsar $a$ and pulsar $b$ \citep{Hellings}, $\tau=2\pi\left(t_{ai}-t_{bj}\right)$ , $\Gamma$ is the gamma function, and $f_L$ is the low cut-off frequency, chosen so that $1/f_L$ is much greater than the duration of the PTA operation." + Introducing f; is a mathematical necessity. since otherwise the GWDB-induced correlation function would diverge.," Introducing $f_L$ is a mathematical necessity, since otherwise the GWB-induced correlation function would diverge." + However. we show below that the low-frequeney part of the GAB is indistinguishable from an extra spin-down of all pulsars which we alreacly correct for. and that our results do not depend on the choice of fj provided that fir«x1.," However, we show below that the low-frequency part of the GWB is indistinguishable from an extra spin-down of all pulsars which we already correct for, and that our results do not depend on the choice of $f_L$ provided that $f_L\tau\ll 1$." + The pulsar timing noise is assumed to be Gaussian. with a certain functional form of the power spectrum.," The pulsar timing noise is assumed to be Gaussian, with a certain functional form of the power spectrum." + The true profile of the millisecond pulsar timing noise spectrum. is not well-known at present time., The true profile of the millisecond pulsar timing noise spectrum is not well-known at present time. + The timing residuals of the most precisely observed: pulsars indicate that pulsar timing noise has a white and. poorly-constrained red. component (J. Verbiest and €i. Hobbs. private communications).," The timing residuals of the most precisely observed pulsars indicate that pulsar timing noise has a white and poorly-constrained red component (J. Verbiest and G. Hobbs, private communications)." + For the purposes of this paper we will always choose the spectra to be of the same functional form for all pulsars. but this is not an inherent limitation of the algorithm.," For the purposes of this paper we will always choose the spectra to be of the same functional form for all pulsars, but this is not an inherent limitation of the algorithm." + We consider 3 cases of pulsar timing noise (1) White (lat) (2) Lorentzian (3) Power-law Obviously. one could also consicer a timing noise which is a superposition of these components: we do not do this at this exploratory stage.," We consider 3 cases of pulsar timing noise (1) White (flat) (2) Lorentzian (3) Power-law Obviously, one could also consider a timing noise which is a superposition of these components; we do not do this at this exploratory stage." +" LE we choose the pulsar timing noise spectrum to be white. with an amplitude AY. the resulting correlation matrix becomes: The Lorentzian spectrum is a red spectrum with a typical frequeney that determines the redness of the timing nolse: which vields the following correlation matrix: where fo isa typical freequeney and iN, is theamplitude."," If we choose the pulsar timing noise spectrum to be white, with an amplitude $N_a$, the resulting correlation matrix becomes: The Lorentzian spectrum is a red spectrum with a typical frequency that determines the redness of the timing noise: which yields the following correlation matrix: where $f_0$ is a typical frequency and $N_a$ is theamplitude." +" ὃν using a power law spectral density with amplitude AN, and spectral index σαν one gets a timine-noise coherence matrix analogous to the one in Iq. (8)):"," By using a power law spectral density with amplitude $N_a$ and spectral index $\gamma_a$, one gets a timing-noise coherence matrix analogous to the one in Eq. \ref{eq:CGW}) ):" + The method: described. in this report is based. upon a Bayesian approach to the parameter inference., The method described in this report is based upon a Bayesian approach to the parameter inference. + The general idea of the method is to (a) assume that the physical processes which produce the timing-residuals can be characterised by several parameters. and (b). use. the Daves theorem to derive. from. the measured. cata the probability distribution of the parameters of our interest.," The general idea of the method is to (a) assume that the physical processes which produce the timing-residuals can be characterised by several parameters, and (b) use the Bayes theorem to derive from the measured data the probability distribution of the parameters of our interest." + In our case. we assume that the timing residuals are created by (1) the GAB: we parametrise it by its amplitude 24 and slope 5. às in equation (6))," In our case, we assume that the timing residuals are created by (1) the GWB; we parametrise it by its amplitude $A$ and slope $\gamma$ , as in equation \ref{eq:spectraldensity})" + In our case. we assume that the timing residuals are created by (1) the GAB: we parametrise it by its amplitude 24 and slope 5. às in equation (6)).," In our case, we assume that the timing residuals are created by (1) the GWB; we parametrise it by its amplitude $A$ and slope $\gamma$ , as in equation \ref{eq:spectraldensity})" +ttelescope images in two passhands. far-UV (FUV)) aud near-UV (NEV) (Martinetal.2005).,"telescope images in two passbands, far-UV ) and near-UV ) \citep{mar05}." +. The ppasshands are aand the photometric system is described in Hewettal.(2006)., The passbands are and the photometric system is described in \citet{hew06}. +. The description of the ssurvev is eiven idu Lawrenceetal.(2007)., The description of the survey is given in \citet{law07}. + Alodel magnitudes. as defined bySDSS.. are not computed by audUlIDSS.," Model magnitudes, as defined by, are not computed by and." +. Therefore. we use Petrosian maguitudes (Petrosiau1976). for aand Wrou-like elliptical aperture magnitudes (INrou1980) for suce Petrosian mnasuitudes are not available in the ccatalogue.," Therefore, we use Petrosian magnitudes \citep{pet76} for and Kron-like elliptical aperture magnitudes \citep{kro80} for since Petrosian magnitudes are not available in the catalogue." + The majority of galaxies iu our sample are not large iu angular size. aud so the differeuce between these magnitudes should not be siguiicaut.," The majority of galaxies in our sample are not large in angular size, and so the difference between these magnitudes should not be significant." + We exclude oohjects which have been debleuded because of a known error in the pipeline that results in erroneous Petrosian uaenitudes for these objects(Smithetal.2009)., We exclude objects which have been deblended because of a known error in the pipeline that results in erroneous Petrosian magnitudes for these objects \citep{smi09}. + Photometric data were obtained from online catalogue:μα via SOL (Structured. Query Lanenage) queries throug[um he CCatalogue Archive Server the ABDNDultinission Archive at STScI (MAST)CAS!°.. and he WWECAAL Science Archive.," Photometric data were obtained from online catalogues via SQL (Structured Query Language) queries through the Catalogue Archive Server, the Multimission Archive at STScI (MAST), and the WFCAM Science Archive." +"(WSA)9., The UV. and jezr-IR. data were obtained by cerossauatchiug the thost galaxy coordinates with the aand ccatalogues using ah” ssearch radius.", The UV and near-IR data were obtained by cross-matching the host galaxy coordinates with the and catalogues using a search radius. + Of the 305 thost galaxies. 198 (65%)) have inuatehes and 178 (58%)) have inatclies within. while 127 )) lave matches in th. aandUIKIDSS.," Of the 305 host galaxies, 198 ) have matches and 178 ) have matches within, while 127 ) have matches in both and." +. We do not require every galaxy to have photometry iu all 11 bands(FOTW.NUV.. vjhk)).," We do not require every galaxy to have photometry in all 11 bands, )." + The addition of UV data helps to coustrain age. metallicity. aud receut star formation. while near-IR data probe the older stellar populations that compose a large portion of the mass.," The addition of UV data helps to constrain age, metallicity, and recent star formation, while near-IR data probe the older stellar populations that compose a large portion of the mass." + For example. adding ddata to ddata has been shown to ereatlv improve estimates of dust optical depth aud star formation rate 2005).," For example, adding data to data has been shown to greatly improve estimates of dust optical depth and star formation rate \citep{sal05}." + The distance modulus for a particular iiu the nunodelis given by where wy (stretch parameter). e (color). and imp (apparent B-baud magnitude at peak) are obtained from ffor cach bby fitting its light curve: a and 2 are cocficicuts which we asstuue to be coustaut: aud AL is the absolute magnitude.," The distance modulus for a particular in the model is given by where $x_1$ (stretch parameter), $c$ (color), and $m_B$ (apparent $B$ -band magnitude at peak) are obtained from for each by fitting its light curve; $\alpha$ and $\beta$ are coefficients which we assume to be constant; and $M$ is the absolute magnitude." + The distance modulus along with à aud > are determined from the output of musing the program ApJ}). which is part of the ppackage.," The distance modulus along with $\alpha$ and $\beta$ are determined from the output of using the program ), which is part of the package." + ls able to caleulate a and .} independent of cosmology bv nüuiuizmg the scatter im the IIubble relation in sanall redshift bins., is able to calculate $\alpha$ and $\beta$ independent of cosmology by minimizing the scatter in the Hubble relation in small redshift bins. + Values of à and . in this work are computed from the sample of tthat pass the lieht-curve cuts iu Section 2.1 and which are cither spectroscopicall-confunnied or photometrically-typed— and lave lost redshifts., Values of $\alpha$ and $\beta$ in this work are computed from the sample of that pass the light-curve cuts in Section \ref{LCcuts} and which are either spectroscopically-confirmed or photometrically-typed and have host redshifts. + —We find the best-fit values to be a=0.121 and |j=2.82. and use these to obtain the distance modulus.jpx.," We find the best-fit values to be $\alpha = 0.121$ and $\beta = 2.82$, and use these to obtain the distance modulus,." +. The IIubble Constant Gvhich is degenerate with AL) is effectively a coustaut offset to aand is an input toSALT2mu: we choose fy=70 km Ἐ t., The Hubble Constant (which is degenerate with $M$ ) is effectively a constant offset to and is an input to; we choose $H_0 = 70$ km $^{-1}$ $^{-1}$. + We define IIubble residuals as UR = pigx-pre.. where Hs the distance modulus obtained from elt curves via aand Hs the distance modulus calculated from the redshift of he and the best-fit cosmologv.," We define Hubble residuals as HR $\equiv$ $-$, where is the distance modulus obtained from light curves via and is the distance modulus calculated from the redshift of the and the best-fit cosmology." + The best-fit cosmology rere is determined by phased on the first-vear ssanaple (I&essloeretal.200923)... 7 0.735.," The best-fit cosmology here is determined by based on the first-year sample \citep{kes09a}, i.e. $\Omega_\mathrm{M} = 0.274,\ \Omega_\Lambda = 0.735$ ." + A wwith a UR >0 siguifies that it is fainter than expected for the best-fit cosmology even after correcting for lelt-curve shape., A with a HR $> 0$ signifies that it is fainter than expected for the best-fit cosmology even after correcting for light-curve shape. +" Tere it is useful to define ""underluuiuous? to refer to wwith IIR. >0 and voverlunineus” to refer to wwith UR <0."," Here it is useful to define “underluminous"" to refer to with HR $> 0$ and “overluminous” to refer to with HR $< 0$." + Exrors in IIR. are derived by adding the OYTOYS Ol aand im quadrature. where the errors on aare caleulated as [Ce|το)plzmrl2.," Errors in HR are derived by adding the errors on and in quadrature, where the errors on are calculated as $[\mu(z+z_{err})-\mu(z-z_{err})]/2$." + Stellar population svuthesis (SPS) codes are commonly used to create model templates of galaxies based ou stellar evolution calculations with the goal of inferring ealaxv properties such as mass. age. metallicity. aud star formation.," Stellar population synthesis (SPS) codes are commonly used to create model templates of galaxies based on stellar evolution calculations with the goal of inferring galaxy properties such as mass, age, metallicity, and star formation." + We use the Flexible Stellar Population Svuthesis code vv2.1) developed by Conroyctal.(2009). and updated in Conrov&πια(2010) to generate spectral energv distributions (SEDs) of composite stellar populations (CSPs)., We use the Flexible Stellar Population Synthesis code v2.1) developed by \citet{con09} and updated in \citet{con10} to generate spectral energy distributions (SEDs) of composite stellar populations (CSPs). + lis simular to codes such as Bruzual&Charlot(2003) , is similar to codes such as \citet{bc03} +"with matter density parameter in the range €,€ [0.2,0.4], M€[10!!,105]Μο A, and z€[0,10], themaximal error is ~1.8% with a mean error of ~0.4%..","with matter density parameter in the range $\Omega_\mm\in[0.2,0.4]$ , $M\in[10^{11},10^{15}]\ M_\odot\ h^{-1}$ and $z\in[0,10]$, themaximal error is $\sim$ with a mean error of $\sim$." +" A similar functional dependence can be found for A,(M,z)."," A similar functional dependence can be found for $\Delta_\vv(M,z)$." + Only a small correction term has to be added to arrive at a satisfactory accuracy., Only a small correction term has to be added to arrive at a satisfactory accuracy. +" We find with a=0.3819, b=0.5379, c=0.7589, and d= 107."," We find with $a=0.3819$, $b=0.5379$, $c=0.7589$, and $d=3.456\times10^{-4}$ ." +" In the same range as above, the maximal error is~5% with a mean error of ~1%..In Fig."," In the same range as above, the maximal error is$\sim$ with a mean error of $\sim$.In Fig." +" [// we plot both 6, and A, as a function of the initial ellipticity e andprolaticity p centered around their expectation values given by Eq.", \ref{fig:influenceEP} we plot both $\delta_\cc$ and $\Delta_\vv$ as a function of the initial ellipticity $e$ andprolaticity $p$ centered around their expectation values given by Eq. + for three different cosmologies., for three different cosmologies. +" For increasing e and decreasing p, both parameters grow qualitatively in the same way as already reported by ? (cf."," For increasing $e$ and decreasing $p$, both parameters grow qualitatively in the same way as already reported by \citet{Sheth2001} (cf." + their Fig., their Fig. + 1)., 1). + Quantitative deviations arise from the differences in the applied algorithm as discussed in Sect. .2]., Quantitative deviations arise from the differences in the applied algorithm as discussed in Sect. \ref{subsec:parameters}. +" For a given mass and virialisation redshift, the initial overdensity for the EdS universe is larger compared to both ACDM and OCDM due to a shorter physical time interval that corresponds to the same redshift interval, resulting in a larger (e) andc, but also in larger curvatures of 6, and A, with respect to e and p."," For a given mass and virialisation redshift, the initial overdensity for the EdS universe is larger compared to both $\Lambda$ CDM and OCDM due to a shorter physical time interval that corresponds to the same redshift interval, resulting in a larger $\langle e \rangle$ and$\sigma_e$, but also in larger curvatures of $\delta_\cc$ and $\Delta_\vv$ with respect to $e$ and $p$." +" These are the sources of the larger error in the approximation (€)=E((e),(p)) discussed in Sect. 2.3}."," These are the sources of the larger error in the approximation $\langle\xi\rangle\approx\xi(\langle e \rangle,\langle p\rangle)$ discussed in Sect. \ref{subsec:epIni}." +" Since the redshift-time relation is not very different between ACDM and OCDM, the dependences of ὃς and A, on e and p are comparable."," Since the redshift-time relation is not very different between $\Lambda$ CDM and OCDM, the dependences of $\delta_\cc$ and $\Delta_\vv$ on $e$ and $p$ are comparable." +" Using Eq.(29).,"," Using Eq.," +" we are able to construct the mass function of dark-matter haloes using the extended Press-Schechter formalism developed by ? and ?,, which is based on the first- distribution of the densitycontrast 6 as a function of the “time variable"" S=a?(M)."," we are able to construct the mass function of dark-matter haloes using the extended Press-Schechter formalism developed by \citet{Bond1991} and \citet{Lacey1993}, which is based on the first-upcrossing distribution of the densitycontrast $\delta$ as a function of the “time variable” $S\equiv\sigma^2(M)$ ." + We shall proceed similarly as ?? and define the scaled variable v=DNIS to derive the mass function for our standard ACDM cosmology.," We shall proceed similarly as \citet{Sheth1999,Sheth2002} and define the scaled variable $\nu\equiv\delta_\mathrm{c,sph}^2/S$ to derive the mass function for our standard $\Lambda$ CDM cosmology." +" As ? pointed out, expressing the first-upcrossing distribution f as a function of v has the advantage that it is only necessary to calculate f(v) for a barrier of height B(v,z) at one arbitrary redshift to infer the mass function n(M) atany other redshift by a simple rescaling."," As \citet{Sheth2002} pointed out, expressing the first-upcrossing distribution $f$ as a function of $\nu$ has the advantage that it is only necessary to calculate $f(\nu)$ for a barrier of height $B(\nu,z)$ at one arbitrary redshift to infer the mass function $n(M)$ atany other redshift by a simple rescaling." +" For a given first-upcrossing distribution f(v), the differential mass function can be calculated using the relation where py is the background density of the Universe."," For a given first-upcrossing distribution $f(\nu)$, the differential mass function can be calculated using the relation where $\rho_\mathrm{b}$ is the background density of the Universe." +" First, we want to find an accurate fit to the first-upcrossing distribution of a moving barrier which is given by the mass-dependent linear overdensity parameter of the ellipsoidal collapse, (see Eq. 9p."," First, we want to find an accurate fit to the first-upcrossing distribution of a moving barrier which is given by the mass-dependent linear overdensity parameter of the ellipsoidal collapse, (see Eq. \ref{eq:fitDeltaC}) )." +" The parameter 6¢,sph is evaluated at z,=0."," The parameter $\delta_\mathrm{c,sph}$ is evaluated at $z_\vv=0$." +" We ran one million random walks and recorded the first-upcrossing values for v€[0.01,20] in 100 equidistant bins in logarithmic space."," We ran one million random walks and recorded the first-upcrossing values for $\nu\in[0.01,20]$ in 100 equidistant bins in logarithmic space." +" The resulting distribution ν/(ν) is nicely expressed by the function Thus, our suggested fitting formula is a mixture of the functional forms proposed by ? and ?.."," The resulting distribution $\nu f(\nu)$ is nicely expressed by the function Thus, our suggested fitting formula is a mixture of the functional forms proposed by \citet{Sheth1999} and \citet{Sheth2002}." +" The remaining best-fit parameters are A=0.357, p=0.212 and a=1.171.The result is shown in Fig.[8]. "," The remaining best-fit parameters are $A=0.357$, $p=0.212$ and $a=1.171$.The result is shown in Fig. \ref{fig:firstUpDist}. ." +"Second, to find a viable mass function from the first-upcrossing distribution, we proceed as ? and ?,, normalise f(v) to unity and rescale the variable a such that we are in agreement with the standard ? massfunction and a mass function based on N-body simulations proposed by ?.."," Second, to find a viable mass function from the first-upcrossing distribution, we proceed as \citet{Sheth1999} and \citet{Sheth2001}, normalise $f(\nu)$ to unity and rescale the variable $a$ such that we are in agreement with the standard \citeauthor{Sheth1999} massfunction and a mass function based on $N$ -body simulations proposed by \citet{Courtin2010}." +" The latter is based on a first-upcrossing distribution that has the same functional form as that proposed by?,, but slightly different best-fit parameters, withA= 0.348, à= 0.695, and p= 0.1."," The latter is based on a first-upcrossing distribution that has the same functional form as that proposed by\citet{Sheth1999},, but slightly different best-fit parameters, with$\tilde{A}=0.348$ , $\tilde{a}=0.695$ , and $\tilde{p}=0.1$ ." +" Note that in their definition of v, the linear density contrast ó;,p, has to be taken at collapse."," Note that in their definition of $\nu$ , the linear density contrast $\delta_\mathrm{c,sph}$ has to be taken at ." +. Normalisingthe first-upcrossing distribution based on the moving barrier of our ellipsoidal-collapse model to unity yieldsa rescaled parameter A—A’= 1.364A.," Normalisingthe first-upcrossing distribution based on the moving barrier of our ellipsoidal-collapse model to unity yieldsa rescaled parameter $A\rightarrow A'=1.364\,A$ ." + We compare the resulting mass function with those by ? and ? for three different redshifts in Fig.[J]., We compare the resulting mass function with those by \citet{Sheth1999} and \citet{Courtin2010} for three different redshifts in Fig. \ref{fig:massFunctions}. + The parameter a was rescaled by a>a’=0.625 a.," The parameter $a$ was rescaled by $a\rightarrow a'=0.625\,a$ ." + Deviations from the ? mass function at, Deviations from the \citeauthor{Sheth1999} mass function at +"CCD stellar photometry in two voung open star clusters Basel 4 and NGC 7067 aiming to investigate the cluster's oie parameters (c.g. reddening. distance and age). mass ""unction and mass segregation etc.","CCD stellar photometry in two young open star clusters Basel 4 and NGC 7067 aiming to investigate the cluster's basic parameters (e.g. reddening, distance and age), mass function and mass segregation etc." + The existing basic informations on both the clusters are given in Table 1., The existing basic informations on both the clusters are given in Table 1. + The an of the paper is as follows., The plan of the paper is as follows. + In Sec., In Sec. + 2 we summarize he previous studies of Basel 4 anc NGC 7067. while Sec.," 2 we summarize the previous studies of Basel 4 and NGC 7067, while Sec." + 3 is dedicated on the observation and. data recluction strategies., 3 is dedicated on the observation and data reduction strategies. + Sec., Sec. + 4 deals with the determination of clusters oic parameters as well as detail study of interstellar extinction. mass function and mass segregation in the clusters under study.," 4 deals with the determination of clusters basic parameters as well as detail study of interstellar extinction, mass function and mass segregation in the clusters under study." + Finally. Sec.," Finally, Sec." + 5 summarizes our findings.4:, 5 summarizes our findings.: + This cluster was studied by Svolopoulos (1965) whotographically first in IU system., This cluster was studied by Svolopoulos (1965) photographically first in RGU system. + According to him the ocation of this cluster coincides with spiral arm. |ELE which could be expected. — if existing at all at a similar distance., According to him the location of this cluster coincides with spiral arm +III which could be expected $-$ if existing at all $-$ at a similar distance. + In any case. it dis remarkable that tvpical representatives of he galactic disk population are located: so far out in the direction of the galactic anticenter.," In any case, it is remarkable that typical representatives of the galactic disk population are located so far out in the direction of the galactic anticenter." +" Ee classified this cluster as a Lil 2m. In addition to this. he also concluded: that Basel dis 10° ves old. and has total apparent ciamoeter of , .4 at a distance. of⋅ 5.9."," He classified this cluster as a III 2m. In addition to this, he also concluded that Basel 4 is $\times$ $^{7}$ yrs old, and has total apparent diameter of $^{\prime}$ .4 at a distance of 5.9." + ⊳∖To our knowledge no other studies. ave been carried out. so7067:: Vhis cluster was first studied by Becker (1963)., To our knowledge no other studies have been carried out so: This cluster was first studied by Becker (1963). + lt is à poor voung open cluster lving in Cygnus. spiral arm., It is a poor young open cluster lying in Cygnus spiral arm. + Lt was again revisited by Becker (1965) and indicated hat the earliest. spectral type of the cluster member. is 90.5., It was again revisited by Becker (1965) and indicated that the earliest spectral type of the cluster member is b0.5. + 11ο also estimated the cluster angular diameter οἱ 2']. which corresponds to a linear diameter of 2.6. pe.," He also estimated the cluster angular diameter of $^\prime$ .1, which corresponds to a linear diameter of 2.6 pc." + Hassan (1973) also studied this cluster photoelectricallv and derived. a distance of about 44 Ixpe having E((D1)=0.83 mag and age less than 10 vears.," Hassan (1973) also studied this cluster photoelectrically and derived a distance of about 4.4 Kpc having $E(B-V) = +0.83$ mag and age less than $10^{7}$ years." + Dias et. al. (, Dias et al. ( +2002) mentioned a distance of 1.3 Ixpe for this cluster.,2002) mentioned a distance of 1.3 Kpc for this cluster. + The distance determination to the cluster is thus quite uncertain., The distance determination to the cluster is thus quite uncertain. + We used CCD imaging to obtain CBV. Johnson and Ri Cousins photometry of the stars in the region of the open clusters Basel 4 and NGC 7067 on 02/03 Jan 2000 and 11/12 Oct 2001 respectively., We used CCD imaging to obtain $UBV$ Johnson and $RI$ Cousins photometry of the stars in the region of the open clusters Basel 4 and NGC 7067 on 02/03 Jan 2000 and 11/12 Oct 2001 respectively. + The cata were obtained using 2A CCD system at the [7/13 C'assegrain focus of the I04-cm Sampurnanand telescope of the State Observatory. Naini Tal.," The data were obtained using $\times$ 2K CCD system at the f/13 Cassegrain focus of the 104-cm Sampurnanand telescope of the State Observatory, Naini Tal." + Log of CCD observations is given in Table 2., Log of CCD observations is given in Table 2. +" ""Phe 07.36/pixel. plate scale. resulted in a [eld of view of 125.3. 127.3.", The $^{\prime\prime}$ .36/pixel plate scale resulted in a field of view of $^{\prime}$ $\times$ $^{\prime}.3$. +" ""Phe read-out noise and gain of the CCD are 5.3 6. and 10 6. /ADU respectively.", The read-out noise and gain of the CCD are 5.3 $^{-}$ and 10 $^{-}$ /ADU respectively. + For the accurate photometric measurements of fainter stars. 2 to 3 deep exposures were taken in cach passband.," For the accurate photometric measurements of fainter stars, 2 to 3 deep exposures were taken in each passband." + Furthermore. observations were taken in 2.2 pixel binning mode to improve the S/N ratio.," Furthermore, observations were taken in $\times$ 2 pixel binning mode to improve the S/N ratio." + An identification map of cluster aud ield regions for both the clusters are shown in Fig 1., An identification map of cluster and field regions for both the clusters are shown in Fig 1. + Besides hem. a number of standard star field: were also observed or calibration purposes.," Besides them, a number of standard star field were also observed for calibration purposes." + We observed. M67 (open cluster) and eld | 051 of Landolt’ (1992) for. calibrating Basel 4 and NGC 7067 respectively., We observed M67 (open cluster) and field $+$ 051 of Landolt (1992) for calibrating Basel 4 and NGC 7067 respectively. + The V. mag range of stars used for calibration is 19 mag in M67 and 16 mag in | 051 while the (V.1) colour range is Ld mag in M67 and 2.0 in |051., The $V$ mag range of stars used for calibration is $-$ 13 mag in M67 and $-$ 16 mag in $+$ 051 while the $(V-I)$ colour range is $-$ 1.1 mag in M67 and $-$ $-$ 2.0 in $+$ 051. + Thus. he standard stars in these fields provide a good magnitude and colour coverage. essential to obtain reliable photometric ransformations.," Thus, the standard stars in these fields provide a good magnitude and colour coverage, essential to obtain reliable photometric transformations." + The standard field are also observed. in UDVRE at dillerent airmasses to obtain a reliable estimate of the atmospheric extinction coelIicients., The standard field are also observed in $UBVRI$ at different airmasses to obtain a reliable estimate of the atmospheric extinction coefficients. + For correcting the nas level to the image. a number of bias frame were taken during the observations while for the flat Geld correction. a number of [at frames were taken on the twilight skv in cach ilter.," For correcting the bias level to the image, a number of bias frame were taken during the observations while for the flat field correction, a number of flat frames were taken on the twilight sky in each filter." + The CCD images were processed using IRAP data reduction package., The CCD images were processed using IRAF data reduction package. + Then. for a given filter. frame of the same exposure time were combined into one. to improve the statistics of the faintest) stars.," Then, for a given filter, frame of the same exposure time were combined into one, to improve the statistics of the faintest stars." + Instrumental magnitucles were derived through Point Spread. Function (PSL) fitting using DAOPLIOT (Stetson 1987) within MIDAS., Instrumental magnitudes were derived through Point Spread Function (PSF) fitting using DAOPHOT (Stetson 1987) within MIDAS. + During the process of determining. PSE. we used. several well isolated stars to construct a single PSP for the entire [rame on cach exposure.," During the process of determining PSF, we used several well isolated stars to construct a single PSF for the entire frame on each exposure." + The bright stars were measured on the frames with short exposure times. as they were saturated in the longer exposure frames.," The bright stars were measured on the frames with short exposure times, as they were saturated in the longer exposure frames." + For transforming the instrumental magnitude to the standard magnitude. the photometric calibration equations are as n=l|O404001L(0.053:0.022(€.—DO.5ON b=B|4A39+001(00240.01)(2V)0:36X r=]408£0.01(001EO.0DCD.V)|O2BN r=|4000.01.(0.0220.01)(V—A)OTS ," For transforming the instrumental magnitude to the standard magnitude, the photometric calibration equations are as $u=U+6.40\pm0.01-(0.03\pm0.02)(U-B)+0.59X$ $b=B+4.39\pm0.01-(0.02\pm0.01)(B-V)+0.36X$ $v=V+4.08\pm0.01-(0.01\pm0.01)(B-V)+0.23X$ $r=R+4.00\pm0.01-(0.02\pm0.01)(V-R)+0.18X$ " +the standard model is a 20 maimain sequence star that has gone through a wind mass loss of 2A... left a neutron star of 1.4A... thus ejecting about 16 wwith a progenitor racius of 3x10 om.,"the standard model is a 20 main sequence star that has gone through a wind mass loss of 2, left a neutron star of 1.4, thus ejecting about 16 with a progenitor radius of $\times10^{13}$ cm." + The energetics of the simulation has a total energv of 1x10°! eres or 1 [oe (ten to the fiftv one eres) and ejects 0.07 79Ni mixed throughout the 6 IIIe core., The energetics of the simulation has a total energy of $\times10^{51}$ ergs or 1 foe (ten to the fifty one ergs) and ejects 0.07 $^{56}$ Ni mixed throughout the 6 He core. + The standard model is similar to SN 1987À except for the larger radius ancl less extensive mixing., The standard model is similar to SN 1987A except for the larger radius and less extensive mixing. + ln this paper the parameter space around this model is In (his paper I show the results of how varving each parameter can inlluence (he shape and absolute magnitude of Type 11 light curves out to 400 days., In this paper the parameter space around this model is In this paper I show the results of how varying each parameter can influence the shape and absolute magnitude of Type II light curves out to 400 days. +" The five parameters explored in this study are: the progenitor radius. envelope mass. explosion energy. ""Ni mass. ancl? Ni mixing."," The five parameters explored in this study are; the progenitor radius, envelope mass, explosion energy, $^{56}$ Ni mass, and $^{56}$ Ni mixing." + All light curves calculated in this paper use the numerically evolved 20 AZ. mmain sequence model with a 6 helium. core from Wooslev aud. Weaver (19380)., All light curves calculated in this paper use the numerically evolved 20 $M{_\odot}$ main sequence model with a 6 helium core from Woosley and Weaver (1980). + The envelope parameters. mass and racius. are varied using homology transformations (section 2).," The envelope parameters, mass and radius, are varied using homology transformations (section 2)." + The models are (hen exploded ina one dimensional. [Inx-Iimited hyedrocdynamical eode with a simple prescription for deposition (section 3).," The models are then exploded in a one dimensional, flux-limited hydrodynamical code with a simple prescription for gamma-ray deposition (section 3)." +""" The bolometric light. curves are calculated and. plotted on an absolute magnitude scale (section 4).", The bolometric light curves are calculated and plotted on an absolute magnitude scale (section 4). + The results are discussed in section For the initial models of all explosions I use the 6 M... helium core from Woosley. aud Weaver (L980) .. originally a 20 A. main sequence star.," The results are discussed in section For the initial models of all explosions I use the 6 $M{_\odot}$ helium core from Woosley and Weaver (1980) \nocite{ww80}, originally a 20 $M{_\odot}$ main sequence star." + The envelope mass and radius are subsequently modilied in a svstematie wav., The envelope mass and radius are subsequently modified in a systematic way. + A total of 8 models were constructed that are identified by a specific mass and radius (Table D)., A total of 8 models were constructed that are identified by a specific mass and radius (Table I). + In this study three different envelope Inasses were used producing total masses of 8. 12. and 16 M...," In this study three different envelope masses were used producing total masses of 8, 12, and 16 $M{_\odot}$." + For each envelope mass. three different radii where used 43 R. (3x107 em). 430 R. (3.x10/7 em). and 4300 R. (3xLol cm).," For each envelope mass, three different radii where used 43 $_\odot$ $3\times10^{12}$ cm), 430 $_\odot$ $3\times10^{13}$ cm), and 4300 $_\odot$ $3\times10^{14}$ cm)." + The original Il rich envelope was modified by homologous transformations to give the various masses and radii (Schwarzschild1958:Chandrasekhar1939).," The original H rich envelope was modified by homologous transformations to give the various masses and radii \citep{s58,c39}." +. For a homologous transformation in radius: where Ris the old radius. R is the new radius. and .r is the percent changed.," For a homologous transformation in radius: where R is the old radius, $'$ is the new radius, and $x$ is the percent changed." + For a homologous transformation in mass :, For a homologous transformation in mass : +density. Z plasma temperature. £j heat flux. & plasma hermal conductivity and 5=5/3.,"density, $T$ plasma temperature, $F_c$ heat flux, $\kappa$ plasma thermal conductivity and $\gamma = 5/3$." + The flare is assumed ο occur on a solar-like star. with solar surface eravity aud radius.," The flare is assumed to occur on a solar-like star, with solar surface gravity and radius." + Plasma thermal conduction is isotropic., Plasma thermal conduction is isotropic. + Radiative osses are those of Ravimoud and Suuith (1977) but are set o zero for Tz:2«10! K. ie. for chromospherie plasma.," Radiative losses are those of Raymond and Smith (1977) but are set to zero for $T \approx 2\times +10^4$ K, i.e. for chromospheric plasma." +" The heating term generally consists of a steady heating erui which iuaintaius the προς, atinosphere im hermal equilibrium and of a transient term. which rigecrs the flare."," The heating term generally consists of a steady heating term which maintains the unperturbed atmosphere in thermal equilibrium and of a transient term, which triggers the flare." + In our simulations. the steady heating das been set to zero both in the chromosphere aud elsewhere. since the transicut heating is switched on. in order to describe the free plasa cooling with no interference from any heating source.," In our simulations, the steady heating has been set to zero both in the chromosphere and elsewhere, since the transient heating is switched on, in order to describe the free plasma cooling with no interference from any heating source." + The trausicut heating term has been assumed as a separable function of space aud time: The spatial distribution of the heating is a 2-D circular Caussian: As for the temporal evolution ο) the impulsive beating has been asstmed to be switched ou at t=0 (0)= 0). kept constant (g(t)= 1) for aeiven time lapse Oty)= 0.," The transient heating term has been assumed as a separable function of space and time: The spatial distribution of the heating is a 2-D circular Gaussian: As for the temporal evolution g(t) the impulsive heating has been assumed to be switched on at t=0 $g(0)=0$ ), kept constant $g(t)=1$ ) for agiven time lapse $0 \leq t \leq t_H$ and then switched off $g(t > +t_H ) = 0$ ." +"bv the color correction factor of 1.09 to place the data on a constant wf, scale. which is also the appropriate color correction (within 254)) for a wide range of possible ealaxy SEDs (see SSC web pages for calibration and color-correction details).","by the color correction factor of 1.09 to place the data on a constant $\nu f_\nu$ scale, which is also the appropriate color correction (within ) for a wide range of possible galaxy SEDs (see SSC web pages for calibration and color-correction details)." + Tn comparison. the calibration correction adopted here is lavecr than the calibration adopted for the xFLS analysis (Fraver ct al.," In comparison, the calibration correction adopted here is larger than the calibration adopted for the xFLS analysis (Frayer et al." + 2006)., 2006). + The flterius of the data is a crucial aspect in the xocessiue., The filtering of the data is a crucial aspect in the processing. + For the 7Ogau photometry mode. calibration stimulator (stim) flashes are used every 6 DCEs. aud ateuts due to these stim flashes acctuulate over time.," For the $\mu$ m photometry mode, calibration stimulator (stim) flashes are used every 6 DCEs, and latents due to these stim flashes accumulate over time." + To remove stim flash lateuts and additional artifacts. we used a inedia cola filter followed by a median Hel-pass tine filter per pixel (with a filter width of 16 DCEx).," To remove stim flash latents and additional artifacts, we used a median column filter followed by a median high-pass time filter per pixel (with a filter width of 16 DCEs)." + The positions of bright sources iu the DCDs were Πασσος so that the filtering corrections were not biased by he presence of sources., The positions of bright sources in the BCDs were flagged so that the filtering corrections were not biased by the presence of sources. + The medium filtering tecliuiques vield sinall offsets from zero iu the average level of the fltered-BCDs (£BCDs)., The median filtering techniques yield small offsets from zero in the average level of the filtered-BCDs (fBCDs). + These offsets correlate with the DCE position within the stim evele aud were removed by subtracting the mecian level frou cach BCD., These offsets correlate with the DCE position within the stim cycle and were removed by subtracting the median level from each fBCD. + The data were coadded onto a sky ος with L” pixels using the SSC imosaicing and source extraction software (ATOPEX. version 112505).," The data were coadded onto a sky grid with $4\arcsec$ pixels using the SSC mosaicing and source extraction software (MOPEX, version 112505)." + Sources were extracted using MODENX point source respouse function (PREF) fitting., Sources were extracted using MOPEX point source response function (PRF) fitting. + Iu crowded regions. the [jn positious (R. Chary ot al.," In crowded regions, the $\mu$ m positions (R. Chary et al.," + in reparation) were used for debleuding., in preparation) were used for deblending. + For optimal source extraction. an accurate uncertainty image is needed.," For optimal source extraction, an accurate uncertainty image is needed." + The uucertzinty image was coustructed by combining the roise per pixel based ou repeated observations with the ocal spatial pixel-to-pixel dispersion after the extraction of bright sources., The uncertainty image was constructed by combining the noise per pixel based on repeated observations with the local spatial pixel-to-pixel dispersion after the extraction of bright sources. + The average level of the uucertiinty nuage was then scaled to match the average empirical »oiut-«ource nolse derived by making multiple aperture ueasureiients at randoni locations throughout the residual mosaic after source extraction., The average level of the uncertainty image was then scaled to match the average empirical point-source noise derived by making multiple aperture measurements at random locations throughout the residual mosaic after source extraction. + The scale factor vetween the aperture derived point source noise Guchiding he aperture correction) and the pixel surface brightucss toixe is c(poiunt source)/o(1” pixels) =10.9+Ld , The scale factor between the aperture derived point source noise (including the aperture correction) and the pixel surface brightness noise is $\sigma$ (point $\sigma(4\arcsec$ pixels) $= 10.9\pm1.1$ )]. +Theaceragepointsouree noise forthe ultra deeparcataftertheceetractionof sources ΕΜ..., The average point source noise for the ultra-deep area (after the extraction of sources) is mJy $1\sigma$ ). + The applicability of the uncertainty image for point source extraction was vorified by obtaining PRF fits with 4?—1 or sources throughout the image., The applicability of the uncertainty image for point source extraction was verified by obtaining PRF fits with $\chi^2\simeq 1$ for sources throughout the image. + Previous survevs withSpitcer aro not deep cnough ) measure the photometric coufusion noise at T0. aud the estimated confusion level is based on the observed bright source counts and models of galaxy evolution (Dole ct al.," Previous surveys with are not deep enough to measure the photometric confusion noise at $\mu$ m, and the estimated confusion level is based on the observed bright source counts and models of galaxy evolution (Dole et al." + 2001b)., 2004b). + With the ultra-deep data of COODS-N. we cau directly measure the confusiou level at TOjau. We define the instrunent noise Guchiding photon noise. detector noise. and noise associated with the data processing) as σι.," With the ultra-deep data of GOODS-N, we can directly measure the confusion level at $\mu$ m. We define the instrument noise (including photon noise, detector noise, and noise associated with the data processing) as $\sigma_I$." +" The total noise (στ) represents the noise after the extraction of sources above a limiting flux deusitv (5/5, ). and the confusion noise (σι) represents fluctuations due to sources with flux deusities below 5;5,,."," The total noise $\sigma_{T}$ ) represents the noise after the extraction of sources above a limiting flux density $S_{lim}$ ), and the confusion noise $\sigma_{c}$ ) represents fluctuations due to sources with flux densities below $S_{lim}$." +" As defined here. 0, is the “photometric” confusion uoise. following the terminology of Dole. Lagache. Puget (2003)."," As defined here, $\sigma_c$ is the “photometric” confusion noise, following the terminology of Dole, Lagache, Puget (2003)." + Iu. the direction of GOODS-N. the contribution of Calactie cirrus to the confusion noise is neeligible (—0.01. nia). based ou the relationship giveu by Dole et al. (," In the direction of GOODS-N, the contribution of Galactic cirrus to the confusion noise is negligible $\sim 0.01$ mJy), based on the relationship given by Dole et al. (" +2003) and the calculations of Jeong et al. (,2003) and the calculations of Jeong et al. ( +2005).,2005). + The iustrunent noise was estimated cimpirically by subtracting pairs of data with the same iutegration time and covering the exact same region on the sky to remove sources and any remamine residuals frou the sky after filtering., The instrument noise was estimated empirically by subtracting pairs of data with the same integration time and covering the exact same region on the sky to remove sources and any remaining residuals from the sky after filtering. +" The measured instruuent uoise integrates down nearly with f£"" (Fig.", The measured instrument noise integrates down nearly with $t^{-0.5}$ (Fig. + 1)., 1). +" For these data. we fiud oFXfOqp£03, where 3=04001 for iuteeratiou tiue f iu units of ks."," For these data, we find $\sigma_{I}^{2} +\propto t^{-1}(1 + \beta t^{0.5})$ , where $\beta=0.04$ for integration time $t$ in units of ks." + The fuuctioual form of this relationship is based on enirical results from several different data sets. and the Jj parameter depends ou the backerouud level aud the quality of the data reduction.," The functional form of this relationship is based on empirical results from several different data sets, and the $\beta$ parameter depends on the background level and the quality of the data reduction." + We use the above function to extrapolate the iustrument noise from half the data to the full data set and derive o;=0.0399+0.0036 sr5., We use the above function to extrapolate the instrument noise from half the data to the full data set and derive $\sigma_{I} = 0.0399\pm 0.0036$ $^{-1}$. + Since the total noise Huage (after source extraction) and mstrinental noise image have nearly Causa distributious. the confusion noise can also be approximated bv a Caussian and is giveu by σι.=(oF ," Since the total noise image (after source extraction) and instrumental noise image have nearly Gaussian distributions, the confusion noise can also be approximated by a Gaussian and is given by $\sigma_c= +(\sigma_T^2-\sigma_I^2)^{0.5}$ ." +"We iterate between source extraction at different LBwiting flux densities and confusion noise measurenienuts until we converge to a solution with 4=S$qg,/o,.5.", We iterate between source extraction at different limiting flux densities and confusion noise measurements until we converge to a solution with $q\equiv S_{\lim}/\sigma_c =5$. +" For the gq=5 solutiou. we derive στ=0.0185+1.003LMIALTy ft aud e,=0.0276d:0.0079 yssr1. or a limiting source fux density of STO=1.5 Tucluding the additional svstematic uncertainties of the solute calibration scale (10543). and the conversion )etween point source noise and surface briehtuess noise1054.. 833). we derive a poiut source confusion noise of a—0.30c015 nuni (yg—5)."," For the $q=5$ solution, we derive $\sigma_{T} = 0.0485\pm +0.0034$ $^{-1}$ and $\sigma_{c} = 0.0276\pm +0.0079$ $^{-1}$, for a limiting source flux density of $=1.5$ Including the additional systematic uncertainties of the absolute calibration scale ) and the conversion between point source noise and surface brightness noise, 3), we derive a point source confusion noise of $\sigma_{c} = 0.30\pm 0.15$ mJy $q=5$ )." + Tn comparison. the predictious of Dole et al. (," In comparison, the predictions of Dole et al. (" +"2003. Ww080) suggest ag=4 photometric confusion level of a,= Ü.28nuuds. depending ou the exact shape of the differential source counts.","2003, 2004b) suggest a $q=5$ photometric confusion level of $\sigma_c\simeq 0.28$ mJy, depending on the exact shape of the differential source counts." + The measured confusion level of 0.3112Jy. agrees well with the predicted photometric confusion level., The measured confusion level of mJy agrees well with the predicted photometric confusion level. + However. the source density criterion (SDC) confusion Lit of 3.2nuuJv. adopted by Dole ct al.," However, the source density criterion (SDC) confusion limit of mJy adopted by Dole et al." + is more than a factor of two higher than the Πιο flux. deusitv derived here., is more than a factor of two higher than the limiting flux density derived here. + The Dole et al., The Dole et al. + SDC ιτ corresponds to 4287 aud a high completeness level of >90%., SDC limit corresponds to $q\simeq7$ and a high completeness level of $>90$. +.. Sources can be extracted at lower completeuess levels. aud counts can be derived reliably well below this SDC limit by making use of the Lian data to help extract the faintest sources.," Sources can be extracted at lower completeness levels, and counts can be derived reliably well below this SDC limit by making use of the $\mu$ m data to help extract the faintest sources." + The source counts were derived separately for the ceutral 10« ultra-deep field. for the wide Lddee? GTO deep field. aud for the 12/9ν intermediate field which inchicdes the ultra-deep field aud the surrounding regions of intermediate depth between the GTO aud ultra-deep survevs (Table 1).," The source counts were derived separately for the central $10^{\prime}\times10^{\prime}$ ultra-deep field, for the wide $^{2}$ GTO deep field, and for the $12\farcm9\times12\farcm9$ intermediate field which includes the ultra-deep field and the surrounding regions of intermediate depth between the GTO and ultra-deep surveys (Table 1)." +" Analvsis was doue ou the ""juterinediate feld for better statistics at STO> [nuudw.", Analysis was done on the “intermediate” field for better statistics at $>4$ mJy. + The central ultra-«deep area has a deficiency (~30 50%)) in nuuber of sources with flux densities between lO0nuuJv iu comparison to typical areas surrounding QGOODS-N. prestunably due to cosmic variance.," The central ultra-deep area has a deficiency $\sim 30$ ) in number of sources with flux densities between mJy in comparison to typical areas surrounding GOODS-N, presumably due to cosmic variance." + The intermediate and GTO £felds allow the measurement of source counts for flux cdeusities 12nuuJwv) not well, The intermediate and GTO fields allow the measurement of source counts for flux densities mJy) not well +The zodiacal light. model used in this paper is derived from the inodel described in (1998).,The zodiacal light model used in this paper is derived from the model described in \citet{Wr98}. +. Three changes liave been mace: The emissivities are ©eiven in Table 6 aud the IRAS baud parameters are ogiven in Table 7..," Three changes have been made: The emissivities are given in Table \ref{tab:zodiemiss} + and the IRAS band parameters are given in Table \ref{tab:bandpar}. ." +Archival Wide-Field/Planetary Camera 2 ΛΕΡΟΣ) observations are available for THO9 and HRI4.,Archival Wide-Field/Planetary Camera 2 (WFPC2) observations are available for TH09 and HR14. + THO9 was observed for a total of 3000s in FSSSW and 6000s in FSΛΑ using a four-point sub-pixel dither pattern. as part of PID 7342 (PI: R. Saunders).," TH09 was observed for a total of 3000s in F555W and 6000s in F814W, using a four-point sub-pixel dither pattern, as part of PID 7342 (PI: R. Saunders)." + These were processed using the package (Fruchter Hook 2002) to recover some of the resolution of the undersampled WFPC? PSF., These were processed using the package (Fruchter Hook 2002) to recover some of the resolution of the undersampled WFPC2 PSF. + HR4 was observed for a total of 5300s in FESI4W as part of PID 6598 (PI: A. Dey) and these data were processed using standard procedures., HR14 was observed for a total of 5300s in F814W as part of PID 6598 (PI: A. Dey) and these data were processed using standard procedures. + Greyscale close-ups of the targets are presented in Figure 3., Greyscale close-ups of the targets are presented in Figure 3. + The GIM2D package (Simard. 1998) was used to fit the two-dimensional surface brightness profiles of THO9 and HRI4 in the WFPC? images., The GIM2D package (Simard 1998) was used to fit the two-dimensional surface brightness profiles of TH09 and HR14 in the WFPC2 images. + We considered bulge-only fits. disc-only fits. and fits containing both bulge and dise components.," We considered bulge-only fits, disc-only fits, and fits containing both bulge and disc components." + Only the fit to THO9 displayed a clear morphological preference. with the bulge-o-total luminosity ratio of the best fit being b.=0.75.+0.13 (95 per cent confidence). and there being no significant preference ‘or this fit over the pure bulge fit (reduced X7/v of L.18 and 1.20. respectively. compared to 1.33 for a pure disce fit).," Only the fit to TH09 displayed a clear morphological preference, with the bulge-to-total luminosity ratio of the best fit being $b=0.75.\pm 0.13$ (95 per cent confidence), and there being no significant preference for this fit over the pure bulge fit (reduced $\chi^2/\nu$ of 1.18 and 1.20, respectively, compared to 1.33 for a pure disc fit)." + The shorter wavelength of the FASSW image of THO9 might be expected to increase the contribution of any dise component. but he lower signal-to-noise ratio of this image precludes a preference being given to any particular model because the fits are poorly constrained (giving a reduced X7/v2 0.4).," The shorter wavelength of the F555W image of TH09 might be expected to increase the contribution of any disc component, but the lower signal-to-noise ratio of this image precludes a preference being given to any particular model because the fits are poorly constrained (giving a reduced $\chi^2/\nu \approx 0.4$ )." + We note however that he preferred composite model has a strong bulge component (93 oer cent of the total luminosity)., We note however that the preferred composite model has a strong bulge component (93 per cent of the total luminosity). + The best fit for HRI4 has a bulge contribution of 3? percent. but the poor sampling and relatively low signal-to-noise ratio mean that all three fits have very similar values of V7.," The best fit for HR14 has a bulge contribution of 32 per cent, but the poor sampling and relatively low signal-to-noise ratio mean that all three fits have very similar values of $\chi^2$." + We show the results of our fits in Table 3 and Figure 2.3., We show the results of our fits in Table \ref{gim2dtab} and Figure \ref{gim2d}. +. We thus conclude that THO9 is morphologically a. bulge-dominated galaxy. and is likely a pure elliptical. but that we are unable on the basis of these images to make a robust morphological classification for HR14.," We thus conclude that TH09 is morphologically a bulge-dominated galaxy, and is likely a pure elliptical, but that we are unable on the basis of these images to make a robust morphological classification for HR14." + We first concentrate our discussion on ΤΗΟΟ., We first concentrate our discussion on TH09. + As noted in the previous section. this galaxy is morphologically an elliptical.," As noted in the previous section, this galaxy is morphologically an elliptical." + To investigate the properties of the stellar population in THO9 we firs used the photometric code (Bolzonello. Mirales Pello. 2000). fixing the redshift at 1.34.," To investigate the properties of the stellar population in TH09 we first used the photometric code (Bolzonello, Mirales Pello, 2000), fixing the redshift at 1.34." + This gave a poor fit for any of the model spectra inHYPERZ: this also applied to the potentia and redshifts described in section 2.1., This gave a poor fit for any of the model spectra in; this also applied to the potential and redshifts described in section 2.1. + However. on examining the best-fit spectrum for >=1.34 in detail. it became apparent that the observed-frame near-IR was in fact a very good fit to an old population.," However, on examining the best-fit spectrum for $z = 1.34$ in detail, it became apparent that the observed-frame near-IR was in fact a very good fit to an old population." + The poorness of the overall fit was caused by the rest-frame UV being too bright for this population. by abou a factor of ten at g-band.," The poorness of the overall fit was caused by the rest-frame UV being too bright for this population, by about a factor of ten at $g$ -band." + We next considered the possibility that THO9 hosts an AGN., We next considered the possibility that TH09 hosts an AGN. + The galaxy is not detected to a three-sigma limit of 18 j/Jy at 8 GHz (Cotter. unpublished data) and a deep ROSAL PSPC image (Kneissl. Sunyaev White 1997) gives alimitof4. 10‘ergs ! 7 inthe 0.5-2.0 keV band.," The galaxy is not detected to a three-sigma limit of 18 $\mu$ Jy at 8 GHz (Cotter, unpublished data) and a deep $ROSAT$ PSPC image (Kneissl, Sunyaev White 1997) gives a limit of $4 \times 10^{-14}$ erg $^{-1}$ $^{-2}$ in the 0.5-2.0 keV band." + Although there are no deep Chandra or XMM images available. which would allow us to rule out hard X-ray emission. these non-detections argue strongly against THO9 being an AGN host.," Although there are no deep Chandra or XMM images available, which would allow us to rule out hard X-ray emission, these non-detections argue strongly against TH09 being an AGN host." + Our detection detection of Ha therefore implies that THO9 is starforming: this means that THO9 cannot be quiescent old elliptical galaxy witha// its stars having formed at an early cosmic epoch., Our detection detection of $\alpha$ therefore implies that TH09 is starforming; this means that TH09 cannot be quiescent old elliptical galaxy with its stars having formed at an early cosmic epoch. + We chose then to model the SED of THO9 as a combination of an old stellar population plus a young starburst population., We chose then to model the SED of TH09 as a combination of an old stellar population plus a young starburst population. + We used the solar metallicity Padua 1994 SSP from Bruzual Charlot (2003: hereafter BCO3). with a model age of 5.5 Gyr (the age of our fiducial universe at 2=1.34) for the old population. as this gave the best fits to the red end of the SED (lower metallicity SSPs were not sufficiently red at this age).," We used the solar metallicity Padua 1994 SSP from Bruzual Charlot (2003; hereafter BC03), with a model age of 5.5 Gyr (the age of our fiducial universe at $z = 1.34$ ) for the old population, as this gave the best fits to the red end of the SED (lower metallicity SSPs were not sufficiently red at this age)." + For the young stellar component we used a continuous starforming model from the same SSP with an age of 70 Myr (tat which are the shape of the SED becomes close to its asymptote). using the rest-frame 2800 Aflux to obtain the SFR.," For the young stellar component we used a continuous starforming model from the same SSP with an age of 70 Myr (at which are the shape of the SED becomes close to its asymptote), using the rest-frame 2800 flux to obtain the SFR." + The next step was to estimate the SFR from the Ha luminosity in our OHS/CISCO spectrum., The next step was to estimate the SFR from the $\alpha$ luminosity in our OHS/CISCO spectrum. + Since our spectral extraction aperture encompasses only a fraction of the total flux from the galaxy. we scale our Ha flux to account for slit losses.," Since our spectral extraction aperture encompasses only a fraction of the total flux from the galaxy, we scale our $\alpha$ flux to account for slit losses." + We measure a difference of one magnitude between the brightness of THO9 in our extraction aperture (as determined from the acquisition images) and its flux in Table 2. and therefore apply a correction factor of 2.5 to our measured emission line flux.," We measure a difference of one magnitude between the brightness of TH09 in our extraction aperture (as determined from the acquisition images) and its flux in Table 2, and therefore apply a correction factor of 2.5 to our measured emission line flux." + This implicitly assumes that the Ha line emission has the same angular extent as the //- light. although we can determine a robust lower limit to the size of this correction of 71.5 by determining how much light from a point source would fall into our spectroscopic aperture. and hence our correction will not be in error by more than pper cent.," This implicitly assumes that the $\alpha$ line emission has the same angular extent as the $H$ -band light, although we can determine a robust lower limit to the size of this correction of $>1.5$ by determining how much light from a point source would fall into our spectroscopic aperture, and hence our correction will not be in error by more than per cent." + Using the relationship between Ha luminosity and star formation rate given by Kennicutt (1998). this implies a star formation rate of ~20M.vr.+.," Using the relationship between $\alpha$ luminosity and star formation rate given by Kennicutt (1998), this implies a star formation rate of $\sim 20 M_{\odot}\,{\rm yr}^{-1}$." + However. adding a suitable constant star-forming component to our model spectrum produces too much emission in the rest-frame ultraviolet.," However, adding a suitable constant star-forming component to our model spectrum produces too much emission in the rest-frame ultraviolet." + At this point we note that. although there is a clear rest-frame UV excess in the spectrum of THO9. it does turn over in the far UV. so we also included a dust extinction. using the reddening law of Calzetti et al. (," At this point we note that, although there is a clear rest-frame UV excess in the spectrum of TH09, it does turn over in the far UV, so we also included a dust extinction, using the reddening law of Calzetti et al. (" +2000) which we applied only to the young stellar population.,2000) which we applied only to the young stellar population. + We tind that by taking an unreddened old stellar population. and adding a young population commensurate to a star formation rate of 50-100. AZ.vr.4+. with dust extinctions of ely=3+ 4. we obtain reduced 47 values of around 3 (in this region of the parameter space. the slope of the «7 surface is quite shallow around the minimum).," We find that by taking an unreddened old stellar population, and adding a young population commensurate to a star formation rate of 50-100 $M_{\odot} {\rm yr}^{-1}$, with dust extinctions of $A_V = +3$ --4, we obtain reduced $\chi^2$ values of around 3 (in this region of the parameter space, the slope of the $\chi^2$ surface is quite shallow around the minimum)." + Moreover. this rate of star formation is then consistent with the observed Ha flux. assuming that it originates only in the star forming regions and suffers the same extinction.," Moreover, this rate of star formation is then consistent with the observed $\alpha$ flux, assuming that it originates only in the star forming regions and suffers the same extinction." + The limit to the 8.4-GHz continuum flux density implies a, The limit to the 8.4-GHz continuum flux density implies a +(Table 1).,(Table 1). + The major changes ave that (wo more Compton-thick sources (NGC 1365 and NGC T5827)) are classified., The major changes are that two more Compton-thick sources (NGC 1365 and NGC ) are classified. + Within the 39 sources. there are 7 radio loud sources (including three blazars). 4 Compton-thick sources and 28 radio quiet Compton-thin Sevlert galaxies.," Within the 39 sources, there are 7 radio loud sources (including three blazars), 4 Compton-thick sources and 28 radio quiet Compton-thin Seyfert galaxies." + In order to increase the number of soft Gamma rav. selected. AGNs. we combine the INTEGRAL Sample and the SWZFT Sample.," In order to increase the number of soft Gamma ray selected AGNs, we combine the $INTEGRAL$ Sample and the $SWIFT$ Sample." + Note that there are 10 objects which were detected bv both of them (see Table 1)., Note that there are 10 objects which were detected by both of them (see Table 1). + Using these 10 objects. we obtained a linear scaling factor from the SIVZET luminosity to the ΓΑTECHRAL one (see Fig.," Using these 10 objects, we obtained a linear scaling factor from the $SWIFT$ luminosity to the $INTEGRAL$ one (see Fig." + 1)., 1). + With the scaling factor.we translate all the STVZ£T luminosity in 14. 195 keV to the the INTEGRAL huninositv in 20 — 100 keV. The combined sample contains 42 radio quiet. Compton-thin objects. 1H radio loud sources (including 6 blazars) and eight Compton-Chick objects.," With the scaling factor,we translate all the $SWIFT$ luminosity in 14 – 195 keV to the the $INTEGRAL$ luminosity in 20 – 100 keV. The combined sample contains 42 radio quiet Compton-thin objects, 14 radio loud sources (including 6 blazars) and eight Compton-thick objects." + In Fig., In Fig. +2 we plot the X-ray absorption column density versus the SWIET Iumninosity for ihe 39 AGNs in the SWIFT sample., \ref{swift} we plot the X-ray absorption column density versus the SWIFT luminosity for the 39 AGNs in the SWIFT sample. +" Consistent with M05. we find a clear drop of Ny, with increasing luninositw."," Consistent with M05, we find a clear drop of $N_H$ with increasing luminosity." + Since soft. gamnia-rav selected samples are not biased to obscuration (except for Compton thick sources). the sample selection is identical for both obscured and unobscured sources.," Since soft gamma-ray selected samples are not biased to obscuration (except for Compton thick sources), the sample selection is identical for both obscured and unobscured sources." +" We can simply study the correlation between Vj, and Ly (or the Inminosity distribution for obscured/unobscured sources) in (he samples without caleulating the Iuminosity. function or folding Iuminosity ΠΙΟΠΟ model with the sample selection.", We can simply study the correlation between $N_H$ and $_X$ (or the luminosity distribution for obscured/unobscured sources) in the samples without calculating the luminosity function or folding luminosity function model with the sample selection. + We performed the Spearman Rank (8I) statistic to eive the correlation between ;Vjj aud Ly., We performed the Spearman Rank (SR) statistic to give the correlation between $N_H$ and $_X$. +" We found a significant anti-correlation between Ny, aud Ly at level.", We found a significant anti-correlation between $N_H$ and $_X$ at level. +" We note that while a [Iux-limited sample would introduce spurious correlation between Iuminosity. and reclshilt (or between luminosities in different bands). such an effect. will not affect. our study. since (he measurement of Ny, is independent of redshift for the local samples."," We note that while a flux-limited sample would introduce spurious correlation between luminosity and redshift (or between luminosities in different bands), such an effect will not affect our study since the measurement of $N_H$ is independent of redshift for the local samples." + With the radio loud and Compton thick sources excluded. (he confidence level of the anti-correlation significantly drops to9856.," With the radio loud and Compton thick sources excluded, the confidence level of the anti-correlation significantly drops to." +".. 18 out of 28 radio quiet Compton-thin objects show Vj, Z 107 7. vielding a fraction of "," 18 out of 28 radio quiet Compton-thin objects show $N_H$ $\gtrsim$ $^{22}$ $^{-2}$, yielding a fraction of ." +6454..., In Fig. +" In Fig. 3 we plot Ny, versus INTEGRAL Iuminosity for the 35 AGNs in the INTEGRAL", \ref{integral} we plot $N_H$ versus INTEGRAL luminosity for the 35 AGNs in the INTEGRAL +simultaneously to the full data set by a non-linear least-squares fit. which produces our tinal set of frequencies and amplitudes.,"simultaneously to the full data set by a non-linear least-squares fit, which produces our final set of frequencies and amplitudes." + Ironically. the simplest feature of the May98 amplitude spectrum is also the most obviously unstable: there is no trace of the mode near 230 s in any of the 1997 amplitude spectra. although it is strong in 2001.," Ironically, the simplest feature of the May98 amplitude spectrum is also the most obviously unstable: there is no trace of the mode near 230 s in any of the 1997 amplitude spectra, although it is strong in 2001." + At first glance. (Pig. 4..," At first glance, (Fig. \ref{fig:mode236}," + upper panels) appears identical to the spectral window in both the May98 and the &JTJune98 FTs., upper panels) appears identical to the spectral window in both the May98 and the June98 FTs. + The lower panels of Fig., The lower panels of Fig. + 4. show the FTs after prewhitening with this signal., \ref{fig:mode236} show the FTs after prewhitening with this signal. + In the May&JJune98 spectrum. with its extended baseline. an additional. low-amplitude component is revealed.," In the June98 spectrum, with its extended baseline, an additional, low-amplitude component is revealed." + If the 230-s signal is a rotationally-split doublet (the most common reason for splitting of DAVY modes). the frequency difference between the components. 0.79 j/Hz. is remarkably small.," If the 230-s signal is a rotationally-split doublet (the most common reason for splitting of DAV modes), the frequency difference between the components, 0.79 $\mu$ Hz, is remarkably small." + If this is an /=1 mode (the most common modes in DAVs). the implied rotation period of the star is 7.3 days (from the properties of pulsational g-modes: see for example Winget et al. [," If this is an $l=1$ mode (the most common modes in DAVs), the implied rotation period of the star is 7.3 days (from the properties of pulsational $g$ -modes; see for example Winget et al. [" +1991.1994]).,"1991,1994])." + This rotation period is much longer than what we would expect for a CV primary., This rotation period is much longer than what we would expect for a CV primary. + A splitting of 0.79 (/Hz corresponds to a beat period of 115 days. which is very close to both the baseline of the May98 dataset. and the gap between the May and June data.," A splitting of 0.79 $\mu$ Hz corresponds to a beat period of 15 days, which is very close to both the baseline of the May98 dataset, and the gap between the May and June data." + However. there are no splittings equal to 0.79 // Hz in the spectral window.," However, there are no splittings equal to 0.79 $\mu$ Hz in the spectral window." + Further evidence that iis a closely-spaced doublet comes from changes in its O-C phases and amplitude over the observing campaign., Further evidence that is a closely-spaced doublet comes from changes in its O-C phases and amplitude over the observing campaign. + In Fig., In Fig. +" 5. we show the O-C and amplitudes of the three principal regions of power.w.,,-. ld css over the baseline of the May&JJune98 dataset."," \ref{fig:ominusc} we show the O-C and amplitudes of the three principal regions of power, and , over the baseline of the June98 dataset." + The points were calculated using the dominant signal in aand an average of the frequencies for each of and listed in Table 2., The points were calculated using the dominant signal in and an average of the frequencies for each of and listed in Table 2. + From the top panels in Fig., From the top panels in Fig. + 5 it can be seen that the curve of Is not flat (Fig. 55).," \ref{fig:ominusc} it can be seen that the curve of is not flat (Fig. \ref{fig:ominusc}) )," + which could indicate that consists of two components., which could indicate that consists of two components. + Fig., Fig. + 5 also shows that the amplitude of appears to be varying sinusoidally. which could indicate the existence of two closely-spaced components beating against each other.," \ref{fig:ominusc} also shows that the amplitude of appears to be varying sinusoidally, which could indicate the existence of two closely-spaced components beating against each other." + The other principal regions of power in the pulsation spectrum of the Μάνος dataset — the structures near 650 s and 370 s — are a great deal more complex than, The other principal regions of power in the pulsation spectrum of the May98 dataset – the structures near 650 s and 370 s – are a great deal more complex than. +"w,.", Fig. +",,.. Fig. 6. shows the 370- and 650-s regions of the May98 and May&JJune98 amplitude spectra in detail.", \ref{fig:yukky} shows the 370- and 650-s regions of the May98 and June98 amplitude spectra in detail. + appears to consist of two triplets. each with components spaced I1. (Hz. apart (Table 2).," appears to consist of two triplets, each with components spaced 1 $\mu$ Hz apart (Table 2)." + One. triplet. centred. at 2645.90 iL Hz or 377.94 s (indicated by the open arrows in Fig. 6..," One triplet, centred at 2645.90 $\mu$ Hz or 377.94 s (indicated by the open arrows in Fig. \ref{fig:yukky}," + which show the three highest-amplitude aliases of the complete triplet). has three closely-spaced components well resolved in both the May98 and May&JJune98 FTs.," which show the three highest-amplitude aliases of the complete triplet), has three closely-spaced components well resolved in both the May98 and June98 FTs." + No feature of the spectral window corresponds to the frequency spacing of the triplet components. so we do not believe that they are an observational artifact.," No feature of the spectral window corresponds to the frequency spacing of the triplet components, so we do not believe that they are an observational artifact." + Ss second structure appears to be an unresolved triplet centred at 2662.94 (/ Hz or 375.52 s (indicated by the solid arrows in Fig. 65., s second structure appears to be an unresolved triplet centred at 2662.94 $\mu$ Hz or 375.52 s (indicated by the solid arrows in Fig. \ref{fig:yukky}) ). + Prewhitening this structure produces 3 signals also |I Az apart., Prewhitening this structure produces 3 signals also 1 $\mu$ Hz apart. + We fitted these three signals simultaneously to the May98 dataset. the May&JJune98 dataset. and two additional datasets containing only the first or the second half of each night.," We fitted these three signals simultaneously to the May98 dataset, the June98 dataset, and two additional datasets containing only the first or the second half of each night." + In all four cases. this feature was consistent with a triplet with components || ji Hz apart.," In all four cases, this feature was consistent with a triplet with components 1 $\mu$ Hz apart." + The presence of both a resolved triplet and an unresolved triplet whose components have the same spacing is not inconsistent: if a light-curve is full of substantial gaps (due to daylight or bad weather. ete). then the resolvability of closely-spaced signals whose beat period is approximately equal to the total run length (as is the case here) depends on how the data and the gaps are distributed across their beat cycle.," The presence of both a resolved triplet and an unresolved triplet whose components have the same spacing is not inconsistent: if a light-curve is full of substantial gaps (due to daylight or bad weather, etc), then the resolvability of closely-spaced signals whose beat period is approximately equal to the total run length (as is the case here) depends on how the data and the gaps are distributed across their beat cycle." + If the data cover regions where the signals are out of phase with each other. the FT is far more likely to resolve the individual signals than if the signals are in phase.," If the data cover regions where the signals are out of phase with each other, the FT is far more likely to resolve the individual signals than if the signals are in phase." + We have modelled pairs of triplets made up of closely-spaced sinusoids sampled in the same way as our data. and we are able to reproduce the appearance of very well.W," We have modelled pairs of triplets made up of closely-spaced sinusoids sampled in the same way as our data, and we are able to reproduce the appearance of very well.," +enge On the other hand. is a partially-resolved tangle of at least 7 closely- but unevenly-spaced signals (Table 2).," on the other hand, is a partially-resolved tangle of at least 7 closely- but unevenly-spaced signals (Table 2)." + It is difficult to know whether these signals represent individual pulsation modes active within the white dwarf. or whether we are seeing the effects of non-stationary behaviour in the pulsation spectrum (.e.. frequency. amplitude or phase modulation).," It is difficult to know whether these signals represent individual pulsation modes active within the white dwarf, or whether we are seeing the effects of non-stationary behaviour in the pulsation spectrum (i.e., frequency, amplitude or phase modulation)." + The O-C curves in Fig., The O-C curves in Fig. + 5 (middle and bottom panels) show noisy modulations. which support our findings that and appear to be made up of several different signals.," \ref{fig:ominusc} (middle and bottom panels) show noisy modulations, which support our findings that and appear to be made up of several different signals." + Linear combination modes are frequently observed in the pulsation spectra of DAVs., Linear combination modes are frequently observed in the pulsation spectra of DAVs. + They arise as a result of non-linear mixing of the real eigenmodes: the thickness of the convection zone is modulated by the pulsations and the signal is not only diminished and delayed. but also distorted.," They arise as a result of non-linear mixing of the real eigenmodes: the thickness of the convection zone is modulated by the pulsations and the signal is not only diminished and delayed, but also distorted." + This latter distortion gives rise to the power seen at linear combinations (Brickhill 1992)., This latter distortion gives rise to the power seen at linear combinations (Brickhill 1992). + We have detected four clusters of signals at frequencies, We have detected four clusters of signals at frequencies +The condition on the inclination. of the candidate orbits (i.c. they. must be prograde) is imposed. to assure the physical correctness of the solutions found. since the formation of retrograde bodies from the Solar Nebula is not If specified by the user. the code can loop the algorithm while varving the orbital position of both the satellite around the planet and the planet around the Sun to avoic selection effects. due to the choice. of particular initia conditions.,"The condition on the inclination of the candidate orbits (i.e. they must be prograde) is imposed to assure the physical correctness of the solutions found, since the formation of retrograde bodies from the Solar Nebula is not If specified by the user, the code can loop the algorithm while varying the orbital position of both the satellite around the planet and the planet around the Sun to avoid selection effects due to the choice of particular initial conditions." + “Phe code also implements the possibility to filter the candidate orbits over a selected ο value of the eccentricitv. in order to control the range of. physica conditions under which the capture event took An open issue with this approach is the physica meaning of the specific impulse α used by the algorithm.," The code also implements the possibility to filter the candidate orbits over a selected $e_{max}$ value of the eccentricity, in order to control the range of physical conditions under which the capture event took An open issue with this approach is the physical meaning of the specific impulse $d\vec{v}$ used by the algorithm." + To the first order ancl for ideally. fully inclastic collisions the interpretation is straightforward. since it represents the change in velocity due to the collision of the parent body with the projectile.," To the first order and for ideally, fully inelastic collisions the interpretation is straightforward, since it represents the change in velocity due to the collision of the parent body with the projectile." + The real case is however complicated by the fact that impacts always involve some level of energy dissipation due to the generation of heat. the formation of craters and fracture lines in the target. body and the excavation of fragments.," The real case is however complicated by the fact that impacts always involve some level of energy dissipation due to the generation of heat, the formation of craters and fracture lines in the target body and the excavation of fragments." + Moreover. things are worse in case of catastrophically disruptive events.," Moreover, things are worse in case of catastrophically disruptive events." + While for. the ejection of [fragments the total excavated mass is usually small in comparison to the mass of the target. ancl the contribution to the change in momentum is limited. in case of catastrophic disruption the mass of the collisional shares could be relevant and the ejection speeds. estimated [rom laboratory experiments and numerical simulations with hyelrocodes to be of the order of 100 m/s (Benz&Aspaugh 1999).. could represent a significant fraction of the specific impulse imposed by the collision.," While for the ejection of fragments the total excavated mass is usually small in comparison to the mass of the target and the contribution to the change in momentum is limited, in case of catastrophic disruption the mass of the collisional shards could be relevant and the ejection speeds, estimated from laboratory experiments and numerical simulations with hydrocodes to be of the order of $100$ m/s \citep{ben99}, could represent a significant fraction of the specific impulse imposed by the collision." + While this problem in eencral has to be dealt with on a case by case basis. we will treat it in major detail for Phoebe in section ??..," While this problem in general has to be dealt with on a case by case basis, we will treat it in major detail for Phoebe in section \ref{phoebe}." + The configuration we used for our investigation of the inverse capture process of Saturn's irregular satellites has been: Since our model emploved the specific impulse as its free parameter. we were not constrained by the size of the bodies in the choice of the ones to be used. as our reference cases.," The configuration we used for our investigation of the inverse capture process of Saturn's irregular satellites has been: Since our model employed the specific impulse as its free parameter, we were not constrained by the size of the bodies in the choice of the ones to be used as our reference cases." + We chose four irregular satellites (νο prograde ancl two retrograde) representative of the main dvnamical configurations for our investigation: Albiorix. Siarnaq. Phoebe and Muncdilfari.," We chose four irregular satellites (two prograde and two retrograde) representative of the main dynamical configurations for our investigation: Albiorix, Siarnaq, Phoebe and Mundilfari." + As their orbits. we used the mean orbital elements we presented in Paper L. Phoebe was a natural choice as one of our case studies since our simulations showed that the secular. variations of its orbit are quite regular. and. limited. (see Paper 1). implying a better preservation of its primordial dynamics.," As their orbits, we used the mean orbital elements we presented in Paper I. Phoebe was a natural choice as one of our case studies since our simulations showed that the secular variations of its orbit are quite regular and limited (see Paper I), implying a better preservation of its primordial dynamics." + Ehe results we obtained are presented from fig., The results we obtained are presented from fig. + 1. to fig. 16...," \ref{aeplot-Albiorix} to fig. \ref{dvplot-Mundilfari}," + where we showed. for increasing values of the specific impulse. the evolution of the solutions to the inverse problem in the: The values of the specific impulse emploved for cach satellite (reported in the captions of the associated figures) produced respectively 101.3101.107.2τοῦὁ«107.12 solutions.," where we showed, for increasing values of the specific impulse, the evolution of the solutions to the inverse problem in the: The values of the specific impulse employed for each satellite (reported in the captions of the associated figures) produced respectively $10^4,\,3\times10^4,10^5,\,2\times10^5,\,6\times10^5,\,1.2\times10^6$ solutions." + These values5 have been chosen to represent. the main features of the evolution of the solutions ancl range from the threshold. values for which. the first. solutions appeared to the values for which the dillerent. families. of solutions overlapped. into a single continuum., These values have been chosen to represent the main features of the evolution of the solutions and range from the threshold values for which the first solutions appeared to the values for which the different families of solutions overlapped into a single continuum. + We found that the minimum change in velocity to be applied in order to capture the irregular satellites lay in general between 450 m/s and 500 m/s.with Phoebe being a separate case requiring a value (2:650 m/s) about 30% While the evolution of the solutions of cach satellite showed its own peculiar features. there were some general conclusions we could. draw.," We found that the minimum change in velocity to be applied in order to capture the irregular satellites lay in general between $450$ m/s and $500$ m/s,with Phoebe being a separate case requiring a value $\approx 650$ m/s) about $30\%$ While the evolution of the solutions of each satellite showed its own peculiar features, there were some general conclusions we could draw." + First. we noticed. that the solutions were grouped into distinct and initially well separated. families (see top panels of figs. 1--16))," First, we noticed that the solutions were grouped into distinct and initially well separated families (see top panels of figs. \ref{aeplot-Albiorix}- \ref{dvplot-Mundilfari}) )" + which. for increasing values of the specifie impulse applied. tended o overlap to finally merge into à more or less continuous distribution (see bottom panels of figs. 1--16)).," which, for increasing values of the specific impulse applied, tended to overlap to finally merge into a more or less continuous distribution (see bottom panels of figs. \ref{aeplot-Albiorix}- \ref{dvplot-Mundilfari}) )." + Second. these zunilies of solutions were related. to. preferential direction of approach. as is particularly evident from the top panels of figs. 1.. 5..," Second, these families of solutions were related to preferential direction of approach, as is particularly evident from the top panels of figs. \ref{aeplot-Albiorix}, \ref{aeplot-Siarnaq}," + 9. and 13.., \ref{aeplot-Phoebe} and \ref{aeplot-Mundilfari}. +" This occurrence is strictly related o the existence of preferential directions of impulse change (i.c. impact ecometry) as is apparent from the plots of figs. 4.. δν,"," This occurrence is strictly related to the existence of preferential directions of impulse change (i.e. impact geometry) as is apparent from the plots of figs. \ref{dvplot-Albiorix}, \ref{dvplot-Siarnaq}," + 12 and 16.., \ref{dvplot-Phoebe} and \ref{dvplot-Mundilfari}. + Third. thefirst solutions to appear for the owestvalues of specific impulse applied: were characterised w high eccentricity values (generally 0.3.<οQT. except in Muncdilfari's case where 0.20«ο 0.5) and semimajor axis spread between ο20 AU (5.30 AU in Albiorixs case). a behaviour contrary to what was generally believed: to occur (e.g. the reservoir of parent bodies. of the irregular satellites being located near their host As a rule of the thumb. prograde and. retrograde satellites. formed: two. distinct. groups in terms of the solutions to the inverse capture problem.," Third, thefirst solutions to appear for the lowestvalues of specific impulse applied were characterised by high eccentricity values (generally $0.3 < e < 0.7$, except in Mundilfari's case where $0.2 < e < 0.5$ ) and semimajor axis spread between $5-20$ AU $5-30$ AU in Albiorix's case), a behaviour contrary to what was generally believed to occur (e.g. the reservoir of parent bodies of the irregular satellites being located near their host As a rule of the thumb, prograde and retrograde satellites formed two distinct groups in terms of the solutions to the inverse capture problem." + Lo we compare the cases with the same number of solutions. the prograde cases cover a wider region of phase space than retrograde cases.," If we compare the cases with the same number of solutions, the prograde cases cover a wider region of phase space than retrograde cases." + The range of inclination values covered by the former is at least one third higher than the one of the latter(OO 0.7$ respectively, see figs. \ref{aeplot-Albiorix}, \ref{aeplot-Siarnaq}, , \ref{aeplot-Phoebe}, , \ref{aeplot-Mundilfari})" +. The solutionsrelated to the orbital region inside Saturn's orbit are the most widespread. in inclination.| ancl acquire the. highest. inclination. values. (see. bottom panels of figs. 2.. 6.. 10... 14)).," The solutionsrelated to the orbital region inside Saturn's orbit are the most widespread in inclination and acquire the highest inclination values (see bottom panels of figs. \ref{aiplot-Albiorix}, , \ref{aiplot-Siarnaq}, , \ref{aiplot-Phoebe}, \ref{aiplot-Mundilfari}) )." + The solutions of Albiorix. Siarnac," The solutions of Albiorix, Siarnaq" +Despite our deep and repeated WSRT observations. we have not been abk' to convincingly detect 22] cu absorption against the raclo source.,"Despite our deep and repeated WSRT observations, we have not been able to convincingly detect 21 cm absorption against the radio source." + This is consisteut with uuisucecesstul WSRT searches in 6 Πές 19993., This is consistent with unsuccessful WSRT searches in 6 HzRGs . +. To date. 22] cin absorption has been solidly «etected iu only oue WzRC. BB? t1902|31 1993).," To date, 21 cm absorption has been solidly detected in only one HzRG, B2 0902+34 ." +. This raises the qiestion as to why DD2 0902|31 stands out., This raises the question as to why B2 0902+34 stands out. + One clue may conie from its bizarre radio morphology 1995)., One clue may come from its bizarre radio morphology . +". areuc that the Hs located in a kpce-zed disc. which can be seen iu absorption duc to a fortuitous orientation of the radio source,"," argue that the is located in a kpc-sized disc, which can be seen in absorption due to a fortuitous orientation of the radio source." + They furier sugeest that a high core fraction nay characterize such orientations: for B2 0902|31. conrpared to and for the 6 IzRCs where 10 21 cni absorption has been detected.," They further suggest that a high core fraction may characterize such orientations: for B2 0902+34, compared to and for the 6 HzRGs where no 21 cm absorption has been detected." + Ilowever. in D3 J2330|3927. we find a core fraction of or (μου Table 3)). depeudiug if we adopt the northern or central radio component as the core (sec 83.2).," However, in B3 J2330+3927, we find a core fraction of or (see Table \ref{B3radio}) ), depending if we adopt the northern or central radio component as the core (see 3.2)." + We conclude that he present sampe of 8 IIZRCs where 22] cn absorptio1i has been searched is clearly too small ο address the origin of the absorbing neutral gas., We conclude that the present sample of 8 HzRGs where 21 cm absorption has been searched is clearly too small to address the origin of the absorbing neutral gas. + The detection of he different ewission and absorption coniponeuts in D3 J2330|3927 suggests it is a Massive svsteni., The detection of the different emission and absorption components in B3 J2330+3927 suggests it is a massive system. + Iu this section. we use the above data to derive 5 indepenuceut lass estimates of the igas axd dust components.," In this section, we use the above data to derive 5 independent mass estimates of the gas and dust components." + We discuss cach component separately. and stuimarize or results in Table 5..," We discuss each component separately, and summarize our results in Table \ref{massestimates}." + We uote that several liegh redshit CO detections wave been helped eyavitational lousing200253., We note that several high redshift CO detections have been helped by gravitational lensing. +. However. from our radio aud optical/near-IR imagine. we find indications that D3 J2330|3927 could be amplified by eravitational leusiug. aud we do rot consider this iu the followiug.," However, from our radio and optical/near-IR imaging, we find no indications that B3 J2330+3927 could be amplified by gravitational lensing, and we do not consider this in the following." + We can estimate the molecular eas content from our CO lime detection by making au asstuuption for the stancard conversion factor YooΠο)0). where is the CO line luminosity measured in I& per1992).," We can estimate the molecular gas content from our CO line detection by making an assumption for the standard conversion factor $X_{\rm CO}=M({\rm H_2})/L^{\prime}_{\rm CO}(1-0)$, where is the CO line luminosity measured in K $^2$." +. 'The standard value for Calactic molecular clouds is, The standard value for Galactic molecular clouds is +"Age estimates [or elobular clusters indicate that they formed. carly in the history of the Milkv Way and represent ""fossil relics’ of the proo-Galaxy (Larson 1990).", Age estimates for globular clusters indicate that they formed early in the history of the Milky Way and represent `fossil relics' of the proto-Galaxy (Larson 1990). + Attempting to uncover this history. researchers have carefully. cxamined a range of properties of the present-davy cluster system. paving particular attention to the cluster kinematic distribution (e.g. Zinn 1993) mass clistribution (ο. Harris DPudritz 1994). metallicity distribution (e.g. Zinn 1985) and age distribution (e.g. Chabover. Demarcue Sarajecini 1996).," Attempting to uncover this history, researchers have carefully examined a range of properties of the present-day cluster system, paying particular attention to the cluster kinematic distribution (e.g. Zinn 1993), mass distribution (e.g. Harris Pudritz 1994), metallicity distribution (e.g. Zinn 1985) and age distribution (e.g. Chaboyer, Demarque Sarajedini 1996)." + These investigations have provided evidence for both accreted and. native components. in the cluster system (Searle Zinn LOTS) and. correlations between kinematics anc metallicity which may trace the collapse of the Galaxy (Zinn 1985: Armancdroll 1989: Zinn 1993)., These investigations have provided evidence for both accreted and native components in the cluster system (Searle Zinn 1978) and correlations between kinematics and metallicity which may trace the collapse of the Galaxy (Zinn 1985; Armandroff 1989; Zinn 1993). + Comparisons with other stellar. populations have revealed. subtletics in the process of Galaxy. formation and evolution., Comparisons with other stellar populations have revealed subtleties in the process of Galaxy formation and evolution. + For example. in the inner Galaxy. the globular cluster distribution is Hatter than the distribution of halo Ποιά stars although their. profiles match well at larger radii.," For example, in the inner Galaxy, the globular cluster distribution is flatter than the distribution of halo field stars although their profiles match well at larger radii." + In addition. the field. star velocity ellipsoid has a strong a radial bias in comparison to the approximately isotropic cluster velocity ellipsoid (e.g. Ostriker. Binney Saha 1989).," In addition, the field star velocity ellipsoid has a strong a radial bias in comparison to the approximately isotropic cluster velocity ellipsoid (e.g. Ostriker, Binney Saha 1989)." + Conversely. Zinn (1985) and ΑναΠοτο (1989) have presented convincing evidence for a high-metallicity disk cluster. population which has broad similarities in kinematics. spatial distribution and metallicity with the," Conversely, Zinn (1985) and Armandroff (1989) have presented convincing evidence for a high-metallicity disk cluster population which has broad similarities in kinematics, spatial distribution and metallicity with the" +"caution, since all the strong emission lines display line-profile variability that could easily be responsible for the observed shifts in RV, whilst the weaker emission lines are found to be more constant, in terms of both morphology and RV.","caution, since all the strong emission lines display line-profile variability that could easily be responsible for the observed shifts in RV, whilst the weaker emission lines are found to be more constant, in terms of both morphology and RV." + The lack of a clear binary signature for 220b and MSP118 is especially surprising given their high X-ray luminosities (see Nazé et citeNRM))., The lack of a clear binary signature for 20b and 18 is especially surprising given their high X-ray luminosities (see Nazé et \\cite{NRM}) ). +" These stars have logLx/Lpo=—6.16 and —5.92 for 220b and 118 respectively, which are significantly larger than for typical single O-type stars and are as large as, or even larger than the value of the interacting wind system 220a (logLx/Lpo1=—6.15, Nazé et citeNRM))."," These stars have $\log{L_{\rm X}/L_{\rm bol}} = -6.16$ and $-5.92$ for 20b and 18 respectively, which are significantly larger than for typical single O-type stars and are as large as, or even larger than the value of the interacting wind system 20a $\log{L_{\rm X}/L_{\rm bol}} = -6.15$, Nazé et \\cite{NRM}) )." +" Since colliding winds have the potential to generate copious amounts of X-rays SStevens, Blondin Pollock 1992)), high X-ray luminosities have traditionally been associated with interacting winds in a binary system."," Since colliding winds have the potential to generate copious amounts of X-rays Stevens, Blondin Pollock \cite{SBP}) ), high X-ray luminosities have traditionally been associated with interacting winds in a binary system." +" However, recent investigations have revealed that interacting windbinaries are not always X-ray overluminous SSana et citeLx,, Nazé 2009)) at least as far as O-star binaries are concerned, and that alternative mechanisms such as magnetically confined winds can also produce high X-ray luminosities BBabel Montmerle 1997))."," However, recent investigations have revealed that interacting windbinaries are not always X-ray overluminous Sana et \\cite{Lx}, Nazé \cite{LxLbol}) ), at least as far as O-star binaries are concerned, and that alternative mechanisms such as magnetically confined winds can also produce high X-ray luminosities Babel Montmerle \cite{BM}) )." +" This implies that colliding winds, and by extension binarity, are neither a necessary nor a sufficient condition for high X-ray luminosities."," This implies that colliding winds, and by extension binarity, are neither a necessary nor a sufficient condition for high X-ray luminosities." +" Nonetheless, the high X-ray luminosities of 118 and 220b make these objects very interesting targets that deserve additional monitoring, in terms of both optical spectroscopy, to search for long-term RV variations, and spectropolarimetry, to search for evidence of magnetic fields or non-spherical winds."," Nonetheless, the high X-ray luminosities of 18 and 20b make these objects very interesting targets that deserve additional monitoring, in terms of both optical spectroscopy, to search for long-term RV variations, and spectropolarimetry, to search for evidence of magnetic fields or non-spherical winds." +" If these stars were indeed single, then their bolometric luminosities would suggest masses in the range 50 — 70Mo, provided that the main-sequence mass-luminosity relation holds for all these objects."," If these stars were indeed single, then their bolometric luminosities would suggest masses in the range 50 – $M_{\odot}$, provided that the main-sequence mass-luminosity relation holds for all these objects." + It has been argued that the most massive stars might actually display an ΠΡ supergiant or hydrogen-rich WN type spectrum rather than a normal O-type spectrum (Crowther et citeCrowther))., It has been argued that the most massive stars might actually display an $^*$ supergiant or hydrogen-rich WN type spectrum rather than a normal O-type spectrum (Crowther et \\cite{Crowther}) ). +" While it is true that the highest ever dynamical masses have been measured for WNLha stars so far (Rauw et citeRauw04,, Niemela et citeNiemela,, Schnurr et"," While it is true that the highest ever dynamical masses have been measured for WNLha stars so far (Rauw et \\cite{Rauw04}, , Niemela et \\cite{Niemela}, , Schnurr et" +With its very early spectral type (O4Infp. Walborn 1972)) and a distance of only ppe (vanLeeuwen.2007:etal.. 2008).. the star Naos. better known as (Cor 666811). Is one of the closest and brightest massive stars.,"With its very early spectral type (O4Infp, \citealt{wal72}) ) and a distance of only pc \citep{van07,mai08}, the star Naos, better known as (or 66811), is one of the closest and brightest massive stars." + It is therefore one of the most studied objects amongst the O-star population., It is therefore one of the most studied objects amongst the O-star population. + However. despite the intense work. many open questions remain on its nature.," However, despite the intense work, many open questions remain on its nature." + Indeed. ddisplays several intriguing properties.," Indeed, displays several intriguing properties." + First. its visible spectrum shows clear signs of helium overabundance and chemical enrichment by CNO-processed material (e.g. Pauldrachetal. 2001)) as well as fast rotation (more than ffor vsin(/). Penny1996;Howarthetal. 1997)).," First, its visible spectrum shows clear signs of helium overabundance and chemical enrichment by CNO-processed material (e.g. \citealt{pau01}) ) as well as fast rotation (more than for $v \sin(i)$, \citealt{pen96,how97}) )." + Second. it is a known runaway (e.g. from Hipparcos data. Moffatetal. 1998).," Second, it is a known runaway (e.g. from Hipparcos data, \citealt{mof98}) )." + These properties have led to speculations on its evolutionary status., These properties have led to speculations on its evolutionary status. + On the one hand. the chemical enrichment and. fast rotation could result from mass and angular momentum exchange through Roche lobe overflow in a binary.," On the one hand, the chemical enrichment and fast rotation could result from mass and angular momentum exchange through Roche lobe overflow in a binary." + ccould therefore have been the secondary component of such à system. the supernova explosion of its companion having ejected it from its birth place a few millions years ago Rensbergenetal.. 1996).," could therefore have been the secondary component of such a system, the supernova explosion of its companion having ejected it from its birth place a few millions years ago \citep{van96}." +. On the other hand. as stars of the Vela R2 (Schaereretal..1997).. and dynamical interactions within this association could have led to the ejection of the (single) O-star (vanRensbergenetal..1996).," On the other hand, as stars of the Vela R2 \citep{sch97}, and dynamical interactions within this association could have led to the ejection of the (single) O-star \citep{van96}." +. In this scenario. the chemical enrichment of wwould be explained by the intense rotational mixing occurring in the fast-rotating main-sequence progenitor (Meynet&Maeder.2000).," In this scenario, the chemical enrichment of would be explained by the intense rotational mixing occurring in the fast-rotating main-sequence progenitor \citep{mey00}." +. In addition. ddisplays double-peaked emission lines. suggested to arise in a rotating wind (Conti&Leep.1974:PetrenzPuls.1996).. and à compression of the wind in the equatorial plane was detected by Harries&Howarth (1996)..," In addition, displays double-peaked emission lines, suggested to arise in a rotating wind \citep{con74,pet96}, and a compression of the wind in the equatorial plane was detected by \citet{har96}. ." + Due to its brightness. wwas one of the first massive stars observed with high-resolution in X-rays (Kahnetal..2001:Cassinellt2001).," Due to its brightness, was one of the first massive stars observed with high-resolution in X-rays \citep{kah01,cas01}." +. At first. tts X-ray lines appeared to match expectations as they did show the broad. blueward-skewed profiles expected for the wind embedded shock model (Owocki&Cohen.2001).," At first, its X-ray lines appeared to match expectations as they did show the broad, blueward-skewed profiles expected for the wind embedded shock model \citep{owo01}." +. However. the devil was 1n the details.," However, the devil was in the details." + When quantitatively fitting the line profiles. Krameretal.(2003) found a much lower wind attenuation than expected on the basis of the mass-loss rate determined from optical and UV observations (see also Oskinovaetal. 2006)).," When quantitatively fitting the line profiles, \citet{kra03} found a much lower wind attenuation than expected on the basis of the mass-loss rate determined from optical and UV observations (see also \citealt{osk06}) )." + They also found that the typical optical depths r.. used in the wind-shock models. seemed independent of wavelength. which can only be explained by invoking porosity (Feldmeieretal...2003:Oskinovaal.. 2006).," They also found that the typical optical depths $\tau_*$, used in the wind-shock models, seemed independent of wavelength, which can only be explained by invoking porosity \citep{fel03, osk06}." + To improve the fitting of the X-ray line profiles. Leuteneggeretal.(2007) included the effect of resonance scattering: better fits were indeed obtained. without the need of a large reduction in the mass-loss rate. but they also showed that some unexplained discrepancies remain.," To improve the fitting of the X-ray line profiles, \citet{leu07} included the effect of resonance scattering: better fits were indeed obtained, without the need of a large reduction in the mass-loss rate, but they also showed that some unexplained discrepancies remain." + Re-analyzing the data ofPuppis.. Cohenetal.(2010) argue in favor of areduced mass-loss rate. without the need of any porosity as their new derivation of the optical depths implies an increase with wavelength. as expected from the bound-free absorption opacity of the (cool) wind.," Re-analyzing the data of, \citet{coh10} argue in favor of a reduced mass-loss rate, without the need of any porosity as their new derivation of the optical depths implies an increase with wavelength, as expected from the bound-free absorption opacity of the (cool) wind." + Except for Leuteneggeretal. (2007).. all above studies relied on a single kks. observation or a kks eexposure taken in 2000.," Except for \citet{leu07}, all above studies relied on a single ks observation or a ks exposure taken in 2000." + Both facilities have their advantages: while gelobally has a higher sensitivity. has a lower background. and a higher spectral resolution and sensivity at short wavelengths for its grating spectra.," Both facilities have their advantages: while globally has a higher sensitivity, has a lower background, and a higher spectral resolution and sensivity at short wavelengths for its grating spectra." + Today. however. much more data are available (see below).," Today, however, much more data are available (see below)." + Considering the uncertainties 1n the line profile resultsand the lack of new variability studies. we decided to re-investigate," Considering the uncertainties in the line profile resultsand the lack of new variability studies, we decided to re-investigate" +values of the parameters of the three Gaussian sources of JL from IMFETT and from our CE technique is shown in Table H1..,values of the parameters of the three Gaussian sources of J1 from IMFIT and from our CE technique is shown in Table \ref{J1_CE_IMFIT}. + Again. both algoritluus found the Camssian paralcters with simular high eficiency.," Again, both algorithms found the Gaussian parameters with similar high efficiency." + Uufortuuatelv. IMETT cannot fit simultaneously more than four Catussian sources.," Unfortunately, IMFIT cannot fit simultaneously more than four Gaussian sources." + To make possible a conrparisou between those algoritlas. we climate source munber 3 of the noisy jet J2. transforming it iuto a four-coniponeut image labeled asJ3!.," To make possible a comparison between those algorithms, we eliminate source number 3 of the noisy jet J2, transforming it into a four-component image labeled as." +. This makes J3 up as a sot of two overlapping components with S/R ~100., This makes J3 map as a set of two overlapping components with S/R $\sim 100$. + We show in Table 12. the mocelfitting values recovered from the CE aud IMEIT fittines as a function of the correct ones., We show in Table \ref{J3_CE_IMFIT} the model-fitting values recovered from the CE and IMFIT fittings as a function of the correct ones. + Unlike the carler comparisons presentec iu this subsection. the CE technique had a superior performance in determining the structural pariuneters of the Gaussian sources. especially in the case of the dinunuest component for which IMIFIT failed to converge to the correct parsuneters.," Unlike the earlier comparisons presented in this subsection, the CE technique had a superior performance in determining the structural parameters of the Gaussian sources, especially in the case of the dimmest component for which IMFIT failed to converge to the correct parameters." + In terms of relative errors. our CE algoritlan was able to recover 7 out of21 parameters within a zero-percent level. aud only one parameter with an error higher than 5 X level (ore precisely. the 6.8% level for the parameter 0 of the diuunest source).," In terms of relative errors, our CE algorithm was able to recover 7 out of 24 parameters within a zero-percent level, and only one parameter with an error higher than 5 $\%$ level (more precisely, the $\%$ level for the parameter $\theta$ of the dimmest source)." + Ou the other hand. the relative errors obtained from IMEIT are systematically lieher in 19 out of 21 parameters.," On the other hand, the relative errors obtained from IMFIT are systematically higher in 19 out of 24 parameters." + In the case of the dinuauest source. the relative errors ranged from 16% to 1004. indicating that the IMEIT did not converge for this coniponent.," In the case of the dimmest source, the relative errors ranged from $\%$ to $\%$, indicating that the IMFIT did not converge for this component." + Iu summary. comparison between the CE optimization algovitlin and IMEIT suegeests that both tools lave simular performance in dealing with nuages that are uot too complex (few aud relatively well-separated sources).," In summary, comparison between the CE optimization algorithm and IMFIT suggests that both tools have similar performance in dealing with images that are not too complex (few and relatively well-separated sources)." + However. our techuique has a better performance when the interferometric 1iap is 110re couples. as in the case of test J3.," However, our technique has a better performance when the interferometric map is more complex, as in the case of test J3." + Note also that our method does not have a limit for the πο of componcuts to be fitted simmltancously in the nage. as in the case of INMETT.," Note also that our method does not have a limit for the number of components to be fitted simultaneously in the image, as in the case of IMFIT." + We have preseuted in previous sections some validation tests necessary to demonstrate the capability of our modelfitting technique of dealing with interferometric images., We have presented in previous sections some validation tests necessary to demonstrate the capability of our model-fitting technique of dealing with interferometric images. + The objective of this section is to check the behavior of our algorithia when applied to real interferometric inaages., The objective of this section is to check the behavior of our algorithm when applied to real interferometric images. + To do this. we selected a naturally weighted J nuage taken from the ALOJAVE/2cm Survey Data Archive (Listerctal.20092) that corresponds to the 15 GITz radio map of the BL Lac 2287 obtained in 1996 Mav 27.," To do this, we selected a naturally weighted $I-$ image taken from the MOJAVE/2cm Survey Data Archive \citep{lis09a} that corresponds to the 15 GHz radio map of the BL Lac 287 obtained in 1996 May 27." + The original fits image of the 2287 is formed by an array of 512 « 512 pixels but only a relatively siuall fraction has a jet signal sigui&cantlv higher than the noise., The original fits image of the 287 is formed by an array of 512 $\times$ 512 pixels but only a relatively small fraction has a jet signal significantly higher than the noise. + Because of this. we decided to crop the original fits inage to maintain ouly the fraction with a useful signal. which meant a 66 < 51 pixel nuage.," Because of this, we decided to crop the original fits image to maintain only the fraction with a useful signal, which meant a 66 $\times$ 51 pixel image." + It is important to cluphasize that this reduction helps the aleorithin to fiud the optimal solutions more rapidly since the parameter space is substantially narrowed in this case., It is important to emphasize that this reduction helps the algorithm to find the optimal solutions more rapidly since the parameter space is substantially narrowed in this case. + Several works iu the literature have asstmed a circular Gaussian shape for jet features (e.g. Lobanovetal.2001:Jorstadctal.2005:Aeudoet2007)).," Several works in the literature have assumed a circular Gaussian shape for jet features (e.g., \citealt{lob01,jor05,agu07}) )." + In this work. we have assumed a two-dimensional elliptical Cassiani fictionas being represeutative of the brightucss distribution of the jet knots. which will be kept for the radio map of the BL Lac 2287.," In this work, we have assumed a two-dimensional elliptical Gaussian function as being representative of the brightness distribution of the jet knots, which will be kept for the radio map of the BL Lac 287." + The justification for this is that our CE model fitting will be executed in the image plane. in which the jet compoucuts are convolved with the elliptical svuthesized CLEAN beam of the interferometric experiment.," The justification for this is that our CE model fitting will be executed in the image plane, in which the jet components are convolved with the elliptical synthesized CLEAN beam of the interferometric experiment." + We applied. our CE algorithm to the cropped image. varvius the number of elliptical. Gaussian sources frou. two to seven.," We applied our CE algorithm to the cropped image, varying the number of elliptical Gaussian sources from two to seven." + For each adopted nuuuber of sources we run the algorithi three times., For each adopted number of sources we run the algorithm three times. +" The model fitting processes exanuned the whole image iu the. aud g/— coordinates. searching for Gaussian sources with structural paraineters in the following ranges: LO€a(pixel)<30. 0xe0.9. 908<090"" (positive values for north to cast direction). and 9.51&10.! 14.0 ). +(5)AII magnitudes in the above equations are in the intrinsic. dereddened 2MASS system (labeled with subscript 0 hereafter). with dereddening applied using the ?. extinction maps.," All magnitudes in the above equations are in the intrinsic, dereddened 2MASS system (labeled with subscript 0 hereafter), with dereddening applied using the \cite{1998ApJ...500..525S} extinction maps." + These selection criteria and the dereddening method are similar to those used by ? to identify the tidal tails of Sagittarius dwarf galaxy., These selection criteria and the dereddening method are similar to those used by \cite{2003ApJ...599.1082M} to identify the tidal tails of Sagittarius dwarf galaxy. + Distance estimates for these stars were made by assuming a uniform metallicity of [Fe/T2.—1.0 and an age of 13.1Gyr and calculating a linear fit to the color magnitude relation of the giant stars using a theoretical isochrone from the Padova database (???).. ," Distance estimates for these stars were made by assuming a uniform metallicity of $[{\rm Fe/H}]=-1.0$ and an age of $13.1 \Gyr$ and calculating a linear fit to the color magnitude relation of the giant stars using a theoretical isochrone from the Padova database \citep{1994AAS..106..275B, 2008AA...482..883M, + 2004AA...415..571B}." +"The best fit relationship is Aj.=3.269.1207N.)y where My is the absolute magnitude of the star and (./.—A, its color.", The best fit relationship is $M_K=3.26-9.42(J-K_s)_0$ where $M_K$ is the absolute magnitude of the star and $(J-K_s)_0$ its color. + Using this relation the distance modulus is then given by (CAI)3.26|9.12(7Tay., Using this relation the distance modulus is then given by (K_s)_0-3.26+9.42(J-K_s)_0. + The specific values of age and metallicity were adopted because a) they roughly correspond to the expected values for the stellar halo and b) they lead to the identification of the largest known stellar halo structure in the data. the tails of the Sagittarius dwarf galaxy. with maximum clarity.," The specific values of age and metallicity were adopted because a) they roughly correspond to the expected values for the stellar halo and b) they lead to the identification of the largest known stellar halo structure in the data, the tails of the Sagittarius dwarf galaxy, with maximum clarity." + To make theoretical predictions of structures in. the stellar halo. we use the eleven stellar halo models of ?.. which were simulated within. the context. of the ACDM cosmological paradigm.," To make theoretical predictions of structures in the stellar halo, we use the eleven stellar halo models of \cite{2005ApJ...635..931B}, which were simulated within the context of the $\Lambda$ CDM cosmological paradigm." + These simulations follow the aceretion of individual satellites modeled as N-body particle systems onto a galaxy whose disk. bulge. and halo potential is represented by time dependent analytical functions.," These simulations follow the accretion of individual satellites modeled as $N$ -body particle systems onto a galaxy whose disk, bulge, and halo potential is represented by time dependent analytical functions." + Semi-analytical prescriptions are used to assign a star formation history to each satellite and a leaky accreting box chemical enrichment model is used to calculate the metallicity as a function of age for the stellar populations (??).. ," Semi-analytical prescriptions are used to assign a star formation history to each satellite and a leaky accreting box chemical enrichment model is used to calculate the metallicity as a function of age for the stellar populations \citep{2005ApJ...632..872R,2006ApJ...638..585F}. ." +The three main model parameters of an accreting satellite are the time since accretion. £44. its luminosity. μι and the circularity of its orbit. defined as e=ων CF being the angular momentum of the orbit and Ίος the angular momentum of a circular orbit having same energy).," The three main model parameters of an accreting satellite are the time since accretion, $t_{\rm + acc}$, its luminosity, $L_{\rm sat}$ , and the circularity of its orbit, defined as $\epsilon=J/J_{\rm circ}$ $J$ being the angular momentum of the orbit and $J_{\rm circ}$ the angular momentum of a circular orbit having same energy)." + The distribution of these three parameters describes the accretion history of a halo., The distribution of these three parameters describes the accretion history of a halo. + To study the sensitivity of the properties of structures in the stellar halo to accretion history. we additionally use a set of six artificial stellar halo models (referred to as ACDM halos) from ?— that have aecretion events that are predominantly () (e.< 0.2). Q1)circular (e> 0.1). Qi)old (face>LL Gat). Qv) (face<8 Cr). (OU) (Lo10* L.). and (vi) Επ.," To study the sensitivity of the properties of structures in the stellar halo to accretion history, we additionally use a set of six artificial stellar halo models (referred to as $\Lambda$ CDM halos) from \cite{2008ApJ...689..936J} that have accretion events that are predominantly (i) $\epsilon<0.2$ ), (ii) $\epsilon>0.7$ ), (iii) $t_{\rm acc}>11 \Gyr$ ), (iv) $t_{\rm acc}<8 \Gyr$ ), (v) $L_{\rm sat}>10^7 \Lsun$ ), and (vi) $L_{\rm sat}<10^7 \Lsun$ )." + Each N-body particle in. the simulations represents a population of stars having a certain stellar mass. a distribution of ages and a monotonic age-metallicity relation.," Each $N$ -body particle in the simulations represents a population of stars having a certain stellar mass, a distribution of ages and a monotonic age-metallicity relation." + The real data from surveys on the other hand are in the form of color-magnitude combinations of individual stars. shaped by observational or other selection criteria.," The real data from surveys on the other hand are in the form of color-magnitude combinations of individual stars, shaped by observational or other selection criteria." + The procedure to convert a simulated stellar halo model to a synthetic survey consists of four steps!:: We use the simulations and the procedure described above to generate five different types of synthetic surveys. namely S1. S2. $3. S4 and S5 (summarized in 1)).," The procedure to convert a simulated stellar halo model to a synthetic survey consists of four steps: We use the simulations and the procedure described above to generate five different types of synthetic surveys, namely S1, S2, S3, S4 and S5 (summarized in )." + Each data set consists of surveys of seventeen stellar halos. eleven of which correspond to halos having ACDM accretion history (ACDM halos).," Each data set consists of surveys of seventeen stellar halos, eleven of which correspond to halos having $\Lambda$ CDM accretion history $\Lambda$ CDM halos)." + The remaining six correspond to artificial accretion histories (non-ACDM halos see 2.2)) and are named as radial. circular. old. young. high luminosity andlow luminosity halos toreflect the properties of the dominant accretion events in them.," The remaining six correspond to artificial accretion histories $\Lambda$ CDM halos see ) and are named as radial, circular, old, young, high luminosity andlow luminosity halos toreflect the properties of the dominant accretion events in them." + Below we briefly describe these data sets and discuss their properties., Below we briefly describe these data sets and discuss their properties. +hat the surface gravities of the WB stars in M79 were uuch lower than predicted by canonical TB evolutionary heory.,that the surface gravities of the HB stars in M79 were much lower than predicted by canonical HB evolutionary theory. + They also referred to the work of Moochler et al. (, They also referred to the work of Moehler et al. ( +1995) who found that individual UB stars in MID with values of lower than 20.000 I& have values of logyg slightly lower (0.2 0.E dex) than predicted by canonical IB evolutionary heorv.,"1995) who found that individual HB stars in M15 with values of lower than 20,000 K have values of $\log g$ slightly lower (0.2 – 0.4 dex) than predicted by canonical HB evolutionary theory." + We point out that the resolution of our svuthetic spectra im Alogg is 0.5., We point out that the resolution of our synthetic spectra in $\Delta \log g$ is 0.5. + Consequently. our svuthetic spectra are not sensitive to the shift towards lower eravities observed amione the BIB stars in a απο of elobular clusters ai therefore do not conflict with these observations.," Consequently, our synthetic spectra are not sensitive to the shift towards lower gravities observed among the BHB stars in a number of globular clusters and therefore do not conflict with these observations." + What is then the reason DDDF predict a Ly a profile significantly broader than observed by WUT?, What is then the reason DDDF predict a Ly $\alpha $ profile significantly broader than observed by HUT? + We sugecst that the reason for this mismatch lies in their svuthesis method rather than in the TB evolutionary theory., We suggest that the reason for this mismatch lies in their synthesis method rather than in the HB evolutionary theory. + Let us consider their Fig., Let us consider their Fig. + 7. where open circles are stars from the Gaussian model that best reproduce the TUT spectrum. albeit a too broad Ly à profile.," 7, where open circles are stars from the Gaussian model that best reproduce the HUT spectrum, albeit a too broad Ly $\alpha$ profile." + We notice that there are no models present in the ranec between 16.000 and 28.000 I in this figure.," We notice that there are no models present in the range between 16,000 and 28,000 K in this figure." + However. the Gaussian mass distribution that reproduces the observed optical CMD docs show masses distributed over the range corresponding to stars with ZAIID between 16.000 aud 28.000 I!," However, the Gaussian mass distribution that reproduces the observed optical CMD does show masses distributed over the range corresponding to stars with ZAHB between 16,000 and 28,000 K!" + This means that there is au Iucousistency between the Caussian distributio- that reproduces the CMD and the distribution in ZAIID that is actually used in calculating the best-fitting Gaussian Bu-UV svuthetic spectrum., This means that there is an inconsistency between the Gaussian distribution that reproduces the CMD and the distribution in ZAHB that is actually used in calculating the best-fitting Gaussian far-UV synthetic spectrum. + As mentioned iu Sect., As mentioned in Sect. + 3.2. about of the cyutribution to the total oeiteerated fiux in our calculations is enütted by models vetween about 16.000 amd abou 25.000 Is. À svuthesis oewhich mocels from this esseutial ranee are not included will provide a broader Ly à profile w overestimatiue the muuber of required cooler IB stars.," 3.2, about of the contribution to the total integrated flux in our calculations is emitted by models between about 16,000 and about 25,000 K. A synthesis in which models from this essential range are not included will provide a broader Ly $\alpha$ profile by overestimating the number of required cooler HB stars." + We conclude tha the Gaussian model that reproduces 16 optica CAID is consistent with the far-UV spectrin. if there isa UV bright star or extra ‘cool’ IIB stars in the central region of the cluster.," We conclude that the Gaussian model that reproduces the optical CMD is consistent with the far-UV spectrum, if there is a UV bright star or extra `cool' HB stars in the central region of the cluster." +" Extremely low eravitics or ""reasonable metallicities are not required to reproduce the £u-UV spectrum. but a smaller amount of o-clemeut chhaucement thaw is usually assuiuied seeuis necessary to reproduce the observed far-UV Si lines."," Extremely low gravities or unreasonable metallicities are not required to reproduce the far-UV spectrum, but a smaller amount of $\alpha $ -element enhancement than is usually assumed seems necessary to reproduce the observed far-UV Si lines." +" There is also an indication for the presence of extreme BIB stars in the center of ΑΙΤΙΟ, which agrees with the presence of some extreme BIB stars that DDDE required to reproduce the wavelength region shortward of Ly 5."," There is also an indication for the presence of extreme BHB stars in the center of M79, which agrees with the presence of some extreme BHB stars that DDDF required to reproduce the wavelength region shortward of Ly $% +\gamma." + Matching the £u-UV spectrum of the elobular cluster AIT9 with a model that is cousisteut with the observed optical CAID Increases our confidence iu or curreut nuderstanding of the late stages of low-nuass star evolution. as well as in our future ability to unuderstaud he integratedC» spectra of distant stellar svsteumis.," Matching the far-UV spectrum of the globular cluster M79 with a model that is consistent with the observed optical CMD increases our confidence in our current understanding of the late stages of low-mass star evolution, as well as in our future ability to understand the integrated spectra of distant stellar systems." +"spectral response theoretically, the range of FWHM varies by less than5%,, for slopes from —2 to +1 in AFy.","spectral response theoretically, the range of FWHM varies by less than, for slopes from $-2$ to $+1$ in $\lambda \ F_{\lambda}$." + Larger PSFs have been measured yielding maxiumum dimensions as high as 7733., Larger PSFs have been measured yielding maxiumum dimensions as high as 3. +" Since only the long axis of the 8 UMa disc exceeds this size, we claim this disc is marginally resolved."," Since only the long axis of the $\beta$ UMa disc exceeds this size, we claim this disc is marginally resolved." + The 6 Leo and 7 Corvi discs are well resolved at 100µπι., The $\beta$ Leo and $\eta$ Corvi discs are well resolved at 100. +. Estimates of deconvolved disc radius have been made from the FWHM., Estimates of deconvolved disc radius have been made from the FWHM. + We call this radius estimate Rj»; (Table 1))., We call this radius estimate $R_{obs}$ (Table \ref{table}) ). + Figure | shows the first resolved images of the disc around 8 Leo., Figure \ref{images} shows the first resolved images of the disc around $\beta$ Leo. + The blackbody temperature and dust luminosity results given in Table 1 are consistent with the values found in previous works (Suetal.2006;Holmes 2003)..," The blackbody temperature and dust luminosity results given in Table \ref{table} are consistent with the values found in previous works \citep{su06,holmes03}. ." + The fractional dust luminosity of 2.3x107? is higher than the estimate from Suetal.(2006)., The fractional dust luminosity of $2.3 \times 10^{-5}$ is higher than the estimate from \cite{su06}. +. The increase is due to a slight increase in dust to match the PACS flux densities., The increase is due to a slight increase in dust to match the PACS flux densities. + The radius estimates found for β Leo are comparable to that of the Kuiper Belt (50 AU)., The radius estimates found for $\beta$ Leo are comparable to that of the Kuiper Belt $\sim 50$ AU). +" This makes the 8 Leo disc one of the smallest disc radii yet resolved at any wavelength (see, for instance, the ’Circumstellar Disks Database’*)) although smaller characteristic orbital radii have been derived based on single temperature blackbody fits to the dust components (e.g.,Rheeetal. 2007).."," This makes the $\beta$ Leo disc one of the smallest disc radii yet resolved at any wavelength (see, for instance, the 'Circumstellar Disks ) although smaller characteristic orbital radii have been derived based on single temperature blackbody fits to the dust components \citep[e.g.,][]{rhee07}." +" The difference between Ro», and Rays; provides an opportunity to learn about the grains within this disc.", The difference between $R_{obs}$ and $R_{dust}$ provides an opportunity to learn about the grains within this disc. +" Because differently sized grains can have the same temperature at different distances from a star, the SED models in refSEDs are degenerate."," Because differently sized grains can have the same temperature at different distances from a star, the SED models in \\ref{SEDs} are degenerate." + This degeneracy is broken by the resolved imaging., This degeneracy is broken by the resolved imaging. +" For example, the ~40 AU radius for the 8 Leo disc is larger than the 23 AU suggested by the blackbody fit."," For example, the $\sim$ 40 AU radius for the $\beta$ Leo disc is larger than the 23 AU suggested by the blackbody fit." +" Therefore, the grains do not emit as blackbodies, but maintain a ~112 K temperature at a greater distance from the star as expected for small grains that emit inefficiently at far-IR wavelengths."," Therefore, the grains do not emit as blackbodies, but maintain a $\sim$ 112 K temperature at a greater distance from the star as expected for small grains that emit inefficiently at far-IR wavelengths." + The inferred characteristic particle radius a is «A/2z=16um.," The inferred characteristic particle radius $a$ is $ < \lambda/2 \pi = +16$." +. Future modeling work that combinesSpitzer IRS spectra and submillimetre images with the data will constrain these grain properties and the spatial dust distribution (L. Churcher et al., Future modeling work that combines IRS spectra and submillimetre images with the data will constrain these grain properties and the spatial dust distribution (L. Churcher et al. +" 2010, in preparation)."," 2010, in preparation)." + Figure | shows that the disc emission around 8 UMa is very compact at 100 and 160µπι., Figure \ref{images} shows that the disc emission around $\beta$ UMa is very compact at 100 and 160. +. The disc is marginally resolved at 100 aand not resolved at 160 um., The disc is marginally resolved at 100 and not resolved at 160 . +. The apparent asymmetry in the 160 ddisc image is likely artificial; it is an effect of interpolation applied to the image at native (Nyquist sampled) resolution., The apparent asymmetry in the 160 disc image is likely artificial; it is an effect of interpolation applied to the image at native (Nyquist sampled) resolution. + The fluxdensities measured for 8 UMa confirmthe earlier 100 and 160 ddetections., The fluxdensities measured for $\beta$ UMa confirmthe earlier 100 and 160 detections. +to oue between the donor aud the black hole.,to one between the donor and the black hole. + From the latter. Leeetal.(2002) predicted the I&err parameter of the black hole.," From the latter, \citet{Lee02} predicted the Kerr parameter of the black hole." + The main poiut developed bv Brown.etal.(2007) was that the rotational cucreyof the binary is roughly inversely proportional to the mass of the donor., The main point developed by \citet{BLMM07} was that the rotational energy of the binary is roughly inversely proportional to the mass of the donor. + This ollows from Ixepler law aud from the fact that in Case C mass transfer (followings the We burning). the initial aj (distance between the eiat and the companion) of 1e binaries are roughly equal," This follows from Kepler's law and from the fact that in Case C mass transfer (following the He burning), the initial $a_i$ s (distance between the giant and the companion) of the binaries are roughly equal." + The fact that. according o Fruchteretal(2006).. the long οταν bursts are in ow-lnctallicity galaxies. does not elucidate the αναος which produce the long bursts.," The fact that, according to \citet{Fruchter06}, the long $\gamma$ -ray bursts are in low-metallicity galaxies, does not elucidate the dynamics which produce the long bursts." + The dynamics result frou he fact that low-nctallicity galaxies tend to have stars of jeher mass than Galactic., The dynamics result from the fact that low-metallicity galaxies tend to have stars of higher mass than Galactic. + The higher mass of the donors slows the binary down sufficicutly that the rotational energv cau be accepted by the ceutral engine., The higher mass of the donors slows the binary down sufficiently that the rotational energy can be accepted by the central engine. + Tn other words. the question of energy is a “Coldilocks” one.," In other words, the question of energy is a “Goldilocks"" one." + It must be not too munich. because in that case the central engine will be dismantled. and not too little. because that would only be sufficient for à subluniuous burst. but for a long high huninosityv οταν burst it must be just right.," It must be not too much, because in that case the central engine will be dismantled, and not too little, because that would only be sufficient for a subluminous burst, but for a long high luminosity $\gamma$ -ray burst it must be just right." + We lave learned enough about herr parameters from our calculations and from the Siiithsonian-Tarvard lcasurements to construct a “eucsstimate”," We have learned enough about Kerr parameters from our calculations and from the Smithsonian-Harvard measurements to construct a “guesstimate""." + Namely. we believe that LMC 3 underwent the closest. (in enerev) explosion in our Galaxy. to a cosmological. GRB. (," Namely, we believe that LMC $-$ 3 underwent the closest (in energy) explosion in our Galaxy, to a cosmological GRB. (" +Of course. one can sav that LAIC N38 is not in our Galaxy. but in the LMC.),"Of course, one can say that LMC $-$ 3 is not in our Galaxy, but in the LMC.)" + We believe that iu its ~1/3 solu metallicity (RussellDopita 1990).. it tends towards the low-inetallicity stars considered by Fruchterοetal.(2006).. that at the least it has somewhere Galactic and the low metallicity favored there.," We believe that in its $\sim1/3$ solar metallicity \citep{Russ90}, it tends towards the low-metallicity stars considered by \citet{Fruchter06}, so that at the least it has somewhere between Galactic and the low metallicity favored there." +" There is uucertaimty in the masses. but Davisetal.(2006) lave a value of a,&0.26 for the present I&err parameter."," There is uncertainty in the masses, but \citet{Davis06} have a value of $a_\star\simeq0.26$ for the present Kerr parameter." + They took 7AL.. as the mass of the black hole. which would Πρίν a donor of from the lower end of the measurements of Cowley (1983).," They took $7\msun$ as the mass of the black hole, which would imply a donor of $\sim4\msun$ from the lower end of the measurements of \citet{Cow83}." +. We take these to be represeutative: other investigators have found other masses. so we sugeest our evolution as only a possible onc.," We take these to be representative; other investigators have found other masses, so we suggest our evolution as only a possible one." + Allofthe binaries in Brown.ctal.(2007) ancl MorenoMeéudezetal.(2007) which had so much energy that they dismantled the black hole accretion disk had douor masses of (lL2)M.. so the donor in LMC N 3 is at least double those masses.," All of the binaries in \citet{BLMM07} and \citet{Mor07} which had so much energy that they dismantled the black hole accretion disk had donor masses of $(1-2)\msun$, so the donor in LMC $-$ 3 is at least double those masses." +" The donor mass is close to the ΟΛΗ, that MorenoMéudoezetal.(2007). estimated would eive the eunergv of a cosmolosical CRD.", The donor mass is close to the $\sim5\msun$ that \citet{Mor07} estimated would give the energy of a cosmological GRB. +" Iu any case, LMC 3 is the closest ""nearby relic of binaries simular to the progenitors of cosmological GRDs."," In any case, LMC $-$ 3 is the closest “nearby"" relic of binaries similar to the progenitors of cosmological GRBs." + We can. therefore. use it as an example to try to reconstruct the explosion and model the enerey of the explosion.," We can, therefore, use it as an example to try to reconstruct the explosion and model the energy of the explosion." + We estimate the mass loss in the explosion. fiudiug it to be substantial.," We estimate the mass loss in the explosion, finding it to be substantial." + It is Likely that the estimated svsteimi velocity can be measured. at least the radial component of it. which should test our prediction.," It is likely that the estimated system velocity can be measured, at least the radial component of it, which should test our prediction." + Iu this paper we wish to also stuumarize results of earlier calculations which have a direct bearing on the papers iu the 31 Angnst 2006 Nature (Young2006:al.2006:evolutionsMazzaliet 2006).. in order to show that useful of black holes have been carried out iu the past. of which the119 astronomers who signed these articles were unaware.," In this paper we wish to also summarize results of earlier calculations which have a direct bearing on the 5 papers in the 31 August 2006 Nature \citep{N0,N1,N2,N3,N4}, in order to show that useful evolutions of black holes have been carried out in the past, of which the 119 astronomers who signed these articles were unaware." +" We show that these previous calculations have a direct bearing ou the 1ieasureimenuts of GRB 060218/8SN 2006aj: namely that the ceutral eugine was a black hole. not the magnetar conjectured by iiost of the authors. aud that the black hole was one of mini black hole mass with au —(18.20)M., ZAMS (Zero Age Main Sequence) progenitor."," We show that these previous calculations have a direct bearing on the measurements of GRB 060218/SN 2006aj; namely that the central engine was a black hole, not the magnetar conjectured by most of the authors, and that the black hole was one of minimum black hole mass with an $\sim(18-20)\msun$ ZAMS (Zero Age Main Sequence) progenitor." + We also correct a uunber of errors in Galactic black hole evolution im the Fruchteretal.(2006) article., We also correct a number of errors in Galactic black hole evolution in the \citet{Fruchter06} article. + WeIo beeinby expanding ou the evolutionary discussions in Brownetal.(2001)., We begin by expanding on the evolutionary discussions in \citet{Bro01}. + The history of black hole evolution in binaries (which is the ouly place where black holes could be studied in detail) was that whatever mass. witlin reasonable limits. oue proposed. the binary would turu out to have had a neutrou star rather than black hole as compact object.," The history of black hole evolution in binaries (which is the only place where black holes could be studied in detail) was that whatever mass, within reasonable limits, one proposed, the binary would turn out to have had a neutron star rather than black hole as compact object." + The first clear explanation of this was eiven by Brownetal.(2001): namely. the evolution of black holes in our Calaxy depeuds upon binarity.," The first clear explanation of this was given by \citet{Bro01}; namely, the evolution of black holes in our Galaxy depends upon binarity." + Namely. in Case A or D mass transfer (nass transfer while the eiaut star is du main sequence or red elaut stage) the stroug winds in our Galaxy blow off sufficicut of the “naked” Πο cuvelope so that the remaining core of nietals was too light to evolve iuto a black hole: rather. it would end up as a neutron star.," Namely, in Case A or B mass transfer (mass transfer while the giant star is in main sequence or red giant stage) the strong winds in our Galaxy blow off sufficient of the “naked"" He envelope so that the remaining core of metals was too light to evolve into a black hole; rather, it would end up as a neutron star." + Ouly in Case C mass transter. i£ mass transfer following Ue burning were carried out. would the remaining core have the possibility of evolving iuto a black hole.," Only in Case C mass transfer, if mass transfer following He burning were carried out, would the remaining core have the possibility of evolving into a black hole." + Now. just what the limit is for the lowest ZAMS mass star that will evolve iuto a black hole is determined by what we call the Woosley Ansatz.," Now, just what the limit is for the lowest ZAMS mass star that will evolve into a black hole is determined by what we call the Woosley Ansatz." + hi our opinion this is one of the most powerful developments in stellar evolution., In our opinion this is one of the most powerful developments in stellar evolution. +" We will combine this ""Ausatz"" with the Betheetal.(1979) considerations of entropy in the Fe core."," We will combine this “Ansatz"" with the \citet{BBAL} considerations of entropy in the Fe core." + The Woosley Ausatz basically divides the υπιο of IC iuto low eucrgv. T— 20keV burning through the Cla 90 process aud the To— s0keV¥ 120 |120 52! NDe ete;," The Woosley Ansatz basically divides the burning of $^{12}$ C into low energy, $T\sim20$ keV burning through the $^{12}$ $+\alpha\rightarrow^{16}$ O process and the $T\sim80$ keV $^{12}$ $+^{12}$ $\rightarrow^{24}$ Mg etc." + process., process. + The ο is produced by a1 ου. »1C: ie. essentially through àατα PC. This is a three body process. going as the square of the density. p?.," The $^{12}$ C is produced by $\alpha+^8$ $^\star\rightarrow^{12}$ C; i.e., essentially through $\alpha+\alpha+\alpha\rightarrow^{12}$ C. This is a three body process, going as the square of the density, $\rho^2$." +" The ο is burned iuto 2Ο by the two body process ο]HO | 5, which goes as p."," The $^{12}$ C is burned into $^{16}$ O by the two body process $^{12}$ $+\alpha\rightarrow^{16}$ $+\gamma$ , which goes as $\rho$." + As loug as PC d8 present. the latter reaction will take place.," As long as $^{12}$ C is present, the latter reaction will take place." + However. withincreasing Mz. the density decreases.," However, with increasing $M_{\rm ZAMS}$ the density decreases." + The eutropy. which goes inversely with the density. is known to increase with Az.," The entropy, which goes inversely with the density, is known to increase with $M_{\rm ZAMS}$." + Therefore. there will be a value of Mzaxj; where the LC is removed by the 5 : ∟≼⊲↖∩≻⊔⇂∪⋜↧↴∖↴↥⋅⋜⋯↕≼∐⋅↖⇁⋜↧↴∖↴↕↑↕↴∖↴↕∪↥⋅⋯↸∖≺∏⋝∙↖↽↑∐↸∖∩↖∩↖∩; ⋅⋅⋟," Therefore, there will be a value of $M_{\rm ZAMS}$ where the $^{12}$ C is removed by the $^{12}$ $+\alpha\rightarrow^{16}$ O as rapidly as it is formed by the $\alpha+\alpha+\alpha$ process." +" At this value⋅ of MagE the ο ο2 97!2 Meprocess, ete.", At this value of $M_{\rm ZAMS}$ the $^{12}$ $+^{12}$ $\rightarrow^{24}$ Mg etc. + shuts off. because there is no 12€: actually. it shuts ice the central carbon abundance is less than ~A because there is not enough: carbon for convective (steady) burniug.," shuts off, because there is no $^{12}$ C; actually, it shuts off once the central carbon abundance is less than $\sim15\%$ because there is not enough carbon for convective (steady) burning." + At this point the burning processes are all of low temperature. T~ 20keV. At this point the uetallicitv is close to zero. independent of the average netallicity of the star.," At this point the burning processes are all of low temperature, $T\sim20$ keV. At this point the metallicity is close to zero, independent of the average metallicity of the star." + Now. this temperature is too low for neutrmno- to carry off appreciable energvaud eutropy (the relativistic p.P pam cross section goes as Tt! power). whereas copious amounts of entropy were carried off bv 2C |PO S?! Me ete;," Now, this temperature is too low for neutrino-pairs to carry off appreciable energyand entropy (the relativistic $\nu$ ,$\bar{\nu}$ pair cross section goes as $T^{11}$ power), whereas copious amounts of entropy were carried off by $^{12}$ $+^{12}$ $\rightarrow^{24}$ Mg etc." + What happens to the entropy which lucreascs withincreasing Qe Mam?, What happens to the entropy which increases with increasing $M_{\rm ZAMS}$ ? +We have shown how the problem of computing the effective area of a Wolter-I mirror with f>>L can be reduced to the computation of an integral (Eq. (25)).,"We have shown how the problem of computing the effective area of a Wolter-I mirror with $f\ \gg L$ can be reduced to the computation of an integral (Eq. \ref{eq:Aeff_fin_offaxis}) )," + or Eq. (26)), or Eq. \ref{eq:Aeff_fin_offaxis0}) ) + as a particular case). on the only conditior that we are able to compute ία). the mirror reflectivity as a function. of the photor wavelength and the meidence angle.," as a particular case), on the only condition that we are able to compute $r_{\lambda}(\alpha)$, the mirror reflectivity as a function of the photon wavelength and the incidence angle." + This can easily be achieved numerically for a source at infinity. as 1n astronomical cases. or for a source at finite distance. as usually done for on- calibrations.," This can easily be achieved numerically for a source at infinity, as in astronomical cases, or for a source at finite distance, as usually done for on-ground calibrations." + For the ideal case of a constant reflectivity r=|. we could solve the integral and obtain of the mirror.," For the ideal case of a constant reflectivity $r =1$, we could solve the integral and obtain of the mirror." + Finally. we presented some examples of the application of the formalism. and checked that its predictions agree with those of a detailed ray-tracing routine.," Finally, we presented some examples of the application of the formalism, and checked that its predictions agree with those of a detailed ray-tracing routine." + The analytical approach undoubtedly has several advantages., The analytical approach undoubtedly has several advantages. + In general. the multilayer reflectivity computation is the Achilles? heel of a ray-tracing program that is aimed at determining the off-axis effective area of a mirror: although conceptually simple. the reflectivity computation consists of summing up the contribution of several layers to the reflectivity. so 1t requires a significant amount of computation time.," In general, the multilayer reflectivity computation is the Achilles' heel of a ray-tracing program that is aimed at determining the off-axis effective area of a mirror: although conceptually simple, the reflectivity computation consists of summing up the contribution of several layers to the reflectivity, so it requires a significant amount of computation time." + A ray-tracing routine often requires 107+10° photons to return sufficient statistics for each photon energy. and the reflectivity routine has to be called for each of them.," A ray-tracing routine often requires $10^4 \div 10^5$ photons to return sufficient statistics for each photon energy, and the reflectivity routine has to be called for each of them." + Hence. the total computation time can reach several hours.," Hence, the total computation time can reach several hours." + If the optic is still to be designed. the entire simulation needs to be run several times. adjusting the parameter values every time. until the optimal solution is reached: the optimization process can thereby take several days.," If the optic is still to be designed, the entire simulation needs to be run several times, adjusting the parameter values every time, until the optimal solution is reached: the optimization process can thereby take several days." + In contrast. the analytical approach presented in this work is completely unaffected by statistical errors.," In contrast, the analytical approach presented in this work is completely unaffected by statistical errors." + Its accuracy is limited only by the applicability of the double cone approximation (discussed in Sect. 2)), Its accuracy is limited only by the applicability of the double cone approximation (discussed in Sect. \ref{DC_WI}) ) + and by the accuracy of the computation of the integral in Eq. (25))., and by the accuracy of the computation of the integral in Eq. \ref{eq:Aeff_fin_offaxis}) ). + In practice. the reflectivity can be computed with. say. a 5 arcsec step of the incidence angle. without noticeably affecting the reflectivity of the multilayer.," In practice, the reflectivity can be computed with, say, a 5 arcsec step of the incidence angle, without noticeably affecting the reflectivity of the multilayer." + This means that. even for a very large off-axis angle. e.g.. 10 aremin. we need to compute the multilayer reflectivity only ~500 times.mosr. instead of more than 107 times as required by à ray-tracing.," This means that, even for a very large off-axis angle, e.g., 10 arcmin, we need to compute the multilayer reflectivity only $\sim 500$ times, instead of more than $10^4$ times as required by a ray-tracing." + For these reasons. the approach presented in this work might be extensively used to compute the effective area of grazing-incidence Wolter-I astronomical mirrors. on- and off-axis. whenever applicable.," For these reasons, the approach presented in this work might be extensively used to compute the effective area of grazing-incidence Wolter-I astronomical mirrors, on- and off-axis, whenever applicable." + On the other hand. às already stated in Sect. ]..," On the other hand, as already stated in Sect. \ref{Intro}," + it wouldvot be applicable to very short focal lengths. or to systems of densely nested mirror shells. obstructing each other in the field of view: in this case a ray- is. as of today. the only viable computational technique.," it would be applicable to very short focal lengths, or to systems of densely nested mirror shells, obstructing each other in the field of view: in this case a ray-tracing is, as of today, the only viable computational technique." + Clearly. a ray-tracing is always necessary to investigate the angular resolution. especially whenever mirror deformations are present.," Clearly, a ray-tracing is always necessary to investigate the angular resolution, especially whenever mirror deformations are present." + We note that. if analytical expressions for Κα) were available. it would be possible to solve explicitly the integral in Eq. (25))," We note that, if analytical expressions for $r_{\lambda}(\alpha)$ were available, it would be possible to solve explicitly the integral in Eq. \ref{eq:Aeff_fin_offaxis}) )" + in the most general case. and obtain area of à Wolter-I mirror.," in the most general case, and obtain area of a Wolter-I mirror." + In this respect. an analytical approach for obtaining μα) of a multilayer was developed by Kozhevnikov et al. (2001)).," In this respect, an analytical approach for obtaining $r_{\lambda}(\alpha)$ of a multilayer was developed by Kozhevnikov et al. \cite{Kozhevnikov}) )," + but a concise expression for the reflectivity appears still to be unavailable., but a concise expression for the reflectivity appears still to be unavailable. + However. if this is achievable. the computation of the effective area. and consequently the optical design and optimization. for astronomical X-ray mirrors of sufficiently large ££ might be simply reduced to the application of a handful of algebraic equations.," However, if this is achievable, the computation of the effective area, and consequently the optical design and optimization, for astronomical X-ray mirrors of sufficiently large $f\#$ might be simply reduced to the application of a handful of algebraic equations." + We derive Eq. (9)).," We derive Eq. \ref{eq:vign}) )," + which returns the geometrical vignetting of a double-reflection mirror. caused by the finite distance of the source.," which returns the geometrical vignetting of a double-reflection mirror, caused by the finite distance of the source." + We consider a radial section of a Wolter-I mirror (Fig. 1).," We consider a radial section of a Wolter-I mirror (Fig. \ref{fig:mirror_section}) )," + in the sz plane. with the primary and secondary segment surfaces intersecting at a 2a angle.," in the $xz$ plane, with the primary and secondary segment surfaces intersecting at a $2\alpha_0$ angle." + We suppose that. as far as the effective area is concerned. the mirror profile can be approximated by a double cone.," We suppose that, as far as the effective area is concerned, the mirror profile can be approximated by a double cone." + If the source were at infinity and on-axis (Fig., If the source were at infinity and on-axis (Fig. + laa). the incoming rays would impinge the primary and secondary segment at αρ.," \ref{fig:mirror_section}a a), the incoming rays would impinge the primary and secondary segment at $\alpha_0$." + We now move the source to a finite. although large. distance D.," We now move the X-ray source to a finite, although large, distance $D$." + The beam is no longer collimated. since it has a nonzero half-divergency ÓxRo/D. where Ro is the radius at the intersection plane (z= 0) of the mirror.," The beam is no longer collimated, since it has a nonzero half-divergency $\delta \approx R_0/D$, where $R_0$ is the radius at the intersection plane $z=0$ ) of the mirror." + Becauseof the small cross-section of the mirror as seen by the distant source. 6 can be considered as a constant.," Becauseof the small cross-section of the mirror as seen by the distant source, $\delta$ can be considered as a constant." + In this configuration. inspection of Fig.," In this configuration, inspection of Fig." + Ibb shows that the incidence angle on the primary segment becomes ay+0. and that on the secondary one. «o—ó.," \ref{fig:mirror_section}b b shows that the incidence angle on the primary segment becomes $\alpha_0+\delta$, and that on the secondary one, $\alpha_0-\delta$." + We consider a ray striking the primary segment at A=(—Ro—zoe.0. zo). with zo«Lj.," We consider a ray striking the primary segment at $A~=~(-R_0-z_0\alpha_0, 0, z_0)$ , with $z_0 $ 1500 K even on the disk surface and only the gaseous disk component can survive. + It is interesting (o note that the power law index of gl=0.75 of the inner disk region equals exactly that what was derived in analytical disk models [or geometrically flat. optically thick disks," It is interesting to note that the power law index of $q1=0.75$ of the inner disk region equals exactly that what was derived in analytical disk models for geometrically flat, optically thick disks" +of dogCAMmas/M.))?=7.9.,of $\langle \log (M_{\mathrm{Bulge}}/M_{\odot}) \rangle = 7.9$. + The resulting distribution of bulges including black holes is depicted in the 2-D histogram. in Fig. 2.., The resulting distribution of bulges including black holes is depicted in the $2$ -D histogram in Fig. \ref{Inilogscatter}. + In this plot we have normalized the number of objects Nan; to the maximum number of objects Ius found in a black hole-bulge. mass bin., In this plot we have normalized the number of objects $N_{\mathrm{objects}}$ to the maximum number of objects $N_{\mathrm{max}}$ found in a black hole-bulge mass bin. + Phe observed AA- AMiascrelation according to 7. is plotted together with the l-c-range of the applied scatter., The observed $M_{\bullet}$ $M_{\mathrm{bulge}}$ -relation according to \citet{Haering} is plotted together with the $1$ $\sigma$ -range of the applied scatter. + Observationallv. we know that the mass function of bulges follows a Seheehter function. (e.g. 2)) rather than a log-normal clistribution.," Observationally, we know that the mass function of bulges follows a Schechter function (e.g. \citealp{Bell03}) ) rather than a log-normal distribution." +" ""Therefore we study the scatter evolution of a Schechter-shaped initial distribution of bulge masses.", Therefore we study the scatter evolution of a Schechter-shaped initial distribution of bulge masses. + We use a fit to the measured Luminosity function (Ix-band magnitude) for red galaxies at redshift z~2 according to? to construct our initial galaxy sample. with the fitting parameters where My are the absolute magnitudes in Ix-band.," We use a fit to the measured luminosity function (K-band magnitude) for red galaxies at redshift $z \sim 2$ according to \citet{Cirasuolo07} to construct our initial galaxy sample, with the fitting parameters where $M_k$ are the absolute magnitudes in K-band." + We convert the luminosity function into a mass function. using the mass-to-light ratios as function of the Ix-band magnitude according to ?:: These mass-to-light ratios were measured. for a population of ellipticals at 2=0 and for simplicity we assume no evolution with redshift., We convert the luminosity function into a mass function using the mass-to-light ratios as function of the K-band magnitude according to \citealp{Cappellari}: These mass-to-light ratios were measured for a population of ellipticals at $z = 0$ and for simplicity we assume no evolution with redshift. + A consequence of this assumption is. that we obtain quite massive galaxies at >=2. although the stellar population was not evolved completely at this time.," A consequence of this assumption is, that we obtain quite massive galaxies at $z=2$, although the stellar population was not evolved completely at this time." + Probably. the mass-to-light ratio was smaller at higher z than the present-clay value leacing to smaller galaxy masses.," Probably, the mass-to-light ratio was smaller at higher $z$ than the present-day value leading to smaller galaxy masses." + However. for our study it is sullicient to see the evolution of statistical properties. which are independent. of the exact choice of the mass-to-light ralio.," However, for our study it is sufficient to see the evolution of statistical properties, which are independent of the exact choice of the mass-to-light ratio." + We scale the resulting mass distribution to a volume of (500Mpc) and. study the evolution of 100000 bulges with black holes. considering only bulge masses larger than 1.610A4. (=log(AMwus/M.)78.2).," We scale the resulting mass distribution to a volume of $(500 \mathrm{Mpc})^3$ and study the evolution of $\sim 100000$ bulges with black holes, considering only bulge masses larger than $1.6 \times 10^{8} M_{\odot}$ $\mathrel{\widehat{=}} \log (M_{\mathrm{Bulge}}/M_{\odot}) > 8.2 $ )." + To keep the Schechter-distribution for the bulge masses we have only applied a log-normal scatter of &=0.6 to the black hole masses (soe Fig. 3))., To keep the Schechter-distribution for the bulge masses we have only applied a log-normal scatter of $\sigma = 0.6$ to the black hole masses (see Fig. \ref{Schechter_ini_z2}) ). + For our fiducial random merging scenario. (depletion Case. Le. without refilling the initial distribution with new ealaxies) we use either the initial log-normal or Schechter distribution as described. above.," For our fiducial random merging scenario (depletion case, i.e. without refilling the initial distribution with new galaxies) we use either the initial log-normal or Schechter distribution as described above." + From the initial pool we randomly select two objects. merge them by adding their slack hole and bulge masses and put the merged object back into the pool.," From the initial pool we randomly select two objects, merge them by adding their black hole and bulge masses and put the merged object back into the pool." + In the next step we again merge two objects randomly. but. now from the new rearranged pool.," In the next step we again merge two objects randomly, but now from the new rearranged pool." + This xocedure is repeated iteratively until. on average. every object has had one merger. ie. only half of the initial objects are left over.," This procedure is repeated iteratively until, on average, every object has had one merger, i.e. only half of the initial objects are left over." + At this point we define one merging generation o be completed., At this point we define one merging generation to be completed. + Then all remaining objects are considered as the initial pool for the next generation., Then all remaining objects are considered as the initial pool for the next generation. +" TPherefore. after he first generation we have ΔΕ)=INi/2 objects and after he n-th generation our pool is reduced to NO)=Niu/2"" objects."," Therefore, after the first generation we have $N(1) = N_{\mathrm{ini}}/2$ objects and after the $n$ -th generation our pool is reduced to $N(n) = N_{\mathrm{ini}}/2^n$ objects." + We note that in one generation some objects can wave merged several times while others have not merged at all., We note that in one generation some objects can have merged several times while others have not merged at all. + Please note that if not stated otherwise. here and in the ollowing we define the number of mergers by counting all mergers that occur for galaxies >»10* M. independent of heir mass ratio.," Please note that if not stated otherwise, here and in the following we define the number of mergers by counting all mergers that occur for galaxies $>10^{4.7}$ $_{\odot}$ independent of their mass ratio." + If we randomly merge the galaxies from the initial log-normal or Schechter distribution in Fig., If we randomly merge the galaxies from the initial log-normal or Schechter distribution in Fig. + 2. and 3. an important consequence of the model is. as already pointed out bv 7. that the sample behaves according to. the (CLE).," \ref{Inilogscatter} and \ref{Schechter_ini_z2}, an important consequence of the model is, as already pointed out by \citet{Pengrandom}, that the sample behaves according to the (CLT)." + This theorem. preclicts that independent. of the initial distribution we always converge owards a Gaussian distribution., This theorem predicts that independent of the initial distribution we always converge towards a Gaussian distribution. + We see this trend.already alter only one merging generation., We see this trendalready after only one merging generation. + In Fig., In Fig. + 4. we show the evolution in the black hole-σος mass plane of the Iog-normal distributed. sample for merece generations n=|8., \ref{RM_bothscatter} we show the evolution in the black hole-bulge mass plane of the log-normal distributed sample for merger generations $n=1-8$. + Again. the black solid. line shows the observed. present day. Aa- νοοαο with he Ί-σ range of the assumed ce;=0.6 initial scatter.," Again, the black solid line shows the observed, present day, $M_{\bullet}$ $M_{\mathrm{bulge}}$ -relation with the $\sigma$ range of the assumed $\sigma_{\mathrm{ini}}=0.6$ initial scatter." + The relation is conserved during all merging generations., The relation is conserved during all merging generations. + ote. however. that here we use the initial scatter in rack hole and bulge masses.," Note, however, that here we use the initial scatter in black hole and bulge masses." + In addition. the overall scatter decreases significantlv with increasing merger generation.," In addition, the overall scatter decreases significantly with increasing merger generation." + The low mass end of the distribution is depleted by merging whereas the high mass end is populated., The low mass end of the distribution is depleted by merging whereas the high mass end is populated. + We also see the trend that the scatter decreases more for more massive black holes ancl bulges than low niass systems., We also see the trend that the scatter decreases more for more massive black holes and bulges than low mass systems. + The evolution of à randomly merging initial Schechter-distribution of bulges is shown in Fig. 5.., The evolution of a randomly merging initial Schechter-distribution of bulges is shown in Fig. \ref{Schechter_merg_z2}. . + In this case the overall slope increases for small merger generations., In this case the overall slope increases for small merger generations. + For high merger generations. when the low mass end is depopulated.," For high merger generations, when the low mass end is depopulated," +height (Wielen1977:Dehnen&Binney1998).,"height \citep{wi77,de98}." +. The large SDSS DR1 sample of galaxies places strong constraints on the best fitting values of j£ and o., The large SDSS DR1 sample of galaxies places strong constraints on the best fitting values of $\mu$ and $\sigma$. + To demonstrate how the goodness of fit varies in (μ.σ] parameter space. Figure 2. shows the isoprobability contours lor the qu data in the / band.," To demonstrate how the goodness of fit varies in $(\mu,\sigma)$ parameter space, Figure \ref{fig:prob_sdss} shows the isoprobability contours for the $q_{\rm am}$ data in the $i$ band." +" Note that the Ctours are drawn at an interval. ofB Alog,,P=à2: the 47L7 probabilityays drops rapidly. as vou move away [rom the best fit. indicated by the filled circle at the center of the innermost our."," Note that the contours are drawn at an interval of $\Delta \log_{10} +P = 2$; the $\chi^2$ probability drops rapidly as you move away from the best fit, indicated by the filled circle at the center of the innermost contour." + At other wavelengths. and using the other shape measure gos. the probability. [alls off with comparable steepness in (jr.0) parameter space.," At other wavelengths, and using the other shape measure $q_{25}$, the probability falls off with comparable steepness in $(\mu,\sigma)$ parameter space." + The log-normal distribution of equation (11)) is not the only functional form to vield an aclequate fit to the data., The log-normal distribution of equation \ref{eq:epsilon}) ) is not the only functional form to yield an adequate fit to the data. + A Gaussian peaking at 2=0. as shown in equation (1)). provides a comparably good fit to the SDSS DRI data.," A Gaussian peaking at $\varepsilon = 0$, as shown in equation \ref{eq:apm}) ), provides a comparably good fit to the SDSS DR1 data." + In the / bauxdl. the best-fitting Gaussian to (he qu data has o=0.26.," In the $i$ band, the best-fitting Gaussian to the $q_{\rm am}$ data has $\sigma_\varepsilon = 0.26$." + The best-litling Gaussian to the qos data has σ.=0.21., The best-fitting Gaussian to the $q_{25}$ data has $\sigma_\varepsilon = 0.21$. + The photometry provided by the SDSS DRI is insufficient. to. distinguish between a Gaussian distribution of ellipticilies. peaking al =0. and a log-normal distribution. peaking al 7>0.," The photometry provided by the SDSS DR1 is insufficient to distinguish between a Gaussian distribution of ellipticities, peaking at $\varepsilon = 0$, and a log-normal distribution, peaking at $\varepsilon > 0$." + Purely photometric studies. il seems. are ill-suited to addressing (he question of whether exactly circular disks. with 7=0. exist. Andersen&Bershady(2003).," Purely photometric studies, it seems, are ill-suited to addressing the question of whether exactly circular disks, with $\varepsilon = 0$, exist. \citet{an03}," +. using the method outlined in Andersenefal(2001).. combined kinematic and /-band photometric data to find the disk ellipticity for a sample ol 28 nearly face-on disk galaxies: the mean inclination of the galaxies is 7=26°.," using the method outlined in \citet{an01}, combined kinematic and $I$ -band photometric data to find the disk ellipticity for a sample of 28 nearly face-on disk galaxies; the mean inclination of the galaxies is $i = 26^\circ$." + The distribution of Ins determined by Andersen&Bershacly(2003) is shown as the histogram in Figure 3.., The distribution of $\ln\varepsilon$ determined by \citet{an03} is shown as the histogram in Figure \ref{fig:loge_ab}. + This distribution is well fitted by a log-normal distribution: the best fit. as fonnd by a 4? test. has parameters yo=—2.80 and oa=0.51.," This distribution is well fitted by a log-normal distribution; the best fit, as found by a $\chi^2$ test, has parameters $\mu = -2.80$ and $\sigma = 0.81$." + However. the best fit to the data in Figure3 is not the best fit to the underlying distribution of disk ellipticities. (hanks to (he selection criteria used in building the sample.," However, the best fit to the data in Figure\ref{fig:loge_ab} is not the best fit to the underlying distribution of disk ellipticities, thanks to the selection criteria used in building the sample." + To ensure that only galaxies with smallinclination were included. Andersen&Bershacly(2003). selected. galaxies with q>0.8606. corresponding to an inclination /<30° for perfectly circular. infinitesimally (hin disks.," To ensure that only galaxies with smallinclination were included, \citet{an03} + selected galaxies with $q \geq 0.866$, corresponding to an inclination $i \leq 30^\circ$ for perfectly circular, infinitesimally thin disks." + To fit the distribution of intrinsic ellipticities in the Andersen-Dershady sample. subject to their selection criterion q>0.866. I started by assuming that the disk ellipticity has the log-normal form given in equation (11)).," To fit the distribution of intrinsic ellipticities in the Andersen-Bershady sample, subject to their selection criterion $q \geq 0.866$, I started by assuming that the disk ellipticity has the log-normal form given in equation \ref{eq:epsilon}) )." + I farther assumed. for simplicity. (hat (he disks are all infinitesimally thin: since the disks in the Andersen-Dershady sample are close to face-on. their exact thiekness doesn't affect the observed axis ratio.," I further assumed, for simplicity, that the disks are all infinitesimally thin; since the disks in the Andersen-Bershady sample are close to face-on, their exact thickness doesn't affect the observed axis ratio." + After assuming values for the parameters po and o. I randomly selected a disk ellipticity 5 as well as a viewing angle (8. 6).," After assuming values for the parameters $\mu$ and $\sigma$ , I randomly selected a disk ellipticity $\varepsilon$ as well as a viewing angle $(\theta,\phi)$ ." +3072 with respect to the Galactic plane.,$\sim 30$ with respect to the Galactic plane. + Since the extent of he Disk in/ and b resembles the dimensions of the 511 keV source. Higdon.Lingenfelter.&Rothschild(2009) suggest hat the positrons reach the disk and annihilate there.," Since the extent of the Disk in$l$ and $b$ resembles the dimensions of the 511 keV source, \citet{2009ApJ...698..350H} suggest that the positrons reach the disk and annihilate there." + To test further the Tilted. Disk model we fit the data with a two-dimensional Caussian allowing for rotation of he major axis., To test further the Tilted Disk model we fit the data with a two-dimensional Gaussian allowing for rotation of the major axis. + Phe results are shown in Fig. 5.., The results are shown in Fig. \ref{fig:rot}. +" Phe best- rotation angle and the widths of the Gaussian in wo directions are @—12"" and Wy=14 Wi,=4 respectively."," The best-fitting rotation angle and the widths of the Gaussian in two directions are $\theta\sim$ and $W_l=14$ , $W_b=4$, respectively." +" The improvement in 47 compared to @=) (and WM;=107. M,—6 1) is Ay?sxY."," The improvement in $\chi^2$ compared to $\theta=0$ (and $W_l=10$, $W_b=6$ ) is $\Delta\chi^2\approx 7$." + As discussed already. the values of Ay? of the order of a few are formally statistically significant. if the errors are due to counting Poisson noise only.," As discussed already, the values of $\Delta\chi^2$ of the order of a few are formally statistically significant if the errors are due to counting Poisson noise only." + The total change of the x7E when a two-dimensional Gaussian is added: to the model is ~SOOQ., The total change of the $\chi^2$ when a two-dimensional Gaussian is added to the model is $\sim 8000$. + Comparing these numbers. it is clear that. even. mocdoest systematies in the data could allect precise derivation of the source spatial characteristics.," Comparing these numbers, it is clear that even modest systematics in the data could affect precise derivation of the source spatial characteristics." + Taking the results shown in Fie., Taking the results shown in Fig. + 5 at face value. a marginally significant improvement in the fit is possible if the annihilation region is tilted by ~12 with respect to the Galactic plane.," \ref{fig:rot} at face value, a marginally significant improvement in the fit is possible if the annihilation region is tilted by $\sim 12$ with respect to the Galactic plane." + Aga [6| increases beyond the Gaussian converges to an almost svmmetric structure.," As $|\theta|$ increases beyond, the Gaussian converges to an almost symmetric structure." +" The tilt of 6~30° corresponds to Ay?z23 for an almost. symmetric Gaussian with Wy)=9 and M,=i", The tilt of $\theta\sim 30$ corresponds to $\Delta\chi^2\approx 23$ for an almost symmetric Gaussian with $W_l=9$ and $W_b=7$. + We therefore conclude that a version of a the ‘Tilted Disk of Ferriere.CGillard.&Jean(2007) is not particularly favored. by SPL data compared to a structure with zero tilt., We therefore conclude that a version of a the Tilted Disk of \citet{2007A&A...467..611F} is not particularly favored by SPI data compared to a structure with zero tilt. +" However. moderate values of the tithe S20"" are allowed by the SPL data."," However, moderate values of the title $\lesssim$ are allowed by the SPI data." + The simple light bucket imaging and. parametric fitting of the 508514 keV ux done in refsec:bucket and 3.2. suggest that a reasonable description of the data in the central racian could. be achieved with an almost svmmetric Gaussian at the centre ancl a more extended component along the plane., The simple light bucket imaging and parametric fitting of the 508–514 keV flux done in \\ref{sec:bucket} and \ref{sec:par} suggest that a reasonable description of the data in the central radian could be achieved with an almost symmetric Gaussian at the centre and a more extended component along the plane. + The stellar bulge and stellar disk are the most obvious structural components of Ίο Galaxy that qualitatively fit this description., The stellar bulge and stellar disk are the most obvious structural components of the Galaxy that qualitatively fit this description. + In fact. rere are plenty of clisk-like structures (cold. gas. massive stars. cosmic rav induced gamama-ray flux. ete) aad very few 'omponents that show a prominent peak at the GC.," In fact, there are plenty of disk-like structures (cold gas, massive stars, cosmic ray induced gamma-ray flux, etc) and very few components that show a prominent peak at the GC." + One of 16 known centrally-peakect cistributions is that of the NI ight. which is a tracer of the old stellar population of the ο.maxy.," One of the known centrally-peaked distributions is that of the NIR light, which is a tracer of the old stellar population of the Galaxy." + For this reason. we decided to restrict our analysis to Ίου simple templates. corresponding to stellar components of the Milky Way. adopted from López-Corredoira.Lavers.&Gorhard(2005). and shown in Fig. 6:," For this reason, we decided to restrict our analysis to three simple templates, corresponding to stellar components of the Milky Way, adopted from \citet{2005A&A...439..107L} and shown in Fig. \ref{fig:mw}:" + This is by no means a comprehensive [ist of possible emplates (see c.g. Ixnócdlsederetal.(2005). for a systematic analysis of various templates)., This is by no means a comprehensive list of possible templates (see e.g. \citet{2005A&A...441..513K} for a systematic analysis of various templates). + However. the hope is hat these spatial templates will capture the most. basic operties of the 508514 keV lux distribution. even if the physical motivation is questionable or the details of shape are not correct.," However, the hope is that these spatial templates will capture the most basic properties of the 508–514 keV flux distribution, even if the physical motivation is questionable or the details of shape are not correct." + We also used slightly. modified (truncated) versions of hese templates: for each template we set to zero the surface xightness in all regions where it is smaller than of he peak value., We also used slightly modified (truncated) versions of these templates: for each template we set to zero the surface brightness in all regions where it is smaller than of the peak value. + The motivation behind this mocification is an attempt to have a template that has a bulge or cisk-vpe morphology at high surface. brightness but lacks the extended low surface brightness regions. which might make a significant contribution to the total Dux.," The motivation behind this modification is an attempt to have a template that has a bulge or disk-type morphology at high surface brightness but lacks the extended low surface brightness regions, which might make a significant contribution to the total flux." + For a given set of templates. the surface brightness for each template is convolved with the simulated SPL response (Sturneretal.2003) vielding an expected count rate in the lIOS514 keV band in individual detectors. during individual observations.," For a given set of templates, the surface brightness for each template is convolved with the simulated SPI response \citep{2003A&A...411L..81S} yielding an expected count rate in the 508–514 keV band in individual detectors during individual observations." + The best-fitting normalizations of the templates are then caleulated in order to minimize the \5 eviation between the raw data and the model., The best-fitting normalizations of the templates are then calculated in order to minimize the $\chi^2$ deviation between the raw data and the model. + Phe 47 values for the various spatial models are given in Table 1.., The $\chi^2$ values for the various spatial models are given in Table \ref{tab:templates}. + Phe fluxes quoted in Table 1 are the integrated model fluxes (with best-fitting normalization) over à square region around the GC., The fluxes quoted in Table \ref{tab:templates} are the integrated model fluxes (with best-fitting normalization) over a square $\times$ region around the GC. + The choice of the region for the calculation of the integrated. model Dux is rather arbitrary., The choice of the region for the calculation of the integrated model flux is rather arbitrary. + The region is not uniformly covered by observations. and areas with the smallest errors (largest exposures) dominate in the determination of the best-fitting normalization.," The $\times$ region is not uniformly covered by observations, and areas with the smallest errors (largest exposures) dominate in the determination of the best-fitting normalization." + On the other hand. underexposed. (or even not observed at all) areas can still provide a significant contribution to the total integrated. flux.," On the other hand, underexposed (or even not observed at all) areas can still provide a significant contribution to the total integrated flux." + An example of a clear overestimation of the flux due to this elfect is seen for the pure “Disk” models in Table 1.., An example of a clear overestimation of the flux due to this effect is seen for the pure “Disk” models in Table \ref{tab:templates}. + Phese models have poor x7.E but predict a large integratedfux. since their normalization is largely. set by the innermost bright. region of the Galaxy.," These models have poor $\chi^2$ , but predict a large integratedflux, since their normalization is largely set by the innermost bright region of the Galaxy." + This becomes an especially severe. problem when dealing with lluxes integrated: over very large areas (e.g. the Dux from the entire Galactic disk)., This becomes an especially severe problem when dealing with fluxes integrated over very large areas (e.g. the flux from the entire Galactic disk). + For this reason.," For this reason," +"results from these randomly resampled coordinates, while the solid line shows the same quantity from the selected sample.","results from these randomly resampled coordinates, while the solid line shows the same quantity from the selected sample." +" The peak value of the solid curve is thus statistically highly significant and occurs for Qp=0.294 (in units of Vo/Ro), in excellent agreement with the value (0.296) obtained from the completely independent ssample."," The peak value of the solid curve is thus statistically highly significant and occurs for $\Omega_p=0.294$ (in units of $V_0/R_0$ ), in excellent agreement with the value (0.296) obtained from the completely independent sample." +" The excess at this frequency is caused by the overdense feature visible in the upper panel slanting upward with negative slope from near the point (1,0)."," The excess at this frequency is caused by the overdense feature visible in the upper panel slanting upward with negative slope from near the point (1,0)." +" Unfortunately, this feature cannot be uniquely attributed to an oof an m=2 pattern, since the loci of corotation and of both Lindblad resonances for m>2 also have similar steep negative slopes in action space, as shown in the lower panel of fig."," Unfortunately, this feature cannot be uniquely attributed to an of an $m=2$ pattern, since the loci of corotation and of both Lindblad resonances for $m\geq2$ also have similar steep negative slopes in action space, as shown in the lower panel of fig." + 5 of Paper I. Thus tests fortrapping at any resonance appear very similar to that shown in the lower panel of Fig., 5 of Paper I. Thus tests for at any resonance appear very similar to that shown in the lower panel of Fig. +" 6, although the almost equally significant excess when other resonances are considered clearly must imply quite different pattern speeds."," 6, although the almost equally significant excess when other resonances are considered clearly must imply quite different pattern speeds." +" Stars that arescattered at a resonance, on the other hand, change both actions in such a way that the Jacobi constant is conserved, which generally shifts a star in a direction in action space that is not parallel to the resonance locus."," Stars that are at a resonance, on the other hand, change both actions in such a way that the Jacobi constant is conserved, which generally shifts a star in a direction in action space that is not parallel to the resonance locus." +" Only at the ddoes the scattering line in action-space have similar, though not identical, slope to the resonance locus; scattering lines at corotation are horizontal while they have positive slope at anOLR."," Only at the does the scattering line in action-space have similar, though not identical, slope to the resonance locus; scattering lines at corotation are horizontal while they have positive slope at an." +". Tests for an excess of stars along lines of positive slope in action space, that would correspond to scattering at anOLR,, confirmed that there are no significant features with this slope, as was also true for the ssample in Paper I. Figure 7 shows the distributions of the two angles conjugate to the actions. ("," Tests for an excess of stars along lines of positive slope in action space, that would correspond to scattering at an, confirmed that there are no significant features with this slope, as was also true for the sample in Paper I. Figure \ref{angplt} shows the distributions of the two angles conjugate to the actions. (" +The physical meaning of these,The physical meaning of these +NSPEC (version 11.3: Arnaud 1996). the ALEINAL plasma emission code (Ixaastra Mewe 1993: incorporating the be-L calculations of Liedhal. Osterheld Goldstein 1995) and the photocleetric absorption models of Balucinska-Church AleCanmunon (1992).,"XSPEC (version 11.3: Arnaud 1996), the MEKAL plasma emission code (Kaastra Mewe 1993; incorporating the Fe-L calculations of Liedhal, Osterheld Goldstein 1995) and the photoelectric absorption models of Balucinska-Church McCammon (1992)." + We have included: standard: correction [actors to account for time-dependent contamination along the instrument light path ancl have incorporated a small correction to the Ligh Resolution Mirror Assembly. mocel in CIAO 3.2.1. which takes the form of an inverse. edge with an energy. ISkkeV and optical depth 70.1 (ορια. Marshall. private communication)," We have included standard correction factors to account for time-dependent contamination along the instrument light path and have incorporated a small correction to the High Resolution Mirror Assembly model in CIAO 3.2.1, which takes the form of an 'inverse' edge with an energy, keV and optical depth $\tau=-0.1$ (Herman Marshall, private communication)." + Only data in the 0.6S.0 keV energy range were used for our analysis., Only data in the $0.6-8.0$ keV energy range were used for our analysis. + The spectra for all annuli or à particular galaxy were mocelled simultaneously in ordv 00 determine the deprojected X-ray gas temperature proiles. under the assumption of spherical svmmetry.," The spectra for all annuli for a particular galaxy were modelled simultaneously in order to determine the deprojected X-ray gas temperature profiles, under the assumption of spherical symmetry." +t.. The emission from cach spherical shell was mocelled as a single phase plasma. with the abundances of all metals in each silb assumed. to vary with a common ratio. Ζ. with resp6ct to Solar values. (," The emission from each spherical shell was modelled as a single phase plasma, with the abundances of all metals in each shell assumed to vary with a common ratio, $Z$, with respect to Solar values. (" +Phe exception o the latter assumption was the analvsis of NGCALSG. reported: separately w Di Matteo (2003). for which he abuncances of kev elements. were permitted. to vary inclependenthy in eac1 shell.),"The exception to the latter assumption was the analysis of NGC4486, reported separately by Di Matteo (2003), for which the abundances of key elements were permitted to vary independently in each shell.)" + Background spectra were extracted. from the blank-ield data sets available from the Chandra. X-ray Center., Background spectra were extracted from the blank-field data sets available from the Chandra X-ray Center. + These were cleaned in an identical manner to the target observations., These were cleaned in an identical manner to the target observations. + In cach case. the normalizations of the xickeround. files were scaled to match the count rates in he target. observations measured. in the 9.5-12ke band.," In each case, the normalizations of the background files were scaled to match the count rates in the target observations measured in the 9.5-12keV band." + Separate photon-weighted response matrices and. effectiveV. area Liles were constructed for cach region using calibration iles appropriate for the period of observation., Separate photon-weighted response matrices and effective area files were constructed for each region using calibration files appropriate for the period of observation. + Azimuthally-averaged surface. brightness. profiles. were constructed from backgroundsubtracted. Hat-fielded images with a 0.4920.402 arcsec? pixel scale (1.1 raw detector pixels).," Azimuthally-averaged surface brightness profiles were constructed from backgroundsubtracted, flat-fielded images with a $0.492\times0.492$ $^2$ pixel scale $1\times1$ raw detector pixels)." + Together with the deprojected spectral temperature profiles. these were used to determine the X-ray gas density profiles (see White. Jones Forman 1997 for details of the technique)," Together with the deprojected spectral temperature profiles, these were used to determine the X-ray gas density profiles (see White, Jones Forman 1997 for details of the technique)." +" For the case of ALS7. the measurement of the central black hole mass. Mpg=3.021.0.10""AL... is from Tremaine (2002) and is based on the data of Harms (1994) and Macchetto (1997)."," For the case of M87, the measurement of the central black hole mass, $M_{\rm BH}=3.0\pm1.0\times10^9$, is from Tremaine (2002) and is based on the data of Harms (1994) and Macchetto (1997)." + For the other galaxies in the sample. the black hole masses have been estimated using the correlation between AMpg ancl velocity. dispersion. o. given bv “Tremaine (2002) with a5δ.]ot2L1.06 and $=4.02£0.32.," For the other galaxies in the sample, the black hole masses have been estimated using the correlation between $M_{\rm BH}$ and velocity dispersion, $\sigma$, given by Tremaine (2002) with $\alpha=8.13\pm0.06$ and $\beta=4.02\pm0.32$." + Our analysis uses a Monte Carlo algorithm to account for the uncertainties in σ ancl the sope of the Alba loge relation., Our analysis uses a Monte Carlo algorithm to account for the uncertainties in $\sigma$ and the slope of the $M_{\rm BH}-$ $\sigma$ relation. + Velocity dispersions for the galaxies are drawn from the work of Jernarc (2002) and are summarized in Table 2.., Velocity dispersions for the galaxies are drawn from the work of Bernardi (2002) and are summarized in Table \ref{table:bondi}. +" The aceretion radius. ra. is the radius within which the eravitational potential of the central black hole dominates over the thermal enerey of the surrounding X-ray. emitting gas Lore € nis the gravitational. constant. e;=V/zaAfTppm ds. the acliabatic sound speed of the gas at the accretion radius. 7 isthe gas temperature at that radius. 50.62 is the mean atomic weight. my is the proton mass and 7, is the adiabatic index of the N-rav emitting gas."," The accretion radius, $r_{\rm A}$, is the radius within which the gravitational potential of the central black hole dominates over the thermal energy of the surrounding X-ray emitting gas Here $G$ is the gravitational constant, $c_s=\sqrt{\gamma_1 +kT/\mu m_p}$ is the adiabatic sound speed of the gas at the accretion radius, $T$ is the gas temperature at that radius, $\mu=0.62$ is the mean atomic weight, $m_p$ is the proton mass and $\gamma_1$ is the adiabatic index of the X-ray emitting gas." + Phe results on the accretion radii. summarized in Table 2.. account for the uncertainties in the central black hole masses (described above) and. σας lemperatires.," The results on the accretion radii, summarized in Table \ref{table:bondi}, , account for the uncertainties in the central black hole masses (described above) and gas temperatures." + ‘Tremaine (2002) measure an intrinsic (systematic), Tremaine (2002) measure an intrinsic (systematic) +these are. (his seems exceedinglv unlikely.,"these are, this seems exceedingly unlikely." + Anv giants would have to be close to the turn-off mass and would experience Roche lobe overflow., Any giants would have to be close to the turn-off mass and would experience Roche lobe overflow. + The resulüng gas in the svstem would give rise lo eclipses. especially if the orbit is highlv inclined (and as we show below. it is) and near conjunction.," The resulting gas in the system would give rise to eclipses, especially if the orbit is highly inclined (and as we show below, it is) and near conjunction." + As it turns out. we see no evidence for eclipses al any orbital phase. including conjuncelion. so a giant seems unlikely," As it turns out, we see no evidence for eclipses at any orbital phase, including conjunction, so a giant seems unlikely." + A blue strageler would also probably cause eclipses or some other timing inregularities in the pulsar., A blue straggler would also probably cause eclipses or some other timing irregularities in the pulsar. + Ii fact. NGC 6544D (mes remarkably well. with no unmocdeled trends in (the data and no need for an error [actor to bring \red2/0.C1.," In fact, NGC 6544B times remarkably well, with no unmodeled trends in the data and no need for an error factor to bring $\chi^2\rmsub{red} = 1$." + llence. we can safelv rule out a significant contribution to w by tidal deformation.," Hence, we can safely rule out a significant contribution to $\dot{\omega}$ by tidal deformation." + Spin orbit coupling is a possibility if the companion is rapidly rotating. but it scales as μα limes a geometrical factor. where wr is the projected semi-major axis: the geometrical factor is expected to be <10 in of cases (e.g.2.andreferences therein)..," Spin orbit coupling is a possibility if the companion is rapidly rotating, but it scales as $|\dot{x}/x|$ times a geometrical factor, where $x$ is the projected semi-major axis; the geometrical factor is expected to be $<10$ in of cases \citep[e.g.][and references +therein]{frb+08}. ." + Our current best limit on implies that. precession due (ο spin-orbit coupling should be smallerthan our extremely small measurement uncertainties in w For the reasons outlined above. we [eel confident that the observed i is due almost entirely to GI.," Our current best limit on $\dot{x}$ implies that precession due to spin-orbit coupling should be smallerthan our extremely small measurement uncertainties in $\dot{\omega}$ For the reasons outlined above, we feel confident that the observed $\dot{\omega}$ is due almost entirely to GR." +" In this case (he total mass of the svstem is given bv where T.=GM.ο*. and DB, is the orbital period."," In this case the total mass of the system is given by where $T_{\Sun} = G \Msun c^{-3}$, and $P\rmsub{b}$ is the orbital period." + Using our measured values. we find Alyy=2.56763(59)M.," Using our measured values, we find $M\rmsub{tot} = +2.56763(59)\; \Msun$." + The total svstem mass of NGC 6544D is fairly high for a pulsar binary system., The total system mass of NGC 6544B is fairly high for a pulsar binary system. + When combined with the observed mass function. it implies a high orbital inclination and massive companion. making NGC 6544D an excellent candidate for a measurement of Shapiro dela.," When combined with the observed mass function, it implies a high orbital inclination and massive companion, making NGC 6544B an excellent candidate for a measurement of Shapiro delay." + We observed the pulsar on ten occasions over a variety of orbital phases. including two eight hour tracks at or near orbitalconjunction.," We observed the pulsar on ten occasions over a variety of orbital phases, including two eight hour tracks at or near orbital." + We used the DDII timing model developed by ?.. which parameterizes (he Shapiro delay as," We used the DDH timing model developed by \citet{fw10},, which parameterizes the Shapiro delay as" +redshift survey covers two long strips in declination. each of which is only about 10 degrees wide. meaning that all galaxies lie within 5 degrees of a catalogue boundary. and many lie significantly closer.,"redshift survey covers two long strips in declination, each of which is only about 10 degrees wide, meaning that all galaxies lie within 5 degrees of a catalogue boundary, and many lie significantly closer." + To estimate the effect that this will have on the surface density calculation. the following procedure was followed: (1) For each galaxy. the value of το was calculated as above.," To estimate the effect that this will have on the surface density calculation, the following procedure was followed: (i) For each galaxy, the value of $r_{10}$ was calculated as above." + 10000 positions were then randomly chosen within a circle of radius yy centred on that galaxy. G, 10000 positions were then randomly chosen within a circle of radius $r_{10}$ centred on that galaxy. ( +i). For each of these 10000 positions. the redshift completeness of the 2dFGRS catalogue was evaluated for galaxies brighter than the apparent magnitude corresponding to an absolute magnitude of Mg=Ü at the redshift of the galaxy under study.,"ii) For each of these 10000 positions, the redshift completeness of the 2dFGRS catalogue was evaluated for galaxies brighter than the apparent magnitude corresponding to an absolute magnitude of $M_{B} = -19$ at the redshift of the galaxy under study." + This ealeulation was carried out using the redshift completeness. limiting magnitude. and j/-masks (see Colless 22001 for details) provided by the 2dFGRS team.," This calculation was carried out using the redshift completeness, limiting magnitude, and $\mu$ -masks (see Colless 2001 for details) provided by the 2dFGRS team." + If a given position lay outside the 2UFGRS region of study. or within one of the survey holes associated with bright stars. then the redshift completeness was set to zero for that position. (," If a given position lay outside the 2dFGRS region of study, or within one of the survey holes associated with bright stars, then the redshift completeness was set to zero for that position. (" +ii) An average redshift completeness was derived for these 10000 positions.,iii) An average redshift completeness was derived for these 10000 positions. + In this way. for each galaxy the average redshift completenessfor galaxies brighterthan Ag<—I9 over the region of sky out to radius rjo was estimated. (," In this way, for each galaxy the average redshift completenessfor galaxies brighter than $M_{B} < -19$ over the region of sky out to radius $r_{10}$ was estimated. (" +"iv) Where the average redshift completeness wasbelowθές, or the value of ry was in excess of 5 degrees. the galaxy was removed from further analvsis: these are predominantly galaxies near the boundaries of the survey region.","iv) Where the average redshift completeness wasbelow, or the value of $r_{10}$ was in excess of 5 degrees, the galaxy was removed from further analysis; these are predominantly galaxies near the boundaries of the survey region." + Removal of these galaxies will no bias any of the results of the paper. since these same cuts are appliec to all of the samples under study. (," Removal of these galaxies will not bias any of the results of the paper, since these same cuts are applied to all of the samples under study. (" +v) The surface densities calculated for the remainder of the galaxies were scaled up by the inverse of their average redshift completeness.,v) The surface densities calculated for the remainder of the galaxies were scaled up by the inverse of their average redshift completeness. + This correction factor provides a rough first-order approximation to the correction and. since all applied corrections are below a factor of 2. any inaccuracies will have a negligible effect on the final results.," This correction factor provides a rough first–order approximation to the correction and, since all applied corrections are below a factor of 2, any inaccuracies will have a negligible effect on the final results." + The [Oth nearest neighbour analysis technique was developed at a time before large spectroscopic catalogues were available. and foreground and background field galaxies had to be statistically subtracted.," The 10th nearest neighbour analysis technique was developed at a time before large spectroscopic catalogues were available, and foreground and background field galaxies had to be statistically subtracted." + The use of redshift information to remove clearly unrelated galaxies greatly improves the reliability of the analysis. and there are clearly many advantages over simple comparisons with. for example. cluster-centric radius.," The use of redshift information to remove clearly unrelated galaxies greatly improves the reliability of the analysis, and there are clearly many advantages over simple comparisons with, for example, cluster-centric radius." + However. this technique still discards some of the information. which is available in a complete spectroscopic dataset. especially in galaxy groups or clusters with over IO members.," However, this technique still discards some of the information which is available in a complete spectroscopic dataset, especially in galaxy groups or clusters with over 10 members." + Using the velocity information available in the 24FGRS and SDSS catalogues. it is in principle possible to determine for each individual galaxy its. exact environment: is it an isolated galaxy. a member of a small group. on the outskirts of a cluster. within a cluster core. ete?," Using the velocity information available in the 2dFGRS and SDSS catalogues, it is in principle possible to determine for each individual galaxy its exact environment: is it an isolated galaxy, a member of a small group, on the outskirts of a cluster, within a cluster core, etc?" + Catalogues of galaxy groups have been constructed from the 2dFGRS by both Merehánn Zandivarez (2) and by Norberg shorteitenor03.. in both cases using an adapted version of the approach first described by Huchra Geller (2).," Catalogues of galaxy groups have been constructed from the 2dFGRS by both Merchánn Zandivarez \shortcite{mer02} and by Norberg \\shortcite{nor03}, in both cases using an adapted version of the approach first described by Huchra Geller \shortcite{huc82}." +. The basis of this approach is as follows., The basis of this approach is as follows. + Two galaxies with anangular separation on the sky of 84». and recession velocities of Vi and V5 with a mean. V=(M34|13)/2) are considered to be linked if they satisfy the following conditions: where D and Vj are the transverse and radial linking lengths respectively.," Two galaxies with anangular separation on the sky of $\theta_{12}$, and recession velocities of $V_1$ and $V_2$ (with a mean, $V = (V_1 + V_2)/2$ ) are considered to be linked if they satisfy the following conditions: where $D_{\rm L}$ and $V_{\rm L}$ are the transverse and radial linking lengths respectively." +"For a survey of fixed apparent magnitude limit. in the standard Huchra Geller formalism the linking lengths Mp and Vj, vary with recession velocity in order to compensate the change in the sampling of the galaxy luminosity functionwith distance. and thus to provide equal sensitivity to groups across all redshifts.","For a survey of fixed apparent magnitude limit, in the standard Huchra Geller formalism the linking lengths $D_{\rm L}$ and $V_{\rm L}$ vary with recession velocity in order to compensate the change in the sampling of the galaxy luminosity functionwith distance, and thus to provide equal sensitivity to groups across all redshifts." +" The linking lengths scale as Dj,=Do and Vj=Vole. where Do and Vo are the linking lengths at some fiducial recession velocityVis and {1 is a sealing factor given by: where Άι and A,» are the absolute magnitudes of the faintest galaxy visible at distances of 1,///o and V///o respectively. and o(M) is the galaxy luminosity function of the sample."," The linking lengths scale as $D_{\rm L} = D_0 R$ and $V_{\rm L} += V_0 R$ , where $D_0$ and $V_0$ are the linking lengths at some fiducial recession velocity$V_{\rm f}$, and $R$ is a scaling factor given by: where $M_{\rm lim}$ and $M_{12}$ are the absolute magnitudes of the faintest galaxy visible at distances of $V_{\rm f}/H_0$ and $V/H_0$ respectively, and $\phi(M)$ is the galaxy luminosity function of the sample." + In the present analysis. such a sealing factor is in principle unnecessary because the adoption of a fixed absolute magnitude imit (Alpe«19. as discussed above) removes this distance dependence of the luminosity function sampling Ge.," In the present analysis, such a scaling factor is in principle unnecessary because the adoption of a fixed absolute magnitude limit $M_B < -19$, as discussed above) removes this distance dependence of the luminosity function sampling (ie." +" My, and AM,» are both equal (ο 19. making 7? unity)."," $M_{\rm lim}$ and $M_{12}$ are both equal to $-19$, making $R$ unity)." + However. the 24FGRS ws a slightly varying magnitude limit. and the spectroscopic completeness varies with position on the sky.," However, the 2dFGRS has a slightly varying magnitude limit, and the spectroscopic completeness varies with position on the sky." + These do require (minor) correction (cf., These do require (minor) correction (cf. + Merehánn Zandivarez 2002). and can be accounted for by redefining the scaling factor as where €'; and C are the redshift completeness for magnitudes brighter than the apparent magnitude corresponding to Λέο=—19 for the redshift of the galaxies in question. at the location in the 2dFGRS of two galaxies whose linkage is being considered.," Merchánn Zandivarez 2002), \nocite{mer02} and can be accounted for by redefining the scaling factor as where $C_1$ and $C_2$ are the redshift completeness for magnitudes brighter than the apparent magnitude corresponding to $M_B = +-19$ for the redshift of the galaxies in question, at the location in the 2dFGRS of two galaxies whose linkage is being considered." + These redshift completeness values can be evaluated using the redshift completeness. limiting magnitude. and sr-masks provided by the 2dFGRS team (see Colless 22001 for details).," These redshift completeness values can be evaluated using the redshift completeness, limiting magnitude, and $\mu$ -masks provided by the 2dFGRS team (see Colless 2001 for details)." + The transverse linking length. D7. is set by defining groupsto be those regions with a mean galaxy density contrast 9p/p in excess of 80 (cf.," The transverse linking length, $D_{\rm L}$, is set by defining groupsto be those regions with a mean galaxy density contrast $\delta \rho / \rho$ in excess of 80 (cf." + Merchánn Zandivarez 2002: Ramella. Pisani Geller 1997).," Merchánn Zandivarez 2002; Ramella, Pisani Geller 1997)." +" This relates to {20 through the expression Taking the Schechter fit to the luminosity function of 2dFGRS galaxies (6°=46.10 °Mpe a= 191. Mj— 20.59. for 44,=65kkmss !Mpe. 1: Norberg 2°002).. for an absolute magnitude limitof Mg= 19). a tiducial transverse linking length of My=1.25 MMpce is derived."," \nocite{mer02,ram97} This relates to $D_0$ through the expression Taking the Schechter fit to the luminosity function of 2dFGRS galaxies $\phi^* = 4.6 \times 10^{-3}$ $^{-3}$ , $\alpha = -1.21$ , $M_B^* += -20.59$ , for $H_0 = 65$ $^{-1}$ $^{-1}$ ; Norberg \nocite{nor02}, , for an absolute magnitude limitof $M_B = -19$ , a fiducial transverse linking length of $D_0 = 1.25$ Mpc is derived." + Regarding the velocity linking length. VL. this needs to be larger than the equivalent distance linking length because peculiar," Regarding the velocity linking length, $V_{\rm L}$ , this needs to be larger than the equivalent distance linking length because peculiar" +valence quarks aresmall as compared. with thoseof CTEQ3distributions. Sincemain,"part of sea (anti)quarks are produced in the cascade processes \ref{eqn:q2B}) \ref{eqn:dq2M}) ), the magnitude" +Let us point out that this corollary is a much more precise version of the well known result which holds for any continuous functüon v6 on Ε that vanishes in a neighbourhood of 0 and that is equal to 1 in a neighbourhood of +x. see for example for a proof of such a result in the three dimensional case and for its use in the proof of asymptotic completeness.,"Let us point out that this corollary is a much more precise version of the well known result which holds for any continuous function $\psi$ on $\R_+$ that vanishes in a neighbourhood of $0$ and that is equal to $1$ in a neighbourhood of $+\infty$, see for example for a proof of such a result in the three dimensional case and for its use in the proof of asymptotic completeness." +" In the framework of Section??. (his result simply savs (hat Py=D,1. but does not sav anvihing about Py and Ps."," In the framework of Section, this result simply says that $\Gamma_3 = \Gamma_4=1$, but does not say anything about $\Gamma_1$ and $\Gamma_2$." + Now. by using the relation(11). the third and the fourth conditions of Corollary can easily be rewritten in terms of the unitary groups generated by D.," Now, by using the relation, the third and the fourth conditions of Corollary can easily be rewritten in terms of the unitary groups generated by $B$." + For example. the (hire condition is equivalent to ⊔∐↲≀↧↴∣↽≻∪∖↽≼↲≼↲⇀↸↕↽≻↕⋅≼↲⋝∖⊽⊳∖⇁↕∪∐⋅↕∐≼⇂≼↲≼↲≼⇂⋅⊔∐↲↓⋟∪∐∪∖∖⊽↕∐≸↽↔↴≼↲≺↥∏≀↧↴∐∐≼↲⊳∖⊽∐∪∐∶ ," For example, the third condition is equivalent to Furthermore, the invariance principle and the intertwining relation allow one to simplifythe above expression." +where In(//) is obtained by functional caleulus on the positive part of the spectrum of 1l.," Indeed, the following equalities hold: where $\ln(H)$ is obtained by functional calculus on the positive part of the spectrum of $H$." + Let us also note that e.In!—eMOTE(IT). where (ΙΓ) denotes the spectral projection on the absolutely. continuous part of 141.," Let us also note that $e^{-i\ln(H)t} = e^{-i\ln(H)t} E_{ac}(H)$, where $E_{ac}(H)$ denotes the spectral projection on the absolutely continuous part of $H$ ." + Finally. one obtains :," Finally, one obtains :" +We note as an aside au alternative to these phenomenological aud observational merecr rates.,We note as an aside an alternative to these phenomenological and observational merger rates. + 7. have instead considered theoretical caleulatious of the mereer rate of galaxy halos., \citet{Menou01} have instead considered theoretical calculations of the merger rate of galaxy halos. +" They perform Moute Carlo sinulatious of the merger history of halos using scui-analytic methods (so-called ""merger trees”) based on nunierieal simulations aud the Press-Schechter formalism aud its extensions.", They perform Monte Carlo simulations of the merger history of halos using semi-analytic methods (so-called “merger trees”) based on numerical simulations and the Press-Schechter formalism and its extensions. + This allows them to vary the black hole mass function aud its relationship to the wnderlving halo mass function as a function of time., This allows them to vary the black hole mass function and its relationship to the underlying halo mass function as a function of time. + Iu this work. however. they do not consider the detailed gravitational wave spectrum that results from their models.," In this work, however, they do not consider the detailed gravitational wave spectrum that results from their models." + Our model is useful bevond the ullz-plIz regime., Our model is useful beyond the $\mu$ Hz regime. + The LISA satellite will be scusitive to the total eveut rate of MBII binary inspirals as they go through their final coalescence., The LISA satellite will be sensitive to the total event rate of MBH binary inspirals as they go through their final coalescence. + This eveut rate is just fiv(.}d: with »(:) given by equation (15)) or equation (17)).," This event rate is just $\int\nu(z)\;dz$, with $\nu(z)$ given by equation \ref{eq:zrate}) ) or equation \ref{eq:numrate}) )." + We show this quautitv iu Figure 2.., We show this quantity in Figure \ref{fig:totalrate}. + For the models we have been considering. the event rate is 0.011 binary coalescence events per vear.," For the models we have been considering, the event rate is 0.01–1 binary coalescence events per year." + However. only a subset of these events will be detected with sufficiently ligh signal-to-noise for a sufficient leneth of time over the different phases of the MBIT binary merecr to enable anieasureineut of their individual masses aud distances (e.g... 2).," However, only a subset of these events will be detected with sufficiently high signal-to-noise for a sufficient length of time over the different phases of the MBH binary merger to enable ameasurement of their individual masses and distances \citep[e.g.,][]{HughesMN2001}. ." +"of R»100, the trajectory along X and Y is a closed loop, called the limit cycle (Left panel of Figure 1)).","of $R > 100$, the trajectory along $X$ and $Y$ is a closed loop, called the limit cycle (Left panel of Figure \ref{lormap}) )." + For any initial condition the system evolves towards the limit cycle., For any initial condition the system evolves towards the limit cycle. + For intermediate values of R the behavior of the system is more complex., For intermediate values of $R$ the behavior of the system is more complex. +" The right panel of Figure 1 shows the trajectory of X and Y for R—28, where the behavior is termed chaotic, i.e. infinitesimally close trajectories diverge exponentially in time."," The right panel of Figure \ref{lormap} shows the trajectory of $X$ and $Y$ for $R = 28$, where the behavior is termed chaotic, i.e. infinitesimally close trajectories diverge exponentially in time." +" Thus, the Lorenz system can exhibit different types of non-linear behavior."," Thus, the Lorenz system can exhibit different types of non-linear behavior." +" Often, in a natural system, only one of the several parameters can be detected and hence the complete dynamic information is not directly available."," Often, in a natural system, only one of the several parameters can be detected and hence the complete dynamic information is not directly available." +" For example, if only the X variable of the Lorenz was known, then from the time series for R—28 (top systempanel of Figure 2)) and the corresponding power spectrum (bottom panel of Figure 2)), the rich complexity of the Lorenz system is not easily identifiable."," For example, if only the $X$ variable of the Lorenz system was known, then from the time series for $R = 28$ (top panel of Figure \ref{lor_pow}) ) and the corresponding power spectrum (bottom panel of Figure \ref{lor_pow}) ), the rich complexity of the Lorenz system is not easily identifiable." +" However, as discussed in the next section, there are non linear techniques by which the complete (qualitative if not quantitative) dynamic nature of such systems can be reconstructed."," However, as discussed in the next section, there are non linear techniques by which the complete (qualitative if not quantitative) dynamic nature of such systems can be reconstructed." +" One of the standard methods to reconstruct the dynamics of a non-linear system from a time series, is the Delay Embedding Technique (Grassberger&Procaccia1983)."," One of the standard methods to reconstruct the dynamics of a non-linear system from a time series, is the Delay Embedding Technique \citep{Gra83}." +" Since the dimension of the system ( ie. the number of governing equations or variables) is not a priori known, one has to construct the for different dimensions."," Since the dimension of the system ( i.e. the number of governing equations or variables) is not a priori known, one has to construct the dynamics for different dimensions." +" In this technique, vectors of dynamicslength N are created from the time series, X(t), by using a delay time 7, i.e. where is the chosen dimension."," In this technique, vectors of length $N$ are created from the time series, $X(t)$, by using a delay time $\tau$, i.e. where $M$ is the chosen dimension." +" Typically, the delay time T is suitablyM chosen such that the vectors are not correlated ie. when the auto-correlation function of X(t) approaches zero."," Typically, the delay time $\tau$ is suitably chosen such that the vectors are not correlated i.e. when the auto-correlation function of $X(t)$ approaches zero." +" For the Lorenz system, such a technique can effectively reconstruct the dynamics as shown in Figure 3,, where the X(t) is plotted versus X(t+7)."," For the Lorenz system, such a technique can effectively reconstruct the dynamics as shown in Figure \ref{lor_Delay}, where the $X(t)$ is plotted versus $X(t+\tau)$." +" Note the similarity between Figures 3 and 1,, with the identification of X(t+7) with Y."," Note the similarity between Figures \ref{lor_Delay} + and \ref{lormap}, with the identification of $X(t +\tau)$ with $Y$." +" One of the difficulties of this technique is the choice of the delay time, 7, which in principle depends on the specific appropriatenature of the system."," One of the difficulties of this technique is the choice of the appropriate delay time, $\tau$, which in principle depends on the specific nature of the system." +" To avoid this ambiguity, a modified technique has been proposed by Broomhead&King(1986) where, a matrix constructed of vectors with unit delay time, is decomposed into eigenvectors which then represent the dynamics."," To avoid this ambiguity, a modified technique has been proposed by \cite{Bro86} where, a matrix constructed of vectors with unit delay time, is decomposed into eigenvectors which then represent the dynamics." + Application of this Singular Value Decomposition (SVD) technique to the Lorenz system is shown in the top two panels of Figure 4 which is again qualitatively similar to Figure 1..," Application of this Singular Value Decomposition (SVD) technique to the Lorenz system is shown in the top two panels of Figure \ref{svdlor} + which is again qualitatively similar to Figure \ref{lormap}." +" To generate Figure 4,, the time series, X(t) has been converted to a uniform deviate, which is convenient when the analysis is undertaken on data obtained from natural (see next section)."," To generate Figure \ref{svdlor}, the time series, $X(t)$ has been converted to a uniform deviate, which is convenient when the analysis is undertaken on data obtained from natural systems (see next section)." + To confirm that the systemsdynamical picture obtained by the Delay Embedding technique is indeed due to an underlying deterministic non-linear system and not of stochastic, To confirm that the dynamical picture obtained by the Delay Embedding technique is indeed due to an underlying deterministic non-linear system and not of stochastic +svuchrotron emission using the Haslun losMITz map with spectral index 0.9.,"synchrotron emission using the Haslam $408\,{\rm MHz}$ map with spectral index $-0.9$." + The dust was assiuined to have a single 18I& component with emissivitv iudex of 2. together witha correlated frec-free like component of spectral iudex 0.15.," The dust was assumed to have a single $18\,{\rm K}$ component with emissivity index of $2$, together with a correlated free-free like component of spectral index $-0.15$." + Figue 1 shows the input CAIB imap. smoothed at the expected resolution of the recistructec niap. aud the error map. which is the difference of the input CMD map and the recovered one.," Figure \ref{fig2} shows the input CMB map, smoothed at the expected resolution of the reconstructed map, and the error map, which is the difference of the input CMB map and the recovered one." + As 1ο latter shows. the overall reconstruction is excellent. although a ew elitches associated with low ealactic latitude ΤΗΙ clouds are visible close to the Galaxy cut.," As the latter shows, the overall reconstruction is excellent, although a few glitches associated with low galactic latitude HII clouds are visible close to the Galaxy cut." + This justifies the removal of the Caudactic plane frou our analysis., This justifies the removal of the Galactic plane from our analysis. + Figure 2 eives the distribution of the reconstructed errors. whose bulk is well approximated by a Gaussian distribution with an rns of 2] μῖν. Note though the low level wings that are likely associated with the residual iupriut of III clouds.," Figure \ref{fig1} gives the distribution of the reconstructed errors, whose bulk is well approximated by a Gaussian distribution with an rms of 24 $\mu $ K. Note though the low level wings that are likely associated with the residual imprint of HII clouds." + The corresponding pixels would probably have to be dropped out from any custne analysis., The corresponding pixels would probably have to be dropped out from any ensuing analysis. + An important feature of Wiener filtering is that the quality of the instrament is au output of the analvsis., An important feature of Wiener filtering is that the quality of the instrument is an output of the analysis. + The expected resolution of the reconstructed map is thus known directly and can be accounted for iu later stages of the statistical analysis., The expected resolution of the reconstructed map is thus known directly and can be accounted for in later stages of the statistical analysis. + Indeed we used it here to couvolve our input CMD map to the expected resolution of the recovered map., Indeed we used it here to convolve our input CMB map to the expected resolution of the recovered map. + For cosmological purposes. the most ΠΠ statistic is the angular power spectrma of the CAIB.," For cosmological purposes, the most important statistic is the angular power spectrum of the CMB." + We therefore show the power spectrum of the recovered CMD maps together with the spectrmu of the reconstruction error in figure 3.., We therefore show the power spectrum of the recovered CMB maps together with the spectrum of the reconstruction error in figure \ref{fig3}. +with impact parameter 5.. which follows (see subsection 3.3 of Lóppez-Corredoira et al.,"with impact parameter $b_*$, which follows (see subsection 3.3 of Lóppez-Corredoira et al." + 2002a) where y is the angle of deviation of the trajectory due to the interaction as represented in Fig. 9.., 2002a) where $\gamma $ is the angle of deviation of the trajectory due to the interaction as represented in Fig. \ref{Fig:orbit}. + The final velocity with respect to the star will be: with the unit vector as specified in Fig. 9..," The final velocity with respect to the star will be: with the unit vector as specified in Fig. \ref{Fig:orbit}," +" and with respect to the centre of the galaxy: Hence. while the initial. velocity with respect to the centre of the galaxy Is This implies an increment of the energy of the particle An approximation for small interactions (y<< 1). using The particles trapped by the galaxy due to this interaction will be those with AEμη (v, as the velocity of the particle at infinite distance always is): that is. those particles with impact parameter For M.=| Ms. v.=200 km/s (the rotation as the main component). v,=50 km/s. for an average case of aw=—457 and vj;100 km/s. the constraint is 5;«2 A.U. With the typical surface density in the galactic dise of 10—100 star/pe- (Lóppez-Corredoira et al."," and with respect to the centre of the galaxy: Hence, while the initial velocity with respect to the centre of the galaxy is This implies an increment of the energy of the particle An approximation for small interactions $\gamma <<1$ ), using \ref{gamma}) ), The particles trapped by the galaxy due to this interaction will be those with $\Delta E<-\frac{1}{2}mv_\infty ^2$ $v_\infty $ as the velocity of the particle at infinite distance always is); that is, those particles with impact parameter For $M_*=1$ $_\odot $, $v_*=200$ km/s (the rotation as the main component), $v_\infty =50$ km/s, for an average case of $\alpha =-45^\circ $ and $v_{dif}\sim 100$ km/s, the constraint is $b_*<\sim 2$ A.U. With the typical surface density in the galactic disc of $10-100$ $^2$ (Lóppez-Corredoira et al." + 2002b). the probability of a particle having an impact parameter less than 2 AU is ~3—30x107.," 2002b), the probability of a particle having an impact parameter less than 2 AU is $\sim 3-30\times 10^{-9}$." + This is just a rough estimate but the order of magnitude should be more or less correct., This is just a rough estimate but the order of magnitude should be more or less correct. + Therefore. the accretion ratio is much lower than the values of A»oo obtained in. $2.2.. and a much lower accretion (totally negligible) is expected to be produced in terms of the star/particle interaction.," Therefore, the accretion ratio is much lower than the values of $R_{200}$ obtained in \ref{.histogram}, and a much lower accretion (totally negligible) is expected to be produced in terms of the star/particle interaction." + It is not straightforward to check this effect on real galaxies., It is not straightforward to check this effect on real galaxies. + We would need to know the complete history of each galaxy. the epoch of formation of its bar and other characteristics which are not directly available.," We would need to know the complete history of each galaxy, the epoch of formation of its bar and other characteristics which are not directly available." + Nonetheless. we can analyse whether spiral galaxies with a prominent bar have different rotation-curve amplitudes from the same type of galaxies without bar.," Nonetheless, we can analyse whether spiral galaxies with a prominent bar have different rotation-curve amplitudes from the same type of galaxies without bar." + Indeed. this analysis cannot be a definitive proof of the present mechanism because there are other possible alternative explanations in terms of the interaction between halo and bar.," Indeed, this analysis cannot be a definitive proof of the present mechanism because there are other possible alternative explanations in terms of the interaction between halo and bar." + For instance. halos might allow bars to become stronger (Athanassoula Misiriotis 2002: Athanassoula 2002. 2003).," For instance, halos might allow bars to become stronger (Athanassoula Misiriotis 2002; Athanassoula 2002, 2003)." + In any case. the present section might be a first step in the search of this effect.," In any case, the present section might be a first step in the search of this effect." + In order to do this. we use first the data from the Mathewson et al. (," In order to do this, we use first the data from the Mathewson et al. (" +1992) catalogue on rotation curves. which contains data for 1355 spiral galaxies.,"1992) catalogue on rotation curves, which contains data for 1355 spiral galaxies." + We subdivide the sample into 12 groups: morphological type from +3 to +8 (equivalently from Sb to Sd) and each of them with or without bar (either SB/SAB or S/SA: according to the classification in this survey similar to the RC3 catalogue)., We subdivide the sample into 12 groups: morphological type from +3 to +8 (equivalently from Sb to Sd) and each of them with or without bar (either SB/SAB or S/SA; according to the classification in this survey similar to the RC3 catalogue). + This is a rough classification. because indeed most of the spiral galaxies should have a bar to some degree (e.g.. Knapen et al.," This is a rough classification, because indeed most of the spiral galaxies should have a bar to some degree (e.g., Knapen et al." + 2000. Fathi 2004).," 2000, Fathi 2004)." + From Mathewson et al. (, From Mathewson et al. ( +1992). we take the maximum rotatio velocity.,"1992), we take the maximum rotation velocity." +" This catalogue includes data from optical H,, rotatio curves and HI profiles.", This catalogue includes data from optical $_\alpha $ rotation curves and HI profiles. + The results are given in Table |.., The results are given in Table \ref{Tab:mathewson}. + The table. although not conclusive. seems to show larger rotatio velocities for earlier types (for +4. the average rotation velocity of barred galaxies is 2.06 higher than the non-barred galaxies) and vice verse for later types (for +7. the average rotatio velocity of barred galaxies is 1o: lower than the non-barrec galaxies).," The table, although not conclusive, seems to show larger rotation velocities for earlier types (for +4, the average rotation velocity of barred galaxies is $\sigma $ higher than the non-barred galaxies) and vice verse for later types (for +7, the average rotation velocity of barred galaxies is $\sigma $ lower than the non-barred galaxies)." + The first thing might be explained in terms of the mechanisms proposed in this paper: throughout their lifetimes. bars help to acerete matter and this is more remarkable 1 earlier types because the bars are more prominent in. these types.," The first thing might be explained in terms of the mechanisms proposed in this paper: throughout their lifetimes, bars help to accrete matter and this is more remarkable in earlier types because the bars are more prominent in these types." + The hypothesis that halos allow bars to become stronger is also a good possible explanation: indeed. the simulations in Athanassoula Misiriotis (2002) and Athanassoula (2002. 2003) refer only to early-type disc. galaxies. with no or hardly any gas. and this would explain why this effect is not necessarily seen in later types.," The hypothesis that halos allow bars to become stronger is also a good possible explanation; indeed, the simulations in Athanassoula Misiriotis (2002) and Athanassoula (2002, 2003) refer only to early-type disc galaxies, with no or hardly any gas, and this would explain why this effect is not necessarily seen in later types." + The second fact is intriguing: it might have to do with the history of the galaxy. in which these late-type galaxies without bars had one in the past. or with a major role of the spiral arms in non-barred galaxy.," The second fact is intriguing: it might have to do with the history of the galaxy, in which these late-type galaxies without bars had one in the past, or with a major role of the spiral arms in non-barred galaxy." + Also. errors in the classification of the galaxy type could be the cause of," Also, errors in the classification of the galaxy type could be the cause of" +absolute magnitude already noticed by Sollima et al. (,absolute magnitude already noticed by Sollima et al. ( +2007) and Milone et al. (,2007) and Milone et al. ( +2008).,2008). +" For this purpose we correlated. the binary fractions £r and 64,7, with age and visual absolute magnitude and computed. the Spearman's rank and Ixendall's 7 coellicients for the sample of OC's and GC's separately and. for the merged. sample.", For this purpose we correlated the binary fractions $\xi_{F}$ and $\xi_{min}$ with age and visual absolute magnitude and computed the Spearman's rank and Kendall's $\tau$ coefficients for the sample of OCs and GCs separately and for the merged sample. + The results for £; are reported inTable 3., The results for $\xi_{F}$ are reported inTable 3. + In Fig., In Fig. +" 6 he core binary [fractions S£,,;, and S£j are xotted as a function of the clusters age (fo).", \ref{age} the core binary fractions $\xi_{min}$ and $\xi_{F}$ are plotted as a function of the clusters age $t_{9}$ ). + As can be seen. a clear anticorrelation between £ ancl fo is evident. among GCs (as already reported. by Sollima ct al.," As can be seen, a clear anticorrelation between $\xi$ and $t_{9}$ is evident among GCs (as already reported by Sollima et al." + 2007)., 2007). + Both correlation tests indicates indeed high probabilities within he GCs sample., Both correlation tests indicates indeed high probabilities within the GCs sample. + OC's. which are sistematically vounger han GCs. have on average higher fraction. of binarics.," OCs, which are sistematically younger than GCs, have on average higher fraction of binaries." + revertheless. within the sample of OC's analvsed here. the raction of binaries seems to be rather independent on age. as indicated by the performed statistical tests.," Nevertheless, within the sample of OCs analysed here, the fraction of binaries seems to be rather independent on age, as indicated by the performed statistical tests." + Unfortunately. he large errors on the measured binary fractions in OC's make cdillicult any firm conclusion on this issue.," Unfortunately, the large errors on the measured binary fractions in OCs make difficult any firm conclusion on this issue." + In ., In Fig. +" 7 the core binary fractions £,,;, and £; are plotted. as a function. of the clusters visual absolute magnitude CV).", \ref{mv} the core binary fractions $\xi_{min}$ and $\xi_{F}$ are plotted as a function of the clusters visual absolute magnitude $M_{V}$ ). + This quantity represents the observational counterpart of the cluster. mass., This quantity represents the observational counterpart of the cluster mass. + In this case. à nice correlation is visible among both GC's and OC's.," In this case, a nice correlation is visible among both GCs and OCs." + According to the two performed. statistical tests. such a correlation seems to be significant in the OC's sample and in the same direction for both OC's and GC's samples.," According to the two performed statistical tests, such a correlation seems to be significant in the OCs sample and in the same direction for both OCs and GCs samples." + Phe statistical significances of the Spearman's rank ancl Wendall’s tau correlation tests on the merged sample are and respectively.," The statistical significances of the Spearman's rank and Kendall's tau correlation tests on the merged sample are and, respectively." + We adopted the same procedure to test the correlations with other general ancl structural parameters. (metallicity. concentration. central density. core radius. ecc.).," We adopted the same procedure to test the correlations with other general and structural parameters (metallicity, concentration, central density, core radius, ecc.)." +" No other significant. corrclators with £r. or £,,;;, have been found among these parameters.", No other significant correlators with $\xi_{F}$ or $\xi_{min}$ have been found among these parameters. + Summoarizing. the above analysis indicates that the mass seenis to be a good correlator with the binary fraction in both type of stellar systems.," Summarizing, the above analysis indicates that the mass seems to be a good correlator with the binary fraction in both type of stellar systems." + A possible dependence of the binary [raction on age cannot be excluded., A possible dependence of the binary fraction on age cannot be excluded. + In this paper we analysed the core binary population of five Galactic OCs with the aim of studying their frequency. in stellar svstems., In this paper we analysed the core binary population of five Galactic OCs with the aim of studying their frequency in stellar systems. + In all the analysed clusters the minimum binary fraction contained within one core radius is greater than 114..., In all the analysed clusters the minimum binary fraction contained within one core radius is greater than . + This, This +"six sources varied by a factor of 2 or greater, two sources increasing, four decreasing (Fig. 3)).","six sources varied by a factor of 2 or greater, two sources increasing, four decreasing (Fig. \ref{fluxdist}) )." +" The two that increased were: 8.139+0.226, which had an MX flux density twice that of the survey cube flux density; and 10.724-0.334, which had an MX peak flux density three times the survey cube value."," The two that increased were: 8.139+0.226, which had an MX flux density twice that of the survey cube flux density; and 10.724-0.334, which had an MX peak flux density three times the survey cube value." + 'The four sources which significantly decreased consisted of two with reduced emission and two which disappeared below the detection threshold of the survey., The four sources which significantly decreased consisted of two with reduced emission and two which disappeared below the detection threshold of the survey. + Both 10.822-0.103 and 12.904-0.031 decreased their emission by a factor of 22 (0.9 to 0.3 Jy and 40 to 20 Jy respectively)., Both 10.822-0.103 and 12.904-0.031 decreased their emission by a factor of $\ge$ 2 (0.9 to 0.3 Jy and 40 to 20 Jy respectively). + The two sources which dropped below our detection threshold represent ideal candidates for variability studies., The two sources which dropped below our detection threshold represent ideal candidates for variability studies. +" The first was the new source 14.230-0.509, which had four epochs of observations: it was seen in the survey cube (2007 August) at 3.62 Jy (3 channels > 2 Jy) then subsequently not seen with the ATCA in 2008 October, before being seen again in 2009 January with the ATCA at 1.4 Jy and then not seen again in 2009 March in an MX observation with Parkes."," The first was the new source 14.230-0.509, which had four epochs of observations: it was seen in the survey cube (2007 August) at 3.62 Jy (3 channels $>$ 2 Jy) then subsequently not seen with the ATCA in 2008 October, before being seen again in 2009 January with the ATCA at 1.4 Jy and then not seen again in 2009 March in an MX observation with Parkes." +" The second was the new source 15.607-0.255, also with four epochs of observations: it was seen in the survey cube data (2007 August) at 0.85 Jy, then reduced to 0.43 Jy in the 2008 March MX before being undetectable in the 2008 August MX (i.e. «0.2 Jy) then rising again to ~0.4 Jy in the ATCA observation in 2008 October."," The second was the new source 15.607-0.255, also with four epochs of observations: it was seen in the survey cube data (2007 August) at 0.85 Jy, then reduced to 0.43 Jy in the 2008 March MX before being undetectable in the 2008 August MX (i.e. $<$ 0.2 Jy) then rising again to $\sim$ 0.4 Jy in the ATCA observation in 2008 October." +" In addition to those already mentioned, a further seven sources within longitudes 6? to 20? are known to be variable (and are individually noted in Section ??))."," In addition to those already mentioned, a further seven sources within longitudes $^{\circ}$ to $^{\circ}$ are known to be variable (and are individually noted in Section \ref{srcnotes}) )." +" Of special note 9.621+0.196 has been shown to periodically flare every 244 days (??),, with possible coincident variability in the magnetic field (?).."," Of special note 9.621+0.196 has been shown to periodically flare every 244 days \citep{goedhart04, walt09}, , with possible coincident variability in the magnetic field \citep{vlemmings09}." +" Our survey cube observations were taken 2007 July 8, MJD 54289.5, lying within the rise of the flare (7) with the maser having a peak flux density of ~5200 Jy."," Our survey cube observations were taken 2007 July 8, MJD 54289.5, lying within the rise of the flare \citep{walt09} with the maser having a peak flux density of $\sim$ 5200 Jy." +" The MX observation was taken 2008 March 17, MJD 54542.5, lying within the rise of the subsequent flare, i.e. separated by approximately a full period from the original observation, again with a peak flux density of ~5200 Jy."," The MX observation was taken 2008 March 17, MJD 54542.5, lying within the rise of the subsequent flare, i.e. separated by approximately a full period from the original observation, again with a peak flux density of $\sim$ 5200 Jy." +" 12.889+0.489 has also been shown to have a periodic flare, with a period of 29.5 days (??).."," 12.889+0.489 has also been shown to have a periodic flare, with a period of 29.5 days \citep{goedhart04, goedhart09}." +" Our survey cube observation was made 2007 August 26, MJD 54338.5, measuring a peak flux density of 79 Jy for the ss! feature."," Our survey cube observation was made 2007 August 26, MJD 54338.5, measuring a peak flux density of 79 Jy for the $^{-1}$ feature." +" Assuming the 29.5 day period and the time series of ?,, our survey cube observation is likely to lie in the declining part of a flare."," Assuming the 29.5 day period and the time series of \citet{goedhart09}, our survey cube observation is likely to lie in the declining part of a flare." +" Our MX observation was made 2008 March 17, MJD 54917.5, measuring a peak flux density of 69 Jy for the same feature."," Our MX observation was made 2008 March 17, MJD 54917.5, measuring a peak flux density of 69 Jy for the same feature." + According to the time series of ? this would place it on the rise of a flare., According to the time series of \citet{goedhart09} this would place it on the rise of a flare. +" Figure 1 shows that the spectra of the masers comprise many narrow spectral features with individual widths often as small as ~0.3kkmss~', spread over a range of velocities."," Figure \ref{spectra} shows that the spectra of the masers comprise many narrow spectral features with individual widths often as small as $\sim$ $^{-1}$, spread over a range of velocities." + The total velocity spread in an individual source is dependent on the sensitivity of the observation and can also change as a result of intrinsicvariability of the components, The total velocity spread in an individual source is dependent on the sensitivity of the observation and can also change as a result of intrinsicvariability of the components +μυ. |DEOL 0., + =0. + ]t is straightforward to see that here we find two distinct solutions: a) when £7fies=0. case in which such mode propagates along standard. null. geodesics. and b) when ἀπο=\.," It is straightforward to see that here we find two distinct solutions: a) when $F^{\alpha\beta} f_{\alpha\beta}=0$, case in which such mode propagates along standard null geodesics, and b) when $F^{\alpha\beta} f_{\alpha\beta}=\chi$." + In the case in which X does not vanish we obtain from equations (5)) and. (7)). the propagation equation for the field discontinuities being given by (Novello et al.," In the case in which $\chi$ does not vanish we obtain from equations \ref{j1}) ) and \ref{j2}) ), the propagation equation for the field discontinuities being given by (Novello et al." + 2004) Ξ ιν, 2004) = 0. +"0 This equation proves that photons propagate Following a geodesic that is not that one of the background space-time described by gf"".", This equation proves that photons propagate following a geodesic that is not that one of the background space-time described by $g^{\mu\nu}$. + Rather. they follow the given by Lq.(S)).," Rather, they follow the given by \ref{63}) )." +" lf one now takes the ae"" derivative of this expression. we can casily obtain (Mosquera Cuesta. de Freitas Pacheco and Salim 2006: Mosquera Cuesta and Salim 2004. Mosquera Cuesta and Salim POOLA) eun2"," If one now takes the $x^a$ derivative of this expression, we can easily obtain (Mosquera Cuesta, de Freitas Pacheco and Salim 2006; Mosquera Cuesta and Salim 2004, Mosquera Cuesta and Salim 2004A) = 4." +13m This expression shows that the nonlincar Lagrangian introduces a term acting as ai [force that accelerates the photon along its path., This expression shows that the nonlinear Lagrangian introduces a term acting as a force that accelerates the photon along its path. + Lt is therefore essential to investigate what are the effects of this peculiar prediction., It is therefore essential to investigate what are the effects of this peculiar prediction. + The occurrence. of this phenomenon over. cosmological distance scales may have a nonneeligible ellect on. the physical properties that are abseribecl to a given source from its astronomical observables., The occurrence of this phenomenon over cosmological distance scales may have a nonnegligible effect on the physical properties that are abscribed to a given source from its astronomical observables. + One example. of this is the cosmological redshift’ (Mosquera. Cuesta. Salim and Novello 2007).," One example of this is the cosmological redshift (Mosquera Cuesta, Salim and Novello 2007)." + Since the photon ought to travel very long distances from cosmic sources until be detected on Earth. then its interaction with the background intergalactic electromagnetic fields should modify the putative (nominal) value of the redshift. or equivalentIy. the actual Iuminosity istance. associated to its emitting source. compared to the proper distance. computed. in a standard. fashion. in 10 context of a particular cosmology.," Since the photon ought to travel very long distances from cosmic sources until be detected on Earth, then its interaction with the background intergalactic electromagnetic fields should modify the putative (nominal) value of the redshift, or equivalently, the actual luminosity distance, associated to its emitting source, compared to the proper distance computed in a standard fashion in the context of a particular cosmology." + In similar lines. we garow next that in the case of EAI radiation coming from [ar distance radio-galaxies and quasars the interaction of the photon with local intergalactic background: LAL fields may significantly modify the actual position of a particular isorption line. from which a potential variation of à can be estimated.," In similar lines, we show next that in the case of EM radiation coming from far distance radio-galaxies and quasars the interaction of the photon with local intergalactic background EM fields may significantly modify the actual position of a particular absorption line, from which a potential variation of $\alpha$ can be estimated." + In this way. an observer on Earth is prone to sav that effectively a has changed for this particular observation.," In this way, an observer on Earth is prone to say that effectively $\alpha$ has changed for this particular observation." + Jut. how exactly does it change?," But, how exactly does it change?" + ln order to investigate whether the photon nonlinear interaction with background fields over large distances docs allect the position of absorption lines. next we present the Lagrangian formulation of this NLIED theory.," In order to investigate whether the photon nonlinear interaction with background fields over large distances does affect the position of absorption lines, next we present the Lagrangian formulation of this NLED theory." +When the wave amplitude approaches the maximal one. the shock formation time goes to zero: at small amplitudes. fy grows as Léa 11).fw.,"When the wave amplitude approaches the maximal one, the shock formation time goes to zero; at small amplitudes, $t_0$ grows as $1/\alpha$ 1)." + Now let us consider the racial low., Now let us consider the radial flow. + In this case the governing equations are written as ∐⇂⋅∪∐∪∖∖⋎⊳∖⇂⋅↓⋅∪⊔↓∣⊲⇀⊲⊏↥⊳∖⊳↿∖∆∖↓⊳↓∶⊰⊳⇀∖↓⊳↓≟⊐↿↓⋯↿∪⊔⋖⊾≼∼⋜⋯↓≻↓⋅⋖⋅⊳∖∢⊾↓∐ the magnetic field as where 6=const.," In this case the governing equations are written as It follows from Eqs.(A1.13, A1.14) that one can present the magnetic field as where $b=\it const$." + IE the [ow is cold. we=na. I5es.CX1.13. ALS. ALG) reduce to Eqs. (," If the flow is cold, $w=nm$, Eqs.(A1.13, A1.15, A1.16) reduce to Eqs. (" +ALL. X12. 1.3) by substitution no=n7.,"A1.1, A1.2, A1.3) by substitution $\widetilde n=nR^2$." + Therefore the above estimate of the shock formation time remains valid. also for the raclial low., Therefore the above estimate of the shock formation time remains valid also for the radial flow. + Let us show that for small amplitude waves. one can separate the energy and momentum of the wave ancl the flow without considering specific waveforms.," Let us show that for small amplitude waves, one can separate the energy and momentum of the wave and the flow without considering specific waveforms." + Let us define the average plasma density. νι ancl velocity. e; by the relations where the angular brackets denote averaging over the wave period.," Let us define the average plasma density, $ +n_*$, and velocity, $v_*$, by the relations where the angular brackets denote averaging over the wave period." + With such a delinition. there is no mass [lux associated with the wave.," With such a definition, there is no mass flux associated with the wave." + The total οποιον and momentum densities are (see Eeq-(ALA-AL.6)) Averaging this values. one can present them as a superposition of a flow part dependent only on average plasma parameters and a wave part dependent on the wave amplitude.," The total energy and momentum densities are (see Eq.(A1.4-A1.6)) Averaging this values, one can present them as a superposition of a flow part dependent only on average plasma parameters and a wave part dependent on the wave amplitude." + Calculations are simplified in the frame where plasma is at rest in average. ry=0.," Calculations are simplified in the frame where plasma is at rest in average, $v_*=0$." + Ina small amplitude wave. the energy. ancl momentunm are of the second. order in the wave amplitude therefore linear relations. like (see I5.CXI.8)) may be used only in the second order terms.," In a small amplitude wave, the energy and momentum are of the second order in the wave amplitude therefore linear relations, like (see Eq.(A1.8)) may be used only in the second order terms." + The average of the first. order terms may be expressed. via the second. order terms expanding Iqs.CX2.1. 2.2) in de ," The average of the first order terms may be expressed via the second order terms expanding Eqs.(A2.1, A2.2) in $\delta v$ " +higher than90%.. while we expected to find only 1.4d1.1 false orbits under the assumption that no real orbits are present.,"higher than, while we expected to find only $1.4 \pm 1.1$ false orbits under the assumption that no real orbits are present." + This suggests that most of them are real., This suggests that most of them are real. + Similarly. we [ind six orbits with significance higher than95%.. while we expected only 0.7d0.8 [false orbits.," Similarly, we find six orbits with significance higher than, while we expected only $0.7 \pm 0.8$ false orbits." + This again suggested that most of these orbits are real., This again suggested that most of these orbits are real. + Further support to this suggestion can be found in the fact that all (he corresponding orbital inclinations. except one. are large. as opposed to the ones of Table 3.," Further support to this suggestion can be found in the fact that all the corresponding orbital inclinations, except one, are large, as opposed to the ones of Table 3." + This is not a surprise., This is not a surprise. + The stellar reflex motion caused by a brown clwarl is mach larger than the one caused by a planet., The stellar reflex motion caused by a brown dwarf is much larger than the one caused by a planet. + Therefore (he minimum semi-major axes. αxsin. ol the brown-dwarf candidates ave closer to the threshold of the Hipparcos detection.," Therefore the minimum semi-major axes, $a\times \sin i$, of the brown-dwarf candidates are closer to the threshold of the Hipparcos detection." + This is reflected. for example. by the fact that out of the 14 brown-dwarl candidate svstems only (wo svstems. wilh short orbital periods. have exsin’ smaller (han 0.1 mcs. while the planets have 34 such orbits out of 47 svstems.," This is reflected, for example, by the fact that out of the 14 brown-dwarf candidate systems only two systems, with short orbital periods, have $a\times +\sin i$ smaller than 0.1 $mas$, while the planets have 34 such orbits out of 47 systems." + Only one of these two brown-dwarl svstems. ILD 37330. was found to have an astrometric orbit with a significance higher than90%.," Only one of these two brown-dwarf systems, HD 87330, was found to have an astrometric orbit with a significance higher than." +. Here again the inclination is suspiciously verv small., Here again the inclination is suspiciously very small. + We therefore suspect that this is a false orbit., We therefore suspect that this is a false orbit. + Alter all we expect 1.4d1.1 svstems to show such false orbits.," After all we expect $1.4 +\pm 1.1$ systems to show such false orbits." + All the significant orbits of the brown-dwarl candidates vielded secondary masses that rendered (he secondary a stellar object., All the significant orbits of the brown-dwarf candidates yielded secondary masses that rendered the secondary a stellar object. + This fact was pointed out already. by Halbwachs οἱ ((2000). who analvzed six of the eight svstems of Table 6. and got very similar results for the secondary masses.," This fact was pointed out already by Halbwachs et (2000), who analyzed six of the eight systems of Table 6, and got very similar results for the secondary masses." + Halbwachs et ((2000) analvzed another five of the brown-cdwarl candidates. which we find their orbit insignificant.," Halbwachs et (2000) analyzed another five of the brown-dwarf candidates, which we find their orbit insignificant." + Although Lalbwachs et ((2000) did nol eive explicitly the significance of (their finding. their derived large uncertainty and the following discussion leave no doubt Chat these orbits are insignificant.," Although Halbwachs et (2000) did not give explicitly the significance of their finding, their derived large uncertainty and the following discussion leave no doubt that these orbits are insignificant." + So. we agree on these five svstenis as well.," So, we agree on these five systems as well." + Note that (hese live svstems include IID 114762. which we still considered a planet.," Note that these five systems include HD 114762, which we still considered a planet." +candidate. In the sample we analyzed we still had six svstems (hat could still be brown-dwarf secondaries., In the sample we analyzed we still had six systems that could still be brown-dwarf secondaries. + To summarize. we [ind no disguised low-mass stellar companions within (he sample of 47 stars that harbor planet companions. while we find 68 such stellar companions in a sample of 14 stars with brown-dwarl candidates.," To summarize, we find no disguised low-mass stellar companions within the sample of 47 stars that harbor planet companions, while we find 6–8 such stellar companions in a sample of 14 stars with brown-dwarf candidates." + The frequency of unknown stellar companions detected as planet candidates depends on the selection of the sample from which the planets are searclied., The frequency of unknown low-mass stellar companions detected as planet candidates depends on the selection of the sample from which the planets are searched. +. Apparently. the planet hunters awoided any known spectroscopic binaries in (their sample. relving on previous lower precision raclial-velocity searches.," Apparently, the planet hunters avoided any known spectroscopic binaries in their sample, relying on previous lower precision radial-velocity searches." + Obviously. some M-star secondaries could have avoided previous detection.," Obviously, some M-star secondaries could have avoided previous detection." + llowever. such binaries must have extremely small inclination angles in order to be erroneously identified as planets.," However, such binaries must have extremely small inclination angles in order to be erroneously identified as planets." + This is why we do not find any such case., This is why we do not find any such case. + On the other hand. even moderate inclinations could turn binaries with stellar secondaries into brown-dwarl candidates.," On the other hand, even moderate inclinations could turn binaries with stellar low-mass secondaries into brown-dwarf candidates." + This is why we find relatively many stellar, This is why we find relatively many stellar +some pulsar models. it is not obvious how that would be accelerated in an oscillating model.,"some pulsar models, it is not obvious how that would be accelerated in an oscillating model." + We conclude that LAE in à LAEW is not a plausible candidate for gamma-ray emission in pulsars., We conclude that LAE in a LAEW is not a plausible candidate for gamma-ray emission in pulsars. + For the photons associated with LAE to produce pairs. their enerey must exceed an MeV. The estimate of a maximum energv of of several tens of kilovolts is sufliciently close to (his threshold to require a more detailed discussion.," For the photons associated with LAE to produce pairs, their energy must exceed an MeV. The estimate of a maximum energy of of several tens of kilovolts is sufficiently close to this threshold to require a more detailed discussion." + Before considering (his. it is relevant (o consider the power in LAE.," Before considering this, it is relevant to consider the power in LAE." + For LAE to be important in generating pairs. (he power in LAE must be a significant Iraction of the total power involved.," For LAE to be important in generating pairs, the power in LAE must be a significant fraction of the total power involved." + It is reasonable to assume that in an oscillating model. (he power released (rom rotational enerey [ον ordinary. pulsars. ancl [rom magnetic energv for magnetars) is Channeled through LAEWs.," It is reasonable to assume that in an oscillating model, the power released (from rotational energy for ordinary pulsars, and from magnetic energy for magnetars) is channeled through LAEWs." + The transfer of energy from the LAEW to pairs through LAE may be regarded as a dissipation process for the LAEW., The transfer of energy from the LAEW to pairs through LAE may be regarded as a dissipation process for the LAEW. + For LAE to be important in generating pairs. not only must its lrequency exceed an MeV but also the LAEW must lose a substantial fraction of its energv to LAE before propagating out of the light cvlinder.," For LAE to be important in generating pairs, not only must its frequency exceed an MeV but also the LAEW must lose a substantial fraction of its energy to LAE before propagating out of the light cylinder." + The damping rate of the LAEW due to LAE maw be estimated by multiplving the power in LAE per particle bv the number of particles. and dividing bv the energy in the LAEW.," The damping rate of the LAEW due to LAE may be estimated by multiplying the power in LAE per particle by the number of particles, and dividing by the energy in the LAEW." + The power per unit volume lollows from the power per background particle. given by (23.4)). times the number density of background particles. 7 sav.," The power per unit volume follows from the power per background particle, given by \ref{Larmor5}) ), times the number density of background particles, ${\bar n}$ say." + Ignoring Iactors οἱ orcler unitv. (he damping rate due to LAE is of order E2zopne. where σ is the Thomson cross section.," Ignoring factors of order unity, the damping rate due to LAE is of order $\Gamma\approx\sigma_T\,{\bar n}c$, where $\sigma_T$ is the Thomson cross section." + The number density determines (he plasma frequency. which is identified as Os (Levinsonοἱal.2005).," The number density determines the plasma frequency, which is identified as $\Omega\gamma_{\rm max}^{1/2}$ \citep{letal05}." +. It follows that the damping decrement. ΓΩ. is of order (ή)ο)μις. where ry is the classical radius of the electron.," It follows that the damping decrement, $\Gamma/\Omega$, is of order $(r_0\Omega/c)\gamma_{\rm max}$, where $r_0$ is the classical radius of the electron." + LAE is important energetically provided that the LAEW remains within the magnetosphere for ~O/T wave periods., LAE is important energetically provided that the LAEW remains within the magnetosphere for $\sim\Omega/\Gamma$ wave periods. +"For star IV we recover the input abundances without any significant offsets, which indicates that for stars with inclination angles >7° we can recover the ‘real’ abundances.","For star IV we recover the input abundances without any significant offsets, which indicates that for stars with inclination angles $> 7^{\circ}$ we can recover the `real' abundances." +" According to Takedaetal.(2008) the inclination angle of Vega is ~7°, in which case we would be able to recover the ‘real’ abundances for this star."," According to \citet{takeda2008} the inclination angle of Vega is $\sim 7^{\circ}$, in which case we would be able to recover the `real' abundances for this star." +" Computations of star IV, with the abundances we obtained for Vega confirm this (see Fig. 7))."," Computations of star IV, with the abundances we obtained for Vega confirm this (see Fig. \ref{abunrottestvega}) )." +" Yoonetal.(2008) used a model for Vega with an inclination angle of 4.54?, which is closer to our test star III."," \citet{yoon2008} used a model for Vega with an inclination angle of $^{\circ}$, which is closer to our test star III." +" They mention that assigning a single abundance and Emicro for all lines of an element with low ionisation and excitation potentials, such as Fe I, is inadequate, because these elements are dominated by the contribution from the equatorial region causing a double-horned shape in the spectral lines."," They mention that assigning a single abundance and $\xi_{micro}$ for all lines of an element with low ionisation and excitation potentials, such as Fe I, is inadequate, because these elements are dominated by the contribution from the equatorial region causing a double-horned shape in the spectral lines." + A single abundance value for each element is however assumed in our procedure., A single abundance value for each element is however assumed in our procedure. +" To further investigate this, we study the distribution of the iron abundances fitted for different spectral regions."," To further investigate this, we study the distribution of the iron abundances fitted for different spectral regions." + The distributions for all four test stars are shown in Fig. 8.., The distributions for all four test stars are shown in Fig. \ref{Fedist}. +" Clearly, star III with the lowest inclination angle has a bimodal distribution and thus the average of the abundance is incorrect for most lines, confirming the findings of Yoonetal.(2008)."," Clearly, star III with the lowest inclination angle has a bimodal distribution and thus the average of the abundance is incorrect for most lines, confirming the findings of \citet{yoon2008}." +. The bimodal effect is already much less pronounced in star IV with an inclination angle of 7.4°., The bimodal effect is already much less pronounced in star IV with an inclination angle of $^{\circ}$. + The distributions of the slowly rotating stars I and II are more symmetric and better centred., The distributions of the slowly rotating stars I and II are more symmetric and better centred. +" In this work, we presented a semi-automatic procedure developed to determine stellar parameters and abundances of elements from helium to mercury for A- and F-type stars."," In this work, we presented a semi-automatic procedure developed to determine stellar parameters and abundances of elements from helium to mercury for A- and F-type stars." + We performed various tests with this stand-alone procedure on synthetic spectra which had a resolving power of 0000 and a wavelength range of 4000-7000À.., We performed various tests with this stand-alone procedure on synthetic spectra which had a resolving power of 000 and a wavelength range of 4000-7000. + Most abundance analyses are applied to a well-observed object like the Sun to verify and demonstrate its performance and dependability., Most abundance analyses are applied to a well-observed object like the Sun to verify and demonstrate its performance and dependability. + In this study we investigate the accuracy of our analyses on synthetic test spectra., In this study we investigate the accuracy of our analyses on synthetic test spectra. +" The main advantage of this is that we can perform the abundance analysis with correct stellar parameters, i.e., the known Teg, log g and vsini for which the test spectrum is computed and use similar log gf values for the ""observation"" as well as for the computations."," The main advantage of this is that we can perform the abundance analysis with correct stellar parameters, i.e., the known $_{\rm eff}$ , $\log$ g and $\upsilon \sin i$ for which the test spectrum is computed and use similar $\log$ gf values for the ""observation"" as well as for the computations." + This approach allows us to test the influence of erroneous stellar parameters on the abundance determination., This approach allows us to test the influence of erroneous stellar parameters on the abundance determination. +" From the analyses of these test spectra, we can conclude that we are able to obtain abundances which are consistent with the input values, within the errors."," From the analyses of these test spectra, we can conclude that we are able to obtain abundances which are consistent with the input values, within the errors." +" When ""reasonable"" changes (ie. changes due to reasonable observational errors) of the stellar parameters are considered, we show that the variance in the resulting abundances is smaller than the difference between the input and the computed values."," When ""reasonable"" changes (i.e. changes due to reasonable observational errors) of the stellar parameters are considered, we show that the variance in the resulting abundances is smaller than the difference between the input and the computed values." +" From this, we conclude that stellar parameters which have a reasonable offset from their ‘real’ values have only minor influence on the abundance determination."," From this, we conclude that stellar parameters which have a reasonable offset from their `real' values have only minor influence on the abundance determination." +" Our method is also tested on an observed spectrum of Vega, which is a fast rotator seen nearly pole-on, and compared with previous studies."," Our method is also tested on an observed spectrum of Vega, which is a fast rotator seen nearly pole-on, and compared with previous studies." + The published results for Vega show that there are rather large differences between the abundances from different studies., The published results for Vega show that there are rather large differences between the abundances from different studies. + Our results are in good agreement with the abundances found by Erspamer&North(2002b) who used data obtained with the same instrument., Our results are in good agreement with the abundances found by \citet{erspamer2002} who used data obtained with the same instrument. +" Although we see only a small fraction of fast-rotating stars nearly pole-on, we might encounter one or more of them."," Although we see only a small fraction of fast-rotating stars nearly pole-on, we might encounter one or more of them." + We investigated this effect by simulating spectra which include fast rotation seen nearly pole-on., We investigated this effect by simulating spectra which include fast rotation seen nearly pole-on. +" The computed abundances for the test star with an inclination angle of =4° are offset from the input values, while this offset is negligible at an inclination angle of 7°."," The computed abundances for the test star with an inclination angle of $\approx 4 ^{\circ}$ are offset from the input values, while this offset is negligible at an inclination angle of $^{\circ}$." + This is also reflected in the bimodal distribution of the iron abundances obtained in different regions of the spectrum., This is also reflected in the bimodal distribution of the iron abundances obtained in different regions of the spectrum. + This bimodal behaviour is likely due to the fact that lines with lower excitation potentials are more influenced by the rapidly rotating equatorial regions than lines with higher excitation potentials., This bimodal behaviour is likely due to the fact that lines with lower excitation potentials are more influenced by the rapidly rotating equatorial regions than lines with higher excitation potentials. + For stars with an inclination angle of >7° the offsets from the input values are negligible and also thedistribution of iron abundances obtained for different spectral regions is almost single-peaked., For stars with an inclination angle of $\ge 7^{\circ}$ the offsets from the input values are negligible and also thedistribution of iron abundances obtained for different spectral regions is almost single-peaked. +star clusters along the edges of the radio lobes (AleNamara et al.,star clusters along the edges of the radio lobes (McNamara et al. + 19962)., 1996a). + In the radio triggered nunoclel. the radio jets collect. pre-existent cold clouds along he edge lobes creating a gas overdensity which triggers or enhancesformation.. which is located in the few central kpe of theIow.. where the jets are confined to.," In the radio triggered model, the radio jets collect pre-existent cold clouds along the edge lobes creating a gas overdensity which triggers or enhances, which is located in the few central kpc of the, where the jets are confined to." + By contrast. in our model. the ooccurs during the process of formation of cold clouds from. »erturbations arising from the hot phase of theIow.. out massive iis allowed. only in the central region of theIow.," By contrast, in our model, the occurs during the process of formation of cold clouds from perturbations arising from the hot phase of the, but massive is allowed only in the central region of the." +. Within the classification scheme of AleNamara (1997).uu[or due structures in cooling Hows. the amorphous tvpoe. encompasses most of the objects and which shows no obvious association with radio sources. could be explained by the model presented in this paper.," Within the classification scheme of McNamara (1997) for blue structures in cooling flows, the amorphous type, which encompasses most of the objects and which shows no obvious association with radio sources, could be explained by the model presented in this paper." + We thank an anonymous referee. for comments which ereatly improved. the presentation of the results. of this paper., We thank an anonymous referee for comments which greatly improved the presentation of the results of this paper. + A.C.S.EF. acknowledges partial support. from. the jMazilian agency. CNPq., A.C.S.F. acknowledges partial support from the Brazilian agency CNPq. + A.C.S.F. ancl LC. acknowledge partial support from the Brazilian Ministry. of Science and Technology through the program PRONEN/FINED., A.C.S.F. and L.C.J. acknowledge partial support from the Brazilian Ministry of Science and Technology through the program PRONEX/FINEP. +shows cuts of the density (continuous line) and temperature (dashed line) along the radius at +zzOOO AU. corresponding to the blob position 40 years since the beginning of the jet/ambiert interaction: the hot (few millions degrees) aad dense blob ts evident for +<10 AU.,"shows cuts of the density (continuous line) and temperature (dashed line) along the radius at $z\approx5000$ AU, corresponding to the blob position 40 years since the beginning of the jet/ambient interaction: the hot (few millions degrees) and dense blob is evident for $r<10$ AU." + The density decreases moving away from the Jet axis along the radial direction ar then. it ηcreases again at the position corresponding to the external part of the cocoon.," The density decreases moving away from the jet axis along the radial direction and, then, it increases again at the position corresponding to the external part of the cocoon." + On the other hand. the temperature monotonously decreases. moving away from the jet axis along the radial direction.," On the other hand, the temperature monotonously decreases, moving away from the jet axis along the radial direction." + The blob. therefore. is expected to be an X-ray source: in. Sect. 3.4.2..," The blob, therefore, is expected to be an X-ray source; in Sect. \ref{Spectral analysis}," + we will show that the X-ray source has luminosity and spectral characteristics consistent with those observed., we will show that the X-ray source has luminosity and spectral characteristics consistent with those observed. + The central panel in Fig., The central panel in Fig. + 3 shows 2-D sections in the (i.1) plane of the mass density and temperature cistributions for the best-fit equal-density model (see Tab. 3)).," \ref{fig:mappe-20yr} shows 2-D sections in the $(r,z)$ plane of the mass density and temperature distributions for the best-fit equal-density model (see Tab. \ref{tab_mod}) )." + The iinteraction between the protostellar jet and the ambient meditm causes the presence of a dense and hot cocoon (0)--~Ll1 mDei T~2\10° K) surrounding the jet.," The interaction between the protostellar jet and the ambient medium causes the presence of a dense and hot cocoon $n\approx1400$ $^{-3}$; $T\approx2\times +10^ {6}$ K) surrounding the jet." + Once again the cocoon is almost uniform for the preserce of the thernal conduction but its temperature decreases with time., Once again the cocoon is almost uniform for the presence of the thermal conduction but its temperature decreases with time. + The cocoor becomes gradually cool and dense with time as in the light-jet case., The cocoon becomes gradually cool and dense with time as in the light-jet case. + Also in this case. the post-shock regio nis a hot and dense blob from which the X-ray emission originates (see Sect.," Also in this case, the post-shock region is a hot and dense blob from which the X-ray emission originates (see Sect." + 3.4.1. for more details).," \ref{Spatial distribution of X-ray +emission} for more details)." + In the heavy-jet case (lower panel in Fig. 43 3)).," In the heavy-jet case (lower panel in Fig. \ref{fig:mappe-20yr}) )," + the jet is surrounded by a cocoon well smoothed by the effects of the thermal conduction and with a radial extension larger than in, the jet is surrounded by a cocoon well smoothed by the effects of the thermal conduction and with a radial extension larger than in +stars (Scliwarzschild Harrin 1965) 1esults from nuclear burning being uuable to raise the overlying hydrogen envelope sulliciently to extinguish tle reactions.,stars (Schwarzschild Härrm 1965) results from nuclear burning being unable to raise the overlying hydrogen envelope sufficiently to extinguish the reactions. + A drastic temperature rise at near constant. pressure eusues., A drastic temperature rise at near constant pressure ensues. + Shortly after reaching its peak temperature. owever. the material does expand aud cool on a rapid ünescale.," Shortly after reaching its peak temperature, however, the material does expand and cool on a rapid timescale." + Note that in contrast to the neutro star example. the layer of [uel in the thin shell helium lash is located inside a star rather than ou he surface of a star.," Note that in contrast to the neutron star example, the layer of fuel in the thin shell helium flash is located inside a star rather than on the surface of a star." + We will focus on a single mocel ol a helium shell flash. namely. tlie M. 1ΟΝ core ola Y ML. star studied by Iben (1977).," We will focus on a single model of a helium shell flash, namely, the M $\sim +1.0 {\rm M}_{\odot}$ core of a 7 $_{\odot}$ star studied by Iben (1977)." + Other uodels tested give qualitatively similar resus., Other models tested give qualitatively similar results. +" Typical shell radii. densities and temperatures at he onset of this thin shell helium flash moclel arecmn. and T — 2x 10"" Kk. respectively."," Typical shell radii, densities and temperatures at the onset of this thin shell helium flash model are, and T $\sim$ $\times$ $^8$ K, respectively." + For these thermocdynaiic conditions. a self-sustained detonation propagates in the lateral direction at Sp 109 cms toa d a laminar ¢ellagration propagates laterally at Sp-- 10 cms ! (Timmes 1999).," For these thermodynamic conditions, a self-sustained detonation propagates in the lateral direction at $S_{\rm D} \sim$ $^9$ cm $^{-1}$ , and a laminar deflagration propagates laterally at $S_{\rm L} \sim$ 10 cm $^{-1}$ (Timmes 1999)." + Purely laminar «e[lagratioi5 al plauar ZND «etonations (Zelclovich (see Ostriker 1992): von veumaun 1912: Dórrlug lL! Md3)represent the stinplest one«lumeusional. steady-state realizations of oxopagatiug burning routs.," Purely laminar deflagrations and planar ZND detonations (Zeldovich (see Ostriker 1992); von Neumann 1942; Dörring 1943) represent the simplest one-dimensional, steady-state realizations of propagating burning fronts." + Ayerods1anic instabililes ln cellagrations. some of which are intrinsic o three-dimeusional opevwatil© Irous and some of whicl are related to the buoyancy of the hot oiurniug products witL respect 1o the cold backgroiud in tie radial direction. give rise to growing »erturbations aud — inless stabilized by ion-linear effects — turbulence.," Hydrodynamic instabilities in deflagrations, some of which are intrinsic to three-dimensional propagating fronts and some of which are related to the buoyancy of the hot burning products with respect to the cold background in the radial direction, give rise to growing perturbations and – unless stabilized by non-linear effects – turbulence." + TIese instabilities deOF he combustion surfac'e. poteutially alteriig the stricture of the reacting I:wers.," These instabilities deform the combustion surface, potentially altering the structure of the reacting layers." + For ceflagralonis. hese instabilities gererally increase the fale al wüch nuclear euergy is 'eleased.," For deflagrations, these instabilities generally increase the rate at which nuclear energy is released." + The deforinec lame [roi| propagates at a speed faster hana pu‘ely lamiuar flame [rou as long as tle sl‘face area lucrease cloiminaes over the reductio1 of loca enuergv generation incuced by κάνεxlyuaiuic strain., The deformed flame front propagates at a speed faster than a purely laminar flame front as long as the surface area increase dominates over the reduction of local energy generation induced by hydrodynamic strain. + For a detonation. these hyclrocvianie instabiities geuerally do not icrease either tlee ey 'eleased. from buruiug or the self-suslained cdetonation speed (e.g.. Fickett Davis 1979.," For a detonation, these hydrodynamic instabilities generally do not increase either the energy released from burning or the self-sustained detonation speed (e.g., Fickett Davis 1979)." +M els or the noi-linear evolution of uustabe or turbulent c'ombustio1 [fronts often involve statistical Ωςjs. and the choice of a1 appropriate too requires kuowledge of the buruiug reeime of the coubistjon ront.," Models for the non-linear evolution of unstable or turbulent combustion fronts often involve statistical tools, and the choice of an appropriate tool requires knowledge of the burning regime of the combustion front." + The Πα puryose of this paper is to evalate the regiues of helium burning frouts i[un he με...ice of btoyancy-cdriven (convective) turlence., The main purpose of this paper is to evaluate the regimes of helium burning fronts in the presence of buoyancy-driven (convective) turbulence. + À siiple dimensional comparison of he relevant leugt1 ancl speed. scales of buoyancyriven turbulence. ZND helium detouations. and alninar helituir cleflagratious determine whetle: the combustion front. is in the flamelet. regime. distributed. btruiug regime. or neither.," A simple dimensional comparison of the relevant length and speed scales of buoyancy-driven turbulence, ZND helium detonations, and laminar helium deflagrations determine whether the combustion front is in the flamelet regime, distributed burning regime, or neither." + It wil always be asstuned in this paper that convective stirring cloudjates over all other instabilities intrinsic to the [lame front., It will always be assumed in this paper that convective stirring dominates over all other instabilities intrinsic to the flame front. + While cellular instabilities behind the cdeonation [rout may be relevant 1 some contexts (Fickett Davis 1979: Merzhanov Rtmanov 1999). they will uot be discussed in thispaper.," While cellular instabilities behind the detonation front may be relevant in some contexts (Fickett Davis 1979; Merzhanov Rumanov 1999), they will not be discussed in thispaper." +assumption is not applicable in general.,assumption is not applicable in general. + One needs to take into account the spatial distribution of the sources., One needs to take into account the spatial distribution of the sources. +" Nevertheless, in the case that the diffusion distance Ry=24/D(tage—tesp) is larger than the radius Res», the distribution function of energetic proton at a distance r can be described as if the CRs were from a point source (see, e.g., Ohira et al."," Nevertheless, in the case that the diffusion distance $R_d=2\sqrt{D(t_{age}-t_{esp})}$ is larger than the radius $R_{esp}$, the distribution function of energetic proton at a distance $r$ can be described as if the CRs were from a point source (see, e.g., Ohira et al." +" 2011) The diffusion coeffcient D=yDjsy, where Disy=1078,/E/10GeVcm?/s (Gabici et al."," 2011) The diffusion coeffcient $D=\chi D_{ISM}$, where $D_{ISM}=10^{28}\sqrt{E/10{\rm GeV}}{\rm cm}^2$ /s (Gabici et al." + 2009; Berezinskii et al., 2009; Berezinskii et al. + 1990)., 1990). + is the spectrum of runaway particles that is integrated f(E)over shock expansion., $f(E)$ is the spectrum of runaway particles that is integrated over shock expansion. + We adopt the routine from Ohira et al. (, We adopt the routine from Ohira et al. ( +2010) here.,2010) here. + If the accelerated particles at a given time is then the general spectrum of protons dispersed from the accelerator is where is the inverse function of Pmax(t)., If the accelerated particles at a given time is then the general spectrum of protons dispersed from the accelerator is where $p^{-1}_{max}(p)$ is the inverse function of $p_{max}(t)$. +" K(t) is a normalization p;,l.(p)factor and can be estimated from In the case of flatter spectrum at the shock front, i.e., a> 0, K(t)ο.U?R3,p."," $K(t)$ is a normalization factor and can be estimated from In the case of flatter spectrum at the shock front, i.e., $a>0$ , $K(t)\propto U^2R_{sh}^3p^{-a}$." + Evaluation of dpmax/dt from Eq.(11)) shows that it can be well represented by a power law in spite of the fact that pmax does not follow an exact power law., Evaluation of $dp_{max}/{dt}$ from \ref{gmax_general}) ) shows that it can be well represented by a power law in spite of the fact that $p_{max}$ does not follow an exact power law. +" Insert and ~ into Eq.18,, we get a universal K(t)power spectrum dpmax/dtf(E)«Pmax/tnEsvE~* with s=2 regardless of the flatter original spectrum at the shock."," Insert $K(t)$ and $dp_{max}/{dt}\simeq p_{max}/t$ into \ref{spectrum_ave}, we get a universal power spectrum $f(E) \propto \eta E_{SN}E^{-s}$ with $s=2$ regardless of the flatter original spectrum at the shock." +. η is the fraction of SN energy converted into CRs., $\eta$ is the fraction of SN energy converted into CRs. + We front?obtain a similar cosmic momentum spectrum as earlier authors Ptuskin rayZirakashvili 2005; Ohira et al.," We obtain a similar cosmic ray momentum spectrum as earlier authors (e.g., Ptuskin Zirakashvili 2005; Ohira et al." +" 2010) without (e.g.,assuming the power law evolution of Pinax(t).", 2010) without assuming the power law evolution of $p_{max}(t)$. +" Pmax(t) in our paper was obtained by considering the balance of the wave growth from the streaming instability, the advection by the shock flow as well as wave damping by the background turbulence."," $p_{max}(t)$ in our paper was obtained by considering the balance of the wave growth from the streaming instability, the advection by the shock flow as well as wave damping by the background turbulence." +" The latter is due to the nonlinear interaction between the wave and the turbulence, and has not been accounted for."," The latter is due to the nonlinear interaction between the wave and the turbulence, and has not been properly accounted for." +" Ptuskin Zirakashvili (2005) considered a properlysimilar process, but assumed isotropy of the MHD turbulence which is not valid."," Ptuskin Zirakashvili (2005) considered a similar process, but assumed isotropy of the MHD turbulence which is not valid." +" Although time evolution of pma,(t) does not follow a power law at high energies?,, the final CR spectrum F(E) at a later age of Sedov phase and a distance r>Rg is well reproduced by the power law form if the diffusion coefficient D(p) has a power law dependence on particle momentum p. This is because high energy CRs are produced at earlier epoch ερ<< SO that Ra can be well approximated by Rg~24/Dtase. tage"," Although time evolution of $p_{max}(t)$ does not follow a power law at high energies, the final CR spectrum $F(E)$ at a later age of Sedov phase and a distance $r> R_d$ is well reproduced by the power law form if the diffusion coefficient $D(p)$ has a power law dependence on particle momentum p. This is because high energy CRs are produced at earlier epoch $t_{esp}\ll t_{age}$ so that $R_d$ can be well approximated by $R_d\simeq 2\sqrt{Dt_{age}}$." +"Adopting the set of parameters for W28 as listed in Tables 1,2, we get the flux of CRs E?F(E)."," Adopting the set of parameters for W28 as listed in Tables 1,2, we get the flux of CRs $E^2F(E)$." +" In Fig.2,, we plot the flux of CRs at different epochs after the SN explosion."," In \ref{CRspectra}, we plot the flux of CRs at different epochs after the SN explosion." + All the values of the parameters except that for turbulence are compatible with those from earlier work ( Fujita et al., All the values of the parameters except that for turbulence are compatible with those from earlier work ( Fujita et al. + 2009; Gabici et al., 2009; Gabici et al. + 2010; Li Chen 2010)., 2010; Li Chen 2010). +" We adopt a turbulence injection scale of 30pc, which is consistent with the scenario that interstellar turbulence is injected from supernovae explosions."," We adopt a turbulence injection scale of $30pc$, which is consistent with the scenario that interstellar turbulence is injected from supernovae explosions." + The CR energy at each peak corresponds to the maximum momentum Pmax(t) reached at each epoch t. The galactic background is also plotted for comparison., The CR energy at each peak corresponds to the maximum momentum $p_{max}(t)$ reached at each epoch t. The galactic background is also plotted for comparison. +" Apparently, the CR intensities are dramatically enhanced in the vicinity of SNRs as compared to the Galactic mean intensities."," Apparently, the CR intensities are dramatically enhanced in the vicinity of SNRs as compared to the Galactic mean intensities." +" In the case F(E) follows a power law distribution, the pion gamma ray emissivity is given by (see Aharonian Atoyan 1996) where ©E,/10 is the corresponding y ray energy, Opp©30x[0.95Ey+0.061n(E, )]mb is the cross section for pp collisions at Ey, f is the/ fractionGeV of energy that is transferred from parent protons to secondary pions, 41.4—1.5 is a parameter to account for the contribution from both cosmic rays and the interstellar gas (Dermer 1986)."," In the case $F(E) $ follows a power law distribution, the pion gamma ray emissivity is given by (see Aharonian Atoyan 1996) where $E_\gamma \approx E_p/10$ is the corresponding $\gamma$ ray energy, $\sigma_{pp}\approx 30\times \left[0.95+0.06\ln (E_p/{GeV})\right]$ mb is the cross section for pp collisions at $E_p$, $f_\pi$ is the fraction of energy that is transferred from parent protons to secondary pions, $\eta_A\simeq 1.4-1.5$ is a parameter to account for the contribution from both cosmic rays and the interstellar gas (Dermer 1986)." +" The total flux then is where M.,d are the mass and the distance of the cloud."," The total flux then is where $M_c,\,d$ are the mass and the distance of the cloud." +" Combining Eqs.(16,,20,,21)), we obtain the flux of gamma ray emission as shown in Fig.3,, where our result is plotted against both Fermi and H.E.S.S. data."," Combining \ref{dist_finl}, \ref{pp}, \ref{gm_flux}) ), we obtain the flux of gamma ray emission as shown in \ref{gamma}, where our result is plotted against both Fermi and H.E.S.S. data." + The GeV and TeV data are adopted from Abdo et al. (, The GeV and TeV data are adopted from Abdo et al. ( +2010) and Aharonian et al. (,2010) and Aharonian et al. ( +"2008), respectively.","2008), respectively." +" Our result produces a power law spectral index 2.75, showing that the steepening of the spectrum of particle can be naturally explained by the propagation effect."," Our result produces a power law spectral index $\sim 2.75$, showing that the steepening of the spectrum of particle can be naturally explained by the propagation effect." +" Indeed, similar fits have been also obtained by other models, e.g., Ohira et al (2011), Li Chen (2010)."," Indeed, similar fits have been also obtained by other models, e.g., Ohira et al (2011), Li Chen (2010)." +" We did not need, however, either to assume Bohm diffusion and phenomenological power law evolution of the momentum of the escaping partciels as in Ohira et al. ("," We did not need, however, either to assume Bohm diffusion and phenomenological power law evolution of the momentum of the escaping partciels as in Ohira et al. (" +"2011), or a steeper","2011), or a steeper" +patterns 0-4 (single and double pixel events) selected for the pn camera and patterns 0-12 for the MOS1 and MOS2 cameras.,patterns 0-4 (single and double pixel events) selected for the pn camera and patterns 0-12 for the MOS1 and MOS2 cameras. +" We extracted source counts within a circular region of rradius defined around the centroid position ofPG12114143,, with the background being taken from a similar region, offset from but close to the source."," We extracted source counts within a circular region of radius defined around the centroid position of, with the background being taken from a similar region, offset from but close to the source." + After removal of data during periods of high background the effective pn exposure was ~49.5 ks while the MOS cameras were combined to give a single-camera-equivalent exposure of ~107 ks., After removal of data during periods of high background the effective pn exposure was $\sim$ 49.5 ks while the MOS cameras were combined to give a single-camera-equivalent exposure of $\sim$ 107 ks. +" Individual spectra were binned to a minimum of 20 counts per bin, to facilitate use of the x? minimalisation technique in spectral fitting."," Individual spectra were binned to a minimum of 20 counts per bin, to facilitate use of the $\chi^2$ minimalisation technique in spectral fitting." +" Spectral fitting was based on the Xspec package (Arnaud 1996), version 11.3."," Spectral fitting was based on the Xspec package (Arnaud 1996), version 11.3." + All spectral fits include absorption due to the line-of-sight Galactic column of Ny=2.85x10?cm? (Murphy 11996) and errors are quoted at the confidence level (Ax?—2.7 for one interesting parameter)., All spectral fits include absorption due to the line-of-sight Galactic column of $N_{H}=2.85\times10^{20}\rm{cm}^{-2}$ (Murphy 1996) and errors are quoted at the confidence level $\Delta \chi^{2}=2.7$ for one interesting parameter). +" Figure 1 reproduces the ratio plot of pn data to a simple power law fit (photon index of [~1.78) over the 1-10 keV band, as modelled in P03."," Figure 1 reproduces the ratio plot of pn data to a simple power law fit (photon index of $\Gamma$$\sim$ 1.78) over the 1–10 keV band, as modelled in P03." +" Marked on the figure are 3 statistically significant ‘narrow’ absorption lines, with their identification as proposed in P03, where they formed a key part of the case for a high velocity outflow."," Marked on the figure are 3 statistically significant `narrow' absorption lines, with their identification as proposed in P03, where they formed a key part of the case for a high velocity outflow." +" Denoted by an asterix in figure 1 is a further ‘absorption line’ at ~1.8 keV, which was not included in the P03 analysis due to prevailing uncertainties in the detector calibration near the neutral Si edge."," Denoted by an asterix in figure 1 is a further `absorption line' at $\sim$ 1.8 keV, which was not included in the P03 analysis due to prevailing uncertainties in the detector calibration near the neutral Si edge." + Repeating the analysis in P03 by successively adding gaussian lines to the power law model in Xspec the observed absorption lines can be quantified., Repeating the analysis in P03 by successively adding gaussian lines to the power law model in Xspec the observed absorption lines can be quantified. +" Fitting first the strongest line at ~7 keV improves the fit by A x? of 69 for 3 fewer degrees of freedom, with a line energy of 7.07+0.03 keV (observer frame), width o=168+46 eV and flux -5.7+0.9 x107° ph cm~? s, corresponding to an equivalent width against the power law continuum of ~210+35 eV. Fitting additional gaussians to the weaker spectral features at ~2.7 and ~1.5 keV, with line width fixed at o=50 eV, gives further significant improvements to the fit, with Ax? of 17 and 16, respectively, each for 2 additional degrees of freedom."," Fitting first the strongest line at $\sim$ 7 keV improves the fit by $\Delta$ $\chi^{2}$ of 69 for 3 fewer degrees of freedom, with a line energy of $\pm$ 0.03 keV (observer frame), width $\sigma$ $\pm$ 46 eV and flux $\pm$ 0.9 $\times 10^{-6}$ ph $^{-2}$ $^{-1}$, corresponding to an equivalent width against the power law continuum of $\sim$ $\pm$ 35 eV. Fitting additional gaussians to the weaker spectral features at $\sim$ 2.7 and $\sim$ 1.5 keV, with line width fixed at $\sigma$ =50 eV, gives further significant improvements to the fit, with $\Delta$$\chi^{2}$ of 17 and 16, respectively, each for 2 additional degrees of freedom." +" The best fit line energies, again in the observer frame, are 2.7+0.03 and 1.47+0.02 keV, with respective fluxes of 4.5x10~° ph cm? s! and -5.7x109 ph cm? s! (EWs of ~30eV and ~14eV, accurate to a factor 2)."," The best fit line energies, again in the observer frame, are $\pm$ 0.03 and $\pm$ 0.02 keV, with respective fluxes of $\times 10^{-6}$ ph $^{-2}$ $^{-1}$ and $\times 10^{-6}$ ph $^{-2}$ $^{-1}$ (EWs of $\sim$ 30eV and $\sim$ 14eV, accurate to a factor $\sim$ 2)." +" Identifying the 3 absorption lines with the resonance Lya transitions of FeXXVI, SXVI and MgXII then yields the mean outflow velocity of —0.0943-0.01c reported in P03."," Identifying the 3 absorption lines with the resonance $\alpha$ transitions of FeXXVI, SXVI and MgXII then yields the mean outflow velocity of $\sim$ $\pm$ 0.01c reported in P03." +" As noted in P03, the outflow velocity of ~0.09c is conservative in that identifying the ~7 keV feature with Fe XXV Heo, rather than FeXXVI Lyo, would require a larger energy shift and correspondingly higher velocity."," As noted in P03, the outflow velocity of $\sim$ 0.09c is conservative in that identifying the $\sim$ 7 keV feature with Fe XXV $\alpha$, rather than FeXXVI $\alpha$, would require a larger energy shift and correspondingly higher velocity." +" Encouraged by the impressive low energy spectra from the (higher resolution) MOS cameras, demonstrated in two recent studies of the Seyfert 2 galaxies Mkn3 (Pounds and Page 2005) and NGC1068 (Pounds and Vaughan 2006) we have re-examined the spectral structure in the oobservation ofPG1211--143,, concentrating on the MOS data."," Encouraged by the impressive low energy spectra from the (higher resolution) MOS cameras, demonstrated in two recent studies of the Seyfert 2 galaxies Mkn3 (Pounds and Page 2005) and NGC1068 (Pounds and Vaughan 2006) we have re-examined the spectral structure in the observation of, concentrating on the MOS data." +" Our aim was to clarify the spectral structure at medium and low energies in the hope of removing the ambiguity in identifying the ~7 keV absorption line, and hence improving confidence in the deduced outflow velocity."," Our aim was to clarify the spectral structure at medium and low energies in the hope of removing the ambiguity in identifying the $\sim$ 7 keV absorption line, and hence improving confidence in the deduced outflow velocity." + With the higher energy resolution of the MOS camera, With the higher energy resolution of the MOS camera +other wavelengths. it. provides information on the physical states and the geometrical distribution of the cireumnuclear gas. which cannot be obtained otherwise.,"other wavelengths, it provides information on the physical states and the geometrical distribution of the circumnuclear gas, which cannot be obtained otherwise." + We have shown in the previous section that NGC 7582 is one of the few nearby obscured AGN where energv-resolved. imaging analysis is indeed. possible with current instrumentation., We have shown in the previous section that NGC 7582 is one of the few nearby obscured AGN where energy-resolved imaging analysis is indeed possible with current instrumentation. + In this section. we will discuss the results obtained in Sect 3 in the context of an overall interpretative scenario for the nuclear region.," In this section, we will discuss the results obtained in Sect \ref{analysis} in the context of an overall interpretative scenario for the nuclear region." +alone: the greater. incidence of clisk-like morphologies and detectable Lla emission demonstrates that star formation is still ongoing in many of these objects. albeit at a relatively ow level ($ 60 per cent of the mean) and a spin-minimum spectrum (count rate $<$ 40 per cent of the mean). + The spectra were fitted with the same model of a 30. bbremsstrablung and an iron line. absorbed by a," The spectra were fitted with the same model of a 30 bremsstrahlung and an iron line, absorbed by a" +because the neutron stars in this EOS are the most compact and tidal effects are the weakest.,because the neutron stars in this EOS are the most compact and tidal effects are the weakest. +" On the other hand, the curve of the least compact neutron stars (the dashed curve, PwPoly30-1395) has already deviated from the curves of TaylorT1 and TaylorT4 before reaching the initial orbital angular velocity MoQinj=0.03, because of the tidal deformation."," On the other hand, the curve of the least compact neutron stars (the dashed curve, PwPoly30-1395) has already deviated from the curves of TaylorT1 and TaylorT4 before reaching the initial orbital angular velocity $M_0 \Omega_{\rm ini}=0.03$, because of the tidal deformation." +" This shows that if we would like to compare the time evolution of the orbital angular velocity obtained by simulations, we need to start the simulations from a much smaller value of the orbital angular velocity for such less-compact neutron star models."," This shows that if we would like to compare the time evolution of the orbital angular velocity obtained by simulations, we need to start the simulations from a much smaller value of the orbital angular velocity for such less-compact neutron star models." +" Figure 23 also shows that the quasi-equilibrium results are closer to those of TaylorT4 than those of TaylorT1, even though our calculation method of the orbital angular velocity as a function of time is similar to that of TaylorT1 (see Equation (67)))."," Figure \ref{fig23} also shows that the quasi-equilibrium results are closer to those of TaylorT4 than those of TaylorT1, even though our calculation method of the orbital angular velocity as a function of time is similar to that of TaylorT1 (see Equation \ref{eq:dodt}) ))." +" We, however, believe that at the limit of test mass, our method gives similar results of TaylorT1."," We, however, believe that at the limit of test mass, our method gives similar results of TaylorT1." + Figures 24--26 compare the results of unequal-mass binaries with those of equal-mass ones with the total mass of Mo=2.7Mo.," Figures \ref{fig24}- \ref{fig26} compare the results of unequal-mass binaries with those of equal-mass ones with the total mass of $M_0=2.7 +M_{\odot}$." +" The equal-mass binary has the mass of MNBA,=MNS},= 1.35Mo, and the unequal-mass binary does ΜΑΡΑ=1.15Mo and ΜΑΡΙ=1.55Mo."," The equal-mass binary has the mass of $M_{\rm ADM}^{\rm +NS1}=M_{\rm ADM}^{\rm NS2}=1.35 M_{\odot}$ , and the unequal-mass binary does $M_{\rm ADM}^{\rm NS1}=1.15 M_{\odot}$ and $M_{\rm +ADM}^{\rm NS2}=1.55 M_{\odot}$." +" The EOSs are the same as those in Figure 23,, but the results for logy)Py=13.95 (PwPoly30-1395), 13.45 (PwPoly30-1345), and 13.15 (PwPoly30-1315) are shown in Figures 24-—26,, respectively."," The EOSs are the same as those in Figure \ref{fig23}, but the results for $\log_{10} P_1=13.95$ (PwPoly30-1395), 13.45 (PwPoly30-1345), and 13.15 (PwPoly30-1315) are shown in Figures \ref{fig24}- \ref{fig26}, respectively." +" From these figures, we find that the curves for unequal-mass binaries are located below those for equal-mass binaries for t>0 and are closer to the post-Newtonian results, in particular for a"," From these figures, we find that the curves for unequal-mass binaries are located below those for equal-mass binaries for $t > 0$ and are closer to the post-Newtonian results, in particular for a" +inetal-poor (—1.60<[Fe/H]€—1.00) and very metal-poor (—2.10<[Fe/H]€—1.60) clusters are collected in Table 2.,metal-poor $(-1.60<[Fe/H]\leq -1.00)$ and very metal-poor $(-2.40<[Fe/H]\leq -1.60)$ clusters are collected in Table 2. + Separate information is provided for (1) all metal-poor clusters. aud (2) with probable companions of the Sagittarius dwarf excluded.," Separate information is provided for (1) all metal-poor clusters, and (2) with probable companions of the Sagittarius dwarf excluded." + Luspection of these data hints at a possible metallicity gracdieut in the expected sense. Le.. with a small excess of the highest metallicity subgroup at παπα. Calactocentric radii.," Inspection of these data hints at a possible metallicity gradient in the expected sense, i.e., with a small excess of the highest metallicity subgroup at small Galactocentric radii." + However. a Ixolmogorov-Simirnov test shows only au probability that this effect is real [or the eive sample. and au probability that it is rea for the sample [rom wuich probable companious to the Sagittarius galaxy have |)een excluded.," However, a Kolmogorov-Smirnov test shows only an probability that this effect is real for the entire sample, and an probability that it is real for the sample from which probable companions to the Sagittarius galaxy have been excluded." + Di sunmauary. it is concluded that the populatio1 of metal-poor Galactic halo cluste* ds too small to establish with certainty if they exhibi a metallicity eradient.," In summary, it is concluded that the population of metal-poor Galactic halo clusters is too small to establish with certainty if they exhibit a metallicity gradient." + For metal-rich globar clusters with [Fe/H]>—1.0 there is no statistically sigulicant evidence for a correation between [Fe/H] «x R., For metal-rich globular clusters with $[Fe/H]>-1.0$ there is no statistically significant evidence for a correlation between $[Fe/H]$ and $R$. + Finally. i In notec that we presently do mot uinlerstancl how some nearby. dwarl sple'olda galaxies were able to fcoiu quite metal-rich οobular (LFe/H]<—1.0) €usters.," Finally, it is noted that we presently do not understand how some nearby dwarf spheroidal galaxies were able to form quite metal-rich globular $([Fe/H]<-1.0)$ clusters." + This contrasts witl the situation in the otler (R>10 ο) regions of the Galaxy that weο apparently never adle to form similarly metal-rich globular clisters., This contrasts with the situation in the outer $(R>10$ $)$ regions of the Galaxy that were apparently never able to form similarly metal-rich globular clusters. + This restlt suggests that the specific globular custer frequency in the Galaxy may have exhibitec La steep decline with increasing metallicity. wlereas the specific cluster frequency may have been less sensitive to metallicity in (some) dwarf sple‘oidal galaxies.," This result suggests that the specific globular cluster frequency in the Galaxy may have exhibited a steep decline with increasing metallicity, whereas the specific cluster frequency may have been less sensitive to metallicity in (some) dwarf spheroidal galaxies." + The metallicity cistributiou of Galactic οobular clusters does not appear to depeucl oi uniuosity., The metallicity distribution of Galactic globular clusters does not appear to depend on luminosity. + ]xolinogorov-5inirnov tests show nuo significait dilfereuces between the metallicity distri)lions of objects brighter and fainter than Ady=—5.0., Kolmogorov-Smirnov tests show no significant differences between the metallicity distributions of objects brighter and fainter than $M_{V}=-5.0$. + The same conclusion holds if the sample is divided at My—6.0., The same conclusion holds if the sample is divided at $M_{V}=-6.0$. + This result is somewhat suroisiug because one mieht have expected [aLL clusters (which mainly occur iu high density regions) to have been preferentially destoyed by bulge aud disk shocks. or eroded by tidal strij»piug.," This result is somewhat surprising because one might have expected faint metal-rich clusters (which mainly occur in high density regions) to have been preferentially destroyed by bulge and disk shocks, or eroded by tidal stripping." + Ou the other hand the most massive (lninous) clusters are expected to be survivors e.g.. Cieclin.(2002).," On the other hand the most massive (luminous) clusters are expected to be survivors e.g., \citet{gne02}." +. The Figure shows little (or no) evidence for a depeudeuce of metallicity ou the central concentration ol uxlex c (μις1962) ol Galactic globular clusters., The Figure shows little (or no) evidence for a dependence of metallicity on the central concentration of index $c$ \citep{kin62} of Galactic globular clusters. + In particular the fraction of globulars with collapsed cores (ezz 2.5) does not appear to depend strongly ou metallicity., In particular the fraction of globulars with collapsed cores $c\approx 2.5$ ) does not appear to depend strongly on metallicity. + The overwhelming majority of clusters with collapsed cores. ie.. those with ez2.5. are Loud to be located at /?«10 kpc.," The overwhelming majority of clusters with collapsed cores, i.e., those with $c\approx 2.5$, are found to be located at $R<10$ kpc." + The reason for this is. no doubt. that globular cluster half-liglit radii tend," The reason for this is, no doubt, that globular cluster half-light radii tend" +The comparison of the observed intensity of the 11-0S(1) line im the ceutral torus of NGC 25316 to the NII98 model predictious shows that the cussion Ci be produced in the hot PDR generated by the radiation of the central star. once the effect of X-rav heating and time-dependent (advecting) clicmustry ds taken iuto account.,"The comparison of the observed intensity of the 1-0S(1) line in the central torus of NGC 2346 to the NH98 model predictions shows that the emission can be produced in the hot PDR generated by the radiation of the central star, once the effect of X-ray heating and time-dependent (advecting) chemistry is taken into account." + The best fit is obtained by models with relatively low deusitv of the neutral eas (in agreement with the low deusitv of the ionized material inferred bv several authors)., The best fit is obtained by models with relatively low density of the neutral gas (in agreement with the low density of the ionized material inferred by several authors). +" However. these PDR models require the i1unuinositv of the hot central star to be siguificautlv higher (L,~250 L..)) than current estimates."," However, these PDR models require the luminosity of the hot central star to be significantly higher $\sim$ 250 ) than current estimates." + If the lines are enüutted in the PDR. we expect to observe a simular iiorphologv iu the ionized aud eemittiue eas.," If the lines are emitted in the PDR, we expect to observe a similar morphology in the ionized and emitting gas." + In NGC 2316. the PDR origin of the lines is supported by the fact that the sane morphology ix seen in aad in Πα (see Walsh 1983).," In NGC 2346, the PDR origin of the lines is supported by the fact that the same morphology is seen in and in $\alpha$ (see Walsh 1983)." + Also. we detect ecnissiou in the two ppeaks. with a N-S profile that follows that of the 1-08(1) line (Fig. 3)).," Also, we detect emission in the two peaks, with a N-S profile that follows that of the 1-0S(1) line (Fig. \ref{fig:cuts}) )." + The intensity of ppredicted bv the models is very low. ofthe order of 8« 1s comparable to the observed values 6.10ο tj).," The intensity of predicted by the models is very low, of the order of $8\times 10^{-6}$ , comparable to the observed values $\times 10^{-6}$ )." +" This supports our estimate ofL,.", This supports our estimate of. +. Iu principle. the observed intensity of tle 11-08(1) liue cau also be accounted for by the emission of the shocked gas produced by the expausion of the torus inside a precursor rec-elant wind.," In principle, the observed intensity of the 1-0S(1) line can also be accounted for by the emission of the shocked gas produced by the expansion of the torus inside a precursor red-giant wind." + BHowever. we estimate (following NII98) that oue needs a rather high value ofthe niass-loss rate iu the red-giaut wiud πα...," However, we estimate (following NH98) that one needs a rather high value of the mass-loss rate in the red-giant wind $\dot M_w/f_w\simgreat 10^{-4}$ )." + This. in turn. implies a high denstv of the pre- eas (2104 1). which is not supported by any existing observation.," This, in turn, implies a high density of the pre-shock gas $\simgreat 10^4$ ), which is not supported by any existing observation." + In fact. as discussed by Zuckerman aud Catley (1988). the main difficulty in ascribing the yvibrationally excited enussion to shocks comes from the hieh momentum rate these mocels require.," In fact, as discussed by Zuckerman and Gatley (1988), the main difficulty in ascribing the vibrationally excited emission to shocks comes from the high momentum rate these models require." + May autlors (see the review by Iwok 1993) have proposed that the formation aud expansion of the PN shell (or torus) is related to the action of the fast wind from the central star., Many authors (see the review by Kwok 1993) have proposed that the formation and expansion of the PN shell (or torus) is related to the action of the fast wind from the central star. + In this case. the ambient eas (pre-shock red eiaut wind) seams momentum approximately at the rate at which momentum is delivered to the torus by the fast wind.," In this case, the ambient gas (pre-shock red giant wind) gains momentum approximately at the rate at which momentum is delivered to the torus by the fast wind." + Since the fast wind is radiation driven. this rate (P) must be SL. fe.," Since the fast wind is radiation driven, this rate $\dot P$ ) must be $\simless$ $c$." + In NGC 22316. we estimate that P is at least ~ὃς1075 ere | 7. hes more than 600 iues the present value of νο (for 22250 L.3) aud 12 times higher than the maxima {ο reached by the star iu its earlier evolution. according to the evolutionary racks of Dlóccker (1995).," In NGC 2346, we estimate that $\dot P$ is at least $\sim 2\times 10^{28}$ erg $^{-1}$ $^{-2}$, i.e., more than 600 times the present value of $c$ (for 250 ) and 12 times higher than the maximum /c reached by the star in its earlier evolution, according to the evolutionary tracks of Blöccker (1995)." + The interpretation of the cecluission iun terms of shocks is often justified in the iterature bv the low measured ratio of the 2-1S(1) to he 1-OS(1) intensity., The interpretation of the emission in terms of shocks is often justified in the literature by the low measured ratio of the 2-1S(1) to the 1-0S(1) intensity. + This aremuenut. however. is not very strong. since in dense PDRs the low vibrational levels are thermalized.," This argument, however, is not very strong, since in dense PDRs the low vibrational levels are thermalized." + The PDR inodels discussed. in &Ll predict a ratio 2-18(1)/1-08(1)—0.15. (uot) very different from the 0.10-0.18 range predicted bv shock nocels: see 81.2). iudependeutly of the deusity aud stellar tuuinosity.," The PDR models discussed in 4.1 predict a ratio $\sim$ 0.15 (not very different from the 0.10-0.18 range predicted by shock models; see 4.2), independently of the density and stellar luminosity." + These values are somewhat higher than the observed ratio (~0.07)., These values are somewhat higher than the observed ratio $\sim$ 0.07). + It is possible. aud worth further investigations. that inodels tend to overestinate the Huorescent componcut of high vibrational lines. possibly vecatise of uncertainties in the collisional deexcitation Yates.," It is possible, and worth further investigations, that models tend to overestimate the fluorescent component of high vibrational lines, possibly because of uncertainties in the collisional deexcitation rates." + Au interesting result of our observations. and oue that we cannot account for with our simple models. is the variation of the 2-189(1)/1-08(1) ratio with position along the slits. rauging from about 0.08 to 0.15 along the W slit. aud from 0.08 to 0.23 alone the E slit (see Fig. 3)).," An interesting result of our observations, and one that we cannot account for with our simple models, is the variation of the 2-1S(1)/1-0S(1) ratio with position along the slits, ranging from about 0.08 to 0.15 along the W slit, and from 0.08 to 0.23 along the E slit (see Fig. \ref{fig:cuts}) )." + These variations are not monotonic with the distance frou the peaks. but show evidence of structures. especially along the W slit.," These variations are not monotonic with the distance from the peaks, but show evidence of structures, especially along the W slit." + It is possible that this is due to density variations. which affect the fluorescent contribution to the 2-]S(1) line.," It is possible that this is due to density variations, which affect the fluorescent contribution to the 2-1S(1) line." + If the ciussion is due to shocks. this could trace variations in the propagation velocity of the shock in an Inhomoecucous mediun.," If the emission is due to shocks, this could trace variations in the propagation velocity of the shock in an inhomogeneous medium." + Further support to the PDR origin of the celission can be obtained by observiug lines from higher vibrational states;, Further support to the PDR origin of the emission can be obtained by observing lines from higher vibrational states. + We show in Table 2 PDR imodclxedieted values for lines not detected so far in NCC 2316. which. however. are accessible frou space.," We show in Table 3 PDR model-predicted values for lines not detected so far in NGC 2346, which, however, are accessible from space." + The lines are very weak with respect to the 1-08(1). with ratios that do rot depend siguificautly on the density.," The lines are very weak with respect to the 1-0S(1), with ratios that do not depend significantly on the density." + We expect that rey will be substautially weaker in shocks., We expect that they will be substantially weaker in shocks. + To complete ie discussion of the sspectrum. we show in Table 1 1uodoel-predieted values of 1ο Intensity of müd-ufrared lines in the v=0-0 baud for our of the PDR 1uodels described oein $£L.1.," To complete the discussion of the spectrum, we show in Table 4 model-predicted values of the intensity of mid-infrared lines in the v=0-0 band for four of the PDR models described in 4.1." + These lines wave been observed by ISO in a uuuber of PNe (amone wun NGC 2316: Barlow ct al., These lines have been observed by ISO in a number of PNe (among them NGC 2346; Barlow et al. + in preparation). aud may )o useful diagnostic of the physical couditious (see NIT98).," in preparation), and may be useful diagnostic of the physical conditions (see NH98)." + This paper is motivated by our interest in undoerstaudiug the origin of the ecluission m PNe., This paper is motivated by our interest in understanding the origin of the emission in PNe. + Recently. Natta Iollenbach. (1998) have computed the evolution with time of the," Recently, Natta Hollenbach (1998) have computed the evolution with time of the" +Sect. 2.1..,Sect. \ref{sect_mathintro}. + The choice of the Gaussians guarantees that the filter gives the best simultaneous confinement in ordinary space and in Fourier space not showing any side lobes in either of them., The choice of the Gaussians guarantees that the filter gives the best simultaneous confinement in ordinary space and in Fourier space not showing any side lobes in either of them. + As the opposite extreme we have also tested a filter measuring the difference between one point in the map and all points displaced by the sharp distance / relative to this pixel., As the opposite extreme we have also tested a filter measuring the difference between one point in the map and all points displaced by the sharp distance $l$ relative to this pixel. + The corresponding A-variance then measures basically the structure function of the map (seee.g.Miesch&Bally.1994:Fricketal.," The corresponding $\Delta$ -variance then measures basically the structure function of the map \citep[see e.g.][]{Miesch94, Frick}." +. 2001).. However. because those tests only confirmed the results from Ossenkopf&MacLow(2002) and Frick et al. (," However, because those tests only confirmed the results from \citet{OML} + and Frick et al. (" +2001) that the structure function ts relatively insensitive to distortions of the power spectrum on particular scales we excluded this filter from the following studies.,2001) that the structure function is relatively insensitive to distortions of the power spectrum on particular scales we excluded this filter from the following studies. + Thus. we restrict ourselves here to the Mexican- and the French-hat filter. where we vary in both cases the diameter ratio v.," Thus, we restrict ourselves here to the Mexican- and the French-hat filter, where we vary in both cases the diameter ratio $v$." + In this way we test both the influence of the general filter shape and of the ratio between core and annulus for each filter on the computed A-variance spectra., In this way we test both the influence of the general filter shape and of the ratio between core and annulus for each filter on the computed $\Delta$ -variance spectra. + Taking into account the finite width of the core and the annulus of both filter functions it is not obvious on which scale variations are actually measured when using a filter with size /., Taking into account the finite width of the core and the annulus of both filter functions it is not obvious on which scale variations are actually measured when using a filter with size $l$. + Here. we compute this scale based on the geometrical properties of the filter.," Here, we compute this scale based on the geometrical properties of the filter." + In the French-hat filter we measure the average distance between a point in the core and a point in the annulus. providing the average scale on which a structure variation in the map should be measured.," In the French-hat filter we measure the average distance between a point in the core and a point in the annulus, providing the average scale on which a structure variation in the map should be measured." + For the Mexican-hat filter. the computation of the average distance includes the additional weighting of each distance by the product of the positive and negative filter values.," For the Mexican-hat filter, the computation of the average distance includes the additional weighting of each distance by the product of the positive and negative filter values." + This reflects the effect of the convolution of a map with this filter., This reflects the effect of the convolution of a map with this filter. + Figure 6 shows the resulting effective filter length relative to the filter size / as a function of the diameter ratio v for the French and the Mexican hat., Figure \ref{v-abstand} shows the resulting effective filter length relative to the filter size $l$ as a function of the diameter ratio $v$ for the French and the Mexican hat. + The length scale traced by the filters is approximately a linear function of the diameter ratio between the core and the annulus ofthe filter., The length scale traced by the filters is approximately a linear function of the diameter ratio between the core and the annulus ofthe filter. + The original A-variance definition using a French hat with v=3 gives an effective length of 1.12 times the core diameter I., The original $\Delta$ -variance definition using a French hat with $v=3$ gives an effective length of 1.12 times the core diameter $l$. + Thus all scales computed previously with that filter should be shifted by the factor 1.12., Thus all scales computed previously with that filter should be shifted by the factor 1.12. + This is only a small correction. not changing the conclusions in any of the papers that have used the A-variance so far.," This is only a small correction, not changing the conclusions in any of the papers that have used the $\Delta$ -variance so far." + In all plots shown in this paper. we use the effective length as the lag of the A-variance to allow a direct comparison of the spectra independent of the filter used.," In all plots shown in this paper, we use the effective length as the lag of the $\Delta$ -variance to allow a direct comparison of the spectra independent of the filter used." + The optimum filter to be used in the A-variance analysis has to fulfil two eriteria: the correct detection of pronounced size scales in the maps and the exact determination of the scaling exponents of the contained structures., The optimum filter to be used in the $\Delta$ -variance analysis has to fulfil two criteria: the correct detection of pronounced size scales in the maps and the exact determination of the scaling exponents of the contained structures. + In the detection of pronounced scales the maximum of the A-variance spectrum. should fall onto the correct lag corresponding to the structure size., In the detection of pronounced scales the maximum of the $\Delta$ -variance spectrum should fall onto the correct lag corresponding to the structure size. + Moreover. the signature of the pronounced scale in the A-variance spectrum should be as sharp as possible with a high contrast relative to other scales.," Moreover, the signature of the pronounced scale in the $\Delta$ -variance spectrum should be as sharp as possible with a high contrast relative to other scales." + As test images we used the chess board field. the sine wave field. and the filled circle field.," As test images we used the chess board field, the sine wave field, and the filled circle field." + In both cases the filter truncation method is used., In both cases the filter truncation method is used. + The dominant, The dominant +It is offen assumed that the narrow emission lines in active galactic nuclei (ACN) are indicative of some approximately stable. quiescent pool of eas thal is being excited or illuminated by the central source.,"It is often assumed that the narrow emission lines in active galactic nuclei (AGN) are indicative of some approximately stable, quiescent pool of gas that is being excited or illuminated by the central source." + Emission lines that originate in the narrow line region (NLR) are commonly used (ο obtain the svstemic redshift (DeRobertis1985:\larzianial.1996:Richardsοἱ2002) or as a proxy [ον (he stellar velocity. dispersion al. 2003).," Emission lines that originate in the narrow line region (NLR) are commonly used to obtain the systemic redshift \citep{derobertis85, +marzianietal96, richardsetal02} or as a proxy for the stellar velocity dispersion \citep{shieldsetal03}." +. Most often it is the [O III] A5007 Ime that is used. as it is usually the strongest and cleanest narrow line in the optical region of the spectrum.," Most often it is the [O III] $\lambda$ 5007 line that is used, as it is usually the strongest and cleanest narrow line in the optical region of the spectrum." + The validity. of the assumptions that the A5007 line is a good indicator of svstenic redshift or stellar velocity dispersion resis primarily on extrapolation of studies of low luminosity objects. such as those by IIleckmanetal. (1931).. Vrtilek (1985)...," The validity of the assumptions that the $\lambda$ 5007 line is a good indicator of systemic redshift or stellar velocity dispersion rests primarily on extrapolation of studies of low luminosity objects, such as those by \citet{heckmanetal81}, , \citet{vrtilek85}, ," +"and produce two electrons with a Lorentz factor: As the optical depth for pair creation is huge all the scattered photons will create pairs with typical energy of ?,m,c?/2.",and produce two electrons with a Lorentz factor: As the optical depth for pair creation is huge all the scattered photons will create pairs with typical energy of $\g_e m_e c^2 /2$. +" As a result we will have colder electrons and positrons with a ratio 2:1 in higher (?,/2) and lower (7, /4&) energies.", As a result we will have colder electrons and positrons with a ratio 2:1 in higher $\g_e /2$ ) and lower $\g_e/4 \xi$ ) energies. + These colder electrons and pairs will Inverse Compton scatter more photons and will produce a second generation of cooler pairs with y./4., These colder electrons and pairs will Inverse Compton scatter more photons and will produce a second generation of cooler pairs with $\gamma_e/4$. + The process will continue until pair creation will stop., The process will continue until pair creation will stop. +" This will happen when Ahwv,/V=m.c?."," This will happen when $\tilde \g h \nu_\gamma /\G \approx m_e +c^2$." +" This situation was considered numerically by Coppi(1992);(1995);Pe'er&Waxman (2005),, and most recently Vurm&Poutanen(2008)."," This situation was considered numerically by \citet{c92,sb95,pw05}, and most recently \citet{vp08}." +". If the physical conditions, like magnetic field and total number of particles are fixed vr, vy and vg as well as the corresponding fluxes will vary as a result of the changing electron energy distribution due to the created pairs."," If the physical conditions, like magnetic field and total number of particles are fixed $\nu_L$, $\nu_\gamma$ and $\nu_H$ as well as the corresponding fluxes will vary as a result of the changing electron energy distribution due to the created pairs." + These variations will be very significant because of the strong dependence (2nd and 4th powers) of the first two on γε., These variations will be very significant because of the strong dependence (2nd and 4th powers) of the first two on $\g_e$. + The dynamical evolution of such a system is interesting by itself., The dynamical evolution of such a system is interesting by itself. +" However, we are interested, here, in the final steady state in which v, and F are fixed as the observed quantities."," However, we are interested, here, in the final steady state in which $\nu_\gamma$ and $F_\gamma$ are fixed as the observed quantities." + In this case we can search for, In this case we can search for +pe for G stars.,pc for G stars. + Hence the number of transits observed in lainter surveys will not continue to erow as d? as in equation (1))., Hence the number of transits observed in fainter surveys will not continue to grow as $d_0^3$ as in equation \ref{equfin}) ). + In previous sections. we ignored (he loss of sensitivity to svstems that are brighter than Vui Which is set by saturation of the detector (or more precisely. bv the flux at. which detector non-linearities can no longer be accurately calibrated).," In previous sections, we ignored the loss of sensitivity to systems that are brighter than $V_{\rm min}$, which is set by saturation of the detector (or more precisely, by the flux at which detector non-linearities can no longer be accurately calibrated)." + This fraction is 100.GAYor lor AV=2. which we therefore adopt as à sensible goal.," This fraction is $10^{-0.6\Delta V}$, or for $\Delta V=2$, which we therefore adopt as a sensible goal." + That is. we wish to optimize the telescope desien for. (In any event. essentially all stars V.—8 have already been survevecl lor NSPs using RV. and the problem of determining which among the planet-bearers have (rausils is (rivial compared to the problem of conducting an all-sky photometric variability survey.)," That is, we wish to optimize the telescope design for, (In any event, essentially all stars $V<8$ have already been surveyed for XSPs using RV, and the problem of determining which among the planet-bearers have transits is trivial compared to the problem of conducting an all-sky photometric variability survey.)" + Optüinization means maximizing the photon collection rate. 5/7. where T is the duration of the experiment and. again. 5 is the total number of photons collected. from a Πάτσα] V—10 mag star.," Optimization means maximizing the photon collection rate, $\gamma/T$, where $T$ is the duration of the experiment and, again, $\gamma$ is the total number of photons collected from a fiducial $V=10$ mag star." + Explicitly. where A@ is (he angular size of the detector. D is the diameter of the primarv-optic. € is the fraction of the time actually spent exposing. and A is a constant that depends on the telescope. filter. aud detector throughput.," Explicitly, where $\Delta\theta$ is the angular size of the detector, $D$ is the diameter of the primary-optic, ${\cal E}$ is the fraction of the time actually spent exposing, and $K$ is a constant that depends on the telescope, filter, and detector throughput." + For our caleulations. we assume cm 7s. which is appropriate for a broad (V+2) filter and the fiducial V.=10 mag star.," For our calculations, we assume $K= K_0\equiv 40 \, e^-\,\rm cm^{-2}\,s$ , which is appropriate for a broad $(V+R)$ filter and the fiducial $V=10$ mag star." + The design problems are brought into sharper relief bv noting that A@=£/DJ. where £ is the linear size of the detector ancl F is the focal ratio. or f//3£.. of the optics.," The design problems are brought into sharper relief by noting that $\Delta\theta = {\cal L}/D{\cal F}$, where ${\cal L}$ is the linear size of the detector and ${\cal F}$ is the focal ratio, or $f$, of the optics." + Equation (4)) then becomes That is. almost regardless of other characteristics of (he svstem. the camera should be made as Last as possible.," Equation \ref{equGam1}) ) then becomes That is, almost regardless of other characteristics of the system, the camera should be made as fast as possible." + We will adopt F=2. bevond which it becomes substantially more dilficult to design the opties.," We will adopt ${\cal F}=2$, beyond which it becomes substantially more difficult to design the optics." + A more remarkable feature of equation (5)) is that all explicit dependence on the size of the primary optic has vanished: a 1 telescope and an 8m telescope would appear equally good!, A more remarkable feature of equation \ref{equGam2}) ) is that all explicit dependence on the size of the primary optic has vanished: a 1” telescope and an 8m telescope would appear equally good! + Actually. as we now show. there is a hidden dependence of £ on D. which favors small telescopes.," Actually, as we now show, there is a hidden dependence of ${\cal E}$ on $D$, which favors small telescopes." + The Ooglobal efficiency € can be broken down into two factors. €=Oes£j£€s. where Ey0 is the fraction of time available [or observing (i.e.. during which the sky is dark. the weather is good. etc.).," The global efficiency ${\cal E}$ can be broken down into two factors, ${\cal E} = {\cal E}_0 {\cal E}_S$, where ${\cal E}_0$ is the fraction of time available for observing (i.e., during which the sky is dark, the weather is good, etc.)," + and Ey is the fraction of this available observing (ime that the shutter is actually open., and ${\cal E}_S$ is the fraction of this available observing time that the shutter is actually open. + The first factor is not affected by telescope design ancl so will be ignored [or, The first factor is not affected by telescope design and so will be ignored for +"Turning to the UV continuum, we measure —6.1x10-15 ffrom our X-shooter spectrum of im1 at observed wavelengths nearAA.","Turning to the UV continuum, we measure $F = 6.1 \times +10^{-18}$ from our X-shooter spectrum of im1 at observed wavelengths near." +". The corresponding rest-frame luminosity near AA,, L,(2800)=1.9x107° eerg s! Hz~"", implies: with the same correction factors as above."," The corresponding rest-frame luminosity near , $L_\nu(2800) = 1.9 \times +10^{29}$ erg $^{-1}$ $^{-1}$, implies: with the same correction factors as above." +" The two values of SFR are in reasonable agreement, given the systematic uncertainties affecting the two estimators, which sample different portions of the IMF (see?).."," The two values of SFR are in reasonable agreement, given the systematic uncertainties affecting the two estimators, which sample different portions of the IMF \citep[see][]{meurer09}." +" At the S/N ratio of the present data, the auroral lines most commonly used for the determination of the electron temperature, A4363, A5755, and [SI]A6312 are below the detection limit."," At the S/N ratio of the present data, the auroral lines most commonly used for the determination of the electron temperature, $\lambda 4363$, $\lambda 5755$, and $\lambda 6312$ are below the detection limit." + The 30 upper limit F(4363)<0.3x10 ttranslates to an upper limit on the temperature Ίο<9900 KK (?)..," The $ 3 +\sigma$ upper limit $F(4363) \leq 0.3 \times 10^{-16}$ translates to an upper limit on the temperature $T_{\rm e} \leq 9900$ K \citep{aller84}. ." +" Turning to density sensitive line ratios, we resolve both the AA3728,3730 and the AA1907,1909 doublets, while 446716, falls between the J and the H bands, where the atmospheric6731 transmission is a few percent only."," Turning to density sensitive line ratios, we resolve both the $\lambda \lambda 3728, +3730$ and the $\lambda \lambda 1907, 1909$ doublets, while $\lambda \lambda 6716, 6731$ falls between the $J$ and the $H$ bands, where the atmospheric transmission is a few percent only." +" We used the package inIRAF,, incorporating the calculations by ?,, to deduce n(e)=315+ 15ccm? from the observed F(3726)/F(3728) ratio, assuming 7.=10000+ 1000KK. Although less tightly constrained, the observed £'(1907)/£(1909) ratio is consistent with the electron density deduced from the higher S/N ratio textscii]] doublet."," We used the package in, incorporating the calculations by \citet{shaw95}, to deduce $n(e) = 315 \pm 15$ $^{-3}$ from the observed $F(3726)/F(3728)$ ratio, assuming $T_{\rm e} = 10\,000 \pm 1000$ K. Although less tightly constrained, the observed $F(1907)/F(1909)$ ratio is consistent with the electron density deduced from the higher S/N ratio ] doublet." +" With many nebular lines detected, we can estimate the abundances of the C, N, O group using a variety of strong emission line diagnostics."," With many nebular lines detected, we can estimate the abundances of the C, N, O group using a variety of strong emission line diagnostics." + Results are collected in Table 4.., Results are collected in Table \ref{tab:abund}. + Oxygen is the element most commonly used to characteriseOxygen. the overall degree of metal enrichment of regions and we thus consider it first., Oxygen is the element most commonly used to characterise the overall degree of metal enrichment of regions and we thus consider it first. +" Among the many calibrations of the oxygen abundance based on the ratios of strong emission lines (e.g. ?), the R23 method first proposed by ? is the one still most commonly applied, at least to low redshift galaxies."," Among the many calibrations of the oxygen abundance based on the ratios of strong emission lines \citep[e.g.][]{kewley08}, , the $R23$ method first proposed by \citet{pagel79} is the one still most commonly applied, at least to low redshift galaxies." +" We used the calibration of the index R23=[F(3728)+F(3730)+F(4960)F(5008)]/ by ?,, appropriate to the lower branch of the double-valued R23 F(H8)vs. O/H relation, to deduce 12+log(O/H)44,=8.28, or approximately of the oxygenabundance in the Sun (?) and in the Orion nebula (?).."," We used the calibration of the index $R23 +\equiv [F(3728) + F(3730) + F(4960) + F(5008)]/F({\rm H}\beta)$ by \citet{kobulnicky04}, appropriate to the lower branch of the double-valued $R23$ vs. O/H relation, to deduce $12 + \log{\rm + (O/H)}_{R23} = 8.28$, or approximately of the oxygenabundance in the Sun \citep[][]{asplund09} and in the Orion nebula \citep[][]{esteban04}." + The random error in the value of log(O/H) is small and negligible compared with the ddex systematic uncertainty in the calibration of the R23 index (?)..," The random error in the value of $\log{\rm + (O/H)}$ is small and negligible compared with the dex systematic uncertainty in the calibration of the $R23$ index \citep{kewley08}." + The lower branch solution is favoured by the lowvalue of the N abundance deduced below., The lower branch solution is favoured by the lowvalue of the N abundance deduced below. +" The calibrationsof the oxygen abundance based on the ratios of nitrogen, oxygen and Balmer lines proposed by ? have the advantages, compared to R23, of being single-valued andrelatively"," The calibrationsof the oxygen abundance based on the ratios of nitrogen, oxygen and Balmer lines proposed by \citet{pettini04} have the advantages, compared to $R23$ , of being single-valued andrelatively" + in the densitv., in the density. + “Phe Hohenberg-Ixohn. theorem then shows that for ground states the density functional. theory possess an exact energv functional and there exists a variational principle for the electron density., The Hohenberg-Kohn theorem then shows that for ground states the density functional theory possess an exact energy functional and there exists a variational principle for the electron density. + Phe INS equation is then an elfective one electron equation where the exchange operator in the EEaurtree-Fock. equation is replaced. by an exchange-correlation operator that depends only on the electron density., The KS equation is then an effective one electron equation where the exchange operator in the Hartree-Fock equation is replaced by an exchange-correlation operator that depends only on the electron density. + “This is exactly what is needed in the present oblem., This is exactly what is needed in the present problem. + The KS equation. then treats the IN. electron »roblem as single electron wave functions., The KS equation then treats the $N$ electron problem as single electron wave functions. + Let n(r)=Spear. where the summation is carried over all electrons. be the electron density.," Let $n({\bf r})=\sum_{l=1}^N +{\left| {\psi_l({\bf r})} \right|}^2$, where the summation is carried over all electrons, be the electron density." + In. our yarticular case. we examine the bound. state of Be (Z=4) (as well as that of the higher Z trace species like C.N etc).," In our particular case, we examine the bound state of Be (Z=4) (as well as that of the higher Z trace species like C, N etc)." + The Be is a trace element. immersed. in a plasma of ‘ually ionized Hydrogen and Helium (mostly) and negligible amounts of heavy elements., The Be is a trace element immersed in a plasma of fully ionized Hydrogen and Helium (mostly) and negligible amounts of heavy elements. + Hence. the major contribution o the electron density comes from the electrons contributed ov Hiedrogen and BHelium.," Hence, the major contribution to the electron density comes from the electrons contributed by Hydrogen and Helium." + This term is essentially given » the environment in which the trace specie is immersed., This term is essentially given by the environment in which the trace specie is immersed. +" teturning to the WS equation. the third. term in the Ks equation is the mutual electron-electron interaction between he bound electron and the free electrons which exist inside he ""effective orbit and it provides the elfective. electron screening of the ion."," Returning to the KS equation, the third term in the KS equation is the mutual electron-electron interaction between the bound electron and the free electrons which exist inside the `effective orbit' and it provides the effective electron screening of the ion." + Lt is easy to estimate when this term »comes important., It is easy to estimate when this term becomes important. + The number of free electrons per Bohr radius. Nig is given by: This term becomes important for Ne~1 or noz1.623107Z?.," The number of free electrons per Bohr radius, $N_B$ is given by: This term becomes important for $N_B \sim 1$ or $n_e \gtrsim 1.623\times 10^{24} Z^{3}$." +" ""Phe forth term is the exchange which is givenL by Οιδη where £ is the exchange energy.", The forth term is the exchange which is given by ${{\partial { E}_{ex}} / {\partial n}}$ where $E_{ex}$ is the exchange energy. + Because of its unique properties. the KS equation. gained popularity with physical chemists.," Because of its unique properties, the KS equation gained popularity with physical chemists." + Phe accuracy of using he KS equation for the calculation of ionization potentials in molecules is described in 2.., The accuracy of using the KS equation for the calculation of ionization potentials in molecules is described in \citet{CRRRP98}. + As a rule. the results of the KS equation are more accurate than those obtained from he Hartree-Fock approximation and reach the accuracy required by quantum chemists.," As a rule, the results of the KS equation are more accurate than those obtained from the Hartree-Fock approximation and reach the accuracy required by quantum chemists." + The implementation of the IWS equation in astrophysics of dense matter is described for he first time by 2.., The implementation of the KS equation in astrophysics of dense matter is described for the first time by \citet{Lai91}. + We solved. for the eigenvalue. of the INS. equation assuming the composition of the present solar core., We solved for the eigenvalue of the KS equation assuming the composition of the present solar core. + We used a variational principle with several trial functions since we are mostly interested in the eigenvalues and not in the wave functions., We used a variational principle with several trial functions since we are mostly interested in the eigenvalues and not in the wave functions. + The results for Be are shown in figure 10 along with the results for the Coulomb potential (and the same boundary condition).," The results for ${\rm +Be}^{7}$ are shown in figure \ref{fig:Be7-ioniz} along with the results for the Coulomb potential (and the same boundary condition)." + Lt appears that the correlations and exchange terms in the WS equation contribute to the further suppression of the energy. level anc complete ionization occurs a là WS at a higher density., It appears that the correlations and exchange terms in the KS equation contribute to the further suppression of the energy level and complete ionization occurs a $\grave{\rm a}$ KS at a higher density. + Note tha for sullicienthy low densities. the KS predicts. significan lowering of the ground state of a clement relative to the continuum.," Note that for sufficiently low densities, the KS predicts significant lowering of the ground state of a element relative to the continuum." + This is a consequence of the exchange term which is mostly. contributed by Hydrogen and Helium ane not by the electrons of the trace ion under consideration., This is a consequence of the exchange term which is mostly contributed by Hydrogen and Helium and not by the electrons of the trace ion under consideration. + The phenomenon does not occur for species which are no trace elements. (see later)., The phenomenon does not occur for species which are not trace elements (see later). + The results with dilferent. tria functions vary a bit and shown are the best (lowest) results., The results with different trial functions vary a bit and shown are the best (lowest) results. + The critical densities and (rz) as obtained in the two approximations are compared in Table 1..," The critical densities and $\langle +r_{Z}\rangle$ as obtained in the two approximations are compared in Table \ref{tbl:crit}." + From the table we see that in the Schródinger approximation (rz) is constant while in the WKS equation it varies ancl increases with the charge of the ion.," From the table we see that in the ${\ddot +{\rm o}}$ dinger approximation $\langle r_{Z}\rangle$ is constant while in the KS equation it varies and increases with the charge of the ion." + A good fit for the value of the critical fry over this range of charges is rz/Z=0.4510.026Z.," A good fit for the value of the critical $\langle r_{Z} +\rangle$ over this range of charges is $r_{Z}/Z=0.451-0.026Z$." + ‘This expression can be easily translated into a termi added to the [ree energy so as to secure pressure ionization., This expression can be easily translated into a term added to the free energy so as to secure pressure ionization. + Based on the WKS equation. we find that the CNO elements are fully ionized in the core of the sun., Based on the KS equation we find that the CNO elements are fully ionized in the core of the sun. + Indeed. a 7=0 the Oxygen still has a bound electron at the densities of the solar core. but the low binding energy. and the high temperature impose complete ionization uncer the conditions in the center of 1ο Sun.," Indeed, at $T=0$ the Oxygen still has a bound electron at the densities of the solar core, but the low binding energy and the high temperature impose complete ionization under the conditions in the center of the Sun." + On the other hand. species with Z=10. like Neon and Iron. still keep their Ix-shell electrons.," On the other hand, species with $Z\ge 10$, like Neon and Iron, still keep their K-shell electrons." + Assuming that all species heavier or equal to Ne are fully ionized introduces a relative error of the order ob SZNO}OXCN).X(CO))/10. or about 10. in the pressure and. speed. of sound.," Assuming that all species heavier or equal to Ne are fully ionized introduces a relative error of the order of $\lesssim +Z(1-X(C)-X(N)-X(O))/10$, or about $10^{-3}$ in the pressure and speed of sound." + Vhe etfect of the boundary condition on the result can be seen in the following way., The effect of the boundary condition on the result can be seen in the following way. + We solved the INS equation under the condition. c(rx)=0 for various densities., We solved the KS equation under the condition $\psi(r \rightarrow \infty)=0$ for various densities. + The result is that as the density increases monotonically. the," The result is that as the density increases monotonically, the" + The results of the extrapolation are illustrated in Fig. l.., The results of the extrapolation are illustrated in Fig. \ref{fig1}. + Various magnetic field structures in the corona are obvious., Various magnetic field structures in the corona are obvious. +" The gray-coded bottom plot shows the weak unipolar magnetic field strength in the photosphere, as derived from data of the MDI instrument."," The gray-coded bottom plot shows the weak unipolar magnetic field strength in the photosphere, as derived from data of the MDI instrument." +" The black line delineates the boundary of the coronal hole, as identified in the EUV images obtained by EIT (Extreme Ultraviolet Imaging Telescope) and SUMER on SOHO."," The black line delineates the boundary of the coronal hole, as identified in the EUV images obtained by EIT (Extreme Ultraviolet Imaging Telescope) and SUMER on SOHO." + The closed magnetic field lines (yellow) in the left frame of Fig., The closed magnetic field lines (yellow) in the left frame of Fig. +" 1 pertain to photospheric fields with strength B>30 G, the open ones (red-brown) in the right frame to stronger fields, with B>100 G. Very few field lines are separately shown, to not confuse the picture by intermingling of magnetic field lines, which would produce a diffuse unresolved pattern."," \ref{fig1} pertain to photospheric fields with strength $B \ge 30$ G, the open ones (red-brown) in the right frame to stronger fields, with $B \ge 100$ G. Very few field lines are separately shown, to not confuse the picture by intermingling of magnetic field lines, which would produce a diffuse unresolved pattern." +" Note that the open magnetic flux (right frame) is concentrated, with linear bundles reaching the top of the simulation box."," Note that the open magnetic flux (right frame) is concentrated, with linear bundles reaching the top of the simulation box." + These bundles are anchored in small (a few seconds of arc in diameter) tubes linked to fine structures with strong unipolar photospheric magnetic flux., These bundles are anchored in small (a few seconds of arc in diameter) tubes linked to fine structures with strong unipolar photospheric magnetic flux. +" Despite their filamentary nature, the flux tubes spread with height, and as coronal funnels fill increasingly larger fractions of the CH at greater altitude."," Despite their filamentary nature, the flux tubes spread with height, and as coronal funnels fill increasingly larger fractions of the CH at greater altitude." +" Not unexpectedly, in the CH there are only low-lying loops."," Not unexpectedly, in the CH there are only low-lying loops." +" They sparsely populate the hole area, consistent with the statistical results of WiegelmannandSolanki (2004)."," They sparsely populate the hole area, consistent with the statistical results of \cite{solanki2004}." +". Note, in contrast, that the strong loops just outside of the hole reach greater heights."," Note, in contrast, that the strong loops just outside of the hole reach greater heights." + This region also has much brighter ultraviolet emission due to a better plasma confinement and higher plasma density., This region also has much brighter ultraviolet emission due to a better plasma confinement and higher plasma density. +" The corresponding radiance maps, Ne Dopplershifts and magnetograms are shown in Fig."," The corresponding radiance maps, Ne Dopplershifts and magnetograms are shown in Fig." + 1 and Fig., 1 and Fig. + 2 of Xiaetal.(2003)., 2 of \cite{xia2003}. +". Here a complementary magnetogram obtained from NSO/Kitt Peak (Jonesetal. (1992))), is overlaid with contours of the Doppler shifts in km s! of the Ne (77 nm) line."," Here a complementary magnetogram obtained from NSO/Kitt Peak \cite{jones1992}) ), is overlaid with contours of the Doppler shifts in km $^{-1}$ of the Ne (77 nm) line." + In Fig., In Fig. +" 2 we present the same Dopplermap, with the Doppler shift over the range of +20 km s7!, and the extrapolated magnetic field lines shown in projection for comparison with the Dopplershift pattern."," \ref{fig2} we present the same Dopplermap, with the Doppler shift over the range of $\pm 20$ km $^{-1}$, and the extrapolated magnetic field lines shown in projection for comparison with the Dopplershift pattern." + Again the closed field lines are yellow and the open ones red-brown., Again the closed field lines are yellow and the open ones red-brown. +" An area of 250""x300"" on the solar disk is shown, covering a large fraction of the equatorial CH and its boundary regions."," An area of $250\arcsec \times +300\arcsec$ on the solar disk is shown, covering a large fraction of the equatorial CH and its boundary regions." +" Note the uniformly yellow domain in the top right corner, which lies outside the hole and corresponds to closed loops shown before in Fig. 1.."," Note the uniformly yellow domain in the top right corner, which lies outside the hole and corresponds to closed loops shown before in Fig. \ref{fig1}." +" The cross-shaped spines of open flux, in the top left corner for instance, mostly coincide with bluish patches and thus indicate sizable plasma outflow in this open field domains, in particular at location(100”,, 250’’))."," The cross-shaped spines of open flux, in the top left corner for instance, mostly coincide with bluish patches and thus indicate sizable plasma outflow in this open field domains, in particular at location, )." +" Furthermore, note that there are many open field lines overarching the smaller yellow patches, which correspond to the closed magnetic carpet."," Furthermore, note that there are many open field lines overarching the smaller yellow patches, which correspond to the closed magnetic carpet." +in (he svstem. but not al the level of a tvpical classical T Tauri star (CTTS).,"in the system, but not at the level of a typical classical T Tauri star (CTTS)." + While the star has no measured infrared excess. an apparent disk ancl jet in Πο have been detected by Demine.Charbonneau&Harrington(2004) and Tokunagaοἱal.(2004).. respectively.," While the star has no measured infrared excess, an apparent disk and jet in $_2$ have been detected by \citet{dem} and \citet{tok}, respectively." + The extremely long duration of the eclipse. currently about one-half of the period. clearly shows that the eclipsing body is not a companion star.," The extremely long duration of the eclipse, currently about one-half of the period, clearly shows that the eclipsing body is not a companion star." + Rather. it appears to be part of a circumstellar or circumbinary disk (Ilerbstetal.2002).," Rather, it appears to be part of a circumstellar or circumbinary disk \citep{h02}." +. During eclipse the svstem becomes both bluer and more highly polarized (1lerbstetal.2002:Agol2004).. suggesting that we are seeing il primarily or entirely in scattered lisht.," During eclipse the system becomes both bluer and more highly polarized \citep{h02, agol}, suggesting that we are seeing it primarily or entirely in scattered light." + There are (wo (ime scales associated with the eclipse. a 48.37 dav evele for the main eclipse aud a secular increase in (he eclipse duration of about. 1 day per vear (Ilerbstοἱal.2002:Winnet2003:Tamilton2004)..," There are two time scales associated with the eclipse, a 48.37 day cycle for the main eclipse and a secular increase in the eclipse duration of about 1 day per year \citep{h02,w03,ham04a}." + Two recent models based on the historic light curve (Winn2004) have proposed (hat the 48 dav eclipse evcle is (he orbital period of a binary system while the secular variation is caused by precession of the circumbinary disk Chiang&Murrav-Clav. 2004).," Two recent models based on the historic light curve \citep{w03,jw04} have proposed that the 48 day eclipse cycle is the orbital period of a binary system while the secular variation is caused by precession of the circumbinary disk \citep{w04,c04}." +. If this is correct it means that. for the first time. we can probe the structure of a disk on leneth scales as small or smaller (han a stellar diameter and monitor events in a possibly planet-forming disk on human time scales!," If this is correct it means that, for the first time, we can probe the structure of a disk on length scales as small or smaller than a stellar diameter and monitor events in a possibly planet-forming disk on human time scales!" + Clearly it is important to understand as much as possible about (his unique PAIS stellar svstem and {ο exploit its fortuitous geometry while the opportunity lasts., Clearly it is important to understand as much as possible about this unique PMS stellar system and to exploit its fortuitous geometry while the opportunity lasts. + One characterisc of T Tauri stars. especially WITS. is that they are procdigious sources ol X-ray emission. although for still largely unknown reasons (FeigelsonFeigelsonetal. 2003).," One characteristic of T Tauri stars, especially WTTS, is that they are prodigious sources of X-ray emission, although for still largely unknown reasons \citep{fm, f03}." +. We hoped to use the periodic eclipse of the IX6-T star behind an optically thick and presumably X-ray opaque circumstellar disk. to allow us to map the structure of the coronal plasma in this WITS.," We hoped to use the periodic eclipse of the K6-7 star behind an optically thick and presumably X-ray opaque circumstellar disk, to allow us to map the structure of the coronal plasma in this WTTS." + As a prelude to this intended. study we searched for archival X-ray data on NGC 2264 and found a long exposure in the archives of the that includes KIL 15D. Ho was obtained during a time interval when the star was oul of eclipse so we expected a relatively strong signal. characteristic of a WITS.," As a prelude to this intended study we searched for archival X-ray data on NGC 2264 and found a long exposure in the archives of the that includes KH 15D. It was obtained during a time interval when the star was out of eclipse so we expected a relatively strong signal, characteristic of a WTTS." + Instead. we found that the total X-ray count oul of eclipse is so small Chat il mav not be possible to learn much by monitoring during an eclipse cvele.," Instead, we found that the total X-ray count out of eclipse is so small that it may not be possible to learn much by monitoring during an eclipse cycle." + This in turn has prompted us to consider the extent to which KIT 15D is unusual in vel another way. namely as a remarkably faint X-ray source fora WTTS.," This in turn has prompted us to consider the extent to which KH 15D is unusual in yet another way, namely as a remarkably faint X-ray source for a WTTS." + In (his paper we present the case that it is. indeed. an unusually weak source of X-ray. enission aud discuss possible implications of this for the system and for the broader question of X-ray. production in solar-like. PAIS stars.," In this paper we present the case that it is, indeed, an unusually weak source of X-ray emission and discuss possible implications of this for the system and for the broader question of X-ray production in solar-like, PMS stars." +regions: in the outer regions violations could be due to more recent and still ongoing slow accretion. since those regions have not reached equilibrium due to the large sound crossing time.,"regions; in the outer regions violations could be due to more recent and still ongoing slow accretion, since those regions have not reached equilibrium due to the large sound crossing time." + Observationallv. Richardetal.(2010) measured an X-rav/Lensing mass cliscrepaney of =1.3$ at $\sigma$ significance level in a sample of 20 strong lensing clusters." + They interpret. this as evidence that the assumption of strict hvclrostatie equilibrium. required. by the X-ray mass estimates is not wholly reliable and the merging activity can add non-thermal pressure support to the IC eas through bulk motions., They interpret this as evidence that the assumption of strict hydrostatic equilibrium required by the X-ray mass estimates is not wholly reliable and the merging activity can add non-thermal pressure support to the IC gas through bulk motions. + Sandersetal.(2010). placed a direct limit on turbulence based. on the non-thermal velocity broadening measured from the emission lines originating in the central 30 kpe of the galaxy cluster Abell 1835., \cite{sanders2010a} placed a direct limit on turbulence based on the non-thermal velocity broadening measured from the emission lines originating in the central 30 kpc of the galaxy cluster Abell 1835. + They. found. that the ratio of turbulent to thermal energy density in the core is less than1, They found that the ratio of turbulent to thermal energy density in the core is less than. +354... Alolnaretal.(2010). analyzed a sample of massive clusters of galaxies crawn from high-resolution cosmological simulations and found a significant contribution 45543) from non-thermal pressure., \cite{molnar2010} analyzed a sample of massive clusters of galaxies drawn from high-resolution cosmological simulations and found a significant contribution ) from non-thermal pressure. + They. also tested the validity. of strict hyclrostatie equilibrium: in. Abell 1059 using gravitational lensing and X-ray observations under the assumption of spherical geometry in order to explain the X-rav/Lensing mass discrepancy: they found a contribution of about from non-thermal pressure within the core region of Abell 1689. sugecsting an alternate explanation for the mass discrepancy. as long as the spherical assumption holds.," They also tested the validity of strict hydrostatic equilibrium in Abell 1689 using gravitational lensing and X-ray observations under the assumption of spherical geometry in order to explain the X-ray/Lensing mass discrepancy: they found a contribution of about from non-thermal pressure within the core region of Abell 1689, suggesting an alternate explanation for the mass discrepancy, as long as the spherical assumption holds." + Our results point to a scenario where the non-thermal component is about 20% of the total energy budget of the IC eas., Our results point to a scenario where the non-thermal component is about $20\%$ of the total energy budget of the IC gas. + This level is quite lower than that found from Molnaretal.(2010). under the assumption of spherical ecometry. suggesting that accounting for the proper triaxial geometry is quite important in evaluating Par accurately.," This level is quite lower than that found from \cite{molnar2010} under the assumption of spherical geometry, suggesting that accounting for the proper triaxial geometry is quite important in evaluating $P_{\rm nt}$ accurately." + Another relevant consideration here is that in our moce we constrained the non-thermal pressure to be à constan [actor of the local thermal pressure throughout the cluster., Another relevant consideration here is that in our model we constrained the non-thermal pressure to be a constant factor of the local thermal pressure throughout the cluster. + The results of Mahbdavietal.(2008) show that there is a racial trend of the N-rav/WL mass ratio. that is interprete as caused by non-thermality increasing toward the outer regions. though their findings hinge on the assumed spherica ecometry. so they did not disentanegle the elect of triaxiality from non-thermal pressure support.," The results of \cite{mahdavi2008} show that there is a radial trend of the X-ray/WL mass ratio, that is interpreted as caused by non-thermality increasing toward the outer regions, though their findings hinge on the assumed spherical geometry, so they did not disentangle the effect of triaxiality from non-thermal pressure support." + In this perspective. we used a linear relation of P. by fixing the slope to that four by Alabdavietal.(2008). and leaving the normalization as a free parameter: the results are. not allectecl appreciably from this. the reason is that the fit is more dominated. by the innermost part (<300 kpe) of the Nray ancl SL data.," In this perspective, we used a linear relation of $P_{\rm nt}$, by fixing the slope to that found by \cite{mahdavi2008} and leaving the normalization as a free parameter: the results are not affected appreciably from this, the reason is that the fit is more dominated by the innermost part $<300$ kpc) of the Xray and SL data." + Aloreover. in order to gauge the likely model dependence of the inferred. non-thermal pressure. we performed a joint analysis bv excluding the temperature constraints (Equation 0)) and assuming a spherical NEN model for the DM.," Moreover, in order to gauge the likely model dependence of the inferred non-thermal pressure, we performed a joint analysis by excluding the temperature constraints (Equation \ref{chi2wwe}) ) and assuming a spherical NFW model for the DM." + Doing so also allows us to make a direct comparison with Lemzeetal.(2008).. who used a similar approach.," Doing so also allows us to make a direct comparison with \cite{lemze2008}, who used a similar approach." +" We found that the ratio between the (de)»ojected leniperature »ofile measured from the X-ray spectrum and that obtained »v assuming strict hyelrostatic equilibrium. (Equation 4 with Par= Buy)is 0.50.6. which is lower than the determination in our triaxial model (P,/P,7 OS)."," We found that the ratio between the (de)-projected temperature profile measured from the X-ray spectrum and that obtained by assuming strict hydrostatic equilibrium (Equation \ref{aa4} with $P_{\rm tot}= P_{\rm +th}$ ) is $\sim0.5-0.6$, which is lower than the determination in our triaxial model $P_{\rm th}/P_{\rm tot}\sim 0.8$ )." + Note hat Lemzeetal.(2008) concluded: that a factor of 0.7 explains most of the temperature discrepancy in bell 1689. whereas we find à somewhat lower value: this stems mostly from the more recent Chandra calibrations adopted in the present work. which led to a lower spectral. temperature profile (by ~20%).," Note that \cite{lemze2008} concluded that a factor of 0.7 explains most of the temperature discrepancy in Abell 1689, whereas we find a somewhat lower value; this stems mostly from the more recent Chandra calibrations adopted in the present work, which led to a lower spectral temperature profile (by $\sim 20\%$ )." + While this test heavily hinges on the model of spherical gcometry. i0 suggests that the small formal error on £ in our triaxial joint analysis merits some caution.," While this test heavily hinges on the model of spherical geometry, it suggests that the small formal error on $\xi$ in our triaxial joint analysis merits some caution." + In this paper we have employed a physical cluster mocel or Abell 1689 with a triaxial mass distribution including support from non-thermal pressure. and. proved. that it is consistent with the X-ray and. SL. observations and the »edietions of CDM mocels.," In this paper we have employed a physical cluster model for Abell 1689 with a triaxial mass distribution including support from non-thermal pressure, and proved that it is consistent with the X-ray and SL observations and the predictions of CDM models." + We demonstrated. that accounting for the three-imensional geometry. and. the non-thermal component of 10 gas allows us to resolve the long-standing cliscrepancy xtween the X-ray and strong lensing mass of Abell 1689 in re Literature. as well as to measure a central slope of the DM and a concentration parameter in agreement with the worctical expectations of the CDAL scenario.," We demonstrated that accounting for the three-dimensional geometry and the non-thermal component of the gas allows us to resolve the long-standing discrepancy between the X-ray and strong lensing mass of Abell 1689 in the literature, as well as to measure a central slope of the DM and a concentration parameter in agreement with the theoretical expectations of the CDM scenario." + We also measured the contribution of the non-thermal 'omponent of the gas (~20% of the total energy. budget of 1¢ LC eas)., We also measured the contribution of the non-thermal component of the gas $\sim 20\%$ of the total energy budget of the IC gas). + This has important consequences for estimating Ίο amount of energy. injected. into clusters from mergers. vecretion of material or feedback from AGN.," This has important consequences for estimating the amount of energy injected into clusters from mergers, accretion of material or feedback from AGN." + The increasing precision of observations now makes it possible to test the assumptions of spherical svmmetry undo fvelrostatic equilibrium., The increasing precision of observations now makes it possible to test the assumptions of spherical symmetry and hydrostatic equilibrium. + Since. important current cosmological tests are based on the knowledge of the masses. shapes. ancl profiles of galaxy clusters. it is important to better characterize their physical. properties by. allowing for realistic triaxial structures as well. as. non-thermal pressure support.," Since important current cosmological tests are based on the knowledge of the masses, shapes, and profiles of galaxy clusters, it is important to better characterize their physical properties by allowing for realistic triaxial structures as well as non-thermal pressure support." + The application of our method to a larger sample of clusters will allow to infer the desired physical parameters of galaxy clusters in a bias-Lree wav. with important implications on the use of galaxy clusters as precise cosmological probes.," The application of our method to a larger sample of clusters will allow to infer the desired physical parameters of galaxy clusters in a bias-free way, with important implications on the use of galaxy clusters as precise cosmological probes." + AAL and RB. acknowledge support bv [sraeb Science Foundation grant. 823/09., A.M. and R.B. acknowledge support by Israel Science Foundation grant 823/09. + ALL. acknowledges the Centre National de la Reeherche Seientifique (CNRS) for its support., M.L. acknowledges the Centre National de la Recherche Scientifique (CNRS) for its support. + The Dark Cosmology Centre is funded by the Danish National Research Foundation., The Dark Cosmology Centre is funded by the Danish National Research Foundation. +jel is ~0.6 CAnglada.et.al.1993;Revnolds.S.P.1986).. the expected flix clensity of the Iree-Iree emission at 3.3 mun becomes 2.47 mJx based on the 3.6 em flux densitv of 0.59 mJv (Reipurthetal...1999).,"jet is ${\sim}0.6$ \citep{ang98, rey86}, the expected flux density of the free-free emission at 3.3 mm becomes 2.47 mJy based on the 3.6 cm flux density of 0.59 mJy \citep{rei99}." +. Thus. the flux densitv. attributed to the cust emission is 21.35 nv at 3.3 nun.," Thus, the flux density attributed to the dust emission is 21.35 mJy at 3.3 mm." + Adopting the dust opacity of 5=0.037engg|(A/400j/)! al.1996).. 2 = 1.0 which is ealeulated from the 1.3 mm and 3.3 mim total [Inxes and Ty. = 26 - 50 Ix (Chinietal.1997:Johnstone2003).. we estimate the mass of the dusty condensation to be 0.36 - 0.72 ML...," Adopting the dust opacity of $\kappa_{\lambda} = 0.037~\rm{cm^2 g^{-1}}~(\lambda/400 \rm{\mu m})^{\beta}$ \citep{oha96}, $\beta$ = 1.0 which is calculated from the 1.3 mm and 3.3 mm total fluxes and $T_{\rm{dust}}$ = 26 - 50 K \citep{chi97, joh03}, we estimate the mass of the dusty condensation to be 0.36 - 0.72 $_{\odot}$." + Figure ?2?cwasimadeonly frointhevisibililydaltlatakenat; 30FÀ (See Table 2)., Figure \ref{cont}$ $c$ was made only from the visibility data taken at $>$ 30 $\lambda$ (See Table 2). + In the higher resolution image. we see an elongated structure along the NE-SW direction.," In the higher resolution image, we see an elongated structure along the NE-SW direction." +" This NE-SW elongation mav imply the presence of a binary with a separation of ~ 1"".9 (corresponds to 830 AU).", This NE-SW elongation may imply the presence of a binary with a separation of $\sim$ $''$ .9 (corresponds to 830 AU). + However. there is no infrared or em counterpart toward the extension of the 3.3 mm enission. and more plausible interpretation is that the [aint continuum feature (traces the hot and dense region heated by tlie associated outflow. since the direction of the elongation ol the 3.3 mm emission is similar to the direction of the 3.6 em fine-scale jet.," However, there is no infrared or cm counterpart toward the extension of the 3.3 mm emission, and more plausible interpretation is that the faint continuum feature traces the hot and dense region heated by the associated outflow, since the direction of the elongation of the 3.3 mm emission is similar to the direction of the 3.6 cm fine-scale jet." + Figure ??ashows!hedistribuliono [theblueshi [led(VUsp 1.0 to 8.7 kms +) and redshifted (Visi12.1 to 13.8 kms 4) PCO(L0) emission in MMS 7 superposed on the 2\[ASS image., Figure \ref{INT}$ $a$ shows the distribution of the blueshifted $V_{\rm{LSR}}$ =7.0 to 8.7 km $^{-1}$ ) and redshifted $V_{\rm{LSR}}$ =12.1 to 13.8 km $^{-1}$ ) $^{12}$ CO(1–0) emission in MMS 7 superposed on the 2MASS K's-band image. + Here. we adopt the svstemic velocity of 10.6 km ! obtained from the single-dish HCO (1:0) spectrum.," Here, we adopt the systemic velocity of 10.6 km $^{-1}$ obtained from the single-dish $^{13}$ $^{+}$ (1–0) spectrum." + The outflow is elongated along the east-west direction and roughly aligned with the direction of the lvee-free jet (Reipurthetal.1999)., The outflow is elongated along the east-west direction and roughly aligned with the direction of the free-free jet \citep{rei99}. +. Both the blue- and recd-shifted. components are seen al Che east and west side of AIMS 7. which suggests that the axis of the bipolar outflow is near the plane of (he sky.," Both the blue- and red-shifted components are seen at the east and west side of MMS 7, which suggests that the axis of the bipolar outflow is near the plane of the sky." + Furthermore. the outflow shows an asvimmnietric structure wilh the stronger red- and blue-shifted components at (he eastern side.," Furthermore, the outflow shows an asymmetric structure with the stronger red- and blue-shifted components at the eastern side." + Figure ο shows velocity channel maps in the PCO(10) emission with a velocity interval of 0.6 km |., Figure \ref{12CO_ch} shows velocity channel maps in the $^{12}$ CO(1–0) emission with a velocity interval of 0.6 km $^{-1}$. + The red-shifted component in the velocity range of Vias 11.6 to 13.3 kms twas already. detected. with the BIMA and the FCRAO 14 m telescope 2003)., The red-shifted component in the velocity range of $V_{\rm{LSR}}$ =11.6 to 13.3 $\rm{km~s^{-1}}$ was already detected with the BIMA and the FCRAO 14 m telescope \citep{wil03}. +. The distribution of this component is consistent with that. [ound by (heir observations., The distribution of this component is consistent with that found by their observations. + We have newly detected other components in the velocity range [rom Vjag-1.6 to 11.0 kms.|., We have newly detected other components in the velocity range from $V_{\rm{LSR}}$ =7.6 to 11.0 $\rm{km~s^{-1}}$. + High-velocity blue-shifted components in the velocity range of Vig 7.6 to 8.7 kms! are seen ad the eastern side of MALS 7., High-velocity blue-shifted components in the velocity range of $V_{\rm{LSR}}$ =7.6 to 8.7 $\rm{km~s^{-1}}$ are seen at the eastern side of MMS 7. + Particularly. the strong and compact CO component is evident at the position of the Ixs-band nebula which is most likely illuminated by MAIS 7.," Particularly, the strong and compact CO component is evident at the position of the K's-band nebula which is most likely illuminated by MMS 7." + The strong blueshifted and redshilted components are only seen al (he eastern side., The strong blueshifted and redshifted components are only seen at the eastern side. + These results suggest that the ΟΙ0) bipolar outflow is slightly inclined from the, These results suggest that the $^{12}$ CO(1–0) bipolar outflow is slightly inclined from the +The conclusion of this brief discussion is (hat in (he Shakura-Sunvaey parameterization of the turbulent viscosity in hvdrodvnanmic disks. either a~107. or ae10(r/Hy. depending on the unknown characteristics of the mechanism which sustains Gurbulence.,"The conclusion of this brief discussion is that in the Shakura-Sunyaev parameterization of the turbulent viscosity in hydrodynamic disks, either $\alpha\sim 10^{-3}$, or $\alpha\sim +10^{-5}(r/H)^2$, depending on the unknown characteristics of the mechanism which sustains turbulence." + In principle. one should also check that Re2Rej: as pele (eoὃς is the velocity dispersion and / the mean [ree path). this translates into /7//>10* in the first case above. and in the second. but both requirements are most probably satisfied evervwhere in astrophysical accretion disks.," In principle, one should also check that $Re > Re_m$; as $\nu\sim l c$ $c\sim c_s$ is the velocity dispersion and $l$ the mean free path), this translates into $H/l \gtrsim 10^3$ in the first case above, and $r^2/Hl +\gtrsim \beta^{-1}\sim 10^5$ in the second, but both requirements are most probably satisfied everywhere in astrophysical accretion disks." + It is unclear how the presence of a magnetic fiekl can modifv lyelrodvnamic shear turbulence., It is unclear how the presence of a magnetic field can modify hydrodynamic shear turbulence. + In particular. even a cdvnamically non dominant field can easily affect the mechanism ol generation of turbulence. and therefore significantly mocily the efficiency of the turbulent viscositv. transport. on top of adding a turbulent resistivity. even if (he MIID flow remains linearlystable.," In particular, even a dynamically non dominant field can easily affect the mechanism of generation of turbulence, and therefore significantly modify the efficiency of the turbulent viscosity transport, on top of adding a turbulent resistivity, even if the MHD flow remains linearly." +.. Reversely. the possible occurrence of hvdrodynamic shear turbulence can possibly affect in a major way our present understanding of MIID. transport ancl dvnamo processes in accretion disks. which mostly relies on the physics of the nonlinear development of the magneto-rotational instability.," Reversely, the possible occurrence of hydrodynamic shear turbulence can possibly affect in a major way our present understanding of MHD transport and dynamo processes in accretion disks, which mostly relies on the physics of the nonlinear development of the magneto-rotational instability." + Clarilving (lese questions is of primary importance for accretion disk theory., Clarifying these questions is of primary importance for accretion disk theory. + To conclude this paper. let me point out that (here is one example of keplerian disk whieh has been observed with a great luxury of details. and whieh is not turbulent. namely saburns vines.," To conclude this paper, let me point out that there is one example of keplerian disk which has been observed with a great luxury of details, and which is not turbulent, namely Saturn's rings." + However. the requirements discussed above fail on several accounts in ring svslenms. because both the particle size d and mean three path / are comparable to Lf.," However, the requirements discussed above fail on several accounts in ring systems, because both the particle size $d$ and mean three path $l$ are comparable to $H$." + For example. in the first limiting case discussed above. the ring is necessarily laminar. while in the," For example, in the first limiting case discussed above, the ring is necessarily laminar, while in the" +they observed in theVane Z bands. with a second but fainter peak visible in the orbital modulation.,"they observed in the and bands, with a second but fainter peak visible in the orbital modulation." + The CV was on average 0.2£0.1 mag brighter during the MDAL observations than during the INT observations., The CV was on average $0.2\pm0.1$ mag brighter during the MDM observations than during the INT observations. + Thus. it might be expected. that the increased. Luminosity of the accretion cise would dilute the contribution from the secondary. removing the associated second peak if such is its source. — from the orbital modulation.," Thus, it might be expected that the increased luminosity of the accretion disc would dilute the contribution from the secondary, removing the associated second peak – if such is its source – from the orbital modulation." + Unfortunately. the phase coverage in our ALDAL bane folded. light. curve (Fie.," Unfortunately, the phase coverage in our MDM -band folded light curve (Fig." + 11 (e)) is insullicient to enable us to discern. the morphology of the orbital modulation., \ref{fig:lcint}~ (c)) is insufficient to enable us to discern the morphology of the orbital modulation. + Vhe N-rav. luminosity of the source in the 0.52.5. keV band was calculated by Hakalaetal.(1997). to be Lyx1.45107 erg ft., The X-ray luminosity of the source in the 0.5–2.5 keV band was calculated by \cite{hakala97} to be $L_{\mathrm{X}} \simeq 1.1 \times 10^{32}$ erg $^{-1}$. + We extrapolate the Dux they measured to find the flux in the 0.56 keV band by fitting with a bremsstrahlung model in finding Fx—10H erg 3 7 (unabsorbed).," We extrapolate the flux they measured to find the flux in the 0.5–6 keV band by fitting with a 3-keV bremsstrahlung model in, finding $F_{\mathrm{X}} \simeq 2.4 \times 10^{-14}$ erg $^{-1}$ $^{-2}$ (unabsorbed)." + We calculate the UV and optical llux using the quiescent V-band magnitude of 20.27£0.04 mag from Ixaluznvetal.(1999). with the formula. logPopt=OAmy 4232. from vanTeeselingetal. (1996).. to find Pcopi23.710L Sores tem27.," We calculate the UV and optical flux using the quiescent -band magnitude of $20.27\pm0.04$ mag from \citet{kaluz99} with the formula, $F_{\mathrm{uv+opt}}=-0.4m_{\mathrm{V}} - 4.32$ , from \citet*{teese96}, to find $F_{\mathrm{uv+opt}} \simeq 3.7 \times 10^{-13}$ erg $^{-1}$ $^{-2}$." + This leads to an X-rav-to-UVfoptical flux ratio of £S ffi 0.06., This leads to an X-ray-to-UV/optical flux ratio of $F_{\mathrm{X}}$ $F_{\mathrm{uv + opt}}\sim 0.06$ . + Previously. the svstem. was seen as faint as 1—22.5 (IXukarkin&Alivonoyv1970).. which would lead to an bs ffion ratio a factor of ten. higher. but there is no evidence for the svstem being this faint during the epoch from which we take the measurements that we use in our calculation.," Previously, the system was seen as faint as $V=22.5$ \citep{kukarkin70}, which would lead to an $F_{\mathrm{X}}$ $F_{\mathrm{uv + opt}}$ ratio a factor of ten higher, but there is no evidence for the system being this faint during the epoch from which we take the measurements that we use in our calculation." + Nevertheless. since we cannot be sure that the system was not fainter at the time the X-ray lux was measured. we consider the bs ffiop ratio estimated above to be a lower limit.," Nevertheless, since we cannot be sure that the system was not fainter at the time the X-ray flux was measured, we consider the $F_{\mathrm{X}}$ $F_{\mathrm{uv + opt}}$ ratio estimated above to be a lower limit." + Previously Webbetal.(2004). found P=1.7040.13 for a power law fit to archival X-ray spectral data for the source: in addition they found. an even softer power law photon index if they added a Gaussian absorption line at 1 keV. which improved their fit.," Previously \citet{webb04} found $\Gamma=1.70\pm0.13$ for a power law fit to archival X-ray spectral data for the source; in addition they found an even softer power law photon index if they added a Gaussian absorption line at 1 keV, which improved their fit." + They. interpreted. this absorption line as possible electron. evclotron resonance in a neutron star pulsar., They interpreted this absorption line as possible electron cyclotron resonance in a neutron star pulsar. + The lack of any evidence for such an absorption line in our data weakens the case for a neutron star pulsar (or LAINB) identification for CV1., The lack of any evidence for such an absorption line in our data weakens the case for a neutron star pulsar (or LMXB) identification for CV1. + The hardness of the X-ray colour of the object. μα=0.89. is also more consistent with a CV than a quiescent LAINB.," The hardness of the X-ray colour of the object, $X_{\mathrm{colour}}=-0.39$, is also more consistent with a CV than a quiescent LMXB." + Thus. based on these A-ray properties of the svstem. it appears much more like a CV than a qLMXD.," Thus, based on these X-ray properties of the system, it appears much more like a CV than a qLMXB." + We also calculated the X-ray luminosity in the ACIS 0.310 keV band. Lx~2.2.107? Org + and found itis at the high end of the range of X-ray luminosities for non-magnetic dwarf novae. but is tvpical for the magnetic IPs.," We also calculated the X-ray luminosity in the ACIS 0.3–10 keV band, $L_{\mathrm{X}}\simeq2.2\times10^{32}$ erg $^{-1}$, and found it is at the high end of the range of X-ray luminosities for non-magnetic dwarf novae, but is typical for the magnetic IPs." + Our best-fitting power-law spectrum is relatively hard. with photon index DL—1.51+0.11.," Our best-fitting power-law spectrum is relatively hard, with photon index $\Gamma=1.51\pm0.11$." + Hleinkeetal.(2008) investigated the relationship between CV subtype anc X-ray spectrum and Luminosity for a sample of CVs comprising confirmed: magnetic CVs (LPs and polars). quiescent. DN and nova-like CVs (NL) and globular cluster CVs.," \citet{heinke08} investigated the relationship between CV subtype and X-ray spectrum and luminosity for a sample of CVs comprising confirmed magnetic CVs (IPs and polars), quiescent DN and nova-like CVs (NL) and globular cluster CVs." + μον founcl the distribution of photon index cdilfered significantly between magnetic CVs. which are harder. N-rav sources(mean L—1.22.0= 0.33). and non-magnetic CVs (mean," They found the distribution of photon index differed significantly between magnetic CVs, which are harder X-ray sources(mean $\Gamma=1.22, \sigma=0.33)$ , and non-magnetic CVs (mean" +which at the location of the OH masers ts possible. but unlikely.,"which at the location of the OH masers is possible, but unlikely." + This also agrees with the Gray et el (1991) model which predicted the absence of 1667 masers at high densities., This also agrees with the Gray et el (1991) model which predicted the absence of 1667 masers at high densities. + To obtain maser emission in both OH and methanol. the Cragg et al.," To obtain maser emission in both OH and methanol, the Cragg et al." + model requires a ratio of methanol to OH column densities in the range 0.1 to 1000. reducing to a range from | to 100 if the lines are both saturated. with a ratio of 10 being typical.," model requires a ratio of methanol to OH column densities in the range 0.1 to 1000, reducing to a range from 1 to 100 if the lines are both saturated, with a ratio of 10 being typical." + Since maser emission from methanol requires methanol abundances of greater than 107. this suggests an OH abundance of ~1077.," Since maser emission from methanol requires methanol abundances of greater than $10^{-6}$, this suggests an OH abundance of $\stackrel{>}{\sim}10^{-7}$." + For a methanol favoured source such as 20126+4104. the models suggest the gas has a density in the range 1077nacem tto I0 aand a gas temperature > 125K with dust at a temperature between 130 K and 230 K. a range of parameters consistent with the absence of 1667 MHz OH masers.," For a methanol favoured source such as $20126+4104$, the models suggest the gas has a density in the range $10^{6.5}$ to $10^8$ and a gas temperature $>125$ K with dust at a temperature between 130 K and 230 K, a range of parameters consistent with the absence of 1667 MHz OH masers." + The gas temperature Is also consistent with the 150-260 K inferred by C97 from observations of CHiCN., The gas temperature is also consistent with the 150-260 K inferred by C97 from observations of $_3$ CN. + The high abundance of methanol suggested by the presence of the nethanol masers could result from the liberation of methanol from grains mantles as the dust is heated or shocked., The high abundance of methanol suggested by the presence of the methanol masers could result from the liberation of methanol from grains mantles as the dust is heated or shocked. + This would also increase the OH abundance as a result of injection of ffollowed by protonation and dissociative recombination., This would also increase the OH abundance as a result of injection of followed by protonation and dissociative recombination. + The “hot core’ chemistry which results when grain mantles are evaporated has recently be modelled by Nomura. Millar (2004).," The `hot core' chemistry which results when grain mantles are evaporated has recently be modelled by Nomura, Millar (2004)." + This model also shows that the gas phase abundance of CH3CN is also significantly enhanced when grain mantles are evaporated. a result also consistent with the observations IRAS 20126-4104 (C97; C99).," This model also shows that the gas phase abundance of $_3$ CN is also significantly enhanced when grain mantles are evaporated, a result also consistent with the observations IRAS 20126+4104 (C97; C99)." + The water masers arise from a region spatially distinct from the OH and mmasers., The water masers arise from a region spatially distinct from the OH and masers. + As suggested by MCR. the location of the eemission appears to associate these masers with the outflow from the source.," As suggested by MCR, the location of the emission appears to associate these masers with the outflow from the source." + Figure 3. plots the location (and velocities) of our water maser observations compared with those detected by MCR., Figure \ref{fig:h2o_comp} plots the location (and velocities) of our water maser observations compared with those detected by MCR. + This figure shows that the spatial and velocity distribution of the maser spots has changed significantly between the two sets of observations., This figure shows that the spatial and velocity distribution of the maser spots has changed significantly between the two sets of observations. + Indeed. it is difficult to identify any common maser spots.," Indeed, it is difficult to identify any common maser spots." + MCR proposed a detailed model for the water masers distribution assuming that the masers lie on the surface of a conical bipolar jet. at the interaction zone between the tonised jet and the surrounding neutral medium. and moving with constant velocity away from the vertex of the cone (assumed to coincide with the embedded YSO).," MCR proposed a detailed model for the water masers distribution assuming that the masers lie on the surface of a conical bipolar jet, at the interaction zone between the ionised jet and the surrounding neutral medium, and moving with constant velocity away from the vertex of the cone (assumed to coincide with the embedded YSO)." +" This model provides a prediction of the maser velocities at any. given. position, and so we can compare the measured velocities of the maser spots detected with MERLIN with the model predictions."," This model provides a prediction of the maser velocities at any given position, and so we can compare the measured velocities of the maser spots detected with MERLIN with the model predictions." + Doing this. we find that the model predicts some velocities close to those observed by a value of 1.17 km s7!. but some predicted model velocities are higher or lower than observed ones by value of 7 to 10 km s7'.," Doing this, we find that the model predicts some velocities close to those observed by a value of 1.17 km $^{-1}$, but some predicted model velocities are higher or lower than observed ones by value of 7 to 10 km $^{-1}$." +" For example. for the maser spot at 2014/726*.027 and 41713/32.59, the model predicts a velocity of -4.13 km s! whereas the measured velocity is --27 km s!."," For example, for the maser spot at $20^h 14^m 26^s.027$ and $41^{\circ} 13' +32''.59$, the model predicts a velocity of -4.13 km $^{-1}$ whereas the measured velocity is $-2.27$ km $^{-1}$." +" Note that before making this comparison. the systematic velocity of —3.5 kms !, used by MCR. was added to the velocity obtained from Eq.(I) of the MCR model."," Note that before making this comparison, the systematic velocity of $-3.5$ km $^{-1}$, used by MCR, was added to the velocity obtained from Eq.(1) of the MCR model." +" If we assume that the mmasers trace a moving shock front then they have travelled a distance of ~0.1"" over the 1587 days between our MERLIN observations and the VLBA observations of MCR.", If we assume that the masers trace a moving shock front then they have travelled a distance of $\sim 0.1''$ over the 1587 days between our MERLIN observations and the VLBA observations of MCR. + This corresponds to a velocity of ~ 190 km s!., This corresponds to a velocity of $\sim$ 190 km $^{-1}$. + This velocity is consistent with the range of velocities inferred for the SiO by C99., This velocity is consistent with the range of velocities inferred for the SiO by C99. + It may also they are a new masers excited by the travelled shock., It may also they are a new masers excited by the travelled shock. + If we consider the uncertainty of the absolute position between for our spots. IO mas. and MCR ones. 30 mas. some of the similar velocities spots of the two observations could be overlaped.," If we consider the uncertainty of the absolute position between for our spots, 10 mas, and MCR ones, 30 mas, some of the similar velocities spots of the two observations could be overlaped." +" IRAS 2012644104 has two different outflow directions: a NW-SE flow on an angular scale of - 10"". seen in HCO and Hs emission (C97) with an SiO jet (C99). and a CO outflow on a 2 angular scale. that is almost N-S. at position angle 171 degrees (Shepherd et al."," IRAS 20126+4104 has two different outflow directions: a NW-SE flow on an angular scale of $\sim$ $''$, seen in $^{+}$ and $_{2}$ emission (C97) with an SiO jet (C99), and a large-scale CO outflow on a $'$ angular scale, that is almost N-S, at position angle 171 degrees (Shepherd et al." + 2000)., 2000). + Shepherd et al., Shepherd et al. + attribute the difference in position angles to precesstor of the Jet., attribute the difference in position angles to precession of the jet. + Our MERLIN measurements of the magnetic field directioi show position angles of -5°+2° and -11?+4° that agree with the position angle of the large-scale CO outflow. (, Our MERLIN measurements of the magnetic field direction show position angles of $^{\circ}\pm2^{\circ}$ and $^{\circ}\pm4^{\circ}$ that agree with the position angle of the large-scale CO outflow. ( +We assume that we are seeing o-components.),We assume that we are seeing $\sigma$ -components.) + The MERLI measurements also agree in position angle with the magnetic field determination by Valléee. Bastien (2000). who found a position angle of +4°+29° based on 760-jum continuum measurements at 14 resolution.," The MERLIN measurements also agree in position angle with the magnetic field determination by Valléee, Bastien (2000), who found a position angle of $^{\circ}\pm29^{\circ}$ based on $\mu$ m continuum measurements at $''$ resolution." + The observations presented here show that IRAS 20126-4104 joins a small group of luminous (.107L.3) young sources where the OH masers originate from within ~1000 AU of the central star and often have a spatial (and in some cases kinematic) morphology consistent the masers being located in. or on the surface of. a circumstellar disk around the source.," The observations presented here show that IRAS 20126+4104 joins a small group of luminous $\sim10^4$ ) young sources where the OH masers originate from within $\sim1000$ AU of the central star and often have a spatial (and in some cases kinematic) morphology consistent the masers being located in, or on the surface of, a circumstellar disk around the source." +" The other such objects are G35.2-0.74N (Hutawarakorn. Cohen 1999), W753N (Hutawarakorn et al."," The other such objects are G35.2-0.74N (Hutawarakorn, Cohen 1999), W75N (Hutawarakorn et al." + 2002) and IRSI. 9 and 11 in NGC7538 (Hutawarakorn. Cohen 2003).," 2002) and IRS1, 9 and 11 in NGC7538 (Hutawarakorn, Cohen 2003)." + The OH masers towards W3(OH) have also recently been interpreted as originating from a circumstellar disk (Wright. Gray. Diamond 2004).," The OH masers towards W3(OH) have also recently been interpreted as originating from a circumstellar disk (Wright, Gray, Diamond 2004)." + Although the OH masers towards 21026+3104 are among the weaker in this group. the 11mG magnetic field strength measured ts the highest among the sample. and is also higher than any of the 100 field values for OH masers studied by Fish et al. (," Although the OH masers towards $21026+4104$ are among the weaker in this group, the 11mG magnetic field strength measured is the highest among the sample, and is also higher than any of the 100 field values for OH masers studied by Fish et al. (" +2002).,2002). + Caswell (1996. 1998) has suggested that OH 1665 MHz maser flux compared to ffülux may be an indicator of the evolutionary stage of a source. increasing as a source evolves.," Caswell (1996, 1998) has suggested that OH 1665 MHz maser flux compared to flux may be an indicator of the evolutionary stage of a source, increasing as a source evolves." + This would suggest that IRAS 20126+4104 is amongst the younger of these sources. which could be consistent with the presence of 1667 MHz maser emission towards the sources with stronger 1665 MHz," This would suggest that IRAS $20126+4104$ is amongst the younger of these sources, which could be consistent with the presence of 1667 MHz maser emission towards the sources with stronger 1665 MHz" +Stars form inside dense cores deep within molecular clouds.,Stars form inside dense cores deep within molecular clouds. +" The similarity of the core mass function (CMF) to the initial mass function of stars (IMF, see Lombardi& Lada|2007)) has sometimes been used [1998] citealtenoch08)) as evidence against theories of core formation where no correspondence is anticipated, iin the competitive accretion picture (Bonnellet_al.||2001}2005)."," The similarity of the core mass function (CMF) to the initial mass function of stars (IMF, see \citealt*{motte98,alves07}) ) has sometimes been used \\citealt{enoch08}) ) as evidence against theories of core formation where no correspondence is anticipated, in the competitive accretion picture \citep{bonnell01,bate05}." +". However, the mapping of a given CMF on to the resultant IMF is complicated by many factors (see citealthatchell08,scubapaper)), such as the cores’ varying (2008),, star-forming efficiencies multiplicity and/or mass-dependent lifetimes (Clark,KTessen&(2008)"," However, the mapping of a given CMF on to the resultant IMF is complicated by many factors (see \\citealt{hatchell08,scubapaper}) ), such as the cores' varying multiplicity \citep{goodwin08}, star-forming efficiencies \citep{swift08} and/or mass-dependent lifetimes \citep*{clark07}." +" In fact, as shown by and BonnellGoodwin2007)..&Kouwenhoven] (7009),, diverse evolutionary schemes can map the observed CMFs on to the"," In fact, as shown by \citet{swift08} and \citet{goodwin09}, , diverse evolutionary schemes can map the observed CMFs on to the" +To remove telluric features in the spectra of EF Evi. the G2V star Η010005 was observed using an identical procedure. but with exposure times of 5 s. At the time of the observation. ID16358 had an airmass of 1.44. whieh is verv close to the mean airmass altained bv EF Evi during the 100 minute observation period.,"To remove telluric features in the spectra of EF Eri, the G2V star HD16358 was observed using an identical procedure, but with exposure times of 5 s. At the time of the observation, HD16358 had an airmass of 1.44, which is very close to the mean airmass attained by EF Eri during the 100 minute observation period." + The resulting dataset was reduced using a procedure common for reducing infrared spectral data in which the images are grouped into sets of five individual exposures., The resulting dataset was reduced using a procedure common for reducing infrared spectral data in which the images are grouped into sets of five individual exposures. + A median of four of these exposures is subtracted from the spectrum of interest (o remove (he skv contamination., A median of four of these exposures is subtracted from the spectrum of interest to remove the sky contamination. + A spectrum is (hen extracted [rom (his skv-subtracted image using (hie normal longslit spectroscopic reduction packages within IRAF. and the process is repeated.," A spectrum is then extracted from this sky-subtracted image using the normal longslit spectroscopic reduction packages within IRAF, and the process is repeated." + Each individual spectrum was wavelength calibrated using the spectrum of an argon lamp obtained shortly before our observations began., Each individual spectrum was wavelength calibrated using the spectrum of an argon lamp obtained shortly before our observations began. + The wavelength calibrated spectra of EF Exi were then divided by the median of the five wavelength calibrated spectra of ILD16358 to remove telluric absorption features., The wavelength calibrated spectra of EF Eri were then divided by the median of the five wavelength calibrated spectra of HD16358 to remove telluric absorption features. + The latter procedure introduces spurious features into the spectra of interest due to weak atomic and molecular absorption lines in the G2V spectrum., The latter procedure introduces spurious features into the spectra of interest due to weak atomic and molecular absorption lines in the G2V spectrum. + To remove (hese weak leatures. we have emploved the procedure described by Maiolino. Rieke. Rieke (1996).," To remove these weak features, we have employed the procedure described by Maiolino, Rieke, Rieke (1996)." + With only a single standard to work with. the tellurie correction for the entire data sel is not as good as can be produced (see Harrison et al.," With only a single standard to work with, the telluric correction for the entire data set is not as good as can be produced (see Harrison et al." + 2004) when a large number of such spectra are available., 2004) when a large number of such spectra are available. + This is evidenced by dips al 2.0 jan and 2.05 san in the NIRD spectra presented below., This is evidenced by dips at 2.0 $\mu$ m and 2.05 $\mu$ m in the NIRI spectra presented below. + The fIux calibration of these data was fairly good. and our spectra revealed the same Large amplitude (AA = 0.8 mag) flux variations as reported by Harrison et al. (," The flux calibration of these data was fairly good, and our spectra revealed the same large amplitude $\Delta$ = 0.8 mag) flux variations as reported by Harrison et al. (" +2003).,2003). + We have assumed that EF Evi has not changed its photometric behavior between the time of the last photometric data set (see below) and the epoch of these observations. allowing us to use the A-band light curve to produce fIux-calibrated spectra.," We have assumed that EF Eri has not changed its photometric behavior between the time of the last photometric data set (see below) and the epoch of these observations, allowing us to use the -band light curve to produce flux-calibrated spectra." + EF Eri was observed using on Keck II on 6 September 2003., EF Eri was observed using on Keck II on 6 September 2003. + We used, We used +"erowth occurs more rapidly as a increases. the overall ellect. on the A ó map. needed to relate the minimum overdensity recquired to produce a detectable lens. Ayn. toa corresponding lincar-theory overdensity 94,554. is fairly small.","growth occurs more rapidly as $w$ increases, the overall effect on the $\Delta$ – $\delta$ map, needed to relate the minimum overdensity required to produce a detectable lens, $\Delta_{\rm{min}}$, to a corresponding linear-theory overdensity $\delta_{\rm{min}}$, is fairly small." + Similarly. the linezr-theory. overdensity at. collapse ὃς does not vary much with ew.," Similarly, the linear-theory overdensity at collapse $\delta_{\rm{c}}$ does not vary much with $w$." + Phe ellect on Ayiy is more significant. however.," The effect on $\Delta_{\rm{vir}}$ is more significant, however." + As dw inereases. structures require. substantially ereater overdensities in order to reach virial equilibrium because they collapse sooner. when the universe was vounger and hotter.," As $w$ increases, structures require substantially greater overdensities in order to reach virial equilibrium because they collapse sooner, when the universe was younger and hotter." + To determine how the power-spectrum amplitude. m. varies with we we considered three possible approaches.," To determine how the power-spectrum amplitude, $\sigma_8$, varies with $w$ we considered three possible approaches." + One was to normalize to the X-ray cluster abundance as was done in WS9S., One was to normalize to the X-ray cluster abundance as was done in WS98. + Another was to normalize to the CODI measurements of CAIB anisotropies on large angular scales., Another was to normalize to the COBE measurements of CMB anisotropies on large angular scales. + These two approaches predict similar. values of ex for the ACDM mocel., These two approaches predict similar values of $\sigma_8$ for the $\Lambda$ CDM model. + However. if all cosmological parameters are held fixed as tw varies. the values of σκ are no longer in accordance.," However, if all cosmological parameters are held fixed as $w$ varies, the values of $\sigma_8$ are no longer in accordance." + This is because the cluster abundance approach is accounting for the earlier. forming. and hence hotter. ealaxy clusters in models with wo>1.," This is because the cluster abundance approach is accounting for the earlier forming, and hence hotter, galaxy clusters in models with $w > -1$." + The COBE normalization. on the other hand. is accounting for the increase in the Integrated: Sachs-Wolle (ISW) effect as ue increases (cL.," The COBE normalization, on the other hand, is accounting for the increase in the Integrated Sachs-Wolfe (ISW) effect as $w$ increases (cf.," + BPB)., BPB). + Given these dillering inlluences. the two approaches are not expected to vield the same es when all the cosmological parameters are held fixed to those of rw [CDM model while t is varied.," Given these differing influences, the two approaches are not expected to yield the same $\sigma_8$ when all the cosmological parameters are held fixed to those of the $\Lambda$ CDM model while $w$ is varied." + This suggests a third ipproach to normalizing the power spectrum: namely. let 10 parameters vary with e such that the cluster abundance normalization matches the CODE normalization.," This suggests a third approach to normalizing the power spectrum; namely, let the parameters vary with $w$ such that the cluster abundance normalization matches the COBE normalization." + In practice we accomplished this by letting just$5 vary with de. as it is 10 parameter most degenerate with as.," In practice we accomplished this by letting just$\Omega_0$ vary with $w$, as it is the parameter most degenerate with $\sigma_8$ ." + The resulting range in Qu for 04 was found to be 0.3,", The above marginalizations are going to inflate the error on $\beta$. + If not predicted properly. the dispersion σι las to be uarginalized over.," If not predicted properly, the dispersion $\sigma_v$ has to be marginalized over." + We propose here a new method to estinate the > xwanmeter that depends just ou the observed. monopole and quadrupole componeuts of the observed correlation πιοπο. and not on their linear theory represcutation. including its dependence ou cosinological parameters.," We propose here a new method to estimate the $\beta$ parameter that depends just on the observed monopole and quadrupole components of the observed correlation function and not on their linear theory representation, including its dependence on cosmological parameters." + To derive our estimator we start in Fourier space o generato as a final product a configuration space expression., To derive our estimator we start in Fourier space to generate as a final product a configuration space expression. + The observational inputs aud them further wandling belong all to configuration space., The observational inputs and their further handling belong all to configuration space. + Our starting volt is ((29)). that was shown to beaplausible convenient description ou scales characterized by," Our starting point is \ref{eq:modelPW}) ), that was shown to be aplausible convenient description on scales characterized by" +conditioned on a known class hypothesis): 3) methods for leuning the mixture model from eiven data were proposed in Miller&Browning(20034). Miller&Browning(2003b).,"conditioned on a known class hypothesis); 3) methods for learning the mixture model from given data were proposed in \citet{pami}, , \citet{Browning}." +. In (hese approaches. individual mixture components learn to represent either known or unknown class data.," In these approaches, individual mixture components learn to represent either known or unknown class data." + We next review Miller&Browning(2003a).. Miller&Browning(2003b) in nore detail.," We next review \citet{pami}, \citet{Browning} in more detail." +" Consider a data set A,={Ap&,P where Y=[Griei).(ta.a)... (ανον) is the abeled subset and A,={taype...ry} is (he unlabeled subset."," Consider a data set ${\cal X}_m = \{{ \cal X}_l,{\cal X}_u\}$, where ${\cal X}_l = \{(\underline{x_1},c_1), (\underline{x_2},c_2), \ldots,$ $(\underline{x_{N_l}},c_{N_l})\}$ is the labeled subset and ${\cal +X}_u = \{\underline{x_{N_l+1}}, \ldots, \underline{x_{N}}\}$ is the unlabeled subset." + Here. à;=(rip.tie...id) is a feature vector and ¢; is a class label [rom the set of known classes 7.," Here, $\underline{x}_i \equiv +(x_{i1},x_{i2},\ldots,x_{id})$ is a feature vector and $c_i$ is a class label from the set of known classes ${\cal P}_c$ ." + This mixed data scenario was considered previously in e.g. Shashahani&Lancerebe(1994).. (1997).. Nigametal.," This mixed data scenario was considered previously in e.g. \citet{Shashahani}, \citet{Miller1}, \citet{Nigam}." + (2000).. Unlike these works. a kev element in Miller& (2003a).. Miller&Browning(2003b) sununarized here. is (hat the fact that a sample is unlabeled is treateddala.," Unlike these works, a key element in \citet{pami}, \citet{Browning} summarized here, is that the fact that a sample is unlabeled is treated." +" Accordingly. we recleline .V,,=CX... where now A=τωT.ey).(.""3.0)⋅⋅⋅⋅⋅Cr-Γον) and X,—αν407b).sss.Cry.om'))."," Accordingly, we redefine ${\cal X}_m = \{{\cal X}_l,{\cal X}_u\}$, where now ${\cal +X}_l = \{(\underline{x_1},{\rm `l'},c_1), (\underline{x_2},{\rm `l' +},c_2), \ldots, (\underline{x_{N_l}},{\rm `l'},c_{N_l})\}$ and ${\cal +X}_u = \{(\underline{x_{N_l+1}},{\rm `m'}), \ldots, (\underline{x_{ +N}},{\rm `m'})\}$." + Here the new random observation £€labelUT.m)J is introduced. taking on values indicating5 a sample is either labeled or missing the ," Here the new random observation ${\cal L } \in +\{{\rm `l'},{\rm `m'}\}$ is introduced, taking on values indicating a sample is either labeled or missing the label." +If a sample is labeled. then it is known the sample originates [rom one of (he known classes.," If a sample is labeled, then it is known the sample originates from one of the known classes." + On the other haad. if the sample is unlabeled. then (here are (wo sources of uncertainty.," On the other hand, if the sample is unlabeled, then there are two sources of uncertainty." + First. under the assumption that (here may be unknown classes present. it is unknown whether or not the given sample originates Irom a known class.," First, under the assumption that there may be unknown classes present, it is unknown whether or not the given sample originates from a known class." + Second. conditioned on its belonging to one of the known classes. the class of origin for the sample is unknown.," Second, conditioned on its belonging to one of the known classes, the class of origin for the sample is unknown." + In Miller&Browning(2003a).. a mixture model was proposed that explains all the observed data. including the presence or absence of a label.," In \citet{pami}, a mixture model was proposed that explains all the observed data, including the presence or absence of a label." + Two tvpes of mixture componen(s were posited. dillering in (he mechanism (μον use lor generating label presence/absence. “," Two types of mixture components were posited, differing in the mechanism they use for generating label presence/absence. “" +Preclelined™ components generate both labeled and unlabeled data and assume labels are missing al random.,Predefined” components generate both labeled and unlabeled data and assume labels are missing at random. +" These components represent the known classes. """, These components represent the known classes. “ +Non-predelined components only generale unlabeled data (hus. inlocalized regions. they capture data subsets (hatare purely unlabeled.,"Non-predefined” components only generate unlabeled data – thus, inlocalized regions, they capture data subsets thatare purely unlabeled." +the sun.,the sun. +" Unfortunately, a significant population of loops in the halo can only arise if the loops manage to lose most of their kinetic energy, and this process is not yet properly quantified."," Unfortunately, a significant population of loops in the halo can only arise if the loops manage to lose most of their kinetic energy, and this process is not yet properly quantified." +" The effect of a straight cosmic string is to induce a 'deficit angle’ a in space, which has the effect of turning parallel rays that pass on either side of a string into a converging beam."," The effect of a straight cosmic string is to induce a 'deficit angle' $\alpha$ in space, which has the effect of turning parallel rays that pass on either side of a string into a converging beam." + Effectively light rays passing the string are bent towards the string by an angle a/2., Effectively light rays passing the string are bent towards the string by an angle $\alpha/2$. +" As a result, background sources that project sufficiently close to a cosmic string are doubly imaged (see Fig. 1))."," As a result, background sources that project sufficiently close to a cosmic string are doubly imaged (see Fig. \ref{fig:bigsrc}) )." +" Because gravitational lensing preserves surface brightness, and because straight strings do not distort the images they produce, a doubly imaged source will be exactly twice as bright as the unlensed source."," Because gravitational lensing preserves surface brightness, and because straight strings do not distort the images they produce, a doubly imaged source will be exactly twice as bright as the unlensed source." +" If a cosmic string were to pass in front of a source therefore, then the lightcurve would show a sharp step up by a factor of two, followed some time later by a decrease in brightness back to the original level."," If a cosmic string were to pass in front of a source therefore, then the lightcurve would show a sharp step up by a factor of two, followed some time later by a decrease in brightness back to the original level." +" The sharpness of the step is determined by the angular size of the source: for a point source the step is instantaneous, but the second image of an extended source will only gradually be built up (down) as the string tracks across the sky, smoothing the increase (decline) in brightness."," The sharpness of the step is determined by the angular size of the source: for a point source the step is instantaneous, but the second image of an extended source will only gradually be built up (down) as the string tracks across the sky, smoothing the increase (decline) in brightness." +" The key point of microlensing is that this lightcurve can be measured even without resolving the double images: provided the lightcurve is sufficiently different from other, astrophysical, variability these events can be found and studied from large monitoring campaigns of many objects."," The key point of microlensing is that this lightcurve can be measured even without resolving the double images: provided the lightcurve is sufficiently different from other, astrophysical, variability these events can be found and studied from large monitoring campaigns of many objects." +" The microlensing described above will only be seen if all of the source is doubly imaged at once, which means that the source must be smaller in angular extent than the lensing angle 60."," The microlensing described above will only be seen if all of the source is doubly imaged at once, which means that the source must be smaller in angular extent than the lensing angle $\delta\theta$." +" The most compact sources that can be seen to cosmological distances are quasars, whose nuclear regions are <1 parsec in radius, corresponding to an angular diameter of 0.08 (mas) at redshift 1."," The most compact sources that can be seen to cosmological distances are quasars, whose nuclear regions are $\la1$ parsec in radius, corresponding to an angular diameter of 0.08 (mas) at redshift 1." +" If 60—a/2 is smaller, not all of the source can be doubly imaged simultaneously, and therefore we will not see the full factor two brightening."," If $\delta\theta\simeq\alpha/2$ is smaller, not all of the source can be doubly imaged simultaneously, and therefore we will not see the full factor two brightening." +" Such lightcurves would not show the characteristic step in brightness either, but a single bump whose shape and peak amplification is determined by the core structure and size."," Such lightcurves would not show the characteristic step in brightness either, but a single bump whose shape and peak amplification is determined by the core structure and size." +" We therefore impose the requirement that the flat top of the light curve lasts at least as long as the rise time (angular diameter of the source less than 60/2), which implies that we are sensitive to cosmic strings with deficit angles with Image configurations and lightcurves for different source sizes are shown in Fig. 2.."," We therefore impose the requirement that the flat top of the light curve lasts at least as long as the rise time (angular diameter of the source less than $\delta\theta/2$ ), which implies that we are sensitive to cosmic strings with deficit angles with Image configurations and lightcurves for different source sizes are shown in Fig. \ref{fig:images}." +" As long as the cosmic string is straight on scales comparable to the source size (and smaller), then the above still holds."," As long as the cosmic string is straight on scales comparable to the source size (and smaller), then the above still holds." +" Otherwise bends in the string will spoil the exact factor-of-two magnification, and may also lead to complex brightness fluctuations as the string tracks across the source."," Otherwise bends in the string will spoil the exact factor-of-two magnification, and may also lead to complex brightness fluctuations as the string tracks across the source." + Such complex lightcurves will be difficult to recognize as, Such complex lightcurves will be difficult to recognize as +"the massive end, we took advantage of the outcomes of large surveys and followed different approaches.","the massive end, we took advantage of the outcomes of large surveys and followed different approaches." +" We fitted the 1/V, points from this study together with those collected from the literature in comparable redshift intervals.", We fitted the $1/V_{max}$ points from this study together with those collected from the literature in comparable redshift intervals. +" We note that in principle, and in contrast to the STY approach, fitting 1/Vinax points involves data binning, thus may in general produce a different fit."," We note that in principle, and in contrast to the STY approach, fitting $1/V_{max}$ points involves data binning, thus may in general produce a different fit." +" We included only those surveys whose results are obtained using a method similar to our own and that sample the high-mass tail of the distribution, typically above M.~3x10? M5."," We included only those surveys whose results are obtained using a method similar to our own and that sample the high-mass tail of the distribution, typically above $M_*\simeq 3 \times 10^{10}M_\odot$ ." +" However, we obtained very similar results when also including the points from the literature at lower masses."," However, we obtained very similar results when also including the points from the literature at lower masses." + We found that a single Schechter function does not seem to reproduce the faint- and the bright-end simultaneously in a satisfactory way., We found that a single Schechter function does not seem to reproduce the faint- and the bright-end simultaneously in a satisfactory way. + This is unsurprising because the Schechter function is itself a poor description of the shape of the GSMF when samples with high quality statistics are used (see discussion in the introduction and in Sect. 3.2))., This is unsurprising because the Schechter function is itself a poor description of the shape of the GSMF when samples with high quality statistics are used (see discussion in the introduction and in Sect. \ref{sec:gsmf}) ). +" However, the inhomogeneity of the data set can also play a role: we collected 1/Vinax points from different surveys, observed in different sky areas, and computed with slightly different methods."," However, the inhomogeneity of the data set can also play a role: we collected $1/V_{max}$ points from different surveys, observed in different sky areas, and computed with slightly different methods." +" We then fitted the ensemble of the 1/V,,;, points from this work plus those collected from the literature with a doublepower-law?..", We then fitted the ensemble of the $1/V_{max}$ points from this work plus those collected from the literature with a double. + The best-fit parameters are shown in Tab. 3.., The best-fit parameters are shown in Tab. \ref{tab:paramdpl}. +" This analytic shape, having one additional degree of freedom than a single Schechter function, provides a tighter fit to the data at all redshifts."," This analytic shape, having one additional degree of freedom than a single Schechter function, provides a tighter fit to the data at all redshifts." + We report the different values of the faint-end slope as a function of redshift in Fig. 8.., We report the different values of the faint-end slope as a function of redshift in Fig. \ref{fig:alpha}. +" It is shown that, regardless of the stellar templates and method adopted and the functional shape fitted to the data, all the results indicate a steepening of the faint-end of the GSMF with redshift up to z~3."," It is shown that, regardless of the stellar templates and method adopted and the functional shape fitted to the data, all the results indicate a steepening of the faint-end of the GSMF with redshift up to $z\sim 3$." +" The trend is robust despite the relatively large error bars, especially at high redshift, and the presence of known overdensities at z~1.6 and ζ2.2—2.3, and it is unaffected by the lack of high quality statistics at the high-mass end typical of small sky areas."," The trend is robust despite the relatively large error bars, especially at high redshift, and the presence of known overdensities at $z\sim 1.6$ and $z\sim 2.2-2.3$, and it is unaffected by the lack of high quality statistics at the high-mass end typical of small sky areas." + The steepening of the faint-end slope with redshift seems to halt at z>3 and the value of o seems to remain constant up to z~4., The steepening of the faint-end slope with redshift seems to halt at $z>3$ and the value of $\alpha$ seems to remain constant up to $z \sim 4$. +" However, although this is confirmed by the use of the outcome of previous large surveys, the results based on our data alone are largely dependent on the choice of the fixed M* parameter."," However, although this is confirmed by the use of the outcome of previous large surveys, the results based on our data alone are largely dependent on the choice of the fixed $M^*$ parameter." + The tendency for the low-mass end of the GSMF tosteepen with redshift was previously found by other authors., The tendency for the low-mass end of the GSMF tosteepen with redshift was previously found by other authors. +" According to the evolutionary STY fit of Fontanaetal. (2006),, α ranges"," According to the evolutionary STY fit of \cite{fontana06}, , $\alpha$ ranges" +Determining the shape of space 1s one of the most important themes in modern cosmology.,Determining the shape of space is one of the most important themes in modern cosmology. +" Together with the assumption of the cosmological principle. Einstein’s General Relativity connects a curvature of space with the average energy density of the universe. and recent observations suggest a flat A-CDM universe (e.g... Qu=1.005070""ποιοι from WMAP++BAO+SN data. by Hinshaw et al."," Together with the assumption of the cosmological principle, Einstein's General Relativity connects a curvature of space with the average energy density of the universe, and recent observations suggest a flat $\Lambda$ -CDM universe (e.g., $\Omega_{\mathrm{tot}}=1.0050^{+0.0060}_{-0.0061}$ from +BAO+SN data, by Hinshaw et al." + 2009)., 2009). + However. while General Relativity describes local geometry (curvature). it predicts nothing about global property of space. namely. topology of the universe.," However, while General Relativity describes local geometry (curvature), it predicts nothing about global property of space, namely, topology of the universe." + Global topology of the Universe is often assumed to be simply connected with no evidence. though it can be rather multiconnected.," Global topology of the Universe is often assumed to be simply connected with no evidence, though it can be rather multiconnected." + A multiconnected space with a nontrivial topology can be imagined as a 2K-polyhedron. called Dirichlet domain. whose K pairs of faces are glued mathematically by holonomies.," A multiconnected space with a nontrivial topology can be imagined as a $2K$ -polyhedron, called Dirichlet domain, whose $K$ pairs of faces are glued mathematically by holonomies." + An object passing through one face immediately returns through the glued face., An object passing through one face immediately returns through the glued face. +" As a result. multiple images of single objects. often referred to as ""ghosts"". appear like those in a kaleidoscope (for detail. see. e.g. Lachiézze-Rey and Luminet 1995)."," As a result, multiple images of single objects, often referred to as “ghosts"", appear like those in a kaleidoscope (for detail, see, e.g. Lachièzze-Rey and Luminet 1995)." + Many methods for constraining cosmic topology are based on this prediction. e.g.. method (Cornish et al.," Many methods for constraining cosmic topology are based on this prediction, e.g., method (Cornish et al." + 1998) is to search for intersections of the last-scattering surface and the faces of our Dirichlet domain., 1998) is to search for intersections of the last-scattering surface and the faces of our Dirichlet domain. + They are circles with the same temperature fluctuation pattern in the CMB map. because they are copies of a physically identical region.," They are circles with the same temperature fluctuation pattern in the CMB map, because they are copies of a physically identical region." + Various authors have searched for matched cireles using the data. and obtained diverse results.," Various authors have searched for matched circles using the data, and obtained diverse results." + For example. Aurich (2008) has found a hint of a 3-torus topology. while Roukema et al. (," For example, Aurich (2008) has found a hint of a 3-torus topology, while Roukema et al. (" +2008) have found a signature of a Poincaré dodecahedral space topology.,2008) have found a signature of a Poincaré dodecahedral space topology. + Contrary to them. Cornish et al. (," Contrary to them, Cornish et al. (" +2004). Key et al. (,"2004), Key et al. (" +2007). and Bielewiez Banday (2011) have found no topological signatures and obtained the lower limit of the size of our Universe.,"2007), and Bielewicz Banday (2011) have found no topological signatures and obtained the lower limit of the size of our Universe." + The most recent constraint is ~27.9 Gpe by Bielewicz Banday (2011)., The most recent constraint is $\sim 27.9$ Gpc by Bielewicz Banday (2011). + These disagreements suggest an existence of methodological problems and bring our interests to the 3D methods. 1.e.. those that are to use distributions of galaxies. galaxy clusters. or active galactic nuclei.," These disagreements suggest an existence of methodological problems and bring our interests to the 3D methods, i.e., those that are to use distributions of galaxies, galaxy clusters, or active galactic nuclei." + 3D methods are to search for unusual positional patterns of objects in a given astronomical catalog. due to an existence of topological copies (e.g.. Lehoucg et al.," 3D methods are to search for unusual positional patterns of objects in a given astronomical catalog, due to an existence of topological copies (e.g., Lehoucq et al." + 1996: Roukema 1996: Uzan et al., 1996; Roukema 1996; Uzan et al. + 1999: Marecki et al., 1999; Marecki et al. + 2005: Fuji Yoshi 2011)., 2005; Fujii Yoshii 2011). + For example. if we live in a 3-torus universe. à pair separation histogram (PSH) of a given catalog will show sharp spikes at the separations corresponding to its fundamental lengths (Lehoucg et al.," For example, if we live in a 3-torus universe, a pair separation histogram (PSH) of a given catalog will show sharp spikes at the separations corresponding to its fundamental lengths (Lehoucq et al." + 1996)., 1996). + Fujii Yoshii (2011) have introduced a new method that is much more sensitive to topological signatures than the prior ones., Fujii Yoshii (2011) have introduced a new method that is much more sensitive to topological signatures than the prior ones. + This method can apply to any of 17 multiconnected Euclidean spaces. even if the whole universe is comparable to the observed region in size. 1.e.. in a case that there are only a few topological ghosts.," This method can apply to any of 17 multiconnected Euclidean spaces, even if the whole universe is comparable to the observed region in size, i.e., in a case that there are only a few topological ghosts." + Our 3D method and others all require spectroscopical observations to calculate the radial distances of objects., Our 3D method and others all require spectroscopical observations to calculate the radial distances of objects. + A wide field spectroscopic survey is usually difficult. especially for high redshift objects in which we are most interested.," A wide field spectroscopic survey is usually difficult, especially for high redshift objects in which we are most interested." + Mainly in order to explore CMB data. Bernui Villela (2006 have extended the PSH method to the pair angular separation histogram (PASH) method that does not require spectroscoptο data when applied to astronomical objects.," Mainly in order to explore CMB data, Bernui Villela (2006) have extended the PSH method to the pair angular separation histogram (PASH) method that does not require spectroscopic data when applied to astronomical objects." + Their method. however. is so insensitive to topological signatures that the signal does not appear unless we average a number of different but statistically equivalent PASHs. which ts almost impossible in practice.," Their method, however, is so insensitive to topological signatures that the signal does not appear unless we average a number of different but statistically equivalent PASHs, which is almost impossible in practice." + A significant number of high redshift objects (galaxies or quasars) are recently found. though most of them are not spectroscopically observed yet.," A significant number of high redshift objects (galaxies or quasars) are recently found, though most of them are not spectroscopically observed yet." + This is a good point in time to examine whether these objects are usable for constraining cosmic topology or not., This is a good point in time to examine whether these objects are usable for constraining cosmic topology or not. + In section 2. we introduce another 2D method to constrain cosmic topology from the distribution of objects projected on the celestial sphere. which is an extension of the 3D method of Fuji Yoshii (2011).," In section 2, we introduce another 2D method to constrain cosmic topology from the distribution of objects projected on the celestial sphere, which is an extension of the 3D method of Fujii Yoshii (2011)." + In section 3. we show that the method is in principle applicable. but in a realistic situation it is no longer useful. similarly to that of Bernui Villela (2006).," In section 3, we show that the method is in principle applicable, but in a realistic situation it is no longer useful, similarly to that of Bernui Villela (2006)." + We conclude therefore that spectroscopically observed 3D catalogs are necessary. in order to reveal the topology of the Universe from the distribution of astronomical objects.," We conclude therefore that spectroscopically observed 3D catalogs are necessary, in order to reveal the topology of the Universe from the distribution of astronomical objects." + Throughout the paper we consider flat universes with zero curvature., Throughout the paper we consider flat universes with zero curvature. +with temperatures of ~ 1 keV and > 7 keV. In analogy withIlva. we deduce that observed the cooling ofthe postshock plasima. as indicated by the theory of the postshock accretion flow.,"with temperatures of $\sim$ 1 keV and $>$ 7 keV. In analogy with, we deduce that observed the cooling of the postshock plasma, as indicated by the theory of the postshock accretion flow." + A remarkable feature of tle rav spectrin of iis the strong iron cussion line whose equivalent width is ~1 keV. To account for this. an irou abundance ercater than Solar by at least 1.3 times is required.," A remarkable feature of the X-ray spectrum of is the strong iron emission line whose equivalent width is $\sim 4$ keV. To account for this, an iron abundance greater than Solar by at least 1.3 times is required." + Frou the combined analysis of theROSAT PSPC and spectra. the ratio of the bolometric Iuninositv of the soft component to the hard is revealed to be greater than 110.," From the combined analysis of the PSPC and spectra, the ratio of the bolometric luminosity of the soft component to the hard is revealed to be greater than 140." +index of the electrons is less than 2. being inconsistent with the shock acceleration theory (Wer Lu 2002).,"index of the electrons is less than 2, being inconsistent with the shock acceleration theory (Wei Lu 2002)." + In addition. the afterglow data of GRB 030226 suggest that its environment might be a low-density wind rather than a constant-density medium. also conflicting with the model (Dai Wu 2003).," In addition, the afterglow data of GRB 030226 suggest that its environment might be a low-density wind rather than a constant-density medium, also conflicting with the model (Dai Wu 2003)." + According to the afterglow jet model (Sari et al., According to the afterglow jet model (Sari et al. +" 1999), the jets half opening angle is given by 0=0.161¢1sysESsli""yl * where E.πο...10°?ergs. fjd= r/lday. οΞnJem™. and i.=0.2 (Frail et al."," 1999), the jet's half opening angle is given by $\theta = +0.161(1+z)^{-3/8}t_{{\rm j},d}^{3/8}E_{\gamma,{\rm iso},52}^{-1/8}n_0^{1/8}\eta_\gamma^{1/8}$ , where $E_{\gamma,{\rm +iso},52}=E_{\gamma,{\rm iso}}/10^{52}{\rm ergs}$, $t_{{\rm j},d}=t_{\rm j}/1\,{\rm day}$ , $n_0=n/1\,{\rm cm}^{-3}$, and $\eta_\gamma=0.2$ (Frail et al." + 2001)., 2001). + Only for few bursts in Table | the medium density was obtained from broadband modelling of the afterglow emission (e.g.. Panaitescu Kumar 2002).," Only for few bursts in Table 1 the medium density was obtained from broadband modelling of the afterglow emission (e.g., Panaitescu Kumar 2002)." +" For those bursts with unknown 1, we assume the median density 7c3em as in Ghirlanda et al. ("," For those bursts with unknown $n$, we assume the median density $n\simeq 3\,{\rm cm}^{-3}$ as in Ghirlanda et al. (" +2004).,2004). + The isotropic-equivalent 5-ray energy of a GRB is calculated by where S. is the fluence (in units of ergecm™) received in some observed bandpass and K is the factor that corrects the observed fluence to the standard rest-frame bandpass (1-107 keV) (Bloom. Frail Sari 2001).," The isotropic-equivalent $\gamma$ -ray energy of a GRB is calculated by where $S_\gamma$ is the fluence (in units of $^{-2}$ ) received in some observed bandpass and $k$ is the factor that corrects the observed fluence to the standard rest-frame bandpass $10^4$ keV) (Bloom, Frail Sari 2001)." + For a Friedmann-Robertson-Walker (FRW) cosmology with mass density Qa; and vacuum energy density O4. the luminosity distance in equation (1) is where c is the speed of light and Hy=100/kms7!Mpe is the present Hubble constant (Carroll. Press Turner 1992).," For a Friedmann-Robertson-Walker (FRW) cosmology with mass density $\Omega_M$ and vacuum energy density $\Omega_\Lambda$, the luminosity distance in equation (1) is where $c$ is the speed of light and $H_0\equiv 100h\,\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$ is the present Hubble constant (Carroll, Press Turner 1992)." +"| In equation (2). OQ,=1O4—O4. and ""sinn"" is sinh for ος>0 and sin for O,«0."," In equation (2), $\Omega_k=1-\Omega_M-\Omega_\Lambda$, and “sinn"" is sinh for $\Omega_k>0$ and sin for $\Omega_k<0$." +" For O,=0. equation (2) turns out to be 12S! times the integral."," For $\Omega_k=0$, equation (2) turns out to be $c(1+z)H_0^{-1}$ times the integral." +" In this section. we assume a flat universe (1.e.. O,= 0) because of both an expected consequence of inflation and the observed characteristic angular size scale of the cosmie microwave background fluctuations (Spergel et al."," In this section, we assume a flat universe (i.e., $\Omega_k=0$ ) because of both an expected consequence of inflation and the observed characteristic angular size scale of the cosmic microwave background fluctuations (Spergel et al." + 2003 and references therein)., 2003 and references therein). +" From equations (1) and (2). we obtain the beaming-corrected 5-ray energy E.jo=(1—CcosOE.ia. that is. Figure | plots E-j versus for the GRB sample listed in Table 1. with O4,20.27. O4E,20.73 and //2 0.71."," From equations (1) and (2), we obtain the beaming-corrected $\gamma$ -ray energy $E_{\gamma,{\rm jet}}=(1-\cos +\theta)E_{\gamma,{\rm iso}}$, that is, Figure 1 plots $E_{\gamma,{\rm jet}}$ versus $E'_p$ for the GRB sample listed in Table 1, with $\Omega_M=0.27$, $\Omega_\Lambda=0.73$ and $h=0.71$ ." +" We find that E.{οι and E, are strongly correlated with a correlation coefficient r,=0.99£0.08 (with a probability of < 107+)."," We find that $E_{\gamma,{\rm jet}}$ and $E'_p$ are strongly correlated with a correlation coefficient $r_s=0.99\pm 0.08$ (with a probability of $<10^{-4}$ )." + The best fit is (E.ο=(1.12£0.12E]/100keV20706 with à reduced Vet-0.53.," The best fit is $(E_{\gamma,{\rm +jet}}/10^{50}{\rm ergs})=(1.12\pm0.12)(E'_p/100\,{\rm keV})^{1.50\pm 0.08}$ with a reduced $\chi^2_{\rm dof}=0.53$." + We note this power to be insensitive to O5., We note this power to be insensitive to $\Omega_M$. +" In addition. although the peak energy E, and the energy spectral index o in Table | appear to evolve with redshift (Amati et al."," In addition, although the peak energy $E'_p$ and the low-energy spectral index $\alpha$ in Table 1 appear to evolve with redshift (Amati et al." + 2002). this evolution doesn't affect the above relation as shown in Figure |.," 2002), this evolution doesn't affect the above relation as shown in Figure 1." + These results imply that GRBs are standard candles., These results imply that GRBs are standard candles. + We first derive the observed luminosity distance the GRB sample., We first derive the observed luminosity distance from the GRB sample. +" Considering a relationship (E.joI0?fromergs)=ClE,,100keV)!° (where C is a dimensionless parameter). we obtain where E,=(12-2) is in units of keV. Thus. the observed distance modulus of a GRB is jigp=5log(d;/1O0pce) with an error of where σε. os.. σι. and o, are the errors in the peak energy. fluence. break time and medium density of the GRB. respectively."," Considering a relationship $(E_{\gamma, {\rm +jet}}/10^{50}{\rm ergs})=C(E'_p/100\,{\rm keV})^{1.5}$ (where $C$ is a dimensionless parameter), we obtain where $E_p=E'_p/(1+z)$ is in units of keV. Thus, the observed distance modulus of a GRB is $\mu_{\rm ob}=5\log +(d_L/10\,{\rm pc})$ with an error of where $\sigma_{E_{p}}$, $\sigma_{S_{\gamma}}$, $\sigma_{t_{{\rm j}}}$, and $\sigma_{n}$ are the errors in the peak energy, fluence, break time and medium density of the GRB, respectively." + We plot a Hubble diagram of our GRB sample in Figure 2 based on equations (4) and (5)., We plot a Hubble diagram of our GRB sample in Figure 2 based on equations (4) and (5). + This figure also presents a Hubble diagram of the current SNe Ia sample., This figure also presents a Hubble diagram of the current SNe Ia sample. + Both Hubble diagrams are consistent with each other., Both Hubble diagrams are consistent with each other. + However. GRBs and SNe la have mean uncertainties of 0.09 and 0.05 in the log of the distance. respectively. and thus GRBs are about twice worse in accuracy than SNe.," However, GRBs and SNe Ia have mean uncertainties of $0.09$ and $0.05$ in the log of the distance, respectively, and thus GRBs are about twice worse in accuracy than SNe." +" For an FRW cosmology with O1; and O4. equation (2) gives the theoretical distance modulus jj,=Slog(d,/lOpe)."," For an FRW cosmology with $\Omega_M$ and $\Omega_\Lambda$, equation (2) gives the theoretical distance modulus $\mu_{\rm th}=5\log (d_L/10\,{\rm pc})$ ." + The likelihood for these cosmological parameters can be determined from a A statistic. where We consider all possible values of the parameters /: and € to be //C(0.68.0.75) (Bennett et al.," The likelihood for these cosmological parameters can be determined from a $\chi^2$ statistic, where We consider all possible values of the parameters $h$ and $C$ to be $h\in (0.68, 0.75)$ (Bennett et al." + 2003) and C(1.00.1.24) (see 82).," 2003) and $C\in(1.00, 1.24)$ (see 2)." + The confidence regions in the O1;-O 4 plane can be found through marginalizing the likelihood functions over / and C (ie. integrating the probability density P»e7 for all values of // and C).," The confidence regions in the $\Omega_M$ $\Omega_\Lambda$ plane can be found through marginalizing the likelihood functions over $h$ and $C$ (i.e., integrating the probability density $P\propto +e^{-\chi^2/2}$ for all values of $h$ and $C$ )." + We plot contours of likelihood (from lo to 30) for unknown curvature ©; in Figure 3., We plot contours of likelihood (from $1\sigma$ to $3\sigma$ ) for unknown curvature $\Omega_k$ in Figure 3. + As shown for a flat universe. with the current sample. ον<0.62 (at the 20 confidence level). and the Io contour containsthe (45.04)=(0.27.0.73) point corresponding to the “concordance” model.," As shown for a flat universe, with the current sample, $\Omega_M<0.62$ (at the $2\sigma$ confidence level), and the $1\sigma$ contour containsthe $(\Omega_M, \Omega_\Lambda)=(0.27, 0.73)$ point corresponding to the “concordance"" model." + We measure Qy20.352512 (Io)., We measure $\Omega_M=0.35\pm^{0.15}_{0.15}$ $1\sigma$ ). + There are several alternative approaches to calculate the luminosity distance (also see Riess et al., There are several alternative approaches to calculate the luminosity distance (also see Riess et al. + 2004)., 2004). + We here consider a flat universe and a constant EOS. w=Py/ppc. of a dark energy component (Garnavich et al.," We here consider a flat universe and a constant EOS, $w=P_{\rm DE}/\rho_{\rm DE}c^2$, of a dark energy component (Garnavich et al." + 1998; Perlmutter et al., 1998; Perlmutter et al. + 1999)., 1999). + In this case we have Figure 4 presents contours of likelihood. in. the Quj2w plane (after marginalizing over /7 and C)., In this case we have Figure 4 presents contours of likelihood in the $\Omega_M$ $w$ plane (after marginalizing over $h$ and $C$ ). +" The solid contours consider a prior of O1,=0.27£0.04 by assuming its Gaussiandistribution. similar to Riess et al. ("," The solid contours consider a prior of $\Omega_M=0.27\pm 0.04$ by assuming its Gaussiandistribution, similar to Riess et al. (" +2004).,2004). + We see w= (lo). which is consistent with the value of iw expected for a cosmological constant (1.6. w2 —1).," We see $w=-0.84\pm^{0.57}_{0.83}$ $1\sigma$ ), which is consistent with the value of $w$ expected for a cosmological constant (i.e., $w=-1$ )." +" The E.jgE!"" relationship withà small dispersion was reported by Ghirlanda et al. ("," The $E_{\gamma,{\rm jet}}\propto {E'_p}^{1.5}$ relationship witha small dispersion was reported by Ghirlanda et al. (" +2004) and confirmed in this Letter.,2004) and confirmed in this Letter. + The advantages of considering this relationship as a probe of theuniverse are (1) that GRBs have been detected at redshifts up to zx 4.5. (2) that > rays suffer from no extinction. and (3) that we don't think of luminosity evolution.," The advantages of considering this relationship as a probe of theuniverse are (1) that GRBs have been detected at redshifts up to $z\simeq 4.5$ , (2) that $\gamma$ rays suffer from no extinction, and (3) that we don't think of luminosity evolution." + These advantages led, These advantages led + connectiton between the flux. spectral and timing properties of," ion between the flux, spectral and timing properties of" +lidentification.,identification. + By assuming a distribution for the intrinsic SEDs. we calculate the average selection xobabilitv as a function of magnitude aud redshitt.," By assuming a distribution for the intrinsic SEDs, we calculate the average selection probability as a function of magnitude and redshift." + To do this. we first produce a large set of galaxy spectra or a given (Misog.:). using the Druzual&Charlot(2003). stellar population svuthesis model with the Salpeter IMF.," To do this, we first produce a large set of galaxy spectra for a given $M_{1300}, z$ ), using the \citet{bru03} stellar population synthesis model with the Salpeter IMF." + The magnitude ου is the absolute AB naenitude at rest-frame 1300A.. and 1300 iis chosen to be close to the z/- baud effective waveleneth OY i~6 galaxies.," The magnitude $M_{1300}$ is the absolute AB magnitude at rest-frame 1300, and 1300 is chosen to be close to the $z'$ -band effective wavelength for $z\sim6$ galaxies." + The input model paramcters will ο described in detail in the next paragraph., The input model parameters will be described in detail in the next paragraph. + We then apply ICM absorption to the model spectra., We then apply IGM absorption to the model spectra. + The neutral TGAL fraction inercases dramatically from 2=5.5 to 2.=6.5.causing complete Comm-Peterson troughs iu sole 202(6 quasar spectra (Fanetal.2006).," The neutral IGM fraction increases dramatically from $z=5.5$ to $z=6.5$,causing complete Gunn-Peterson troughs in some $z>6$ quasar spectra \citep{fan06}." +. It is hus critical to predict (2! colors., It is thus critical to predict $i'-z'$ colors. + We calculate ICAI absorption in the wav used by Fanetal.(2001) αμα Jiangetal.(2008)., We calculate IGM absorption in the way used by \citet{fan01} and \citet{jia08}. +. Finally we measure the apparent uaenitudes from the model spectra with the SDF filter ransiuission curves., Finally we measure the apparent magnitudes from the model spectra with the SDF filter transmission curves. + We also incorporate photometric errors into each band., We also incorporate photometric errors into each band. + It is particularly important for aut objects; as a non-neeheible fraction of real galaxies uav have been scattered out of the selection region due o large photometric errors.," It is particularly important for faint objects, as a non-negligible fraction of real galaxies may have been scattered out of the selection region due to large photometric errors." + The selection. probability or this galaxy (M4309. 2) is then the fraction of mode ealaxies that mect all our criteria.," The selection probability for this galaxy $M_{1300}, z$ ) is then the fraction of model galaxies that meet all our criteria." + The intrinsic SEDs of ealaxics depend on their plivsica xoperties such as age. metallicity. aud dust extinction.," The intrinsic SEDs of galaxies depend on their physical properties such as age, metallicity, and dust extinction." + However. we know very little about physical properties of 2>6 galaxies.," However, we know very little about physical properties of $z>6$ galaxies." + We deteriune input parameters or the above svuthesis models from our JST iux Spitzer observations of 20) spectroscopicallv-confiruie LAEs aud LBCs at 5.6<:7 in SDF (E. Ee et abl.," We determine input parameters for the above synthesis models from our $HST$ and $Spitzer$ observations of 20 spectroscopically-confirmed LAEs and LBGs at $5.6100$ Myr and young galaxies with ages $\sim1$ Myr." + The dust extinction is low to uoderate. consistent with the eeneral trend that hieher-redshift galaxies have bluer UV continuum slope and ower dust extinction (Douweusetal.2009).," The dust extinction is low to moderate, consistent with the general trend that higher-redshift galaxies have bluer UV continuum slope and lower dust extinction \citep{bou09}." +. Dased ou hese results. our model paraiueters are set as follows.," Based on these results, our model parameters are set as follows." + At a eiven redshift (rom 5.5 to 7.2). we choose to use a iixed erid of six ages [L. 2. 5. 10. 10. 100| Myr aud που dust extinction values E(BV) = 0.02. 0.1. 0.3].," At a given redshift (from 5.5 to 7.2), we choose to use a mixed grid of six ages [1, 2, 5, 10, 40, 100] Myr and three dust extinction values E(B–V) = [0.02, 0.1, 0.3]." + The metallicity for the models with ages of 1 and 2 Myr is 0.005 Z... for the models of with ages of 5 aud 10 Myr is 0.02 Z... and for the models of with ages of 10 aud 100 Abvrds 0.2 2...," The metallicity for the models with ages of 1 and 2 Myr is 0.005 $Z_{\sun}$, for the models of with ages of 5 and 10 Myr is 0.02 $Z_{\sun}$, and for the models of with ages of 40 and 100 Myr is 0.2 $Z_{\sun}$." + The selection functiou is not sensitive to these physical parameters such as age. metallicity. aud dust extinction.," The selection function is not sensitive to these physical parameters such as age, metallicity, and dust extinction." + After we generate the galaxy. coutimmun spectra using the Druzual&Charlot(2003) model. we add eenission lines to the spectra.," After we generate the galaxy continuum spectra using the \citet{bru03} model, we add emission lines to the spectra." + The eenission i our galaxies is strong. and has siguificaut contribution (0.1 mag) to the 2 baud plotometry.," The emission in our galaxies is strong, and has significant contribution $\sim0.4$ mag) to the $z'$ -band photometry." + As we discussed in Section 3. we kuow very little about the statistics of sstroneths at 2~6.," As we discussed in Section 3, we know very little about the statistics of strengths at $z\sim6$." + Therefore we asune that the EWs of aat lo6 have a distribution similar to that of 2—3 (Reddy&Steidel2009).., Therefore we assume that the EWs of at $z\sim6$ have a distribution similar to that of $z\sim3$ \citep{red09}. . + Figure 1 shows the selection fictionas a function of AMisogo aud +., Figure 4 shows the selection functionas a function of $M_{1300}$ and $z$. + The contours iu the figure are selection probabilities from to with an interval of54., The contours in the figure are selection probabilities from to with an interval of. +. The sharp decrease of the probability at το6 is due to the color cut of (20>1.7., The sharp decrease of the probability at $z\sim6$ is due to the color cut of $i'-z'>1.7$. + The solid circles are the locations of the 19 2>6 galaxies in our sample., The solid circles are the locations of the 19 $z>6$ galaxies in our sample. + Figure 1 does not include two simall constant iucompletenesses., Figure 4 does not include two small constant incompletenesses. + Que is from slit conflict during DEIMOS slit assiguiueut: candidates were not allocated slits., One is from slit conflict during DEIMOS slit assignment; $\sim8$ candidates were not allocated slits. +" The other one is due to the existence of strong sky ΟΠ lines: enmission lines that happen to be ou these ΟΠ lines are mich more difficult to identity,", The other one is due to the existence of strong sky OH lines; emission lines that happen to be on these OH lines are much more difficult to identify. + Although iu principle this incompleteness is also a function of mmaeuitude aud redshift. we fud that is a good approximation for our sample in the rauge of 85009000 (e.g.Starketal.2010).," Although in principle this incompleteness is also a function of magnitude and redshift, we find that is a good approximation for our sample in the range of 8500–9000 \citep[e.g.][]{sta10}." +". Figure L does uot take iuto account the rejection of +—6.5 LAEs either. otherwise there willbe a ""dip. at 2—6.5 in the selection function of Fieure 1."," Figure 4 does not take into account the rejection of $z\sim6.5$ LAEs either, otherwise there willbe a `dip' at $z\sim6.5$ in the selection function of Figure 4." + We derive the volume density of the galaxies at 2>6 using the traditional η method., We derive the volume density of the galaxies at $z>6$ using the traditional $1/V_{a}$ method. + The available volume for a galaxy with absolute maguitude ουν and redshitt > ina dnagnitude bin AAS aud a redshift biu A: is where pCAZ4599.2) is the probability function used to correct for all the sample iucounipletenesses described above.," The available volume for a galaxy with absolute magnitude $M_{1300}$ and redshift $z$ in a magnitude bin $\Delta M$ and a redshift bin $\Delta z$ is where $p(M_{1300},z)$ is the probability function used to correct for all the sample incompletenesses described above." + Then the spatial densitv and dts statistical nucertaity can be written as (Page&Carrera2000) where Nga? d the nuuber of galaxies iu the biu CAM. Az).," Then the spatial density and its statistical uncertainty can be written as \citep{pag00} + where $N_{gal}$ is the number of galaxies in the bin $\Delta M, \Delta z$ )." + The inagnitude aud redshift distributions of the ealaxies in our suple are shown in Fieure Lt., The magnitude and redshift distributions of the galaxies in our sample are shown in Figure 4. + We ieasure galaxy deusitics iu one redshift bin 5.52<6.5 and three magnitude bins |19.1. 20.1). aud |21.1. 23).," We measure galaxy densities in one redshift bin $5.86.6$ (see subsection 4.5 for discuss) and the LAEs at $z\sim6.56$ are being targeting in another program (see Section 2). + Figure 5 shows our imeasurenmieuts of the spatial deusities (the filled circles with error bars) in the three inaguitude bius at (2)6.2., Figure 5 shows our measurements of the spatial densities (the filled circles with error bars) in the three magnitude bins at $\langle z\rangle \sim6.2$. + It also compares with the UV LEs at 2= 5. 5.9. and 6.8 from other studies(Bowensetal.2007:MeLure2009:Ouchi 2011)..," It also compares with the UV LFs at $z=5$ , 5.9, and 6.8 from other studies\citep{bou07,mcl09,ouc09,bou11}. ." + Douweusetal.(2007) obtained a large saunple of LBC candidates from the QUDF aud other Πο datasets., \citet{bou07} obtained a large sample of LBG candidates from the HUDF and other $HST$ datasets. + They derived the UV, They derived the UV +A triple isolation of the spectrograph is the basis of precise thermal control.,A triple isolation of the spectrograph is the basis of precise thermal control. + The spectrograph bench is completely packed by a box of demountable 60-mm panels of polyurethane sandwiched between thin steel sheets., The spectrograph bench is completely packed by a box of demountable 60-mm panels of polyurethane sandwiched between thin steel sheets. +" Inside this box, thermal dissipation is minimal and limited to the photo multiplier of the exposure metre (~250 mW) and the actuator for the miniature shutter."," Inside this box, thermal dissipation is minimal and limited to the photo multiplier of the exposure metre $\sim$ 250 mW) and the actuator for the miniature shutter." + The latter is a bistable solenoid that only dissipates for a few milliseconds during opening or closing of the shutter., The latter is a bistable solenoid that only dissipates for a few milliseconds during opening or closing of the shutter. +" The inner room, built from the same 60-mm isolating panels, surrounds the spectrograph box."," The inner room, built from the same 60-mm isolating panels, surrounds the spectrograph box." +" A LakeShore Model331 temperature controller with 50-Watt heater actively stabilises the temperature of this room at 18+ 0.01°C. Finally, similar 100-mm walls for the outer room isolate the spectrograph further from the outside world."," A LakeShore Model331 temperature controller with 50-Watt heater actively stabilises the temperature of this room at $18\pm0.01^{\circ}$ C. Finally, similar 100-mm walls for the outer room isolate the spectrograph further from the outside world." +" An air conditioning system keeps the temperature in this room at 14+0.1°C. Apart of temperature, atmospheric pressure changes also have an effect on the refractive index of air, causing a spectral shift."," An air conditioning system keeps the temperature in this room at $14\pm0.1^{\circ}$ C. Apart of temperature, atmospheric pressure changes also have an effect on the refractive index of air, causing a spectral shift." + Fig., Fig. +" 9 shows typical pressure fluctuations including the (semi-)ddiurnal atmospheric tide (Lindzen 1979),, together with the resulting radial velocity offset that amounts to 0.05 pixel/hPa or 0.08 hhPa)."," \ref{fig:pressure} shows typical pressure fluctuations including the diurnal atmospheric tide \citep{Lindzen79}, together with the resulting radial velocity offset that amounts to 0.05 pixel/hPa or 0.08 hPa)." + Housing the spectrograph in a vacuum tank would have been the obvious approach for avoiding pressure-induced instrumental drift., Housing the spectrograph in a vacuum tank would have been the obvious approach for avoiding pressure-induced instrumental drift. +" However, practical and financial limitations prohibited this solution."," However, practical and financial limitations prohibited this solution." +" As an alternative, we have started the installation of a system that should stabilise the spectrograph at a constant absolute pressure of ~ hhPa, a value close to the maximum atmospheric pressure that occurs at the altitude of the observatory."," As an alternative, we have started the installation of a system that should stabilise the spectrograph at a constant absolute pressure of $\sim$ hPa, a value close to the maximum atmospheric pressure that occurs at the altitude of the observatory." +" To allow for over-pressure of maximum ~220hhPa in the spectrograph room during periods of low atmospheric pressure (observing conditions never occur when atmospheric pressure is below hhPa), the walls of the outer room have been reinforced by a structure of 40-mm steel tubes."," To allow for over-pressure of maximum $\sim$ hPa in the spectrograph room during periods of low atmospheric pressure (observing conditions never occur when atmospheric pressure is below hPa), the walls of the outer room have been reinforced by a structure of 40-mm steel tubes." + The large dimensions of HERMES prohibit the installation of the instrument at the telescope focal plane., The large dimensions of HERMES prohibit the installation of the instrument at the telescope focal plane. + The obvious, The obvious +even in Equation 3) does predict flux profiles that are simular to those observed at μα for values of ry iu the range of sand à in the range 2.53.5.,given in Equation \ref{MODELEQ} does predict flux profiles that are similar to those observed at mm for values of $r_0$ in the range of and $\alpha$ in the range 2.5–3.5. + The model density profile that we use to ft the observed fux profiles of Perhol5 and Perbo58 docs not provide a unique solution to what the true density profiles of these core are. aud other models that have a flat inner profile that steepens at larger radii can be consistent with our observations.," The model density profile that we use to fit the observed flux profiles of Perbo45 and Perbo58 does not provide a unique solution to what the true density profiles of these core are, and other models that have a flat inner profile that steepens at larger radii can be consistent with our observations." + If one uses different asstuptionus about the temperature profile aud allows he enüssivitv to vary with radius. it might even be yossible to fit the πμ flux profile with a power-aw density profile.," If one uses different assumptions about the temperature profile and allows the emissivity to vary with radius, it might even be possible to fit the mm flux profile with a power-law density profile." + What we have shown here is that he density profiles of PerbolS and Perbo5s are not recessarily different from typical starless cores. aud the reason that they are detected in our survey while other cores are not is most Likely due to their relatively large nasses for their size.," What we have shown here is that the density profiles of Perbo45 and Perbo58 are not necessarily different from typical starless cores, and the reason that they are detected in our survey while other cores are not is most likely due to their relatively large masses for their size." + Of the 11 starless cores that were observed with CARAIA. 2 were detected (Perbol5 aud Perbohs) aud 9 were not.," Of the 11 starless cores that were observed with CARMA, 2 were detected (Perbo45 and Perbo58) and 9 were not." + Neither of the detected starless cores are seen to break iuto multiple componcuts., Neither of the detected starless cores are seen to break into multiple components. + The non-detection of the majority of the starless cores is not duc to low sensitivity (the median uppoer lint for the nou-detections is - see Section 3.1.0 for details). but iustead is likely he result of a lack of compact sub-structures within the cores.," The non-detection of the majority of the starless cores is not due to low sensitivity (the median upper limit for the non-detections is - see Section \ref{MASS} for details), but instead is likely the result of a lack of compact sub-structures within the cores." + If all ofthe mass in cach of the uou-detected cores iwl been contained within a few compact structures. every core would have been detected in the CARMA observations (sce Section 3.1.0 for an explanation of row the mass upper lanits in Table ο were derived).," If all of the mass in each of the non-detected cores had been contained within a few compact structures, every core would have been detected in the CARMA observations (see Section \ref{MASS} for an explanation of how the mass upper limits in Table \ref{MMFITSTAB} were derived)." + For example. the median 26 upper lait on the mass of the non-detected cores is a factor of 7 smaller than he core mass derived frou. the Bolocaim map.," For example, the median $\sigma$ upper limit on the mass of the non-detected cores is a factor of 7 smaller than the core mass derived from the Bolocam map." + Therefore. we areue that the nou-detection of iiultiple compoucuts in all 1l cores in our suple is a significaut result.," Therefore, we argue that the non-detection of multiple components in all 11 cores in our sample is a significant result." + Furthermore. eiven the high rate of multiplicity in Class Yand Class I protostars (Looneyctal.2000) and the ow rate of nmultiplieitv iu starless cores. we sugecst hat fragmentation iuto binaries takes place duriug the collapse of a prestellar core or during the Class 0 stage.," Furthermore, given the high rate of multiplicity in Class 0 and Class I protostars \citep{Looney00} and the low rate of multiplicity in starless cores, we suggest that fragmentation into binaries takes place during the collapse of a prestellar core or during the Class 0 stage." + The density profiles of many starless cores have con measured from (ub)inillimeter contiuuun emission naps and it has generally. been found that the density xofiles are cousistent with an r? power-law at Óurge radi that flattens towards the center of the core (e.g.Ward-Thompsonetal.1991.1999:Shirley 2000).," The density profiles of many starless cores have been measured from (sub)millimeter continuum emission maps and it has generally been found that the density profiles are consistent with an $r^{-2}$ power-law at large radii that flattens towards the center of the core \citep[e.g.][]{Ward-Thompson94, Ward-Thompson99, Shirley00}." +. To study the deusitv profiles of the starless cores in our saluple. we use the mass and radius derived from the l.luuun observations to predict the 2122uu flux at the center of each core with the asstuuptions that the deusity profile gocs as r2. that the ciuissivity spectral index is eiven bv 9=2. and that the cores are isothermal.," To study the density profiles of the starless cores in our sample, we use the mass and radius derived from the mm observations to predict the mm flux at the center of each core with the assumptions that the density profile goes as $r^{-2}$, that the emissivity spectral index is given by $\beta = 2$, and that the cores are isothermal." + We would have been able to detect (at the 3o level) all 17 cores in our saiuple if these assimuptions were valid. bu in fact we onlv detect two starless cores.," We would have been able to detect (at the $\sigma$ level) all 11 cores in our sample if these assumptions were valid, but in fact we only detect two starless cores." + As noted in Section 3.1.0.0 76 9=1 then the detection rate of cores. and any substructure m them. would be easier than if j—2.," As noted in Section \ref{MASS}, if $\beta=1$ then the detection rate of cores, and any substructure in them, would be easier than if $\beta=2$." + Because we expect starless cores to be colder iu their centers than at the edees the fux profile of a “real” starless core will be somewhat flatter than our isotlerma model would predict., Because we expect starless cores to be colder in their centers than at the edges the flux profile of a “real” starless core will be somewhat flatter than our isothermal model would predict. + Nevertheless. we conclude that the density profiles for the majority of the starless cores m our saauple are flatter than aur 2 profile at their centers. in aerecinent with other survevs.," Nevertheless, we conclude that the density profiles for the majority of the starless cores in our sample are flatter than an $r^{-2}$ profile at their centers, in agreement with other surveys." + The low vate of οταν continuum detections towards 1l of tho brightest (2200—mJxbeamlatldoannmueithBoloeam: in this study is in agreement with the results of Oluietal.(2005) who detect only 1 out of 6 dense cores ij Perseus., The low rate of mm continuum detections towards 11 of the brightest \citep[$>$200 mJy beam$^{-1}$ at mm with in this study is in agreement with the results of \citet{Olmi05} who detect only 1 out of 6 dense cores in Perseus. + The largest augular scale to which the interferometer was sensitive aud the median noise in the maps dn this study aaud 0.7 uty beam3) are similar to that iu Olinietal.(20LO”and1-1.5iiJybeam1: 2005).," The largest angular scale to which the interferometer was sensitive and the median noise in the maps in this study and 0.7 mJy $^{-1}$ ) are similar to that in \citet[20\arcsec--40\arcsec\ and +1-1.5 mJy beam$^{-1}$ ." + There is no overlap in the sample of sources mapped in this study and in Olinietal.(2005)., There is no overlap in the sample of sources mapped in this study and in \citet{Olmi05}. +. There are 67 starless cores detected bv Enochetal.(2008) in the Perseus molecular cloud. of which we observed 11.," There are 67 starless cores detected by \citet{Enoch08} in the Perseus molecular cloud, of which we observed 11." + Because we selected our sample based on their high peak fluxes. there is no reason to expect that the other starless cores in Perseus would have a higher detection rate at 21inun.," Because we selected our sample based on their high peak fluxes, there is no reason to expect that the other starless cores in Perseus would have a higher detection rate at mm." + The low rate (0/11) of finding iiutiple nuu componeuts at rresolution within uum cores observed with resolution is consistent with the Sima contin OVRO observations of dense cores in Perseus carried out bv Olunietal.(2005).. who fouud that none of the cores (out of six) wore seen to be composed of multiple colmpoucuts.," The low rate (0/11) of finding mutiple mm components at resolution within mm cores observed with resolution is consistent with the mm continuum OVRO observations of dense cores in Perseus carried out by \citet{Olmi05}, who found that none of the cores (out of six) were seen to be composed of multiple components." + We argue that starless core mass functions eenerated from single dish bolometer maps of Perseus (e.g.Enochetal.2008:Tatchell&Fuller2008). are not strouglv biased by the blending of compact. close cores iuto more massive single cores.," We argue that starless core mass functions generated from single dish bolometer maps of Perseus \citep[e.g.][]{Enoch08, Hatchell08} are not strongly biased by the blending of compact, close cores into more massive single cores." + Given that niauv stars are found im multiple svstenis (Duqueunoy&Mavor1991). aud that may protostars are also multiples (Looneyetal.2000:Tlaisch 2001). it is worthwhile to examine when fragmentation akes place.," Given that many stars are found in multiple systems \citep{Duquennoy91} and that many protostars are also multiples \citep{Looney00, Haisch04}, it is worthwhile to examine when fragmentation takes place." + If starless cores fragment before formation of an embedded: object. then we would expect to be able to detect these sub-cores.," If starless cores fragment before formation of an embedded object, then we would expect to be able to detect these sub-cores." + On the other laud. if ragiueutation takes place after the first protostar las ornued. then a survey of starless cores wout find any evidence of fragmentation.," On the other hand, if fragmentation takes place after the first protostar has formed, then a survey of starless cores won't find any evidence of fragmentation." + In this studs. we find that rone of the eleven starless cores show any evidence of rasniecntation.," In this study, we find that none of the eleven starless cores show any evidence of fragmentation." + If these cores will eventually fragment. hen this must happen during aud/or after the collapse and formation of the first protostar.," If these cores will eventually fragment, then this must happen during and/or after the collapse and formation of the first protostar." + Late fragimoeutatiou on sinall scales. which is consistent with the results of this survey. is predicted by theories that create binaries from disk fragiucutation (e.g.Bonnell&Bate1991:Ἱνταττοetal. 2010).," Late fragmentation on small scales, which is consistent with the results of this survey, is predicted by theories that create binaries from disk fragmentation \citep[e.g.][]{Bonnell94, +Kratter10}." +. The observations deseribed iu this paper are iu agreement with the results of other receut survevs m Perseus., The observations described in this paper are in agreement with the results of other recent surveys in Perseus. + Kirketal.(2007). compared the line. profiles of CASO (2-1) and Χο) (1-0) toward a sample of 150 candidate deuse cores. both prestellar and protostellar.," \citet{Kirk07} compared the line profiles of $^{18}$ O (2-1) and $_2$ $^+$ (1-0) toward a sample of 150 candidate dense cores, both prestellar and protostellar." + They found that the NoII! lines. represeutiug the densest sas within the core. displav nearly thermal liue widths. indicating little non-thermal activity at the core center.," They found that the $_2$ $^+$ lines, representing the densest gas within the core, display nearly thermal line widths, indicating little non-thermal activity at the core center." + While the CO eas shows significant non- broadening. the velocity centroids of the two species are very similar. mdicatiug that the counection," While the $^{18}$ O gas shows significant non-thermal broadening, the velocity centroids of the two species are very similar, indicating that the connection" +the masses to a Salpeter IMF (as used in Maraston et al.,the masses to a Salpeter IMF (as used in Maraston et al. +" 2009) using scale-factors: M$etpeter_1gyKroura—1.78MC""these— ΜΕΝ, ", 2009) using these scale-factors: $M_\star^{Salpeter} = 1.6 M_\star^{Kroupa} = 1.78 M_\star^{Chabrier}= 2 M_\star^{B\&G}$ . +"In addition, to account for differences in stellar population models we rescaled the Bezanson et al."," In addition, to account for differences in stellar population models we rescaled the Bezanson et al." + data multiplying their stellar masses by 0.7 (as e.g. in Mancini et al., data multiplying their stellar masses by 0.7 (as e.g. in Mancini et al. +" 2010, see also Muzzin et al."," 2010, see also Muzzin et al." + 2009) and by 0.5 for the Damjanov et al., 2009) and by 0.5 for the Damjanov et al. + stellar masses., stellar masses. + The evidence for small sizes at z~2 is not uncontested., The evidence for small sizes at $z\sim 2$ is not uncontested. + Mancini et al. (, Mancini et al. ( +"2010) have argued that neglect of low surface brightness features will bias re to small values (while the bias in M, is small — C. Mancini private communication).",2010) have argued that neglect of low surface brightness features will bias $r_e$ to small values (while the bias in $M_*$ is small – C. Mancini private communication). + Accounting for this effect in a sample at z~1.5 yields the open squares in Figure 5.., Accounting for this effect in a sample at $z\sim 1.5$ yields the open squares in Figure \ref{fig:comp1}. +" Evidently, these objects are not small for their M. compared to z=0 objects."," Evidently, these objects are not small for their $M_*$ compared to $z=0$ objects." + If both Mancini et al., If both Mancini et al. + and Bezanson et al., and Bezanson et al. +" are correct, and both probe the massive end of the population at their respective mean redshifts, then there must have been significant evolution in size and stellar mass between z—2.3 and z— 1.5."," are correct, and both probe the massive end of the population at their respective mean redshifts, then there must have been significant evolution in size and stellar mass between $z=2.3$ and $z=1.5$ ." +" In view of this discussion, it is remarkable that the z=2.3 compact galaxies appear to trace the small size and M. end of the relation we find at z~O0, for fixed c (solid line)."," In view of this discussion, it is remarkable that the $z=2.3$ compact galaxies appear to trace the small size and $M_*$ end of the relation we find at $z\sim 0$, for fixed $\sigma$ (solid line)." + The z~1.5 sample of Mancini et al. (, The $z\sim 1.5$ sample of Mancini et al. ( +"2010) is confined to a narrower range of M,, making it difficult to define a relation.","2010) is confined to a narrower range of $M_*$, making it difficult to define a relation." +" However, at this M., the difference between the solid line (c~400 km s!) and the others (bulk of early-type population) is a factor of two or less."," However, at this $M_*$, the difference between the solid line $(\sigma\sim 400$ km $^{-1}$ ) and the others (bulk of early-type population) is a factor of two or less." +" It will be interesting if future measurements show the z—2.3 objects to have σ~400 km s~', and even more so if this is also true for the most compact of the objects in the Mancini et al."," It will be interesting if future measurements show the $z=2.3$ objects to have $\sigma \sim 400$ km $^{-1}$, and even more so if this is also true for the most compact of the objects in the Mancini et al." + sample., sample. +" We now turn to a slightly different version of the correlation between size and mass, namely that between average density and mass."," We now turn to a slightly different version of the correlation between size and mass, namely that between average density and mass." +" For this purpose, it is useful to define the average density within r."," For this purpose, it is useful to define the average density within $r$." +" In what follows, we will pay special attention to pe and pi: the mean density within the de Vaucouleurs radius re, and within 1 kpc, respectively."," In what follows, we will pay special attention to $\bar{\rho}_e$ and $\bar{\rho}_1$: the mean density within the de Vaucouleurs radius $r_e$, and within 1 kpc, respectively." +" Whereas pe can be thought of as a characteristic density, pi is more like the central density (recall that, for this sample, Te©10 kpc)."," Whereas $\bar\rho_e$ can be thought of as a characteristic density, $\bar{\rho}_1$ is more like the central density (recall that, for this sample, $r_e\approx 10$ kpc)." +" Theright-hand panel of Figure 6 shows the correlation between pe and M., using the same format as for the panel on the left."," Theright-hand panel of Figure \ref {fig:comp2} shows the correlation between $\bar{\rho}_e$ and $M_*$, using the same format as for the panel on the left." + Fitting to the relation defined by our dynamically estimated M. yields This characteristic density is a sharply declining function of stellar mass — the decline is significantly steeper than previously reported for a sample which includes the full range of early-types (e.g. Bernardi et al., Fitting to the relation defined by our dynamically estimated $M_*$ yields This characteristic density is a sharply declining function of stellar mass – the decline is significantly steeper than previously reported for a sample which includes the full range of early-types (e.g. Bernardi et al. + 2003; Hyde Bernardi 2009)., 2003; Hyde Bernardi 2009). +" Following our discussion of the re—M. relation⋅ above, the more relevant comparison⋅ may be with⋅ the p.B—M. relation. at fixed c, for which- the slope is: —1.8 (Bernardi et al."," Following our discussion of the $r_e-M_*$ relation above, the more relevant comparison may be with the $\bar\rho_e-M_*$ relation at fixed $\sigma$, for which the slope is $-1.8$ (Bernardi et al." + 2008)., 2008). +" Our current estimate is slightly steeper, perhaps because our mass estimate is less noisy."," Our current estimate is slightly steeper, perhaps because our mass estimate is less noisy." +" To see this, note that could have derived the slope from the fact that peοςM./rzwsM,, where the final expression uses the fact that the scatter between Τε and M. is small (which we argued was a consequence of the fact that our sample has only a small range of c, a small range in re/rap, and that Figure 2 has small scatter)."," To see this, note that we could have derived the slope from the fact that $\bar\rho_e\propto M_*/r_e^3 \propto M_*^{-2.21}$, where the final expression uses the fact that the scatter between $r_e$ and $M_*$ is small (which we argued was a consequence of the fact that our sample has only a small range of $\sigma$, a small range in $r_e/r_{ap}$, and that Figure \ref{fig:lambda} has small scatter)." +" We note that, while the z=2.3 objects have p. orders of magnitude larger than the bulk of the z—0 objects of the sameM.. (compare diamonds with dashed or dotted curves), they are only slightly denser than z=0 objects of the same M,, if such objects had ao~400 km s! (extrapolate solid line to small M.)."," We note that, while the $z=2.3$ objects have $\bar\rho_e$ orders of magnitude larger than the bulk of the $z=0$ objects of the same$M_*$ (compare diamonds with dashed or dotted curves), they are only slightly denser than $z=0$ objects of the same $M_*$ , if such objects had $\sigma\sim 400$ km $^{-1}$ (extrapolate solid line to small $M_*$ )." + 'The steepness of this relation stands in stark contrast, The steepness of this relation stands in stark contrast +the IAL and RAL.,the IMF and RMF. + However. the results are much less sensitive to our choice of IME or IRME than to the other nmocel parameters.," However, the results are much less sensitive to our choice of IMF or RMF than to the other model parameters." + Given the uncertainty in current composition and structure of ColtoT-7 b. our model of coupled. orbit evolution and evaporativo mass loss cannot uniquely determine the mass of the gaseous envelope that C'oltoT-7 b may originally have had.," Given the uncertainty in current composition and structure of CoRoT-7 b, our model of coupled orbit evolution and evaporative mass loss cannot uniquely determine the mass of the gaseous envelope that CoRoT-7 b may originally have had." + ColtoT-7 b may have begun as a gàs giant with a core mass slightly larger thanColtolT-7 bs curent mass (sav. 7 Agaun).," CoRoT-7 b may have begun as a gas giant with a core mass slightly larger thanCoRoT-7 b's current mass (say, 7 $M_{Earth}$ )." +" After evaporation stripped the original atmosphere. it could. also remove ~ 1 Mew, Wom the original core to give the mass seen today."," After evaporation stripped the original atmosphere, it could also remove $\sim$ 1 $M_{Earth}$ from the original core to give the mass seen today." + Consequently. in order to test the hypothesis that C'oltoT-3 b started out as a gas giant. we consider a range of masses for the core of the original planet (Alou). ranging from ColtoT-7 b's current mass (in which case. the planet. very recently [ost its original atmosphere) up to LO Mun.," Consequently, in order to test the hypothesis that CoRoT-7 b started out as a gas giant, we consider a range of masses for the core of the original planet $M_{core}$ ), ranging from CoRoT-7 b's current mass (in which case, the planet very recently lost its original atmosphere) up to 19 $M_{Earth}$." +" In our simulations. we run time backward. allowing the solid mass of the planet to increase until M, reaches our assumed: AZ..."," In our simulations, we run time backward, allowing the solid mass of the planet to increase until $M_p$ reaches our assumed $M_{core}$." +" From that point continuing back in time. we assume the planet “gains” mass in the form of H/LIe Once the planet has a thick enough. atmosphere. we define the planets radius. Ze, to be the altitude level at which most of the stellar. NUM. is absorbed. (227)..."," From that point continuing back in time, we assume the planet “gains” mass in the form of H/He Once the planet has a thick enough atmosphere, we define the planet's radius $R_p$ to be the altitude level at which most of the stellar XUV is absorbed \citep{2007A&A...472..329E, 2004Icar..170..167Y, 2009A&A...506..399L}." +" For Al,»OOLSALa). Ry, corresponds to the 1 mbar pressure level."," For $M_p \ge 0.018 M_{Jup}$, $R_p$ corresponds to the 1 mbar pressure level." +" Lo determine A2, as a function of AZ, and age for these planets. we use an updated version of the model described in ?.. C"," To determine $R_p$ as a function of $M_p$ and age for these planets, we use an updated version of the model described in \citet{2007ApJ...659.1661F}. (" +"Phis model provides #2, at à series of grid points in Aly. e and age. and we linearly. interpolate between mocel erid points.)","This model provides $R_p$ at a series of grid points in $M_p$, $a$ and age, and we linearly interpolate between model grid points.)" +" Although recent studies of evaporation. of exoplanet atmospheres suggest taking 2, at the 1 mbar level is the most appropriate choice (7).. previous studies suggest Z2, should be taken at about the 0.1 nbar level (2).."," Although recent studies of evaporation of exoplanet atmospheres suggest taking $R_p$ at the 1 mbar level is the most appropriate choice \citep{2004Icar..170..167Y}, previous studies suggest $R_p$ should be taken at about the 0.1 nbar level \citep{1981Icar...48..150W}." +" ‘This choice would significantly increase our calculated mass loss rate because 2), would be much larger than what we've chosen. and our estimates here would. provide lower limits on the total mass lost."," This choice would significantly increase our calculated mass loss rate because $R_p$ would be much larger than what we've chosen, and our estimates here would provide lower limits on the total mass lost." +" Lor M,«0.015 Mara. the previous model for £?,, breaks down. so. for planets with such masses. we determine R, by assuming the planet's density. remains constant ab its value when AZ,=0.015 Αν."," For $M_p < 0.018$ $M_{Jup}$ , the previous model for $R_p$ breaks down, so, for planets with such masses, we determine $R_p$ by assuming the planet's density remains constant at its value when $M_p = 0.018$ $M_{Jup}$." +" This assumption uncloubtecdhy introcuces some error into the value for 72. but the relationshi» of radius to mass remains uncertain for planets transitioning [rom eas gians to rocky planets with atmospheres o ""several Earth masses."," This assumption undoubtedly introduces some error into the value for $R_p$, but the relationship of radius to mass remains uncertain for planets transitioning from gas giants to rocky planets with atmospheres of several Earth masses." + The atmospheric structure for. these planets is a compicateck function. of atmospheric. Compesition (?7)..," The atmospheric structure for these planets is a complicated function of atmospheric composition \citep{2010arXiv1001.0976M, 2009arXiv0912.3288R}." + Our aoproximalion gives roughly the correc radii lor Neptune ancl Neptune-Like extra-solar planets :uid has been applied tore C2).., Our approximation gives roughly the correct radii for Neptune and Neptune-like extra-solar planets and has been applied before \citep{2008ApJ...678.1396J}. + Thus. it should sullice for the current study," Thus, it should suffice for the current study." + Weve also assumed that the mass loss has a negligible ellect on t1e planets thermal evolution. consistent with previous work(e.g... 2))," We've also assumed that the mass loss has a negligible effect on the planet's thermal evolution, consistent with previous work, \citealt{1998ApJ...500..428T}) )." + Vo model the effects of tides on the orbit. we use a standard tidal model that has been applied in many studies of solar and extra-solar svstems (?27?7?).. ," To model the effects of tides on the orbit, we use a standard tidal model that has been applied in many studies of solar and extra-solar systems \citep{1963MNRAS.126..257G, 1966Icar....5..375G, 1996ApJ...470.1187R, 2008CeMDA.101..171F, 2008ApJ...678.1396J}." +Like many other close-in exoplanets. Colto'T-7 b raises significant tidal bulges on its host star.," Like many other close-in exoplanets, CoRoT-7 b raises significant tidal bulges on its host star." + For planets that revolve more quickly on circular orbits than their lost stars rotate. like ColtoT-7 b. the tical bulec on the host star lags behind the planet.," For planets that revolve more quickly on circular orbits than their host stars rotate, like CoRoT-7 b, the tidal bulge on the host star lags behind the planet." +" This interaction results in a torque that spins up thehost star ancl reduces the orbital semi-major axis e as: where Ad. is the stellar mass. Ze, is the stellar radius. and QA is the modified tidal dissipation parameter for the star (?227)..:"," This interaction results in a torque that spins up thehost star and reduces the orbital semi-major axis $a$ as: where $M_*$ is the stellar mass, $R_*$ is the stellar radius, and $Q_*^{\prime}$ is the modified tidal dissipation parameter for the star \citep{1966Icar....5..375G, 2008ApJ...678.1396J, 2007ApJ...661.1180O}." +" Because constraints. on 6), are poor(e.g... .2)) we consider a range of values: 107. 10'""and LO’. In using Equation 4.. we assume ColtoT-7 b's orbital eccentricity has been negligible since /=0.1 Cr."," Because constraints on $Q_{*}^{\prime}$ are poor, \citealt{2008ApJ...678.1396J}) ), we consider a range of values: $10^5$, $10^6$, and $10^7$ In using Equation \ref{eqn:dadt}, we assume CoRoT-7 b's orbital eccentricity has been negligible since $t = 0.1$ Gyr." + ColtoT-7 c might play a role in planet. bs orbital evolution bv pumping up its orbital eccentricity (2)..., CoRoT-7 c might play a role in planet b's orbital evolution by pumping up its orbital eccentricity \citep{2010ApJ...709L..95B}. + However. tides probably keep ColtoI-7 b's eccentricity. camped to small values.," However, tides probably keep CoRoT-7 b's eccentricity damped to small values." + We also assume planet c has experienced negligible mass loss and tidal evolution over its lifetime. due to its &ereater distance from the host star.," We also assume planet c has experienced negligible mass loss and tidal evolution over its lifetime, due to its greater distance from the host star." + Orbital evolution at that clistance for a planet with a mass as small as CoRoT-7 Cs minimum mass is also much smaller (?).., Orbital evolution at that distance for a planet with a mass as small as CoRoT-7 c's minimum mass is also much smaller \citep{2008ApJ...678.1396J}. +" To constrain Coltold-7 b's initial mass (M,;,54) and senmi-major axis (e;,;:). we numerically integrate Equations 1 and 4 together. backward: and forward. in time. and continually evaluate all the other equations along the way."," To constrain CoRoT-7 b's initial mass $M_{p, init}$ ) and semi-major axis $a_{init}$ ), we numerically integrate Equations \ref{eqn:dMpdt} and \ref{eqn:dadt} together, backward and forward in time, and continually evaluate all the other equations along the way." + We consider the full range of current. system. parameters allowed: by observational uncertainty. and run a unique integration for cach combination of system parameters.," We consider the full range of current system parameters allowed by observational uncertainty, and run a unique integration for each combination of system parameters." +" That is. we run models with ColtoT-7 b's current mass Mu, 4.0. 4.8 and 5.6 Mew, and with its current semi-major axis (tu,= 0.01601. 0.0172. and 0.01749 AU."," That is, we run models with CoRoT-7 b's current mass $M_{p, cur} = $ 4.0, 4.8 and 5.6 $M_{Earth}$ and with its current semi-major axis $a_{cur} =$ 0.01691, 0.0172, and 0.01749 AU." + ColtoT-T age is reported to lie between. 1.2 €ivr ancl 2.3 Cyr (2)). 8s so we also run models with the planct’s current age equal to 1.2 and 2.3 vr.," CoRoT-7's age is reported to lie between 1.2 Gyr and 2.3 Gyr \citet{2009A&A...506..303Q}) ), so we also run models with the planet's current age equal to 1.2 and 2.3 Gyr." + Along with the range of model parameters we also consider. altogether we run more than 10.000. unique calculations.," Along with the range of model parameters we also consider, altogether we run more than 10,000 unique calculations." + Our results show that the coupling of mass loss and orbita evolution may have played a significant role in ColtoT-7 bs history: Loss of planetary mass can reduce the rate of orbita evolution because the rate of orbital evolution scales as the mass (Equation 4))., Our results show that the coupling of mass loss and orbital evolution may have played a significant role in CoRoT-7 b's history: Loss of planetary mass can reduce the rate of orbital evolution because the rate of orbital evolution scales as the mass (Equation \ref{eqn:dadt}) ). + At the same time. even mocdest orbita evolution can significantly modify the mass loss history of the planet because the mass loss rate depends so sensitively on the planet-star distance (Equations 1 and 2)).," At the same time, even modest orbital evolution can significantly modify the mass loss history of the planet because the mass loss rate depends so sensitively on the planet-star distance (Equations \ref{eqn:dMpdt} and \ref{eqn:Ktide}) )." + In this section. we first. consider the orbital ancl mass evolution if ColoT-7 b has always been a solid planet.," In this section, we first consider the orbital and mass evolution if CoRoT-7 b has always been a solid planet." + Then we consider the evolution ifColtoT-7 b started out as a gas giant., Then we consider the evolution ifCoRoT-7 b started out as a gas giant. + First we consider mass loss with negligible orbital evolution., First we consider mass loss with negligible orbital evolution. +" ligure 2 shows the mass evolution of CoholT-7 b backward: and forward in time. assuming αρ=0.0172 AV. My=5.6 Man. and ""n=16 Hpoan- which"," Figure \ref{fig:plot_evol_notide_solid} shows the mass evolution of CoRoT-7 b backward and forward in time, assuming $a_{cur} = 0.0172$ AU, $M_{p, cur} = 5.6$ $M_{Earth}$ , and $R_p = 1.6$ $R_{Earth}$ , which" +"greatest challenge to theory. especially at high redshift where. for example. black holes with masses Ali,=110°AL. already appear to have been in place less than | billion years after the Big Bang (Fan et al.","greatest challenge to theory, especially at high redshift where, for example, black holes with masses $M_{bh} > 1 \times 10^{9}\,{\rm M_{\odot}}$ already appear to have been in place less than 1 billion years after the Big Bang (Fan et al." + 2001. 2003: Willott et al.," 2001, 2003; Willott et al." + 2007: Mortlock et al., 2007; Mortlock et al. + 2011)., 2011). + However. extracting reliable information on the host galaxies of these overwhelmingly bright AGN presents a formidable technical challenge.," However, extracting reliable information on the host galaxies of these overwhelmingly bright AGN presents a formidable technical challenge." + At low redshift (2< 0.4) this challenge was effectively met when the first refurbishment of the (HST) enabled optical imaging of the necessary depthand exquisitetstable angular resolution to allow the scalelengths and morphologies of low-redshift quasar hosts to be reliably determined for the first time (e.g. Disney et al., At low redshift $z < 0.4$ ) this challenge was effectively met when the first refurbishment of the ) enabled optical imaging of the necessary depth exquisite+stable angular resolution to allow the scalelengths and morphologies of low-redshift quasar hosts to be reliably determined for the first time (e.g. Disney et al. + 1995: MeLure et al., 1995; McLure et al. + 1999: Dunlop et al., 1999; Dunlop et al. + 2003: Floyd et al., 2003; Floyd et al. + 2004)., 2004). + Indeed. the results of these deepHST optical imaging programs of quasar hosts. when combined with “virial” measurements of the black-hole masses in the same objects. were instrumental in demonstrating that these most active objects displayed the same black-hole:host-galaxy mass proportionality as found in quiescent galaxies (McLure Dunlop 2002).," Indeed, the results of these deep optical imaging programs of quasar hosts, when combined with “virial” measurements of the black-hole masses in the same objects, were instrumental in demonstrating that these most active objects displayed the same black-hole:host-galaxy mass proportionality as found in quiescent galaxies (McLure Dunlop 2002)." + However. extending the effective study of quasar host galaxies out to higher redshifts. and in particular into the “quasarepoch” üt 2;22. has proved to be extremely difficult.," However, extending the effective study of quasar host galaxies out to higher redshifts, and in particular into the “quasarepoch” at $z > 2$, has proved to be extremely difficult." + There are a number of reasons for this., There are a number of reasons for this. + First. there is the obvious cosmological dimming of the host-galaxy light.," First, there is the obvious cosmological dimming of the host-galaxy light." + Second there is the necessity of observing in the near-infrared. in order to continue to sample the rest-frame optical light of the host galaxy (both for comparison with low-redshift studies. and to avoid the host-galaxy light being completely swamped by the UV-bright quasar).," Second there is the necessity of observing in the near-infrared, in order to continue to sample the rest-frame optical light of the host galaxy (both for comparison with low-redshift studies, and to avoid the host-galaxy light being completely swamped by the UV-bright quasar)." + Some success in detecting the hosts of quasars out to 2c was achieved with the NICMOS infrared camera onAST (Kukula et al., Some success in detecting the hosts of quasars out to $z \simeq 2$ was achieved with the NICMOS infrared camera on (Kukula et al. + 2001. Ridgway et al.," 2001, Ridgway et al." + 2001: Peng et al., 2001; Peng et al. + 2006b) but. even with this high-resolution near-infrared imaging. obtaining reliable measurements of host-galaxy luminosities and scalelengths proved extremely difficult.," 2006b) but, even with this high-resolution near-infrared imaging, obtaining reliable measurements of host-galaxy luminosities and scalelengths proved extremely difficult." + We now know that this was almost certainly in part due to the fact that. in general. massive galaxies at high-redshift have since been discovered to be generally much more compact than their low-redshift counterparts (Daddi et al.," We now know that this was almost certainly in part due to the fact that, in general, massive galaxies at high-redshift have since been discovered to be generally much more compact than their low-redshift counterparts (Daddi et al." + 2005: Trujillo et al., 2005; Trujillo et al. + 2006. 2007: Longhetti et al.," 2006, 2007; Longhetti et al." + 2007: Zirm et al., 2007; Zirm et al. + 2007: Cimatti et al., 2007; Cimatti et al. + 2008: van Dokkum et al., 2008; van Dokkum et al. + 2008: Buitrago et al., 2008; Buitrago et al. + 2008: Szomoru et al., 2008; Szomoru et al. + 2010: Targett et al., 2010; Targett et al. + 2011)., 2011). + If this is also true for quasar hosts. then the separation of galaxyand nuclear light in quasars at 2 will inevitably be even more problematic than was perhaps first anticipated.," If this is also true for quasar hosts, then the separation of galaxyand nuclear light in quasars at $z \ge 2$ will inevitably be even more problematic than was perhaps first anticipated." + Nonetheless. these difficulties have not deterred several groups from attempting to repeat this experiment at redshifts as high as 24.5.," Nonetheless, these difficulties have not deterred several groups from attempting to repeat this experiment at redshifts as high as $z \simeq 4 - 5$." + Such studies have been encouraged (at least in part) by the advent of active/adaptive opties on ground-based 8-m class telescopes. and by the fact that +— is the natural limit for ground-based studies of quasar host galaxies if one hopes to detechost-galaxy light longward of the 4000À//Balmer break in the JV -band.," Such studies have been encouraged (at least in part) by the advent of active/adaptive optics on ground-based 8-m class telescopes, and by the fact that $z \simeq 4$ is the natural limit for ground-based studies of quasar host galaxies if one hopes to detecthost-galaxy light longward of the /Balmer break in the $K$ -band." + However. perhaps unsurprisingly. existing studies of the hos galaxies of quasars at οστ4 have met with very limited success.," However, perhaps unsurprisingly, existing studies of the host galaxies of quasars at $z \simeq 4$ have met with very limited success." + For example. usingAST NICMOS //-band data. Peng et al. (," For example, using NICMOS $H$ -band data, Peng et al. (" +2006b) attempted to measure the luminosities and sizes of the hosts of two gravitationally-lensed quasars at >=4.1 and >=4.5 via two-dimensional modelling.,2006b) attempted to measure the luminosities and sizes of the hosts of two gravitationally-lensed quasars at $z=4.1$ and $z=4.5$ via two-dimensional modelling. +" Although reliable host-galaxy luminosities were claimed. theAS7 images sampled High shortward of A,,.,;=4000 aand. in addition. the complexity of the lensing model led the authors to conclude that the extracted morphological parameters could not be trusted."," Although reliable host-galaxy luminosities were claimed, the images sampled light shortward of $\lambda_{rest} = 4000$ and, in addition, the complexity of the lensing model led the authors to conclude that the extracted morphological parameters could not be trusted." + In an alternative ground-based approach. Hutchings (2003. 2005) observed seven quasars at >25 with the Gemini 8-m telescope in the JJ. //. and /&-bands.," In an alternative ground-based approach, Hutchings (2003, 2005) observed seven quasars at $z \simeq 5$ with the Gemini 8-m telescope in the $J$, $H$, and $K$ -bands." +" Using point- function (PSF) subtraction. host-galaxy luminosities were estimated from the PSF-subtracted images. although no evidence of smooth centrally-concentrated host galaxies was found and. again. this time due to the decision to observe quasars at 2o5, this imaging sampled rest-frame wavelengths À,,.,;«4000AA.. limiting the usefulness of the extracted luminosities."," Using point-spread function (PSF) subtraction, host-galaxy luminosities were estimated from the PSF-subtracted images, although no evidence of smooth centrally-concentrated host galaxies was found and, again, this time due to the decision to observe quasars at $z \simeq 5$, this imaging sampled rest-frame wavelengths $\lambda_{rest} < 4000$, limiting the usefulness of the extracted luminosities." + Most recently. McLeod Bechtold (2009) observed 34 2—4 quasars in the A-band with the Magellan I and Gemini North telescopes.," Most recently, McLeod Bechtold (2009) observed 34 $z \simeq 4$ quasars in the $K$ -band with the Magellan I and Gemini North telescopes." + However. despite the use of well-controlled PSF subtraction. only four host galaxies were detected in their deepest and sharpest data. at an average quasar redshift (2)=3.8.," However, despite the use of well-controlled PSF subtraction, only four host galaxies were detected in their deepest and sharpest data, at an average quasar redshift $\langle z \rangle = 3.8$." + Host-galaxy luminosity and size estimates were attempted from the PSF-subtracted images of these 4+ quasars. although the authors noted that the surface-brightness limit of these data was really of inadequate depth for the accurate recovery of host-galaxy sizes.," Host-galaxy luminosity and size estimates were attempted from the PSF-subtracted images of these 4 quasars, although the authors noted that the surface-brightness limit of these data was really of inadequate depth for the accurate recovery of host-galaxy sizes." + The deepest imaging obtained by these authors (3.5 hours per source on 8-m class telescopes) would thus seem to represent a minimum requirement for the discovery and study of quasar host galaxies at zc4., The deepest imaging obtained by these authors $\simeq 3.5$ hours per source on 8-m class telescopes) would thus seem to represent a minimum requirement for the discovery and study of quasar host galaxies at $z \simeq 4$. + In this paper we present and analyse even deeper (25.5 hours per source) European Southern Observatory (ESO) 8.2-m Very Large Telescope (VLT) /vs-band imaging of two ς=d Sloan Digital Sky Survey (SDSS) quasars., In this paper we present and analyse even deeper $\simeq 5.5$ hours per source) European Southern Observatory (ESO) 8.2-m Very Large Telescope (VLT) $K_S$ -band imaging of two $z \simeq 4$ Sloan Digital Sky Survey (SDSS) quasars. + These two quasars were carefully chosen to have a redshift which ensures line-free imaging of the host-galaxy stellar population at Αγιο24000AA... and to have a star of comparable brightness within an angular radius of 40 arcsec. in order to provide a robust. high signal:noise ratio. on-detector representation of the VET /vs-band PSF over the complete duration of the host-galaxy imaging.," These two quasars were carefully chosen to have a redshift which ensures line-free imaging of the host-galaxy stellar population at $\lambda_{rest} > 4000$, and to have a star of comparable brightness within an angular radius of 40 arcsec, in order to provide a robust, high signal:noise ratio, on-detector representation of the VLT $K_S$ -band PSF over the complete duration of the host-galaxy imaging." + This care in quasar target selection. combined with deliberate (flexibly scheduled) use of only the very best seeing conditions (and the deliberate avoidance of adaptive optics). has enabled us to achieve robust detections of the host galaxies of both quasars. despite the fact that. with 1;«—2S. these objects are representative of the most luminous/massive black holes in existence at this (or indeed any) epoch.," This care in quasar target selection, combined with deliberate (flexibly scheduled) use of only the very best seeing conditions (and the deliberate avoidance of adaptive optics), has enabled us to achieve robust detections of the host galaxies of both quasars, despite the fact that, with $M_i < -28$, these objects are representative of the most luminous/massive black holes in existence at this (or indeed any) epoch." + This paper is structured as follows., This paper is structured as follows. + In Section 2 we describe our observing strategy. our target selection. and summarise the new near-infrared data obtained with the VLT.," In Section 2 we describe our observing strategy, our target selection, and summarise the new near-infrared data obtained with the VLT." + Next. in Section 3 we explain the PSF subtraction technique used to separate host and nuclear light.," Next, in Section 3 we explain the PSF subtraction technique used to separate host and nuclear light." + Then. in Section 4 we describe the determination of host-galaxy properties and the estimation of the central hole masses.," Then, in Section 4 we describe the determination of host-galaxy properties and the estimation of the central black-hole masses." + Finally. in Section 5 we attempt to place our results in the context of studies of other galaxy populations at. both high and low redshift. and briefly explore the consequences of this study for the inferred cosmic evolution of the black hole- mass ratio.," Finally, in Section 5 we attempt to place our results in the context of studies of other galaxy populations at both high and low redshift, and briefly explore the consequences of this study for the inferred cosmic evolution of the black hole-to-galaxy mass ratio." +" Throughout we adopt a cosmology with ll,=TOkkmss + DOO,= 003. and Q4= 0.7."," Throughout we adopt a cosmology with $H_{0}=70$ $^{-1}$ $^{-1}$ , $\Omega_{m}=0.3$ , and $\Omega_{\Lambda}=0.7$ ." + Unless otherwise noted. we report all magnitudes in the Vega system to ease comparison with previous studies. but our {νο ραπ photometry can be simply converted to the AB magnitude system via dvsagἐννα| 155.," Unless otherwise noted, we report all magnitudes in the Vega system to ease comparison with previous studies, but our $K_S$ -band photometry can be simply converted to the AB magnitude system via $K_{S,AB} = K_{S,Vega} + 1.85$ ." + The deep /vs-band imaging presented here was performed with, The deep $K_S$ -band imaging presented here was performed with +The key to tuucerstauding the evolution of late-type galaxy. systems is their star formation history.,The key to understanding the evolution of late-type galaxy systems is their star formation history. + For while a majority of their stellar mass originates [rom the epoch of galaxy. formation. their current visual appearance is clriven by star formation over the last Gyr (Gallagher 1981).," For while a majority of their stellar mass originates from the epoch of galaxy formation, their current visual appearance is driven by star formation over the last Gyr (Gallagher 1984)." + Thus. studies of the characteristics of star forming galaxies is a glimpse into the process oL star formation and. thus. a window into the conditions that played a role during the galaxy formation era.," Thus, studies of the characteristics of star forming galaxies is a glimpse into the process of star formation and, thus, a window into the conditions that played a role during the galaxy formation era." + Late-type galaxies Come in a range of morphological appearances aud their study has been. for decades. been dominated by the extremely bright. actively star forming examples such as NGC," Late-type galaxies come in a range of morphological appearances and their study has been, for decades, been dominated by the extremely bright, actively star forming examples such as NGC" +"between the spectral index of Seyferts and quasars Is measured in CAIXA (Ls,=1.66+ 0.05: Toso=1.80x0.05: B09).",between the spectral index of Seyferts and quasars is measured in CAIXA $\Gamma_{Sy}=1.66\pm0.05$ ; $\Gamma_{QSO}=1.80\pm0.05$: B09). + We showed in BO9 that the introduction of a luminosity-dependent Compton reflection component to the baseline model does not remove the difference between these two populations., We showed in B09 that the introduction of a luminosity-dependent Compton reflection component to the baseline model does not remove the difference between these two populations. + Further tests should be performed to understand the real driver for this difference., Further tests should be performed to understand the real driver for this difference. + Similarly. we do not find a significant correlation between the photon index and the BH mass or the Eddington rate. but the significances found by ? are lower than our threshold. and the results recently found by ? are strongly dependent on how the BH masses are calculated.," Similarly, we do not find a significant correlation between the photon index and the BH mass or the Eddington rate, but the significances found by \citet{pico05} are lower than our threshold, and the results recently found by \citet{kelly08} are strongly dependent on how the BH masses are calculated." + On the other hand. the correlation with the Eddington ratio found by ?. is more significant than our threshold. but only when high-z and quasars are taken into account.," On the other hand, the correlation with the Eddington ratio found by \citet{shem08} is more significant than our threshold, but only when high-z and high-luminosity quasars are taken into account." + , +"Mo=nM, and to set A and B equal.",$M_0 = \eta M_c$ and to set $A$ and $B$ equal. +" Without loss of generality ΛΜ.=1 is adopted(i.e., M. is defined as the unit of mass) for purposes of plotting and giving numerical values."," Without loss of generality $M_c = 1$ is adopted, $M_c$ is defined as the unit of mass) for purposes of plotting and giving numerical values." + We can then obtain the following: given that Mo«M.X«πας., We can then obtain the following: given that $M_0< M_c < X < M_{max}$. + It is easy to see that the addition of V will increase the probability that Mr is smaller than X., It is easy to see that the addition of $\frac{\eta}{\sqrt{1-\eta^2}}$ will increase the probability that $M_T$ is smaller than $X$. +" Furthermore, if Mo2. no third image is produced.," In particular, for $\beta>2$, no third image is produced." + For large ry. the cusp must conform to the value ο)=1.91 derived above.," For large $r_b$, the cusp must conform to the value $\beta=1.91$ derived above." + As ry becomes smaller. the inner mass distribution must become shallower (ο compensate lor the steeper mass distribution at large radii.," As $r_b$ becomes smaller, the inner mass distribution must become shallower to compensate for the steeper mass distribution at large radii." + For the purpose of finding central odd images. the best svstems are racio-Ioud (wo-image quasars with a large magnification ratio between the (vo bright images.," For the purpose of finding central odd images, the best systems are radio-loud two-image quasars with a large magnification ratio between the two bright images." + Radio loudness is important because the radio components can be observed through the lens galaxy. whereas optical components are likely to be hidden by the lens galaxy.," Radio loudness is important because the radio components can be observed through the lens galaxy, whereas optical components are likely to be hidden by the lens galaxy." + Free-[ree absorption is potentially significant. but. can be overcome by observing at. high [requencies., Free-free absorption is potentially significant but can be overcome by observing at high frequencies. + Dwo-image svstems are better than four-image svstems. as emphasized recently by Ixeeton(2002).," Two-image systems are better than four-image systems, as emphasized recently by \citet{keeton02}." +.. This is because the projected source position in four-image svstems is usually closer to the lens center. where the central image magnification is smallest.," This is because the projected source position in four-image systems is usually closer to the lens center, where the central image magnification is smallest." + In addition. lour-image svstems are subject to a larger magnilieation bias than two-image svstems (Wallington&Naravan1993:KingBrowne1996:Keeton.IXochanek.&SeljakL997:RusinTeemark2001:Finchetal. 2002).. leading to a smaller intrinsic source flux and a fainter odd image.," In addition, four-image systems are subject to a larger magnification bias than two-image systems \citep{wn93,king96,kks97,rt01,finch02}, leading to a smaller intrinsic source flux and a fainter odd image." + Among two-image svstenms. (he asvamnetric doubles are [avorable because (he source position is close to (he radial caustic. producing the brightest possible central image for a given mass distribution.," Among two-image systems, the asymmetric doubles are favorable because the source position is close to the radial caustic, producing the brightest possible central image for a given mass distribution." + The subject of this paper. PAIN J1632.0033. is exactly this tvpe of svstemr: an asvuunelric (wo-image radio lens.," The subject of this paper, PMN J1632–0033, is exactly this type of system: an asymmetric two-image radio lens." + For (his reason. it seemed reasonable (hat the (third component found by Winnetal.(2002) could be an example of the elusive and long-sought central odd images.," For this reason, it seemed reasonable that the third component found by \citet{winn02} + could be an example of the elusive and long-sought central odd images." + llowever. we have shown (hat the third component has a spectral index Chat dillers by 360 from those of the two bright quasar images.," However, we have shown that the third component has a spectral index that differs by $3\sigma$ from those of the two bright quasar images." + We have argued (hat the two most plausible interpretations are that (he central component is emission from the lens galaxy. or else (hat it is a third image with the extra complication that its spectral index has been mocified by free-Iree absorption.," We have argued that the two most plausible interpretations are that the central component is emission from the lens galaxy, or else that it is a third image with the extra complication that its spectral index has been modified by free-free absorption." + The data are quantitatively consistent with either scenario., The data are quantitatively consistent with either scenario. + Lens galaxies are rarely radio-Ioud. but the {his density of ihe component is consistent wilh (vpical radio powers of active ealactic nuclei.," Lens galaxies are rarely radio-loud, but the flux density of the component is consistent with typical radio powers of active galactic nuclei." + No central image has ever been securely identified for a radio lens. nor has Iree-DIree absorption by a lens galaxy ever been reported (will one possible exception. D01284437: BBrowne 2002. private communication). but one might expect the two phenomena to be related due," No central image has ever been securely identified for a radio lens, nor has free-free absorption by a lens galaxy ever been reported (with one possible exception, B0128+437; Browne 2002, private communication), but one might expect the two phenomena to be related due" +As already evident [rom the measurements aud from previous moclels of the evolution of the planet (Satoetal.2005:Fortuey2006).. HD119026b is surprisingly small. aud should possess either a big core or a large aunount of heavy. elements in its interior.,"As already evident from the measurements and from previous models of the evolution of the planet \citep{Sato05,Fortney06}, HD149026b is surprisingly small, and should possess either a big core or a large amount of heavy elements in its interior." + Iu this work. we attempt to constrain the core mass by using a variety of evolutionary models bevoud those explored by Sato et al.," In this work, we attempt to constrain the core mass by using a variety of evolutionary models beyond those explored by Sato et al." + aud Fortuey et al., and Fortney et al. + In doing so. we will show that HDI19026b indeed contains a significant amount of heavy elements. in apparent contradiction with current inodels of the formation of giant plauets.," In doing so, we will show that HD149026b indeed contains a significant amount of heavy elements, in apparent contradiction with current models of the formation of giant planets." + The evolution of a giant planet is essentially goverued by a Iwelvin-Helimboltz cooling aud contraction similar to a stellar pre-main sequence evolution but slightly modified by clegeneracy effects. aud by the inteuse stellar irradiatiou that slows the cooling through the growth of a deep radiative region that ca1 exteud to kbar levels (Guillotetal.1996:Cuillot2005).," The evolution of a giant planet is essentially governed by a Kelvin-Helmholtz cooling and contraction similar to a stellar pre-main sequence evolution but slightly modified by degeneracy effects, and by the intense stellar irradiation that slows the cooling through the growth of a deep radiative region that can extend to kbar levels \citep{Guillot96, Guillot05}." +". The level of the irradiation received by the planet is calculated from the observations by (2005):: We adopt vaues of the stellar radius (2,=1.15 Ro.) aud temperature (74;=61501.) aud the orbital cistance of ()016 AU to derive zero-albedo equilibrium temperature Tijς=lol. We use this value as a miniuum lor the atinospheric temperature at the 1 bar level (he correspouding temperature found by Fortueyetal.(2006) is between 2000 aud Why. and. using the moclel of Iro.Bézard.&Cuilot(2005).. we find a value of IIS)."," The level of the irradiation received by the planet is calculated from the observations by \citet{Sato05}: We adopt values of the stellar radius $R_*=1.45\,\rm R_\odot$ ) and temperature $T_*=6150\,$ K) and the orbital distance of $0.046\,$ AU to derive zero-albedo equilibrium temperature $T_{\rm eq}^*=1740\,$ K. We use this value as a minimum for the atmospheric temperature at the 1 bar level (the corresponding temperature found by \citet{Fortney06} is between 2000 and K, and using the model of \citet{IBG05}, we find a value of K)." + We use the 1 bar level as outer boundary condition [or the evolution models (seeGuillot2005)., We use the 1 bar level as outer boundary condition for the evolution models \citep[see][]{Guillot05}. +. Standard models are calculated on the basis of structure consisting of a central rock/ice core aud of au envelope of solar composition. aud further assumius that the planet bas either formed or moved rapidly to its present location. so that throughout its evolution it lias received a constant stellar beat [lux to slow its cooling.," Standard models are calculated on the basis of structure consisting of a central rock/ice core and of an envelope of solar composition, and further assuming that the planet has either formed or moved rapidly to its present location, so that throughout its evolution it has received a constant stellar heat flux to slow its cooling." +" For the core. we use the equations of state for ""rocks"" auc “ices” obtained by (1989)."," For the core, we use the equations of state for “rocks” and “ices” obtained by \citet{HM89}." +. For the envelope. we use the H-He EOS from Saumon.Chabrier. (1995).," For the envelope, we use the H-He EOS from \citet*{SCVH95}." +. The structure ol the core with Hubbard&Marley (1989)s EOS is uxlepeudeut of its temperature. but this simplification is reasonable because it has muchli smaller effects than chauges in the (unknown) core «‘omposition.," The structure of the core with \citet{HM89}' 's EOS is independent of its temperature, but this simplification is reasonable because it has much smaller effects than changes in the (unknown) core composition." + Although it has little effecton the models. we assume that the core luminositynH isH due both to radioactiveH decay (withíH lonondeitie&410>eres!M 1j and cooliHlg (asstuning that in the core the temperature is uniform and the specilic heat is ejz10*erggtis +).," Although it has little effecton the models, we assume that the core luminosity is due both to radioactive decay (with $l_{\rm chondritic}\approx +10^{20}\rm\,erg\,s^{-1}\,\mearth^{-1}$ ) and cooling (assuming that in the core the temperature is uniform and the specific heat is $c_v\approx +10^7\rm\,erg\,g^{-1}\,K^{-1}$ )." + Iuternal opacities are calculated from Rosselaud opacity tables provided by Allardοἱal.(2001)., Internal opacities are calculated from Rosseland opacity tables provided by \citet{Allard01}. +. The calculations are mace for various core masses aud core Compositions aud compared to the observational constraints in Fig. 1.., The calculations are made for various core masses and core compositions and compared to the observational constraints in Fig. \ref{fig:evol_std}. + As discussed by Satoetal.(2005) and by Fortneyetal. (2006).. the small planetary. radius implies that it contaius a large fraction of its mass in heavy elemeuSs," As discussed by \citet{Sato05} and by \citet{Fortney06}, , the small planetary radius implies that it contains a large fraction of its mass in heavy elements." +De Vaucouleurs (1961. 1970) first sugeested. din an attempt to explain observed non-circular eas orbits. tha the Calaxy imdght be barred.,"De Vaucouleurs (1964, 1970) first suggested, in an attempt to explain observed non-circular gas orbits, that the Galaxy might be barred." + Since then. a large body of observational evidence has been accunuulated tha supports this hvpothesis (see Carzóunu 1999 for a review).," Since then, a large body of observational evidence has been accumulated that supports this hypothesis (see Garzónn 1999 for a review)." + Axial asviunietries in the Πο Calaxy lave been detected iu star counts (Nakada ect al., Axial asymmetries in the inner Galaxy have been detected in star counts (Nakada et al. + 1991: Weinberg 1992: Whitelock et al., 1991; Weinberg 1992; Whitelock et al. + 1992: Stanek ct al., 1992; Stanek et al. + 1991: Tlanuuersley et al., 1994; Hammersley et al. + 1991. 1999. 2000 Wozzuiak Stauck 1996: Nikolaev Weinberg 1997: Unavaue Ciluore 1998: Loppez-Corredoira et al.," 1994, 1999, 2000 Wózzniak Stanek 1996; Nikolaev Weinberg 1997; Unavane Gilmore 1998; Lóppez-Corredoira et al." + 1997. 2000) and by surface photometry at different wavelengths (Blitz Spergel 1991: Weiland et al.," 1997, 2000) and by surface photometry at different wavelengths (Blitz Spergel 1991a; Weiland et al." + 1991: Dwek ct al., 1994; Dwek et al. + 1995: Freudenreich 1998). mucroleusing (Stanek 1995: Diunev et al," 1995; Freudenreich 1998), microlensing (Stanek 1995; Binney et al." + 2000) and analvsis of internal motions of the eas (Peters 1975: Liszt Durtou 1980: Yuan 1981: Nakai 1992: Cerhard 1996)., 2000) and analysis of internal motions of the gas (Peters 1975; Liszt Burton 1980; Yuan 1984; Nakai 1992; Gerhard 1996). + Various models have been constructed to explain the observed features. may of which include a bar (e.g.. Binney et al.," Various models have been constructed to explain the observed features, many of which include a bar (e.g., Binney et al." + 1991: Weiner Selhvood 1999)., 1991; Weiner Sellwood 1999). + The observed nou-axisviuuetrv. however. varies considerably between the various papers. although “bar” ds the term normally used.," The observed non-axisymmetry, however, varies considerably between the various papers, although “bar” is the term normally used." + Unufortuuatelv. this criminology is ambiguous aud has led to uaich confusion aud controversy. as has been commented ou in several pers (duijkeu 1996: Ne 1998: Lóppez-Corredoia et al.," Unfortunately, this terminology is ambiguous and has led to much confusion and controversy, as has been commented on in several papers (Kuijken 1996; Ng 1998; Lóppez-Corredoira et al." + 1999)., 1999). + This is more than a mere question of words. rowever.," This is more than a mere question of words, however." + Many authors have classed what is a short fat structure as a bar. when possibly a more appropriate teri would be a triaxial bulee.," Many authors have classed what is a short fat structure as a bar, when possibly a more appropriate term would be a triaxial bulge." + Other authors have found a ong thin structure. which. if it exists. would be what is raditionallv cousidered to be a bar. aud such a feature is inherently differcut from a triaxial bulec.," Other authors have found a long thin structure, which, if it exists, would be what is traditionally considered to be a bar, and such a feature is inherently different from a triaxial bulge." + Nhülst evidence for the triaxial bulge is now overwhehnumg aud the results are vasically consistent. there is still discussion ou the presence of the lone thin bar.," Whilst evidence for the triaxial bulge is now overwhelming and the results are basically consistent, there is still discussion on the presence of the long thin bar." + Badio maps show significant non-axisviunetry in the motions of the eas iu the inner ealaxy., Radio maps show significant non-axisymmetry in the motions of the gas in the inner galaxy. + Peters (1975) analysed the ITE maps aud showed that a bar inclined at about 15? to the SunGalactic Centre line would produce the features secu., Peters (1975) analysed the HI maps and showed that a bar inclined at about $^\circ$ to the Sun–Galactic Centre line would produce the features seen. + Nakai (1992) found a simular anele when analvsiug CO maps. aud a rough calculation places the euds of the bar a P~30° aud /=20.IRAS," Nakai (1992) found a similar angle when analysing CO maps, and a rough calculation places the ends of the bar at $l\sim 30^\circ$ and $l=-20^\circ$." + star counts in the plane have a very asviuinoetric distribution iu longitude (c.g. Garzoun 1999). with mere stars at positive than at negative longitudes.," star counts in the plane have a very asymmetric distribution in longitude (e.g. Garzónn 1999), with more stars at positive than at negative longitudes." + These asvuuuetrics stretch from about 7—307 το 307 and are far larger than the asvuumetries caused by a triaxial bulee. in both extent aud magnitude.," These asymmetries stretch from about $l=30^\circ$ to $-30^\circ$ and are far larger than the asymmetries caused by a triaxial bulge, in both extent and magnitude." + Weinberg (1992) analysed theFRAS star counts in the plane and proposed that there was an in-plane stellar bar with a position angele of 36 X107 and hilf-leusth of about 5 kpc., Weinberg (1992) analysed the star counts in the plane and proposed that there was an in-plane stellar bar with a position angle of 36 $\pm 10^\circ$ and half-length of about 5 kpc. + Wamunersley et al. , Hammersley et al. ( +1991. hereafter ΠΟ1) exainined data from the Two Microu lanlactic Survey (TAICS) aud showed that there is a high chsity of voung stars in the plaue at /=277 and 217 that is not seen either towards the bulge or at longitudes ereater /=277.,"1994, hereafter H94) examined data from the Two Micron Galactic Survey (TMGS) and showed that there is a high density of young stars in the plane at $l=27^\circ$ and $21^\circ$ that is not seen either towards the bulge or at longitudes greater $l=27^\circ$." + An analysis of the COBE/DIRBE jan surface brightness maps showed that the form was consistent with an in-plane bar., An analysis of the /DIRBE $\mu$ m surface brightness maps showed that the form was consistent with an in-plane bar. + Further evidence for the bar at positive onegitudes is xeseuted by Carzonn et al. (, Further evidence for the bar at positive longitudes is presented by Garzónn et al. ( +1997) aud Lóppez-Corredoira et al. (,1997) and Lóppez-Corredoira et al. ( +]999)who made a spectroscopic analysis of the xiehtes stars in an infrared-sclectecl sample of objects close to the Galactic plane at /=27° showing a strikinely Heh fraction of superegiauts. characteristic of a strong star ornation region.,"1999),who made a spectroscopic analysis of the brightest stars in an infrared-selected sample of objects close to the Galactic plane at $l=27^\circ $ showing a strikingly high fraction of supergiants, characteristic of a strong star formation region." + The typical distance to these sources was found to be 6 kpc., The typical distance to these sources was found to be 6 kpc. + It was argued that this result is consistent with this region being the near chad of he Galactic bar., It was argued that this result is consistent with this region being the near end of the Galactic bar. + Such regions can form due to the concentrations of shocked gas where the stellar bar mcets he dise. as is observed at the cuds of the bars of face-ou external ealaxies (Sandage Dedke 1991).," Such regions can form due to the concentrations of shocked gas where the stellar bar meets the disc, as is observed at the ends of the bars of face-on external galaxies (Sandage Bedke 1994)." + IHuunerslev et al. (, Hammersley et al. ( +2000. hereafter HOO) exiiuiued iufrared colouruaenitude diagrams mn a nuuber of regious iu the plane.,"2000, hereafter H00) examined infrared colour--magnitude diagrams in a number of regions in the plane." + Thev show that there is a major cluster of IKM elauts at a distance of 5.7 £ 0.5 kpc at /=277 which is not preseut at $=327.," They show that there is a major cluster of K–M giants at a distance of 5.7 $\pm$ 0.5 kpc at $l=27^\circ$, which is not present at $l=32^\circ$." + This cluster is seu at iiost longitudes smaller than /=27° (the exception being regions of extremely lugh extinction) and the distance from he Sun to the cluster mereases with decreasing longitude uutil about, This cluster is seen at most longitudes smaller than $l=27^\circ$ (the exception being regions of extremely high extinction) and the distance from the Sun to the cluster increases with decreasing longitude until about +e—Jp».,$\sim -45^\circ$. + €Jn the night side tiere are two regions of cooling: where hot air lias bee1 adivected [roi the day side across the east leriinator. aid where air bas been heated w the sliock-like feature al c135°.," On the night side there are two regions of cooling: where hot air has been advected from the day side across the east terminator, and where air has been heated by the shock-like feature at $\sim135^\circ$." +" This feature is cliscussed in more cletail in BRauscjer&Meiou(2010): it ix a steady feattre that exteuds across 1jally pressure evels aud is associated with ho regions. consistent with aclial""alic heating from downward flow induced by the stroug iorizontal cOnvergelce."," This feature is discussed in more detail in \citet{RM10}; it is a steady feature that extends across many pressure levels and is associated with hot regions, consistent with adiabatic heating from downward flow induced by the strong horizontal convergence." + Note that iu Figu el there is a region of night side APE loss associated w‘ith this feature., Note that in Figure \ref{fig:eq} there is a region of night side APE loss associated with this feature. + While the j»otential energy veneration [ron both the racjative aud [rictico1al heating will be weiehted by the local temperature through the efficiency factoTIT. the 'adiative heating is nore strougly «lependeut ou the temperature structsre. while the frictioual heaing is clepencent o the pattern o[ wiud speeds.," While the potential energy generation from both the radiative and frictional heating will be weighted by the local temperature through the efficiency factor $T_r/T$, the radiative heating is more strongly dependent on the temperature structure, while the frictional heating is dependent on the pattern of wind speeds." +" The ""missing"" potenial energy. generation shown iu the right paiel of Figure 2 follows the same structure as the sinetic energy al this leve."," The “missing"" potential energy generation shown in the right panel of Figure \ref{fig:150} follows the same structure as the kinetic energy at this level." + We can see this row the [OW |yattern iu Figure +)3.. where the strougest winds are on the uieh| side. inaxinized iu an equaorial jet and with significant flow in curviug branches at high latitucle.," We can see this from the flow pattern in Figure \ref{fig:Tv}, where the strongest winds are on the night side, maximized in an equatorial jet and with significant flow in curving branches at high latitude." + Not all of the strongly irraciated close-in gas giauts are o circular orbits: tlepe are Maly known with significant uozero eccentricities. the most extreme bei1& HD 80606b. with an eccentricity of 0.931 (Moutouetal.2009)..," Not all of the strongly irradiated close-in gas giants are on circular orbits; there are many known with significant non-zero eccentricities, the most extreme being HD 80606b, with an eccentricity of 0.934 \citep{Moutou2009}." + These eccentric planets iuay be Subject to the saije drag uechanisims that have been pro»osed for circular bot Jupiters. but with te added complicaion that ie leve of stelar irraciatio1 will chauge throughout the orbit.," These eccentric planets may be subject to the same drag mechanisms that have been proposed for circular hot Jupiters, but with the added complication that the level of stellar irradiation will change throughout the orbit." + During |yerlasiron passage here wi| )e luteise stelar heating tiat will drive up the potentia| enerey of te atiuosphere. sone of wich wil be converted iuto kinetic energy and then dissipated.," During periastron passage there will be intense stellar heating that will drive up the potential energy of the atmosphere, some of which will be converted into kinetic energy and then dissipated." + The temyerature and. velocity structures of atinosphe'e will va‘y throughout the orbit., The temperature and velocity structures of the atmosphere will vary throughout the orbit. + The radiative APE generation shotId closely follow teniperattwe evolution of the atinosphere. while the [rictional dissipation will ollow the evolt of he kinelic enerey.," The radiative APE generation should closely follow the temperature evolution of the atmosphere, while the frictional dissipation will follow the evolution of the kinetic energy." + At any point in the orljt there may |ye a Lulsmatch between the rate: APE generation. conversion to kine16 energy. ali clissipatiou. eacling to a teiiporary build : APE or kinetic energy.," At any point in the orbit there may be a mismatch between the rates of APE generation, conversion to kinetic energy, and dissipation, leading to a temporary build up of APE or kinetic energy." + This delay i Leberey (ranser ls seen in he three-dimerslonal model of the eccentric 100 Neptune C136b («=0.02872AUaxle0.15.Lewisetal.2010).. where they [iix that the peak in wiud speeds occurs. 1-8 hours afer periasticoi passage.," This delay in energy transfer is seen in the three-dimensional model of the eccentric hot Neptune GJ436b \citep[$a=0.02872$ AU and $e=0.15$,][]{Lewis2010}, where they find that the peak in wind speeds occurs 4-8 hours after periastron passage." + The evolving cissipatior may then lead to a secondary period of APE generation from tle frictional heati igaid. depending ou the delayed rates of energy trausfer. this could be late enough aler periastrοι passage that the [rictional heating might domiuate over the stellar heating.," The evolving dissipation may then lead to a secondary period of APE generation from the frictional heating and, depending on the delayed rates of energy transfer, this could be late enough after periastron passage that the frictional heating might dominate over the stellar heating." + As we call see. steacly state assiiuptions aud tinplicit time-averages are uo louger valid lor eccentric: plauet atmospheres and a more detailed analysis of the energetics will require further study.," As we can see, steady state assumptions and implicit time-averages are no longer valid for eccentric planet atmospheres and a more detailed analysis of the energetics will require further study." +If the emission comes from the secondary star. it must come from its irradiated face. which is closer to the centre of mass of the binary so will have a velocity amplitude smaller than Κ..,"If the emission comes from the secondary star, it must come from its irradiated face, which is closer to the centre of mass of the binary so will have a velocity amplitude smaller than $K_2$." +" The most extreme possibility is where the emission comes from Roche LI point. in which case the true K» is related to the observed Ky by where(LE 7j, quuis the mEradius of the inner Lagrangian point im units of the semimajor axis."," The most extreme possibility is where the emission comes from Roche L1 point, in which case the true $K_2$ is related to the observed $K_2^{\rm\,obs}$ by where $r_{\rm L1}$ is the radius of the inner Lagrangian point in units of the semimajor axis." + For d=0.15 and KY=202kms!.. this leads to Ks=317kms!.," For $q = 0.15$ and $K_2^{\rm\,obs} = 202$, this leads to $K_2 = 317$." +. This in turn gives rap=0.29> n. allowing the implied dise radius to exceed the circularisation radius.," This in turn gives $r_{\rm AD} = 0.29 > r_{\rm h}$ , allowing the implied disc radius to exceed the circularisation radius." + But there is another problem., But there is another problem. + If the central spike emission is coming from the irradiated. face of the donor. it should peak in strength at orbital phases 0.25-0.75 when the face is pointing towards the observer (phase zero is defined by superior conjunction of the WD).," If the central spike emission is coming from the irradiated face of the donor, it should peak in strength at orbital phases 0.25–0.75 when the face is pointing towards the observer (phase zero is defined by superior conjunction of the WD)." + The level of modulation will depend on inclination. with edge-on systems showing modulation and face-on systems no modulation.," The level of modulation will depend on inclination, with edge-on systems showing modulation and face-on systems no modulation." + The brightness modulation measured by our four-Gaussian model (above) is 20x4% in amplitude., The brightness modulation measured by our four-Gaussian model (above) is $20 \pm 4$ in amplitude. + This quantity is subject to unknow! systematics since the central spike is crossed by the bright spot and our fit is far from perfect. but it is clear that the modulation is not strong.," This quantity is subject to unknown systematics since the central spike is crossed by the bright spot and our fit is far from perfect, but it is clear that the modulation is not strong." + We then calculated the emission line to be expected from the irradiated face of the secondary by computing a gric covering the star and assigning an emissivity to each element proportional to the flux it receives from the WD and boundary layer., We then calculated the emission line to be expected from the irradiated face of the secondary by computing a grid covering the star and assigning an emissivity to each element proportional to the flux it receives from the WD and boundary layer. + We calculated the modulation (7) from the minimum anc maximum fluxes at orbital phases 0.0 and 0.5 (finin and. fi) using This was done both for optically thick emission and for the less likely possibility of optically thin emission., We calculated the modulation $m$ ) from the minimum and maximum fluxes at orbital phases 0.0 and 0.5 $f_\mathrm{min}$ and $f_\mathrm{max}$ ) using This was done both for optically thick emission and for the less likely possibility of optically thin emission. + The results are plotted versus orbital inclination in Fig. Ὁ.., The results are plotted versus orbital inclination in Fig. \ref{fig:modplot}. + They show that 1f the central spike comes from the irradiated face of the secondary star. the orbital inclination must be low (;<10° for optically thick and /<25° for optically thin emission).," They show that if the central spike comes from the irradiated face of the secondary star, the orbital inclination must be low $i < 10^\circ$ for optically thick and $i < 25^\circ$ for optically thin emission)." + We can obtain a second constraint on the orbital inclination from the full width at zero intensity (FWZD of the Ha emission line profile. which we measure to be 2000+100kms7!.," We can obtain a second constraint on the orbital inclination from the full width at zero intensity (FWZI) of the $\alpha$ emission line profile, which we measure to be $2000 \pm 100$." +. With a mass-radius relation for WDs [Bergeronetal.(1995).. supplemented by Hamada&Salpeter(1961) for masses M4]|. the FWZI σινὲς an upper limit on i (as a function of WD mass) for which the innermost part of the disc is on a Keplerian orbit which is not inside the WD surface.," With a mass-radius relation for WDs \citet{Bergeron++95apj}, supplemented by \citet{HamadaSalpeter61apj} for masses ], the FWZI gives an upper limit on $i$ (as a function of WD mass) for which the innermost part of the disc is on a Keplerian orbit which is not inside the WD surface." + We can also rule out high inclinations (¢2757; Hellier 2001))as the system is not eclipsing refsec:phot))., We can also rule out high inclinations $i \ga 75^\circ$; \citealt{Hellier01book}) )as the system is not eclipsing \\ref{sec:phot}) ). + These two constraints are visualised in reffig:iconstraint. and show that requiring ;«10° (257) leads to WD masses of Mwp21.40 ((0.97 Mis)., These two constraints are visualised in \\ref{fig:iconstraint} and show that requiring $i < 10^\circ$ $25^\circ$ ) leads to WD masses of $M_{\rm WD} \ga 1.40$ $0.97$ ). + If the central spike comes from optically thin gas situated at the Roche L1 point. then 7.<25° and Mywp20.97M.," If the central spike comes from optically thin gas situated at the Roche L1 point, then $i < 25\degr$ and $M_{\rm WD} \ga 0.97$." +... The validity of these constraints can be tested using simulated spectra of the system in order to connect Asi with the true Κ.., The validity of these constraints can be tested using simulated spectra of the system in order to connect $K_{\rm spike}$ with the true $K_2$ . + We therefore computed synthetic Ha emission lines. for specific g and Kwp+A> values. as would arise from optically," We therefore computed synthetic $\alpha$ emission lines, for specific $q$ and $K_{\rm WD}+K_2$ values, as would arise from optically" +Galaxy clusters are. the voungest and largest. organized structures known to exist. and their ensemble. properties can shed light on many cosmological problems.,"Galaxy clusters are the youngest and largest organized structures known to exist, and their ensemble properties can shed light on many cosmological problems." + They. arise rom significantly overdense regions on cosmological scales. which are exponentially rare events in a Gaussian initial perturbation spectrum.," They arise from significantly overdense regions on cosmological scales, which are exponentially rare events in a Gaussian initial perturbation spectrum." + The shape and normalisation of the cluster mass function are therefore extremely sensitive to he statistical properties of the primordial density field., The shape and normalisation of the cluster mass function are therefore extremely sensitive to the statistical properties of the primordial density field. +" The evolution of cluster number densities is also tightly. coupled o the cosmic expansion rate. and can precisely constrain £8,,."," The evolution of cluster number densities is also tightly coupled to the cosmic expansion rate, and can precisely constrain $\Omega_m$." +" Much elfort has been expended owards a measurement of the cluster mass ""unction and its evolution (sec| Henry 2000 for a summary of recent work in this area) IuU much remains to be understood about the clusters themselves rcfore we can be confident of such results."," Much effort has been expended towards a measurement of the cluster mass function and its evolution (see Henry 2000 for a summary of recent work in this area), but much remains to be understood about the clusters themselves before we can be confident of such results." + The properties of the local mass function. can be constrained by using either stancare Press-Seheeter (1974) (also Bond οἱ al., The properties of the local mass function can be constrained by using either standard Press-Schecter (1974) (also Bond et al. + 1991. Lacey Cole 1993) theory. a more sophisticated analytical model of the cosmic mass 'unction (c.g. Sheth. Mo. Tormen 1999). or fitting formua based on large-scale sructure simulations (Jenkins et al.," 1991, Lacey Cole 1993) theory, a more sophisticated analytical model of the cosmic mass function (e.g. Sheth, Mo, Tormen 1999), or fitting formula based on large-scale structure simulations (Jenkins et al." + 2000)., 2000). + οσο methoes predict the number density of dark matter ialoes as a funcion of mass and redshift., These methods predict the number density of dark matter haloes as a function of mass and redshift. + Some relaionship »etween: model variables (1.0.. the total mass within some clensity threshod) and a more casily observed. cuantitv (c.g. NXrav temperature. NX.ray luminosity. or weak lensing mass) must therefore be assumed. to match cosmological predictions to the results of cluster surveys.," Some relationship between model variables (i.e., the total mass within some density threshold) and a more easily observed quantity (e.g. X–ray temperature, X–ray luminosity, or weak lensing mass) must therefore be assumed to match cosmological predictions to the results of cluster surveys." + Intracluster mecdium (ICM) X.ray temperatures show particular promise in this regard. since they demonstrate a tight. (<20% scatter) correlation with cluster mass components in both simulations (Alathiesen Evrarcl 2001. total mass) and observations (Mohr. Mathiesen. Evrard 1999. ICM mass). and the cluster Xrav temperature function (NTE) currently provides the tightest constraints on the cluster mass function.," Intracluster medium (ICM) X–ray temperatures show particular promise in this regard, since they demonstrate a tight $\lesssim 20\%$ scatter) correlation with cluster mass components in both simulations (Mathiesen Evrard 2001, total mass) and observations (Mohr, Mathiesen, Evrard 1999, ICM mass), and the cluster X–ray temperature function (XTF) currently provides the tightest constraints on the cluster mass function." +" It therefore sccms likely that our best structure formation measurements of ον, will rely on mecium-redshift measurements of the NTE. and it is essential to make sure that our interpretation of cluster temperature functions is correct."," It therefore seems likely that our best structure formation measurements of $\Omega_m$ will rely on medium-redshift measurements of the XTF, and it is essential to make sure that our interpretation of cluster temperature functions is correct." + A modified. form of the mass function allowing Lor differences between a clusters formation redshift ancl observed: recishift was first proposed. by Witavama Suto (1996). and has begun to be commonly. implemented in deriving constraints on the power spectrum. normalization ay at low redshfits (Ixitavama Suto 1997. Kay Bower 1999. Viana Liclelle 999).," A modified form of the mass function allowing for differences between a cluster's formation redshift and observed redshift was first proposed by Kitayama Suto (1996), and has begun to be commonly implemented in deriving constraints on the power spectrum normalization $\sigma_8$ at low redshfits (Kitayama Suto 1997, Kay Bower 1999, Viana Liddle 1999)." +" ""This extension to the theory produces little change in the shape of he predicted: mass function. but can have an appreciable effect on the predicted temperature function 1f one assumes that. clusters scatter around a nass-temperature scaling relation appropriate to"," This extension to the theory produces little change in the shape of the predicted mass function, but can have an appreciable effect on the predicted temperature function if one assumes that clusters scatter around a mass-temperature scaling relation appropriate to" +In Εναetal.(2006) we eruclely estimated the activity of the bursting behavior of bby comparing the time curing which the source is observed {ο be active to the total amount of observing time.,In \cite{hlrrkn06} we crudely estimated the activity of the bursting behavior of by comparing the time during which the source is observed to be active to the total amount of observing time. + With the addition of 40 hr of 330 MIIz VLA observations analvzed in 2006. with no detection. the total observing lime is ~120 hr.," With the addition of $\sim$ 40 hr of 330 MHz VLA observations analyzed in 2006, with no detection, the total observing time is $\sim$ 120 hr." + The 2002 September 30 - October 1 bursts lasted for at least 6 hr. and since only a single burst was detected on 2003 september 28 and on 2004 March 20. we assume that the source was active For 1 hr in each of these epochs.," The 2002 September 30 - October 1 bursts lasted for at least 6 hr, and since only a single burst was detected on 2003 September 28 and on 2004 March 20, we assume that the source was active for $\sim$ 1 hr in each of these epochs." + Thus. hhas exhibited bursting activity approximately of the time it was observed.," Thus, has exhibited bursting activity approximately of the time it was observed." + The 2002 and 2003 detections of ooccured in late September auc the 2004 detection occurred in late March. suggesting a roughly 6-month interval between active periods.," The 2002 and 2003 detections of occured in late September and the 2004 detection occurred in late March, suggesting a roughly 6-month interval between active periods." + Although we find no detections in our 1998. 2002. 2005. and 2006 observations in March and September. it is still possible that bursting activity did occur in these months but was either too faint or lasted too short a time to be detected.," Although we find no detections in our 1998, 2002, 2005, and 2006 observations in March and September, it is still possible that bursting activity did occur in these months but was either too faint or lasted too short a time to be detected." + Similarly. while our database has many observations in 2002. 2003. aud 2006. we did not monitor for transients nearly as often in 2004 and 2005. and useful archival data dis very limited in those vears.," Similarly, while our database has many observations in 2002, 2003, and 2006, we did not monitor for transients nearly as often in 2004 and 2005, and useful archival data is very limited in those years." + Since we have now detected iin three significantly different. observed. states (1 Jv versus ~50 mJy burst strenetls. ~10 min.," Since we have now detected in three significantly different observed states $\sim$ 1 Jy versus $\sim$ 50 mJy burst strengths, $\sim$ 10 min." + versus ~2 min., versus $\sim$ 2 min. + burst durations. ancl regularly repeating versus isolated bursts). future detections may vel exhibit additional properties (e.g.. emission in other lrequency bands and polarizecl emission) that will lead to a definitive unclerstanding of the nature ofJ1745—3009.," burst durations, and regularly repeating versus isolated bursts), future detections may yet exhibit additional properties (e.g., emission in other frequency bands and polarized emission) that will lead to a definitive understanding of the nature of." +. Given the high variability in flux densitv already. detected. and the very steep spectrum of the 2004 burst. it is even conceivable that bursts much stronger (han e-] Jv will be detected at 330 MIIz ancl lower Irequencies. although it is also possible (hat the bursts are now continually decreasing in strength at all [requencies.," Given the high variability in flux density already detected, and the very steep spectrum of the 2004 burst, it is even conceivable that bursts much stronger than $\sim$ 1 Jy will be detected at 330 MHz and lower frequencies, although it is also possible that the bursts are now continually decreasing in strength at all frequencies." + We note that all three detections suggest strongly that Hvimanetal.(2005).. 3...," We note that all three detections suggest strongly that \cite{hlkrmy-z05}, \ref{fig:lightcurve04}." +The group of supernova remnant (SNRs) which are known to host a radio-quiet but X-ray bright. central compact object (CCO) is a slowly growing one.,The group of supernova remnant (SNRs) which are known to host a radio-quiet but X-ray bright central compact object (CCO) is a slowly growing one. + Thanks to more sensitive X-ray observatories it currently includes Cas-A (CXOU J232327.9-584842: Tananbaum 1999). RX J0852.0-4622. (CXOU J085201.4—461753; Aschenbach 1998). RX H713.7—3946 (RX J1713.4—3949: Pfeffermann Aschenbach 1996). 1103 (IE 161348-5055: Tuohy Garmire 1980).JO822—4300:; Petre et al.," Thanks to more sensitive X-ray observatories it currently includes $-$ A (CXOU J232327.9+584842; Tananbaum 1999), RX $-$ 4622 (CXOU $-$ 461753; Aschenbach 1998), RX $-$ 3946 (RX $-$ 3949; Pfeffermann Aschenbach 1996), 103 (1E 161348-5055; Tuohy Garmire 1980),; Petre et al." + 1982: Petre. Becker. Winkler 1996; Hui Becker 2006). PKS 1209-51/52 (IE 1207.4—5209; Helfand Becker 1984) and Kes 79 (CXOU J185238.6+004020; Seward et al.," 1982; Petre, Becker, Winkler 1996; Hui Becker 2006), PKS 1209-51/52 (1E $-$ 5209; Helfand Becker 1984) and Kes 79 (CXOU $+$ 004020; Seward et al." + 2003: Gotthelf et al., 2003; Gotthelf et al. + 2005)., 2005). + Was first noticed in one of the EINSTEIN HRI images of the ssupernova remnant (Petre et al., was first noticed in one of the EINSTEIN HRI images of the supernova remnant (Petre et al. + 1982)., 1982). + However. it appeared in this data only as a faint X-ray feature.," However, it appeared in this data only as a faint X-ray feature." +" It is not until the era of ROSAT when it became evident that Is the central compact stellar remnant which was formed in the supernova event (Petre. Becker. Winkler 1996),"," It is not until the era of ROSAT when it became evident that is the central compact stellar remnant which was formed in the supernova event (Petre, Becker, Winkler 1996)." + Recently. Hui Becker (2006) presented results from a detailed analysis of Which made use of all XMM-Newton and Chandra data available from it by beginning of 2005.," Recently, Hui Becker (2006) presented results from a detailed analysis of which made use of all XMM-Newton and Chandra data available from it by beginning of 2005." + The spectral analysis of XMM-Newton data revealed that the X-ray emission from Is in agreement with being of thermal origin., The spectral analysis of XMM-Newton data revealed that the X-ray emission from is in agreement with being of thermal origin. +" A double blackbody model with the temperatures T,=(2.35-2.91)x10° Κ. T;=(4.84—5.3)x10° K and the projected blackbody emitting radii Rj2(2.55—4.41) km and R>=(600—870) m gave the best description of the observed point source spectrum among various spectral models tested."," A double blackbody model with the temperatures $T_{1}=(2.35-2.91)\times10^{6}$ K, $T_{2}=(4.84-5.3)\times10^{6}$ K and the projected blackbody emitting radii $R_{1}=(2.55-4.41)$ km and $R_{2}=(600-870)$ m gave the best description of the observed point source spectrum among various spectral models tested." + The X-ray images taken with the Chandra HRC-I camera allowed for the first time to examine the spatial nature of with sub-aresecond resolution., The X-ray images taken with the Chandra HRC-I camera allowed for the first time to examine the spatial nature of with sub-arcsecond resolution. + Besides an aecurate measurement of the source position. this observation constrained the point source nature of down to 0.59+0.01 aresee (FWHM) for the first time.," Besides an accurate measurement of the source position, this observation constrained the point source nature of down to $0.59\pm0.01$ arcsec (FWHM) for the first time." + Despite the effort in searching for coherent radio pulsations. has not been detected as a radio pulsar (Kaspi et al.," Despite the effort in searching for coherent radio pulsations, has not been detected as a radio pulsar (Kaspi et al." + 1996)., 1996). + Similar to many other CCOs. it has no optical counterpart down to a limiting magnitude of B225.0 and R223.6 (Petre. Becker. Winkler 1996).," Similar to many other CCOs, it has no optical counterpart down to a limiting magnitude of $B\ga 25.0$ and $R\ga 23.6$ (Petre, Becker, Winkler 1996)." + Together with the lack of long term flux variation (Hui Becker 2006). all these evidences rule out many types of X-ray sources as a likely counterpart ofJ0822—4300.. except a neutron star.," Together with the lack of long term flux variation (Hui Becker 2006), all these evidences rule out many types of X-ray sources as a likely counterpart of, except a neutron star." + is located about ~6 aremin distant from the optical expansion center ofPuppis—A.. which is at RAZ08222745 and Decz-4257'28.67 (J2000) (cf.," is located about $\sim 6$ arcmin distant from the optical expansion center of, which is at $08^{\rm h}22^{\rm m}27.45^{\rm s}$ and $-42^{\circ}57'28.6""$ (J2000) (cf." + Winkler Kirshner 1985; Winkler et al., Winkler Kirshner 1985; Winkler et al. + 1988)., 1988). + The age of the supernova remnant. as estimated from the kinematics of oxygen-rich filaments ts -3700 years (Winkler et al.," The age of the supernova remnant, as estimated from the kinematics of oxygen-rich filaments is $\sim 3700$ years (Winkler et al." + 1988)., 1988). + If these estimates are correct. should have a proper motion of the order of ~100 mas/yr to a direction away from its proposed birth place.," If these estimates are correct, should have a proper motion of the order of $\sim 100$ mas/yr to a direction away from its proposed birth place." + In this letter we test this hypothesis by making use of archival Chandra HRC-I data spanning an epoch of somewhat more than five years., In this letter we test this hypothesis by making use of archival Chandra HRC-I data spanning an epoch of somewhat more than five years. + The expected positional displacement for un this time span is of the order of ~0.5 aresec., The expected positional displacement for in this time span is of the order of $\sim 0.5$ arcsec. + This is in the range of the Chandra accuracy given the possibility to correct for pointing uncertainties by using X-ray counterparts of stars with accurate position and which are serendipitously located in the field of view., This is in the range of the Chandra accuracy given the possibility to correct for pointing uncertainties by using X-ray counterparts of stars with accurate position and which are serendipitously located in the field of view. + Owing to the fact that there are only few bad pixels in the Chandra HRC-I and the pixel size of 0.13187 arcsec oversamples the point spread function (PSF) by a factor of ~5. the HRC-I appears to be the most suitable detector to perform astrometric measurements of X-ray sources.," Owing to the fact that there are only few bad pixels in the Chandra HRC-I and the pixel size of 0.13187 arcsec oversamples the point spread function (PSF) by a factor of $\sim 5$, the HRC-I appears to be the most suitable detector to perform astrometric measurements of X-ray sources." + Checking the Chandra archive for suitable data we found that by mid of 2006 Was observed twice with the HRC-I. The first observation was performed in 1999 December 21 (MJD 51533) for an exposure time of about 16 ksec., Checking the Chandra archive for suitable data we found that by mid of 2006 was observed twice with the HRC-I. The first observation was performed in 1999 December 21 (MJD 51533) for an exposure time of about 16 ksec. + The second observation was done in 2005 April 25 (MJD 53485) for an on-source time of ~33 ksec., The second observation was done in 2005 April 25 (MJD 53485) for an on-source time of $\sim 33$ ksec. + In the April 2005 observation. the target was displaced onlv," In the April 2005 observation, the target was displaced only" + In the April 2005 observation. the target was displaced onlvá," In the April 2005 observation, the target was displaced only" +"debris disk structure postulates belts of planetesimals that produce a range of dust grain sizes through a collisional cascade (e.g.?,andreferencestherein)..",debris disk structure postulates belts of planetesimals that produce a range of dust grain sizes through a collisional cascade \citep[e.g.][and references therein]{wya08}. +" The “birth rings"" in which dust is generated are typically assumed to be relatively radially narrow, and millimeter-size grains are predicted to be confined near the birth population while smaller grains are smeared to far larger distances through the effects of stellar radiation (e.g.??).."," The “birth rings” in which dust is generated are typically assumed to be relatively radially narrow, and millimeter-size grains are predicted to be confined near the birth population while smaller grains are smeared to far larger distances through the effects of stellar radiation \citep[e.g.][]{str06, +kuc10}." +" In this context, it is interesting to compare the morphology of the disks derived at millimeter wavelengths to the results of spatially resolved imaging at optical and infrared wavelengths."," In this context, it is interesting to compare the morphology of the disks derived at millimeter wavelengths to the results of spatially resolved imaging at optical and infrared wavelengths." + The broad ring model derived for HD 107146 bears a striking similarity to the features of the scattered light observations of ??..," The broad ring model derived for HD 107146 bears a striking similarity to the features of the scattered light observations of \citet{ard04,ert11}." + They infer the presence of a broad dust ring with peak optical depth at a distance of 130AAU from the star and FWHM , They infer the presence of a broad dust ring with peak optical depth at a distance of AU from the star and FWHM AU. +"The um SMA data have peak brightness at a AAU.distance of 5” from the central star, with models of the spatially (~115AAU)resolved data implying a broad ring extending from 50 to AAU, similar to the extent measured in the optical."," The $\mu$ m SMA data have peak brightness at a distance of 5” $\sim$ AU) from the central star, with models of the spatially resolved data implying a broad ring extending from 50 to AU, similar to the extent measured in the optical." +" The negative surface density power law of p~—0.3 implies a near-constant surface brightness with radius, similar to the two-power-law behavior (with optical depth increasing to a radius of AAU and decreasing beyond that described for the scattered light."," The negative surface density power law of $p\sim-0.3$ implies a near-constant surface brightness with radius, similar to the two-power-law behavior (with optical depth increasing to a radius of AU and decreasing beyond that radius) described for the scattered light." +" However, it is not at radius)all obvious that the morphology of the jum datashould be so well matched to that of the F606W and F814WHST data, given the birth ring scenario and the prediction that the spatial extent of the small scatterers should exceed that of the millimeter-size particles."," However, it is not at all obvious that the morphology of the $\mu$ m data be so well matched to that of the F606W and F814W data, given the birth ring scenario and the prediction that the spatial extent of the small scatterers should exceed that of the millimeter-size particles." +" If enough molecular gas lingers in the system, it is possible that even the large dust grains could remain entrained in gas."," If enough molecular gas lingers in the system, it is possible that even the large dust grains could remain entrained in gas." + It is also possible that the grain size distribution is concentrated at small sizes; multiwavelength imaging at higher to-noise would be required to confirm this., It is also possible that the grain size distribution is concentrated at small sizes; multiwavelength imaging at higher signal-to-noise would be required to confirm this. + The HR 8799 disk is known to posess a large and surprisingly massive halo of small dust grains extending between ~300-1000 AAU from the star and resolved in emission withSpitzer, The HR 8799 disk is known to posess a large and surprisingly massive halo of small dust grains extending between $\sim$ AU from the star and resolved in $\mu$ m emission with \citep{su09}. +" The mass of grains in Τθµπιthe halo is about 15 times (?)..higher than expected for a static collisionally dominated disk (?),, similar to the halo observed around Vega."," The mass of grains in the halo is about 15 times higher than expected for a static collisionally dominated disk \citep{wya07}, similar to the halo observed around Vega." +" This implies that the production of small grains is enhanced in these systems, most likely due to heavy dynamical stirring (?).."," This implies that the production of small grains is enhanced in these systems, most likely due to heavy dynamical stirring \citep{su09}." + The broad ring of millimeter emission suggested by the SED model of ? that is consistent with the jum visibilities is likely to be generated by the same stirring process responsible for the enhanced production of small grains in the halo.," The broad ring of millimeter emission suggested by the SED model of \citet{su09} + that is consistent with the $\mu$ m visibilities is likely to be generated by the same stirring process responsible for the enhanced production of small grains in the halo." + The other aspect of morphology worth mentioning is the degree of axisymmetry., The other aspect of morphology worth mentioning is the degree of axisymmetry. + There is no statistically significant evidence for deviations from axisymmetry in the disks that might point to dynamical resonances with a large planet., There is no statistically significant evidence for deviations from axisymmetry in the disks that might point to dynamical resonances with a large planet. +" The 30 negative residual in the HR 8799 observation coincides roughly with the position of the emissionpeak in the um CSO map presented in ?,, a likely indication that both features are in fact simply noise in the data."," The $\sigma$ negative residual in the HR 8799 observation coincides roughly with the position of the emission in the $\mu$ m CSO map presented in \citet{pat11}, a likely indication that both features are in fact simply noise in the data." + We do not confirm the azimuthal asymmetry suggested by CSO observations in ? despite higher resolution and signal-to-noise; within the (large) uncertainties the data are so far consistent with a symmetric disk., We do not confirm the azimuthal asymmetry suggested by CSO observations in \citet{pat11} despite higher resolution and signal-to-noise; within the (large) uncertainties the data are so far consistent with a symmetric disk. + The inset in the center image panel of Fig., The inset in the center image panel of Fig. + 2 illustrates how emission morphology in low signal-to-noise data sets may be misleading., \ref{fig:hr8799} illustrates how emission morphology in low signal-to-noise data sets may be misleading. +" We also note that the challenge of interpreting faint emission morphology from debris disk has lead to spurious detections of clumpy structure in the Vega (???) and HD 107146 (?,thiswork) debris disks."," We also note that the challenge of interpreting faint emission morphology from debris disk has lead to spurious detections of clumpy structure in the Vega \citep{koe01,wil02,pie11} + and HD 107146 \citep[][this work]{cor09} debris disks." +" Given these difficulties, greater sensitivity is necessary to point conclusively to a deviation from axisymmetry."," Given these difficulties, greater sensitivity is necessary to point conclusively to a deviation from axisymmetry." +" Of course, the lack of deviations from axisymmetry does not necessarily imply a lack of giant planets; for example, ? predict that the dynamical influence of Neptune should be invisible at millimeter wavelengths in our own solar system, and that the smoothing effect of collisions would be enhanced for larger optical depths comparable to the disks observed in this paper."," Of course, the lack of deviations from axisymmetry does not necessarily imply a lack of giant planets; for example, \citet{kuc10} predict that the dynamical influence of Neptune should be invisible at millimeter wavelengths in our own solar system, and that the smoothing effect of collisions would be enhanced for larger optical depths comparable to the disks observed in this paper." + The location of the inner edge of the dust belt has profound implications for our understanding of the directly-imaged planetary system orbiting HR 8799., The location of the inner edge of the dust belt has profound implications for our understanding of the directly-imaged planetary system orbiting HR 8799. + The visibilities alone constrain the inner radius of, The visibilities alone constrain the inner radius of + Long seriod variables (LPW) form au mnuportaut class of τος eiat stars., Long period variables (LPV) form an important class of red giant stars. + They show amore or less reeular photometric variability with amplitudes reaching up to & magnitudes and periods up to 600 days., They show more or less regular photometric variability with amplitudes reaching up to 8 magnitudes and periods up to 600 days. + They traditionally conrprise Aras. semiveeular (SR) aud ivreeular (L) variables according to the amplitude and the regularitv of their visual light curves.," They traditionally comprise Miras, semi-regular (SR) and irregular (L) variables according to the amplitude and the regularity of their visual light curves." + They ave known to be either rich or C-vich. and comprise thus M. S and C stars.," They are known to be either O-rich or C-rich, and comprise thus M, S and C stars." + More receutly OILIBR sources have been fouud from infrared and radio observations showing that they beloug to the LPV »pulatiou with periods up to 2000x davs., More recently OH-IR sources have been found from infrared and radio observations showing that they belong to the LPV population with periods up to 2000 days. + Those sources enit iu the infrared and radio svaveleuethis. aud are not associated with any detectable counterpart in optical waveleugthlis.," Those sources emit in the infrared and radio wavelengths, and are not associated with any detectable counterpart in optical wavelengths." + The brightest LPVs are uuinous euough to be observed at long distances. providing information ou the host galaxw. like the Magellanic Clouds (see Van Loon et al.," The brightest LPVs are luminous enough to be observed at long distances, providing information on the host galaxy, like the Magellanic Clouds (see Van Loon et al.," + 1999 as an example)., 1999 as an example). + While the rauges of masses and ages of LPVs are still the subject of discussion. it is eenerallv accepted that thev are large. aud are therefore considered as very good tracers of galactic history.," While the ranges of masses and ages of LPVs are still the subject of discussion, it is generally accepted that they are large, and are therefore considered as very good tracers of galactic history." + The determination of the characteristics of individual LPVs is usually a delicate ask due to the complexity of the dynamic and chemical phenomena to be considered., The determination of the characteristics of individual LPVs is usually a delicate task due to the complexity of the dynamic and chemical phenomena to be considered. + A statistical study using all available data of a large sample of LPVs is often rwecded., A statistical study using all available data of a large sample of LPVs is often needed. + A rough example of such an approach could be the relation between the neal visual light curves aud the infrared colors of C aud O-vich LPVs already preseutec oei Mennesscr et al. (, A rough example of such an approach could be the relation between the mean visual light curves and the infrared colors of C and O-rich LPVs already presented in Mennessier et al. ( +19972).,1997a). + Iu this paper. WIPPARCOS astrometric data aud the available multi-wavelcueth (IX. IRAS 12 and 25) infrared photometric measurements allow us to calibrate niulti-wavelength luninosities and to discriminate between different galactic populations and thus different ranges of initial masses Αν) amoug the LPVs according to their kinematical properties.," In this paper, HIPPARCOS astrometric data and the available multi-wavelength (K, IRAS 12 and 25) infrared photometric measurements allow us to calibrate multi-wavelength luminosities and to discriminate between different galactic populations – and thus different ranges of initial masses ${\cal M}_{ms}$ ) – among the LPVs according to their kinematical properties." + Iu a second step. individual KK and IRAS absolute magnitudes are estimated for all the SOO considered LPVs using a powerful statistical Our sample of LPV stars and the data used are described in Sect. 2..," In a second step, individual K and IRAS absolute magnitudes are estimated for all the 800 considered LPVs using a powerful statistical Our sample of LPV stars and the data used are described in Sect. \ref{Sect:sample}." + The statistical method specifically developed for the study of TIPPARCOS samples is stnunarized in Sect. 3.., The statistical method specifically developed for the study of HIPPARCOS samples is summarized in Sect. \ref{Sect:statistics}. + Sect., Sect. + L presents the discriminated eroups of LPVs resulting from our statistical analysis. while Sect.," \ref{Sect:groups} presents the discriminated groups of LPVs resulting from our statistical analysis, while Sect." + ο analvzes the results derived. for incivicual stars.," \ref{Sect:individual} + analyzes the results derived for individual stars." + Finally. Sect.," Finally, Sect." + 6 reviews the crossed properties derived from the analysis at differcut wavelenueths., \ref{sec_propgrups} reviews the crossed properties derived from the analysis at different wavelengths. +We then show in the right panel of Fig.,We then show in the right panel of Fig. + 5 that ffor high-redshift galaxies is consistent with the ratios from local LIRGs and ULIRGs with significantly lowerL(TIR)., \ref{q24} that for high-redshift galaxies is consistent with the ratios from local LIRGs and ULIRGs with significantly lower. +. Consider the SMGs atz~2.4 with ~10155Lo: the correlation in Fig.," Consider the SMGs at$z \sim +2.4$ with $\sim 10^{13.5}$; the correlation in Fig." +" 4 suggests L(TIR)their starburst environment to be similar to local ULIRGs with L(TIR)~10"" aand iis clearly inconsistent with the extrapolation for local ULIRGs at 1013.5 wwhile agreeing with the SED for e»1013 llocal ULIRGs.", \ref{LTIR_density_z} suggests their starburst environment to be similar to local ULIRGs with $\sim 10^{12}$ and is clearly inconsistent with the extrapolation for local ULIRGs at $\sim 10^{13.5}$ while agreeing with the SED for $\sim 10^{12}$ local ULIRGs. + Another way to interpret this is illustrated by Fig., Another way to interpret this is illustrated by Fig. + 6 that the aromatic features are significantly stronger compared to local SED templates at redshifts greater than z~1., \ref{q24_z_ratio} that the aromatic features are significantly stronger compared to local SED templates at redshifts greater than $z \sim 1$. +" Second, we consider a result from Rigbyetal. (2008),, specifically their Fig."," Second, we consider a result from \citet{Rigby08}, , specifically their Fig." +" 3, that shows aromatic emissions"," 3, that shows aromatic emissions" +Gamma-ray bursts (GRBs) are enigmatic explosions. detected usually at cosmological distances.,"Gamma-ray bursts (GRBs) are enigmatic explosions, detected usually at cosmological distances." + They appear to come in two distinct flavors according to their duration (seee.g.Gehrelsetal..2009.fora review).., They appear to come in two distinct flavors according to their duration \citep[see e.g.][for a review]{gehrels09}. + Powerful explosions usually leave long-living remnants behind that potentially could be studied in the local Universe as relics of the original events., Powerful explosions usually leave long-living remnants behind that potentially could be studied in the local Universe as relics of the original events. + Long bursts (duration longer than about 2 s) are generally considered to be launched by the death of a massive star and several structures in our Galaxy have been suggested to be the remnants of such events., Long bursts (duration longer than about 2 s) are generally considered to be launched by the death of a massive star and several structures in our Galaxy have been suggested to be the remnants of such events. + These proposed remnants are in many cases linked to sources of very-high-energy (VHE. >100 GeV) gamma-ray emission.," These proposed remnants are in many cases linked to sources of very-high-energy (VHE, $>$ 100 GeV) gamma-ray emission." + The VHE gamma-ray source HESS J1303-631 (Aharonianetal..2005) has been suggested as the remnant of a long GRB that happened >10* years ago (Atoyanetal..2006)., The VHE gamma-ray source HESS J1303-631 \citep{aharonian05} has been suggested as the remnant of a long GRB that happened $\gtrsim 10^4$ years ago \citep{atoyan06}. +. Also the structure W49B has been suspected to be a remnant of a GRB (lokaet 2004)., Also the structure W49B has been suspected to be a remnant of a GRB \citep{ioka04}. +. Recently it has been argued that the population of unidentified TeV sources (seee.g.Aharonianetal..2008) may be dominated by GRB/Hypernova remnants (Ioka&Mészáros. 2010)., Recently it has been argued that the population of unidentified TeV sources \citep[see e.g.][]{aharonian08} may be dominated by GRB/Hypernova remnants \citep{ioka09}. +. For short GRBs (duration shorter tha 2 s). compact binary Mergers as central engine have been identified as the preferred scenario (e.g.Gehrelsetal..2005:Lee2005).," For short GRBs (duration shorter than 2 s), compact binary mergers as central engine have been identified as the preferred scenario \citep[e.g.][]{gehrels05,lee05}." +. Such compact binaries may be efficiently created i globular clusters since these environments feature high densities of very old stars in their. cores., Such compact binaries may be efficiently created in globular clusters since these environments feature high densities of very old stars in their cores. + Indeed in the globular cluster M 15 already a close system that consists of two neutron stars (NS) has been discovered (Andersonetal..1990)., Indeed in the globular cluster M 15 already a close system that consists of two neutron stars (NS) has been discovered \citep{anderson90}. +. Based on these facts. it has been argued that a considerable fraction of all NSNS binaries are formed in globular clusters (Grindlayetal..2006).," Based on these facts, it has been argued that a considerable fraction of all NSNS binaries are formed in globular clusters \citep{grindlay06}." + It has been claimed that the rate of short bursts in the local Universe is dominated by mergers of dynamically formed compact binaries in globular clusters (Salvateraetal..2008:Guetta&Stella. 2009).," It has been claimed that the rate of short bursts in the local Universe is dominated by mergers of dynamically formed compact binaries in globular clusters \citep{salvaterra08,guetta09}." +. Therefore. globular clusters might be the prime environment for seeking remnants of short GRBs.," Therefore, globular clusters might be the prime environment for seeking remnants of short GRBs." + Potential signatures of remnants of compact binary mergers have already been discussed 2008)..," Potential signatures of remnants of compact binary mergers have already been discussed \citep[see][]{domainko05,domainko08}." + The H.E.S.S. collaboration has very recently reported the detection of à VHE gamma-ray source HESS J1747-248 in the direction of the galactic globular cluster Terzan 5 (Abramowskietal.2011) with. a flux above [440 GeV of (1.220.3)x 107. em? s7!.," The H.E.S.S. collaboration has very recently reported the detection of a VHE gamma-ray source HESS J1747-248 in the direction of the galactic globular cluster Terzan 5 \citep{hesspaper} with a flux above 440 GeV of $\pm$ $\times$ $^{-12}$ $^{-2}\,$ $^{-1}$." +" The source is extended with intrinsic extension of 9’.642’.4. [ and there appears to be an offset from the cluster core position by about. 47.0417.9,"," The source is extended with intrinsic extension of $^\prime$ $ \pm $ $^\prime$ .4, and there appears to be an offset from the cluster core position by about $^\prime$ $ \pm $ $^\prime$ .9." +" Terzan 5 is located at a distance of 5.9 kpe (Ferraro2009).. at RA(Q2000) 1748""0:P.85 and Dec —24°46'44’"".6 (I 3.87. b 1.77). and exhibits a core radius of 0.15"" a half-mass radius of 0.52 and a tidal radius of 4.6 (Lanzonietal..2010)."," Terzan 5 is located at a distance of 5.9 kpc \citep{ferraro2009}, at RA(J2000) $^\mathrm{h}$ $^\mathrm{m}$ $^\mathrm{s}$ .85 and Dec $-24^{\circ}$ $^\prime$ $^{\prime\prime}$ .6 (l $^{\circ}$, b $^{\circ}$ ), and exhibits a core radius of 0.15' a half-mass radius of 0.52' and a tidal radius of 4.6' \citep{lanzoni2010}." +. Terzan 5 is the globular cluster with the highest expected rates of close stellar encounters (Pooley&Hut.2006) and with the largest population of millisecond pulsars (33) discovered up to now (Ransom.2008)., Terzan 5 is the globular cluster with the highest expected rates of close stellar encounters \citep{pooley06} and with the largest population of millisecond pulsars (33) discovered up to now \citep{ransom08}. +. Gamma rays of likely magnetospheric origin produced by millisecond pulsars have been detected in the GeV range in Terzan 5 (Kongetal..2010:Abdo 2010a).," Gamma rays of likely magnetospheric origin produced by millisecond pulsars have been detected in the GeV range in Terzan 5 \citep{kong10,abdo10}." +. Diffuse X-ray emission extending beyond the half- radius has also been reported (Egeretal..2010)., Diffuse X-ray emission extending beyond the half-mass radius has also been reported \citep{eger2010}. +. In the vicinity of Terzan 5 several structures in the radio band have been found (ClapsonetaL.2011)., In the vicinity of Terzan 5 several structures in the radio band have been found \citep{clapson2011}. +. Terzan 5 Is à predicted VHE gamma-ray emitter where energetic electrons produced by the large population of millisecond pulsars up-scatter stellar photons to gamma-ray energies (Venteretal..2009:Bednarek&Sitarek. 2007).," Terzan 5 is a predicted VHE gamma-ray emitter where energetic electrons produced by the large population of millisecond pulsars up-scatter stellar photons to gamma-ray energies \citep{venter2009,bednarek2007}." +. In. contrast to these models here VHE gamma-ray emission originating from collisions of hadronic cosmic rays with ambient target nuclet and subsequent π0 decay is explored., In contrast to these models here VHE gamma-ray emission originating from collisions of hadronic cosmic rays with ambient target nuclei and subsequent $\pi^0$ decay is explored. + A short GRB is adopted as the accelerator of the cosmic rays., A short GRB is adopted as the accelerator of the cosmic rays. + The paper is organized as follows: In Sect., The paper is organized as follows: In Sect. + ?? potential indications for à hadronie VHE gamma-ray production in Terzan 5 are discussed. in Sect.," \ref{sec:hadronic} potential indications for a hadronic VHE gamma-ray production in Terzan 5 are discussed, in Sect." + ??. signatures left behind by the ultrarelativistic outflow of an ancient GRB in Terzan 5 are assessed. in Sect.," \ref{sec:ultra_rel} signatures left behind by the ultrarelativistic outflow of an ancient GRB in Terzan 5 are assessed, in Sect." + ?? signatures related to the subrelativistic ejecta are explored. and in Sect.," \ref{sec:sub_rel} signatures related to the subrelativistic ejecta are explored, and in Sect." + ?? potential traces of tonizing radiation emitted by the GRB are investigated., \ref{sec:ionization} potential traces of ionizing radiation emitted by the GRB are investigated. + Some of the properties of the VHE gamma-ray source that were detected in the direction of Terzan 5 appear to challenge, Some of the properties of the VHE gamma-ray source that were detected in the direction of Terzan 5 appear to challenge + he photous from a poiut-like nucleus would fall within the extraction region used for tle NW extensiou.,of the photons from a point-like nucleus would fall within the extraction region used for the NW extension. + The ratio of the 3-10 keV flux (which excludes most of the soft the‘ual X-ray emissiot) he NW extension to that of the nucleis ds ον0.5%. or twice that expected [rom the telescope F.," The ratio of the 3–10 keV flux (which excludes most of the soft thermal X-ray emission) of the NW extension to that of the nucleus is $\simeq +0.5$, or twice that expected from the telescope PSF." + We have also compared the hard flux of the NW extension with the IlIX lh a region at te 1ο distauce Grom the nucleus where {1ere is no detected diffuse etission [rom Ci‘cluus (e.g. wards the SE)., We have also compared the hard flux of the NW extension with the flux in a region at the same distance from the nucleus where there is no detected diffuse emission from Circinus (e.g. towards the SE). + Tie 3-10 keV count rates of the NW extension aud a regioito the 5E with tle je area are (1.7+0.3)x103 cis La xl (1.2£0.2)x10“etsu 1 respectively.," The 3–10 keV count rates of the NW extension and a region to the SE with the same area are $(1.7 \pm 0.3) \times 10^{-3}$ cts $^{-1}$ and $(1.2 \pm +0.2) \times 10^{-3}$ cts $^{-1}$ respectively." + TIerelore. Wwe tatively conclude that the hard power-aw COLDyonent in the NW extensi[9]Lis real.," Therefore, we tentatively conclude that the hard power-law component in the NW extension is real." + A plausibe erpretation is that this hard power-law compotent is nuclear flux scattered by electrous in an ized gas above the plaie of the galaxy., A plausible interpretation is that this hard power-law component is nuclear flux scattered by electrons in an ionized gas above the plane of the galaxy. + The flux aud equivalent width of tje Fe Ixo. emission liiT he NW extensici areape (1.2.1οαςL0)x10.? photons cmτς land 2.7“y=οnn keV. respectively.," The flux and equivalent width of the Fe $\alpha$ emission line in the NW extension are $(1.2^{+1.0}_{-0.8}) \times 10^{-6}$ photons $^{-2}$ $^{-1}$ and $2.7^{+2.4}_{-1.9}$ keV, respectively." + The triT e flux will be smaller tjan this value. because the telescope PSF contribues 7.5x10.* photonJd. 57s 5! from⋅ FeMN Ka emission line iu the nuclear spectrum.," The true line flux will be smaller than this value, because the telescope PSF contributes $7.5 +\times 10^{-7}$ photons $^{-2}$ $^{-1}$ from Fe $\alpha$ emission line in the nuclear spectrum." + However. Fe Ina euiission lines of large equivalent width cau reacily occur if a small fraction of the nuclear emission is scattered by a warui πο (Rirolik&EKallijiuLOST:Bandetal.1990).," However, Fe $\alpha$ emission lines of large equivalent width can readily occur if a small fraction of the nuclear emission is scattered by a warm “mirror” \citep{kk87,ban90}." +. A similar specral fitting approach was adopted for the spectrum of the SW exteusion as that ised for the spectrum of the WW region., A similar spectral fitting approach was adopted for the spectrum of the SW extension as that used for the spectrum of the NW region. + Several lines are evident in the spectrum (Figure 9)). he most prominett being the Fe Ίνα aud Ix? emission lines at 6.1100.055o.u27 OLL 7.0300.030uusi keV 'espectively.," Several lines are evident in the spectrum (Figure \ref{fig9}) ), the most prominent being the Fe $\alpha$ and $\beta$ emission lines at $6.410^{+0.035}_{-0.027}$ and $7.030^{+0.039}_{-0.035}$ keV respectively." + A two-component uodel consisting ofa thermal bremisstraliluug phs power-law continuum (model B+P) provides a poor it to the data with 4?=12.5 for 21 d.o.L. (, A two-component model consisting of a thermal bremsstrahlung plus power-law continuum (model B+P) provides a poor fit to the data with $\chi^{2} = 42.5$ for 24 d.o.f. ( +the orobability that the nodel describes t1e data aud that Q exCeecs the observed value by chance is 156)): he parameters are given ii Table τ..,the probability that the model describes the data and that $\chi^{2}$ exceeds the observed value by chance is $1$ ); the best-fitting parameters are given in Table \ref{tbl-4}. + Repacing the thermal bremesstrallne continuum with a solar-metallicity HXOcel gives a ΙΟ] better fit to the data (model MI-P. Table 7)).," Replacing the thermal bremsstrahlung continuum with a solar-metallicity model gives a much better fit to the data (model M1+P, Table \ref{tbl-4}) )." + A significaut (at >99.5% confidence) imJovenent in the fit is obtained for a netal abundance of 0.085τω0.0520.031 times solar (inodel M24-P. Table 7 |.," A significant (at $> 99.5$ confidence) improvement in the fit is obtained for a metal abundance of $0.088^{+0.052}_{-0.031}$ times solar (model M2+P, Table \ref{tbl-4}) )." + A two MERKALs 1uodel (1nocel MI+M1. each witl solar metallicity) οives a worse fit to tle data than does the MI--P model.," A two s model (model M1+M1, each with solar metallicity) gives a worse fit to the data than does the M1+P model." + Alhough a sieuificant (al 99.7% conlidence) improveruent iu the fit is obtalned when the 1jetal aloiundauce is alOWerc to vary Gnodel M2--M2. both MERALs are asstuned to have the same metalliciy. Table 7)). the fit is worse than tha for the M24-P. tmoce.," Although a significant (at $> 99.7$ confidence) improvement in the fit is obtained when the metal abundance is allowed to vary (model M2+M2, both s are assumed to have the same metallicity, Table \ref{tbl-4}) ), the fit is worse than that for the M2+P model." + Thus. we preer the plis power-law cdescription of the SW extension," Thus, we prefer the plus power-law description of the SW extension." + It is notable thatal values of the :vbsorbing colt density in Table 7 excee the Galactic colunu. luclicating that significan absorj»tion occurs witlin the disk of the Circinus galaxy.," It is notable thatall values of the absorbing column density in Table \ref{tbl-4} exceed the Galactic column, indicating that significant absorption occurs within the disk of the Circinus galaxy." + None of tle iocels reproduce the strong Fe a aud Fe Ij lineS., None of the models reproduce the strong Fe $\alpha$ and Fe $\beta$ lines. + Given the close prcxinuitv of the SW region to he nucleus. appOxüinately 1% of the 3-10 keV flux of a poiut-like iucleus would fall witliu the extraction region used for the SW exteusiou.," Given the close proximity of the SW region to the nucleus, approximately $1$ of the 3–10 keV flux of a point-like nucleus would fall within the extraction region used for the SW extension." + The ratio of the (backgrouud subtracted) 3-10 keV couit rates of the SW extension to that of the nucleus is 2 154.. in agreement with that expeced [ror ithe telescope PSF.," The ratio of the (background subtracted) 3–10 keV count rates of the SW extension to that of the nucleus is $\simeq 1$ , in agreement with that expected from the telescope PSF." + Therefore. we conclude," Therefore, we conclude" +The WMAP mission makes measurements of temperature with two antennas. A and D. and record in time-order the dillerence between the (wo antenna temperatures. Z4—Z5. which is called the time-order data (LOD).,"The WMAP mission makes measurements of temperature with two antennas, A and B, and record in time-order the difference between the two antenna temperatures, $T_A-T_B$, which is called the time-order data (TOD)." + The observed CMD signal is contaminated by Doppler effect induced by the joint motion of the solar svstem and (the spacecraft., The observed CMB signal is contaminated by Doppler effect induced by the joint motion of the solar system and the spacecraft. +" The aroused dipole difference signal can be calculated by where J)=2.725 WIN is the CMD monopole. e is the speed of light. v is the joint velocity. n, and n, are the unit direction vectors of the antenna A and D respectively"," The aroused dipole difference signal can be calculated by where $T_0=2.725$ K is the CMB monopole, $c$ is the speed of light, $\bf{v}$ is the joint velocity, $\bf{n}_{_A}$ and $\bf{n}_{_B}$ are the unit direction vectors of the antenna A and B respectively" +main host.,main host. +" Figure 8 shows the fraction of metals at redshift 3 that was released to gas particles at overdensity ó(z—3) before redshifts z=4,5,6.1,6.8,7.9."," Figure \ref{fig8} shows the fraction of metals at redshift 3 that was released to gas particles at overdensity $\delta(z=3)$ before redshifts $z=4,5,6.1,6.8,7.9$." + The epoch at which a gas element is enriched is clearly a sensitive function of its overdensity at some later time., The epoch at which a gas element is enriched is clearly a sensitive function of its overdensity at some later time. +" The diffuse IGM is typically enriched earlier than high density regions, a trend that is in agreement with the results of and Oppenheimeretal."," The diffuse IGM is typically enriched earlier than high density regions, a trend that is in agreement with the results of and \citet{Oppenheimer11}." +" More than (35%)) of all z=3 metals at(2011).. the average density were synthesized before z—5 (z—6), while newly produced metals are mostly confined to high overdensities."," More than ) of all $z=3$ metals at the average density were synthesized before $z=5$ $z=6$ ), while newly produced metals are mostly confined to high overdensities." + There are two possible causes for this “outside-in” (a term we borrow from Oppenheimeretal. 2011)) enrichment of ErisMC’s CGM: 1) metals released at earlier times into the high-density regions of ErisMC main host and transported into the IGM via galactic winds on timescales that are comparable to the age of the universe at z—3; and metals released at earlier times in dwarf galaxies and 2)shed into the surrounding intergalactic and circumgalactic medium before and/or during infall.," There are two possible causes for this “outside-in"" (a term we borrow from \citealt{Oppenheimer11}) ) enrichment of ErisMC's CGM: 1) metals released at earlier times into the high-density regions of ErisMC main host and transported into the IGM via galactic winds on timescales that are comparable to the age of the universe at $z =3$; and 2) metals released at earlier times in dwarf galaxies and shed into the surrounding intergalactic and circumgalactic medium before and/or during infall." +" Dwarf galaxies are referred to as “nearby dwarfs” if they are still orbiting outside Ry, at z=3, and as “satellite progenitors” if they have been accreted by the main host before redshift 3."," Dwarf galaxies are referred to as “nearby dwarfs"" if they are still orbiting outside $R_{\rm vir}$ at $z=3$, and as “satellite progenitors"" if they have been accreted by the main host before redshift 3." +" To identify the time, location, and source of enrichment of a given gas particle, we define a metal mass-weighted redshift as in Wiersmaetal. (2010):: where Amz, is the metal mass gained by the gas particle in an enrichment event at redshift z;>3, and >>, is the total metal mass of the particle at z=3."," To identify the time, location, and source of enrichment of a given gas particle, we define a metal mass-weighted redshift as in \citet{Wiersma10}: where $\Delta m_{Z,i}$ is the metal mass gained by the gas particle in an enrichment event at redshift $z_i \ge 3$, and $\sum_i \Delta m_{Z,i}$ is the total metal mass of the particle at $z=3$." +" Gas Amz,;particles in ErisMC typically receive metals more than once, with about half of them enriched in more than three events."," Gas particles in ErisMC typically receive metals more than once, with about half of them enriched in more than three events." +" For every enrichment episode we also derive the mass of the satellite or nearby dwarf in which the gas particle resides, M;,; and the distance between the"," For every enrichment episode we also derive the mass of the satellite or nearby dwarf in which the gas particle resides, $M_{h,i}$ and the distance between the" +ENIM and attenuations of 30 arcmin and 30 dB. and 4 degrees and 50 dB. respectively.,"FWHM and attenuations of 30 arcmin and 30 dB, and 4 degrees and 50 dB, respectively." + This convolution produces multiple velocities at cach .X position in the CV.V) positionvelocity diagrams derived from the model. in the same way as multiple velocities arise naturally in the data cube.," This convolution produces multiple velocities at each $X$ position in the $(X,V)$ position--velocity diagrams derived from the model, in the same way as multiple velocities arise naturally in the data cube." + Fig.l shows positionvelocity diagrams for observational data at 39+y50 arcsec. where yo—1.2.3.," \ref{fig-offaxis} shows position–velocity diagrams for observational data at $Y = \pm \, y \times 50$ arcsec, where $y = 1, +2, 3$." + Overlavecd are Derman's best [it models oedietions. convolved with the POCRAO bean function which should. if the model is correct. approximately enclose he observations on every plot.," Overlayed are Berman's best fit model's predictions convolved with the FCRAO beam function which should, if the model is correct, approximately enclose the observations on every plot." + In this. as in all of the comparisons below. the model has been interpolated to it the positions of the observations.," In this, as in all of the comparisons below, the model has been interpolated to fit the positions of the observations." + Although the &eneral rends of the predictions and the observations are similar. he mocel data enclose a narrower range of velocities than he observations and are further from the svstemic velocity han the observations.," Although the general trends of the predictions and the observations are similar, the model data enclose a narrower range of velocities than the observations and are further from the systemic velocity than the observations." + The discrepancies are just as large or greater for models with dillerent. input parameters., The discrepancies are just as large or greater for models with different input parameters. + In xwticular. it is not reasonable to use a smaller. rotation velocity.," In particular, it is not reasonable to use a smaller rotation velocity." + This would help reconcile the predictions of the model. proposed. by Berman (2001) with the data in the central regions. but would predict velocities much too small al distances larger than about 40 arcmin from the centre.," This would help reconcile the predictions of the model proposed by Berman (2001) with the data in the central regions, but would predict velocities much too small at distances larger than about 40 arcmin from the centre." + The same “beard phenomenon is seen in the positionvelocity diagrams of the spiral galaxy. NCC 2403 11 of Schaap ct 22000)., The same `beard' phenomenon is seen in the position--velocity diagrams of the spiral galaxy NGC 2403 1 of Schaap et 2000). + The arguments presented in that xiper conclude that the beard is either caused by a thick veh censity eas laver with a half width at half maxinium (LIWWLIAT) intensity of 500 pe or a lower density [aver with LWLIAL of 1.75 kpe. rotating more slowly than the standard hin clisk.," The arguments presented in that paper conclude that the beard is either caused by a thick high density gas layer with a half width at half maximum (HWHM) intensity of 500 pc or a lower density layer with HWHM of 1.75 kpc, rotating more slowly than the standard thin disk." + Phis conclusion is motivated by ealactic fountain models (Spitzer 1990) in which hot gas from supernova explosions anc galactic winds rises from the disk into the ialo., This conclusion is motivated by galactic fountain models (Spitzer 1990) in which hot gas from supernova explosions and galactic winds rises from the disk into the halo. + As it rises. the gravitational attraction towards the centre of the galaxy lessens. the gas moves outwarcds and. by conservation of angular momentum. its azimuthal velocity decreases.," As it rises, the gravitational attraction towards the centre of the galaxy lessens, the gas moves outwards and, by conservation of angular momentum, its azimuthal velocity decreases." + Thick molecular disks have been seen in CO in the Milkv Way Galaxy (Dame Phaccleus 1994). and the edge.on spiral galaxy NGC SOL (Careia-Burillo et 11992).," Thick molecular disks have been seen in CO in the Milky Way Galaxy (Dame Thaddeus 1994), and the edge–on spiral galaxy NGC 891 (Garcia-Burillo et 1992)." + To recover the small magnitude anc [large range of velocities of the observations of M31. the bulge mocdel of Jerman (2001) is augmented. by the kinematics of a thick disk which has been rotated and inclined to the observer's frame.," To recover the small magnitude and large range of velocities of the observations of M31, the bulge model of Berman (2001) is augmented by the kinematics of a thick disk which has been rotated and inclined to the observer's frame." + Lhe vertical density distribution follows Schaap et ((2000) in taking a Gaussian forni where po and Xo are the density and surface density respectively at z=0. ane co is the vertical scale height of the gas.," The vertical density distribution follows Schaap et (2000) in taking a Gaussian form where $\rho_0$ and $\Sigma_0$ are the density and surface density respectively at $z = 0$, and $z_0$ is the vertical scale height of the gas." + The half width at half maximum intensity στο=1.18 z5.," The half width at half maximum intensity $z_{1/2} = 1.18 \, +z_0$ ." + The intensities at CY.) are convolved in 2D with the function representing the FCRAO beam as described earlier. to produce positionvelocity plots for Y—cg50 arcsec. where y=1.2.3.," The intensities at $(X,Y)$ are convolved in 2D with the function representing the FCRAO beam as described earlier, to produce position–velocity plots for $Y = \pm \, y \times 50$ arcsec, where $y += 1,2,3$." + reffie-fast3d0 compares the observational data with the results from a model with sy=400 pc. the lowest value of the scale height that adequately encloses the vast majority of the observations for Yo750 aremin.," \\ref{fig-fast3d} compares the observational data with the results from a model with $z_0~=~400$ pc, the lowest value of the scale height that adequately encloses the vast majority of the observations for $X > -50$ arcmin." +" For this model. 2,-5 = 472 pc."," For this model, $z_{1/2}$ = 472 pc." + This is very large when compared to the thick disk observed by Dame Thaceleus (1994) in the Milky Wax. for whieh LAWLAL is between 71 ancl 133 pe depencing on position. but smaller than the thick disk of NGC SOL (Garcia-Burillo et 11992). where LAVLIAL is larger than 1 kpe.," This is very large when compared to the thick disk observed by Dame Thaddeus (1994) in the Milky Way, for which HWHM is between 71 and 133 pc depending on position, but smaller than the thick disk of NGC 891 (Garcia-Burillo et 1992), where HWHM is larger than 1 kpc." + We now follow Schaap (2000) ancl clrop the implicit asstunption that the thick disk is corotating with the .=0 plane ancl reduce the velocities of the gas where 2σὲ0., We now follow Schaap (2000) and drop the implicit assumption that the thick disk is corotating with the $z~=~0$ plane and reduce the velocities of the gas where $z~\neq~0$. + Velocities parallel to the z axis staw fixed. at zero., Velocities parallel to the $z$ axis stay fixed at zero. + A slow thick disk is implied. by the galactic fountain models. and was also invoked by Swaters et ((1997) to explain the oobservations of NGC SOL., A slow thick disk is implied by the galactic fountain models and was also invoked by Swaters et (1997) to explain the observations of NGC 891. + We take the linear velocity distribution used in both papers: where vo is the velocity in the z=0 plane. > is the velocity lost per kpe and z is the height.," We take the linear velocity distribution used in both papers: where ${\bf v}_0$ is the velocity in the $z = 0$ plane, $\gamma$ is the velocity lost per kpc and $z$ is the height." + By slowing the gas down above and below the plane of the disk. the range of velocities at a particular scale height is extended.," By slowing the gas down above and below the plane of the disk, the range of velocities at a particular scale height is extended." + It can be seen in reffig-slow3d that a similar range of velocities to both the observations and the corotating model is produced. if the scale height is just 200 pe and 5=0.3 Le. the gas loses of its speed. per kpe away from the plane of the disk., It can be seen in \\ref{fig-slow3d} that a similar range of velocities to both the observations and the corotating model is produced if the scale height is just 200 pc and $\gamma = 0.3$ i.e. the gas loses of its speed per kpc away from the plane of the disk. + This implies that στο = 236 pe which is closer to but still lareer than the values quoted for the Milkv. Way in Dame Phackleus (1994) and much smaller than the value. for NGC 891., This implies that $z_{1/2}$ = 236 pc which is closer to but still larger than the values quoted for the Milky Way in Dame Thaddeus (1994) and much smaller than the value for NGC 891. + ὃν including a thick disk. the mocdel initially proposed bv Berman (2001) is able to match. the 3D CO cata of Loinarel et ((1999) reasonably well.," By including a thick disk, the model initially proposed by Berman (2001) is able to match the 3D CO data of Loinard et (1999) reasonably well." + Phe most noticeable discrepancy is found. around Y=+2025 arcmin. S 45 kms a position that the original mocel found. dillicult to account for even along the line of nodes of the disk.," The most noticeable discrepancy is found around $X = +\pm 20-25$ arcmin, $V \sim~-$ 45 km $^{-1}$, a position that the original model found difficult to account for even along the line of nodes of the disk." + Lt is plausible that some vertical or turbulent eas motions not included in our model can account for these remaining discrepancies., It is plausible that some vertical or turbulent gas motions not included in our model can account for these remaining discrepancies. + As mentioned above. galactic fountain models are often invoked to account for thick gaseous disks in the centres of ealaxies.," As mentioned above, galactic fountain models are often invoked to account for thick gaseous disks in the centres of galaxies." + However. they are probably. not justifiable in M31 since it does not harbour à great deal of star. formation.," However, they are probably not justifiable in M31 since it does not harbour a great deal of star formation." + Moreover. whilst the thick disk found by Dame Thacddeus (1994) in the Milkv Way appears to be much fainter in CO than the Galactic mid.plane. the present modelling requires that in M3L it be just as bright.," Moreover, whilst the thick disk found by Dame Thaddeus (1994) in the Milky Way appears to be much fainter in CO than the Galactic mid–plane, the present modelling requires that in M31 it be just as bright." + A plausible alternative follows from the recent work by Martos Cox (1998). who describe many numerical simulations combining magnetic fields. with hvdrodynamies to create postshock regions in which large pressure gradients exist near to the mid.plane causing the gas laver to expand. vertically.," A plausible alternative follows from the recent work by Martos Cox (1998), who describe many numerical simulations combining magnetic fields with hydrodynamics to create postshock regions in which large pressure gradients exist near to the mid–plane causing the gas layer to expand vertically." +" “Phe result is a ""hydraulie jump! in which a build up of gas in the vertica direction. can be seen with scale heights. of hundreds: of WESCOS.", The result is a `hydraulic jump' in which a build up of gas in the vertical direction can be seen with scale heights of hundreds of parsecs. + Another. perhaps more controversial. possibility shoul x» mentioned here.," Another, perhaps more controversial, possibility should be mentioned here." + Prinele et al. (, Pringle et al. ( +2001) contend tha much of the ISM in spiral galaxies is molecular. but. too cold to be easily detectable in CO.,"2001) contend that much of the ISM in spiral galaxies is molecular, but too cold to be easily detectable in CO." + In this view. only he parts of molecular clouds illuminated by newly formec stars are bright in CO.," In this view, only the parts of molecular clouds illuminated by newly formed stars are bright in CO." + The CObright thin disk. coul hen correspond to the thin laver where stars form mos actively. whereas the thick cisk would correspond to the rea otal extent of the molecular laver.," The CO–bright thin disk could then correspond to the thin layer where stars form most actively, whereas the thick disk would correspond to the real total extent of the molecular layer." + Phe existence of large quantities of cold molecular gas in the inner regions of M3, The existence of large quantities of cold molecular gas in the inner regions of M31 +detection limit. so the lighteurve bevond ~120 d i$ a mix of detections and upper bounds whose lo limits are not very. different. [rom the level of some of the last detections.,"detection limit, so the lightcurve beyond $\simeq 120$ d is a mix of detections and upper bounds whose $1\sigma$ limits are not very different from the level of some of the last detections." +" To describe (his lighteurve parametricallv. we fit the data for />τα to a model of the form Fi)=Ab” lor) dy and F(/)=D for !/>¢,."," To describe this lightcurve parametrically, we fit the data for $t > 7$ d to a model of the form $F(t) = A t^{-n}$ for $t < t_b$ and $F(t) = B$ for $t \geq t_b$." + The minima in \-squarecd was found Lor n=L9 and /j120 d: this best-fit model is shown as the solid line in Figure 3.., The minimum in $\chi$ -squared was found for $n = 1.9$ and $t_b \simeq 120$ d; this best-fit model is shown as the solid line in Figure \ref{fig:lc}. +" That A? is reduced by: a value of /, within the span of the data supports our prediction that (he jet Iuninosity should become nearly constant. after an initial period of decline.", That $\chi^2$ is reduced by a value of $t_b$ within the span of the data supports our prediction that the jet luminosity should become nearly constant after an initial period of decline. + To use (he procedure just outlined. we take /=LO d. as that appears to be the point ab which power-law decline begins.," To use the procedure just outlined, we take $t_0 = 10$ d, as that appears to be the point at which power-law decline begins." + Following the results of our fit to the lishteurve. we set lia=120 d. uncertain as that identification may be. and η=1.9 rather than 5/3.," Following the results of our fit to the lightcurve, we set $t_{\rm jet} = 120$ d, uncertain as that identification may be, and $n=1.9$ rather than 5/3." + The difference in (he parameter inferences due {ο the latter choice are probably smaller than the intrinsic error in the method., The difference in the parameter inferences due to the latter choice are probably smaller than the intrinsic error in the method. + Using these numbers. we find and That is. we estimate that the black hole is in the upper range of masses al which tidal disruptions of main sequence stars can occur. aid the penetration factor is «quite modest.," Using these numbers, we find and That is, we estimate that the black hole is in the upper range of masses at which tidal disruptions of main sequence stars can occur, and the penetration factor is quite modest." + The expected mass might be a bit smaller if the stellar mass is less than solar: in (hat case. €c0.2. and © would increase.," The expected mass might be a bit smaller if the stellar mass is less than solar; in that case, $\xi \simeq 0.2$, and $\beta$ would increase." + The luminositv in this flare appears to be dominated by hard X-ravs (photon energies =10 keV) and peaked (in nominal isotropic terms) al ~3x107 erg ! (or perhaps a [actor of a few more when contributions from still harder N-ravs are considered)., The luminosity in this flare appears to be dominated by hard X-rays (photon energies $\gtrsim 10$ keV) and peaked (in nominal isotropic terms) at $\sim 3 \times 10^{47}$ erg $^{-1}$ (or perhaps a factor of a few more when contributions from still harder X-rays are considered). + The constraint on the jet parameters (equ. 24)), The constraint on the jet parameters (eqn. \ref{eq:qbeta}) ) + then becomes, then becomes +LPVs are particularly interesting red giants for two nian reasons.,LPVs are particularly interesting red giants for two main reasons. + Ou the one hand. the brightest LPVs are huninous cnough to be observed at large distances. providing information on the host galaxy (Van Loon ct al.," On the one hand, the brightest LPVs are luminous enough to be observed at large distances, providing information on the host galaxy (Van Loon et al.," + 199983)., 1999a). + On the other laud. although their precise ranges of masses and ages reniadn controversial. if ds clear that they are large enough.," On the other hand, although their precise ranges of masses and ages remain controversial, it is clear that they are large enough." + Thus LPVs are very good tracers of the galactic history., Thus LPVs are very good tracers of the galactic history. + Moreover the final evolution along the AGB. aud peculiarly the carbou surface curichment and the change of the cuvelope chemistry. is very couples.," Moreover the final evolution along the AGB, and peculiarly the carbon surface enrichment and the change of the envelope chemistry, is very complex." + It depends on may factors (as convection. overshooting. internal chemical process. niass-loss. pulsation. etc).," It depends on many factors (as convection, overshooting, internal chemical process, mass-loss, pulsation, etc.)," + the relative effects of wuch depend on the mass and metallicity. among other Tia previous paper (CMoeunessier et al..," the relative effects of which depend on the mass and metallicity, among other In a previous paper (Mennessier et al.," + 2000). hereafter Paper L IHPPARCOS astrometric data and multi-waveleugth photometric 1ieasuremoents of a sauple of 800 LPVs (seniaegular a and b. nregular L aud Mira. with O.S and C spectral types} were analyzed using the LM eorithin (Lavi. Meunuessier et al..," 2000), hereafter Paper I, HIPPARCOS astrometric data and multi-wavelength photometric measurements of a sample of 800 LPVs (semi-regular a and b, irregular L and Mira with O,S and C spectral types) were analyzed using the LM algorithm (Luri, Mennessier et al.," + 1996)., 1996). + VAX and IRAS 12 and 25 huninosities were calibrated.," V,K and IRAS 12 and 25 luminosities were calibrated." + The EM aleorithiu classified the stars according to the ealactic population associated with the initial mass and netallieitv of the stars) and to the circumstellar cuvelope thickuess id expansion., The LM algorithm classified the stars according to the galactic population (associated with the initial mass and metallicity of the stars) and to the circumstellar envelope thickness and expansion. + Several eroups were obtained iu this Classification: Tjose groups were obtained by comiuiie I aud IRÁS results., Several groups were obtained in this classification: These groups were obtained by combining K and IRAS results. + From kinematic properties. the dis- 1 »opulation was fou to be 1-1 10? vy old. disk 2 populaion LS 10? xx old aud the old diss population older tlal S 109 wr. up to 1019 Vr Or even nare.," From kinematic properties, the disk 1 population was found to be 1-4 $10^9$ yr old, disk 2 population 4-8 $10^9$ yr old and the old disk population older than 8 $10^9$ yr, up to $10^{10}$ yr or even more." + An extended disk was assuined to be composed of verv old. metaldeficient sars.," An extended disk was assumed to be composed of very old, metal-deficient stars." +" Tjio lower lins of the main sequence initial mass. Mong were estined to be in the range 2-1. Mi:. Mos. aud 1.15-1M for disk 1. lish 2 and old disk. populations respecively,"," The lower limits of the main sequence initial mass, ${\cal M}_{ms}$, were estimated to be in the range 2-1.4 ${\cal M}_{\sun}$, 1.4-1.15 ${\cal +M}_{\sun}$, and 1.15-1 ${\cal M}_{\sun}$ for disk 1, disk 2 and old disk populations respectively." + Moreover. in paper L statistical estimates were coie to quantify how much eroups axd various variability aud spectral tvpes attract or repel each other.," Moreover, in paper I, statistical estimates were done to quantify how much groups and various variability and spectral types attract or repel each other." + Each star of tje sunple was assigned to a ealac population and its individual Ky aud IRAS 12 aud 25 absolute maguiticleSs Were estinated., Each star of the sample was assigned to a galactic population and its individual K and IRAS 12 and 25 absolute magnitudes were estimated. +" A table with these values is available in electronic orm at CDS 5,They aSO are available in the ASTRID secialized database Iu this paper. we use the exlated Ποάνοια stellar absolute πλαστάτιcle (ON) τουςher with properties of the circulisellar enveOpes (deduced from IRAS absohte lnaeuitides) alc the assigue ealactic population to define an evolutive scenario of simultancous stelar oaxd circuustellhu evohtion of LPVs alone the AsvuptolC Cuan Brauch (ACD)."," A table with these values is available in electronic form at CDS .They also are available in the ASTRID specialized database In this paper, we use the estimated individual stellar absolute magnitudes (K) together with properties of the circumstellar envelopes (deduced from IRAS absolute magnitudes) and the assigned galactic population to define an evolutive scenario of simultaneous stellar and circumstellar evolution of LPVs along the Asymptotic Giant Branch (AGB)." + We ained to link the cπα evohtion your O-vich o παν LPVs or OIL emitters (througi the inernediate states of S and/or Το LPVs) aud he sellar and circtustellar evolution. depenudiug on the σαactic pomulation. Le. on the initial mass. as cisctssed in sect. 2..," We aimed to link the chemical evolution from O-rich to C-rich LPVs or OH emitters (through the intermediate states of S and/or Tc LPVs) and the stellar and circumstellar evolution, depending on the galactic population, i.e. on the initial mass, as discussed in sect. \ref{sec_chemev}." + Iu Sect., In Sect. + 3. we examine the first stages of O-rich LPVs aud their correlatio1 with iniial mass., \ref{sec_gap} we examine the first stages of O-rich LPVs and their correlation with initial mass. + More precisely. we propose and critically study several possible explanations for fje gap observed iu the distribution of O-rich LPVs. separating those wi hand wihout a cireunstellar shell.," More precisely, we propose and critically study several possible explanations for the gap observed in the distribution of O-rich LPVs, separating those with and without a circumstellar shell." +"suppressed by Compton down-scattering, and the intrinsic luminosity must be corrected by a factor e*, where tT=Nyo, and c,=6.65x10? cm? is the Thomson cross-section.","suppressed by Compton down-scattering, and the intrinsic luminosity must be corrected by a factor $e^{\tau}$, where $\tau=N_{\rm H}\sigma_\tau$ and $\sigma_\tau = 6.65 \times 10^{-25}$ $^{2}$ is the Thomson cross-section." + This model provides now a good fit for the 0.5-30 keV spectrum (y?/dof=164/145; see Fig., This model provides now a good fit for the 0.5–30 keV spectrum $\chi^2/\rm{dof}=164/145$; see Fig. + 2 upper panel and Table ] model A)., 2 upper panel and Table 1 model A). +" However, we found a low value of the reflection fraction with respect to this primary absorbed power law component (R« 0.1)."," However, we found a low value of the reflection fraction with respect to this primary absorbed power law component $R<0.1$ )." + This suggests that the line and the hard 2-10 keV spectrum are unlikely to be produced by reflection off cold material., This suggests that the line and the hard 2–10 keV spectrum are unlikely to be produced by reflection off cold material. +" Indeed, the broad band continuum could be also reproduced by a model without the reflected component (see Table 1 model B)."," Indeed, the broad band continuum could be also reproduced by a model without the reflected component (see Table 1 model B)." +" Statistically this model gives a slightly worse fit (y?/dof= 181/146) than the previous one, but it is not able to account for the hardness of the 2-10 keV emission."," Statistically this model gives a slightly worse fit $\chi^2/\rm{dof}=181/146$ ) than the previous one, but it is not able to account for the hardness of the 2–10 keV emission." + In particular clear residuals are present in the 5-10 keV band where the reflected component dominates (see Fig., In particular clear residuals are present in the 5–10 keV band where the reflected component dominates (see Fig. + 2 top panel)., 2 top panel). +" Finally, if we allow the photon index to vary, we found that although the fit improves we again need an unusually hard photon index of the power law component (I=1.207011, Ny24x1x10 cm""; see Table 1 model One of the main results of this observation is that, although we can confirm the presence of a strong Fe line as detected withXMM-Newton,, the centroid of this line is now at 6.67+0.05 keV in the rest frame (EW~0.7 keV; for the model without the reflected component), consistent with He-like Fe."," Finally, if we allow the photon index to vary, we found that although the fit improves we again need an unusually hard photon index of the power law component $\Gamma=1.20^{+0.11}_{-0.04}$, $N_{\rm H}=4\pm 1\times 10^{24}$ $^{-2}$; see Table 1 model One of the main results of this observation is that, although we can confirm the presence of a strong Fe line as detected with, the centroid of this line is now at $ 6.67\pm 0.05 $ keV in the rest frame $EW\sim 0.7$ keV; for the model without the reflected component), consistent with He-like Fe." +" Furthermore, the line appears to be marginally broad (σ=0.12+0.06 keV)."," Furthermore, the line appears to be marginally broad $\sigma=0.12\pm 0.06$ keV)." + The inclusion of the line in the model improves the fit by Ay?=51 for 3 degree offreedom®., The inclusion of the line in the model improves the fit by $\Delta\chi^2= 51$ for 3 degree of. +". However, if we constrain the line to be unresolved the fit is worse only by Ay?=5."," However, if we constrain the line to be unresolved the fit is worse only by $\Delta\chi^2=5$." +" In order to check the energy and the intrinsic width of the Fe line detected in the XIS, we examined the spectra of the ??Fe calibration source lines, which are located on two corners of each XIS."," In order to check the energy and the intrinsic width of the Fe line detected in the XIS, we examined the spectra of the $^{55}$ Fe calibration source lines, which are located on two corners of each XIS." + The calibration source produces lines from Mn Και at 5.899 keV and Mn Kaz at 5.899keV. From the spectrum of the calibration source we found that the line energy is shifted red-wards by about 25," The calibration source produces lines from Mn $ +\mathrm{K}\alpha_{1}$ at 5.899 keV and Mn $ \mathrm{K}\alpha_{2}$ at 5.899keV. From the spectrum of the calibration source we found that the line energy is shifted red-wards by about 25" +period.,period. + To reduce the effects of the dispersion due to the observational conditious. averaging the iaages of each welt turus out to be a crucial step.," To reduce the effects of the dispersion due to the observational conditions, averaging the images of each night turns out to be a crucial step." + The fluctuations due to secing variations have heen corrected for., The fluctuations due to seeing variations have been corrected for. + We associate an error bar with each measurement. and these careful estimates together with the study of possible svstematics are used in the companion papers for the detection of iutriusic huuiuositv variations.," We associate an error bar with each measurement, and these careful estimates together with the study of possible systematics are used in the companion papers for the detection of intrinsic luminosity variations." + This study is the starine poiut for the comprehensive nicroleusimg search described in Paper IL., This study is the starting point for the comprehensive microlensing search described in Paper II. + The οἱ estimates cuter the definition of he selection criteria and constitute an muporant uereieut for mücroleusimg ALonte-C'arlo Smaulatious required to quantity the eficiency of the pixel mucrolensing method., The error estimates enter the definition of the selection criteria and constitute an important ingredient for microlensing Monte-Carlo simulations required to quantify the efficiency of the pixel microlensing method. + The study of the|ckeround of variable stars will be addressed in Paper ΤΠ., The study of the background of variable stars will be addressed in Paper III. +majority of the molecular and atomic gas.,majority of the molecular and atomic gas. + All of the northern massive star forming GMCs with masses of 103 to 10° MM. are covered by the longitude range of our survey (Dame Thaddeus (198530)., All of the northern massive star forming GMCs with masses of $^4$ to $^6$ $_\odot$ are covered by the longitude range of our survey (Dame Thaddeus \cite{1985ApJ...297..751D}) ). + It includes the Galactic Ring at a galactocentric radius of Skkpe. where star formation is particularly intense.," It includes the Galactic Ring at a galactocentric radius of kpc, where star formation is particularly intense." + Indeed. the scale-height for OB stars in our Galaxy is of the order of ppe (Reed (2000)... Elias et al. (200600).," Indeed, the scale-height for OB stars in our Galaxy is of the order of pc (Reed \cite{2000AJ....120..314R}, Elias et al. \cite{2006AJ....132.1052E}) )." + This is a clear indication that much of the massive star formation occurs within the latitude range of our survey., This is a clear indication that much of the massive star formation occurs within the latitude range of our survey. + An unbiased survey was preferred over a survey which targets specitic regions based on. e.g. low-resolution CO maps or galactic radio surveys. for a number of reasons.," An unbiased survey was preferred over a survey which targets specific regions based on, e.g. low-resolution CO maps or galactic radio surveys, for a number of reasons." + An unbiased survey. by its very nature. provides more reliable statistics for a sizeable portion of the Galactic Plane.," An unbiased survey, by its very nature, provides more reliable statistics for a sizeable portion of the Galactic Plane." + Also. the UWISH? survey not only addresses star formation. but also evolved stars: the latter will not necessarily be associated with massive molecular clouds or bright radio sources.," Also, the UWISH2 survey not only addresses star formation, but also evolved stars; the latter will not necessarily be associated with massive molecular clouds or bright radio sources." + Thirdly. given the abundance of high and low mass cores along the Galactic Plane. we assumed that most regions in the survey would contain emission-line sources.," Thirdly, given the abundance of high and low mass cores along the Galactic Plane, we assumed that most regions in the survey would contain emission-line sources." + This assumption was to some extent based on preliminary WFCAM JHK and oobservations of a region that included the well-known high-mass star forming regions 221 and (Davis et al. (2007):, This assumption was to some extent based on preliminary WFCAM JHK and observations of a region that included the well-known high-mass star forming regions 21 and N (Davis et al. \cite{2007MNRAS.374...29D}; + Kumar et al. (2007)))., Kumar et al. \cite{2007MNRAS.374...54K}) ). + In this area (/2881.77... bo440.5 d--222-3kkpe jets. outflows. PDRs and young clusters were identified in separate regions: in the main 221 and NN high mass cores. but also along the western periphery of the NN core wwest of NN) and towards a newly-discovered low mass cloud. dubbed EE. wwest of 221.," In this area $l$, $b$; kpc), jets, outflows, PDRs and young clusters were identified in separate regions: in the main 21 and N high mass cores, but also along the western periphery of the N core west of N) and towards a newly-discovered low mass cloud, dubbed E, west of 21." + These latter regions would not necessarily show up as major features in low resolution dust continuum. radio or CO surveys. and therefore could be missed in a pointed survey of GMCs.," These latter regions would not necessarily show up as major features in low resolution dust continuum, radio or CO surveys, and therefore could be missed in a pointed survey of GMCs." + Of course. there have been numerous other infrared imaging studies of low and high mass star forming regions which reveal an abundance of lline-emission features associated with jets and outflows from YSOs (e.g. Davis Eislófffel (1995): Miralles et al. (1997):," Of course, there have been numerous other infrared imaging studies of low and high mass star forming regions which reveal an abundance of line-emission features associated with jets and outflows from YSOs (e.g. Davis Eislöfffel \cite{1995A&A...300..851D}; ; Miralles et al. \cite{1997ApJ...488..749M};" + Hodapp Davis (20023:: Walawender. ReipurthBally (2009): Ginsburg et al. (2009):," Hodapp Davis \cite{2002ApJ...575..291H}; Walawender, ReipurthBally \cite{2009AJ....137.3254W}; Ginsburg et al. \cite{2009ApJ...707..310G};" + Varricatt et al. (2010):, Varricatt et al. \cite{2010MNRAS.404..661V}; + Buckle et al. (QO0I I»)., Buckle et al. \cite{2011MNRAS.inpress.B}) ). + The GLIMPSE survey itself also hints at the existence of many extended line-emission objects at locations along the Galactic Plane., The GLIMPSE survey itself also hints at the existence of many extended line-emission objects at locations along the Galactic Plane. + Dubbed Extended Green Objects (EGOs}. the of colourthese features may result from enhanced line emission in the SSpitzer-IRAC band (Cyganowski et al. (2008)..," Dubbed Extended Green Objects (EGOs), the colour of these features may result from enhanced line emission in the Spitzer-IRAC band (Cyganowski et al. \cite{2008AJ....136.2391}," + Stecklum et al. (20091)., Stecklum et al. \cite{2009pjc..book..619S}) ). + These are often regarded as pure-rotational wwhich in these extended objects may be associated with outflows from voung stars., These are often regarded as pure-rotational which in these extended objects may be associated with outflows from young stars. + However. there is growing evidence that the observed emission at least in some objects can be alternatively attributed to scattered continuum emission (e.g. Qiu et al. (2008):," However, there is growing evidence that the observed emission at least in some objects can be alternatively attributed to scattered continuum emission (e.g. Qiu et al. \cite{2008ApJ...685.1005Q};" + De Buizer Vacca (2010): Chen et al. (2010)))., De Buizer Vacca \cite{2010AJ....140..196D}; Chen et al. \cite{2010ApJ.submitted.C}) ). + Follow-up observations at higher resolution. like those presented in this paper. are needed to reveal the true nature of these objects.," Follow-up observations at higher resolution, like those presented in this paper, are needed to reveal the true nature of these objects." + The narrow-band images that constitute UWISH2 are being obtained with the Wide-Field Camera (WFCAM. Casali et al. (200731) ," The narrow-band images that constitute UWISH2 are being obtained with the Wide-Field Camera (WFCAM, Casali et al. \cite{2007A&A...467..777C}) )" +at the United Kingdom Infrared Telescope (UKIRT)., at the United Kingdom Infrared Telescope (UKIRT). + The camera uses four Rockwell Hawaii-II (HgCdTe 22048) arrays., The camera uses four Rockwell Hawaii-II (HgCdTe $\times$ 2048) arrays. + The gaps between the four arrays are equivalent to ofσα contiguous area covering 0.75 square degrees on the sky (a WFCAM tile) is imaged by observing at four discrete positions., The gaps between the four arrays are equivalent to of; a contiguous area covering 0.75 square degrees on the sky (a WFCAM tile) is imaged by observing at four discrete positions. + In order to correct for image artifacts. bad pixels. and to fully sample the point spread function. a 22 micro-stepping pattern is repeated at three jitter positions.," In order to correct for image artifacts, bad pixels, and to fully sample the point spread function, a $\times$ 2 micro-stepping pattern is repeated at three jitter positions." + The jitter positions are offset by (specificallyQ7..07::6.47.07:: 9: at each jitter position we microstep with offsets of + (N+1/2 pixels on the IR arrays and an integral number of autoguider pixels)., The jitter positions are offset by (specifically; ); at each jitter position we microstep with offsets of $\pm$ (N+1/2 pixels on the IR arrays and an integral number of autoguider pixels). + This results in a pixel scale of iin the final stacked images., This results in a pixel scale of in the final stacked images. + An exposure time of ss is employed: the total per-pixel integration time is thus ssec., An exposure time of s is employed; the total per-pixel integration time is thus sec. + The images are acquired through a narrow-band filter (AA= ) centred on the 1-OSS¢1) line of molecular hydrogen. at 2.)pim. 22All WFCAM data are reduced by the Cambridge Astronomical Survey Unit (CASU) and are distributed through a dedicated archive hosted by the Wide Field Astronomy Unit (WFAU) in Edinburgh. U.K.. The CASU reduction steps are deseribed in detail by Dye et al. (2006):," The images are acquired through a narrow-band filter $\Delta\lambda =$ ) centred on the S(1) line of molecular hydrogen at $\mu$ m. All WFCAM data are reduced by the Cambridge Astronomical Survey Unit (CASU) and are distributed through a dedicated archive hosted by the Wide Field Astronomy Unit (WFAU) in Edinburgh, U.K.. The CASU reduction steps are described in detail by Dye et al. \cite{2006MNRAS.372.1227D};" + astrometric and photometric calibrations (Hodgkin et al. (2009))), astrometric and photometric calibrations (Hodgkin et al. \cite{2009MNRAS.394..675H}) ) + are. achieved using 2MASS (Skrutskie et al. (2006)..," are achieved using 2MASS (Skrutskie et al. \cite{2006AJ....131.1163S}," + Dye et al. (2006):, Dye et al. \cite{2006MNRAS.372.1227D}; + Hewett et al. (2006)., Hewett et al. \cite{2006MNRAS.367..454H}) ). + Data are then downloaded in bulk from WFAU and are made available (initially only to members of the UWISH2 consortium) via a dedicatedweb-site., Data are then downloaded in bulk from WFAU and are made available (initially only to members of the UWISH2 consortium) via a dedicated. +. However. all data are available directly from WFAU. and are made publicly available without restriction mmonths after they are acquired.," However, all data are available directly from WFAU, and are made publicly available without restriction months after they are acquired." + The same applies to data access via our dedicated web-site., The same applies to data access via our dedicated web-site. + In order to continuum subtract our narrow band images we use the K-band data obtained as part of the UKIDSS GPS (Lucas et al. (2008)))., In order to continuum subtract our narrow band images we use the K-band data obtained as part of the UKIDSS GPS (Lucas et al. \cite{2008MNRAS.391..136L}) ). + The aand K-band images are aligned using the astrometric calibration parameters stored in the file headers and scaled to the same size., The and K-band images are aligned using the astrometric calibration parameters stored in the file headers and scaled to the same size. + The flux scaling between aand K-band is done for each star individually., The flux scaling between and K-band is done for each star individually. + We then determine a map of the median flux scaling factor with a resolution of1’., We then determine a map of the median flux scaling factor with a resolution of. +. This is required since the scaling factor between aand K-band changes for regions with high extinction., This is required since the scaling factor between and K-band changes for regions with high extinction. + To subtract the continuum as accurately as possible. Le. getting the least amount of residuals for stars we also apply a Gaussian smoothing to the image with the better seeing to ensure the same full width half maximum in both images before continuum subtraction.," To subtract the continuum as accurately as possible, i.e. getting the least amount of residuals for stars we also apply a Gaussian smoothing to the image with the better seeing to ensure the same full width half maximum in both images before continuum subtraction." +" Naturally. this process leads to ""negative bowl effects. which can be used to identify K-band reflection nebulae."," Naturally, this process leads to 'negative bowl' effects, which can be used to identify K-band reflection nebulae." + The continuum subtracted images will be made available on our dedicated web-site., The continuum subtracted images will be made available on our dedicated web-site. + Please note. that we have used these images only for the identification of line-emission sources.," Please note, that we have used these images only for the identification of line-emission sources." + They should not be used for photometry., They should not be used for photometry. + To facilitate and simplify the continuum subtraction. we have tiled our survey field in exactly the same way as the GPS.," To facilitate and simplify the continuum subtraction, we have tiled our survey field in exactly the same way as the GPS." + Due to the inclination of the Galactic to the Equatorial Plane. at least fourtiles are required to ensure that all regions with |b|< aare completely covered.," Due to the inclination of the Galactic to the Equatorial Plane, at least fourtiles are required to ensure that all regions with $|b| <$ are completely covered." + Thus. our survey (once completed) will cover a somewhat larger area. with |b]< z: in some regions we will reach as far as|b]= oor [.," Thus, our survey (once completed) will cover a somewhat larger area, with $|b| \le$ ; in some regions we will reach as far as$|b| =$ or ." +8.. Hence. an area of approximately ssquare degrees in total will be imaged.," Hence, an area of approximately square degrees in total will be imaged." +of standard stellar theory.,of standard stellar theory. +magnitude.,magnitude. + We the1 derive the (B-R) color of a given object by compare its magnitudes with its ucighbor stars (with B-R coor from). GSC2 catalog) iu pairs of blue vs redyellow ]dates taken from the sine night or very close iu time (uostlv within a week)., We then derive the (B-R) color of a given object by comparing its magnitudes with its neighbor stars (with B-R color from GSC2 catalog) in pairs of blue vs red/yellow plates taken from the same night or very close in time (mostly within a week). + Each pair of plates eives a (B-R) color of the object at that time., Each pair of plates gives a (B-R) color of the object at that time. + More details are describec in Taug ct al. (, More details are described in Tang et al. ( +20102).,2010a). + We bin some plae pairs close iu time. and plot the color evolution of tje three variables by the red open squares in Fieure 1.," We bin some plate pairs close in time, and plot the color evolution of the three variables by the red open squares in Figure 1." + The color evolution data are limited mainly by the small nuuber of red and vellow plates usually: available., The color evolution data are limited mainly by the small number of red and yellow plates usually available. + Both «105020 aud JO736 are redder when they are fainter. at τσ and 36 level. respectively.," Both J0830 and J0736 are redder when they are fainter, at $\sigma$ and $\sigma$ level, respectively." +" We didu't detect anv color change in J0751, although we do uot have red or vellow plates available duriug its major dinuuiug phase (1930-19L0)."," We didn't detect any color change in J0754, although we do not have red or yellow plates available during its major dimming phase (1930-1940)." + Spectra were acquired with FAST spectrograph on tle, Spectra were acquired with FAST spectrograph on the + z=3 :=0 2%2. 2s3 A (ACDAT) =1 ," $z=3$ $z=0$ $z \approx 2,$ $z \approx 3$ $\Lambda$ $\Lambda$ $\approx 1$ " +Depending on the selection technique and the definition used. about to of the quasars detected in recent surveys show the presence of the broad absorption line (BAL) troughs associated with the emission lines in their rest frame UV spectrum (e.g. Knigge et al. 2008..,"Depending on the selection technique and the definition used, about to of the quasars detected in recent surveys show the presence of the broad absorption line (BAL) troughs associated with the emission lines in their rest frame UV spectrum (e.g. Knigge et al. \cite{kn08}," + Ganguly et al. 2008))., Ganguly et al. \cite{ga08}) ). + These BALs. reminiscent of the P Cygnr-type. profiles seen in the spectra of massive stars. are mainly observed in high ionization lines like and and are sometimes detected in lower ionization species likeim.," These BALs, reminiscent of the P Cygni-type profiles seen in the spectra of massive stars, are mainly observed in high ionization lines like and and are sometimes detected in lower ionization species like." + They reveal strong outflows from quasars (Scargle 1972)). which can reach velocities up to 0.2 € (Foltz et al. 1983)).," They reveal strong outflows from quasars (Scargle \cite{sc72}) ), which can reach velocities up to 0.2 c (Foltz et al. \cite{fo83}) )." + Despite the large number of observations. the physical and geometrical properties of the wind at the origin of the BALs remainlargely unknown (e.g. Brotherton 2007)).," Despite the large number of observations, the physical and geometrical properties of the wind at the origin of the BALs remainlargely unknown (e.g. Brotherton \cite{br07}) )." + Moreover. the distance at which those objects are found (z>1.5. so that is shifted in the optical domain) hampers direct observation of the regions at the origin of the BALs even with the best telescopes presently available.," Moreover, the distance at which those objects are found $z \geq 1.5$, so that is shifted in the optical domain) hampers direct observation of the regions at the origin of the BALs even with the best telescopes presently available." + Thus. all the information we can get about the inner regions of BAL quasars comes mainly from indirect observations.," Thus, all the information we can get about the inner regions of BAL quasars comes mainly from indirect observations." + The first attempts to model the BAL profiles considered the resonant scattering of photons emitted by a continuum source in a spherically symmetric stellar-like wind (e.g. Scargle et al. 1972..," The first attempts to model the BAL profiles considered the resonant scattering of photons emitted by a continuum source in a spherically symmetric stellar-like wind (e.g. Scargle et al. \cite{sc72}," + Surdej Hutsemékkers 1987))., Surdej Hutsemékkers \cite{su87}) ). + However. the growing number of observed spectra displaying a huge variety of line profiles (Korista et al. 1993))," However, the growing number of observed spectra displaying a huge variety of line profiles (Korista et al. \cite{ko93}) )" + revealed the need for other wind models., revealed the need for other wind models. + Facing the diversity of line profiles. Turnshek (1984a)) proposed that BAL quasars could be broadly divided into two samples: those quasars that exhibit smooth P Cyeni-type profiles. and other ones that display an absorption trough that is detached in velocity from the associated weaker and wider emission peak.," Facing the diversity of line profiles, Turnshek \cite{tu84a}) ) proposed that BAL quasars could be broadly divided into two samples: those quasars that exhibit smooth P Cygni-type profiles, and other ones that display an absorption trough that is detached in velocity from the associated weaker and wider emission peak." + These observations indicate that the properties of the wind are more complex than the simple spherically symmetric outflow inferred for stellar winds (Lee Blandford 1997))., These observations indicate that the properties of the wind are more complex than the simple spherically symmetric outflow inferred for stellar winds (Lee Blandford \cite{le97}) ). + However. as emphasized by Turnshek (1984b)). it is very likely that distinct types of BAL QSOs do not exist but are instead different manifestations of the same phenomenon.," However, as emphasized by Turnshek \cite{tu84b}) ), it is very likely that distinct types of BAL QSOs do not exist but are instead different manifestations of the same phenomenon." + The similarities of the emission line. optical continuum. and infrared properties of BAL and non-BAL QSOs (e.g. Weymann et al. [99]..," The similarities of the emission line, optical continuum, and infrared properties of BAL and non-BAL QSOs (e.g. Weymann et al. \cite{we91}," +. Gallagher et al. 1999..," Gallagher et al. \cite{ga99}," + Reichard et al. 2003..," Reichard et al. \cite{re03}," + Gallagher et al. 2007).," Gallagher et al. \cite{ga07}) )," +" as well as the spectropolarimetric observations (e.g. Schmidt Hines 1999., Ogle et al. 1999.."," as well as the spectropolarimetric observations (e.g. Schmidt Hines \cite{sc99}, Ogle et al. \cite{og99}," + Lamy Hutsemékkers 2004)). favor a unification by orientation scheme for the BAL QSOs over the evolutionary scheme (Hazard et al. 1984..," Lamy Hutsemékkers \cite{la04}) ), favor a unification by orientation scheme for the BAL QSOs over the evolutionary scheme (Hazard et al. \cite{ha84}," + Becker et al. 2000))., Becker et al. \cite{be00}) ). + In the unification by orientation scheme. only a fraction (roughly corresponding to the observed fraction of BAL QSOs) of the continuum source is covered by optically thick material producing the broad absorption lines. which suggests a disk- equatorial geometry for the BAL region (e.g. Turnshek 1984a.. Hamann et al. 1993..," In the unification by orientation scheme, only a fraction (roughly corresponding to the observed fraction of BAL QSOs) of the continuum source is covered by optically thick material producing the broad absorption lines, which suggests a disk-like equatorial geometry for the BAL region (e.g. Turnshek \cite{tu84a}, Hamann et al. \cite{ha93}," + Murray et al. 1995..," Murray et al. \cite{mu95}," + Elvis et al. 2000..," Elvis et al. \cite{el00}," + Yamamoto 2002))., Yamamoto \cite{ya02}) ). + Such a geometry is supported by theoretical studies and commonly accepted. since the QSOs are thought to be powered by accretion of matter onto a supermassive black hole in the form of a disk. from which the wind could be launched.," Such a geometry is supported by theoretical studies and commonly accepted, since the QSOs are thought to be powered by accretion of matter onto a supermassive black hole in the form of a disk, from which the wind could be launched." + However. the recent discovery of radio loud BAL QSOs (e.g. Becker et al. 2000))," However, the recent discovery of radio loud BAL QSOs (e.g. Becker et al. \cite{be00}) )" + and subsequent radio variability studies reveal polar outflows in at least some of them (Brotherton et al. 2006..," and subsequent radio variability studies reveal polar outflows in at least some of them (Brotherton et al. \cite{br06}," + Zhou et al. 2006..," Zhou et al. \cite{zh06}," + Ghosh Punsly 2007))., Ghosh Punsly \cite{gh07}) ). + Models combining polar and equatorial components have also been suggested (e.g. Lamy Hutsemékkers 2004)) and evaluated from a theoretical point of view (Pereyra et al. 2004..," Models combining polar and equatorial components have also been suggested (e.g. Lamy Hutsemékkers \cite{la04}) ) and evaluated from a theoretical point of view (Pereyra et al. \cite{pe04}," + Proga et al. 2000..," Proga et al. \cite{pr00}," + Proga 2003.. Proga Kallman 2004)) In this context and given the similarities between typical BAL profiles (e.g. Korista et al. 1993))," Proga \cite{pr03}, Proga Kallman \cite{pr04}) ) In this context and given the similarities between typical BAL profiles (e.g. Korista et al. \cite{ko93}) )" + and the line profiles produced by a two component polart+equatorial wind like the one presented by Bjorkman et al. (1994)).," and the line profiles produced by a two component polar+equatorial wind like the one presented by Bjorkman et al. \cite{bj94}) )," + our goal in this first paper is to determine whether such a simple two-component wind can qualitatively reproduce the various types of line profiles observed among the BAL QSOs., our goal in this first paper is to determine whether such a simple two-component wind can qualitatively reproduce the various types of line profiles observed among the BAL QSOs. + We also try to identify the key ingredients needed to reproduce BAL profiles., We also try to identify the key ingredients needed to reproduce BAL profiles. + In a second paper. we will investigate the effect of microlensing on these profiles. aiming at a realistic interpretation of the spectral differences observed in gravitationally lensed BAL QSOs like HI413+117 (cf.," In a second paper, we will investigate the effect of microlensing on these profiles, aiming at a realistic interpretation of the spectral differences observed in gravitationally lensed BAL QSOs like H1413+117 (cf." + Hutsemékkers et al. 2009)., Hutsemékkers et al. \cite{hu09}) ). + In Sect.2.. we present MCRT. the Monte Carlo radiative transfer code we implemented in order to simulate resonance line profiles in a two-component axisymmetrie wind.," In \ref{sec1}, , we present MCRT, the Monte Carlo radiative transfer code we implemented in order to simulate resonance line profiles in a two-component axisymmetric wind." + In Sect.3 we briefly identify the influence of the wind model parameters, In \ref{parmstud} we briefly identify the influence of the wind model parameters +Lt is worthy of a mention that the model results presented above constitute a first. ancl preliminary step in our computations of globular cluster star formation.,It is worthy of a mention that the model results presented above constitute a first and preliminary step in our computations of globular cluster star formation. + In fact. several aspects are still to be worked out.," In fact, several aspects are still to be worked out." + We now give some examples of these. which our future developments will have ο encompass.," We now give some examples of these, which our future developments will have to encompass." + This paper has presented the results of simulations dedicate to the transverse collapse of shells of eas resulting [rom the sweeping of gaseous GC progenitors by SNeLL, This paper has presented the results of simulations dedicated to the transverse collapse of shells of gas resulting from the sweeping of gaseous GC progenitors by SNeII. + In these simulations. the erowth of an initial perturbation in the shel surface density is followed by solving the linear. perturbec equations of continuity ancl motion for transverse flows in a spherical shell of gas.," In these simulations, the growth of an initial perturbation in the shell surface density is followed by solving the linear perturbed equations of continuity and motion for transverse flows in a spherical shell of gas." + Such a collapse depends on severa parameters. namely the number of SNeLL the backgroun presure. the sound: speed. of the shell gas and the initia conditions of the perturbation (i.e. the number of clumps. the initial perturbecl surface density and velocity anc the corresponding phase cilference).," Such a collapse depends on several parameters, namely the number of SNeII, the background presure, the sound speed of the shell gas and the initial conditions of the perturbation (i.e. the number of clumps, the initial perturbed surface density and velocity and the corresponding phase difference)." + ALL these parameters have been discussed in turn., All these parameters have been discussed in turn. +" The results show that the pressure 27, of the hot. protogalactic background. (17,~101° delwne.cm7. Fall Rees 1985. Murray Lin 1992) and the numbers No of. SNell allowed by the disruption criterion (i.e. smaller than 200. Paper L) can indeed. lead to a successful shell transverse collapse. and thereby to the formation of new stars. assuming some reasonable initial conditions for the perturbation (see Fig."," The results show that the pressure $P_h$ of the hot protogalactic background $P_h \sim 10^{-10}$ $^{-2}$, Fall Rees 1985, Murray Lin 1992) and the numbers $N$ of SNeII allowed by the disruption criterion (i.e. smaller than 200, Paper I) can indeed lead to a successful shell transverse collapse, and thereby to the formation of new stars, assuming some reasonable initial conditions for the perturbation (see Fig." + 8)., 8). + The metallicities achieved in the shells able to. collapse agrees with the metallicity range of Galactic halo GCs. namely. 2.5xFefM]SL.," The metallicities achieved in the shells able to collapse agrees with the metallicity range of Galactic halo GCs, namely, $-2.5 \lesssim {\rm [Fe/H]} \lesssim -1$ ." +" Furthermore. while No and D, determine the metallicity achieved. through self-enrichment. they also control the probability of triggered star formation and the ability of these second generation stars to form a bound GC."," Furthermore, while $N$ and $P_h$ determine the metallicity achieved through self-enrichment, they also control the probability of triggered star formation and the ability of these second generation stars to form a bound GC." + Such a property is the most interesting since it opens the way to the understanding of the halo metallicity distribution functions. for both stars ancl clusters.," Such a property is the most interesting since it opens the way to the understanding of the halo metallicity distribution functions, for both stars and clusters." + ] am grateful to. Richard Sceullaire. for fruitful acyvices and. discussions., I am grateful to Richard Scuflaire for fruitful advices and discussions. +" Supports from Polle dAttraction Interuniversitaire through grant. 5/36. (ΤΟ. Belgium) and. from the European Commission through erant IPMCE-C""E-2000-00132 are gratefully acknowledged."," Supports from Pôlle d'Attraction Interuniversitaire through grant P5/36 (SSTC, Belgium) and from the European Commission through grant HPMT-CT-2000-00132 are gratefully acknowledged." +is not the whole story.,is not the whole story. + Fig., Fig. + shows there is a clear excess of sources with P(x2)<0.1., \ref{fig:nsources_vs_threshold} shows there is a clear excess of sources with $P(\chi_{\rm lc}^2)< 0.1$. +" While we cannot determine whether a particular source’s variation is attributable to measurement errors or true variation, we can compare the number of apparently variable sources to the expected number if only Gaussian measurement errors were present."," While we cannot determine whether a particular source's variation is attributable to measurement errors or true variation, we can compare the number of apparently variable sources to the expected number if only Gaussian measurement errors were present." +" If we conservatively take the ‘expected’ line as the number of non-varying sources, we arrive at an excess of 200 sources, corresponding to a lower limit on the the two-epoch areal density of variable sources at 843 MHz of 0.072deg"," If we conservatively take the `expected' line as the number of non-varying sources, we arrive at an excess of 200 sources, corresponding to a lower limit on the the two-epoch areal density of variable sources at 843 MHz of $0.072 \unit{deg^{-2}}$." +" This would appear to be an underestimate, as the actual number?. of sources with P(x?)<0.2 is substantially less than the expected number, due to over-estimated errors."," This would appear to be an underestimate, as the actual number of sources with $P(\chi_{\rm lc}^2)< 0.2$ is substantially less than the expected number, due to over-estimated errors." +" If we extrapolate the actual number of sources from P(x?.)=0.2, we arrive an an excess of approximately 350 sources with P(x2.)«0.2 at 843 MHz with flux densities between 15 and 100mJybeam~!, which corresponds to a two-epoch areal density of variable sources at 843 MHz of 0.126deg"," If we extrapolate the actual number of sources from $P(\chi_{\rm lc}^2)= 0.2$, we arrive an an excess of approximately 350 sources with $P(\chi_{\rm lc}^2)< 0.2$ at 843 MHz with flux densities between 15 and $\unit{mJy~beam^{-1}}$, which corresponds to a two-epoch areal density of variable sources at 843 MHz of $0.126 \unit{deg^{-2}}$." +" After accounting for completeness of 47 per cent, the areal ?.density rises to 0.268deg in 2 epochs."," After accounting for completeness of 47 per cent, the areal density rises to $0.268 \unit{deg^{-2}}$ in 2 epochs." + A definitive statement? about the number of variable Sources requires a caveat on the time-scale of the variability., A definitive statement about the number of variable sources requires a caveat on the time-scale of the variability. + Our data are not regularly sampled and so we can only make broad statements about variability on time-scales greater than 1 day and less than about 10 years., Our data are not regularly sampled and so we can only make broad statements about variability on time-scales greater than 1 day and less than about 10 years. +" At 843 MHz, our observations are firmly in the strong or refractive regime of interstellar scintillation."," At 843 MHz, our observations are firmly in the strong or refractive regime of interstellar scintillation." + In these conditions ? derives the maximum rate of change of flux of sources with a brightness of Ti»x10’?K at latitudes |b]>10? as giving a range of (dS/dt)maz for a source with a brightness temperature at the inverse Compton limit of between 12.5 and 30 mJy day~!., In these conditions \citet{Rickett86} derives the maximum rate of change of flux of sources with a brightness of $T_{12} \times 10^{12}\unit{K}$ at latitudes $|b| \geq 10\degree$ as giving a range of $(dS/dt)_{max}$ for a source with a brightness temperature at the inverse Compton limit of between 12.5 and 30 mJy $^{-1}$. +" As our data are sparsely sampled in the time domain, this limit is easily satisfied for all of our sources."," As our data are sparsely sampled in the time domain, this limit is easily satisfied for all of our sources." + Some 30 per cent of the variable sources have no optical counterpart., Some 30 per cent of the variable sources have no optical counterpart. +" In the absence of more data, we cannot positively identify these sources."," In the absence of more data, we cannot positively identify these sources." +" Transient emission on characteristic time-scales of less than the full synthesis time is unlikely to be detected by our technique, because a significant change in flux density would result in a distorted synthesised beam for that source, which would result in large errors in a Gaussian fit and ultimately rejection from the analysis."," Transient emission on characteristic time-scales of less than the full synthesis time is unlikely to be detected by our technique, because a significant change in flux density would result in a distorted synthesised beam for that source, which would result in large errors in a Gaussian fit and ultimately rejection from the analysis." +" Therefore, we will omit from our discussion source classes such giant pulsesfrom neutron stars (?) as well as flares from extrasolar planets (?) and fast extragalactic transients (?),, which have time-scales much shorter than 12 h. Also, a source that is constant over 12 h but bright (>100 mJy), or in a region containing bright sources (such as the Galactic plane), is unlikely to be detected due to image artefacts or large formal errors in source fitting."," Therefore, we will omit from our discussion source classes such giant pulsesfrom neutron stars \citep{Hankins03} as well as flares from extrasolar planets \citep{Bastian00} and fast extragalactic transients \citep{lorimer2007bmr}, which have time-scales much shorter than 12 h. Also, a source that is constant over 12 h but bright $>100~\unit{mJy}$ ), or in a region containing bright sources (such as the Galactic plane), is unlikely to be detected due to image artefacts or large formal errors in source fitting." +" Table [d shows 15 sources that satisfied our definition of a transient with a flux density above 14mJybeam"", corresponding to an areal density of transient sources at 843 MHz of 6x107?deg? in 2 epochs."," Table \ref{tab:transients} shows 15 sources that satisfied our definition of a transient with a flux density above $14 \unit{mJy~beam^{-1}}$, corresponding to an areal density of transient sources at 843 MHz of $6 \times 10^{-3} \unit{deg^{-2}}$ in 2 epochs." +" After accounting for completeness of 47 per cent, the areal density rises to 1.3x10?deg? in 2 epochs."," After accounting for completeness of 47 per cent, the areal density rises to $1.3 \times 10^{-2} \unit{deg^{-2}}$ in 2 epochs." +" ? compute a two-epoch areal density of transient sources of l.5deg? above 370pJy at 5GHz and a flux density distribution following $ with y= 1.5, which"," \citet{bower2007sta} compute a two-epoch areal density of transient sources of $1.5 \unit{deg^{-2}}$ above $370 \unit{\mu Jy}$ at $5 \unit{GHz}$ and a flux density distribution following $S^{-\gamma}$ with $\gamma=1.5$ , which" +used is 0.5 mag.,used is 0.5 mag. + This control field may not be far enough from the cluster to derive the field star contribution., This control field may not be far enough from the cluster to derive the field star contribution. + Hf so. we might have oversubtracted the field contribution. obtaining Hatter luminosity functions than true luminosity functions.," If so, we might have oversubtracted the field contribution, obtaining flatter luminosity functions than true luminosity functions." + However. the fraction of the cluster members in this field must be. i£ any. very low. because the surface number density of this region is almost constant with the radius as shown in Fig.," However, the fraction of the cluster members in this field must be, if any, very low, because the surface number density of this region is almost constant with the radius as shown in Fig." + 3., 3. + The luminosity function of the C-region in Fig., The luminosity function of the C-region in Fig. + O(a) increases rapidly up to Vz16.5 mag. and stavs almost Hat for V2»16.5 mae.," 9(a) increases rapidly up to $V\approx 16.5$ mag, and stays almost flat for $V>16.5$ mag." + The luminosity functions of the N-region and the (19Fir)-region are steeper than that of the C-region., The luminosity functions of the N-region and the (R+Fir)-region are steeper than that of the C-region. + A remarkable drop is seen at V=16.2 mag (M=1.5 mag) in the luminosity function of the C-region based on smaller bin size of 0.2 mag in Fig.9(b)., A remarkable drop is seen at $V=16.2$ mag $M_V = 1.5$ mag) in the luminosity function of the C-region based on smaller bin size of 0.2 mag in Fig.9(b). + This corresponds to the main sequence eap described above., This corresponds to the main sequence gap described above. + We have investigated. the structure of NGC 2192. using starcounts., We have investigated the structure of NGC 2192 using starcounts. + We could. not. use the centroid. method. to estimate the centre of this cluster. because this cluster is too sparse.," We could not use the centroid method to estimate the centre of this cluster, because this cluster is too sparse." + So we have used eve-estimate to determine the centre of the cluster to be at the position of CX=465 pixel. )j=930 pixel).," So we have used eye-estimate to determine the centre of the cluster to be at the position of $X = 465$ pixel, $Y=930$ pixel)." + Fig., Fig. + 10 —:lustrates the projected: surface number density profile derived. from counting stars with V«15 mag in the entire CCD field., 10 illustrates the projected surface number density profile derived from counting stars with $V<18$ mag in the entire CCD field. + The magnitude cutoll Or slarcounts was set so that the counts should be [ree of any photometric incompleteness problem., The magnitude cutoff for starcounts was set so that the counts should be free of any photometric incompleteness problem. + Fig., Fig. +" 10 shows hat most of the stars in NGC 2192 are concentrated within he radius of 200 pixel (=100 ). and that the outskirts of he cluster extend out. to about 440 pixel (= 220"") from he centre."," 10 shows that most of the stars in NGC 2192 are concentrated within the radius of 200 pixel $= 100''$ ), and that the outskirts of the cluster extend out to about 440 pixel $=220''$ ) from the centre." + Therefore the approximate size of NGC 2192 is estimated: to be about 440° in Hosdiameterwhich. corresponds o a linear size of 7.5 pe for the distance of NGC 2192 as determined below.," Therefore the approximate size of NGC 2192 is estimated to be about $440''$ in diameter,which corresponds to a linear size of 7.5 pc for the distance of NGC 2192 as determined below." + Figs., Figs. + lland 12show the Vo(D. V)and V.(V.1) color-magnitude diagrams of the measured stars in the observe regions in NGC 2192., 11 and 12 show the $V-(B-V)$ and $V-(V-I)$ color-magnitude diagrams of the measured stars in the observed regions in NGC 2192. + Phe distinguishable features seen in the color-magnitude diagrams of the C-region are: (a) There is a well-defined main sequence the top of which is located a VmI4 mag: (b) There are a group of red giant clump stars αἲ (D.1)2LI and V—142 mag. which are remark by the small box in the figures: and (c) There are a smal number of stars along the locus of the red giant. branch.," The distinguishable features seen in the color-magnitude diagrams of the C-region are: (a) There is a well-defined main sequence the top of which is located at $V \approx 14$ mag; (b) There are a group of red giant clump stars at $(B-V)=1.1$ and $V=14.2$ mag, which are remarked by the small box in the figures; and (c) There are a small number of stars along the locus of the red giant branch." + NGC 2192 is located. 11 degrees above the galactic plane in the anti-galactic centre direction (b=107.64 and 737.41) but higher than NGC 1798 so that it is expected that the reddening toward this cluster is significant but smaller than that of NGC 179s., NGC 2192 is located 11 degrees above the galactic plane in the anti-galactic centre direction $b=10^\circ.64$ and $l=173^\circ.41$ ) but higher than NGC 1798 so that it is expected that the reddening toward this cluster is significant but smaller than that of NGC 1798. + We have estimated the reddening for NGC 2192 using two methods as applied. for NGC 1798., We have estimated the reddening for NGC 2192 using two methods as applied for NGC 1798. + First we have used the mean color of the red. giant ‘lump., First we have used the mean color of the red giant clump. + “Phe mean color of the red. giant clump in the is estimated to be (pees=LOSEO01 (V=LOTEOOL and (C—Bypee=0.61£0.02). and 16 corresponding mean magnitude is Vee=14:20x0.05.," The mean color of the red giant clump in the C-region is estimated to be $(B-V)_{RGC}=1.08 \pm 0.01$ $(V-I)_{RGC}=1.07 \pm 0.01$ , and $(U-B)_{RGC}=0.61\pm0.02$ ), and the corresponding mean magnitude is $V_{RGC} = 14.20 \pm 0.05$." +r V. ds estimated to be 0.6250.2. which is similar to the value erived by Phelps ct ((1994).," $\delta V$ is estimated to be $0.6\pm 0.2$, which is similar to the value derived by Phelps et (1994)." + From these data we have erived a value of the reddening. (5132—019£0.03.," From these data we have derived a value of the reddening, $E(B-V) = 0.19 \pm 0.03$." + Secondly we have used the color-color diagram to estimate the reddening and the metallicity simultaneously., Secondly we have used the color-color diagram to estimate the reddening and the metallicity simultaneously. + We have fitted the mean colors of the stars in the C-region with the color-color relation used in the Padova isochrones Bertellietal.1994)., We have fitted the mean colors of the stars in the C-region with the color-color relation used in the Padova isochrones \cite{ber94}. +.. Eig., Fig. + 13 illustrates the results of fitting inthe (0.D)(B13 color-color diagram., 13 illustrates the results of fitting in the $(U-B)-(B-V)$ color-color diagram. + It is shown in this figure that the stars in NGC 2192 are reasonably itted by the color-color relation of the isochrones for. F1] =0.31£0.15 dex with a reddening value of 0Y)—21 0.01., It is shown in this figure that the stars in NGC 2192 are reasonably fitted by the color-color relation of the isochrones for [Fe/H] $= -0.31 \pm 0.15$ dex with a reddening value of $E(B-V)=0.21 \pm 0.01$ . + Phe error for the metallicity. 0.15. was estimated w comparing isochrones with different metallicities.," The error for the metallicity, 0.15, was estimated by comparing isochrones with different metallicities." + As a reference the mean locus of the giant. for solar abundance given by Schmidt-Ixaler is also plotted in Fig., As a reference the mean locus of the giant for solar abundance given by Schmidt-Kaler is also plotted in Fig. + 13., 13. + Finally we derive à mean value of the two estimates for the reddening. οV)=0.2030.05.," Finally we derive a mean value of the two estimates for the reddening, $E(B-V) = 0.20 \pm 0.03$." + We have estimated. the distance to NGC 2192 using two methods as for NGC 1798., We have estimated the distance to NGC 2192 using two methods as for NGC 1798. + First we have used the mean magnitude of the red giant clump., First we have used the mean magnitude of the red giant clump. + We have derived a value of the apparent distance modulus 0A)=13.61+£0.10 from the values for the mean magnitudes of the red giant clump stars described. previously., We have derived a value of the apparent distance modulus $(m-M)_V = 13.61 \pm 0.10$ from the values for the mean magnitudes of the red giant clump stars described previously. + Secondly we have used the ZAAIS fitting., Secondly we have used the ZAMS fitting. + Before the ZANMS fitting. we subtractecl statistically the contribution due to the field stars in the CMDs of the C-reeion using the CMDs of the E-region.," Before the ZAMS fitting, we subtracted statistically the contribution due to the field stars in the CMDs of the C-region using the CMDs of the F-region." + The size of the bin used for the subtraction is NY=0.25 and ACBY)—0I., The size of the bin used for the subtraction is $\Delta V = 0.25$ and $\Delta (B-V) = 0.1$. + The resulting CALDs are clisplaved in Fig., The resulting CMDs are displayed in Fig. + 14., 14. + We used the metallicity of ο) = O31 as derived. before. and adopted Y-—0.28., We used the metallicity of [Fe/H] = –0.31 as derived before and adopted $Y=0.28$. + Using this method. we have obtained a value of the apparent. distance modulus. (nAl\y=19.1€ 0.2., Using this method we have obtained a value of the apparent distance modulus $(m-M)_V = 13.1 \pm 0.2$ . + Finally we caleulate a mean value of the two estimates. (i.AL)=13.350.2.," Finally we calculate a mean value of the two estimates, $(m-M)_V = 13.3 \pm 0.2$." + Adopting the extinction law of Ay=BPEV). we derive a value of the intrinsic distance modulus GrAL)y=12.7£0.2.," Adopting the extinction law of $A_V = 3.2 E(B-V)$, we derive a value of the intrinsic distance modulus $(m-M)_0 = 12.7 \pm 0.2$." + This corresponds to a distance of d=3.53:0.3 kpc., This corresponds to a distance of $d=3.5\pm 0.3$ kpc. + We have estimated the age of NGC 2192 using two methods as follows., We have estimated the age of NGC 2192 using two methods as follows. + First we have used the morphological age index., First we have used the morphological age index. + From the value of 9Y derived above. 0.60.2 mag. we obtain a value for the age. ALAL =1.140.2 Gyes.," From the value of $\delta V$ derived above, $0.6\pm0.2$ mag, we obtain a value for the age, MAI $= 1.1\pm0.2$ Gyrs." + Secondly we have estimated the age of the cluster using the theoretical isochrones given by the Padova group (Bertellietal. 1994)., Secondly we have estimated the age of the cluster using the theoretical isochrones given by the Padova group \cite{ber94}. . +"The diagonal elements of the Ricci tensor f,=qRag;j, ake nonzero while the off-diagonal ones are zero.","The diagonal elements of the Ricci tensor $R_{\mu\nu} = g^{\alpha\beta} +R_{\alpha\mu\beta\nu}$ are nonzero while the off-diagonal ones are zero." +" 2= ESTE = = ign-- Πω. |Sgn Do= (( \2) | jg""? (t ERNJj Eus L176)⋅−⋅ Thecurvature /2=IP, is given as follows: ", = ] F_0 = = = ] F_x = ( )^2 ] + ( )^2 ] F_r Thecurvature $R = R^{\lambda}_{\;\;\lambda}$ is given as follows: R = F_0 + 3F_x + F_r. +Lastly we come to the invariant --, Lastly we come to the invariant =. +"gg""rgnallo(78) For the background metric this reduces toRP ον P9) which can be written as = 9P (Gaὑπ ) 3,29re Y) 439 (t P D» "" (Gu PEP", For the background metric this reduces to = 2 )^2 which can be written as = 3 ( )^2 + 3 )^4 + 3 ( )^2 ] )^2 + ( )^2 ] )^2 . +"where n, aud yy are dimensionless parameters which define the relative strengths of the poloidal and toroidal components respectively.",where $\eta_p$ and $\eta_t$ are dimensionless parameters which define the relative strengths of the poloidal and toroidal components respectively. + Ehe function 7(a) takes the form 3(a)=(a1Yy fora xzLand (0)20 elsewhere. conlining the toroidal field to the region where a exceeds unity. the value taken by a at (0:8)=(1.7/2): the current density goes continuously to zero at this boundary.," The function $\beta(\alpha)$ takes the form $\beta(\alpha)=(\alpha-1)^2$ for $\alpha\geqslant 1$ and $\beta(\alpha)=0$ elsewhere, confining the toroidal field to the region where $\alpha$ exceeds unity, the value taken by $\alpha$ at $(r,\theta)=(1,\pi/2)$; the current density goes continuously to zero at this boundary." + The flux function a(r0) is taken to be f(r)sin?&.," The flux function $\alpha(r,\theta)$ is taken to be $f(r)\sin^2\theta$." + Note that this particular form of a(r.0) is only applicable when we try to match our field to an external dipole: other multipoles match dilferent 6-dependences.," Note that this particular form of $\alpha(r,\theta)$ is only applicable when we try to match our field to an external dipole; other multipoles match different $\theta$ -dependences." + The radial dependence ofa is given by The function. f(r) is postulated to be of this form to ensure that the field described by I2qs. (, The radial dependence of $\alpha$ is given by The function $f(r)$ is postulated to be of this form to ensure that the field described by Eqs. ( +1)(2) is continuous with a dipole field outside the star. that there are no surface currents. and that the current density is finite at the origin for à more thorough derivation. sec Aketinetal. (2011)]].,"1)–(2) is continuous with a dipole field outside the star, that there are no surface currents, and that the current density is finite at the origin [for a more thorough derivation, see \citet{aetal11}] ]." + A schematic diagram of the field is shown in Eig. 1., A schematic diagram of the field is shown in Fig. \ref{field}. +7 It represents just one possibility amongst many. chosen for simplicity and mathematical convenience: possible configurations involving higher multipoles are not ruled out hy observations 2002).," It represents just one possibility amongst many, chosen for simplicity and mathematical convenience; possible configurations involving higher multipoles are not ruled out by observations \citep{a93,tlk02}." +. We now caleulate the small changes dp and dp to the pressure and density of a star in hyelrostatic equilibrium caused by this field. whieh satisfy the force balance equation (Ioasson&Pethick1977:AketinWas," We now calculate the small changes $\delta p$ and $\delta\rho$ to the pressure and density of a star in hydrostatic equilibrium caused by this field, which satisfy the force balance equation \citep{ep77,aw08} + In Eq. (" +serman2008) In Eq. (3). H=ή is the magnetic intensity. 9 is the eravitational potential (the Cowling approximation has been taken. with 0= 0). and se is the magnetic permeability.,"3), ${\bf{H}}={\bf{B}}/\mu$ is the magnetic intensity, $\Phi$ is the gravitational potential (the Cowling approximation has been taken, with $\delta\Phi=0$ ), and $\mu$ is the magnetic permeability." + Phis allows for à superconducting interior (where ji is smaller than the vacuum permeability jo). às analysed in Sec.," This allows for a superconducting interior (where $\mu$ is smaller than the vacuum permeability $\mu_0$ ), as analysed in Sec." + 3., 3. + The assumption that the changes to density and pressure are small enough that they can be treated as perturbations on the steady state is justified., The assumption that the changes to density and pressure are small enough that they can be treated as perturbations on the steady state is justified. +posterior’... EMipticity is then calculated from the perturbecl density., Ellipticity is then calculated from the perturbed density. + Again. the non-barotropic assumption is essential.," Again, the non-barotropic assumption is essential." + Lf barotropy is assumed. instead. pressure must be a function of density only. to all orders: arestriction is then imposed on the magnetic field configuration. because the poloical and toroidal components must be related in such a way that ép is purely a function of op e.g.. Haskelletal. (2008)... (2009).. and. Ciolfi.Ferrari.&Gualtieri (2010)]].," If barotropy is assumed instead, pressure must be a function of density only, to all orders; arestriction is then imposed on the magnetic field configuration, because the poloidal and toroidal components must be related in such a way that $\delta p$ is purely a function of $\delta\rho$ [e.g., \citet{hetal08}, , \citet{lj09}, and \citet{cfg10}] ]." +" For the initial unperturbed hydrostatie equilibrium. we adopt a parabolic density. profile PSP where p,=15A/(Szdri) is the density at the core. Ad, is the mass of the star. and. £, is the radius of the star."," For the initial unperturbed hydrostatic equilibrium, we adopt a parabolic density profile _c where $\rho_c=15\mstar/(8\pi\rstar^3)$ is the density at the core, $\mstar$ is the mass of the star, and $\rstar$ is the radius of the star." + While this is one particular. simple choice of density profile. chosen to render the calculations tractable. we showed in Sec.," While this is one particular, simple choice of density profile, chosen to render the calculations tractable, we showed in Sec." + 3.3 of Alastranoetal.(2011) that the resulting ellipticity is within of that obtained using the more common n»=1 polytrope., 3.3 of \citet{metal11} that the resulting ellipticity is within of that obtained using the more common $n=1$ polytrope. + We define the parameter A as the ratio of poloidal field. energy. to total field. energy., We define the parameter $\Lambda$ as the ratio of poloidal field energy to total field energy. + The energies are obtained. by integrating the squares of the poloidal and total magnetic intensities over the star: note that this definition is slightly cilferent [rom that given by Mastranoetal.2011)... who integrated He over all space.," The energies are obtained by integrating the squares of the poloidal and total magnetic intensities over the star; note that this definition is slightly different from that given by \citet{metal11}, who integrated ${\bf{H}}^2$ over all space." + We have A=1 for a purely poloidal field configuration and A=0 for a purely toroidal configuration., We have $\Lambda=1$ for a purely poloidal field configuration and $\Lambda=0$ for a purely toroidal configuration. +" In terms of A. for a with po=pry. the ellipticity ο takes the form where D, is. the surfaceB magnetic. field⋅ strength at the equator. and A. is. the Solar1 mass."," In terms of $\Lambda$, for a with $\mu=\mu_0$, the ellipticity $\epsilon$ takes the form where $B_{\mathrm{s}}$ is the surface magnetic field strength at the equator, and $M_\odot$ is the Solar mass." + As expected. one finds⋅ €x2By.," As expected, one finds $\epsilon\propto B_\mathrm{s}^2$." + The mass quadrupole moment vanishes for A=0.351. that is. when the poloicdal field energy. is of the total magnetic field energy.," The mass quadrupole moment vanishes for $\Lambda=0.351$, that is, when the poloidal field energy is of the total magnetic field energy." +" Note that both our model and the generalised ""twisted torus! model of Ciolfi.Ferrari.&Cualtieri(2010). predict €4o10P for à canonical ""magnetar-like! neutron star with a purely poloidal field of strength 2,—5«101 T. Armed with Eq. (", Note that both our model and the generalised `twisted torus' model of \citet{cfg10} predict $\epsilon\sim 4\times 10^{-6}$ for a canonical `magnetar-like' neutron star with a purely poloidal field of strength $B_\mathrm{s}=5\times 10^{10}$ T. Armed with Eq. ( +"5). we can use spin-down measurements of D, and eravitational-wave upper limits on ο to constrain A and hence the internal magnetic field for various classes of object.","5), we can use spin-down measurements of $B_{\mathrm{s}}$ and gravitational-wave upper limits on $\epsilon$ to constrain $\Lambda$ and hence the internal magnetic field for various classes of object." + In Fig. 2.. ," In Fig. \ref{eps}, ," +"we plot themost up-to-date LIGO (triangles) and spin-down (dots) gravitational-wave upper limits on the absolute value of¢ for SI knownmillisecond radio pulsars as a function of D, (Abbottetal. 2010)...", we plot themost up-to-date LIGO (triangles) and spin-down (dots) gravitational-wave upper limits on the absolute value of $\epsilon$ for 81 knownmillisecond radio pulsars as a function of $B_\mathrm{s}$ \citep{aetal10}. . + As expected. the indirect," As expected, the indirect" +with the interpretation of the radio emission as gyrosynchrotron radiation.,with the interpretation of the radio emission as gyrosynchrotron radiation. + Assuming that L=R. the electron density is 1.6«10* em.," Assuming that $L=R$, the electron density is $n_e\approx 1.6\times +10^6$ $^{-3}$." + Several conclusions can be drawn from this discussion., Several conclusions can be drawn from this discussion. + First. the magnetic field strength is larger than the average solar field or the magnetic field of Jupiter. but is somewhat lower than the ~| KG fields inferred in some active early M dwarfs (Smithe£Johns-Krull&Valenti1996;Stepanoveral... 2001).," First, the magnetic field strength is larger than the average solar field or the magnetic field of Jupiter, but is somewhat lower than the $\sim 1$ kG fields inferred in some active early M dwarfs \citep{sdj+75,sl85,hsr91,jv96,skz+01}." +". We note however. that the surface magnetic field of mmay be an order of magnitude larger than that inferred for the emission region ifL=Rw|.4R,. placing it in the same range of early M dwarfs."," We note however, that the surface magnetic field of may be an order of magnitude larger than that inferred for the emission region if $L\approx R\approx +1.4R_s$, placing it in the same range of early M dwarfs." + Second. the radio emission. and in particular the high fraction of circular polarization. requires a large-scale. long-lived ordered magnetic field with a large covering fraction.," Second, the radio emission, and in particular the high fraction of circular polarization, requires a large-scale, long-lived ordered magnetic field with a large covering fraction." + This is again similar to the conditions inferred for early M dwarfs (Saar&Linsky1985;Johns-KrullValenti1996).," This is again similar to the conditions inferred for early M dwarfs \citep{sl85,jv96}." +". Finally. the density of emitting electrons is similar to. that inferred in the emission zones (coronae) of early M dwarfs (Stepanoveral,2001:Ostenetaf,2004)."," Finally, the density of emitting electrons is similar to that inferred in the emission zones (coronae) of early M dwarfs \citep{skz+01,oha+04}." +. Thus. the physical conditions in the L3.5 rresemble those found in active early M dwarf. but the Ho and X-ray emission are strongly suppressed.," Thus, the physical conditions in the L3.5 resemble those found in active early M dwarf, but the $\alpha$ and X-ray emission are strongly suppressed." + We finally note that the plasma-beta. ./=2paP/B. of the corona. using 71.6«10° em™. a typical temperature K (Giampapaetaf...1996). and B—175 G. is 3~3« 107°.," We finally note that the plasma-beta, $\beta=2\mu_0P/B^2$ , of the corona, using $n\sim 1.6\times 10^6$ $^{-3}$, a typical temperature $T\sim 2\times 10^6$ K \citep{grk+96}, and $B\sim 175$ G, is $\beta\sim 3\times 10^{-8}$ ." + The typical photospheric pressure of an L dwarf is P~3<10° dyne env? (Burrowserui20010)... resulting in jo2.," The typical photospheric pressure of an L dwarf is $P\sim 3\times 10^5$ dyne $^{-2}$ \citep{bhl+01}, resulting in $\beta\sim 2$." + These conditions are again similar to those found in M dwarfs (Giampapaerαἰ.1996) and the Sun., These conditions are again similar to those found in M dwarfs \citep{grk+96} and the Sun. + Thus. even small perturbations in the coronal field of aare capable of supporting the pressure gradients produced by the radio-emitting material.," Thus, even small perturbations in the coronal field of are capable of supporting the pressure gradients produced by the radio-emitting material." + The simultaneous radio and X-ray observations allow us for the first time to directly investigate the radio/X-ray correlation in an. L dwarf., The simultaneous radio and X-ray observations allow us for the first time to directly investigate the radio/X-ray correlation in an L dwarf. + Similar observations of coronally active stars (including the Sun) reveal a tight correlation between Lj and Ly (Figure 4:: Guedel&Benz1993: 1994)).," Similar observations of coronally active stars (including the Sun) reveal a tight correlation between $L_R$ and $L_X$ (Figure \ref{fig:gb}; ; \citealt{gb93,bg94}) )." + This correlation holds for both flaring and persistent emission. and for single stars and binary systems.," This correlation holds for both flaring and persistent emission, and for single stars and binary systems." + For M dwarfs the correlation holds to spectral type M7 (Gudeletal1993)., For M dwarfs the correlation holds to spectral type M7 \citep{gsb+93}. +. The persistent emission follows Lj=3«107*L« Hz! (Guedel 1993).. and extends over six orders of magnitude in Ly.," The persistent emission follows $L_R\approx +3\times 10^{-16}L_X$ $^{-1}$ \citep{gb93}, , and extends over six orders of magnitude in $L_R$." + The relation for radio and X-ray flares is non-linear. Lyx1.3<107°L2 Hz! (Benz&Guedel1994).. and holds over eight orders of magnitude in Ly.," The relation for radio and X-ray flares is non-linear, $L_R\propto 1.3\times 10^{-26}L_X^{0.73}$ $^{-1}$ \citep{bg94}, and holds over eight orders of magnitude in $L_R$." +" For wwe find Lyz2.5«10 ere so! Hz! and Ly<9.7«107 erg s!, ", For we find $L_R\approx 2.5\times 10^{13}$ erg $^{-1}$ $^{-1}$ and $L_X<9.7\times 10^{24}$ erg $^{-1}$ . +Thus. Lg/Ly>2.6«1077 Hz! is at least 8600 times higher than predicted by the radio/X-ray correlation (Figure 4)).," Thus, $L_R/L_X\gtrsim +2.6\times 10^{-12}$ $^{-1}$ is at least 8600 times higher than predicted by the radio/X-ray correlation (Figure \ref{fig:gb}) )." + A similar result. from non-simultaneous data. was obtained for the M9.5 brown dwarf LP944-20 (BOL) with a ratio that exceeded the expected value by a factor of 10 (flares) and >8500 (persistent emission).," A similar result, from non-simultaneous data, was obtained for the M9.5 brown dwarf LP944-20 (B01) with a ratio that exceeded the expected value by a factor of $10^4$ (flares) and $>8500$ (persistent emission)." + Similarly. for the M9.5 dwarf 00021-0214 the radio luminosity exceeded the X-ray upper limit by at least a factor of 10° (B02).," Similarly, for the M9.5 dwarf 0021-0214 the radio luminosity exceeded the X-ray upper limit by at least a factor of $10^3$ (B02)." + Thus. the radio anc X-ray luminosities appear to de-correlate over a narrow range in spectral type (between about M7 and M9) and remain uncorrelated at least to mid-L (Figure 4)).," Thus, the radio and X-ray luminosities appear to de-correlate over a narrow range in spectral type (between about M7 and M9) and remain uncorrelated at least to mid-L (Figure \ref{fig:gb}) )." + Incidentally. this is the same range over which both the fraction of Ha ane X-ray active sources and the strength of the activity drop precipitously.," Incidentally, this is the same range over which both the fraction of $\alpha$ and X-ray active sources and the strength of the activity drop precipitously." + The violation of the radio/X-ray correlation is surprising given that the magnetic and emission region properties derived for aare not dissimilar from those found on early M dwarts refsec:gyro))., The violation of the radio/X-ray correlation is surprising given that the magnetic and emission region properties derived for are not dissimilar from those found on early M dwarfs \\ref{sec:gyro}) ). + This suggests that either. the origin of the magnetic field is different than in M dwarfs or the atmospheric conditions are not conducive for the support of a chromosphere and/or a corona., This suggests that either the origin of the magnetic field is different than in M dwarfs or the atmospheric conditions are not conducive for the support of a chromosphere and/or a corona. + The radio/X-ray correlation has been interpreted in. the context of magnetic reconnection., The radio/X-ray correlation has been interpreted in the context of magnetic reconnection. + In this scenario. the flares are produced when coronal magnetic loops reconnect. release energy. and create a current sheet along which ambient electrons are accelerated.," In this scenario, the flares are produced when coronal magnetic loops reconnect, release energy, and create a current sheet along which ambient electrons are accelerated." + The accelerated electrons drive an outflow of hot plasma into the corona as they interact with and heat the underlying chromospheric material., The accelerated electrons drive an outflow of hot plasma into the corona as they interact with and heat the underlying chromospheric material. + The interaction of the outflowing plasma with the electrons produces X-ray emission via the bremsstrahlung process (Neupert1968:Hawleyefal1995;Guedelerαἰ. 1996).," The interaction of the outflowing plasma with the electrons produces X-ray emission via the bremsstrahlung process \citep{neu68,hfs+95,gbs+96}." +. This so-called Neupert effect points to a causal connection between particle acceleration. which ts the source of radio emission. and plasma heating. which results in X-ray emission.," This so-called Neupert effect points to a causal connection between particle acceleration, which is the source of radio emission, and plasma heating, which results in X-ray emission." + Thus. the X-ray thermal energy should simply be related by a constant of proportionality to the integrated radio flux.," Thus, the X-ray thermal energy should simply be related by a constant of proportionality to the integrated radio flux." + Guedel&Benz(1993) discuss this correlation in terms of the relation Le/Lyz1072B2?(afbyro(4a) Hz! where a is the fractional efficiency of accelerating electrons. b is the fraction of coronal energy radiated in X-rays. 7 is the average lifetime of the low-energy electrons. and α is the power law relating the electron lifetime to its energy.," \citet{gb93} discuss this correlation in terms of the relation $L_R/L_X\approx 10^{-22}B^{2.5}(a/b)\tau_0(1+\alpha)$ $^{-1}$, where $a$ is the fractional efficiency of accelerating electrons, $b$ is the fraction of coronal energy radiated in X-rays, $\tau_0$ is the average lifetime of the low-energy electrons, and $\alpha$ is the power law relating the electron lifetime to its energy." + The observed tight correlation suggests that the combination B?(«/b)n is nearly unchanged for a wide range of stars., The observed tight correlation suggests that the combination $B^{2.5}(a/b)\tau_0$ is nearly unchanged for a wide range of stars. +" Since in the case of aand the other radio active late-M and L dwarts Lj/Ly is higher by several orders of magnitude while the inferred value of B is not unusual compared to M dwarfs. this indicates that either the fraction of energy emitted in X-rays. b. is suppressed by a factor of ~I0"". or the typical lifetime of the electrons. 7. is longer by a similar factor."," Since in the case of and the other radio active late-M and L dwarfs $L_R/L_X$ is higher by several orders of magnitude while the inferred value of $B$ is not unusual compared to M dwarfs, this indicates that either the fraction of energy emitted in X-rays, $b$, is suppressed by a factor of $\sim +10^4$, or the typical lifetime of the electrons, $\tau_0$, is longer by a similar factor." + In particular. for «/b of order unity and Bz175 G. we find a mean electron lifetime 7~1 d. In this case. the X-ray emission is suppressed because the electrons do not lose their energy to coronal heating on a sufficiently rapid timescale.," In particular, for $a/b$ of order unity and $B\approx 175$ G, we find a mean electron lifetime $\tau\sim 1$ d. In this case, the X-ray emission is suppressed because the electrons do not lose their energy to coronal heating on a sufficiently rapid timescale." + On the other hand. the violation. of the radio/X-ray correlation may be due to an inefficient. production. of. rays. Le.. a low value of 5.," On the other hand, the violation of the radio/X-ray correlation may be due to an inefficient production of X-rays, i.e., a low value of $b$." + In the case of L dwarfs this may be explained by the increasingly neutral atmospheres and the reduction m the density of tons available for X-ray emission (Mohantyefαἱ.2002)., In the case of L dwarfs this may be explained by the increasingly neutral atmospheres and the reduction in the density of ions available for X-ray emission \citep{mbs+02}. +. However. it is not clear if this can account for the late-M dwarfs LP944-20 and 00021-0214. or for the sudden transition between spectral types M7 and M9.," However, it is not clear if this can account for the late-M dwarfs LP944-20 and 0021-0214, or for the sudden transition between spectral types M7 and M9." + More likely. the reduction in. X-ray luminosity. or the over-production of radio emission. may be related to the magnetic structureacross the atmosphere. chromosphere and corona or efficient trapping of the electrons (1.e.. longlifetime).," More likely, the reduction in X-ray luminosity, or the over-production of radio emission, may be related to the magnetic structureacross the atmosphere, chromosphere and corona or efficient trapping of the electrons (i.e., longlifetime)." + We note that recentradio and X-ray observations of the dM4.5e star EV Lac also reveal a breakdown of the Neupert effect. which Osten interpret in the same context discussed here. namelyefficient trapping or a low value of 5.," We note that recentradio and X-ray observations of the dM4.5e star EV Lac also reveal a breakdown of the Neupert effect, which \citet{oha+04} interpret in the same context discussed here, namelyefficient trapping or a low value of $b$ ." + To this point we have discussed the properties of the integrated radio emission during the entire 7.8 hour, To this point we have discussed the properties of the integrated radio emission during the entire 7.8 hour +The simulations with the same box size are run with the same initial condition.,The simulations with the same box size are run with the same initial condition. + There are three main novel features to our simulations., There are three main novel features to our simulations. +" First. we use the new ""conservative entropy formulation of SPII (Springel&Ποιος2002) which explicitly conserves entropy (in regions without shocks). as well as momentum and energv. even when one allows for Lully adaptive smoothing lengths (seee.g.Llernquist1993)."," First, we use the new “conservative entropy” formulation of SPH \citep{SH02} which explicitly conserves entropy (in regions without shocks), as well as momentum and energy, even when one allows for fully adaptive smoothing lengths \citep[see e.g. ][]{Hern93}." +. ‘Phiis formulation moderates the overcooling problem. present. in earlier. formulations of SPLI (seealsoYoshidaetal.2002:Pearceοἱal.1999:Croftct 2001).," This formulation moderates the overcooling problem present in earlier formulations of SPH \citep[see also][]{Yoshida02, Pearce99, Croft01}." +. Second. highly over-dense gas particles are. treated with an effective sub-vesolution multiphase ISM model. as described by Springel&Llernquist(2003a).," Second, highly over-dense gas particles are treated with an effective sub-resolution multiphase ISM model, as described by \citet{SH03a}." +. In this model. each eas particle represents a statistical mixture of cold clouds and a hot ambient. phase.," In this model, each gas particle represents a statistical mixture of cold clouds and a hot ambient phase." + Cold. clouds. can grow bv radiative cooling. out. of the hot. medium. and form the reservoir of neutral gas for star formation.," Cold clouds can grow by radiative cooling out of the hot medium, and form the reservoir of neutral gas for star formation." + Once star formation takes place. supernova explosions deposit energy into the hot eas. heating the gas and evaporating the cold clouds. transferring cold gas back into the hot phase.," Once star formation takes place, supernova explosions deposit energy into the hot gas, heating the gas and evaporating the cold clouds, transferring cold gas back into the hot phase." + This Feedback establishes a self-regulated evele of star formation., This feedback establishes a self-regulated cycle of star formation. + Third. a phenomenological mocel for galactic winds is implemented.," Third, a phenomenological model for galactic winds is implemented." + In this model. gas particles are stochastically. driven out of the dense star-forming region by assigning an extra momentum in random directions. with a rate and magnitude chosen to reproduce mass-Ioads and wind speeds similar to those observed. (," In this model, gas particles are stochastically driven out of the dense star-forming region by assigning an extra momentum in random directions, with a rate and magnitude chosen to reproduce mass-loads and wind speeds similar to those observed. (" +See Springel&Hernequist(20032) for a detailed discussion. of this method.),See \citet{SH03a} for a detailed discussion of this method.) +" Most of our simulations eniploy a ""strong? wind of speed 4S4kms.+. but for the O3. P3. Q3-runs. we also varied the wind strength to examine the elfect of feedback from galactic winds."," Most of our simulations employ a “strong” wind of speed $484\,{\rm +km\,s^{-1}}$, but for the O3, P3, Q3-runs, we also varied the wind strength to examine the effect of feedback from galactic winds." + The runs with 10h.!Mpe boxes are collectively called the Ὁ-series’. and the resolution is increased from (3 to O4. and to Q5.," The runs with $10\,\himpc$ boxes are collectively called the `Q-series', and the resolution is increased from Q3 to Q4, and to Q5." + Phe other series CD-'and “G-Serics’) extend the strong wind results to larger box sizes and hence lower redshift., The other series (`D-'and `G-Series') extend the strong wind results to larger box sizes and hence lower redshift. + Our naming convention is such that runs of the same moclel (box size and included physics) are designated with the same letter. with an additional number specifving the particle resolution.," Our naming convention is such that runs of the same model (box size and included physics) are designated with the same letter, with an additional number specifying the particle resolution." + Our caleulations include a uniform UV. background radiation feld with a modified Πααταί&Macau(1996) spectrum. where reionisation takes place at z=6 (seeDaveetal.1999) as suggested by the quasar observations (e.g.Beckeretal.2001) and radiative transfer calculations of the impact of the stellar SOUrCeS dn Our simulations on the IGM (e.g.Sokasianetal.2003).," Our calculations include a uniform UV background radiation field with a modified \citet{Haa96} spectrum, where reionisation takes place at $z\simeq 6$ \citep[see][]{Dave99} as suggested by the quasar observations \citep[e.g.][]{Beck01} and radiative transfer calculations of the impact of the stellar sources in our simulations on the IGM \citep[e.g.][]{Sok03}." +. The early reionisation at higher redshift. as suggested. by. the WALAD satellite. should not allect the results presented in this paper because we are mainly dealing with halos with virial temperatures above 107 Why and the infalling eas will raciatively cool even if it was photoionised by the reionisation at 22»10 before falling into the halo (seeSpringel&Llernquist 2003b).," The early reionisation at higher redshift, as suggested by the WMAP satellite, should not affect the results presented in this paper because we are mainly dealing with halos with virial temperatures above $10^4$ K and the infalling gas will radiatively cool even if it was photoionised by the reionisation at $z>10$ before falling into the halo \citep[see][]{SH03b}." +. “Phe radiative cooling and heating rate is computed as described by Ixatzetal.(1996) assuming that the gas is optically thin and in ionisation equilibrium., The radiative cooling and heating rate is computed as described by \citet{Katz96} assuming that the gas is optically thin and in ionisation equilibrium. + The adopted: cosmological parameters of all runs are (Q4.04...σε.h)=(0.3.0.7.0.04.0.9.0.7).," The adopted cosmological parameters of all runs are $(\Om,\Ol,\Ob,\sigma_8, h)= (0.3, 0.7, 0.04, 0.9, 0.7)$." + The simulations were performed. on the Athlon-\LP cluster at the Center for Parallel Astrophysical Computing (CPAC) at the Llarvard-Smithsonian Center for Astrophysics. using a mocified version of the parallel code (Springel.Yoshida&White 2001).," The simulations were performed on the Athlon-MP cluster at the Center for Parallel Astrophysical Computing (CPAC) at the Harvard-Smithsonian Center for Astrophysics, using a modified version of the parallel code \citep{Gadget}." +". We identify, simulated: galaxies às isolated: groups of stars using a simplified variant of the algorithm proposed by Springelοἱal.(2001).", We identify simulated galaxies as isolated groups of stars using a simplified variant of the algorithm proposed by \citet{Spr01}. +. In detail we first compute an adaptively smoothed. barvonic densiv Ποιά for all star ancl gas particles. allowing us to robustly identify centres of individual galaxies as isolated density »eaks.," In detail, we first compute an adaptively smoothed baryonic density field for all star and gas particles, allowing us to robustly identify centres of individual galaxies as isolated density peaks." + We Lin 1e Full extent of these galaxies by processing the eas and star particles in the order of declining density. adding particles one by one to the galaxies.," We find the full extent of these galaxies by processing the gas and star particles in the order of declining density, adding particles one by one to the galaxies." +" Lf all of the 32 nearest neighbours of a particle have lower density. this particle is considered to be à new galaxy ""seed."," If all of the 32 nearest neighbours of a particle have lower density, this particle is considered to be a new galaxy `seed'." + Otherwise. the particle is attached to the galaxy that its nearest. denser neighbour already belongs to.," Otherwise, the particle is attached to the galaxy that its nearest denser neighbour already belongs to." + H£ the two nearest clenser neighbours belong to cillerent galaxies. ancl one of these galaxies has less than 32 particles. these galaxies are merged.," If the two nearest denser neighbours belong to different galaxies, and one of these galaxies has less than 32 particles, these galaxies are merged." + Η the two nearest denser neighbours belong to cdillerent. ealaxies and both of these galaxies have more than 32. particles. then the particle is attached to the larger eroup of the two. leaving the other one intact.," If the two nearest denser neighbours belong to different galaxies and both of these galaxies have more than 32 particles, then the particle is attached to the larger group of the two, leaving the other one intact." + Finally. we restrict. the," Finally, we restrict the" +just obtained. we need to include a probability penalty due to parameter selection.,"just obtained, we need to include a probability penalty due to parameter selection." + This is fixed by performing my MonteCarlo realizations of the cosmic-ray data set. which are drawn from a isotropic distribution but they are also selected in such away that they mimic the events which the Pierre Auger Observatory might detect. due to declination dependence of the exposure.," This is fixed by performing $n_{\rmn{MC}}$ MonteCarlo realizations of the cosmic-ray data set, which are drawn from a isotropic distribution but they are also selected in such a way that they mimic the events which the Pierre Auger Observatory might detect, due to declination dependence of the exposure." + Therefore. the mock. cosmic ray data set assume isotropic Lux but the probability of a given arrival direction (0.9) is proportional to the exposure function of the Auger observatory on that. position (see e.g. 7)).," Therefore, the mock cosmic ray data set assume isotropic flux but the probability of a given arrival direction $\alpha,\delta$ ) is proportional to the exposure function of the Auger observatory on that position (see e.g. \citealt{2006JCAP...01..009C}) )." + The isotropic samples are obtained as usual by generating randoni points on the sphere. i. picking uniformly cistributecl random numbers in. sind and a. so that the number cdensitwy. of points. is. completely homogeneous over the solid angle unit dQ=cosódóoda.," The isotropic samples are obtained as usual by generating random points on the sphere, i.e. picking uniformly distributed random numbers in $\sin\delta$ and $\alpha$, so that the number density of points is completely homogeneous over the solid angle unit $\mathrm{d}\Omega = \cos\delta\mathrm{d}\delta\mathrm{d}\alpha$." + To account for the Auger observed. sky. we accept à random point on the sphere if an uniformly distributed: random number between O and Lis smaller than the relative exposure w normalized. bv its maximum value μις. otherwise this point is rejected.," To account for the Auger observed sky, we accept a random point on the sphere if an uniformly distributed random number between 0 and 1 is smaller than the relative exposure $\omega$ normalized by its maximum value $\omega_{\rmn{max}}$ , otherwise this point is rejected." + According to 2. the relative exposure is In]eiven by:et where A=—35 is the latitude corresponding to the location of the Pierre Auger Observatory. ¢ is given by: (funy=7/3 is the cut in zenith angle @ of the arrival directions applied by Auger). and ἂν is defined as follows: Therefore. if we perform the same exploratory scan in the same wav as in the beginning of this Section. for cach dillerent. set 7 of Monte Carlo generated. arrival directions (i—l1....Dc). we can just count the number of trials ni for which the absolute minimum (over the entire parameter space) of the probability. of isotropic Dux. is lower than the actually observed. minimum. {μμxPasta.," According to \citet{2001APh....14..271S}, the relative exposure is given by: where $\lambda \simeq -35^{\circ}$ is the latitude corresponding to the location of the Pierre Auger Observatory, $\zeta$ is given by: $\theta_{\rmn{max}}=\pi/3$ is the cut in zenith angle $\theta$ of the arrival directions applied by Auger), and $\alpha_m$ is defined as follows: Therefore, if we perform the same exploratory scan in the same way as in the beginning of this Section, for each different set $i$ of Monte Carlo generated arrival directions $(i=1,\ldots,n_{\rmn {MC}})$, we can just count the number of trials $n^*_{\rmn{MC}}$ for which the absolute minimum (over the entire parameter space) of the probability of isotropic flux is lower than the actually observed minimum, $P^i_{\rmn{min}} \leq P_{\rmn{data}}$." + The chance probability of observing £u is (2): We can consider this value as an estimate of the chance probability of correlation due to isotropic lux. as in ?..," The chance probability of observing $P_{\rmn{data}}$ is \citep{2004APh....21..359F}: We can consider this value as an estimate of the chance probability of correlation due to isotropic flux, as in \citet{2008APh....29..188T}." + We performed 10 Monte Carlo realizations of the Auger cosmic rav data set. in order to keep our uncertainties below0.," We performed $10^6$ Monte Carlo realizations of the Auger cosmic ray data set, in order to keep our uncertainties below." +154... The value we obtain for this probability after correcting for parameter selection is the following one: We find that the probability of chance correlation of he highest energy. (££: 55]5eV) Auger events with nearby ealaxies [rom the ? catalogue is around0., The value we obtain for this probability after correcting for parameter selection is the following one: We find that the probability of chance correlation of the highest energy $E>55$ EeV) Auger events with nearby galaxies from the \citet{2004AJ....127.2031K} catalogue is around. +964... Phis small obabilitv. corresponds to a 2.66 correlation between both samples., This small probability corresponds to a $2.6\sigma$ correlation between both samples. + We point out that more than the hall of the 27 Auger events above ££2 55eV. are within 4° of a nearby (D« 10Mpc) galaxy. which made it worth of exploring.," We point out that more than the half of the 27 Auger events above $E>55$ EeV are within $4^{\circ}$ of a nearby $D<10$ Mpc) galaxy, which made it worth of exploring." + Tis result goes along the same direction as the previous studies. inding a hint of violation of isotropy in the Auger sample.," This result goes along the same direction as the previous studies, finding a hint of violation of isotropy in the Auger sample." + Phere are 5 out of 27 correlating events. while only 1.5 should be expected on average in the case of isotropic lux. as the elfective fraction of the sky for the values of he parameters at the minimum is p=0.018.," There are 5 out of 27 correlating events, while only 0.5 should be expected on average in the case of isotropic flux, as the effective fraction of the sky for the values of the parameters at the minimum is $p=0.018$." + Of course he number of correlating events is much lower than he value found by ? (20 out of 27. with 5.6 expected in the case of isotropic Dux). but it should be considered that the elfective [fraction of the sky covered (at the minimum Z4) bv 442 objects in the Vérron-C'etty AGN catalogue with τς0.017 is much larger (ντ 0.21) than the 31 objects with our parameters (p= 0.018).," Of course the number of correlating events is much lower than the value found by \citet{2008APh....29..188T} (20 out of 27, with 5.6 expected in the case of isotropic flux), but it should be considered that the effective fraction of the sky covered (at the minimum $P_{\rmn{data}}$ ) by 442 objects in the Vérron-Cetty AGN catalogue with $z\leq 0.017$ is much larger $p\simeq 0.21$ ) than the 31 objects with our parameters $p=0.018$ )." + The galaxies which correlate with the arrival directions of the cosmic rays. are δές200 (spiral galaxy. twpe SA). Νέας)ΙΡ (Ον2). NCGC5102 (LIED) and NC5128 (832).," The galaxies which correlate with the arrival directions of the cosmic rays, are NGC300 (spiral galaxy type SA), NGC4945 (Sy2), NGC5102 (HII) and NGC5128 (Sy2)." + With exception ofNGC300. they mostly show nuclear activity and both Seyfert galaxies are. included in the ACN catalogue used by 2..," With exception of NGC300, they mostly show nuclear activity and both Seyfert galaxies are included in the AGN catalogue used by \citet{2008APh....29..188T}." + In. particular NGC5128. which is associated with 2 cosmic-ray events. is inside the well known Cen A region.," In particular NGC5128, which is associated with 2 cosmic-ray events, is inside the well known Cen A region." + Thus. it might happen that the correlation we find could. just be inherited bythe correlation. found. by the," Thus, it might happen that the correlation we find could just be inherited bythe correlation found by the" +"The spectra of quasars show a ""Iorest of absorption lines blueward of the Ly-a emission line (Lvnds 1971. Sargent et 11930. Wevmann. Carswell. Smith 1981).","The spectra of quasars show a $``$ forest"" of absorption lines blueward of the $\alpha$ emission line (Lynds 1971, Sargent et 1980, Weymann, Carswell, Smith 1981)." + Observational and theoretical work in recent vears has shown that most of this absorption can be attributed io neutral hydrogen in galaxies ancl large-scale structure along the line of sight (Cen et 11994. Lanzetta et 11995.1996. Zhang et 11995. Hernequist et 11996. Miralda-Escudé et 11996. Di Davidsen 1997. Chen et 11993. Theuns et 11993. Ortiz-Gil et 11999. Iupex. Petry. Flint 1999. Dave et 11999. Brvan et 11999).," Observational and theoretical work in recent years has shown that most of this absorption can be attributed to neutral hydrogen in galaxies and large-scale structure along the line of sight (Cen et 1994, Lanzetta et 1995,1996, Zhang et 1995, Hernquist et 1996, Miralda-Escudé et 1996, Bi Davidsen 1997, Chen et 1998, Theuns et 1998, Ortiz-Gil et 1999, Impey, Petry, Flint 1999, Davé et 1999, Bryan et 1999)." + In aggregate. QSO spectra show an increasing line density. wilh increasing redshift such that LN/dzzx(1.42) (Sargent et 11930. Wevimann. Carswell. Smith 1931. Young et 11982. Murdoch et 11936. Lu. Wolle. Turnshek. 1991. Beehtold 1994. Kim et 11997).," In aggregate, QSO spectra show an increasing line density with increasing redshift such that $dN/dz \propto +(1.+z)^{\gamma}$ (Sargent et 1980, Weymann, Carswell, Smith 1981, Young et 1982, Murdoch et 1986, Lu, Wolfe, Turnshek, 1991, Bechtold 1994, Kim et 1997)." + But the line density within an individual quasar spectrum decreases with proximidiwv to the Ly-a emission line (Wevmann. Carswell. Smith 1931. Murdoch et 11936).," But the line density within an individual quasar spectrum decreases with proximity to the $\alpha$ emission line (Weymann, Carswell, Smith 1981, Murdoch et 1986)." + This is generally thought (o be due to enhanced ionization of neutral hydrogen in the vicinity of the quasar due to ionizing photons from the quasar itself., This is generally thought to be due to enhanced ionization of neutral hydrogen in the vicinity of the quasar due to ionizing photons from the quasar itself. +" This “proximity elect"" can be used to measure the mean intensitv of the UV background. denoted έν) (Carswell et 11987. Bajtlik. Duncan. Ostriker 1988. hereafter BDO)."," This $``$ proximity effect"" can be used to measure the mean intensity of the UV background, denoted $J(\nu_{0})$ (Carswell et 1987, Bajtlik, Duncan, Ostriker 1988, hereafter BDO)." + ον). has been measured al z21.7 bv a variely of authors (BDO. Lu. Wolle. Turnshek 1991. Giallongo et 11993.1996. Dechtold 1994. Williser et 11994. Cristiani οἱ 11995. Fernánndez-Soto et 11995. Lu οἱ 11996. Savaglio et 11997. Cooke et," $J(\nu_{0})$ has been measured at $z > 1.7$ by a variety of authors (BDO, Lu, Wolfe, Turnshek 1991, Giallongo et 1993,1996, Bechtold 1994, Williger et 1994, Cristiani et 1995, Fernánndez-Soto et 1995, Lu et 1996, Savaglio et 1997, Cooke et" +A single illuminating source is assumed for the dusty disk: in this case the red giant.,A single illuminating source is assumed for the dusty disk; in this case the red giant. + Thus. the contribution from the companion in both the heating and shaping processes is not included and cannot be reproduced.," Thus, the contribution from the companion in both the heating and shaping processes is not included and cannot be reproduced." + This drawback may partly explain the difficulty in fitting the spectral energy distribution., This drawback may partly explain the difficulty in fitting the spectral energy distribution. + The binary interactions lead us to consider a different disk geometry., The binary interactions lead us to consider a different disk geometry. + Due to the limited number of baselines. our selection of geometric parameters was restricted.," Due to the limited number of baselines, our selection of geometric parameters was restricted." + We have found an acceptable disk model to fit the observational data. which implies a general agreement in terms of emission and spatial distribution of the bulk of the dust in the core of the system.," We have found an acceptable disk model to fit the observational data, which implies a general agreement in terms of emission and spatial distribution of the bulk of the dust in the core of the system." + Despite this. it is also true that the source is complex. probably engulfing a binary. and that the passive disk model is probably not a good deseription of the reality.," Despite this, it is also true that the source is complex, probably engulfing a binary, and that the passive disk model is probably not a good description of the reality." + This source clearly requires interferometric imaging either with aperture masking techniques (?) or with MATISSE/VLTI (?).., This source clearly requires interferometric imaging either with aperture masking techniques \citep{2006SPIE.6272E.103T} or with MATISSE/VLTI \citep{2008SPIE.7013E..70L}. + Spectrophotometry of the core has shown an intrinsic amount of (high-excitation) iron emission lines ([Fe and2)., Spectrophotometry of the core has shown an intrinsic amount of (high-excitation) iron emission lines \citep[\ion{[Fe}{ and. + This gives an electron temperature for the core ~ 10.000 K and an electron density of 10em? (similartoMz3.?)..," This gives an electron temperature for the core $\sim$ 10,000 K and an electron density of $10^{7}\,\rm cm^{-3}$ \citep[similar to Mz3,][]{2003MNRAS.342..383S}." + As it is mentioned in that work. at such high core densities collisional de-excitation prevails and weak forbidden nitrogen lines in the core are not a surprise.," As it is mentioned in that work, at such high core densities collisional de-excitation prevails and weak forbidden nitrogen lines in the core are not a surprise." + Iron. was found in the northern lobe as well (Fig. 3))., Iron was found in the northern lobe as well (Fig. \ref{fig:spitzer}) ). + ? have also detected iron lines. that have a high ionization potential. evidencing the presence of a particle beam or supersonic shock interface inside M2-9.," \citet{1994ApJ...437..281H} have also detected iron lines that have a high ionization potential, evidencing the presence of a particle beam or supersonic shock interface inside M2-9." + Πα emission from the core is optically thick with broad wings due to scattering (22)..," $\alpha$ emission from the core is optically thick with broad wings due to scattering \citep{1989AJ.....97..476B,0067-0049-147-1-97}." + Polarisation measurements in the optical revealed an elliptical polarisation in the core of M2-9. which was consistent in every observed waveband (namely B. R and D.," Polarisation measurements in the optical revealed an elliptical polarisation in the core of M2-9, which was consistent in every observed waveband (namely B, R and I)." + ? explain this as scattered continuum from the central ionizing source by an extended ionized dusty torus around the core (diameter € 4))., \citet{1984A&A...134..333A} explain this as scattered continuum from the central ionizing source by an extended ionized dusty torus around the core (diameter $\lesssim4$ ). + All this indicates that the illuminatiisi source of M2-9 must be a hot and compact star., All this indicates that the illuminating source of M2-9 must be a hot and compact star. + A lifetime of a planetary nebula is ~ 10.000 years and that of a white dwarf billions of years.," A lifetime of a planetary nebula is $\sim$ 10,000 years and that of a white dwarf billions of years." + Thus. material ejected by what is now the secondary. a white dwarf. is already dissolved in the interstellar medium.," Thus, material ejected by what is now the secondary, a white dwarf, is already dissolved in the interstellar medium." + We expect that the material that composes M2-9 at the moment. originates from what is now the primary. an evolved giant. either an AGB or a post-AGB star.," We expect that the material that composes M2-9 at the moment, originates from what is now the primary, an evolved giant, either an AGB or a post-AGB star." + According to ?. shaping of the ejecta of a tight-waist PN is possible by an aceretion disk around the secondary., According to \citet{2008MNRAS.391.1063A} shaping of the ejecta of a tight-waist PN is possible by an accretion disk around the secondary. + An accretion disk would be bright enough and illuminate part of the disk that has been detected by MIDI., An accretion disk would be bright enough and illuminate part of the disk that has been detected by MIDI. + We believe that the disk found in the core of M2-9. engulfs an evolved star (AGB or post-AGB) and a WD. namely the primary and secondary components of the binary.," We believe that the disk found in the core of M2-9, engulfs an evolved star (AGB or post-AGB) and a WD, namely the primary and secondary components of the binary." + The first one is the main heating source for the dust at ~2 2.500 Le (Table 3)). while the latter obtains its luminosity from an accretion disk. although it is the main ionizing source for the nebula (lighthouse beam).," The first one is the main heating source for the dust at $\sim$ 2,500 $_{\sun}$ (Table \ref{tab:param}) ), while the latter obtains its luminosity from an accretion disk, although it is the main ionizing source for the nebula (lighthouse beam)." + The most probable scenario to explain the observables of ? is that the mass-losing star transfers material onto the secondary at a rate of M.=10° Moyr- at supersonic speeds (5-10kms7!) feeding the aceretion disk of a white dwarf.," The most probable scenario to explain the observables of \citet{1997A&A...319..267S} is that the mass-losing star transfers material onto the secondary at a rate of $\dot{M}_{*}=10^{-6}$ $_{\sun}$ $^{-1}$ at supersonic speeds $\rm{km\,s^{-1}}$ ) feeding the accretion disk of a white dwarf." + A luminosity of ~100 Le was estimated for the ionizing source from radio observations (?).., A luminosity of $\sim$ 100 $_{\sun}$ was estimated for the ionizing source from radio observations \citep{1982MNRAS.198..321P}. +" The following equation by ?. was used in order to calculate accretion luminosities for the white dwarf: where M. is the mass accretion rate. M. is the mass-loss rate of the primary. Myp is the mass of the accreting white dwarf. a is the binary separation and v, is the wind speed."," The following equation by \citet{2004MNRAS.350.1366S} was used in order to calculate accretion luminosities for the white dwarf: where $\dot{M}_{\rm acc}$ is the mass accretion rate, $\dot{M}_{*}$ is the mass-loss rate of the primary, $M_{\rm WD}$ is the mass of the accreting white dwarf, $a$ is the binary separation and $v_{s}$ is the wind speed." + Table 4 displays a range of accretion luminosities Ga GMMwp/Rwp) for different secondary masses for the above-mentioned accretion rates and velocities. assuming a binary separation of 30 AU and a WD radius of 6.000 km.," Table \ref{tab:lumos} displays a range of accretion luminosities $L_{\rm acc}$ $\dot{M}_{\rm acc}M_{\rm WD}/R_{\rm WD}$ ) for different secondary masses for the above-mentioned accretion rates and velocities, assuming a binary separation of 30 AU and a WD radius of 6,000 km." + Our findings confirm a WD mass of 0.6-0.8 Mo. previously suggested by ? and in accordance to ?..," Our findings confirm a WD mass of 0.6–0.8 $_{\sun}$, previously suggested by \citet{2001ApJ...552..685L} and in accordance to \citet{2007A&A...467L..29G}." + We can see that the accretion luminosities. for a wind velocity ~10kms7! aren't high enough to evaporate dust up to 15 AU (inner rim).," We can see that the accretion luminosities for a wind velocity $\sim$ $\rm km\,s^{-1}$ aren't high enough to evaporate dust up to 15 AU (inner rim)." + The cool primary’s luminosity (2.500 La) is sufficient though.," The cool primary's luminosity (2,500 $_{\sun}$ ) is sufficient though." + It has long been believed that M2-9 engulfs a binary system., It has long been believed that M2-9 engulfs a binary system. + The light-house effect is an indirect. but rather convincing evidence of binarity.," The light-house effect is an indirect, but rather convincing evidence of binarity." + The assumption of circularity is based on the fact that no evident acceleration nor deceleration of the lighthouse's angular velocity has been observed to date (R. Corradi. private," The assumption of circularity is based on the fact that no evident acceleration nor deceleration of the lighthouse's angular velocity has been observed to date (R. Corradi, private." +"communication)"". ? have used a typical mass for a white dwarf of 0.6 Mg and 0.8 Mo for a post-AGB star. leading to an orbital separation of 27 AU. assuming a circular orbit."," \citet{2001ApJ...552..685L} have used a typical mass for a white dwarf of 0.6 $_{\sun}$ and 0.8 $_{\sun}$ for a post-AGB star, leading to an orbital separation of 27 AU, assuming a circular orbit." + The VLTI observations of a compact dusty structure impose some constraints. which are not trivial for the interpretation of this system.," The VLTI observations of a compact dusty structure impose some constraints, which are not trivial for the interpretation of this system." + However. these interferometric observations are also limited in the sense that they do not provide any closure phase. nor absolute astrometry as in radio interferometry.," However, these interferometric observations are also limited in the sense that they do not provide any closure phase, nor absolute astrometry as in radio interferometry." + It is therefore not possible to locate precisely the position of the compact dusty structure., It is therefore not possible to locate precisely the position of the compact dusty structure. +"displays the 8 um, uum and wm maps.","displays the $8\,\mu$ m, $\mu$ m and $\mu$ m maps." + We use theDustEM dust model described in Compiégneal.(2010) to analyse the data., We use the dust model described in \citet{compiegne2010} to analyse the data. +" We consolidated the standard four grain populations into three: the Polycyclic Aromatic Hydrocarbons Small Amorphous Carbons representing the Very (PAH),Small Grains (VSG) and we merged Large Amorphous Carbons and Silicates into a single Dig Grains (BG) population."," We consolidated the standard four grain populations into three: the Polycyclic Aromatic Hydrocarbons (PAH), Small Amorphous Carbons representing the Very Small Grains (VSG) and we merged Large Amorphous Carbons and Silicates into a single Big Grains (BG) population." +" Using the (Markwardt IDL minimizationroutine"", we choose to adjust the 2009)following four parameters to fit the observed SED for each pixel: the (i) PAH and (ii) VSG abundances relative to BG, Ypan and Yyso, (iii) the BG opacity, Taq, and Uypas a scaling factor of the “solar neighborhood"" (iv)Mathisetal.(1983) (hereafter MMPS83) exciting radiation field."," Using the \citep{markwardt2009} IDL minimization, we choose to adjust the following four parameters to fit the observed SED for each pixel: the (i) PAH and (ii) VSG abundances relative to BG, $Y_{PAH}$ and $Y_{VSG}$, (iii) the BG opacity, $\tau_{BG}$ , and $U_{MMP83}$ a scaling factor of the “solar neighborhood” \citet{mathis83} (hereafter MMP83) exciting radiation field." +" Self-extinction along the line of sight can be significant at 8um and is accounted for assuming I)=lo,Le” where Jo, is the integrated emissivityand 74 the total dust opacity that is computed from the dust model using ΥΡΑΗ, Yvsc and tga."," Self-extinction along the line of sight can be significant at $\mu$ m and is accounted for assuming $I_\lambda\,=\,I_{0,\lambda}\,\frac{1-e^{-\tau_\lambda}}{\tau_\lambda}$ where $I_{0,\lambda}$ is the integrated emissivityand $\tau_\lambda$ the total dust opacity that is computed from the dust model using $Y_{PAH}$, $Y_{VSG}$ and $\tau_{BG}$." +" Since in this first analysis we do not perform any separation of the components along the line of sight, the derived parameters result from the spatial mixing of different physical conditions."," Since in this first analysis we do not perform any separation of the components along the line of sight, the derived parameters result from the spatial mixing of different physical conditions." +" Fortunately, at 1~59°, we expect only contributions from the Vulpecula star formation region (d~2kkpc) and the Perseus arm (d~8.5kkpc)."," Fortunately, at $l\sim59\degr$, we expect only contributions from the Vulpecula star formation region $\sim$ kpc) and the Perseus arm $\sim$ kpc)." +" We focus on the smallest particles behavior and VSG) and hence, we do not assume any variation(PAH of the BG properties (i.e. rpG/Ng constant)."," We focus on the smallest particles behavior (PAH and VSG) and hence, we do not assume any variation of the BG properties (i.e. $\tau_{BG}/N_H$ constant)." +" In that case and to ease the following discussion, we can convert TBG into the hydrogen column density, Ny, and assume the relative abundances of PAH and VSG, YpAg and Yvsg to be their abundance relative to hydrogen."," In that case and to ease the following discussion, we can convert $\tau_{BG}$ into the hydrogen column density, $N_H$, and assume the relative abundances of PAH and VSG, $Y_{PAH}$ and $Y_{VSG}$ to be their abundance relative to hydrogen." +" Indeed, emissivity and/or abundance of the BG is known to evolve Stepniketal.2003;Désert2008) and can be studied(e.g. using theHerschel data (seeParadisetal.2010) but to take such variations into account is beyond the scope of this paper."," Indeed, emissivity and/or abundance of the BG is known to evolve \citep[e.g.][]{stepnik2003, desert2008} and can be studied using the data \citep[see][]{paradis2010} but to take such variations into account is beyond the scope of this paper." +reffig:spectra illustrates the obtained fitted spectra for two observed SEDs.,\\ref{fig:spectra} illustrates the obtained fitted spectra for two observed SEDs. + The photometric points computed from a modeled spectrum take into account the color corrections., The photometric points computed from a modeled spectrum take into account the color corrections. +" Schematically, the 160, 250, 350 and wm photometric points give constraints on Uyyyps3 and τῃς (Ng) through the BG emission."," Schematically, the 160, 250, 350 and $\mu$ m photometric points give constraints on $U_{MMP83}$ and $\tau_{BG}$ $N_H$ ) through the BG emission." +" The shape of the BG SED depends on Uyypaa as this grain population is at thermal equilibrium, in contrast with the stochastically heated grains (PAH and VSG) whose SED shape is invariant regarding the radiation field intensity (seeDraine&Li2007;Compiégneetal. 2010)."," The shape of the BG SED depends on $U_{MMP83}$ as this grain population is at thermal equilibrium, in contrast with the stochastically heated grains (PAH and VSG) whose SED shape is invariant regarding the radiation field intensity \citep[see][]{draine2007, +compiegne2010}." +". Hence, given UwyMpPsa3 the absolute level of the BG SED constrains Ng."," Hence, given $U_{MMP83}$ the absolute level of the BG SED constrains $N_H$." +" Finally, the 8 and jum constrain the abundances of the two stochastically heated population since the intensity of their emission scales as YxNyUypaa."," Finally, the 8 and $\mu$ m constrain the abundances of the two stochastically heated population since the intensity of their emission scales as $Y \times N_H \times U_{MMP83}$." +" reffig:fitres shows maps of the YpAg, Yvsc, Ng and UwMPsa3 parameters and a map of the product YpAgxNuXxUmrs3- "," \\ref{fig:fitres} shows maps of the $Y_{PAH}$ , $Y_{VSG}$, $N_H$ and $U_{MMP83}$ parameters and a map of the product $Y_{PAH} \times N_H \times U_{MMP83}$ ." +XeeducedS2 for all pixels over these maps., $\chi^2_{reduced}\la2$ for all pixels over these maps. + Ng is given in unit of 102°Ηcm-? and Uypss is dimensionless.," $N_H$ is given in unit of $10^{20}\,H\,cm^{-2}$ and $U_{MMP83}$ is dimensionless." +" YpAg and Yygg are given relative to the value for the diffuse high galactic latitude medium (DHGL, ||= 15°), Mpan/My=7.81075 and Mvsa/My=1.651073 (seeCompiégneetal.2010)."," $Y_{PAH}$ and $Y_{VSG}$ are given relative to the value for the diffuse high galactic latitude medium (DHGL, $|b| \ga 15\degr$ ), $M_{PAH}/M_{H}\,=\,7.8\,10^{-4}$ and $M_{VSG}/M_{H}\,=\,1.65\,10^{-4}$ \citep[see][]{compiegne2010}." +. Notice that Μησα/Μη=9.2510-?.," Notice that $M_{BG}/M_{H}\,=\,9.25\,10^{-3}$." + The uncertainties on these parameters are given as computed inMPFIT from the covariance matrix., The uncertainties on these parameters are given as computed in from the covariance matrix. +" The column density lies between ~1.51033Hcm? for the most diffuse part and 1.11035cm-? toward the dense filamentary structures, with a relativeH uncertainty of ~18%.."," The column density lies between $\sim$$1.5\,10^{22}\,H\,cm^{-2}$ for the most diffuse part and $\sim$$1.1\,10^{23}\,H\,cm^{-2}$ toward the dense filamentary structures, with a relative uncertainty of $\sim$." +" The Uyps3 ranges between ~0.5 and ~1.5 with a relative uncertainty of ~22%,, which is consistent with the absence of young stellar cluster over our field."," The $U_{MMP83}$ ranges between $\sim$ 0.5 and $\sim$ 1.5 with a relative uncertainty of $\sim$ , which is consistent with the absence of young stellar cluster over our field." +" In agreement with the fact that the radiation field is shielded, we see that Uypsa decreases toward the highest column density regions."," In agreement with the fact that the radiation field is shielded, we see that $U_{MMP83} $ decreases toward the highest column density regions." + These Uyps3 and Ng values are in agreement with previous estimates (seeBernardetal. 2010)., These $U_{MMP83}$ and $N_H$ values are in agreement with previous estimates \citep[see][]{bernard2010}. +. YpAg goes from ~1.0 to ~2.0 with a relative uncertainty of ~16%.., $Y_{PAH}$ goes from $\sim$ 1.0 to $\sim$ 2.0 with a relative uncertainty of $\sim$ . +" The obtained Yysq spans a wider range than Yp Ag, going from ~0.5 to ~3.0 but with a relative uncertainty going from ~40% for the highest values to ~60% forthe smallest values."," The obtained $Y_{VSG}$ spans a wider range than $Y_{PAH}$ , going from $\sim$ 0.5 to $\sim$ 3.0 but with a relative uncertainty going from $\sim$ for the highest values to $\sim$ forthe smallest values." + The variations of these parameters over the map are therefore significant., The variations of these parameters over the map are therefore significant. + shows theaveraged SED over the two boxesseen on and illustrate the wide Yygg variations., \\ref{fig:spectra} shows theaveraged SED over the two boxesseen on \\ref{fig:fitres} and illustrate the wide $Y_{VSG}$ variations. +" For the top (bottom) panel spectrum we have (2.5-Ε0.5102?Hcm 2),"," For the top (bottom) panel spectrum we have $N_{H}\,=\, 5.1$$\pm$$0.9\,10^{22} \,H\,cm^{-2}$ $2.5$$\pm$$0.5\,10^{22}\,H\,cm^{-2}$ )," +For the bootstrap analysis. we generated 200 sets of sin; values of equal size to the observed sample (d.c. 9T stars) bv randomly selecting values with replacement frou the list of observed siu; values.,"For the bootstrap analysis, we generated 200 sets of $\sin i$ values of equal size to the observed sample (i.e. 97 stars) by randomly selecting values with replacement from the list of observed $\sin i$ values." + For cach of the 200 sets. a best fit distance was derived using the KS procedure described above.," For each of the 200 sets, a best fit distance was derived using the KS procedure described above." + The resultant distribution of distance estimates is shown in Fie. 10.., The resultant distribution of distance estimates is shown in Fig. \ref{bootstrapfinal}. + We derive a σ confidence range for our distance estimate from the width of the velocity region that encloses 67% of the best-fit distances measured with the bootstrap procedure., We derive a $\sigma$ confidence range for our distance estimate from the width of the velocity region that encloses $67 \%$ of the best-fit distances measured with the bootstrap procedure. + Combining this uucertaintyv estimate with the best fit distance measured in 61.5 vields a distance estimate to NGC 2261 of 91310 pc.," Combining this uncertainty estimate with the best fit distance measured in $\S$ \ref{kolmogorov} + yields a distance estimate to NGC 2264 of $913 \pm 40$ pc." + Our distauce imieasurenient iucludes statistical ucertaintics due to sampling effects. απ calculated above. but also potential systematic errors due to the assuniptious that underlie our models.," Our distance measurement includes statistical uncertainties due to sampling effects, as calculated above, but also potential systematic errors due to the assumptions that underlie our models." +" Factors that could introduce systematic errors iuto our analysis include: the error prescriptions and binary fraction adopted iu our calculation of (sin/),: the esiu; cutoff we imposed on our modeled aud observed siu distributions: biases oei the stellar properties derived for stars as a function of their evolutionary state: aud finallv. the uuderlviug assunptiou of isotropically distributed rotation axes."," Factors that could introduce systematic errors into our analysis include: the error prescriptions and binary fraction adopted in our calculation of $(\sin i)_{m}$; the $v \sin i$ cutoff we imposed on our modeled and observed $\sin i$ distributions; biases in the stellar properties derived for stars as a function of their evolutionary state; and finally, the underlying assumption of isotropically distributed rotation axes." + We consider in turn the potential müpact of cach of these effects on our analysis., We consider in turn the potential impact of each of these effects on our analysis. + The impact of differeut sources of observational error ou the distance deteriunation can be seen im Fie. 9..," The impact of different sources of observational error on the distance determination can be seen in Fig. \ref{ks_errs}," + where we compare the Piss vs. distance relations produced by comparing our observed sample to models that neglect various compoucuts of the sin/ error budget., where we compare the $P_{KS}$ vs. distance relations produced by comparing our observed sample to models that neglect various components of the $\sin i$ error budget. + The solid line represeuts the case where all of the errors are Chosen randomly from the actual error distributions. and the remaining curves represent cases where the errors ina particular variable have been set to 0.," The solid line represents the case where all of the errors are chosen randomly from the actual error distributions, and the remaining curves represent cases where the errors in a particular variable have been set to 0." + It is clear frou Fig., It is clear from Fig. + 9 that the assuued errors have a nou-ucsligible inpact on both the best-fit distance as well as the height of the Piss curve., \ref{ks_errs} that the assumed errors have a non-negligible impact on both the best-fit distance as well as the height of the $P_{KS}$ curve. +" For instance. negating the Iuninosity errors has the effect of reducing the best-fit distance by 1“.. while climinating the Ty, errors iuereases the best- distance by roughly 6%."," For instance, negating the luminosity errors has the effect of reducing the best-fit distance by 4, while eliminating the $T_{eff}$ errors increases the best-fit distance by roughly 6." +". Eliminating the esins errors not only increases the best fit distance by 1%... but also strouely reduces the peak νο, suggesting that the errors In οσαι{ contribute significantly to the shape of the sin/ distribution."," Eliminating the $v +\sin i$ errors not only increases the best fit distance by 4, but also strongly reduces the peak $P_{KS}$, suggesting that the errors in $v \sin i$ contribute significantly to the shape of the $\sin i$ distribution." + To the extent that the error distrbutious we adopt in our model (see 51.3)) do not reflect the true error distributions of our data. our distance estimate will be skewed.," To the extent that the error distributions we adopt in our model (see $\S$ \ref{error_distribution}) ) do not reflect the true error distributions of our data, our distance estimate will be skewed." + As shown above. the error distributions we do adopt are influcucing our derived distance at the level. sugeesting any systematic crror iu our derived distance due to adopting nuproper error cistributious would likely be ~5% as well," As shown above, the error distributions we do adopt are influencing our derived distance at the $\sim$ level, suggesting any systematic error in our derived distance due to adopting improper error distributions would likely be $\sim$ as well." + Our error distributious. however. are consistent with those estimated by other authors for the same parameters. and the error distributions push the derived distance im different directions. such that inultiple svstematic errors should offset one another to some degree.," Our error distributions, however, are consistent with those estimated by other authors for the same parameters, and the error distributions push the derived distance in different directions, such that multiple systematic errors should offset one another to some degree." + Perhaps most Woltisolme is the asvnunetrie shape of the lhuninositv error distribution. but lacking a more robust means of characterizing the lhunünositv errors. we are unable to remove this potential svsteiatic effect from our analysis.," Perhaps most worrisome is the asymmetric shape of the luminosity error distribution, but lacking a more robust means of characterizing the luminosity errors, we are unable to remove this potential systematic effect from our analysis." + Fie., Fig. + ll shows the effect of the assmmed binary fraction on the best fit distance., \ref{ks_binary} shows the effect of the assumed binary fraction on the best fit distance. + As the binary fraction is iuereased. the average lunimositv of the modeled stars ds ducreased. causing the sins distribution to move to lower sin; as per Eq. 6..," As the binary fraction is increased, the average luminosity of the modeled stars is increased, causing the $\sin i$ distribution to move to lower $\sin i$ as per Eq. \ref{sinim}." + In order for the observed sini distribution to remain well matched to the modeled distribution. the assumed distance nist therefore increase according to Eq. 5..," In order for the observed $\sin i$ distribution to remain well matched to the modeled distribution, the assumed distance must therefore increase according to Eq. \ref{siniL}." + Thus. we see that as the modeled binary fraction chauges from B=0.0 to B=0.75. the best-fit distance goes from ~860 pc to 970 pc. a chanee of roughly13%.," Thus, we see that as the modeled binary fraction changes from $B = 0.0$ to $B = 0.75$, the best-fit distance goes from $\sim 860 $ pc to $\sim 970$ pc, a change of roughly." +. This is conusisteut with the results of Jeffries(2007).. who found in lis ONC study that increasing the binary fraction by 0.2 led to a inerease in lis modeled best fit distance.," This is consistent with the results of \citet{Jeffries}, who found in his ONC study that increasing the binary fraction by 0.2 led to a increase in his modeled best fit distance." + Biases in the parameters derived for stars in different evolutionary states could also the results of our analysis., Biases in the parameters derived for stars in different evolutionary states could also the results of our analysis. + As noted by Jeffries(2007).. if may be more difficult to derive accurate temperatures. Iuninosities. aud. thus. radii for classical T Tauri stars than more evolved weak T Tami stars: classical T Tauri stars typically possess Iarger extinctions. are nreeularly variable. aud have siguificaut contributions to their total luminosity from accretion aud re-radiationr2 from their circumstellar disk. all of which can complicate the derivation of their intrinsic stellar properties.," As noted by \citet{Jeffries}, it may be more difficult to derive accurate temperatures, luminosities, and, thus, radii for classical T Tauri stars than more evolved weak T Tauri stars; classical T Tauri stars typically possess larger extinctions, are irregularly variable, and have significant contributions to their total luminosity from accretion and re-radiation from their circumstellar disk, all of which can complicate the derivation of their intrinsic stellar properties." + Following Ladaetal.(2006).. we used au IRAC [3.6 - s] color cut to ideutify classical T Tauri stars in our saunple: eheu these CTTSs are excluded frou our sample. the best fit distauce to NGC 2261 mmereases to ~950 pc.," Following \citet{Lada2006}, we used an IRAC [3.6 - 8] color cut to identify classical T Tauri stars in our sample; when these CTTSs are excluded from our sample, the best fit distance to NGC 2264 increases to $\sim$ 950 pc." + This effect is contrary to that seen bv Jeffries(2007).. who found a decreased best fit distauce to the ONC once CTTSs were excluded from liis sample.," This effect is contrary to that seen by \citet{Jeffries}, who found a decreased best fit distance to the ONC once CTTSs were excluded from his sample." + Cuven these coutracictory results. and that the effect of removing CTTSs from our sample is comparable to the other systematic effects probed here. we have chosen not to exclude CTTSs frou our main analysis.," Given these contradictory results, and that the effect of removing CTTSs from our sample is comparable to the other systematic effects probed here, we have chosen not to exclude CTTSs from our main analysis." + Our technique assumes that all of the stars in NGC 226[ are at the same distance from Earth., Our technique assumes that all of the stars in NGC 2264 are at the same distance from Earth. + Iu reality. the cluster has some line of sight depth. predicted to be," In reality, the cluster has some line of sight depth, predicted to be" +Note that in a similar way one can prove that is no longer true when,Note that in a similar way one can prove that is no longer true when +ruling its dynamics. and extending it to several tens of solar radit. progressively generating. and shaping a circumstellar envelope around coolest objects.,"ruling its dynamics, and extending it to several tens of solar radii, progressively generating, and shaping a circumstellar envelope around coolest objects." + However. to date. the magnetic nature of these shock waves has never been identified or deeply investigated. while since the 60s. theoretical studies of shock waves propagating throughout gaseous media of atmospheric density predict there is an electric field (therefore a magnetic field) in the shock region (see for instance: ? +?); 2)).," However, to date, the magnetic nature of these shock waves has never been identified or deeply investigated, while since the 60s, theoretical studies of shock waves propagating throughout gaseous media of atmospheric density predict there is an electric field (therefore a magnetic field) in the post-shock region (see for instance: \citealt{Jaffrin65} ; \citealt{Lu74} ; \citealt{Vidal95}) )." + Moreover. because of the complexity of the problem. this magnetic nature has never been introduced in shock structure or shock propagation modelling.," Moreover, because of the complexity of the problem, this magnetic nature has never been introduced in shock structure or shock propagation modelling." + Also. its impact on astrophysical processes. such as radial pulsation or chaotic behaviour. atmospheric dynamics. circumstellar envelope formation and structure. mass loss. and grain formation. has never been investigated so far.," Also, its impact on astrophysical processes, such as radial pulsation or chaotic behaviour, atmospheric dynamics, circumstellar envelope formation and structure, mass loss, and grain formation, has never been investigated so far." + In the late 70s. narrow- and broad-band polarimetric observations were performed on cool evolved stars hosting circumstellar envelopes in order to investigate the grain distribution in. stellar environments.," In the late 70s, narrow- and broad-band polarimetric observations were performed on cool evolved stars hosting circumstellar envelopes in order to investigate the grain distribution in stellar environments." + With this technique. in a study devoted to the one-year-period variable Mira. star. omicron Ceti. ? were the first to detect a strongly linear polarized flux in the emission lines of the Balmer series.," With this technique, in a study devoted to the one-year-period variable Mira star, omicron Ceti, \cite{mlc1978} were the first to detect a strongly linear polarized flux in the emission lines of the Balmer series." + Based on just a single observation limited to the maximum luminosity. the polarization in the hydrogen lines (from HB to HIO) was noticed as two to three times greater than the polarization measured in the nearby continumm.," Based on just a single observation limited to the maximum luminosity, the polarization in the hydrogen lines (from $H\beta$ to H10) was noticed as two to three times greater than the polarization measured in the nearby continumm." + To date. this observational fact is still an enigma.," To date, this observational fact is still an enigma." + It has also never been reproduced on any Mira star or on another pulsating star. or even characterized during a complete pulsating cycle.," It has also never been reproduced on any Mira star or on another pulsating star, or even characterized during a complete pulsating cycle." + Moreover. recet modelling of the linear polarization of optical emission in red giants (?)) which investigates light scattering by dust grains in axisymmetric circumstellar envelopes. has even failed to explai such a high polarization rate.," Moreover, recent modelling of the linear polarization of optical emission in red giants \citealt{Fadeyev07}) ) which investigates light scattering by dust grains in axisymmetric circumstellar envelopes, has even failed to explain such a high polarization rate." + Recently. a new generation of instruments has been made available: spectropolarimeters.," Recently, a new generation of instruments has been made available: spectropolarimeters." + Over a large spectral domain. they combine high-resolution spectroscopy and information in polarized light. and they open new observational windows for astrophysical objects. mainly focussing on stellar magnetism.," Over a large spectral domain, they combine high-resolution spectroscopy and information in polarized light, and they open new observational windows for astrophysical objects, mainly focussing on stellar magnetism." + With these instruments. it is now possible to collect spectral information through the four Stokes parameters (V. characterizing circular polarization; Q and U. characterizing linear polarization: L the classical spectrum).," With these instruments, it is now possible to collect spectral information through the four Stokes parameters (V, characterizing circular polarization; Q and U, characterizing linear polarization; I, the classical spectrum)." + ? present spectropolarimetric observations of Post-AGB stars and RV Tauri stars and report. for most of these objects. the detection of linear (Stokes Q and Stokes U) polarimetric signatures associated to the Ha lines.," \cite{Harrington09} present spectropolarimetric observations of Post-AGB stars and RV Tauri stars and report, for most of these objects, the detection of linear (Stokes Q and Stokes U) polarimetric signatures associated to the $H\alpha$ lines." + In most objects. the morphology of the polarization feature presents short timescale variability that suggests the presence of absorbing polarizing gas close to the star. according to the optical pumping model deseribed by ?..," In most objects, the morphology of the polarization feature presents short timescale variability that suggests the presence of absorbing polarizing gas close to the star, according to the optical pumping model described by \cite{Kuhn07}." + Stong mass loss. progressively shaping circumstellar environments. ts very common in these stars. and the shock waves propagating throughout their atmosphere and inducing ballistic motions has also been reported (?.. ?)).," Stong mass loss, progressively shaping circumstellar environments, is very common in these stars, and the shock waves propagating throughout their atmosphere and inducing ballistic motions has also been reported \citealt{Lebre91}, \citealt{Lebre96}) )." + It is thus now possible for the very first time to estimate the linear and the circular polarization evolution in the emission lines of Mira stars., It is thus now possible for the very first time to estimate the linear and the circular polarization evolution in the emission lines of Mira stars. + Ás we are convinced that the hydrogen emission lines are polarized by a physical process inherent to the mechanism responsible for the emission line formation (1e. the shock wave itself). a spectropolarimetric survey performed during the cycle of pulsation of Mira stars appears to be a good tool for tackling this problem.," As we are convinced that the hydrogen emission lines are polarized by a physical process inherent to the mechanism responsible for the emission line formation (i.e, the shock wave itself), a spectropolarimetric survey performed during the cycle of pulsation of Mira stars appears to be a good tool for tackling this problem." + In section 2. we present our observations of omicron Ceti as collected with the NARVAL spectropolarimeter.," In section 2, we present our observations of omicron Ceti as collected with the NARVAL spectropolarimeter." + In. section. 3. we interpret the obtained results in term of shock wave characterization.," In section 3, we interpret the obtained results in term of shock wave characterization." + In section 4. we draw a conclusion from this spectropolarimetrie analysis.," In section 4, we draw a conclusion from this spectropolarimetric analysis." + We performed a spectropolarimetric monitoring along three consecutive pulsation cycles of the bright star omicron Ceti. the prototype of oxygen-rich Mira stars.," We performed a spectropolarimetric monitoring along three consecutive pulsation cycles of the bright star omicron Ceti, the prototype of oxygen-rich Mira stars." + During one of its typical eycles of luminosity (with à mean period of pulsation of 331 days). the visual magnitude of omicron Ceti presents an average variation amplitude of eight and its spectral type varies from M3e to M9e (see General Catalogue of Variable Stars and AAVSO website).," During one of its typical cycles of luminosity (with a mean period of pulsation of 331 days), the visual magnitude of omicron Ceti presents an average variation amplitude of eight and its spectral type varies from M5e to M9e (see General Catalogue of Variable Stars and AAVSO website)." + Omicron Ceti has the peculiarity of hosting a companion (VZ Ceti) at ~70 A.U. believed to be either a white dwarf (?.. 2)) or a main sequence star (?)).," Omicron Ceti has the peculiarity of hosting a companion (VZ Ceti) at $\sim$ 70 A.U. believed to be either a white dwarf \citealt{Karovska97}, \citealt{Karovska06}) ) or a main sequence star \citealt{Ireland07}) )." + We consider 1t to be too far to have any influence on the dynamics of the lower atmosphere of omicron Ceti., We consider it to be too far to have any influence on the dynamics of the lower atmosphere of omicron Ceti. + The spectropolarimetric data come from the NARVAL instrument mounted on the Téllescope Bernard Lyot (TBL) in the Pie du Midi Observatory. France.," The spectropolarimetric data come from the NARVAL instrument mounted on the Téllescope Bernard Lyot (TBL) in the Pic du Midi Observatory, France." + The polarimeter is made with optical elements (a series of half-wave. quarter-wave. and half-wave rhombs) that analyse the circular or linear polarization state of a signal (2)).," The polarimeter is made with optical elements (a series of half-wave, quarter-wave, and half-wave rhombs) that analyse the circular or linear polarization state of a signal \citealt{donatial1997}) )." + The processed signal is thus transmitted in an achromatic way via an optical fiber to the cross-dispersion spectrometer doing the spectral analysis over a very wide part of the spectrum (from 375 to 0050nnm) and over 40 orders., The processed signal is thus transmitted in an achromatic way via an optical fiber to the cross-dispersion spectrometer doing the spectral analysis over a very wide part of the spectrum (from 375 to nm) and over 40 orders. + The polarimetric mode gives us a spectral resolution of 0000. and the velocity bin is then Av 4.4kkms!.," The polarimetric mode gives us a spectral resolution of 000, and the velocity bin is then $\Delta$ $\sim\,$ $^{-1}$." + The monitoring was from the 5 September 2007 to the 10 February 2010. covering three luminosity cycles of omicron Ceti.," The monitoring was from the 5 September 2007 to the 10 February 2010, covering three luminosity cycles of omicron Ceti." +" To provide phases during these cycles. we used as heliocentric julian date of reference at Juminosity maximum (see AAVSO website): HJD, = 2454150."," To provide phases during these cycles, we used as heliocentric julian date of reference at luminosity maximum (see AAVSO website): $\mathrm{HJD}_\mathrm{r}$ = $2\,454\,150$." +" The phase ᾧ is then the ratio between HJD,— and the period (see Fig.", The phase $\varphi$ is then the ratio between $\mathrm{HJD}_\mathrm{o}-\mathrm{HJD}_\mathrm{r}$ and the period (see Fig. + 1. and Table 1)»., \ref{cdl} and Table \ref{tab1}) ). + The Libre-ESpRIT software (?)) processing data collected by NARVAL allows us to obtain polarimetric spectra., The Libre-ESpRIT software \citealt{donatial1997}) ) processing data collected by NARVAL allows us to obtain polarimetric spectra. + The outputs of Libre-ESpRIT process are the four Stokes parameters divided by a pseudo-continuum:, The outputs of Libre-ESpRIT process are the four Stokes parameters divided by a pseudo-continuum: +For the past wears. there have been great successes ii nieasureineut of CAIB anisotropy bv eround aud satellite observations (Buuvauaudetal.2003:Adesonetal.2010:Jarosik 2010)..,"For the past years, there have been great successes in measurement of CMB anisotropy by ground and satellite observations \citep{ACBAR,QUaD1,WMAP5:powerspectra,QUaD:instrument,WMAP5:basic_result,WMAP5:parameter,QUaD2,ACBAR2008,WMAP7:powerspectra,WMAP7:basic_result}." + By comparing the ieular power spectrum of the CAIB anisotropy with theoretical predictions. we may inipose strong constraints ou cosinological models (LiddleaudLyth2000:Dodel-son2003:Muklauov2005:Weinberg 2008)..," By comparing the angular power spectrum of the CMB anisotropy with theoretical predictions, we may impose strong constraints on cosmological models \citep{Inflation,Modern_Cosmology,Foundations_Cosmology,Cosmology}." + In. spite of remarkable eoodness of fit (οιίναandetal.2009.Ww HO).. there are some features of WALIAP data. which are not well explained by the WALAP concordance model (Chiangetal.2003:deOliveira-Costa2001:Copietal.2010:Copi 2010)..," In spite of remarkable goodness of fit \citep{WMAP5:Cosmology,WMAP7:Cosmology}, there are some features of WMAP data, which are not well explained by the WMAP concordance model \citep{Chiang_NG,Tegmark:Alignment,Multipole_Vector1,Hemispherical_asymmetry,cold_spot1,Universe_odd,alfven,lowl,fnl_power,odd,odd_origin,WMAP7:anomaly,lowl_anomalies}." + In particular. the power contrast anomaly between even and odd multipoles is explicitly associated with the augular power spectrin. which are mainly used to fit cosmological uodels (Latepusoetal.2010:Bennett 2010)..," In particular, the power contrast anomaly between even and odd multipoles is explicitly associated with the angular power spectrum, which are mainly used to fit cosmological models \citep{Universe_odd,odd,odd_origin,odd_bolpol,WMAP7:anomaly}." + Tlaving note: this. we have investigated whether eveu(odd) multipole data set is consistent with the WMADP concordance model.," Having noted this, we have investigated whether even(odd) multipole data set is consistent with the WMAP concordance model." + Our investigation shows there exist some leve of tension. which may be an indication of uuaccouutec contanination or iuissine ineredicuts iu the assume piuiuuetrie model such as the flat ACDAM 1nodel.," Our investigation shows there exist some level of tension, which may be an indication of unaccounted contamination or missing ingredients in the assumed parametric model such as the flat $\Lambda$ CDM model." +" We may consider CMD anisotropy as the sui of even and odd parity functions: where Using the parity property of spherical harmonics Yn)={LVn) CArfkeunandWeber2000).. it is straightforward to show Obvioush. the power spectrum of even aud odd multipoles are associated with Tan) aud T(m) respectively,"," We may consider CMB anisotropy as the sum of even and odd parity functions: where Using the parity property of spherical harmonics $Y_{lm}(\hat{\mathbf n})=(-1)^l\,Y_{lm}(-\hat{\mathbf n})$ \citep{Arfken}, it is straightforward to show Obviously, the power spectrum of even and odd multipoles are associated with $T^{+}(\hat{\mathbf n})$ and $T^{-}(\hat{\mathbf n})$ respectively." + Cüven the ACDM model. we do not expec any features distinct between even and odd inultipoles.," Given the $\Lambda$ CDM model, we do not expect any features distinct between even and odd multipoles." + However. there have been reported power contras vetween even aud odd inultipoles of WALAP TT power spectriuu (LaudaudMagueijo2005:Iamaud.Naselskv2010a.b:Cruppusoetal.2010:Bennett 2010).," However, there have been reported power contrast between even and odd multipoles of WMAP $TT$ power spectrum \citep{Universe_odd,odd,odd_origin,odd_bolpol,WMAP7:anomaly}." +.. A ovest imultipoles (2<7< 22). there is odd iuultipok oxeference (1.6. power excess in odd iultipoles aud defici in even multipoles) (LaudaudMagueijo2005:IiiNaselskv2010a.b:Camppusoetal. 2010).. and even uultipole preference at interiuediate multipoles (200.<|x 100) (Bennettetal.2010).," At lowest multipoles $2\le l\le 22$ ), there is odd multipole preference (i.e. power excess in odd multipoles and deficit in even multipoles) \citep{Universe_odd,odd,odd_origin,odd_bolpol}, , and even multipole preference at intermediate multipoles $200\le l \le400$ ) \citep{WMAP7:anomaly}." +.. Additionally. we have investigated TE correlation. and noticed odd multipole reference at (LOOSFxz 200) and even multipole reference at (200=7X 100). though its statistical sienificance is not hieh enough. due to low Signal-to-Noise Ratio of polarization data.," Additionally, we have investigated TE correlation, and noticed odd multipole preference at $100\lesssim l\lesssim 200$ ) and even multipole preference at $200\lesssim l \lesssim400$ ), though its statistical significance is not high enough, due to low Signal-to-Noise Ratio of polarization data." + Not surprisingly. these oower contrast anonalies are explicitly associated with he augular power spectrum data. which are mainly used o fif cosinological models.," Not surprisingly, these power contrast anomalies are explicitly associated with the angular power spectrum data, which are mainly used to fit cosmological models." + Waving noted this. we have investigated whether the eveutodd) multipole data setis consistent with the concordance model.," Having noted this, we have investigated whether the even(odd) multipole data setis consistent with the concordance model." + For a cosmological imodel. we have considered ACDM | SZ effect. | weak-leusiug. where cosmological," For a cosmological model, we have considered $\Lambda$ CDM + SZ effect + weak-lensing, where cosmological" +Although many of the features seen. here are also seen in andS.. there are two additional ones which we will comment on now.,"Although many of the features seen here are also seen in and, there are two additional ones which we will comment on now." + One such feature is the bimodality in the satellite clistribution of halo 1., One such feature is the bimodality in the satellite distribution of halo 1. + In this Figure there seems to be two distinct (live and dead) satellite populations orbiting within the dark matter halo., In this Figure there seems to be two distinct (live and dead) satellite populations orbiting within the dark matter halo. + As we saw. particularly in4.. this dark matter halo lies in a rich area being fed by (at least) two filaments.," As we saw, particularly in, this dark matter halo lies in a rich area being fed by (at least) two filaments." + Perhaps these two satellite populations are a remnant of the Glamentary large-scale structure surrounding the host?, Perhaps these two satellite populations are a remnant of the filamentary large-scale structure surrounding the host? + Lfthat is true. it is interesting that the satellites still maintain their dynamical distinctiveness. after. several orbits.," If that is true, it is interesting that the satellites still maintain their dynamical distinctiveness after several orbits." + In addition there appears to be a distinct population of satellites with an extremely tight between eccentricities e=0.60.9 anc pericentres pz0.3.y0.8 in many halos., In addition there appears to be a distinct population of satellites with an extremely tight between eccentricities $e \approx 0.6-0.9$ and pericentres $p\approx 0.3-0.8$ in many halos. + Upon detailed investigation these satellites were identified to have completed one orbit and were entering the halo for the first time., Upon detailed investigation these satellites were identified to have completed one orbit and were entering the halo for the first time. + This is consistent. with the notion of the satellites infalling on radial orbits., This is consistent with the notion of the satellites infalling on radial orbits. + We investigate this point in the next section. namely the evolution. of eccentrieltvy.," We investigate this point in the next section, namely the evolution of eccentricity." + In the previous section we considered the orbital characteristies of the satellites at redshift 2=0., In the previous section we considered the orbital characteristics of the satellites at redshift $z=0$. + We now investigate the evolution of the orbital eccentricities of the satellite family., We now investigate the evolution of the orbital eccentricities of the satellite family. + shows the eecentricity of each satellite (represented by the crosses) versus the number of orbits the satellite has completed., shows the eccentricity of each satellite (represented by the crosses) versus the number of orbits the satellite has completed. + Phere is a clear trend for eccentricity to decrease as the number of orbits of a satellite increases., There is a clear trend for eccentricity to decrease as the number of orbits of a satellite increases. +" ‘This is also demonstrated by the histogram. which is not the “binned” results of the crosses. but is instead. the average eccentricity for all satellites that hack &INous orbits llere. e;(Noite) is the eccentricity of satellite { after Manis orbits and Now(2Norns) is the number of satellites with equal or more than INaig, Orbits."," This is also demonstrated by the histogram, which is not the “binned” results of the crosses, but is instead the average eccentricity for all satellites that had $\geq N_{\rm orbits}$ orbits Here, $e_i(N_{\rm orbits})$ is the eccentricity of satellite $i$ after $N_{\rm orbits}$ orbits and $N_{\rm sat}({\ge N_{\rm orbits}})$ is the number of satellites with equal or more than $N_{\rm orbits}$ orbits." + For example. a satellite that has had 3 orbits contributes its respective value of eccentricity to the average eecentricity in the bins for 1. 2. and 3 orbits.," For example, a satellite that has had 3 orbits contributes its respective value of eccentricity to the average eccentricity in the bins for 1, 2, and 3 orbits." + This histogram shows a, This histogram shows a +mean cell density is unity). and the secouc panel shows the value of B: both of these factor in eq. [5].,"mean cell density is unity), and the second panel shows the value of $B$; both of these factor in eq. \ref{eqn:rhocrit}] ]," + which in turn plays a major part in determining the tree distribution., which in turn plays a major part in determining the tree distribution. + Various aspects of this clistribution are shown iu the remaining curves., Various aspects of this distribution are shown in the remaining curves. + The third panel shows the size of the largest cubical subvolume required (in units of PM grid cells)., The third panel shows the size of the largest cubical subvolume required (in units of PM grid cells). + Initially small. this grows extremely rapidly as σ rises [roin its initial value of 0.3 to ~1: iu response B is iucreased.," Initially small, this grows extremely rapidly as $\sigma$ rises from its initial value of 0.3 to $\sim 1$; in response $B$ is increased." + When this size is αἱ its greatest (at ozzp 1.6). the percentages of total volume aud mass in trees (shown iu the next two panels) are still quite sinall.," When this size is at its greatest (at $\sigma\approx 1.6$ ), the percentages of total volume and mass in trees (shown in the next two panels) are still quite small." + The trees at this time tend to follow caustics— they are only slightly overcdense aud uot very massive. but because of their filamentary nature they can have a large spatial extent.," The trees at this time tend to follow caustics— they are only slightly overdense and not very massive, but because of their filamentary nature they can have a large spatial extent." + These caustics then fragment aud collapse. so— even while the total mass in trees aid the number of trees (shown iu the third pauel (rom the bottom) iucrease— the rnaxiuimun subvolume size decreases.," These caustics then fragment and collapse, so— even while the total mass in trees and the number of trees (shown in the third panel from the bottom) increase— the maximum subvolume size decreases." + The changes in B allect mainly the iiaximum subvoluime size: tlie number ol trees and volume coutaiued iu tree regious both increase at a steady rate up to z—1., The changes in $B$ affect mainly the maximum subvolume size; the number of trees and volume contained in tree regions both increase at a steady rate up to $z$ =1. + The nuuber oL tree particles increases monotonically throughout the simulation., The number of tree particles increases monotonically throughout the simulation. + Alter 2—1 (by far the bulk of the computational time). the characteristies of the simulation Change much more slowly.," After $z=1$ (by far the bulk of the computational time), the characteristics of the simulation change much more slowly." + Roughly half the particles are in ~2700 trees ranging from a few to 10? particles but occupying only of the simulation volume., Roughly half the particles are in $\sim$ 2700 trees ranging from a few to $10^5$ particles but occupying only of the simulation volume. + The penultimate panel shows the uumber of particles tu the first aud third largest trees: by z=1 the growth in mass of these objects has slowed to a fairly coustaut. low rate.," The penultimate panel shows the number of particles in the first and third largest trees; by $z=1$ the growth in mass of these objects has slowed to a fairly constant, low rate." + Trees are distributed in mass roughly as a power law. with of the trees having fewer than 100 particles and less than 1000.," Trees are distributed in mass roughly as a power law, with of the trees having fewer than 100 particles and less than 1000." + Most tree particles take two or four steps per PAL step. but some are taking up to GE: there were LOTS PM steps total in this run.," Most tree particles take two or four steps per PM step, but some are taking up to 64; there were 1075 PM steps total in this run." + Aso increases. so does the limiting density above which all cells are treated at full resolution.," As $\sigma$ increases, so does the limiting density above which all cells are treated at full resolution." + [t is important to keep track of this limit when interpreting the results of a TPM run., It is important to keep track of this limit when interpreting the results of a TPM run. + The bottor-— pauel shows the highest value of the deusity among those cells evolved only with PN., The bottom panel shows the highest value of the density among those cells evolved only with PM. + By 2=1 this deusity is 120 times the mean. correspondiug to 15 particles iuside a cell.," By $z=1$ this density is 120 times the mean, corresponding to 15 particles inside a cell." + By the end of the computation. the densest PM-only cell contaius 26 particles: so trying to make statements abou objects smaller than this will be complicated by the varying spatial resolution of TPM.," By the end of the computation, the densest PM–only cell contains 26 particles; so trying to make statements about objects smaller than this will be complicated by the varying spatial resolution of TPM." + Note tha most objects with VooS25 will in [ασ be followed at full resolution— substructures inside larger objects because they are in regions of higher density. aud suall isolated halos because they presen a density contrast to their surroundings.," Note that most objects with $N\la 25$ will in fact be followed at full resolution— substructures inside larger objects because they are in regions of higher density, and small isolated halos because they present a density contrast to their surroundings." + To be cautious we will limit our analysis to objects larger than this limit. LO particles or LOM1AL..," To be cautious we will limit our analysis to objects larger than this limit, 40 particles or $10^{11}h^{-1}M_\odot$." + As seen in the previous section. during later epochs— which take up most of the computational time needed for a ruu— the mass distribution of trees is generally well fit by a power law raugiug [rom a few particles up to of order 0.01.," As seen in the previous section, during later epochs— which take up most of the computational time needed for a run— the mass distribution of trees is generally well fit by a power law ranging from a few particles up to of order $N$." +N. The actual mass of the largest tree will depeud on the ratio of the largest non-linear scale in the box to the box size: as this ratio becomes larger so does the mass of the largest tree., The actual mass of the largest tree will depend on the ratio of the largest non-linear scale in the box to the box size; as this ratio becomes larger so does the mass of the largest tree. + Furthermore. the amouut of computation required for a tree with A; ," Furthermore, the amount of computation required for a tree with $N_t$ " +The physical number density »(M.z:) of virialized dark halos of masses between. M. and M+dAl is expressed as n(M.z)=nGM.z)(14z)* and eCM.z) is the cross-section defined in the lens plane for forming multiple images.,"The physical number density $\bar{n}(M,z)$ of virialized dark halos of masses between $M$ and $M+dM$ is expressed as $\bar{n}(M,z)=n(M,z)(1+z)^3$ and $\sigma(M,z)$ is the cross-section defined in the lens plane for forming multiple images." + In the standard hierarchical theory of structure formation. (he comoving number density of virialized dark halos per unit mass A at redshift z can be given bv (the Press and Schechter (PS) formula (?):: nCM.z)—dN/dM=pyf(M.z)/M where po is the mean mass density of the universe (today and. instead of PS formula in this letter. the mass function /(M.2z) takes the form of an empirical fit [rom high-resolution simulation (7?) Ilere. ACAL.2)=ACADD6 and D(z)=e(Q(z))fe(Q4(12) is the linear growth function of density perturbation (?).. in which ο.)=2.5r/(L/70+209%/140—47/140eh) and O(:)=μα+z)'/E?(:).," In the standard hierarchical theory of structure formation, the comoving number density of virialized dark halos per unit mass $M$ at redshift $z$ can be given by the Press and Schechter (PS) formula \citep{1974ApJ...187..425P}: $n(M,z)=dN/dM=\rho_0 +f(M,z)/M$ where $\rho_0$ is the mean mass density of the universe today and, instead of PS formula in this letter, the mass function $f(M,z)$ takes the form of an empirical fit from high-resolution simulation \citep{2001MNRAS.321..372J} + Here, $\Delta(M,z)=\Delta(M)D(z)$ and $D(z)=e(\Omega(z))/e(\Omega_{\mathrm{m}})(1+z)$ is the linear growth function of density perturbation \citep{1992ARA&A..30..499C}, in which $e(x)=2.5x/(1/70+209x/140-x^2/140+x^{4/7})$ and $\Omega(z)=\Omega_{\mathrm{m}}(1+z)^3/ E^2(z)$." +" The present variance of the fluctuations within a spherecontaining a mass Af can be expressed as ΑΛ).=nery DO8?ΤΙ». where Whryy)=3[in(erg)/Gery)!—cos(ery)/(rgapP] is the Top-hat window function in Fourier space and ry,=(BALπρι)ο."," The present variance of the fluctuations within a spherecontaining a mass $M$ can be expressed as $\Delta^2(M)=\frac{1}{2\pi^2}\int^{\infty}_0P(k) +W^2(kr_{\mathrm{M}})k^2dk$ , where $W(kr_{\mathrm{M}})=3[\sin(kr_{\mathrm{M}})/(kr_{\mathrm{M}})^3- +\cos(kr_{\mathrm{M}})/(kr_{\mathrm{M}})^2]$ is the Top-hat window function in Fourier space and $ +r_{\mathrm{M}}=(3M/4\pi\rho_0)^{1/3}$." +" The power spectrum of CDM density fluctuations is Pk)=DPO)T? where the matter transfer function ΤΗ) isgiven by ?.. and P,(h) is the primordial power spectrum of density fluctuation."," The power spectrum of CDM density fluctuations is $P(k)=P_p(k)T^2(k)$ where the matter transfer function $T(k)$ isgiven by \cite{1999ApJ...511....5E}, and $P_p(k)$ is the primordial power spectrum of density fluctuation." +" The scaleanvariant primordial power spectrum in the PL-ACDM model is given by ΠΟ)=AL""5 with index n;—1 and that in the RSI-ACDM model is assumed to be P,(h)=DOG/kyy. where the index n.(h) is a [unetion of length scale The pivot scale 4520.05 bh |. Πιν (η)... and dnαἱΠα k--0.03 are the best-fil values to the combination data of the recent CMD experiments ancl (wo other large-scale structure observations (?).."," The scale-invariant primordial power spectrum in the $\Lambda$ CDM model is given by $P_p(k)=Ak^{n_s}$ with index $n_s$ =1 and that in the $\Lambda$ CDM model is assumed to be $P_p(k)=P(k_0)(k/k_0)^{n_{s}(k)}$, where the index $n_{s}(k)$ is a function of length scale The pivot scale $k_0$ =0.05 h $^{-1}$, $n_{\rm s}(k_0)$ =0.93, and $dn_{s}/d\ln k$ =-0.03 are the best-fit values to the combination data of the recent CMB experiments and two other large-scale structure observations \citep{2003ApJS..148..175S}." +" For both PL-ACDAL and BRSI-ACDAM models. (he amplitude of primordial power spectrum. A and Phy). arenormalized to e=A(ry,8h.! Mpe). which is (he rms mass fluctuations when present universe is smoothed using a window Iunction on a scale of 8h t\Mpe."," For both $\Lambda$ CDM and $\Lambda$ CDM models, the amplitude of primordial power spectrum, $A$ and $P(k_0)$ , arenormalized to $\sigma_8=\Delta +(r_{\mathrm{M}}=8h^{-1}\mathrm{Mpc})$ , which is the rms mass fluctuations when present universe is smoothed using a window function on a scale of $8h^{-1}\mathrm{Mpc}$ ." +"(ratio of magnetic to initial particle kinetic energev) of the svstem as where e,=ny(mp+m,)?(50—DL,νοον, (L,, being the simulation box dimension in the +; direction). and r=Low/L,,.","(ratio of magnetic to initial particle kinetic energy) of the system as where $\epsilon_p = n_0 (m_p+m_e)c^2(\gamma_0-1) L_{x_1} L_{x_2} L_{x_3}$ $L_{x_i}$ being the simulation box dimension in the $x_i$ direction), and $r = L_\mathrm{sat}/L_{x_3}$." +" We measure from the simulation at saturation oc4 (rc 0.2) for the subrelativistic case. vielding ep/e,—4x10.|. and à~15 (r&0.19) for the relativistic case. yielding e5/e,=1.2x10.ni7. which are comparable with the simulations results (Figure 4))."," We measure from the simulation at saturation $\alpha \simeq 4$ $r \simeq 0.2$ ) for the subrelativistic case, yielding $\epsilon_B/\epsilon_p = 4 \times 10^{-4}$, and $\alpha \simeq 15$ $r \simeq 0.19$ ) for the relativistic case, yielding $\epsilon_B/\epsilon_p = 1.2 \times 10^{-3}$, which are comparable with the simulations results (Figure \ref{fig:bevol}) )." + We may also estimate the maxinunm value of equipartiüon which is found at the shear surfaces by averaging around the interaction region. which has a typical thickness on the order of Lu: vielding 2x10? for the subrelativistic case and 7xLO% for the relativistic case.," We may also estimate the maximum value of equipartition which is found at the shear surfaces by averaging around the interaction region, which has a typical thickness on the order of $L_\mathrm{sat}$: yielding $2 \times 10^{-3}$ for the subrelativistic case and $7 \times 10^{-3}$ for the relativistic case." +" A hieher efficiency. of conversion of particle kinetic enerev (o magnetic fields is observed in (he relativistic case since (he thickness of the proton currents sheets (5,4) is much higher {han in (he subrelativistic case.", A higher efficiency of conversion of particle kinetic energy to magnetic fields is observed in the relativistic case since the thickness of the proton currents sheets $L_\mathrm{sat}$ ) is much higher than in the subrelativistic case. + Most of the energy in the svstem. however. is still contained in the ions which remain unperturbed at (these (ime-scales.," Most of the energy in the system, however, is still contained in the ions which remain unperturbed at these time-scales." +" We expect (he svstem to reach hieher levels of equipartition once the protons undergo the proton-scale KIT. which would occur ab roughly ρω.κιcLOO(mi/me)t*feyL000/e,."," We expect the system to reach higher levels of equipartition once the protons undergo the proton-scale KHI, which would occur at roughly $t_\mathrm{proton-KHI} \simeq 100 ~ (mi/me)^{1/2} /\omega_p \simeq 4000 /\omega_p$." + The long-lived large-scale DC magnetic field can (hus be sustained up to the proton time-scale which is roughly long enough lor prompt GRB emission and early afterglow (Piran1999)., The long-lived large-scale DC magnetic field can thus be sustained up to the proton time-scale which is roughly long enough for prompt GRB emission and early afterglow \citep{Piran99}. +. In this Letter. we present the first self-consistent 3D PIC simulations of the NII in munaenelized eleclron-prolon plasmas and analvze (heir evolution on the electron scale.," In this Letter, we present the first self-consistent 3D PIC simulations of the KHI in unmagnetized electron-proton plasmas and analyze their evolution on the electron time-scale." + Our results show that the multidimensional physics of the KIL is extremely. rich ancl that kinetic effects plav an important role. in particular. in the transverse dynamics of the WI (which is dominant over the longitudinal NII cdvnamics in relativistic shears}. and in ihe generation of a strong large-scale DC magnetic field.," Our results show that the multidimensional physics of the KHI is extremely rich and that kinetic effects play an important role, in particular, in the transverse dynamics of the KHI (which is dominant over the longitudinal KHI dynamics in relativistic shears), and in the generation of a strong large-scale DC magnetic field." + The transverse dynamics of the NIL consists of a Weibel-like electron bunching process. leading to the formation of electron. current. filaments which are then accelerated across the shear surface. forming finger-like structures.," The transverse dynamics of the KHI consists of a Weibel-like electron bunching process, leading to the formation of electron current filaments which are then accelerated across the shear surface, forming finger-like structures." + At the electron saturation time-scale. the magnetic field has evolved to a large-scale DC field structure that extends over the entire," At the electron saturation time-scale, the magnetic field has evolved to a large-scale DC field structure that extends over the entire" +"are also distributions of the third-order moments in unlensed galaxy profiles which create an ""intrinsic flexion"" signal.",are also distributions of the third-order moments in unlensed galaxy profiles which create an “intrinsic flexion” signal. +" This unlensed-shape-induced scatter is best characterized by the scatter in the dimensionless products o,,V4 and AopsV¥3, where oy, is the observed, image plane size of the image."," This unlensed-shape-induced scatter is best characterized by the scatter in the dimensionless products $\alpha_{\text{obs}}\Psi_1$ and $\alpha_{\text{obs}}\Psi_3$ , where $\alpha_{\text{obs}}$ is the observed, image plane size of the image." +" The intrinsic flexion scatter should not be correlated with the astrophysically-sourced lensing flexion, so each component of the flexion fields can be used as an independent probe of the scatter along a single coordinate axis."," The intrinsic flexion scatter should not be correlated with the astrophysically-sourced lensing flexion, so each component of the flexion fields can be used as an independent probe of the scatter along a single coordinate axis." +" Table 2] lists the mean and standard deviation of these dimensionless products o,V, for the flexion fields measured in A1689, characterized in three different object samples for each flexion field."," Table \ref{tab:intflex} lists the mean and standard deviation of these dimensionless products $\alpha_{\text{obs}}\Psi_{mn}$ for the flexion fields measured in A1689, characterized in three different object samples for each flexion field." + The full sample includes all objects used for the flexion analysis in refsec:realdata.. “, The full sample includes all objects used for the flexion analysis in \\ref{sec:realdata}. “ +"Low error” and “high error"" samples are defined independently for 1-flexion and 3-flexion based on the sum in quadrature of their respective flexion parameter error estimates: the full sample is divided about the median 1-flexion error of 0.029 arcsec! and the median 3-flexion error of 0.049 arcsec!.",Low error” and “high error” samples are defined independently for 1-flexion and 3-flexion based on the sum in quadrature of their respective flexion parameter error estimates: the full sample is divided about the median 1-flexion error of 0.029 $^{-1}$ and the median 3-flexion error of 0.049 $^{-1}$. +" The scatter we observe is similar to values previously reported, though caution is warranted when directly comparing numerical values, due to the difference between our treatment of the mass-sheet degeneracy and that of(2007)."," The scatter we observe is similar to values previously reported, though caution is warranted when directly comparing numerical values, due to the difference between our treatment of the mass-sheet degeneracy and that of." +" Another notable feature is the higher 1-flexion scatter in the low error subsample than in the high error sample, which we attribute to the astrophysical flexion signal."," Another notable feature is the higher 1-flexion scatter in the low error subsample than in the high error sample, which we attribute to the astrophysical flexion signal." + The low error sample are those objects most likely to include a non-zero measured flexion value., The low error sample are those objects most likely to include a non-zero measured flexion value. +" The objects which have larger true flexion field values are more likely to be well-constrained by the AIM fitting, and thus will more likely be in the low error sample and increase the scatter in our unitless figure-of-merit."," The objects which have larger true flexion field values are more likely to be well-constrained by the AIM fitting, and thus will more likely be in the low error sample and increase the scatter in our unitless figure-of-merit." +" Sub-dividing the full sample by their radius from the cluster center has no discernible effect on the scatter, which is expected."," Sub-dividing the full sample by their radius from the cluster center has no discernible effect on the scatter, which is expected." +" The flexion signal is less dependent on the overall cluster potential, and more dependent on the local substructure."," The flexion signal is less dependent on the overall cluster potential, and more dependent on the local substructure." + A detailed study of the scatter in the measuredflexion fields and the relative contributions, A detailed study of the scatter in the measuredflexion fields and the relative contributions +aat a redshift of1.,at a redshift of. +2.. For a total of ssources. our data sullice to construct SEDs.," For a total of sources, our data suffice to construct SEDs." + The measured ISO [Iuxes for them are presented in table 1., The measured ISO fluxes for them are presented in table 1. + Interpretation of the IR. spectra requires detailed. knowledge of the energv sources and the distribution and composition of gas ancl dust which absorbs ancl re-Utransmits the radiation., Interpretation of the IR spectra requires detailed knowledge of the energy sources and the distribution and composition of gas and dust which absorbs and re-transmits the radiation. + In the case of the AGNs discussed in this paper. the primary energy source is the central engine in the nucleus enshrouded by dust clouds.," In the case of the AGNs discussed in this paper, the primary energy source is the central engine in the nucleus enshrouded by dust clouds." + Dust close to the nucleus absorbs (he radiation Grom the nucleus and reaadiates it., Dust close to the nucleus absorbs the radiation from the nucleus and re-radiates it. + This emission depends mostly on the total power and spectrum of the central engine. and the distribution and properties of dust.," This emission depends mostly on the total power and spectrum of the central engine, and the distribution and properties of dust." + While (he composition of (he dust can reasonably assumed to be similar to local dust aud is therefore well constrained. its distribution around the power source of the AGN is largely unknown.," While the composition of the dust can reasonably assumed to be similar to local dust and is therefore well constrained, its distribution around the power source of the AGN is largely unknown." + I1 is generally assumed that the geometrical distribution of dust around ACNs is similar to a torus or warped disk (e.g..UrrvandPclovani1995).," It is generally assumed that the geometrical distribution of dust around AGNs is similar to a torus or warped disk \citep[e.g.,][]{review}." +. However. observations of dust leatures close to the nucleus of AGNs with the IST reveal a variety of morphologies 2000)..," However, observations of dust features close to the nucleus of AGNs with the HST reveal a variety of morphologies \citep{Mat2}." + These observations and the [act that dust at distance much larger than the size of the putative torus shapes the ALR spectrum (Farrahetal.2003) motivated us to adopt a simple approach to the modelling of dust SEDs in AGNs., These observations and the fact that dust at distance much larger than the size of the putative torus shapes the MIR spectrum \citep{Far} motivated us to adopt a simple approach to the modelling of dust SEDs in AGNs. + Instead of choosing between possible geometrical configurations. we carried oul spherical radiative transfer ealeulations wilh a central heating source.," Instead of choosing between possible geometrical configurations, we carried out spherical radiative transfer calculations with a central heating source." + In (his approach. (he size of the model sphere depends on the viewing angle because of the intrinsic asvmmetry of AGNs.," In this approach, the size of the model sphere depends on the viewing angle because of the intrinsic asymmetry of AGNs." +" We used a power law Lxp""* between A=LOA aand μην as the input spectrum of the central sources.", We used a power law $L \propto\nu^{-0.7}$ between $\lambda=10$ and $2\mu$ m as the input spectrum of the central sources. + The exciting radiation field is jerefore. significantly harder than for star bursts leading to stronger photo-cdestruction of V.nall grains (Siebenmorgen.R., The exciting radiation field is therefore significantly harder than for star bursts leading to stronger photo-destruction of small grains \citep{Timmi}. +etal.2003b).. Had. we used a more distributed source οἱ Mjergv within the nucleus. the predicted PAI] emission would have been much stronger.," Had we used a more distributed source of energy within the nucleus, the predicted PAH emission would have been much stronger." + We numerically solved the radiative (ransfer equations for a grid of models. varving 1e (otal luminosity of the central engine. the total extinction and the outer radius of the dust clouds.," We numerically solved the radiative transfer equations for a grid of models, varying the total luminosity of the central engine, the total extinction and the outer radius of the dust clouds." + The dust in our model consists of carbon grains. silicate grains and PALIs.," The dust in our model consists of carbon grains, silicate grains and PAHs." + The initial density within the sphere is constant. but dust evaporation and PAIL destruction are taken into account in a self-consistent wav.," The initial density within the sphere is constant, but dust evaporation and PAH destruction are taken into account in a self-consistent way." +" We computed model SEDs for outer radii ranging [rom 0.125 to L6kpe. luminosities ranging from 10? to 10!!L,.. and visual extinction ranging [rom 1 to 128 magnitudes."," We computed model SEDs for outer radii ranging from 0.125 to 16kpc, luminosities ranging from $10^{9}$ to $10^{14}$, and visual extinction ranging from 1 to 128 magnitudes." + The full set of models is available αἱmodels.html., The full set of models is available at. + The parameters of the best fitting model for each observed SED, The parameters of the best fitting model for each observed SED +Bate (2007) have investigated the influence of initially perpendicular rotation axis and magnetic field.,Bate (2007) have investigated the influence of initially perpendicular rotation axis and magnetic field. +" More realistic initial conditions, including non uniform density field, turbulent velocity field and rotation axis non aligned with the magnetic field, will be considered in future studies."," More realistic initial conditions, including non uniform density field, turbulent velocity field and rotation axis non aligned with the magnetic field, will be considered in future studies." +" In particular, we determine the lowest value of pt, the mass-to-flux over critical mass-to-flux ratio for which fragmentation is suppressed."," In particular, we determine the lowest value of $\mu$, the mass-to-flux over critical mass-to-flux ratio for which fragmentation is suppressed." + It turns out that the results depend strongly on the amplitude of the initial perturbation., It turns out that the results depend strongly on the amplitude of the initial perturbation. + 'The paper is organized as follow., The paper is organized as follow. +" In the first section, we consider the same initial conditions as used in paper I, namely a spherical uniform one solar mass dense core."," In the first section, we consider the same initial conditions as used in paper I, namely a spherical uniform one solar mass dense core." + The thermal over gravitational energy of the core is equal to ~0.37 and the rotation over gravitational energy is 0.045., The thermal over gravitational energy of the core is equal to $\simeq$ 0.37 and the rotation over gravitational energy is 0.045. + Note that such rotation are typical of (may be slightly larger than) values observed in dense cores (Goodman et al., Note that such rotation are typical of (may be slightly larger than) values observed in dense cores (Goodman et al. + 1993)., 1993). +" The initial density is about ~5x1071? g cm? and the cloud radius, Ro 70.016 pc."," The initial density is about $\simeq \, 5 \times 10^{-18}$ g $^{-3}$ and the cloud radius, $R_0 \simeq$ 0.016 pc." + The freefall time is thus of the order of 3x104 years., The freefall time is thus of the order of $3 \times 10^4$ years. +" We use a barotropic equation of state: C2=(C9)?x(1+(p/p.)*/9)1/2, where C,c0.2 km/s is the sound speed and p,=107% g cm-?."," We use a barotropic equation of state: $C_s^2 = (C_s^0)^2 \times (1 + (\rho/\rho_c)^{4/3})^{1/2}$, where $C_s \simeq 0.2$ km/s is the sound speed and $\rho_c=10^{-13}$ g $^{-3}$." + This set of cloud parameters is known to give rise to a disk that unambiguously fragments in the pure hydrodynamics case., This set of cloud parameters is known to give rise to a disk that unambiguously fragments in the pure hydrodynamics case. +" The only difference with paper Iis that an m—2 perturbation of amplitude A—0.1 in the density field, p(r,0,z)=pox(1+Acos(m8)), as well as in the B, field, is added."," The only difference with paper Iis that an $m=2$ perturbation of amplitude $A=0.1$ in the density field, $\rho(r,\theta,z) = \rho_0 \times (1 + A {\rm cos} (m \theta) )$, as well as in the $B_z$ field, is added." +" In the second section, we further discuss the physical interpretation of the results obtained in our simulations and we estimate analytically the critical value of µ for which it is expected that the magnetic field stabilizes the disk."," In the second section, we further discuss the physical interpretation of the results obtained in our simulations and we estimate analytically the critical value of $\mu$ for which it is expected that the magnetic field stabilizes the disk." +" In the third section, we consider initial density perturbations of amplitude 0.5 and show that in this case, fragmentation can be obtained for a much wider range of µ."," In the third section, we consider initial density perturbations of amplitude 0.5 and show that in this case, fragmentation can be obtained for a much wider range of $\mu$." +" The fourth section provides a discussion on possible mechanisms leading to disk fragmentation and the formation of binaries, even in the presence of magnetic fields."," The fourth section provides a discussion on possible mechanisms leading to disk fragmentation and the formation of binaries, even in the presence of magnetic fields." + The sixth section concludes the paper., The sixth section concludes the paper. + We investigate the fragmentation in the case where the amplitude of the perturbations is initially A 0.1., We investigate the fragmentation in the case where the amplitude of the perturbations is initially $A=0.1$ . + In this case it is found that without rotation no fragmentation occurs., In this case it is found that without rotation no fragmentation occurs. +" Therefore, we call this type of initial condition, rotationally driven fragmentation."," Therefore, we call this type of initial condition, rotationally driven fragmentation." +" We next consider various values of the magnetic mass-to-flux over critical mass-to-flux ratio, namely µ—1000 (quasi hydrodynamical case), 4=50, 20, 5, 2 and 1.25."," We next consider various values of the magnetic mass-to-flux over critical mass-to-flux ratio, namely $\mu=1000$ (quasi hydrodynamical case), $\mu=50$, 20, 5, 2 and 1.25." +" Recalling that 44=1 corresponds to the case of a cloud supported by the magnetic field, the last value corresponds to a strongly magnetized supercritical cloud."," Recalling that $\mu=1$ corresponds to the case of a cloud supported by the magnetic field, the last value corresponds to a strongly magnetized supercritical cloud." +" In the following, we display the inner part of the collapsing cloud."," In the following, we display the inner part of the collapsing cloud." + The size of each plot is about Ro/10., The size of each plot is about $\simeq R_0/10$. + This corresponds to a physical size of 1.6x107? pc or about 7300 AU., This corresponds to a physical size of $1.6 \times 10^{-3}$ pc or about $\simeq$ 300 AU. + We present the hydrodynamical case (4=1000)., We present the hydrodynamical case $\mu=1000$ ). + Figure 1 shows three snapshots., Figure \ref{mu1000_Ap0.1} shows three snapshots. + Equatorial density and velocity field are displayed., Equatorial density and velocity field are displayed. + The first snapshot is taken shortly after the formation of the first Larson core., The first snapshot is taken shortly after the formation of the first Larson core. +" A rotationally supported structure has formed and since it is very unstable, a strong spiral pattern is developing."," A rotationally supported structure has formed and since it is very unstable, a strong spiral pattern is developing." +" This is very similar to the results obtained by other authors (e.g. Matsumoto Hanawa 2003, Hennebelle et al."," This is very similar to the results obtained by other authors (e.g. Matsumoto Hanawa 2003, Hennebelle et al." +" 2004, Goodwin et al."," 2004, Goodwin et al." + 2004)., 2004). +" The next snapshot shows that the central bar-like structure, fragments into two objects whereas the spiral pattern keeps growing and expanding due to further accretion of mass and momentum."," The next snapshot shows that the central bar-like structure, fragments into two objects whereas the spiral pattern keeps growing and expanding due to further accretion of mass and momentum." + The last snapshot shows that the centrifugally supported structure continues fragmenting and that 5 fragments have developed., The last snapshot shows that the centrifugally supported structure continues fragmenting and that 5 fragments have developed. +" Altogether, this is very similar to the results reported by many authors investigating the fragmentation of hydrodynamical rotating cores."," Altogether, this is very similar to the results reported by many authors investigating the fragmentation of hydrodynamical rotating cores." +" We note that in spite of the strongly non-linear evolution, the result remains remarkably symmetric due to proper resolution of the Jeans length (10 numerical cells per Jeans length)."," We note that in spite of the strongly non-linear evolution, the result remains remarkably symmetric due to proper resolution of the Jeans length (10 numerical cells per Jeans length)." +" We present results for the weak field cases, 4=50 and L1=20."," We present results for the weak field cases, $\mu=50$ and $\mu=20$." + Figure 2. shows results for u=50., Figure \ref{mu50_Ap0.1} shows results for $\mu=50$. +" Due to the difference in the initial magnetic strengths, it is not possible to compare the simulations at exactly the same times."," Due to the difference in the initial magnetic strengths, it is not possible to compare the simulations at exactly the same times." + The first snapshot shows a spiral pattern which is similar to the one seen in the previous case., The first snapshot shows a spiral pattern which is similar to the one seen in the previous case. +" A difference however, is that the central bar-like structure appears to be much shorter."," A difference however, is that the central bar-like structure appears to be much shorter." + This is likely due to the central magnetic field which is strongly amplified by the rapid twisting of field lines., This is likely due to the central magnetic field which is strongly amplified by the rapid twisting of field lines. +" As a result, the cloud first fragments into three fragments instead of two."," As a result, the cloud first fragments into three fragments instead of two." +" This is due to the fact that since the central bar-like structure does not fragment in two objects as in the previous case, more material and angular momentum is available in its vicinity to produce one object on each side."," This is due to the fact that since the central bar-like structure does not fragment in two objects as in the previous case, more material and angular momentum is available in its vicinity to produce one object on each side." + The next snapshots show that a symmetry breaking occurs due to one of the two satellites having merged with the central more massive fragment., The next snapshots show that a symmetry breaking occurs due to one of the two satellites having merged with the central more massive fragment. + The structure in the outer part (z>0.05 80) is still quite symmetric., The structure in the outer part $x>0.03 R_0$ ) is still quite symmetric. + Further fragments are forming in the outer part of the spiral pattern at zx= +0.05Ro., Further fragments are forming in the outer part of the spiral pattern at $x=\pm0.05 R_0$ . +" From these results, one concludes that even for values of µ as large as 50, the magnetic fieldhas a significant"," From these results, one concludes that even for values of $\mu$ as large as 50, the magnetic fieldhas a significant" +7-ray 50% z>6 redshifts of z=1—4 PPerley et 22009).,$\gamma$ $50$ $z>6$ redshifts of $z=1-4$ Perley et 2009). + 0080607 at redshift zajj=3.0363 is a unique case of a highly extinguished (Ayz3 mag) afterglow that was yet sufficiently bright for high-quality spectroscopy (Prochaska 22009)., 080607 at redshift $z_{\rm GRB} = 3.0363$ is a unique case of a highly extinguished $A_V \approx 3$ mag) afterglow that was yet sufficiently bright for high-quality spectroscopy (Prochaska 2009). + The afterglow spectrum displays positive detections of CO A-X bandheads (Morton Noreau 1994) that have also been seen through translucent molecular gas of the Milky Way SSonnentrucker 22007)., The afterglow spectrum displays positive detections of CO $A-X$ bandheads (Morton Noreau 1994) that have also been seen through translucent molecular gas of the Milky Way Sonnentrucker 2007). + The presence of III 1602 and II 1355 absorption features indicates that the host ISM has been enriched to roughly solar metallicity., The presence of II 1602 and I 1355 absorption features indicates that the host ISM has been enriched to roughly solar metallicity. + Identifications of vibrationally excited H» indicate the presence of substantial molecular gas at a few hundred pe from the burst (Sheffer 22009)., Identifications of vibrationally excited $_2$ indicate the presence of substantial molecular gas at a few hundred pc from the burst (Sheffer 2009). + The large gas surface mass density (400M pew?) and large molecular gas content found in 0080607.. are unprecedented among either damped aabsorbers along random QSO sightlines or GRB host galaxies SSrianand 22008: Noterdaeme 22009) Contrary to the common expectation of GRBs occurring preferentially in low-mass and low-metallicity environments FFruchter 220006). the observed large metal and dust contents. together with the mass-metallicity relation known for z22—3 galaxies MMannuceci 22009). imply that the host galaxy is massive and intrinsically luminous.," The large gas surface mass density $\approx 400\,{\rm M}_\odot\, {\rm pc}^{-2}$ ) and large molecular gas content found in 080607 are unprecedented among either damped absorbers along random QSO sightlines or GRB host galaxies Srianand 2008; Noterdaeme 2009) Contrary to the common expectation of GRBs occurring preferentially in low-mass and low-metallicity environments Fruchter 2006), the observed large metal and dust contents, together with the mass-metallicity relation known for $z=2-3$ galaxies Mannucci 2009), imply that the host galaxy is massive and intrinsically luminous." + Searching for the host galaxy of 0080607 therefore bears significantly on our general understanding of GRB host galaxies and particularly the dark burst population., Searching for the host galaxy of 080607 therefore bears significantly on our general understanding of GRB host galaxies and particularly the dark burst population. + Here we report the discovery of the host galaxy of 0080607 in an extensive imaging follow-up campaign., Here we report the discovery of the host galaxy of 080607 in an extensive imaging follow-up campaign. + The observed broad-band spectral energy distribution (SED) from optical toIR wavelengths. together with known dust," The observed broad-band spectral energy distribution (SED) from optical toIR wavelengths, together with known dust" +"AGAPE (7) made a survey of several fields in the central part of M31 to look for eravitationa mucrolensing eveuts,",AGAPE \cite{AGAPE1} made a survey of several fields in the central part of M31 to look for gravitational microlensing events. + As a major by-product. this survey discovered 1579 variable objects in à Ll’«10 field ceutred ou M31.," As a major by-product, this survey discovered 1579 variable objects in a $14' \times 10'$ field centred on M31." + The zin of this paper is to catalogue these objects., The aim of this paper is to catalogue these objects. + Due to the lieh star background. pixel leusine techniques have to be used to detect fix variations of individual stars.," Due to the high star background, pixel lensing techniques have to be used to detect flux variations of individual stars." +" Since we are observing brightuess fluctuations of unresolved stars. variable stars. particularly those that are intrinsically faint. are a significantOo backeroundC» in the detection of real iiicroleusiug events,"," Since we are observing brightness fluctuations of unresolved stars, variable stars, particularly those that are intrinsically faint, are a significant background in the detection of real microlensing events." + Ou the other hand. variable stars are also of high interest in their own right.," On the other hand, variable stars are also of high interest in their own right." + Svstcmatic surveys looking for variable stars in AI31 have bec first done by IIubble (2)aaud Baade aud Swope (?:?)..," Systematic surveys looking for variable stars in M31 have been first done by Hubble \cite*{hubble29}a and Baade and Swope \cite*{baade63,baade65}." + Recent surveys ou luwee fields have been used to search for Cepheids (7) and cosimuiological calibrators (DIRECT project (2)))., Recent surveys on large fields have been used to search for Cepheids \cite{magnier97} and cosmological calibrators (DIRECT project \cite{kaluzny98}) ). + ILowever. except for novae and N-ray sources INiuuwct (7?).. Tsong et al. €2).," However, except for novae and X-ray sources Kaaret \cite*{kaaret02}, Kong et al. \cite*{kong02}," +. published work avoid the bulge region., published work avoid the bulge region. + Our study is then the first oue done ou this central zone aud it leads to the identification of some variable stars poorly known in M31: Miras aud long period objects., Our study is then the first one done on this central zone and it leads to the identification of some variable stars poorly known in M31: Miras and long period objects. + Our catalogue is drawn from J-easous of nüeasuremaents and our field las significant intersection with those of other studies ((?).. DIRECT field E. (?3)) and the Point ACAPE collaboration using the INT (?)..," Our catalogue is drawn from 3-seasons of measurements and our field has significant intersection with those of other studies \cite{crotts96}, DIRECT field E, \cite{riffeser01}) ) and the Point AGAPE collaboration using the INT \cite{kerins01}." + Sect., Sect. + 2 presents ACAPE observations aud variable selection., 2 presents AGAPE observations and variable selection. + Sect., Sect. + 3 preseuts the astrometiy as well as our photometry and period search (Time Series Analysis)., 3 presents the astrometry as well as our photometry and period search (Time Series Analysis). + Sect., Sect. + L discusses our type-ideutified variable stars aud sect., 4 discusses our type-identified variable stars and sect. + 5 presents our complete catalogue as well as some conclusious., 5 presents our complete catalogue as well as some conclusions. + The ACADPE observations were made at the aun Bernard Lyot telescope (TBL) of the Pic du Midi Observatory with he £/8 spectro-reducer ISARD., The AGAPE observations were made at the m Bernard Lyot telescope (TBL) of the Pic du Midi Observatory with the f/8 spectro-reducer ISARD. + A thin Tektrouik 10211021 CCD was used with a useful field of Lsο) with 0.3” Xxels., A thin Tektronik $1024\times1024$ CCD was used with a useful field of $4' \times 4.5'$ with $0.3''$ pixels. + Since the feld of ISARD is small. 6 fields (called A. D. C. D. E. E) were necessary to cover one Ll’«104 field centred on M31 aud oricuted along its main axis.," Since the field of ISARD is small, 6 fields (called A, B, C, D, E, F) were necessary to cover one $14' \times 10'$ field centred on M31 and oriented along its main axis." + The exposure times were generally nunin in the BUR) χιπρα., The exposure times were generally min in the $B(R)$ passband. + Am additional field. Z. ceutred on the uucleus of M31 and with laree overlap with A and D fields. was aken at the beeimmine of each night. as a reference to iclp in the pointing of the telescope.," An additional field, Z, centred on the nucleus of M31 and with large overlap with A and B fields, was taken at the beginning of each night, as a reference to help in the pointing of the telescope." + The exposures were as short as in th the B and MR passhands for the Z ceutral field., The exposures were as short as min in both the $B$ and $R$ passbands for the Z central field. + Since the short exposures prevent detection of faint or stuall auiplitude variable objects ouly novae are presented for the Z field data in this paper.," Since the short exposures prevent detection of faint or small amplitude variable objects, only novae are presented for the Z field data in this paper." + The observing canupaigu ran roni 1991 to 1996., The observing campaign ran from 1994 to 1996. + It turned out that it was mupossible to monitor all the fields iu both colours, It turned out that it was impossible to monitor all the fields in both colours +Inmiinosity of galaxies. but in (his case the regulating parameter e does not have a theoretical counterpart.,"luminosity of galaxies, but in this case the regulating parameter $a$ does not have a theoretical counterpart." + The second transformation is where Τα is an exponent that connects the mass to the Iuminositv., The second transformation is where 1/a is an exponent that connects the mass to the luminosity. + The pdf (13. ) is therefore transformed into the following: where V is a normalisation [actor which defines the overall density of galaxies. a nunmber per cubic AMpe.," The pdf \ref{psi} ) is therefore transformed into the following: where $\Psi^*$ is a normalisation factor which defines the overall density of galaxies, a number per cubic $Mpc$." + The mathematical range of existence is 0xL<2€: conversely (he astronomical range is Li] and a no-zero value of fo is required from the data (see Fig. 39).," Moreover, I can estimate from the observables the ratio $R_{\rm gas} = (\Omega_{\rm b}/\Omega_{\rm m} -f_{\rm gal}/B) +/ f_{\rm gas} \times (Y B C) \approx (f_{\rm ob}/f_{\rm gas} +1)$ and to evaluate the probability that $R_{\rm gas} > 1$ and a no-zero value of $f_{\rm ob}$ is required from the data (see Fig. \ref{fig:macho}) )." + L obtain values of 2a... between 1.300=1.6 lyand 1.7 (5=1.15.€ 1.151. with an interval accepted at the 95 per cent contidence level of 0.5—2.7.," I obtain values of $R_{\rm gas}$ between 1.3 $B=1, C=1$ ) and 1.7 $B=1.15, C=1.15$ ), with an interval accepted at the 95 per cent confidence level of 0.5–2.7." + More signiticantly. this ratio has to be larger than | a 76.6 (5D=1.€ lrand 92.5 (5.=115.€ 1.15) per cent confidence level.," More significantly, this ratio has to be larger than 1 at 76.6 $B=1, C=1$ ) and 92.5 $B=1.15, C=1.15$ ) per cent confidence level." + This result gives a high confidence to the conclusion that a significant amount of baryons has to be presen apart from what is observed both at X-ray and optical wavelength., This result gives a high confidence to the conclusion that a significant amount of baryons has to be present apart from what is observed both at X-ray and optical wavelength. +" By comparing the recent. cosmological constraints from measurements of the angular power spectrum of the temperature anisotropy in the CMB done with WMAP with the observed distribution of the gas mass fraction in clusters of galaxies. I conclude that It is very unlikely that galactic objects. such as ""colored"" (red. brown, white. beige) dwarfs. stellar remnants and other species of MACHOs (see review in Gilmore 1999 and Evans 2003). or intergalactic ones formed from tidal disruption of cluster dwarfs. ike planetary nebulae (e.g. Ciardullo et al."," By comparing the recent cosmological constraints from measurements of the angular power spectrum of the temperature anisotropy in the CMB done with WMAP with the observed distribution of the gas mass fraction in clusters of galaxies, I conclude that It is very unlikely that galactic objects, such as “colored"" (red, brown, white, beige) dwarfs, stellar remnants and other species of MACHOs (see review in Gilmore 1999 and Evans 2003), or intergalactic ones formed from tidal disruption of cluster dwarfs, like planetary nebulae (e.g. Ciardullo et al." + 2002). red-giant-branch stars (e.g. Ferguson et al.," 2002), red-giant-branch stars (e.g. Ferguson et al." + 1998) and supernovae (Gal-Yam et al., 1998) and supernovae (Gal-Yam et al. + 2003). can beresponsible for such amount of baryons.," 2003), can beresponsible for such amount of baryons." + It is reasonable to believe that they can contribute by about 0.2 times fost. οἳ O04fu.," It is reasonable to believe that they can contribute by about 0.2 times $f_{\rm gal}$, or $0.04 f_{\rm gas}$." + The most plausible suspect to give so large contribution is then a X-ray warm (107 K <2 10* Ko intracluster medium (W-ICM)., The most plausible suspect to give so large contribution is then a X-ray warm $10^5$ K $< T <$ $10^7$ K) intracluster medium (W-ICM). + Large scale cosmological and hydrodynamical simulations by Cen Ostriker (1999) and Dave et al. (, Large scale cosmological and hydrodynamical simulations by Cen Ostriker (1999) and Davé et al. ( +"2001) show that the mass fraction at redshift O is largely dominated from a warm medium. with a relative contribution in mass that 1s about 2 times larger than the amount of hot (/°LO"" K) baryons.","2001) show that the mass fraction at redshift 0 is largely dominated from a warm medium, with a relative contribution in mass that is about 2 times larger than the amount of hot $T > 10^7$ K) baryons." + However. less than 30 per cent of it falls in overdensities 60 that are typical for bound structures in a ACDM universe.," However, less than 30 per cent of it falls in overdensities $\ge 60$ that are typical for bound structures in a $\Lambda$ CDM universe." + Furthermore. Bonamente et al. (," Furthermore, Bonamente et al. (" +2002) present evidence of excess in the soft emission between 0.2—0.4 keV in SO per cent of the 38 clusters in their sample of PSPC observations.,2002) present evidence of excess in the soft X-ray emission between 0.2–0.4 keV in 50 per cent of the 38 clusters in their sample of PSPC observations. + They list several suggestions on how to explain this excess. originally observed in extreme ultraviolet (Lieu et al.," They list several suggestions on how to explain this excess, originally observed in extreme ultraviolet (Lieu et al." + 1996). both as thermal and non-thermal component.," 1996), both as thermal and non-thermal component." + If we assign this emission to the baryons that are lacking in our budget. we interpret it as thermal emission due either to the diffuse/halo component of unresolved X-ray. faint cluster galaxies or. W-ICM.," If we assign this emission to the baryons that are lacking in our budget, we interpret it as thermal emission due either to the diffuse/halo component of unresolved X-ray faint cluster galaxies or W-ICM." + In the first case. we are forced to consider an inexplicable large amount of X-ray emitting member galaxies.," In the first case, we are forced to consider an inexplicable large amount of X-ray emitting member galaxies." + More plausible is then the hypothesis of W-ICM. even hough its cooling time tends to be very short with the bulk of he radiation in emission line if this gas is not primordial.," More plausible is then the hypothesis of W-ICM, even though its cooling time tends to be very short with the bulk of the radiation in emission line if this gas is not primordial." + Fabian (1997) suggested that it can be located in turbulent mixing layers ying between embedded cold clouds and the ICM., Fabian (1997) suggested that it can be located in turbulent mixing layers lying between embedded cold clouds and the ICM. + However. he traditional picture on the efficiency of cooling processes in he cluster cores is not supported anymore after that XMM and Chandra observations did not report evidence of gas cooler than 1—2 keV te.g. Peterson et al.," However, the traditional picture on the efficiency of cooling processes in the cluster cores is not supported anymore after that XMM and Chandra observations did not report evidence of gas cooler than 1–2 keV (e.g. Peterson et al." + 2003) and showed a strong interplay between ICM. the central active galaxy (e.g. Fabian 2002) and merging cool clumps (e.g.Markevitch et al.," 2003) and showed a strong interplay between ICM, the central active galaxy (e.g. Fabian 2002) and merging cool clumps (e.g.Markevitch et al." + 2000. Mazzotta et al.," 2000, Mazzotta et al." + 2003)., 2003). + On the other side. the production of thermal energy per xrticle due to supernovae related to the star formation activity is in the order of Εν10yore37.Mau) keV fora given efficiency n in converting the kinetic energy of the explosion into thermal energy through galactic winds. and adopting typical values of the cluster gas mass and number of type IT supernovae as required from the observed ICM metallicity.," On the other side, the production of thermal energy per particle due to supernovae related to the star formation activity is in the order of $0.4 (\eta/0.1) (N_{\rm SNII}/10^9) +(10^{13} M_{\odot} / M_{\rm gas})$ keV for a given efficiency $\eta$ in converting the kinetic energy of the explosion into thermal energy through galactic winds, and adopting typical values of the cluster gas mass and number of type II supernovae as required from the observed ICM metallicity." + While this energy per gas particle is not enough to stop cooling the hot ICM. it can easily accommodate for the survival of the warm component.," While this energy per gas particle is not enough to stop cooling the hot ICM, it can easily accommodate for the survival of the warm component." + Intriguingly. the stronger soft excess detected in data from Bonamente et al. (," Intriguingly, the stronger soft excess detected in data from Bonamente et al. (" +2002) is measured in objects like ASS and ΑΙΤΟΣ. that are the ones lacking most of the baryons with respect to the cosmic budget as plotted in Fig. |..,"2002) is measured in objects like A85 and A1795, that are the ones lacking most of the baryons with respect to the cosmic budget as plotted in Fig. \ref{fig:dat}." + Signiticant detection is also present in A2029. A?199 and A3571. whereas a marginal detection is associated to A?142.," Significant detection is also present in A2029, A2199 and A3571, whereas a marginal detection is associated to A2142." + Nevalainen et al. (, Nevalainen et al. ( +2003: see also Kaastra et al.,2003; see also Kaastra et al. + 2003) confirm with XMM the excess in the soft X-ray emission in A1795 and that this excess is best fitted by a thermal component with a characteristic temperature of 0.8 keV. which is about an order of magnitude higher than what required from data but still consistent with our energetic arguments.," 2003) confirm with XMM the excess in the soft X-ray emission in A1795 and that this excess is best fitted by a thermal component with a characteristic temperature of 0.8 keV, which is about an order of magnitude higher than what required from data but still consistent with our energetic arguments." + Using their estimation of the atom density of the W-ICM in the core of A1795. and assuming that it is broadly distributed like the ICM. one ean infer à fwgeifons=Husloc]O43.," Using their estimation of the atom density of the W-ICM in the core of A1795, and assuming that it is broadly distributed like the ICM, one can infer a $f_{\rm W-ICM} / f_{\rm gas} = +R_{\rm gas} -1 \approx 0.43$." + In general. values of fwacufans between 0.1 and 0.5 are expected.," In general, values of $f_{\rm W-ICM} / f_{\rm gas}$ between 0.1 and 0.5 are expected." + To summarize. clusters seem to have similar behavior in accumulating the same relative amount of baryons.," To summarize, clusters seem to have similar behavior in accumulating the same relative amount of baryons." + It is then their peculiar thermal history due to the interplay of merging actions and/or activity of the central active galaxy that provides the baryonic ingredients and cook the baryonic pie that we taste and show in Figure 4.., It is then their peculiar thermal history due to the interplay of merging actions and/or activity of the central active galaxy that provides the baryonic ingredients and cook the baryonic pie that we taste and show in Figure \ref{fig:pie}. + To prepare it. I have considered only the eight nearby clusters which provide a more reliable estimate of f.i and are less affected from systematics in the determination of f... (see discussion in Ettori et al.," To prepare it, I have considered only the eight nearby clusters which provide a more reliable estimate of $f_{\rm gal}$ and are less affected from systematics in the determination of $f_{\rm gas}$ (see discussion in Ettori et al." + 2003)., 2003). + I have also corrected the gas fraction by the depletion factor 3=0.92., I have also corrected the gas fraction by the depletion factor $Y \approx 0.92$. + The baryonic pie is then made of 70 per cent of ICM. with Lo range between 56 and 89 per cent and a distribution of the calculated fan./Awarar that spans between 28 and 143 per cent at 27 confidence level (higher upper limit observed in A426 that has a most probable fas./Avatar value of 115 per cent).," The baryonic pie is then made of 70 per cent of ICM, with $1 \sigma$ range between 56 and 89 per cent and a distribution of the calculated $f_{\rm gas}/f_{\rm WMAP}$ that spans between 28 and 143 per cent at $2 \sigma$ confidence level (higher upper limit observed in A426 that has a most probable $f_{\rm gas}/f_{\rm WMAP}$ value of 115 per cent)." + The cold. stellar component is responsible for 13 (1o: 8-19) per cent. with an observed distribution in the sample between 2 and 37 per cent (20 lower and upper limit. with," The , stellar component is responsible for 13 $1 \sigma$ : 8–19) per cent, with an observed distribution in the sample between 2 and 37 per cent $2 \sigma$ lower and upper limit, with" +The outliers in these plots are also interesting.,The outliers in these plots are also interesting. +" The clusters which give strong overestimates of Y and Mj, typically result from line-of-sight overlap of multiple structures.", The clusters which give strong overestimates of $Y$ and $M_{gas}$ typically result from line-of-sight overlap of multiple structures. +" This enhances the integrated SZE signal in projection, but overestimates the true value for the main cluster."," This enhances the integrated SZE signal in projection, but overestimates the true value for the main cluster." +" The clusters with low estimated values of Y and/or Mgas typically have poor quality 6-model fits (as measured by a x? statistic), and appear to have systematically low fitted values for the core radius."," The clusters with low estimated values of $Y$ and/or $M_{gas}$ typically have poor quality $\beta$ -model fits (as measured by a $\chi^2$ statistic), and appear to have systematically low fitted values for the core radius." +" Some of these clusters appear to have weak cool cores, not meeting the cool core criteria, and thus were not excluded from the sample."," Some of these clusters appear to have weak cool cores, not meeting the cool core criteria, and thus were not excluded from the sample." + It is interesting that the clusters with mass underestimates do not all generate underestimates of Y., It is interesting that the clusters with mass underestimates do not all generate underestimates of $Y$ . + This effect warrants further study., This effect warrants further study. + Table 3 also shows the result of this analysis., Table \ref{y500_tab} also shows the result of this analysis. +" When using isothermal models, the median estimated value of Ysoo is larger than the true value mean is a "," When using isothermal models, the median estimated value of $Y_{500}$ is larger than the true value (the mean is a overestimate)." +"Additionally, when (theestimating the gas mass, the overestimate).median estimated value is a overestimate."," Additionally, when estimating the gas mass, the median estimated value is a overestimate." +" In previous work (Hallmanetal.2006),, we have shown that the magnitude of the overestimate via X-ray £-model methods is lower than this, but in that case we assumed one could correctly calculate the value of rsgo with no error."," In previous work \citep{hall06}, we have shown that the magnitude of the overestimate via X-ray $\beta$ -model methods is lower than this, but in that case we assumed one could correctly calculate the value of $r_{500}$ with no error." +" In either case, this overestimate is consistent with our previous work, and with that of others (Mohretal.1999;Mathiesen1999)."," In either case, this overestimate is consistent with our previous work, and with that of others \citep{mohr99, math99}." +". The overestimate in mass results from substructure, merging and other physical processes not described by a simple model."," The overestimate in mass results from substructure, merging and other physical processes not described by a simple model." +" In the current analysis, the value of rso9 is deduced directly from the 8-model."," In the current analysis, the value of $r_{500}$ is deduced directly from the $\beta$ -model." +" In contrast, the U-8 method gets closer to the correct value for Yso9, with a median value higher than the true value."," In contrast, the $\beta$ method gets closer to the correct value for $Y_{500}$, with a median value higher than the true value." +" For the mass, the U-@ method gets an estimate close to the true mass, a median overestimate of only4%."," For the mass, the $\beta$ method gets an estimate close to the true mass, a median overestimate of only." +". Additionally, using the U-5 method reduces the scatter in Y5oo values, as shown in Figure 7.."," Additionally, using the $\beta$ method reduces the scatter in $Y_{500}$ values, as shown in Figure \ref{yhist}." +" The distribution of values is more sharply peaked, with a smaller high end tail in addition to a reduced bias compared to the isothermal method."," The distribution of values is more sharply peaked, with a smaller high end tail in addition to a reduced bias compared to the isothermal method." +" In mass, the result is a reduced bias in the median values with a slight improvement in the scatter as shown in Figure 8.."," In mass, the result is a reduced bias in the median values with a slight improvement in the scatter as shown in Figure \ref{mhist}. ." + 'There is an inconsistency between X-ray and SZE fitted model parameters that leads to a bias in deduced values of Y5oo and when using isothermal 8-models.," There is an inconsistency between X-ray and SZE fitted model parameters that leads to a bias in deduced values of $Y_{500}$ and $M_{500,gas}$ when using isothermal $\beta$ -models." +" Using our U-8 Mso0,gasmodel reduces the bias and scatter, resulting in a more precise and accuratedetermination of the y- Mscaling relation for clusters."," Using our $\beta$ model reduces the bias and scatter, resulting in a more precise and accuratedetermination of the $y$ $M$scaling relation for clusters." +The most important parameter from the CMB data is the acoustic scale.,The most important parameter from the CMB data is the acoustic scale. +" In this paper the stretch parameter R=QI?H.(1+zps)DA(zrs)/c (Bond, Efstathiou Tegmark 1997; Wang Mukherjee 2006) is not used, but the acoustic scale £, evaluated at the mean baryon and dark matter densities is used in its place."," In this paper the stretch parameter $R = \Omega_M^{1/2} H_\circ (1+z_{LS}) D_A(z_{LS})/c$ (Bond, Efstathiou Tegmark 1997; Wang Mukherjee 2006) is not used, but the acoustic scale $\ell_a$ evaluated at the mean baryon and dark matter densities is used in its place." + The acoustic scale is defined as (Page 22003) t, The acoustic scale is defined as (Page 2003) _a = +confirms previous studies in the mid-IR that show large fractions of star-forming galaxies closer to the dense cores of galaxy clusters.,confirms previous studies in the mid-IR that show large fractions of star-forming galaxies closer to the dense cores of galaxy clusters. + The combined results of our analysis show that the cluster members identified at sub-mm wavelengths can be part of a population of evolved systems on the verge of transition from the population of blue active galaxies to the quenched systems (ellipticals and SOs) dominating the cluster cores. and suggests that environmental effects at distances of order of play a role regulating formation activity during this transition.," The combined results of our analysis show that the cluster members identified at sub-mm wavelengths can be part of a population of evolved systems on the verge of transition from the population of blue active galaxies to the quenched systems (ellipticals and S0s) dominating the cluster cores, and suggests that environmental effects at distances of order of play a role regulating star-formation activity during this transition." + Deeper and more complete studies of galaxy clusters at far- and sub-mm wavelengths withHerschel and SCUBA-2 should oovide more complete coverage of the physical processes at work in cluster galaxies., Deeper and more complete studies of galaxy clusters at far-IR and sub-mm wavelengths with and SCUBA-2 should provide more complete coverage of the physical processes at work in cluster galaxies. + In particular. combining the higher sensitivity and resolution of SPIRE and the spectral coverage offered by xrallel. observations with PACS and SPIRE will allow for the detection and characterization of cluster galaxies down to smaller uminosities and masses. providing amore complete description of he star-formation activity in galaxy clusters.," In particular, combining the higher sensitivity and resolution of SPIRE and the spectral coverage offered by parallel observations with PACS and SPIRE will allow for the detection and characterization of cluster galaxies down to smaller luminosities and masses, providing a more complete description of the star-formation activity in galaxy clusters." +which are observed to be generally more diffuse.,which are observed to be generally more diffuse. +" Other factors which influence the concentration parameter include the mass and velocity dispersion, both of which are low for the dwarf galaxy sample."," Other factors which influence the concentration parameter include the mass and velocity dispersion, both of which are low for the dwarf galaxy sample." + The MUGS sample of simulated galaxies in Figure 6 appears to extend to higher values of concentration than both the UW sample of Milky Way-like galaxies and the Dwarf sample., The MUGS sample of simulated galaxies in Figure \ref{ColourConc} appears to extend to higher values of concentration than both the UW sample of Milky Way-like galaxies and the Dwarf sample. +" This is most likely due to the presence of earlier-type discs that have greater masses within the unbiased MUGS sample (c.f.,"," This is most likely due to the presence of earlier-type discs that have greater masses within the unbiased MUGS sample (c.f.," +" with the UW sample, which were chosen a priori to more closely resemble later-type discs)."," with the UW sample, which were chosen a priori to more closely resemble later-type discs)." +" Moreover, the MUGS sample of galaxies have a higher density threshold for star formation (1 cm~3), which could lead to preferential star formation in the denser (central) regions of the galaxy (Agertz, Teysier Moore 2010), although this behaviour is not seen in dwarf galaxy simulations (Governato et al."," Moreover, the MUGS sample of galaxies have a higher density threshold for star formation (1 $^{-3}$ ), which could lead to preferential star formation in the denser (central) regions of the galaxy (Agertz, Teysier Moore 2010), although this behaviour is not seen in dwarf galaxy simulations (Governato et al." + 2010)., 2010). +" The MUGS sample also has a greater average circular velocity (150 - 250 km/s), compared to the other simulated samples of galaxies, which is a parameter known to correlate with concentration (?).."," The MUGS sample also has a greater average circular velocity (150 - 250 km/s), compared to the other simulated samples of galaxies, which is a parameter known to correlate with concentration \citep{Graham2001}." +" In Figure 7,, the observed galaxy sample demonstrates a strong anti-correlation between asymmetry and colour."," In Figure \ref{ColourAsym}, the observed galaxy sample demonstrates a strong anti-correlation between asymmetry and colour." +" This correlation stems from the bluer, younger galaxies generally containing spiral arms with dust lanes and star forming regions, and the older, elliptical galaxies generally being devoid of structure."," This correlation stems from the bluer, younger galaxies generally containing spiral arms with dust lanes and star forming regions, and the older, elliptical galaxies generally being devoid of structure." +" The simulated galaxies follow an approximately identical trend to that of the observed galaxies, however, due to the bluer nature of the selected simulations, they form a blue extension of the observed galaxy trend."," The simulated galaxies follow an approximately identical trend to that of the observed galaxies, however, due to the bluer nature of the selected simulations, they form a blue extension of the observed galaxy trend." + ? showed that there was a distinct region in the bottom left corner of the colour-asymmetry plot where no galaxies were bluer and more symmetric., \citet{Conselice2003} showed that there was a distinct region in the bottom left corner of the colour-asymmetry plot where no galaxies were bluer and more symmetric. + This region is well-defined by the simulations which demonstrate a very strong correlation between colour and asymmetry., This region is well-defined by the simulations which demonstrate a very strong correlation between colour and asymmetry. +" The earlier-types within the MUGS sample are redder in colour with respect to the other simulations, and tend to be more symmetric."," The earlier-types within the MUGS sample are redder in colour with respect to the other simulations, and tend to be more symmetric." +" Again there is a strong distinction between the various Hubble types, which is similar to the correlation demonstrated by the observed galaxy sample."," Again there is a strong distinction between the various Hubble types, which is similar to the correlation demonstrated by the observed galaxy sample." +" However, due to the lack of redder simulated galaxies with low, approximately zero, asymmetry values, this trend does not extend to the upper left corner of Figure 7,, where the redder, symmetric, galaxies reside in nature."," However, due to the lack of redder simulated galaxies with low, approximately zero, asymmetry values, this trend does not extend to the upper left corner of Figure \ref{ColourAsym}, where the redder, symmetric, galaxies reside in nature." +" Again, this can be traced to the ongoing late-time star formation in the earlier-type simulations which is not seen in nature."," Again, this can be traced to the ongoing late-time star formation in the earlier-type simulations which is not seen in nature." + In Figure 7 some of the dwarf simulated galaxies appear to be excessively asymmetric relative to the other simulations., In Figure \ref{ColourAsym} some of the dwarf simulated galaxies appear to be excessively asymmetric relative to the other simulations. + The large variation of apparent flux levels within these systems is most likely the cause of this increased in asymmetry., The large variation of apparent flux levels within these systems is most likely the cause of this increased in asymmetry. + ? showed that it is almost always the inclined galaxies that contribute to the scatter in the colour-asymmetry diagram and that the less inclined galaxies are systematically higher., \citet{Conselice2000b} showed that it is almost always the inclined galaxies that contribute to the scatter in the colour-asymmetry diagram and that the less inclined galaxies are systematically higher. +" In Figure 8,, the edge-on and face- galaxies have different symbols, and from this it can"," In Figure \ref{ColourAsymN}, the edge-on and face-on galaxies have different symbols, and from this it can" +We carry ont a study of SiO outflows toward the high-mass star forming regions 118264 and 123151.,We carry out a study of SiO outflows toward the high-mass star forming regions I18264 and I23151. + According to the IIPCO observations and SiO line profiles. (he SiO emission in these two sources can be caused by the interaction between the jet or wind from the central voung stars and the dense ambient gas.," According to the $^{13}$ $^+$ observations and SiO line profiles, the SiO emission in these two sources can be caused by the interaction between the jet or wind from the central young stars and the dense ambient gas." +" The mass-velocity relation of the IC of the SE outflow in [18264 and the blueshifted outflows in 123151 also can be fitted by a broken power law with the slopes steeping αἱ about 10 ! with respective to the svstemic velocity,", The mass-velocity relation of the HC of the SE outflow in I18264 and the blueshifted outflows in I23151 also can be fitted by a broken power law with the slopes steeping at about 10 $^{-1}$ with respective to the systemic velocity. + With the PV characteristic of the terminal velocities decreasing with the distance from the driving source. the low velocity (|Av<10 !) gas probably comprises the ambient gas entrained by the high velocity (|Av>10 !) gas.," With the PV characteristic of the terminal velocities decreasing with the distance from the driving source, the low velocity $|{\Delta}v|<10$ $^{-1}$ ) gas probably comprises the ambient gas entrained by the high velocity $|{\Delta}v|>10$ $^{-1}$ ) gas." + Toward 118264. al least two quasi-perpencicular oulllows with high collimation [actors (c3— 4) are resolved.," Toward I18264, at least two quasi-perpendicular outflows with high collimation factors $\sim3-4$ ) are resolved." + The VIIC of the SE outflow has verv high velocities up to Ar~60 +., The VHC of the SE outflow has very high velocities up to ${\Delta}v\sim60$ $^{-1}$. + db ds north offset from the HIC. and its downstream peak is [arther away [rom the driving source.," It is north offset from the HC, and its downstream peak is farther away from the driving source." + Comparing wilh the outflows in the well studied low-mass source L1157. we suggest the SE outflow can be entrained by an widerlving precessing jet.," Comparing with the outflows in the well studied low-mass source L1157, we suggest the SE outflow can be entrained by an underlying precessing jet." + The characteristics of the IC and VIIC of the SE outflow in the mass-velocity and PV diagrams also support the processing jet scenario., The characteristics of the HC and VHC of the SE outflow in the mass-velocity and PV diagrams also support the processing jet scenario. + For 23151. the blueshilted SiO emission (races a quasi-parabolic shaped outflow which can be identified in the 3.4 mm continuum and 0Ο — emission and coincide with (he near-inlrared nebulositv in the literature.," For I23151, the blueshifted SiO emission traces a quasi-parabolic shaped outflow which can be identified in the 3.4 mm continuum and $^{13}$ $^+$ emission and coincide with the near-infrared nebulosity in the literature." + This outflow can be interpreted as (he molecular gas entrained bv the underlving wide-angle wind., This outflow can be interpreted as the molecular gas entrained by the underlying wide-angle wind. + The core masses estimated [rom the 3.4 mam conünuunm are 570 AL. and 7300 M. respectively for the near and far distances for 113264 and 170 A. for 123151., The core masses estimated from the 3.4 mm continuum are 570 $M_{\odot}$ and 7300 $M_{\odot}$ respectively for the near and far distances for I18264 and 170 $M_{\odot}$ for I23151. +" With the assumption of (he momentum conservation between the outflow and the driving agent. the estimated outflow rates lead to accretion rates of 1.2xLOM.yrFl and 4.2x10294,yr! respectively for the near and [ar distances lor 118264 and 1.9x10M,yr for I23151."," With the assumption of the momentum conservation between the outflow and the driving agent, the estimated outflow rates lead to accretion rates of $1.2\times10^{-3}M_{\odot}\,yr^{-1}$ and $4.2\times10^{-2}M_{\odot}\,yr^{-1}$ respectively for the near and far distances for I18264 and $1.9\times10^{-5}M_{\odot}\,yr^{-1}$ for I23151." + Taking into account the missing flux due to the (he missing short spacings lor 123151. the accretion rate in (his region should be higher.," Taking into account the missing flux due to the the missing short spacings for I23151, the accretion rate in this region should be higher." + Thus for both sources the accretion rates are hieh enough to overcome the radiation pressure from the central objects and form massive slars., Thus for both sources the accretion rates are high enough to overcome the radiation pressure from the central objects and form massive stars. + To summarize. our molecular outflow: cata derived [rom high resolution observations toward (wo Iuminous sources show morphologies and kinematics similar to those of the sources.," To summarize, our molecular outflow data derived from high resolution observations toward two luminous sources show morphologies and kinematics similar to those of the low-mass sources." + The outflows can be interpreted by jet or wide-angle wind entrainment moclels., The outflows can be interpreted by jet or wide-angle wind entrainment models. + The presented data and analvsis further support that massive stars up to 10L. (e30MM. ) form via disk mediated accretion processes as low-mass stars., The presented data and analysis further support that massive stars up to $10^5 L_{\odot}$ $\sim30 M_{\odot}$ ) form via disk mediated accretion processes as low-mass stars. +Partial covering phenomena have recently been detected with NADENewton in broad- and unarrow-line ACN 11 707-195. Boller et al.,"Partial covering phenomena have recently been detected with XMM-Newton in broad- and narrow-line AGN (1H 0707-495, Boller et al." + 2002: IRAS 13221-3809. Boller et al.," 2002; IRAS 13224-3809, Boller et al." + in preparation: PG 12111651. Reeves. in preparation. and PDS 651. O'Brien. in preparation).," in preparation; PG 1211+654, Reeves, in preparation, and PDS 654, O'Brien, in preparation)." + Compton thick naterial partially covers the central source. resulting in strong neutral or partially iouised Fe EK absorption edees. Fe I& re-enission features with fluorescent vields ο] 0.323. and stroug soft N-rav cussion.," Compton thick material partially covers the central source, resulting in strong neutral or partially ionised Fe K absorption edges, Fe K re-emission features with fluorescent yields below 0.33, and strong soft X-ray emission." +" Ποπονα, je Dhauted spectral coverage of the Chandra LETC PAoectrum does not allow us to coustrain partial coverer PAoectral compoucuts."," However, the limited spectral coverage of the Chandra LETG spectrum does not allow us to constrain partial coverer spectral components." + NMNI-Nowton is required to test us livpothesis., XMM-Newton is required to test this hypothesis. + Most probably. the absorbing material has o be Compton thick for X-ray aux optical light (cf.," Most probably, the absorbing material has to be Compton thick for X-ray and optical light (cf." + Boller al., Boller et al. + 2002). which would not be in disagreement with the optical extinction derived for LES 1927|651.," 2002), which would not be in disagreement with the optical extinction derived for 1ES 1927+654." + We note that the XN-rav observations were uot taken siuultaneouslv with the optical observations and it is possible that the obscuration is a strong function of time., We note that the X-ray observations were not taken simultaneously with the optical observations and it is possible that the obscuration is a strong function of time. + However. this possibility is not very likely as the N-rax observations are spread over a time scale of 12 years which also holds for the optical spectroscopic data (see e.9.. Porhlnan et al.," However, this possibility is not very likely as the X-ray observations are spread over a time scale of 12 years which also holds for the optical spectroscopic data (see e.g., Perlman et al." + 1996)., 1996). + Whenever we observe LES 1927|651 at A-ravs. it clisplavs strong and rapid variability.," Whenever we observe 1ES 1927+654 at X-rays, it displays strong and rapid variability." + The optical spectitun also shows consistency. over time., The optical spectrum also shows consistency over time. + Near-intrared spectroscopy is required to further constraiu the optical extinction for the BLR in LES 1927|651. e.g. observations of Pad. Pao. Br? aud Bra.," Near-infrared spectroscopy is required to further constrain the optical extinction for the BLR in 1ES 1927+654, e.g. observations of $\rm \beta$ , $\rm \alpha$ , $\rm \gamma$ and $\rm \alpha$." + Assuming that we will detect broad components in these lines. this will allow us to determine wpper linits for the Ay value up to about 65 (cf.," Assuming that we will detect broad components in these lines, this will allow us to determine upper limits for the $\rm A_V$ value up to about 68 (cf." + Goodrich et al., Goodrich et al. + 1991)., 1994). + O.5cem We have preseuted an extreme and unique colubination of optical aud X-ray properties in. LES | G51., 0.5cm We have presented an extreme and unique combination of optical and X-ray properties in 1ES $+$ 654. + Clearly it is crucial to search for simular features in other galaxies., Clearly it is crucial to search for similar features in other galaxies. + If such features are comuuou in other objects. this will further constrain therange ofsuitable models.," If such features are common in other objects, this will further constrain therange ofsuitable models." +"functions estimated. from ""whullled catalogues in. which satellitecentral galaxy populations are randomly exchanged between halos of similar mass.",functions estimated from “shuffled” catalogues in which satellite–central galaxy populations are randomly exchanged between halos of similar mass. + H£ halo assembly history is indeed. independent. of halo environment. such shullling should have no effect on the estimated. correlations.," If halo assembly history is indeed independent of halo environment, such shuffling should have no effect on the estimated correlations." + Alore specifically. for cach FOL dark matter halo we first. record. the position oll-sets of all its galaxies wil-— respect to the central’ galaxy.," More specifically, for each FOF dark matter halo we first record the position off-sets of all its galaxies with respect to the `central' galaxy." + This central galaxy sits at the bottom of the halo's potential well. while further galaxiega are satellites which may or may not be associated with subhalos catalogued bySUBEIND.," This central galaxy sits at the bottom of the halo's potential well, while further galaxies are satellites which may or may not be associated with subhalos catalogued by." +" We then rank-orcler all halos by virial mass and divide them into mass bins of width logMya,=0.1 (although because of the rapidly decreasing number of halos in the tail of the mass function the two most massive bins are widened to logMy=14.815.0 and logMj;=15.015.5."," We then rank-order all halos by virial mass and divide them into mass bins of width $\log \Delta {\rm M}_{\rm vir} = 0.1$ (although because of the rapidly decreasing number of halos in the tail of the mass function the two most massive bins are widened to $\log\, {\rm M}_{\rm vir} = +14.8-15.0$ and $\log\, {\rm M}_{\rm vir} = 15.0-15.5$." + Note that the gradient of the assembly bias ellect across this mass range is small. as shown in Figure 3 o£ ?..," Note that the gradient of the assembly bias effect across this mass range is small, as shown in Figure 3 of \cite{Wechsler2006}." + Note also that here and elsewhere we define Alay as the mass within the largest: sphere surrounding the halo's potential minimum with mean enclosed. density at least 200 times the critical value)., Note also that here and elsewhere we define $M_{\rm vir}$ as the mass within the largest sphere surrounding the halo's potential minimum with mean enclosed density at least 200 times the critical value). + We then rancdomly shullle the galaxy populations of the halos in cach bin., We then randomly shuffle the galaxy populations of the halos in each bin. + When doing this. we take the new central galaxy of cach halo to have the same position as the original central galaxy and we determine the positions of the new satellites using their recorded olf-sets from their central galaxy.," When doing this, we take the new central galaxy of each halo to have the same position as the original central galaxy and we determine the positions of the new satellites using their recorded off-sets from their central galaxy." + Each central ealaxy thus moves together with its own set of satellites., Each central galaxy thus moves together with its own set of satellites. + In the language of HOD mocdellers (e.g.7). this procedure preserves all 1-halo contributions to galaxy clustering statistics., In the language of HOD modellers \citep[e.g.][]{Cooray2002} this procedure preserves all 1-halo contributions to galaxy clustering statistics. + Any clillerences between the original and the shullled catalogues can arise from 2-halo terms only., Any differences between the original and the shuffled catalogues can arise from 2-halo terms only. + The shullling is done 10 times with clifferent rancom seeds. to create 10 cilferent shullled galaxy catalogues., The shuffling is done 10 times with different random seeds to create 10 different shuffled galaxy catalogues. + Lt can also be carried out among halos for which a second variable. such as halo formation redshift. has been matched in addition to halo mass.," It can also be carried out among halos for which a second variable, such as halo formation redshift, has been matched in addition to halo mass." + We show the cllect of such extra constraints in Section 4.3.., We show the effect of such extra constraints in Section \ref{results2}. + To quantify the dilference in clustering between the actual and the shullled galaxy catalogues we measure the 2-point autocorrelation function for cach ancl plot. their relative bias. 6(r). defined by lere Souur is the 2-point function of the. shullled catalogue at pair separation r. and £o is the corresponding 2-point function for the original (unshullled) catalogue.," To quantify the difference in clustering between the actual and the shuffled galaxy catalogues we measure the 2-point autocorrelation function for each and plot their relative bias, $b(r)$, defined by Here $\xi_{\rm shuff}$ is the 2-point function of the shuffled catalogue at pair separation $r$, and $\xi_{\rm orig}$ is the corresponding 2-point function for the original (unshuffled) catalogue." + Note that a value of 671 implies that the shullling cilutes the clustering of the original distribution., Note that a value of $b\!>\!1$ implies that the shuffling dilutes the clustering of the original distribution. + Note also that whenever we estimate 6 below. exactly the same galaxy. set is use to estimate both Sarin and Sanur.," Note also that whenever we estimate $b$ below, exactly the same galaxy set is use to estimate both $\xi_{\rm orig}$ and $\xi_{\rm shuff}$." + Only the positions of the galaxies are changed by the shullling., Only the positions of the galaxies are changed by the shuffling. + 1n Fig., In Fig. + 1 we plot the relative. bias between our 10 shullled galaxy catalogues and the original Millennium Run catalogue as a function of pair separation. and for subsets of galaxies selected. in various wavs.," \ref{fig1} we plot the relative bias between our 10 shuffled galaxy catalogues and the original Millennium Run catalogue as a function of pair separation, and for subsets of galaxies selected in various ways." +" In this subsection we show results for subcatalogues which contain only galaxies in subhalos with mass (asdefinedbySUBLIND.. greater han Mπο10175.1M, (ie. 64 simulation particles)."," In this subsection we show results for subcatalogues which contain only galaxies in subhalos with mass \citep[as defined by +{\small SUBFIND}, greater than $M_{\rm +vir}\!=\!5.5\times 10^{10} h^{-1} {\rm M}_{\odot}$ (i.e. $>64$ simulation particles)." + This means that we consider only galaxies which reside in well-resolved. dark matter (sub)structures at z=0., This means that we consider only galaxies which reside in well-resolved dark matter (sub)structures at $z=0$. + In the op panel. relative bias functions are shown for this sample as à whole and for subsamples split by colour at B.V=0.8 (sceLig.9of?2)..," In the top panel, relative bias functions are shown for this sample as a whole and for subsamples split by colour at ${\rm B\!-\!V}=0.8$ \citep[see Fig.~9 of][]{Croton2006}." + The bottom panel presents à. similar analvsis but further restricts the catalogues to contain only he central galaxies of the halos., The bottom panel presents a similar analysis but further restricts the catalogues to contain only the central galaxies of the halos. + Note that for all statistics here is a very small scatter between the 10 relative bias measurements., Note that for all statistics there is a very small scatter between the 10 relative bias measurements. + This demonstrates that ‘small sample ellects are negligible for the questions we address here., This demonstrates that `small sample' effects are negligible for the questions we address here. + Consider first the top panel of Fig. l.., Consider first the top panel of Fig. \ref{fig1}. + The galaxy population as a whole (the solid lines) shows a svstematic bias of ~3% on laree scales., The galaxy population as a whole (the solid lines) shows a systematic bias of $\sim\!3\%$ on large scales. + Shullling has reduced. the streneth of clustering by a small but significant. amount., Shuffling has reduced the strength of clustering by a small but significant amount. + Note that this result is independent of the galaxy formation model. since shullling does not change the set. of central galaxy positions but. merely reassigns populations of well-resolved subhalos among halos of similar mass.," Note that this result is independent of the galaxy formation model, since shuffling does not change the set of central galaxy positions but merely reassigns populations of well-resolved subhalos among halos of similar mass." + Clearly the asscmibly histories of dark halos are independent of their clustering properties (as CiISWO5 already. showed) ancl this allect. galaxyclustering., Clearly the assembly histories of dark halos are independent of their clustering properties (as GSW05 already showed) and this affect galaxy. +. Hed galaxies. (long-dashed lines) are biased in the same way as the sample as a whole but at the 15% level. while blue &alaxies. (cashed-cotted lines) are biased. with the opposite sign at the ~5% level.," Red galaxies (long-dashed lines) are biased in the same way as the sample as a whole but at the $\sim\!15\%$ level, while blue galaxies (dashed-dotted lines) are biased with the opposite sign at the $\sim\!5\%$ level." + ‘These results do. of course. depend on the galaxy formation model which determines whether galaxies are τοῦ or blue.," These results do, of course, depend on the galaxy formation model which determines whether galaxies are red or blue." + ‘The overall bias is cllectively a weighted average of these two partially compensating effects., The overall bias is effectively a weighted average of these two partially compensating effects. + Note that bias is negligible on small scales and grows toa value which is almost constant Dor c23h*Alpe.," Note that bias is negligible on small scales and grows to a value which is almost constant for $r \simgt 3 +h^{-1}{\rm Mpc}$." + This rellects the fact that only the 2-halo term contributes (Le. clustering between galaxies which live in halos)., This reflects the fact that only the 2-halo term contributes (i.e. clustering between galaxies which live in halos). + Vhis is diluted on small scales by 1-halo clustering which is identical in all catalogues., This is diluted on small scales by 1-halo clustering which is identical in all catalogues. + The change in clustering amplitude for galaxies (here (1.0)?Z5 30%) is smaller than that found by CiSWO5 for dark matter halos (whieh was up to a factor of ~ 5)., The change in clustering amplitude for galaxies (here $(1\!-\!b)^2 \simlt 30\%$ ) is smaller than that found by GSW05 for dark matter halos (which was up to a factor of $\sim\!5$ ). + This is because we sum clustering contributions from halos with a wide range in mass. thereby diluting the predominantly low-mass GSWO5 cllect.," This is because we sum clustering contributions from halos with a wide range in mass, thereby diluting the predominantly low-mass GSW05 effect." + When we consider the clustering of central galaxies only the total number of galaxies in these catalogues is reduced by approximately and the relative bias functions change considerably., When we consider the clustering of central galaxies only the total number of galaxies in these catalogues is reduced by approximately and the relative bias functions change considerably. + By definition. there is now one and only one ealaxy in each dark halo so there is no l-halo contribution to the correlation functions.," By definition, there is now one and only one galaxy in each dark halo so there is no 1-halo contribution to the correlation functions." + In addition. the correlation function for the population as a whole is invariant uncer shullling.," In addition, the correlation function for the population as a whole is invariant under shuffling." + Thus the solid. lines in the lower panel of Fig., Thus the solid lines in the lower panel of Fig. + 1 all coincide with br)=I., \ref{fig1} all coincide with $b(r)=1$. + There are. however. substantial elfects when the population is split by colour. demonstrating that the colour of the central galaxy in a halo of given mass depends significantly on the halo's environment.," There are, however, substantial effects when the population is split by colour, demonstrating that the colour of the central galaxy in a halo of given mass depends significantly on the halo's environment." + Lalos with red central galaxies show a strong relative bias (40% on, Halos with red central galaxies show a strong relative bias $\sim\!40\%$ on +A. Melehiorri aud N. Strammann for useful discussions.,A. Melchiorri and N. Straumann for useful discussions. + This work was partially supported by the Swiss National Science Foundation., This work was partially supported by the Swiss National Science Foundation. +"""true? dirty image D às N increases.",`true' dirty image $D$ as $N$ increases. + And rapid convergence in the sky plane is surely linked to rapid convergence of the basis function expansion in the U-V plane., And rapid convergence in the sky plane is surely linked to rapid convergence of the basis function expansion in the U-V plane. + However. it is difficult to predict which set will best meet this criterion. for two reasons.," However, it is difficult to predict which set will best meet this criterion, for two reasons." + Firstly the light curves encountered im practice may be very diverse: a basis set which converges rapidly to one sort may not do so for another., Firstly the light curves encountered in practice may be very diverse: a basis set which converges rapidly to one sort may not do so for another. + Secondly. there appears to be at present no analysis which predicts the image residuals.," Secondly, there appears to be at present no analysis which predicts the image residuals." + Thus trial and error. as with traditional CLEAN. probably remains the best guide here too.," Thus trial and error, as with traditional CLEAN, probably remains the best guide here too." + In the present section. we compare two sets of basis functions for the expansion of light curves. namely Fourier sinusoids and Chebyshev polynomials.," In the present section we compare two sets of basis functions for the expansion of light curves, namely Fourier sinusoids and Chebyshev polynomials." + If a standard Fourier series 1s employed. the expansion will suffer from Gibbs phenomenon at the boundaries. unless the light curve is periodic continuous (in fact periodic analytic) over the chosen observation interval.," If a standard Fourier series is employed, the expansion will suffer from Gibbs phenomenon at the boundaries, unless the light curve is periodic continuous (in fact periodic analytic) over the chosen observation interval." + Gibbs ringing can however be much reduced by the following treatment., Gibbs ringing can however be much reduced by the following treatment. + Let the duration of the observation be denoted by 7. and the light curve at a given sky direction by f(t).," Let the duration of the observation be denoted by $T$, and the light curve at a given sky direction by $f(t)$." + Suppose one doubled the observation time. and filled the new interval with a function £ defined such that The new function g Is periodic continuous in the interval [0.27]. so there should be no zeroth-order Gibbs ringing in its Fourier expansion.," Suppose one doubled the observation time, and filled the new interval with a function $g$ defined such that The new function $g$ is periodic continuous in the interval $[0,2T]$, so there should be no zeroth-order Gibbs ringing in its Fourier expansion." + e is also symmetric about zero. so only cosine terms will remain in the expansion.," $g$ is also symmetric about zero, so only cosine terms will remain in the expansion." + If the resulting Fourier basis functions are truncated back to [0.7] they are seen to be given by Similar tricks can be used to enforce boundary differentiability to higher orders if desired.," If the resulting Fourier basis functions are truncated back to $[0,T]$ they are seen to be given by Similar tricks can be used to enforce boundary differentiability to higher orders if desired." + If there are gaps in the time sequence of data values - patches of bad data perhaps. or even planned. periodic observations of a phase calibrator - such gaps might be expected to cause additional Gibbs-type problems.," If there are gaps in the time sequence of data values - patches of bad data perhaps, or even planned, periodic observations of a phase calibrator - such gaps might be expected to cause additional Gibbs-type problems." + A normal Fourier expansion of a function which suddenly drops to zero at intervals would suffer Gibbs ringing at the discontinuities., A normal Fourier expansion of a function which suddenly drops to zero at intervals would suffer Gibbs ringing at the discontinuities. +" However. Conway decomposition is not ""normal expansion’ in the basis functions."," However, Conway decomposition is not `normal expansion' in the basis functions." + The actual basis onto which the dirty image is projected consists of the set of beams: and the construction of each beam from the corresponding basis function in. the UV plane effectively disconnects it from any trregularities in the support of the basis functions., The actual basis onto which the dirty image is projected consists of the set of beams; and the construction of each beam from the corresponding basis function in the UV plane effectively disconnects it from any irregularities in the support of the basis functions. + Orthonormal basis functions won't necessarily produce orthonormal beams. and vice versa.," Orthonormal basis functions won't necessarily produce orthonormal beams, and vice versa." + A final point to note is that this technique cannot disentangle or unwrap an observation which spans more than 24 hours at the same frequency: in this case all that can be obtained is the net (cyclic superimposed) light curve., A final point to note is that this technique cannot disentangle or unwrap an observation which spans more than 24 hours at the same frequency: in this case all that can be obtained is the net (cyclic superimposed) light curve. + Figures | to 4. refer to a simulation constructed as follows., Figures \ref{fig_a} to \ref{fig_c} refer to a simulation constructed as follows. + Artificial visibilities were calculated. for a single time-varying source which was located at the phase centre., Artificial visibilities were calculated for a single time-varying source which was located at the phase centre. + The array parameters were those of MERLI the chosen source declination was +40°: integration time was 10s. and 32 channels of 1 MHz width starting at 6 GHz were used.," The array parameters were those of MERLIN; the chosen source declination was $+40^\circ$; integration time was 10s, and 32 channels of 1 MHz width starting at 6 GHz were used." + Perfect calibration was assumed and no instrumental noise was added., Perfect calibration was assumed and no instrumental noise was added. + A gap was introduced into the data sequence between approximately 4 and 6.5 hours postmeridian., A gap was introduced into the data sequence between approximately 4 and 6.5 hours postmeridian. + Figures |.. 2 and 3 show the effect of different basis expansions on the Gibbs phenomenon: figure + concerns the relative efficiency of Hóggbom versus Sault-Wieringa cleans for time-variable sources.," Figures \ref{fig_a}, \ref{fig_b1} and \ref{fig_b2} show the effect of different basis expansions on the Gibbs phenomenon; figure \ref{fig_c} concerns the relative efficiency of Höggbom versus Sault-Wieringa cleans for time-variable sources." + In figure {.. the light curve of the source (solid line) is compared firstly to a direct. Fourier expansion of this light curve to order 10 (dashed line). and secondly to the light curve reconstructed after Conway decomposition into 6 beams (i.e. to order 5) from the half-frequeney cosine basis functions prescribed by equation 7.. followed by 1000 cycles of Sault-Wieringa cleaning with loop gain 0.1 (dotted line).," In figure \ref{fig_a}, the light curve of the source (solid line) is compared firstly to a direct Fourier expansion of this light curve to order 10 (dashed line), and secondly to the light curve reconstructed after Conway decomposition into 6 beams (i.e. to order 5) from the half-frequency cosine basis functions prescribed by equation \ref{equ_m}, followed by 1000 cycles of Sault-Wieringa cleaning with loop gain 0.1 (dotted line)." + The Gibbs ringing of the standard Fourier expansion at boundaries and other discontinuities is very obvious. as is the almost complete absence of such an effect in the Sault-Wieringa result.," The Gibbs ringing of the standard Fourier expansion at boundaries and other discontinuities is very obvious, as is the almost complete absence of such an effect in the Sault-Wieringa result." + Figure | shows clearly that Gibbs phenomenon can be largely avoided in Sault-Wieringa cleaning of time-varying sources., Figure \ref{fig_a} shows clearly that Gibbs phenomenon can be largely avoided in Sault-Wieringa cleaning of time-varying sources. + It is of interest however to explore a little more deeply into the difference between boundary discontinuities and data gaps. and the relative efficacy. of different basis functions.," It is of interest however to explore a little more deeply into the difference between boundary discontinuities and data gaps, and the relative efficacy of different basis functions." + Figures 2 and 3 serve this purpose., Figures \ref{fig_b1} and \ref{fig_b2} serve this purpose. + For these figures. the same input data are used. but the plotting style is different to figure ..," For these figures, the same input data are used, but the plotting style is different to figure \ref{fig_a}. ." +changes over cosmological (imeseales (Uzan2003).,changes over cosmological timescales \citep{uza03}. +. Astrophvsies offers a possible test to constrain the parameters of such theories by directly measuring the values of such constants through the comparison of properties of objects al different. evolutionary epochs of the Universe., Astrophysics offers a possible test to constrain the parameters of such theories by directly measuring the values of such constants through the comparison of properties of objects at different evolutionary epochs of the Universe. + Reviews of the techniques used have been presented by LandauanclSimeone(2008)... IXanekaretal.(2008) ancl others.," Reviews of the techniques used have been presented by \citet{lan08}, \citet{kan08} and others." + The biggest observational effort to constrain the values of physical constants in the past has been directed at the fine structure constant (a= che) which plavs a fundamental role in the characterization of electromagnetic interaction.," The biggest observational effort to constrain the values of physical constants in the past has been directed at the fine structure constant $\alpha \equiv e^2/\hbar c$ ), which plays a fundamental role in the characterization of electromagnetic interaction." + Several methods have been developed based on the analvsis of cosmic microwave background data (Nakashimaetal.2008).. Dig Dang nucleosvnthesis (Ichikawaetal...2002).. and the fine structure splitting of several atomie lines in QSO spectra (see below).," Several methods have been developed based on the analysis of cosmic microwave background data \citep{nak08}, Big Bang nucleosynthesis \citep{ich02}, and the fine structure splitting of several atomic lines in QSO spectra (see below)." + A review on the techniques ancl observational constraints can be found in Garcia-Berroοἱal.(2007)., A review on the techniques and observational constraints can be found in \citet{gar08}. +. llere. we mention only those methods based on fine structure splitting.," Here, we mention only those methods based on fine structure splitting." + The splitting ratio (Às—À4)/(Àa+Ay) at (wo dillerent epochs gives the relative dillerence in a between these (wo epochs., The splitting ratio $\lambda_2-\lambda_1)/(\lambda_2+\lambda_1)$ at two different epochs gives the relative difference in $\alpha$ between these two epochs. + It is shown (Uzan2003) that where A» and Ay are (he wavelengths of the pairs of the doublet. ancl the subscripts z ancl Q reler to the values at recdshift z aud local respectively.," It is shown \citep{uza03} that where $\lambda_2$ and $\lambda +_1$ are the wavelengths of the pairs of the doublet, and the subscripts $z$ and $0$ refer to the values at redshift $z$ and local respectively." + The method has been emploved to measure the relative separation of absorption lines in (he spectra of QSOs. including (he alkali doublet (Dahcalletal.1967).. and the many multiplet method (MML). (Webbetal.1999).," The method has been employed to measure the relative separation of absorption lines in the spectra of QSOs, including the alkali doublet \citep{bah67}, and the many multiplet method (MML), \citep{web99}." +. The best constraints obtained using the alkali doublet method are those by Chandetal.(2005). [Na/a.=(0.15+0.44)x10. 7] over the range 1.59<2< 2.32].," The best constraints obtained using the alkali doublet method are those by \citet{cha05} $\Delta \alpha/\alpha=(0.15\pm +0.44)\times 10^{-5}$ ] over the range $1.59\le z \le 2.32$ ]." + The MALL simultaneously analyzes many doublets of many abomic species. and due to (the large number of lines used. higher precision than with the alkali doublet method.," The MML simultaneously analyzes many doublets of many atomic species, and due to the large number of lines used, higher precision than with the alkali doublet method." + The MML is the only method that has resulted in claims for the detection of variation of a (Webbetal.1999:Murphy2003) Aa/a=(—0.5742:0.102)x10? in the range Q.2<2<3.7. although these results are controversial (Chaneetal.2006).. (but. see also (Murphyetal.2008) on the opposite view). ancl are at odds with similar studies 2004:Levshakovοἱal.2007 ).," The MML is the only method that has resulted in claims for the detection of variation of $\alpha$ \citep{web99,mur03} $\Delta \alpha/\alpha=(-0.574\pm 0.102)\times 10^{-5}$ in the range $0.2\le z\le 3.7$, although these results are controversial \citep{cha06}, (but see also \citep{mur08} on the opposite view), and are at odds with similar studies \citep{cha04,sri04,lev07}." +. The MAIL method suffers from several uncertainties and might be affected by possible svstemalties. as was pointed out bv Bahealletal.(2004) among others.," The MML method suffers from several uncertainties and might be affected by possible systematics, as was pointed out by \citet{bah04} among others." + Another group (Levshakovetal.2005) has developed a slight modification of (he MML method in which only one atomic ion (Fe II) is used. avoiding many of (he assumptions ancl uncertainties inherent to the MAIL method.," Another group \citep{lev05} has developed a slight modification of the MML method in which only one atomic ion (Fe II) is used, avoiding many of the assumptions and uncertainties inherent to the MML method." + Their latest analvsis, Their latest analysis +We consider now the chemical aud. thermal evolution of the preealactic gas in the framework of a Friediuauu cosniological model.,We consider now the chemical and thermal evolution of the pregalactic gas in the framework of a Friedmann cosmological model. + We start the caleulations at 2=101 with all atomic species fully ionized and we follow their recombination down to to τ=0 asstuning that no relonizing eveuts have taken place in the Universe., We start the calculations at $z=10^4$ with all atomic species fully ionized and we follow their recombination down to to $z=0$ assuming that no reionizing events have taken place in the Universe. + Tn order to calculate the abundances of the 21 clemeuts iucluded in the network. we have solved the set of coupled chemical rate equations of the form μι des where Moray nado Άρα are the formation anc destruction reaction rates ciscussed iu Sect.," In order to calculate the abundances of the 21 elements included in the network, we have solved the set of coupled chemical rate equations of the form n_j , where $k_{\rm form}$ and $k_{\rm dest}$ are the formation and destruction reaction rates discussed in Sect." + 2. aud p; is the number density of thereactant species /.," 2, and $n_i$ is the number density of thereactant species $i$ ." +Galaxy interactions provide strong clues aout the structure aud dynamics of galaxies. aud a powerful nechanisin for the origin of very massive ceiral star ormnatiou eveuts;,"Galaxy interactions provide strong clues about the structure and dynamics of galaxies, and a powerful mechanism for the origin of very massive central star formation events." + Besides. the development of oue tical ails of stellar aud gaseous material during the encounter. which can be observed aud comuted ia numerical simulations. has posed the question of the fate of this idally ejected material.," Besides, the development of long tidal tails of stellar and gaseous material during the encounter, which can be observed and computed in numerical simulations, has posed the question of the fate of this tidally ejected material." + Zwicky (1956) was the first to oopose ftat some of this material wielt survive in the ong terni in the form of sclferavitating dwiirf galaxies., Zwicky (1956) was the first to propose that some of this material might survive in the long term in the form of self-gravitating dwarf galaxies. +" Evidence in favor of this scenario for the origin of dwarfs comes from the identification of blue coudcusations in the ips ofthe tails of galaxy mergers with typical llASSCR raneie yon 5«105 to 610"" ALL.", Evidence in favor of this scenario for the origin of dwarfs comes from the identification of blue condensations in the tips of the tails of galaxy mergers with typical masses ranging from $5\times 10^{8}$ to $6\times 10^{9}$ $M_{\odot}$. + AGirabel et a. (, Mirabel et al. ( +1992) and Duc et al. (,1992) and Duc et al. ( +1998) have shown that objecs snudar ο dwarf nireeulars or blue compacts are found iu the ails.,1998) have shown that objects similar to dwarf irregulars or blue compacts are found in the tails. + These small galaxies of tical «igi are potential xoesenitors of detached systeus. nach. isolaeck dwart ealaxies (Sanders Mirabol 1996. Braine ct al.," These small galaxies of tidal origin are potential progenitors of detached systems, namely, isolated dwarf galaxies (Sanders Mirabel 1996, Braine et al." + 2001)., 2001). + Niunerical simulations of iuteracions between disk ealaxies show that tidal tails are the natural restIt of such oocesses (Barnes lleruquist 1996)., Numerical simulations of interactions between disk galaxies show that tidal tails are the natural result of such processes (Barnes Hernquist 1996). + Also. if the nneraction is strong enough. selfsravitatiug chuups of eax aud stars are ikelv to forma alone the tails (Schwager 1978).," Also, if the interaction is strong enough, self-gravitating clumps of gas and stars are likely to form along the tails (Schweizer 1978)." + Several exanples of stelar coudcusations at tie tips of long tidal ails have been reported. like NCC 1252 (Wibbard ct al.," Several examples of stellar condensations at the tips of long tidal tails have been reported, like NGC 7252 (Hibbard et al." + 1991). Arp 105 (Duc Mirabel 1991) aud Arp 215 (Duc et al.," 1994), Arp 105 (Duc Mirabel 1994) and Arp 245 (Duc et al." + 20n., 2000). + The possibility that these chuups »ocomie madependen dwazrt compaious has been proposed w Barnes IIoiquist. (1992) aud Elmeereen et al. (, The possibility that these clumps become independent dwarf companions has been proposed by Barnes Hernquist (1992) and Elmegreen et al. ( +1993).,1993). + In. addilon. sole inaterial — both easeous aud stellar is ejected roni the disks of the pareut salaxies. forning lower lass compexes that are probabY ot Endf-eravitaine.," In addition, some material – both gaseous and stellar – is ejected from the disks of the parent galaxies, forming lower mass complexes that are probably not self-gravitating." + It is expeced that oulv t1ο outermost ejected material may evenually abandonτσ the potential W“oll of the arent galaxy axd formas dwarf galaxies., It is expected that only the outermost ejected material may eventually abandon the potential well of the parent galaxy and form dwarf galaxies. + The lOYluost material would sQW.v fall back to the xuenut ealaxy., The innermost material would slowly fall back to the parent galaxy. + Civeu that the further out the material is. he wer Is jo. fine for return. dwarf objects in he πιWroullingos of the iuteracΠιο pairs would be exrected or a loug tine. even well afer the relaxatio1 time.," Given that the further out the material is, the longer is the time for return, dwarf objects in the surroundings of the interacting pairs would be expected for a long time, even well after the relaxation time." + These X5-eravitaΠιο condoeusatioi of stars odIn. t1C SO-called Tida Dwart Galaxies (heneeforth TDC). would e significautly iu optica wavelengths in the (ανν that ows their formation. as soon as the gas is appreciably exhausted by the starburs (Weilbacher et al.," These self-gravitating condensations of stars and, the so-called Tidal Dwarf Galaxies (henceforth TDG), would fade significantly in optical wavelengths in the Gyr that follows their formation, as soon as the gas is appreciably exhausted by the starburst (Weilbacher et al." + 2000)., 2000). + In dition. tidal stripping from the pareut galaxw may be iu he long term a significait source of mass loss. thereby LC4(πο��ο the TDG to a very low surface brightucss chwart (Maver et al.," In addition, tidal stripping from the parent galaxy may be in the long term a significant source of mass loss, thereby reducing the TDG to a very low surface brightness dwarf (Mayer et al." + 2001)., 2001). + ALL these circumsta1COR COUSPILE to make senumne dwarf galaxies hard to ¢lotect. uuless cartograpiv as well as spectroscopic surveys around merecrs are performed.," All these circumstances conspire to make genuine dwarf galaxies hard to detect, unless cartography as well as spectroscopic surveys around mergers are performed." + Iu the o»yeseut study we investigate if strong interactions vetween galaxies can produce a sieuificaut ibaucenent on the number of «wart galaxies around 1ie systeni., In the present study we investigate if strong interactions between galaxies can produce a significant enhancement on the number of dwarf galaxies around the system. +" Lacki1ο spectroscopic data. which are very cifficult to obtain due to the faintuess and small size the wee majority of TDG candidates. we choose ) addsss this questio1 statistically, bv comparing the rototric sunple of extended objects - or dwart uididaes- catalogued in the previous work of Dece oet ("," Lacking spectroscopic data, which are very difficult to obtain due to the faintness and small size of the large majority of TDG candidates, we choose to address this question statistically, by comparing the photometric sample of extended objects - or dwarf candidates- catalogued in the previous work of Deeg et al. (" +1998. hereafter Paper I) witi background ealaxy imnber counts;,"1998, hereafter Paper I) with background galaxy number counts." + By doiis so. We expect to include both axmung aud evolved TDC. arriving at au estimate of the amudauce of TDC forued bv field interacting galaxies.," By doing so, we expect to include both young and evolved TDG, arriving at an estimate of the abundance of TDG formed by field interacting galaxies." + From the fields around 15 interacting systems catalogued in Paper 1. we have selected those fields that were observed in two filters (V. and LR).fF). had a statisticallytatistically significasiguificaut," From the fields around 15 interacting systems catalogued in Paper I, we have selected those fields that were observed in two filters $V$ and $R$ ), had a statistically significant" + , +"with fant sources (like NACIIO-LMC-5). the parameters that are well constrained bv the fils are not uy. dye. and FL. separately. but rather the parameter combinations Piya,=Fig.log=ul. ancl their product Fur=Fg.","with faint sources (like MACHO-LMC-5), the parameters that are well constrained by the fits are not $u_0$ , $t_\e$ , and $F_s$, separately, but rather the parameter combinations $F_{\rm max}=F_s/u_0$,$t_{\rm eff}=u_0 t_\e$, and their product $F_{\rm max}t_{\rm eff} = F_s t_\e$." +" To test this. I show in the sixth line of Table 1. the best fit zero-parallax solution with Fyjy, constrained to the value of the first parallax solution."," To test this, I show in the sixth line of Table 1, the best fit zero-parallax solution with $F_{s,R}$ constrained to the value of the first parallax solution." + The parameters of this solution show much better agreement with those of the parallax solutions. while V7 is increased by less than unity (for one more degree of freedom).," The parameters of this solution show much better agreement with those of the parallax solutions, while $\chi^2$ is increased by less than unity (for one more degree of freedom)." + llence. the geocentric worldview is confirmed.," Hence, the geocentric worldview is confirmed." + To compare the direction of motion of the parallax solution with that of the proper- measurement. yoy=13874 (which reflects the time-averaged motion of the Earth and so is basically heliocentric). (he parallax measurement must be converted [rom geocentric to heliocentric coordinates.," To compare the direction of motion of the parallax solution with that of the proper-motion measurement, $\theta_{HST}=138.\hskip-2pt ^\circ 4$ (which reflects the time-averaged motion of the Earth and so is basically heliocentric), the parallax measurement must be converted from geocentric to heliocentric coordinates." + This requires (wo steps., This requires two steps. + First. the parallax must be converted (o the geocentric projected velocity. Next. one must add the Earth's instantaneous velocity al fy to obtain the heliocentric projected velocity. Finally. since (he projected Einstein radius. rye=eq. is (he same in both frames. the heliocentric Einstein crossing time is. These steps are illustrated in Figure 4..," First, the parallax must be converted to the geocentric projected velocity, Next, one must add the Earth's instantaneous velocity at $t_0$ to obtain the heliocentric projected velocity, Finally, since the projected Einstein radius, $\tilde r_\e=\tilde v t_\e$, is the same in both frames, the heliocentric Einstein crossing time is, These steps are illustrated in Figure \ref{fig:projvel}." +" Also shown in this figure is the direction 444,4 as measured byLST.", Also shown in this figure is the direction $\bmu_\rel$ as measured by. + Note that both parallax solutions are reasonably aligned. with this direction. although the new solution is about twice as far from it as the original solution.," Note that both parallax solutions are reasonably aligned with this direction, although the new solution is about twice as far from it as the original \citet{alcock01} solution." + See Table I., See Table 1. + ] now combine (heT proper motion wilh each of the (wo parallax solutions to produce likelihood contours in lens mass ancl distance., I now combine the proper motion with each of the two parallax solutions to produce likelihood contours in lens mass and distance. +" For simplicity. and because the7/57 angular nmeasurenient error (170) is so much smaller than the difference between it and either parallax solution. I treat theHST pi,4 as a constraint. Le.. as having zero error."," For simplicity, and because the angular measurement error $1.\hskip-2pt ^\circ 0$ ) is so much smaller than the difference between it and either parallax solution, I treat the $\bmu_\rel$ as a constraint, i.e., as having zero error." +" For each lens trial distance D,~Απο. I derive a heliocentricprojectedvelocity. VagΑμqmac Dip."," For each lens trial distance $D_l\simeq {\rm AU}\pi_\rel^{-1}$, I derive a heliocentricprojectedvelocity, $\tilde \bv_{\rm hel} = {\rm AU}\bmu_\rel \pi_\rel \simeq D_l\bmu_\rel$ ." + ] convert this to a geocentric projected velocity v by inverting equation (24))., I convert this to a geocentric projected velocity $\tilde \bv$ by inverting equation \ref{eqn:helvel}) ). + Next. for each," Next, for each" +conrpared with the case of a coustaut deusitv.,compared with the case of a constant density. + The larger loss of planets is caused by the effect that according to this scaling law the initial deusitv is smaller by about a factor of 2., The larger loss of planets is caused by the effect that according to this scaling law the initial density is smaller by about a factor of 2. + As expected. the effect is less pronounced for planets with higher The derived mass function could be compared with the observed mass distribution of known planets.," As expected, the effect is less pronounced for planets with higher The derived mass function could be compared with the observed mass distribution of known planets." + However. we prefer to avoid to compare our predictions with the preseut day planetary mass distribution because of the complex biases present iun the observed," However, we prefer to avoid to compare our predictions with the present day planetary mass distribution because of the complex biases present in the observed" +have become possible(eg... Burles Tytler 1998a l1908b: Webb et al 1997:,"have become possible, Burles Tytler \cite{bt1} \cite{bt2}; Webb et al. \cite{webb97};" + see also Dulles Tytler 19986. for a review)., see also Burles Tytler \cite{burles_revue_98} for a review). + Taken altogether. the abundances of deuterium seen to decrease with time. as expected. although the dispersion remains rather large.," Taken altogether, the abundances of deuterium seem to decrease with time, as expected, although the dispersion remains rather large." + These various measurements aud their treuds are reviewed iu detal in Lemoime et al. (1999)).," These various measurements and their trends are reviewed in detail in Lemoine et al. \cite{lemoine99}) )," + and we refer the reader to this review for more details., and we refer the reader to this review for more details. + The first measurements of the interstellar deuteriuui abundance(D/ID;sar. representativo of the present epoch. were reported by Rogerson York (1973)) through Lian absorption ou the line of sight of ο) Cen. usingC," The first measurements of the interstellar deuterium abundance, representative of the present epoch, were reported by Rogerson York \cite{ry73}) ) through Lyman absorption on the line of sight of $\beta$ Cen, using." +"opernicus, Their value of (D/IDtsarc1.40502«107 has not changed ever since and twenty vears later. Liusky et al"," Their value of $\simeq1.4\pm0.2\times10^{-5}$ has not changed ever since and twenty years later, Linsky et al." + (1993 19953) measured =1.6040.09|o«107 in the direction of Capella usiug IIST-, \cite{linsky93} \cite{linsky95}) ) measured $=1.60 \pm 0.09 ^{+0.05}_{-0.10}\times 10^{-5}$ in the direction of Capella using HST-GHRS. + But it turns out that determinations of the iratio do not eenerallv aeree on a single value. even im the very local medium (Vidal-Madjar et al.," But it turns out that determinations of the ratio do not generally agree on a single value, even in the very local medium (Vidal-Madjar et al." + 1978. 19806.. ADurthy et al.," \cite{avm78} \cite{avm86}, Murthy et al." + 1987. 1990))., \cite{murty87} \cite{murty90}) ). + While many measurements are in aegrecinent with the value of Liusky et al., While many measurements are in agreement with the value of Linsky et al. + (1993 1995)). παν sighthnes exhibit differcut values.," \cite{linsky93} \cite{linsky95}) ), many sightlines exhibit different values." + For iustance. (D/ID);sarjl0.7 toward A Sco (York. 1983)). (D/ID;sar7.«LO© toward 8 Ori aud ε Ori (Laurent et al 1979)) (D," For instance, $<10^{-5}$ toward $\lambda$ Sco (York \cite{york83}) ), $\simeq7.\times10^{-6}$ toward $\delta$ Ori and $\epsilon$ Ori (Laurent et al. \cite{laurent79}) )," +/ID;sajg5.«109 toward 0 Car (Allen et al. 1992))., $\simeq5.\times10^{-6}$ toward $\theta$ Car (Allen et al. \cite{allen92}) ). + Finally. thanks to uew IIST-CGIIRS observations of 101-020. Vidal-Madjar et al. (1998))," Finally, thanks to new HST-GHRS observations of G191-B2B, Vidal-Madjar et al. \cite{avm98}) )" + detected variations of bbyv at least ~30% within the local interstellar media on the sighthue of G191-B2B. aud Jeulins ct al. (1999))," detected variations of by at least $\sim30$ within the local interstellar medium on the sightline of G191-B2B, and Jenkins et al. \cite{jenkins99}) )" + up to ~50% toward 6 Ori. using IMAPS.," up to $\sim50$ toward $\delta$ Ori, using IMAPS." + We can also report the measurement of the 92cm hyperfiue trausitio- 6: by Cheugalur et al. (19973).," We can also report the measurement of the 92cm hyperfine transition of by Chengalur et al. \cite{chengalur97}) )," + showing n3.90EL0.10 7., showing $\simeq3.9\pm1.0\times10^{-5}$ . + Although several scenarios have bee- proposed to explain these putative viriatious(6.9... VidaAMacdjar et al. 1978:," Although several scenarios have been proposed to explain these putative variations, Vidal-Madjar et al. \cite{avm78};" + Jura 1982)). the above measurementy. are still unaccounted for (Lemoine et al. 1999)).," Jura \cite{jura}) ), the above measurements are still unaccounted for (Lemoine et al. \cite{lemoine99}) )." + We introduced in Cycle 1 of UST a jew type of target. white dwarts in he high temperature range. for which the depth of the pphotospheric absorption liue is reduced. aud whose stellar continu remains smooth.," We introduced in Cycle 1 of HST a new type of target, white dwarfs in the high temperature range, for which the depth of the photospheric absorption line is reduced, and whose stellar continuum remains smooth." + These targets also allow the study of lines of other species. such as andOr which are shown to be reliable tracers of in the ISAL (Ferlet 1981: York et al. 19521).," These targets also allow the study of lines of other species, such as and, which are shown to be reliable tracers of in the ISM (Ferlet \cite{ferlet81}; York et al. \cite{york_etal83}) )." + These tarects mav also be chosen close to the Sun so that the cohuun deusity is not too high and the velocity strucure of the line of sight not too complex., These targets may also be chosen close to the Sun so that the column density is not too high and the velocity strucure of the line of sight not too complex. + We have already observed the white dwarf CI91-D2D in UST Cycle 1 (Lemoime et al. 1996)), We have already observed the white dwarf G191-B2B in HST Cycle 1 (Lemoine et al. \cite{lemoine96}) ) + and Cyele 5. (Vidal-Madjar. ct al. 1998))., and Cycle 5 (Vidal-Madjar et al. \cite{avm98}) ). + Continuing that program. we present here new ultraviolet observations of Sirius A and its white chvarf colpanion Sinus D performed with UST-CURS.," Continuing that program, we present here new ultraviolet observations of Sirius A and its white dwarf companion Sirius B performed with HST-GHRS." + Previous IST-CGIIRS observations of Sirius A reveal the velocity structure iucluding two conmponeuts on this sightline (Lallemeut et al. 199 9).," Previous HST-GHRS observations of Sirius A reveal the velocity structure including two components on this sightline (Lallement et al. \cite{lalle}) )," + and also the possible detection of a diffuse interstellar cloud boundary (Bertin et al. 1995a)), and also the possible detection of a diffuse interstellar cloud boundary (Bertin et al. \cite{bert1}) ) + and the detection of a stellar wind trom Sirius A (Bertin et al. 1995b))., and the detection of a stellar wind from Sirius A (Bertin et al. \cite{bert2}) ). + From a subset of these new observatious. the identifications of the Sirius A emission lines have been made beforehand (van Noort et al. 1998)).," From a subset of these new observations, the identifications of the Sirius A emission lines have been made beforehand (van Noort et al. \cite{noort}) )." + Tere. following the presentation of these spectroscopic observations aud the data reduction iu Section 2.. we study the structure of the line of sight iu Section 3.. he aaborption features includiug sstudy in Section L. aud the ionization and metal abundances in Section 5...," Here, following the presentation of these spectroscopic observations and the data reduction in Section \ref{Observations_and_data_reduction}, we study the structure of the line of sight in Section \ref{Study_of_sightline_structure}, the aborption features including study in Section \ref{Study_of_the_lya_lines_toward_Sirius_A_and_Sirius_B}, and the ionization and metal abundances in Section \ref{Analysis_of_the_metallic_lines}." + We finally discuss our results in Section 6.., We finally discuss our results in Section \ref{Discussion}. + Our observations of the stars Sirius A and Sirius D were performed with GIIRS (the Spectrograph) ouboard the i Novetber 1996. in the frame of Cycle 6 Guest. Observer proposals TD οδς and ID 65828.," Our observations of the stars Sirius A and Sirius B were performed with GHRS (the ) onboard the in November 1996, in the frame of Cycle 6 Guest Observer proposals ID 6800 and ID 6828." + A first attemp was made iu September 1996 but failed because the stars were not correctly located within the GURS eutrauce slit., A first attempt was made in September 1996 but failed because the stars were not correctly located within the GHRS entrance slit. + The observations were finally repeated with a different pointing strateev which was filly successful and allowed for extremely eood observations of both stars., The observations were finally repeated with a different pointing strategy which was fully successful and allowed for extremely good observations of both stars. + The spectra were acquired at high and medium spectral resolution (Echelle-A and GLIOM evatines)., The spectra were acquired at high and medium spectral resolution (Echelle-A and G140M gratings). + Most of them have a very good quality aud show clearly iuterstellar lines., Most of them have a very good quality and show clearly interstellar lines. + The wavelengths ranges of the spectra are listed in Table 1.., The wavelengths ranges of the spectra are listed in Table \ref{obs}. + The GLLOAL erating provides a resolving power 2=AfAXzz 20.000. aa spectral resolution of 15Do," The G140M grating provides a resolving power $R=\lambda/\Delta\lambda\simeq20,000$ , a spectral resolution of $\sim15$." + With the Echelle-A erating we have obtained a resolving power R285.000. aa spectral resolution of ~3.51," With the Echelle-A grating we have obtained a resolving power $R\simeq85,000$, a spectral resolution of $\sim3.5$." + AWe used only the Sinall Science Aperture (SSA). correspouding to 0.257 ou the skv and ilunünatiug one diode to achieve the best )ossible resolving power.," We used only the Small Science Aperture (SSA), corresponding to 0.25"" on the sky and illuminating one diode to achieve the best possible resolving power." + For further details ou the iustrunentation. see Duncan 1992)].," For further details on the instrumentation, see Duncan \cite{duncan}) )." + Our data were reduced with the huage Reduction aud Analysis Facility (IRAE) software. using the STSDAS package.," Our data were reduced with the Image Reduction and Analysis Facility (IRAF) software, using the STSDAS package." + During the observations. we used the FP-SPLIT mode which splits the total exposure time into successive cycles of four sub-exposures. cach correspouding to a slightly different projection of the spectu on the photocathode.," During the observations, we used the FP-SPLIT mode which splits the total exposure time into successive cycles of four sub-exposures, each corresponding to a slightly different projection of the spectrum on the photocathode." +" We used the ""quarter stepping” mode. which provides"," We used the “quarter stepping” mode, which provides" +fallback matter (Wang Mésszárros. 2007).,"fallback matter (Wang Mésszárros, 2007)." +" Fora typical magnetar with neutron star radius Πρνς~050kia aud mass LAY... the ram pressure can be written as fa,Tp.m5.qu⋅XruMPEET(Be)⇁⊳−“hyere st. where cee=(2GMRpxys)'? is the free-fall velocity aud AL is the mass infalline rate in units of AM.«s!, "," For a typical magnetar with proto-neutron star radius $R_{PNS}\sim +50 \ {\rm km}$ and mass $M_0\sim 1.4 M_\sun$ , the ram pressure can be written as $P_{\rm ram}=\frac{\dot{M} v_{ff}}{4\pi R_{PNS}^2}\simeq +5\times10^{26}\dot{M}_{-2}M_0^{1/2}\left(\frac{R_{PNS}}{50{\rm +km}}\right)^{-5/2} {\rm erg\ s^{-1}}$ , where $v_{ff}=(2GM/R_{PNS})^{1/2}$ is the free-fall velocity and $\dot{M}$ is the mass infalling rate in units of $M_{\sun} {\rm\ s^{-1}}$." +The magnetic field pressure can be written as Pp=LsLOBFergs +.," The magnetic field pressure can be written as $P_B=B_f^2/8\pi\simeq 4\times10^{28}B_{f,15}^2{\rm erg\ +{\rm s}^{-1}}$ ." + Comparing the two. one can eet By>1033C.," Comparing the two, one can get $B_f \gtrsim 10^{14}\ G$." +" Such a maeuctized jet internally dissipates aud powers the observed gauuna-rav cussion. (οιο, Zhaug Yan 2011: Metzger et al.", Such a magnetized jet internally dissipates and powers the observed gamma-ray emission (e.g. Zhang Yan 2011; Metzger et al. + 2011). (, 2011). ( +2) After the maenetar slows down. the magnetic outflow stresses decrease. so the ram. pressure of the Παπιο matter becomes donünanut.,"2) After the magnetar slows down, the magnetic outflow stresses decrease, so the ram pressure of the infalling matter becomes dominant." +" Thus the activity of the iuagnetar is suppressed curing the accretion xocess,", Thus the activity of the magnetar is suppressed during the accretion process. + The accretion onto the maguctar docs not lead o GRB cuuission. since the hot NS likely launches a dirty jeutrino-driven wind with heavy barvou loading.," The accretion onto the magnetar does not lead to GRB emission, since the hot NS likely launches a dirty neutrino-driven wind with heavy baryon loading." + Iu order ο forii a BIL a total accreting mass of 1AL. is needed.," In order to form a BH, a total accreting mass of $1\ M_\sun$ is needed." + Assundug a redshift z=2. the accretion rate is about MxονTAL.12)zeO.O0GAL£s. which is consistent with heoretical predictions in the supernova fallback scenario (see e.g... MacFadyen ct al.," Assuming a redshift z=2, the accretion rate is about $\dot{M}\sim +\frac{1M_\sun}{500s/(1+z)} \simeq 0.006 M_\sun/s$, which is consistent with theoretical predictions in the supernova fallback scenario (see e.g., MacFadyen et al." + 2001). (, 2001). ( +3) The accretiou finally loads the maguetar to collapse o à black hole.,3) The accretion finally leads the magnetar to collapse to a black hole. + The second sub-burst is produced either roni a barvonic or a nmaeguetie jet., The second sub-burst is produced either from a baryonic or a magnetic jet. + The spectrum will © softer either because the accretion leads the eas near he ceutral eugime to be more barvon-loaded so that the jet is slower or because the pre-existing chaunel from he first sub-burst may not have time to close so that he wide channel results in a slower jet and a softer spectrum., The spectrum will be softer either because the accretion leads the gas near the central engine to be more baryon-loaded so that the jet is slower or because the pre-existing channel from the first sub-burst may not have time to close so that the wide channel results in a slower jet and a softer spectrum. + The spectral evolution of the two stages would © expected to be different. since they are due to different Xwesieal process.," The spectral evolution of the two stages would be expected to be different, since they are due to different physical process." + These model features appear to be in concordance with the observed facts (see Fig 7))., These model features appear to be in concordance with the observed facts (see Fig \ref{fig:ept}) ). + The similarity of the two sub-bursts raises the question of whether they could be produced by gravitational leuxiug of a single CRB located behind a foreground ealaxy., The similarity of the two sub-bursts raises the question of whether they could be produced by gravitational lensing of a single GRB located behind a foreground galaxy. + To investigate this possibility. we first examined Chandra observations of CRB 110709D at 11:15:04 UT ou 23 July 2011 (dav Ll: 15.05 ks exposure time: Observation ID 12921) aud at 19:50:31 UT on 31 October 2011 (day lll: 10 ks exposure time: Observation ID 11237).," To investigate this possibility, we first examined Chandra observations of GRB 110709B at 14:15:04 UT on 23 July 2011 (day 14; 15.05 ks exposure time; Observation ID 12921) and at 19:50:34 UT on 31 October 2011 (day 114; 10 ks exposure time; Observation ID 14237)." + We downloaded the public Chandra data from the Chandra and processed them using the standard CTAO tools (version L3)., We downloaded the public Chandra data from the Chandra and processed them using the standard CIAO tools (version 4.3). + The first Chandra observation las two X-ray point sources in the Ποια of CRB 110700D. with nearly identical ποιος» (37.10% s1202-8 keV) aud separated by ouly 3.1 arcseconds (Fig. 11)).," The first Chandra observation has two X-ray point sources in the field of GRB 110709B, with nearly identical brightness $3.7\times 10^{-3}$ $ {\rm s}^{-1} $, 0.2-8 keV) and separated by only 3.4 arcseconds (Fig. \ref{fig:chandra}) )." + Source Lis located 0.67 arcsecouds from the refined. ART position. within the refined NRT error circle.," Source 1 is located 0.67 arcseconds from the refined XRT position, within the refined XRT error circle." + Both sources are within the NRT poiut-spread function (18 arcsecouds Half-Power-Diuneter). and the stun of their fluxes is consistent with the total NRT fiux 1nieasured during the first epoch. while the fiux of Source l is consistent with the extrapolation of the NRT licht curve (Fie. 2)).," Both sources are within the XRT point-spread function (18 arcseconds Half-Power-Diameter), and the sum of their fluxes is consistent with the total XRT flux measured during the first epoch, while the flux of Source 1 is consistent with the extrapolation of the XRT light curve (Fig. \ref{fig:xrtlc}) )." + The feld was unobservable by both Chandra and Swift from about ὃ August 2011 uutil 28 October 2011., The field was unobservable by both Chandra and Swift from about 8 August 2011 until 28 October 2011. + In the second Chandra observation. taken shortly after the field αμασος. from the Chandra Sun (pitch augle) coustraimt. Source 1 has vanished. while Source 2 is still prescut. with a πο] lower couut rate of ~2.5«10? 1 (0.248 keV). cousistent with being a backeround N-rav source such as an AGN.," In the second Chandra observation, taken shortly after the field emerged from the Chandra Sun (pitch angle) constraint, Source 1 has vanished, while Source 2 is still present, with a slightly lower count rate of $\sim 2.7 \times 10^{-3}$ $^{-1}$ (0.2-8 keV), consistent with being a background X-ray source such as an AGN." + The upper limit for the Source 1 fux is still consistent with the extrapolation of the NRT Πο curve (Fig. 2))., The upper limit for the Source 1 flux is still consistent with the extrapolation of the XRT light curve (Fig. \ref{fig:xrtlc}) ). + The fact that Source 1 vanished while Source 2 did not clearly rules out any possibility that the two Chancra N-rav sources in the double burst field are due to gravitational leusing., The fact that Source 1 vanished while Source 2 did not clearly rules out any possibility that the two Chandra X-ray sources in the double burst field are due to gravitational lensing. + Ou the other hand. assuuine the time delav (— 1l minutes) between two sub-bursts is caused by eravitational lensing. we calculated that the angular separation of the two lensed iuages would be —103 arcsecond (Walker Lewis 2003). which is hevoud Chanda best resolution capacity (~ 0.5 axcsecond).," On the other hand, assuming the time delay $\sim$ 11 minutes) between two sub-bursts is caused by gravitational lensing, we calculated that the angular separation of the two lensed images would be $\sim 10^{-2} $ arcsecond (Walker Lewis 2003), which is beyond Chanda best resolution capacity $\sim$ 0.5 arcsecond)." + We ound that a typical dwarf galaxy at 2~1 would be able ο serve as the massive leusiug object and cause such a separation., We found that a typical dwarf galaxy at $z\sim 1$ would be able to serve as the massive lensing object and cause such a separation. + In this scenario. the difference between the oilse structure of the two sib-bursts can be understood w taking iuto account a structured jet aud the so-called iuoleusine effect (Walker Lewis 2003).," In this scenario, the difference between the pulse structure of the two sub-bursts can be understood by taking into account a structured jet and the so-called nanolensing effect (Walker Lewis 2003)." +" However the different E, aud spectral evolution. (sce 83) of the two sub-bursts are still difficult to explain.", However the different $E_p$ and spectral evolution (see 3) of the two sub-bursts are still difficult to explain. + We thus cisfavor he eravitational lensing explanation for this burst., We thus disfavor the gravitational lensing explanation for this burst. + GRD 110709D is à unique event., GRB 110709B is a unique event. + It is one out of 613 CRBs detected by Susift/NRT so fax (as of 30 December 2011: Evans et al., It is one out of 613 GRBs detected by /XRT so far (as of 30 December 2011; Evans et al. + 2009. 2011).," 2009, 2011)." + Since nearly half ofSusff GRBs have X-ray flares (Maxhliuu Zhang. 2009). it is roughly one out of ~300 CRBs with flares.," Since nearly half of GRBs have X-ray flares (Maxham Zhang, 2009), it is roughly one out of $\sim 300$ GRBs with flares." + Comparing with other CRBs. one may wouder whether this is a burst with a huge precursor (the firstsub-burst). a huge X-ray flare (the second. sub-burstj. or simply a long GRD that has an extremely long quiescent gap in between.," Comparing with other GRBs, one may wonder whether this is a burst with a huge precursor (the firstsub-burst), a huge X-ray flare (the second sub-burst), or simply a long GRB that has an extremely long quiescent gap in between." + We address these possibilities in turn., We address these possibilities in turn. +JI51114.66+060742.9) is inlerred to be a mid L/mid T binary by ?/— and was marginally too red in J—ff. while the other (SDSS J120602.514-231328.7) was too blue in y—J by less than 0.02 magnitudes.,"J151114.66+060742.9) is inferred to be a mid L/mid T binary by \cite{Burgasser2010} and was marginally too red in $J-H$, while the other (SDSS J120602.51+281328.7) was too blue in $y-J$ by less than 0.02 magnitudes." + Additionally one object was excluded due to a noisy (o>0.2) y baud measurement. while three objects lav close to USNO or SuperCOSMOS cletections.," Additionally one object was excluded due to a noisy $\sigma>0.2$ ) $y$ band measurement, while three objects lay close to USNO or SuperCOSMOS detections." + AcldiGonally we extracted y band images from the conunissioning data for all T. dwarfs in with no v-band double detection., Additionally we extracted $y$ band images from the commissioning data for all T dwarfs in \cite{Faherty2009} with no y-band double detection. + One object appeared in only one y band detection., One object appeared in only one $y$ band detection. + Four objects were in (he footprints of multiple images but fell into masked regions such as chip gaps or poor cells., Four objects were in the footprints of multiple images but fell into masked regions such as chip gaps or poor cells. + These four objects ave of T. dwarls which fell into the footprint of (wo or more PS1 commissioning images., These four objects are of T dwarfs which fell into the footprint of two or more PS1 commissioning images. + This number is in agreement with the loss or area estimated in the fill [actor used to caleulate our survey area., This number is in agreement with the loss or area estimated in the fill factor used to calculate our survey area. + We obtained follow-up imaging of canclicdates using WECAM (?)) on the Ul Infrared Telescope (UIXIRT)., We obtained follow-up imaging of candidates using WFCAM \citealt{Casali2007}) ) on the UK Infrared Telescope (UKIRT). + As our PSI data are separated by ten vears from 2MASS. many of our supposedly red high proper motion objects will in fact be anonvmous blue 11 objects paired with 2MAÀSS transient sources such as uneataloged asteroids.," As our PS1 data are separated by ten years from 2MASS, many of our supposedly red high proper motion objects will in fact be anonymous blue 1 objects paired with 2MASS transient sources such as uncataloged asteroids." + Such PS1 sources will be too faint to appear in 2421ASS. USNO-D or SuperCOSMOS.," Such PS1 sources will be too faint to appear in 2MASS, USNO-B or SuperCOSMOS." + Additionally many of our sample are low signal to noise single J band detections in 2\IASS., Additionally many of our sample are low signal to noise single $J$ band detections in 2MASS. + While these could be (he most scientifically interesting (due to their faint. blue infrared photometry). many are expected to be noise spikes or other image artefacts.," While these could be the most scientifically interesting (due to their faint, blue infrared photometry), many are expected to be noise spikes or other image artefacts." + Follow-up infrared imagine allows us to confirm that the candidates are as red in y—J as the PSI and 2MASS photometry suggest and to improve on the signal-to-noise of our 2ATASS infrared photometry., Follow-up infrared imaging allows us to confirm that the candidates are as red in $y-J$ as the PS1 and 2MASS photometry suggest and to improve on the signal-to-noise of our 2MASS infrared photometry. + Over the course of three and a half nights. a total of 195 candidates were imaged in Y. J. HE and ἐν on the 16-19 June 2010 (IIST).," Over the course of three and a half nights, a total of 195 candidates were imaged in $Y$, $J$, $H$ and $K$ on the 16-19 June 2010 (HST)." + Observations were reduced at the Cambridge Astronomical Survey Unit using the WFECAM survey pipeline (??)..," Observations were reduced at the Cambridge Astronomical Survey Unit using the WFCAM survey pipeline \citep{Irwin2004, Hodgkin2009}." + Additionally 56 objects had four band photometry in the UIKIDSS Large Area Survey (2).., Additionally 56 objects had four band photometry in the UKIDSS Large Area Survey \citep{Lawrence2007}. . + As many of our candidates will in [act be spurious associations. we plotted the difference between the J band magnitudes [rom 2MASS and WFCAMJ/URKIDSS.," As many of our candidates will in fact be spurious associations, we plotted the difference between the $J$ band magnitudes from 2MASS and WFCAM/UKIDSS." + This produced a bimodal distribution with a division al 0.6 magnitudes., This produced a bimodal distribution with a division at 0.6 magnitudes. + We chose this as the division between objects will good and discrepant We then selected objects which appeared to be red (ie. yerκο> 2.0)., We chose this as the division between objects with good and discrepant We then selected objects which appeared to be red (i.e. $y_{P1}-J_{MKO}>2.0$ ). + These were egiven further visual screeninge andhad their photometry from the Sloan Digital, These were given further visual screening andhad their photometry from the Sloan Digital + These were egiven further visual screeninge andhad their photometry from the Sloan Digitale, These were given further visual screening andhad their photometry from the Sloan Digital + These were egiven further visual screeninge andhad their photometry from the Sloan Digitalex, These were given further visual screening andhad their photometry from the Sloan Digital +"halos, i.e. defining the spherical region inside the virial radius as the halo.","halos, i.e. defining the spherical region inside the virial radius as the halo." +" Unless FOF groups are organised in a way that the smoothly accreted mass is outside the virial radius and the merger accreted mass is inside, significant deviations from our results should not arise."," Unless FOF groups are organised in a way that the smoothly accreted mass is outside the virial radius and the merger accreted mass is inside, significant deviations from our results should not arise." +" The case is probably the opposite, because when FOF groups have very shapes it is mainly because a few substructures areaspherical connected together, i.e. it is not that the outskirts of FOF groups constitute mainly of smoothly accreted material."," The case is probably the opposite, because when FOF groups have very aspherical shapes it is mainly because a few substructures are connected together, i.e. it is not that the outskirts of FOF groups constitute mainly of smoothly accreted material." + Many theoretical models focus on the role of major mergers in galaxy evolution., Many theoretical models focus on the role of major mergers in galaxy evolution. + In this paper we have shown that it is minor mergers (x> 10) and smooth accretion that actuallydominate halo growth by accounting for ~70% of the accretion rate onto halos., In this paper we have shown that it is actually minor mergers $x>10$ ) and smooth accretion that dominate halo growth by accounting for $\approx70\%$ of the accretion rate onto halos. +" Therefore, halos grow mainly continuously rather than in bursts with short duty cycles."," Therefore, halos grow mainly continuously rather than in bursts with short duty cycles." +" This mode of accretion is more favourable for disk formation at all redshifts, and may in particular help in understanding galaxies at high redshift that show extreme star-formation rates but no signs of major mergers (e.g. Genzeletal.2008;Genel2008;ForsterSchreiberetal. 2009))."," This mode of accretion is more favourable for disk formation at all redshifts, and may in particular help in understanding galaxies at high redshift that show extreme star-formation rates but no signs of major mergers (e.g. \citealp{GenzelR_08a,GenelS_08a,FoersterSchreiberN_09a}) )." +" If there is a truly smooth accretion component, simulations from cosmological initial conditions naturally include it."," If there is a truly smooth accretion component, simulations from cosmological initial conditions naturally include it." +" Indeed, our result is consistent with hydrodynamical simulations that show that most baryonic accretion onto galaxies does not arrive in the form of mergers (Muralietal.etal. 2009a)."," Indeed, our result is consistent with hydrodynamical simulations that show that most baryonic accretion onto galaxies does not arrive in the form of mergers \citep{MuraliC_02a,SemelinB_05a,MallerA_06a,DekelA_09a}." +". Our findings suggest that as the resolution of future simulations increases, the mass contribution of small halos to the formation of galaxy-size halos will hardly increase further."," Our findings suggest that as the resolution of future simulations increases, the mass contribution of small halos to the formation of galaxy-size halos will hardly increase further." +"This implies that ~40% is a strong limit on the mean fraction of pristine IGM gas in the baryons accreted onto halos of any given mass or redshift, since this smooth gas was never bound to any subhalos and is therefore not expected to have formed stars or to have become significantly enriched with metals, regardless of the star-formation efficiency and history of the baryons in the merging halos.","This implies that $\approx40\%$ is a strong lower-limit on the mean fraction of pristine IGM gas in the baryons accreted onto halos of any given mass or redshift, since this smooth gas was never bound to any subhalos and is therefore not expected to have formed stars or to have become significantly enriched with metals, regardless of the star-formation efficiency and history of the baryons in the merging halos." +" It may also be expected that this ~40% did not experience feedback from star-formation in smaller halos, and is likely ""cold"" when finally accreted onto a halo, with T=10K set by photoheating of IGM gas."," It may also be expected that this $\approx40\%$ did not experience feedback from star-formation in smaller halos, and is likely ""cold"" when finally accreted onto a halo, with $T\gtrsim10^4K$ set by photoheating of IGM gas." +" In the context of the ""cold flow"" mode of gas accretion onto galaxies (Birnboim&Dekel2003;Birnboim2006;Kere§etal. 2005),, our results suggest that roughly half of the incoming gas is not clumpy, thus processes like tidal stripping and dynamical friction are irrelevant forit?."," In the context of the ""cold flow"" mode of gas accretion onto galaxies \citep{BirnboimY_03a,Dekel06_a,KeresD_05a}, our results suggest that roughly half of the incoming gas is not clumpy, thus processes like tidal stripping and dynamical friction are irrelevant for." +". Theoretical or semi-analytical galaxy formation models, for example EPS-based models, may benefit from taking the smooth accretion component into account, as many properties of galaxies, such as size and morphology, depend on the way they accrete their baryons."," Theoretical or semi-analytical galaxy formation models, for example EPS-based models, may benefit from taking the smooth accretion component into account, as many properties of galaxies, such as size and morphology, depend on the way they accrete their baryons." +" Even if an extrapolation of the power-law index of the merger rate beyond x=10? is not valid and mergers of higher mass ratios do make up for the ""missing"" ~40%, our results are still significant."," Even if an extrapolation of the power-law index of the merger rate beyond $x=10^5$ is not valid and mergers of higher mass ratios do make up for the ""missing"" $\approx40\%$, our results are still significant." +" Since the MS2 resolves all halos with Tu,>10*K atz<3 (MZ;1.9xIO Mo), we do resolve most of the accretion of halos that have experienced star-formation, that is if star-formation is prohibited in halos with Την«10K (e.g. 2010))."," Since the MS2 resolves all halos with $T_{vir}>10^4K$ at $z\lesssim3$ $M\gtrsim1.9\times10^{8}\Msun$ ), we do resolve most of the accretion of halos that have experienced star-formation, that is if star-formation is prohibited in halos with $T_{vir}<10^4K$ (e.g. )." +" Current models of galaxy formation derive, assume or require strong suppression of cooling and/or star-formation below a virial temperature threshold that is even higher than 10K (e.g. Bouchéetal.2009;Kravtsov 2010,, and references therein)."," Current models of galaxy formation derive, assume or require strong suppression of cooling and/or star-formation below a virial temperature threshold that is even higher than $10^4K$ (e.g. \citealp{BoucheN_10a,KravtsovA_10a}, and references therein)." + The fraction of the mass that arrives either smoothly or by accretion of small halos can be read off Figure 2 as the complement of the merger contribution., The fraction of the mass that arrives either smoothly or by accretion of small halos can be read off Figure \ref{f:growth} as the complement of the merger contribution. +" However, for the convenience of the reader we explicitly show in Figure 9 the fraction of accretion that arrives smoothly, for different values of a threshold mass below which accretion of baryons is assumed smooth."," However, for the convenience of the reader we explicitly show in Figure \ref{f:fraction_below_UV_threshold} the fraction of accretion that arrives smoothly, for different values of a threshold mass below which accretion of is assumed smooth." + The results shown in Figure 9 do not depend on any extrapolation, The results shown in Figure \ref{f:fraction_below_UV_threshold} do not depend on any extrapolation +Once the probability (ΝΤ) and the galaxy circular velocity V(M) are given. we can calculate the velocity function. of galaxies from the mass function of dark halos: For the mass function dn/dM. we adopt a fitting form derived by Sheth&Tormen(1999):: This fitting form coincides more accurately with numerical simulations than the analytic mass function derived by Press&Schechter (1974).,"Once the probability $p_g(M)$ and the galaxy circular velocity $v_{\rm +c}(M)$ are given, we can calculate the velocity function of galaxies from the mass function of dark halos: For the mass function $dn/dM$, we adopt a fitting form derived by \citet{sheth99}: This fitting form coincides more accurately with numerical simulations than the analytic mass function derived by \citet{press74}." +". The velocity function is sometimes expressed in terms of logv, as In this calculation we neglect the contribution from “substructures” (r.e.. galaxies in groups and clusters). because this mainly changes the normalization of the velocity function which we do not use as a constraint on the model parameters (see $3.1) )."," The velocity function is sometimes expressed in terms of $\log v_{\rm +c}$ as In this calculation we neglect the contribution from “substructures” (i.e., galaxies in groups and clusters), because this mainly changes the normalization of the velocity function which we do not use as a constraint on the model parameters (see \ref{sec:const:vf}) )." + Substructures. however. may affect the fraction of dark halo lenses directly. because it changes only the number of galaxy lenses.," Substructures, however, may affect the fraction of dark halo lenses directly, because it changes only the number of galaxy lenses." + Therefore we consider the effect of substructures in predicting the fraction of dark halo lenses (see $4)), Therefore we consider the effect of substructures in predicting the fraction of dark halo lenses (see \ref{sec:frac}) ). +" Bearing the picture deseribed in MM$2.1. lossinsin mind. we calculate the probability of gravitational caused by brightgalaxies and dark halos separately: where zs Is the source redshift. zi, is the lens redshift. £ is the lummosity of the source. and dn/dM is the comoving number density of dark halos (eq. [7]])."," Bearing the picture described in \ref{sec:th:baryon} in mind, we calculate the probability of gravitational lensing caused by brightgalaxies and dark halos separately: where $z_{\rm S}$ is the source redshift, $z_{\rm L}$ is the lens redshift, $L$ is the luminosity of the source, and $dn/dM$ is the comoving number density of dark halos (eq. \ref{st}] ])." + Lensing cross sections σεις and CNpw are given by where μμ is the radius of the radial caustic at source plane (e.g..Schneider.Ehlers.&Falco1992) and Doc. Dos. and Djs are the angular diameter distances to the lens. to the source. and between the lens and source. respectively.," Lensing cross sections $\sigma_{\rm SIS}$ and $\sigma_{\rm NFW}$ are given by where $\eta_{\rm rad}$ is the radius of the radial caustic at source plane \citep*[e.g.,][]{schneider92} and $D_{\rm OL}$, $D_{\rm OS}$, and $D_{\rm LS}$ are the angular diameter distances to the lens, to the source, and between the lens and source, respectively." + The one-dimensional velocity dispersion σ in equation (11)) can be represented as a function of halo mass M: where equation (5)) is used., The one-dimensional velocity dispersion $\sigma$ in equation\ref{cs_sis}) ) can be represented as a function of halo mass $M$: where equation \ref{gammav}) ) is used. + The lower limit of integral by mass. Maj. is determined by solving the equation οMinin-οςσι).," The lower limit of integral by mass, $M_{\rm min}$, is determined by solving the equation $\theta=\theta(M_{\rm min},z_{\rm S},z_{\rm L})$ ." +" The magnification bias al.1984) 1s included in B as follows: whereο Φος,DML) is the luminosity function of sources and piGp is the factor at i."," The magnification bias \citep{turner80,turner84} is included in $B$ as follows: where $\Phi(z_{\rm S}, L)$ is the luminosity function of sources and $\mu(\vec{\eta})$ is the magnification factor at $\vec{\eta}$." + The total lensing probability with image separation. larger than Ó Is given by The velocity function. is valuable because it Is easy to handle theoretically. and ts useful to test the model of galaxy formation and cosmology (Cole&Kaiser1989;Shimasaku1993:Gonzalezetal.2000:Kochanek&White 2001)..," The total lensing probability with image separation larger than $\theta$ is given by The velocity function is valuable because it is easy to handle theoretically, and is useful to test the model of galaxy formation and cosmology \citep{cole89,shimasaku93,gonzalez00,kochanek01b}." + Using the model described in. $2.2.. we can calculate the velocity function of galaxies from the mass function. of dark halos.," Using the model described in \ref{sec:th:vf}, we can calculate the velocity function of galaxies from the mass function of dark halos." +" By comparing the theoretical velocity function withobserved velocity functions. one can constrain the model parameters such as oy. My. and 7,."," By comparing the theoretical velocity function withobserved velocity functions, one can constrain the model parameters such as $\delta_{\rm +h}$, $M_{\rm h}$ , and $\gamma_v$." + The definite theoretical prediction. however. needs the value of cosmological parameters such as oy.," The definite theoretical prediction, however, needs the value of cosmological parameters such as $\sigma_8$." + Therefore we use the normalized velocity function instead of V(v)., Therefore we use the normalized velocity function instead of $\Psi(v_{\rm c})$. + Moreover. by using ος) we can neglect the effect of the overall factor of p.(M).," Moreover, by using $\psi(v_{\rm c})$ we can neglect the effect of the overall factor of $p_{\rm g}(M)$." + For the observed velocity functions. we use five velocity functions derived by Gonzalezetal.(2000): velocity functions derived from Southern Sky Redshift Survey (SSRS2). Automatic Plate Measuring facility survey (APM). United Kingdom Schmidt Telescope survey (UKST). Las Campanas Redshift Survey (LCRS). and K-band survey by Gardneretal.(1997).," For the observed velocity functions, we use five velocity functions derived by \citet{gonzalez00}: velocity functions derived from Southern Sky Redshift Survey (SSRS2), Automatic Plate Measuring facility survey (APM), United Kingdom Schmidt Telescope survey (UKST), Las Campanas Redshift Survey (LCRS), and K-band survey by \citet{gardner97}." +". We restrict the comparison with observations in the region 200km/s 500km/s) (Gonzalezetal.2000).", One reason is that observed velocity functions are not reliable at the high velocity region $v_{\rm c}>500{\rm km/s}$ ) \citep{gonzalez00}. +. The other reason is the obvious difference between observed and theoretical number density of galaxies at the low velocity region 200km /s).," The other reason is the obvious difference between observed and theoretical number density of galaxies at the low velocity region $v_{\rm c}<200{\rm +km/s}$ )." + The reason of this difference is that in our model we neglect effects of e.g.. supernovae feedback (Dekel&Silk1986) which substantially suppress the number of galaxies in low-mass halos (e.g..Gonzalezetal.2000;Nagamineal. 2001).," The reason of this difference is that in our model we neglect effects of e.g., supernovae feedback \citep{dekel86} which substantially suppress the number of galaxies in low-mass halos \citep[e.g.,][]{gonzalez00,nagamine01}." +. However we are interested in the gravitational lensing with angular separation larger than current angular resolution (0~ 0.3”).thus we can safely neglect such low- galaxies which have little impact on our lensing results.," However we are interested in the gravitational lensing with angular separation larger than current angular resolution $\theta\sim0.3''$ ),thus we can safely neglect such low-velocity galaxies which have little impact on our lensing results." + Figure 1. shows constraints on model parameters from observed velocity functions., Figure \ref{fig:chis} shows constraints on model parameters from observed velocity functions. + Contours are calculated from ratios of combined likelihood £«T]exp(—4\7)., Contours are calculated from ratios of combined likelihood ${\cal L}\propto\prod\exp(-\frac{1}{2}\chi_i^2)$. + Errors of observed velocity functions are estimated from errors of fitting parameters of velocity functions (seeGonzalezetal. 2000)., Errors of observed velocity functions are estimated from errors of fitting parameters of velocity functions \citep[see][]{gonzalez00}. . +. As easily seen from the upper panel of Figure 1.. we can put useful constraints on àp and vj=v (Mj).," As easily seen from the upper panel of Figure \ref{fig:chis}, , we can put useful constraints on $\delta_{\rm h}$ and $v_{\rm h}\equiv v_{\rm +c}(M_{\rm h})$ ." + The bestfit parameter set is (Op.vg)&(0.78.238Km/s).," The bestfit parameter set is $(\delta_{\rm h},v_{\rm +h})\simeq(0.78,238{\rm km/s})$ ." +" This means that there still remains strong degeneracy between Mj and 7,: parameter combinations which yield the same vj cannot be discriminated from. the velocity functions.", This means that there still remains strong degeneracy between $M_{\rm h}$ and $\gamma_v$ : parameter combinations which yield the same $v_{\rm h}$ cannot be discriminated from the velocity functions. + This fact is also shown in the lower panel, This fact is also shown in the lower panel +is lintriguiug. as we find no evicence lor a difference in the SDs of the low aud high inclination eroups.,"is intriguing, as we find no evidence for a difference in the SDs of the low and high inclination groups." + It is possible that their results are a cousequence of not cousicering calibration aud density ollsets when perlorming the likelihood calculations. as we have done bere.," It is possible that their results are a consequence of not considering calibration and density offsets when performing the likelihood calculations, as we have done here." + Clearly however. more observations are needed which probe the entire range of current observations before these results can be clarified.," Clearly however, more observations are needed which probe the entire range of current observations before these results can be clarified." +" The best-fit parameters for the LF presented in Equation { imply that the size clistribution is a power-law with slope q,~L5 for large objects. which breaks to a shallower slope at ciameter Dy~50-99 kin assumiug albedos."," The best-fit parameters for the LF presented in Equation \ref{eq:Fraser2008} imply that the size distribution is a power-law with slope $q_1\sim 4.8$ for large objects, which breaks to a shallower slope at diameter $D_b\sim 50-95$ km assuming albedos." + Comparison of this size distribution to models which evolve a population of planetesimals and track their size distribution as a function of time in the Ixuiper belt region can place a constraint ou the formation processes aud the duration of accretion in that region (???)..," Comparison of this size distribution to models which evolve a population of planetesimals and track their size distribution as a function of time in the Kuiper belt region can place a constraint on the formation processes and the duration of accretion in that region \citep{Kenyon2001, Kenyon2002, Kenyon2004}." + In the early stagese of formation. run-away eerowtl occurs. aud very rapidly eerow objects as largee as ~10 kun in the Ixuiper belt (?)..," In the early stages of formation, run-away growth occurs, and very rapidly grow objects as large as $\sim 10^3$ km in the Kuiper belt \citep{Kenyon2002}." +" During this process. a steep-sloped large object size distribution develops. which flattens with time as more objects become ""large""."," During this process, a steep-sloped large object size distribution develops, which flattens with time as more objects become “large”." + Caleulatious preseuted in 2.. which simulate planet accretion for coucditious in the Ixuiper belt expected for the early solar system. üunply that. in tle absence of influences [rom Neptune. the mocderu-day large object slope would be shallower than that observed if accretion lasted the age of the solar system.," Calculations presented in \citet{Kenyon2002}, which simulate planet accretion for conditions in the Kuiper belt expected for the early solar system, imply that, in the absence of influences from Neptune, the modern-day large object slope would be shallower than that observed if accretion lasted the age of the solar system." + They find that for au initial Ixuiper be{ inass similar to that predicted from the minimunm-moass solar nebula model (?) - muuch more massive than the current belt (2). - accretion must have been halted after 100 Myr., They find that for an initial Kuiper belt mass similar to that predicted from the minimum-mass solar nebula model \citep{Hayashi1981} - much more massive than the current belt \citep{Fuentes2008} - accretion must have been halted after $\sim 100$ Myr. + If IKBOs are weaς (easier to disrupt). then accretion might liave gone on for as loug as | Gyr ?)..," If KBOs are weak (easier to disrupt), then accretion might have gone on for as long as 1 Gyr \citep[see Figures 9, and 10 from][]{Kenyon2002}." + Some event(s) must have halted this process by clearing the majority ofinitial mass ott of the belt belore the slope becaine too shallow., Some event(s) must have halted this process by clearing the majority of initial mass out of the belt before the slope became too shallow. + ? has deuxyustratecd that weaker bodies will exhibit a size distribution with a larger break diameter Dy tha1 stronger bodies would if they underwent the same evolutionary history., \citet{Kenyon2004} has demonstrated that weaker bodies will exhibit a size distribution with a larger break diameter $D_b$ than stronger bodies would if they underwent the same evolutionary history. + They calculated the size distribution expected. [rom a Ixuiper belt uncer the gravitational influence of Neptune which evolved for the age of the solar system., They calculated the size distribution expected from a Kuiper belt under the gravitational influence of Neptune which evolved for the age of the solar system. + In this model. break diameters as large as 60 kim were produced ouly [or the weakest bodies they cousidered.," In this model, break diameters as large as 60 km were produced only for the weakest bodies they considered." + This moclel however. produced a large object slope iuuchli too shallow to be cousistent with the observatious. implyiug that accretion over the age of the solar system cannot have occurrect.," This model however, produced a large object slope much too shallow to be consistent with the observations, implying that accretion over the age of the solar system cannot have occurred." + The existenre of sucha large break diameter in the NBO SD implies that. ΕΣ must be quite weak (streugthless rubble piles). aud have uudergone a period of increased collisional evolution.," The existence of such a large break diameter in the KBO SD implies that, KBOs must be quite weak (strengthless rubble piles), and have undergone a period of increased collisional evolution." + This suggests a scenario in which the event responsible for the early end to accretion. aud the clearing of the majority of the mass in the Ixuiper belt. also increased the rate of collisional evolution lor a time. pushing the break diameter to the large value we see today.," This suggests a scenario in which the event responsible for the early end to accretion, and the clearing of the majority of the mass in the Kuiper belt, also increased the rate of collisional evolution for a time, pushing the break diameter to the large value we see today." + C'ollisional disruption would be substantially increased for a period of time duriug tlie scattering, Collisional disruption would be substantially increased for a period of time during the scattering +identical parameters.,identical parameters. + In any case. equation. (9)) is ον an approximation as the derivation assumes the WI approximation. while the non-linear saturation of the HDI occurs on global scales).," In any case, equation \ref{eqn:B_field_hbi}) ) is only an approximation as the derivation assumes the WKB approximation, while the non-linear saturation of the HBI occurs on global scales)." + In this paper. we will deliberately ignore this possibility.," In this paper, we will deliberately ignore this possibility." + Observationallv. the strength. of the magnetic field in the ICM is ~ CG and has a large scatter of about an order of magnitude within the ICM and between clusters (2): moreover. there are considerable observational uncertainties in these values. as mentioned above.," Observationally, the strength of the magnetic field in the ICM is $\sim\mu$ G and has a large scatter of about an order of magnitude within the ICM and between clusters \citep{carilli}; moreover, there are considerable observational uncertainties in these values, as mentioned above." + Numerical simulations show that the LIBI still develops for pi fields (1. Parrish. priv.," Numerical simulations show that the HBI still develops for $\sim\mu$ G fields (I. Parrish, priv." + comm.).," comm.)," + although it can be celaved for increased. Ποια strengths., although it can be delayed for increased field strengths. + Given the large uncertainty in whether observed field. strengths are capable of stabilizing he HBL. past studies of LIBL (e.g... 227773) focused on the regime where the magnetic tension is unimportant.," Given the large uncertainty in whether observed field strengths are capable of stabilizing the HBI, past studies of HBI (e.g., \citet{parrish09, bogdanovic09, ruszkowski10, parrish10}) ) focused on the regime where the magnetic tension is unimportant." + We also adopt the same approach here. and. study if volumc-filling urbulence can stabilize the HDI.," We also adopt the same approach here, and study if volume-filling turbulence can stabilize the HBI." + More specifically. we consider plasma 3l and note that. as long as the ield is not dynamically important. its exact. value does not av a role.," More specifically, we consider plasma $\beta\gg 1$ and note that, as long as the field is not dynamically important, its exact value does not play a role." + In this case. the magnetic field strength scales out of the problem and only serves as a medium to redirect he heat Low via anisotropic thermal conduction.," In this case, the magnetic field strength scales out of the problem and only serves as a medium to redirect the heat flow via anisotropic thermal conduction." + We can herefore study the elfects of turbulence alone without the yossibly confouncding ellects of magnetic tension., We can therefore study the effects of turbulence alone without the possibly confounding effects of magnetic tension. + ‘Turbulence impacts the thermodynamics of the Euid through its elfect on thermal conduction. both randomizing ancl amplifving the magnetic field.," Turbulence impacts the thermodynamics of the fluid through its effect on thermal conduction, both randomizing and amplifying the magnetic field." + Both of these suppress the LBL. and allow thermal conduction at ~1/3 the Spitzer value.," Both of these suppress the HBI, and allow thermal conduction at $\sim 1/3$ the Spitzer value." + llowever. turbulence can also cirecthy allect the thermal state of the plasma through dissipation of turbulent motions (direct. heating). or allowing heat transport via turbulent cilfusion (??.. and references therein).," However, turbulence can also directly affect the thermal state of the plasma through dissipation of turbulent motions (direct heating), or allowing heat transport via turbulent diffusion \citet{kim03,dennis05}, and references therein)." + Phe heating rate [rom dissipation of kinetic and magnetic energy. is: where ej ds a dimensionless constant of order unity and /. the dominant. velocity length-scale. is unknown but almost certainly a function of radius: a reasonable ansatz might be /zar|fy (?7).. where à is some adjustable constant of order unity. and fo is some minimal lengthscale.," The heating rate from dissipation of kinetic and magnetic energy is: where $c_{\rm diss}$ is a dimensionless constant of order unity and $l$, the dominant velocity length-scale, is unknown but almost certainly a function of radius; a reasonable ansatz might be $l\approx \alpha r + l_{0}$ \citep{dennis05}, where $\alpha$ is some adjustable constant of order unity, and $l_{0}$ is some minimal lengthscale." + On the other hand. the heating rate from turbulent heat clilfusion is: where s=C'yln(p/p>) is the specific entropy. ancl the turbulent cliffusivity is: where the second factor of (efepy)? takes into account the damping of radial heat transport by. buoyaney [forces (7)..," On the other hand, the heating rate from turbulent heat diffusion is: where $s=C_{\rm V} {\rm ln}(p/\rho^{\gamma})$ is the specific entropy, and the turbulent diffusivity is: where the second factor of $(\omega/\omega_{\rm BV})^{2}$ takes into account the damping of radial heat transport by buoyancy forces \citep{dennis05}." + Phe fact that Sign~04 ds of order. the hvdrodsnamic value even for ai magnetized plasma was found in MIID. simulations by 7..., The fact that $\kappa_{\rm turb} \sim u l$ is of order the hydrodynamic value even for a magnetized plasma was found in MHD simulations by \citet{cho03}. + Nonetheless. equation (11)) should be understood to be only approximate. since it assumes that [uid clements are transported. acliabatically. whieh neec not. be the case when anisotropic conduction is operating.," Nonetheless, equation \ref{eqn:heat_diffusion}) ) should be understood to be only approximate, since it assumes that fluid elements are transported adiabatically, which need not be the case when anisotropic conduction is operating." +" In. reality. both the thermal conduction. diffusion coelficient Wspizes=Pb]OUem?sFl(nf10Fem7)!UP/2keV)? anc the turbulent heat illusion coellicient μιoLO""em?sL(uf200kms1)20kpc) can be comparable. and either could dominate in a specific situation."," In reality, both the thermal conduction diffusion coefficient $\kappa_{\rm Spitzer} = v_{e} l_{\rm mfp} \sim 10^{30} {\rm cm^{2} \, s^{-1}} \, (n/10^{-2} \, {\rm cm^{-3}})^{-1} (T/2 \, {\rm keV})^{5/2}$ and the turbulent heat diffusion coefficient $\kappa_{\rm turb} \sim 10^{30} \, {\rm cm^{2} \, s^{-1}} \, (u/200\, {\rm km \, s^{-1}})(l/20 \, {\rm kpc})$ can be comparable, and either could dominate in a specific situation." + Vhermal conduction may indirectly assist with urbulent heat cdilfusion. as it reduces the impact of »iovanev forces (and thus reduces sq ).," Thermal conduction may indirectly assist with turbulent heat diffusion, as it reduces the impact of buoyancy forces (and thus reduces $\omega_{\rm BV}$ )." + Indeed. simulations w ? show that metal mixing in a stratified plasma is much more cLlicient once conduction is at. play. allowing much ooader metallicity profiles. for this very. reason.," Indeed, simulations by \citet{sharma09a} show that metal mixing in a stratified plasma is much more efficient once conduction is at play, allowing much broader metallicity profiles, for this very reason." + Naively. if we think of gas entropy. as a scalar to be advected: by urbulent motions. similar conclusions should hold. althoug= of course the interaction between heat transport and dynamics requires detailed simulations.," Naively, if we think of gas entropy as a scalar to be advected by turbulent motions, similar conclusions should hold, although of course the interaction between heat transport and dynamics requires detailed simulations." + We shall investigate he relative role of all these heating processes in our simulations., We shall investigate the relative role of all these heating processes in our simulations. + The details of the numerical setup are described in Ruszkowski Ob (2010: hereafter ROLO)., The details of the numerical setup are described in Ruszkowski Oh (2010; hereafter RO10). + Llere we summarize key differences., Here we summarize key differences. + The cluster parameters used here are similar to those corresponding to cool-core cluster A2199., The cluster parameters used here are similar to those corresponding to cool-core cluster A2199. + In addition to the NEW potential of the eluster halo. we also include the contribution from the central brightest cluster galaxy (BCC). which was not included in 11010.," In addition to the NFW potential of the cluster halo, we also include the contribution from the central brightest cluster galaxy (BCG), which was not included in RO10." +" The gravitational potential is described by the sum of the term due to an NEW profile with a softened where r, is the smoothing core radius (r,—20 kpc). r.c390 kpe is the usual NEW scale radius. and the BCG contribution which has a Ixing profile: where a—rfrns. Mes=3 kpe is the core radius for he BCC and one,=200 km Jis its line-ol-sight velocity dispersion."," The gravitational potential is described by the sum of the term due to an NFW profile with a softened where $r_{c}$ is the smoothing core radius $r_{c}= 20$ kpc), $r_{s}=390$ kpc is the usual NFW scale radius, and the BCG contribution which has a King profile: where $x=r/r_{\rm bcg}$, $r_{\rm bcg}=3$ kpc is the core radius for the BCG and $\sigma_{\rm bcg}=200$ km $^{-1}$ is its line-of-sight velocity dispersion." +" The parameter AL,=3.8«10AZ. in equation (14)) determines the cluster mass and. is of the order of he total cluster mass. Moo)=6.6107Ag."," The parameter $M_{o}=3.8\times 10^{14}M_{\odot}$ in equation \ref{eqn:NFW_potential}) ) determines the cluster mass and is of the order of the total cluster mass, $M_{\rm 200}=6.6 \times 10^{14} \, M_{\odot}$." + We then solve the equation of hyelrostatic equilibrium assuming the entropy distribution as parametrizecl by 2:: sce equations (16) (17) of ROLO., We then solve the equation of hydrostatic equilibrium assuming the entropy distribution as parametrized by \citet{cavagnolo09}; see equations (16) (17) of RO10. + Note that we do not include the eravitational contribution from other galaxies (83.2)) in our initial conditions. so the svstem is not initially in full ivdrostatic equilibrium.," Note that we do not include the gravitational contribution from other galaxies \ref{section:galaxies}) ) in our initial conditions, so the system is not initially in full hydrostatic equilibrium." + However. after an initial transient. it rapidly relaxes to a new equilibrium configuration.," However, after an initial transient, it rapidly relaxes to a new equilibrium configuration." + The addition of the BCG has two ellects., The addition of the BCG has two effects. + Firstly. due Oo the increased. gravitational acceleration. it results. in uigher gas densities compared to the models we considered in Ruszkowski Ob (2010).," Firstly, due to the increased gravitational acceleration, it results in higher gas densities compared to the models we considered in Ruszkowski Oh (2010)." + This allows for a more conservative analysis of the elfect. of cooling., This allows for a more conservative analysis of the effect of cooling. + In fact. the central density here is à factor of ~3.5 times higher. which.," In fact, the central density here is a factor of $\sim 3.5$ times higher, which," +atomic number derived [rom (he average mass number. (he Ἐν. and (he neutron and alpha mass fractions al Ty=2.5 in Woosleyοἱal.(1994).,"atomic number derived from the average mass number, the $_e$, and the neutron and alpha mass fractions at $_9$ =2.5 in \citet{woosley94}." +. We justilv this by noting that the distribution is twpically sharply peaked near Ty=2.5., We justify this by noting that the heavy-nuclide distribution is typically sharply peaked near $_9$ =2.5. + An adiabatic expansion was assumed for each trajectory in the nucleosvnthesis. with entropy constant within a trajectory but varving between trajectories. again consistent with the approach of for mes at which the temperature Ty«2.5.," An adiabatic expansion was assumed for each trajectory in the nucleosynthesis, with entropy constant within a trajectory but varying between trajectories, again consistent with the approach of \citet{woosley94} for times at which the temperature $_9<$ 2.5." + The material was taken to expand at constant velocity on a timescale consistent with that derived from Woosleyetal.(1994)., The material was taken to expand at constant velocity on a timescale consistent with that derived from \citet{woosley94}. +. For each trajectory the caleulation was continued until neutron capture reactions had ceased and the abundance distribution versus mass number had frozen out., For each trajectory the calculation was continued until neutron capture reactions had ceased and the abundance distribution versus mass number had frozen out. + Our representation of the full r-process abundances. shown as the dots in Figure 1.. is not as good as that achieved by Wooslevetal.(1994).. but our calculations do produce the basic features of the full r-process. namely the mass 130 and 195u peaks.," Our representation of the full r-process abundances, shown as the dots in Figure \ref{woo_traj}, is not as good as that achieved by \citet{woosley94}, but our calculations do produce the basic features of the full r-process, namely the mass 130 and 195u peaks." + The simulation of Wooslevetal.(1994). that produced a good r-process representation began with trajectory number 24 and summed the nucleosvnthesis vields [rom the remaining 16 elements since all of these trajectories would have been ejected. into the interstellar medium., The simulation of \citet{woosley94} that produced a good r-process representation began with trajectory number 24 and summed the nucleosynthesis yields from the remaining 16 elements since all of these trajectories would have been ejected into the interstellar medium. + We also began with trajectory 24. and perlormed a mass weighted sum of the nucleosvithesis from the trajectories up to some hieher number trajectory to observe the resulting nucleosvnthesis when the trajectories bevond our maximum trajectory were assumec to be consumed bv the collapse to a black hole.," We also began with trajectory 24, and performed a mass weighted sum of the nucleosynthesis from the trajectories up to some higher number trajectory to observe the resulting nucleosynthesis when the trajectories beyond our maximum trajectory were assumed to be consumed by the collapse to a black hole." + This produced a result similar to that οἱ Wooslevetal.(1994) when all trajectories [rom 24 to 40 were included., This produced a result similar to that of \citet{woosley94} when all trajectories from 24 to 40 were included. + The results are shown in Figure l.., The results are shown in Figure \ref{woo_traj}. + There it can be seen that truncating the r-process al increasing (rajectory number does terminate (he r-process nucleosvuthesis al increasingly hieher nuclear mass., There it can be seen that truncating the r-process at increasing trajectory number does terminate the r-process nucleosynthesis at increasingly higher nuclear mass. + Note that although the curve representing trajectories 24 through 31 does reach the mass 195u peak. the abundance produced in that ealeulation is nearly (wo orders of magnitude below that of the full r-process. which would render the higher mass nuclides difficult to observe.," Note that although the curve representing trajectories 24 through 31 does reach the mass 195u peak, the abundance produced in that calculation is nearly two orders of magnitude below that of the full r-process, which would render the higher mass nuclides difficult to observe." + The abundances for (hat calculation would therelore appear observationallv to terminate at a mass of about 140 u. In Figure 2 we compare several (r-process calculations with the derived elemental abundance pattern in the metal poor halo star HD. 122563., The abundances for that calculation would therefore appear observationally to terminate at a mass of about 140 u. In Figure \ref{ele_abun} we compare several tr-process calculations with the derived elemental abundance pattern in the metal poor halo star HD 122563. + This low-metallicity star ([Fe/1l] = -2.7) is deficient in (he heavy neutron-capture elements (Ba and heavier) relative to the light. neutron-capture elements (Sr through. Cel) when compared with the scaled Solar pattern., This low-metallicity star ([Fe/H] = -2.7) is deficient in the heavy neutron-capture elements (Ba and heavier) relative to the light neutron-capture elements (Sr through Cd) when compared with the scaled Solar r-process pattern. + The HD 122563 abundances are a very poor match to the scaled Solar s-process pattern., The HD 122563 abundances are a very poor match to the scaled Solar s-process pattern. + Hs abundance pattern matches the scaled Solar r-process pattern better up to an atomic mass of about 70 (mass of 114 u). but even this fit is unsatislving (Sneden 2006).," Its abundance pattern matches the scaled Solar r-process pattern better up to an atomic mass of about 70 (mass of $\sim$ 174 u), but even this fit is unsatisfying \citep{sneden83, honda06}." +. Stars like IID 122563 may be. candidates for enrichment bv the ti-process., Stars like HD 122563 may be candidates for enrichment by the tr-process. + Figure 2. demonstrates that the ta-process predictions. while far [from a perfect match to the individual abundances. can reproduce the relative," Figure \ref{ele_abun} demonstrates that the tr-process predictions, while far from a perfect match to the individual abundances, can reproduce the relative" +"A]LSkv Survey. which vields the observed treud of Ly with M, without having to invoke effects from supposed Star-Planct Interactious.","All-Sky Survey, which yields the observed trend of $L_X$ with $M_p$ without having to invoke effects from supposed Star-Planet Interactions." +" Also without performing a PCA onu this sample. the dependencies ofLy aud M, ou d are revealed by rauk correlation tests."," Also without performing a PCA on this sample, the dependencies of$L_X$ and $M_p$ on $d$ are revealed by rank correlation tests." + We calculate Spearman's f. a rank correlation coefficieut which displays a perfect correlation by a value of 1l. perfect auticorrelation by —1 aud no correlation by 0.," We calculate Spearman's $\rho$, a rank correlation coefficient which displays a perfect correlation by a value of $1$, perfect anticorrelation by $-1$ and no correlation by $0$." +" For the full ?— suuple. we fiud strong correlations of both Ly aud M, with d. indicated by p values of0.19/0.5[ respectively. trauslati1ο to probabilities of 0.6/0.2% that sucha correlation can be reached by pure chance."," For the full \cite{Scharf2010} sample, we find strong correlations of both $L_X$ and $M_p$ with $d$, indicated by $\rho$ values of $0.49/0.54$ respectively, translating to probabilities of $0.6/0.2 \%$ that such a correlation can be reached by pure chance." +" This correlation analysis vields the same result as ιο PCA: the stellar distance is the crucial parameter iu us saniple which causes the Ly/M, correlation.", This correlation analysis yields the same result as the PCA; the stellar distance is the crucial parameter in this sample which causes the $L_X/M_p$ correlation. +" This is also reflected in the behavior of Ly/L,,. where rere Is no significant correlation with planetary mass for stars with close-in planets. see Fig. l.."," This is also reflected in the behavior of $L_X/L_{bol}$, where there is no significant correlation with planetary mass for stars with close-in planets, see Fig. \ref{fig1}." + We also checked us visual result with a Spearman's p test while excluding 1ο data from the two incomparable stars., We also checked this visual result with a Spearman's $\rho$ test while excluding the data from the two incomparable stars. + This vields p— 4.05. Le. a very weak positive correlation: the probability at such a p value is reached by chance is 87%.," This yields $\rho = 0.05$ , i.e. a very weak positive correlation; the probability that such a $\rho$ value is reached by chance is $87\%$." +" This is rot surprising: if the trend m Ly is a distance selection effect and not related to the stellar activity level. theu the quantity Ly(Ly... which measures the intrinsic stellar activity level. should be indepeudent from the planetary mass,"," This is not surprising: if the trend in $L_X$ is a distance selection effect and not related to the stellar activity level, then the quantity $L_X/L_{bol}$, which measures the intrinsic stellar activity level, should be independent from the planetary mass." + Tn our further analysis. we use the data presented in ?.. which consists of all known planet-hosting stars within a distance of 30 pc from the Sun. with ταν properties derived from audROSAT data.," In our further analysis, we use the data presented in \cite{Poppenhaeger2010}, which consists of all known planet-hosting stars within a distance of $30$ pc from the Sun, with X-ray properties derived from and data." + As discssed iu detail in 2.. we exclude unresolved binary stars and early stars without outer convection zones frou our analysis.," As discussed in detail in \cite{Poppenhaeger2010}, we exclude unresolved binary stars and early stars without outer convection zones from our analysis." + The errors given are Poissonian errors plus an additional uncertainty of 30% ou the N-rav huinosity to account for short-time variations. suce a large part of our salple consists of pointed obervatious.," The errors given are Poissonian errors plus an additional uncertainty of $30\%$ on the X-ray luminosity to account for short-time variations, since a large part of our sample consists of pointed obervations." + We use the same sample sclection criterion on these data as was used in’? (planets at a<0.15 AU)., We use the same sample selection criterion on these data as was used in \cite{Scharf2010} (planets at $a<0.15$ AU). +" We show the relation between Ly aud M, iu Fig. 3.."," We show the relation between $L_X$ and $M_{pl}$ in Fig. \ref{fig3}," + lett pauchk data from stars which are also present iu the sample from ? are plotted as ercen filled sviibols., left panel; data from stars which are also present in the sample from \cite{Scharf2010} are plotted as green filled symbols. + These stars lie close to a straight line. simülu to Fie. l.. ," These stars lie close to a straight line, similar to Fig. \ref{fig1}, ," +although the data was collected in single poiutiues and not averaged over larger portions of the planetary orbit., although the data was collected in single pointings and not averaged over larger portions of the planetary orbit. + This shows that the averaging process is not crucial for this kind of analysis:, This shows that the averaging process is not crucial for this kind of analysis; +enerev deposition laver.,energy deposition layer. + With this approach thev found the escape rates to depend on the position of the heating laver as well as on the amount of energy input. wilh the escape rate exponentially increasing wilh (he heating rate.," With this approach they found the escape rates to depend on the position of the heating layer as well as on the amount of energy input, with the escape rate exponentially increasing with the heating rate." + Tianetal.(2005) also Found Watson's escape [Iuxes to be too high when low density hydrogen atmospheres are involved (as in the case IID 2094583b)., \cite{Tetal:05} also found Watson's escape fluxes to be too high when low density hydrogen atmospheres are involved (as in the case HD 209458b). + At hydrogen number densities higher than 10! 7. Tianetal.(2005). find hieher scape rates than Watson.," At hydrogen number densities higher than $^{14}$ $^{-3}$, \cite{Tetal:05} find higher scape rates than Watson." + Generally. the simulations produce higher escape rates (han the ones given bv Eq.," Generally, the simulations produce higher escape rates than the ones given by Eq." + 10. for £ = 3 as the density increases., \ref{loss} for $\xi$ = 3 as the density increases. + This is (he result of the hieher total amount of energv. absorbed in an extended atmosphere. as opposed to that absorbed in a single laver (the approximation used to obtain Eq. 10)).," This is the result of the higher total amount of energy absorbed in an extended atmosphere, as opposed to that absorbed in a single layer (the approximation used to obtain Eq. \ref{loss}) )." + The mass-loss rates (obtained by using €= 3 in Eq. 10)), The mass-loss rates (obtained by using $\xi~=$ 3 in Eq. \ref{loss}) ) + from a 1 planet for central stars (al 360000 IXIX) with different masses are plotted in Fig. 5.. ," from a 1 planet for central stars (at 000 K) with different masses are plotted in Fig. \ref{hydro}, ," +versus the orbital distance., versus the orbital distance. + Note that the value of& used in Fig., Note that the value of $\xi~$ used in Fig. + 5. is always smaller than that obtained by Evkaevetal.(2006) for the exoplanets in which the mass. radius ancl stellar parameters are known.," \ref{hydro} is always smaller than that obtained by \cite{Erk:06} for the exoplanets in which the mass, radius and stellar parameters are known." + The different lines account for the different central star masses considered. with the mass-loss rates increasing with the stellar mass.," The different lines account for the different central star masses considered, with the mass-loss rates increasing with the stellar mass." + It is important (o note that for theblow-off 2004) to operate. the planet has to be in a very. close orbit to the parent star which is never the case for planets to be found around PN central stars.," It is important to note that for the \citep{Letal:04} to operate, the planet has to be in a very close orbit to the parent star which is never the case for planets to be found around PN central stars." + Moreover. none of the calculations in the literature includes heating rates as high as the ones expected for a planet orbiting a PN central star. and as it has been shown by Cecchi-Pestellinietal.(2006).. the inclusion of X-ray irradiation from the star strongly increases (he heating in planetary exospheres.," Moreover, none of the calculations in the literature includes heating rates as high as the ones expected for a planet orbiting a PN central star, and as it has been shown by \cite{Cp:06}, the inclusion of X-ray irradiation from the star strongly increases the heating in planetary exospheres." + ‘Therefore. {he mass-loss rates given in Fig.," Therefore, the mass-loss rates given in Fig." + 5Hr should be considered merely as order of magnitude approximations {ο the actual mass-loss rates [rom a planet exposed to a PN central star., \ref{hydro} should be considered merely as order of magnitude approximations to the actual mass-loss rates from a planet exposed to a PN central star. + In addition. it is very likely that the planet will inflate as radiation is iransformed into heal inside i(s atmosphere. which will lead to further increase in (he planets evaporation rate with our approach.," In addition, it is very likely that the planet will inflate as radiation is transformed into heat inside its atmosphere, which will lead to further increase in the planet's evaporation rate with our approach." + An appropriate determination of the escape rate will require a solution of the hvdrodynanmic escape equations for the case under consideration., An appropriate determination of the escape rate will require a solution of the hydrodynamic escape equations for the case under consideration. + Central stars of PN do not maintain high huninosities for an extended. period of time and therefore (he evaporation rates shown in Fig., Central stars of PN do not maintain high luminosities for an extended period of time and therefore the evaporation rates shown in Fig. + 5. will change as (he star evolves., \ref{hydro} will change as the star evolves. + In Fig., In Fig. + 6 we show the evolution of the evaporation rate of a planet orbiting a 0.56 PN central star at two orbital distances: 1.5AAU and AAU (solid and dashed lines respectively)., \ref{hydro_time} we show the evolution of the evaporation rate of a planet orbiting a 0.56 PN central star at two orbital distances: AU and AU (solid and dashed lines respectively). + The evaporation rate has been computed using £=3 in Eq., The evaporation rate has been computed using $\xi=3$ in Eq. + 10. anclthe evolution of the stellar flux from the models of Vassiliadis&Wood(1994) extended to the white chwarl cooling, \ref{loss} andthe evolution of the stellar flux from the models of \cite{Vw:94} extended to the white dwarf cooling +"where μι denotes the use of Q,,, and af,""(E) in Eq. (14)).",where $R_{\mu \nu}$ denotes the use of $Q_{\mu \nu}$ and $\sigma_{1 2}^{\mu \rightarrow \nu}(E)$ in Eq. \ref{eq:R-Formal}) ). + Inserting Eq. (19)), Inserting Eq. \ref{eq:Ratio of Reaction Rates munu}) ) + into Eq. (18)), into Eq. \ref{sigmac-star}) ) +" and using the fact that Ομ=O-E3,+E),,. we can write where R represents an average correction factor among all thermally populated states."," and using the fact that $Q_{\mu \nu} = Q - E_{3 \nu} + E_{1 \mu}$, we can write where $R$ represents an average correction factor among all thermally populated states." + As demonstrated below. R is nearly independent of the detailed nuclear. structure.," As demonstrated below, $R$ is nearly independent of the detailed nuclear structure." + Hence. we can simply utilize the ground-state Q-value as à representative average over the distribution of Q-values among the thermally populated states.," Hence, we can simply utilize the ground-state $Q$ -value as a representative average over the distribution of $Q$ -values among the thermally populated states." + Also. the spin factors above are now replaced by the relevant nuclear partition functions G;: where o denotes the individual states m nucleus 7.," Also, the spin factors above are now replaced by the relevant nuclear partition functions $G_{i}$: where $\alpha$ denotes the individual states in nucleus $i$." + Stellar reaction rate tables are usually listed as functions of temperature 7) in units of 10? K and are given as [MitavTo)]., Stellar reaction rate tables are usually listed as functions of temperature $T_9$ in units of $10^9$ K and are given as $\bigl[ N_A \langle \sigma v(T_9) \rangle^* \bigr]$. + Thus. we can rewrite Eq. (20))," Thus, we can rewrite Eq. \ref{eq:thermal}) )" + as where now N4 is Avagadro’s number so that [MatovCTo] is in units of em? mol! s7!. Q is in units of MeV and j: is the reduced mass in atomic mass units.," as where now $N_A$ is Avagadro's number so that $\bigl[ N_A \langle \sigma v(T_9) \rangle^* \bigr]$ is in units of $^3$ $^{-1}$ $^{-1}$, $Q$ is in units of MeV and $\hat \mu$ is the reduced mass in atomic mass units." + Equations (20)) and (229) are in a convenient form because in the limit ofRA> 0. they reduce to usual photodisintegration rates available from. various. compilations (e.g... Fowler.Caughlan.&Zimmerman(1967. 1975); Holmesetal. (1976):; Woosleyet.al. (1978); Caughlan&Fowler (1988): NACRE. Anguloetal.(1990): TALYS. Goriely.Hilaire.&Konig (2008):: NONSMOKER. Rauscher&Thielemann(2000) or REACLIB. Cyburtetal. (2010))).," Equations \ref{eq:thermal}) ) and \ref{eq:thermalT9}) ) are in a convenient form because in the limit of $R \rightarrow 0$ , they reduce to usual photodisintegration rates available from various compilations (e.g., \cite{fow67,fow75}; \cite{Holmes76}; \cite{Woosley78}; \cite{CF88}; NACRE, \cite{NACRE}; TALYS, \cite{Goriely08}; NONSMOKER, \cite{Rauscher00} or REACLIB, \cite{REACLIB}) )." +" The combined factors multiplying £ov?,. in Eq. (22))", The combined factors multiplying $ {\langle\sigma v\rangle_{12}^*} $ in Eq. \ref{eq:thermalT9}) ) +" are usually referred to as the ""reverse ratio"" as this factor gives the reverse reaction rate in terms of the forward rate."," are usually referred to as the ""reverse ratio"" as this factor gives the reverse reaction rate in terms of the forward rate." + In this work. we show that there is a simple correction (1+) to this reverse ratio due to the difference between Planckian and Maxwell-Boltzmann statistics.," In this work, we show that there is a simple correction $(1 + R)$ to this reverse ratio due to the difference between Planckian and Maxwell-Boltzmann statistics." + For most of the remainder of this manuscript. our goal will be to derive a simple analytic form for R for ease in correcting existing tabularized reverse reaction rates.," For most of the remainder of this manuscript, our goal will be to derive a simple analytic form for $R$ for ease in correcting existing tabularized reverse reaction rates." + We will also derive simple analytic approximations to clarify the essential physies of this correction and summarize examples of which astrophysical conditions may be most affected by these correction factors., We will also derive simple analytic approximations to clarify the essential physics of this correction and summarize examples of which astrophysical conditions may be most affected by these correction factors. + Before leaving this discussion. however. it is worth emphasizing again that the above rate does not imply equilibrium. but only detailed balance and à thermal population of photons and nuclear excited states.," Before leaving this discussion, however, it is worth emphasizing again that the above rate does not imply equilibrium, but only detailed balance and a thermal population of photons and nuclear excited states." + Nevertheless. the situation of equilibrium between capture and photodissociation frequently occurs m astrophysical environments and is referred to as nuclear statistical equilibrium (NSE).," Nevertheless, the situation of equilibrium between capture and photodissociation frequently occurs in astrophysical environments and is referred to as nuclear statistical equilibrium (NSE)." + It is of note that the conditions of NSE are also modified from the usual Saha equation by the above quantum corrections., It is of note that the conditions of NSE are also modified from the usual Saha equation by the above quantum corrections. + Moreover. in conditions of NSE. one sometimes synthesizes nuclei for which Q/AT~| and the corrections can become larger.," Moreover, in conditions of NSE, one sometimes synthesizes nuclei for which $Q/kT \sim 1$ and the corrections can become larger." + Examples of this include the formation of nuclei near the proton drip line in the hot hydrogen burning rp-process. or the synthesis of nuclei near the neutron drip line in the neutron-capture +-process. as discussed below.," Examples of this include the formation of nuclei near the proton drip line in the hot hydrogen burning $rp$ -process, or the synthesis of nuclei near the neutron drip line in the neutron-capture $r$ -process, as discussed below." + To see the revised conditions of NSE consider the evolution of a nucleus undergoing rapid particle captures and photodissociation., To see the revised conditions of NSE consider the evolution of a nucleus undergoing rapid particle captures and photodissociation. + This can be written as ⊤∣↴⊜⊜↳∣⋯⋯↴∣⋪⋯⋯∁⋂⋯∐⊓∪∏⋖∠∣∣≀∣∠∣∩∶∩⋔⊜∣⋪⊖↑↴⋯⋪⊜↳↿⊜⋯∐⋯↿⋋ that or in terms of mass fractions and temperature. it is more convenient for stellar models to write In the limit that R>O. Eqs. (24))," This can be written as The equilibrium condition $(dn_1/dt) = 0$ therefore demands that or in terms of mass fractions and temperature, it is more convenient for stellar models to write In the limit that $R \rightarrow 0$, Eqs. \ref{sahaeq}) )" + and (25)) represent the usual nuclear Saha equation (Saha1921) of statistical equilibrium which also invokes the Maxwellian approximation given in Eq. (12)), and \ref{sahaeqT9}) ) represent the usual nuclear Saha equation \citep{saha21} of statistical equilibrium which also invokes the Maxwellian approximation given in Eq. \ref{approx}) ) + either directly or indirectly in its derivation (ef. Clayton(1968):Ihadis (2007))).," either directly or indirectly in its derivation (cf. \cite{cla68,Iliadis07}) )." + The deviation of NSE due to quantum statistics may impact the evolution of explosive nucleosynthesis environments for which one can encounter nuclei with small photodissociation thresholds. e.g.. near the neutron or proton drip lines.," The deviation of NSE due to quantum statistics may impact the evolution of explosive nucleosynthesis environments for which one can encounter nuclei with small photodissociation thresholds, e.g., near the neutron or proton drip lines." + To the extent that such nuclei are beta-decay waiting points. for example. the altered statistics will affect the timescale for the build up of abundances.," To the extent that such nuclei are beta-decay waiting points, for example, the altered statistics will affect the timescale for the build up of abundances." + Another possible application of the corrections deduced here is for the ionization equilibrium of atomic or molecular species with a low ionization potential in stellar atmospheres., Another possible application of the corrections deduced here is for the ionization equilibrium of atomic or molecular species with a low ionization potential in stellar atmospheres. + However. we will not consider that case further here.," However, we will not consider that case further here." + It is worth noting that quantum effects always tend to speed up photodisintegration rates because the Planck distribution places many more photons at low energy than à Maxwell-Boltzmann distribution of the same temperature or energy density., It is worth noting that quantum effects always tend to speed up photodisintegration rates because the Planck distribution places many more photons at low energy than a Maxwell-Boltzmann distribution of the same temperature or energy density. + In other words. R is always positive definite.," In other words, $R$ is always positive definite." + Hence. even though it is often small. it is worth including.," Hence, even though it is often small, it is worth including." + This correction could of course always be evaluated by direct numerical integration of Eq. (14)), This correction could of course always be evaluated by direct numerical integration of Eq. \ref{eq:R-Formal}) ) + or Eq. (11)., or Eq. \ref{eq:Inverse Reaction Rate 2}) ). + In a large etwork calculation with evolving temperature. however. the repeated numerical integrations would slow the computation time. moreover. 1t Is a tedious task to assemble all of the relevant cross section data.," In a large network calculation with evolving temperature, however, the repeated numerical integrations would slow the computation time, moreover, it is a tedious task to assemble all of the relevant cross section data." + Nevertheless. the advantage of introducing the R in Eq. (20))," Nevertheless, the advantage of introducing the $R$ in Eq. \ref{eq:thermal}) )" + is that it gives the quantum correction as a small of the classical Maxwellian result., is that it gives the quantum correction as a small of the classical Maxwellian result. + Hence. for implementation in large networks. an analytic approximation to the exact numerical integration for R is both adequate and desirable.," Hence, for implementation in large networks, an analytic approximation to the exact numerical integration for $R$ is both adequate and desirable." + Moreover. we show that an accurate analytic correction 1s readily available based upon theinput from existing reaction rate tables (either in analytic or tabularized form).," Moreover, we show that an accurate analytic correction is readily available based upon theinput from existing reaction rate tables (either in analytic or tabularized form)." + We also show that A is nearly independent of the nuclear cross sections. and to leading order only depends upon the Q-value and the Gamow and/or resonance energy.," We also show that $R$ is nearly independent of the nuclear cross sections, and to leading order only depends upon the $Q$ -value and the Gamow and/or resonance energy." +free parameters of the model.,free parameters of the model. + In this work we neglect the presence of a possible contamination from Soft Cimma-Itay Repeaters at low redshifts (Hurley et al., In this work we neglect the presence of a possible contamination from Soft Gamma-Ray Repeaters at low redshifts (Hurley et al. + 2005) which is still dillieult to quantify. (see Chapman οἱ al., 2005) which is still difficult to quantify (see Chapman et al. + 2008)., 2008). +" We then compute the expected SGRB rate in the 15 keV band ofSuwiff adopting a field of view AQ,=LA sr. ancl a 2-vear mission."," We then compute the expected SGRB rate in the 15--150 keV band of adopting a field of view $\Delta \Omega_s=1.4$ sr, and a 2-year mission." + For a correct comparison between model results ancl data. we calculate the photon peak Εαν forSwiff SGRBs in a timing window similar to the one used on BATSE.," For a correct comparison between model results and data, we calculate the photon peak flux for SGRBs in a timing window similar to the one used on BATSE." + Peak Uuxes of Swift GRBs are calculated on clilferent integration times. spanning from 64 to 448 ms. in order to match common significance criteria and compatibly with the duration of the peak itself.," Peak fluxes of Swift GRBs are calculated on different integration times, spanning from 64 to 448 ms, in order to match common significance criteria and compatibly with the duration of the peak itself." + These are consistent. within uncertainties with the corresponding values integrated on a fixed 64-ms window., These are consistent within uncertainties with the corresponding values integrated on a fixed 64-ms window. + This makes the comparison with BATSE well grounded., This makes the comparison with BATSE well grounded. + The photon Ηχος fo. for the SGRBs observed with are collected. in ‘Table 2., The photon fluxes $P_{64}$ for the SGRBs observed with are collected in Table 2. + The few dttections do not. allow to construct a reliable differential peak Εαν cistribution., The few detections do not allow to construct a reliable differential peak flux distribution. +" However. we expect ~9LOSCRBs per vear with 23,22 phs + em? for all our models. in agreement with the TSCRBs per vear detected by at 10 same [lux limit."," However, we expect $\sim 9-10$ SGRBs per year with $P_{64}\ge 2$ ph $^{-1}$ $^{-2}$ for all our models, in agreement with the 7 SGRBs per year detected by at the same flux limit." + Note that this is a lower limit since we do not consider here SCliDs that are identified in the ground. analysis (eg. GRB 051114) and rose long GRBs that could be tentatively ascribed to the garort category. (e.g... GRB 060614. ancl 060505).," Note that this is a lower limit since we do not consider here SGRBs that are identified in the ground analysis (e.g., GRB 051114) and those long GRBs that could be tentatively ascribed to the short category (e.g., GRB 060614, and 060505)." + Lowering ve Swiff photon Lux threshold down to 1 ph 5| 7. je expected SGRB detections largely exceed. the number X identified SGORBs.," Lowering the photon flux threshold down to 1 ph $^{-1}$ $^{-2}$, the expected SGRB detections largely exceed the number of identified SGRBs." + This fact may be related to a different nergy band and trigeer procedure of and BATSE., This fact may be related to a different energy band and trigger procedure of and BATSE. + We ius choose the threshold of 2 ph s| em.7 as measured in a 64 ms timing window as reliable detection limit forτί]., We thus choose the threshold of 2 ph $^{-1}$ $^{-2}$ as measured in a 64 ms timing window as reliable detection limit for. + In Table 2 we list. all SCRBs detected. by until march 2007 with. when present. the redshift.," In Table 2 we list all SGRBs detected by until march 2007 with, when present, the redshift." + We note that GRB 050509D. 050906. and 051210 are not included in our analysis being their photon flux in the 64 ms timing window below the threshold. limit we adopted.," We note that GRB 050509B, 050906, and 051210 are not included in our analysis being their photon flux in the 64 ms timing window below the threshold limit we adopted." + To be conservative. we assume that GRB 050813 lies at 2=0.72 instead. of >=Ls.," To be conservative, we assume that GRB 050813 lies at $z=0.72$ instead of $z=1.8$." + The shaded area in Fig., The shaded area in Fig. + 1 accounts for the observed cumulative 2 distribution including the uncertainties due the lack of a secure redshift determination for some SCliDs., 1 accounts for the observed cumulative $z$ –distribution including the uncertainties due the lack of a secure redshift determination for some SGRBs. + Alodel results computed. for the different DNS formation channels are shown in Fig., Model results computed for the different DNS formation channels are shown in Fig. + 1: solid line refers to the Lele scenario. dot.short dashed for GCL. dotted for GC2. dashec for ας3. and dot.lone dashed for GCA.," 1: solid line refers to the field scenario, dot–short dashed for GC1, dotted for GC2, dashed for GC3, and dot–long dashed for GC4." + For the field scenario our fit is close to model Gi) of Guetta Piran (2007)., For the field scenario our fit is close to model (ii) of Guetta Piran (2007). + For the GC scenario. we note that in spite of the dilleren assumptions of the GC formation rate. the expected SCGIUD > distributions are not remarkably dillerent.," For the GC scenario, we note that in spite of the different assumptions of the GC formation rate, the expected SGRB $z$ –distributions are not remarkably different." + Phe key resul is that DNSs from dynamical interactions in GC may account only for the lowest redshift SGRBs. Le. 2<0.2.0.3.," The key result is that DNSs from dynamical interactions in GC may account only for the lowest redshift SGRBs, i.e. $z<0.2-0.3$." + We find that only of SCIUBs in GC should lie above >=0.65., We find that only of SGRBs in GC should lie above $z=0.6$. + This result is expected owing to the longer delay times in the formation and coalescence of DNSs in. GCs relative to the field., This result is expected owing to the longer delay times in the formation and coalescence of DNSs in GCs relative to the field. + Field Όλος form carlicr and. for this reason they can account for the SGRB distribution above =(KS. Instead. the field scenario. results inconsistent with data below this redshift.," Field DNSs form earlier and for this reason they can account for the SGRB distribution above $z=0.8.$ Instead, the field scenario results inconsistent with data below this redshift." + This appears to be little alfected by our choice of à in theluminosity function. although the bestfit. parameters in Table 1 may vary significantly.," This appears to be little affected by our choice of $\alpha$ in theluminosity function, although the best–fit parameters in Table 1 may vary significantly." +C-0.02-0.07 is a group of LTT regions (three compact and oue ultracompact) in⋅ the Galactic: center (hereafter‘ GC) which lie ~6 parsecs in projection from the ceutral supermassive black hole.,G-0.02-0.07 is a group of 4 regions (three compact and one ultracompact) in the Galactic center (hereafter GC) which lie $\sim6$ parsecs in projection from the central supermassive black hole. + Dudividually. the regions are also identified as Ser A-A through Ser A-D. as they were first identified iu radio mages of the Ser A couples of ionized. eas surrounding Ser A*. the radio counterpart of the central black hole(2).," Individually, the regions are also identified as Sgr A-A through Sgr A-D, as they were first identified in radio images of the Sgr A complex of ionized gas surrounding Sgr A*, the radio counterpart of the central black hole." +.. All four regions are projected to lie aloug the edge of the Ser A East supernova relat (sce Figure 1)) which lies between these reeious aud Ser Ae, All four regions are projected to lie along the edge of the Sgr A East supernova remnant (see Figure \ref{radiofig}) ) which lies between these regions and Sgr A*. + Severa studies have been made of the C-0.02-0.07 coniplex. both in radio contimmun and recombiuation lines sas well as in mic infrared fine structure linesS92).. including the recent work of?.," Several studies have been made of the G-0.02-0.07 complex, both in radio continuum and recombination lines, as well as in mid infrared fine structure lines, including the recent work of." +. These observations have shown that the regious are consistent with each being ionized by a single late O-tvpe star., These observations have shown that the regions are consistent with each being ionized by a single late O-type star. + The radial velocities of all four regions have also been measured to be very similar. ranging from L3 to 19)+... indicating that these reeious ire kinematically associated both with each other. aud with A\L-0.02-0.07. the nearby 50 kan + cloud.," The radial velocities of all four regions have also been measured to be very similar, ranging from 43 to 49, indicating that these regions are kinematically associated both with each other, and with M-0.02-0.07, the nearby 50 km $^{-1}$ cloud." +" The regions appear to lie along a spatially coincident dense ridge of the cloud. denoted the tnolecnar NAle? N""ich shows evidence of interaction with the Ser A AST MSTLο ΠΕ"," The regions appear to lie along a spatially coincident dense ridge of the cloud, denoted the molecular by, which shows evidence of interaction with the Sgr A East supernova remnant." + the suggestive ATASCLxt of the regions along the periphery of Ser A East. cstimates of its age sneeost that the sar formation event that produced the C-0.02-0.07. conu]ex predates the explosion. as the lifetimes of ultracoupact regions. precursors to compact rTOglons. are believed to span 10 vears(?).," Despite the suggestive arrangement of the regions along the periphery of Sgr A East, estimates of its age suggest that the star formation event that produced the G-0.02-0.07 complex predates the explosion, as the lifetimes of ultracompact regions, precursors to compact regions, are believed to span $10^5$ years." +". In particular. region D. ikelv the vouneest of the four. has a minimal, aee oeof at 1east a few times 104 years. estimated from the mass loss rate of the cenral star. aud the expansion rate of the nehula(?)."," In particular, region D, likely the youngest of the four, has a minimum age of at least a few times $10^4$ years, estimated from the mass loss rate of the central star, and the expansion rate of the nebula." +. Although these regiois are thus unlikely to be au exanple of supernova-tr188OOered star formation. they are valuable t«» study not on vas the closest episode of receut (within 0.1.1 Myrs) massive star formation to he center of the Galaxy. but also as one of very few exaples of recent massive star formation m the centra Iiudred parsecs.," Although these regions are thus unlikely to be an example of supernova-triggered star formation, they are valuable to study not only as the closest episode of recent (within $0.1-1$ Myrs) massive star formation to the center of the Galaxy, but also as one of very few examples of recent massive star formation in the central hundred parsecs." + The ceutral huudred parsecs of the οalaxy are estimated to have a star formation rate of at cast 0.05 A\L.xr |7). and likely higher(?7).. are hostto three vouug star clusters with initial masses in excess of 10! Εμ“... aud at least |<109 solar masses of molecular lateral 7).," The central hundred parsecs of the galaxy are estimated to have a star formation rate of at least $0.05$ $_{\odot}$ $^{-1}$, and likely higher, are hostto three young star clusters with initial masses in excess of $10^4$ $_{\odot}$, and at least $4\times10^6$ solar masses of molecular material ." + However the C-0.02-0.07 couples. of, However the G-0.02-0.07 complex of +vector of the parameters defining the model: triaxial virial mass Alooy. concentration 6). minor axis ratio e. intermediate axis ratio b. and two orientation angles @ and ©.,"vector of the parameters defining the model: triaxial virial mass $M_{200}$, concentration $C$, minor axis ratio $a$, intermediate axis ratio $b$, and two orientation angles $\theta$ and $\phi$." + In our MCMC sampler we employ a 6D two-sided Gaussian transfer function. and use the covariance matrix of an early run to sample in an optimised basis aligned with the degeneracies of the posterior.," In our MCMC sampler we employ a 6D two-sided Gaussian transfer function, and use the covariance matrix of an early run to sample in an optimised basis aligned with the degeneracies of the posterior." + We tune the step sizes of the sampler to achieve an average acceptance rate of |/3 in each basis direction. run three independent MCMC chains. started at randomly chosen positions in parameter space. for each lens system. and sample the distribution space until the standard vartehain meanYmean(cehain var) indicator is less than 0.2. indicating chain convergence.," We tune the step sizes of the sampler to achieve an average acceptance rate of 1/3 in each basis direction, run three independent MCMC chains, started at randomly chosen positions in parameter space, for each lens system, and sample the distribution space until the standard var(chain mean)/mean(chain var) indicator is less than 0.2, indicating chain convergence." + We utilise the GetDist package from the standard CosmoMC (Lewis&Bridle 2002)) distribution to calculate convergence statistics. parameter contours. and marginalized parameter estimates.," We utilise the GetDist package from the standard CosmoMC \citealt{lewis}) ) distribution to calculate convergence statistics, parameter contours, and marginalized parameter estimates." + We employ 40 bins in the Gaussian smoothing of the contours. chosen because. for the spherical case. this smoothing length best matches the contours obtained using this MCMC method to those of a standard \7 approach.," We employ 40 bins in the Gaussian smoothing of the contours, chosen because, for the spherical case, this smoothing length best matches the contours obtained using this MCMC method to those of a standard $\chi^2$ approach." + We note that while the angles are defined over a range O«60$. + Hence they are all stable against. axisvmmetric perturbations., Hence they are all stable against axisymmetric perturbations. + We next consider. non-axisvmumetric instabilities., We next consider non-axisymmetric instabilities. + We have 3—0.23.0.26 For the cold EOS mocdels and 0.14 for the hot EOS models (Lable 3))., We have $\beta=0.23 - 0.26$ for the cold EOS models and $\beta=0.13 - 0.14$ for the hot EOS models (Table \ref{tab:prop}) ). + Phe hot models are probably dynamically stable but may be secularly unstable., The hot models are probably dynamically stable but may be secularly unstable. + llowever. since they are evolving to cold neutron stars in about 20 s and their structures are continually changing on times comparable to the secular timescale. we shall not cliscuss secular instabilities of these hot models here.," However, since they are evolving to cold neutron stars in about 20 s and their structures are continually changing on times comparable to the secular timescale, we shall not discuss secular instabilities of these hot models here." + Vhe values of 3 for the three cold neutron. stars are slightlv less than the traditional critical value for, The values of $\beta$ for the three cold neutron stars are slightly less than the traditional critical value for +images. wherever applicable.,"images, wherever applicable." + The polynomial functions used to fit the heights of the events are further used to determine errors in velocity and acceleration., The polynomial functions used to fit the heights of the events are further used to determine errors in velocity and acceleration. + The errors in heights are used in the error propagation formula. and (he maximum errors in velocity ancl acceleration are found to be dOkms! and 25s7. respectively.," The errors in heights are used in the error propagation formula, and the maximum errors in velocity and acceleration are found to be $40\kmps$ and $25\mpss$, respectively." + Both the STEREO spacecraft observed this event as a faint and slow CME on the south-west limb of the Sun (Figure 1))., Both the STEREO spacecraft observed this event as a faint and slow CME on the south-west limb of the Sun (Figure \ref{F:img16nov}) ). + The CME first appeared in the AA field of view (FOV) at ULT. and in BB FOV at O8:15UUT.," The CME first appeared in the A field of view (FOV) at UT, and in B FOV at UT." + The CAIE entered the AA FOV at 10:2:Τι and in the BB FOV two hours later at UUT.," The CME entered the A FOV at UT, and in the B FOV two hours later at UT." + EUVIAA images show a surge eruption on the far-side of the Sun., A images show a surge eruption on the far-side of the Sun. + The surge eruption commenced al ULT. and could be observed up to UUT.," The surge eruption commenced at UT, and could be observed up to UT." + Figure 7 shows results of the stereoscopic reconstruction technique applied to a feature on the LE of this CME., Figure \ref{F:res16nov} shows results of the stereoscopic reconstruction technique applied to a feature on the LE of this CME. + The plots on the left in Figure 7. show change in height. and the resultant speed and acceleration obtained from derivatives of a polynomial function fitted to (he (ive height. as a function of time.," The plots on the left in Figure \ref{F:res16nov} show change in height, and the resultant speed and acceleration obtained from derivatives of a polynomial function fitted to the true height, as a function of time." + The plots on the right show speed and acceleration as a function of true height., The plots on the right show speed and acceleration as a function of true height. + From this figure we find that the CME speed increases very rapidly in the COR] FOV. and is almost constant in COR? FOV.," From this figure we find that the CME speed increases very rapidly in the COR1 FOV, and is almost constant in COR2 FOV." + The acceleration of the CME in the CORL FOV is 50ms7. but it [alls rapidly. and is down to Llms7 at about 3.71...," The acceleration of the CME in the COR1 FOV is $50\mpss$, but it falls rapidly, and is down to $11\mpss$ at about $3.7\Rsun$." + Thus. maximum value of acceleration. and the height at which the CME attained," Thus, maximum value of acceleration, and the height at which the CME attained" + DSM/Irfu/SPP. CEA/Saclay. F-91191 Gif-sur-Yvette Cedex," DSM/Irfu/SPP, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex" +Figure 2. shows the velocity dispersion (bottom panel) aud mass-to-light ratios. AL/Ly (top pauel). as a function of V-baud luminosity of the new and old dwarls from observations in comparison to simulated fossils.,"Figure \ref{SL} shows the velocity dispersion (bottom panel) and mass-to-light ratios, $M/L_V$ (top panel), as a function of V-band luminosity of the new and old dwarfs from observations in comparison to simulated fossils." + The sviubols are the same as in the previous figures., The symbols are the same as in the previous figures. + Whie 1Dnass data is available for all the previously known dwarls. we found no published o values for 9 dlrr. E dE aud 3 dSph (Autila. Phoenix and ασ) (??)..," While mass data is available for all the previously known dwarfs, we found no published $\sigma$ values for 9 dIrr, 4 dE and 3 dSph (Antila, Phoenix and SagDIG) \citep{Mateo98, Strigarietal08}." + We observe a good agreement betwee1 tlie statistical properties of the new dwarf galaxies and he RGOS predictions for the fossils. although simulated cdwarfs slow a slightly larger iuass-to-ligl| ratios than observed ones at tlje. low uminosity eud. Ly«10 L...," We observe a good agreement between the statistical properties of the new dwarf galaxies and the RG05 predictions for the fossils, although simulated dwarfs show a slightly larger mass-to-light ratios than observed ones at the low luminosity end, $L_V <10^4$ $_\odot$." +" Theoretical and observed «vnuamical masses are calculated tle samme way. [rom the velocity «lispersiot sol stars(ie... Al=2)""ul207/G . aud do not necessarily relect the total mass of the da‘k halo a virializatiou."," Theoretical and observed dynamical masses are calculated the same way, from the velocity dispersions of stars, $M=2r_{1/2}\sigma^2/G$ ), and do not necessarily reflect the total mass of the dark halo at virialization." + hudeed. tje simulaion provides some iusiglt οιi why the oserved value of he clyuenical mass. Ad~(1255)x10*M... reimalns 'elative coistaib as a [uu‘tion of Ly.," Indeed, the simulation provides some insight on why the observed value of the dynamical mass, $M \sim (1 \pm 5) \times +10^7$$_\odot$, remains relative constant as a function of $L_V$." + Sintlatious low that in pre-reionizaiou dwars. the ratio of he radius of he stellar s»heroid to the vi‘ial racs of the dark halo deereases with lucreasing «l:wk halo 1jass.," Simulations show that in pre-reionization dwarfs, the ratio of the radius of the stellar spheroid to the virial radius of the dark halo decreases with increasing dark halo mass." + The lowest mass cdwarls Lave stell:| speroids comparable ii size to their virial racii (see RGSOS., The lowest mass dwarfs have stellar speroids comparable in size to their virial radii (see RGS08). + As the haο Lass and viria racius increases. the stellar spleroid becomes increasi1ely couceuated tn the deepest yart of |the ryoteial well. thus the ratio of the cdyuaimical mass within the largest stellar orbits to otal clarkar 1ια{οι mass is reduced.," As the halo mass and virial radius increases, the stellar spheroid becomes increasingly concentrated in the deepest part of the potential well, thus the ratio of the dynamical mass within the largest stellar orbits to total dark matter mass is reduced." + This effect maintains the vale of the «yuatical mass willin he stelar spheroid (measured by the velocity dispersion of he stars) remarkably coustaut evel hough the otal mass of the halo iucreases., This effect maintains the value of the dynamical mass within the stellar spheroid (measured by the velocity dispersion of the stars) remarkably constant even though the total mass of the halo increases. + If «warts are uudergoing tidal disruption. Ursa Major II). the velocity dispersious could )e artiliclafly inflated.," If dwarfs are undergoing tidal disruption, Ursa Major II), the velocity dispersions could be artificially inflated." + However. the agreeuent with theory is rather good for all the new «walls.," However, the agreement with theory is rather good for all the new ultra-faint dwarfs." + The data on the lowest luniuosity cdwarls in οuw simulatious are the least reliable. )ecause {1ev are very close to the resolutic1 units of the simulation (we resolve halos of aOU 10? M. with 100 particles).," The data on the lowest luminosity dwarfs in our simulations are the least reliable, because they are very close to the resolution limits of the simulation (we resolve halos of about $10^5$ $_\odot$ with 100 particles)." + Let us assume we Call trust the sinulajon ancl the observational cala. even [or tie lowest. luminosity dwar(s aux he discrepaucy )ebween simulation and observation al the low luminosity end is real.," Let us assume we can trust the simulation and the observational data, even for the lowest luminosity dwarfs and the discrepancy between simulation and observation at the low luminosity end is real." + The dynnical mass is AJxr307., The dynamical mass is $M \propto r_{1/2}\sigma^2$. + There is good agreetlet between o»ervations and sinulatious for o in faint dwarls., There is good agreement between observations and simulations for $\sigma$ in faint dwarfs. + Thus. it is likely that the the reason for disagreemet tin M/Ly is due to the valte of rq;5. being simalle: for the observed. dwarls μαι the simula edojes.," Thus, it is likely that the the reason for disagreement in $M/L_V$ is due to the value of $r_{1/2}$, being smaller for the observed dwarfs than the simulated ones." + This cotId be partly due an observational bias rat selec‘ts prefereutially «Splis Wwith hieher su‘face brightuess aud smaller ο (see Figure 1))., This could be partly due an observational bias that selects preferentially dSphs with higher surface brightness and smaller $r_{1/2}$ (see Figure \ref{Kor}) ). + Anojer explanation. is a dynaica elfect not inelt(ed in our situtlation that reduces he stellar radius «X cdwarls after virializatio: for ]ustance. 1ical «stripping or relaxatiou.," Another explanation, is a dynamical effect not included in our simulation that reduces the stellar radius of dwarfs after virialization; for instance, tidal stripping or relaxation." + A larger sauple size of distatt cdwarls. including kineles OL Anc NID ar( And XIV. oth: believed to be οἱ their ist approach to M31. would be useul to jetter characterize this disc'epanicy.," A larger sample size of distant dwarfs, including kinematics on And XII and And XIV, both believed to be on their first approach to M31, would be useful to better characterize this discrepancy." + Tle velocity dispersious of the stars [or the oBELVEC new dwarfs aud the simulated fossi sare just beow 10 km s1! for luidnosities <10° Lo., The velocity dispersions of the stars for the observed new dwarfs and the simulated fossils are just below $10$ km $^{-1}$ for luminosities $<10^6$ $_V$. + Tle scatter of the predicted aud observed veOcity dispersious as a Function of dwarf luninosity suggests tlat dwarfs with the same luminosity may ye fourd iu a broad distribution of halos masses., The scatter of the predicted and observed velocity dispersions as a function of dwarf luminosity suggests that dwarfs with the same luminosity may be found in a broad distribution of halos masses. + These results are in agreement with Figure L.. showing that the faintest primordial galaxies of a given |uuinosity may form in halos with a total," These results are in agreement with Figure \ref{fstar}, , showing that the faintest primordial galaxies of a given luminosity may form in halos with a total" +line at this point.,line at this point. + We find that. at least for the ranges that are considered here for the parameters. spontaneous cussion viclds results that differ ueeligibly from those obtained for incident continui radiatiou with 7.—$.," We find that, at least for the ranges that are considered here for the parameters, spontaneous emission yields results that differ negligibly from those obtained for incident continuum radiation with $I_{c} =S$." + We thus present results labelled only according to the Z.. but with the uuderstancding that they are applicable for S$=Z. as well.," We thus present results labelled only according to the $I_{c}$, but with the understanding that they are applicable for $S = I_{c}$ as well." + The relevaut characteristics for the profiles in reffIP 5NW(0.7.aurelans1.38)=C(7.2.1«10 (ArpsISE(0.5.1810 53.andforafourthprofile observed by Sarmaetal.(2001) bbut not D.Atleastshowninthefieure.(0.5.8.5«10.," The relevant characteristics for the profiles in \\ref{fMP} are $\Delta v_{1/2}$, $\delta$ ) = (0.7, 2.4 $\times$ }), NW (0.7, 2.4 $\times$ }), SE (0.5, 1.8 $\times$ }), and for a fourth profile observed by \citet{str01} but not shown in the figure, (0.5, 8.5 $\times$ })." + within the relevant range of values for Z. that is considered in refflvsT.. the values of ἐν at which ó occur are essentially independent of 7. when 90 specific," At least within the relevant range of values for $I_{c}$ that is considered in \\ref{fIvsT}, the values of $I_{p}$ at which specific $\delta$ occur are essentially independent of $I_{c}$ when $\delta \lesssim$ }." +°Hence.tobe=10 conrpatible with the observed profiles iu refsOBS ffor which three 7.theintensitymustciterhave6<10 be quite large (2 100) or it mst be somewhat less than 1 according to reftkL..," Hence, to be compatible with the observed profiles in \\ref{sOBS} for which three have $\delta$ $\lesssim$ }, the intensity must either be quite large $\gtrsim$ 100) or it must be somewhat less than 1 according to \\ref{fKL}." + We reject the Ligh saturation solutions because (4) the required saturation seenis excessive. but lore objectively because (1) the eas temperatures TZ that would be indicated (2 100 TS for Aeys = 0.5 1)) in roffIvsT aare below what secs to be required for the chemistry and pumping of these masers. aud (ii) the 22 GIIz maser feature probably consists of a bleud of three hyperfine componeuts.," We reject the high saturation solutions because (i) the required saturation seems excessive, but more objectively because (ii) the gas temperatures $T$ that would be indicated $\simeq$ 100 K for $\Delta v_{1/2}$ = 0.5 ) in \\ref{fIvsT} are below what seems to be required for the chemistry and pumping of these masers, and (iii) the 22 GHz maser feature probably consists of a blend of three hyperfine components." + Uwperfine structure is omitted here. but would cause regular profiles at temperatures of a few hundred Ik. At these temperatures. ος is too μα]. iu comparison with the hvperfne splittiues for the conrponeuts to meree completely.," Hyperfine structure is omitted here, but would cause irregular profiles at temperatures of a few hundred K. At these temperatures, $v_t$ is too small in comparison with the hyperfine splittings for the components to merge completely." +" In addition. (1v) the “kurtosis” of the four line profiles that are observed is positive as is expected from retfl ffor maserL profiles at Z 0.3. but not for larger Z,."," In addition, (iv) the “kurtosis” of the four line profiles that are observed is positive as is expected from \\ref{fKL} for maser profiles at $I_{p}\ \lesssim$ 0.3, but not for larger $I_{p}$ ." +" Also. the residuals at the J,intensity peak for two of the three profiles in reffIP ({aucl for a fourth profile that is not shown) are positive. directly indicating that the observed profiles are more sharply peaked (positive kurtosis) than the Cassia fit."," Also, the residuals at the intensity peak for two of the three profiles in \\ref{fMP} (and for a fourth profile that is not shown) are positive, directly indicating that the observed profiles are more sharply peaked (positive kurtosis) than the Gaussian fit." + For the third profile shown in ((anaser SE). the peak in theresidual is shifted by one velocity channel from the peak in the observed profile.," For the third profile shown in \\ref{fMP} (maser SE), the peak in theresidual is shifted by one velocity channel from the peak in the observed profile." +" Now consider the likely ranges for Z. °T_AO and S~ ""AQ(A/AA). where the backeround continui intensity has been expressed as a brightuess teniperature T, and the usual estimate for the 22 GIIz masers [ =2"," Now consider the likely ranges for $I_{c}\ \simeq$ $T_c\Delta\Omega$ and $S \simeq$ $\Delta\Omega(\Lambda/\Delta\Lambda)$ , where the background continuum intensity has been expressed as a brightness temperature $T_c$ and the usual estimate for the 22 GHz masers $\Gamma$ =2" +ol SIM in 8.,of SIM in 4. + In 85 we summarize our main fiudiugs aud couclusious., In 5 we summarize our main findings and conclusions. + We have conducted. Monte Carlo simulations to anticipate the number and properties of extrasolar planets that the narrow augle SIM planet search is likely to detect., We have conducted Monte Carlo simulations to anticipate the number and properties of extrasolar planets that the narrow angle SIM planet search is likely to detect. + First. we generate a list of target stars appropriate lor SIM.," First, we generate a list of target stars appropriate for SIM." + Next. we assieu hypothetical planets. specified by a mass aud orbital period or seiui-major axis. to these stars usiug au empirical fit to the known extrasolar planet tmass-periocd distribution from Tabachuik Tremaine (2002).," Next, we assign hypothetical planets, specified by a mass and orbital period or semi-major axis, to these stars using an empirical fit to the known extrasolar planet mass-period distribution from Tabachnik Tremaine (2002)." + Then. we determiue which of these planets SIM would discover using empirical fits to the detailed simulations of Sozzetti (2002).," Then, we determine which of these planets SIM would discover using empirical fits to the detailed simulations of Sozzetti (2002)." + Finally. we analyze the iunber aud the properties of planets discovered to anticipate the discovery. poteutial of SIM.," Finally, we analyze the number and the properties of planets discovered to anticipate the discovery potential of SIM." + For the sake of comparisou. we apply a simplistic model to estimate the number aud properties of planets which could be discovered by a radial velocity survey of the sale stars.," For the sake of comparison, we apply a simplistic model to estimate the number and properties of planets which could be discovered by a radial velocity survey of the same stars." + We begin by selecting stars [rom the Hipparcos catalog within 100 pe of the Sun (ESA 1997)., We begin by selecting stars from the Hipparcos catalog within $100$ pc of the Sun (ESA 1997). + Next. we restrict the sample to stars brighter than V.=10.5.," Next, we restrict the sample to stars brighter than $V = 10.5$." + For dimmer stars the photon noise would clominate the instrumental uncertainties (~1.7 μας) in a 30 second integration. demanding longer integratiou times to achieve the specified astrometric precision.," For dimmer stars the photon noise would dominate the instrumental uncertainties $\sim1.7$ $\mu$ as) in a 30 second integration, demanding longer integration times to achieve the specified astrometric precision." + Provided that V.<10.5. there is little gain in astrometric precision or observing elficieney by observing brighter stars. due to systematic uncertainties /index.htinl)).," Provided that $V < 10.5$, there is little gain in astrometric precision or observing efficiency by observing brighter stars, due to systematic uncertainties )." +" We require that the stars not be a member of a known spectroscopic binary or have an observed compato within I"".", We require that the stars not be a member of a known spectroscopic binary or have an observed companion within $1''$. + Of the stars which meet the above criteria. we select [V/E stars of each of the four spectral types F. C. Ix. aud M. for a total of N stars iu tlie sample.," Of the stars which meet the above criteria, we select $N/4$ stars of each of the four spectral types F, G, K, and M, for a total of $N$ stars in the sample." + Since the Hipparcos catalog includesW. Iuminosity classificatious for only about half of these stars. we do not exclude giant stars;," Since the Hipparcos catalog includes luminosity classifications for only about half of these stars, we do not exclude giant stars." + We estimate that and not more than 105€ of the stars in our samples are giant stars.," We estimate that $\sim5\%$, and not more than $10\%$ of the stars in our samples are giant stars." + The actual SIM target list would likely replace these stars with maln-sequeuce stars at slightly larger distances., The actual SIM target list would likely replace these stars with main-sequence stars at slightly larger distances. +" Since obtainingfon) a singlee measurement precision of oydp<3 pas requires averaginge[eJ the results of multiple 302 second observing blocks. the necessary observing time scales approximately as ~0,72 for og<3 pras;"," Since obtaining a single measurement precision of $\sigma_d \le 3$ $\mu$ as requires averaging the results of multiple 30 second observing blocks, the necessary observing time scales approximately as $\sim\sigma_d^{-2}$ for $\sigma_d \le 3$ $\mu$ as." +" Assuming constant mission time. the number of stars that can be surveyed therefore scales as ον>ση. provided. that there is. no additionaln overhead (e.g../ slewing.. acquiringna guide"" stars)."," Assuming constant mission time, the number of stars that can be surveyed therefore scales as $\sim\sigma_d^2$, provided that there is no additional overhead (e.g., slewing, acquiring guide stars)." + While a target star and its reference stars must fit within a 1° diameter fiekl of view. several target stars cau be observed across a 15° diameter field of regard. (FoR) without slewing or significant. additional missiou time.," While a target star and its reference stars must fit within a $\sim1^\circ$ diameter field of view, several target stars can be observed across a $\sim15^\circ$ diameter field of regard (FoR) without slewing or significant additional mission time." + Within a oue hour observing interval. the augles between oue target star aud four reference stars (all V.< 10.5) may be measured at a precision of gy=1 µας.," Within a one hour observing interval, the angles between one target star and four reference stars (all $V<10.5$ ) may be measured at a precision of $\sigma_d = 1$ $\mu$ as." + Alternatively. in the same hour interval two or four target stars could be measured at a precision," Alternatively, in the same hour interval two or four target stars could be measured at a precision" +assumed characteristic Pop III mass of 10041.,assumed characteristic Pop III mass of $100 \msun$. + We see that with these parameter choices. our simple recipe reproduces (he simulation resulis fairly well.," We see that with these parameter choices, our simple recipe reproduces the simulation results fairly well." + Of course. we do not really expect Pop HI star formation to continue to z3.," Of course, we do not really expect Pop III star formation to continue to $z\sim3$." + However. in the absence of more detailed modeling of metal production and mixing. we do not know when the Pop III mode will ‘shut oll’.," However, in the absence of more detailed modeling of metal production and mixing, we do not know when the Pop III mode will `shut off'." + Fie., Fig. + 3aa also shows the prediction of the halo collapse model for Pop II stars. with ME corresponding to a of 101 IX andl efficiencies of eh=0.1 and 1.0.," \ref{fig:sfrd}a a also shows the prediction of the halo collapse model for Pop II stars, with $M^{\rm II}_{\rm crit}$ corresponding to a of $10^{4}$ K and efficiencies of $e^{\rm II}_{*}=0.1$ and $e^{\rm II}_{*}=1.0$ ." + The e!=1 halo collapse model represents a sort of upper limit for star formation in halos that cool via Ly. as it would require all new gas flowing into these halos to cool and form stars instantaneously.," The $e^{\rm II}_{*}=1$ halo collapse model represents a sort of upper limit for star formation in halos that cool via $_{\rm I}$, as it would require all new gas flowing into these halos to cool and form stars instantaneously." + The predicted SFRD max be compared will observational estimates and limits on this quantity at ‘low redshift 3S26 (see figure caption)., The predicted SFRD may be compared with observational estimates and limits on this quantity at `low' redshift $3 \la z \la 6$ (see figure caption). + The assumed efficiencies of e!=0.1 and e=1 approximately bracket the range in observational estimates.," The assumed efficiencies of $e^{\rm II}_{*}=0.1$ and $e^{\rm +II}_{*}=1$ approximately bracket the range in observational estimates." + We note in passing (hat the Lanzetta et al., We note in passing that the Lanzetta et al. + high estimate exceeds even (lie extreme case of el!= Lal z—8 10., high estimate exceeds even the extreme case of $e^{\rm II}_{*}=1$ at $z=8$ –10. + We also show the star formation history produced in the more realistic semi-analvtic merger tree models described in Section 3.., We also show the star formation history produced in the more realistic semi-analytic merger tree models described in Section \ref{sec:sam}. + To study the sensitivity of our results to our recipes for star formation. photoionization squelchine. aud supernova feedback. we investigate different choices of ingredients and parameters.," To study the sensitivity of our results to our recipes for star formation, photoionization squelching, and supernova feedback, we investigate different choices of ingredients and parameters." + The merger (ree models are summarized in Table 2.., The merger tree models are summarized in Table \ref{tab:models}. + The reader only interested in the main result may skip directly to Section 4.2.., The reader only interested in the main result may skip directly to Section \ref{sec:phot}. + Models MT-1a and NET-1b do not include supernova feedback or photoionization sequelching., Models MT-1a and MT-1b do not include supernova feedback or photoionization squelching. +" Star formation is (hen regulated only by the rate at which gas can cool via atonmie processes and collapse. ancl by the star formation (nmescale τι=maq4/12,."," Star formation is then regulated only by the rate at which gas can cool via atomic processes and collapse, and by the star formation timescale $\tau_* = m_{\rm cold}/\dot{m}_*$." + We consider (wo choices for this timescale. which we refer to as ‘constant efficiency and ‘accelerating.," We consider two choices for this timescale, which we refer to as `constant efficiency' and `accelerating'." +" In the constant efficiency (CE) recipe. 7, is a constant (we lake 7,= 0.1)."," In the constant efficiency (CE) recipe, $\tau_*$ is a constant (we take $\tau_*=0.1$ )." +" In the ""accelerating recipe. T.Xlau Where fasXrus/csus is Che dynamical time of the halo."," In the `accelerating' recipe, $\tau_* \propto t_{\rm dyn}$, where $t_{\rm +dyn} \propto \rvir/\vvir$ is the dynamical time of the halo." + This is similar to the scaling observed in nearby galaxies (??) ancl is commonly used as an empirical basis for star formation recipes in senii-analviic models and hydrodsnamie simulations.," This is similar to the scaling observed in nearby galaxies \citep{kennicutt:83,kennicutt:98} and is commonly used as an empirical basis for star formation recipes in semi-analytic models and hydrodynamic simulations." + Relerring to Fig., Referring to Fig. + 3aa. we see that the ‘accelerating sealing leads to dramatically more star formation at hieh redshift compared with the constant efficiency scaling.," \ref{fig:sfrd}a a, we see that the `accelerating' scaling leads to dramatically more star formation at high redshift compared with the constant efficiency scaling." + We use this recipe in the rest of ihe models., We use this recipe in the rest of the models. + In models MT-2ac. we include the effect of photoionization squelching (but no SN feedback). with different assumed reionization histories. motivated bv the joint. aand ceconstraints discussed above.," In models MT-2a–c, we include the effect of photoionization squelching (but no SN feedback), with different assumed reionization histories, motivated by the joint and constraints discussed above." + We show in Fig., We show in Fig. + 3aa a model in which hydrogen is reionized, \ref{fig:sfrd}a a a model in which hydrogen is reionized +Iu this paper. I point out that dirty. fireballs observed on-axis may be ideutifiecl in orpliau alterglow searches through their multiwavelength properties.,"In this paper, I point out that dirty fireballs observed on-axis may be identified in orphan afterglow searches through their multiwavelength properties." + By using quautities whose evolution changes sign at the jet break. we obtain tests that are robust to the uncertainty in fy.," By using quantities whose evolution changes sign at the jet break, we obtain tests that are robust to the uncertainty in $t_1$." + Accditionally. ] examiue the cistributiou of /4 expected under a simple orphan afterglow search strategy. in order to constraiu the typical monitoring period A/ required to reliably fit both /4 aud a.," Additionally, I examine the distribution of $t_1$ expected under a simple orphan afterglow search strategy, in order to constrain the typical monitoring period $\Delta t$ required to reliably fit both $t_1$ and $\alpha$." + Iu simple models. au afterglow is characterized by three spectral break frequencies aud a peak lux deusity (Sari. Pirau. Narayan 1998).," In simple models, an afterglow is characterized by three spectral break frequencies and a peak flux density (Sari, Piran, Narayan 1998)." + The breaks are η. correspouxliug to the observed yeak of syuchrotron emission for the minimum everey of the electron power aw distribution: n. COITespOldiug to the observe peak of svucluotrot euission for electrons whose cooling titje equals he dynauical age of the remnaut: aud vy. the syuclrot‘ou sellabsorptiou [recueucy.," The breaks are $\num$, corresponding to the observed peak of synchrotron emission for the minimum energy of the electron power law distribution; $\nuc$, corresponding to the observed peak of synchrotron emission for electrons whose cooling time equals the dynamical age of the remnant; and $\nua$, the synchrotron self-absorption frequency." +" The spectral »eak is fran""m).", The spectral peak is $\fnumax \equiv \fnu(\num)$. +" Ana[terglow model precicts the evolution of each of hese quantities in erms of johysical quantities tla1 coutrol the fireb:ill evoutiou aud elission: Tle initial energy Ep. he ambient density 1=pj""mnp). and the Cractions of the total available οιerey converted iuto 'elativisti¢ electrous £. and iuto magnetic fields £y at he forward shock of he expaucing blast wave."," An afterglow model predicts the evolution of each of these quantities in terms of physical quantities that control the fireball evolution and emission: The initial energy $E_0$, the ambient density $n = \rho / +(\mu m_p)$, and the fractions of the total available energy converted into relativistic electrons $\xie$ and into magnetic fields $\xib$ at the forward shock of the expanding blast wave." + Coumon generalizatious include noisplierical expOslOnls. Wlhi initial opering angle ¢. and a 1i0nuniformi ambient 1jeciium. with densitκ κr7. (," Common generalizations include nonspherical explosions, with initial opening angle $\zeta$, and a nonuniform ambient medium, with density $n \propto r^{-\delta}$. (" +Usually. ο]er ó=0 for a uniforin medium or ὃ=2 as expected Kk) à constaut velocity wind from the GRB progenitor).,"Usually, either $\delta = 0$ for a uniform medium or $\delta = 2$ as expected for a constant velocity wind from the GRB progenitor)." + The ligh Curve o. an afterglow depeuds on the time evolutiOL ol the spectrum in a way t depends ou ie details of the model (e.g.. spherical or «‘Ollimatect low. uuiform or wind jeclit but in all cases sunupes ouly a fraction of the full. information provided by the inultilreque behavior of je. transient.," The light curve of an afterglow depends on the time evolution of the spectrum in a way that depends on the details of the model (e.g., spherical or collimated flow, uniform or wind medium) but in all cases samples only a fraction of the full information provided by the multifrequency behavior of the transient." + Thus. when HDLO? examined the possibilities for distinguishing cirty fireballs from off-axis jets primarily using the ligjt curve αἱ a sitele observed [requency. tey used a subset ofte nvallable tools axl reached. ματy pessimistic conclusious.," Thus, when HDL02 examined the possibilities for distinguishing dirty fireballs from off-axis jets primarily using the light curve at a single observed frequency, they used a subset of the available tools and reached unduly pessimistic conclusions." +" Consider a quality or that behaves as a pc»wver law of the lune elapsed since the listir fy)""."," Consider a quantity $x$ that behaves as a power law of the time elapsed since the burst, $x \propto (t-t_0)^{q}$ ." + Folowing HDLO2. sup2056 we do not kiow fy but have made a guess /obsoomIacT that is in error by auount 7.," Following HDL02, suppose we do not know $t_0$ but have made a guess $t_0^{obs} = t_0 + +T$ that is in error by amount $T$." + Then wex(/—TinT))*.," Then $x \propto (t - (t_0^{obs} - +T))^{q}$." + Without loss of generality. we can set te origin ol time to the assumed burst trigger. =0. uplilving the previous expression to wrx(," Without loss of generality, we can set the origin of time to the assumed burst trigger, $t_0^{obs} = 0$, simplifying the previous expression to $x\propto (t+T)^{q}$." + Then the instantaneotis slope njeasurement becomes q?(1)=dlog/dlog(/)qt/(+T).," Then the instantaneous slope measurement becomes $q^{obs}(t) \equiv d\log{x}/d\log(t) = q t / +(t+T)$." +" our measurement of q will be sibstautially in error uuless |Z“κε/""1. we see that the sie is unallectec. ("," While our measurement of $q$ will be substantially in error unless $|T|/t \ll 1$, we see that the sign of $q^{obs}$ is unaffected. (" +Note that (+T) is always positive. since our fi‘st observation cannot precede t actial trigeerMD time.),"Note that $(t+T)$ is always positive, since our first observation cannot precede the actual trigger time.)" + We shoid therefore measure the behavior of oue or more q1antities whose sigu elianges al te transition [rom ellectively spherical to effectively jetlike belavicx., We should therefore measure the behavior of one or more quantities whose sign changes at the transition from effectively spherical to effectively jetlike behavior. + Table 1 lists several potentiaV appicable qlautities. together with their expected evolutiou alte tlie jet break aud before the break in elther a iuilorm deusity anbient medium or a wiud euvirouuent.," Table 1 lists several potentially applicable quantities, together with their expected evolution after the jet break and before the break in either a uniform density ambient medium or a wind environment." + Spherically syiuuetric CRB, Spherically symmetric GRB +This is needed to calibrate the leakage of linear polarization into circular.,This is needed to calibrate the leakage of linear polarization into circular. + For the 4800 MlIlz and S640MLELZ observations. 16 VLA calibrator 1923|210 was used. as a polarization alibrator for both epochs.," For the 4800 MHz and 8640MHz observations, the VLA calibrator 1923+210 was used as a polarization calibrator for both epochs." + Calibrator confusion and low incar polarization. however. precluded the use of any of 16 observed. calibrators as polarization calibrators for the January 1384 MlIZ ancl 2496 MlIz observations.," Calibrator confusion and low linear polarization, however, precluded the use of any of the observed calibrators as polarization calibrators for the January 1384 MHz and 2496 MHz observations." + As a result. we were forced to use calibration solutions derived: using 1 “weakly-polarized” equations with the APCA primary calibrator. 1934-638.," As a result, we were forced to use calibration solutions derived using the ""weakly-polarized"" equations with the ATCA primary calibrator, 1934-638." + The use of the “weakly-polarized™ equations will cause a time-varving leakage of linear. polarization into circular.," The use of the ""weakly-polarized"" equations will cause a time-varying leakage of linear polarization into circular." + In tests. peak leakages of of the linear polarization into circular have been observed.," In tests, peak leakages of of the linear polarization into circular have been observed." + For the 1384 MIEEZ observations. the low linear polarization of GRS 1915]105 implies the elfect. of such leakage is negligible.," For the 1384 MHz observations, the low linear polarization of GRS 1915+105 implies the effect of such leakage is negligible." + Even for the 2496 AI. observations. where the linear polarization rises rapidly during the observation. in the the leakage would be only half the Stokes V. error due to thermal noise.," Even for the 2496 MHz observations, where the linear polarization rises rapidly during the observation, in the the leakage would be only half the Stokes V error due to thermal noise." + The full polarisation ATCA data for both epochs are presented in big 2., The full polarisation ATCA data for both epochs are presented in Fig 2. + The Alulti Element Badio Linked. Interferometer Network (ALERLUN) consists of six individual antennae with a twpical diameter of 25m and a maximum baseline of 217 km (Thomasson 1986)., The Multi Element Radio Linked Interferometer Network (MERLIN) consists of six individual antennae with a typical diameter of 25m and a maximum baseline of 217 km (Thomasson 1986). + Ehe observations presented. here were undertaken in continuum mode at a frequency of 4994 MIE[IZ with a total bancwidth of 16 Mllz., The observations presented here were undertaken in continuum mode at a frequency of 4994 MHz with a total bandwidth of 16 MHz. + As ALERLIN measures all four correlation products as a matter of course when in this mode. full. polarimetric information can be derived from all images.," As MERLIN measures all four correlation products as a matter of course when in this mode, full polarimetric information can be derived from all images." + Ongoing work is seeking to establish the reliability of Stokes V measurements with ALERLIN: these will not be reported here., Ongoing work is seeking to establish the reliability of Stokes V measurements with MERLIN; these will not be reported here. + GRS 1915)105 was. observed. eleven. times with ALERLIN following the [are observed on 2001. March 22/23.," GRS 1915+105 was observed eleven times with MERLIN following the flare observed on 2001, March 22/23." + The first five epochs. corresponding to daily observations between 2001 March 24 and March 27 and again on March 20. are presented in this paper (rig 3): further. details and analysis of the full set of MERLIN observations will be published in MeCormick et al. (," The first five epochs, corresponding to daily observations between 2001 March 24 and March 27 and again on March 29, are presented in this paper (Fig 3); further details and analysis of the full set of MERLIN observations will be published in McCormick et al. (" +in. prop).,in prep). + 1n cach case a flux calibrator. 3€286. a point source. OQ208. and a phase calibrator. 1919|OSG. were included in the observing schedule.," In each case a flux calibrator, 3C286, a point source, OQ208, and a phase calibrator, 1919+086, were included in the observing schedule." + The flux calibrator and point source. calibrator were observed at the beginning and end of the run whilst the rest of the observation was devoted to a evele of 1.5 minutes on the phase calibrator and 5 minutes on GRS 1915|105., The flux calibrator and point source calibrator were observed at the beginning and end of the run whilst the rest of the observation was devoted to a cycle of 1.5 minutes on the phase calibrator and 5 minutes on GRS 1915+105. + Initial data editing and calibration were performed using the standard ALERLIN doograns and the data were then transferred to the NRAO Astronomical. Image Processing System (ALPS)., Initial data editing and calibration were performed using the standard MERLIN d-programs and the data were then transferred to the NRAO Astronomical Image Processing System (AIPS). + Within ALPS the cata were processed via the MIEILIN pipeline. which calibrates and images the phase reference source and then applies. these solutions to the target. source.," Within AIPS the data were processed via the MERLIN pipeline, which calibrates and images the phase reference source and then applies these solutions to the target source." + This process also. derives instrumental polarisation corrections and calibrates the lincar polarisation position angle. using 36286 as the calibrator and assuming a position angle of [or its [5 vector.," This process also derives instrumental polarisation corrections and calibrates the linear polarisation position angle, using 3C286 as the calibrator and assuming a position angle of for its E vector." + The position angles. measured. by MIZRLIN ancl ATCA are consistent with the same value. indepencdentIv confirming the position angle calibration of each array.," The position angles measured by MERLIN and ATCA are consistent with the same value, independently confirming the position angle calibration of each array." + Further self. calibration was then carried. out. within AIPS and GRS 1915)105 imaged in total intensity and μαokes Q ancl U. These maps were then combined using the AIDS task PCNTR to produce the final maps with total intensity contours ancl veetors denoting the direction. aud μαreneth of linear polarisation., Further self calibration was then carried out within AIPS and GRS 1915+105 imaged in total intensity and stokes Q and U. These maps were then combined using the AIPS task PCNTR to produce the final maps with total intensity contours and vectors denoting the direction and strength of linear polarisation. + Note that we can be confident both from. previous studies (e.g. Alirabel Rodriguez: 1994: Fender οἱ al., Note that we can be confident both from previous studies (e.g. Mirabel Rodriguez 1994; Fender et al. + 1999) and these data (AleCormick et al., 1999) and these data (McCormick et al. + in. prep) that 16 component(s) to the south cast (labelled in Fig 3 as SEL) is ‘approaching’. and component(s) to the north west are ‘receding (although in fact both sides of the jet have Doppler factors à.< 1).," in prep) that the component(s) to the south east (labelled in Fig 3 as `SE1') is `approaching', and component(s) to the north west are `receding' (although in fact both sides of the jet have Doppler factors $\delta < 1$ )." + In both sets of ATCA observations. CIUS 1915|105. is unambiguously detected as a source of circularly polarised raclio emission (Stokes V).," In both sets of ATCA observations, GRS 1915+105 is unambiguously detected as a source of circularly polarised radio emission (Stokes V)." + In 2001 January (Fig 2. left panels). significant CP is nieasured at all four ATCA frequencies. from 19 CllIz.," In 2001 January (Fig 2, left panels), significant CP is measured at all four ATCA frequencies, from 1–9 GHz." + The total lux density is clearly declining. indicating the decay phase ofa major Dare. but there is also significant variability," The total flux density is clearly declining, indicating the decay phase of a major flare, but there is also significant variability" +We detect aas well as the aand dedoublets throughout the whole field of view.,We detect as well as the and doublets throughout the whole field of view. + lis in fact observed. on a much larger. scale. as nicely emphasized with the maps produced by Plana (1998).," is in fact observed on a much larger scale, as nicely emphasized with the maps produced by Plana (1998)." + From our dedata. we cut out regions where the intensity of the [laG6583 emission line was less than 5 times the 1 (0 noise level to avoid spurious features in the maps.," From our data, we cut out regions where the intensity of the 6583 emission line was less than 5 times the 1 $\sigma$ noise level to avoid spurious features in the maps." + This of course implies a lower {lux threshold for the [lines which are significantly weaker than the Hines., This of course implies a lower flux threshold for the lines which are significantly weaker than the lines. + However. we kept the same field size for all lines to avoid any confusion.," However, we kept the same field size for all lines to avoid any confusion." + Spectral profiles of the emission lines show large line widths in the centre., Spectral profiles of the emission lines show large line widths in the centre. + This is true for both aand the forbidden linesNu]. Su])). so that it is not due to the presence of a Broad-Line Region of an active galactic nucleus (AGN).," This is true for both and the forbidden lines, ), so that it is not due to the presence of a Broad-Line Region of an active galactic nucleus (AGN)." + Spatial mapping of the ionized eas showing such broad. lines shows that it is spatially unresolved in the cdata., Spatial mapping of the ionized gas showing such broad lines shows that it is spatially unresolved in the data. + We therefore modelled it with a fixed radial velocity ide Dd dispersion eit.," We therefore modelled it with a fixed radial velocity $v_{{\rm wide}}$ and dispersion $\sigma_{{\rm + wide}}$." + Phe values for reise ancl oue were determined on the central spectrum. in which the wings have the best contrast. ancl signal-to-noise ratio: we find Coat=1965 tancd oes.=460+.," The values for $v_{\rm wide}$ and $\sigma_{\rm wide}$ were determined on the central spectrum, in which the wings have the best contrast and signal-to-noise ratio: we find $v_{wide} = 1965$ and $\sigma_{wide}= 460$." + Errors bars on these values are dillieult to derive since it should include both the formal error bar as well as the uncertainty due to the noise in the data., Errors bars on these values are difficult to derive since it should include both the formal error bar as well as the uncertainty due to the noise in the data. + We estimated them using the 25 spectra which are within ool the centre and were found to exhibit. such a wide component., We estimated them using the 25 spectra which are within of the centre and were found to exhibit such a wide component. + “Phese central 25 spectra were fitted with an additional Gaussian component., These central 25 spectra were fitted with an additional Gaussian component. + and we then find rms uncertainties of 35 land 61 ton the velocity and velocity dispersion respectively., and we then find rms uncertainties of 35 and 61 on the velocity and velocity dispersion respectively. + All other spectra were fitted with a single Gaussian., All other spectra were fitted with a single Gaussian. + The Icla66583 emission-line [ux map is presented in Fig., The 6583 emission-line flux map is presented in Fig. + ϱ with spectra illustrating the variations of line profiles and. line ratios over the field., \ref{fig:NIIwithspec} with spectra illustrating the variations of line profiles and line ratios over the field. + Other maps aand E10)) are presented in Fig. 10.., Other maps and ) are presented in Fig. \ref{fig:otherlines}. + They all exhibit à two- spiral structure that is consistent. from one emission line to the other. wih an additional brigi central. peak.," They all exhibit a two-arm spiral structure that is consistent from one emission line to the other, with an additional bright central peak." + The SW arm (negative abscissa) is brighter than the NE one., The SW arm (negative abscissa) is brighter than the NE one. + In the inner part of each arm. the emission-line profiles are complex.," In the inner part of each arm, the emission-line profiles are complex." + This is oobablyv caused by. tje superposition of components at clillerent velocities., This is probably caused by the superposition of components at different velocities. + Note that a sime check of the validity of the stellar continuum subtration. method. described. in Sect., Note that a simple check of the validity of the stellar continuum subtration method described in Sect. + 2.1.2. can [x| done by reconstructing the 4455200 intensity map and comparing it with the, \ref{sec:contsub} can be done by reconstructing the two-dimensional 5200 intensity map and comparing it with the +evenis much more intensively (han (he survey groups in order to identify anomalous behavior that can signal (he presence of a planet. associated will the lens star.,events much more intensively than the survey groups in order to identify anomalous behavior that can signal the presence of a planet associated with the lens star. + High-maenification events in particular (those with ly210) attract the attention of follow-up groups since il is (hese (hat are most likely (ο give detectable planetary signals (Griest&Safizadel1995:Gaudi.Naber&Sackett 1993).," High-magnification events in particular (those with $A_{\rm 0} \gtrsim 10$ ) attract the attention of follow-up groups since it is these that are most likely to give detectable planetary signals \citep{Griest98,Gaudi98}." +. In addition. for high magnification events the angular size of the source star may be non-negligible in comparison to (he lens-source angular separation.," In addition, for high magnification events the angular size of the source star may be non-negligible in comparison to the lens-source angular separation." + In these cases the liehtcurves of (he events can provide the possibility to determine the lens- relative proper motion (Gould1994:Alcocketal.1997b). and atmospheric properties ol the source (IIevrovsky.2003).," In these cases the lightcurves of the events can provide the possibility to determine the lens-source relative proper motion \citep{Gould94,Alcock97b} + and atmospheric properties of the source \citep{Heyrovsky03}." +. In the first vears of operation. when microlensing alerts came primarily from the NLACIIO collaboration. detected event rates were low enough that PLANET could monitor almost all potentially interesting events with ease.," In the first years of operation, when microlensing alerts came primarily from the MACHO collaboration, detected event rates were low enough that PLANET could monitor almost all potentially interesting events with ease." + For the last (wo vears (the 2002 and 2003 Dulge seasons). this has not been the case. due to (he much improved alert rate since the advent of ihe OGLE III early warning et.svstem (EWS). (Udalskietal.1994b:Udalski2003).," For the last two years (the 2002 and 2003 Bulge seasons), this has not been the case, due to the much improved alert rate since the advent of the OGLE III early warning system (EWS), \citep{Udalski94b,Udalski03}." +. In exeess of 400 events were alerted by the EWS in each of these vears., In excess of 400 events were alerted by the EWS in each of these years. + In addition. approximately 75 events were alerted in 2003 by the MOAÀ collaboration (Bondetal.2002) although some of these were duplicates of EWS events.," In addition, approximately 75 events were alerted in 2003 by the MOA collaboration \citep{Bond02} although some of these were duplicates of EWS events." + We are now in an era in which a careful selection of events is necessary (o optimize planet detection. aud exclusion productivitv., We are now in an era in which a careful selection of events is necessary to optimize planet detection and exclusion productivity. + For this reason. follow-up groups require accurate predictions of eventual maximum amplicatious in the early davs following a detection.," For this reason, follow-up groups require accurate predictions of eventual maximum amplications in the early days following a detection." + For the remainder of this paper I will locus exclusively on events detected by the OGLE 11 EWS., For the remainder of this paper I will focus exclusively on events detected by the OGLE III EWS. + Most microlensing; events are well fitted by a point-source point-mass-lens (PSPL) moclel for the magnification -l(/)} al time /. The impact parameter « is (he angular separation between (he source and lens measured," Most microlensing events are well fitted by a point-source point-mass-lens (PSPL) model for the magnification $A(t)$ at time $t$, The impact parameter $u$ is the angular separation between the source and lens measured" +to [IHICO! |/tde/dr)=1«10Spet L|. ic. ! 77. and the ! surface filling factor to (see dashed aud dotted lines in Fig. 3)).,"to $^+$ ${\rm d}v/{\rm d}r) = 1 \times 10^{-8.5}\,{\rm +pc}\,$ $^{-1}$, i.e., $^+$ $^{-3.5}$, and the $^+$ surface filling factor to (see dashed and dotted lines in Fig. \ref{f3}) )." + Overall. the models sugeest a relatively lieh median eas densitv in this galaxy. and that the CO aud the TCO! emission likely trace the same wari. dense molecular ISM phase. with ICO! tracing the deusest ~15 of the eas.," Overall, the models suggest a relatively high median gas density in this galaxy, and that the CO and the $^+$ emission likely trace the same warm, dense molecular ISM phase, with $^+$ tracing the densest $\sim$ of the gas." + Given that the ICO! lines have only ~2/3 of the width of the CO lines. this may suggest that the cussion region with the densest eas is more spatially couccutrated than the overall CO emission. such as. C... dn a nuclear starburst.," Given that the $^+$ lines have only $\sim$ 2/3 of the width of the CO lines, this may suggest that the emission region with the densest gas is more spatially concentrated than the overall CO emission, such as, e.g., in a nuclear starburst." + Tigher spatial resolution ! observations are required to confirun this scenario. and to investigate potential differential lensing effects.," Higher spatial resolution $^+$ observations are required to confirm this scenario, and to investigate potential differential lensing effects." + We have detected bright. but subthermalhy excited eenission towardL the Cloverleaf quasar at :—2.56.," We have detected bright, but subthermally excited emission toward the Cloverleaf quasar at $z$ =2.56." + Based on excitation modcling. we find that tho wari. deuse gas traced by ICO! appears to be associated with the wari. eas phase traced by the CO lines. picking out its densest reelous.," Based on excitation modeling, we find that the warm, dense gas traced by $^+$ appears to be associated with the warm gas phase traced by the CO lines, picking out its densest regions." + The IICO! excitation iu the Cloverleaf is consisteut with that seen in the starburst nucleus of 2253. with IICO! J—1 23/1 »0 ratios of rjj lSt0.11 and 0.53 (Ixuucdsen et citevearkunt7)). respectively.," The $^+$ excitation in the Cloverleaf is consistent with that seen in the starburst nucleus of 253, with $^+$ $J$ $\to$ $\to$ 0 ratios of $r_{41}$ $\pm$ 0.11 and 0.53 (Knudsen et \\citeyear{knu07}) ), respectively." + Intriguingly. the Cloverleat and the nucleus of 2253 also have comparable /IICN 7-1 50 line ratios of —O0.5.," Intriguingly, the Cloverleaf and the nucleus of 253 also have comparable $^+$ /HCN $J$ $\to$ 0 line ratios of $\sim$ 0.8." + The rg in he Cloverleaf is higher than that iu the infrared-tninous galaxies 662LO 1250.06) and 2220 (0.332E0.12: Creve et citevearerc09))., The $r_{41}$ in the Cloverleaf is higher than that in the infrared-luminous galaxies 6240 $\pm$ 0.06) and 220 $\pm$ 0.12; Greve et \\citeyear{gre09}) ). + ITowever. this is likely due to the fact hat the line ratios are averaged over virtually the entire uolecular line cussion regions. rather than just the wiclei.," However, this is likely due to the fact that the line ratios are averaged over virtually the entire molecular line emission regions, rather than just the nuclei." + As shown by Jono ct ((2007:: their Fig., As shown by Iono et \citeyear{ion07}; their Fig. + 10). the ry iu 66210 scatters up to values of ~0.6 within he -cumitting region. indicating that the ratio is comparable to the Cloverleaf in the densest regions.," 10), the $r_{41}$ in 6240 scatters up to values of $\sim$ 0.6 within the $^+$ -emitting region, indicating that the ratio is comparable to the Cloverleaf in the densest regions." + Thus. it secius plausible that the dense gas excitation in the Cloverleaf is comparable to what is found in the unclear regions of nearby starburst galaxies aud Iuninous infrared. galaxies.," Thus, it seems plausible that the dense gas excitation in the Cloverleaf is comparable to what is found in the nuclear regions of nearby starburst galaxies and luminous infrared galaxies." + The relatively high iuedian eas deusitv iu the Cloverleaf sueeested by the ICO! aud CO observatious is also consistent with its location ou the ICO! infrared Iuuinositv relation (Ricchers et citevearric0G6)) within the framework of the model description of Iuuhlolz Thompson (2007))., The relatively high median gas density in the Cloverleaf suggested by the $^+$ and CO observations is also consistent with its location on the $^+$ --far-infrared luminosity relation (Riechers et \\citeyear{rie06}) ) within the framework of the model description of Krumholz Thompson \citeyear{kt07}) ). + In fact. it may be the most direct evidence that the increasing slope in deuse gas-star formation relations observed toward the most Iuniuous. bieh redshift svstcems (Cao ct citeveargaot7:: Riechers et is indeed related to an elevated median eas density relative to lower-Iuninosity svstenis.," In fact, it may be the most direct evidence that the increasing slope in dense gas-star formation relations observed toward the most luminous, high redshift systems (Gao et \\citeyear{gao07}; Riechers et \\citeyear{rie07b}) ) is indeed related to an elevated median gas density relative to lower-luminosity systems." + Besides 008279]5255 (2=3.91). the Cloverleaf is only the second ligh-: galaxy in which iuultiple transitious of a deuse gas tracer were detected (c.g. Waee ct citevearwagetüb:: Carcia-Birillo ct citeveargar06: eet citevearwei07:: Guelin et citevearguet7:: Riechers et citevearieü9.. 20101).," Besides 08279+5255 $z$ =3.91), the Cloverleaf is only the second $z$ galaxy in which multiple transitions of a dense gas tracer were detected (e.g., Wagg et \\citeyear{wag05}; Garcia-Burillo et \\citeyear{gar06}; et \\citeyear{wei07}; Guelin et \\citeyear{gue07}; Riechers et \\citeyear{rie09}, \citeyear{rie10}) )." + Modeliug of the IICN line ladder πι APMOO08279|5255 suggests that the cussion in lieh-J IICN transitious is substantially eulhauced by radiative excitation through pumping of mud-intrarec vibrational lines eet citevearweiü7:: Ricchers et citeveairielü)., Modeling of the HCN line ladder in 08279+5255 suggests that the emission in $J$ HCN transitions is substantially enhanced by radiative excitation through pumping of mid-infrared ro-vibrational lines et \\citeyear{wei07}; Riechers et \\citeyear{rie10}) ). + In contrast. the ICO! excitation in the Cloverleaf is consistent with purely collisional excitation.," In contrast, the $^+$ excitation in the Cloverleaf is consistent with purely collisional excitation." + Given the comparable critical densities of Πο aud IICO!. this sugeests that we have ideutified a clear difference in the dense gas excitation conditious between these two hiel-z svsteuis.," Given the comparable critical densities of HCN and $^+$, this suggests that we have identified a clear difference in the dense gas excitation conditions between these two $z$ systems." + This investigation highlights the importance of studving the excitation of dense gas tracers to nuderstand differences in the conditions for star formation iu. high redshift ealaxies., This investigation highlights the importance of studying the excitation of dense gas tracers to understand differences in the conditions for star formation in high redshift galaxies. + Such studies will become routine with the advent of broad instantaneous bandwidth svstemis as part of future facilities such as the Atacama Large (sub-) Millimeter Array (ALMA). which will allow to frequently cover mes of multiple deuse gas tracers as part of standi hieh-: CO observations.," Such studies will become routine with the advent of broad instantaneous bandwidth systems as part of future facilities such as the Atacama Large (sub-) Millimeter Array (ALMA), which will allow to frequently cover lines of multiple dense gas tracers as part of `standard' $z$ CO observations." + We thauk the referee for holpful suggestions. Chiistian IIleukel for the original version of the LVG code. aud Jean-Paul KIucib for à CO image of the Cloverleaf.," We thank the referee for helpful suggestions, Christian Henkel for the original version of the LVG code, and Jean-Paul Kneib for a CO image of the Cloverleaf." + DR acknowledges support from from NASA through Hubble Fellowship eraut IIST-ITE-51235.01. awarded by Τσο]. operated by AURA for NASA. under contract NAS 5-," DR acknowledges support from from NASA through Hubble Fellowship grant HST-HF-51235.01 awarded by STScI, operated by AURA for NASA, under contract NAS 5-26555." + The IRAM PdBI is supported by INSU/CNRS (France). MPG (Germany) aud IGN (Spain).," The IRAM PdBI is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain)." +Many ganmmnia-ray burst counterparts have now been identified using the rapid. precise localizations available from the BeppoSAX spacecraft. as well as [rom the Ross? Αα Timing Explorer.. starting with GIAD970228 (Costa et al.,"Many gamma-ray burst counterparts have now been identified using the rapid, precise localizations available from the BeppoSAX spacecraft, as well as from the Rossi X-Ray Timing Explorer, starting with GRB970228 (Costa et al." + 1997; van Paraclijs et al., 1997; van Paradijs et al. + 1997)., 1997). + Such detections occur at a low rate (Sy 1). and thev have been limited to the longduration events so far. but they have confirmed the cosmological origin of at least (his class of bursts.," Such detections occur at a low rate $\sim 8 \, y^{-1}$ ), and they have been limited to the long–duration events so far, but they have confirmed the cosmological origin of at least this class of bursts." + Since 1971. interplanetary networks of omnidirectional GRB detectors have provided precise iriangulations of both short and long bursts at rates up to L/week. but often the networks have been incomplete. or the data return from (the interplanetary spacecraft has been slow.," Since 1977, interplanetary networks of omnidirectional GRB detectors have provided precise triangulations of both short and long bursts at rates up to $\sim$ 1/week, but often the networks have been incomplete, or the data return from the interplanetary spacecraft has been slow." + The present. 21d LPN is now complete with Ulysses and NEAR as its distant points (Cline et al.," The present, 3rd IPN is now complete with Ulysses and NEAR as its distant points (Cline et al." + 1999) and. in conjunction with numerous," 1999) and, in conjunction with numerous" +55hRO. BLRG and NLRG for which spectroscopical information is present in al least one ol Narrow Field Instruments (ΝΕΟΙ LECS (Parmaretal.1997).. MECS elal. 1997).. and PDS (Fronteraetal.1997).,"SSRQ, BLRG and NLRG for which spectroscopical information is present in at least one of Narrow Field Instruments (NFI): LECS \citep{par97}, MECS \citep{boe97}, and PDS \citep{fro97}." +. The resulting sample includes 35 AGN (10 DLRG. 3 NLRG. 6 SSRQ. 16 FSRQ) for a total of 61 observations.," The resulting sample includes 35 AGN (10 BLRG, 3 NLRG, 6 SSRQ, 16 FSRQ) for a total of 61 observations." + Most of the radiogalaxies (9) show a Fanarof-Bilev II CER. H) morphology. one source. 3C120. is a FR 1. while three objects have uncertain/unknown radio morphology.," Most of the radiogalaxies (9) show a Fanaroff-Riley II (FR II) morphology, one source, 3C120, is a FR I, while three objects have uncertain/unknown radio morphology." + The sample. shown in Figure 1. (left panel). spans about four orders of magnitude in luminosity (Loquio~LOM+LO” erg s1). and about (wo in redshift (2=0.027+3.9).," The sample, shown in Figure \ref{fig:Lum} (left panel), spans about four orders of magnitude in X-ray luminosity $L_{\rm 2-10\;keV}\sim10^{43}\div10^{47}$ erg $s^{-1}$ ), and about two in redshift $z=0.027\div3.9$ )." + Table D. lists the relevant information of all the analvzecl AGN., Table \ref{tab:sam} lists the relevant information of all the analyzed AGN. + The Badio Core Dominance value. A. reported in Table Lis defined as R=δα[Stat—Scare]. being 5&4; and Syo1 the core and total fux densities al 5 Gllz. respectively.," The Radio Core Dominance value, $R$, reported in Table \ref{tab:sam} is defined as $R=S_{\rm core}/[S_{\rm tot}-S_{\rm core}]$, being $S_{\rm core}$ and $S_{\rm tot}$ the core and total flux densities at 5 GHz, respectively." + 22 is considered an indicator of the orientation of the beamed radiation with respect to (he lime o sight (Orr&Browne1932)., $R$ is considered an indicator of the orientation of the beamed radiation with respect to the line of sight \citep{orr82}. +. In agreement with the unilied schemes. objects with large 2 are expected to have their beamed radiation emitted in a direction closer to the line of sight. and therefore with a higher beam boosting. even if the N-ravs from the jet ave not necessarily beamed as the radio ones.," In agreement with the unified schemes, objects with large $R$ are expected to have their beamed radiation emitted in a direction closer to the line of sight, and therefore with a higher beam boosting, even if the X-rays from the jet are not necessarily beamed as the radio ones." + A study of radio cores of a complete subsample of radio sources taken from the 2.7 Gllz Wall sample (Morgantietal.1997). has indeed shown Chat /? increases going from NLRG to FSRQ. with BLRG between NLRG aud $5RCG.," A study of radio cores of a complete subsample of radio sources taken from the 2.7 GHz \citet{wap85} sample \citep{mor97} has indeed shown that $R$ increases going from NLRG to FSRQ, with BLRG between NLRG and SSRQ." + The values of 2 in Table 1 are from Morgaantietal.(1993) and Fan&Zhang(2003)., The values of $R$ in Table \ref{tab:sam} are from \citet{mor93} and \citet{fan03}. +. Fan&Zhang(2003) caleulated. 2 at 5 GlIIz using extended Iumninosities al 1.4 GlIIz., \citet{fan03} calculated $R$ at 5 GHz using extended luminosities at 1.4 GHz. + They assumed (wo possible values of the extended spectral index (a=0.5 and a= 1.0) to convert the 1.4 Gllz luminosity into 5 GIIz luminosity and gave two values of 22 for each analvzed source., They assumed two possible values of the extended spectral index $\alpha=0.5$ and $\alpha=1.0$ ) to convert the 1.4 GHz luminosity into 5 GHz luminosity and gave two values of $R$ for each analyzed source. +" Table 1. shows (he average value /2—(2,-0.5+R424)/2. together with (he associated on=MHsus—R4 [/2. which represents the allowed range covered by 2."," Table \ref{tab:sam} shows the average value $R=(R_{\alpha=0.5}+R_{\alpha=1})/2$, together with the associated $\sigma_{\rm R}=|R_{\alpha=0.5}-R_{\alpha=1}|/2$ , which represents the allowed range covered by $R$." + Figure 1. (right panel) shows. the different classes of the sample on the LeΊων—1 plane.," Figure \ref{fig:Lum} (right panel) shows, the different classes of the sample on the $L_{\rm 2-10\;keV}-R$ plane." + In agreement wilh (he unilied schemes. (here is a general increasing trend of HR. ie. of the contribution of the Doppler-enhanced non-(hermal radiation. [rom Raclio-Galaxies to Quasars.," In agreement with the unified schemes, there is a general increasing trend of $R$, i.e. of the contribution of the Doppler-enhanced non-thermal radiation, from Radio-Galaxies to Quasars." + FSRQ occupy the upper region above 2>0.1. the two NLRG are in the lower region of the plane. and most BLRG are in the intermediate region. while SSRQ are equally distributed in the FSRQ and BLRG regions.," FSRQ occupy the upper region above $R>0.1$, the two NLRG are in the lower region of the plane, and most BLRG are in the intermediate region, while SSRQ are equally distributed in the FSRQ and BLRG regions." + Table 2. summarizes the logof observations., Table \ref{tab:jou} summarizes the logof observations. + LECS. MECS and PDs event files and spectra.available from the ASI Scientific Data Center (ASDC). were generated by," LECS, MECS and PDS event files and spectra,available from the ASI Scientific Data Center (ASDC), were generated by" +The plasma frequency plays a key role here in the electrodynamics. and we show how the plasma frequency must be dependent on the magnetic field. since the latter causes the matter deformation and compression that enables the perfectly conducting. anisotropie transport of electrons along flux tubes to exist.,"The plasma frequency plays a key role here in the electrodynamics, and we show how the plasma frequency must be dependent on the magnetic field, since the latter causes the matter deformation and compression that enables the perfectly conducting, anisotropic transport of electrons along flux tubes to exist." + The sections that follow address key issues in sequence: the magnetic compression. and its influence over the plasma frequency: the dynamics of |-D electrostatic waves and oscillations: the modelling of the Fermi energy. and the associated maximum energy gain in an electron wave: and a selection of possible candidate pulsars showing non-thermal features that correlate with the prediction of radiation at the internal plasma frequency.," The sections that follow address key issues in sequence: the magnetic compression, and its influence over the plasma frequency; the dynamics of 1-D electrostatic waves and oscillations; the modelling of the Fermi energy, and the associated maximum energy gain in an electron wave; and a selection of possible candidate pulsars showing non-thermal features that correlate with the prediction of radiation at the internal plasma frequency." + Concluding remarks finish the paper. and an explanatory Appendix gives more detail on the relativistic ealeulation of the Fermi energy.," Concluding remarks finish the paper, and an explanatory Appendix gives more detail on the relativistic calculation of the Fermi energy." + The process of extracting electrons from the outer crust. requires the description of the structure of matter there. and this has to be supported with the study of the structure of atoms in strong magnetic fields.," The process of extracting electrons from the outer crust, requires the description of the structure of matter there, and this has to be supported with the study of the structure of atoms in strong magnetic fields." + There are various exotic descriptions of atoms in extreme magnetic fields. showing how the basic lattice structure of the conducting metal is severely distorted. with implications for the conduction electrons.," There are various exotic descriptions of atoms in extreme magnetic fields, showing how the basic lattice structure of the conducting metal is severely distorted, with implications for the conduction electrons." + Such models are controversial. and in some respects. difficult to reconcile (for example. the literature (Neuhauseretal.1986.1987:Lieb1992) is undecided about the complex nature of the bonding between iron atoms under such conditions).," Such models are controversial, and in some respects, difficult to reconcile (for example, the literature \citep{1986PhRvA..33.2084N,1987PhRvA..36.4163N, 1992PhRvL..69..749L} is undecided about the complex nature of the bonding between iron atoms under such conditions)." + However. the more general concept is widely accepted. namely that the magnetic compression of the atoms leads to an effective iron atomic radius /? given by (Lai2001) where Z is the atomic number (26 for Fe) b.=DDy is the ratio of the pulsar magnetic field to the critical field 2)=mleejh?=2.35 ΙΤ and ay=5.29«10 Hm is the Bohr radius.," However, the more general concept is widely accepted, namely that the magnetic compression of the atoms leads to an effective iron atomic radius $R$ given by \citep{2001RvMP...73..629L} + where $Z$ is the atomic number (26 for Fe), $b=B/B_0$ is the ratio of the pulsar magnetic field to the critical field $B_0=m_e^2e^3c/\hbar ^3=2.35\times 10^5$ T and $a_0= 5.29 \times 10^{-11}$ m is the Bohr radius." +" For the typical pulsar field of 107T. 6=426 and Hc9.10 tm. The classical of radiusFe is Ryo=1.4:10. 1m (Slater 19643.. so that the compression leads to an increase in matter density of (11,Ry)=3.7510°."," For the typical pulsar field of $10^8$ T, $b\approx 426$ and $R\approx 9\times 10^{-12}$ m. The classical radius of Fe is $R_\text{Fe}=1.4\times 10^{-10}$ m \citep{1964JChPh..41.3199S}, , so that the compression leads to an increase in matter density of $(R_{Fe}/R)^3\approx 3.75\times 10^3$." + Of course. the free electron density is also increased as a direct consequence of this compression.," Of course, the free electron density is also increased as a direct consequence of this compression." + Taking the free electron density of Fe under standard terrestrial conditions as n'*=1.7. 10πι* ¢Asheroft 1976).. we can arrive at an electron number density for the pulsar n;* from atomic compression by applying the same scaling: which is a lower limit. since it is likely that there are more electrons able to access the conduction band under compression than in the classical limit.," Taking the free electron density of Fe under standard terrestrial conditions as $n_e^\text{Fe}=1.7\times 10^{29}$ $^{-3}$ \citep{ash+merm}, we can arrive at an electron number density for the pulsar $n_{e}^{A}$ from atomic compression by applying the same scaling: which is a lower limit, since it is likely that there are more electrons able to access the conduction band under compression than in the classical limit." + However. there is another way of deriving the empirical electron number density in the pulsar crust.," However, there is another way of deriving the empirical electron number density in the pulsar crust." +" Iron has a monatomic body-centred cubic (bec) ervstal structure under standard terrestrial conditions. with inter-atomic spacing ej;=2.8710 ""m (Ashcroft&Mermin1976)."," Iron has a monatomic body-centred cubic (bcc) crystal structure under standard terrestrial conditions, with inter-atomic spacing $a_{\text{Fe}}=2.87\times 10^{-10}$ m \citep{ash+merm}." +. Assuming that the iron on the surface of the pulsar is also bee (Ruderman1971)... this means. that the compression factor here can be calculated in terms of the effective atom spacing in the pulsar environment compared with the terrestrial one.," Assuming that the iron on the surface of the pulsar is also bcc \citep{1971PhRvL..27.1306R}, this means that the compression factor here can be calculated in terms of the effective atom spacing in the pulsar environment compared with the terrestrial one." +" The presence of extraordinarily large magnetic fields distorts the iron crystal from being isotropic to being severely anisotropic in transport terms: the iron is very highly conducting in the ""irection parallel to the magnetic field. but perpendicular transport is severely inhibited."," The presence of extraordinarily large magnetic fields distorts the iron crystal from being isotropic to being severely anisotropic in transport terms: the iron is very highly conducting in the direction parallel to the magnetic field, but perpendicular transport is severely inhibited." + The overall picture is of a set of perfectly conducting ‘tubes’ aligned locally with the ambient magnetic field direction along which electrons are able to move relatively freely: this description is qualitatively consistent with the ‘distorted atoms in a strong field’ model., The overall picture is of a set of perfectly conducting `tubes' aligned locally with the ambient magnetic field direction along which electrons are able to move relatively freely; this description is qualitatively consistent with the `distorted atoms in a strong field' model. + This is essentially the structure proposed by Ruderman(1971):: Canuto&Ventura(1977). show that the conductivity parallel to the magnetic field is on average 20 times greater than that of the field-free case: conversely. the transverse conductivity has a strong dependence on the magnetic field and the Fermi energy. and is typically orders of magnitude smaller than the longitudinal case.," This is essentially the structure proposed by \citet{1971PhRvL..27.1306R}; \citet{1977FCPh....2..203C} show that the conductivity parallel to the magnetic field is on average 20 times greater than that of the field-free case; conversely, the transverse conductivity has a strong dependence on the magnetic field and the Fermi energy, and is typically orders of magnitude smaller than the longitudinal case." + With this simple picture we can capture the essence of the electron. motion: parallel momentum is unconstrained. but perpendicular momentum is quantised.," With this simple picture we can capture the essence of the electron motion; parallel momentum is unconstrained, but perpendicular momentum is quantised." + In Ruderman's simple one-dimensional flux tube (Ruderman1971).. the radius of the flux tube is set equal to the mean orbital radius associated with the Landau ground state: where we have taken D=107T. In so doing. the simple 1-D flux tube model assumes dominant parallel motion along the magnetic field. and assumes that the transport anisotropy is sufficient to render all non-trivial Landau levels as unimportant. effectively contining the electron to a single flux tube.," In Ruderman's simple one-dimensional flux tube \citep{1971PhRvL..27.1306R}, the radius of the flux tube is set equal to the mean orbital radius associated with the Landau ground state: where we have taken $B=10^8$ T. In so doing, the simple 1-D flux tube model assumes dominant parallel motion along the magnetic field, and assumes that the transport anisotropy is sufficient to render all non-trivial Landau levels as unimportant, effectively confining the electron to a single flux tube." + The scale-length ῥ is then the effective inter-atom spacing in the compressed bee structure. leading to a compression of (0fp)?zcLA107. and an electron number density nz. based on lattice compression of Since we now have possible electron number densities ranging over more than 2 orders of magnitude. we shall take the geometric meanas the characteristic pulsar interior electron number density nol where we have assumed a magnetic field of 2= 107T. that is. bzx426.," The scale-length $\hat\rho$ is then the effective inter-atom spacing in the compressed bcc structure, leading to a compression of $(a^\text{Fe}/\hat\rho)^3\approx 1.4\times 10^6$, and an electron number density $n_{eL}$ based on lattice compression of Since we now have possible electron number densities ranging over more than 2 orders of magnitude, we shall take the geometric meanas the characteristic pulsar interior electron number density $n_e$: where we have assumed a magnetic field of $B=10^8$ T, that is, $b\approx 426$." +" The geometric mean compression yields a mass density of approximately LO°kem ? for ""Fe. which is consistentwith the conventional assumptions of density on the surface (Shapiro& 20060. "," The geometric mean compression yields a mass density of approximately $10^6$ $^{-3}$ for $^{56}$ Fe, which is consistentwith the conventional assumptions of density on the surface \citep{shapiro,2006RPPh...69.2631H}. ." +The electron number density is a critical parameter for plasmas. since it defines the basic collective timescale. namely," The electron number density is a critical parameter for plasmas, since it defines the basic collective timescale, namely" +Consiler a blob of plasma moving relativisücally with a bulk Lorentz factor D and velocity oc. at an angle 8 to the observers line of sight.,"Consider a blob of plasma moving relativistically with a bulk Lorentz factor $\Gamma$ and velocity $\beta c$, at an angle $\theta$ to the observer's line of sight." + In the frame of the blob the electrons are characterized by an isotropic power-law density. distribution n'(5/). ∖∖⇁↥∐↲↕⋅≼↲↰∣↕⋟∖⇁⊔∐↲∟∪↕⋅≼↲∐↥∠↓⋟≀↧↴≺∢↥∪↕⋅∪↓⋟⊔∐↲≼↲↥≼↲≺∢⊔⋅∪∐⋅∣⋅⊲↕⋟∖⇁≀↧↴≺∢∪∐⋟∖⊽↥≀↧↴↕∐⋅≀↧↴↕∐⇂∫∍⋖⋡↴↓⋅↴⊋⋅↴↕⋝∶↓↓⋟∪↕⋅ ↶⇩↴↓≤↶↵≤↷↴↴↴⋅↽−≻⋅≀↧↴∐≼⇂∠≼↲↕⋅∪∪⊔∐↲↕⋅∖∖⊽↕⊳∖⊽≼↲⋅↧∕⊽∐≼⇂≼↲↕⋅⊔∐↲≀↧↪∖," In the frame of the blob the electrons are characterized by an isotropic power-law density distribution $n'(\gamma')$, where $\gamma'$ is the Lorentz factor of the electron, $k$ is a constant, and $P(\gamma_1,\gamma_2,\gamma)=1$ for $\gamma_{1}\leq \gamma\leq \gamma_2$ , and zero otherwise." +⊽⊳∖⇁∏∐↓↕↽≻∐∪∐⊔⋯↴↥↷↴↴↴∣⋗⋗↕⇁⋅∪∐≼↲≺∢≀↧↴∐∏⋅≼↲≀↧↴↥⊔∐↲ ≼↲↥≼↲≺∢⊔⋅∪∐⋟∖⇁≀↧⊍∖⊽≀↧↴↕↽≻∐∪∩≻∐≸≟≀↧↪∖⊽≀↕↴↕∐⇂∐⋯↴↳↽≼↲∏⋟∖⊽↩∪↓⊔∐↲∟∪↕⋅≼↲∐↥∠∐↥∖⇁≀↕↴↕⋅↕≀↧↴↕∐≺⇂∏≀↧↴↕∐∐⋡∖⇁∣∣∕∕∕↰−⋅," Under the assumption that $\gamma' \gg \Gamma$, one can treat the electrons as a photon gas and make use of the Lorentz invariant quantity $n/\gamma^2$." +∏∐↲∟∪↕⋅≼↲∐↥∠ ↓⋟≀↧↴≺∢↥∪↕⋅↶↵∪↓⋟≀↧↴∐≼↲↥≼↲≺∢∏⋅∪∐↕∐⊔∐↲↥≀↧, The Lorentz factor $\gamma$ of an electron in the lab. +↴∣↽≻⋅↓⋟↕⋅≀↧↴∐∐↲↕⋟∖⊽⊔∐↲∐↴∶∣∑∣↰↶↵∣≀↕↴∐≼⇂⊔∐↲≼↲↥≼↲≺∢⊔⋅∪↕⊔⇂≼↲∐⋟∖⊽∐⋡∖↽∣∣⋜⋡↶↵↕⋝↕∐⊔∐↲ lal., frame is then $\gamma={\cal D} \gamma'$ and the electron density $n(\gamma)$ in the lab. + frame is Given that the effective volume Voy of the blob is Vy=VD (see Appendix A). where V. is the volume of the blob in the blob frame. the energy distribution of the effective number of electrons Neg(4.1) is: Cousider now that (his electron. distribution. will Comptonscatter seed photons of an arbitrary angular distribution.," frame is Given that the effective volume $V_{\rm eff}$ of the blob is $ V_{\rm eff}=V{\cal D}$ (see Appendix A), where $V$ is the volume of the blob in the blob frame, the energy distribution of the effective number of electrons $N_{\rm eff}(\gamma,\mu)$ is: Consider now that this electron distribution will Compton–scatter seed photons of an arbitrary angular distribution." + Since 51. we can make the approximation usually made in svnchrotron theory that the outgoing photons move in (he same direction as the scattering electron.," Since $\gamma\gg 1$, we can make the approximation usually made in synchrotron theory that the outgoing photons move in the same direction as the scattering electron." + Therelore. when observing under a certain angle only electrons moving in this direction contribute to the Compton Iuminosity.," Therefore, when observing under a certain angle only electrons moving in this direction contribute to the Compton luminosity." + Since (he effective number of these electrons is proportional to D?7. the Compton specific Iuminosity (observed luminosity per energy interval per solid angle) is also proportional to D?.," Since the effective number of these electrons is proportional to ${\cal D}^{3+p}$, the Compton specific luminosity (observed luminosity per energy interval per solid angle) is also proportional to ${\cal D}^{3+p}$." + Different seed photon angular distributions will introduce an angledependent multiplication term in the caleulation of ihe external Compton luminosity., Different seed photon angular distributions will introduce an angle–dependent multiplication term in the calculation of the external Compton luminosity. +" An extreme case of a photon angular distribution is a monodirectional photon beampropagating along the direction of motion of the blob. for whieh Dermer.Schlickeiser.&Alastichiaclis(1992) caleulated the beaming factor of Compton scattering to be D?ΕΙ—ji)?P7,"," An extreme case of a photon angular distribution is a monodirectional photon beampropagating along the direction of motion of the blob, for which \citet{dermer92} calculated the beaming factor of Compton scattering to be ${\cal D}^{3+p} (1-\mu)^{(p+1)/2}$." + Note here that for 9.=0° the inverse Compton luminosity is zero., Note here that for $\theta=0^o$ the inverse Compton luminosity is zero. +" It can easily be shown that for a monoclirectional photon beam propagating in the direction opposite to the direction of motion of the blob. as may be the case for the mirror model of Ghisellini&Madan(1996).. the beaming factor is Εμ)be,"," It can easily be shown that for a monodirectional photon beam propagating in the direction opposite to the direction of motion of the blob, as may be the case for the mirror model of \citet{ghisellini96}, the beaming factor is ${\cal D}^{3+p} (1+\mu)^{(p+1)/2}$." + We now consider that the plasma blob is propagating through an environmentpermeatect bv an isotropic monoenereelic photon fielcl of οποιον density C., We now consider that the plasma blob is propagating through an environmentpermeated by an isotropic monoenergetic photon field of energy density $U$ . + The lab., The lab. + fame rate of, frame rate of +jet iauplies higher deusitv of the external photous in the dob. if the reflection of clouds in broad line region works. and therefore stronger absorption of high cuerey 5-ravs (Colotti. Fabian Rees 1998).,"jet implies higher density of the external photons in the blob, if the reflection of clouds in broad line region works, and therefore stronger absorption of high energy $\gamma$ -rays (Celotti, Fabian Rees 1998)." + Tere we argue based on the wpothesis of Clhisellini Madau (1996) that the energy density of reflected svuchrotroun. photon is high enough Or pair production via iteraction of eanunmnia-ray photons woinverse Compton scattering with reflected svuchrotrou photons if the bulk velocity is high cnough., Here we argue based on the hypothesis of Ghisellini Madau (1996) that the energy density of reflected synchrotron photon is high enough for pair production via interaction of gamma-ray photons by inverse Compton scattering with reflected synchrotron photons if the bulk velocity is high enough. + Further we apply the present coustraint to the represeutative individual objects. Mik 121 aud 3C 279.," Further we apply the present constraint to the representative individual objects, Mrk 421 and 3C 279." + (κοπή Madau (1996) have calculated the energy density. of reflected. svuchrotron (Rsv) cussion. anc compared with the other reflected components.," Ghisellini Madau (1996) have calculated the energy density of reflected synchrotron (Rsy) emission, and compared with the other reflected components." + They draw a concluxiou that the οποιον deusitv of Rsv componcut dominates over 10 times of that of reflected commponcut of accretion disk radiation., They draw a conclusion that the energy density of Rsy component dominates over 10 times of that of reflected component of accretion disk radiation. + Iu this section we make an attempt to use the observables quantities to express the intrinsic constraiuts on τον high cuerey enuüssou., In this section we make an attempt to use the observables quantities to express the intrinsic constraints on very high energy emission. + Theoverall νΕν spectrum of blazars shows that there are two power peaks: the first is low cnerev oue between IR/soft N-rav baud. aud the second is high energy one peaking iu the MeVGeV rauge (vou Montieuy ct al 1995. Samibruua. Maraschi Urry 1906. Comasti et al 1997. Kubo et al 1998).," Theoverall $\nu F_{\nu}$ spectrum of blazars shows that there are two power peaks: the first is low energy one between IR/soft X-ray band, and the second is high energy one peaking in the MeV/GeV range (von Montigny et al 1995, Sambruna, Maraschi Urry 1996, Comastri et al 1997, Kubo et al 1998)." + This characteristic can be explained by the simple context of onc-zone homogeneous SSC or EC model., This characteristic can be explained by the simple context of one-zone homogeneous SSC or EC model. +" The low energy peak denoted ;4 is caused by svuchrotrou radiation of relativistic clectrous. and the second peak denoted É4. or Mae results from the Compton scattering off the svuchrotron or reflected svuchrotron photons by the sale population of clectrous. respectively,"," The low energy peak denoted $\nu_{\rm s}$ is caused by synchrotron radiation of relativistic electrons, and the second peak denoted $\nu_{\rm c}$, or $\nursc$ results from the Compton scattering off the synchrotron or reflected synchrotron photons by the same population of electrons, respectively." + We take the two peaks aud their corresponding fluxes as four observable quautities., We take the two peaks and their corresponding fluxes as four observable quantities. + From the RSC model the magnetic field B can be approximately expressed by the observational quantities., From the RSC model the magnetic field $B$ can be approximately expressed by the observational quantities. + The observed frequeney of svuchrotron photon is vo=DiaDB (m=2.8s 10°). and the frequency of reflected svuchrotron Compton pliotous reads Mae=D(2D)?3/44 D. and we can get the estimation of magnetic field 5 while iuo pure SSC inodel the magnetic feld is approximately as Bo=νεπμ). where vm is the frequency of photous enitte dby SSC.," The observed frequency of synchrotron photon is $\nu_{\rm s}=\cd \nu_0 \gamma_{\rm b}^2B$ $\nu_0=2.8\times 10^6$ ), and the frequency of reflected synchrotron Compton photons reads $\nursc=\cd (2\Gam)^2\gamma_{\rm b}^4\nu_0B$ , and we can get the estimation of magnetic field $B$ while in pure SSC model the magnetic field is approximately as $B=\nu_{\rm s}^2/(\cd\nu_0\nu_{\rm c})$, where $\nu_{\rm c}$ is the frequency of photons emitted by SSC." + The Doppler factor Ῥ--]ΓΗwlP27)) where pi= cosis the cosine of the orientated angle of jet relative to the observer.," The Doppler factor $\cd=1/\Gam [1-\mu(1-\Gam^{-2})^{1/2}]$, where $\mu=\cos \theta$ is the cosine of the orientated angle of jet relative to the observer." + Equation (1)is similar to the wodel of Sikora. Degelinan Rees (1991) (also see Sambruna. Miiraschni σπιν 1996).," Equation (1) is similar to the model of Sikora, Begelman Rees (1994) (also see Sambruna, Maraschi Urry 1996)." + Comparing with the above two formula. we learn that RSC model needs stronger magnetic field than SSC model does whereas the energy of relativistic electrous is lower iu RSC model than in SSC model.," Comparing with the above two formula, we learn that RSC model needs stronger magnetic field than SSC model does whereas the energy of relativistic electrons is lower in RSC model than in SSC model." + The reflected svuchrotrou Compton (RSC) mainly depends on two parameters: the reflection albedo. namely. the Thomson scattering optical depth (7BER E and the Lorentz factor D of the relativistic jet.," The reflected synchrotron Compton (RSC) mainly depends on two parameters: the reflection albedo, namely, the Thomson scattering optical depth $\tblr$ ), and the Lorentz factor $\Gamma$ of the relativistic jet." + Iu the case of power-law distribution of clectrous. ΑνΞNowU. (ainX05Xtax}. Where Nis the nunber deusitv of relativistic electrons. and 5 is the Loreutz factor of electron. the svuchrotron clusion cocficiency ls Ipprosiiaatelvls eiven by ον=e5(ayNyBE(νου4yk Tere," In the case of power-law distribution of electrons, $N=N_0\gam^{-\al}$ , $\gam_{\rm min}\leq \gam \leq \gam_{\rm max}$ ), where $N$ is the number density of relativistic electrons, and $\gam$ is the Lorentz factor of electron, the synchrotron emission coefficiency is approximately given by $\veps_{\nu}=c_5(\al)N_0B^{1+\al \over 2}(\nu/2c_1)^{1-\al \over 2}$." + ey=ithin6.27and οσα) is tabulated in Pacholezy (1970) w the frequency range mp<<νvy. where Vy»=MmBrrr?lulli'/lnuax0).," Here $c_1=6.27\times 10^{18}$, and $c_5(\al)$ is tabulated in Pacholczyk (1970) within the frequency range $\nu_1\leq \nu \leq \nu_2$, where $\nu_{1,2}=\nu_0B(\gam^2_{\rm min},\gamma^2_{\rm max})$." + The average eucrey deusity per frequency DEP in a region with diuensiou s in the jet comoving frame can be obtained where Ne=Nos.," The average energy density per frequency $u^{\prime}_{\rm syn,\nu^{\prime}}$ in a region with dimension $s$ in the jet comoving frame can be obtained where $N_T=N_0s$." + The number deusitv of svuchrotron pliotous can be obtained by aud poto) reads here P is Planck constant. and εἰ=i!deriveμι," The number density of synchrotron photons can be obtained by and $n_0(\al)$ reads here $h$ is Planck constant, and $\epsp=h\nu'/m_ec^2$." +",We have ee relationship n2=Πιν)ide’ to equation 3).", We have employed relationship $n_{\epsp}=n_{\nu'}d\nu'/d\epsp$ to derive equation (3). + The mean eucrev density is expressed by for a«3., The mean energy density is expressed by for $\al< 3$. + Defining fo. as we lave where ή denotes 14., Defining $\lssc$ as we have where $\nusp$ denotes $\nu_2^{\prime}$. + Since the opening angle of jet (7/I?) is much less than 27. it is then reasonable to assume that the DER reflection approxiuates to plane mürror with thickness AHfpyjg aud electron. number deusitv s.," Since the opening angle of jet $\pi/\Gam^2$ ) is much less than $2\pi$, it is then reasonable to assume that the BLR reflection approximates to plane mirror with thickness $\Delta R_{\rm BLR}$ and electron number density $n_e$." + The distauce distribution of reflected svuchrotron photous has been discussed by Cdiseliià Madaui (1996)., The distance distribution of reflected synchrotron photons has been discussed by Ghisellini Madau (1996). + The angular distribution has not been issued., The angular distribution has not been issued. + Since the thickness of uiror is zero. the energy density of reflected svuchrotrou cnuission sharply increases when blob is close to the mirror.," Since the thickness of mirror is zero, the energy density of reflected synchrotron emission sharply increases when blob is close to the mirror." + Iu fact if we drop the asstuuption of zero-thickucss of wirror. this characteristic will disappear.," In fact if we drop the assumption of zero-thickness of mirror, this characteristic will disappear." + We will deal with his sophisticate model im future., We will deal with this sophisticate model in future. + Because the reflectec svuchrotron emission is isotropic in observers frame. the dob receives the reflected photon beamed within a solic anele z/I?.," Because the reflected synchrotron emission is isotropic in observer's frame, the blob receives the reflected photon beamed within a solid angle $\pi/\Gam^2$ ." + The subsequent section will pay atteution tolis effects., The subsequent section will pay attention tothis effects. + Neglecting the anele-dependeut distribution of reflected. photon field. we approximate the Doppler actor D=20 (0z 0).," Neglecting the angle-dependent distribution of reflected photon field, we approximate the Doppler factor $\cd \approx 2\Gam$ $\theta \approx 0$ )." +" For simplicity. we assume the uiirror (reflecting clouds in broad line regiou) has Thomson scattering optical depth τι,=6,noABmon Rau"," For simplicity, we assume the mirror (reflecting clouds in broad line region) has Thomson scattering optical depth $\tblr=\st n_e\Delta \rblr \approx \st n_e \rblr$ ." +Figure 1:FUSE specirum of VW II with lines identified.,Figure 1: spectrum of VW Hyi with lines identified. + The sharp emission lines are not intrinsic (o the source. (hey are due to air glow.," The sharp emission lines are not intrinsic to the source, they are due to air glow." +" Figure 2:FUSE spectrum of VW IIi together with the synthetic spectrum for a single white dwarf model with T—26.000K. Vi,sin;=400km |. and the composition as specified in the text (model 1 in Table 2)."," Figure 2: spectrum of VW Hyi together with the synthetic spectrum for a single white dwarf model with T=26,000K, $V_{rot}\sin{i}=400$ km $^{-1}$, and the composition as specified in the text (model 1 in Table 2)." +" Figure 3:FUSE spectyum of VW Lyi together with the svnthetic spectrum for an accretion disk model with a 1.02.U. central star. M.=LOx10A, vr.|. and a disk inclination of 81 degrees (model 6 in Table 2)."," Figure 3: spectrum of VW Hyi together with the synthetic spectrum for an accretion disk model with a $1.03M_{\odot}$ central star, $\dot{M}=1.0 \times 10^{-10.5} M_{\odot}$ $^{-1}$, and a disk inclination of 81 degrees (model 6 in Table 2)." + Figure 4:FUSE spectrum of VW II together with the svnthetic spectrum lor a composite model fit. consisting of a WD (dotted line) and an accretion disk (dashed line)., Figure 4: spectrum of VW Hyi together with the synthetic spectrum for a composite model fit consisting of a WD (dotted line) and an accretion disk (dashed line). +" The WD model has Z;;;=23. 000K. V,sin;= 400km ! and the disk has an accretion rate of 3.16xLOHM vr.1H and an inclination of 81 degrees."," The WD model has $T_{eff} = 23,000$ K, $V_{rot}\sin{i}=400$ km $^{-1}$ and the disk has an accretion rate of $3.16 \times 10^{-11} +M_{\odot}$ $^{-1}$ and an inclination of 81 degrees." + The combination fit is shown with the solid line. (, The combination fit is shown with the solid line. ( +model 10 in Table 2) Figure 5:FUSE spectrum of VW II together with the svnthetic spectrum for a composite model fit consisting of a WD and an accretion. belt.,model 10 in Table 2) Figure 5: spectrum of VW Hyi together with the synthetic spectrum for a composite model fit consisting of a WD and an accretion belt. +" The white dwarl model has M4=0.96.4... T—23.000I. Vi,sini= 400km !. and the composition as specified in the text. together with an accretion belt with T=48. 000I&. and Visini= 4.000km |."," The white dwarf model has $M_{wd}=0.96 M_{\odot}$, T=23,000K, $V_{rot}\sin{i}=400$ km $^{-1}$, and the composition as specified in the text, together with an accretion belt with $T=48,000$ K, and $V_{belt}\sin{i}=4,000$ km $^{-1}$." + The white dwarf photosphere flux is shown with the dotted line. (he accretion belt. [Iux is shown with the dashed line and their combined flux is shown with the solid line. (," The white dwarf photosphere flux is shown with the dotted line, the accretion belt flux is shown with the dashed line and their combined flux is shown with the solid line. (" +model 12 in Table 2) Figure 6:FUSE spectrum of VW II together with the svnthetic spectrum lor a composite model fit consisting of a WD and an accretion. belt.,model 12 in Table 2) Figure 6: spectrum of VW Hyi together with the synthetic spectrum for a composite model fit consisting of a WD and an accretion belt. +" The white dwarl model has M4;=0.86.M.. T—22.000N. Vi,sini= 400km !. and solar composition. together with an accretion belt with T=50. 000K. and Vj;sini= 3.000km !."," The white dwarf model has $M_{wd}=0.86 M_{\odot}$, T=22,000K, $V_{rot}\sin{i}=400$ km $^{-1}$, and solar composition, together with an accretion belt with $T=50,000$ K, and $V_{belt}\sin{i}=3,000$ km $^{-1}$." + The white cwarl photosphere flux is shown with the dotted line. the accretion belt flix is shown with the dashed line and their combined fIux is shown with the solid line. (," The white dwarf photosphere flux is shown with the dotted line, the accretion belt flux is shown with the dashed line and their combined flux is shown with the solid line. (" +model 13 in Table 2),model 13 in Table 2) +As observations of one field in WLM containing 23 Cepheid variables for which previous optical light eurves. were presented in Paper L With the PANIC camera we were able to observe three additional smaller fields partly overlapping with the SOFI field. under photometric conditions.,"$Ks$ observations of one field in WLM containing 23 Cepheid variables for which previous optical light curves were presented in Paper I. With the PANIC camera we were able to observe three additional smaller fields partly overlapping with the SOFI field, under photometric conditions." + The locations of all these fields are shown in Fig., The locations of all these fields are shown in Fig. + | and their coordinates are given in Table 1., 1 and their coordinates are given in Table 1. + ÁAlltogether. the four observed fields in WLM contain 31 Cepheids.," Alltogether, the four observed fields in WLM contain 31 Cepheids." + In order (o account lor the rapid variations of the skv brightness in (he bands we used a dithering technique. as described in the previous papers of the Arancaria Project reporting inlrared photometry of Cepheid variables.," In order to account for the rapid variations of the sky brightness in the near-infrared bands we used a dithering technique, as described in the previous papers of the Araucaria Project reporting infrared photometry of Cepheid variables." + Total integration iimes were 15 min in the / and GO min in the A band., Total integration times were 15 min in the $J$ and 60 min in the $K$ band. + All the reductions and calibrations were perlormed with the pipeline developed in the course of the Araucaria Project and deseribed in detail in earlier papers of this series., All the reductions and calibrations were performed with the pipeline developed in the course of the Araucaria Project and described in detail in earlier papers of this series. + The subtraction of the skv brightness was done in a (wo-slep process which included the masking ol stars with the IRAF xdimsum package (Pietrzvnski Gieren 2002)., The subtraction of the sky brightness was done in a two-step process which included the masking of stars with the IRAF xdimsum package (Pietrzynski Gieren 2002). + Next. each single image was flat-lielded: and stacked. into the final deep [ield image.," Next, each single image was flat-fielded and stacked into the final deep field image." + PSF photometry and aperture corrections were performed as desribed in Pielvzvuski et al. (, PSF photometry and aperture corrections were performed as desribed in Pietrzynski et al. ( +2002).,2002). + The calibration of the photometry onto the standard system was based on the observations of 22 standarcl stars from the UIXIRT list (Llawarden et al., The calibration of the photometry onto the standard system was based on the observations of 22 standard stars from the UKIRT list (Hawarden et al. + 2001)., 2001). + All of them were observed along with the target fields in WLM at different airmasses aud under photometric conditions., All of them were observed along with the target fields in WLM at different airmasses and under photometric conditions. + The large nunmber of stancard stars observed on each of the six photometric nights for this programme allowed us to obtain the absolute photometric zero points wilh an accuracy close to 0.01 mag. in both filters.," The large number of standard stars observed on each of the six photometric nights for this programme allowed us to obtain the absolute photometric zero points with an accuracy close to 0.01 mag, in both filters." + Deviations of the photometric zero points obtained independently for different nights never exceeded 0.02 mag. for both SOFI ancl PANIC data.," Deviations of the photometric zero points obtained independently for different nights never exceeded 0.02 mag, for both SOFI and PANIC data." + This is demonstrated in Fig., This is demonstrated in Fig. + 2., 2. + For an external check of our photometry. we compared our calibrated magnitudes with those of the 2MAÀSS catalog for the (small) sample of common stars. not finding anv evidence lor a signilicant zero point difference in J and/or Ix (see Fig.," For an external check of our photometry, we compared our calibrated magnitudes with those of the 2MASS catalog for the (small) sample of common stars, not finding any evidence for a significant zero point difference in J and/or K (see Fig." + 3)., 3). + We present the calibrated individual near-infrared magnitudes for all Cepheids located in the observed fields in Table 2 which lists the stars’ IDs. heliocentric Julian days of the observations (mid-integrations). and (he measurements in J and I| with their standard deviations.," We present the calibrated individual near-infrared magnitudes for all Cepheids located in the observed fields in Table 2 which lists the stars' IDs, heliocentric Julian days of the observations (mid-integrations), and the measurements in J and K with their standard deviations." + Depending on the positions of the Cepheids in the galaxy. the number of individual JIx observations range [rom one (o six.," Depending on the positions of the Cepheids in the galaxy, the number of individual JK observations range from one to six." + On average. we were able to collect 3 JIX observations per star.," On average, we were able to collect 3 JK observations per star." + The WLM C'epheids observed in the near-infrared span a period range [rom 54 down to 2.5 davs., The WLM Cepheids observed in the near-infrared span a period range from 54 down to 2.5 days. + The intensity mean magnitudes of the Cepheids were derived by taking a straight average, The intensity mean magnitudes of the Cepheids were derived by taking a straight average +in the MOS aud PN cameras.,in the MOS and PN cameras. + In order to circiuunveut this difficulty we have computed from the actual data the ratio of MOSL. MOS2 and PN source couuts.," In order to circumvent this difficulty we have computed from the actual data the ratio of MOS1, MOS2 and PN source counts." + The median of the ratio of PN and siugle-MOS collected counts. in the LO keV band. is ~ 2.5. re. on average the PN camera collects 2.5 times more counts than cach sinele MOS camera.," The median of the ratio of PN and single-MOS collected counts, in the 0.3--4.0 keV band, is $\sim$ 2.5, i.e. on average the PN camera collects 2.5 times more counts than each single MOS camera." + This factor has been included in the derivation of the sunuued exposure map., This factor has been included in the derivation of the summed exposure map. + We recognize that a) this factor could be a function of source intrinsic spectra aud b) its determination is subject to uncertainties since nieasured ratios have a somewhat large scatter., We recognize that a) this factor could be a function of source intrinsic spectrum and b) its determination is subject to uncertainties since measured ratios have a somewhat large scatter. +" Iu deriving N-rav flux we have assmunued a conversion factor from counts to intrinsic source flux in the 0.1ο keV.pass?.. as computer (using PIMA3) for a Ravinoud-Siunith spectrmm with &7—0.5L keV iux NH—d5100 7, of 7.1«410E1?P forB à singleB MOS.B camera."," In deriving X-ray flux we have assumed a conversion factor from counts to intrinsic source flux in the 0.1–4.0 keV, as computed (using PIMMS) for a Raymond-Smith spectrum with $kT$ =0.54 keV and $N_H = 7.5\times 10^{20}$ $^{-2}$, of $7.1\times 10^{-12}$ for a single MOS camera." + We note that this xoacd baud conversion factor is rather lnscusitive to πλοίαlicity variatiois up to a factor 3., We note that this broad band conversion factor is rather insensitive to metallicity variations up to a factor 3. + With the above conversion factor. the net exposure tine of ~ 33 ks of he sunmed DIC data set. translates to an equivalent 150 ks of a single MOS camera (or to au equivalent 60 ks of the PN camera).," With the above conversion factor, the net exposure time of $\sim$ 33 ks of the summed B+C data set, translates to an equivalent $\sim$ 150 ks of a single MOS camera (or to an equivalent $\sim$ 60 ks of the PN camera)." + The siugle-MOS equivalent rate of weaker sources is ~3.3.10! cut (indeed we have detected ouly three sources below this value). that corresponds to ~2.35S10D ere 7. well below the Πιο sensitivitv (~6«10.1? erg 1 7). achieved by the GU ksROSAT-PSPC observation analyzed bv. Jetfries et al. (," The single-MOS equivalent rate of weaker sources is $\sim 3.3\times 10^{-4}$ cnt $^{-1}$ (indeed we have detected only three sources below this value), that corresponds to $\sim 2.35\times 10^{-15}$ erg $^{-1}$ $^{-2}$, well below the limiting sensitivity $\sim 6\times 10^{-15}$ erg $^{-1}$ $^{-2}$ ), achieved by the 60 ks observation analyzed by Jeffries et al. (" +"1997). and with a spatial resolution (EPIC FWIAL ~ G"") better than the PSPC whose PSF had a FWIINE of ~ 20"".","1997), and with a spatial resolution (EPIC FWHM $\sim$ $^{\prime\prime}$ ) better than the PSPC whose PSF had a FWHM of $\sim$ $^{\prime\prime}$." + Sunuuiue all the available data allows us to reachthe deepest possible limiting seusitivitv., Summing all the available data allows us to reachthe deepest possible limiting sensitivity. + With the data taken just with observation Bowe would have reached a iuiting scusitivity of ~8«LO1? and ~3.5.10Pore for a sinele MOS and the PN calucras. respectively.," With the data taken just with observation B we would have reached a limiting sensitivity of $\sim 8\times 10^{-15}$, and $\sim 3.5\times 10^{-15}$ for a single MOS and the PN cameras, respectively." + Sumunine up the data of all cameras or the observation Bowe would have reached a limiting ↴∖↴↸∖∐↴∖↴↕↑↕↖↽↕↑⋅↖↽∪⋅⋅⋅ SB 101↸⊳↕⊔−∙≼∐∖↑↸∖↸⊳⊓∐∶↴⋁∪∐↕⋅↖↽ ⋅ about 160 sources.," Summing up the data of all cameras for the observation B we would have reached a limiting sensitivity of $\sim 3\times 10^{-15}$, detecting only about 160 sources." + From the above mmubers. is is also clear ∐⋜↧↑∙↕⋟∪↥⋅↸∖⊼↻∪↴∖↴↿∐⋅↸∖∶↴∙⊾↥⋅↸∖⋜↧↑↸∖↥⋅↑∐⋜⊔∿⊇∩ ss EPIC enters in ∐↸∖↴⋝⋯⊳↨↘↽∶↴∙↕⋅≺∏∐≼⊔↕⋯↕↑↸∖≼↧↥⋅↸∖∶↴∙⊾↕∐∐∖⋜⋯≼⊔↕∐∖ Huiting seusitivitv does not scale nearly with exposure time!.," From the above numbers, is is also clear that, for exposure greater than $\sim$ 20 ks EPIC enters in the background-limited regime and the limiting sensitivity does not scale linearly with exposure ." +. ⊺↕∐∖≼∐∖↸↰⋉∖↴∖↴↑⋖↕∙↸∖∙∪∐≓⋜⋯↕↴∖↴⋟∐∐∏↑↕∐∶↴⋁↴∖↴↸∖∐↴∖↴↕↑↕↖⇁↕↑⋅↖↽∪↕⋟↑↕∐∖ ∐⋅↸∖↴∖↴↸∖∐↑⊀∖⊽⊀∐⊀∐⋉↼∖⊽↙↕⊓⋎↑∪∣∣∶≩∶≩↨↘↽↴∖↴∪↴⋝↴∖↴↸∖↥⋅↖↽⋜↧↑↕∪↓↕↴∖↴↴∖↴↕⋯∐⋜∐⋅↑∪↑∐⋜↧↑ attained. again on-axis with a ~ 20 ss ACIS-Il observation (ILlundenetal.20003). and it varies bv a factor 2 within the central 1l arcnmün region (to be compared with a factor 5 variation in the case of Chandra): in other words the present observation has a total 5oOrasp (forà the ΕΟΝ inu comune) that is ~ 2 iues better than the onc.," The deepest (i.e. on-axis) limiting sensitivity of the present 33 ks observation is similar to that attained, again on-axis, with a $\sim$ 20 ks ACIS-I observation \cite{H++00}) ), and it varies by a factor 2 within the central 11 arcmin region (to be compared with a factor 5 variation in the case of ); in other words the present observation has a total grasp (for the FOV in common) that is $\sim$ 2 times better than the one." + Since the present observation has been doue with the thick filter we expect hat. under the assuniption of an approximately constaut vackeround level. the attainable limiting seusitivitv (iu he somewhat soft baud we have considered) could benefit roni the use of the οςατα (or the hin) filter.," Since the present observation has been done with the thick filter we expect that, under the assumption of an approximately constant background level, the attainable limiting sensitivity (in the somewhat soft band we have considered) could benefit from the use of the medium (or the thin) filter." + Tn order to gain furher couficdence in the adopted xocedure we have compared the EPIC Nevay luminosities with those derived frou observatious (ILundenetal. 2000)) for the 1nenubers detected by both observatories., In order to gain further confidence in the adopted procedure we have compared the EPIC X-ray luminosities with those derived from observations \cite{H++00}) ) for the members detected by both observatories. + The resulting scatter plo in Fie., The resulting scatter plot in Fig. + 3 shows a good agreciment. especially if one considers source variability. of which we lave fouud clear evidence in the cata. as well as differen source spectra.," \ref{fig:Lx_Lx} shows a good agreement, especially if one considers source variability, of which we have found clear evidence in the data, as well as different source spectra." + As matter of fact we have detected 105 ou of the LIT. ACIS-I sources. and we have detected 3l new sources in the common FOV.," As matter of fact we have detected 108 out of the 147 ACIS-I sources, and we have detected 34 new sources in the common FOV." +" A Large fraction of the new sources falls in the external part of the ΕΟΝ,", A large fraction of the new sources falls in the external part of the FOV. + About half of the sources missed with EPIC have been detected in the ceutral part of the FOV correspouding to a somewhat external aud less sensitive region of the EPIC) ΕΟΝ. the others are likely to be variable.," About half of the sources missed with EPIC have been detected in the central part of the FOV corresponding to a somewhat external and less sensitive region of the EPIC FOV, the others are likely to be variable." + As stated above we Lave foun clear evidence of variability that will be discussed iu a forthcoming paper., As stated above we have found clear evidence of variability that will be discussed in a forthcoming paper. + Deeper liniting sensitivity will be reached by including iu a future analysis the data from observations A aud D ., Deeper limiting sensitivity will be reached by including in a future analysis the data from observations A and D . +. Coloranaenitude diagrams (CMD) of the NGC2516 photometrically determined members in the preseut, Color-magnitude diagrams (CMD) of the NGC2516 photometrically determined members in the present +We have computed a new generation of interior models for Jupiter and Saturn. with an emphasis on improving the treatment of the EOS of hydrogen ancl of elements heavier than ID and He.,"We have computed a new generation of interior models for Jupiter and Saturn, with an emphasis on improving the treatment of the EOS of hydrogen and of elements heavier than H and He." + In. particular. we have used 7 different EOS of hvdrogen that were chosen to reproduce (he range of possibilities indicated by first and second shock Hugoniot data.," In particular, we have used 7 different EOS of hydrogen that were chosen to reproduce the range of possibilities indicated by first and second shock Hugoniot data." + This allows. lor the first time. a determination of the effects of the present uncertainty on the EOS of hydrogen on the interior structure of jovian planets.," This allows, for the first time, a determination of the effects of the present uncertainty on the EOS of hydrogen on the interior structure of jovian planets." + The parameters of interest. which characterize the total mass of heavy. elements ancl their radial distribution in both Jupiter and Saturn are now constraimed reliably. by (his study.," The parameters of interest, which characterize the total mass of heavy elements and their radial distribution in both Jupiter and Saturn are now constrained reliably by this study." + It is interesting lo compare the results to previous models (Guillotet1999) lor which a third parameter was added (to (he optimization: a discontinuity in the abundance of heavy elements accross the helium-poor/helium region (located αἱ the transition between molecular and metallic hydrogen in the 3-laver model).," It is interesting to compare the results to previous models \citep{ggh97, guillot99} for which a third parameter was added to the optimization: a discontinuity in the abundance of heavy elements accross the helium-poor/helium region (located at the transition between molecular and metallic hydrogen in the 3-layer model)." + Our results for Jupiter are very similar. in particular concerning the low central core mass and highly uncertain (otal mass of heavy elements.," Our results for Jupiter are very similar, in particular concerning the low central core mass and highly uncertain total mass of heavy elements." + Differences arise in the case of Saturn. for which some models (GQuillot1999) were found to fit the planets gravitational field with no central dense core.," Differences arise in the case of Saturn, for which some models \citep{guillot99} were found to fit the planet's gravitational field with no central dense core." + However. these previous models consisted in solutions with a high abundance discontinuitv al the molecular/metallic transition (a large abundance of heavy. elements in the heliumn-rich region mimicking the effect of a central dense core).," However, these previous models consisted in solutions with a high abundance discontinuity at the molecular/metallic transition (a large abundance of heavy elements in the helium-rich region mimicking the effect of a central dense core)." + We can thus be relatively confident that even with a simple (hree-laver model with (vo free parameters GVous ancl M;J one can constrain the global structures of Jupiter ancl Saturn., We can thus be relatively confident that even with a simple three-layer model with two free parameters $M_{\rm core}$ and $M_{\sss Z}$ ) one can constrain the global structures of Jupiter and Saturn. + On the other hand. we shoul— keep in mind that (he real structures of these (wo planets maybe more complex so that the actual interpretation of these parameters is not precisely defined (e.g. the central core coul— be either diluted or present as a well-delined structure).," On the other hand, we should keep in mind that the real structures of these two planets maybe more complex so that the actual interpretation of these parameters is not precisely defined (e.g. the central core could be either diluted or present as a well-defined structure)." +" Quantitatively. we confirm that both Jupiter and Saturn are enriched in heavy elements compared to the Sun. by factors of 1.5 Gand ο 14. respectively,"," Quantitatively, we confirm that both Jupiter and Saturn are enriched in heavy elements compared to the Sun, by factors of 1.5 – 6 and 6 – 14, respectively." + Maximum compression ratios of e4 along the principal IIugoniot are supported by three independent experiments (Ixnucsonetal.2001:Belov2002:Doriskovοἱ20023:IXnudson2003.2004). and by most ab initio EOS simulations (Lenosky. Kress Collins 1997: Militzer Ceperley 2000: Galli et al.," Maximum compression ratios of $\sim 4$ along the principal Hugoniot are supported by three independent experiments \citep{knudson01, belov02, +boriskov03, knudson03, knudson04}, and by most ab initio EOS simulations (Lenosky, Kress Collins 1997; Militzer Ceperley 2000; Galli et al." + 2000: Desjarlais 2003)., 2000; Desjarlais 2003). + This tvpe of Hugoniot response is represented by the LM-SOCP and the SESAME-p EOS., This type of Hugoniot response is represented by the LM-SOCP and the SESAME-p EOS. + Interestingly. both EOS lead to very small core masses (MooreS33 )in Jupiter. and a substantial amount of heavy elements in (he envelope.," Interestingly, both EOS lead to very small core masses $M_{\rm +core} \wig< 3\,M_\oplus$ ) in Jupiter, and a substantial amount of heavy elements in the envelope." + The same LOS predict a more massive core in Saturn (10. 20M. ).," The same EOS predict a more massive core in Saturn (10 – $\,M_\oplus$ )." + Changing the IIe-SCVII helium EOS for the He-SESAME-p EOS has a modest effect on the structure of Jupiter and increases (he total amount of heavy elements by a lew Earth masses. split more or less evenly between the core and the envelope.," Changing the He-SCVH helium EOS for the He-SESAME-p EOS has a modest effect on the structure of Jupiter and increases the total amount of heavy elements by a few Earth masses, split more or less evenly between the core and the envelope." + This does not change (he qualitative picture that, This does not change the qualitative picture that +phase 0 corresponds to the accretion disk most open towards the observer ( almost edge on for phase ~0.3).,phase 0 corresponds to the accretion disk most open towards the observer ( almost edge on for phase $\sim$ 0.3). + In contrast. the ESO NTT data of Schmidtobreick Blundell (2006a.b) were taken over a single 30 day period in 2004. starting at JD 2453245 and ending JD 2453274.," In contrast, the ESO NTT data of Schmidtobreick Blundell (2006a,b) were taken over a single 30 day period in 2004, starting at JD 2453245 and ending JD 2453274." + These data covered more than two orbits and the precessional phase varied from 0 at JD +245 to + 0.32 at +274. [, These data covered more than two orbits and the precessional phase varied from 0 at JD +245 to + 0.2 at +274. [ +There are also spectra taken almost every night between JD +287 and +310 but they do not concern me here because the Ha line broadened in an optical flare preceding a radio flare.,There are also spectra taken almost every night between JD +287 and +310 but they do not concern me here because the $\alpha$ line broadened in an optical flare preceding a radio flare. + Two wings corresponding to red and blue shifted velocities of more than 500 km s! appeared and the signals | deal with here were confused - matters were made worse by P Cygni absorption troughs.|, Two wings corresponding to red and blue shifted velocities of more than 500 km $^{-1}$ appeared and the signals I deal with here were confused - matters were made worse by P Cygni absorption troughs.] + A qualitative comparison of Fig.2 of Li Yan (2010) and Fig., A qualitative comparison of Fig.2 of Li Yan (2010) and Fig. + 2 of Schmidtobreick Blundell (2006a) shows the stationary Ha line to have. in both sets of data. a two hornec structure on top of a broader component.," 2 of Schmidtobreick Blundell (2006a) shows the stationary $\alpha$ line to have, in both sets of data, a two horned structure on top of a broader component." + In Schmidtobreick Blundell the bluer horn is dominant at JD +245 and the spectral shape evolves through a symmetric configuratio (equal heights) at +248 to red horn dominant at about +253t (there was no observation on JD +252). just before orbital phase 0 at JD +255.," In Schmidtobreick Blundell the bluer horn is dominant at JD +245 and the spectral shape evolves through a symmetric configuration (equal heights) at +248 to red horn dominant at about +253 (there was no observation on JD +252), just before orbital phase 0 at JD +255." + The pattern of oscillation from blue hor strength to red horn dominance and back repeats throughout the 30 day period: the red becomes slowly more dominant (or equivalently blue is slowly more depleted than red) as time goes on., The pattern of oscillation from blue horn strength to red horn dominance and back repeats throughout the 30 day period; the red becomes slowly more dominant (or equivalently blue is slowly more depleted than red) as time goes on. + The Li Yan data show red dominance at orbital phase ~ 0. evolving through a symmetric configuration at orbital phase ~ 0.5 and returning to red dominance as orbital phase continues to 1.," The Li Yan data show red dominance at orbital phase $\sim$ 0, evolving through a symmetric configuration at orbital phase $\sim$ 0.5 and returning to red dominance as orbital phase continues to 1." + These two sets of data are qualitatively both consistent with the red and blue horns oscillating in antiphase and with blue progressively more strongly absorbed after a precessional phase of -θ.ἱ. (, These two sets of data are qualitatively both consistent with the red and blue horns oscillating in antiphase and with blue progressively more strongly absorbed after a precessional phase of $\sim$ 0.1. ( +The He I spectra in Schmidtobreick Blundell 2006a show very strong periodic swings from red to blue and back. throughout the 30 day period.),"The He I spectra in Schmidtobreick Blundell 2006a show very strong periodic swings from red to blue and back, throughout the 30 day period.)" + In order to make quantitative comparisons I digitised the 17 spectra presented in Fig., In order to make quantitative comparisons I digitised the 17 spectra presented in Fig. + 2 of Li Yan (2010) and fitted each to à sum of three Gaussians., 2 of Li Yan (2010) and fitted each to a sum of three Gaussians. + The variables were the positions of the centroids. the standard deviations of the Gaussians and the heights at the centroids.," The variables were the positions of the centroids, the standard deviations of the Gaussians and the heights at the centroids." + The fits achieved a good representation of the spectra in all cases: the red and blue horns were generated by two Gaussians about 10 aapart and of standard deviation 3-4, The fits achieved a good representation of the spectra in all cases; the red and blue horns were generated by two Gaussians about 10 apart and of standard deviation 3-4. + These sit on a broader Gaussian of standard deviation approximately 13., These sit on a broader Gaussian of standard deviation approximately 13. +. Fig.] displays two samples of my digitised Purple Mountain spectra. together with the fitted curves and the three Gaussian components.," Fig.1 displays two samples of my digitised Purple Mountain spectra, together with the fitted curves and the three Gaussian components." + Fig.2 shows the centroids of the three fitted Gaussians as a function of orbital phase and is designed to be compared directly with Fig.1 of Blundell et al (2008) (which however covers over two orbital periods)., Fig.2 shows the centroids of the three fitted Gaussians as a function of orbital phase and is designed to be compared directly with Fig.1 of Blundell et al (2008) (which however covers over two orbital periods). + The symbols + and x denote the centroids of the blue and red horn Gaussians respectively: « denotes the centroid of the broad component identified with the wind from the disk in Blundell et al (2008)., The symbols $+$ and x denote the centroids of the blue and red horn Gaussians respectively; $*$ denotes the centroid of the broad component identified with the wind from the disk in Blundell et al (2008). + The two narrow components run almost railroad straight and the wind centroid wanders from one side to the other with the orbital period. just as in Fig.," The two narrow components run almost railroad straight and the wind centroid wanders from one side to the other with the orbital period, just as in Fig." + | of Blundell et al (2008)., 1 of Blundell et al (2008). + Fig.3 presents the data of Fig.2 in a different way., Fig.3 presents the data of Fig.2 in a different way. + The upper panel shows half the difference in recessional velocity of the two horn centroids: that is. approximately the rotational speed of the eircumbinary ring which | have supposed responsible.," The upper panel shows half the difference in recessional velocity of the two horn centroids; that is, approximately the rotational speed of the circumbinary ring which I have supposed responsible." + This ts to be compared with the upper panel of Fig.3 of Blundell et al (2008) or with the upper panel of Fig.7 of Bowler (2010)., This is to be compared with the upper panel of Fig.3 of Blundell et al (2008) or with the upper panel of Fig.7 of Bowler (2010). + In both cases this supposed rotational speed is rather constant at approximately 200 km s! (the Purple Mountain speed is maybe a bit larger than that from Chile)., In both cases this supposed rotational speed is rather constant at approximately 200 km $^{-1}$ (the Purple Mountain speed is maybe a bit larger than that from Chile). + The middle panel is the complement: it is the mean speed of the horns and again can be compared with the upper panels of Fig., The middle panel is the complement; it is the mean speed of the horns and again can be compared with the upper panels of Fig. + 3 of Blundell et al (2008) or Fig.7 of Bowler (2010)., 3 of Blundell et al (2008) or Fig.7 of Bowler (2010). + The nominal systemic speed of the horns looks a bit larger in the Purple Mountain data., The nominal systemic speed of the horns looks a bit larger in the Purple Mountain data. + The lowest panel displays the recessional speed of the centroid of the wind component (s in Fig.2) as a function of orbital phase., The lowest panel displays the recessional speed of the centroid of the wind component $*$ in Fig.2) as a function of orbital phase. + This can be compared with the top panel of Fig.2 of Blundell et al (2008)., This can be compared with the top panel of Fig.2 of Blundell et al (2008). + In both data sets the wind centre is receding fastest, In both data sets the wind centre is receding fastest +08.12.1;07.19.2)The The still recent discovery of the first extrasolar planet. around 51 Peg (Alavor Queloz. 1995). has since bec followed by umauyv more.,"08.12.1;\tikzmark{mainBodyEnd2} % Stars: late-type + \tikzmark{mainBodyStart3}07.19.2)\tikzmark{mainBodyEnd3} % Solar system: general, + \tikzmark{mainBodyStart4}}\tikzmark{mainBodyEnd4} +% +\title{The closest extrasolar planet} + +\subtitle{ A giant planet around the M4 dwarf Gl~876} + +\thanks{Partly based on observations made at the Observatoire de Haute Provence +(CNRS)} + +\thanks{Partly based on observations obtained with the swiss 1.2m telescope at the European Southern Observatory +} + +\author{X.~Delfosse \inst{1}\inst{2} + \and T.~Forveille \inst{2} + \and M.~Mayor \inst{1} + \and C.~Perrier \inst{2} + \and D.~Naef \inst{1} + \and D.~Queloz \inst{3}\inst{1} +} + +\offprints{Xavier Delfosse, e-mail: Xavier.Delfosseobs.unige.ch} + +\institute{ Observatoire de Gen\`eve, + 51 Ch des Maillettes, + 1290 Sauverny, + Switzerland +\and + Observatoire de Grenoble, + 414 rue de la Piscine, + Domaine Universitaire de S$^{\mathrm t}$ Martin d'H\`eres, + F-38041 Grenoble, + France +\and + Jet Propulsion Laboratory, % California Institute of Technology, + Mail Stop 306-473, 4800 Oak Grove Drive, Pasadena, + \tikzmark{mainBodyStart5}CA\tikzmark{mainBodyEnd5} \tikzmark{mainBodyStart6}91109,\tikzmark{mainBodyEnd6} + \tikzmark{mainBodyStart7}USA\tikzmark{mainBodyEnd7} +\tikzmark{mainBodyStart8}} The still recent discovery of the first extrasolar planet, around 51 Peg (Mayor Queloz, 1995), has since been followed by many more." + The count currently ruus to 1l very low mass companions (Marcy Butler. 1998: Queloz. 1999). with minima masses (M sin’) which range between 0.5 aud 10 times the mass of Jupiter.," The count currently runs to 11 very low mass companions (Marcy Butler, 1998; Queloz, 1999), with minimum masses (M $\sin{i}$ ) which range between 0.5 and 10 times the mass of Jupiter." + Asides from their Jupiter-like masses. which largelv reflect the sensitivity threshold of current radial velocity programs. the known extra-solu planets are a very diverse class.," Asides from their Jupiter-like masses, which largely reflect the sensitivity threshold of current radial velocity programs, the known extra-solar planets are a very diverse class." + Some of them have large eccentricities when others have nearly circular orbits. aud their periods rauge between 3.3 davs and L1 years.," Some of them have large eccentricities when others have nearly circular orbits, and their periods range between 3.3 days and 4.4 years." + Ciaut planets can thus have very much shorter periods than in our solar svsteni which clearly does not represent the only possible outcome of planetary system formation and evolution.," Giant planets can thus have very much shorter periods than in our solar system, which clearly does not represent the only possible outcome of planetary system formation and evolution." + To date on the other iud. planets have mostly beeu looked for around solar type stars. auc. pulsar companions asides. they lave only been found orbiting such stars.," To date on the other hand, planets have mostly been looked for around solar type stars, and, pulsar companions asides, they have only been found orbiting such stars." + This reflects to some extent an understandable desire to identify close analogs to our own solar system. which could perhaps coutain life sustaining planets.," This reflects to some extent an understandable desire to identify close analogs to our own solar system, which could perhaps contain life sustaining planets." + Also. the selection function of the radial velocity planet searches has a relatively sharp optiumn around spectral class Ci. Essentially all stars hotter than approximately FS have fast rotation (Wolf et al.," Also, the selection function of the radial velocity planet searches has a relatively sharp optimum around spectral class G. Essentially all stars hotter than approximately F5 have fast rotation (Wolf et al.," + 1982). so that it is impossible to measure their radia velocity to the 01s Loaccuracev needed to detect planets;," 1982), so that it is impossible to measure their radial velocity to the $\sim$ $^{-1}$ accuracy needed to detect planets." + At the other cud of the mass spectrum. nost AL chwarts have slow rotation (Dolfosse et al..," At the other end of the mass spectrum, most M dwarfs have slow rotation (Delfosse et al.," + 1998a) aud their velocity can be measured accurately. as we discuss below.," 1998a) and their velocity can be measured accurately, as we discuss below." + Their Iunuinosities however are much lower than those of solar tvpe stars., Their luminosities however are much lower than those of solar type stars. + At a given distauce a imuch longer integration time is thus needed to obtain a eiven radial velocity precision on an M dwarf than on a € dwarf., At a given distance a much longer integration time is thus needed to obtain a given radial velocity precision on an M dwarf than on a G dwarf. + All planet search programs have thus uuderstandably concentrated on solar type stars., All planet search programs have thus understandably concentrated on solar type stars. + C chwarts however ouly represent a siuall fraction of the disk stellar population. with the lower dass AD dwarfs outumuberius them by about an order of magnitude (Cdliese Jabreiss. 1991).," G dwarfs however only represent a small fraction of the disk stellar population, with the lower mass M dwarfs outnumbering them by about an order of magnitude (Gliese Jahreiss, 1991)." + It is thus likely that uost planets in our galaxy orbit stars whose mass and huninesitv are significantly lower than the Suus (Boss. 1995). tuless sole as vet uideuti&ed plysical process restricts planet formation to the euvironment of sufficicutly niassve stars.," It is thus likely that most planets in our galaxy orbit stars whose mass and luminosity are significantly lower than the Sun's (Boss, 1995), unless some as yet unidentified physical process restricts planet formation to the environment of sufficiently massive stars." + It is clearly important to establish whether such à mechauisiu exists., It is clearly important to establish whether such a mechanism exists. + For the last three years. we have been motoring the radial velocities of à nominally volue limited sample of 125 nearby AI chwarts.," For the last three years, we have been monitoring the radial velocities of a nominally volume limited sample of 125 nearby M dwarfs." + The two main goals of this large observing program (~30 nielits/vear) are to establish the controversial (e.g. Kroupa. 1995. and Reid Cizis. 1997. for two contrasted views) multiplicity statistics of ficld M dwarf svsteis. aud to pin down the still uncertain mass-huninosity relation at the bottom of the main sequence.," The two main goals of this large observing program $\sim$ 30 nights/year) are to establish the controversial (e.g. Kroupa, 1995, and Reid Gizis, 1997, for two contrasted views) multiplicity statistics of field M dwarf systems, and to pin down the still uncertain mass-luminosity relation at the bottom of the main sequence." + Deltosse et al (1998b) presen prelininary results for the stellar companion search. with 12 new compoucuts found in these nearby AL dwarf systems. including the third detached AL dwarf eclipsing binary (Delfosse et al.," Delfosse et al (1998b) present preliminary results for the stellar companion search, with 12 new components found in these nearby M dwarf systems, including the third detached M dwarf eclipsing binary (Delfosse et al.," + 1998e)., 1998c). + A byproduct of this program.C» related to the angular," A byproduct of this program, related to the angular" + A byproduct of this program.C» related to the angularc," A byproduct of this program, related to the angular" + A byproduct of this program.C» related to the angularc»," A byproduct of this program, related to the angular" +Aledium Deep Survey images.,Medium Deep Survey images. + These. however. have not vet been confirmed and remain only as candidates.," These, however, have not yet been confirmed and remain only as candidates." + It is now recognized (hat galaxies which act as gravitational lenses are extremely important tools lor studving a variety of cosmological problems including (he nature and evolution of the lensing galaxies themselves (Ixochaneketal.2000:Naravan&Dartelmann1999:Relsdalsurdej1994:Schneider 1996).," It is now recognized that galaxies which act as gravitational lenses are extremely important tools for studying a variety of cosmological problems including the nature and evolution of the lensing galaxies themselves \citep{Koc00,Nar99,Ref94, Schn96}." +. For example. Im.Griffiths&Ratnatunea(1997). showed (hat observations of seven galaxy lenses favor a nonzero cosmological constant. while Ixochianek and Ixeeton.Nochanek&Falco(1998) present results on the properties of the lensing galaxies. most of which are earlv-tvpe.," For example, \citet{Im97} showed that observations of seven galaxy lenses favor a nonzero cosmological constant, while \citet{Koc00} and \citet{Kee98} present results on the properties of the lensing galaxies, most of which are early-type." + Since the lens models give data on the total (dark + visible) distribution of mass. investigations like (he latter are extremely powerlul. especially for studying the properties of galaxies at high redshifts where (racditional methods become increasinely difficult.," Since the lens models give data on the total (dark + visible) distribution of mass, investigations like the latter are extremely powerful, especially for studying the properties of galaxies at high redshifts where traditional methods become increasingly difficult." + Einstein ring lenses provide additional constraints ancl hence are even more important to the determination of mass distributions of the lensing galaxies (IXochanek.Keeton&MeLeod20011., Einstein ring lenses provide additional constraints and hence are even more important to the determination of mass distributions of the lensing galaxies \citep{Koc01}. + Even though Einstein ring lenses are predicted to be much more common at optical wavelengths (han radio. only one opticallv-idenüified svstem has so [ar been confirmed: 004- (Warrenοἱal.1998.1999).," Even though Einstein ring lenses are predicted to be much more common at optical wavelengths than radio, only one optically-identified system has so far been confirmed: 0047-2808 \citep{War98, War99}." +. Rather than being initially recognised [rom an image as a “rine. Chis lens was detected through superposition of emission lines [rom (he lensed object on the spectrum of the foreground galaxy.," Rather than being initially recognised from an image as a “ring"", this lens was detected through superposition of emission lines from the lensed object on the spectrum of the foreground galaxy." + Hewettetal.(2000) and Halletal.(2000) recently report finding additional candidate lenses in (his manner. but these remain to be confirmed.," \citet{Hew00} and \citet{Hal00} recently report finding additional candidate lenses in this manner, but these remain to be confirmed." + These authors arene (hat spectroscopic observation of distant early (vpe galaxies is one of the best methods of detecting galaxy. lenses. particularly. because the presence of spectroscopic features from (he source implies that the crucial redshifts of both (he source and deflector can be determined.," These authors argue that spectroscopic observation of distant early type galaxies is one of the best methods of detecting galaxy lenses, particularly because the presence of spectroscopic features from the source implies that the crucial redshifts of both the source and deflector can be determined." + In practice. however. (his method is only viable for background galaxies with strong emission lines.," In practice, however, this method is only viable for background galaxies with strong emission lines." + Furthermore. galaxy lens candidates are quite easily recognizable with images trom JST or ground-based adaptive optic svstems. and disentangling the spectral features arising from the source and deflector galaxies is no longer as difficult with the improved spatial resolution being achieved on modern large ground. based telescopes.," Furthermore, galaxy lens candidates are quite easily recognizable with images from $HST$ or ground-based adaptive optic systems, and disentangling the spectral features arising from the source and deflector galaxies is no longer as difficult with the improved spatial resolution being achieved on modern large ground based telescopes." + In this paper we report on a detailed analvsis of the JST images of the lens ancl source ealaxies related to CEBRS03.1077., In this paper we report on a detailed analysis of the $HST$ images of the lens and source galaxies related to CFRS03.1077. + We also present spectra of these galaxies obtained with the Canada-Fraice-IHawali Telescope (CFUT) and derive the redshift of the source - a galaxy without strong enission lines., We also present spectra of these galaxies obtained with the Canada-France-Hawaii Telescope (CFHT) and derive the redshift of the source - a galaxy without strong emission lines. + Finally. a simple model of (he lens-source svstem is described.," Finally, a simple model of the lens-source system is described." +Some difference in emission or absorption properties (e.g... a different gas-to-dust ratio) is needed to make the tail visible as is clear from the density plot but it is a dynamical possibility for tail production.,"Some difference in emission or absorption properties (e.g., a different gas-to-dust ratio) is needed to make the tail visible as is clear from the density plot but it is a dynamical possibility for tail production." + Important diagnostic information comes from the tail velocity structure in knot 38 given by Meaburnetal.(1998)., Important diagnostic information comes from the tail velocity structure in knot 38 given by \citet{Meaburn:1998}. +. In view of our model limitations. we use mass-weighted velocities for comparison with the data.," In view of our model limitations, we use mass-weighted velocities for comparison with the data." + In Fig., In Fig. + + we show mass-weighted velocity profiles along tails for several incident Mach numbers and two stream-source gas temperature ratios., \ref{fig:vz} we show mass-weighted velocity profiles along tails for several incident Mach numbers and two stream-source gas temperature ratios. + We give results only for the transonic and supersonic isothermal-isothermal flows that are relevant to the present paper., We give results only for the transonic and supersonic isothermal-isothermal flows that are relevant to the present paper. + For streams that are roughly in excess of transonic. the velocity increases quickly over a few injection radit.," For streams that are roughly in excess of transonic, the velocity increases quickly over a few injection radii." + The initial increase is followed by a velocity decrease for Mach numbers less than about 3 then the velocity rises to a roughly coasting velocity., The initial increase is followed by a velocity decrease for Mach numbers less than about 3 then the velocity rises to a roughly coasting velocity. + Once the Mach number is around 3. the initial increase is just followed by a very gentle rise or even roughly constant velocity over distances of tens of injection radii.," Once the Mach number is around 3, the initial increase is just followed by a very gentle rise or even roughly constant velocity over distances of tens of injection radii." + Appreciably greater distances are probably not relevant to the Helix tails where the very longest tail (knot 38) has a length about 100 times its head diameter and we display results accordingly., Appreciably greater distances are probably not relevant to the Helix tails where the very longest tail (knot 38) has a length about 100 times its head diameter and we display results accordingly. + The final velocity. reachec depends on the temperature contrast between the stream anc source gas and is higher (in terms of the stream velocity. Ys) the lower the temperature contrast.," The final velocity reached depends on the temperature contrast between the stream and source gas and is higher (in terms of the stream velocity, $V_{\rm S}$ ) the lower the temperature contrast." + This is às expected since the temperature contrast determines crudely the stream-injected gas density contrast and there is more momentum transfer from unit mass of the stream to unit mass of injected gas the less this contrast., This is as expected since the temperature contrast determines crudely the stream-injected gas density contrast and there is more momentum transfer from unit mass of the stream to unit mass of injected gas the less this contrast. + At sufficiently high incident Mach number and low enough temperature contrast. the tail material achieves supersonic velocities in terms of the sound speed in the stream anc obviously as well that of the injected gas (since the injected gas is either at the same temperature or cooler than the stream gas).," At sufficiently high incident Mach number and low enough temperature contrast, the tail material achieves supersonic velocities in terms of the sound speed in the stream and obviously as well that of the injected gas (since the injected gas is either at the same temperature or cooler than the stream gas)." + To compare the tail models with the observational data we assume that a stream of velocity Vs interacts with a clump which has a velocity Vc. where both velocities are measured in the stellar frame.," To compare the tail models with the observational data we assume that a stream of velocity $V_{\rm S}$ interacts with a clump which has a velocity $V_{\rm C}$, where both velocities are measured in the stellar frame." + The relative velocity 1s therefore (Vs— Ve)., The relative velocity is therefore $V_{\rm S}-V_{\rm C}$ ). + We concentrate on knot 38 of Meaburnetal.(1998)., We concentrate on knot 38 of \citet{Meaburn:1998}. +. The gas at the end of this tail has a velocity Vj=22kms! relative to the head (Meaburn&Redman2003)., The gas at the end of this tail has a velocity $V_{\rm T} = 22\;\kmps$ relative to the head \citep{Meaburn:2003}. +. Since this knot has a tail length-to-head diameter ratio of around 100:1 we take this to be equal to the coasting velocity from our calculations reached at 100 injection radit., Since this knot has a tail length-to-head diameter ratio of around 100:1 we take this to be equal to the coasting velocity from our calculations reached at 100 injection radii. +2009).,. +". From the clear elongation observed in the WFC3 images, one can exclude the possibility that it is a brown dwarf."," From the clear elongation observed in the WFC3 images, one can exclude the possibility that it is a brown dwarf." +" The 2-D and 1-D spectra of G2_11408 are shown in Fig.2 The spectral feature is extended over 4 pixels in the spatial direction, consistent with the average seeing."," The 2-D and 1-D spectra of 1408 are shown in \ref{spectrum} The spectral feature is extended over 4 pixels in the spatial direction, consistent with the average seeing." +" The FWHM is ~10À,, significantly larger than any feature due to noise."," The FWHM is $\simeq 10$, significantly larger than any feature due to noise." + The weak emission line has a total observed flux of 3.4x107!8erg cm-?s-!., The weak emission line has a total observed flux of $ 3.4 \times 10^{-18}$ erg $^{-2}$ $^{-1}$. +" The formal S/N is 7, but this estimate does not include systematic errors, and should be considered as an upper limit."," The formal S/N is 7, but this estimate does not include systematic errors, and should be considered as an upper limit." + We made extensive tests to verify the reliability of this detection., We made extensive tests to verify the reliability of this detection. +" We verified that the feature is present both in the Polyn and in the ABBA reductions, as shown in Fig.2.."," We verified that the feature is present both in the Polyn and in the ABBA reductions, as shown in \ref{spectrum}." +" We then inspected all the 75 individual spectra to ensure that the feature is not due to an artifact, and that it is still detected when we separately summed the data in two halves."," We then inspected all the 75 individual spectra to ensure that the feature is not due to an artifact, and that it is still detected when we separately summed the data in two halves." +" Because of the large color break (z—Y>2.1) measured in the HUDF data and the non-detection in the BVI bands, an identification of this line with a lower redshift [ΟΠ] or Ha would imply a very peculiar SED, unlike that of currently known galaxies."," Because of the large color break $z-Y>2.1$ ) measured in the HUDF data and the non--detection in the $BVI$ bands, an identification of this line with a lower redshift [OII] or $\alpha$ would imply a very peculiar SED, unlike that of currently known galaxies." + 'This cannot be excluded a priori., This cannot be excluded a priori. +" We note that there is no evidence of the asymmetry that is expected (but not required, see discussion below) for a z~7 galaxy, although the S/N is too poor to reach any firm conclusion about this."," We note that there is no evidence of the asymmetry that is expected (but not required, see discussion below) for a $z\simeq 7$ galaxy, although the S/N is too poor to reach any firm conclusion about this." +" Based on these tests, we conclude that the feature is likely real and due to emission from a z—6.972 galaxy =6.970 if computed at the blue edge of the line),(z although this should be validated by independent and possibly deeper observations."," Based on these tests, we conclude that the feature is likely real and due to emission from a $z=6.972$ galaxy $z=6.970$ if computed at the blue edge of the line), although this should be validated by independent and possibly deeper observations." +" No continuum is detected in the spectrum: if we estimate it from the Hawk-I Y-band magnitude (Table 1), the line flux translates into an observed EW of103À,, corresponding to 13À if placed at z—6.972."," No continuum is detected in the spectrum: if we estimate it from the Hawk–I Y-band magnitude (Table 1), the line flux translates into an observed EW of, corresponding to $13$ if placed at $z=6.972$." + We do not identify any other emission lines from objects in our sample., We do not identify any other emission lines from objects in our sample. +" We only detect a faint continuum from two objects, namely 22370 (the brightest in our sample) and the brown dwarfG2. candidate of Mannuccietal."," We only detect a faint continuum from two objects, namely 2370 (the brightest in our sample) and the brown dwarf candidate of \citet{Mannucci2007}." +" In both cases, the continuum is consistent with the (2007)..broad-band magnitudes but the low S/N prevents us from deriving any robust information about their spectral type or redshift."," In both cases, the continuum is consistent with the broad–band magnitudes but the low S/N prevents us from deriving any robust information about their spectral type or redshift." +" The key result of our observations is the lack of prominent emission lines in our sample, which may imply a rapid evolution in the physical properties of z>6 galaxies and/or in the surrounding IGM."," The key result of our observations is the lack of prominent emission lines in our sample, which may imply a rapid evolution in the physical properties of $z>6$ galaxies and/or in the surrounding IGM." +" To quantify this issue, we have carried out the following Monte Carlo simulations under the assumptions thata) all our 7 candidates are indeed z~7 galaxies; and the distribution of the intensity in galaxies as a function6) of their rest-frame continuum magnitude Myy does not change significantly from z=4—6 to z—T."," To quantify this issue, we have carried out the following Monte Carlo simulations under the assumptions that all our 7 candidates are indeed $z\simeq 7$ galaxies; and the distribution of the intensity in galaxies as a function of their rest–frame continuum magnitude $M_{UV}$ does not change significantly from $z=4-6$ to $z=7$." +" For the redshift distribution expected for our sample we use the result by C10 (see their Fig 7), which has a broad maximum from z=6.4 to z=7.1 and tails that extend to z—6 and z—7.5."," For the redshift distribution expected for our sample we use the result by C10 (see their Fig 7), which has a broad maximum from $z=6.4$ to $z=7.1$ and tails that extend to $z=6$ and $z=7.5$." +" The distribution of the intensity in galaxies at z=3—6 has been investigated in a numberof studies (S07, V09, $10, D10), showing that the intensity of is anti-correlated with"," The distribution of the intensity in galaxies at $z=3-6$ has been investigated in a numberof studies (S07, V09, S10, D10), showing that the intensity of is anti–correlated with" +intervene vears lave revealed that the broad orbital modulation drifts im both phase aud modulation depth. aud that the spin pulse profile varies too i both shape aud sieuificauce.,"intervening years have revealed that the broad orbital modulation drifts in both phase and modulation depth, and that the spin pulse profile varies too in both shape and significance." + However. there is no evidence for a svetematic chanee in N-rav flux or column deusity of NY Ari (as the disc presumably settles into quicscence following its 1996 outburst) to explain the observed changes in behaviour.," However, there is no evidence for a systematic change in X-ray flux or column density of XY Ari (as the disc presumably settles into quiescence following its 1996 outburst) to explain the observed changes in behaviour." + lustead we sugeest that a precessing. tilted accretion disc may cause both the changes in the broad orbital modulation and the changes in the pulse profile.," Instead we suggest that a precessing, tilted accretion disc may cause both the changes in the broad orbital modulation and the changes in the pulse profile." + At its outer edge. the precessing disce will move the absorbing bulee in orbital phase and may remove it from our line of sight entirely," At its outer edge, the precessing disc will move the absorbing bulge in orbital phase and may remove it from our line of sight entirely." +" At its inner οσο, the precessiug disc will alter our view through the accretion curtains that are anchored there. aud may also hide our view of the lower role."," At its inner edge, the precessing disc will alter our view through the accretion curtains that are anchored there, and may also hide our view of the lower pole." + The tilt and precession of the dise may be induced bx he action of the inclined. rotating magnetic field lines at he disc’s mner edge: it is uulikely to be dviven by radiation rou the central source.," The tilt and precession of the disc may be induced by the action of the inclined, rotating magnetic field lines at the disc's inner edge; it is unlikely to be driven by radiation from the central source." + We conclude by notius tha suce NY Avi is the oulv deeply eclipsing IP. in this source we are probing natter which is less than 6° above the orbital plane.," We conclude by noting that since XY Ari is the only deeply eclipsing IP, in this source we are probing matter which is less than $6^{\circ}$ above the orbital plane." + Other IPs may also possess precessiug. tilted accretion dises.," Other IPs may also possess precessing, tilted accretion discs." + However. the iuflueuce of such a structure is more apparent in NY Avi han in other svstems where we see an N-ray orbital modulation. because m those cases our line of sight is up to 30° above the orbital planc.," However, the influence of such a structure is more apparent in XY Ari than in other systems where we see an X-ray orbital modulation, because in those cases our line of sight is up to $30^{\circ}$ above the orbital plane." + With the additional characteristic of showing outbursts on a timescale which may be ~10 vr. NY An therefore allows us a unique view ofthe accretion dise structure amougst magnetic cataclysunic variables.," With the additional characteristic of showing outbursts on a timescale which may be $\sim 10$ yr, XY Ari therefore allows us a unique view of the accretion disc structure amongst magnetic cataclysmic variables." +ils own particular distinguishing characteristics.,its own particular distinguishing characteristics. + In doing so we also wish to address a conclusion of Parnell et al. (, In doing so we also wish to address a conclusion of Parnell et al. ( +2010a) who suggested (hat separator reconnection does not appear to involve the nulls that lie at both ends of the separator as well as the recent findines (Parnell 2010b) of verv large numbers of separators sometimes appearing in numerical MIID experime=WV.,2010a) who suggested that separator reconnection does not appear to involve the nulls that lie at both ends of the separator as well as the recent findings (Parnell 2010b) of very large numbers of separators sometimes appearing in numerical MHD experiments. + Accordingly the aim of the present work is to describe in detail the nature of an isolated 3D reconnection event in the vicinity of a separator., Accordingly the aim of the present work is to describe in detail the nature of an isolated 3D reconnection event in the vicinity of a separator. + We do so using a simple analvtical model whieh is described in detail in Section 2.., We do so using a simple analytical model which is described in detail in Section \ref{ref:themodel}. + The model allows us to consider (vpical magnetic field connectivities resulting [rom separator reconnection in Section 2. and the nature of the magnetic flix evolution in Section 4.., The model allows us to consider typical magnetic field connectivities resulting from separator reconnection in Section \ref{sec:bif} and the nature of the magnetic flux evolution in Section \ref{sec:evolve}. + We consider how reconnection rates nav be determined in separator configurations in Section 5.Hr before discussing our findings and concluding in Sections 6. 7.., We consider how reconnection rates may be determined in separator configurations in Section \ref{sec:rates} before discussing our findings and concluding in Sections \ref{sec:discussion} \ref{sec:conc}. + A fully self-consistent model for reconnection must incorporate a dvnanmie evolution which generates current sheet(s) as well as the reconnection that takes place at. (hose current. sheets and changes the magnetic lield topology., A fully self-consistent model for reconnection must incorporate a dynamic evolution which generates current sheet(s) as well as the reconnection that takes place at those current sheets and changes the magnetic field topology. + An example in the solar corona is ihe emergence of a magnetic flix tube from the convection zone and reconnection with the pre-existing coronal magnetic field., An example in the solar corona is the emergence of a magnetic flux tube from the convection zone and reconnection with the pre-existing coronal magnetic field. + Inherent in such events is an enormous separation of scales between the global dynamic process and the local reconnection events., Inherent in such events is an enormous separation of scales between the global dynamic process and the local reconnection events. + Accordingly. a (vpical approach to model reconnection itself is (ο start with a local magnetic field configuration (hat is considered susceptible to current sheet formation (such as. in two dimensions. an X-tvpe null point of the field).," Accordingly, a typical approach to model reconnection itself is to start with a local magnetic field configuration that is considered susceptible to current sheet formation (such as, in two dimensions, an X-type null point of the field)." + In simulations the magnetic field is then confined to a finite region and the boundaries driven in such a manner as (ο initiate a reconnection event which can Chen be studied in detail., In simulations the magnetic field is then confined to a finite region and the boundaries driven in such a manner as to initiate a reconnection event which can then be studied in detail. + Determining physically realistic, Determining physically realistic +central concentration. such that the y=[4 model is the most concentrated and the y=1.8 is the least.,"central concentration, such that the $\gamma=1.4$ model is the most concentrated and the $\gamma=1.8$ is the least." + It might be worth also to recall that models with larger y are less compressible than models with lower y., It might be worth also to recall that models with larger $\gamma$ are less compressible than models with lower $\gamma$. + Finally. we introduce the black hole as a point mass at the origin and we displace the star so as to place its center of mass on the required parabolie orbit (since the star is an extended object this actually means that the total mechanical energy of the star is slightly negative. amounting to roughly -0.005 in our units).," Finally, we introduce the black hole as a point mass at the origin and we displace the star so as to place its center of mass on the required parabolic orbit (since the star is an extended object this actually means that the total mechanical energy of the star is slightly negative, amounting to roughly -0.005 in our units)." + The initial distance from the black hole is three times the pericentre distance (in other simulations not described here. we have also used a larger initial distance and found no significant difference).," The initial distance from the black hole is three times the pericentre distance (in other simulations not described here, we have also used a larger initial distance and found no significant difference)." +" Our code units are A, for length and M, for mass. which ensure that our results are deseribed in the same dimensionless variables as described in Section 2."," Our code units are $R_{\star}$ for length and $M_{\star}$ for mass, which ensure that our results are described in the same dimensionless variables as described in Section 2." + The black hole is modelled as a sink onto which SPH particles can be accreted if they come closer to the black hole that a distance 0.25 in code units., The black hole is modelled as a sink onto which SPH particles can be accreted if they come closer to the black hole that a distance 0.25 in code units. + However. in practice. given that our pericentre is very large and that we do not follow the evolution of the debris long after the interaction. no particles are actually accreted during the course of our simulations.," However, in practice, given that our pericentre is very large and that we do not follow the evolution of the debris long after the interaction, no particles are actually accreted during the course of our simulations." + Before comparing the results obtained with various polytropic indices. we start by describing the results that we have obtainec in the y=5/3. which is directly comparable to the simulations discussed in previous papers.," Before comparing the results obtained with various polytropic indices, we start by describing the results that we have obtained in the $\gamma=5/3$, which is directly comparable to the simulations discussed in previous papers." + In particular. this simulation is essentially a higher resolution version of the one initially discussed in ?..," In particular, this simulation is essentially a higher resolution version of the one initially discussed in \citet{evans89}." + Two snapshots of the integrated density profile of the star are shown in the lower left panels of Fig. , Two snapshots of the integrated density profile of the star are shown in the lower left panels of Fig. \ref{fig:image}( ( +αι). at two ditferen times. that is when the star is at pericentre and when it is a roughly two times the pericentre distance. after the encounter.,"a,b), at two different times, that is when the star is at pericentre and when it is at roughly two times the pericentre distance, after the encounter." + The overall structure of the star looks qualitatively similar to the one shown in ?.., The overall structure of the star looks qualitatively similar to the one shown in \citet{evans89}. + It is interesting to notice that at pericentre the star is already quite distorted with respect to its initial configuration and in particular it has expanded somewhat (recall that its initial radius is | in code units)., It is interesting to notice that at pericentre the star is already quite distorted with respect to its initial configuration and in particular it has expanded somewhat (recall that its initial radius is 1 in code units). + This occurs because. in isolation. the star is in hydrostatic equilibrium between its pressure and its self-gravity.," This occurs because, in isolation, the star is in hydrostatic equilibrium between its pressure and its self-gravity." + As the star approaches the black hole the tidal tield etfectively acts as to reduce the stellar gravity. making pressure forces unbalanced and therefore ‘inflating’ the star.," As the star approaches the black hole the tidal field effectively acts as to reduce the stellar gravity, making pressure forces unbalanced and therefore `inflating' the star." + This ettect is expected to be more significant for small than for large y., This effect is expected to be more significant for small than for large $\gamma$. + This reflects the fact that the radius of a polytrope with small y is more sensitive to the effective gravity., This reflects the fact that the radius of a polytrope with small $\gamma$ is more sensitive to the effective gravity. + A more quantitative comparison can be done by looking at the distribution of specitic energies of the disrupted star., A more quantitative comparison can be done by looking at the distribution of specific energies of the disrupted star. + This is shown in Fig., This is shown in Fig. + 5 at four ditferent times during the simulations: at |=0 (upper left panel). at pericentre (upper right). and after the encounter. when the star is roughly at four times the pericentre distance (lower left) and ten times the pericentre distance (lower right).," \ref{fig:evans} + at four different times during the simulations: at $t=0$ (upper left panel), at pericentre (upper right), and after the encounter, when the star is roughly at four times the pericentre distance (lower left) and ten times the pericentre distance (lower right)." + For ease of comparison with ?.. only for this plot we have used a logarithmie scale for the distribution.," For ease of comparison with \citet{evans89}, only for this plot we have used a logarithmic scale for the distribution." + It can be seen that initially the distribution is very narrow and centered at e=O0. which just reflect the fact that the whole star is initially on a parabolic orbit.," It can be seen that initially the distribution is very narrow and centered at $\epsilon=0$, which just reflect the fact that the whole star is initially on a parabolic orbit." + As the star approaches the black hole. the distribution becomes wider and indeed approaches the width predicted by the simple analysis of Section 2 (which is equal to unity in the units adopted here).," As the star approaches the black hole, the distribution becomes wider and indeed approaches the width predicted by the simple analysis of Section 2 (which is equal to unity in the units adopted here)." + The lower left panel. in particular. showing the distribution at four times the pericentre. compares almost exactly with the distribution shown by ? (their fig.," The lower left panel, in particular, showing the distribution at four times the pericentre, compares almost exactly with the distribution shown by \citet{evans89} (their fig." + 3). confirming that indeed our simulations replicate accurately their results.," 3), confirming that indeed our simulations replicate accurately their results." + However. one can see that the density distribution keeps evolving until the star is at roughly 10 pericentre distances. where it finally settles down in the configuration shown in the lower right panel of Fig. 5..," However, one can see that the density distribution keeps evolving until the star is at roughly 10 pericentre distances, where it finally settles down in the configuration shown in the lower right panel of Fig. \ref{fig:evans}." + We thus see that the distribution is characterized by a central peak at lower energies. followed by two ‘wings’ at larger energies.," We thus see that the distribution is characterized by a central peak at lower energies, followed by two `wings' at larger energies." + The presence of a central peak is expected based on the analytical model described above., The presence of a central peak is expected based on the analytical model described above. + The wings. on the other hand. refer to the stellar material at the surface of the star. which at pericentre is somewhat distorted from its initially spherical shape (as ean be seen in Fig. 4..," The wings, on the other hand, refer to the stellar material at the surface of the star, which at pericentre is somewhat distorted from its initially spherical shape (as can be seen in Fig. \ref{fig:image}," + lower left panel) and would obviously show some discrepancies with respect to the simple “spherical” model of Section 2., lower left panel) and would obviously show some discrepancies with respect to the simple `spherical' model of Section 2. + Fig., Fig. + 6 (solid line) shows the distribution of specitic energies averaged over 10 time units. when the stars has reached ~20 pericentre distances and the distribution has settled down.," \ref{fig:spec1} (solid line) shows the distribution of specific energies averaged over 10 time units, when the stars has reached $\sim 20$ pericentre distances and the distribution has settled down." + This is compared with the prediction of the analytical model of Section 2 (cf., This is compared with the prediction of the analytical model of Section 2 (cf. + Fig. 2..," Fig. \ref{fig:analytic}," + left panel). which is shown with a dashed line.," left panel), which is shown with a dashed line." + Since the profiles are all normalized to |. in order to compare the shape of the distribution at the peak. we have scaled down the analytical," Since the profiles are all normalized to 1, in order to compare the shape of the distribution at the peak, we have scaled down the analytical" +"Since the WFPC2 fields only cover about half the area of the ACS fields, some objects will only have three-band photometry (BV I), while others will have all four colors.","Since the WFPC2 fields only cover about half the area of the ACS fields, some objects will only have three-band photometry $BVI$ ), while others will have all four colors." + Objects that satisfy the three criteria listed above are considered as star cluster candidates in the rest of the paper., Objects that satisfy the three criteria listed above are considered as star cluster candidates in the rest of the paper. +" However, as found in many previous studies, there is no unique combination of objective criteria that can lead to a successful detection of bona-fide clusters and no false detections."," However, as found in many previous studies, there is no unique combination of objective criteria that can lead to a successful detection of bona-fide clusters and no false detections." + Our cluster candidates were therefore visually inspected to determine whether they resemble star clusters., Our cluster candidates were therefore visually inspected to determine whether they resemble star clusters. +" Based on this, we classified the cluster candidates into three categories: Accepted, Suspected, and Rejected."," Based on this, we classified the cluster candidates into three categories: Accepted, Suspected, and Rejected." + Figure 3 presents some examples of each category., Figure \ref{fig:rejects} presents some examples of each category. +" In this figure, the first row presents the Accepted objects, which are clearly extended objects with normal measured sizes and magnitudes."," In this figure, the first row presents the Accepted objects, which are clearly extended objects with normal measured sizes and magnitudes." +" The second row presents the Suspected objects, where the size/magnitude measurements may be affected by crowding, where the shape appears irregular, or where the contrast against the background is not strong."," The second row presents the Suspected objects, where the size/magnitude measurements may be affected by crowding, where the shape appears irregular, or where the contrast against the background is not strong." + The last (third) row presents examples of the Rejected objects., The last (third) row presents examples of the Rejected objects. +" Table 3 summarizes the total number of objects detected that have size measurements (2""7 column), the total number of objects with three-band photometry and have sizes over the limits imposed (3""7 column), the total number of accepted objects with three- and four band photometry (4 and 5' columns), the total number of suspected objects with three- and four band photometry (6* and 7* columns), and the total number of rejected objects (813 column)."," Table \ref{tab:clustersdetected} summarizes the total number of objects detected that have size measurements $2^{nd}$ column), the total number of objects with three-band photometry and have sizes over the limits imposed $3^{rd}$ column), the total number of accepted objects with three- and four band photometry $4^{th}$ and $5^{th}$ columns), the total number of suspected objects with three- and four band photometry $6^{th}$ and $7^{th}$ columns), and the total number of rejected objects $8^{th}$ column)." + Shaded areas are the total numbers per galaxy., Shaded areas are the total numbers per galaxy. +" Figure 4 shows two-color diagrams for accepted plus suspected clusters with four band photometry (all the fields combined per galaxy), corrected for foreground extinction with the values presented in Table 1.."," Figure \ref{fig:twoc-obs} shows two-color diagrams for accepted plus suspected clusters with four band photometry (all the fields combined per galaxy), corrected for foreground extinction with the values presented in Table \ref{tab:setparam}." +" Overplotted is a theoretical track that a cluster will follow between 4 Myr and 1 Gyr using Galev models (?),, assuming LMC metallicity and no extinction."," Overplotted is a theoretical track that a cluster will follow between 4 Myr and 1 Gyr using Galev models \citep{andersfritze03}, assuming LMC metallicity and no extinction." +" We see that the clusters generally tend to align with the model sequence, but with significant scatter around it."," We see that the clusters generally tend to align with the model sequence, but with significant scatter around it." + Below we investigate to what extent this scatter may come from stochastic color variations due to random sampling of the stellar IMF., Below we investigate to what extent this scatter may come from stochastic color variations due to random sampling of the stellar IMF. +3d) 95 at.;,3d) 95 at.; +" in (3a), substitute an H atom to the CH3 group attached to the O-capped pentagon; 3e) 95 at.;"," in (3a), substitute an H atom to the $_{3}$ group attached to the O-capped pentagon; 3e) 95 at.;" +" in (3a), substitute an H atom to the CH3 group attached to the CH2-capped trio; 3f) 102 at.;"," in (3a), substitute an H atom to the $_{3}$ group attached to the $_{2}$ -capped trio; 3f) 102 at.;" +" in (3a), replace the O-bridges with short CH» chains."," in (3a), replace the O-bridges with short $_{2}$ chains." + Figure 11 displays the concatenated spectra of the 4 families of composite structures., Figure 11 displays the concatenated spectra of the 4 families of composite structures. + Comparison with Fig., Comparison with Fig. + 5 demonstrates the efficiency of the adopted procedure in the way of increasing the density of active lines in the bands that are to be simulated., 5 demonstrates the efficiency of the adopted procedure in the way of increasing the density of active lines in the bands that are to be simulated. +" Although there is room for further improvement in this direction, e.g. by extending the list of families and variants in each family, it is instructive, at this stage, to try and produce a synthetic spectrum for comparison with observed UIBs."," Although there is room for further improvement in this direction, e.g. by extending the list of families and variants in each family, it is instructive, at this stage, to try and produce a synthetic spectrum for comparison with observed UIBs." +" In the dust model envisioned here, the UIB spectrum is the sum of contributions from all the structures described above."," In the dust model envisioned here, the UIB spectrum is the sum of contributions from all the structures described above." +" Although, the emission spectrum depends on the excitation process, we assume, here, for simplicity, that it is"," Although, the emission spectrum depends on the excitation process, we assume, here, for simplicity, that it is" +extinction law for Cepheids in NGC 5128 based solely on observations of SN 1986G is not favoured.,extinction law for Cepheids in NGC 5128 based solely on observations of SN 1986G is not favoured. + The classical Cepheid distance to NGC 5128 disagrees with other indicators by ~—20% by2007)mainBodyCitationEnd1125]ha09., The classical Cepheid distance to NGC 5128 disagrees with other indicators by $\simeq -20$ by. +" The distances cited above should be interpreted cautiously, irrespective of the aforementioned discrepancy."," The distances cited above should be interpreted cautiously, irrespective of the aforementioned discrepancy." +" The Type II Cepheid estimate exhibits small statistics and large uncertainties, as expected."," The Type II Cepheid estimate exhibits small statistics and large uncertainties, as expected." +" The distances computed for the classical Cepheids exhibit a dependence on colour and CCD chip (§4.2,, Fig. 5))."," The distances computed for the classical Cepheids exhibit a dependence on colour and CCD chip \ref{asources}, , Fig. \ref{fig9}) )." + Additional concerns arise because that population is amongst the most obscured in the extragalactic sample (§4.2))., Additional concerns arise because that population is amongst the most obscured in the extragalactic sample \ref{asources}) ). +" It has been argued that metal-rich classical Cepheids may exhibit a shallower steeper) Wesenheit slope than metal-poor ones, thereby introducing a potential source of uncertainty into the present analysis since the chemical composition of the Cepheids in NGC 5128 is unknown."," It has been argued that metal-rich classical Cepheids may exhibit a shallower steeper) Wesenheit slope than metal-poor ones, thereby introducing a potential source of uncertainty into the present analysis since the chemical composition of the Cepheids in NGC 5128 is unknown." +" However, a plot of the Wesenheit slopes inferred from ground-based observations of classical Cepheids in the Milky Way, LMC, NGC 6822, SMC, and IC 1613, demonstrates that the galaxies are characterized by a common slope over a sizeable abundance baseline (Fig. 2,,"," However, a plot of the Wesenheit slopes inferred from ground-based observations of classical Cepheids in the Milky Way, LMC, NGC 6822, SMC, and IC 1613, demonstrates that the galaxies are characterized by a common slope over a sizeable abundance baseline (Fig. \ref{fig2}," + a=—3.34+0.08(20) A[Fe/H]~ 1)., $\alpha=-3.34\pm0.08(2\sigma)$ $\Delta$ $\simeq1$ ). + The slope of the Wesenheit function is therefore insensitive to metallicity to within the uncertainties., The slope of the Wesenheit function is therefore insensitive to metallicity to within the uncertainties. + The contrasting interpretations and evidence presented by and should be considered., The contrasting interpretations and evidence presented by and should be considered. +" The Galactic calibration employed to secure the distance to NGC 5128 and construct figure 2 is based in part on HST parallaxes for 10 nearby classical Cepheids, which anchored the Milky Way calibration."," The Galactic calibration employed to secure the distance to NGC 5128 and construct figure \ref{fig2} is based in part on HST parallaxes for 10 nearby classical Cepheids, which anchored the Milky Way calibration." +" questioned the reliability of the HST parallaxes since the resulting period-My,; relations inferred from that sample do not match their functions2004),, which were constructed from the best available data at the time."," questioned the reliability of the HST parallaxes since the resulting $M_{V,I}$ relations inferred from that sample do not match their functions, which were constructed from the best available data at the time." +" Their relations were derived prior to the publication of the HST parallaxes and the parameters for longer-period classical Cepheids tied to Galactic associations have since been revised2010),, although continued work is needed to secure new calibrators and revise existing The implied assertion that the HST parallaxes are awry is not supported by the results of or figure 2.."," Their relations were derived prior to the publication of the HST parallaxes and the parameters for longer-period classical Cepheids tied to Galactic associations have since been revised, although continued work is needed to secure new calibrators and revise existing The implied assertion that the HST parallaxes are awry is not supported by the results of or figure \ref{fig2}." + A central conclusion of was that the classical Cepheid period-luminosity relation tied to the HST sample is in agreement with that inferred from cluster Cepheids., A central conclusion of was that the classical Cepheid period-luminosity relation tied to the HST sample is in agreement with that inferred from cluster Cepheids. +" Moreover, the slope of the Wesenheit function inferred from theHST parallaxes matches that of"," Moreover, the slope of the Wesenheit function inferred from theHST parallaxes matches that of" +Researchers use (he term “escape traction” in several mocdel-depencdent wavs.,"Researchers use the term “escape fraction"" in several model-dependent ways." + The most conceptually straightlorwarel definition is (he number of ionizing photons escaping (he galaxy divided by the total number of ionizine photons emitted by stars within il. ie. Li. = Nose δομή.," The most conceptually straightforward definition is the number of ionizing photons escaping the galaxy divided by the total number of ionizing photons emitted by stars within it, i.e., $_{esc}$ = $_{esc}$ $_{emit}$." + Llowever. to avoid anv dependence on models. theobserved limit of 1500 to 900 {flux is sometimes euoted. for comparison with (he value which would be expected if all ionizing photons escapecl.," However, to avoid any dependence on models, the limit of 1500 to 900 flux is sometimes quoted, for comparison with the value which would be expected if all ionizing photons escaped." + CastellanosandDiaz(2002) used photoionization models of well studied extragalactic eiant II II regions and predicted escape fractions of ionizing photons < Li. 5 with total escape fractions Li. >20%.," In a recent study of the influence of supershells and galactic outflows, \citet{fuj02} conclude that starburst galaxies may have played an important role in ionizing the universe at z $>$ 5 with total escape fractions $_{esc}$ $>$." + The simple theoretical picture of a calm. uniform disk galaxy. fully shrouded in I I aud opaque to jionizing photons. is unlikely to be realistic. particularly in Cae vounger Universe.," The simple theoretical picture of a calm, uniform disk galaxy, fully shrouded in H I and opaque to ionizing photons, is unlikely to be realistic, particularly in the younger Universe." + In the Milkv Wax. radio maps reveal large-scale bubbles and chimuevs (hat appear to have been blasted (hrough the interstellar gas of the disk by (he combined effects of many supernovae and vigorous stellar winds (Lleiles 1937: also in M82 Devine Bally 1999).," In the Milky Way, radio maps reveal large-scale bubbles and chimneys that appear to have been blasted through the interstellar gas of the disk by the combined effects of many supernovae and vigorous stellar winds (Heiles 1987; also in M82 Devine Bally 1999)." + These evacuated or ionized holes max open up escape paths for ionizine photons heading out of the disk 1998).," These evacuated or ionized holes may open up escape paths for ionizing photons heading out of the disk \citep{roz99,kun98}." +. Detection of ionized gas well above the plane of (he Milky Way (the “Revnolds laver and the Magellanic Stream) has been interpreted as meaning that 5 - of hvdrogen ionizing photons escape [rom our own galaxy (Reynolds. 1999).," Detection of ionized gas well above the plane of the Milky Way (the “Reynolds layer"" and the Magellanic Stream) has been interpreted as meaning that 5 - of hydrogen ionizing photons escape from our own galaxy \citep{rey85,bla99}." +. It is also possible that the detection of strong ionized ealeium absorption along most lines of sieht through the Milky Way. halo requires (hie escape of a substantial number of ionizing photons [rom the disk (Savage1985)., It is also possible that the detection of strong ionized calcium absorption along most lines of sight through the Milky Way halo requires the escape of a substantial number of ionizing photons from the disk \citep{sav88}. +. WUT obtained strong upper limits on the Lyman conünuunm escaping from 3 low-redshift galaxies (and less sensitive observations of a fourth galaxy) (Leitherer.HeckmanandLowenthal 1995).," HUT obtained strong upper limits on the Lyman continuum escaping from 3 low-luminosity, low-redshift galaxies (and less sensitive observations of a fourth galaxy) \citep{lei95}." +". After correction for Milkv. way absorption. these observations translate into five-o [lux upper limits of F, ES 1x10 Pergs bem2 A4! (IIurwitz.JelinskyandDixon1997:Ferguson2001)."," After correction for Milky way absorption, these observations translate into $\sigma$ flux upper limits of $_{\lambda ~ 900\AA}$ $<$ $ \times $ $^{-15}$ ergs $^{-1}$ $^{-2}$ $\AA^{-1}$ \citep{hur97,fer01}." +. Dased on models. the implied fraction of escaping Lyman continuum photons L4. « 8 (five-o. upper limits).," Based on models, the implied fraction of escaping Lyman continuum photons $_{esc}$ $<$ 8 — $\sigma$ upper limits)." + FUSE has, FUSE has +A132 where the light is probably dominated by a single bright AGD-tip star.,M32 where the light is probably dominated by a single bright AGB-tip star. + It can be anticipated (that. when compared with blends. unblended sources (1) will be fainter. ancl (2) will be in areas of lower projected stellar density.," It can be anticipated that, when compared with blends, unblended sources (1) will be fainter, and (2) will be in areas of lower projected stellar density." + The brightnesses and local backeround levels of all fourteen locations were measured [rom the A images discussed by Dawvidge et al. (, The brightnesses and local background levels of all fourteen locations were measured from the $K$ images discussed by Davidge et al. ( +2000).,2000). + The locations with broad lines tend to be almost 2x brighter in A than those with narrow lines. and are in regions where (he background within 0.2 arcsec of the source is ~LOM higher.," The locations with broad lines tend to be almost $2 \times$ brighter in $K$ than those with narrow lines, and are in regions where the background within 0.2 arcsec of the source is $\sim 10\%$ higher." + With the caveat that a large lraction of the brightest stars are LPVs (Davicdee Rieaut 2004). the sources with low velocity dispersions thus tend to be fainter than the hieh velocity-dispersion sources aud are located in areas with lower background evels. as expected if (hev are not blends of many objects will comparable brightness.," With the caveat that a large fraction of the brightest stars are LPVs (Davidge Rigaut 2004), the sources with low velocity dispersions thus tend to be fainter than the high velocity-dispersion sources and are located in areas with lower background levels, as expected if they are not blends of many objects with comparable brightness." +" While (he sample of single stars detected here is ΒΙΑ, modest insights can be gained into the bright stellar content near the center of N22."," While the sample of single stars detected here is small, modest insights can be gained into the bright stellar content near the center of M32." + The objects that are dominated by one or two bright stars are almost certainly evolving near the ACD-tip. and these all have an ΔΕΟ spectral (vpe.," The objects that are dominated by one or two bright stars are almost certainly evolving near the AGB-tip, and these all have an M5III spectral type." + These spectral (wpe measurements are not biased by a single strong feature. such as the (2.0) CO band head.," These spectral type measurements are not biased by a single strong feature, such as the (2,0) $^{12}$ CO band head." + The uniformity in spectral (wpe is consistent with the distinct red cut-off in the CK.—N) CMD of the central regions of M22 found by Daowvidge et al. (," The uniformity in spectral type is consistent with the distinct red cut-off in the $(K, H-K)$ CMD of the central regions of M32 found by Davidge et al. (" +2000).,2000). + It also suggests that the J—A color of the AGD-tip near the center ol M32 is consistent with that at large radii. indicating that the homogeneous nature of the AGB sequence in M32 measured by Davidge Jensen (2007) extends into the central arcsec ol the galaxy.," It also suggests that the $J-K$ color of the AGB-tip near the center of M32 is consistent with that at large radii, indicating that the homogeneous nature of the AGB sequence in M32 measured by Davidge Jensen (2007) extends into the central arcsec of the galaxy." + The spectra also suggest that there are modest star-to-star metallicity differences among the brightest stars in M32., The spectra also suggest that there are modest star-to-star metallicity differences among the brightest stars in M32. + When the narrow-line spectra are cross-correlated wilh a reference spectrum in the 2.1— 2.28/0n interval. one source 1 has a significantly lower peak in the correlation function. by an amount that suggests it has a metallieitv that is zz0.2 dex lower than (he other stars.," When the narrow-line spectra are cross-correlated with a reference spectrum in the $2.1 - 2.28\mu$ m interval, one source – 1 – has a significantly lower peak in the correlation function, by an amount that suggests it has a metallicity that is $\approx 0.2$ dex lower than the other stars." + Metallicity differences of (his size Fall well within the spread seen in other spheroidal svstems. ancl are consistent with the spread in J—A color seen amongst AGB stars in the outer region of M32 (Davidge Jensen 2007).," Metallicity differences of this size fall well within the spread seen in other spheroidal systems, and are consistent with the spread in $J-K$ color seen amongst AGB stars in the outer region of M32 (Davidge Jensen 2007)." + Many of the bright ACID stars in M32 are LPVs (Davidee Bigaut 2004). and there is an obvious bias to detect these objects when they are brightest.," Many of the bright AGB stars in M32 are LPVs (Davidge Rigaut 2004), and there is an obvious bias to detect these objects when they are brightest." + Observations at future epochs imav [ind new locations near the center of M32 that are dominated by single LPVs that are near the peak of their light variation. bul were in a part of their light curve that rendered (hem too faint to be resolved in the present data.," Observations at future epochs may find new locations near the center of M32 that are dominated by single LPVs that are near the peak of their light variation, but were in a part of their light curve that rendered them too faint to be resolved in the present data." + By Che same token. (he sources found here may not be detected if they are variable and in a faint phase of their light cvele at (he time of fature observation.," By the same token, the sources found here may not be detected if they are variable and in a faint phase of their light cycle at the time of future observation." + This raises the possibility that (he sample of stars near the center of M32 can be increased by observing al different. epochs., This raises the possibility that the sample of spectroscopically-identified stars near the center of M32 can be increased by observing at different epochs. + This will provide a larger sample of objects from which to measure. lor example. a more," This will provide a larger sample of objects from which to measure, for example, a more" +supermassive blackhole from a small seed blackhole.,supermassive blackhole from a small seed blackhole. + Without any further assumption. azz4 is consistent with the range of the decay. rate obtained by observational data [from cooling flow clusters.," Without any further assumption, $\alpha +\approx 4$ is consistent with the range of the decay rate obtained by observational data from cooling flow clusters." +" In this article. we first eive a brief review on three popular analytic models that explain the Alpi,—e relation."," In this article, we first give a brief review on three popular analytic models that explain the $M_{BH,f}- \sigma$ relation." + Then we will give a detailed description of our model and compare il wilh other existing models., Then we will give a detailed description of our model and compare it with other existing models. +" Ixing(2003) presented a model to explain the Mjj,—& relation."," \citet{King2} presented a model to explain the $M_{BH,f}-\sigma$ relation." + He assumed that the eas density profile of a protogalaxy is isothermal (p~r7) (INing2003.2005)..," He assumed that the gas density profile of a protogalaxy is isothermal $\rho \sim r^{-2}$ ) \citep{King2,King}." +" Therelore {he gas mass inside racius /2 is: where /,20.16 is the cosmological ratio of baryon to total mass. assumed to be the same in a galaxy. and the Virial Theorem is used."," Therefore the gas mass inside radius $R$ is: where $f_g \approx 0.16$ is the cosmological ratio of baryon to total mass, assumed to be the same in a galaxy, and the Virial Theorem is used." + Consider a super-Ecdineton accretion onto a seed blackhole., Consider a super-Eddington accretion onto a seed blackhole. + The accretion feedback. produces a momentunr-diiven superbubble that sweeps ambient gas into a thin shell which expands to the galaxy., The accretion feedback produces a momentum-driven superbubble that sweeps ambient gas into a thin shell which expands to the galaxy. + The equation of molion 19 where Legg=μμπαλοί. wilh & the opacity aud Αμ.) the mass of the central blackhole at time /.," The equation of motion is where $L_{edd}=4 \pi G M_{BH}(t)c/ \kappa$, with $\kappa$ the opacity and $M_{BH}(t)$ the mass of the central blackhole at time $t$ ." + Integrating (vice and assuming >GMy¢/o7. one gels: where Ry= Ral R=Ry. with My some large radius CGMpy /o7). and πι”.," Integrating twice and assuming $R \gg +GM_{BH,f}/ \sigma^2$, one gets: where $\dot{R}_0=\dot{R}$ at $R=R_0$, with $R_0$ some large radius $\gg +GM_{BH,f}/ \sigma ^2$ ), and $M_{\sigma} \equiv f_g \kappa \sigma^4/ +\pi G^2$ ." +" Therefore. the maximum radius 2, is given by When μμ) approaches ζω. P4, becomes very large such that the cooling of the shocked wind. is. inellicient.n asthe cooling. (me. /,,,;,4XΠΠL7 and the accretion. is. stopped as"," Therefore, the maximum radius $R_{\rm max}$ is given by When $M_{BH}(t)$ approaches $M_{\sigma}$, $R_{\rm max}$ becomes very large such that the cooling of the shocked wind is inefficient asthe cooling time $t_{cooling} \propto R^2$ and the accretion is stopped as" +‘This is an estimate of the time for a nuclide to settle down over a pressure scale height a negative value means that the nuclide ascends.,This is an estimate of the time for a nuclide to settle down over a pressure scale height — a negative value means that the nuclide ascends. +" This timescale is typically around a few vears lor the envelope and. about 10"" vr for the outer crust (p«107 ο ) for Silicon-28. in a background. of Iron-56.", This timescale is typically around a few years for the envelope and about $10^6$ yr for the outer crust $\rho < 10^{12}$ g $^{-3}$ ) for Silicon-28 in a background of Iron-56. +" In. particular until the bulk of the Niekel-56 has decaved the settling time for Silicon-28 is much [arger because 41»Z,—ALZo1: consequently. the nucleons dillerentiate gravitationallv after the nuclear reactions ellectively cease. Le. ZeaTu"," In particular until the bulk of the Nickel-56 has decayed the settling time for Silicon-28 is much larger because $A_2Z_1-A_1Z_2 \ll 1$; consequently, the nucleons differentiate gravitationally after the nuclear reactions effectively cease, i.e. $\tau_{\rm rxn} < \tau_s$." + For the modified. Urea case we also caleulated the reaction rate time scales by making use of the subroutines intorch., For the modified Urca case we also calculated the reaction rate time scales by making use of the subroutines in. + Each of the rate calculations depends only on the input temperature and the densities of the various species., Each of the rate calculations depends only on the input temperature and the densities of the various species. + As there are many cilferent wavs to make a specific isotope. e. 77 8L the rates which lead to the creation of the isotope are added together to getthe timescale of the reaction rate. Tyxn-," As there are many different ways to make a specific isotope, e.g $^{28}$ Si, the rates which lead to the creation of the isotope are added together to getthe timescale of the reaction rate, $\tau_{\rm rxn}$." + In order to calculate. the abundance. of the alpha particles and the other species we make use of the nuclear statistical Saha equations as implemented innge., In order to calculate the abundance of the alpha particles and the other species we make use of the nuclear statistical Saha equations as implemented in. + We assume that a particular species freezes out of equilibrium. when the reaction timescale exceeds the cooling timescale., We assume that a particular species freezes out of equilibrium when the reaction timescale exceeds the cooling timescale. + The abundance in nuclear statistical equilibrium at the freeze out temperature gives an alternative estimate of the final abundance of the nuclides., The abundance in nuclear statistical equilibrium at the freeze out temperature gives an alternative estimate of the final abundance of the nuclides. + In order to determine the expected. composition. of the aatmosphoere. in the cases of the modified Urea and the thick crust. we examined a density of 10 g/em.," In order to determine the expected composition of the atmosphere, in the cases of the modified Urca and the thick crust we examined a density of $10^7{\rm g/cm}^3$ ." + For the thin crust a density of 10&/em? would. ervstallize before any of the isotopes had time to reach the surface. so we examined a density of 10g/cm.," For the thin crust a density of $10^7{\rm g/cm^3}$ would crystallize before any of the isotopes had time to reach the surface, so we examined a density of $10^6{\rm + g/cm^3}$." + The results from the nuclear reaction network are compared with those of a semi-analvtic [reeze-out calculation in the modified Urea case., The results from the nuclear reaction network are compared with those of a semi-analytic freeze-out calculation in the modified Urca case. + Each of the three cases are discussed below., Each of the three cases are discussed below. + At a density of 10g/eni the corresponding pressure is: 1077. dvne/em?., At a density of $10^7{\rm g/cm}^3$ the corresponding pressure is: $\times 10^{24}$ $^2$. + At this. pressure the column. density to the surface is: 4.4 l00g/em.," At this pressure the column density to the surface is: 4.4 $\times 10^9 {\rm + g/cm}^2$." +" DonThe resulting. required. minimun mass fraction required for an isotope to be optically thick on the surface I 3210i,"," The resulting required minimum mass fraction required for an isotope to be optically thick on the surface is: $\times +10^{-10}$." + Isotopes with a mass fraction greater than 2.3.10lU will have a surface density of Lefem?., Isotopes with a mass fraction greater than $\times 10^{-10}$ will have a surface density of ${\rm g/cm}^2$. + The lightest elements to be optically thick on the surface and have time to reach the surface before crystallization of the laver occurs. are shown in Figure 2.. where the horizontal line indicates the minimum mass fraction required to be optically thickon the surface.," The lightest elements to be optically thick on the surface and have time to reach the surface before crystallization of the layer occurs are shown in Figure \ref{fig:surf7}, where the horizontal line indicates the minimum mass fraction required to be optically thickon the surface." +" The lightest elements to rise to the surface whichare optically thick are: ο οἱ, n EXE78. n *!8. and ""P Ar."," The lightest elements to rise to the surface whichare optically thick are: $^{28}$ Si, $^{32}$ S, $^{34}$ S, and $^{36}$ Ar." + In particular the abundance of LON77 Si Gesis about 3..10.) soalaver ~IO0g/cnr 3 of silicon [ies on the surface of the star., In particular the abundance of $^{28}$ Si is about $3\times 10^{-9}$ so a layer $\sim 10$ $^{3}$ of silicon lies on the surface of the star. + Using the steps outlined in £4. we have calculated the cooling (τι). settling (τι). and the nuclear reaction (7534) timescales or thecase of Si.," Using the steps outlined in \ref{freezesteps} we have calculated the cooling $\tau_c$ ), settling $\tau_s$ ), and the nuclear reaction $\tau_{\rm rxn}$ ) timescales for thecase of $^{28}$ Si." + The results of these caleulations are displayed in Figure 6.., The results of these calculations are displayed in Figure \ref{fig:timfreeze}. . +" Phese calculations compare the age of he neutron star to the settling. ervstallization temperature. creation and destructiontimescales of οἱ for two densities: 191g/cm and 10127gem""."," These calculations compare the age of the neutron star to the settling, crystallization temperature, creation and destructiontimescales of $^{28}$ Si for two densities: $10^7 \; +\rm{g/cm}^3$ and $10^{12} \; \rm{g/cm}^3$." +" The temperatures at. which he lavers crystallize are 4.8«10 lx. anc 2.2 Lo"". [or he densities o£ 10g/em? and LOMg/em. respectively."," The temperatures at which the layers crystallize are $4.8\times 10^7$ K and $2.2\times 10^9$ K, for the densities of $10^7{\rm g/cm^3}$ and $10^{12}{\rm g/cm^3}$, respectively." + The creation and destruction rates are dInX;/df. where NX; is the abundance of the “Si isotope.," The creation and destruction rates are $d\ln X_i/dt$, where $X_i$ is the abundance of the $^{28}$ Si isotope." + These rates are calculated »v using the routines in to determine the energy release per unit mass. these are then multiplied. by. the abundances calculated from the code.," These rates are calculated by using the routines in to determine the energy release per unit mass, these are then multiplied by the abundances calculated from the code." + The abundances were also calculated using the nuclear Saha equation and are the output of the routine., The abundances were also calculated using the nuclear Saha equation and are the output of the routine. + Thetwo different methods for calculating the relative abundances. the output [rom and using are clisplaved in Figure 2..," Thetwo different methods for calculating the relative abundances, the output from and using are displayed in Figure \ref{fig:tde}. ." + Lt is clearthat the results from do not follow nuclear statistical equilibrium precisely., It is clearthat the results from do not follow nuclear statistical equilibrium precisely. + 6 , \ref{fig:timfreeze} +Finally. we have three stars in common with ?..,"Finally, we have three stars in common with \citet{Asplundetal2006}." + Using Sy = 0 we obtain temperatures for two of the stars that are hotter than ? by 97 K and 151 K. The third star is CD—3371173. for which we calculated a negative temperature correction. and which is cooler in our study by 97 K. The temperatures for all three stars are hotter in our study than in ? when using Sy = I.," Using $\rm S_{H}$ = 0 we obtain temperatures for two of the stars that are hotter than \citet{Asplundetal2006} by 97 K and 151 K. The third star is $-$ $^{\circ}$ 1173, for which we calculated a negative temperature correction, and which is cooler in our study by 97 K. The temperatures for all three stars are hotter in our study than in \citet{Asplundetal2006} when using $\rm S_{H}$ = 1." + Here the average difference is 110 K. values ranging from 37 K to 207 K. If the ? temperatures are affected by NLTE. as stated by ? who expects a 100 K increase in Balmer line temperatures. this would bring the 7. scales back into agreement.," Here the average difference is 110 K, values ranging from 37 K to 207 K. If the \citet{Asplundetal2006} temperatures are affected by NLTE, as stated by \citet{Barklem2007} who expects a 100 K increase in Balmer line temperatures, this would bring the $T_{\rm eff}$ scales back into agreement." + Another problem facing the Balmer line method is the effects of granulation. due to convection. on the line wings (2)..," Another problem facing the Balmer line method is the effects of granulation, due to convection, on the line wings \citep{Ludwigetal2009}." + It has been found (Bonifacio — private communication) that inclusion. of these effects would increase the effective temperatures derived with this method., It has been found (Bonifacio – private communication) that inclusion of these effects would increase the effective temperatures derived with this method. + In particular a value of Ty = 6578 K has been found for the star LP815—43., In particular a value of $T_{\rm eff}$ = 6578 K has been found for the star $-$ 43. + Although this is 176 K hotter than our result for the SGB case with Sy = 0. Le. Tay = 6402 K. it is in good agreement with the values Taj = 6522 K (Sy = 1) for the SGB case and 7 = 6551 K (Sy = 0) or Tay = 6607 K (Sy = 1) for the MS ease. calculated in this work.," Although this is 176 K hotter than our result for the SGB case with $\rm S_{H}$ = 0, i.e. $T_{\rm eff}$ = 6402 K, it is in good agreement with the values $T_{\rm eff}$ = 6522 K $\rm S_{H}$ = 1) for the SGB case and $T_{\rm eff}$ = 6551 K $\rm S_{H}$ = 0) or $T_{\rm eff}$ = 6607 K $\rm S_{H}$ = 1) for the MS case, calculated in this work." + We now address the new Li abundances and their effect on the lithium problem., We now address the new Li abundances and their effect on the lithium problem. +" We see that the introduction of NLTE corrections to the 7, scale has led to temperatures that are of order 100 K hotter than LTE temperature scales. with the obvious exception of the ? scale."," We see that the introduction of NLTE corrections to the $T_{\rm eff}$ scale has led to temperatures that are of order 100 K hotter than LTE temperature scales, with the obvious exception of the \citet{MelendezRamirez2004} scale." + This will then lead to an increase in the mean lithium abundance., This will then lead to an increase in the mean lithium abundance. + Table 2. lists A(LI) for the new temperatures., Table \ref{Table2} lists $A$ (Li) for the new temperatures. + With these new Τομ). we calculate a mean Li abundance of A(L1) = 2.19 dex with a scatter of 0.072 dex when using Sy = 0. and A(Li) = 2.21 dex with a scatter of 0.058 dex for the Sy = | case.," With these new $T_{\rm eff}$ 's, we calculate a mean Li abundance of $A$ (Li) = 2.19 dex with a scatter of 0.072 dex when using $\rm S_{H}$ = 0, and $A$ (Li) = 2.21 dex with a scatter of 0.058 dex for the $\rm S_{H}$ = 1 case." + Consistent with the temperature increase. these values are higher than those found by other," Consistent with the temperature increase, these values are higher than those found by other" +NGC9183.,NGC9183. +" The latter appears to be a rather ordered galaxy, although some deviations from regularity were noted (Bosma1981;vanAlbadaetal.1985;Begeman1989)."," The latter appears to be a rather ordered galaxy, although some deviations from regularity were noted \citep{{bosma81}, {vanAlbada}, {Begeman}}." +. The H; column densities do not exceed 5x10??cm so the optical depth is rather small., The $H_I$ column densities do not exceed $5\times 10^{20} cm^{-2}$ so the optical depth is rather small. + The data presented ?in Table 2., The data presented in Table 2. + of Begeman(1989) show a very flat rotation curve for radial distances in the range 1.5’—11’ corresponding to 4.1kpc—29.9kpc., of \cite{Begeman} show a very flat rotation curve for radial distances in the range $1.5' - 11'$ corresponding to $4.1\ kpc - 29.9\ kpc$. + This is the range of radial distances to which the proposed test is applied., This is the range of radial distances to which the proposed test is applied. + The residuals (with respect to the mean value) are plotted in Fig., The residuals (with respect to the mean value) are plotted in Fig. + 2 as function of radial distance in units of arcminutes., 2 as function of radial distance in units of arcminutes. +" Up to 3’, the radial distances are spaced by 0.25’ and later by 0.5’."," Up to 3', the radial distances are spaced by 0.25' and later by 0.5'." +" Since the computation of power Spectra requires even spacings, we omitted the data points at positions 1.75’,2.25’,2.75’ thus there remain overall 20 evenly spaced data points."," Since the computation of power spectra requires even spacings, we omitted the data points at positions $1.75',\ 2.25', \ 2.75'$ thus there remain overall 20 evenly spaced data points." + Note that the uncertainties are (2—3)km/s; substantially smaller than the 15.5 km/s uncertainty in a single measurement (Begeman1989)., Note that the uncertainties are $(2-3)km/s$; substantially smaller than the 15.5 km/s uncertainty in a single measurement \citep{Begeman}. +. This arises from the use of many measurements along the ring and demonstrates the advantage of using a rotation curve rather than a PV data., This arises from the use of many measurements along the ring and demonstrates the advantage of using a rotation curve rather than a PV data. + 'The residual velocity shown in Fig., The residual velocity shown in Fig. +" 2 does seem to exhibit fluctuations, as function of radial distance."," \ref{vel} + does seem to exhibit fluctuations, as function of radial distance." + But one has yet to test whether these fluctuations do indeed represent a large scale turbulence., But one has yet to test whether these fluctuations do indeed represent a large scale turbulence. +" The Mathematica7(2010) software was used to compute the power spectrum of the residual rotation curve velocity as function of the wavenumberwas q=2π/1, with l denoting the corresponding spatial scale."," The \cite{mathematica} software was used to compute the power spectrum of the residual rotation curve velocity as function of the wavenumberwas $q= 2\pi/l$, with $l$ denoting the corresponding spatial scale." +" Because of the cyclic nature of the discrete Fourier transform, the power spectrum is obtained for relative wavenumbers in the range 1--11 with g=1 corresponding {ο=25.8kpc, the largest spatial scale of the turbulence and q=11 corresponds to 2.35kpc, which is about twice the radial spacing between the observations used in the present analysis."," Because of the cyclic nature of the discrete Fourier transform, the power spectrum is obtained for relative wavenumbers in the range $1-11$ with $q=1$ corresponding $l_0=25.8 kpc$, the largest spatial scale of the turbulence and $q=11$ corresponds to $2.35 \ kpc$, which is about twice the radial spacing between the observations used in the present analysis." + To obtain the error bars for the observational power spectrum we performed 104 simulations of “observational” velocity sets., To obtain the error bars for the observational power spectrum we performed $10^4$ simulations of “observational” velocity sets. + At each position a velocity was randomly chosen from a normal distribution with a mean equal to the observational value at this position and a standard deviation equal to the observational uncertainty at this position., At each position a velocity was randomly chosen from a normal distribution with a mean equal to the observational value at this position and a standard deviation equal to the observational uncertainty at this position. +" For each such set, the power spectrum was computed and subsequently the standard deviations, at each wavenumber, of the logarithm of the simulated power spectra."," For each such set, the power spectrum was computed and subsequently the standard deviations, at each wavenumber, of the logarithm of the simulated power spectra." + These standard deviations were taken as the uncertainties in the logarithm of the observational power spectrum of the residual rotation velocity., These standard deviations were taken as the uncertainties in the logarithm of the observational power spectrum of the residual rotation velocity. + The standard deviation of the observational residual rotation velocity of Fig., The standard deviation of the observational residual rotation velocity of Fig. + 2 is 3.6km/s., \ref{vel} is $3.6 km/s$. +" Hence, if it indeed represents a turbulence the latter must be subsonic(in the isotropic case Viurs=V33.66.2 km/s)."," Hence, if it indeed represents a turbulence the latter must be subsonic(in the isotropic case $v_{turb} = \sqrt{3} 3.6 = 6.2 \ km/s$ )." +" The theoretical fit is thus chosen to be a turbulence spectral function with m=11/6.The depth D, along the line of sight and the overall normalization of the function given by Eq. (13))"," The theoretical fit is thus chosen to be a turbulence spectral function with $m=11/6$.The depth D, along the line of sight and the overall normalization of the function given by Eq. \ref{prot}) )" + to minimize the reduced x? value., to minimize the reduced $\chi^2$ value. + The observational power spectrum of the residual rotation curve velocity is shown in Fig., The observational power spectrum of the residual rotation curve velocity is shown in Fig. + 3 together with two such fits., \ref{powers} together with two such fits. + The lower one is the best fit with x?—0.43., The lower one is the best fit with $\chi^2 = 0.43$. +" It has a depth along the line of sight D—7.31kpc translated into a scale height for neutral hydrogen Hy,=1130pc.", It has a depth along the line of sight $D= 7.31 \ kpc$ translated into a scale height for neutral hydrogen $H_{H_I} = 1130 \ pc$. + The law value of x? suggests that the uncertainties in (1989) are probably overestimated., The law value of $\chi^2$ suggests that the uncertainties in \cite{Begeman} are probably overestimated. +" 'This analysis implies that the residuals are consistent with being a manifestation of a subsonic turbulence with a largest scale of 25.8 pc, a turbulent velocity of 3.6km/s, and a lifetime scale of the order of 7Gyr."," This analysis implies that the residuals are consistent with being a manifestation of a subsonic turbulence with a largest scale of $25.8 \ pc$ a turbulent velocity of $3.6 km/s$ , and a lifetime scale of the order of $7 Gyr$." + About of the x? value is contributed by the point at relative wavenumber q=7 corresponding to a scale of about 3.7kpc., About of the $\chi^2 $ value is contributed by the point at relative wavenumber $q=7$ corresponding to a scale of about $3.7 \ kpc$. + The upper curve in Fig., The upper curve in Fig. + 3 is the best fit to the power spectrum with this point excluded., \ref{powers} is the best fit to the power spectrum with this point excluded. +" It has a X!=0.11, and a depth D=3.78kpc corresponding to a scale height Hy,=584pc."," It has a $\chi^2 = 0.11$, and a depth $D=3.78\ kpc$ corresponding to a scale height $H_{H_I} = 584 \ pc$." + This latter is more consistent with observational values for disk galaxies 2010).., This latter is more consistent with observational values for disk galaxies \citep{Bagetakos}. +" For each of the two fits there is a correlation between the normalization of the fit and the value of D, resulting in a flat dependence of x? on D. Thus,in each case the calculated D and the corresponding scale heightvary in a range of about 43-2096."," For each of the two fits there is a correlation between the normalization of the fit and the value of $D$ , resulting in a flat dependence of $\chi^2$ on D. Thus,in each case the calculated D and the corresponding scale heightvary in a range of about $\pm 20\%$ ." +aabuudance tuto good agreement with observations but leaving the precieted number of ssystenis substantially below the observed uumber.,abundance into good agreement with observations but leaving the predicted number of systems substantially below the observed number. + Tn Gardner ((1997b: GINWH hereafter). we applied the atv.) relation derived [or SCDM to other cosumological models. obtaining more general predictious lor aand aabsorption under the assumption that the relation between halo Ὁ aud gas absorption cross-section was iucdependeut of cosmological parameters.," In Gardner (1997b; GKWH hereafter), we applied the $\alpha(v_c)$ relation derived for SCDM to other cosmological models, obtaining more general predictions for and absorption under the assumption that the relation between halo $v_c$ and gas absorption cross-section was independent of cosmological parameters." + In this paper. we present results of simulatious of several variants of the inflatiou+CDMscenario (see. citealt khw99)) aud improve upon the CIXWH results by using these simulatious to predict aand aabsorptiou iu these moclels.," In this paper, we present results of simulations of several variants of the inflation+CDMscenario (see, \\citealt{khw99}) ) and improve upon the GKWH results by using these simulations to predict and absorption in these models." + We contiuue to use a Press-Schechter based extrapolation (witli the mass function of Jenkinsetal. 2001)) to compute the contribution of sinaller halos to aaud statistics. emploviug au improved methodology that significantly changes the (ΗΛ predictions for absorption by low mass systems.," We continue to use a Press-Schechter based extrapolation (with the mass function of \citealt{jenkins01}) ) to compute the contribution of smaller halos to and statistics, employing an improved methodology that significantly changes the GKHW predictions for absorption by low mass systems." +" Using an improved fittiug procedure. we obtain more accurate error estimates of our fitted a(e,.) to the sinulated data."," Using an improved fitting procedure, we obtain more accurate error estimates of our fitted $\alpha(v_c)$ to the simulated data." + We fud that our largest error iu estimating the universal auinount of aand aabsorptiou arises [rom the uncertainty in the exact c. at which halos cease to harbor these absorbers., We find that our largest error in estimating the universal amount of and absorption arises from the uncertainty in the exact $v_c$ at which halos cease to harbor these absorbers. +" Given the large number of halos at 0,4;2zLOkms1. a simall variation in the exact value or form of this cutoll leads to significant deviatious in the estimation of total aaud aabsorptiou cross sectious."," Given the large number of halos at $v_{c,min} \approx 40\;\vunits$, a small variation in the exact value or form of this cutoff leads to significant deviations in the estimation of total and absorption cross sections." + In lieht of these results. we find that we are not vet able to test the four cosmologies we consider against the observed aud aabuudances.," In light of these results, we find that we are not yet able to test the four cosmologies we consider against the observed and abundances." +" Iustead. we have adopted the approach of determining the value of 0,5, in each moclel that yields best agreement with the observations."," Instead, we have adopted the approach of determining the value of $v_{c,min}$ in each model that yields best agreement with the observations." + The nature of the galaxies that host ssystetus has been a controversial topic for many years., The nature of the galaxies that host systems has been a controversial topic for many years. + Two competing hypotheses lave defined the poles of the debate: the idea that most ssystetus are large. rotating gas disks citealtschiiauno90)). aud the idea that a large fraction of aabsorptiou arises in dwarf galaxies citettvsonss)).," Two competing hypotheses have defined the poles of the debate: the idea that most systems are large, rotating gas disks \\citealt{schiano90}) ), and the idea that a large fraction of absorption arises in dwarf galaxies \\citet{tyson88}) )." + The strongest empirical argument for the chwarl hypothesis is that some imagiug studies reveal sinall galaxies near the lineof sight but uo clear caucliclates for large galaxies produciug the absorption citealtfontana060:: LeBrunetal. 1997: Moller&Warren 1998))., The strongest empirical argument for the dwarf hypothesis is that some imaging studies reveal small galaxies near the lineof sight but no clear candidates for large galaxies producing the absorption \\citealt{fontana96}; ; \citealt{lebrun97}; ; \citealt{moller98}) ). + The recent study of two, The recent study of two +Before proceeding. we make a small correction.,"Before proceeding, we make a small correction." + For clouds. the observed nass function o(AL) represcuts the true ass function at formation «{Al) (ie. the birthrate) weighted bw the lifetime: oC)x(AL (AL).," For clouds, the observed mass function $\psi_o(M)$ represents the true mass function at formation $\psi(M)$ (i.e., the birthrate) weighted by the lifetime: $\psi_o(M) \propto \psi(M)\tau_l(M)$ ." +" We assume. as before. that lifetime is proportional. to crossing. time:: 7;XzxMUD17,2"," We assume, as before, that lifetime is proportional to crossing time: $\tau_l \propto \tau_c \propto M^{(3\alpha - 1)/2}$." +" Thon: the exponcuts of the true aud observed mass functions are related by3=3,(3n1)/2.", Then the exponents of the true and observed mass functions are related by$\beta = \beta_o - (3\alpha - 1)/2$. + Inserting this iuto Equatious (2a)) aud (2b)). we obtain We now evaluate ΤαΊος (2a)]) and (3b)) with )= ly. the observed exponent of the mass functiou of molecular clouds (Rosolowsky2005:Reid&Wilson 2008)..," Inserting this into Equations \ref{beta1e}) ) and \ref{beta1p}) ), we obtain We now evaluate Equations \ref{betastar:energy}) ) and \ref{betastar:momentum}) ) with $\beta_o = -1.7$ , the observed exponent of the mass function of molecular clouds \citep{rosolowsky05b, reid06b, munoz07a, wong08a, fukui08a}." + For coustaut mean surface density (a= 1/2). we Bud 4=Ls in the cuereyv-driven regime and 4=2.0 in the momentumedriven regime.," For constant mean surface density $\alpha = 1/2$ ), we find $\beta_* = -1.8$ in the energy-driven regime and $\beta_* = -2.0$ in the momentum-driven regime." +" These predictions agree nicely with the observed exponents of the mass ""ucetfious of vounsg star clusters. ονm2.0 (with vpical uncertainty A4,z 0.2)."," These predictions agree nicely with the observed exponents of the mass functions of young star clusters, $\beta_* \approx -2.0$ (with typical uncertainty $\Delta\beta_* \approx 0.2$ )." + Our model is clearly idealized.but the scaliugs. aud thus the agreecimeut νου the aud predietedobserved 3... should robust.," Our model is clearly idealized,but the scalings, and thus the agreement between the predicted and observed $\beta_*$, should be robust." + For constaut size (a= 0). however. we find ἐνbe=L.l in ith. the cnerev-driven and imonienutuin-driven reginies. in definite conflict with observations.," For constant size $\alpha = 0$ ), however, we find $\beta_* = -1.1$ in both the energy-driven and momentum-driven regimes, in definite conflict with observations." + The mass function of star clisters older than ~10° vr depends ou the proportion that remain gravitationally bound., The mass function of star clusters older than $\sim 10^7$ yr depends on the proportion that remain gravitationally bound. + This in tur depends on the cticiency of star formation £ and the timescale for ISAD rcmoval Af relative to the crossing time 7.., This in turn depends on the efficiency of star formation ${\cal E}$ and the timescale for ISM removal $\Delta t$ relative to the crossing time $\tau_c$. +" Both analytical aretnents and N-body sinuuations indicate that voune clusters lose most of their stars tfor €=0.3 aud At«7, but retain most of them for £20.5 or Af27, (Illls1980:IKroupaetal.2001:Iroupa&Doilv2002:Bamneardt&Kroupa2007 Lk."," Both analytical arguments and $N$ -body simulations indicate that young clusters lose most of their stars for ${\cal E} \la 0.3$ and ${\Delta t} \ll \tau_c$ but retain most of them for ${\cal E} \ga 0.5$ or ${\Delta t} \gg \tau_c$ \citep{hills80, kroupa01b, kroupa02a, +baumgardt07a}." + Thus. as lone as £ aud Afír. are. on average. indeudent of AM. as they are for protoclusters with consaut ean surface density (a= 1/2) and momentuim-drjvenu feedback. ISM removal will uot alter the shape oftje Inass function (although its amplitude will decline).," Thus, as long as ${\cal E}$ and ${\Delta t}/\tau_c$ are, on average, independent of $M$, as they are for protoclusters with constant mean surface density $\alpha = 1/2$ ) and momentum-driven feedback, ISM removal will not alter the shape of the mass function (although its amplitude will decline)." + This is consistent with the observed exponeuts 3.%—2.0 for clusters both vounger and older than 10* vr in the Antennae aud LMC (Zhlaug&Fall1999:etal.2009:Chandar 2010).," This is consistent with the observed exponents $\beta_* \approx -2.0$ for clusters both younger and older than $10^7$ yr in the Antennae and LMC \citep{zhang99b, fall09a, chandar09a}." +. Iu all other cases. €c increases with AL. aud a higher proportion of low-niass clusters is disrupted. causing a flattening or a bend at &=O030.5 in the ias function.," In all other cases, ${\cal E}$ increases with $M$, and a higher proportion of low-mass clusters is disrupted, causing a flattening or a bend at ${\cal E} \approx 0.3 - 0.5$ in the mass function." + The exact shape depends on Afr. cIunipiness within protoclusters. and otlrer uncertain factors.," The exact shape depends on $\Delta t/\tau_c$, clumpiness within protoclusters, and other uncertain factors." +" If the efficicney has a weal clependence on nues. as it does for constant mean surface density (0= 1/2) aud cucrev-driven feedback (€x AM, the predicted ο wight be mareially consisteut with «jbservations over a lanited range of masses (101A.XAL= 10°AL.)."," If the efficiency has a weak dependence on mass, as it does for constant mean surface density $\alpha = 1/2$ ) and energy-driven feedback ${\cal E} \propto M^{1/4}$ ), the predicted $\beta_*$ might be marginally consistent with observations over a limited range of masses $10^4 M_{\odot} \la M \la 10^6 M_{\odot}$ )." + However. for coustaut size (a= 0). the variations are so strong (©xAP? and £x AL) that we expect major differences between the mass functions of clusters vounger aud older than 105 vr. in clear coutracliction with observations.," However, for constant size $\alpha = 0$ ), the variations are so strong ${\cal E} \propto M^{3/2}$ and ${\cal E} \propto M$ ) that we expect major differences between the mass functions of clusters younger and older than $10^7$ yr, in clear contradiction with observations." +" Our sinle analytical model aerees. at least qualitatively, with the merical calculations Y Bamueardtetal.(2008). ancl Parmentieretal.(2008)."," Our simple analytical model agrees, at least qualitatively, with the numerical calculations by \citet{baumgardt08a} and \citet{parmentier08a}. ." +". They present results for cnerev-driven feedback by supernovae iu protoclusters with uncorrelated sizes aud nasses,", They present results for energy-driven feedback by supernovae in protoclusters with uncorrelated sizes and masses. +" Iu some cases. they find a beud in the mass ""uncfion of young clusters at AL10AL... while in others. they find a flattened power law with Jj.=1 (see Figure { of Bammeardtetal. 2008))."," In some cases, they find a bend in the mass function of young clusters at $M \sim 10^5 M_{\odot}$, while in others, they find a flattened power law with $\beta_* \approx -1$ (see Figure 4 of \citealt{baumgardt08a}) )." + As we have already. noted. these results are expected for a=0. aud they are inconsistent with the observed mass functions of vouug clusters.," As we have already noted, these results are expected for $\alpha = 0$, and they are inconsistent with the observed mass functions of young clusters." + We now consider five specific feedback mechlianisaus: siperhovac. mnaiu-sequence winds. protostellar outflows. photoionized eas. and radiation pressure.," We now consider five specific feedback mechanisms: supernovae, main-sequence winds, protostellar outflows, photoionized gas, and radiation pressure." + For the first four. we review results from the literature.," For the first four, we review results from the literature." + Supernova feedback beeins only after the >3.6 Alwr Ποιος of massive stars., Supernova feedback begins only after the $>3.6$ Myr lifetimes of massive stars. + Unless turbulence within a protocluster is nidntained by feedback or external forcing. stars would form rapidly and consuue its ISM. with €»1 in 12 crossing times.," Unless turbulence within a protocluster is maintained by feedback or external forcing, stars would form rapidly and consume its ISM, with ${\cal E} \rightarrow 1$ in $1-2$ crossing times." +" This implies that supernovae can donuüuate onlv for 27,cV3.6 Myr unless another niechanisni somehow keeps € σπα. without expelling much ISM (νο&Matzuer2009).."," This implies that supernovae can dominate only for $2\tau_c \ga +3.6$ Myr unless another mechanism somehow keeps ${\cal E}$ small without expelling much ISM \citep{krumholz09d}." + However. even iu this coutrived situation. supernovae would plav oulv a secondary role.," However, even in this contrived situation, supernovae would play only a secondary role." + Maiu-sequeuce winds are not effective. if their enerev is able to leak out of the bubbles they blow (Ibupor-Clhuk&Murray.2009).., Main-sequence winds are not effective if their energy is able to leak out of the bubbles they blow \citep{harper-clark09a}. +. As a result of this leakage. winds simply provide au nuity euhancenieut to radiation pressure (INruiuholz& 2009)..," As a result of this leakage, winds simply provide an order-unity enhancement to radiation pressure \citep{krumholz09d}." + Protostellar outflows can oulv remove the ISM from protoclusters with escape velocities below about 7 | (Matzner&Melee 2000).., Protostellar outflows can only remove the ISM from protoclusters with escape velocities below about 7 $^{-1}$ \citep{matzner00}. . + Photoionized eas is dportant as a feedback mechanisin ouly wheu its pressure exceeds that of radiation throughout most of au ireegion., Photoionized gas is important as a feedback mechanism only when its pressure exceeds that of radiation throughout most of an region. +" This in παπι requires that the iregion be larger thanthe radius ra, at which P4=Das a condition harder to satisfv iu massive. compact protoclusters (I&xuiiholz&Matzner 2009)."," This in turn requires that the region be larger thanthe radius $r_{\rm ch}$ at which $P_{\rm rad} = P_{\rm gas}$, a condition harder to satisfy in massive, compact protoclusters \citep{krumholz09d}. ." + We summarize these results iu Table 1 aud Figure 2.., We summarize these results in Table \ref{Table} and Figure \ref{Fig:ejection}. . + Asthe plot shows. the mechanisms discussed./ thus," Asthe plot shows, the mechanisms discussed thus" +Cübbs sauupliug iu the polarization case is csscutially the same as in the temperature case. with objects involved in the sampling re-defined to account for the additional information.,"Gibbs sampling in the polarization case is essentially the same as in the temperature case, with objects involved in the sampling re-defined to account for the additional information." + For full details on the methodology of Cabbs sampling as applied to CMD analysis. see Jowelletal. (2001): Wandeltetal.(2001): and Euksenctal.(2001).," For full details on the methodology of Gibbs sampling as applied to CMB analysis, see \citet{jewell:2004}; ; \citet{wandelt:2004}; ; and \citet{eriksen:2004}." +". Specifically, the CAIB signal is generalized to a vector of harmonics cocficients for each ( and m. Where the letters 7. E. (al.aud DBab. standab) for teuiperature. electziic/eradieunt. and magnetic/curl respectively."," Specifically, the CMB signal is generalized to a vector of harmonics coefficients $(a_{\ell m}^T, a_{\ell m}^E, a_{\ell m}^B)$ for each $\ell$ and $m$, where the letters $T$, $E$, and $B$ stand for temperature, electric/gradient, and magnetic/curl respectively." + The covariance matrix S of the CMD signal then becomes block-diagonal. with an identical οον3 sub-imatrix for cach i9 value at a given f: The data are pixelized maps m of the Stokes paralcters £.Q.0 of the form where A is a linear operator that includes convolutio with an instimucut beam aud the trausformatiou oτσ the T.E.DB compoucuts of the signal s iuto the Stokey. paranieters.," The covariance matrix $\BS$ of the CMB signal then becomes block-diagonal, with an identical $3\times 3$ sub-matrix for each $m$ value at a given $\ell$: The data are pixelized maps $\Bm$ of the Stoke's parameters $I,Q,U$ of the form where $\mathbf{A}$ is a linear operator that includes convolution with an instrument beam and the transformation of the $T,E,B$ components of the signal $\Bs$ into the Stokes parameters." + Note that for the rest of this paper. we wi assune both the iustruucutal beam to be svuunetric and the noise n to be uucorrelated. having a diagonua covariauce matrix IN.," Note that for the rest of this paper, we will assume both the instrumental beam to be symmetric and the noise $\Bn$ to be uncorrelated, having a diagonal covariance matrix $\BN$." + These are the reasons we eau wor- with maps instead of tinue-ordered data., These are the reasons we can work with maps instead of time-ordered data. + However. te siuplifr the notation we disregard in the following a issues concerning data format. beam couvolutions. multi-frequency observatious etc..," However, to simplify the notation we disregard in the following all issues concerning data format, beam convolutions, multi-frequency observations etc.," + and model our data as a siuple sun of a signal term aud a noise term., and model our data as a simple sum of a signal term and a noise term. + For the full expressions. see Appendix. A..," For the full expressions, see Appendix \ref{app:signal_sampling}." + Application of a galactic mask is implemented bv Increasing the noise variance to Παπά for masked pixels. or rather. bv setting the inverse noise τν.covariance to zero.," Application of a galactic mask is implemented by increasing the noise variance to infinity for masked pixels, or rather, by setting the inverse noise covariance to zero." + For full details. we refer the interested reader to 1)..," For full details, we refer the interested reader to \citet{eriksen:2004}." + Asin the tempcrature-ouly case discussed in Jewelletal.(2001) and Wandeltetal.(2001).. we wish to sample from the P(S]d) posterior.," As in the temperature-only case discussed in \citet{jewell:2004} and \cite{wandelt:2004}, we wish to sample from the $P(\BS | \Bd)$ posterior." + Tt is typically not easy. to evaluate P(S}d) directly. because of a large and dense (S|N) covariance matrix. nor is it easy to sample from it directlv.," It is typically not easy to evaluate $P(\BS | \Bd)$ directly, because of a large and dense $(\BS + \BN)$ covariance matrix, nor is it easy to sample from it directly." + This is precisely the motivation for Cübbs suupliug. which allows sampling from a joiut density hrough the corresponding conditional deusities.," This is precisely the motivation for Gibbs sampling, which allows sampling from a joint density through the corresponding conditional densities." + For the case of CAIB power spectrum estimation. this is done w first sampling from P(S.s|d) using P(S|s.d) and P(s|S.d). (ucither of which requires inversion of deuse (S|Nj) matrices). and then mareializing over s.," For the case of CMB power spectrum estimation, this is done by first sampling from $P(\BS, \Bs | \Bd)$ using $P(\BS | \Bs, \Bd)$ and $P(\Bs| \BS, \Bd)$, (neither of which requires inversion of dense $(\BS + \BN)$ matrices), and then marginalizing over $\Bs$." + Using he fact that. given a full-sky signal map the conditional density for the signal matrix is iudependent of the data P(S|s.d)=P(S|s). the basic Cabbs sampling scheme nay be written iu the following form. Here the svinbol 49 indicates sampling from the distribution ou the melt haud side.," Using the fact that, given a full-sky signal map the conditional density for the signal matrix is independent of the data $P(\BS|\Bs,\Bd) = P(\BS|\Bs)$, the basic Gibbs sampling scheme may be written in the following form, Here the symbol $\leftarrow$ indicates sampling from the distribution on the right hand side." + The only remaining problem is to establish the correct sampling aleoritlinus for cach of the two conditional distributions for polarized data. and this is the topic of the following sections.," The only remaining problem is to establish the correct sampling algorithms for each of the two conditional distributions for polarized data, and this is the topic of the following sections." + Note that if a continuous distribution for P(S|d) is desired. as opposed to a set of individual samples. one niav take advantage of the known analytical form of the distribution P(S|s) by applviug the BlackwellRao estimator.," Note that if a continuous distribution for $P(\BS|\Bd)$ is desired, as opposed to a set of individual samples, one may take advantage of the known analytical form of the distribution $P(\BS|\Bs)$ by applying the Blackwell-Rao estimator." + This procedure was discussed iu detail bv Wandeltetal(2001) and Chuetal.(2005)— for the temperatiure-only case. and the generalization to polarization is once again straightforward.," This procedure was discussed in detail by \cite{wandelt:2004} and \cite{chu:2005} for the temperature-only case, and the generalization to polarization is once again straightforward." + Tle required modifications are written out in Section 2.5.., The required modifications are written out in Section \ref{sec:blackwell_rao}. . + The signal samplue equatious for polarization are identical to those for temperature-onlv data. talking into account the eeneralizations mentioned above.," The signal sampling equations for polarization are identical to those for temperature-only data, taking into account the generalizations mentioned above." + Specifically. the skv signal (s=x|y) is sampled (given the current covariance matrix S) by solving for the mean field. x. and fluctuation. y. maps where © and X are random maps contaiume Caussiau unit variates (zero inean and unit variance) in each pixel for cach of the 1. Q. aud Ucompouents?.," Specifically, the sky signal $\Bs=\Bx+\By$ ) is sampled (given the current covariance matrix $\BS$ ) by solving for the mean field, $\Bx$, and fluctuation, $\By$, maps where $\mathbf{\xi}$ and $\mathbf{\chi}$ are random maps containing Gaussian unit variates (zero mean and unit variance) in each pixel for each of the $I$, $Q$, and $U$." +. Note that the sviubols in these equations may be interpreted either in terms of pixel space or spherical harmonic space objects., Note that the symbols in these equations may be interpreted either in terms of pixel space or spherical harmonic space objects. + In practice. this is implemented iu terms of conversions between pixel aud larimonic space with standard spherical harmonics transforms.," In practice, this is implemented in terms of conversions between pixel and harmonic space with standard spherical harmonics transforms." + For example. the mmerse noise covariance matrix is given by Niu pixel space and YNHY in harmonic space. where Y and Y7 are the inverse aud standard spherical harmonics transforms. respectively.," For example, the inverse noise covariance matrix is given by $\mathbf{N}^{-1}$ in pixel space and $\mathbf{Y}^T +\mathbf{N}^{-1} \mathbf{Y}$ in harmonic space, where $\mathbf{Y}$ and $\mathbf{Y}^T$ are the inverse and standard spherical harmonics transforms, respectively." + For explicit details ou such conrputations. see Eriksenetal. (2006)..," For explicit details on such computations, see \citet{eriksen:2006}. ." + The signal saunplug operation is by far the most demanding step of the Cabbs sampler. because it requires the solution of a verv large linear system.," The signal sampling operation is by far the most demanding step of the Gibbs sampler, because it requires the solution of a very large linear system." + Formally speaking. this corresponds to inverting a ~ος10 matrix. which clearly is uot computationally feasible through brute-force methods.," Formally speaking, this corresponds to inverting a $\sim 10^6 +\times 10^6$ matrix, which clearly is not computationally feasible through brute-force methods." +" Πωπονα, as described in detail by. e.g.. Exikseuetal.(2001).. the systems πι cquatious 5. aud 6 iav be solved by means of Conjugate Cracdicuts (CC)."," However, as described in detail by, e.g., \citet{eriksen:2004}, the systems in equations \ref{sampleMean} and \ref{sampleFluctuation} may be solved by means of Conjugate Gradients (CG)." + The computational scaling is thus reduced to the most expeusive step for applviug the operator on the left haud side of the equations. which for svuuuetre beams and uucorrelated noise is a standard spherical harmonic traustorm.," The computational scaling is thus reduced to the most expensive step for applying the operator on the left hand side of the equations, which for symmetric beams and uncorrelated noise is a standard spherical harmonic transform." + The cficiency of the CC technique depends critically ou the condition umuber of the matrix under consideration., The efficiency of the CG technique depends critically on the condition number of the matrix under consideration. + For our case. this is simply the highest signal-to-noise ratio of any mode in the system.," For our case, this is simply the highest signal-to-noise ratio of any mode in the system." + As an example. for a fixed. pre-conditioncr it takes about GU iterationsto solve for the first-vear WMAP data. about 120 iterations to solve for thethree-vear WALAPdata.aud about 300 iterations to solve for the Plauck GGIIz data.," As an example, for a fixed pre-conditioner it takes about 60 iterationsto solve for the first-year WMAP data, about 120 iterations to solve for thethree-year WMAPdata,and about 300 iterations to solve for the Planck GHz data." +us a result that is related (o expression (1): The universe behaves as a quanti black hole 2010)).,us a result that is related to expression (1): The universe behaves as a quantum black hole ). + All that is needed is to generalize Planck's constant., All that is needed is to generalize Planck's constant. +" Applying (1) to the universe. with ReLOem. mass 7Mz10g and characteristic time /j243.x10855. we get the conjugate black hole: where im,1=(he/G)'? is Planck's mass and /,1=(Gh/c)!? is Planck's time."," Applying (1) to the universe, with $R \approx 10^{28} cm$, mass $M \approx 10^{56} g$ and characteristic time $t_0 \approx 4.3 \ \times 10^{17} s$, we get the conjugate black hole: where $m_p = (\hbar c/G)^{1/2}$ is Planck's mass and $t_p = (G \hbar /c^5)^{1/2}$ is Planck's time." + The mass mzzLOο of the conjugate black hole of the universe has been identified with the quantum of the gravitational potential field 2011aa) and the bit 2011bb)., The mass $m \approx 10^{-65} g$ of the conjugate black hole of the universe has been identified with the quantum of the gravitational potential field a) and the bit b). + This is in line with the suggestion that this is a possible way to univ eravitv with quantum (theory., This is in line with the suggestion that this is a possible way to unify gravity with quantum theory. + Besides. (he information-entropy. relation. based on the bit. the Padmanabhan (2010aa. 2010bb and relerences therein) proposal (hat gravity has an entropic or thermodynamic origin. and the Verlinde interpretation of eravily as an emerging entropic force 2011)). gives us a hope in (his direction.," Besides, the information-entropy relation, based on the bit, the Padmanabhan a, b and references therein) proposal that gravity has an entropic or thermodynamic origin, and the Verlinde interpretation of gravity as an emerging entropic force ), gives us a hope in this direction." + The physical properties of the bit in (2) clearly imply. a iunber of bits lor the universe of AL/mzz10155., The physical properties of the bit in (2) clearly imply a number of bits for the universe of $M/m \approx 10^{122}$. + On the other hand the Hawking entropy for a black hole 1975)). (the Bekenstein limit. see 1972)) is for the universe:," On the other hand the Hawking entropy for a black hole ), (the Bekenstein limit, see ) is for the universe:" +this and also fud that the bias iu deyy is reduced. but at the cost of a cousicerable merease m vardauce i Eyy.,"this and also find that the bias in $\hat{\beta}_{EXY}$ is reduced, but at the cost of a considerable increase in variance in $\hat{\beta}_{EXY}$." + In general. our simulations iuplyv that the variance of the FITENY estimator is comparable to that of the BCES(Y” X) estimator if one does not iterate the minimization of vg. aud the variance of Jgyy Is larecr if one does iterate.," In general, our simulations imply that the variance of the FITEXY estimator is comparable to that of the $Y|X$ ) estimator if one does not iterate the minimization of $\chi^2_{EXY}$, and the variance of $\hat{\beta}_{EXY}$ is larger if one does iterate." +" Towever. since Opeges ix approximately unbiased when R, is not too large. opers should be preferred over jgxyy."," However, since $\hat{\beta}_{BCES}$ is approximately unbiased when $R_x$ is not too large, $\hat{\beta}_{BCES}$ should be preferred over $\hat{\beta}_{EXY}$." + In addition. when the measureimieut errors are large the FITENY estimate of σ is conmmonly opyy=0. similar to the BCES-type estimate of the intrinsic dispersion.," In addition, when the measurement errors are large the FITEXY estimate of $\sigma$ is commonly $\hat{\sigma}_{EXY} = 0$, similar to the BCES-type estimate of the intrinsic dispersion." + The masximauuo-likchlood estimator based on the Gaussian structural model performs better than the OLS. BCES. aud FITENY cstimators. aud gives fÉürlv consistent estimates even in the presence of severe measurement error and low seuuple size.," The maximum-likelihood estimator based on the Gaussian structural model performs better than the OLS, BCES, and FITEXY estimators, and gives fairly consistent estimates even in the presence of severe measurement error and low sample size." + The MLE is approximately unbiased. in spite of the fact that the MILE incorrectly assumes that the independent variables are normally distributed.," The MLE is approximately unbiased, in spite of the fact that the MLE incorrectly assumes that the independent variables are normally distributed." +" The variance in the MEE of the slope. εξ. is stnaller than that of Opers and oryy. particularly when A, is large."," The variance in the MLE of the slope, $\hat{\beta}_{MLE}$, is smaller than that of $\hat{\beta}_{BCES}$ and $\hat{\beta}_{EXY}$, particularly when $R_x$ is large." + In coutrast to the OLS estimate of the slope. the dispersion in λες duereases as the measurement errors inercases. reflecting the additional uncertainty iu ayer caused bv the measurement errors.," In contrast to the OLS estimate of the slope, the dispersion in $\hat{\beta}_{MLE}$ increases as the measurement errors increases, reflecting the additional uncertainty in $\hat{\beta}_{MLE}$ caused by the measurement errors." + Finally. iu contrast to the other estimators. the MILE of the iutriusic variance is always positive. aud the probability of obtaimine Tuer= Nis uceheible for these sinmmlations.," Finally, in contrast to the other estimators, the MLE of the intrinsic variance is always positive, and the probability of obtaining $\hat{\sigma}_{MLE} = 0$ is negligible for these simulations." + Tareucd in L1 that assunüug a uniform distribution on & docs not lead to better estimates than the usual OLS case., I argued in \ref{s-normreg} that assuming a uniform distribution on $\xi$ does not lead to better estimates than the usual OLS case. + I also used these simulations to estimate the sampling density of the MLE assmuine p)x1., I also used these simulations to estimate the sampling density of the MLE assuming $p(\xi) \propto 1$. + The results were nearly indistinguishable from the OLS estimator. supporting our conjecture that assuming p(£)«X1 does not offer an improvement over OLS.," The results were nearly indistinguishable from the OLS estimator, supporting our conjecture that assuming $p(\xi) \propto 1$ does not offer an improvement over OLS." + While it is informative to compare the sampling distribution of our proposed maxiuuunu-lükclibhood estimator with those of the OLS. DCES(Y LV). and FITENY estimators. Edo uot derive the uncertainties iu the reeression parameters from the sampling distribution of the MLE.," While it is informative to compare the sampling distribution of our proposed maximum-likelihood estimator with those of the OLS, $Y|X$ ), and FITEXY estimators, I do not derive the uncertainties in the regression parameters from the sampling distribution of the MLE." + As described in 6.2.. we derive the uncertainties iu the regression paraucters by simulating draws from the posterior distribution. p(0.clc.y).," As described in \ref{s-markov}, we derive the uncertainties in the regression parameters by simulating draws from the posterior distribution, $p(\theta,\psi|x,y)$." + This allows a straight-forward method ofinterpreting the paramcter uncertainties that does not rely on approximations. as the posterior distribution is the probability distribution of the parameters. even he observed data.," This allows a straight-forward method of interpreting the parameter uncertainties that does not rely on large-sample approximations, as the posterior distribution is the probability distribution of the parameters, given the observed data." +" The posterior distributions of p.J. aud σ for a simulated data set with 5»=50.0,~7. aud o,~7 is shown in Figure 6.."," The posterior distributions of $\rho, \beta,$ and $\sigma$ for a simulated data set with $n = 50, + \sigma_x \sim \tau,$ and $\sigma_y \sim \sigma$ is shown in Figure \ref{f-post1d}." + When estimating these posteriors. I used A=2 Gaussians in the mixture nodel.," When estimating these posteriors, I used $K = 2$ Gaussians in the mixture model." +" Ax cau be seen from Figure 6.. the true values of p.ο, and σ are coutained within the regions of 10n-neelieible posterior probability."," As can be seen from Figure \ref{f-post1d}, the true values of $\rho, \beta,$ and $\sigma$ are contained within the regions of non-negligible posterior probability." + I have estimated posteriors for other simulated data sets; varving the nunher of data points and the degree of measurement error.," I have estimated posteriors for other simulated data sets, varying the number of data points and the degree of measurement error." + As one would expect. the uncertainties in the regression paraiueters. represented by the widths of the posterior distributions. increase as the size of the neasunrenient errors merease and the sample size decreases.," As one would expect, the uncertainties in the regression parameters, represented by the widths of the posterior distributions, increase as the size of the measurement errors increase and the sample size decreases." + A «ώμο frequentist approach is to compute the covariance matrix of the MILE by inverting the estimated Fisher information matiix. evaluated at the AILE.," A common frequentist approach is to compute the covariance matrix of the MLE by inverting the estimated Fisher information matrix, evaluated at the MLE." + Then. uuder certain regularity couditious. the MILE of the parameters is asvinpotically normally distributed with mean equal to the true value of the araluctors and covariance matrix equal to the inverse ofthe Fisher information matrix.," Then, under certain regularity conditions, the MLE of the parameters is asympotically normally distributed with mean equal to the true value of the parameters and covariance matrix equal to the inverse of the Fisher information matrix." + Furthermore. wader hese reeularity couditious the posterior distribution aud sampling distribution of the MILE are asviuiptoticallv he same.," Furthermore, under these regularity conditions the posterior distribution and sampling distribution of the MLE are asymptotically the same." + Figure 7 compares the posterior distribution of the slope for a simulated data set with that inferred from the MEE., Figure \ref{f-fbcompare} compares the posterior distribution of the slope for a simulated data set with that inferred from the MLE. + The posterior and MLE was calculated asstuning A—1 Gaussian., The posterior and MLE was calculated assuming $K = 1$ Gaussian. +" As can be seen. he posterior distribution for Jis considerably different from the approximation based ou the MLE of ο, aud hus the two have not couverecd for this sample."," As can be seen, the posterior distribution for $\beta$ is considerably different from the approximation based on the MLE of $\beta$, and thus the two have not converged for this sample." + In particular. the posterior is more skewed aud heavy-tailed. lacing more probability ou values of 3>O than docs the distribution approximated by the MILE.," In particular, the posterior is more skewed and heavy-tailed, placing more probability on values of $\beta > 0$ than does the distribution approximated by the MLE." +" Therefore. ""uncertainties in the MEE should be interpreted with caution if using the asviiptotie approximation to the siuupling distribution of the MLE."," Therefore, uncertainties in the MLE should be interpreted with caution if using the asymptotic approximation to the sampling distribution of the MLE." +velocity make it problematic for SN 1961V to conform to other prestuned SN impostors auc known LBVs.,velocity make it problematic for SN 1961V to conform to other presumed SN impostors and known LBVs. + They argue that the lieht curve is consistent with the superposition of a normal Type U-Plateau SN light curve and a SN IIn-lixe light curve. with additional Iuuinosity arising from chhanced interaction at late times with an existing cireunistellar medium.," They argue that the light curve is consistent with the superposition of a normal Type II-Plateau SN light curve and a SN IIn-like light curve, with additional luminosity arising from enhanced interaction at late times with an existing circumstellar medium." + rely almost entirely on an analysis of the wud-intrared dust cluission in the SN enviroment., rely almost entirely on an analysis of the mid-infrared dust emission in the SN environment. + Their bypothesis is that. since the prediction is that a LBV survivor of SN 1961V would be cloaked by £L5 magnitudes of visual extinction. this dust shell should be easily detectable iu the thermal infrared (IR) as an IR jj Car analog.," Their hypothesis is that, since the prediction is that a LBV survivor of SN 1961V would be cloaked by 4–5 magnitudes of visual extinction, this dust shell should be easily detectable in the thermal infrared (IR) as an IR $\eta$ Car analog." + The lack of detectable mid-IR cinissiou at the SN positiou led to conclude that SN. 1961V. ust have been a true SN. which has now faded below optical detectability.," The lack of detectable mid-IR emission at the SN position led to conclude that SN 1961V must have been a true SN, which has now faded below optical detectability." + There lave been multiple observations of SN. L961V at a wide range of wavelengths iu the last fifty vears., There have been multiple observations of SN 1961V at a wide range of wavelengths in the last fifty years. + Depending ou the assuniptious used iu iuterpretiug these data sets; one can cole to several plausible couclusious.," Depending on the assumptions used in interpreting these data sets, one can come to several plausible conclusions." + Tere. and in 77.. we male the case that the overall picture across the clectromaeuetic spectrum is simpler and more consistent with SN 1961V as an eruptive LBY.," Here, and in \ref{analysis}, we make the case that the overall picture across the electromagnetic spectrum is simpler and more consistent with SN 1961V as an eruptive LBV." + We obtained from the VLA data archive the 6 cii data. originally collected by(2001).. and produced a map using standard routines in NRAO‘s Astronomical huage Processing System (AIPS).," We obtained from the VLA data archive the 6 cm data, originally collected by, and produced a map using standard routines in NRAO's Astronomical Image Processing System (AIPS)." + We obtained from the archive the STIS 50CCD image from and applied a very accurate astrometric erid. £0702 in both right ascension and declination. to the image. using the tasks and inI," We obtained from the archive the STIS 50CCD image from and applied a very accurate astrometric grid, $\pm +0{\farcs}02$ in both right ascension and declination, to the image, using the tasks and in." +RAE! We then registered this image to our version of the radio map., We then registered this image to our version of the radio map. + This analysis first appeared im(2005)., This analysis first appeared in. +. The radio emission overlaid on the image is shown in Figure 1.., The radio emission overlaid on the image is shown in Figure \ref{radiomap}. . + The objects from and are labeled in the figure., The objects from and are labeled in the figure. + We place the accurate optical absolute position of SN 1961V iu the fieure as well, We place the accurate optical absolute position of SN 1961V in the figure as well. + It is clear from the Ποιο that the optical SN position is most coiucideut with Object 7coincidence)., It is clear from the figure that the optical SN position is most coincident with Object 7. +.. However. the ceutroid of the radio source. Which both aud claiii to be associated with the SN. is significantly displaced. by ~071 southeast (ie. 2 19). roni the optical position.," However, the centroid of the radio source, which both and claim to be associated with the SN, is significantly displaced, by $\sim 0{\farcs}4$ southeast (i.e., $\gtrsim 4\sigma$ ), from the optical position." + Furthermore. the nonthermal radio cussion does rot appear that well correlated with the stellay objects in the environment.," Furthermore, the nonthermal radio emission does not appear that well correlated with the stellar objects in the environment." + Iustead. we consider it far more ikelv that it is cussion associated with what appears ο be a complex. turbulent interstellar medimm.," Instead, we consider it far more likely that it is emission associated with what appears to be a complex, turbulent interstellar medium." + Note the “finger” of radio cuuission that extends to the northeast roni the main central concentration of cussion. which appears to follow the arcs of nebular cliission secu in the STIS nuage toward the central cluster of stars.," Note the “finger” of radio emission that extends to the northeast from the main central concentration of emission, which appears to follow the arcs of nebular emission seen in the STIS image toward the central cluster of stars." + The unfiltered STIS nuage2001).. which clearly inchices uehbular ciaission lines. alludes to such a spectacular interstellar environment Gvhich is vorv conspicuous as being the most optically Iuniuous extranuclear eniüssion regiou iu the host galaxy).," The unfiltered STIS image, which clearly includes nebular emission lines, alludes to such a spectacular interstellar environment (which is very conspicuous as being the most optically luminous extranuclear emission region in the host galaxy)." +" This is the ""easteru region” from seeu at miaich higher spatial resolution.", This is the “eastern region” from seen at much higher spatial resolution. + Additionally. our flux deusitv measurement from the2000 radio 6 cin data is 250.005. idv.," Additionally, our flux density measurement from the2000 radio 6 cm data is $\pm$ 0.005 mJy." +.. Comparing this to O.11250.03 mJy from 19861988).. it is not eutirely obvious that the radio flux deusitv had. iu fact. actually declined iu that time interval. as claimed.," Comparing this to $\pm$ 0.03 mJy from 1986, it is not entirely obvious that the radio flux density had, in fact, actually declined in that time interval, as claimed." + Therefore. we consider it to be quite convincing that the radio cussion is not that of a fading radio SN. nor does the radio cussion have any direct relation at all to SN 1961V. We have analyzed archival UST/WFPC2 images. specifically of SN. 1961V. obtained in 2008 August bv program GO-10877 (PI: W. Li).," Therefore, we consider it to be quite convincing that the radio emission is not that of a fading radio SN, nor does the radio emission have any direct relation at all to SN 1961V. We have analyzed archival /WFPC2 images, specifically of SN 1961V, obtained in 2008 August by program GO-10877 (PI: W. Li)." + These are exposures of 360 sec total iu PSSSW and 800 sec total in F658N (the narrow baud that includes Ta at approximately the host ealaxy redshift)., These are exposures of 360 sec total in F555W and 800 sec total in F658N (the narrow band that includes $\alpha$ at approximately the host galaxy redshift). + The images are shown in Figure 2.., The images are shown in Figure \ref{hstimage}. . + The stars that are visible in the figure from and(2002).. again. are labeled.," The stars that are visible in the figure from and, again, are labeled." + Achuittedly not of the highest sigual-to-noise ratio (S/N). it is clear from the figure that Object. 7 is well detected in both bands (at 5.70 iu both E555W. and F658N).," Admittedly not of the highest signal-to-noise ratio $S/N$ ), it is clear from the figure that Object 7 is well detected in both bands (at $5.7\sigma$ in both F555W and F658N)." + In fact. Object 7 is the solitary Πα source in the inunediate ceutral cluster.," In fact, Object 7 is the solitary $\alpha$ source in the immediate central cluster." + Object LO GQvhich from Figure l is most Likely an ciission region) aud possibly another. umnuunbered object to the northeast of Object T. are the oulv other detected poiut-like sources in that uae.," Object 10 (which from Figure \ref{radiomap} is most likely an emission region) and possibly another, unnumbered object to the northeast of Object 7, are the only other detected point-like sources in that image." + We measured photometry for these images using the routine USTphot2000a.b).. which automatically accounts for WFEDPC2 poiut-spread function (PSF) variations aud charge-transfer effects across the chips. zeropoiuts. aperture corrections. etc.," We measured photometry for these images using the routine HSTphot, which automatically accounts for WFPC2 point-spread function (PSF) variations and charge-transfer effects across the chips, zeropoints, aperture corrections, etc." + IISTphot was run ou both bands with a 3e detection threshold., HSTphot was run on both bands with a $\sigma$ detection threshold. + Object 7 is detected at mpsssy=2L7T0250.19 and omgossw=20.15+0.19 mae.," Object 7 is detected at $m_{\rm F555W}=24.70 \pm 0.19$ and $m_{\rm F658N} = 20.45 +\pm 0.19$ mag." + We can compare the gspassswy dnnueasurenment for Object 7 from these 2008 data with that from the WE/PC-1 observations by(1995). Le. pss=2122£0.07 mae. and the WEPC2 FOOGW ieasurement by(2002).. Le. mMeguew=2.8L40.11 mag.," We can compare the $m_{\rm F555W}$ measurement for Object 7 from these 2008 data with that from the WF/PC-1 observations by, i.e., $m_{\rm F555W}=24.22 \pm 0.07$ mag, and the WFPC2 F606W measurement by, i.e., $m_{\rm F606W}=23.84 \pm 0.14$ mag." +" Furthermore. we can measure the brightness of Object 7 from the archival STIS 50CCD nuage (unorinaliziug to a 2lpixelaradius. or l72-radius. aperture. which iucludes of the encircled. cucrey. following the online STIS DIustriuncut Taudbool). adopting the appropriate zero poiut for the clear (CL) bandpass from(2000).. ancl Bud ey,=2LIL40.01 @which is ~V. if we assiue VoF045 mae)."," Furthermore, we can measure the brightness of Object 7 from the archival STIS 50CCD image (normalizing to a 24-pixel-radius, or $1{\farcs}2$ -radius, aperture, which includes of the encircled energy, following the online STIS Instrument Handbook), adopting the appropriate zero point for the clear (CL) bandpass from, and find $m_{\rm CL}=24.41 \pm 0.04$ (which is $\sim$ V, if we assume $V-I\simeq 0.5$ mag)." + Although it is likely that we caunot directly compare observations made withHST with differeut detectors aud different baudpasses to better than 1056. the ingsssw aud wey all agree relatively well. while the memgogw: differs pretty significantly frou the others.," Although it is likely that we cannot directly compare observations made with with different detectors and different bandpasses to better than $\sim$ , the $m_{\rm F555W}$ and $m_{\rm CL}$ all agree relatively well, while the $m_{\rm F606W}$ differs pretty significantly from the others." + However. we have checked the photometry," However, we have checked the photometry" +There are currently two models proposed. for ultraluminous Xray SOULCES (ULXs).,There are currently two models proposed for ultraluminous X–ray sources (ULXs). + In one they are identified as intermediatemass black holes (LNIBII) accreting at rates below their. Exldington limits., In one they are identified as intermediate–mass black holes (IMBH) accreting at rates below their Eddington limits. + In. the alternative model. ULXs represent a very bright and unusual phase of Xrav binary evolution. in which the compact object is fed mass al a rate Mo well above the usual Eddington value Ale.," In the alternative model, ULXs represent a very bright and unusual phase of X--ray binary evolution, in which the compact object is fed mass at a rate $\dot M$ well above the usual Eddington value $\dot M_E$." +" In the picture proposed by Shakura Sunvacy (1973) radiation pressure becomes important at the spherization radius Royc2TCALALRA where By=261£0. is the Schwarzschild radius of the accreting black hole of mass Al, (Shakura Sunvacy. 1973: see also Begelman οἱ al.."," In the picture proposed by Shakura Sunyaev (1973) radiation pressure becomes important at the spherization radius $R_{\rm sph} \simeq +27(\dot M/\dot M_E)R_s/4$, where $R_s = 2GM_1/c^2$ is the Schwarzschild radius of the accreting black hole of mass $M_1$ (Shakura Sunyaev, 1973; see also Begelman et al.," + 2006: Poutanen et al..," 2006; Poutanen et al.," +. 2007)., 2007). + Within this raclius the clise remains close to the local radiation pressure limit., Within this radius the disc remains close to the local radiation pressure limit. + Matter is therefore blown away so that the accretion rate decreases with disce radius as (2)cALHau)MpeU/I).," Matter is therefore blown away so that the accretion rate decreases with disc radius as $\dot M(R) \simeq \dot +M(R/R_{\rm sph}) \simeq \dot M_E(R/R_s)$." + As the disc wind has the local escape velocity at each radius. we see [rom mass conservation that the wind is dense near Zea and tenuous near the inner disc edge. and there is à vacuunr funnel along the central disc axis through which radiation CSCADCS.," As the disc wind has the local escape velocity at each radius, we see from mass conservation that the wind is dense near $R_{\rm sph}$ and tenuous near the inner disc edge, and there is a vacuum funnel along the central disc axis through which radiation escapes." + In this model the large apparent Xrav luminosity Lx=10Lig vesults from two elfeets of superEddington acerction (Degelman et al..," In this model the large apparent X–ray luminosity $L_X = +10^{40}L_{40}$ $^{-1}$ results from two effects of super--Eddington accretion (Begelman et al.," +. 2006: Poutanen et al.," 2006; Poutanen et al.," + 2000)., 2000). + First. the bolometric luminosity is larger than the usual Ecddington limit by a factor ~1|In(AL/Alp). which can be of order ο10 for the high mass transfer rates encountered at various stages of the evolution of a compact stellarmass binary.," First, the bolometric luminosity is larger than the usual Eddington limit by a factor $\sim 1 + \ln(\dot M/\dot M_E)$, which can be of order $5 -10$ for the high mass transfer rates encountered at various stages of the evolution of a compact stellar–mass binary." + Second. the luminosity of a ULX is collimated by a beaming factor b via scattering olf the walls of the central funnel. (," Second, the luminosity of a ULX is collimated by a beaming factor $b$ via scattering off the walls of the central funnel. (" +Note that here and thoughout this paper. ‘beaming’ simply means geometrical collimation. and not relativistic beaming.),"Note that here and thoughout this paper, `beaming' simply means geometrical collimation, and not relativistic beaming.)" + These conditions could occur in a state of high mass transfer (ef Wing. 2001. Rappaport et αἱ.," These conditions could occur in a state of high mass transfer (cf King, 2001, Rappaport et al.," + 2005) or conceivably à transient. outburst (xing. 2002).," 2005) or conceivably a transient outburst (King, 2002)." + In this picture one would expect on physical grounds that the I5ddington ratio mi—AL/ALge should determine the beaming [actor b., In this picture one would expect on physical grounds that the Eddington ratio $\dot m = \dot M/\dot M_E$ should determine the beaming factor $b$. + Llowever current mocelling has not vet derived this connection. allowing a spurious extra degree of freeclom in comparing this picture with observations.," However current modelling has not yet derived this connection, allowing a spurious extra degree of freedom in comparing this picture with observations." + A clue here comes from the fact that bright ULXs have spectra Consisting of a power law plus a soft (AT~0.10.3 keV) excess which can be modelled as a blackbodyv., A clue here comes from the fact that bright ULXs have spectra consisting of a power law plus a soft $kT \sim 0.1 - 0.3$ keV) excess which can be modelled as a blackbody. + This is usually taken as a multicolour disc with the maximum, This is usually taken as a multicolour disc with the maximum +"The basic idea of BOO was to build a unique interaction list that allows the force for a of particles inside a region: Le. a cell C,,,4, Of the treecell). to be computed reducing the uuuboer of tree iuspectious to build the Z£s.","The basic idea of B90 was to build a unique interaction list that allows the force for a of particles inside a region; i.e., a cell $C_{group}$ of the tree, to be computed reducing the number of tree inspections to build the $ILs$." +" D90 builds an IL that applies evervwhere within C,,,,,, aud reuses this IL for cach particle pCC,,,,5 3n turi.", B90 builds an IL that applies everywhere within $C_{group}$ and reuses this IL for each particle $p \in C_{group}$ in turn. + Iu this way it is possible to reduce the tree inspection phase., In this way it is possible to reduce the tree inspection phase. +" The CPU time T, for BOO may be written as where Iu the following paragraphs we will compare the T, time with the Z5, time cousideriug the generic case 0=OS.", The CPU time $T_g$ for B90 may be written as where In the following paragraphs we will compare the $T_g$ time with the $T_o$ time considering the generic case $\theta=0.8$. + We notice that different values of 0 eive similar results. as shown by the acconipauying figures.," We notice that different values of $\theta$ give similar results, as shown by the accompanying figures." + The original DII algorithin adopts an opening criterion (pg. based ou the distance between the position of the p particle aud the ceuter of mass of the remote cells. the IL length (Lj5) beiug proportional to (055)ουν.," The original BH algorithm adopts an opening criterion $\theta_{BH}$ , based on the distance between the position of the $p$ particle and the center of mass of the remote cells, the $IL$ length $L_{IL}$ ) being proportional to ${(\theta_{BH}^3)}^{-1} logN$." + Iu order to have the same accuracy as the original algorvitlin. the iuteraction list of the eroupiug cell is formed usine Eq. (1))," In order to have the same accuracy as the original algorithm, the interaction list of the grouping cell is formed using Eq. \ref{eq:un}) )" + but now the d teyii is computed in terms of the distance from the ceuter of mass of an inspected cell and the edee of the erouping cell. as shown in Fie.," but now the $d$ term is computed in terms of the distance from the center of mass of an inspected cell and the edge of the grouping cell, as shown in Fig." + 1(doy is used iustead of dp)., 1$d_{B90}$ is used instead of $d_{BH}$ ). +The mean plate magnitudes or 19 stars. as nieasured on 90 plates. are shown as open circles in Fig.,"The mean plate magnitudes for 19 stars, as measured on 90 plates, are shown as open circles in Fig." + 6 plotted against their DT. (Tycho-2) magnitudes., \ref{derived_mags} plotted against their BT (Tycho-2) magnitudes. + For conrparisou a 1:l relation is shown as the solid lue with upright crosses., For comparison a 1:1 relation is shown as the solid line with upright crosses. +" The observed relationship between late aud catalogued magnitudes is reasonably linear for the faiuter stars. but ccarly falls off (bs"" about 1 mag) for the brightest stars as saturation effects heconlο lInore significait."," The observed relationship between plate and catalogued magnitudes is reasonably linear for the fainter stars, but clearly falls off (by about 1 mag) for the brightest stars as saturation effects become more significant." + That saturation is the cause is clear from the aperture photometrv magnitudes determined for the saturated. svuthetic profiles shown iu the rieht hand panel of Fig. 1.," That saturation is the cause is clear from the aperture photometry magnitudes determined for the saturated, synthetic profiles shown in the right hand panel of Fig. \ref{synthetic}," + ming a circular aperture of 20 pixels. (, using a circular aperture of 20 pixels. ( +The same flux saturatioi level was used as that which produced the results of Fig. 5..,The same flux saturation level was used as that which produced the results of Fig. \ref{radius_comp}. + The vertical off«tis arbitrary for the plate and svuthetic magnitudes. and has been adjusted so the data overlap near ~12. which is the same zeropoiut as was used to ot the solid line in Fig. 5..)," The vertical offset is arbitrary for the plate and synthetic magnitudes, and has been adjusted so the data overlap near $\sim$ 12, which is the same zero–point as was used to plot the solid line in Fig. \ref{radius_comp}. .)" + The svuthetic photometry results are shown iu Fie., The synthetic photometry results are shown in Fig. + 6 bv the solid line with uo svinbols., \ref{derived_mags} by the solid line with no symbols. + The ecneral ποια of this line matches quite well he observed plate magnitudes (circles)., The general trend of this line matches quite well the observed plate magnitudes (circles). +" It is relatively straighforward to derive a ρουαι transformation from plate to standard ο,", It is relatively straightforward to derive a polynomial transformation from plate to standard $^{6}$. + We have not attempted to optimise thefit to the radii of saturation (Fig. 5)), We have not attempted to optimise thefit to the radii of saturation (Fig. \ref{radius_comp}) ) + wea anore careful selection of the svuthetic saturation level. or to inixove the aerecluent bv secking a better match between the svuthetic prele and the stellar profiles obtained from the Bamberg plates.," by a more careful selection of the synthetic saturation level, or to improve the agreement by seeking a better match between the synthetic profile and the stellar profiles obtained from the Bamberg plates." + The purpose of tles tudy was ο illustrate that the known. extended stellar raclial profile. when ¢lieiΊος as a xioto-positive from a photographic plate. cau Ὃς| aused. successfully for aperture photometry. even though (indeed. because) the stellar image is nostvy saturated.," The purpose of the study was to illustrate that the known, extended stellar radial profile, when digitised as a photo-positive from a photographic plate, can be used successfully for aperture photometry, even though (indeed, ) the stellar image is mostly saturated." + Such a result was well known to iris photoimotrists (e.c. Moffatt. cr) but nay be less widely appreciated in the modern dieial age.," Such a result was well known to iris photometrists (e.g. $^{\rm {4}}$, $^{\rm {5}}$ ), but may be less widely appreciated in the modern digital age." + We thaik tjo staff of the Dr. Reieis Observatory. Bauberg. for access to their plate οςJlectio1 for hospitality over several visits.," We thank the staff of the Dr. Remeis Observatory, Bamberg, for access to their plate collection for hospitality over several visits." + M. Tsvetkov and A. Dorisova were supported by the Alexander von IIuuboldt Fouidation wader the “Pact of saülitv of Sotth-East Europe’ programune. aud eraut strom BAS/DFG 186-BUL!1 /120/0-2aud the Bulearian National Scieuce Fui (NES T-1103/2001).," M. Tsvetkov and A. Borisova were supported by the Alexander von Humboldt Foundation under the `Pact of stability of South-East Europe' programme, and grants from BAS/DFG 436-BUL110/120/0-2 and the Bulgarian National Science Fund (NFS I-1103/2001)." + D. Coates thanks Pro| C. Simon for access to the facilities of the School of Physics aXx Alaterials Euginceriug., D. Coates thanks Prof G. Simon for access to the facilities of the School of Physics and Materials Engineering. +" We used IRAE. from the US National Optical Astronomial οoervatories. for the photometric nieasurenieits,"," We used IRAF, from the US National Optical Astronomical Observatories, for the photometric measurements." + This research has made use of the o1iline SIMBAD data facility of the Stellar Data Ceutre (CDS). Strasbourg. the NASA ADS database. aud the Sofia Wide Field Plate Database (WEPDB).," This research has made use of the on–line SIMBAD data facility of the Stellar Data Centre (CDS), Strasbourg, the NASA ADS database, and the Sofia Wide Field Plate Database (WFPDB)." + This research has made use of the o1iline SIMBAD data facility of the Stellar Data Ceutre (CDS). Strasbourg. the NASA ADS database. aud the Sofia Wide Field Plate Database (WEPDB). ," This research has made use of the on–line SIMBAD data facility of the Stellar Data Centre (CDS), Strasbourg, the NASA ADS database, and the Sofia Wide Field Plate Database (WFPDB)." + This research has made use of the o1iline SIMBAD data facility of the Stellar Data Ceutre (CDS). Strasbourg. the NASA ADS database. aud the Sofia Wide Field Plate Database (WEPDB). R," This research has made use of the on–line SIMBAD data facility of the Stellar Data Centre (CDS), Strasbourg, the NASA ADS database, and the Sofia Wide Field Plate Database (WFPDB)." + This research has made use of the o1iline SIMBAD data facility of the Stellar Data Ceutre (CDS). Strasbourg. the NASA ADS database. aud the Sofia Wide Field Plate Database (WEPDB). Re," This research has made use of the on–line SIMBAD data facility of the Stellar Data Centre (CDS), Strasbourg, the NASA ADS database, and the Sofia Wide Field Plate Database (WFPDB)." + This research has made use of the o1iline SIMBAD data facility of the Stellar Data Ceutre (CDS). Strasbourg. the NASA ADS database. aud the Sofia Wide Field Plate Database (WEPDB). Ref," This research has made use of the on–line SIMBAD data facility of the Stellar Data Centre (CDS), Strasbourg, the NASA ADS database, and the Sofia Wide Field Plate Database (WFPDB)." + This research has made use of the o1iline SIMBAD data facility of the Stellar Data Ceutre (CDS). Strasbourg. the NASA ADS database. aud the Sofia Wide Field Plate Database (WEPDB). Refe," This research has made use of the on–line SIMBAD data facility of the Stellar Data Centre (CDS), Strasbourg, the NASA ADS database, and the Sofia Wide Field Plate Database (WFPDB)." + This research has made use of the o1iline SIMBAD data facility of the Stellar Data Ceutre (CDS). Strasbourg. the NASA ADS database. aud the Sofia Wide Field Plate Database (WEPDB). Refer," This research has made use of the on–line SIMBAD data facility of the Stellar Data Centre (CDS), Strasbourg, the NASA ADS database, and the Sofia Wide Field Plate Database (WFPDB)." + This research has made use of the o1iline SIMBAD data facility of the Stellar Data Ceutre (CDS). Strasbourg. the NASA ADS database. aud the Sofia Wide Field Plate Database (WEPDB). Referc," This research has made use of the on–line SIMBAD data facility of the Stellar Data Centre (CDS), Strasbourg, the NASA ADS database, and the Sofia Wide Field Plate Database (WFPDB)." + This research has made use of the o1iline SIMBAD data facility of the Stellar Data Ceutre (CDS). Strasbourg. the NASA ADS database. aud the Sofia Wide Field Plate Database (WEPDB). Referco," This research has made use of the on–line SIMBAD data facility of the Stellar Data Centre (CDS), Strasbourg, the NASA ADS database, and the Sofia Wide Field Plate Database (WFPDB)." + This research has made use of the o1iline SIMBAD data facility of the Stellar Data Ceutre (CDS). Strasbourg. the NASA ADS database. aud the Sofia Wide Field Plate Database (WEPDB). Refercon," This research has made use of the on–line SIMBAD data facility of the Stellar Data Centre (CDS), Strasbourg, the NASA ADS database, and the Sofia Wide Field Plate Database (WFPDB)." + This research has made use of the o1iline SIMBAD data facility of the Stellar Data Ceutre (CDS). Strasbourg. the NASA ADS database. aud the Sofia Wide Field Plate Database (WEPDB). Referconc," This research has made use of the on–line SIMBAD data facility of the Stellar Data Centre (CDS), Strasbourg, the NASA ADS database, and the Sofia Wide Field Plate Database (WFPDB)." + This research has made use of the o1iline SIMBAD data facility of the Stellar Data Ceutre (CDS). Strasbourg. the NASA ADS database. aud the Sofia Wide Field Plate Database (WEPDB). Referconce," This research has made use of the on–line SIMBAD data facility of the Stellar Data Centre (CDS), Strasbourg, the NASA ADS database, and the Sofia Wide Field Plate Database (WFPDB)." + This research has made use of the o1iline SIMBAD data facility of the Stellar Data Ceutre (CDS). Strasbourg. the NASA ADS database. aud the Sofia Wide Field Plate Database (WEPDB). Referconces," This research has made use of the on–line SIMBAD data facility of the Stellar Data Centre (CDS), Strasbourg, the NASA ADS database, and the Sofia Wide Field Plate Database (WFPDB)." +ere ? + (Sobezaketal.2000).. the source huninosity would have been Ly~5x10 eres +.,"erg $^{-2}$ $^{-1}$ \citep{sobczak2000}, the source luminosity would have been $_X\sim5\times$ $^{38}$ erg $^{-1}$." + In this case. we would have measured V.~17.5 three weeks later (Jainetal.1999). 0.9 mag fainter than the peak of V=16.6 (Liuetal.2001).," In this case, we would have measured $V\sim17.5$ three weeks later \citep{jain1999}, , 0.9 mag fainter than the peak of $V=16.6$ \citep{liu2001}." +. The later optical measurement would have vielded My=—0.9[2 and a period prediction of 1.17! days., The later optical measurement would have yielded $_V = -0.9^{+1.2}_{-0.8}$ and a period prediction of $1.1^{+13.3}_{-1.0}$ days. + The actual period of NTE J1550-564 is 1.55 days (Oroszetal.2002).. within (he predicted range.," The actual period of XTE J1550-564 is 1.55 days \citep{orosz2002j1550}, within the predicted range." + euccinctlv. theZ8T data show that r2-71 is not an HLMXD. and therefore may be an LMXD.," Succinctly, the data show that r2-71 is not an HMXB, and therefore may be an LMXB." + The vanParadij&MeClintock.(1994) correlation provides reliable orbital period range predictions for such objects even when the observations are separated by 3 weeks and the relation is applied to a complex transient lighteurve., The \citet{vanparadijs1994} correlation provides reliable orbital period range predictions for such objects even when the observations are separated by 3 weeks and the relation is applied to a complex transient lightcurve. + We therefore. apply the correlation to our measurements of 12-11 under the assumption that. as in the above Galactic examples. the errors in absolute V. magnitude and in the correlation are sufficient to account for complications in the lightνο ancl (he 3-week gap between N-ray and optical observations.," We therefore apply the correlation to our measurements of r2-71 under the assumption that, as in the above Galactic examples, the errors in absolute $V$ magnitude and in the correlation are sufficient to account for complications in the lightcurve and the 3-week gap between X-ray and optical observations." + We note that these predictions rely on the assumption that 12-71 behaves in a similar way (0 many Galactic XlNe., We note that these predictions rely on the assumption that r2-71 behaves in a similar way to many Galactic XRNe. + Qur L-band brightness upper-limit of D>25.5. [rom our completeness results. can be converted (o a V-band luminosity bv assuming the same foreground extinction we assumec for the X-ray spectral lit and converting to optical extinction using the relation of (1995).," Our $B$ -band brightness upper-limit of $B\geq25.5$, from our completeness results, can be converted to a $V$ -band luminosity by assuming the same foreground extinction we assumed for the X-ray spectral fit and converting to optical extinction using the relation of \citet{predehl1995}." +. Assuming i—M=24.47. Mj>0.6.," Assuming $m-M = 24.47$, $_B \geq 0.6$." + Then using the mean D—V colors of Galactic LAINBs in the Liuetal.(2001) catalog (-0.09 +/- 0.14). M20.5.," Then using the mean $B-V$ colors of Galactic LMXBs in the \citet{liu2001} + catalog (-0.09 +/- 0.14), $_V \geq 0.5$." + Placing this upper-limit on the optical huninosity and our 0.3.7 keV X-ray huninositv of 3.9 x107* ere Linto the vanParadijs&MeClintock(1994) correlation. including their quoted errors. we obtain a prediction for the period of the LMXD svstem r2-71 of P?x1.6 days.," Placing this upper-limit on the optical luminosity and our 0.3–7 keV X-ray luminosity of 3.9 $\times 10^{37}$ erg $^{-1}$ into the \citet{vanparadijs1994} + correlation, including their quoted errors, we obtain a prediction for the period of the LMXB system r2-71 of $P\leq1.6$ days." + We have constrained (he N-rav and optical properties of a repeating N-rav Gansient source in the M31 bulge. which we have named CXOMS1 JO04233.4+411703 or 12-71.," We have constrained the X-ray and optical properties of a repeating X-ray transient source in the M31 bulge, which we have named CXOM31 J004233.4+411703 or r2-71." +" This source has undergone at least (wo X-ray outbursts brighter (han 10"" erg Fin the past two decades.", This source has undergone at least two X-ray outbursts brighter than $^{37}$ erg $^{-1}$ in the past two decades. + Previous X-ray. observations reveal that the source has varied by at least a factor of 100 in X-ray. Iuminositv. and ourChandra monitoring program shows that the outburst in May of 2004 had an e-folding decay. time of less than a month.," Previous X-ray observations reveal that the source has varied by at least a factor of 100 in X-ray luminosity, and our monitoring program shows that the outburst in May of 2004 had an $e$ -folding decay time of less than a month." + The observed activity of the source from 1979 to the present suggests (hab it has a duty evele of (ra., The observed activity of the source from 1979 to the present suggests that it has a duty cycle of $^{+0.06}_{-0.03}$. + Optical observations of the location of 12-71 with //5T' ACS before. during. and alter the X-ray outburst show no clear optical counterpart to this (rausient N-ray event in (he M31 bulee.," Optical observations of the location of r2-71 with $HST$ ACS before, during, and after the X-ray outburst show no clear optical counterpart to this transient X-ray event in the M31 bulge." + The stellar content of (he region rules out thepresence of an HMXD (ransient svstem, The stellar content of the region rules out thepresence of an HMXB transient system +of Ser before the occurrence of anv tidal stripping. My= LL ,"of Sgr before the occurrence of any tidal stripping, $M_V\simeq -14$ ." +estimated that in he Ser Stream there are as many stars as in the present uudiszupted body of the galaxy. thus the total inuinositv of the Ser dSpl was roughly two times the xeseut value.," estimated that in the Sgr Stream there are as many stars as in the present undisrupted body of the galaxy, thus the total luminosity of the Sgr dSph was roughly two times the present value." + ence the total absolute magnitude at that nue was Myloe(2)=Lhd1998).., Hence the total absolute magnitude at that time was $M_V-\log(2)\simeq -14.1$. + The excellent agreement between the two independent estimates of the iuitial Ay fully supports the ausibility of the proposed scenario., The excellent agreement between the two independent estimates of the initial $M_V$ fully supports the plausibility of the proposed scenario. + According to the results presented. it emerges that the Ser dSph was not only au nauportaut coutributor of halo ποια stars but it also had a significant role iu the building-wp of the globular clusters system of the. Milky Wav.," According to the results presented, it emerges that the Sgr dSph was not only an important contributor of halo field stars but it also had a significant role in the building-up of the globular clusters system of the Milky Way." + ALD. and F.R.F. acknowledge the financial support to this research by the italian (MURST) through the eraut p. 2001028879. assigned to the projectSpheroid.," M.B. and F.R.F. acknowledge the financial support to this research by the italian (MURST) through the grant p. 2001028879, assigned to the project." + This research has mace use of NASAs Astrophysics Data System Abstract Service., This research has made use of NASA's Astrophysics Data System Abstract Service. +as that [or a single star appears to be quite good throughout this ghase.,as that for a single star appears to be quite good throughout this phase. + This cau probably be iuterpreted as being adequate for any stars which are not. compact objects because the sinallest separation case was about as small as we could make it on the ZAKS for these two masses., This can probably be interpreted as being adequate for any stars which are not compact objects because the smallest separation case was about as small as we could make it on the ZAMS for these two masses. + The differences in structure become noticeable a about one quarter of the radius (equivaleut to abot an iuterior mass of ONL.) for the moclel jus prior to Roche lobe overflow., The differences in structure become noticeable at about one quarter of the radius (equivalent to about an interior mass of $\Msun$ ) for the model just prior to Roche lobe overflow. + The surface is reasonably well approximated bv the Roche surface until very close to the beginning of Roche lobe overflow., The surface is reasonably well approximated by the Roche surface until very close to the beginning of Roche lobe overflow. + As Rocte lobe overflow is approached the contour lines in tle direction of the secondary. become very sesilively «epeudent on the value of the equipotential. aud the variatious between the Roche poterial and tie equipotential determined from the mocle reflect this.," As Roche lobe overflow is approached the contour lines in the direction of the secondary become very sensitively dependent on the value of the equipotential, and the variations between the Roche potential and the equipotential determined from the models reflect this." + It is also true that the timescae for the surface chauge becomes very short as Rocle lobe overflow is approached. raisiug the possibility hat the assumptiou that the surface is au equipotential is not valid.," It is also true that the timescale for the surface change becomes very short as Roche lobe overflow is approached, raising the possibility that the assumption that the surface is an equipotential is not valid." + It is difficult to identify aiv consequence of this from the staudpoit of the evolution caleulations. but it uay play a role 1 the details of the mass transfer within the systel.," It is difficult to identify any consequence of this from the standpoint of the evolution calculations, but it may play a role in the details of the mass transfer within the system." +" One linportant assumption we 1rake in the calcuatious is that we neglect the radiation from the secoucary component. aud this racdiation could make a considerae difference to the elTective lemperawe aaud observed surface fux of the prima""wo star. particularly iu the direction of the secondary."," One important assumption we make in the calculations is that we neglect the radiation from the secondary component, and this radiation could make a considerable difference to the effective temperature and observed surface flux of the primary star, particularly in the direction of the secondary." +" We cab estimate the ""trte” effective tem;»erature of the primary star by calculati the effecjve teuperature at the surf:ce of the prinary 1sing the secondarys Iuminosity axd p. where La is the ZAMS |uuinosity of he OM model ceterminect w the 2D evolution code. σ je Stefan-Boltzinann constant. Ap the «Istanee from the center of the secondary to the Surface o. the primary and ζω the effective teniperatwe."," We can estimate the “true” effective temperature of the primary star by calculating the effective temperature at the surface of the primary using the secondary's luminosity and $L_{\rm S} = 4 \pi \sigma T_{\rm eff}^{4} R_{\rm D}$ , where $L_{\rm S}$ is the ZAMS luminosity of the $\Msun$ model determined by the 2D evolution code, $\sigma$ the Stefan-Boltzmann constant, $R_{\rm D}$ the distance from the center of the secondary to the surface of the primary and $T_{\rm eff}$ the effective temperature." + If we take the a11H. Case as a represen.ative example and the radius of the pritlary jus before RLOF. which is IB... tlen Ry=G.88OR. (where tie ZANIS radius of the SNL. 2D inodel is 2.785R..).," If we take the $a = 14\Rsun$ case as a representative example and the radius of the primary just before RLOF, which is $\Rsun$, then $R_{\rm D} = 6.886\Rsun$ (where the ZAMS radius of the $\Msun$ 2D model is $\Rsun$ )." + Using La=529L. we find that the effective teuperature at the surface o ‘the pμιαν usiug the secoudarys luminosity to be 102611. At tle angilar zoue closest to the seconda'v. the effective temperature of the primary just before RLOF was determined to be 131761s. which is hotter than the effective temperature calculated. using the luiuosity of the secondary. inocel.," Using $L_{\rm S} = 529\Lsun$ we find that the effective temperature at the surface of the primary using the secondary's luminosity to be 10561K. At the angular zone closest to the secondary, the effective temperature of the primary just before RLOF was determined to be 13476K, which is hotter than the effective temperature calculated using the luminosity of the secondary model." + We have also calculated the effective temperature at the surface of the pritjury using the secondarys Luminosity just alter the ZAMS., We have also calculated the effective temperature at the surface of the primary using the secondary's luminosity just after the ZAMS. + This effecive temperature was loud4 to be about 23 times less than te effective temperature of the primary calculated by the 2D evolutionolt code., This effective temperature was found to be about 2.3 times less than the effective temperature of the primary calculated by the 2D evolution code. + The üunplication of this 'esult for the models near RLOF js that the surface flux of tle primary. [or example as show i Fig.," The implication of this result for the models near RLOF is that the surface flux of the primary, for example as shown in Fig." + 9. shouk Clearly be higher at the angular zones closest to he companion.," 9, should clearly be higher at the angular zones closest to the companion." + This also means lizi the observec| dip iu the flux is uot completely real auc iuxleed. the effective temperature of thee primary closes to the companion should be substantially hotter than what we have calculated it to be using the 2D stellar evolution code.," This also means that the observed dip in the flux is not completely real and indeed, the effective temperature of the primary closest to the companion should be substantially hotter than what we have calculated it to be using the 2D stellar evolution code." + What ellect the secoucarys racliatiou has on the interior properties oftve SAL. primary are vet to be determined aud we leave tlat for future work., What effect the secondary's radiation has on the interior properties of the $\Msun$ primary are yet to be determined and we leave that for future work. + We do note that this effect will mostly be important when the prilary ds rapidly approaching RLOF aud the evolution of the system at this stage is quick enough that the raclation, We do note that this effect will mostly be important when the primary is rapidly approaching RLOF and the evolution of the system at this stage is quick enough that the radiation +The temperature profiles are calculated (rom the brightuess ratio of the X-ray. profiles in the three energy bauds. AD=0.5—1.5.1.23.04443.010keV.,"The temperature profiles are calculated from the brightness ratio of the X-ray profiles in the three energy bands, $kT = 0.5-1.5, 1.5-3.0 and 3.0-10 keV$." + We assumed that there were no racial eradients in metal abuudance auc HI absorption., We assumed that there were no radial gradients in metal abundance and HI absorption. + The typical temperature profiles of our sample are shown in Figure 1. together with a comparison with the previous rueasurements.," The typical temperature profiles of our sample are shown in Figure 1, together with a comparison with the previous measurements." + The total mass of a dark balo can be calculated [rom the gas deusity and the temperature profiles of ICML assuming the hydrostatic equilibrium.," The total mass of a dark halo can be calculated from the gas density and the temperature profiles of ICM, assuming the hydrostatic equilibrium." +" If the observed. X-ray. surface. brightuess profile Sig, is described by the ;7— model. "". where 0. 0. and 3 are the angular radius. the core radius aud the 3 parameter respectively. aud the radial gradient of temperatures is relatively small as compared with that of the eas deusity. the total mass within radius r is given by where T. b. gan, aud ry. are the gas temperature. the zmauu's coustant. the mean molecular weieht of the hot eas aud the core radius respectively."," If the observed X-ray surface brightness profile $S_{(\theta)}$ is described by the $\beta-$ model, $S(\theta)=S_{0} (1+(\theta/\theta_{c})^{2} )^{-3 \beta +0.5}$ , where $\theta$, $\theta_{c}$ and $\beta$ are the angular radius, the core radius and the $\beta$ parameter respectively, and the radial gradient of temperatures is relatively small as compared with that of the gas density, the total mass within radius r is given by where $ T$, $k$, $\mu m_{p}$ and $r_{c}$ are the gas temperature, the $^\prime$ s constant, the mean molecular weight of the hot gas and the core radius respectively." + We found that ο. 9 aud AL were uot coustaut in a sinele cluster. but changed slowly with radius.," We found that $r_{c}$, $\beta$ and $kT$ were not constant in a single cluster, but changed slowly with radius." + The angular profiles of two parameters. rig) aud ο]. were calculated by fitting the 5— model to the local brightness profiles of 0+0.30.," The angular profiles of two parameters, $r_{c (\theta)}$ and $\beta_{(\theta)}$ , were calculated by fitting the $\beta-$ model to the local brightness profiles of $\theta\pm 0.3 \theta$." + Although the angular profiles. Γρ. oy) aud (0) ATi). ave the luminosity weightedo properties of the hot oeas alonee the line of sieht.D these are nearly equal to the radial profiles. ο] rj). (n)μι amd (n)AT). if the radial ogradient of ogas densitv (or ορ)(0) is much larger than those ofr.. 9 and £T.," Although the angular profiles, $r_{c (\theta)}$, $\beta_{(\theta)}$ and $kT_{(\theta)}$ , are the luminosity weighted properties of the hot gas along the line of sight, these are nearly equal to the radial profiles, $r_{c (r)}$ , $\beta_{(r)} $ and $kT_{(r)}$, if the radial gradient of gas density (or $S_{(\theta)}$ ) is much larger than those of $r_{c}$, $\beta$ and $kT$." + In our sample. reg). δρ) aud πρι change factor 2 at most. while the Sig; changes 2 or 3 orders of maguitude.," In our sample, $r_{c (\theta)}$, $\beta_{(\theta)}$ and $kT_{(\theta)}$ change factor 2 at most, while the $S_{(\theta)}$ changes 2 or 3 orders of magnitude." + We therefore assumed that the observed augular proliles represented the radial profiles of these parameters., We therefore assumed that the observed angular profiles represented the radial profiles of these parameters. +" The local gas density. profile was therefore. given. by ny,=wy.LF(r/raqu)""PE|3572?> and the total mass AL, was calculated from. the equation (2).", The local gas density profile was therefore given by $n_{(r)} = n_{0} (1+(r/r_{c (r)})^{2})^{-3\beta_{(r)} /2} $ and the total mass $M_{(r)}$ was calculated from the equation (2). +" The mass density pp.ose)=GMdey—Mj)erdr) was obtained from Mj, and Mj4,4. keeping dr=2arcsec."," The mass density $\rho_{(r+0.5dr)} = (M_{(r+dr)}-M_{(r)} )/(4 \pi r^{2} dr)$ was obtained from $M_{(r)}$ and $M_{(r+dr)}$, keeping $ dr=26arcsec$." + We have coustructed the models of gas halos bound by the NEW dark halos to evaluate the systematic errors in our iruethod., We have constructed the models of gas halos bound by the NFW dark halos to evaluate the systematic errors in our method. + The mass profiles were calculated from the model profiles. which correspond to typical galaxies. poor clusters aud rich elusters. by applying the same method.," The mass profiles were calculated from the model profiles, which correspond to typical galaxies, poor clusters and rich clusters, by applying the same method." + The best-fit 0. aud re are then calculated by fitting the NEW model to the mass profiles., The best-fit $\delta_{c}$ and $r_{s}$ are then calculated by fitting the NFW model to the mass profiles. + Comparing the caleulated 5. aud ri with the original values. we have coulirmecd that the systematic errors of our method were much smaller than the typical photon noise of our sample objects.," Comparing the calculated $\delta_{c}$ and $r_{s}$ with the original values, we have confirmed that the systematic errors of our method were much smaller than the typical photon noise of our sample objects." + Inour analvsis. thebrightness profile within 0.«Q.barcmin were excluded toavoid the contribution of the cooling flow compouent.," Inour analysis, thebrightness profile within $\theta<0.5 arcmin$ were excluded toavoid the contribution of the cooling flow component." + The maximum radii were extending up to 10—IQarcimin , The maximum radii were extending up to $10-40 arcmin$ +predicted confusion is predouminautly iustrunental. because the sources are typically unresolved (see &66.1).,"predicted confusion is predominantly instrumental, because the sources are typically unresolved (see 6.4)." + We find approximately 100 sources within 430°) of atitude aud longitude of the Galactic Centre an area of roughly 23100.deg?., We find approximately 100 sources within $\pm30^\circ$ of latitude and longitude of the Galactic Centre – an area of roughly $3400\;{\rm deg^2}$. +" Dx conrparison the poiut-spread-fuuction of EGRET has a Full-Width. ILf-Maxiuumn (FEWIIMS) of approxinatelv (μου 866.1). implying hat this eutire region appears. to EGRET. to be ""covered"" with overlapping sources."," By comparison the point-spread-function of EGRET has a Full-Width Half-Maximum (FWHM) of approximately $4^\circ$ (see 6.4), implying that this entire region appears, to EGRET, to be “covered” with overlapping sources." + The spectrum predicted by the present model is given in Ohishi. Mori auc Walker (2003): it exhibits a peak power Le. a peak in E°dN/dE at several-liuudred MeV. At lis point the spectrum rolls over from dN/LExE. |. at low energies. approaching E277 at Ec1 GeV. Iu comparing this prediction with the data (e.g. Merck et al 1996). there are two iuportaut poiuts o bear in nünd.," The spectrum predicted by the present model is given in Ohishi, Mori and Walker (2003): it exhibits a peak power – i.e. a peak in $E^2{\rm d}N/{\rm d}E$ – at several-hundred MeV. At this point the spectrum rolls over from ${\rm d}N/{\rm d}E\propto E^{-1}$ , at low energies, approaching $E^{-2.75}$ at $E\gg1$ GeV. In comparing this prediction with the data (e.g. Merck et al 1996), there are two important points to bear in mind." + First. the model gamma-ray Cluission spectruni is unique only by default: we donut know the cosmic-ray spectrun clsewhere in he Galaxy.," First, the model gamma-ray emission spectrum is unique only by default: we don't know the cosmic-ray spectrum elsewhere in the Galaxy." + The simple fact that various eamuna-rav spectra are observed should therefore mot ο sed as an argument agaiust the present uodel., The simple fact that various gamma-ray spectra are observed should therefore not be used as an argument against the present model. + We note that the diffuse Calactic plane enüsson at Ez1 GeV (Iblunter ct al 1997) is difücult to understand if the Calactic cosiic-rav spectrum is everywhere the same as du the solar neighbourhood. sugecstingOO that the typical cosmic-ray spectrum may be harder than measured locally (Mori 1997).," We note that the diffuse Galactic plane emission at $E\ga1$ GeV (Hunter et al 1997) is difficult to understand if the Galactic cosmic-ray spectrum is everywhere the same as in the solar neighbourhood, suggesting that the typical cosmic-ray spectrum may be harder than measured locally (Mori 1997)." + Secondly. the sources are predicted to be extended. with low-intensity wines on the profile extending out to ~2 typically.," Secondly, the sources are predicted to be extended, with low-intensity wings on the profile extending out to $\sim2^\circ$, typically." + Although the spectrin should be uniforui across the source. the fact that the poiut-spread function of the detector chauges with enerewv. coupled with the low-level “wines” on the source profile. could lead to spurious estimates of spectral shapes.," Although the spectrum should be uniform across the source, the fact that the point-spread function of the detector changes with energy, coupled with the low-level “wings” on the source profile, could lead to spurious estimates of spectral shapes." + In particular. some fraction of the source flux will be absorbed into the estimate of the backeround intensity. aud this fraction will vary with photon euergv.," In particular, some fraction of the source flux will be absorbed into the estimate of the background intensity, and this fraction will vary with photon energy." + These problems. coupled with the low signal-to-noise ratio of niuiv of the UID sources. male it difficult to assess the success of the model spectral predictions.," These problems, coupled with the low signal-to-noise ratio of many of the UID sources, make it difficult to assess the success of the model spectral predictions." + The model we have preseuted involves emission which is intrinsically steady on observationally accessible time-scales: it is therefore not relevant to anv sources Which are kuown to vary siguificautly., The model we have presented involves emission which is intrinsically steady on observationally accessible time-scales; it is therefore not relevant to any sources which are known to vary significantly. + Most of the UID EGRET sources are not bright enough to permit strong coustraimts on their variability., Most of the UID EGRET sources are not bright enough to permit strong constraints on their variability. + There is no consensus in the literature regarding the variability of the UID sources: AleLaughlin ct al (1996) find that only a siall fraction. roughly one in six. of the UID EGRET sources are significantly variable (see also Wallace et al 2000): by contrast Torres et al (2001) suggest that the fraction mav be as huge as one third. in the case of low-latitude UID sources (see also Torres. Pessal aud Romero. 2001. and. Tomplius 1999).," There is no consensus in the literature regarding the variability of the UID sources: McLaughlin et al (1996) find that only a small fraction, roughly one in six, of the UID EGRET sources are significantly variable (see also Wallace et al 2000); by contrast Torres et al (2001) suggest that the fraction may be as large as one third, in the case of low-latitude UID sources (see also Torres, Pessah and Romero, 2001, and Tompkins 1999)." + We note that large-uuplitude variations do not sit casily with the multiple/exteuded. source designation carried by —50 of the UID EGRET sources (Iartinan et al 1999)., We note that large-amplitude variations do not sit easily with the multiple/extended source designation carried by $\sim$ of the UID EGRET sources (Hartman et al 1999). + Although the cstimated angular sizes of the detectable nüui-ialos are large (of order degrees]. the resolving power of EGRET is quite modest. with a poiut-spread-functiou. of 5 Full--Width-TaltA\lasximuun CPFWIIM) at 100 MeV. CPhonipso- et al 1993). (," Although the estimated angular sizes of the detectable mini-halos are large (of order degrees), the resolving power of EGRET is quite modest, with a point-spread-function of $5^\circ$ Full-Width-Half-Maximum (FWHM) at 100 MeV (Thompson et al 1993). (" +The in-flight calibration data are consisteut with the pre-launch calibration in respect of the poiut-spread-function — Esposito ¢+ al 1999.),The in-flight calibration data are consistent with the pre-launch calibration in respect of the point-spread-function — Esposito et al 1999.) + The ECRET angular resolution improvesμα with increasing euergv. scaling roughly as E0.53.," The EGRET angular resolution improves with increasing energy, scaling roughly as $E^{-0.534}$." + However. if (UNAE is close to £7. half of the photous contributing to a source detection are within a factor ~2 of the low-energy. threshold.," However, if ${\rm d}N/{\rm d}E$ is close to $E^{-2}$, half of the photons contributing to a source detection are within a factor $\sim2$ of the low-energy threshold." + We therefore adopt a PFWIIM of 17 as the relevant instrumental width: sources would thus ποσα to ve at least 87 across m order to be fully resolved., We therefore adopt a FWHM of $4^\circ$ as the relevant instrumental width; sources would thus need to be at least $8^\circ$ across in order to be fully resolved. + For an isothermal deusity distribution withiu each uini-halo (855). half of the total fiw is contained within a diameter approximately equal to 6.," For an isothermal density distribution within each mini-halo 5), half of the total flux is contained within a diameter approximately equal to $\theta_t$." + Referring o figure Lowe then find that oulv a inv fraction of the svuthetic popul:ion could be ally resolved by EGRET., Referring to figure 4 we then find that only a tiny fraction of the synthetic population could be fully resolved by EGRET. + If the iustrmuuental FWIIM is comparable to he source size then the source structure will rot be resolved. but the datacan nevertheless indicate that the source is extended. by virtue of he observed intensity profile being broader than," If the instrumental FWHM is comparable to the source size then the source structure will not be resolved, but the datacan nevertheless indicate that the source is extended, by virtue of the observed intensity profile being broader than" +1n Cold) Dark Matter models. structure formation evolves in à hierarchical. fashion with aggregation of smaller mass units along large-scale anisotropic structures.,"In Cold Dark Matter models, structure formation evolves in a hierarchical fashion with aggregation of smaller mass units along large-scale anisotropic structures." + since virialization processes tend to sphericalize initial anisotropic distributions of matter. the shape of cosmic. structures is related. to their. formation processes ancl evolutionary stage and thus it is extremely important to unambiguouslv determine their intrinsic shapes.," Since virialization processes tend to sphericalize initial anisotropic distributions of matter, the shape of cosmic structures is related to their formation processes and evolutionary stage and thus it is extremely important to unambiguously determine their intrinsic shapes." + Apart from disk galaxies all cosmic structures on Larger scales appear to be dominated by prolate like shapes., Apart from disk galaxies all cosmic structures on larger scales appear to be dominated by prolate like shapes. + This is been shown to be the case for clusters of galaxies (cL., This has been shown to be the case for clusters of galaxies (cf. + Carter Aletealfe 1980: Plionis.. Barrow Frenk 1991: Cooray 1999: Jasilakos. lionis Maddox 2000) as well as for superclusters which show a precominance of ilamentary like shapes both observationally. theoretically and in Cosmological N-body simulations (ο Zeldovich. Einasto Shancarin 1982: Shandarin Zelclovich 1983: Broadhurst οἱ al.," Carter Metcalfe 1980; Plionis, Barrow Frenk 1991; Cooray 1999; Basilakos, Plionis Maddox 2000) as well as for superclusters which show a predominance of filamentary like shapes both observationally, theoretically and in Cosmological N-body simulations (cf Zeldovich, Einasto Shandarin 1982; Shandarin Zeldovich 1983; Broadhurst et al." + 1990: de Lapparent. Geller. Lluehra 901: Plionis. Jing Valdarnini 1992: Jaaniste et. al 908: Sathvaprakash et al.," 1990; de Lapparent, Geller Huchra 1991; Plionis, Jing Valdarnini 1992; Jaaniste et al 1998; Sathyaprakash et al." + 1998: Valdarnini. Chizzardi Bonometto 1999: Jasilakos. Plionis Rowan-Robinson 2001).," 1998; Valdarnini, Ghizzardi Bonometto 1999; Basilakos, Plionis Rowan-Robinson 2001)." + In the case of Hickson or Shakhhazian compact groups it has been shown that they are even flatter than clusters ancl most. probably prolate-like configurations with typical true axial ratios 0.3 (Vardanian AMelik-Alaverdian 1978: Hickson et al., In the case of Hickson or Shakhbazian compact groups it has been shown that they are even flatter than clusters and most probably prolate-like configurations with typical true axial ratios $\sim 0.3$ (Vardanian Melik-Alaverdian 1978; Hickson et al. + 1984: AMalvkh Orlov 1986: Oleak et al., 1984; Malykh Orlov 1986; Oleak et al. + 1995)., 1995). + Lt is obvious that the intrinsic shape of cosmic structures can be lost when projected. on the plane of the sky and herefore it is important. to deal. with such and. other systematic effects that can hide the true shape of cosmic structures., It is obvious that the intrinsic shape of cosmic structures can be lost when projected on the plane of the sky and therefore it is important to deal with such and other systematic effects that can hide the true shape of cosmic structures. + Different studies have attempted: to recover he distribution of intrinsic shapes from the corresponding apparent distribution using inversion techniques based on he assumption the| their orientations are random., Different studies have attempted to recover the distribution of intrinsic shapes from the corresponding apparent distribution using inversion techniques based on the assumption that their orientations are random. + The plan of the paper is the following: In. Section 2 we deseribe the eroup sample that we use., The plan of the paper is the following: In Section 2 we describe the group sample that we use. + We attempt o identify the extent of projection contamination and we describe the projected. shape determination. method., We attempt to identify the extent of projection contamination and we describe the projected shape determination method. + ba Section 3 we invert the projected. axial ratio distribution and recover the corresponding intrinsic one., In Section 3 we invert the projected axial ratio distribution and recover the corresponding intrinsic one. + The discussion and our conclusions are presented in Section 4., The discussion and our conclusions are presented in Section 4. + We use the recent UZC-SSRS2 eroup catalogue (Itamella et al 2002) which is based on the Updated Zwicky Catalogue (UZC: Falco et al., We use the recent UZC-SSRS2 group catalogue (Ramella et al 2002) which is based on the Updated Zwicky Catalogue (UZC; Falco et al. + 1999) and the Southern Sky Redshift Survey (SSRS2: da Costa et al 1998). to measure the projected. group shape distribution and. hence. attempt to estimate their intrinsic. shape.," 1999) and the Southern Sky Redshift Survey (SSRS2; da Costa et al 1998), to measure the projected group shape distribution and hence attempt to estimate their intrinsic shape." + The catalogue. has a, The catalogue has a +the luminosities produced by primary electrons are higher in models with a=1.,the luminosities produced by primary electrons are higher in models with $a=1$. +" On the other hand, luminosities produced by hadrons and muons are higher in models with a static corona and diffusion of the relativistic particles."," On the other hand, luminosities produced by hadrons and muons are higher in models with a static corona and diffusion of the relativistic particles." +" This is because in models with advection an important fraction of protons and pions are swallowed by the black hole, while with diffusion these particles are able to lose their energy before falling onto the compact object or escaping from the system."," This is because in models with advection an important fraction of protons and pions are swallowed by the black hole, while with diffusion these particles are able to lose their energy before falling onto the compact object or escaping from the system." +" In models with a=100, the non-thermal emission at E,>1 MeV is dominated by synchrotron and IC radiation of secondary pairs."," In models with $a=100$, the non-thermal emission at $E_{\gamma}>1$ MeV is dominated by synchrotron and IC radiation of secondary pairs." +" At very high energies, the main contributions to the spectrum are due to photo-meson production in all models."," At very high energies, the main contributions to the spectrum are due to photo-meson production in all models." + We note that below ~150 keV the source will be totally dominated by thermal Comptonization (not shown in the figures for clarity)., We note that below $\sim 150$ keV the source will be totally dominated by thermal Comptonization (not shown in the figures for clarity). +" From Fig. 3,"," From Fig. \ref{fig:SEDs}," + we conclude that there are two parameters that determine the relevant radiative processes: the hadronic content in the plasma and the advection velocity., we conclude that there are two parameters that determine the relevant radiative processes: the hadronic content in the plasma and the advection velocity. +" If the hadronic content is high, then a large number of secondary particles are expected to increase the emission at high energies."," If the hadronic content is high, then a large number of secondary particles are expected to increase the emission at high energies." + This is precisely what happens in our model for a high value of the parameter a., This is precisely what happens in our model for a high value of the parameter $a$. +" However, the advection also has an important role, because in a corona with convection a significant part of the proton content will be engulfed by the black hole reducing the emission."," However, the advection also has an important role, because in a corona with convection a significant part of the proton content will be engulfed by the black hole reducing the emission." + The overall SED predicted by a particular model is then the result of the specific balance between the two main free parameters., The overall SED predicted by a particular model is then the result of the specific balance between the two main free parameters. +" 'There are other physical quantities that are important to our model, such as the magnetic field and the background thermal luminosity, but the values of these parameters are restricted by observations of sources, such as Cygnus X-1."," There are other physical quantities that are important to our model, such as the magnetic field and the background thermal luminosity, but the values of these parameters are restricted by observations of sources, such as Cygnus X-1." +propertiess of ssystems.J,"s of systems.," +propertiess of ssystems.J1,"s of systems.," +propertiess of ssystems.J17,"s of systems.," +propertiess of ssystems.J175,"s of systems.," +propertiess of ssystems.J1758,"s of systems.," +propertiess of ssystems.J17585,"s of systems.," +propertiess of ssystems.J17585-,"s of systems.," +propertiess of ssystems.J17585-3,"s of systems.," +propertiess of ssystems.J17585-30,"s of systems.," +propertiess of ssystems.J17585-305,"s of systems.," +propertiess of ssystems.J17585-3057,"s of systems.," +propertiess of ssystems.J17585-3057.,"s of systems.," +propertiess of ssystems.J17585-3057..,"s of systems.," +effective radius of 2.75kpe. and amass of Lx10/2M.. (2)..,"effective radius of $2.75\,{\rm kpc}$, and a mass of $1 \times 10^{10} M_\odot$ \citep{BinneyMerrifield98}." + Note that although this model is only intended to very approximately reproduce the phase-space properties of the Milkv Way's bulge. the maximum phase-space dersity that it produces in Fig.," Note that although this model is only intended to very approximately reproduce the phase-space properties of the Milky Way's bulge, the maximum phase-space density that it produces in Fig." + | agrees well with the value of ~107M.pe?(km/s)7* inferred by ?..," \ref{fig:mwphase} agrees well with the value of $\sim 10^{-5}M_\odot\,{\rm pc}^{-3}\,({\rm km/s})^{-3}$ inferred by \citet{Wyse98}." + The maximum phase density decreases with luminosity in typical spheroidal components (?).. so even this relatively small bulge adds in sufficient stars at high phase densities to generate the missing high-density extreme of the elliptical.," The maximum phase density decreases with luminosity in typical spheroidal components \citep{MaoMo98}, so even this relatively small bulge adds in sufficient stars at high phase densities to generate the missing high-density extreme of the elliptical." + Thus. there would be noviolation of the mixing constraint of Eq. (2))," Thus, there would be noviolation of the mixing constraint of Eq. \ref{eq:mixing}) )" + in turning this disk-dominated galaxy into a typical elliptical galaxy through collisionless mixing processes., in turning this disk-dominated galaxy into a typical elliptical galaxy through collisionless mixing processes. + Although the above test case is interesting. 1t does not place any strong limits on the possible general evolutionary. paths for galaxies. since for any individual case one could always find potential progenitors with structural parameters such that the mixing constraint is not violated.," Although the above test case is interesting, it does not place any strong limits on the possible general evolutionary paths for galaxies, since for any individual case one could always find potential progenitors with structural parameters such that the mixing constraint is not violated." + It is therefore more interesting to consider the properties of the entire population of galaxies. to determine more globally what evolutionary. paths the whole population may or may not have followed.," It is therefore more interesting to consider the properties of the entire population of galaxies, to determine more globally what evolutionary paths the whole population may or may not have followed." + An important first step in this direction was made by 9?.. who explored the phase density as a function of absolute magnitude for a reasonably large sample of disk and elliptical galaxies.," An important first step in this direction was made by \citet{MaoMo98}, who explored the phase density as a function of absolute magnitude for a reasonably large sample of disk and elliptical galaxies." + They also went beyond considering just the extrema of the phase density distribution by also calculating an average “effective phase density” for these galaxies., They also went beyond considering just the extrema of the phase density distribution by also calculating an average “effective phase density” for these galaxies. + Through. this analysis. they were able to show that disk- and galaxies follow distinct sequences of phase space density as a function. of absolute magnitude.," Through this analysis, they were able to show that disk- and galaxies follow distinct sequences of phase space density as a function of absolute magnitude." + However. they did not possess the decompositions of individual galaxies into spheroids and disks that would have allowed them to model multiple components within single systems.," However, they did not possess the decompositions of individual galaxies into spheroids and disks that would have allowed them to model multiple components within single systems." + Thus. they were not in a position to calculate the full stellar phase space density distribution to ascertain whether. for example. the bulge components of disk galaxies might be sufficient to eliminate any apparent violation of mixing constraints. às was illustrated in Sect. 2.3..," Thus, they were not in a position to calculate the full stellar phase space density distribution to ascertain whether, for example, the bulge components of disk galaxies might be sufficient to eliminate any apparent violation of mixing constraints, as was illustrated in Sect. \ref{sec:MWmodel}." + In addition. the galaxies they analyzed comprised à somewhat heterogeneous sample. so they did not have access to a statistically complete sample that would have enabled them to determine the stellar phase density of the local Universe in a well-defined volume.," In addition, the galaxies they analyzed comprised a somewhat heterogeneous sample, so they did not have access to a statistically complete sample that would have enabled them to determine the stellar phase density of the local Universe in a well-defined volume." + We therefore seek to extend this analysis by considering the data from the Millennium Galaxy (MGC:?).., We therefore seek to extend this analysis by considering the data from the Millennium Galaxy \citep[MGC;][]{Liskeetal03}. + This survey over 37.5deg. complete to mp=24. provides a well-defined and thorough sampling of galaxies in the local Universe. and the availability of colour data offers at least a crude conversion from B-band luminosity to stellar mass (?).. although the connection between these quantities 1s necessarily indirect due to the effects of varying stellar populations and extinctio.," This survey over $37.5\,{\rm deg}^2$, complete to $m_B = 24$, provides a well-defined and thorough sampling of galaxies in the local Universe, and the availability of colour data offers at least a crude conversion from B-band luminosity to stellar mass \citep{BelldeJong01}, although the connection between these quantities is necessarily indirect due to the effects of varying stellar populations and extinction." + Moreover. ? have show1 that the MGC images of these galaxies are of sufficient quality to be decomposed with some confidence into separate disk and spheroidal components.," Moreover, \citet{Allenetal06} + have shown that the MGC images of these galaxies are of sufficient quality to be decomposed with some confidence into separate disk and spheroidal components." +" In carrying out such decompositions. ? found that a relatively modest fraction of ""pseudo-bulges"" are better fitted by a less centrally-concentrated spheroid function than a de Vaucouleurs law. but that a de Vaucouleurs law spheroid plus an exponential disk was a generally reasonable approximation to the observed photometry. allowing us to employ the simple phase-space components adopted in the current analysis."," In carrying out such decompositions, \citet{Driveretal07} found that a relatively modest fraction of “pseudo-bulges” are better fitted by a less centrally-concentrated spheroid function than a de Vaucouleurs law, but that a de Vaucouleurs law spheroid plus an exponential disk was a generally reasonable approximation to the observed photometry, allowing us to employ the simple phase-space components adopted in the current analysis." + Estimating the stellar phase density distribution of the local Universe from these data is relatively straightforward., Estimating the stellar phase density distribution of the local Universe from these data is relatively straightforward. + For each of the 100095 galaxies in the MGC for which the decomposition into exponential disk and de Vaucouleurs spheroid has beer made. one calculates the model phase space densities of the two components as in Sect. 2..," For each of the 095 galaxies in the MGC for which the decomposition into exponential disk and de Vaucouleurs spheroid has been made, one calculates the model phase space densities of the two components as in Sect. \ref{sec:model}." + These components are then converted from luminosity phase densities into mass phase densities using the colour prescription of ?.., These components are then converted from luminosity phase densities into mass phase densities using the colour prescription of \citet{BelldeJong01}. + Finally. the contribution of each galaxy is weighted according to its total absolute magnitude to allow for the different volumes sampled by this survey at different absolute magnitudes. such that each absolute magnitude bin of galaxies in the MGC contributes a signal proportional to the galaxy lummosity function at that magnitude. as derived by ?..," Finally, the contribution of each galaxy is weighted according to its total absolute magnitude to allow for the different volumes sampled by this survey at different absolute magnitudes, such that each absolute magnitude bin of galaxies in the MGC contributes a signal proportional to the galaxy luminosity function at that magnitude, as derived by \citet{Driveretal07}." + The results of this analysis are presented in Fig. 3.., The results of this analysis are presented in Fig. \ref{fig:MGCphase}. . + It is notable that. even with the large data set of the MGC.," It is notable that, even with the large data set of the MGC," +denotes the external driving force per unit volume exerted by the gravitational waves.,denotes the external driving force per unit volume exerted by the gravitational waves. + The linear cdillerential operators £ and D act on arbitrary differentiable vector fields X according to The model of viscosity adopted. here corresponds. to the kelvinVoigt model considered by Ortega(1907). and Lobo&Ortega(1998)., The linear differential operators $\mathcal{L}$ and $\mathcal{D}$ act on arbitrary differentiable vector fields $\bmath{X}$ according to The model of viscosity adopted here corresponds to the Kelvin–Voigt model considered by \citet{Ortega} and \citet{LoboOrtega}. +. For the present. paper. however. it sullices to consider the damping operator D as some general abstract operator that is linear in its argument and does not involve any time derivatives.," For the present paper, however, it suffices to consider the damping operator $\mathcal{D}$ as some general abstract operator that is linear in its argument and does not involve any time derivatives." + “Phese are the only properties that enter ancl allect the caleulation conducted in Section 5., These are the only properties that enter and affect the calculation conducted in Section 5. + Hence. in principle. anv other (phenomenological) mocel may be emploved. provided. that the resulting damping operator has the aforementioned properties.," Hence, in principle, any other (phenomenological) model may be employed, provided that the resulting damping operator has the aforementioned properties." + The normal modes of an clastic sphere. formi a basis. of solutions to the homogeneous equation of motion without a damping term. This equation of motion has to be supplemented. with the appropriate boundary condition ater= Ro where A! and jÓ£6 are set to zero. n;Surifr is the unit normal in Cartesian coordinates anc /? denotes the racius of the sphere.," The normal modes of an elastic sphere form a basis of solutions to the homogeneous equation of motion without a damping term, This equation of motion has to be supplemented with the appropriate boundary condition at $r=R$ , where $\lambda'$ and $\mu'$ are set to zero, $n_i\equiv x_i/r$ is the unit normal in Cartesian coordinates and $R$ denotes the radius of the sphere." + In order to find the normal niocles. one can assume the displacement to have a harmonical time dependence. Inserting equation (15)) into equation (13)) vielcls the eigenvalue problem Solving for the cigenfunctions and eigenfrequencies of £ subject to the bouncary conditions given by equation (14)) is à standard problem in elasticity theory und thus shall not be reconsidered here.," In order to find the normal modes, one can assume the displacement to have a harmonical time dependence, Inserting equation \ref{eq:sepAn}) ) into equation \ref{eq:EOM_hom}) ) yields the eigenvalue problem Solving for the eigenfunctions and eigenfrequencies of $\mathcal{L}$ subject to the boundary conditions given by equation \ref{eq:boundary}) ) is a standard problem in elasticity theory und thus shall not be reconsidered here." + We solely quote the final result. below for later use in Section 5 (ef, We solely quote the final result below for later use in Section 5 (cf. + e.g. Ashby&Dreitlein1975: Lobo 1995:: Maggiore 2008))., e.g. \citealt{AshbyDreitlein}; \citealt{Lobo}; \citealt{Mag}) ). + There are two families of solutions to equation (16))., There are two families of solutions to equation \ref{eq:eigenvalprob}) ). + The Esyheroical modes can be written as where DO=imxV is the angular momentum operator., The spheroidal modes can be written as where $\bmath{L}\equiv-\rmn{i}\bmath{x\times\nabla}$ is the angular momentum operator. + Phe normalization is fixed by requiring where / is normally set equal to the mass AZ of the sphere and V denotes its volume., The normalization is fixed by requiring where $I$ is normally set equal to the mass $M$ of the sphere and $V$ denotes its volume. +" For /=0. the spheroidal modes are purely racial. that is. b,o(r)=0."," For $l=0$, the spheroidal modes are purely radial, that is, $b_{n0}(r)=0$." + The toroidal modes are given by the expression where /zcl1. and are normalized in the same way as the spheroidal modes.," The toroidal modes are given by the expression where $l\ge 1$ , and are normalized in the same way as the spheroidal modes." + “Phe orthogonality ancl normalization properties of the eigenfunctions of £ can be summarized as where JNtrimSor} is an abridged. index.," The orthogonality and normalization properties of the eigenfunctions of $\mathcal{L}$ can be summarized as where $N\equiv\{nlm;S\,\rmn{or}\,T\}$ is an abridged index." + Lt is important to stress that in the present paper we are not interested. in detailed. analytical expressions. for the coellicient. functions. μι). μμ) and οί). we rather reat them: as variables. ie. we express the final results as unctions of these coellicient functions.," It is important to stress that in the present paper we are not interested in detailed analytical expressions for the coefficient functions $a_{nl}(r)$, $b_{nl}(r)$ and $c_{nl}(r)$, we rather treat them as variables, i.e. we express the final results as functions of these coefficient functions." + In deriving equation. (10)). ellects of sell-stress. caused » the intrinsic gravitational field of the sphere were neglected.," In deriving equation \ref{eq:stress_ten}) ), effects of self-stress caused by the intrinsic gravitational field of the sphere were neglected." + However. these elfects are expected to be non- for spheres as massive as astronomical objects (Ashby&Dreitlein.1975).," However, these effects are expected to be non-negligible for spheres as massive as astronomical objects \citep{AshbyDreitlein}." +. Including these ellects into the oesent. formalism: vields a dillerent. dilferential operator £ in equation (112). (Ashby&Dreitlein1975)... where uniform elastic constants were assumed and all quantities. GQ such as pressure. density. gravitational potential V. ete.," Including these effects into the present formalism yields a different differential operator $\mathcal{L}$ in equation \ref{eq:EOM3}) ), \citep{AshbyDreitlein}, where uniform elastic constants were assumed and all quantities $Q$ such as pressure, density, gravitational potential $V$, etc." + have been expanded to first order in h;;. Q=Quo|QU. where (Qu denotes the zeroth-order quantity and €1 the first-order correction.," have been expanded to first order in $h_{ij}$, $Q=Q_0+Q^{(1)}$, where $Q_0$ denotes the zeroth-order quantity and $Q^{(1)}$ the first-order correction." +" Due to spherical svnunetry. however. the clecnlunetions of E are ol the same type as in equation (17)) and (19)). but having cdillerent. coellicient. Functions (er). bur) and. e,(0)."," Due to spherical symmetry, however, the eigenfunctions of $\tilde{\mathcal{L}}$ are of the same type as in equation \ref{eq:sphmodes}) ) and \ref{eq:tor_modes}) ), but having different coefficient functions $\tilde{a}_{nl}(r)$ , $\tilde{b}_{nl}(r)$ and $\tilde{c}_{nl}(r)$." + In case of uniform density. po=const. the spheroidal coellicient functions. μι). and barr) are computed. explicitlv by Ashby&Dreitlein.(1975).," In case of uniform density, $\rho_0=\rmn{const.}$, the spheroidal coefficient functions $\tilde{a}_{nl}(r)$ and $\tilde{b}_{nl}(r)$ are computed explicitly by \citet{AshbyDreitlein}." +.. Since details of the analytical expressions of αμ). bur) and er) do not enter and allect the caleulations in Section 5 and 6. we simply assume eigenfunctions of the tvpe given by equation (17)) and (19)). regardless of whether effects of self-stress have been included or not.," Since details of the analytical expressions of $a_{nl}(r)$, $b_{nl}(r)$ and $c_{nl}(r)$ do not enter and affect the calculations in Section 5 and 6, we simply assume eigenfunctions of the type given by equation \ref{eq:sphmodes}) ) and \ref{eq:tor_modes}) ), regardless of whether effects of self-stress have been included or not." + In this section. the (complex) internal velocity fieldοία).£) of the star due to the external gravitational waves iscalculated from equation (11)).," In this section, the (complex) internal velocity field$\bmath{v}(\bmath{x},t)$ of the star due to the external gravitational waves iscalculated from equation \ref{eq:EOM3}) )." + Since the eigenfunctions of £ form a complete orthogonal set. the complex. velocity field can be expanded as where shy denote complex time-dependent. expansion cocllicients the amplitudesof the velocity. cigenmodes and N=[ném:—SorT] summarizes all indices ofa particular cigenfunction.," Since the eigenfunctions of $\mathcal{L}$ form a complete orthogonal set, the complex velocity field can be expanded as where $A_N$ denote complex time-dependent expansion coefficients – the amplitudesof the velocity eigenmodes – and $N\equiv\{nlm;S\,\rmn{or}\,T\}$ summarizes all indices of a particular eigenfunction." +any significant difference with the local galaxies.,any significant difference with the local galaxies. +" Since we have not applied any evolutionary corrections, the implication is that in the last ~2.5 Gyr average) the galaxy populations have experienced no (onmeasurable evolution except stellaraging®."," Since we have not applied any evolutionary corrections, the implication is that in the last $\sim 2.5$ Gyr (on average) the galaxy populations have experienced no measurable evolution except stellar." +". We also include the ACDM toy models in Fig. 3,,"," We also include the $\Lambda$ CDM toy models in Fig. \ref{fig: +fig3}," +" and see that some fpm--age anticorrelation is expected, which can be traced to the anti-correlation between aand age."," and see that some -age anticorrelation is expected, which can be traced to the anti-correlation between and age." +" However, there are indications in every mass bin that the observed fpw--age slope is steeper than in the models."," However, there are indications in every mass bin that the observed -age slope is steeper than in the models." +" Some systematic link between age and egr is possible, but the models shown in Fig."," Some systematic link between age and $\epsilon_{\rm SF}$ is possible, but the models shown in Fig." +" 3 suggest that this would not be a strong enough effect, as changes in virial mass do not propagate strongly to changes in central DM content (and in fact earlier collapsing halos should havedenser centers, which goes in the wrong way to explain the observations)."," \ref{fig: fig3} suggest that this would not be a strong enough effect, as changes in virial mass do not propagate strongly to changes in central DM content (and in fact earlier collapsing halos should have centers, which goes in the wrong way to explain the observations)." +" The alternatives as discussed in NRT10 are that AC is more effective in younger galaxies, or that older galaxies have ""lighter"" IMF's (e.g., Kroupa versus Salpeter1955 for the younger galaxies)."," The alternatives as discussed in NRT10 are that AC is more effective in younger galaxies, or that older galaxies have “lighter” IMFs (e.g., Kroupa versus \citealt{Salpeter55} for the younger galaxies)." + We have analyzed the central DM content of a sample of intermediate-z lenses from the latest release of the SLACS survey (A+09)., We have analyzed the central DM content of a sample of $z$ lenses from the latest release of the SLACS survey (A+09). +" Following the phenomenological framework introduced in T+09 and NRT10 we have discussed scaling relations between DM fraction, galaxy size, and formation epoch."," Following the phenomenological framework introduced in T+09 and NRT10 we have discussed scaling relations between DM fraction, galaxy size, and formation epoch." +" Gravitational lensing and dynamical analyses are used to constrain the total mass profile, while synthetic spectral populations are used to infer the stellar mass and other stellar properties such as galaxy age."," Gravitational lensing and dynamical analyses are used to constrain the total mass profile, while synthetic spectral populations are used to infer the stellar mass and other stellar properties such as galaxy age." + ETGs at z0.2 are found to be similar to local ones; future work will include extending the baseline to higher redshifts., ETGs at $z \sim 0.2$ are found to be similar to local ones; future work will include extending the baseline to higher redshifts. + The somewhat surprising findings of NRT10 are now confirmed with an independent and arguably more robust data set., The somewhat surprising findings of NRT10 are now confirmed with an independent and arguably more robust data set. +" The DM fraction within iis found to strongly correlate withReg,, because larger length-scales probe a more DM dominated region."," The DM fraction within is found to strongly correlate with, because larger length-scales probe a more DM dominated region." +" On these scales, the DM mean density decreases with aas (ppm)ος|, which argues for cuspy DM halos for ETGs out to Reg.z~0.5 was discussed in NRT10 for local galaxies)."," On these scales, the DM mean density decreases with as $\langle\rho_{\rm DM}\rangle \, \propto \Re^{-1.7}$, which argues for cuspy DM halos for ETGs out to $z\sim0.5$ (as was discussed in NRT10 for local galaxies)." +" At a fixed (asstellar mass and length-scale, we have found that the DM halos of ETGs are denser than those of local spiral galaxies, providing a critical test for the merging formation scenario (see also Cardone&Tortora 2010))."," At a fixed stellar mass and length-scale, we have found that the DM halos of ETGs are denser than those of local spiral galaxies, providing a critical test for the merging formation scenario (see also \citealt{CT10}) )." +" Finally, we have confirmed our earlier finding that central DM content anti-correlates with stellar age."," Finally, we have confirmed our earlier finding that central DM content anti-correlates with stellar age." + The strength of this correlation appears to exceed what is expected from size-age effects., The strength of this correlation appears to exceed what is expected from size-age effects. +" A fundamental connection between galactic structure and star formation history is implied, which we propose is a consequence of variations with formation epoch of either DM halo contraction or stellar IMF."," A fundamental connection between galactic structure and star formation history is implied, which we propose is a consequence of variations with formation epoch of either DM halo contraction or stellar IMF." +" In future work, we plan to investigate the impact on these results of more complex total and DM galaxy profiles (e.g. Cardoneetal.2005,, Tortoraetal. 2007)) along the lines of recent work in Cardoneetal.(2009) and Cardone&Tortora(2010).."," In future work, we plan to investigate the impact on these results of more complex total and DM galaxy profiles (e.g. \citealt{Cardone05}, \citealt{Tortora2007}) ) along the lines of recent work in \cite{Cardone+09} and \cite{CT10}." + New high-quality data are also expected with the advent of future surveys both in the local Universe and at larger redshifts., New high-quality data are also expected with the advent of future surveys both in the local Universe and at larger redshifts. +" Such surveys will include larger samples of gravitational lenses along with more detailed spectroscopic information, and could be used to verify and extend the results presented here, providing a clearer picture of the physical processes of ETG assembly."," Such surveys will include larger samples of gravitational lenses along with more detailed spectroscopic information, and could be used to verify and extend the results presented here, providing a clearer picture of the physical processes of ETG assembly." +winds by ?..,winds by \citet{1988ApJ...329..299B}. + Dlócekers MILR formula is: and a variant. Apo. has Mzqas replaced by 44..," Blöccker's MLR formula is: and a variant, $\Mdot_{\rm B2}$ , has $M_{ZAMS}$ replaced by $\Mstar$." + 6., 6. + Yet another modification of Reimerss formula. intended for cool winds that are not driven by molecules or dust. is given by 2.. τη with κο=8(-E1)x10.1.," Yet another modification of Reimers's formula, intended for cool winds that are not driven by molecules or dust, is given by \citet{2005ApJ...630L..73S}, \citet{2007A&A...465..593S}: with $\etasc= 8(\pm 1)\times 10^{-14}\, $." + Here two new [actors are included. taking into account the dependence of chromospheric height on surface gravity and the dependence of the mechanical enerev flux on the effective temperature.," Here two new factors are included, taking into account the dependence of chromospheric height on surface gravity and the dependence of the mechanical energy flux on the effective temperature." + In applying anv of the MLB expressions. instead of turning it on suddenly. we multiply it bv à Fermi weight function where {ρουμ is an MLB threshold radius. which we (vpically choose between 1. and 50.," In applying any of the MLR expressions, instead of turning it on suddenly, we multiply it by a Fermi weight function where $R_{thresh}$ is an MLR threshold radius, which we typically choose between 1 and 50." + lis precise value is not important. so long as the MLB is negligible for R=R4.," Its precise value is not important, so long as the MLR is negligible for $R=R_{thresh}$." +" As H, increases. F(H,) varies smoothly near {Τρ from O to 1. over a width of 0.057255..."," As $\Rstar$ increases, $F(\Rstar)$ varies smoothly near $R_{thresh}$ from 0 to 1, over a width of $0.05R_{thresh}$." + This prevents an on-off situation. which can ruin the convergence of the iteration process bv which the difference equations of reluum. are solved.," This prevents an on-off situation, which can ruin the convergence of the iteration process by which the difference equations of \\ref{num} are solved." + The question remains. which formula to use?," The question remains, which formula to use?" + The code includes an algorithm that identifies the evolutionary stage of the stellar model by testing various parameters (such as luminosity. radius. composition profiles) aud their rates of change.," The code includes an algorithm that identifies the evolutionary stage of the stellar model by testing various parameters (such as luminosity, radius, composition profiles) and their rates of change." + Therefore. one may pass | inasmooth manner — from one formula to another.," Therefore, one may pass — in a smooth manner — from one formula to another." + In this work. we used for the RGB and for later stages.," In this work, we used for the RGB and for later stages." + The parameter opo was taken progressively higher with increasing initial mass., The parameter $\etareim$ was taken progressively higher with increasing initial mass. + The effect of ρω and nog on the results will be briefly discussed 1n section $+..., The effect of $R_{thresh}$ and $\etareim$ on the results will be briefly discussed in section \ref{ifmr}. + Using the evolution code described in the previous section. we performed calculations over a wide range of initial stellar masses and metallicities.," Using the evolution code described in the previous section, we performed calculations over a wide range of initial stellar masses and metallicities." + Ii the following sections we address representative results. outcome of continuous calculations(hat vield complete evolutionary tracks. starting [rom an initial pre-main-sequence state and ending with either a cooling," In the following sections we address representative results, outcome of continuous calculationsthat yield complete evolutionary tracks, starting from an initial pre-main-sequence state and ending with either a cooling" +from gravitationally settling.,from gravitationally settling. + This leads to the disappearance of the superticial He convection zone and renders the atmosphere more stable., This leads to the disappearance of the superficial He convection zone and renders the atmosphere more stable. + Once the medium is stable enough. atomic diffusion can dominate there. leading to abundance anomalies and vertical abundance stratification. of the chemical elements through. the migration of the particles caused by the disbalance of gravity and radiative forces. and yielding superficial abundance anomalies.," Once the medium is stable enough, atomic diffusion can dominate there, leading to abundance anomalies and vertical abundance stratification of the chemical elements through the migration of the particles caused by the disbalance of gravity and radiative forces, and yielding superficial abundance anomalies." + Stratification of the elements has an effect on the physical structure of the atmosphere through the change in the opacities. thus leading to photometric anomalies. and to a change of the shape of the Balmer lines. explaining the low values of surface gravity obtained by fitting of these lines. if one uses canonical models.," Stratification of the elements has an effect on the physical structure of the atmosphere through the change in the opacities, thus leading to photometric anomalies, and to a change of the shape of the Balmer lines, explaining the low values of surface gravity obtained by fitting of these lines, if one uses canonical models." + The scenario outlined above. where atomic diffusion takes place in the atmospheres of hot BHB stars. may therefore explain the various observational anomalies observed for these stars.," The scenario outlined above, where atomic diffusion takes place in the atmospheres of hot BHB stars, may therefore explain the various observational anomalies observed for these stars." + Hui-Bon-Hoa. LeBlane and Hauschildt (2000) constructed stellar atmosphere models of BHB stars with vertical stratification of the elements. and self-consistent atmospheric structure.," Hui-Bon-Hoa, LeBlanc and Hauschildt (2000) constructed stellar atmosphere models of BHB stars with vertical stratification of the elements, and self-consistent atmospheric structure." + These models were successful in qualitatively reproducing the above-mentioned anomalies when assuming that atomic diffusion becomes efficient in BHB stars with Τμ 11500 K tie. the temperature above which the vast majority of the BHB stars rotate slowly)., These models were successful in qualitatively reproducing the above-mentioned anomalies when assuming that atomic diffusion becomes efficient in BHB stars with $T_{\rm eff} > $ 11500 K (i.e. the temperature above which the vast majority of the BHB stars rotate slowly). + These models have been improved recently (LeBlanc et al., These models have been improved recently (LeBlanc et al. + 2009). and the aim of this paper is to apply these new models to BHB stars and to compare the results to observational data.," 2009), and the aim of this paper is to apply these new models to BHB stars and to compare the results to observational data." + Among the improvements. the convergence scheme to obtain self-consistent abundance stratification was ameliorated in these models.," Among the improvements, the convergence scheme to obtain self-consistent abundance stratification was ameliorated in these models." + Also. the diffusion coefficients now used take into account the interaction between the ions and neutral hydrogen.," Also, the diffusion coefficients now used take into account the interaction between the ions and neutral hydrogen." + Moreover. in these new models. upper and lower abundance limits were imposed to avoid that certain elements attain extremely large (for the test-particle approximation of the diffusion theory to still be valid) or small (to avoid numerical problems) abundances at certain depths (see Section 3 of LeBlanc et al.," Moreover, in these new models, upper and lower abundance limits were imposed to avoid that certain elements attain extremely large (for the test-particle approximation of the diffusion theory to still be valid) or small (to avoid numerical problems) abundances at certain depths (see Section 3 of LeBlanc et al." + 2009 for more details)., 2009 for more details). + First the new model atmospheres with elemental stratification will be briefly deseribed., First the new model atmospheres with elemental stratification will be briefly described. + Theoretical vertical stratification of Fe in models of various Ίο will be compared to the observational results of Khalack et al. (, Theoretical vertical stratification of Fe in models of various $T_{\rm eff}$ will be compared to the observational results of Khalack et al. ( +2007. 2008 and 2010).,"2007, 2008 and 2010)." + The synthetic photometry obtained with these models will then be presented. checking if they are able to reproduce observed photometric jumps and gaps for globular cluster BHB sequences.," The synthetic photometry obtained with these models will then be presented, checking if they are able to reproduce observed photometric jumps and gaps for globular cluster BHB sequences." + Synthetic Balmer lines are also compared between models with different prescriptions. to show how the diffusion model can account for the low values of gravity derived when using canonical models.," Synthetic Balmer lines are also compared between models with different prescriptions, to show how the diffusion model can account for the low values of gravity derived when using canonical models." + The process of elemental stratification relies on the diffusion velocity. which causes the migration of the different chemical elements within stars.," The process of elemental stratification relies on the diffusion velocity, which causes the migration of the different chemical elements within stars." + The leading terms that cause this velocity are gravity and the radiative acceleration resulting from the momentum transfer between the radiation tield and each chemical species (e.g. Gonzalez et al., The leading terms that cause this velocity are gravity and the radiative acceleration resulting from the momentum transfer between the radiation field and each chemical species (e.g. Gonzalez et al. + 1995)., 1995). + This transfer depends on the opacity of the species under consideration and the local monochromatic radiation field. which. in turn. via the monochromatic opacities. depends on the local abundances of the different species.," This transfer depends on the opacity of the species under consideration and the local monochromatic radiation field, which, in turn, via the monochromatic opacities, depends on the local abundances of the different species." + The stratification of the abundances is thus a time-dependent process and it is therefore complex to treat it thoroughly., The stratification of the abundances is thus a time-dependent process and it is therefore complex to treat it thoroughly. + As the radiative transfer equation has to be solved explicitly in stellar atmospheres. which are optically thin media. time-dependent calculations are not feasible at the present time.," As the radiative transfer equation has to be solved explicitly in stellar atmospheres, which are optically thin media, time-dependent calculations are not feasible at the present time." + Studies of abundance stratification can however be performed assuming that an equilibrium state can be reached. when the diffusion velocity of each element is nil at each laver of the atmosphere.," Studies of abundance stratification can however be performed assuming that an equilibrium state can be reached, when the diffusion velocity of each element is nil at each layer of the atmosphere." + This is the framework within which our calculations are performed., This is the framework within which our calculations are performed. + Even though the elemental stratification profiles can possibly differ from those computed time-dependently. this approximation can be used to gauge the impact of vertical P2stratification of the abundances on the atmospheric structure and on certain observed quantities.," Even though the elemental stratification profiles can possibly differ from those computed time-dependently, this approximation can be used to gauge the impact of vertical stratification of the abundances on the atmospheric structure and on certain observed quantities." + For a more detailed discussion surrounding time-dependent diffusion and equilibrium solution. the reader is referred to Alecian Stift (2007) in which Ap stars are studied.," For a more detailed discussion surrounding time-dependent diffusion and equilibrium solution, the reader is referred to Alecian Stift (2007) in which Ap stars are studied." + The model atomspheres presented here are calculated with a modified version of the PHOENIX code (Hauschildt. Allard Baron 1999) as described by LeBlane et al. (," The model atomspheres presented here are calculated with a modified version of the PHOENIX code (Hauschildt, Allard Baron 1999) as described by LeBlanc et al. (" +2009).,2009). + The models computed here are in LTE and include 39 elements (H-Ga. Kr-Nb. Ba and La.," The models computed here are in LTE and include 39 elements (H-Ga, Kr-Nb, Ba and La)." + To build the stratification profile for each element. the code seeks iteratively a solution where the atmospheric structure and the vertical abundance stratitications yield a nil diffusion velocity for each chemical species (i.e. the equilibrium solution).," To build the stratification profile for each element, the code seeks iteratively a solution where the atmospheric structure and the vertical abundance stratifications yield a nil diffusion velocity for each chemical species (i.e. the equilibrium solution)." + Indeed. as the abundance of each species changes locally. so do the opacities. and thus the atmospheric structure.," Indeed, as the abundance of each species changes locally, so do the opacities, and thus the atmospheric structure." + The resulting model atmospheres are thus self-consistent from this point of view., The resulting model atmospheres are thus self-consistent from this point of view. + For the evaluation of the radiative accelerations. both bound-bound and bound-free transitions are considered for each species while assuming LTE (Hui-Bon-Hoa et al.," For the evaluation of the radiative accelerations, both bound-bound and bound-free transitions are considered for each species while assuming LTE (Hui-Bon-Hoa et al." + 2002)., 2002). + As the radiative transfer is solved with the opacity sampling method. the radiative accelerations. along with the radiative flux. are calculated using a sufficiently fine frequency grid to ensure adequate precision (e.g. LeBlanc. Michaud Richer 2000).," As the radiative transfer is solved with the opacity sampling method, the radiative accelerations, along with the radiative flux, are calculated using a sufficiently fine frequency grid to ensure adequate precision (e.g. LeBlanc, Michaud Richer 2000)." + Several improvements were brought to the models presented here as compared to the models used in Hui-Bon-Hoa. LeBlanc Hauschildt (2000).," Several improvements were brought to the models presented here as compared to the models used in Hui-Bon-Hoa, LeBlanc Hauschildt (2000)." + For example. the convergence scheme used to compute the stratification of the abundances has been moditied.," For example, the convergence scheme used to compute the stratification of the abundances has been modified." + Also. more precise diffusion coefficients are used.," Also, more precise diffusion coefficients are used." + More details concerning the improvements brought to the atmospheric code are found in LeBlane et al. (, More details concerning the improvements brought to the atmospheric code are found in LeBlanc et al. ( +2009).,2009). + A series of BHB model atmospheres from τω = 11000 to 18000 K (see Tab. 13) , A series of BHB model atmospheres from $T_{\rm eff}$ = 11000 to 18000 K (see Tab. \ref{tab:parameters}) ) +were constructed while including abundance stratitications., were constructed while including abundance stratifications. + The surface gravities and masses used here are those of the zero-age horizontal-branch (ZAHB) models of VandenBerg et al. (, The surface gravities and masses used here are those of the zero-age horizontal-branch (ZAHB) models of VandenBerg et al. ( +2000).,2000). + The stratification of the elements predicted at equilibrium strongly modifies the physical structure of the stellar atmospheres of hot BHB stars., The stratification of the elements predicted at equilibrium strongly modifies the physical structure of the stellar atmospheres of hot BHB stars. + Figure |. shows the ratio of the temperature as a function of optical depth in several of these models as compared to the temperature of corresponding models (with the same fundamental parameters) with homogeneous models with a metallicity of -1.5 dex solar., Figure \ref{fig:Rapport_T} shows the ratio of the temperature as a function of optical depth in several of these models as compared to the temperature of corresponding models (with the same fundamental parameters) with homogeneous models with a metallicity of -1.5 dex solar. + The abundances used for these homogeneous models are chosen to be -I.5 dex compared to solar abundances which are typical of well-studied globular cluster, The abundances used for these homogeneous models are chosen to be -1.5 dex compared to solar abundances which are typical of well-studied globular cluster +(54 clusters are found in the vicinity of plate-holes or crowded regions aud thus are excluded).,(54 clusters are found in the vicinity of plate-holes or crowded regions and thus are excluded). + We will also use the NBAC (Ebelingοἱal.1996) and BCS (Ebelingetal.1998) ROSAT N-rav cluster samples (o lest whether (here is anv indications of a recent evolution of the ICM temperature., We will also use the XBAC \citep{Ebel} and BCS \citep{Ebel1} ROSAT X-ray cluster samples to test whether there is any indications of a recent evolution of the ICM temperature. + Details of the sample construction can be found in (he original papers., Details of the sample construction can be found in the original papers. +" We only note that the NBAC's has a flux-limit of f,>5xLOP ! ? and contains 283 Abell clusters. while the BCS. with its low-fIux extension (Ebelingοἱal.2001).. has a [lux limit of [,>2.8x10.© eres t 7 and contains 304 clusters."," We only note that the XBACs has a flux-limit of $f_x>5 \times 10^{-12}$ $^{-1}$ $^{-2}$ and contains 283 Abell clusters, while the BCS, with its low-flux extension \citep{Ebel2}, , has a flux limit of $f_x > 2.8 \times 10^{-12}$ ergs $^{-1}$ $^{-2}$ and contains 304 clusters." +" Most of the listed ICAL temperatures are estimated from the £,—7 relation of Whiteetal.(1997).. but a reasonable number of clusters have measured temperatures [see Table 1 of (1997)]]."," Most of the listed ICM temperatures are estimated from the $L_x-T$ relation of \cite{WhiteF}, but a reasonable number of clusters have measured temperatures [see Table 1 of \cite{WhiteF}] ]." +" The fhix-limited nature of these samples create an apparent {ντz relation. as can be seen in Figure 1. aud in order (o avoid reproducing an artificial redshift evolution we construct volume limited subsamples (the delineated regions of Fig.l); one is a low-Iuminosity (L,>10! eves/sec) subsample. which spans a limited redshift range (2<0.07 and 0.09 for the NBACS and BC'S. receptivelv) and one high-huninosity subsample (L,>8x10H ergs/sec). spanning a much larger redshift range (2<0.19 and 0.24 for the NDACS and BCS. respectively)."," The flux-limited nature of these samples create an apparent $L_{x}-z$ relation, as can be seen in Figure 1, and in order to avoid reproducing an artificial redshift evolution we construct volume limited subsamples (the delineated regions of Fig.1); one is a low-luminosity $L_{x}>10^{44}$ ergs/sec) subsample, which spans a limited redshift range $z\lesssim 0.07$ and 0.09 for the XBACs and BCS, receptively) and one high-luminosity subsample $L_{x}> 8 \times 10^{44}$ ergs/sec), spanning a much larger redshift range $z\lesssim 0.19$ and 0.24 for the XBACs and BCS, respectively)." + Figure 2 shows the distribution of APM cluster ellipticities as a function of redshift (2:< 0.15]., Figure 2 shows the distribution of APM cluster ellipticities as a function of redshift $z<0.18$ ). + The filled circles represent ADM. clusters that are also in the Abell/ACO cablalogue., The filled circles represent APM clusters that are also in the Abell/ACO catalogue. + There is a definite trend. of ellipticity with redshift in the direction expected from an evolution of the dvnanmical status of clusters. supporting similar claims of (2001)..," There is a definite trend of ellipticity with redshift in the direction expected from an evolution of the dynamical status of clusters, supporting similar claims of \citet{MelC}." + Table 1 summarizes the quantitative correlation results for all tests., Table 1 summarizes the quantitative correlation results for all tests. + The Pearson correlation coefficient for (he €—z correlation is r~0.2 and with a probability of being a chance correlation of P~10.7., The Pearson correlation coefficient for the $\epsilon-z$ correlation is $r\simeq 0.2$ and with a probability of being a chance correlation of ${\cal P}\simeq 10^{-8}$. + This result is robust to changes of the sample size by [actors of two or three. depending on whether we use clusters with observed redshilts or different cluster richness (see Table 1).," This result is robust to changes of the sample size by factors of two or three, depending on whether we use clusters with observed redshifts or different cluster richness (see Table 1)." + Tests were performed to investigate whether systematic effects in the shape-parameter determination method could be responsible for the ellipticitv-redshift trend., Tests were performed to investigate whether systematic effects in the shape-parameter determination method could be responsible for the ellipticity-redshift trend. + Already in Dasilakosetal.(2000) à detailed analvsis of the performance of (he method as a function of sampling. distance aud the presence of a projected random background galaxy distribution las predicted by the Iuminosity function of APM galaxies: Maddoxetal. (1996)]] showed that such effects will tend to overestimate by. ~0.1—0.15 the ellipticity of nearly sphericalclusters (more so for distant clusters - but only bv more). (hey will underestimate the ellipticity of flat clusters. more so al laree-reclshilts.," Already in \cite{BPM} a detailed analysis of the performance of the method as a function of sampling, distance and the presence of a projected random background galaxy distribution [as predicted by the luminosity function of APM galaxies; \cite{Mad96}] ] showed that such effects will tend to overestimate by $\sim 0.1-0.15$ the ellipticity of nearly sphericalclusters (more so for distant clusters - but only by more), they will underestimate the ellipticity of flat clusters, more so at large-redshifts," +laboratories for studving the large amounts of dust (Dunlopetal. 1991: Ivisonetal.1998)) andl molecular eas (Papadopoulosetal. 1999)). which are observed to accolmpany the formation of the first Orniüug niassive ealaxies.,"laboratories for studying the large amounts of dust \cite{dun94}; ; \cite{ivi98}) ) and molecular gas \cite{pap99}) ), which are observed to accompany the formation of the first forming massive galaxies." + Using newly available. large radio surveys we have beeun a systematic search for 2> WzRGs to be followed bv. mere detailed studies of selected objects.," Using newly available, large radio surveys we have begun a systematic search for $z>4$ HzRGs to be followed by more detailed studies of selected objects." + Tn this Letter. we present deep intermediate resolution VLT/FORSL spectroscopy of wwhicdh. ato.=Lll. was the first :>| radio ealaxy discovered in the southern hemisphere (DeBreucketal. 1999a)). aud is one of the brightest aud most Iuminous oobjects of its class.," In this Letter, we present deep intermediate resolution VLT/FORS1 spectroscopy of which, at $z = 4.11$, was the first $z > 4$ radio galaxy discovered in the southern hemisphere \cite{deb99a}) ), and is one of the brightest and most luminous objects of its class." + Tn $82. we describe the discovery aud previous observations of.," In 2, we describe the discovery and previous observations of." +1912.. In 83 we describe our VLT observatious. and in &L we discuss some of the Huplications of our results.," In 3 we describe our VLT observations, and in 4 we discuss some of the implications of our results." + Throughout this paper we will asstuue {10=65 ans tMIpe +. 4420.15. and A=0.," Throughout this paper we will assume $H_0 = 65$ km $^{-1}$ $^{-1}$, $q_0$ =0.15, and $\Lambda=0$." + At 2=LIL. this nuplies a linear size scale of 7.5. kpe/arcsec.," At $z=4.11$, this implies a linear size scale of 7.5 kpc/arcsec." + The iiethod we are using to find distant radio galaxies is based on the empirical correlation between redshift aud observed spectral index in suuples of low-frequency selected radio sources απetal. 1999))., The method we are using to find distant radio galaxies is based on the empirical correlation between redshift and observed spectral index in samples of low-frequency selected radio sources \cite{car99}) ). + Selecting radio sources with ultra steep spectra (USS) dramatically increases he probability of piupolutius lieh-z radio galaxies. as conrpared Το observius racio ealaxies with more common radio spectra.," Selecting radio sources with ultra steep spectra (USS) dramatically increases the probability of pinpointing high-z radio galaxies, as compared to observing radio galaxies with more common radio spectra." +" This method. which can to a large extent be explained as a Wk-correction induced by a curvature of the radio spectra. has been shown to be extremely efücieut Cliuubers,Miley&vanDreugel1990: vanBrenecletal. 1999a))."," This method, which can to a large extent be explained as a K-correction induced by a curvature of the radio spectra, has been shown to be extremely efficient \cite{cha90}; \cite{wvb99a}) )." +" WeA constructedpoenateneted sucheneh aon USSTES suupleou. (omgld—«c1.30:S,x i"": DeBreucketal. 19991)). consisting of 669 objects. using several radio catalogs which. in the southern hemisphere. iuclude the Texas 365 MITz catalog (Douglasetal. 1996)) and the NVSS ντ αν catalog (Condonetal. 1998))."," We constructed such a USS sample $\alpha^{\rm 1.4 GHz}_{\rm 365 +MHz} < -1.30 ;S_\nu \propto \nu^\alpha$ ; \cite{deb99b}) ), consisting of 669 objects, using several radio catalogs which, in the southern hemisphere, include the Texas 365 MHz catalog \cite{dou96}) ) and the NVSS 1.4 GHz catalog \cite{con98}) )." +" As part of our searchprogram ο observed (ashe—004,31 0.07) with the ESO 3.611 telescope in 1997 March and April (DeBreuclsetal. 1999a))."," As part of our search–program we observed $\alpha^{\rm 1.4 +GHz}_{\rm 365 MHz} = -1.31\pm0.07$ ) with the ESO 3.6m telescope in 1997 March and April \cite{deb99a}) )." + The radio source was first identified by takine a 10 minute R band nuage., The radio source was first identified by taking a 10 minute $R-$ band image. + Followup spectroscopy then showed the radio galaxy to be at a redshift of 2=L183d:0.02. based on a stroug detection ofLya.. aud weak confriiius παπα1610.," Followup spectroscopy then showed the radio galaxy to be at a redshift of $z=4.13 \pm 0.02$, based on a strong detection of, and weak confirming and." +.. At this redshift its derived restfune low frequency (178. MIIZz) radio Iuninositv is comparable to that of the most huuinous 3CR sources., At this redshift its derived rest–frame low frequency (178 MHz) radio luminosity is comparable to that of the most luminous 3CR sources. + More detailed radio information was obtained with the VLA at L71 GIIz and 5.16. GIIz on 1998 March 2] as part of a survey to measure rotation measures in UzRCs (Peutericesetal.1999)).," More detailed radio information was obtained with the VLA at 4.71 GHz and 8.46 GHz on 1998 March 24, as part of a survey to measure rotation measures in HzRGs \cite{pen99}) )." +. We deteet two radio colmpoucnts.wate (S3|NAY76g._—=9721.9¢ uty:e 5755.GSE=1.1 uJv) separated by 5755 in the field of the radio galaxy (Fie. 1)., We detect two radio components $S_{4.7 GHz}^{NW} = 21.9$ mJy; $S_{4.7 GHz}^{SE} = 1.1$ mJy) separated by 5 in the field of the radio galaxy (Fig. \ref{kradio}) ). +" The bright NW conponent has a very faint radio companion (S$-,,,=0.) mJy) at ULL to the SE."," The bright NW component has a very faint radio companion $S_{4.7 GHz}^{C} += 0.3$ mJy) at 4 to the SE." + Our preseut observations show that all compoucuts lave very steep radio spectra with ayeCHENIT)~1.6. at20H8E)~Ls and aj26H£(C)—1.," Our present observations show that all components have very steep radio spectra with $\alpha^{\rm +8.5~GHz}_{\rm 4.7~GHz}(NW) \sim -1.6$, $\alpha^{\rm 8.5~GHz}_{\rm +4.7~GHz}(SE) \sim -1.8$, and $\alpha^{\rm 8.5~GHz}_{\rm 4.7~GHz}(C) +\sim -1.0$." + The proximity and aliguinent of such rare USS compoucuts stronely sugeests that they are related and part of one source., The proximity and alignment of such rare USS components strongly suggests that they are related and part of one source. +" While further observations over a vider frequency ranee would be useful to confirm this. for now we couclude that lis a verv asvuuuetric radio source. and identity component C a A200=1338"" πι ὅρυυυ=ἹοτP31 with the radio core."," While further observations over a wider frequency range would be useful to confirm this, for now we conclude that is a very asymmetric radio source, and identify component C at $\alpha_{2000} = 13^h38^m26\fs10$ and $\delta_{2000}=-19\degr 42\arcmin 31\farcs1$ with the radio core." + Such asvinmnctric radio sources are ot unconiion AIeCarthy.vanBreugel&Iapali 1991))..— and are usually thought to be due to strong interaction of one of its radio lobes with very dense gas or a neighiborimg ealaxy (see for example Feiusteiuetal.1999).," Such asymmetric radio sources are not uncommon \cite{mcc91}) ), and are usually thought to be due to strong interaction of one of its radio lobes with very dense gas or a neighboring galaxy (see for example \cite{fei99}) )." + We also obtained a A/baud image with the Near lufrared Camera (NIRC: Mathews&Soifer199 0} at the Keck I telescope on UT 1998 April 15., We also obtained a $K-$ band image with the Near Infrared Camera (NIRC; \cite{mat94}) ) at the Keck I telescope on UT 1998 April 18. + The inteeratio- time was 61 iinutes in photometric conditions with 755 secius., The integration time was 64 minutes in photometric conditions with 5 seeing. + Observing procedures. calibration aud data reduction techniques were similar to those described iu vau Breugel et al. (," Observing procedures, calibration and data reduction techniques were similar to those described in van Breugel et al. (" +1998).,1998). + Using a circular aperture of3”. enconipassiue the eutire object. we measure fy=19.0.2 (we do not expect a significant contribution from emission lues at the redshift of the galaxy).," Using a circular aperture of, encompassing the entire object, we measure $K=19.4 \pm 0.2$ (we do not expect a significant contribution from emission lines at the redshift of the galaxy)." + In a 61 kpc metric aperture. the maeuitude is A5;=19.2£0.3. which puts aat the bright eud. but within the scatter. of the A relationship (vanBreueeletal. 1998)).," In a 64 kpc metric aperture, the magnitude is $K_{64}=19.2 \pm 0.3$, which puts at the bright end, but within the scatter, of the $K-z$ relationship \cite{wvb98}) )." + We determined the astrometric positions in our 5.5 R baud image usiue the USNO PAMAL catalog (Mouctetal. 1998)).," We determined the astrometric positions in our $5\arcmin \times +5\arcmin$ $R-$ band image using the USNO PMM catalog \cite{mon98}) )." + We nest used the positions of niue stars on the R-band nuage in conuuou with the Keck IW baud to solve the astrometry on the Vo.1 AW baud nuaec.," We next used the positions of nine stars on the R-band image in common with the Keck $K-$ band to solve the astrometry on the $1\arcmin +\times 1\arcmin$ $K-$ band image." + The eror in therelative nearIR/radio astrometry is donmuünated by the absolute uncertainty of the optical reference frame. which is οLL couficdence But: Deutsch 19993).," The error in the near–IR/radio astrometry is dominated by the absolute uncertainty of the optical reference frame, which is $\sim$ 4 confidence limit; \cite{deu99}) )." + Tn figure 1.. we show the overlay of the radio and dy baud Bo baud) nuages.," In figure \ref{kradio}, we show the overlay of the radio and $K-$ band $B-$ band) images." + The NW hotspot coincides within 00035 of the peak of the A Daud emission. while some faint diffuse extensions can be seen towards the radio core aud bevoud the lobe.," The NW hotspot coincides within 035 of the peak of the $K-$ band emission, while some faint diffuse extensions can be seen towards the radio core and beyond the lobe." + The positional difference between the peak of the A band euissiou aud the radio core is LE (—lo). which suggests that the AGN aud peaks of the A band aud eenussion nav not be cocentered.," The positional difference between the peak of the $K-$ band emission and the radio core is 4 $\sim 4\sigma$), which suggests that the AGN and peaks of the $K-$ band and emission may not be co–centered." +future. broadband observ:ations of very high-z GRBs should open new windows onto he cosmic reilonization epoch.,"future, broadband observations of very $z$ GRBs should open new windows onto the cosmic reionization epoch." + Even if HE-inducec spectral features are detected. a generic problem for ο absorption stuclics is clistineuishing them from spectral cuto(fs intrinsic to the source.," Even if IRF-induced spectral features are detected, a generic problem for $\gamma\gamma$ absorption studies is distinguishing them from spectral cutoffs intrinsic to the source." + In. this regard. spectral variability should. olfer an important clue.," In this regard, spectral variability should offer an important clue." + oth blazars and GRBs are highly variable ganmia-rav emitters. and in general. changes in physical conditions of ie source that cause variations in [lux should. also. be accompanied by variations of the intrinsic cutoll energy. whether it is due to injection of freshly accelerated particles. changes in the magnetic fields. internal radiation fields. bulk How velocity. ete.," Both blazars and GRBs are highly variable gamma-ray emitters, and in general, changes in physical conditions of the source that cause variations in flux should also be accompanied by variations of the intrinsic cutoff energy, whether it is due to injection of freshly accelerated particles, changes in the magnetic fields, internal radiation fields, bulk flow velocity, etc." + In contrast. cutolls of HE origin shoul be stable in time and independent of the variability state of cach object.," In contrast, cutoffs of IRF origin should be stable in time and independent of the variability state of each object." + Acquisition of time-resolved. spectra shoul thus allow the deconvolution of the two elfects., Acquisition of time-resolved spectra should thus allow the deconvolution of the two effects. + Another indication should come from statistical stuclics of a sullicien sample of measurements., Another indication should come from statistical studies of a sufficient sample of measurements. + LU-related. eutoffs should. occur al similar energies for sources at similar z. and also exhibi a systematic evolution toward lower energies lor higher whereas there is no strong reason to expect such trencds for intrinsic cutolls.," IRF-related cutoffs should occur at similar energies for sources at similar $z$, and also exhibit a systematic evolution toward lower energies for higher $z$, whereas there is no strong reason to expect such trends for intrinsic cutoffs." + Both the above strategies motivate the construction of future. high-sensitivity multi-GeV. facilities such as CEA. AGIS and5065. which should be powerful tools to probe the evolution of UV LIES in the cosmic reionization era through το absorption in very high-z sources.," Both the above strategies motivate the construction of future, high-sensitivity multi-GeV facilities such as CTA, AGIS and 55, which should be powerful tools to probe the evolution of UV IRFs in the cosmic reionization era through $\gamma\gamma$ absorption in very $z$ sources." + We thank EF. Xharonian. P. Coppi. Y. Inoue. N. Ixawai. E. AMiniai. N. Omodei. J. Rhoads. M. Teshima and T. Totani for valuable discussions. T. Ixneiske for making her models available. and the anonymous referee for very helpful and constructive comments.," We thank F. Aharonian, P. Coppi, Y. Inoue, N. Kawai, F. Miniati, N. Omodei, J. Rhoads, M. Teshima and T. Totani for valuable discussions, T. Kneiske for making her models available, and the anonymous referee for very helpful and constructive comments." + S. L is supported by Cirants-cin-Vid for Scientific Research Nos., S. I. is supported by Grants-in-Aid for Scientific Research Nos. +" 19047004 and. 19540283 and [or the Global COL Program ""The Next Generation of Physics. Spun from Universality and Emergence” from the Ministry obl I.CS.ST. CMIENT) of Japan."," 19047004 and 19540283 and for the Global COE Program ""The Next Generation of Physics, Spun from Universality and Emergence"" from the Ministry of E.C.S.S.T. (MEXT) of Japan." +"of elapsed time Af is where inate is the ΠΟΠ faction at Af=0. f,=(Eia|on i Deo is the electron density. and aff) is the recombination ον3 lot)n]lis 77(:)1 2. «Προς Dua A,—0.15 A,EN Lye Ly =LOcApe From these two propositions. one cau place an interesting lower bound on μοι in z 10eMpe regions.","of elapsed time $\Delta t$ is where $x_{\rm HeII, 0}$ is the HeII fraction at $\Delta t=0$, $t_{\rm eq} \equiv (\Gamma_{\rm HeII} + \alpha \, n_e)^{-1}$ , $n_e$ is the electron density, and $\alpha(T)$ is the recombination $z\sim 3$ $[\alpha(T) \, n_e]^{-1}$ $H(z)^{-1}$ \ref{fig:HeIIfrac} $x_{\rm HeII, eq}$ $\Gamma_{\rm HeII}$ $\Delta_b=0.15$ $\Delta_b=1$ $\alpha$ $\alpha$ $\gtrsim 10\,$ From these two propositions, one can place an interesting lower bound on $x_{\rm HeII}$ in $\gtrsim 10\,$ cMpc regions." +" To see this. let us take our constraut of rp0.008 at A,=(0.15 (Section 2))."," To see this, let us take our constraint of ${x}_{\rm HeII}>0.008$ at $\Delta_b =0.15$ (Section \ref{sec1}) )." +" Using the two propositions aud equation (1) to infer the ionization state of neighboring gas elemieuts (which provides the scaling DITSA;vtyD j we fud that nearby elemeuts with A,=1 should have egg>0.6031."," Using the two propositions and equation (4) to infer the ionization state of neighboring gas elements (which provides the scaling $x_{\rm HeII} \propto \Delta_b^{1 - 0.7 (\gamma - 1)}$ ), we find that nearby elements with $\Delta_b = 1$ should have ${x}_{\rm HeII} > 0.034$." + See the intersection of the solid vertical linc in Fieure 20 with the thick solid curve., See the intersection of the solid vertical line in Figure \ref{fig:HeIIfrac} with the thick solid curve. +" In addition. the intersection of this vertical line with the two dashed curves in Figure 2. represcuts the lower limit ou the volume- aud imasseweighted Tell fractions iu the region surrouncdiuse the opaque voids witli ΜΗΠΟ=0.005 at Ay,=0.15. or UUCILYW=0.026 and ΠΟΠD0.052 (excluding A;>LO in these averages)."," In addition, the intersection of this vertical line with the two dashed curves in Figure \ref{fig:HeIIfrac} represents the lower limit on the volume- and mass-weighted HeII fractions in the region surrounding the opaque voids with ${x}_{\rm HeII}>0.008$ at $\Delta_b=0.15$, or ${x}_{\rm HeII, V}>0.026$ and ${x}_{\rm HeII, M}>0.052$ (excluding $\Delta_b > 10$ in these averages)." + This calculation ofthe volune-aud mass-weighted Tellfractionsusestheeas density probability distribution function (PDF) measured from simulations inMiralda- and it uses the fact that a," This calculation ofthe volume-and mass-weighted HeIIfractionsusesthegas density probability distribution function (PDF) measured from simulations in\citet{miralda00}, and it uses the fact that a" +inversion.,inversion. + The latter denotes the presence of positive fields., The latter denotes the presence of positive fields. + The MISMA code correctly interprets such a profile as emerging from a pixel in which opposite polarities coexist., The MISMA code correctly interprets such a profile as emerging from a pixel in which opposite polarities coexist. +" Such an interpretation is consistent with the COG map, showing how the pixel from which the profile is taken lies in the frontier between positive and negative field patches."," Such an interpretation is consistent with the COG map, showing how the pixel from which the profile is taken lies in the frontier between positive and negative field patches." + The central panel of Fig., The central panel of Fig. + 4 shows the Stokes V profile of a pixel next to the previous one in the direction of the positive polarity concentration., \ref{figs} shows the Stokes $V$ profile of a pixel next to the previous one in the direction of the positive polarity concentration. + It is very different from its neighbor - the profile in Fig., It is very different from its neighbor – the profile in Fig. + 4 is dominated by a negative red lobe and presents a small positive blue lobe., \ref{figs} is dominated by a negative red lobe and presents a small positive blue lobe. + The MISMA code interprets such a profile as emerging from a pixel in which only positive fields are present., The MISMA code interprets such a profile as emerging from a pixel in which only positive fields are present. +" In this case the inversion is also consistent with the COG magnetogram, which shows the pixel lying on a positive polarity patch."," In this case the inversion is also consistent with the COG magnetogram, which shows the pixel lying on a positive polarity patch." +" Figure 5 presents two examples of full Stokes inversion, i.e., inversions including Q and U."," Figure \ref{figf} presents two examples of full Stokes inversion, i.e., inversions including $Q$ and $U$." + Such examples illustrate the linear polarization signals we considered to be invertible., Such examples illustrate the linear polarization signals we considered to be invertible. + The upper panel of Fig., The upper panel of Fig. + 5 shows the inversion of a pixel very close to the example in the upper panel of Fig. 3.., \ref{figf} shows the inversion of a pixel very close to the example in the upper panel of Fig. \ref{figpm}. + In this case the linear polarization signal is strong enough to be analyzed and the MISMA code succeeds in the inversion., In this case the linear polarization signal is strong enough to be analyzed and the MISMA code succeeds in the inversion. +" It is important to notice that in such a pixel, similarly to what found in the upper panel of Fig. 3,,"," It is important to notice that in such a pixel, similarly to what found in the upper panel of Fig. \ref{figpm}," + polarization profiles are still interpreted by the code as emerging from a mixed polarity pixel., polarization profiles are still interpreted by the code as emerging from a mixed polarity pixel. + In the lower panel of Fig., In the lower panel of Fig. + a full inversion of an IN pixel is represented.," \ref{figf} + a full inversion of an IN pixel is represented." +" In this case, even if the pixel is almost on the frontier between opposite polarity regions, a single polarity is measured."," In this case, even if the pixel is almost on the frontier between opposite polarity regions, a single polarity is measured." + In the two cases the magnetic field strengths at the base of the photosphere are in the kG regime., In the two cases the magnetic field strengths at the base of the photosphere are in the kG regime. + The examples discussed here illustrate not only the goodness of the fits but also the soundness of the MISMA interpretation of SOT/SP measurements., The examples discussed here illustrate not only the goodness of the fits but also the soundness of the MISMA interpretation of SOT/SP measurements. + Such measurements are often characterized by important asymmetries in Stokes V profiles; Figs., Such measurements are often characterized by important asymmetries in Stokes $V$ profiles; Figs. + 3 and 4 show three examples of Stokes V profiles whose NCP>0.3., \ref{figpm}~ and \ref{figs} show three examples of Stokes $V$ profiles whose $NCP\geq0.3$. + From the maps in Fig. 2.., From the maps in Fig. \ref{fig2}. +" we notice that such values for the NCP are very common in the selected 29.52""x31.70"" subfield and, by extrapolation, they should be very common in the full FOV as well."," we notice that such values for the $NCP$ are very common in the selected $29.52''\times31.70''$ subfield and, by extrapolation, they should be very common in the full FOV as well." +" The common presence of large asymmetries demands a refined inversion method to interpret quiet Sun SOT/SP profiles, such as the MISMA inversion we are employing."," The common presence of large asymmetries demands a refined inversion method to interpret quiet Sun SOT/SP profiles, such as the MISMA inversion we are employing." + Detail on the percentage of asymmetric are reported in 4.., Detail on the percentage of asymmetric profiles are reported in \ref{res}. + The inversion code succeeded in the inversion of 11600 profiles which represent 29% of the selected subfield., The inversion code succeeded in the inversion of $11600$ profiles which represent $29\%$ of the selected subfield. + The total time needed to perform such an analysis about two days when the inversion analysis is split, The total time needed to perform such an analysis is about two days when the inversion analysis is split +It was ?. who first found cases of outward migration due to a coorbital torque in their three-dimensional radiative transfer models.,It was \cite{PaaMel2006} who first found cases of outward migration due to a coorbital torque in their three-dimensional radiative transfer models. + They found that this coorbital torque could be prevented from saturating if the radiation diffusion timescale was shorter than the libration timeseale of gas in the horseshoe region., They found that this coorbital torque could be prevented from saturating if the radiation diffusion timescale was shorter than the libration timescale of gas in the horseshoe region. + This enabled temperature asymmetries to be maintained beyond a single libration period., This enabled temperature asymmetries to be maintained beyond a single libration period. + They also showed that reducing the opacity (further shortening the radiation diffusion timescale) of their dise could lead to results in agreement with previous isothermal calculations., They also showed that reducing the opacity (further shortening the radiation diffusion timescale) of their disc could lead to results in agreement with previous isothermal calculations. + This was further described by ?.. who make clear that the radiation diffusion timescale must be greater than the period of a single horseshoe orbit to avoid returning to an isothermal like migration. and that outward migration can be related to the dise's radial entropy. gradient.," This was further described by \cite{BarMas2008}, who make clear that the radiation diffusion timescale must be greater than the period of a single horseshoe orbit to avoid returning to an isothermal like migration, and that outward migration can be related to the disc's radial entropy gradient." + Many numerical models have since also found evidence of outward migration in the Type I regime (2: ?:: 2u ?u ?u ?p»., Many numerical models have since also found evidence of outward migration in the Type I regime \citealt{PaaMel2008}; ; \citealt{PaaPap2008}; ; \citealt{KleCri2008}; \citealt*{KleBitKla2009}; \citealt{AylBat2010}; \citealt{YamIna2011}) ). + Periods of outward migration can help to increase the overall migration timescale of a forming planet embedded in a disc. as is required by synthesis models to explain the population of exoplanets that has been observed (22)," Periods of outward migration can help to increase the overall migration timescale of a forming planet embedded in a disc, as is required by synthesis models to explain the population of exoplanets that has been observed \citep*{IdaLin2008, MorAliBen2009}." + More recently there has been an extension. of analytical descriptions of the non-linear coorbital torque. called the horseshoe drag. to describe it in both its unsaturated and saturated states (2:: 2:: 2).," More recently there has been an extension of analytical descriptions of the non-linear coorbital torque, called the horseshoe drag, to describe it in both its unsaturated and saturated states \citealt{PaaBarCriKle2010}; \citealt*{PaaBarKle2011}; \citealt{MasCas2010}) )." + These works give expressions for the total torque acting on a planet due to both Lindblad torques and the coorbital component., These works give expressions for the total torque acting on a planet due to both Lindblad torques and the coorbital component. + As such they can deseribe planet migration for a large range of scenarios. taking into account the dise's density and temperature profiles. as well as its thermal ditfusivity.," As such they can describe planet migration for a large range of scenarios, taking into account the disc's density and temperature profiles, as well as its thermal diffusivity." + Outward migration is fastest in disces with steep radial temperature profiles. becoming more marginal at typical gradients such as Fwr|.," Outward migration is fastest in discs with steep radial temperature profiles, becoming more marginal at typical gradients such as $T \propto r^{-1}$." +" This paper is intended to explore protoplanet migration in a series of discs with radial temperature gradients from r"" to r7.", This paper is intended to explore protoplanet migration in a series of discs with radial temperature gradients from $r^{0}$ to $r^{-2}$. + We conduct three dimensional global dise models. using smoothed particle hydrodynamies (SPH). that include self-gravity and which use a planetary surface to allow modelling of gas flow to well within —qe Hill sphere and the self-consistent formation of an atmosphere.," We conduct three dimensional global disc models, using smoothed particle hydrodynamics (SPH), that include self-gravity and which use a planetary surface to allow modelling of gas flow to well within the Hill sphere and the self-consistent formation of an atmosphere." + We conduct a few isothermal models to investigate whether or not the temperature profile alone has an impaet on the migration rate. but otherwise our calculations all include radiative transfer using a flux-limited diffusion approximation.," We conduct a few isothermal models to investigate whether or not the temperature profile alone has an impact on the migration rate, but otherwise our calculations all include radiative transfer using a flux-limited diffusion approximation." + In Section 2.. we describe our computational method. in Section we explain how we obtained our results which are then presented3. in Section 4..," In Section \ref{sec:setup}, we describe our computational method, in Section \ref{sec:calc} we explain how we obtained our results which are then presented in Section \ref{sec:results}." + Section 5 discusses these results. whilst a summary and our conclusions are given in Section 6..," Section \ref{sec:discussion} discusses these results, whilst a summary and our conclusions are given in Section \ref{sec:summary}." + The calculations deseribed herein have been performed using a three-dimensional SPH code., The calculations described herein have been performed using a three-dimensional SPH code. + This SPH code has its origins in a version first developed by ? (?z 2)) but it has undergone substantial moditication in subsequent years., This SPH code has its origins in a version first developed by \citeauthor{Ben1990} \citeyear{Ben1990}; \citealt{BenCamPreBow1990}) ) but it has undergone substantial modification in subsequent years. + Energy and entropy are conserved to timestepping accuracy by use of the variable smoothing length formalism of 2?) and ? with our specific implementation being described in ?.., Energy and entropy are conserved to timestepping accuracy by use of the variable smoothing length formalism of \cite{SprHer2002} and \cite{Mon2002} with our specific implementation being described in \cite{PriBat2007}. . + Gravitational forces are calculated and neighbouring particles are found using a binary tree., Gravitational forces are calculated and neighbouring particles are found using a binary tree. + Radiative transfer is modelled in the two temperature (gas. 7... and radiation. 7;) flux-limited diffusion approximation using the method developed by ?. and ?..," Radiative transfer is modelled in the two temperature (gas, $T_{\rm g}$, and radiation, $T_{\rm r}$ ) flux-limited diffusion approximation using the method developed by \citet*{WhiBatMon2005} and \citet{WhiBat2006}." + Integration of the SPH equations is achieved using a second-order Runge-Kutta-Fehlberg integrator with particles having individual timesteps (2).., Integration of the SPH equations is achieved using a second-order Runge-Kutta-Fehlberg integrator with particles having individual timesteps \citep{Bat1995}. + The code has been parallelised by M. Bate using OpenMP., The code has been parallelised by M. Bate using OpenMP. + We present a few calculations performed using a locally-isothermal equation of state. as well as many more calculations which include radiative transfer.," We present a few calculations performed using a locally-isothermal equation of state, as well as many more calculations which include radiative transfer." + In locally-isothermal models the temperature of the gas in the dise remains as a function of radius throughout the calculations., In locally-isothermal models the temperature of the gas in the disc remains as a function of radius throughout the calculations. +" For the radiation hydrodynamical calculations we use the ideal gas equation of state. p=ofA,/p where Αι is the gas constant. p is the density. 7, is the gas temperature. and gc is the mean molecular mass."," For the radiation hydrodynamical calculations we use the ideal gas equation of state, $p=\rho T_{g} R_{g}/\mu$ where $R_{g}$ is the gas constant, $\rho$ is the density, $T_{g}$ is the gas temperature, and $\mu$ is the mean molecular mass." + The equation of state takes into account the translational. rotational. and vibrational degrees of freedom of molecular hydrogen (assuming a 3:1 mix of ortho- and para-hydrogen: see 2).," The equation of state takes into account the translational, rotational, and vibrational degrees of freedom of molecular hydrogen (assuming a 3:1 mix of ortho- and para-hydrogen; see \citealt{BolHarDurMic2007}) )." + It also includes the dissociation of molecular hydrogen. and the ionisations of hydrogen and helium.," It also includes the dissociation of molecular hydrogen, and the ionisations of hydrogen and helium." + The hydrogen and helium mass fractions are X=0.70 and Y=0.35. respectively. whilst the contribution of metals to the equation of state is neglected.," The hydrogen and helium mass fractions are $X=0.70$ and $Y=0.28$ , respectively, whilst the contribution of metals to the equation of state is neglected." + More details on the implementation of the equation of state can be found in 2.., More details on the implementation of the equation of state can be found in \cite{WhiBat2006}. + The radiative transfer in these calculations is performed using the flux-limited ditfusion approximation. as implemented by ? and ὃν. in which work and artificial viscosity (including both bulk and shear components) increase the thermal energy of the gas.," The radiative transfer in these calculations is performed using the flux-limited diffusion approximation, as implemented by \cite{WhiBatMon2005} and \cite{WhiBat2006}, in which work and artificial viscosity (including both bulk and shear components) increase the thermal energy of the gas." + Work done on the radiation field increases the radiative energy which can be transported via flux-limited ditfusion., Work done on the radiation field increases the radiative energy which can be transported via flux-limited diffusion. + The energy transfer between the gas and radiation fields is dependent upon their relative emperatures. the gas density. and the opacity. κ.," The energy transfer between the gas and radiation fields is dependent upon their relative temperatures, the gas density, and the opacity, $\kappa$." + Energy is lost from he system by the radiation field into the vacuum surrounding the dise: this is performed numerically through the use of a radiation boundary., Energy is lost from the system by the radiation field into the vacuum surrounding the disc; this is performed numerically through the use of a radiation boundary. +" This boundary is positioned at a height from the dise midplane at which the radiation path through the gas from this reight outwards has an optical depth of το,=I: Le. the radiation can be expected to reach the vacuum.", This boundary is positioned at a height from the disc midplane at which the radiation path through the gas from this height outwards has an optical depth of $\tau_{\rm op} \approx 1$; i.e. the radiation can be expected to reach the vacuum. + As a result. two layers of xurticles. one above and one below the disc. are made to comprise he radiation boundary.," As a result, two layers of particles, one above and one below the disc, are made to comprise the radiation boundary." + These particles are compelled to follow the initial temperature profile of the disc. causing them to function as energy sinks which impose a minimum temperature to which the dise can cool (see?.forafullerdeseription)..," These particles are compelled to follow the initial temperature profile of the disc, causing them to function as energy sinks which impose a minimum temperature to which the disc can cool \citep[see][for a fuller description]{AylBat2010}." + The use of steep radial temperature profiles in some of our models in this work leads to very high temperatures towards the inner boundary of these circumstellar dises., The use of steep radial temperature profiles in some of our models in this work leads to very high temperatures towards the inner boundary of these circumstellar discs. + This material forms an unrealistically hot annulus at the inner boundary. from which radiation ditfuses out through the dise. changing its structure out to the environs of the embedded. protoplanet.," This material forms an unrealistically hot annulus at the inner boundary, from which radiation diffuses out through the disc, changing its structure out to the environs of the embedded protoplanet." + To remedy this situation. the disc out to 2 auis compelled to maintain its initial temperature profile throughout the simulation. which quashes any ditfusion in this region.," To remedy this situation, the disc out to 2 auis compelled to maintain its initial temperature profile throughout the simulation, which quashes any diffusion in this region." + This rule was applied in all the calculations for consistency. including the shallower temperature profile calculations where it has no discernible ettect.," This rule was applied in all the calculations for consistency, including the shallower temperature profile calculations where it has no discernible effect." + The opacities used here are those of ? and ?. (the IVa King model). with the former providing the grain opacities and the latter the gas opacities at temperatures beyond the grain sublimation point.," The opacities used here are those of \cite{PolMcKChr1985} and \cite{Ale1975} (the IVa King model), with the former providing the grain opacities and the latter the gas opacities at temperatures beyond the grain sublimation point." + In some calculations the grain opacity is reduced by a factor of 100 to emulate possible modification of the population due to agglomeration processes (see?.forfurtherdetails)., In some calculations the grain opacity is reduced by a factor of 100 to emulate possible modification of the population due to agglomeration processes \citep[see][for further details]{AylBat2009}. +" We model a protoplanetary dise with radial bounds of0.1 - 3> (0.52: - 15.6 au. where iis the initial orbital radius of our embeddedry protoplanets. takingr, avalue of5.2 au."," We model a protoplanetary disc with radial bounds of0.1 - 3 (0.52 - 15.6 au), where is the initial orbital radius of our embedded protoplanets, taking avalue of5.2 au." + The dise is represented by 2 million SPH particles. a number found to deliver satisfactory resolution (see ?)..," The disc is represented by 2 million SPH particles, a number found to deliver satisfactory resolution \citep[see][]{AylBat2010}. ." + This leads to smoothing lengths at, This leads to smoothing lengths at +equilibrium between phases (Fieldefaf1969:Melee&Ostriker1977:Wolfiread1995).. (his is predicted to have a temperature of approximately 8000Ix. high enough to collisionally dissociate II.,"equilibrium between phases \citep{fgh,mo,wolf}, this is predicted to have a temperature of approximately $8000 \: \rm{K}$, high enough to collisionally dissociate $\mHt$." + ILowever. recent observations (IIeiles&Troland2002) and simulations that include the effects of turbulence (Gazolefαἱ.2001:MacLowal.2001) suggest that much of this gas is actually at much lower temperatures: for instance. Ποιος&Troland quote a temperature range of 500«T'5000Ix.," However, recent observations \citep{ht2} and simulations that include the effects of turbulence \citep{gaz,mac} suggest that much of this gas is actually at much lower temperatures; for instance, \citeauthor{ht2} quote a temperature range of $500 < T < 5000 \: \rm{K}$." + Taking representative values for the temperature and ionization of the WNM to be T=2000K and +=10? Ποιος2001).. I find that In other words. gas-phase formation would dominate if we could ignore the effects of the raciation field.," Taking representative values for the temperature and ionization of the WNM to be $T = 2000 \: \rm{K}$ and $x = 10^{-2}$ \citep{hei}, I find that In other words, gas-phase formation would dominate if we could ignore the effects of the radiation field." + In. practice. this is not possible: at the densities characteristic of the WNM (n0.1]em 3). we have and equation 37 becomes These two examples demonstrate (hat gas-phase Is formation is unimportant in the bulk of the gas in the Milky Wavy: either the temperature and ionization are (oo low. as in molecular clouds. or the gas is too diffuse and II» formation is suppressed by the photocdissociation of Il and IL.," In practice, this is not possible; at the densities characteristic of the WNM $n \simeq 0.1 \: \rm{cm}^{-3}$ ), we have and equation \ref{WNM} becomes These two examples demonstrate that gas-phase $\mHt$ formation is unimportant in the bulk of the gas in the Milky Way: either the temperature and ionization are too low, as in molecular clouds, or the gas is too diffuse and $\mHt$ formation is suppressed by the photodissociation of $\Hm$ and $\mHtp$." + llowever. there are a few counterexamples.," However, there are a few counterexamples." + For instance. gas-phase Il» formation has long been known to play an important role in the chemistry of nova ejecta (Rawlings and protostellar outflows (Glassgolde£a£.1989).. where the gas initially has little or no dust (although more generally forms later) ancl where (he high gas densities help mitigate the effects of photodissociation.," For instance, gas-phase $\mHt$ formation has long been known to play an important role in the chemistry of nova ejecta \citep{raw} and protostellar outflows \citep{gmh}, where the gas initially has little or no dust (although more generally forms later) and where the high gas densities help mitigate the effects of photodissociation." + Gas-phase formation is also predicted to dominate the molecular chemistry of [reelv-expanding supernova remnants such as SN1987A (Culhane&MeCray 1995)., Gas-phase formation is also predicted to dominate the molecular chemistry of freely-expanding supernova remnants such as SN1987A \citep{cm}. +. Finally. Lepp&MeCray(1983). suggest (hal gas-phase formation max dominate in X-rav dissociation regions (dense clouds illuminated by hard N-ravs): modelling by (1996) would appear to confirm (his.," Finally, \citet{lmc} suggest that gas-phase formation may dominate in X-ray dissociation regions (dense clouds illuminated by hard X-rays); modelling by \citet{mht} would appear to confirm this." + These are somewhat unusual conditions. however. and in general dust abundances sgnificamtlv below the (vpical galactic value are required. before gas-phase Ils formation becomes competitive with exgrain-catalvzed formation.," These are somewhat unusual conditions, however, and in general dust abundances significantly below the typical galactic value are required before gas-phase $\mHt$ formation becomes competitive with grain-catalyzed formation." +"the recognition that inclusion of the more highly deuterated species Doll and D, in (he chemical calculations. increases at least bv a factor of 2 the gas phase D/II ratio (Robertsetal.2003).","the recognition that inclusion of the more highly deuterated species $_2$ $^+$ and $_3^+$ \citep{phillips02} in the chemical calculations, increases at least by a factor of 2 the gas phase D/H ratio \citep{roberts03}." +. The identified most abundant components of the molecular mantles found on interstellar dust erains are [oO and CO (lorrelerences.seeTeixeira&Emerson1999).," The identified most abundant components of the molecular mantles found on interstellar dust grains are $_2$ O and CO \citep[for references, see][]{teixeira99}." +". The large range of condensation temperatures (seeNakagawa1950) spannecl by LeO (DL, ~ 90 IX) and CO CL. ~ 16 IX) suggests that molecules with intermediate condensation temperatures could also be present in (he grain mantles.", The large range of condensation temperatures \citep[see][]{nakagawa80} spanned by $_2$ O $_c$ $\sim$ 90 K) and CO $_c$ $\sim$ 16 K) suggests that molecules with intermediate condensation temperatures could also be present in the grain mantles. + For example. LoS has a condensation temperature ol ~ 39 Ik (Nakagawa1980).," For example, $_2$ S has a condensation temperature of $\sim$ 39 K \citep{nakagawa80}." +. This molecule and other sulfiu-bearing molecules have been observed in (hie gas phase in cold. dark cloudswhere hish-temperature processes should not be important (Minhetal.1989:IrvineFuenteοἱ 1990): ΧΡ) = 3 x ? al the SO peak of LI34N. < 5 x LO! at the evanopolvvne peak towards TMCI and ~ 7x LO! towards the NIL; peak position of TMCL.," This molecule and other sulfur-bearing molecules have been observed in the gas phase in cold, dark cloudswhere high-temperature processes should not be important \citep{minh89,irvine89,fuente90}: : $_2$ S) = 3 $\times$ $^{-9}$ at the SO peak of L134N, $<$ 5 $\times$ $^{-10}$ at the cyanopolyyne peak towards TMC1 and $\sim$ 7 $\times$ $^{-10}$ towards the $_3$ peak position of TMC1." + These values can be compared to the range 11 - I! obtained [or steady-state gas-phase models (Millaretal. 1997).," These values can be compared to the range $^{-11}$ - $^{-10}$ obtained for steady-state gas-phase models \citep{millar90,millar97}." +. Therefore. it poses a problem [ον gas phase chemistry.," Therefore, it poses a problem for gas phase chemistry." + The gas-phase reactions proposed for the formation of Iles are endothermic (see Section 3) and other mechanisms such as shock chemistvy or high temperature chemistry are unlikely to be important in dark clouds., The gas-phase reactions proposed for the formation of $_2$ S are endothermic (see Section 3) and other mechanisms such as shock chemistry or high temperature chemistry are unlikely to be important in dark clouds. + Grain surface reactions have then been suggested as an alternative patliway to 1155 molecule formation (Dulevetal.1980)., Grain surface reactions have then been suggested as an alternative pathway to $_2$ S molecule formation \citep{duley80}. +. Because sulfur is chemically similar to oxvgen. it is tempting to study (his molecule to eain insight to the Π.Ο deuteration processes.," Because sulfur is chemically similar to oxygen, it is tempting to study this molecule to gain insight to the $_2$ O deuteration processes." + Like IIO. it is possible that 1. originates on erain surfaces. where it was formed by accretion and hydrogenation of sulfur atoms during core formation (Tielens&Allamancdola1987).," Like $_2$ O, it is possible that $_2$ S originates on grain surfaces, where it was formed by accretion and hydrogenation of sulfur atoms during core formation \citep{tielens87}." +. The comparison between LoS. IIDS and DoS would be useful for a complete study of the deuteration processes.," The comparison between $_2$ S, HDS and $_2$ S would be useful for a complete study of the deuteration processes." + In this letter. we report the observations of the IIDS and DoS ground transitions. accessible at the Caltech Submillimeter Observatory (CSO).," In this letter, we report the observations of the HDS and $_2$ S ground transitions, accessible at the Caltech Submillimeter Observatory (CSO)." + This observatory is a 10.1 meter single-dish antenna located on top of Mana Ixea in Lawaii., This observatory is a 10.4 meter single-dish antenna located on top of Mauna Kea in Hawaii. +" At 240 GlIIz. the telescope has an FWIIM beam size of 31""."," At 240 GHz, the telescope has an FWHM beam size of $^{\prime\prime}$ ." + The observations ofthese molecules were carried out between March. 2002 and September 2002., The observations ofthese molecules were carried out between March 2002 and September 2002. + Weather conditions were average with zenith opacities between 0.05 and 0.2 al 225 GIIz., Weather conditions were average with zenith opacities between 0.05 and 0.2 at 225 GHz. +Aeauwhile. Shull (1996) have estimated the radii of local clouds to be ~LOOkpe at cobuuus of NO~100n 7. aud Blitz (1998) have found the upper lait cloud radius. constrained by the tidal feld of the Local Group. to be z25 kpe at colhuuus of N~101?cu7.,"Meanwhile, Shull (1996) have estimated the radii of local clouds to be $\sim 100 \kpc $ at columns of $N \sim 10^{13} \cmtw $ , and Blitz (1998) have found the upper limit cloud radius, constrained by the tidal field of the Local Group, to be $\simeq 25$ kpc at columns of $N \simeq 10^{19} \cmtw$." + While these Seures mv make the simulated cloud sizes at hiehredshift sccm low. the 50fold drop in the farUV ietagalactic flux at the Lxauan μπιτ from its value at 2=2.5 (Πααταί Madan 1996) will help to account for this apparent disparity in absorption cross section.," While these figures may make the simulated cloud sizes at high–redshift seem low, the 50–fold drop in the far--UV metagalactic flux at the Lyman limit from its value at $z=2.5$ (Haardt Madau 1996) will help to account for this apparent disparity in absorption cross section." + Iu a study of the lensed quasar (2315| OOTA.B. Foltz (1981) have placed a lower Bit on the characteristic diameters of clouds at (2)=1.95 of 5.25 kpe (the uncertaintv stems from the ακουσα redshitt of the leus).," In a study of the lensed quasar $Q2345+007$ A,B, Foltz (1984) have placed a lower limit on the characteristic $diameters$ of clouds at $\langle z +\rangle = 1.95$ of $5 - 25$ kpc (the uncertainty stems from the unknown redshift of the lens)." + These values simply reflect the range of possible distances between beams., These values simply reflect the range of possible distances between beams. + However. a \Moute Carlo analysis of the correlated absorption svsteis in the spectra of Q313| 2610A. D (Dinshaw 199D. which lias a similar ratio of κ to “iisses” (hmc 2). found an imferred cloud diameter 2.5 times that of the median bean separation.," However, a Monte Carlo analysis of the correlated absorption systems in the spectra of $1343+2640$ A, B (Dinshaw 1994), which has a similar ratio of “hits” to “misses” $\simeq 2$ ), found an inferred cloud diameter 2.5 times that of the median beam separation." + If this correction is applied to the Foltz (1981) data. the cloud range in radii becomes 7.562.55.tkpe.," If this correction is applied to the Foltz (1984) data, the cloud range in $radii$ becomes $7.5 - +62.5 \hkpc$." +" However. recent work correlating absorption svstenis of double aud eroup quasars (e.g.. Fang 1996: Crotts Faug 1998) fud much larger values (typically « 100. of kpc). but it is not clear that these are large individual clouds rather than the largerscale clustering of much sanaller individual clouds that we lave been discussing. which could be expected to give ""cloud diameters” of from ~3005002.3 Epe. depending ou the equivalent widths probed aud the methodof analysis — consistent with their results."," However, recent work correlating absorption systems of double and group quasars (e.g., Fang 1996; Crotts Fang 1998) find much larger values (typically $\times$ 100s of kpc), but it is not clear that these are large individual clouds rather than the larger–scale clustering of much smaller individual clouds that we have been discussing, which could be expected to give “cloud diameters” of from $\sim 300 - 500 h^{-1}$ kpc, depending on the equivalent widths probed and the methodof analysis – consistent with their results." + For high redshift clouds (25 3) 1 adopt a fiducial radius of 25 5Xpc for individual IT I clouds at columuis of LogNzLL.," For high redshift clouds $z \sim 2-3$ ) I adopt a fiducial radius of 25 $\hkpc$ for individual H I clouds at columns of ${\rm Log} \, N +\simeq 14$." +" A line density of dNf/dz~100 at a vedshitt of 2~3 is asstued. based on data normalized to an equivalent width limit of 1Y,,20.2LA (Weviann 1998). which. for T2 «10!K. is quite close to a column deusitv. VN=10them2, "," A line density of $d{\rm N}/d {\rm z} \approx 100$ at a redshift of $z\sim 3$ is assumed, based on data normalized to an equivalent width limit of $W_o = 0.24 { \rm\AA }$ (Weymann 1998), which, for $\rm T \approx 2 \times 10^4 $ K, is quite close to a column density, $N=10^{14} \cmtw $." +Substituting these values iuto Eq., Substituting these values into Eq. + 3. we find. For ο=Ll. nj;=SA?MpeP7. Comparison of Eqs.," 3, we find, For $\Omega = 1$, $n_{cl}=8.4 \, \rm{h^3 \, Mpc^{-3}}$ Comparison of Eqs." + 2 aud [ shows ny.zn., 2 and 4 shows $n_{gc} \approx n_{cl}$. + Ἡ there is a spectrum of cloud. sizes (I find the largest dominated the absorption luedeusitv). then since cloud number deusitv. οXr7? (Eq.," If there is a $spectrum$ of cloud sizes (I find the largest dominated the absorption line–density), then since cloud number density, $n_{cl} \propto +r^{-2}$ (Eq." + 3) the total nuniber deusity of clouds iav be sienificautlv. larger. which may help the nuubers to look better for open cosinologies.," 3), the total number density of clouds may be significantly larger, which may help the numbers to look better for open cosmologies." + Also. if replenishiment is οσαας at hiehredshift bv the condensation of clouds in voids and subsequent movement toward neighboring ealaxies. then the total nunuber of potential mipactors could be substantially exeater than estimated above.," Also, if replenishment is occurring at high–redshift by the condensation of clouds in voids and subsequent movement toward neighboring galaxies, then the total number of potential impactors could be substantially greater than estimated above." + For a modest sized protogalaxy. the infall velocities of an intergalactic cloud can be expected to be in excess of 60 kan/sec.," For a modest sized protogalaxy, the infall velocities of an intergalactic cloud can be expected to be in excess of 60 km/sec." + In order to form a cluster. therefore. some simall fraction of the pluugiug cloud iust survive tle supersouic shock iu a compact form.," In order to form a cluster, therefore, some small fraction of the plunging cloud must survive the supersonic shock in a compact form." + Numerical simulations of honiogeueous clouds subjected to interstellar shocks have found that clouds are cestroved ou fine scales of a sound crossing time(e.g... Kleiu. MelIsee Colella 1991: πιακαὶ Ikeuchi 1993).," Numerical simulations of homogeneous clouds subjected to interstellar shocks have found that clouds are destroyed on time scales of a sound crossing time, Klein, McKee Colella 1994; Murakami Ikeuchi 1993)." +" However. ποΊσα studies of he survival of iutergalactie. cold dark matterheld. ""uiniwo” clouds (Rees 1986) subjected to supersouie flows (Murakauni Useuchi 1991) have shown that the cores of clouds confined by a dark halo may survive extended seriods of exposure to supersonic wind as long as the ceutral cloud density exceeds that of the ambicut medium hrough which it passes."," However, numerical studies of the survival of intergalactic, cold dark matter–held, ``mini--halo'' clouds (Rees 1986) subjected to supersonic flows (Murakami Ikeuchi 1994) have shown that the cores of clouds confined by a dark halo may survive extended periods of exposure to supersonic wind as long as the central cloud density exceeds that of the ambient medium through which it passes." + Tn the context of accretion to a galaxy. this will require that the central density of the cloud should increase m time in order that if may survive he increasing deusitics it will eucounter as it falls iuc.," In the context of accretion to a galaxy, this will require that the central density of the cloud should increase in time in order that it may survive the increasing densities it will encounter as it falls inward." + This in turn will require cooling., This in turn will require cooling. +" For a stable compression xocess, therefore. the cooling time scale. 7. must remain sanaller than the timescale for the iucrease in the ambicut xotosalaxv eas density. Ty. at cach stage of the cloud’s journey."," For a stable compression process, therefore, the cooling time scale, $\tau_c$, must remain smaller than the time–scale for the increase in the ambient protogalaxy gas density, $\tau_{d}$, at each stage of the cloud's journey." +" The timescale for change of deusitv is expressible x the equation. I prestune. for the sake of iniplicity. that the eas aud the DM are distributed in au isothermal profile with density law. p=Aftἐπ), where R is the ealactocentiic distauco. and A is a unit of mass per unit leneth."," The timescale for change of density is expressible by the equation, I presume, for the sake of simplicity, that the gas and the DM are distributed in an isothermal profile with density law, $\rho={\cal{K}}/(4 \pi R^2)$, where $R$ is the galactocentric distance, and ${\cal{K}}$ is a unit of mass per unit length." + A. will be referred to as the system massdistribution constant.," ${\cal +K}$ will be referred to as the system mass–distribution constant." + For au £ galaxv. C=KP?zmLAE10*M.pe|," For an $L^*$ galaxy, ${\cal{K}}={\cal{K}}^*\approx 1.14 \times 10^{7} +\Msun \pc^{-1}$." + Falso presiuaue that the distribution is truncated at a distance A., I also presume that the distribution is truncated at a distance $R_t$. + Then for RooBy. MR)=KR. aud for RB. M(QR)=Ks.," Then for $ R < R_t$, $M(R) = {\cal{K}} R$, and for $R > R_t$, $M(R) = {\cal{K}} R_t$." + Manipulating Eq., Manipulating Eq. + 5.Γ we fud. ος is the mfall velocity.," 5, we find, where $v_i$ is the infall velocity." + With the assumed mass distribution. we can calculate the potential: where Ry is the location. presmmed in this case to be ~2Apc. of the turiaround radius. aud at which the potential is set to zero.," With the assumed mass distribution, we can calculate the potential: where $R_0$ is the location, presumed in this case to be $\sim 2$, of the turn–around radius, and at which the potential is set to zero." + Ry is assumed to be 500 kpe for an LU type object., $R_t$ is assumed to be 500 kpc for an $L^*$ –type object. + Conservation of energy requires that the infall velocity be eiveu by the equation. ΟΠ30$, cannot be stored sufficiently accurately in single precision." + This requirement is of relevance to GPU implementation. as the greatest. processing speccd-ups ollered by the current generation of GPUs is for single precision. and reduces the overall memory required. by storing as 32-bit rather than O4-bit values.," This requirement is of relevance to GPU implementation, as the greatest processing speed-ups offered by the current generation of GPUs is for single precision, and reduces the overall memory required by storing as 32-bit rather than 64-bit values." + Given the strong degree of parallelism exhibited by the algorithm. the ability to efficiently cache the input data and take advantage of à very high arithmetic intensity. the ability to pre-compute the shapelet integral terms. and the fact that the core of the algorithm can be reduced to simple multiply-adel operations. we conclude that an implementation of the shapelet decomposition algorithm on a CPU would. likely achieve a level of performance very near the peak capability of the hardware.," Given the strong degree of parallelism exhibited by the algorithm, the ability to efficiently cache the input data and take advantage of a very high arithmetic intensity, the ability to pre-compute the shapelet integral terms, and the fact that the core of the algorithm can be reduced to simple multiply-add operations, we conclude that an implementation of the shapelet decomposition algorithm on a GPU would likely achieve a level of performance very near the peak capability of the hardware." + Shapelet decomposition thus stands. to benefit significantly [rom current trends in. commocity computing hardware. and may have an additional advantage over related: methods that are unable to take advantage of massively-parallel architectures.," Shapelet decomposition thus stands to benefit significantly from current trends in commodity computing hardware, and may have an additional advantage over related methods that are unable to take advantage of massively-parallel architectures." + The extension. of the above algorithm analysis to. d-dimensional shapelet decompositions should be straightforward. and we expect the conclusions| to remain— unchanged: however. implementation complexity is likely to increase. particularly in the general case.," The extension of the above algorithm analysis to $d$ -dimensional shapelet decompositions should be straightforward, and we expect the conclusions to remain unchanged; however, implementation complexity is likely to increase, particularly in the general case." + For the application domain we now explore. viz.," For the application domain we now explore, viz." + 3-cl Cartesian shapelet representations of simulated dark matter haloes. we have used a CPU-only implementation of the decomposition algorithm.," 3-d Cartesian shapelet representations of simulated dark matter haloes, we have used a CPU-only implementation of the decomposition algorithm." + If the only use of the shapelet approach was to calculate the analytic expressions of Section 3. then it would. be a somewhat incllecient one. Compared to direct. numerical integration of equations (24)). (300). (35)). (39)). and (42).," If the only use of the shapelet approach was to calculate the analytic expressions of Section 3, then it would be a somewhat ineffecient one, compared to direct numerical integration of equations \ref{eqn:ana1}) ), \ref{eqn:ana2}) ), \ref{eqn:ana3}) ), \ref{eqn:ana4}) ), and \ref{eqn:ana5}) )." + The benefit of the shapelet decomposition is that we now have additional information concerning the shape., The benefit of the shapelet decomposition is that we now have additional information concerning the shape. + Opportunities for classifving threc-dimensional structures based. on the shapelet terms may be mace through identification of the dominant shapelet terms. or. by investigating relative weights of particular shapelet orders.," Opportunities for classifying three-dimensional structures based on the shapelet terms may be made through identification of the dominant shapelet terms, or by investigating relative weights of particular shapelet orders." + In this section. we demonstrate. how threc-dimensional shapelet. analvsis of dark matter halos suggests. a new method for automatically classifying halo types.," In this section, we demonstrate how three-dimensional shapelet analysis of dark matter halos suggests a new method for automatically classifying halo types." + For some time. it has been known that Cold Dark Matter (CDAD) cosmologies predict the formation of triaxial haloes (on average). with a slight preference for prolate haloes over oblate ones (Davis et al.," For some time, it has been known that Cold Dark Matter (CDM) cosmologies predict the formation of triaxial haloes (on average), with a slight preference for prolate haloes over oblate ones (Davis et al." + 1985: Barnes Lfstathiou LOST: Frenk et al., 1985; Barnes Efstathiou 1987; Frenk et al. + 1988: Dubinski Carlberg 1991: Dubinski 1994: Cole Lacey 1996: Jing Suto 2002: Ixasun IE5vrard 2005:, 1988; Dubinski Carlberg 1991; Dubinski 1994; Cole Lacey 1996; Jing Suto 2002; Kasun Evrard 2005; +brightest galaxies. the measured fiux docs uot deviate significantly from the input value.,"brightest galaxies, the measured flux does not deviate significantly from the input value." +" At isi)22 mags. however. we systematically uuderestimate the iuput flux by ~0:3 aes aud maxinuun raudoni errors increase to Ams,70.5 across the range of B/T."," At $m_{814}>22$ mags, however, we systematically underestimate the input flux by $\sim0.3$ mags and maximum random errors increase to $\Delta m_{814}>0.5$ across the range of $B/T$." +" With the exception of three galaxies (of 173). all of the CL 1358|62 sample are brighter than 4,—22 mags."," With the exception of three galaxies (of 173), all of the CL 1358+62 sample are brighter than $m_{814}=22$ mags." + The bottom paucl of Fig., The bottom panel of Fig. + 77 emphasizes how faint ealaxies. and in particular low surface brightuess ones. are adversely affected by decreasing signal-to-noise ratios.," \ref{1358flux_rh} emphasizes how faint galaxies, and in particular low surface brightness ones, are adversely affected by decreasing signal-to-noise ratios." + Iu cach subpancl. we underestimate the total flux as nieasured increases. £60. as the average surface brightuess decreases;," In each subpanel, we underestimate the total flux as measured increases, $i.e.$ as the average surface brightness decreases." + Even at fairly bright magnitudes (κιX21 mags). flax loss cau be significant for ealaxies with ο kpc.," Even at fairly bright magnitudes $m_{814}\leq21$ mags), flux loss can be significant for galaxies with $>5$ kpc." +" Fortunately, the median halt-light radius of the CL 1358|62 cluster sample is 2.11.28 kpe so this «hould not affect our conclusions."," Fortunately, the median half-light radius of the CL 1358+62 cluster sample is $2.4\pm1.2$ kpc so this should not affect our conclusions." + Figure ?7 illustrates how the measured bulge fraction I Τοντ] differs from its put value as a function of measured sy). DAT. auc ;5.," Figure \ref{1358bt_comp4} illustrates how the measured bulge fraction $(B/T)_{OUT}$ ] differs from its input value as a function of measured $m_{814}$, $B/T$, and ." +". Above our maguitude cut of sy,= 21. the systematic differences between iuput and measured B/T are negligible aud the random errors are «0.2 (see Fig. ??))."," Above our magnitude cut of $m_{814}=21$ , the systematic differences between input and measured $B/T$ are negligible and the random errors are $<0.2$ (see Fig. \ref{1358dbt_deV}) )." + These results leud confidence to measurement of the bulge/total luminosity for galaxies im our cluster sample., These results lend confidence to measurement of the bulge/total luminosity for galaxies in our cluster sample. + Figure ?7. (top panel) shows the fractional difference between input and measured values of as a function of bulge fraction., Figure \ref{1358r_comp4} (top panel) shows the fractional difference between input and measured values of as a function of bulge fraction. + Recovery of the laltlight radius is robust for maj;<21 mags galaxies with systematic and randoni errors of less than and respectively., Recovery of the half-light radius is robust for $m_{814}\leq21$ mags galaxies with systematic and random errors of less than and respectively. + This is reiterated in the top panel of Fig. ??.., This is reiterated in the top panel of Fig. \ref{1358rscales_bt}. + Here we show the average input and measured values as a function of input bulee fraction., Here we show the average input and measured values as a function of input bulge fraction. + Ouly for the most bulec-dominated systems (B/T> 0.7) axe the differences systematically larger than lo as due to the long wings of the de Vaucouleurs profile. flux at large radii cau be lost in the sky backeround.," Only for the most bulge-dominated systems $B/T\geq0.7$ ) are the differences systematically larger than $1\sigma$ as due to the long wings of the de Vaucouleurs profile, flux at large radii can be lost in the sky background." + Recovery of disk exponential scale leugth for G/T<0. ealaxies is excellent., Recovery of disk exponential scale length for $B/T<0.4$ galaxies is excellent. + At nai;x21 mags svstematic and randoni errors for disk-dominated objects (B/T< 0.1) are zero aud <15% respectivelv Guiddle panel. Fie. ?7?)).," At $m_{814}\leq21$ mags, systematic and random errors for disk-dominated objects $B/T<0.4$ ) are zero and $<15\%$ respectively (middle panel, Fig. \ref{1358r_comp4}) )." + Iu fact. the simulations show that ry measurements are robust up to B/T~0.5 (middle panel. Fie. ??)).," In fact, the simulations show that $r_d$ measurements are robust up to $B/T\sim0.8$ (middle panel, Fig. \ref{1358rscales_bt}) )." + Iu comparison. measurements of the bulee scale leneth are not as robust: ο teuds to be underestimated (~10 20:4)) at all magnitudes (bottom panel. Fies.," In comparison, measurements of the bulge scale length are not as robust: $r_e$ tends to be underestimated $\sim10-20$ ) at all magnitudes (bottom panel, Figs." + ?? ?7))., \ref{1358r_comp4} \ref{1358rscales_bt}) ). + Random errors. even for the most bulge-dominated systenas. also are larecr than those associated with the disk scale leugth.," Random errors, even for the most bulge-dominated systems, also are larger than those associated with the disk scale length." + While this result is not surprising when considering the shape of the de Vaucouleurs profile. it can iutroduce a bias that would be particularly detrimental to laree. bulge-doiniuated. low huninosity syvstenis.," While this result is not surprising when considering the shape of the de Vaucouleurs profile, it can introduce a bias that would be particularly detrimental to large, bulge-dominated, low luminosity systems." + From these simulations. we determine that for the CL 1358162 cluster sample: 1) Measurements of halfhelt radius across the range of B/T are robust:2) Disk scale leugths are reliable for ealaxics with substantial disks (2B/T« 0.6): aud 3) The svstematic uncertaiuties associated with imeasmiug bulge scale leugthns requires that care be applied iu their interpretation. especially for ealaxies with a small bulee componeut (2/7«0.1).," From these simulations, we determine that for the CL 1358+62 cluster sample: 1) Measurements of half-light radius across the range of $B/T$ are robust;2) Disk scale lengths are reliable for galaxies with substantial disks $B/T<0.6$ ); and 3) The systematic uncertainties associated with measuring bulge scale lengths requires that care be applied in their interpretation, especially for galaxies with a small bulge component $B/T<0.4$ )." + To test the robustucss of our results concerning ellipticals. aud. SOs. we compare input and measured values of bulge cllipticity aud disk inclination.," To test the robustness of our results concerning ellipticals and S0's, we compare input and measured values of bulge ellipticity and disk inclination." + Figure ?? shows the average differences in bulge ellipticity aud disk inclinations for artificial galaxies as a function of nieasured BiT aud apparent magnitude., Figure \ref{1358cosi_ell4} shows the average differences in bulge ellipticity and disk inclinations for artificial galaxies as a function of measured $B/T$ and apparent magnitude. +" At ms,<21. both paralcters are recovered well with iuedian differences between input and measured values of approximately zero."," At $m_{814}\leq21$, both parameters are recovered well with median differences between input and measured values of approximately zero." + The associated random errors iu both ellipticity aud cos 7 aro <<(LL., The associated random errors in both ellipticity and cos $i$ are $<0.1$. + As expected. random errors dn the bulge cllipticity are largest for disk-donmünated svstenis. aud errors n cos / largest im bulge-donminated svstenis.," As expected, random errors in the bulge ellipticity are largest for disk-dominated systems, and errors in cos $i$ largest in bulge-dominated systems." + We fund that fitting Séirsic bulecs with exponcutial disks to the cluster members results iu a siguificant correlation between visual type and bulee fraction (see Fie. ??))., We find that fitting Sérrsic bulges with exponential disks to the cluster members results in a significant correlation between visual type and bulge fraction (see Fig. \ref{1358profiles}) ). +" By fitting Sévrsic profiles. however. we must test our ability to recover the true bulge power η,"," By fitting Sérrsic profiles, however, we must test our ability to recover the true bulge power $n$." + To do so. we create an artificial galaxy catalog of L500 ealaxies in the FalAWW filter with bulee fraction z0.5 and bulee power » between 0.2 and 6: all other structural parameters are the same as for the deVaucouleurs bulee|exponential disk artificial catalog.," To do so, we create an artificial galaxy catalog of $1500$ galaxies in the F814W filter with bulge fraction $\geq0.5$ and bulge power $n$ between 0.2 and 6; all other structural parameters are the same as for the deVaucouleurs bulge+exponential disk artificial catalog." + As before. we discuss results ouly for galaxies with κιE21 mags.," As before, we discuss results only for galaxies with $m_{814}\leq21$ mags." + For most galaxies )). we are within 0.5 of the true Sérrsic bulee power » (Fie. ??:," For most galaxies ), we are within 0.5 of the true Sérrsic bulge power $n$ (Fig. \ref{1358dnb_plot};" + top panel)., top panel). + Approximately of the catalog. however. has An21 and. in some cases. An can be as iimcli as £L.," Approximately of the catalog, however, has $\Delta n\geq1$ and, in some cases, $\Delta n$ can be as much as $\sim4$." + Even more disconcerting is the comparison of input versus iieasured bulee fraction (Fig. 27:, Even more disconcerting is the comparison of input versus measured bulge fraction (Fig. \ref{1358dnb_plot}; + lower panel)., lower panel). + The distribution is skewed heavily towards underestinmatiug the true bulee fraction Guedian A(B/T)~ Lll) and of the galaxies are now considered disk-dominated systems even though uoue have input B/T<0.5.," The distribution is skewed heavily towards underestimating the true bulge fraction (median $\Delta (B/T)\sim14\%$ ), and of the galaxies are now considered disk-dominated systems even though none have input $B/T<0.5$." + These siuulatious emphasize that measuring reliable Séórrsje ps and the corresponding bulee fraction requires 1) a combination of excellent resolution aud high signal-to-noise: 2) understanding how noise affects the measurements: and 3) rigorous testing of structural piriuneters derived for cach galaxy., These simulations emphasize that measuring reliable Sérrsic $n$ and the corresponding bulge fraction requires 1) a combination of excellent resolution and high signal-to-noise; 2) understanding how noise affects the measurements; and 3) rigorous testing of structural parameters derived for each galaxy. + With the artificial catalog of Sérrsic bulge|exponcutial disk galaxies. we address the question of how serious the errors would be if we modeled them as," With the artificial catalog of Sérrsic bulge+exponential disk galaxies, we address the question of how serious the errors would be if we modeled them as." +"Bulges, Fieure 2 courpares the input Sénse DB/T compared to that recovered using the de Vaucouleurs profile.", Figure \ref{1358dbt_cross} compares the input Sérrsic $B/T$ compared to that recovered using the de Vaucouleurs profile. + The distributionisas skewed towards uuderestimating the true bulee fraction as iu Fie. ??::, The distributionisas skewed towards underestimating the true bulge fraction as in Fig. \ref{1358dnb_plot}; + this is due prunarily to lich B/T systems with bulee vw—1 beige confused as disk-«donunated svstems (see 855.3]., this is due primarily to high $B/T$ systems with bulge $n\sim1$ being confused as disk-dominated systems (see 5.3). +" Even for galaxies with hieher Sérrsic indices (η7 3). the average A(B/T) is still larger than if the true bulee profile Is jp,"," Even for galaxies with higher Sérrsic indices $n>3$ ), the average $\Delta (B/T)$ is still larger than if the true bulge profile is $r^{1/4}$ ." + (Ivudinetal.1991). > ;di(QUa Dichl&Tiuuues(19908) (Theetal.1996: (7.041.7)10? (3.320.6)το°? citeplIvudiu97.. L110. (Fronteraetal.1997)..," \citep{Iyudin94} $\rightarrow$ $\rightarrow$ \citet{Diehl98} \citep{The96,Rothschild97,Vink00}, $(7.0 \pm 1.7)\ 10^{-5}$ $(3.3 \pm 0.6)\ 10^{-5}$ \\citep{Iyudin97}, $4.1\ 10^{-5}$ \\citep{Vink00}. \citep{Frontera97}. \citep{cookbook}," +"with 3= 60. cs,=0.2 and f.=5.","with $\beta = 60$ , $\epsilon_{SN} = 0.2$ and $f_c = 5$." + These values are well within the uncertainties of observations by Kennicutt (1998) ancl Bosma (1981) for the star formation cllicleney and the gaseous extent of colcl disks. respectively.," These values are well within the uncertainties of observations by Kennicutt (1998) and Bosma (1981) for the star formation efficiency and the gaseous extent of cold disks, respectively." + Numerical simulations by e.g. Phornton et al. (, Numerical simulations by e.g. Thornton et al. ( +"1998) tend to give values closer to 0.1 for feedback elliciencv: however our higher value is a consequence of an attempt to reduce the number of small objects overestimated by the Press-Sehechter prescription. as well as a means to cure the “cooling catastrophe"". where too much gas cools in low mass halos at high redshift.","1998) tend to give values closer to 0.1 for feedback efficiency; however our higher value is a consequence of an attempt to reduce the number of small objects overestimated by the Press-Schechter prescription, as well as a means to cure the “cooling catastrophe”, where too much gas cools in low mass halos at high redshift." +" “Phe qualitative elfect of each ofthese parameters can be summed up in the following way: The main drawback of DCGO0 is their modelling of ultraluminous clusty starbursts: they use anhoc fraction of massive objects £. calibrated. locally on the Iuminosity function anc which is evolving with redshift as Fox(1|2)""."," The qualitative effect of each of these parameters can be summed up in the following way: The main drawback of DG00 is their modelling of ultraluminous dusty starbursts: they use an fraction of massive objects $F$, calibrated locally on the luminosity function and which is evolving with redshift as $F \propto (1+z)^6$." +" In this paper. we replace this ""recipe"" by a physically motivated: collision model which allows us to differentiate between disks and ellipticals."," In this paper, we replace this “recipe” by a physically motivated collision model which allows us to differentiate between disks and ellipticals." + To separate disk galaxies from spheroids we use the prescription proposed in. BSSOS., To separate disk galaxies from spheroids we use the prescription proposed in BSS98. + It is based on the amount of energv exchanged by a galaxy with its neighbours via eravitational interactions during its lifetime., It is based on the amount of energy exchanged by a galaxy with its neighbours via gravitational interactions during its lifetime. + Interactions are modelled as rapid. non-mereing collisions following the Spitzer impulse approximation (Spitzer 1958)., Interactions are modelled as rapid non-merging collisions following the Spitzer impulse approximation (Spitzer 1958). +" I£ we denote by A the instantaneous relative rate of cnerey exchange. (LPEdEfdl. at epoch f. the cumulative clleet of interactions occurring throughout the galaxy Lifetime (from its birth at the redshift 2,; at which its host halo collapses to the redshift, z of observation) is obtained by integration: In the above expression. the main parameters describing an interaction (impact parameter. relative velocity between the interacting galaxies. relative mass. number density of neighbouring galaxies) enter through the quantity A."," If we denote by ${\dot \Delta}$ the instantaneous relative rate of energy exchange, $(1/E)dE/dt$, at epoch $t$, the cumulative effect of interactions occurring throughout the galaxy lifetime (from its birth at the redshift $z_{nl}$ at which its host halo collapses to the redshift $z$ of observation) is obtained by integration: In the above expression, the main parameters describing an interaction (impact parameter, relative velocity between the interacting galaxies, relative mass, number density of neighbouring galaxies) enter through the quantity ${\dot \Delta}$." + The scalings with these parameters are derived. [rom the numerical simulations of Aguilar White (1985)., The scalings with these parameters are derived from the numerical simulations of Aguilar White (1985). + In this wav. it ds possible to overcome the dilliculty of modelling analytically the details of the interaction. which is a highly non-linear process.," In this way, it is possible to overcome the difficulty of modelling analytically the details of the interaction, which is a highly non-linear process." + The ellects of cosmology enter. equation. (1)) via the conversion of the loockback time / into redshift z and the scaling of the interaction parameters with redshift., The effects of cosmology enter equation \ref{eqdelt}) ) via the conversion of the loockback time $t$ into redshift $z$ and the scaling of the interaction parameters with redshift. +" For instance. in the present cosmology (see table 1). the relative velocity between two interacting galaxies is given by: The evaluation of equation (1)) for a galaxy in the field (sce BSSOS for details) gives (in a Dat. 0|Ay=1. universe): with A,zm1.3510! for h=0.65."," For instance, in the present cosmology (see table 1), the relative velocity between two interacting galaxies is given by: The evaluation of equation \ref{eqdelt}) ) for a galaxy in the field (see BSS98 for details) gives (in a flat, $\Omega_0+\lambda_0=1$, universe): with $\Delta_\star\approx 1.35\times 10^{-4}$ for $h=0.65$." +" It is easy to verily that in the limit Ag7O equation (3)) reduces to Af.)=Av(lLdocu)(1|2Y] which is the result for an Q,=1 universe (BSSOS)."," It is easy to verify that in the limit $\lambda_0 \rightarrow 0$ equation \ref{eqdelt2}) ) reduces to $\Delta(z) = \Delta_\star[(1+z_{nl})^3- +(1+z)^3]$ which is the result for an $\Omega_0=1$ universe (BSS98)." + Alorphological tvpes are then defined according to the value of A using the following rules: The values of Ay); andAvy are [fixed by. requiring that the model produces the observed: amount of each tvpe in the field at the present epoch., Morphological types are then defined according to the value of $\Delta$ using the following rules: The values of $\Delta_{spi}$ and$\Delta_{ell}$ are fixed by requiring that the model produces the observed amount of each type in the field at the present epoch. + Typical values. are iN0]ALIO. and Avyzm107. ancl are not very sensitive to the cosmological moclel assumed. (standard or ΝΤ).," Typical values are $\Delta_{spi}\approx 3.10^{-3}$ and $\Delta_{ell}\approx 10^{-2}$, and are not very sensitive to the cosmological model assumed (standard or )." +" The above conditions on A can then be inverted to obtain conditions on the formation redshift 2,:(2) of galaxy types.", The above conditions on $\Delta$ can then be inverted to obtain conditions on the formation redshift $z_{nl}(z)$ of galaxy types. + Lt is important to realize that the formation redshift) of a galaxv of a given type at epoch z depends on z., It is important to realize that the formation redshift of a galaxy of a given type at epoch $z$ depends on $z$. + That is to say that in our model the morphology of a galaxy is not fixed. once ancl for all by initial conditions but. on the contrary. it evolves progressively from. late-type to early-type.," That is to say that in our model the morphology of a galaxy is not fixed once and for all by initial conditions but, on the contrary, it evolves progressively from late-type to early-type." + However. contrary to most other semi-analvtic approaches. this progression is monotonic: once a spiral galaxy has become SO it can only evolve to the elliptical stage. and it can only remain elliptical once it reaches that stage.," However, contrary to most other semi-analytic approaches, this progression is monotonic: once a spiral galaxy has become SO it can only evolve to the elliptical stage, and it can only remain elliptical once it reaches that stage." +" The condition for a galaxy to be elliptical at redshift zis thatits formation redshilt 2,; is such that: where sos) is defined by equating εδ) to Av) and solving for σε.", The condition for a galaxy to be elliptical at redshift $z$ is thatits formation redshift $z_{nl}$ is such that: where $z_{ell}(z)$ is defined by equating $\Delta(z)$ to $\Delta_{ell}$ and solving for $z_{nl}$ . + Equivalently. spirals at epoch z are those ealaxies that turned non-linear at an epoch such that:," Equivalently, spirals at epoch $z$ are those galaxies that turned non-linear at an epoch such that:" +when fitting either the rise (lower measurement) or decay (upper measurement) phases of an outburst.,when fitting either the rise (lower measurement) or decay (upper measurement) phases of an outburst. + It is important to note that while there are considerable uncertainties in the absolute normalisation and form of the relation betwen radio luminosity and total jet power what we have measured here is a fairly well-definedranking., It is important to note that while there are considerable uncertainties in the absolute normalisation and form of the relation betwen radio luminosity and total jet power what we have measured here is a fairly well-defined. + In this context it is important to note that the source with the lowest reported spin. Cygnus is also one of the best constrained. being at a relatively small distance and with detailed studies of the jets (Gallo et al.," In this context it is important to note that the source with the lowest reported spin, Cygnus X-1, is also one of the best constrained, being at a relatively small distance and with detailed studies of the jets (Gallo et al." + 2005: Heinz 2006)., 2005; Heinz 2006). + Note also that XTE J1650-500 (see Corbel et al., Note also that XTE J1650-500 (see Corbel et al. + 2004 for more details) elearly shows the pattern of the global correlation. but at à lower normalisation than the rest (Fig 2). despite having a relatively high reported spin (0.79+ 0.01).," 2004 for more details) clearly shows the pattern of the global correlation, but at a lower normalisation than the rest (Fig 2), despite having a relatively high reported spin $0.79 \pm 0.01$ )." + Overall. we conclude that while there may be evidence for the requirement of an additional parameter determining jet power in hard state black hole binaries. such a parameter in no way correlates with reported estimates of black hole spin.," Overall, we conclude that while there may be evidence for the requirement of an additional parameter determining jet power in hard state black hole binaries, such a parameter in no way correlates with reported estimates of black hole spin." + It is worth noting that while there may be some unknown systematics. which may exceed our 0.3 dex estimate it seems very unlikely indeed that these systematics could be enough to hide a genuinely strong trend with reported spin.," It is worth noting that while there may be some unknown systematics, which may exceed our 0.3 dex estimate it seems very unlikely indeed that these systematics could be enough to hide a genuinely strong trend with reported spin." + For the powerful. transient. jets we may potentially explore both jet power and jet speed (since we have proper motions in several cases) as functions of estimated black hole spin (whereas for the hard state jets there are no clear speed measurements}. although as we will see below we only really have lower limits to the Jet speeds and cannot make much progress.," For the powerful, transient, jets we may potentially explore both jet power and jet speed (since we have proper motions in several cases) as functions of estimated black hole spin (whereas for the hard state jets there are no clear speed measurements), although as we will see below we only really have lower limits to the jet speeds and cannot make much progress." + It is not straightforward to measure the power associated with the transient ejection events., It is not straightforward to measure the power associated with the transient ejection events. + Typically we calculate the minimum energy associated with some synchrotron event. and divide by the rise time to get the average power going into the jet.," Typically we calculate the minimum energy associated with some synchrotron event, and divide by the rise time to get the average power going into the jet." + This approach is useful to provide lower limits on. and order of magnitude estimates of. jet power but is very susceptible to errors resulting from poor sampling of events. uncertainties in Doppler boosting. assumptions about equipartition etc.," This approach is useful to provide lower limits on, and order of magnitude estimates of, jet power but is very susceptible to errors resulting from poor sampling of events, uncertainties in Doppler boosting, assumptions about equipartition etc." + As a result both the normalisation and ranking of jet powers between different sources is less accurate than for the hard state., As a result both the normalisation and ranking of jet powers between different sources is less accurate than for the hard state. + Nevertheless we can make a comparison. and for this purpose we will use the transient Jet powers estimated in FBGOA. compared with the spin measurements compiled in this paper.," Nevertheless we can make a comparison, and for this purpose we will use the transient jet powers estimated in FBG04, compared with the spin measurements compiled in this paper." + In Fig we pot as a function of X-ray luminosity the estimated transient je powers for five systems listed in FBGO+ for which there are repor'ed spin measurements., In Fig we plot as a function of X-ray luminosity the estimated transient jet powers for five systems listed in FBG04 for which there are reported spin measurements. + The fitted lines are of fixed slope +0.5 (as fitted to the ensemble of transient jet powers by FBGO4). and so we may compare the fitted normalisations in à process analogous to that employed for the hard state radio and near-IR measurements earlier in the paper.," The fitted lines are of fixed slope +0.5 (as fitted to the ensemble of transient jet powers by FBG04), and so we may compare the fitted normalisations in a process analogous to that employed for the hard state radio and near-IR measurements earlier in the paper." + The normalisations. c. in this case are: In Fig we compare these fitted normalisations with the reported measurements of black hole spin.," The normalisations, $c$, in this case are: In Fig we compare these fitted normalisations with the reported measurements of black hole spin." + While the disc measurements again show no correlation with the estimated jet power. there is an intriguing apparent correlation between jet power and spin for the reflection measurements.," While the disc measurements again show no correlation with the estimated jet power, there is an intriguing apparent correlation between jet power and spin for the reflection measurements." + We caution the reader not to over-interpret this. given all the uncertainties outlined above. and discuss it further in section 3..," We caution the reader not to over-interpret this, given all the uncertainties outlined above, and discuss it further in section \ref{discussion}." + As discussed already in Fender (2003) and FBGOA. in nearly all cases it is only possible to place a lower limit on the speed ofjets rom X-ray binaries when basing the estimates on measurements of proper motions alone.," As discussed already in Fender (2003) and FBG04, in nearly all cases it is only possible to place a lower limit on the speed of jets from X-ray binaries when basing the estimates on measurements of proper motions alone." + This is because the distance uncertainties ypically encompass a range of possible solutions for the Lorentz uctor from 2DXo.," This is because the distance uncertainties typically encompass a range of possible solutions for the Lorentz factor from $2 +\leq \Gamma \leq \infty$." + A different approach was taken in Tiller-Jones. Fender Nakar (2005) in which estimates of the jet Lorentz factor were made under the assumption of free relativistic expansion in the rest frame of the jet. with ime dilation causing he apparently very small opening angles (i.e. retarded. apparent expansion).," A different approach was taken in Miller-Jones, Fender Nakar (2005) in which estimates of the jet Lorentz factor were made under the assumption of free relativistic expansion in the rest frame of the jet, with time dilation causing the apparently very small opening angles (i.e. retarded apparent expansion)." + A third approach to estimating he Lorentz factor of jets is available from the ratio of approaching to receding jets., A third approach to estimating the Lorentz factor of jets is available from the ratio of approaching to receding jets. + Unfortunately in all cases we still end up with lower limits on the Lorentz factor., Unfortunately in all cases we still end up with lower limits on the Lorentz factor. + All of these three approaches have their uncertainties: we summarize these estimates. for sources with reported spin measurements. in table 3..," All of these three approaches have their uncertainties; we summarize these estimates, for sources with reported spin measurements, in table \ref{speed}." + Once again. there is no evidence for any correlation with reported black hole spin measurements.," Once again, there is no evidence for any correlation with reported black hole spin measurements." + Furthermore it is worth noting that currently the highest speed measured for a jet from an. X-ray binary is that from thestar system Circinus X-1 (Fender et al., Furthermore it is worth noting that currently the highest speed measured for a jet from an X-ray binary is that from the system Circinus X-1 (Fender et al. + 2004: Tudose et al., 2004; Tudose et al. + 2009). although this may be a jet quite unlike those observed from accreting black holes.," 2009), although this may be a jet quite unlike those observed from accreting black holes." + Because these measurements are all lower limits. it is more," Because these measurements are all lower limits, it is more" +data vector or for an overestimation of the source redshifts would produce both a tighter upper bound and a looser lower bound on the neutrino mass.,data vector or for an overestimation of the source redshifts would produce both a tighter upper bound and a looser lower bound on the neutrino mass. + The matter power spectrum also contributes as a source of uncertainties., The matter power spectrum also contributes as a source of uncertainties. +" The prescription used, Eq. (10)),"," The prescription used, Eq. \ref{eq:Pnl}) )," +" does not consider clustering of neutrinos on CDM structures, which occurs when the neutrino thermal velocity drops below the velocity dispersion, v, of forming clusters; for instance, it takes place at z~2.3 for ve1000 km/s and m,~0.5 eV. The corresponding neutrino halo profile is flatter in the centre than a pure CDM Navarro-Franck-White (Ringwald&Wong2004)."," does not consider clustering of neutrinos on CDM structures, which occurs when the neutrino thermal velocity drops below the velocity dispersion, $v$, of forming clusters; for instance, it takes place at $z\sim 2.3$ for $v\sim + 1000$ km/s and $m_\nu\sim 0.5$ eV. The corresponding neutrino halo profile is flatter in the centre than a pure CDM Navarro-Franck-White \cite{nuprofile}." +". Including it in the 1-halo term of the halo model, Abazajian (2005) showed that it decreases the non-linear matter power spectrum."," Including it in the 1-halo term of the halo model, Abazajian (2005) showed that it decreases the non-linear matter power spectrum." +" Accordingly, in this work the term Pl.4p is expected to be overestimated by ~1% on scales around k=0.5h Mpc-! for my~0.5 eV. Alternatively, results from perturbation theory with neutrinos (Wong2008) also indicate an overestimation of the matter power spectrum, as already mentioned in Sect."," Accordingly, in this work the term $P_{\cdm+\baryons}^\nonlin$ is expected to be overestimated by $\sim1\%$ on scales around $k=0.5\,h$ $^{-1}$ for $m_\nu \sim 0.5$ eV. Alternatively, results from perturbation theory with neutrinos \cite{Wong08} also indicate an overestimation of the matter power spectrum, as already mentioned in Sect." + 2.1., 2.1. +" The non-linear power spectrum is computed with theHALOFIT, which declares a uncertainty on scales k<10 h/Mpc at z<3 (Smithetal.2003),, which are thus of the same order as the supposed shear measurement bias."," The non-linear power spectrum is computed with the, which declares a uncertainty on scales $k<10$ h/Mpc at $z<3$ \cite{halofit}, which are thus of the same order as the supposed shear measurement bias." + This uncertainty is effectively both redshift- and scale-independent over the data redshift and scale ranges., This uncertainty is effectively both redshift- and scale-independent over the data redshift and scale ranges. +" Marginalizing over a uncertainty, the corresponding joint constraint is »5m,<0.56 eV. Furthermore, the does not take account of the effects of cooling baryons and hot intra-cluster baryons, which are degenerate with the neutrinos, affecting the power spectrum by a few percent on small scales (White2005;Zhan&Knox2004;Jingetal. 2006).."," Marginalizing over a uncertainty, the corresponding joint constraint is $\sum m_\nu<0.56$ eV. Furthermore, the does not take account of the effects of cooling baryons and hot intra-cluster baryons, which are degenerate with the neutrinos, affecting the power spectrum by a few percent on small scales \citep{psbaryons1, psbaryons2, psbaryons3}." + We have investigated the potential of cosmic shear to constrain the mass of neutrinos., We have investigated the potential of cosmic shear to constrain the mass of neutrinos. +" In the sub-free-streaming regime, the constraining power originates, for a fixed density of baryons, in the tendency of relativistic (hot) dark matter particles to escape from collapsed regions."," In the sub-free-streaming regime, the constraining power originates, for a fixed density of baryons, in the tendency of relativistic (hot) dark matter particles to escape from collapsed regions." +" Therefore additional amounts of CDM are needed to produce the same cosmic-shear distortion, shifting the Qm—og degeneracy towards larger values of CO, with respect to the analysis without massive neutrinos (Fig. 2)),"," Therefore additional amounts of CDM are needed to produce the same cosmic-shear distortion, shifting the $\Om-\sigma_8$ degeneracy towards larger values of $\Om$ with respect to the analysis without massive neutrinos (Fig. \ref{fig:nufu}) )," +" producing a «eam—wy, degeneracy favoring higher amounts of CDM for higher amounts of massive neutrinos (Fig. 3)).", producing a $\omega_\cdm-\omega_\nu$ degeneracy favoring higher amounts of CDM for higher amounts of massive neutrinos (Fig. \ref{fig:wlcont}) ). +" The analysis of CFHTLS-T0003 data alone yields a loose constraint of Σιν<3.3 eV at the C.L., for our particular choice of priors."," The analysis of CFHTLS-T0003 data alone yields a loose constraint of $\sum +m_\nu<3.3$ eV at the C.L., for our particular choice of priors." +" We have explored larger angular scales using a synthetic data vector extended to 20? to explore the possibility of breaking the weam—w, degeneracy using", We have explored larger angular scales using a synthetic data vector extended to $20\degr$ to explore the possibility of breaking the $\omega_\cdm-\omega_\nu$ degeneracy using +"Intermediate polars (LPs). form a class. of cataclysmic variables ancl consist of a white-dwarl ""pulsar and a το dwarf companion.",Intermediate polars (IPs) form a class of cataclysmic variables and consist of a white-dwarf `pulsar' and a red dwarf companion. + The white-chwarl ‘pulsar is a magnetic white dwarl (107$ 0.6 $^{-1}$ )." +We have studied one case of a sunspot penumbra displaviug a neutral line all alone ai sector of 10 umbra (Fieire 9))., We have studied one case of a sunspot penumbra displaying a neutral line all along a sector of the penumbra (Figure \ref{F:9}) ). + This uectral line is deected at he peπμυτα ])ouncdary but al) enipliasized. by a large Opposie polariv concentration nearby., This neutral line is detected at the penumbral boundary but also emphasized by a large opposite polarity concentration nearby. + Tuterestinglv. lis peuunibral sector shows no uoat flow.," Interestingly, this penumbral sector shows no moat flow." + We interpret his evidence as au iudicatio Lot he Evershed fkny being orced o go into deeper subphotospleric lavers a a faster oue than what is normally trough to occur in peuumbral PC@IOUS not associated to neutral ines (WesteudorpPlazaetal.]0077 )., We interpret this evidence as an indication of the Evershed flow being forced to go into deeper subphotospheric layers at a faster pace than what is normally though to occur in penumbral regions not associated to neutral lines \citep{westendorp1997}. +. A simular case. but in a sheare« neutral ine of a é-xpot. was found w VargasDonelezotal. (2007)..," A similar case, but in a sheared neutral line of a $\delta$ -spot, was found by \citet{vargas2007}. ." + Thoreh there is increasing evidence linking fhe moat flows and the Evershed flow along the peuumbral filaments. the debate reguing the existeuce o [n moat," Though there is increasing evidence linking the moat flows and the Evershed flow along the penumbral filaments, the debate regarding the existence of a moat" +We can now recursively use the above reasoning to show that there does not exist an ΑΝ that can satisfy eq.(77)).,We can now recursively use the above reasoning to show that there does not exist an $N$ that can satisfy \ref{Gamma_1_chain_rule2}) ). + Therefore. we can never find CSES of the type defined in eq.675)).," Therefore, we can never find CSEs of the type defined in \ref{requirement_stronger}) )." + TFhough. one may still expect to find CSEs based on the most general. requirement defined. in e0.(5.3)).," Though, one may still expect to find CSEs based on the most general requirement defined in \ref{requirement_again}) )." + However. even in this case. CSEs reduce to highly nonlinear forms for galaxies of pure elliptical shapes when the PSE ellect is small. as we have shown in refspingst," However, even in this case, CSEs reduce to highly nonlinear forms for galaxies of pure elliptical shapes when the PSF effect is small, as we have shown in \\ref{spin_2_esti}." + hisfeatureisalreadgsuf ficient forarguingagainstlheirusefulnessinpraclice , This feature is already sufficient for arguing against their usefulness in practice. +"above Let us now calculate. the terms 0, and. ὃν defined. in (41)).", Let us now calculate the terms $\delta_1$ and $\delta_2$ defined in \ref{shear12PSF_wrong}) ). + The averages of the spatial derivatives. of the surface brightness field of a single galaxy can be related to the Fourier modes of the image., The averages of the spatial derivatives of the surface brightness field of a single galaxy can be related to the Fourier modes of the image. + The Fourier transformation has been defined in eq.(66)) in Appendix €. Following the notations of Appendix C. we find: and where S is the total area of the map containing the ealaxy.," The Fourier transformation has been defined in \ref{Fourier}) ) in Appendix C. Following the notations of Appendix C, we find: and where $S$ is the total area of the map containing the galaxy." + Similarly. one can derive the following relation: Eq.(S80)) and eq.(81)) allow us to transform eq.(41)) into its version in Fourier space: where Note that 4=Pi|2/0»Lay.," Similarly, one can derive the following relation: \ref{RF_derivative_aves}) ) and \ref{RF_derive2}) ) allow us to transform \ref{shear12PSF_wrong}) ) into its version in Fourier space: where Note that $D_4=P_{40}+2P_{22}+P_{04}$." + Lis now clear that the method of ZOS basically utilizes the quadrupole moments in the Fourier space to measure the cosmic shear., It is now clear that the method of Z08 basically utilizes the quadrupole moments in the Fourier space to measure the cosmic shear. + Using eq.(690)). we can find out how £75; transform under lensing: eq.(41))," Using \ref{f_O2}) ), we can find out how $P_{ij}$ transform under lensing: \ref{shear12PSF_wrong})" + Using eq.(690)). we can find out how £75; transform under lensing: eq.(41)):," Using \ref{f_O2}) ), we can find out how $P_{ij}$ transform under lensing: \ref{shear12PSF_wrong})" +This paper has demonstrated the utility of the SPIRE FTS an μη efficient broad band spectral observations of very bright astronomical sources and the ability to provide acenrately calibrated spectra when SPIRE is operated in its “bright source mode.,This paper has demonstrated the utility of the SPIRE FTS in making efficient broad band spectral observations of very bright astronomical sources and the ability to provide accurately calibrated spectra when SPIRE is operated in its “bright source” mode. + This was not ecpected to be the case before launch and it represents a significant enhancement to the observation capabilities ofro., This was not expected to be the case before launch and it represents a significant enhancement to the observation capabilities of. + We haee taken the first continuous submillimeter spectrum of the planet Mars and shown the ability to ΠΙΟΗΕ all water and carbon monoridc lines between 600 und 1550 GIs with yood photometric accuracy in a single short observation., We have taken the first continuous submillimetre spectrum of the planet Mars and shown the ability to measure all water and carbon monoxide lines between 600 and 1550 GHz with good photometric accuracy in a single short observation. + Our preliminary analysis of the spectrum shows that a imodel with abundances of GOO ppin. for CO and L00 ppi for Ποο best fits the observed line depths., Our preliminary analysis of the spectrum shows that a model with abundances of 900 ppm for CO and 100 ppm for $_2$ O best fits the observed line depths. + Both these values ere in line with previously established fuptres., Both these values are in line with previously established figures. + A more sophiscated modeling approach is clearly needed to make the best use of these end futic data sets that will be obtained during the ΗΜΩΝ and this will be the subject of future work., A more sophiscated modeling approach is clearly needed to make the best use of these and future data sets that will be obtained during the mission and this will be the subject of future work. +of magnitudes higher than that of the AS 205N model.,of magnitudes higher than that of the AS 205N model. +" However, there are more bona-fide isolated disks in our"," However, there are more bona-fide isolated disks in our" +"a region where the disc has a large positive surface density gradient, close to the outer edge of the partial gap formed by the 22.5 Mg body.","a region where the disc has a large positive surface density gradient, close to the outer edge of the partial gap formed by the 22.5 $\mearth$ body." +" This results in large positive corotation torques, leading to the observed outward migration of the outermost planet."," This results in large positive corotation torques, leading to the observed outward migration of the outermost planet." +" This process is likely to operate until the planet reaches a fixed point located near the gap edge, where the total torque (corotation plus Lindblad) cancels (Masset et al."," This process is likely to operate until the planet reaches a fixed point located near the gap edge, where the total torque (corotation plus Lindblad) cancels (Masset et al." + 2006)., 2006). +" This result is consistent with that found in Section ?? where the inner and outer planet masses were 20 and 5 Mg, respectively."," This result is consistent with that found in Section \ref{qge1} where the inner and outer planet masses were 20 and 5 $\mearth$, respectively." + We now turn to the question of the long-term evolution of the planetary systems obtained in the five-planet simulations., We now turn to the question of the long-term evolution of the planetary systems obtained in the five-planet simulations. +" Because the interaction with the gas disc tends to damp eccentricities, it is necessary to examine the dynamical stability of the planets after the disc dispersal to establish long term stability."," Because the interaction with the gas disc tends to damp eccentricities, it is necessary to examine the dynamical stability of the planets after the disc dispersal to establish long term stability." +" Each of the previous simulations was restarted at a point corresponding to the end of the run, but with the gas surface density decaying exponentially with an e—folding time με=2x10°."," Each of the previous simulations was restarted at a point corresponding to the end of the run, but with the gas surface density decaying exponentially with an e–folding time $t_{dec}= 2\times 10^3$." +" Once these systems had evolved for ~104 binary orbits, by which time the surface density in the discs had decreased by a factor of ~10°, we continued the simulations with a pure N-body code, ignoring any residual effects of the remaining gas."," Once these systems had evolved for $\sim 10^4$ binary orbits, by which time the surface density in the discs had decreased by a factor of $\sim 10^3$, we continued the simulations with a pure N-body code, ignoring any residual effects of the remaining gas." +" For each of the five-planet models the results of this procedure are presented in Fig. 9,,"," For each of the five-planet models the results of this procedure are presented in Fig. \ref{model1}," + which displays the time evolution of the orbital radii of the planets., which displays the time evolution of the orbital radii of the planets. +" In Modell, the eccentricity growth resulting from the disc dispersal gives rise, at the beginning of the simulation, to numerous scattering events that eventually lead to collisions."," In Model1, the eccentricity growth resulting from the disc dispersal gives rise, at the beginning of the simulation, to numerous scattering events that eventually lead to collisions." + At time f~8x10* a system of two planets with masses of, At time $t\sim 8\times 10^4$ a system of two planets with masses of +considered the Fe-K and Ni-K fluorescence lines and thus we can constrain the reflection component by the prominent Fe-K line.,considered the Fe-K and Ni-K fluorescence lines and thus we can constrain the reflection component by the prominent Fe-K line. +" In this case, the gaussian model for the Fe-K line is not included for fitting (model E)."," In this case, the gaussian model for the Fe-K line is not included for fitting (model E)." +" Figure 10 shows a confidence contour between the soft and hard powerlaw photon index, where we plot the confidence contours of three 2009 observations."," Figure \ref{contpo2} shows a confidence contour between the soft and hard powerlaw photon index, where we plot the confidence contours of three 2009 observations." +" The photon index of the soft and hard component is constrained to be around 1.9 and 1.6, respectively, for all 2009 observations."," The photon index of the soft and hard component is constrained to be around 1.9 and 1.6, respectively, for all 2009 observations." +" The photon index of the hard component depends on the assumed absorption; when the absorption is weaker, the photon index becomes smaller and the fraction of the hard component in the softer X-ray band becomes smaller."," The photon index of the hard component depends on the assumed absorption; when the absorption is weaker, the photon index becomes smaller and the fraction of the hard component in the softer X-ray band becomes smaller." + Thus the photon index of 1.6 is considered to give an upper limit of the hard component., Thus the photon index of 1.6 is considered to give an upper limit of the hard component. +" Then, we fixed the photon indices of the two powerlaw components to 1.6 and 1.9."," Then, we fixed the photon indices of the two powerlaw components to 1.6 and 1.9." +" Table 8 summarized the fitting results, and figure 11 shows the best-fit model and spectra."," Table \ref{fite} summarized the fitting results, and figure \ref{specmde} + shows the best-fit model and spectra." +" The x? value is smaller than those of the model D for the 2009 1st observation, but almost the same as those of"," The $\chi^2$ value is smaller than those of the model D for the 2009 1st observation, but almost the same as those of" +" (~1010"" ?) (~ (Ehtzurotal.1989).", $\sim10^8-10^9$ $^{-3}$ $\sim$ \citep{Eli89}. +. Tj~1012. Cawinnctal.(1992) spots. which were used for a statistical study.," $\sim10^{13}$ $T_b\sim10^{12}$ \citet{Gwi92} spots, which were used for a statistical study." + A iascr spot is an individual component of the maser cussion occuriue at a given velocity channel aud position., A maser spot is an individual component of the maser emission occurring at a given velocity channel and position. + Maser spots teud to cluster in position aud Doppler velocity. typically d AU and 0.5 lan s| (Cavinn1991a).," Maser spots tend to cluster in position and Doppler velocity, typically 1 AU and 0.5 km $^{-1}$ \citep{Gwi94a}." +. Such clusters or eroups of mmascr spots are called maser features., Such clusters or groups of maser spots are called maser features. + Plivsically. miaser features should be small clouds supporting population iuversion by a punipiug mechanism (Cwiuu1991b).," Physically, maser features should be small clouds supporting population inversion by a pumping mechanism \citep{Gwi94b}." +. The statistical analysis of spatial and velocity distributions for both spots aud features reveals that turbulent motious dominate on a spatial scale of ~L300 AU (Cavinn199la)., The statistical analysis of spatial and velocity distributions for both spots and features reveals that turbulent motions dominate on a spatial scale of $\sim$ 1–300 AU \citep{Gwi94a}. + Tinaictal.(2002). carried out a similar study using Verv Lone Bascline Array (VLBA) maser data of the SFR W3 IRS 5., \citet{Ima02} carried out a similar study using Very Long Baseline Array (VLBA) maser data of the SFR W3 IRS 5. + For the statistics. Tmaictal.(2002) used 905 maser spots erouped in 152 mascr catires.," For the statistics, \citet{Ima02} used 905 maser spots grouped in 152 maser features." + They found that spots form features with a vpical size of ~0.5 AU., They found that spots form features with a typical size of $\sim$ 0.5 AU. +" The statistical analvsis of the Doppler velocities. specifically, the velocity correlation πιοος for maser spots follow a power-law depenudeuce in the range of 300 AU with an iudex of ~0.29 hat is consistent with the I&oluogorov value of 1/: he value expected for incompressible fuids with a urbuleut velocity feld (Nolmoeorov1911:Streluitski 2007)."," The statistical analysis of the Doppler velocities, specifically, the velocity correlation functions for maser spots follow a power-law dependence in the range of $-$ 300 AU with an index of $\sim$ 0.29, that is consistent with the Kolmogorov value of 1/3, the value expected for incompressible fluids with a turbulent velocity field \citep{Kol41,Str07}." +. Simular results have been also obtained bv Streluit«kietal.(2002) in other five SFRs., Similar results have been also obtained by \citet{Str02} in other five SFRs. + VLDÀ water maser observations toward the SFRs Cepheus A and W75 N revealed remarkable nucrostructures (Torrellesetal.2001b.2003).," VLBA water maser observations toward the SFRs Cepheus A and W75 N revealed remarkable microstructures \citep{Tor01b,Tor03}." +. These nücrostrüctures exhibit a coherent anc well-ordered spatio-kinematical behavior at AU scales (Uscanugaet 2005)., These microstructures exhibit a coherent and well-ordered spatio-kinematical behavior at AU scales \citep{Usc05}. +. Properauotiou measurements of water mascrs Sugeest the presence of organized motious of structures with sizes from tens to a few hundreds of AUs (Torrelles 2003)..," Proper-motion measurements of water masers suggest the presence of organized motions of structures with sizes from tens to a few hundreds of AUs \citep{Tor01b,Tor03}. ." + Tere we study the spatial aud velocity distribution of the water masers in these two SERs using a statistical analysis to iuvestigate whether, Here we study the spatial and velocity distribution of the water masers in these two SFRs using a statistical analysis to investigate whether +Planetary Nebulae (PNe) constitute one of the most valuable chemical tracers of the past abundances in the interstellar medium (ISM).,Planetary Nebulae (PNe) constitute one of the most valuable chemical tracers of the past abundances in the interstellar medium (ISM). + Their chemical compositions allow us to determine the abundances of some chemical elements present in the ISM when their progenitor stars were born., Their chemical compositions allow us to determine the abundances of some chemical elements present in the ISM when their progenitor stars were born. + PNe are produced by stars with initial masses from ~ 1 Πο - 8 aand also with a large age spread (from 0.1 to 9 Gyr. Allen et al.," PNe are produced by stars with initial masses from $\sim$ 1 to $\sim$ 8 and also with a large age spread (from 0.1 to 9 Gyr, Allen et al." + 1998)., 1998). + Therefore PN characteristics are important as observational constraints in chemical evolution models. allowing us to improve the inferred chemical history (Hemánndez-Martínnez et al.," Therefore PN characteristics are important as observational constraints in chemical evolution models, allowing us to improve the inferred chemical history (Hernánndez-Martínnez et al." + 2009. hereafter HPCGO9: Richer MeCall 2007; Buzzoni et al.," 2009, hereafter HPCG09; Richer McCall 2007; Buzzoni et al." + 2006: Maciel et al., 2006; Maciel et al. + 2006)., 2006). + Despite the fact that PNe show some bright emission lines. deep observations are needed to determine their physical conditions and accurate chemical abundances. which are based on much fainter lines.," Despite the fact that PNe show some bright emission lines, deep observations are needed to determine their physical conditions and accurate chemical abundances, which are based on much fainter lines." + In addition. gaseous nebulae are an important key m the chemical abundances determination of noble gases (e.g.. Ne and Ar) and other elements like Cl and. therefore. in the test of stellar yields of these elements.," In addition, gaseous nebulae are an important key in the chemical abundances determination of noble gases (e.g., Ne and Ar) and other elements like Cl and, therefore, in the test of stellar yields of these elements." + The determination of this type of elements in stars is not so reliable and. in previous papers (e. g.. Timmes et al.," The determination of this type of elements in stars is not so reliable and, in previous papers (e. g., Timmes et al." + 1995: Romano et al., 1995; Romano et al. + 2010: Kobayashi et al., 2010; Kobayashi et al. + 2011). the authors were not able to test Ne. Cl. and Ar yields. due to the lack of stellar abundances.," 2011), the authors were not able to test Ne, Cl, and Ar yields, due to the lack of stellar abundances." + The chemical evolution equations (e.g.. Tinsley 1974) take into account many physical parameters: galactic infalls. galactic outflows. the initial mass function. the star formation rate. and a set of stellar yields for different masses.," The chemical evolution equations (e.g., Tinsley 1974) take into account many physical parameters: galactic infalls, galactic outflows, the initial mass function, the star formation rate, and a set of stellar yields for different masses." + Therefore these equations are complex and have to be solved using numerical methods., Therefore these equations are complex and have to be solved using numerical methods. + However they can be simplified assuming the (IRA. Talbot Arnett 1971).," However they can be simplified assuming the (IRA, Talbot Arnett 1971)." + For this approximation the lifetimes of all stars more massive than | aare negligible compared with the age of the galaxies., For this approximation the lifetimes of all stars more massive than 1 are negligible compared with the age of the galaxies. + This approximation allows us to solve the chemical evolution equations analytically., This approximation allows us to solve the chemical evolution equations analytically. + Despite its simplicity. IRA Is a good first approximation for elements produced mainly by massive stars (MS). but not for the elements produced partially by low and intermediate mass stars (LIMS).," Despite its simplicity, IRA is a good first approximation for elements produced mainly by massive stars (MS), but not for the elements produced partially by low and intermediate mass stars (LIMS)." + There are intermediate methods to calculate chemical evolution models. which consist in analytical approximations that consider the delays in chemical enrichment produced by LIMS.," There are intermediate methods to calculate chemical evolution models, which consist in analytical approximations that consider the delays in chemical enrichment produced by LIMS." + Several authors have presented their own analytical approximations (e.g.. Serrano Peimbert 1983: Pagel 1989: Franco Carigi 2008).," Several authors have presented their own analytical approximations (e.g., Serrano Peimbert 1983; Pagel 1989; Franco Carigi 2008)." + They propose some time-delay prescription for the chemical enrichment produced by LIMS., They propose some time-delay prescription for the chemical enrichment produced by LIMS. + These time-delay terms make the LIMS to bring out to the ISM the processed nuclear material at a single time after their formation. while the contribution due to MS is instantaneous. like in the IRA approximation.," These time-delay terms make the LIMS to bring out to the ISM the processed nuclear material at a single time after their formation, while the contribution due to MS is instantaneous, like in the IRA approximation." + In this paper we calculate chemical evolution models for the dwarf irregular galasy 66822 following the method used by Franco Carigi (2008)., In this paper we calculate chemical evolution models for the dwarf irregular galaxy 6822 following the method used by Franco Carigi (2008). + This method was modified by Hernánndez-Martínez (2010) to include numerically infalls. outflows. and star formation rates.," This method was modified by nez (2010) to include numerically infalls, outflows, and star formation rates." + Also. in this new code we have increased the number of chemical elements considered. from 5 to 27.," Also, in this new code we have increased the number of chemical elements considered, from 5 to 27." + NGC 6822. a galaxy of the Local Group. is located at 460 kpe from the Milky Way (Gieren et al.," NGC 6822, a galaxy of the Local Group, is located at 460 kpc from the Milky Way (Gieren et al." + 2006)., 2006). + It presents à recent increase 1n the star formation rate as shown by its bright regions., It presents a recent increase in the star formation rate as shown by its bright regions. + These features make it easy to determine the present-day chemical abundances of the ISM., These features make it easy to determine the present-day chemical abundances of the ISM. + Thus. it is suitable for chemical evolution modeling.," Thus, it is suitable for chemical evolution modeling." + Carigi et al. (, Carigi et al. ( +2006. hereafter CCPO6) performed chemical and photometric evolution models for 66822.,"2006, hereafter CCP06) performed chemical and photometric evolution models for 6822." + Based on a cosmological approach they obtained the gas infall rate adequate to form the galaxy and. based on the photometric properties. they derived a robust star formation history.," Based on a cosmological approach they obtained the gas infall rate adequate to form the galaxy and, based on the photometric properties, they derived a robust star formation history." + Their chemical evolutior models were built to reproduce the present component of the ISM. as given by the chemical abundances of the region HV. determined from recombination lines (RLs).," Their chemical evolution models were built to reproduce the present component of the ISM, as given by the chemical abundances of the region HV, determined from recombination lines (RLs)." + HPCGO09 determined abundances from collisionally excited lines (CELs) for 11. PNe and one region., HPCG09 determined abundances from collisionally excited lines (CELs) for 11 PNe and one region. + From these data. they confirmed the chemical homogeneity of the present component in the ISM and found the presence of two populations of PNe.," From these data, they confirmed the chemical homogeneity of the present component in the ISM and found the presence of two populations of PNe." + Based on these results they built a preliminary chemical evolution model to reproduce the chemical behavior of 66822., Based on these results they built a preliminary chemical evolution model to reproduce the chemical behavior of 6822. + One of the aims of this work, One of the aims of this work +"UK The 3.29 infrared emission feature (EF). discovered in the planetary nebula (Merrill.Soifer.&Russell1975).. is the shortest wavelength [EF among what used to be known as ""the unidentified infrared features.”"," The 3.29 infrared emission feature (IEF), discovered in the planetary nebula \citep*{MSR75}, is the shortest wavelength IEF among what used to be known as “the unidentified infrared features.”" + The IEFs are observed at 3.29µπι.. 6.2um... 7.7um. 8.6pam... 11.3µπι.. and 12.7 µηι.," The IEFs are observed at 3.29, 6.2, 7.7, 8.6, 11.3, and 12.7 ." +. Duley&Williams(1981) were the first to suggest that the 3.29 ΠΕΕ is due to the stretching mode of an aromatic (sp) C—H. This identification is now widely accepted 1999)..," \citet{DW81} were the first to suggest that the 3.29 IEF is due to the stretching mode of an aromatic $sp^2$ ) H. This identification is now widely accepted \citep*[see reviews by][]{ATB89,PL89,Se90,Se94,PCG96,To97,Ge97,Sa99}." + The 3.29 HEF emission in visual reflection nebulae. such as7023.. has always been observed to be accompanied by near-infrared (NIR) continuum emission at 2-4 citep?SWD83.Se84.JDG90a.JDG90b.S WA96.Joblin96.. which is not due to reflected starlight erstein 1992).," The 3.29 IEF emission in visual reflection nebulae, such as, has always been observed to be accompanied by near-infrared (NIR) continuum emission at 2-4 \\citep*{SWD83,Se84,JDG90a,JDG90b,SWA96,Joblin96}, which is not due to reflected starlight \citep*{SWD92}." +. The temperature of dust grains in equilibrium with the incident stellar radiation for these visual reflection nebulae is observed to befar too low to produce any detectable NIR radiation (Harvey.Thronson.&Gatley1980;WhitcombSellgren.&Werner1987:Luan.1990a:Casey199];YoungOwletal. 2002).," The temperature of dust grains in equilibrium with the incident stellar radiation for these visual reflection nebulae is observed to befar too low to produce any detectable NIR radiation \citep*{HTG80,WGH81,CSW87,SLW90,Ca91,YO02}." +. Observations of aat 55-400uim.. in particular. are best fit by an equilibrium dust temperature of - 50 K (Whitcombetal.1981;Casey1991).. in clear disagreement with the characteristic temperature. - 1000 K. of the NIR continuum emission 1984).," Observations of at 55-400, in particular, are best fit by an equilibrium dust temperature of $\sim$ 50 K \citep{WGH81,Ca91}, in clear disagreement with the characteristic temperature, $\sim$ 1000 K, of the NIR continuum emission \citep{SWD83,Se84}." +. This NIR continuum emission in visual reflection nebulae has beenattributed to single stellar photons that transiently heat tiny (] nm radius) grains to high temperature (Sellgrenetal.1983;Sellgren1984):: to vibrational or electronic fluorescence from polycyclic aromatic hydrocarbon (PAH) molecules (Léger&Puget1984:1985. 1989): or to photoluminescence of larger hydrogenated amorphous carbon (HAC) grains or carbon nanoparticles (Duley&Williams1988;Duley1988.2001).," This NIR continuum emission in visual reflection nebulae has beenattributed to single stellar photons that transiently heat tiny (1 nm radius) grains to high temperature \citep{SWD83,Se84}; to vibrational or electronic fluorescence from polycyclic aromatic hydrocarbon (PAH) molecules \citep*{LP84,ATB85,ATB89}; or to photoluminescence of larger hydrogenated amorphous carbon (HAC) grains or carbon nanoparticles \citep*{DW88,Du88,Du01}." +. When an ultraviolet (UV) source. such as a hot star. illuminates a molecular cloud. it forms a photodissociation region (PDR: also referred to as a photon-dominated region) where absorption of UV photons in the Lyman-Werner bands nm) of molecular hydrogen (H:)) dissociateH».," When an ultraviolet (UV) source, such as a hot star, illuminates a molecular cloud, it forms a photodissociation region (PDR; also referred to as a photon-dominated region) where absorption of UV photons in the Lyman-Werner bands (91.2-110 nm) of molecular hydrogen ) dissociate." +. These same photons also pump fluorescent quadrupole ro-vibrational eemission lines. and thus fluorescent eemission delineates the ttransition region in a PDR.," These same photons also pump fluorescent quadrupole ro-vibrational emission lines, and thus fluorescent emission delineates the transition region in a PDR." + Observations ofthe Bar.. the PDR adjoining the southeastern ionization front of the (Sellgren.Tokunaga.&Nakada1990b:Tielensetal. 1993).. and of the planetary nebula," Observations ofthe , the PDR adjoining the southeastern ionization front of the \citep{STN90,TMW93}, , and of the planetary nebula" +remains unknown.,remains unknown. + In their seminal review. Wakker van Woerden (1997) distinguished. three. dilferent origins of UVCs: Galactic fountain. particularly for those clouds seen in absorption against halo stars within the Milky. Way. the tidal debris of the Alagellanic Stream. ancl “others”.," In their seminal review, Wakker van Woerden (1997) distinguished three different origins of HVCs: Galactic fountain, particularly for those clouds seen in absorption against halo stars within the Milky Way, the tidal debris of the Magellanic Stream, and “others""." + Blitz ο al. (, Blitz et al. ( +"1999) proposed that some of the ""other? IIV€'Ss could. be distant. extragalactic LL clouds distributed throughout the Local. Group.","1999) proposed that some of the “other"" HVCs could be distant, extragalactic HI clouds distributed throughout the Local Group." + They suppose such ΗΝος could. in fact represent primordial gas clouds or protogalaxies. which could be interpreted as the leftover building blocks from whieh Local Group galaxies have formed.," They suppose such HVCs could in fact represent primordial gas clouds or protogalaxies, which could be interpreted as the leftover building blocks from which Local Group galaxies have formed." + These Ηλος are compact. ancl isolated from the large IVC complexes.," These HVCs are compact, and isolated from the large HVC complexes." + Blitz et al., Blitz et al. + suggest that these compact ancl isolated: LEVCS. have a characteristic mean. distance ol about 1 Alpe.," suggest that these compact and isolated HVCs, have a characteristic mean distance of about 1 Mpc." + Do compact. isolated HIVCs trace the substructures predicted by CDM simulations?," Do compact, isolated HVCs trace the substructures predicted by CDM simulations?" + 3aun& Burton (1999. 2000) identified an intial catalog ol 65 Compact μα... and: conducted detailed: follow-up observations.," Braun Burton (1999, 2000) identified an intial catalog of 65 Compact HVCs, and conducted detailed follow-up observations." +" CLIIVCs have a mean infall velocity of 100 km in the Local. Group reference. frame. have angular sizes less than 2"" FAWHIAL. are isolated. and. at an distance of 1 Alpe. have LL masses of a [ew times LOO M..."," CHVCs have a mean infall velocity of 100 km $^{-1}$ in the Local Group reference frame, have angular sizes less than $^o$ FWHM, are isolated, and, at an distance of 1 Mpc, have HI masses of a few times $^7$ $_{\odot}$." + Their rotation curves imply a high. dark-to-visible mass ratio of 10 to 50., Their rotation curves imply a high dark-to-visible mass ratio of 10 to 50. + Deep integrated HIE maps reveal a core-halo structure (Brünns. Ixerp Pagels 2001).," Deep integrated HI maps reveal a core-halo structure (Brünns, Kerp Pagels 2001)." + The highest column density ancl colclest HIE gas is situatec in à compact region no more than several aremin across. whereas the large-scale eas distribution consists of warm. lower column density gas.," The highest column density and coldest HI gas is situated in a compact region no more than several arcmin across, whereas the large-scale gas distribution consists of warm, lower column density gas." + The cold. dense regions. woutle be the regions which are most conducive to star formation.," The cold, dense regions, would be the regions which are most conducive to star formation." + The HIE column densities of these regions are in excess of ΠΠ 1077 ? (LHerbstmeier. Heithausen. and Mebolc 1993). sullicienthy high to form molecules ancl star-forming cores.," The HI column densities of these regions are in excess of $_{HI}$$>$ $\times$ $^{20}$ $^{-2}$ (Herbstmeier, Heithausen, and Mebold 1993), sufficiently high to form molecules and star-forming cores." + Putman et al. (, Putman et al. ( +2002) recently identified acdditiona CUVCs in the LIE Parkes All-Sky Survey (LUPASS).,2002) recently identified additional CHVCs in the HI Parkes All-Sky Survey (HIPASS). + There are 179 objects on the southern hemipshere which share many of the properties of the original CLIWC's identified by 3aun Burton., There are 179 objects on the southern hemipshere which share many of the properties of the original CHVCs identified by Braun Burton. + Additionally. de Ueij. Braun Burton (2002) re-analyzed the Leiden/Dwingeloo Survey data [rom which the original Braun Burton list was clrawn. and recognise 67 CLVCs.," Additionally, de Heij, Braun Burton (2002) re-analyzed the Leiden/Dwingeloo Survey data from which the original Braun Burton list was drawn, and recognise 67 CHVCs." + The current source count of CLIIVC'S thus stands at 246., The current source count of CHVCs thus stands at 246. + A major hurdle in understanding the nature of IIVC's in general. and that of CIIVCSs in. particular. has been the lack of distance information.," A major hurdle in understanding the nature of HVCs in general, and that of CHVCs in particular, has been the lack of distance information." + Braun (2001) recently reviewed existing. anc hitherto unsuccessful. attempts to derive distances.," Braun (2001) recently reviewed existing, and hitherto unsuccessful, attempts to derive distances." + The goal of identifving stars associated with CLIVCS is that stars would supply distance indicators., The goal of identifying stars associated with CHVCs is that stars would supply distance indicators. + Yet. CIIVCS have no optical counterparts on sky SULVON Mates: this rules out. resolved. stars down to Vz2].," Yet, CHVCs have no optical counterparts on sky survey plates; this rules out resolved stars down to $\approx$ 21." + An associated content of bright voung supergiants seems highly unlikely., An associated content of bright young supergiants seems highly unlikely. + Simon Blitz (2002) recently inspected digitized Palomar Sky Survey (POSS) plates with a spatial filtering method. for 264 northern ΕΟΝ.," Simon Blitz (2002) recently inspected digitized Palomar Sky Survey (POSS) plates with a spatial filtering method, for 264 northern HVCs." + The surface. brightness imits reached by their analysis (26 magnitudes Do.7 in V) would. have recovered. all known Local Group galaxies except for four of the very diffuse. extended ανα Spheroidal (dSph) galaxies within LOO kpe of the Milkv Way.," The surface brightness limits reached by their analysis (26 magnitudes $^{-2}$ in V) would have recovered all known Local Group galaxies except for four of the very diffuse, extended dwarf Spheroidal (dSph) galaxies within 100 kpc of the Milky Way." + Follow-up imaging of several “suspicious” CLIVC's at. 1-m and. 3-m telescopes did not reveal a stellar content to a typical imiting stellar magnitude of Ry = 22.2.," Follow-up imaging of several “suspicious"" CHVCs at 1-m and 3-m telescopes did not reveal a stellar content to a typical limiting stellar magnitude of $_S$ = 22.2." + Simon Blitz rule out the possibility. that LIWCs are associated with a sub-population of clwarl galaxies within the range of known dwarf galaxy. properties., Simon Blitz rule out the possibility that HVCs are associated with a sub-population of dwarf galaxies within the range of known dwarf galaxy properties. + Other attempts to resolve a 2int stellar content in CIIVCSs with 44m class telescopes have aileck due to crowding of potential stars in CIIVC'S with oreground stars and background. galaxies at the aresee evel. although Braun (2001) reports there is tantalizing evidence of the possible detection. of tip-ol-the-rec-giant-ΥΠΟ (PROB) stars in a low. which awaits confirmation.," Other attempts to resolve a faint stellar content in CHVCs with 4-m class telescopes have failed due to crowding of potential stars in CHVCs with foreground stars and background galaxies at the arcsec level, although Braun (2001) reports there is tantalizing evidence of the possible detection of tip-of-the-red-giant-branch (TRGB) stars in a few, which awaits confirmation." + We here esent two new and complementary searches or the elusive stellar content of CLIVCs., We here present two new and complementary searches for the elusive stellar content of CHVCs. + The firs approach uses deep imaging in the optical with the S.2-m Very. Large Telescopes (VET)., The first approach uses deep imaging in the optical with the 8.2-m Very Large Telescopes (VLT). + The data are presented and discussed in section 2., The data are presented and discussed in section 2. + The VLT data consist of optical imaging with a reasonably sized. field of view. 6/88 x 688. centered on the highest. column. density. regions of five CLIVCs.," The VLT data consist of optical imaging with a reasonably sized field of view, 8 x 8, centered on the highest column density regions of five CHVCs." + We show that these observations have sulliciently high angular resolution and limiting magnitude to be sensitive to red giant branch stars (the brightest phase of a 1.12 Cir stellar, We show that these observations have sufficiently high angular resolution and limiting magnitude to be sensitive to red giant branch stars (the brightest phase of a 1–12 Gyr stellar +viscous timescale (Changctal.2010).,viscous timescale \citep{Chang+10}. +. In standard steacdvy-state thin-disc models the viscosity is an increasing function of radius. so this drainage occurs on timescales shorter than that of the binarys orbital decay.," In standard steady-state thin-disc models the viscosity is an increasing function of radius, so this drainage occurs on timescales shorter than that of the binary's orbital decay." + When the mass of the secondary becomes comparable to the local clise mass. the orbital clecay slows clown with respect to the local viscous time.," When the mass of the secondary becomes comparable to the local disc mass, the orbital decay slows down with respect to the local viscous time." +" The gas piles up immediately outside the cavity. forming a decretion region in which the viscous torque 7,=AseNOLRP is nearly constant with radius (Pringle1991)."," The gas piles up immediately outside the cavity, forming a decretion region in which the viscous torque $\mathcal{T}_{\nu}=3\pi\nu\Sigma \Omega R^{2}$ is nearly constant with radius \citep{Pringle91}." +. We apply the analytic moclel of Ivanov.Papaloizou&Polnarey(1999) to calculate the residency time for this scconcary-dominated migration stage: qo," We apply the analytic model of \cite{IPP99} + to calculate the residency time for this secondary-dominated migration stage: )." +m Note that lzH3there identare two competing cllects influencing fio.faecl2 the decay slows down as the local disc mass decreases with respect to the secondary. but this is mitigated to a small extent by the fact that X outside the cavity increases due to pile-up.," Note that there are two competing effects influencing $t_{\rm + res}^{\rm (sec)}$: the decay slows down as the local disc mass decreases with respect to the secondary, but this is mitigated to a small extent by the fact that $\Sigma$ outside the cavity increases due to pile-up." + Phe enhancement of X relative to that of a cisc around a solitary SML of the same mass as the binary (equation 25)) has thefunctional Form. (Ivanov.Papaloizou&Polnarey1999) in the neighbourhood RozRy.," The enhancement of $\Sigma$ relative to that of a disc around a solitary SMBH of the same mass as the binary (equation \ref{eq:Sig1BH}) ) has thefunctional form \citep{IPP99} + ] in the neighbourhood $R\gta R_{\lambda}$." + Above. ReUU is the radius of the cavity when the transition [rom clise- to secondarv-dominated: migration occurs. ie. when yAl=AnAX).," Above, $R_{\lambda}^{\rm(disc/sec)}$ is the radius of the cavity when the transition from disc-dominated to secondary-dominated migration occurs, i.e. when $\eta M=4\pi R_{\lambda}^{2}\Sigma(R_{\lambda})$." + For reasonable parameter values. nyUUowLOCALAC," For reasonable parameter values, $R_{\lambda}^{\rm(disc/sec)}>10^{3}GM/c^{2}$." + Γιο dimensionless quantities 4d and D in equation 28. depend on the viscosity and mass profiles of the dise. (seeIvanov.Papaloizou&Polnarey1999.[or details)., The dimensionless quantities $A$ and $B$ in equation \ref{eq:pileup} depend on the viscosity and mass profiles of the disc \citep[see][for details]{IPP99}. . +. We typically find that zd~4 and 2~0.2 in our disce mocels: Le. the fractional surface densitv enhancement during secondarv-dominated migration is no greater than (41.1207~14.," We typically find that $A\sim 4$ and $B\sim 0.2$ in our disc models; i.e., the fractional surface density enhancement during secondary-dominated migration is no greater than $(1+A)^{B}\sim 1.4$." + At vet smaller separations. the binary’s orbital evolution begins to be driven by GAV emission.," At yet smaller separations, the binary's orbital evolution begins to be driven by GW emission." + Since binaries of interest. hereare far [rom merging. GA emission. can be approximated by the leading term in the Newtonian quacdrupole.," Since binaries of interest hereare far from merging, GW emission can be approximated by the leading term in the Newtonian quadrupole." + For circular orbits. the residence time is given bv Peters(1964) As the binarv's BLOForbital decayqc accelerates due to GW emission. the pileup caused. by. seconcdary-dominated migration spreads out.," For circular orbits, the residence time is given by \cite{Peters64} + As the binary's orbital decay accelerates due to GW emission, the pileup caused by secondary-dominated migration spreads out." + Past the point where nUee1.(Ry). the binary begins to outrun the disc. as the decay timescale [or e becomes rapidly shorter than that on which the disc can viscously spread.," Past the point where $t_{\rm res}^{\rm (GW)}\approx t_{\nu}(R_{\lambda})$, the binary begins to outrun the disc, as the decay timescale for $a$ becomes rapidly shorter than that on which the disc can viscously spread." + Let us now discuss the gravitational stability of the disc. based on the stability criteria of a radiation-pressure dominated: [uid summarized by Thompson(2008).," Let us now discuss the gravitational stability of the disc, based on the stability criteria of a radiation-pressure dominated fluid summarized by \cite{Thompson08}." +. If. the radiative cdillusion timescale is much shorter than the dynamical timescale. then the radiation pressure does not μαabilize the [uid and gravitational fragmentation occurs on 10 sume length scales as it would in the absence of radiation pressure.," If the radiative diffusion timescale is much shorter than the dynamical timescale, then the radiation pressure does not stabilize the fluid and gravitational fragmentation occurs on the same length scales as it would in the absence of radiation pressure." + Lf the radiative diffusion timescale is much longer iun the dynamical time. which we find to be the case for our disc models. then radiation pressure acts to make the Iiic moreJeans-stable/!.," If the radiative diffusion timescale is much longer than the dynamical time, which we find to be the case for our disc models, then radiation pressure acts to make the fluid more." +. We invoke the Toomre criterion. and assume that the disc is gravitationally stable when the imensionless parameter is greater than unity.," We invoke the Toomre criterion, and assume that the disc is gravitationally stable when the dimensionless parameter Q(R) is greater than unity." + Note that the Κον ellect of radiation pressure in this context is that the sound. speed ὃς is computed. from. the total pressure. not just the gas pressure.," Note that the key effect of radiation pressure in this context is that the sound speed $c_{\rm s}$ is computed from the total pressure, not just the gas pressure." + A counterintuitive result is that in radiation pressure-dominated. discs. increasing the surface density or equivalently. the accretion rate ab fixecl radius and disc parameters (a. @ ete.)," A counterintuitive result is that in radiation pressure-dominated discs, increasing the surface density — or equivalently, the accretion rate — at fixed radius and disc parameters $\alpha$, $\theta$, etc.)" + makes it stable against fragmentation., makes it stable against fragmentation. + This is a significant point. because it allows for the existence of a copious amount of hot. gravitationally stable gas near the binary.," This is a significant point, because it allows for the existence of a copious amount of hot, gravitationally stable gas near the binary." + We demonstrate this behavior as follows., We demonstrate this behavior as follows. + Combining equations 24 and 30. we may write in general Q=«ντo. where urpπέν)c1 is the ratio of the pressure in the disk to its self-eravity.," Combining equations \ref{eq:cs} and \ref{eq:Q}, we may write in general $Q=4\sqrt{x^{2}-x}$, where $x\equiv p/(4\pi G \Sigma^{2})\ge 1$ is the ratio of the pressure in the disk to its self-gravity." + lt follows directly that the stability. criterion Q=1 is equivalent to the condition .r2(2|V5)42Ll., It follows directly that the stability criterion $Q>1$ is equivalent to the condition $x>(2+\sqrt{5})/4\approx 1.1$. + Some algebraic manipulation of the disc equations. (20 243) gives another general expression for the region dominated by electron scattering and radiation pressure: In standard @ ancl 37 1x51)disces. increasing the surface density with all other propertics held constant increases the midplane temperature.," Some algebraic manipulation of the disc equations \ref{eq:nutherm} $-$ \ref{eq:cs}) ) gives another general expression for the region dominated by electron scattering and radiation pressure: In standard $\alpha$ and $\beta$ discs, increasing the surface density with all other properties held constant increases the midplane temperature." + This raises the value of 7. and the eravbods [actor Z decreases orremains constant (ee. =—1 for blackbody discs).," This raises the value of $\nu$ , and the graybody factor $\Xi$ decreases orremains constant (e.g., $\Xi\equiv 1$ for blackbody discs)." + Fhus. in radiation pressure-dominated discs the parameters c and (2 increase with an increase inNX oor the aceretion parameter ra.," Thus, in radiation pressure-dominated discs the parameters $x$ and $Q$ increase with an increase in$\Sigma$ or the accretion parameter $\dot{m}$ ." + Increasing the accretion rate heats ancl “pulls up” the radiation pressure-cdominated, Increasing the accretion rate heats and “puffs up” the radiation pressure-dominated +molecular absorption in hot Jupiters - using the multi-linear decorrelation techniques. described in. SOS and. repeatedly used: since.,molecular absorption in hot Jupiters - using the multi-linear decorrelation techniques described in S08 and repeatedly used since. + Indeed. there is no physical reason why the systematics should be described by a linear combination of the selected state parameters.," Indeed, there is no physical reason why the systematics should be described by a linear combination of the selected state parameters." + In the absence of a better systematics removal technique. there appears to be a ~0.1 All of the data presented in this paper were obtained from the Multimission Archive at the Space Telescope Science Institute (ALAS).," In the absence of a better systematics removal technique, there appears to be a $\sim$ All of the data presented in this paper were obtained from the Multimission Archive at the Space Telescope Science Institute (MAST)." + S'TScel is operated by the Association of Universities for Rescarch in Astronomy. Inc.. under NASA contract NASS-26555.," STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555." + Support. lor ALAS for. non-LIST data is provided by the NASA Ollice of Space Science via erant NNNOOAPOSC ancl by other erants ancl contracts., Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts. +" N. P. G and ο, AX. acknowledge support from STEC grant ST/C002266/2.", N. P. G and S. A. acknowledge support from STFC grant ST/G002266/2. + We are very grateful to D. Sing for providing limb darkening co-cllicients for the NICALOS wavelength Channels., We are very grateful to D. Sing for providing limb darkening co-efficients for the NICMOS wavelength channels. + Finally. we thank the referee. whose insightful comments helped improve the clarity of this paper.," Finally, we thank the referee, whose insightful comments helped improve the clarity of this paper." +assiniption of equal iux for the R- aud L-handed circular polarizations.,assumption of equal flux for the R- and L-handed circular polarizations. + As a result the circular polarization spectra are forced to he anti-viunietric. as discussed below.," As a result the circular polarization spectra are forced to be anti-symmetric, as discussed below." + Later. diving the analysis of the circular polarization spectra. we still have to correct for simall replicas of the total power profiles due to remaining small eain differences.," Later, during the analysis of the circular polarization spectra, we still have to correct for small replicas of the total power profiles due to remaining small gain differences." + After the gain calibration. we used he calibrators to determine the R-L dela offset aud he RR-LL phase offset.," After the gain calibration, we used the calibrators to determine the R-L delay offset and the RR-LL phase offset." + The delay offset is expected to ο stable over the duration of the observation (Brown et al., The delay offset is expected to be stable over the duration of the observation (Brown et al. + 1989) and cau be deteriuned from a single οὐπα scan in which the cross-haud fringes RL aud LR are well detected., 1989) and can be determined from a single continuum scan in which the cross-hand fringes RL and LR are well detected. + The RR-LL phase offset varies over the observation and are deteruiued from calibrators which are assumed to show 10 circular polarization., The RR-LL phase offset varies over the observation and are determined from calibrators which are assumed to show no circular polarization. + The solutious were again copied roni the mocest resolution date aud applied to the high resohtion data., The solutions were again copied from the modest resolution date and applied to the high resolution data. + Then friuge fitting aud self-calibration for he two separate data-sets were performed on a strong naser feature., Then fringe fitting and self-calibration for the two separate data-sets were performed on a strong maser feature. + Finally. corrections were made for the iustrunental feed polarization using a range of frequency channels on the maser source. in which the expected linear volarization or the frequeney averaged sumi of the linear xilarization is low.," Finally, corrections were made for the instrumental feed polarization using a range of frequency channels on the maser source, in which the expected linear polarization or the frequency averaged sum of the linear polarization is low." + After the solutious were applied to oth data sets image cubes could be created., After the solutions were applied to both data sets image cubes could be created. + We observed 1 late type stars. the supereiauts ο Per. VY CMa and NAIL Cyg and the Mira variable star U Πα.," We observed 4 late type stars, the supergiants S Per, VY CMa and NML Cyg and the Mira variable star U Her." + They are listed in Table., They are listed in Table. +" 1. with type. position. distance. perioc and velocity,"," \ref{sample} with type, position, distance, period and velocity." + The sources were selected. on the basis of 2 criteria: strong Πο masers and previous SiO and ΟΠ maser polarization observations., The sources were selected on the basis of 2 criteria; strong $_2$ O masers and previous SiO and OH maser polarization observations. + The peak fluxes measured in these observations are also shown im Table. 1.., The peak fluxes measured in these observations are also shown in Table. \ref{sample}. + Ou the total intensity channel maps with high spectral resolution. the noise is dominated by dynamic rauge effects aud lies between zz0.080.3 Jv.," On the total intensity channel maps with high spectral resolution, the noise is dominated by dynamic range effects and lies between $\approx 0.08 - 0.3$ Jy." + Ou the circular polarization maps we have noise of z0.010.03 Jv., On the circular polarization maps we have noise of $\approx 0.01 - 0.03$ Jy. + The circular polarization of the SiO masers around VY CMa has previously been observed with a single dish by Barvainis ct al. (, The circular polarization of the SiO masers around VY CMa has previously been observed with a single dish by Barvainis et al. ( +1987).,1987). + They fud circular polarization of 6.5 4. nmicating a field streugth of Dui~65 Ci Observatious of the 1612 MITz main line ΟΠ maser bv Cohen ct al. (," They find circular polarization of $6.5~\%$ , indicating a field strength of $B_{\rm SiO}\approx 65$ G. Observations of the 1612 MHz main line OH maser by Cohen et al. (" +1987) give Boyzm2 mG. Suith et al.(2001) concluded from erouud based aud Itubble Space Telescope optical observation. that lieh maenuetic fields of at least 1l € are necessary to explain the outtlow of matter observed in VY CMa.,"1987) give $B_{\rm OH}\approx +2$ mG. Smith et al.(2001) concluded from ground based and Hubble Space Telescope optical observation, that high magnetic fields of at least $1$ G are necessary to explain the outflow of matter observed in VY CMa." + Cohen et al., Cohen et al. +" also detected fields of z2 116 on the 1612 MIIz OII masers around NAIL νο, while Mashleder et al. ("," also detected fields of $\approx 2$ mG on the 1612 MHz OH masers around NML Cyg, while Masheder et al. (" +1999) estimated a feld of =1 mC on the OI masers aroud S Per.,1999) estimated a field of $\approx 1$ mG on the OH masers around S Per. + Ou U Her. Paen Fix (2000) observed pairs of R- aud L-polarized maser features. for the 1665 aud 1667 MITz ΟΠ masers.," On U Her, Palen Fix (2000) observed pairs of R- and L-polarized maser features, for the 1665 and 1667 MHz OH masers." + Although uot many of these Zeeman pairs were fouud they estimate a inagnetic field of Boy2 Linc. We lave examined the strongest IIO maser features around the1 stars observed., Although not many of these Zeeman pairs were found they estimate a magnetic field of $B_{\rm OH}\approx 1$ mG. We have examined the strongest $_2$ O maser features around the4 stars observed. + The results are shown iu, The results are shown in +the LF is calculated as where c/ is the time of visibility i the rest-fraine at which each SN Ia is «observed.,the LF is calculated as where $ct^i$ is the time of visibility in the rest-frame at which each SN Ia is observed. + If the SN would be observed just at oue epoch. as was clone in a number of observations to derive the SN rate. the visibility time will be a tile span over which each SNe cau be detected above the detection limit: in this case a fainter SNe would have a slorter visibility time.," If the SN would be observed just at one epoch, as was done in a number of observations to derive the SN rate, the visibility time will be a time span over which each SNe can be detected above the detection limit: in this case a fainter SNe would have a shorter visibility time." + In ou‘case. however. observations have been 1iade for the sai1ο field of sky «'ontiiuously with the maeittide Lit set for peak brightuess.," In our case, however, observations have been made for the same field of sky continuously with the magnitude limit set for peak brightness." + The visibility time will then be a tiue span of the survey observation., The visibility time will then be a time span of the survey observation. + From the criteria ou the date o μιακ brieuuess. the visibility time in tlie observed fame is 65 days. and hence cl=65/(1+at) days in the rest-frame.," From the criteria on the date of maximum brightness, the visibility time in the observed frame is 65 days, and hence $ct^i = 65 / (1+z^i)$ days in the rest-frame." + For SNe la M is absolute peak B-passband inagnitu«ce of SNe Ia. wlose apparent rest-[rame magiude is estimated [rom SALT2.," For SNe Ia $M^i$ is absolute peak $B$ -passband magnitude of SNe Ia, whose apparent rest-frame magnitude is estimated from SALT2." + For host galaxies 1 tis absolute magnitude in the rest-[rame estimated usiugkcorrect., For host galaxies it is absolute magnitude in the rest-frame estimated using. + The (actor e(z) is the completeless correction. eq. (1)).," The factor $\epsilon(z)$ is the completeness correction, eq. \ref{eqn:completeness}) )." + The LE is represented. i1 uuits of per Mpe’. aud 7 (vear) absorbs the time ol the duration of observability when we deal wihi SNe.," The LF is represented in units of per $^3$, and $\tau$ (year) absorbs the time of the duration of observability when we deal with SNe." + We take 7=1 vr as the unit., We take $\tau = 1$ yr as the unit. + We describe in Appenclix simulations we made to show that sample incompleteness auc our corrections do not itduce particular systematic errors to our analysis aud our procedures allow us to recover the true LE. SN rate aud related quantities.," We describe in Appendix simulations we made to show that sample incompleteness and our corrections do not induce particular systematic errors to our analysis and our procedures allow us to recover the true LF, SN rate and related quantities." + To estimate the intrinsic brightiess of SNe Ia. we must correct for dust extinetion withi1 host @alanies.," To estimate the intrinsic brightness of SNe Ia, we must correct for dust extinction within host galaxies." + In Lact. SNe Ia show the vwiation in colour that could be attributed to dust. exti1Ctlont within host galaxies and/or interpreed as au intrinsic colour variation.," In fact, SNe Ia show the variation in colour that could be attributed to dust extinction within host galaxies and/or interpreted as an intrinsic colour variation." + The colour informalon ls obtained from the colour excess parajeter c of SALT2. which is defined by at B-passband maximum brightness. where the second term is colour of the SN Ia teuplet.," The colour information is obtained from the colour excess parameter $c$ of SALT2, which is defined by $c = (B-V)_{\rm +max} - \langle(B-V)_{\rm max}\rangle$ at $B$ -passband maximum brightness, where the second term is colour of the SN Ia templet." + Figure 5 shows the distribution of t1is colour excess ec=E(B—V)., Figure \ref{fig:ebvhist} shows the distribution of this colour excess $c=E(B-V)$. + The distribution is asyinnetric with respect to E(B—V)=0. similar to that of the SNLS sample (Astieretal.2006).," The distribution is asymmetric with respect to $E(B-V) = +0$, similar to that of the SNLS sample \citep{SNLS}." +. I we aποσταλλο the color distributio las all exponelial distribution exp(—E(B—V)/.N) smeared by inTinslc Gaussian color cistribution with tle dispersion of σ. the observed distribution ean be fittec |wiil A0.0IS aud σ=0.071 as in Figwe 5..," If we assume the color distribution as an exponential distribution $\propto +\exp(-E(B-V)/\Delta)$ smeared by intrinsic Gaussian color distribution with the dispersion of $\sigma$ , the observed distribution can be fitted with $\Delta = 0.048$ and $\sigma = 0.074$ as in Figure \ref{fig:ebvhist}." + This value of A is smaller than A=0.138 obtaiec for the 1earby SN Ia sample by Jlaelal.(2007).," This value of $\Delta$ is smaller than $\Delta = +0.138$ obtained for the nearby SN Ia sample by \citet{Jha07}." +. The mean and dispersion (c)οτοτε0.230 are compared with (E(B—V))0.128d-0.173 from Jhaetal.(2007)., The mean and dispersion $\langle c\rangle = 0.176\pm 0.280$ are compared with $\langle E(B-V)\rangle = 0.128 \pm 0.173$ from \citet{Jha07}. +. Several data poinS Wwiil hieh valie of E(B—V) greater tlal 0.5 coutribute significantly to c., Several data points with high value of $E(B-V)$ greater than 0.5 contribute significantly to $c$. + IC they would be remove the mea1 aud dispersion will become (e=0.061£0.107., If they would be removed the mean and dispersion will become $\langle c\rangle = 0.061\pm 0.107$. + One may suspect that our sample may lack highly extinct or very red SNe cdie to selection effects., One may suspect that our sample may lack highly extinct or very red SNe due to selection effects. + It is unlikely. however. that we droppe stich SNe atleast at lower z where SNe are surveyed deep enough to reach briglitness siguilicantly," It is unlikely, however, that we dropped such SNe atleast at lower $z$ where SNe are surveyed deep enough to reach brightness significantly" +Recent measurements of stellar obliquity in transiting exoplanctary systems using the Itossiter-MeLaughlin effect have shown that a significant [fraction of hot Jupiter systems have misaligned stellar spin with respect to the planetary angular momentum axis (e.g.. Hébbrard et al.,"Recent measurements of stellar obliquity in transiting exoplanetary systems using the Rossiter-McLaughlin effect have shown that a significant fraction of hot Jupiter systems have misaligned stellar spin with respect to the planetary angular momentum axis (e.g., Hébbrard et al." + 2008: Winn οἱ al., 2008; Winn et al. + 2009.2010.2011: Johnson ct al.," 2009,2010,2011; Johnson et al." + 2009: Narita et al., 2009; Narita et al. + 2009: ‘Triaucl et al., 2009; Triaud et al. + 2010: Pont ct al., 2010; Pont et al. + 2010: Simpson οἱ al., 2010; Simpson et al. + 2011: Aloutou et al., 2011; Moutou et al. + 2011)., 2011). + This suggests that a laree population hot Jupiters are formed. through dynamical. planet-planet scatterings (e.g. Rasio Ford 1996: Weiclenschilling AMarzari 1996: Zhou et al.," This suggests that a large population hot Jupiters are formed through dynamical planet-planet scatterings (e.g., Rasio Ford 1996; Weidenschilling Marzari 1996; Zhou et al." + 2007: Chatterjee et al., 2007; Chatterjee et al. + 2008: Juric ‘Tremaine 2008) and more importantly. through secular interactions between multiple planets or Ixozai effect induced by a distant companion (e.g.. Wu Murray. 2003: Fabrveky Tremaine 2007: Nagasawa ct al.," 2008; Juric Tremaine 2008) and more importantly, through secular interactions between multiple planets or Kozai effect induced by a distant companion (e.g., Wu Murray 2003; Fabrycky Tremaine 2007; Nagasawa et al." + 2008: Naoz et al., 2008; Naoz et al. + 2011a.b: Wu Lithwick 2011: lxatz et al.," 2011a,b; Wu Lithwick 2011; Katz et al." + 2011). although other ellects involving star-disc interactions (Lai et al.," 2011), although other effects involving star-disc interactions (Lai et al." + 2011: LFoucart Lai 2011) and the assembly of protoplanetary discs (Bate et al., 2011; Foucart Lai 2011) and the assembly of protoplanetary discs (Bate et al. + 2010: Phies et al., 2010; Thies et al. + 2011) may also plav a role in producing spin-orbit misalignment., 2011) may also play a role in producing spin-orbit misalignment. + Reeent observations have also revealed. an intriguing correlation between stellar obliquity Ο and effective temperature Zi: Winn et al. (, Recent observations have also revealed an intriguing correlation between stellar obliquity $\Theta$ and effective temperature $T_{\rm eff}$: Winn et al. ( +2010) found that the misaligned svstems tend to have hotter parent stars,2010) found that the misaligned systems tend to have hotter parent stars +"and their depeudeuce on SSP metallicity is. therefore. naturally prone to more entaugled age effects aud to OTHERthor mnodoeidopoenaenticdlout features,features. SUCHsuch as COLVOCCTIOLLecti akaud inass loss proporties (both coustraining the AGB/RGB tip location).","and their dependence on SSP metallicity is, therefore, naturally prone to more entangled age effects and to other model-dependent features, such as convection and mass loss properties (both constraining the AGB/RGB tip location)." + The Fe5270444 location for the illustrative case of different simple stellar populations (SSPs). with varvine either age or |Fo/II]. is shown in Fig. 3..," The $_{\rm max}$ location for the illustrative case of different simple stellar populations (SSPs), with varying either age or [Fe/H], is shown in Fig. \ref{f2}." + A glance to the fieure makes clear that E5270 lomoagencously probes the ubiquitous componcut of IK1-I&3 ITI stars within each stellar system., A glance to the figure makes clear that Fe5270 homogeneously probes the ubiquitous component of K1-K3 III stars within each stellar system. + The collection of enmipidcal estinates of τος for several open aud elobular clusters of the Calaxy. according to the Gorgasetal.(1993)— database. is sununarized in Fie. L.," The collection of empirical estimates of $_{\rm max}$ for several open and globular clusters of the Galaxy, according to the \citet{gorgas93} database, is summarized in Fig. \ref{f4}." + These results are collected iu Table 1. where we report for cach cluster the strougest value reached by the Fe5270 index among the sampled stars. together with the sample size iu cach system. aud ιο adopted cluster metallicity.," These results are collected in Table 1, where we report for each cluster the strongest value reached by the Fe5270 index among the sampled stars, together with the sample size in each system, and the adopted cluster metallicity." + Note that. as Feh270 streneth peaks amoueg increasinely brighter red eiauts with decreasing metallicity (sce left panel of Fig. 3)).," Note that, as Fe5270 strength peaks among increasingly brighter red giants with decreasing metallicity (see left panel of Fig. \ref{f2}) )," +" just a handful set of bright stars iu metal-poor elobular clusters is sufficient to suitably pick up Fe52704,44.", just a handful set of bright stars in metal-poor globular clusters is sufficient to suitably pick up $_{\rm max}$. + A slightly deeper spectroscopy ds required. instead. for netalrich systems. but even in this case a dozen of stars taken at low spectral resolution are fully sufficient o suitably coustrain the iudex tip.," A slightly deeper spectroscopy is required, instead, for metal-rich systems, but even in this case a dozen of stars taken at low spectral resolution are fully sufficient to suitably constrain the index tip." + As an interesting exainple.am] in this regard.a we uualso overplotpo in Fig.," As an interesting example, in this regard, we also overplot in Fig." +or 1 ιο full sample of field eiauts (class AUN III or ogg€ 3) studied by Duzzonietal.(1991).. and Buzzouietal. (2001): it is evident that the upper envelope of 1ο Feh270 distribution for the eutire stellar dataset ffectivelv matches the overall cluster treud.," \ref{f4} + the full sample of field giants (class MK III or $1 \le \log g \le 3$ ) studied by \citet{buzzoni94}, and \citet{buzzoni01}; it is evident that the upper envelope of the Fe5270 distribution for the entire stellar dataset effectively matches the overall cluster trend." + The data of Fig., The data of Fig. + { are also compared with theoretical owedietfious from. population svuthesis models., \ref{f4} are also compared with theoretical predictions from population synthesis models. + The displaved models refer to 12.5 Car SSPs with differcut netallicity from Duzzonui(1989.1995a).," The displayed models refer to 12.5 Gyr SSPs with different metallicity from \citet{buzzoni89,buzzoni95a}." +. The case of vounecr (5 Car) populations: is: also accounted for: the nctallicitytallicity rangetanec of opena A Bt⋅ to all svutliesis. models of≯∙ Fig. 1.," The case of younger (5 Gyr) populations is also accounted for the metallicity range of open A fit to all synthesis models of Fig. \ref{f4}," +" excluding. the [Fe/HM| =2.27 case, provides with the displaved cocficient uncertainty at 1o level."," excluding the [Fe/H] $= -2.27$ case, provides with the displayed coefficient uncertainty at $\sigma$ level." + Compared to the original stellar fitting function of eq. (1)).," Compared to the original stellar fitting function of eq. \ref{eq:fe52}) )," + we report here a slightly steeper slope (ic. a more scusitive depeudeuce) iu the Fe5270 1)).," we report here a slightly steeper slope (i.e., a more sensitive dependence) in the Fe5270 )." + This is due to the reinforcing effect of the logg variation. which increases among metal-rich eiants. for fixed SSP age.," This is due to the reinforcing effect of the $\log{g}$ variation, which increases among metal-rich giants, for fixed SSP age." + Entering eq. (5)), Entering eq. \ref{eq:fitssp}) ) +" with the cluster values for E5270, roni Table we could assess the statistical performance of our theoreticalb. calibration as |Fe/II| predictor."," with the cluster values for $_{\rm max}$ from Table \ref{tab1} + we could assess the statistical performance of our theoretical calibration as [Fe/H] predictor." +" One ias fo bear in und. however. that this procedure is clearly biased toward underestimating cluster metallicity we wight ."" e MN MAU H"," One has to bear in mind, however, that this procedure is clearly biased toward underestimating cluster metallicity as we might be missing the real Fe5270 maximum." +" ueverter beput T ro rendnds I castz o )ositive and quterestnegative ratherresiduals (in the sense ""observedution. - xedieted:- [Fe;ΤΠ). separately."," Of better interest may rather be to study the distribution of positive and negative residuals (in the sense “observed - predicted” [Fe/H]), separately." +" In summary. the relevant are ⋅↜⋅↴⋅the followine: ""PMHeures where the rms for the total sample residuals sside of the equation) comes in fact from a skeweddistribution"," In summary, the relevant figures are the following: where the rms for the total sample residuals side of the equation) comes in fact from a skewed distribution" +"the mnaxiuuni temperature seen in the rine and this temperature determuncs LyR35,",the maximum temperature seen in the ring and this temperature determines $L_S/R_D^2$. + Here Ly d the total stellar hunuiuositv aud Rp is the dust radius from the center of mass, Here $L_S$ is the total stellar luminosity and $R_D$ is the dust radius from the center of mass. + Therefore. a increase in flux £F could represent a ~ merease in the ring radius from radiative trausfer modeling.," Therefore, a increase in flux $F$ could represent a $\sim$ increase in the ring radius from radiative transfer modeling." +" The temperature coutrast around the ring for optically thin dust with opacity KY~A teoes as FLO, meaning that the temperature around the ring ranges from ~136 KI to LISI. Grav dust would vary from ~133 KK to IKK. Although this contrast is only moderate. it may present an additional challenge iu detailed spectral fitting. as the models of D'Alessioetal.(2005). required. cinission from a single temperature only."," The temperature contrast around the ring for optically thin dust with opacity $\kappa_\lambda \propto +\lambda^{-1}$ goes as $F^{1/5}$, meaning that the temperature around the ring ranges from $\sim$ K to K. Gray dust would vary from $\sim$ K to K. Although this contrast is only moderate, it may present an additional challenge in detailed spectral fitting, as the models of \citet{DAlessio05} required emission from a single temperature only." + One way fo reconcile the gap radius from radiative trauster modeling with that from dynamical considerations would be if the Lhuunmositv of ον Tau/l is significantly underestinated., One way to reconcile the gap radius from radiative transfer modeling with that from dynamical considerations would be if the luminosity of CoKu Tau/4 is significantly underestimated. +" If we keep the dust temperature and therefore LsR3, constant. increasing Ls increases the model Rp."," If we keep the dust temperature and therefore $L_S/R_D^2$ constant, increasing $L_S$ increases the model $R_D$." + Au uncertiiuty iu distance due to the depth of Taurus (e.g.Torresetal.2007) can not reconcile this discrepancy. as both Ry determined from radiative trausfer imodoeliug and the münnuuni Rp determined by dynamical consideratious both increase Lnearly with the distauce estimate.," An uncertainty in distance due to the depth of Taurus \cite[e.g.][]{Torres07} can not reconcile this discrepancy, as both $R_D$ determined from radiative transfer modeling and the minimum $R_D$ determined by dynamical considerations both increase linearly with the distance estimate." + Towever. an uncertaintwv in the reddening of Colkkw Τα translates to a hpuuinositv uucertaiuty.," However, an uncertainty in the reddening of CoKu Tau/4 translates to a luminosity uncertainty." + The probable reddening calculated in Section 3.1 is ower than that used bv D'Alessioetal.(2005).. but uncertainties are considerable. and it may be possible hat a larger bolometric reddening could imerease the eap radius derived from radiative transter modeling.," The probable reddening calculated in Section \ref{sectProperties} is lower than that used by \citet{DAlessio05}, but uncertainties are considerable, and it may be possible that a larger bolometric reddening could increase the gap radius derived from radiative transfer modeling." + Iu order to independoeutlv estimate the dust radius roni raciative transfer modeling aud appreciate possible παπα complexities. we will exinume a very simple uodoel.," In order to independently estimate the dust radius from radiative transfer modeling and appreciate possible further complexities, we will examine a very simple model." +" This model contains sinall grains of amorplous olivine (ie. the limit where the erain radius is much sanaller than the blackbody cmussion peak). with optical constants frou, Dorschueretal.(1995)."," This model contains small grains of amorphous olivine (i.e. the limit where the grain radius is much smaller than the blackbody emission peak), with optical constants from \cite{Dorschner95}." +. We assign a dust temperature To=LiIS IKE and a stellar Tuuünosity of O.61L.. as in D'Alessioetal.(2005).. and a stellar temperature of au ALL. star of Ty=3600 Wy (Lulunan 1999).," We assign a dust temperature $T_D$ K and a stellar luminosity of $L_\sun$ as in \citet{DAlessio05}, and a stellar temperature of an M1.5 star of $T_S=$ K \citep{Luhman99}." +. The stellar radius for each of the two stars is 3Bus equivalent to a siugle star of radius R...," The stellar radius for each of the two stars is $R_\sun$, equivalent to a single star of radius $R_\sun$." + We assunie a blackbody spectrum for thestar?., We assume a blackbody spectrum for the. +. The dust is assiunnued optically thin (which could represeut the outer lavers of an opticallv-thück disk). so that the dust radius is then eiven by: Iu this simple model. the dust radius is Rp215 AAU. roughly cousisteunt with disk truncation radi from dynamical considerations.," The dust is assumed optically thin (which could represent the outer layers of an optically-thick disk), so that the dust radius is then given by: In this simple model, the dust radius is $R_D=$ AU, roughly consistent with disk truncation radii from dynamical considerations." + With the many possible paralucters to tweak in a more complete model. aud the possibility of the optically-thin dust being additionally heated by surrounding dust. increasing Zj aud driving the model radius outwards. it appears likely that a detailed radiative trausfer model could indeced be made to natch the dyuauical triucatiou radius.," With the many possible parameters to tweak in a more complete model, and the possibility of the optically-thin dust being additionally heated by surrounding dust, increasing $T_D$ and driving the model radius outwards, it appears likely that a detailed radiative transfer model could indeed be made to match the dynamical truncation radius." + The edge in the spectrum of disk cinission frou Colku Tau/1 at. ~9 yan coincides with a sharp rise in silicate enissivity. nieaniug hat the interplay between teniperature. extinction. ecolctry and dust composition is all the more complex or this source.," The edge in the spectrum of disk emission from CoKu Tau/4 at $\sim$ $\mu$ m coincides with a sharp rise in silicate emissivity, meaning that the interplay between temperature, extinction, geometry and dust composition is all the more complex for this source." + We hope that this preliminary discussion will motivate other authors to examine possible models iu more detail., We hope that this preliminary discussion will motivate other authors to examine possible models in more detail. + The ciceunbiuary nature of the Colsu Tau/lt disk bees the question: are other so-called transition disks also likely cireuuubinarvy in nature?, The circumbinary nature of the CoKu Tau/4 disk begs the question: are other so-called transition disks also likely circumbinary in nature? + The other well-kuown cold disks in Taurus. DAL Tau. LkCa 15. UN Tau and GAL Aur. ave also generally assumed to be single stars.," The other well-known cold disks in Taurus, DM Tau, LkCa 15, UX Tau and GM Aur, are also generally assumed to be single stars." + Although all these systems differ from oue another. Colksu Tau/ lis perhaps most uuique because of its very low accretion rate.," Although all these systems differ from one another, CoKu Tau/4 is perhaps most unique because of its very low accretion rate." + Our apertureanaskiug observations of these svstenis (paper in preparation) can so far elininate stellar (ass ratio 4.20.1) companions over a 160numas projected separation range. but can sax little about the possibility. of closer companions.," Our aperture-masking observations of these systems (paper in preparation) can so far eliminate stellar (mass ratio $q>0.1$ ) companions over a mas projected separation range, but can say little about the possibility of closer companions." + Accurate (στlkhnss 1) radial velocity mouitorine of these systenas is required to determine if auy of them harbor a close CE LAAT) companion., Accurate $\sigma \la1$ $^{-1}$ ) radial velocity monitoring of these systems is required to determine if any of them harbor a close $\la$ AU) companion. + Radial velocity monitoring is most applicable to DM. Tau. where the cleared tuner hole is expected to have ouly a AAU radius (Calvetetal. 2005).," Radial velocity monitoring is most applicable to DM Tau, where the cleared inner hole is expected to have only a AU radius \citep{Calvet05}." +. Simonetal(2000)— used resolved CO 2-1 observations of disks around several T Toi stars to measure their masses directly., \citet{Simon00} used resolved CO 2-1 observations of disks around several T Tauri stars to measure their masses directly. + These measurements would have resulted iu the total mass of the stellar primarics and auv unresolved companious., These measurements would have resulted in the total mass of the stellar primaries and any unresolved companions. + The total masses of O81c 0.05. 0.97+0.03 and. 0.55+0.03. for GAL Aur. LkCa 15 and DAL Tau respectively provide convincing evidence that these svstems do not harbor companions with mass ratios q20.3.," The total masses of $0.84\pm0.05$ , $0.97\pm0.03$ and $0.55\pm0.03$ for GM Aur, LkCa 15 and DM Tau respectively provide convincing evidence that these systems do not harbor companions with mass ratios $q>0.3$." + Tn sunmuuw. Colu Tau/l is a binary star system. with a current projected separation of τις AAT. aud a nlass ratio near uuitv.," In summary, CoKu Tau/4 is a binary star system with a current projected separation of $\sim$ AU, and a mass ratio near unity." + The disk suirouncdiug Col&u Tau/1 is therefore a οποια disk. with the disk ιο edee set bv dynamical truncation.," The disk surrounding CoKu Tau/4 is therefore a circumbinary disk, with the disk inner edge set by dynamical truncation." + The ανασα. disk runcation radius of Z13.16 AAU is inconsistent with he disk radius derived from previous spectral iodoeliug. mt it is likely that a different choice of reddening law aud correction. dust composition and ecometry will resolve his small discrepancy.," The dynamical disk truncation radius of $\ga13-16$ AU is inconsistent with the disk radius derived from previous spectral modeling, but it is likely that a different choice of reddening law and correction, dust composition and geometry will resolve this small discrepancy." + We sugecst that systematic racial velocity monitoring and aperture masking surveys arerequired to determine if other so-called transition disks are in fact niultiple svsteuis., We suggest that systematic radial velocity monitoring and aperture masking surveys arerequired to determine if other so-called transition disks are in fact multiple systems. +sources follow a well known q-shaped pattern in the colour-intensity diagram (e.g. Dunn et al.,sources follow a well known q-shaped pattern in the colour-intensity diagram (e.g. Dunn et al. +" 2010), which means that their X-ray spectral properties are typical of GBHs."," 2010), which means that their X-ray spectral properties are typical of GBHs." +" Hence, we believe that the data we selected are representative of a GBH behaviour during the luminosity rise and decay phases of an outburst."," Hence, we believe that the data we selected are representative of a GBH behaviour during the luminosity rise and decay phases of an outburst." +" We extracted archival Standard 2 spectra for detector 2, top layer, in the 3-20 keV band and HEXTE spectra from both detectors in the 20-200 keV band."," We extracted archival Standard 2 spectra for detector 2, top layer, in the 3–20 keV band and HEXTE spectra from both detectors in the 20–200 keV band." +" The details on data reduction are given in Sobolewska, Gierlinisski Siemiginowska (2009)."," The details on data reduction are given in Sobolewska, Gierlińsski Siemiginowska (2009)." +" Standard methods were used to subtract the background, create response matrices and deal with systematic errors."," Standard methods were used to subtract the background, create response matrices and deal with systematic errors." + We obtained one spectrum per pointed observation., We obtained one spectrum per pointed observation. +" Of all the available RXTE observations, we chose to study the data when the source’s high energy spectrum has photon index [«2, as found from the PCA+HEXTE 3-200 keV model fits including thermal Comptonisation component (Sobolewska et al."," Of all the available RXTE observations, we chose to study the data when the source's high energy spectrum has photon index $\Gamma < 2$, as found from the PCA+HEXTE 3–200 keV model fits including thermal Comptonisation component (Sobolewska et al." + 2009)., 2009). +" Figure 1 shows the X-ray luminosity in Eddington units plotted as a function of time, for the selected RXTE observations of the two sources."," Figure \ref{fig:fig1} shows the X-ray luminosity in Eddington units plotted as a function of time, for the selected RXTE observations of the two sources." + The rising/decaying phases of the outbursts can be clearly seen., The rising/decaying phases of the outbursts can be clearly seen. +" In all cases, the source luminosity was lower than of the Eddington limit for aand for339-4.."," In all cases, the source luminosity was lower than of the Eddington limit for and for." +" Consequently, both systems during"," Consequently, both systems during" +000.,000. + We also ran one head-on collision with 10? particles., We also ran one head-on collision with $10^6$ particles. + The details of the collisions are shown in ‘Table 1.., The details of the collisions are shown in Table \ref{description}. +" We give a single letter name for cach run. the pericentre separation ry in solar radii. the number of particles. the initial value of the smoothing length fy in solar radii. the minimum and iamaximunm particle masses in solar masses. and the amount of mass lost from the svstem during the collision in. solar Masses,"," We give a single letter name for each run, the pericentre separation $r_p$ in solar radii, the number of particles, the initial value of the smoothing length $h_0$ in solar radii, the minimum and } (M_v/)^b$, that a fraction, $\eta_t$, of the $P dV$ work, done by subclusters crossing the main clusters during mergers goes into turbulence." +" The frequency vs, defined as the frequency at which the spectral slope of the halos becomes a>1.9 (P(v)«v*), depends on the acceleration efficiency in the ICM, y, on the magnetic field in the ICM, B, and on the energy density of the cosmic microwave background radiation (CMB) as: v,ος(By2)/(B?+B2.?."," The frequency $\nu_s$, defined as the frequency at which the spectral slope of the halos becomes $\alpha\geq1.9$ $P(\nu)\propto \nu^{-\alpha}$ ), depends on the acceleration efficiency in the ICM, $\chi$, on the magnetic field in the ICM, $B$, and on the energy density of the cosmic microwave background radiation (CMB) as: $\nu_s\propto (B\,\chi^2)/(B^2+B_{cmb}^2)^2$." +" The frequency v, is a more practical re-definition of the synchrotron break frequency, vp, and, in the case of homogeneous models is v,~7vy (C09)."," The frequency $\nu_s$ is a more practical re-definition of the synchrotron break frequency, $\nu_b$, and, in the case of homogeneous models is $\nu_s\sim 7\,\nu_b$ (C09)." +" According to C09, in the case of a single major merger between a cluster of mass M, and a subcluster with mass AM, v; is where Βωμν=3.2(1+z)°uG is the equivalent magnetic field strength of the CMB, and R, is the cluster virial radius."," According to C09, in the case of a single major merger between a cluster of mass $M_v$ and a subcluster with mass $\Delta M$, $\nu_s$ is where $B_{cmb}=3.2 (1+z)^2 \mu G$ is the equivalent magnetic field strength of the CMB, and $R_v$ is the cluster virial radius." +" It is expected that mergers may generate halos with larger v; in more massive clusters, and that halos in clusters with the same mass M, (and magnetic field) and redshift could have different v, depending on the properties of the merger event responsible for their generation."," It is expected that mergers may generate halos with larger $\nu_s$ in more massive clusters, and that halos in clusters with the same mass $M_v$ (and magnetic field) and redshift could have different $\nu_s$ depending on the properties of the merger event responsible for their generation." +" Halos with v,> 1.4 GHz must be generated in connection with the most energetic merger-events in the Universe since only these mergers may allow for the efficient acceleration that is necessary to have relativistic electrons emitting at these frequencies.", Halos with $\nu_s \geq$ 1.4 GHz must be generated in connection with the most energetic merger-events in the Universe since only these mergers may allow for the efficient acceleration that is necessary to have relativistic electrons emitting at these frequencies. +" Present surveys carried out at νο~ 1 GHz detect radio halos only in the most massive and merging clusters Buote 2001, Venturi et al."," Present surveys carried out at $\nu_o \sim$ 1 GHz detect radio halos only in the most massive and merging clusters Buote 2001, Venturi et al." + 2008)., 2008). +" On the other hand, radio halos with smaller values of v, must be more common, since they can be generated in connection with less energetic phenomena, major mergers between less massive systems or minor mergers in massive systems, that are more frequent in the Universe."," On the other hand, radio halos with smaller values of $\nu_s$ must be more common, since they can be generated in connection with less energetic phenomena, major mergers between less massive systems or minor mergers in massive systems, that are more frequent in the Universe." +" This has been addressed quantitatively by means of Monte Carlo calculations that allow us to derive the fraction of clusters with radio halos with different v, as a function of the cluster mass and redshift.", This has been addressed quantitatively by means of Monte Carlo calculations that allow us to derive the fraction of clusters with radio halos with different $\nu_s$ as a function of the cluster mass and redshift. +" The expected population of radio halos is indeed constituted by a mixture of halos with different spectra, with steep spectrum halos being more common in the Universe; ~200 radio halos with 120«v,600 MHz are expected in future LOFAR surveys at 120 MHz (C09)."," The expected population of radio halos is indeed constituted by a mixture of halos with different spectra, with steep spectrum halos being more common in the Universe; $\sim 200$ radio halos with $120<\nu_s<600$ MHz are expected in future LOFAR surveys at 120 MHz (C09)." +" According to this model the monochromatic luminosity of radio halos at a given frequency, vo«νι, increases with increasing v,."," According to this model the monochromatic luminosity of radio halos at a given frequency, $\nu_0<\nu_s$, increases with increasing $\nu_s$." +" For a fixed cluster mass (or X-ray luminosity), the relation between the radio luminosity at vo of halos with Ys=Vs) and νεο. Py,(vo,Lx) and P,,,(vo,Lx) respectively, is (C09) where a~1.3 Ferrari et al."," For a fixed cluster mass (or X-ray luminosity), the relation between the radio luminosity at $\nu_0$ of halos with $\nu_s=\nu_{s,1}$ and $\nu_{s,2}$, $P_{\nu_{s,1}}(\nu_0,L_X)$ and $P_{\nu_{s,2}}(\nu_0,L_X)$ respectively, is (C09) where $\alpha\approx 1.3$ Ferrari et al." + 2008) is the radio spectral index., 2008) is the radio spectral index. + A correlation between the radio power Pg of halos and the mass (and X-ray luminosity) of the hosting clusters is expected (C06)., A correlation between the radio power $P_R$ of halos and the mass (and X-ray luminosity) of the hosting clusters is expected (C06). + In the simplest case that halos are generated by a single major merger this is where the parameter Γ is defined by TοΜΙ (T~2/3 in the virial scaling)., In the simplest case that halos are generated by a single major merger this is where the parameter $\Gamma$ is defined by $T\propto M^{\Gamma}$ $\Gamma\simeq 2/3$ in the virial scaling). + Eq., Eq. + 3 implies that more massive clusters host more luminous radio halos., \ref{Eq:PM} implies that more massive clusters host more luminous radio halos. +" By considering halos with v,=1.4 GHz, C06 showed that the slope of this scaling is consistent with that of the observed P(1.4)—M, correlation, provided that the model parameters (Bzy.,b,7j) lie within a fairly constrained range of values (see Fig."," By considering halos with $\nu_s\geq1.4$ GHz, C06 showed that the slope of this scaling is consistent with that of the observed $P(1.4)-M_v$ correlation, provided that the model parameters $(B_{}, b , \eta_t)$ lie within a fairly constrained range of values (see Fig." + 7 in C06)., 7 in C06). + We refer the reader to Sects., We refer the reader to Sects. + 3.3 and 4.1 of C06 for a more detailed discussion on model parameters and on their constraints., 3.3 and 4.1 of C06 for a more detailed discussion on model parameters and on their constraints. +" Following C09, we adopt a reference set of parameters?:: Beys= 1.94G, b= 1.5, n,=0.2, that falls in that range and sets ay=3.3, with P(1.4)αM?""."," Following C09, we adopt a reference set of : $B_{}=1.9\, \mu$ G, $b=1.5$ , $\eta_t=0.2$, that falls in that range and sets $\alpha_M=3.3$, with $P(1.4)\propto M_v^{\alpha_M}$." +" This implies P(1.4)oL7? assuming the Lx—M, correlation for galaxy clusters as derived in C06.", This implies $P(1.4)\propto L_X^{2.25}$ assuming the $L_X-M_v$ correlation for galaxy clusters as derived in C06. + Since the bulk of radio halos in our calculations is found to be associated with clusters of mass ~[1—2]x10?Μο the adopted values of B and b imply typical average magnetic fields ~1—3 4G. These values of B are similar to those derived from rotation measurements Govoni Feretti 2004; Bonafede et al.," Since the bulk of radio halos in our calculations is found to be associated with clusters of mass $\sim[1-2]\times 10^{15}\,M_{\odot}$ the adopted values of $B$ and $b$ imply typical average magnetic fields $\sim 1-3$ $\mu$ G. These values of $B$ are similar to those derived from rotation measurements Govoni Feretti 2004; Bonafede et al." + 2010) and equipartition assumption (EnBlin et al., 2010) and equipartition assumption lin et al. + 1998; Govoni et al., 1998; Govoni et al. + 2001)., 2001). +" The observed P(1.4)—Ly correlation shows an intrinsic scatter across the radio luminosity 6P/P~+2 Brunetti et al.2009).In principle, in our model a scatter in the P(1.4)—Ly "," The observed $P(1.4)-L_X$ correlation shows an intrinsic scatter across the radio luminosity $\delta P/P\simeq \pm 2$ Brunetti et al.2009).In principle, in our model a scatter in the $P(1.4)-L_X$ " +from the secondary star.,from the secondary star. + However. we can see Dux moculatec with the companions motion in the trailed spectra shown in Fig.," However, we can see flux modulated with the companion's motion in the trailed spectra shown in Fig." + 4 indicating the presence of such an irradiatec region near the inner Lagrangian point., 4 indicating the presence of such an irradiated region near the inner Lagrangian point. + We believe that this behaviour is a consequence of irradiation of the companion bv the inner disc anc white ανα uncer the influence of shadowing by the disc., We believe that this behaviour is a consequence of irradiation of the companion by the inner disc and white dwarf under the influence of shadowing by the disc. + Fig., Fig. + T shows an edge-on view of aassuming that the disc is thick enough to shield. the companion almost entirely., \ref{res:diag} shows an edge-on view of assuming that the disc is thick enough to shield the companion almost entirely. + Only a region near the poles of the companion star can see the inner disc and white dwarf. ancl therefore we expect to see emission displaced from the L1 point. towards the centre of mass of the secondary star.," Only a region near the poles of the companion star can see the inner disc and white dwarf, and therefore we expect to see emission displaced from the L1 point towards the centre of mass of the secondary star." + This displacement survives the process of Doppler tomography. even though it does not strictly satisfy the assumptions which underly it: in Fig.," This displacement survives the process of Doppler tomography, even though it does not strictly satisfy the assumptions which underly it: in Fig." + S. we show maps derived taking shadowing and Roche lobe geometry. into account for 74/4?= 0.0. 0.15. and 0.30 (anything lareer than 0.31. prevents all light from reaching the secondary star).," \ref{res:compsim} we show maps derived taking shadowing and Roche lobe geometry into account for $H/R = 0.0$ , $0.15$, and $0.30$ (anything larger than 0.31 prevents all light from reaching the secondary star)." + Comparing this figure with the real maps. suggests that the cise has an cllective 0.2.," Comparing this figure with the real maps, suggests that the disc has an effective $H/R \approx 0.2$ ." + Phe 12/2 may. be able to vary owing to waveloneth-dependent opacity at the EUV wavelengths appropriate for photoionisation of the various species involved., The $H/R$ may be able to vary owing to wavelength-dependent opacity at the EUV wavelengths appropriate for photoionisation of the various species involved. + For instance. the Balmer lines require photons with fy13.6eV. compared to 24eV for aand 54eV forA4686 X..," For instance, the Balmer lines require photons with $h \nu +> 13.6\,{\rm eV}$, compared to $24\,{\rm eV}$ for and $54\,{\rm + eV}$ for." +.We would expect the opacity at 13.6eV to be largest (because of neutral hydrogen). and thus the dise to appear thickest for the Balmer lines.," We would expect the opacity at $13.6\,{\rm eV}$ to be largest (because of neutral hydrogen), and thus the disc to appear thickest for the Balmer lines." + Our data are suggestive of this οσοι. although not conclusive.," Our data are suggestive of this effect, although not conclusive." + Ligher resolution observations would be of use because apart from the Balmer emission. the irracliated features are not resolved in our data.," Higher resolution observations would be of use because apart from the Balmer emission, the irradiated features are not resolved in our data." + We have discovered. spiral shocks in the August 1994 outburst of the dwarf nova 55 and 6 davs after the system went into outburst and with no noticeable diminution in strength from one day to the next., We have discovered spiral shocks in the August 1994 outburst of the dwarf nova 5 and 6 days after the system went into outburst and with no noticeable diminution in strength from one day to the next. + Our data extend the duration over which spiral structure is known to remain strong. and suggest that they could last the entire outburst.," Our data extend the duration over which spiral structure is known to remain strong, and suggest that they could last the entire outburst." + The eclipses of the emission lines are shifted by about 0.015.0.045 towards earlier phases than that of the white dwarf., The eclipses of the emission lines are shifted by about 0.015–0.045 towards earlier phases than that of the white dwarf. + These shifts towards earlier phases require a large-scale asvnimetry about the line of centres of the two stars larger than the spiral shocks suggest., These shifts towards earlier phases require a large-scale asymmetry about the line of centres of the two stars larger than the spiral shocks suggest. + We cannot explain this., We cannot explain this. + The cise is also apparently variable on short timescales as we see several strong Hares in. both 3almier and emission lines., The disc is also apparently variable on short timescales as we see several strong flares in both Balmer and emission lines. + Doppler maps of line emission on the companion suw show that it is located between the inner Lagrangian point and the poles of the star. and that it avoids the equator.," Doppler maps of line emission on the companion star show that it is located between the inner Lagrangian point and the poles of the star, and that it avoids the equator." + This is strong evidence for shielding of the companion star w the dise., This is strong evidence for shielding of the companion star by the disc. + From comparison with models. the shielding must be substantial. requiring a height-to-radius ratio in the cise of 4/1?zz0.2.," From comparison with models, the shielding must be substantial, requiring a height-to-radius ratio in the disc of $H/R \approx 0.2$." + There is some evidence for variability in he loc:ion of the emission. as might be expected. if the disc appears to vary in thickness according to the threshold wavelength needed to drive the respective emission line.," There is some evidence for variability in the location of the emission, as might be expected if the disc appears to vary in thickness according to the threshold wavelength needed to drive the respective emission line." + The Balmer emission from the companion is clearly broader than he other emission lines. supporting evidence from detached inaries for non-Doppler broadening in this line.," The Balmer emission from the companion is clearly broader than the other emission lines, supporting evidence from detached binaries for non-Doppler broadening in this line." + The Isaac Newton ‘Telescope is operated on the island of La Palma by the Isaac. Newton Group in the Spanish Observatorio del Itoque de los Muchachos of the Instituto de Astrolissica cle Canarias., The Isaac Newton Telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de sica de Canarias. + In. this research. we have used. and acknowledge with thanks. data from the AAVSO International Database. based. on observations submitted to the AAVSO by variable star observers worlwide.," In this research, we have used, and acknowledge with thanks, data from the AAVSO International Database, based on observations submitted to the AAVSO by variable star observers worldwide." + The reduction ancl analysis of the data were carried. out. on the Southampton node ofthe SEXRLINIS network., The reduction and analysis of the data were carried out on the Southampton node ofthe STARLINK network. + LM- wishes to thank L. Gonzállez Hernánndez for computer support., LM-R wishes to thank L. Gonzállez Hernánndez for computer support. +it through the ISM.,it through the ISM. + Note that the SN Ia ejecta appears to be distributed less homogencously: the reason for this is the low SNe la rate., Note that the SN Ia ejecta appears to be distributed less homogeneously; the reason for this is the low SNe Ia rate. + X deeper discussion on this point. and its consequences on the chemical evolution. will be presented in the next subsection.," A deeper discussion on this point, and its consequences on the chemical evolution, will be presented in the next subsection." + The periodic evolution of the ISAT can be better seen in Fig., The periodic evolution of the ISM can be better seen in Fig. + 4. (upper panel) where the behaviour of the gas content of the galaxy is plotted. as a function of the time., \ref{fig:mhot} (upper panel) where the behaviour of the gas content of the galaxy is plotted as a function of the time. + In this figure three different phases of the gas are shown: cold gas with Z«2 warm gas with 2.lol ks Tox10? Ix and hot gas with 7>10 Kk. This distinction helps us to understand the thermal evolution of the gas and the exchange among the cold. warm ancl hot phases.," In this figure three different phases of the gas are shown: cold gas with $T < +2 \times 10^4$ K, warm gas with $2 \times 10^4$ K $\le T \le 10^6$ K and hot gas with $T > 10^6$ K. This distinction helps us to understand the thermal evolution of the gas and the exchange among the cold, warm and hot phases." + The warm and hot eas phases reside mainly in the stellar region. and their time evolution is indicated by the dashed and dashed lines. respectively.," The warm and hot gas phases reside mainly in the stellar region, and their time evolution is indicated by the dashed and dot-dashed lines, respectively." + For the sake of simplicity. in Fig.," For the sake of simplicity, in Fig." + 4. we show only the evolution during five evcles in the time interval 0«/300 Awe., \ref{fig:mhot} we show only the evolution during five cycles in the time interval $0 < t < 300$ Myr. + The evolution over the entire period of 3 Gyr shows essentially the same periodicity. as can be seen in bie.," The evolution over the entire period of 3 Gyr shows essentially the same periodicity, as can be seen in Fig." + 5 (upper panel) where the cold gas mass content of the galaxy is plotted up to 3 Gye., \ref{fig:mcold} (upper panel) where the cold gas mass content of the galaxy is plotted up to 3 Gyr. + Despite its oscillatory behaviour. nearly of the initial gas is located bevond the galactic region.," Despite its oscillatory behaviour, nearly of the initial gas is located beyond the galactic region." + Llowever.," However," +Additional feedback by accretion frou stellar roeiinaut dack holes or subsequent SN explosions may become imuportant as well.,Additional feedback by accretion from stellar remnant black holes or subsequent SN explosions may become important as well. + However. iu the preseut work. we choose to nof include more than one SN. since we )dlieve it is essential to understaud the effects of a single SN before attempting to follow the evolution of Itiple. interacting SNe.," However, in the present work, we choose to not include more than one SN, since we believe it is essential to understand the effects of a single SN before attempting to follow the evolution of multiple, interacting SNe." + We therefore assune that all stars formed in nünihalos collapse directly to black roles after they die., We therefore assume that all stars formed in minihalos collapse directly to black holes after they die. + Recent investigations have shown hat accretion outo these stellar reiinaut black holes is inefficient as a result of the low density of the eas after shotoheating (οσοι&Broun2007:Alvarezet 2009).. at least for regions of the universe that are not wart of au unusually large overdensity (ec...Gaoetal. 2005).," Recent investigations have shown that accretion onto these stellar remnant black holes is inefficient as a result of the low density of the gas after photoheating \citep{jb07,awa09}, at least for regions of the universe that are not part of an unusually large overdensity \citep[e.g.,][]{gao05}." +. This leads us to ucelect radiative feedback from carly müniquasus (e.@..Iulileu&Macdau2005)..," This leads us to neglect radiative feedback from early miniquasars \citep[e.g.,][]{km05b}." +" Iu light of the complexity. induced by imuultiple star formation sites. we have chosen to run two distinct sinulatious: in simulation A (Sim A). we insert a 50AL, Pop III star whenever the density in a minibalo exceeds my=100cnm7 and subsequently solve for the IL region according to the prescription in Section 2.2."," In light of the complexity induced by multiple star formation sites, we have chosen to run two distinct simulations: in simulation A (Sim A), we insert a $50~M_{\odot}$ Pop III star whenever the density in a minihalo exceeds $n_{\rm H}=100~{\rm cm}^{-3}$, and subsequently solve for the H region according to the prescription in Section 2.2." + After of order 50 stars lave formed. we stop the rav-traciug routine and instead form sink particles.," After of order $50$ stars have formed, we stop the ray-tracing routine and instead form sink particles." + This ensures that the sinulatiou doces not become exceedingly complex., This ensures that the simulation does not become exceedingly complex. + Ouce a sink particle is created. all eas particles within the zinoothiug leusth correspoudiug to the above deusity threshold are iuniecdiatelv accreted.," Once a sink particle is created, all gas particles within the smoothing length corresponding to the above density threshold are immediately accreted." + Further accretion is eoverned by the criterion that a particle must fall within this smoothing Ieneth (details on the implementation may be fouud im Ja»psenetal. (2005)3)., Further accretion is governed by the criterion that a particle must fall within this smoothing length (details on the implementation may be found in \citet{jappsen05}) ). + Iu simulation D (Sim D). we orn sink particles aud do not iuclude anv radiative feedback bevoud that of the verv first star.," In simulation B (Sim B), we form sink particles and do not include any radiative feedback beyond that of the very first star." + This distiuction allows us to investigate the effects of photoheating ou the distribution of metals aud the assembly of the galaxy., This distinction allows us to investigate the effects of photoheating on the distribution of metals and the assembly of the galaxy. + Iu this section. we discuss the evolution of the SN remnant and its influence on the surrounding medi. followed by a detailed investigation of the distribution of metals in both simulations.," In this section, we discuss the evolution of the SN remnant and its influence on the surrounding medium, followed by a detailed investigation of the distribution of metals in both simulations." + This will then allow us to discuss the cousequeuces of metal enrichment for eeneration star formation in Section L., This will then allow us to discuss the consequences of metal enrichment for second-generation star formation in Section 4. +" The expansion of the SN remnant into the TCAD is depicted in Figures 1 aud 2. where we show the ceutral LOOkpe (comoving) of Sim A aud D. After ~15λίαν, the SN remuaut has propagated to =1kpc iu radius. roughly the size of the original IT11 region."," The expansion of the SN remnant into the IGM is depicted in Figures 1 and 2, where we show the central $100~{\rm kpc}$ (comoving) of Sim A and B. After $\simeq 15~{\rm Myr}$, the SN remnant has propagated to $\simeq 1~{\rm kpc}$ in radius, roughly the size of the original H region." + Both simulations are identical at this poiut. siuce no other nünibhalos have collapsed vet.," Both simulations are identical at this point, since no other minihalos have collapsed yet." + Iu a few cases. the shock aliead of the SN remnant has disrupted neighhborime mnünihalos that are just inthe process of collapsing.," In a few cases, the shock ahead of the SN remnant has disrupted neighboring minihalos that are just in the process of collapsing." + However. most ninilialos renun unaffected since they are either too far away or have collapsed to Ligh enough deusities (Cen&Riquelme 2008).," However, most minihalos remain unaffected since they are either too far away or have collapsed to high enough densities \citep{cr08}." +. The distinction between digupted and larecly unaffected iminilalos leads to an iuterestius result that will be discussed iu Section L., The distinction between disrupted and largely unaffected minihalos leads to an interesting result that will be discussed in Section 4. + After roughly 100Myr. or a Hubble time at : 30. the SN remnant comes iuto pressure equilibriui with the surrounding mediun aud stalls.," After roughly $100~{\rm Myr}$, or a Hubble time at $z\simeq 30$ , the SN remnant comes into pressure equilibrium with the surrounding medium and stalls." + Divine this period. multiple ucighboring minibalos uudergo ruuawayv collapse aud form stars.," During this period, multiple neighboring minihalos undergo runaway collapse and form stars." + Tn Sim A. the cnsuing Tu regions then partially overlap with the SN remnaut aud he comoving volume ofthe nascent galaxy.," In Sim A, the ensuing H regions then partially overlap with the SN remnant and the comoving volume of the nascent galaxy." + At this point. he complexity of the simulation dramatically iucreases and a multi-phase iiediuun forms.," At this point, the complexity of the simulation dramatically increases and a multi-phase medium forms." + In Figure 3. we show he distribution o| the gas in deusitv aud tenperature space within the lnieh resolution region atf :10. excluding eas accreted onto sink particles.," In Figure 3, we show the distribution of the gas in density and temperature space within the high resolution region at $z\simeq 10$ excluding gas accreted onto sink particles." +" It occupies nore than six orders of magnitude in density. ranging youn spp=[s107 to 100cm.7. and more than three orders of rnaguitude in teniperature. ranging from Z7""=10 o l1<10!K."," It occupies more than six orders of magnitude in density, ranging from $n_{\rm H}=4\times 10^{-5}$ to $100~{\rm cm}^{-3}$, and more than three orders of magnitude in temperature, ranging from $T=10$ to $4\times 10^{4}~{\rm K}$." + Most of the eas is shock-heated to the virial temperature and cools once the density exceeds BpLem/. but some parcels of gas in Suu A are shotoheated to 10!EK and have cooled down to T~1000I bv :10.," Most of the gas is shock-heated to the virial temperature and cools once the density exceeds $n_{\rm H}\sim 1~{\rm cm}^{-3}$, but some parcels of gas in Sim A are photoheated to $10^{4}~{\rm K}$ and have cooled down to $T\simeq 1000~{\rm K}$ by $z\simeq 10$." + This wari. diffuse mediun resides in the low-density ICM at ay~107? 105n? and will not be available for further star formation for 210° vas the approximate IGM free-fall time.," This warm, diffuse medium resides in the low-density IGM at $n_{\rm H}\sim 10^{-3}$ – $10^{-4}~{\rm cm}^{-3}$ and will not be available for further star formation for $\ga 10^8$ yr, the approximate IGM free-fall time." + A third phase. consisting of eas shock-heated by the SN remuaut. ias cooled down from an initial temperature of ~105Is o 10K aud has become mdistinguishable frou the relic IT region gas.," A third phase, consisting of gas shock-heated by the SN remnant, has cooled down from an initial temperature of $\sim 10^{8}~{\rm K}$ to $\sim 10^{4}~{\rm K}$ and has become indistinguishable from the relic H region gas." + Conconutant to the onset of star formation in other winihalos. the potential well of the nascent galaxy assembles at the ceuter of a massive filament (sce bottoni xuicls of Fieures b aud 2).," Concomitant to the onset of star formation in other minihalos, the potential well of the nascent galaxy assembles at the center of a massive filament (see bottom panels of Figures 1 and 2)." + Accreted halos are subject o tidal stripping aud rapidly lose their mass. simular o the disvuption of satellite galaxies cutering the halo of the Milky Way.," Accreted halos are subject to tidal stripping and rapidly lose their mass, similar to the disruption of satellite galaxies entering the halo of the Milky Way." + In some cases. they complete a few orbits before being disrupted. or undergo a iiajor merger.," In some cases, they complete a few orbits before being disrupted, or undergo a major merger." + luterestingly. virial shocks around halos in Sim D are hotter aud more distinct than in Sim A. The additional plotoheating in Sim A increases the pressure at larger radii reducing the iufall velocity aud. ii consequence. the post-shock temperature of the eas.," Interestingly, virial shocks around halos in Sim B are hotter and more distinct than in Sim A. The additional photoheating in Sim A increases the pressure at larger radii, reducing the infall velocity and, in consequence, the post-shock temperature of the gas." + For the same reason. structures in Sim D are generally more pronounced. which is particularly true at the ceuter of the galaxy (see inlays}.," For the same reason, structures in Sim B are generally more pronounced, which is particularly true at the center of the galaxy (see inlays)." + During the first few iillion wears after tle SN explosion. the metals are distributed iuto the ICAL by the bulk motion of the blast wave. which leads to a tieht correlation between teimiperature aud ietallicity.," During the first few million years after the SN explosion, the metals are distributed into the IGM by the bulk motion of the blast wave, which leads to a tight correlation between temperature and metallicity." + This becomes evident from the top panucls shown iu Figures 1 aud 2., This becomes evident from the top panels shown in Figures 1 and 2. + Once the SN remnant stalls. mixine is facilitated by agents that act on various scales.," Once the SN remnant stalls, mixing is facilitated by agents that act on various scales." + Ou the largest scales. flamentary accretion dominates (6.9..Wise&Abel2007:Greifetal. 2008).. while ou smaller scales photolheating by neighborig stars as well as dynamical iuteractions associated with the virialization of the galaxy become important.," On the largest scales, filamentary accretion dominates \citep[e.g.,][]{wa07b,greif08}, while on smaller scales photoheating by neighboring stars as well as dynamical interactions associated with the virialization of the galaxy become important." + As can be seen in the muddle and bottom panels of Figures 1 aud 2. these all interact to create a complex hierarchy of turbulent motions that cficieutly mis the eas.," As can be seen in the middle and bottom panels of Figures 1 and 2, these all interact to create a complex hierarchy of turbulent motions that efficiently mix the gas." + In Figure 1. we show the resulting deusitvAnetallicitv relation for the three output times in Figures 1 and 2.," In Figure 4, we show the resulting density-metallicity relation for the three output times in Figures 1 and 2." + At carly times. a distinct correlation arises: Hot. uuderdeuse reeious of the ICAL tend to be enriched to Z~10.72Z. or higher. while the densest regions. stich as nearby iniuilialos.remain aluost devoid of metals.," At early times, a distinct correlation arises: Hot, underdense regions of the IGM tend to be enriched to $Z\sim 10^{-3}~Z_{\odot}$ or higher, while the densest regions, such as nearby minihalos,remain almost devoid of metals." + Ouce the potential well of the ealaxy assenmibles. metalaich eas acemnuulates at hieh densities and leads to a flattening of the relation.," Once the potential well of the galaxy assembles, metal-rich gas accumulates at high densities and leads to a flattening of the relation." +Ou the other hand one can argue that before the second supernova explosion the stars are tidally locked. which would prevent the uewly born neutrou star fron beconune a pulsar. provided that the orbit before the explosion is wide cnough.,"On the other hand one can argue that before the second supernova explosion the stars are tidally locked, which would prevent the newly born neutron star from becoming a pulsar, provided that the orbit before the explosion is wide enough." + There are two effects bracketing the size of orbit of biumries before second supernova explosion. aud they have chance (depeudi18o on evolutionary parameters) to select binaries. which are tidaly locked before second superuova explosion and are not too tight at that time.," There are two effects bracketing the size of orbit of binaries before second supernova explosion, and they have chance (depending on evolutionary parameters) to select binaries, which are tidaly locked before second supernova explosion and are not too tight at that time." + The first selection occurs duri18o the first supernova explosion which tends to disrupt the widest binaries. as theiy binding energv is small.," The first selection occurs during the first supernova explosion which tends to disrupt the widest binaries, as their binding energy is small." + After, After +"Taking the dot product of Bwithbothsidesof Equation(57))givesB Vi Vj)—0. which results in the following algebraic relation for ey: can be differentiated to give ef, for use iu Equation (61)).","Taking the dot product of $B$ with both sides of Equation \ref{eq:momentad})) gives $B$ $ \cdot \left(\mbox{\boldmath$ $}_{\rm i} - \mbox{\boldmath$ $}\right) = 0$, which results in the following algebraic relation for $v_{\rm{i}\mathit{\phi}}$: which can be differentiated to give $v_{\rm{i}\mathit{\phi}}^{\prime}$ for use in Equation \ref{eq:virphiprime}) )." + Tuow have a system of 8 ordinary cliffereutial equations in the variables ων fs 6042 050. 01 πρι δρ and bu.," I now have a system of 8 ordinary differential equations in the variables $x$, $\tilde{\rho}$, $v_{r}$, $v_{\phi}$, $v_{z}$, $v_{\rm{i}\mathit{r}}$, $b_{r}$ and $b_{\phi}$." + This system differs from that of LOG in the treatment of the induction equation., This system differs from that of L96 in the treatment of the induction equation. + A solution of tliis version of the disk equations and a matching wind solution are prescuted in Section ??.., A solution of this version of the disk equations and a matching wind solution are presented in Section \ref{res}. + That solution assmues a functional form for the matterfold coupling paramcter YXῥι that differs from the one used iu L96while L96 assumes that Y increases monotonically with height. I take Y to be coustant along a field Lue. as would be the case when the ion density is constant (WIN93).," That solution assumes a functional form for the matter–field coupling parameter $\Upsilon \propto \tilde \rho_{\rm i}$ that differs from the one used in L96—while L96 assumes that $\Upsilon$ increases monotonically with height, I take $\Upsilon$ to be constant along a field line, as would be the case when the ion density is constant (WK93)." + Iu fact. the coupling parameter is expected to with height in the upper reaches of real protostellar disks not too far from the origin (Salinerou&Wardle2005).. reflecting the decrease of the ion mass density ϱ with height (which occurs even though the ionization fraction increases witli height because the neutral mass density p drops rapidly with :).," In fact, the coupling parameter is expected to with height in the upper reaches of real protostellar disks not too far from the origin \citep{sw05}, reflecting the decrease of the ion mass density $\tilde\rho_{\rm i}$ with height (which occurs even though the ionization fraction increases with height because the neutral mass density $\tilde \rho$ drops rapidly with $z$ )." + On the other haud. the coupling parameter mcereases ith radial position because the Keplerian frequency decreases.," On the other hand, the coupling parameter increases with radial position because the Keplerian frequency $\Omega_{\rm K}$ decreases." + Taking Yo constant d8 a compromise ween these competing effects as the iuteeration Oceeds upwards and outwards aloug a field line., Taking $\Upsilon$ constant is a compromise between these competing effects as the integration proceeds upwards and outwards along a field line. +" inally. the solution prescuted here differs frou the ποutions presented in L96 in that Einitiate the wmuerical integration of the disk equations using a Tavlor series expansion (see Appendix 77)). whereas LOG uses the approxination Ct,=eps du a sinall region near the uudplane to obtain algebraic relations for c, aud ος."," Finally, the solution presented here differs from the solutions presented in L96 in that I initiate the numerical integration of the disk equations using a Taylor series expansion (see Appendix \ref{taylorAD}) ), whereas L96 uses the approximation $v_{z} = v_{r} s$ in a small region near the midplane to obtain algebraic relations for $v_{r}$ and $v_{\phi}$." +" From Equation (63)). ty.=ep0l’?, "," From Equation \ref{eq:virz}) ), $v_{\rm{i}\mathit{r},0} = -\epsilon_{\rm +B} \theta^{1/2}$." +The r conrponeut of momentum conservatiou (Equation (8))). with Equation (57)) used to replace the Loreutz force term with an ion-neutral drag force term. vields Equation (13) of L96.," The $r$ component of momentum conservation (Equation \ref{eq:moment}) )), with Equation \ref{eq:momentad}) ) used to replace the Lorentz force term with an ion-neutral drag force term, yields Equation (13) of L96." +" At the midplanc. this equation reduces to Or which gives ου dn terms of the parameters 0. ο, Ty. €. and ep."," At the midplane, this equation reduces to or which gives $v_{\phi,0}$ in terms of the parameters $\theta$, $\zeta$ , $\Upsilon_{0}$, $\epsilon$ , and $\epsilon_{\rm B}$." + Continuity of ο. nauplies ej;9=0. aud the o component of the momentum equation (cf.," Continuity of $v_{\rm{i}\mathit{z}}$ implies $v_{\rm{i}\mathit{z},0} = 0$, and the $\phi$ component of the momentum equation (cf." + Equation (11) of L96) evaluated at the midplane gives which can be used to calculate ου.," Equation (14) of L96) evaluated at the midplane gives which can be used to calculate $v_{\rm{i}\mathit{\phi},0}$ ." + Combining Amperre’s law {Equation (9))) with Equation (57)) yields equations for bf and ή (ct., Combining Ampèrre's law (Equation \ref{eq:amp}) )) with Equation \ref{eq:momentad}) ) yields equations for $b_{r}^{\prime}$ and $b_{\phi}^{\prime}$ (cf. + Equations (17)(19) of L96): evaluating at the midplane vields aud The expression for eg (see Table 1)) remainsuuchiauged.," Equations (17)–(19) of L96); evaluating at the midplane yields and The expression for $v_{z,0}^{\prime}$ (see Table \ref{tab:bcs}) ) remainsunchanged." + The Tavlor expansion procedure used to iuitiate the intceration isdescribed in Appendix ??.., The Taylor expansion procedure used to initiate the integration isdescribed in Appendix \ref{taylorAD}. . +studies. in particular ?.. who found a value of A(L1) = 2.08 (+£0.08) dex using a similar iron excitation energy technique but without the NLTE corrections. ? with A(L1) = 2.10 (£0.09) using a Balmer line wing temperature scale. and ΑΕ) = 2.16 dex or A(Li) = 2.10 depending on the evolutionary state from ?..,"studies, in particular \citet{Spiteetal1996}, who found a value of $A$ (Li) = 2.08 $\pm$ 0.08) dex using a similar iron excitation energy technique but without the NLTE corrections, \citet{Bonifacioetal2007} with $A$ (Li) = 2.10 $\pm$ 0.09) using a Balmer line wing temperature scale, and $A$ (Li) = 2.16 dex or $A$ (Li) = 2.10 depending on the evolutionary state from \citet{Hosfordetal2009}." + The NLTE corrections have moved the mean Li abundance closer to. but not consistent with. the WMAP value of A(Li) = 2.72 dex. and thus still leaves the lithium problem unsolved.," The NLTE corrections have moved the mean Li abundance closer to, but not consistent with, the WMAP value of $A$ (Li) = 2.72 dex, and thus still leaves the lithium problem unsolved." + It 15 noted that even the ? scale. whilst bringing the observed and theoretical Li abundances closer. still failed to solve the lithium problem.," It is noted that even the \citet{MelendezRamirez2004} scale, whilst bringing the observed and theoretical Li abundances closer, still failed to solve the lithium problem." + Fig., Fig. + 10. shows the lithium abundances versus [Fe/H] and Tj. least squares fits have been performed for both sets of data.," \ref{Fig:met/teff-li} shows the lithium abundances versus [Fe/H] and $T_{\rm eff}$, least squares fits have been performed for both sets of data." + In the fit to metallicity we get the values: for Sy = 0 and for Sy = I., In the fit to metallicity we get the values: for $\rm S_{H}$ = 0 and for $\rm S_{H}$ = 1. + For Sy= 0. we see a similar values to the coefficient of metallicity as 2... whilst for Sy = 1. we have a value that is about half the size. and has a negative slope.," For $\rm S_{H}$= 0, we see a similar values to the coefficient of metallicity as \citet{Ryanetal1999}, whilst for $\rm S_{H}$ = 1, we have a value that is about half the size, and has a negative slope." + However. our errors are much larger. due to the large random errors and small sampleof stars. and therefore no statistically relevant trend can be deduced.," However, our errors are much larger, due to the large random errors and small sampleof stars, and therefore no statistically relevant trend can be deduced." + For Tay. we get the equations: for Sy = 0 and for Sy = |.," For $T_{\rm eff}$, we get the equations: for $\rm S_{H}$ = 0 and for $\rm S_{H}$ = 1." + Here we see no statistically relevant trend with Tay for either Sy value., Here we see no statistically relevant trend with $T_{\rm eff}$ for either $\rm S_{H}$ value. + We also perform the fit as described by ?.. such that: where ¢ measures the primordial abundance of Li and 5. is a probe of galactic chemical evolution.," We also perform the fit as described by \citet{Ryanetal2000}, such that: where $a^{'}$ measures the primordial abundance of Li and $b^{'}$ is a probe of galactic chemical evolution." + For this fit. we obtain the primordial values of = (1.47 + 0.27)x10 for Sy = O and = (1.80 + 0.16)%107' for Sy = I.," For this fit, we obtain the primordial values of = (1.47 $\pm$ $\times10^{-10}$ for $\rm S_{H}$ = 0 and = (1.80 $\pm$ $\times10^{-10}$ for $\rm S_{H}$ = 1." + Both of these values are far from the high value of = 5.245/1x107 (?)ffrom WMAP and BBN., Both of these values are far from the high value of = $5.24^{+0.71}_{-0.62}\times10^{-10}$ \citep{Cyburt2008}f from WMAP and BBN. + We see then that the addition of NLTE corrections has led to an merease in Τομ for most stars., We see then that the addition of NLTE corrections has led to an increase in $T_{\rm eff}$ for most stars. + This equates to an increase in A(Li) but it is still not high enough to reconcile the lithium problem., This equates to an increase in $A$ (Li) but it is still not high enough to reconcile the lithium problem. + Through the efforts of ?. and this study it is safe to conclude that systematic errors in the metal-poor Tar scale are almost certainly not large enough to be the source of the A(Li) discrepancy between observation and WMAP + BBN predictions., Through the efforts of \citet{Hosfordetal2009} and this study it is safe to conclude that systematic errors in the metal-poor $T_{\rm eff}$ scale are almost certainly not large enough to be the source of the $A$ (Li) discrepancy between observation and WMAP + BBN predictions. + This outcome lends strength to other possible explanations. such as processing in the stars. e.g. diffusion. processing in earlier generations of stars. and/or different BBN networks. or more exotic solutions requiring physics beyond the standard model.," This outcome lends strength to other possible explanations, such as processing in the stars, e.g. diffusion, processing in earlier generations of stars, and/or different BBN networks, or more exotic solutions requiring physics beyond the standard model." + It should be noted that while we have computed Fe lines in NLTE to constrain the temperature. our Li abundances are calculated from a grid of abundance versus equivalent width that was constructed under the assumptions of LTE. see Paper I for details.," It should be noted that while we have computed Fe lines in NLTE to constrain the temperature, our Li abundances are calculated from a grid of abundance versus equivalent width that was constructed under the assumptions of LTE, see Paper I for details." + Several studies of the effects of NLTE Li line formation have been conducted., Several studies of the effects of NLTE Li line formation have been conducted. + Two of these studies are those of ? and ?:: they find Li abundance corrections of ~ +0.013 — +0.020 dex and ~ +0.01 — +0.03 dex respectively for the temperature. log ¢ and [Fe/H] range in this study.," Two of these studies are those of \citet{Carlssonetal1994} and \citet{Lindetal2009}; they find Li abundance corrections of $\sim$ +0.013 – +0.020 dex and $\sim$ +0.01 – +0.03 dex respectively for the temperature, log g and [Fe/H] range in this study." + Due to the very small size of these corrections we find the use of the LTE grid. combined with our NLTE effective temperatures. to be acceptable in determining Li abundances. and that the introduction of NLTE Li abundances will not significantly aid in solving the lithium problem.," Due to the very small size of these corrections we find the use of the LTE grid, combined with our NLTE effective temperatures, to be acceptable in determining Li abundances, and that the introduction of NLTE Li abundances will not significantly aid in solving the lithium problem." + Having discussed the effects of NLTE corrections on the Τομ: scale and the lithium abundances. it is also of interest to note the effect or an aspect of abundance analysis. specifically ionization equilibrium often used in the determination of log g.," Having discussed the effects of NLTE corrections on the $T_{\rm eff}$ scale and the lithium abundances, it is also of interest to note the effect on an aspect of abundance analysis, specifically ionization equilibrium often used in the determination of log $g$." + We can also nake a preliminary investigation into constraints we can place on the value of Sy from our results., We can also make a preliminary investigation into constraints we can place on the value of $\rm S_{H}$ from our results. + Ithas been noted previously (?) that lines are relatively unaffected by NLTE., It has been noted previously \citep{Gehrenetal2001} that lines are relatively unaffected by NLTE. + In this work we have also found this to be the case with values for abundance corrections of order 0.01 dex., In this work we have also found this to be the case with values for abundance corrections of order 0.01 dex. + Our NLTE calculations induce a mean difference between AA(Fe 0) and AA(Fe i) of 0.39 dex for Sy = 0 and 0.27 dex for Sy = I., Our NLTE calculations induce a mean difference between $\Delta A$ ) and $\Delta A$ ) of 0.39 dex for $\rm S_{H}$ = 0 and 0.27 dex for $\rm S_{H}$ = 1. + Knowing that a 0.1 dex change in log g induces a difference of 0.05 dex between and abundance. for there to be ionization balance. one would need a correction of ~ + 0.8 dex and + 0.5 dex in log g for Sy = 0 and | respectively.," Knowing that a 0.1 dex change in log g induces a difference of 0.05 dex between and abundance, for there to be ionization balance, one would need a correction of $\sim$ + 0.8 dex and + 0.5 dex in log $g$ for $\rm S_{H}$ = 0 and 1 respectively." + That is. due to overionization. foreing ionization balance for," That is, due to overionization, forcing ionization balance for" +expect that satellite color is an excellent indicator of satelli stellar mass. regardless of the mass of the host halo.,"expect that satellite color is an excellent indicator of satellite stellar mass, regardless of the mass of the host halo." + The approximate independence of satellite Iuminosity functions on group size also suggests that the extreme value statistics of the sort pioneered by Scott (1957) should provide a &ood cleseription of the luminosity function. of the most luminous satellites., The approximate independence of satellite luminosity functions on group size also suggests that the extreme value statistics of the sort pioneered by Scott (1957) should provide a good description of the luminosity function of the most luminous satellites. + Note that most. previous work has used extreme value statistics to model the luminosity function of the central rather than satellite galaxies (e.g. Bhavsar Barrow 1985)., Note that most previous work has used extreme value statistics to model the luminosity function of the central rather than satellite galaxies (e.g. Bhavsar Barrow 1985). + ‘This is the subject of work in progress (also see Vale Ostriker 2007)., This is the subject of work in progress (also see Vale Ostriker 2007). + More recent work has phrased this discussion in terms of the luminosity gap between the first ancl second. or second. ancl third ranked galaxies in clusters.," More recent work has phrased this discussion in terms of the luminosity gap between the first and second, or second and third ranked galaxies in clusters." + For example. Milosavljevic et al. (," For example, Milosavljevic et al. (" +"2006) suggest that the gap. between first. and. second ranked. galaxies is correlated with the dynamical age of the system: ""fossil, groups. poor clusters. and rich clusters are distinguished by the time since their last major merger. so their luminosity gaps ciller.","2006) suggest that the gap between first and second ranked galaxies is correlated with the dynamical age of the system: “fossil” groups, poor clusters, and rich clusters are distinguished by the time since their last major merger, so their luminosity gaps differ." + In addition. van den Bosch et al. (," In addition, van den Bosch et al. (" +2007) find that the average luminosity gap and the fossil eroup fraction both increase with decreasing host halo mass.,2007) find that the average luminosity gap and the fossil group fraction both increase with decreasing host halo mass. + This last finding is particularly easy to. understand in the context of our results., This last finding is particularly easy to understand in the context of our results. + At. small halo masses. the luminosity of the central galaxy grows linearly with halo mass. but the growth is only logarithmic at. large. masses (equation 6)).," At small halo masses, the luminosity of the central galaxy grows linearly with halo mass, but the growth is only logarithmic at large masses (equation \ref{LMapprox}) )." + On the other hand the number of satellites erows slightly more strongly than linearly. (equation. 4))., On the other hand the number of satellites grows slightly more strongly than linearly (equation \ref{sdssNg}) ). + Η the satellite luminosity function is independent. of halo mass. then massive haloes are allowed more draws from the universal satellite luminosity Function.," If the satellite luminosity function is independent of halo mass, then massive haloes are allowed more draws from the universal satellite luminosity function." + Lf this function has an exponential tail. and equations (9)) ancl (10)) suggest hat it does. then the most luminous of these draws grows ogarithmically with the number of draws. so dU grows ogarithmically with halo mass.," If this function has an exponential tail, and equations \ref{phisat}) ) and \ref{phiLsat}) ) suggest that it does, then the most luminous of these draws grows logarithmically with the number of draws, so it grows logarithmically with halo mass." + Thus. the luminosity gap is larger at small masses. ancl decreases at larger masses.," Thus, the luminosity gap is larger at small masses, and decreases at larger masses." + This οσοι is further helped by the fact that (1) the satellite unminosity function is not quite independent of halo massmean satellite luminosity increases slightlv with halo mass: (ii) in equation (4)). AdiCL)z23πμ but the factor of 23 is replaced by a smaller factor at large L.," This effect is further helped by the fact that (i) the satellite luminosity function is not quite independent of halo mass---mean satellite luminosity increases slightly with halo mass; (ii) in equation \ref{sdssNg}) ), $M_1(L)\approx 23\,M_{\rm min}(L)$, but the factor of 23 is replaced by a smaller factor at large $L$." + In effect. this allows for even more luminous satellites in massive haloes.," In effect, this allows for even more luminous satellites in massive haloes." + If satellite galaxies are associated with the subhaloes of dark matter haloes. then the halo model predicts that central and satellite galaxies of the same luminosity should differ in mass by factors of about 90/23~4 (the centrals being more massive). whereas the stellar masses at. [ixed Luminosity are unlikely to be very. cillerent (equation 16)).," If satellite galaxies are associated with the subhaloes of dark matter haloes, then the halo model predicts that central and satellite galaxies of the same luminosity should differ in mass by factors of about $90/23\sim 4$ (the centrals being more massive), whereas the stellar masses at fixed luminosity are unlikely to be very different (equation \ref{satM2L}) )." + Weak-lensing analyses should soon be able to test this prediction (e.g. Yang et al., Weak-lensing analyses should soon be able to test this prediction (e.g. Yang et al. + 2006). as should. analyses of satellite dvnamics (c.g. Melxay ct al.," 2006), as should analyses of satellite dynamics (e.g. McKay et al." + 2002)., 2002). + In. practice. there is likely to be more scatter between subhalo mass and luminosity than there is between parent. halo mass and luminositw: we expect this to alter our conclusions quantitatively but not qualitatively.," In practice, there is likely to be more scatter between subhalo mass and luminosity than there is between parent halo mass and luminosity; we expect this to alter our conclusions quantitatively but not qualitatively." + Εις too can be checked by lensing analyses., This too can be checked by lensing analyses. + At the time or writing. Limousin et al. (," At the time or writing, Limousin et al. (" +2007) have concluded a weak-Iensing study of five clusters.,2007) have concluded a weak-lensing study of five clusters. + They report a cdillerence between central and satellite masses (at. fixed. luminosity) of about a factor of 5., They report a difference between central and satellite masses (at fixed luminosity) of about a factor of 5. + Dynamical mass is proportional to £207. so since tidal stripping usually does not significantly allect velocity dispersion. the smaller sizes of cluster galaxies compared. to field. ealaxics at the same luminosity implies that the satellite galaxies are less massive by a similar factor.," Dynamical mass is proportional to $R\,\sigma^2$, so since tidal stripping usually does not significantly affect velocity dispersion, the smaller sizes of cluster galaxies compared to field galaxies at the same luminosity implies that the satellite galaxies are less massive by a similar factor." + Phe measurements are still quite uncertain. but. constraints from lensing are improving.," The measurements are still quite uncertain, but constraints from lensing are improving." + We look forward to more such data. since our analysis has shown that such studies are rather closely related to studies of the luminosity dependence of galaxy clustering.," We look forward to more such data, since our analysis has shown that such studies are rather closely related to studies of the luminosity dependence of galaxy clustering." + Uf the cdilference between the factors of 23 (in the halo model description of the mass required to host one satellite) and 90 (in the subhalo mass function) is associated with mass lost to stripping processes as satellites become incorporated into parent haloes. then the mass of a satellite prior to stripping is about 90/23~4 times larger than its current mass: about of its mass is stripped.," If the difference between the factors of 23 (in the halo model description of the mass required to host one satellite) and 90 (in the subhalo mass function) is associated with mass lost to stripping processes as satellites become incorporated into parent haloes, then the mass of a satellite prior to stripping is about $90/23\sim 4$ times larger than its current mass: about of its mass is stripped." +" ""This is slightly larger than the ~60 mass-loss factors seen in simulations which only include the dark matter component (e.g. Nagai Ixravtsoy. 2005).", This is slightly larger than the $\sim 60\%$ mass-loss factors seen in simulations which only include the dark matter component (e.g. Nagai Kravtsov 2005). + Given that the halo-moclel argument is based. on relating the subhalo population in simulations toobservations. it is remarkable that the two estimates are similar.," Given that the halo-model argument is based on relating the subhalo population in simulations to, it is remarkable that the two estimates are similar." + Our analysis of the connection between subhaloes. ealaxics and the halo model has another interesting consequence.," Our analysis of the connection between subhaloes, galaxies and the halo model has another interesting consequence." + Phe mass fraction in subhaloes is where we have used equation (11)) for the subhalo mass Function. dNZdim.," The mass fraction in subhaloes is where we have used equation \ref{dNgao}) ) for the subhalo mass function, $dN/dm$." + LH stars only form in sullicicntly massive objects. the lower limit to this integral may be greater than zero: this will change the quantitative estimates which follow. but not the qualitative conclusions.," If stars only form in sufficiently massive objects, the lower limit to this integral may be greater than zero: this will change the quantitative estimates which follow, but not the qualitative conclusions." + Our estimate of the mass lost to stripping processes. when combined. with equation (18)) for the mass fraction in subhaloes. leaves about half the mass of a 10775.ΑΙ. xvent halo unaccounted for.," Our estimate of the mass lost to stripping processes, when combined with equation \ref{massfrac}) ) for the mass fraction in subhaloes, leaves about half the mass of a $10^{12}h^{-1}M_\odot$ parent halo unaccounted for." + For a LOMA134. mass halo his fraction is about twenty percent., For a $10^{15}h^{-1}M_\odot$ mass halo this fraction is about twenty percent. + For comparison. using he model of subhalo mass-loss due to stripping in. Vale Ostriker (2005: see their Figure 1) with equation (18)). hese corresponding fractions are about thirty percent. and wentv percent. when subhaloes with m2»1045TAL. are considered. C," For comparison, using the model of subhalo mass-loss due to stripping in Vale Ostriker (2005; see their Figure 1) with equation \ref{massfrac}) ), these corresponding fractions are about thirty percent and twenty percent, when subhaloes with $m>10^{11}h^{-1}M_\odot$ are considered. (" +Phese mass fraction estimates are highly sensitive to their model of the amount of mass stripped from he numerous very low mass haloes. however.),"These mass fraction estimates are highly sensitive to their model of the amount of mass stripped from the numerous very low mass haloes, however.)" + Presumably. his mass is associated with the central galaxy itself. and/or with subhaloes that were completely disrupted by the parent alo.," Presumably this mass is associated with the central galaxy itself, and/or with subhaloes that were completely disrupted by the parent halo." + HE these objects hosted stars. then these stars may have »en incorporated into the central object. or they may now contribute to intracluster light.," If these objects hosted stars, then these stars may have been incorporated into the central object, or they may now contribute to intracluster light." + Indeed. results from recent studies of intracluster light support the idea that much of the ight in the LCL comes from the stripping. disruption. ancl mereing of satellite galaxies (Gonzalez et al.," Indeed, results from recent studies of intracluster light support the idea that much of the light in the ICL comes from the stripping, disruption, and merging of satellite galaxies (Gonzalez et al." + 2005: Zibetti et al., 2005; Zibetti et al. + 2005)., 2005). + Consider a 1075ΣΑΙ. cluster. for which. the halo model predicts about eighty percent. of the stellar mass is associated with satellite galaxies: the rest is in the BCC or in the intracluster medium.," Consider a $10^{15}h^{-1}M_\odot$ cluster, for which the halo model predicts about eighty percent of the stellar mass is associated with satellite galaxies; the rest is in the BCG or in the intracluster medium." + IH the luminosity and color of the BCG. are observed (as is the case for the SDSS). reasonable assumptions about its stellar mass allow one to predict the stellar mass associated with the LOL.," If the luminosity and color of the BCG are observed (as is the case for the SDSS), reasonable assumptions about its stellar mass allow one to predict the stellar mass associated with the ICL." +" For example. the halo model says the BCG is about 4.5 times more luminous than the satellite galaxies brighter than Al,<19.9. and that there should be about TO such satellites."," For example, the halo model says the BCG is about 4.5 times more luminous than the satellite galaxies brighter than $M_r<-19.9$, and that there should be about 70 such satellites." + Lf the stellar mass to light ratio is independent of £L. (for the red. galaxies in a cluster this should. be a reasonable assumption). then," If the stellar mass to light ratio is independent of $L$ (for the red galaxies in a cluster this should be a reasonable assumption), then" +lt is becoming increasingly clear that the extreme ultraviolet (EUV) regime can provide unique insight into the phenomenon of active galactic nuclei (AGN).,It is becoming increasingly clear that the extreme ultraviolet (EUV) regime can provide unique insight into the phenomenon of active galactic nuclei (AGN). + Consider. for instance. the emerging subclass of AC: known as narrow-line Sevfert 1 galaxies (NLSIs).," Consider, for instance, the emerging subclass of AGN known as narrow-line Seyfert 1 galaxies (NLS1s)." + Phe extreme properties of NLSIs have prompted comparison with Galactic black hole candidates in their high states (Pounds. Done Osborne 1995) leading to the suggestion that they may represent a class of AGN in which accretion (onto a supermassive black hole) proceeds at à rate close to the Eddington limit (Ross. Fabian Mineshige 1992).," The extreme properties of NLS1s have prompted comparison with Galactic black hole candidates in their high states (Pounds, Done Osborne 1995) leading to the suggestion that they may represent a class of AGN in which accretion (onto a supermassive black hole) proceeds at a rate close to the Eddington limit (Ross, Fabian Mineshige 1992)." + These objects were first identified (Osterbrock Posee 1985: Goodrich 1989) by virtue of the fact that their optical permitted. lines are much. narrower (1.7 PWIA z2000 km/s) than in “normal” broacd-lIine Sevlert 1: galaxies 121919).," These objects were first identified (Osterbrock Pogge 1985; Goodrich 1989) by virtue of the fact that their optical permitted lines are much narrower $\beta$ FWHM $ \ls 2000 $ km/s) than in “normal"" broad-line Seyfert 1 galaxies (BLS1s)." + Llowever. more recently. largely on the basis of oobservations. NLSIs have also been shown to exhibit extremely soft X-ray spectra and to be variable in the soft X-ray band (Boller. Brandt Fink Ml199.," However, more recently, largely on the basis of observations, NLS1s have also been shown to exhibit extremely soft X-ray spectra and to be highly variable in the soft X-ray band (Boller, Brandt Fink 1996)." +" This. in nd""turn. suggests that an excellent wav ο construct a sample of NLSI objects might »e via EUV-selection."," This, in turn, suggests that an excellent way to construct a representative sample of NLS1 objects might be via EUV-selection." + Unfortunately. the dillieulties of working in at EUY wavelengths have until now prevented the definition. of complete and unbiased samples of EUW-bright extragalactic sources.," Unfortunately, the difficulties of working in at EUV wavelengths have until now prevented the definition of complete and unbiased samples of EUV-bright extragalactic sources." + These clillicultics include the relative insensitivity of instruments Lown to date compounded by the fact that most ines of sight to the extragalactic Universe are opaque in he EUY due to photoelectrie absorption in the interstellar medium of our Galaxy., These difficulties include the relative insensitivity of instruments flown to date compounded by the fact that most lines of sight to the extragalactic Universe are opaque in the EUV due to photoelectric absorption in the interstellar medium of our Galaxy. + During 1990. performed. an all-skv survey in both the soft. X-ray (0.12.4 keV) and EUV (602 V) bands.," During 1990, performed an all-sky survey in both the soft X-ray (0.1--2.4 keV) and EUV (60–210 eV) bands." +" “Phe former employed he XXN-ay telescope ancl position sensitive. detector (PSPC: Trümmper 1991) and the latter the coaligned Ul Wide Field €""amera (NEC: Sims 1990).", The former employed the X-ray telescope and position sensitive detector (PSPC; Trümmper 1991) and the latter the coaligned UK Wide Field Camera (WFC; Sims 1990). + Phe result has been the publication of the BBright Source Catalogue (RBSC: Voges 1996) and the WEC RE and 2RE catalogues. (Pounds 1993: Pye 1995)., The result has been the publication of the Bright Source Catalogue (RBSC; Voges 1996) and the WFC RE and 2RE catalogues (Pounds 1993; Pye 1995). +" dueHere we utilize the WEC all-sky survey database to the first reasonably large and complete sample of EUV-selectecl extragalactic objects. all of which are identified as AGN,"," Here we utilize the WFC all-sky survey database to produce the first reasonably large and complete sample of EUV-selected extragalactic objects, all of which are identified as AGN." + The remainder of this paper is organised. as follows., The remainder of this paper is organised as follows. + Me first discuss the selection criteria used to. define a preliminary list of LEUV-selected.: sources and then describe, We first discuss the selection criteria used to define a preliminary list of EUV-selected sources and then describe +that cick include the gravity of the stars (Pittard 1998: Stevens Pollock 1991) bad parameters that are not relevant toy Car. aud did not consider accretion.,"that did include the gravity of the stars (Pittard 1998; Stevens Pollock 1994) had parameters that are not relevant to $\eta$ Car, and did not consider accretion." + Iu the present study we conduct numerical simulatious of the collision of the two wiuds iu the y Car binary system., In the present study we conduct numerical simulations of the collision of the two winds in the $\eta$ Car binary system. + We perform Cartesian 3D uumerical simulations., We perform Cartesian 3D numerical simulations. + Our results suggestMO that accretion is very likely to occur Wear periastron passage., Our results suggest that accretion is very likely to occur near periastron passage. + There are some uncertainties as to the exact binary parameters of jj Car (Ixashi Soker 2000c)., There are some uncertainties as to the exact binary parameters of $\eta$ Car (Kashi Soker 2009c). + We here take the common parameters as used by many others. e.g. list of papers in section l.," We here take the common parameters as used by many others, e.g., list of papers in section 1." + The stellar inasses are AJ]=120A... aud M2BOAL.. the eccentricity is e=0.9. and the orbital period is 2021 days. hence the semi-major axis is ¢=16.61AU anc periastron occurs at ro—1.66AU.," The stellar masses are $M1 = 120 M_\odot$, and $M2 = 30 M_\odot$, the eccentricity is $e = 0.9$ , and the orbital period is $2024$ days, hence the semi-major axis is $a = 16.64 \AU$ and periastron occurs at $r = 1.66 \AU$." + The mass loss rates and velocities of the winds are Mq=3xLO1M.yr? and Mo=10M.vrLl and ey=500kms| and v»=3000lans.4. respectively.," The mass loss rates and velocities of the winds are $\dot M_1= 3 \times 10^{-4} M_\odot \yr^{-1}$ and $\dot M_2= 10^{-5} M_\odot \yr^{-1}$, and $v_1 = 500 \km \s^{-1}$ and $v_2 = 3000 \km \s^{-1}$, respectively." + The simulatious are performed with Virginia Hydrodsuamics-I (VH-1). a high resolution uultiduiueusioual astrophysical hydrodsuzinies code developed by Johu Bloucin aud. co-workers (Blondin et al.," The simulations are performed with Virginia Hydrodynamics-I (VH-1), a high resolution multidimensional astrophysical hydrodynamics code developed by John Blondin and co-workers (Blondin et al." + 1990: Stevens et al.," 1990; Stevens et al.," + 1992: Blondiu 1991)., 1992; Blondin 1994). + We have added radiative cooling to the code at all temperatures of T>2x107IX.," We have added radiative cooling to the code at all temperatures of $T > 2 +\times 10^4 \K$." + Namely. the radiative cooling is set to zero for temperatures of T«2x107Ix. but we allow adiabatic cooling to continue below that temperature.," Namely, the radiative cooling is set to zero for temperatures of $T<2 \times 10^4 \K$, but we allow adiabatic cooling to continue below that temperature." + adiative coolinge is carefully treated near contact discontiuuities. to prevent largee temperature eradients from causing unuplhivsical results.," Radiative cooling is carefully treated near contact discontinuities, to prevent large temperature gradients from causing unphysical results." + The cooling function A(T) Cor solar abundauces) is taken from Sutherland Dopita (1993: their table 6)., The cooling function $\Lambda (T)$ (for solar abundances) is taken from Sutherland Dopita (1993; their table 6). + Gravity by the secondary star is included. as this is the sole issue of this studs.," Gravity by the secondary star is included, as this is the sole issue of this study." + Iu two ruus we added the gravity of the primary star. and slow it cannot prevent accretion.," In two runs we added the gravity of the primary star, and show it cannot prevent accretion." + However. as the acceleration zone of the primary star is large aud we canuot add radiative pressure. the primary gravity is not fully sell-consistent.," However, as the acceleration zone of the primary star is large and we cannot add radiative pressure, the primary gravity is not fully self-consistent." + We start by imposiugOm undisturbed winds iu the numerical egrid. aud let the How reach a steady state without gravity.," We start by imposing undisturbed winds in the numerical grid, and let the flow reach a steady state without gravity." + Only then we turn ou gravity. aud let the flow reach the new steady state with the gravity included.," Only then we turn on gravity, and let the flow reach the new steady state with the gravity included." + The flow does not reach a strict steady state. but rather it posses au erratic motion of the winds collision region that we term wigeliug.," The flow does not reach a strict steady state, but rather it posses an erratic motion of the winds collision region that we term wiggling." + The collision region moves back auc forth. ie.. its distauce from the stars is not constant. and to the sides. ie.. the axi-svuunetry around the liue connecting the two stars is broken.," The collision region moves back and forth, i.e., its distance from the stars is not constant, and to the sides, i.e., the axi-symmetry around the line connecting the two stars is broken." + We perform the numerical simulations iu the Cartesian geometry Gr.gy.z) mode of the code (a 3D calculation).," We perform the numerical simulations in the Cartesian geometry $(x,y,z)$ mode of the code (a 3D calculation)." + Results are presented iu the (κιν) plane that contains the two stars.," Results are presented in the (x,y) plane that contains the two stars." + Iu most runs there were 112 equal-size grid points along each axis., In most runs there were 112 equal-size grid points along each axis. + The distance between the two stars is half the leneth of the x-axis., The distance between the two stars is half the length of the x-axis. + To coufirm the adequacy. of the resolutiou. we run one case with gravity. aud an orbital separation of r=2AU andwith 175 cells along each axis (instead of 112).," To confirm the adequacy of the resolution, we run one case with gravity and an orbital separation of $r=2 \AU$ andwith 175 cells along each axis (instead of 112)." + We found, We found +aud for the atlas and PSF images respectively.,and for the atlas and PSF images respectively. + requires a bandpass and object ID as inputs while cau output a SDSS-provided PSF at auv object position (given bvrowc. colc) ina given baucdpass.," requires a bandpass and object ID as inputs while can output a SDSS-provided PSF at any object position (given by, ) in a given bandpass." + There is no uuique procedure for deblending objects and defining their object-Ey boundaries on astronomical nuages., There is no unique procedure for deblending objects and defining their object-sky boundaries on astronomical images. + Two different approaches can be adopted to tackle this problem. aud these two approaches are excluplified by the SDSSPHOTO pipeline aud the SExtractor software (Bertin&Arnouts1996).," Two different approaches can be adopted to tackle this problem, and these two approaches are exemplified by the SDSS pipeline and the SExtractor software \citep{bertin96}." +. Both approaches are shown in Figure 3.., Both approaches are shown in Figure \ref{deblending-comparison}. + In tle case of SDSS debleudiug (Section ??)). the pipeline tries to isolate ιο flux in a given object to create a new nuage of what this object would look like if ouly this flux was shown.," In the case of SDSS deblending (Section \ref{sdss-deblend}) ), the pipeline tries to isolate the flux in a given object to create a new image of what this object would look like if only this flux was shown." + The object area of interest is then determined roni this new debleuded iaage., The object area of interest is then determined from this new deblended image. + It is iaportaut to note iat this object area may extend to areas that used to )o occupied by neighboring galaxies. auc may affect the photometry if some flux from the ucighboring galaxies rat were removed is left behind.," It is important to note that this object area may extend to areas that used to be occupied by neighboring galaxies, and may affect the photometry if some flux from the neighboring galaxies that were removed is left behind." + SExtractor deblending Section ??)) does uot attempt to create a new inage showing the deblended object., SExtractor deblending (Section \ref{sex-deblend}) ) does not attempt to create a new image showing the deblended object. + It uses a muiuti-thyeshold ucthod to look at the ux tree of the object in its original inge., It uses a multi-threshold method to look at the flux tree of the object in its original image. + As it moves up the tree goiug from one isophotal evel to the next. it looks at the fiux in each branch.," As it moves up the tree going from one isophotal level to the next, it looks at the flux in each branch." + If he flux ina brauch is above a set ήπια fraction of he total fux in the tree. then this brauch is deemed to )o a separate object altogether.," If the flux in a branch is above a set minimum fraction of the total flux in the tree, then this branch is deemed to be a separate object altogether." + Once all the objects have cen ideutified. SExtractor then produces a seguieutatiou nuage that assieus pixels to the different objects.," Once all the objects have been identified, SExtractor then produces a segmentation image that assigns pixels to the different objects." +" In the case of a ealaxy with a close neighbor. the uct result is a Urklee"" of scemmentation values at the saddle point )etwoeen the two adjaceut objects"," In the case of a galaxy with a close neighbor, the net result is a “ridge"" of segmentation values at the saddle point between the two adjacent objects." + The segmoeutation of an object never extends over the area occupied by its wighbors (see upper left-hand panel of Figure 3))., The segmentation of an object never extends over the area occupied by its neighbors (see upper left-hand panel of Figure \ref{deblending-comparison}) ). + It is clear from Figure 32. that cach object segmentatiou area nisses a significant fraction of the flux in the object jecause it spills over iuto the seenmentation area of its wighbor., It is clear from Figure \ref{deblending-comparison} that each object segmentation area misses a significant fraction of the flux in the object because it spills over into the segmentation area of its neighbor. + The SExtractor magnitudes measured from. hese areas would therefore svstematically uuderestiniate he brightuesses of the two objects., The SExtractor magnitudes measured from these areas would therefore systematically underestimate the brightnesses of the two objects. + However. if we also fit some surface brightness model (e.g.. bulee|disk) to he flux inside a given object segmentation area and hen iutegrate the fux in this model out to large radii. hen the missing flux is recovered.," However, if we also fit some surface brightness model (e.g., bulge+disk) to the flux inside a given object segmentation area and then integrate the flux in this model out to large radii, then the missing flux is recovered." + As we will show later. such combination of SExtractor deblendingend model photometry cau produce more reliable magnitudes aud colors in crowded environments.," As we will show later, such combination of SExtractor deblending model photometry can produce more reliable magnitudes and colors in crowded environments." + The atlas nuages provide object fluxes in pixels deemed to belong to the object bv the SDSS debleudiug aleorithii (Luptouctal.2001). and they have zero object fux evervwhere else.," The atlas images provide object fluxes in pixels deemed to belong to the object by the SDSS deblending algorithm \citep{lupton01}, and they have zero object flux everywhere else." +" The SDSS pipeline adds a constant ""softbias level of 1000 counts to all pixels in the atlas and PSF nuages.", The SDSS pipeline adds a constant “softbias” level of 1000 counts to all pixels in the atlas and PSF images. + This softbias level was subtracted from the nuages. so the atlas tuage skv jxel« therefore have a value of zero.," This softbias level was subtracted from the images, so the atlas image sky pixels therefore have a value of zero." + However. these atlas inages cannot be used as is for our morphological analysis.," However, these atlas images cannot be used as is for our morphological analysis." + The isophotal cut chosen to define iui object is oo high. aud the wines of galaxw profiles where uscful information can still be found have been truncated from hese images as a result of this choice.," The isophotal cut chosen to define an object is too high, and the wings of galaxy profiles where useful information can still be found have been truncated from these images as a result of this choice." + Our science Inunbnail images were therefore produced by extending he object pixel area in the atlas images using pixels roni the corrected damage of the field in which the object resides., Our science thumbnail images were therefore produced by extending the object pixel area in the atlas images using pixels from the corrected image of the field in which the object resides. + We van SExtractor ou the corrected ππασο to identity skv pixels., We ran SExtractor on the corrected image to identify sky pixels. + Pixels from the corrected lnaee were added to the science ΕΕΕΠ oulv if they were identified as sky. pixels., Pixels from the corrected image were added to the science thumbnail only if they were identified as sky pixels. + The mask image is a critical clement of the analysis as it specifies the object pixel brigltuess distribution that will be “seen” by the fitting algorithin.," The mask image is a critical element of the analysis as it specifies the object pixel brightness distribution that will be “seen"" by the fitting algorithm." + Mask pixels could take ou three different values: 1 (object). O (skv) aud 2 (excluded from fit).," Mask pixels could take on three different values: 1 (object), 0 (sky) and $-$ 2 (excluded from fit)." + Tuitially. our main consideration was to remain consistent with the object debleudiug performed by the SDSS pipeline.," Initially, our main consideration was to remain consistent with the object deblending performed by the SDSS pipeline." + We did not perform our own object deblending at first., We did not perform our own object deblending at first. + We used the atlas image itself as a starting point for the creation of the mask nuage., We used the atlas image itself as a starting point for the creation of the mask image. + For pixels in the mask nuage overlapping with the atlas image. we assigued them a value of 1 when the atlas nuage pixel value was greater than 1000 aud a value of | 2 otherwise.," For pixels in the mask image overlapping with the atlas image, we assigned them a value of 1 when the atlas image pixel value was greater than 1000 and a value of $-$ 2 otherwise." + We then used the SExtractor seeieutation duaee of the corrected image to complete the masks., We then used the SExtractor segmentation image of the corrected image to complete the mask. + Pixels iu the final iiask were assigued a value of lifatlas mask pixel value was 1 aud a value of 0 if atlas mask was 2 and SExtractor mask value was 0., Pixels in the final mask were assigned a value of 1 if atlas mask pixel value was 1 and a value of 0 if atlas mask was $-$ 2 and SExtractor mask value was 0. + The not result was a 1iask with the same dimensions as the atlas nuage but with more sky pixels than the original atlas jmaees that preserves the object debleudiug of the SDSS pipeline., The net result was a mask with the same dimensions as the atlas image but with more sky pixels than the original atlas images that preserves the object deblending of the SDSS pipeline. + The procedure for preparing GIM2D postage stamp nuages using SExtractor rather than SDSS debleudiug is considerably simpler., The procedure for preparing GIM2D postage stamp images using SExtractor rather than SDSS deblending is considerably simpler. + It starts directlv from the SDSS corrected nage frame on which the object is ocated., It starts directly from the SDSS corrected image frame on which the object is located. + SExtractor was run ou this corrected frame o ineasure the paruneters IMAGE. IMAGE. BACKGROUND. aud TIAIAGE using a value of 0.00005 for the SExtractor debleunding coutrast xuimeter DEBLENDMMINCONT aud a 1-7 isophote or the analvsis area.," SExtractor was run on this corrected frame to measure the parameters IMAGE, IMAGE, BACKGROUND, and IMAGE using a value of 0.00005 for the SExtractor deblending contrast parameter MINCONT and a $\sigma$ isophote for the analysis area." + The area extracted around cach object for the GIM2D postage stamp nuages was set o five times the area eiven by ISOAREATIAIACE., The area extracted around each object for the GIM2D postage stamp images was set to five times the area given by IMAGE. + The GIM2D decompositions were performed over al jxxels flageed as objector backeround in the SExtractor seenieutation image., The GIM2D decompositions were performed over all pixels flagged as object background in the SExtractor segmentation image. + Objects in the scementation images of the SDSS corrected frames are sharply deliucatec w the location of the isophote corresponding to the detection threshold) because SExtractor considers al κος below this ποιοί to be background pixels., Objects in the segmentation images of the SDSS corrected frames are sharply delineated by the location of the isophote corresponding to the detection threshold because SExtractor considers all pixels below this threshold to be background pixels. + Ilowever. precious information on the outer parts of he ealaxy profile μας. be contained iu the pixels vclow that threshold. and fits should therefore not ο restricted only to object pixels to avoid throwing hat information away (This is an analogous problem o the sharp isophotal Limit in SDSS atlas images).," However, precious information on the outer parts of the galaxy profile may be contained in the pixels below that threshold, and fits should therefore not be restricted only to object pixels to avoid throwing that information away (This is an analogous problem to the sharp isophotal limit in SDSS atlas images)." +with soft spectra to the X/K ratio.,with soft spectra to the X/K ratio. + Indeed. the data is roughly consistent with the Nj; dependence for emission with a power-law spectrum with the slope [=2.," Indeed, the data is roughly consistent with the $N_H$ dependence for emission with a power-law spectrum with the slope $\Gamma=2$." + The value obtained for the solar neighborhood also fits this dependence well., The value obtained for the solar neighborhood also fits this dependence well. + On the other hand. à much steeper dependence would be expected if a significant fraction (e.g. a half of the unabsorbed flux) of the 0.3—0.7 keV emission had a blackbody spectrum with temperature of 50 eV. This suggests that the contribution of sources with soft emission spectra. Το~SO—75 eV is not dominant.," On the other hand, a much steeper dependence would be expected if a significant fraction (e.g. a half of the unabsorbed flux) of the $0.3 - 0.7$ keV emission had a blackbody spectrum with temperature of $50$ eV. This suggests that the contribution of sources with soft emission spectra, $kT_{bb}\sim 50-75$ eV is not dominant." +" The discrepancy decreases quickly. with the temperature of the soft emission and becomes negligible for the blackbody temperature of &7,,-100 eV. which has approximately the same dependence as a I=2 power-law."," The discrepancy decreases quickly, with the temperature of the soft emission and becomes negligible for the blackbody temperature of $kT_{bb}\sim 100$ eV, which has approximately the same dependence as a $\Gamma=2$ power-law." + Therefore the contribution of the sources with harder spectra could not be constrained using this method., Therefore the contribution of the sources with harder spectra could not be constrained using this method. + Because of the remaining. dispersion in the data points caused by unknown systematic. effects. the data cannot be adequately fitted in a strict statistical sense by à combination of power-law and soft spectral components with. reasonable parameters.," Because of the remaining dispersion in the data points caused by unknown systematic effects, the data cannot be adequately fitted in a strict statistical sense by a combination of power-law and soft spectral components with reasonable parameters." + For this reason quantitative constraints on. the contribution of sources with soft spectra would not be feasible., For this reason quantitative constraints on the contribution of sources with soft spectra would not be feasible. +" However. the qualitative conclusion from the analysis of the Nj; dependence of the Ly/L, ratio generally agrees with the result of Sazonovetal.(2006).. who conclude that the emission from accreting white dwarfs contributes <1/3 to the Ly/Ly ratio of the solar neighborhood in the 0.1—2.4 keV energy band."," However, the qualitative conclusion from the analysis of the $N_H$ dependence of the $L_X/L_K$ ratio generally agrees with the result of \citet{sazonov}, who conclude that the emission from accreting white dwarfs contributes $ \lesssim 1/3 $ to the $L_X/L_K$ ratio of the solar neighborhood in the $ 0.1-2.4 $ keV energy band." +" We did not find any obvious correlations of the corrected Ly/L, ratios with the mass. metallicity (TerlevichForbes. 2002).. and age (Fig. 5))"," We did not find any obvious correlations of the sensitivity-corrected $L_X/L_K$ ratios with the mass, metallicity \citep{terlevich}, and age (Fig. \ref{fig:agedistribution}) )" + of the host galaxy., of the host galaxy. + In particular. we tentatively conclude that there is no significant difference between younger (~3—4 Gyrs) and older (~6—12 Gyrs) early-type galaxies in our sample (but see the comment at the end of Sect.," In particular, we tentatively conclude that there is no significant difference between younger $\sim 3-4$ Gyrs) and older $\sim 6-12$ Gyrs) early-type galaxies in our sample (but see the comment at the end of Sect." + 4.2. regarding the possible effect of the inconstant LMXB X/K ratio on the result of the sensitivity correction applied to the two youngest galaxies in our sample)., \ref{sec:xtokvalues} regarding the possible effect of the inconstant LMXB X/K ratio on the result of the sensitivity correction applied to the two youngest galaxies in our sample). + Using archival data. we measured the X-ray to K-band luminosity ratio in the 0.3—0.7 keV energy band in a sample of nearby gas-poor. early-type galaxies.," Using archival data, we measured the X-ray to K-band luminosity ratio in the $ 0.3-0.7 $ keV energy band in a sample of nearby gas-poor, early-type galaxies." + In computing the X/K ratios. we retained only those components of X-ray emission that could be associated with the emisstot of steady nuclear-burning white dwarfs. namely unresolved emission and emission of resolved supersoft sources.," In computing the X/K ratios, we retained only those components of X-ray emission that could be associated with the emission of steady nuclear-burning white dwarfs, namely unresolved emission and emission of resolved supersoft sources." + To this end. we excluded gas-rich galaxies from our sample and removed the contribution of resolved low-mass X-ray binaries.," To this end, we excluded gas-rich galaxies from our sample and removed the contribution of resolved low-mass X-ray binaries." + Our final sample contains seven external galaxies covering a broad range of stellar masses and galaxy ages., Our final sample contains seven external galaxies covering a broad range of stellar masses and galaxy ages. + It was complemented by the solar neighborhood data., It was complemented by the solar neighborhood data. + We measured a fairly uniform set of X/K ratios with an average value of Ly/Ly=(2.4404)-107ergs!Ly.," We measured a fairly uniform set of X/K ratios with an average value of $L_X/L_K=(2.4\pm0.4)\cdot 10^{27} \ \mathrm{erg \ s^{-1} \ L_{K,\odot}^{-1}}$." + The error associated with this number corresponds to the rms of the values obtained for individual galaxies., The error associated with this number corresponds to the rms of the values obtained for individual galaxies. + We estimated that unresolved low-mass X-ray binaries contribute ~15 per cent of this value., We estimated that unresolved low-mass X-ray binaries contribute $\sim 15$ per cent of this value. + We did not find any significant dependence of X/K ratios on the parameters of the galaxies. such as their mass. age. or metallicity.," We did not find any significant dependence of X/K ratios on the parameters of the galaxies, such as their mass, age, or metallicity." +" There appears to be a weak anti-correlation of X/K ratios with the galactic absorption column N,;.", There appears to be a weak anti-correlation of X/K ratios with the galactic absorption column $N_H$. +" The relative flatness of this dependence suggests that contribution of the sources with soft spectra Τρ,x50—75 eV to this ratio does not dominate.", The relative flatness of this dependence suggests that contribution of the sources with soft spectra $kT_{bb}\lesssim 50-75$ eV to this ratio does not dominate. + The remaining dispersion in the data points precludes more rigorous and quantitative conclusions., The remaining dispersion in the data points precludes more rigorous and quantitative conclusions. +Measurements of the abuudance of the Hsotope in stellar atmospheres are of considerable iuterest and have attracted much attention since the frst detection of in the metal-poor turnoff star by Sinith et al. (1993)).,Measurements of the abundance of the isotope in stellar atmospheres are of considerable interest and have attracted much attention since the first detection of in the metal-poor turnoff star by Smith et al. \cite{smith93}) ). + The reason for this interest is threefold: Detection of iu halo turnoff stars puts strong limits on the possible depletion ofLi. and thus allows better determination of the primordial aabunudauce from the observed Li abuudance of stars on the “Spite plateau. (," The reason for this interest is threefold: Detection of in halo turnoff stars puts strong limits on the possible depletion of, and thus allows better determination of the primordial abundance from the observed Li abundance of stars on the `Spite plateau'. (" +Copi ct al. 1997..,"Copi et al. \cite{copi97}," + Piusouncault et al. 1998]) , Pinsonneault et al. \cite{pin98}) ) +aabundauces as a fuuction of pprovide an additional test of theories for the production of the light clements Li. Be and D by interactions between fast nuclei aud aibieut oues (Ramaty et al. 1996...," abundances as a function of provide an additional test of theories for the production of the light elements Li, Be and B by interactions between fast nuclei and ambient ones (Ramaty et al. \cite{ramaty96}, ," + Yoshii et al. 1997..," Yoshii et al. \cite{yoshii97}," + Fields Olive 199943... Vangioni-Fhun et al. 1999).," Fields Olive \cite{fields99}, Vangioni-Flam et al. \cite{flam99}) )." + Tuformation ou depletion of as a function of stellar nass and metallicity puts new constraints on stellar models in addition to those set by dadepletion., Information on depletion of as a function of stellar mass and metallicity puts new constraints on stellar models in addition to those set by depletion. + This is so because the protou capture cross section of Hs nmceh lareer than that of‘, This is so because the proton capture cross section of is much larger than that of. +"Li, Heuce. at a given inetallicity there will be a mass interval. where bbut not lis being destroved according to standard stellar models (Chahover 199 1)."," Hence, at a given metallicity there will be a mass interval, where but not is being destroyed according to standard stellar models (Chaboyer \cite{cha94}) )." + Altoscther. aabunudauces may contribute to the study of such different fields as Big Bang uucleosvuthesis. cosmic ray plivsies aud stellar structure.," Altogether, abundances may contribute to the study of such different fields as Big Bang nucleosynthesis, cosmic ray physics and stellar structure." + It will. lowever. require a rather large data set of aabundances to ect information in all these areas.," It will, however, require a rather large data set of abundances to get information in all these areas." + The most 1netal-poor stars around the turnoff are of particular interest iu connection with the determinationof the primordial, The most metal-poor stars around the turnoff are of particular interest in connection with the determinationof the primordial +Ty=10! Ws. the upper limit to the radio source size would be very close to the diameter of the BLR. or ~4x10.7 pe.,"$T_{\rm B}\gtrsim 10^{10}$ K, the upper limit to the radio source size would be very close to the diameter of the BLR, or $\sim 4\times 10^{-3}$ pc." + This limit of about 2000 gravitational radii is comparable to the limits for several low-liminositv AGNs in galaxies found at similar distances (Ulvest2001:Andersonοἱal. 2004).," This limit of about 2000 gravitational radii is comparable to the limits for several low-luminosity AGNs in galaxies found at similar distances \citep{ulv01,and04}." +. The apparent flat-spectrum component δα. which appears relatively prominent at 15 GHz and not obvious at 8.4 GIIz. has a lower brightness temperature limit of Ty>5x10* Ix. This component could well represent a shock in the inner jet. less than 0.1 pe from the AGN.," The apparent flat-spectrum component D3a, which appears relatively prominent at 15 GHz and not obvious at 8.4 GHz, has a lower brightness temperature limit of $T_{\rm B} > 5\times 10^7$ K. This component could well represent a shock in the inner jet, less than 0.1 pc from the AGN." + One might speculate (hat D3a could be a location where the jet collides with material in the inner narrow-line region. as may be seen on larger scales (Muncdelletal.2003).," One might speculate that D3a could be a location where the jet collides with material in the inner narrow-line region, as may be seen on larger scales \citep{mun03}." +.. However. the inability of optical emission-line imaging lo probe a scale similar to that seen by VLBI makes it difficult to test (his possibility.," However, the inability of optical emission-line imaging to probe a scale similar to that seen by VLBI makes it difficult to test this possibility." + An alternative hypothesis for the flat-spectrum radio components would be that their spectral shapes are caused by Iree-[ree absorption bv ionizecl gas in the inner torus. line in front of svnchrotron-emitüng plasma.," An alternative hypothesis for the flat-spectrum radio components would be that their spectral shapes are caused by free-free absorption by ionized gas in the inner torus, lying in front of synchrotron-emitting plasma." + Since D3a ancl D3b have fairly [lat spectra between 8 and 15 Gllz. the presence of [ree-DIree absorption would imply an optical depth τιx1 al a frequency of ~10 GIIz: for a gas temperature near 8000 Ix. this implies an emission measure of n2dLzz3x105 “pe.," Since D3a and D3b have fairly flat spectra between 8 and 15 GHz, the presence of free-free absorption would imply an optical depth $\tau_{\rm ff}\approx 1$ at a frequency of $\sim 10$ GHz; for a gas temperature near 8000 K, this implies an emission measure of $n_e^2 dL\approx 3\times 10^8$ $^{-6}$ pc." + IE all of component D3 were enveloped in an ionized torus of radius 3 pe (Mundelletal.2003).. (hen (he average density in (hat torus (for a filling factor of unitv) would be ~10 7. somewhat below the value inferred by (2003).," If all of component D3 were enveloped in an ionized torus of radius $\sim 3$ pc \citep{mun03}, then the average density in that torus (for a filling factor of unity) would be $\sim 10^4$ $^{-3}$, somewhat below the value inferred by \citet{mun03}." +. ILowever. il seems apparent that (here is some steep-specirunm enission in D3 (e.g.. between D3a and D3b. as shown in Figure 5)).," However, it seems apparent that there is some steep-spectrum emission in D3 (e.g., between D3a and D3b, as shown in Figure \ref{fig:sliceD}) )." +" This would imply à very. patchy torus. and would make one wonder why the densest ionized gas ""coincidentallv lies in front of the radio components."," This would imply a very patchy torus, and would make one wonder why the densest ionized gas “coincidentally” lies in front of the radio components." + Thus. the more likely scenario for Iree-DIree absorption. if it caused the flat spectra. might be an ionized “skin” around the radio components.," Thus, the more likely scenario for free-free absorption, if it caused the flat spectra, might be an ionized “skin” around the radio components." +" This thermal gas would have a path length shorter than 0.1 pe. and therefore an ionized densitv n,210? emoM"""," This thermal gas would have a path length shorter than 0.1 pc, and therefore an ionized density $n_e \gtrsim 10^5$ $^{-3}$." + In fact. we consider the most likely inference to be that we have detected svnchrotron and no [ree-Iree absorption.," In fact, we consider the most likely inference to be that we have detected synchrotron self-absorption and no free-free absorption." +" Then. (he presence of some steep-spectrum radio enussion al 8 Gllz simply limits (he overall emission measure of a «quasi-uniform ionized medium: to S105NL Ga,""pc."," Then, the presence of some steep-spectrum radio emission at 8 GHz simply limits the overall emission measure of a quasi-uniform ionized medium to $\lesssim 10^8$ $^{-6}$ pc." + We note that (he flux density measured [ον component D3 at 15.3 GllIz is above the upper limit previously reported by Ulvestadetal.(1998)., We note that the flux density measured for component D3 at 15.3 GHz is above the upper limit previously reported by \citet{ulv98}. +. The difference might result from source variability by a factor of (wo. certainiy a viable possibility given the strong variability ol the hard and medium-energy. N-ravs from the galaxy nucleus (Perottial. 1994).," The difference might result from source variability by a factor of two, certainly a viable possibility given the strong variability of the hard and medium-energy X-rays from the galaxy nucleus \citep{per81,wea94}." +. However. the 1996.43 VLBI phliase-relerencing observations (Ulvestad also could have suffered Irom substantial loss of atmospheric coherence.," However, the 1996.43 VLBI phase-referencing observations \citep{ulv98} also could have suffered from substantial loss of atmospheric coherence." + In 2002.37. there was sienilicant coherence loss in (he initial phase referencing. which was recovered by (he use," In 2002.37, there was significant coherence loss in the initial phase referencing, which was recovered by the use" +Double-peaked. low-ionizalion broad lines are detected in over 150 AGNs now.,Double-peaked low-ionization broad lines are detected in over 150 AGNs now. + Most of these objects were discovered either during the spectroscopic survey of radio loud AGNs (Eracleous Halpern 2003. herealter E103) or curing the Sloan Digital Skv Survey (SDSS. Strateva οἱ al.," Most of these objects were discovered either during the spectroscopic survey of radio loud AGNs (Eracleous Halpern 2003, hereafter EH03) or during the Sloan Digital Sky Survey (SDSS, Strateva et al." + 2003. herealter $03).," 2003, hereafter S03)." + The incidence of such lines is particularly. hieh in racio loud AGNs (~20%.:; EIIO3). and in Low Ionization Nuclear Emission Line Reeions (LINERs) with broad emission lines (Shields et al.," The incidence of such lines is particularly high in radio loud AGNs $\sim$; EH03), and in Low Ionization Nuclear Emission Line Regions (LINERs) with broad emission lines (Shields et al." + 2000 and references therein)., 2000 and references therein). + The double-peaked line profile was proposed to be the characteristic feature of lines emitted [rom an accretion disk (Chen lIlalpern 1989. hereafter CIIS9). from a binary," The double-peaked line profile was proposed to be the characteristic feature of lines emitted from an accretion disk (Chen Halpern 1989, hereafter CH89), from a binary" +nuueasureiment together with the previous results is consistent with : constant spin-down rate.,measurement together with the previous results is consistent with a constant spin-down rate. + The observations are not vet sufficient to clearly ideutity any siguificaut variation from a constaut spiu-dowu rate., The observations are not yet sufficient to clearly identify any significant variation from a constant spin-down rate. + Iu the source5937.. departure frou a incar spin-down is already known (Alereehetti 1995:: Oosterbroeketal. 1998)).," In the source, departure from a linear spin-down is already known \cite{mere95a}; ; \cite{oost98}) )." + In this source. an order of inagnitude larger spin-down rate aud better pulse xriod immeasuremients (AP/P~ 9). owing to a Heh pulse fraction (~75%). help us to identity τος different epochs of spin-down history.," In this source, an order of magnitude larger spin-down rate and better pulse period measurements $({{\Delta {\rm P}} / {\rm P}} \sim $ $^{-6})$, owing to a high pulse fraction $(\sim 75\%)$, help us to identify three different epochs of spin-down history." + Though he method adopted for calculating the errors in the ulse period is not known for all the observations aud he uncertainty level is likely to be ποποσα. a constant spin-down trend cau be ruled out without any doubt.," Though the method adopted for calculating the errors in the pulse period is not known for all the observations and the uncertainty level is likely to be nonuniform, a constant spin-down trend can be ruled out without any doubt." + A linear fit to the pulse period history with the reported errors gives a reduced 4? of L500 for 11 degrees of freedom., A linear fit to the pulse period history with the reported errors gives a reduced $\chi ^2$ of 4500 for 11 degrees of freedom. + Including the 1998 oobservation (see Fieure 6) with the recent aud oobservatious. we find that from 1996 the source has a spiu-down rate of (1.67£0.02)«10lla 1," Including the 1998 observation (see Figure 6) with the recent and observations, we find that from 1996 the source has a spin-down rate of $(1.67 \pm 0.02) +\times 10^{-11}$ s $^{-1}$." + This is a factor of 2 smaller than the spin-down rate of (3.2940.03).10H s s+ during the 19911996 period., This is a factor of 2 smaller than the spin-down rate of $(3.29 \pm 0.03) \times 10^{-11}$ s $^{-1}$ during the 1994–1996 period. + The preseut spin-down rate is closer to the value of (1.520.5)«101 s &Ἐν measured durius theEinstein... aad oobservations made in the period 19791988.," The present spin-down rate is closer to the value of $(1.5 \pm 0.5) \times 10^{-11}$ s $^{-1}$, measured during the, and observations made in the period 1979–1988." +" The spin-down rate is nmch closer to beige constant caring hese three epochs with reduced X? of O8. 7.7. and 36 or 3. 3. and 1 deerees of freedom respectively,"," The spin-down rate is much closer to being constant during these three epochs with reduced $\chi ^2$ of 0.8, 7.7, and 36 for 3, 3, and 1 degrees of freedom respectively." + These two sources do uot show flux variability ou ine scales from a few Πίος to days., These two sources do not show flux variability on time scales from a few minutes to days. + Iu the oobservations of both the sources separated by E years we have found that the overall iuteusity aud spectral xuwanueters have remarkable stability., In the observations of both the sources separated by 4 years we have found that the overall intensity and spectral parameters have remarkable stability. + Ao differcuce tween the CIS aud SIS photon iudex that has oen found in61. is due to calibration uncertainties.," A difference between the GIS and SIS photon index that has been found in, is due to calibration uncertainties." + The spectral parameters obtained from 1e 1998 GIS and SIS observations are identical to the —99L values., The spectral parameters obtained from the 1998 GIS and SIS observations are identical to the 1994 values. + The spectral parameters obtained frou je slunultancous fitting of the CUS and SIS spectra re suunilaa to the vvalues obtained during 19971998., The spectral parameters obtained from the simultaneous fitting of the GIS and SIS spectra are similar to the values obtained during 1997–1998. + Tn61.. ie flux history shows a rius variatiou of around ic average value (Figure 5). aud multiple nieasuremenuts with the same instriuncut xl BeppoSAN)) eave alinost identical tux.," In, the flux history shows a rms variation of around the average value (Figure 5), and multiple measurements with the same instrument and ) gave almost identical flux." +" InΠΟΤΕ, 16 over all intensity durius the two oobservatious and one oobservation in between are within LOW of the average value."," In, the over all intensity during the two observations and one observation in between are within $10\%$ of the average value." + The 2.010.0 keV fluxes duriug the aand oobservations are estimated by extrapolating the nieasureimoenuts in the low cnerev bands of 0.2[.0 keV and 0.52.5 keV respectively. aud using a rather low photon iudex of 2.26. obtained byENOSAT.," The 2.0–10.0 keV fluxes during the and observations are estimated by extrapolating the measurements in the low energy bands of 0.2–4.0 keV and 0.5–2.5 keV respectively, and using a rather low photon index of 2.26, obtained by." +. The flux diving the oobservation ds estimated by coneriug the pulsed fluxes curving the aand oobservations and assmnuiuse that the pulse fraction remained same., The flux during the observation is estimated by comparing the pulsed fluxes during the and observations and assuming that the pulse fraction remained same. + The fiux measurements frou the previous observations as shown in the bottom paucl of Figure 6 are about a factor 3 higher than the receut nieasureiments with, The flux measurements from the previous observations as shown in the bottom panel of Figure 6 are about a factor 3 higher than the recent measurements with + , +he various components).,the various components). + Higher resolution optical spectra of the trace neutral species would. provide more stringent constraints on the temperature in the main component., Higher resolution optical spectra of the trace neutral species would provide more stringent constraints on the temperature in the main component. + Determination of the recombination behaviour ofCril.. as a function of temperature. would aid in understanding he hieh abundance of and the role of. dielectronic recombination.," Determination of the recombination behaviour of, as a function of temperature, would aid in understanding the high abundance of and the role of dielectronic recombination." + Continued. monitoring of the interstellar absorption toward these two stars could provide insights into he structure ancl properties of interface regions between warm and cool gas., Continued monitoring of the interstellar absorption toward these two stars could provide insights into the structure and properties of interface regions between warm and cool gas. + We are. grateful to M. Rejkuba anc Ας Cioni (ESO/Paranal) for their assistance with the UVES observations. to Thorburn for. performing initial oocessing of the UVES data. and to S. Nahar for communicating preliminary results on the recombination toCri.," We are grateful to M. Rejkuba and M.-R. Cioni (ESO/Paranal) for their assistance with the UVES observations, to J. Thorburn for performing initial processing of the UVES data, and to S. Nahar for communicating preliminary results on the recombination to." + T. S. acknowledges support from. RIEU erant NSE-1353854 to the University of Chicago., T. S. acknowledges support from REU grant NSF-0353854 to the University of Chicago. + This work has been supported ον NASA Long-Term Space Astrophysics grants XC-4445 and NAX5-114413 to the University of Chicago., This work has been supported by NASA Long-Term Space Astrophysics grants NAGW-4445 and NAG5-11413 to the University of Chicago. + The CGLIBGS data for HD. 72127. were originally obtained uncer NASA grant. 6O-2251.01-87X to the University. of Chicago., The GHRS data for HD 72127A were originally obtained under NASA grant GO-2251.01-87A to the University of Chicago. +the Einstein Telescope. and space detectors such as DECIGO.,"the Einstein Telescope, and space detectors such as DECIGO." +"Three iain radiation proccesses Considered to account for the uouthermal Αννα e1uüission iu knots and hot spots of tie extended jets discovered bv the are svuchrotron. svuchrotron scl-Conpon (SSC). and Compton scattering of externa plotous contributed imostlv bv the CBR (οιο,ος, IhurisandWrawezvuski(2002):Stawarz(2 OB).","Three main radiation processes considered to account for the nonthermal X-ray emission in knots and hot spots of the extended jets discovered by the are synchrotron, synchrotron self-Compton (SSC), and Compton scattering of external photons contributed mostly by the CMBR (e.g., \citet{hk02,sta03}) )." +" Ini X-ray knots of quasar jets with projected lengths 210) kpe. where the X-ray spectrum is nof a sooth exteusion of the radio/optical spectrun. a currentvo favored interpretation Is the external Compton (EC) model (TaveceΠωetal.2000:Celotti,Clisclliai.&Cliaberee200] )."," In X-ray knots of quasar jets with projected lengths $\gtrsim 100$ kpc, where the X-ray spectrum is not a smooth extension of the radio/optical spectrum, a currently favored interpretation is the external Compton (EC) model \citep{tav00,cgc01}." + Iu this model. the N-rav Cluission fron shots such as WIN7.8 of PISS 0637-752 is argued to due to CAIB photons that are Comptonpsc:uttered by nonthermal electrons from kpc-scale enting regious in bulk relativistic motion at οςalices up to several huudred kpc away frou the conral engine.," In this model, the X-ray emission from knots such as WK7.8 of PKS 0637-752 is argued to be due to CMB photons that are Compton-upscattered by nonthermal electrons from kpc-scale emitting regions in bulk relativistic motion at distances up to several hundred kpc away from the central engine." + We note. however. that iu the framework of this miodel it is problematic to explain a clear trend observed from many exteuded jets of radio quasars. such as of 3€ 273," We note, however, that in the framework of this model it is problematic to explain a clear trend observed from many extended jets of radio quasars, such as of 3C 273" +(5% )) radiative efficiency. then the luminosity of the jet is likely to exceed of the observed: X-ray luminosity. and is furthermore likely to scale linearly with the N-ray lux.,"$\la 5$ ) radiative efficiency, then the luminosity of the jet is likely to exceed of the observed X-ray luminosity, and is furthermore likely to scale linearly with the X-ray flux." + All this evidence supports a jet.disc “svmbiosis’ moclel Faleke Biermann 1996. L999) in which the jet luminosity is some fixed. and. probably large. fraction of the accretion uminositv.," All this evidence supports a jet–disc `symbiosis' model (Falcke Biermann 1996, 1999) in which the jet luminosity is some fixed, and probably large, fraction of the accretion luminosity." + The observed comparable correlation. between he radio (jet) ancl hard. X-ray. (Comptonised) emission in different svstems implies that these two components do not nave very dillerent beaming: this in turn implies that unless he hard. X-ray emission is stronely beamed (possibly via synchrotron seli-Compton in the jet) then the jet in the Low/llard state is unlikely to have a very large. Lorentz actor (D£55 or so)., The observed comparable correlation between the radio (jet) and hard X-ray (Comptonised) emission in different systems implies that these two components do not have very different beaming; this in turn implies that unless the hard X-ray emission is strongly beamed (possibly via synchrotron self-Compton in the jet) then the jet in the Low/Hard state is unlikely to have a very large Lorentz factor $\Gamma \la 5$ or so). + Further observations to determine the high-[requency extent of the [lat spectral component are οἱ great importance., Further observations to determine the high-frequency extent of the flat spectral component are of great importance. + Confirmation of a high fraction of the accretion luminosity being civertec into the jet during haud. power-law-cdominatecd X-ray spectral states will have great significance for our understanding of the accretion [ow near a black hole. not least. for models of advection-dominated accretion.," Confirmation of a high fraction of the accretion luminosity being diverted into the jet during hard, power-law-dominated X-ray spectral states will have great significance for our understanding of the accretion flow near a black hole, not least for models of advection-dominated accretion." + ] would like to thank many people including Stephane Corbel. Chris Done. Heino Faleke. 3ob Ljecllming. Ixinwah Wu. Catherine Brocksopp. Mariano Mendez. Chris Shracder and Michiel van der. Whis for useful discussions and information.," I would like to thank many people including Stephane Corbel, Chris Done, Heino Falcke, Bob Hjellming, Kinwah Wu, Catherine Brocksopp, Mariano Mendez, Chris Shrader and Michiel van der Klis for useful discussions and information." + In addition E would like to thank Luis guez and. Felix. Mirabel for supplying the maps presented in Fig 2., In addition I would like to thank Luis guez and Felix Mirabel for supplying the maps presented in Fig 2. + Finally E would like to thank the referee. Ralph Spencer. for many in-depth. comments. which helped. to improve the paper.," Finally I would like to thank the referee, Ralph Spencer, for many in-depth comments which helped to improve the paper." + This research has made use of the SIMDBAD database. operated at CDS. Strasbourg. France.," This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France." + RPE was supported during the initial period of this research by EC Marie Curie Fellowship ERBEAIBIC'T 972436., RPF was supported during the initial period of this research by EC Marie Curie Fellowship ERBFMBICT 972436. + [warmly thank the organizers of this enjoyable and interesting meeting for the invitation and the financial support.,I warmly thank the organizers of this enjoyable and interesting meeting for the invitation and the financial support. + I sincerely congratulate them for the success of their Gracduate School., I sincerely congratulate them for the success of their Graduate School. + This work has been partly supported by the Italian MURST through Cofin2000., This work has been partly supported by the Italian MURST through Cofin2000. +llere we assume that the Williamsetal.(1996) imunber counts are correct.,Here we assume that the \citet{W96} number counts are correct. + Comparing the n(Gn)-estimated oj; obtained using Williamsetal.(1996). data and SBF-measured The. it can be seen that the former are much larger.," Comparing the $n(m)$ -estimated $\sigma_{\rm BG}^2$ obtained using \citet{W96} data and SBF-measured $\sigma_{\rm BG}^2$, it can be seen that the former are much larger." + There are only two possible sources to account [ον Chis discrepancy: first. a faint unresolved stellar population. belonging to the Milky Way halo. could be responsible of the excess in the SBF signal: and second. the faint end of n(m) is different from the fitted one used here to evaluate the n(m)-estimated oj.," There are only two possible sources to account for this discrepancy: first, a faint unresolved stellar population, belonging to the Milky Way halo, could be responsible of the excess in the SBF signal; and second, the faint end of $n(m)$ is different from the fitted one used here to evaluate the $n(m)$ -estimated $\sigma_{\rm BG}^2$." + In the [inst case. SBF results may be used (to characterize such a halo population.," In the first case, SBF results may be used to characterize such a halo population." + In the second ease. SBF results may be used to deduce a new faint end of n(m) able to account [or the SBF-neasured oj.," In the second case, SBF results may be used to deduce a new faint end of $n(m)$ able to account for the SBF-measured $\sigma_{\rm BG}^2$." + We shall analyze both possibilities in detail ancl discuss the feasibility of each one and its compatibility with (he observations: finally. we shall deduce its implications for (i).," We shall analyze both possibilities in detail and discuss the feasibility of each one and its compatibility with the observations; finally, we shall deduce its implications for $n(m)$." + llere. we will consider a Milkv Way halo population of faint stars be responsible of the observed excess in (he SBF signal.," Here, we will consider a Milky Way halo population of faint stars be responsible of the observed excess in the SBF signal." + We will firstly deduce the halo population necessary {ο cause this SBF signal excess., We will firstly deduce the halo population necessary to cause this SBF signal excess. + In orcler to check the feasibility of (his hypothesis. the obtained halo population will then be compared with observations in the IIDE.," In order to check the feasibility of this hypothesis, the obtained halo population will then be compared with observations in the HDF." + Lets consider a simple population of objects with absolute magnitude M. following the standard spatial distribution used by Binney&Tremaine(1981): where p(r)dr is the number of objects per pc* at a distance from the Milkv Way center between kr and r+ dria ds the core radius. and po is the object density in the Milkv. Way center.," Lets consider a simple population of objects with absolute magnitude $M$ following the standard spatial distribution used by \citet{BT87}: where $\rho(r)dr$ is the number of objects per $^3$ at a distance from the Milky Way center between $r$ and $r+dr$; $a$ is the core radius, and $\rho_0$ is the object density in the Milky Way center." + For simpliciiwv we take a=2., For simplicity we take $\alpha=2$. + To derive the SBF signal from the former population. we must first express (he equations in terms of distance from the Sun (9).," To derive the SBF signal from the former population, we must first express the equations in terms of distance from the Sun $\delta$ )." + This can be clone using: where ry is the galactocentric radius. i.e.. the distance from the Sun to the Milkv. Way center. and (5.7) are galactic coordinates.," This can be done using: where $r_0$ is the galactocentric radius, i.e., the distance from the Sun to the Milky Way center, and $(b,l)$ are galactic coordinates." + The spatial distribution of objects expressed in, The spatial distribution of objects expressed in +aud the following section includes coments on a nunnber of the sources in these three categories.,and the following section includes comments on a number of the sources in these three categories. +"shows ai,max for η=0.7 (left figure) and η=5 (right figure).","shows $a_{\rm i,max}$ for $\eta=0.7$ (left figure) and $\eta=5$ (right figure)." +" In general, less mass loss leads to tidal engulfment at slightly larger distances."," In general, less mass loss leads to tidal engulfment at slightly larger distances." +" By coupling stellar evolution models with various tidal theories, we determined the maximum separation at which a companion might be tidally captured."," By coupling stellar evolution models with various tidal theories, we determined the maximum separation at which a companion might be tidally captured." +" Companions slightly exterior to di,max are never engulfed by the envelope of the primary but their orbital dynamics are still subject to the effects of mass loss and tidal torques."," Companions slightly exterior to $a_{\rm i,max}$ are never engulfed by the envelope of the primary but their orbital dynamics are still subject to the effects of mass loss and tidal torques." +" By continuing to follow the orbital evolution, we can predict the minimum final separation for each binary configuration."," By continuing to follow the orbital evolution, we can predict the minimum final separation for each binary configuration." + The minimum of this set is the minimum separation exterior to which one would expect to find planetary companions around white dwarfs., The minimum of this set is the minimum separation exterior to which one would expect to find planetary companions around white dwarfs. +" In the following two sections, we determine the maximum separation at which a companion can survive CE evolution."," In the following two sections, we determine the maximum separation at which a companion can survive CE evolution." +" Interior to this separation, we would expect to find companions to white dwarfs."," Interior to this separation, we would expect to find companions to white dwarfs." +" Taken together, the minimum and maximum form a separation gap between which we expect an absence of planetary and brown dwarf companions around white dwarfs."," Taken together, the minimum and maximum form a separation gap between which we expect an absence of planetary and brown dwarf companions around white dwarfs." +" For the solar system, tides and mass-loss compete and determine whether the inner planets plunge into the Sun or evade tidal engulfment (??).."," For the solar system, tides and mass-loss compete and determine whether the inner planets plunge into the Sun or evade tidal engulfment \citep{Rybicki:2001fk, Sackmann:1993lr}." +" Under the assumption f=1, Venus plunges into the Sun for all of our 1 Mo evolutionary models."," Under the assumption $f=1$, Venus plunges into the Sun for all of our 1 $M_\odot$ evolutionary models." +" Earth however, evades tidal engulfment with the orbit expanding for all of our evolutionary models, consistent with the results of ?.."," Earth however, evades tidal engulfment with the orbit expanding for all of our evolutionary models, consistent with the results of \citet{Rasio:1996yq}." +" In addition, none of the planets beyond Earth are swallowed."," In addition, none of the planets beyond Earth are swallowed." +" Upon tidal engulfment, the companion enters a common envelope with the primary star (??7)."," Upon tidal engulfment, the companion enters a common envelope with the primary star \citep{Paczynski:1976fj, Iben:1993kx, Nordhaus:2006oq}." + The velocity difference between the orbital motion of the companion and the common envelope generates drag., The velocity difference between the orbital motion of the companion and the common envelope generates drag. + The resulting loss of orbital energy leads to rapid in-spiral on week- to month-timescales (?).., The resulting loss of orbital energy leads to rapid in-spiral on week- to month-timescales \citep{Nordhaus:2006oq}. + The orbital energy released as the companion in-spirals can be used to overcome the binding energy of the envelope., The orbital energy released as the companion in-spirals can be used to overcome the binding energy of the envelope. +" If sufficient energy is released from the orbit during in-spiral, the companion can eject the envelope and survive the CE."," If sufficient energy is released from the orbit during in-spiral, the companion can eject the envelope and survive the CE." +" This is expressed as the following: where Epina is the binding energy of the envelope, a is the fraction of orbital energy that goes toward ejecting the envelope and AE, is the change in orbital energy of the companion."," This is expressed as the following: where $E_{\rm bind}$ is the binding energy of the envelope, $\alpha$ is the fraction of orbital energy that goes toward ejecting the envelope and $\Delta E_{\rm orb}$ is the change in orbital energy of the companion." +" The change in orbital energy of the companion is given aS Éorb,n,—Éorb,a, Where Forb,r, is the orbital energy at tidal engulfment (a= Εικ) and Eorb,a is the orbital energy at semimajor axis a inside the CE (ie. a«R,)."," The change in orbital energy of the companion is given as $E_{{\rm + orb},R_\star} - E_{{\rm orb},a}$, where $E_{{\rm orb},R_\star}$ is the orbital energy at tidal engulfment $a = R_\star$ ) and $E_{{\rm + orb}, a}$ is the orbital energy at semimajor axis $a$ inside the CE (i.e. $a1." +According to equation (13)) this critical angular frequency. corresponds to optically thick reeiue onlv ifieosmasQUILOEO]lo).," According to equation \ref{eq:tau_thick}) ) this critical angular frequency corresponds to optically thick regime only if$\dot m\gtrsim +\alpha_{\nu}^{(10+4\beta)/(7+4\beta)}$." +" In the optically thin case background viscosity reeulates disk at ⋅≻↴⋅⋅⋅≻↴PFO «d., and this ον corresponds to 7<1 provided that iiXap(UpLayer|ls ."," In the optically thin case background viscosity regulates disk at , <1, and this $\omega_\nu$ corresponds to $\tau<1$ provided that $\dot m\lesssim +\alpha_{\nu}^{(10+4\beta)/(7+4\beta)}$ ." +" Tuside the region where the background viscosity dominates (at woo w,) equations governing disk structure change.", Inside the region where the background viscosity dominates (at $\omega>\omega_\nu$ ) equations governing disk structure change. + Previously. when considering the eravitoturbulent transport. we did not have a constraiut ou a but instead had a relationship between T anc “in the form of equation (12)). ariing from the requirement of the marginal eravitational instability.," Previously, when considering the gravitoturbulent transport, we did not have a constraint on $\alpha$ but instead had a relationship between $T$ and $\Sigma$ in the form of equation \ref{eq:T}) ), arising from the requirement of the marginal gravitational instability." + However. with the backeround viscosity dominating the aneular momentum transport a is constraüued to be equal to αν. Which leads to an overdetermined svsteni of equations if we also try to keep the condition Q= Qu.," However, with the background viscosity dominating the angular momentum transport $\alpha$ is constrained to be equal to $\alpha_{\nu}$ , which leads to an overdetermined system of equations if we also try to keep the condition $Q=Q_0$ ." + This contradiction is naturally avoided by dropping the latter coustraint. ic. allowing the disk uot to bemareinally eravitatioually unstable when aΞ αν.," This contradiction is naturally avoided by dropping the latter constraint, i.e. allowing the disk not to bemarginally gravitationally unstable when $\alpha=\alpha_\nu$ ." +of the quantity.,of the quantity. + Because we did not know the true nature of observed period changes of P(t) we chose standard low-orders polynomials for their description., Because we did not know the true nature of observed period changes of $P(t)$ we chose standard low-orders polynomials for their description. + The period changes P(r) (see refFigcu)) can be adequately approximated by a cubic parabola with the origin at the time ¢=Το. where A and /7 are parameters expressing the amplitude and timescale of the observed period changes. and @ is à time- function.," The period changes $P(t)$ (see \\ref{Figcu}) ) can be adequately approximated by a cubic parabola with the origin at the time $t=T_0$, where $A$ and $\mathit{\Pi}$ are parameters expressing the amplitude and timescale of the observed period changes, and $\mathit{\Theta}$ is a time-like function." +" The instant period P(t) reaches its local extrema Po€A at Qj»=c, where Pp is the period at the time of (6=0)Ty."," The instant period $P(t)$ reaches its local extrema $P_0\mp A$ at $\mathit{\Theta}_{1,2}=\mp\textstyle{\frac{1}{2}}$, where $P_0$ is the period at the time of $t(\mathit{\Theta}=0)=T_0$." + The value /7 then equals the duration of the rotation deceleration epoch that took place in the time interval tra2To*ig.," The value $\mathit{\Pi}$ then equals the duration of the rotation deceleration epoch that took place in the time interval $t_{1,2}=T_0\mp\textstyle{\frac{1}{2}}\mathit{\Pi}$." + Applying the equality #=1/P(r). we obtain the following approximation for the phase function in the form of the order polynomial of time where y is the phase function for a linear ephemeris with the origin at My=2446730.4447 and the basic period Po.," Applying the equality $\dot{\vartheta}=1/P(t)$, we obtain the following approximation for the phase function in the form of the fourth-order polynomial of time where $\vartheta_0$ is the phase function for a linear ephemeris with the origin at $M_0 \equiv 2\,446\,730.4447$ and the basic period $P_0$." +" Using the above formulated phenomenological model. we derive Py= 0/52069415(8). 7=13260070)d36.29(19) yr. Ty=2446636(24) or 1986.56(7). A=1.915(10) s. and B=0.5643(29) d. The period P(r) reached its local minimum im the year 1968.4. Pj=0152067198(7). and its local maximum in 2004.7: P4,=0152071631018)."," Using the above formulated phenomenological model, we derive $P_0 = +0\fd52069415(8)$ , $\mathit{\Pi} = 13260(70)\,\mathrm{d} = 36.29(19)$ yr, $T_0 = 2\,446\,636(24)$ or 1986.56(7), $A = 1.915(10)$ s, and $B=0.5643(29)$ d. The period $P(t)$ reached its local minimum in the year 1968.4, $P_{\mathrm{min}}= 0\fd52067198(7)$, and its local maximum in 2004.7: $P_{\mathrm{max}}= 0\fd52071631(18)$." + The rotational deceleration rate reached its maximum P= O0.I58ssyyr! in the year 1986.6., The rotational deceleration rate reached its maximum $\dot{P}=0.158$ $^{-1}$ in the year 1986.6. +" The zero phase times of ccan be evaluated using the relation JD(K)Biτος— 0.4), where K is an integer and ὃς=(My+Pok—To/ H."," The zero phase times of can be evaluated using the relation $\textit{JD}(k)\cong +M_0+P_0\,k+B\,(\textstyle{\frac{3}{2}}\mathit{\Theta_k}^2-\mathit +{\Theta_k}^4)$ , where $k$ is an integer and $\mathit{\Theta}_k=(M_0+P_0\,k-T_0)/\mathit{\Pi}$ ." + The basic model fits the observed long-term period changes very well and enables us to predict the zero phase times with an accuracy of 0.001 d. However. the analysis of the residuals from the accepted polynomial model reveals an additional variation.," The basic model fits the observed long-term period changes very well and enables us to predict the zero phase times with an accuracy of 0.001 d. However, the analysis of the residuals from the accepted polynomial model reveals an additional variation." + Between 1988 and 1998. for which there i5 excellent photometric coverage (Adelmanetal.1992:Pyper1998).. we find a small modulation of the period on a timescale of several years refFigdetail)).," Between 1988 and 1998, for which there is excellent photometric coverage \citep{ade92,pyper98}, we find a small modulation of the period on a timescale of several years \\ref{Figdetail}) )." + For the phase function of wwe adopted polynomials in the form of the third-order expansion. also used in Mikuláseketal.(2008): where Ó 1s the phase function for the linear ephemeris with the origin at Mo.," For the phase function of we adopted polynomials in the form of the third-order Taylor-expansion, also used in \citet{mik901}: where $\vartheta_0$ is the phase function for the linear ephemeris with the origin at $M_0$." + Po and Po are the instantaneous period and its first derivative at Mo., $P_0$ and $\dot{P}_0$ are the instantaneous period and its first derivative at $M_0$. + We assumed that the second derivative of the period. P. is constant throughout the interval of observations.," We assumed that the second derivative of the period, $\ddot{P}$, is constant throughout the interval of observations." +" We put the origin. Mo=2449967.969(5). at a brightness maximum (in 1999),"," We put the origin, $M_0 = 2\,449\,967.969(5)$, at a brightness maximum (in 1999)." + Our fitted parameter values include the instantaneous period at time Ma. and Py=1130.7)x10?=0356(Q3)ss yyr! and P=—44(6)x107do!=—1.38(19)x102 yyr7. the first and second time derivatives.," Our fitted parameter values include $P_0 = 1\fd538756(3)$ , the instantaneous period at time $M_0$, and $\dot{P}_0 = +11.3(0.7)\times 10^{-9} = 0.356(23)$ $^{-1}$ and $\ddot{P}=-4.4(6)\times +10^{-12}\mathrm{d}^{-1}=-1.38(19)\times10^{-5}$ $^{-2}$, the first and second time derivatives." + The negative value of P is now established with 74r certainty., The negative value of $\ddot{P}$ is now established with $\sigma$ certainty. + Accordingly. the star reached its longest period. Pray=115387709(15). in 2002.8+L1. and is now accelerating again (see refFig901)).," Accordingly, the star reached its longest period, $P_{\mathrm{max}}= 1\fd5387709(15)$, in $2002.8\pm1.1$, and is now accelerating again (see \\ref{Fig901}) )." +" The zero-phase timing can be calculated by the relation DU)=Mo+Potkπαλ.PSPΚΟ, where k is an integer."," The zero-phase timing can be calculated by the relation $\textit{JD}(k)\cong +M_0+P_0\,(k+\textstyle{\frac{1}{2}}\dot{P}_0\,k^2+ +\textstyle{\frac{1}{6}}P_0\ddot{P}\,k^3)$, where $k$ is an integer." + There is no indication of any short-term period modulation analogous to that seen inVir., There is no indication of any short-term period modulation analogous to that seen in. +. We were able to reveal unexpected alternating lengthenings and shortenings in the periods of aand oowing to simultaneous processing of all available observational material obtained during many decades. including our own observations made in 2007-11.," We were able to reveal unexpected alternating lengthenings and shortenings in the periods of and owing to simultaneous processing of all available observational material obtained during many decades, including our own observations made in 2007–11." + The period evolutions of both stars were modelled by polynomials of low degrees., The period evolutions of both stars were modelled by polynomials of low degrees. + In the case of wwe also tested a fit with a harmonie function (Mikulaseketal. and a Gaussian functioncorresponding to the transient nature of the phenomenon., In the case of we also tested a fit with a harmonic function \citep{unstead} and a Gaussian functioncorresponding to the transient nature of the phenomenon. + The only differences among them are noticeable at the very beginning of our observations. which slightly favour the latter two alternatives.," The only differences among them are noticeable at the very beginning of our observations, which slightly favour the latter two alternatives." + The possible harmonie-like changes of the observed periods of both stars together with the strict constancy of the, The possible harmonic-like changes of the observed periods of both stars together with the strict constancy of the + During the past wear. a suite of jw nearinfrared (NIR) surveys has exteuded the searedl for starforming ealaxies to redshift 6.5<2.x10 using the well Lxiuaubreak technique (Cuewalisco2002.audreferences therein).," During the past year, a suite of new near–infrared (NIR) surveys has extended the search for star–forming galaxies to redshift $6.5 \leq +z\leq 10$ using the well--proven Lyman–break technique \citep[][and +references therein]{Giavalisco2002}." + With respect to ower redshift. the munhber density of UV.selected. galaxies decreases (6.9..2010:Bowweusetal.2010a:Willàus€tt 2OLOD).. their UV contimmun becomes bluer implyπιο either reduced dust obscuration or poorer metal ewichinent or both (oe.Finkelsteinetal.2009:Dowweusot20105:Schaerer&deBarros 2010).. aud treir stellar masses are. oni average. stnaller than those of their lower redshift counterparts (ee...Labbéetal.201n.," With respect to lower redshift, the number density of UV–selected galaxies decreases \citep[e.g.,][]{Ouchi2009, Mclure2009b, + Castellano2010, Bouwens2009b, Wilkins2010}, their UV continuum becomes bluer implying either reduced dust obscuration or poorer metal enrichment or both \citep[e.g.,][]{Finkelstein2009,Bouwens2010b,Schaerer2010}, and their stellar masses are, on average, smaller than those of their lower redshift counterparts \citep[e.g.,][]{Labbe2010}." + Unfortunately. these results are based on color-selected samples with no spectroscopic validation.," Unfortunately, these results are based on color-selected samples with no spectroscopic validation." + At the time of writing. spectroscopic detections of only a few incividual objects have been obtained at z26.6 (Iveetal.2006:Greiner2009)..," At the time of writing, spectroscopic detections of only a few individual objects have been obtained at $z>6.6$ \citep{Iye2006,Greiner2009,Salvaterra2009,Tanvir2009}." + The lack of knowledge of the true redshifts of the curent +~T candidates places significant lmitatk-y. on our ability to robustly measure the properties of the ealaxies at this critical cosmic epoch., The lack of knowledge of the true redshifts of the current $z\sim 7$ candidates places significant limitations on our ability to robustly measure the properties of the galaxies at this critical cosmic epoch. + For example. the yaction of imterlopers aud the redslift distribution of he sample galaxies are uccessary to robustly measure he UV huumositv fiction (¢.e..Reddy&Steidel 20093.," For example, the fraction of interlopers and the redshift distribution of the sample galaxies are necessary to robustly measure the UV luminosity function \citep[e.g.,][]{Reddy2009}." +. Currently. the former renmiidns uuknuown. aud the atter is estimated with Monte Carlo siunlatious wader various assuniptious for the iutriusic (listributions of UV spectral cuerey distribution (SED). surface brightucss iuid imorphologv. with the result that the measure of the huninosity function remains subject to uucontrolled svstematic errors.," Currently, the former remains unknown, and the latter is estimated with Monte Carlo simulations under various assumptions for the intrinsic distributions of UV spectral energy distribution (SED), surface brightness and morphology, with the result that the measure of the luminosity function remains subject to uncontrolled systematic errors." + Iu practice. Oogiven the maried decrease in seusitivitv of current spectroscopic observations at increasing redshift. the spectral confirmation of galaxies at :>5Γ relies heavily on their enussion liue. (Starketal.2010:Vanzella2009.SIOanV09inthe following).," In practice, given the marked decrease in sensitivity of current spectroscopic observations at increasing redshift, the spectral confirmation of galaxies at $z>5$ relies heavily on their emission line, \citep[][S10 and V09 in the following]{Stark2010, + Vanzella2009}." +. Indeed. redshifts derived without typically have lower confidence. although their umber may be comparable (Douglasetal.2010.D10inthe followiug)..," Indeed, redshifts derived without typically have lower confidence, although their number may be comparable \citep[][D10 in the following]{Douglas2010}." + The line in itself is au important (liaguostic of pliysical processes at work in the galaxies (e.g...Cuüavaliscoetal.1996:Peutericci2010:Shapleyetal. 2003).. since its streneth and velocity xofile depeud on the instantancous star-formation rate. (lust content. metallicity. kiuneniatics aud ecometry of he interstellar wedi.," The line in itself is an important diagnostic of physical processes at work in the galaxies \citep[e.g.,][]{Giavalisco1996,Pentericci2010,Shapley2003}, since its strength and velocity profile depend on the instantaneous star-formation rate, dust content, metallicity, kinematics and geometry of the interstellar medium." + Particularly relevant here is he evidence that the fraction of cutters iu selected samples increases with redshift (VWOO.SLOReddyowing) and that the fraction of galaxies with a larec equivalent width (EW) is substantially larger at zduter UV Iuninosities.," Particularly relevant here is the evidence that the fraction of emitters in UV--selected samples increases with redshift \citep[V09,S10][S07 in +the following]{Reddy2009,Stanway2007} and that the fraction of galaxies with a large equivalent width (EW) is substantially larger at fainter UV luminosities." + Finally. the very visibility of the line during the (ding phases of the cosiuic reionization is subject to he damping effect of an iucreasing neutral intergalactic neditun (IGM) (e...Zheneetal.2010:Davalct 2010).. expected to attenuate most of its luminosity aud uake the earliest galaxies consequently more difficult to identify.," Finally, the very visibility of the line during the ending phases of the cosmic re–ionization is subject to the damping effect of an increasing neutral intergalactic medium (IGM) \citep[e.g.,][]{Zheng2010,Dayal2010b}, , expected to attenuate most of its luminosity and make the earliest galaxies consequently more difficult to identify." + Heuce. the line profile aud. the evolutiou of its," Hence, the line profile and the evolution of its" +"spatial resolution, evidencing a cascade of spatial scales in the internetwork.","spatial resolution, evidencing a cascade of spatial scales in the internetwork." + The very quict Sun magnetism is thus very complex and we are forced to employ sophisticated statistical modeling tools to infer its properties., The very quiet Sun magnetism is thus very complex and we are forced to employ sophisticated statistical modeling tools to infer its properties. +"Simulation was performed with exactly the same setup as(G09b),, but with eight times less particles.","Simulation was performed with exactly the same setup as, but with eight times less particles." + This leads to a two times lower spatial resolution., This leads to a two times lower spatial resolution. +" Nevertheless, the morphology is comparable to the high resolution case (Fig 3,, panel 2)."," Nevertheless, the morphology is comparable to the high resolution case (Fig \ref{FIG_compare}, panel 2)." + The only noticeable difference is that the second largest structure in this case has already merged with the third structure., The only noticeable difference is that the second largest structure in this case has already merged with the third structure. +" Furthermore, tiny structures are less frequent."," Furthermore, tiny structures are less frequent." + The physical properties (see Table 2)) are similar as well., The physical properties (see Table \ref{TAB_compare}) ) are similar as well. +" The structures in the low resolution case tend to be a bit more massive, which can be expected."," The structures in the low resolution case tend to be a bit more massive, which can be expected." +" Altogether, the morphology and the global physical properties are comparable and thus, we conclude that is reasonably converged."," Altogether, the morphology and the global physical properties are comparable and thus, we conclude that is reasonably converged." + In the other test case we investigate the boundary condition in the negative x-direction., In the other test case we investigate the boundary condition in the negative x-direction. + In this boundary is not reflecting., In this boundary is not reflecting. + Instead the gas is allowed to stream away freely., Instead the gas is allowed to stream away freely. + This leads subsequently to a lower density in the ionized region., This leads subsequently to a lower density in the ionized region. +" As a consequence (Fig. 3,,"," As a consequence (Fig. \ref{FIG_compare}," +" panel 3) looks similar to (panel 8, see 3.5)) as the radiation is able to penetrate further into the computational domain."," panel 3) looks similar to (panel 8, see \ref{RES_flux}) ), as the radiation is able to penetrate further into the computational domain." +" Nevertheless, the formation of pillars still takes place and is not strongly affected."," Nevertheless, the formation of pillars still takes place and is not strongly affected." + Even density and mass assembly of the most prominent structure are alike., Even density and mass assembly of the most prominent structure are alike. +" T'herefore, the choice of the boundary condition does not influence the overall scenario significantly."," Therefore, the choice of the boundary condition does not influence the overall scenario significantly." + As it is more realistic to assume hot gas is already present in the region between the ionizing source and the simulated part of the molecular cloud we keep the reflecting boundary condition in all other simulations., As it is more realistic to assume hot gas is already present in the region between the ionizing source and the simulated part of the molecular cloud we keep the reflecting boundary condition in all other simulations. + These reflection can be interpreted as flux conservation at the left border of the simulation: as much gas streams from the area towards the source into the region as is streaming outwards., These reflection can be interpreted as flux conservation at the left border of the simulation: as much gas streams from the area towards the source into the region as is streaming outwards. +Such type of photometric variability is seen on the long-term light curves of GAL Cop constructed by Xiao et al. (,Such type of photometric variability is seen on the long-term light curves of GM Cep constructed by Xiao et al. ( +2010).,2010). + The authors indicate that the variability of GAL Cep is more likely due to dips caused by extinction iustead of outbursts caused by accretion., The authors indicate that the variability of GM Cep is more likely due to dips caused by extinction instead of outbursts caused by accretion. + The search for periodicity performed by Xiao et al. (, The search for periodicity performed by Xiao et al. ( +2010) show no siguificaut periods iu the range between 0.5 and 100 davs.,2010) show no significant periods in the range between 0.5 and 100 days. + But periods of longer duration are not excluded and the collection of a lone set of homogeneous multicolor observatious cau be used in a new search for periodicity., But periods of longer duration are not excluded and the collection of a long set of homogeneous multicolor observations can be used in a new search for periodicity. + Using our photometric data the color-magnitude diagrams of GM Cop are constructed aud presented ou Fig., Using our photometric data the color-magnitude diagrams of GM Cep are constructed and presented on Fig. + 3., 3. + The values of the three color indices Bo V. VR and V. Foe plotted according to the V stellar magnitude.," The values of the three color indices $B-V$ , $V-R$ and $V-I$ are plotted according to the $V$ stellar magnitude." + The observed change of color iudices sugecst for exisence of a color reversal in the nininma helt. a typical feature of the PMS stays from UNor type.," The observed change of color indices suggest for existence of a color reversal in the minimum light, a typical feature of the PMS stars from UXor type." + The result is evience that the variability of GAL Cep is dominated by variable extinction from the circuuusteHar euvironmenut., The result is evidence that the variability of GM Cep is dominated by variable extinction from the circumstellar environment. + The effect of color reversal (or co-called πιο} has been studied aud explained by mauv authors (Bibo The 1990. Caimin et al.," The effect of color reversal (or co-called ""blueing"") has been studied and explained by many authors (Bibo Thé 1990, Grinin et al." + 1991. Grady et al.," 1994, Grady et al." + 1995. Tlerbst Shevehcuke 1999).," 1995, Herbst Shevchenko 1999)." + The widely accepted explanation of color reversal effect js Vvarlatious of [ume column density of dust in the line of sight to re star. but the nature aud origin of these dust nips or filaments is still debated.," The widely accepted explanation of color reversal effect is variations of the column density of dust in the line of sight to the star, but the nature and origin of these dust clumps or filaments is still debated." + According to 1e niodoel of dust cbunips obscuration (ui alternative nool see in Herbst Shevchenko 1999) he observed color reversal is caused by the scattered light from je sinall dust eraius., According to the model of dust clumps obscuration (an alternative model see in Herbst Shevchenko 1999) the observed color reversal is caused by the scattered light from the small dust grains. + Normally the stay becomes redder when its lelt is covered bv dust clumps or filaments on the line of sight., Normally the star becomes redder when its light is covered by dust clumps or filaments on the line of sight. + Du when the obscuration rises sufficiently the part of the scattered in the total observed Leht become siguificaut the star color ects bluer., But when the obscuration rises sufficiently the part of the scattered light in the total observed light become significant and the star color gets bluer. + Simmltancously with the decrease iu brightucss the percentage of polarization in the optical light imereases dramatically (πι et al., Simultaneously with the decrease in brightness the percentage of polarization in the optical light increases dramatically (Grinin et al. + 1991)., 1994). + One of the first explanations of this phenomenon is hat the sars are surrounded by uuuber of protocometary clous or cometary bodies (Curadyv et al., One of the first explanations of this phenomenon is that the stars are surrounded by number of protocometary clouds or cometary bodies (Grady et al. + 2000. 2x references therein)., 2000 and references therein). + The more receut alternative niocl of Dulleiiond et al. (, The more recent alternative model of Dullemond et al. ( +2003) proposes that UXor stars have sel£shadowed discs. aud the livdrodyuauie fiuctuatious in the puffed-aip mner riu of the disk can cause short time scale extinction events.,"2003) proposes that UXor stars have self-shadowed discs, and the hydrodynamic fluctuations in the puffed-up inner rim of the disk can cause short time scale extinction events." + As we noted above CGAL Cep can be classified as ETTS. consequently it may show variability typical for both CTTS aud WAEBE stars.," As we noted above GM Cep can be classified as ETTS, consequently it may show variability typical for both CTTS and HAEBE stars." + The broad Πα ciission lue and the presence of a massive circumstellar disk are amoung the most inportaut attributes of CTT stars., The broad $\alpha$ emission line and the presence of a massive circumstellar disk are among the most important attributes of CTT stars. + The strong P Cre xofile of Πα lime is interpreted bv Sicilia-Aguilar ct al. (, The strong P Cyg profile of $\alpha$ line is interpreted by Sicilia-Aguilar et al. ( +2008) as evidence of very strong acerction.,2008) as evidence of very strong accretion. + Thus. the observed switching frou hieh-hrightuecss level to low-brightuess level in the lelt curve of CAL Cop (Xiao et al. (," Thus, the observed switching from high-brightness level to low-brightness level in the light curve of GM Cep (Xiao et al. (" +2010) can be explained by variable accretion rate typical of CTT stars (vau Bockel et al.,2010) can be explained by variable accretion rate typical of CTT stars (van Boekel et al. + 2010)., 2010). + This type of variability may explain also the rapid changes in brightuess and the observed dispersion of the points on color-maguitude diagrams (especially on V/BVW)., This type of variability may explain also the rapid changes in brightness and the observed dispersion of the points on color-magnitude diagrams (especially on $V/B-V$ ). + The analysis of all collected data sugecst that photometric properties of CAL Cop can be explained * superposition of both: (1) magnetically chauneled variable accretion from the cireunstellar disk. aud (2) occultation from cimceuustellar clouds of dust or fro catures of ai circuustellar disk.," The analysis of all collected data suggest that photometric properties of GM Cep can be explained by superposition of both: (1) magnetically channeled variable accretion from the circumstellar disk, and (2) occultation from circumstellar clouds of dust or from features of a circumstellar disk." + Such a conclusion is mentioned in the paper of Sicilia-Aguilar et al. (, Such a conclusion is mentioned in the paper of Sicilia-Aguilar et al. ( +2008). but the variable accretion is supposed to be he stronger contributor.,"2008), but the variable accretion is supposed to be the stronger contributor." + Our photometric results for he period Jun. 2008 - Feb. 201] sugecst that the variable extinction dominates the variability of CAL Cop., Our photometric results for the period Jun. 2008 - Feb. 2011 suggest that the variable extinction dominates the variability of GM Cep. + Analyzing the magnitude hisoeranus frou loue-iue light curves of GAL Cep Xiao et al. (, Analyzing the magnitude histograms from long-time light curves of GM Cep Xiao et al. ( +2010) reach a sinilu conclusion. the star spend most of ifs time in a nearly constaut bright state. thus the variability is not dominated by flares caused by accretion.,"2010) reach a similar conclusion, the star spend most of its time in a nearly constant bright state, thus the variability is not dominated by flares caused by accretion." + Iu ow accretion raes both types of variability can act independently during different tine periods and the result is the complicated helt curve of GAL Cop., In low accretion rates both types of variability can act independently during different time periods and the result is the complicated light curve of GM Cep. + Due o the complex circumstellar cuviromment around PAIS stars. such a musture of different types of plotometric variability can be expected.," Due to the complex circumstellar environment around PMS stars, such a mixture of different types of photometric variability can be expected." + A similar superposition of wo types of variability is secu on the loue-term liebt curve of another PAIS stay V1181 Tau (Semkov 2006. Senmikov et al.," A similar superposition of two types of variability is seen on the long-term light curve of another PMS star V1184 Tau (Semkov 2006, Semkov et al." + 2008)., 2008). + But in this case the observed light curve is due to the phenomena of both: the typical for WTT stis periodic variability (Tackett et al., But in this case the observed light curve is due to the phenomena of both: the typical for WTT stars periodic variability (Tackett et al. + 2003) and variable obscuration from UXor type (Dirsunova et al., 2003) and variable obscuration from UXor type (Barsunova et al. + 2006)., 2006). + At this stageoO if is most uulikelv that the plotometric variability of GM. Cep can be attribued to outmusts from FUor or EXor type., At this stage it is most unlikely that the photometric variability of GM Cep can be attributed to outbursts from FUor or EXor type. + The one-time light curves of GAL Cop show that the star spends much iore time iu hielh-brishtuess level than in low-brightuess level., The long-time light curves of GM Cep show that the star spends much more time in high-brightness level than in low-brightness level. + Our study indicates that the high amplitude variability aud the observed color reversal in the nünimuu lielt are caused by variable extinction from the circumstellar environnieut., Our study indicates that the high amplitude variability and the observed color reversal in the minimum light are caused by variable extinction from the circumstellar environment. + Siuultaucouslv. brieltucss variability as a result of a variableaccretion from the circumstellar disk are observed.," Simultaneously, brightness variability as a result of a variableaccretion from the circumstellar disk are observed." +]O0M.. which leads us to conclude that the mass of the black hole in 6-30-15 is ~10°—10°. smaller than anticipated.,"$\rm \sim 10 M_{\odot}$, which leads us to conclude that the mass of the black hole in $-$ 6-30-15 is $\sim 10^5-10^6$, smaller than anticipated." + Our mass estimate agrees with that of Hayashida et al. (, Our mass estimate agrees with that of Hayashida et al. ( +1998) and Nowak Chiang (1999) who also used the break frequency and scaling arguments.,1998) and Nowak Chiang (1999) who also used the break frequency and scaling arguments. + However. such mass estimates should be treated with extreme caution.," However, such mass estimates should be treated with extreme caution." + The break frequencies in any one given GBHC can vary by one or two orders of magnitude depending upon the exact flux/spectral state of the source., The break frequencies in any one given GBHC can vary by one or two orders of magnitude depending upon the exact flux/spectral state of the source. + Given hat we do not know how to map AGN spectral states into analogous GBHC states. the mass estimate derived above (and hat of Nowak Chiang 1999) will also be uncertain by up to wo orders of magnitude.," Given that we do not know how to map AGN spectral states into analogous GBHC states, the mass estimate derived above (and that of Nowak Chiang 1999) will also be uncertain by up to two orders of magnitude." + Additionally. it is not entirely clear what imescales to identify the cutoff frequency with.," Additionally, it is not entirely clear what timescales to identify the cutoff frequency with." + A small black hole mass (Le. « 2.LO? M.) would also imply the presence of a Eddington black hole in 6-30-15., A small black hole mass (i.e. $<$ $\rm 2 \times 10^6 M_\odot$ ) would also imply the presence of a super-Eddington black hole in $-$ 6-30-15. + Finally. we address what implications a 33 hr period would have on the black hole mass in 6-30-15.," Finally, we address what implications a 33 hr period would have on the black hole mass in $-$ 6-30-15." +" Tf we make the assumption that this is the orbital time scale for e.g. a flare to circumnavigate the black hole in 6-30-15. then we can estimate the mass via the relation: where /? is the distance from the center. and /?,—2r, is he Schwarzschild radius (the gravitational radius of the black hole rymGMfc and fos is in days)."," If we make the assumption that this is the orbital time scale for e.g. a flare to circumnavigate the black hole in $-$ 6-30-15, then we can estimate the mass via the relation: where $R$ is the distance from the center, and $R_s \equiv 2r_g$ is the Schwarzschild radius (the gravitational radius of the black hole $r_g \equiv GM/c^2$, and $t_{orb}$ is in days)." +" The diskline model constrains #;,, and /7,,; assuming some yower law emissivity function 6x.[4 ""9 that declines to larger radii. (", The diskline model constrains $R_{in}$ and $R_{out}$ assuming some power law emissivity function $\propto R^{- \alpha}$ ) that declines to larger radii. ( +"We note that beyond r,,; the line emission is negligible.)",We note that beyond $r_{out}$ the line emission is negligible.) + Accordingly. we expect that most of the power is concentrated in he inner radii.," Accordingly, we expect that most of the power is concentrated in the inner radii." +" 196 and 199 constrain using time averaged data rj,(6.7cO.S)r, for 6-30-15.", I96 and I99 constrain using time averaged data $r_{in} \sim (6.7 \pm 0.8) r_g $ for $-$ 6-30-15. +" This combined with /,,4 33hr ¢= 1.375 days) give a mass for the black hole in 6-30-15—2.6.10ML..."," This combined with $t_{orb} \sim$ 33hr (= 1.375 days) give a mass for the black hole in $-$ 6-30-15 $\rm \sim 2.6 \times 10^7 +\thinspace M_{\odot}$." + We summarize below the spectral and timing results of this paper., We summarize below the spectral and timing results of this paper. + It is clear that complicated processes are present. the nature of which is not obviously apparent. and may prove to be a challenge to present theoretical models.," It is clear that complicated processes are present, the nature of which is not obviously apparent, and may prove to be a challenge to present theoretical models." + We thank Juri Poutanen for useful discussions about cross correlation techniques., We thank Juri Poutanen for useful discussions about cross correlation techniques. + We thank all the members of the, We thank all the members of the +power and cross spectra were calculated.,power and cross spectra were calculated. + The power spectra were fitted with a constant (representing the dead-time mocified Poisson noise). a power-law (for the low-frequenevy noise component). and one or more Lorentzians (for the »ealked noise component and the QPOs).," The power spectra were fitted with a constant (representing the dead-time modified Poisson noise), a power-law (for the low-frequency noise component), and one or more Lorentzians (for the peaked noise component and the QPOs)." + The uncertainties in the fit. parameters were calculated: using x7=1 and upper limits using N47=2.7 which vields confidence evels., The uncertainties in the fit parameters were calculated using $\Delta\chi^2 = 1$ and upper limits using $\Delta \chi^2 = 2.7$ which yields confidence levels. + The phase lags of the QPOs were calculated for a requencey interval equal to the EWILIM of the Lorentzians used to fit the QPOs. centred. on the peak frequency of hese Lorentzians.," The phase lags of the QPOs were calculated for a frequency interval equal to the FWHM of the Lorentzians used to fit the QPOs, centred on the peak frequency of these Lorentzians." + To correct for the small ceacd-time ellects on the phase lags. we subtracted the average 50125 Lz cross vector from the cross spectra (see van cer Wis et al.," To correct for the small dead-time effects on the phase lags, we subtracted the average 50–125 Hz cross vector from the cross spectra (see van der Klis et al." + 1987)., 1987). + The single bit and the event mode data were used to search for high frequency (2 100 Lz) QPOs., The single bit and the event mode data were used to search for high frequency $>$ 100 Hz) QPOs. +" The all skv monitor (ASAI"")) light curve (1.512 keV) of the source is shown in Figure La (see also Borozdin et al.", The all sky monitor ) light curve (1.5–12 keV) of the source is shown in Figure \ref{fig:asm}{ (see also Borozdin et al. + 1998: Borozdin “Lruclolvuboy 2000)., 1998; Borozdin Trudolyubov 2000). + The outburst light curve of GRS 1739.278 can be classified as a tvpical fast rise. exponential decay light curve. although with multiple maxima in the decay.," The outburst light curve of GRS 1739–278 can be classified as a typical fast rise, exponential decay light curve, although with multiple maxima in the decay." + At the peak of the outburst the Lux was about 1 Crab. which makes this source a bright X-ray ransient.," At the peak of the outburst the flux was about 1 Crab, which makes this source a bright X-ray transient." + The 512 keV/1.53 keV count rate ratio curveis shown in Figure 15. which shows that the spectrum was iudest at the start of the outbursts (during the rise. before he peak of the outburst) and gradually became softer.," The 5–12 keV/1.5–3 keV count rate ratio curveis shown in Figure \ref{fig:asm}{, which shows that the spectrum was hardest at the start of the outbursts (during the rise, before the peak of the outburst) and gradually became softer." + The 5 Iz QPO was discovered during the 1996 March 31RAPE observation. which is day 90 in this figure. at à time when he source was already considerable weaker than at the peak of the outhurst. and the X-ray spectrum hacl significantly softened compared to previous clays.," The 5 Hz QPO was discovered during the 1996 March 31 observation, which is day 90 in this figure, at a time when the source was already considerable weaker than at the peak of the outburst, and the X-ray spectrum had significantly softened compared to previous days." + The 260 keV light curve. of the TE/PCAX observation of 1996. March. 31 is shown in Figure 2a., The 2–60 keV light curve of the /PCA observation of 1996 March 31 is shown in Figure \ref{fig:lc_colours}{ . + The, The +significantly in the interacting system.,significantly in the interacting system. + The reason for this difference is the fact that in an interacting system the kinematic axis is not well defined and does in general not coincide with the photometric axis of the system., The reason for this difference is the fact that in an interacting system the kinematic axis is not well defined and does in general not coincide with the photometric axis of the system. +" Thus, the slit does in general not follow the kinematic axis of the galaxy."," Thus, the slit does in general not follow the kinematic axis of the galaxy." + Only the knowledge of the full 2D velocity field allows to determine the kinematic axis., Only the knowledge of the full 2D velocity field allows to determine the kinematic axis. + The plots of the radial behaviour of the kinemetry parameters in Fig., The plots of the radial behaviour of the kinemetry parameters in Fig. + 5 do not yield clear evidence for a distorted VF at z=0.5., \ref{plotsdis} do not yield clear evidence for a distorted VF at z=0.5. + Only the outermost data point of ks/ki shows a significant increase., Only the outermost data point of $k_5/k_1$ shows a significant increase. + The situation is even worse for the resolution obtained with FLAMES/GIRAFFE., The situation is even worse for the resolution obtained with FLAMES/GIRAFFE. +" Although the maximum rotational velocity of the RC becomes similar to the one of the isolated galaxy due to the smearing out of the VF, a misclassification as undistorted galaxy would result in systematic errors in Tully-Fisher studies."," Although the maximum rotational velocity of the RC becomes similar to the one of the isolated galaxy due to the smearing out of the VF, a misclassification as undistorted galaxy would result in systematic errors in Tully-Fisher studies." + The luminosity of the system is possibly enhanced due to a merger induced starburst., The luminosity of the system is possibly enhanced due to a merger induced starburst. + In Fig., In Fig. +" 7 we show the 2D velocity field of this example for redshift z= 0.05, z=0.3, z=0.8, and z=1.0."," \ref{distevo} we show the 2D velocity field of this example for redshift $z=0.05$ , $z=0.3$, $z=0.8$, and $z=1.0$." +" It is clearly visible, how substructures are smeared out at higher redshift."," It is clearly visible, how substructures are smeared out at higher redshift." + We studied the effects of different interaction geometries on the results presented above., We studied the effects of different interaction geometries on the results presented above. +" For this purpose we considered a counter-rotating unequal mass merger (simulation 4) and an unequal massmerger, where"," For this purpose we considered a counter-rotating unequal mass merger (simulation 4) and an unequal massmerger, where" +of helium expelled into the intracluster medium by each model.,of helium expelled into the intracluster medium by each model. + We herealter refer to the Campbell et al., We hereafter refer to the Campbell et al. +" models as ""our models.", models as “our” models. + We also show the Z=0.001 vields from. [or comparison and note that the vields agree to within ~30%., We also show the $Z=0.001$ yields from \citet{ventura02} for comparison and note that the yields agree to within $\sim 30$. +. Our vields (and average Y) are svstematically larger for m>3.5M.. reflecting the different. input phivsies used in the two computations.," Our yields (and average $Y$ ) are systematically larger for $m > 3.5\Msun$, reflecting the different input physics used in the two computations." + Venturaetal.(2002) use a different convective model (Full Spectrum of Turbulence instead of the mixing-length theory) and mass-loss rate. and observe shallower dredge-up.," \citet{ventura02} use a different convective model (Full Spectrum of Turbulence instead of the mixing-length theory) and mass-loss rate, and observe shallower dredge-up." + In Table 20 an important resull can be seen (he average Y from our models does not monotonically increase with increasing stellar mass but instead peaks al 5M..., In Table \ref{table1} an important result can be seen – the average $Y$ from our models does not monotonically increase with increasing stellar mass but instead peaks at $\Msun$. + We observe ellicient ΤΟ: and IBB plus our models spend longer on the AGB thanks to the Vassiliadis&Wood(1993) mass-loss rate (seediscussionetal. 2006b)., We observe efficient TDU and HBB plus our models spend longer on the AGB thanks to the \citet{vw93} mass-loss rate \citep[see discussion in][]{karakas06a}. +. On the other hand. the models of Venturaetal.(2002) have more efficient envelope convection resulting in larger luminosities and shorter AGB lifetimes. owing to their choice of a Iuminositv-driven mass-loss rate (Ventura&D'Antona2005a).," On the other hand, the models of \citet{ventura02} have more efficient envelope convection resulting in larger luminosities and shorter AGB lifetimes, owing to their choice of a luminosity-driven mass-loss rate \citep{ventura05a}." +. This results in smaller helium. vields and consequently less helium in the cluster gas for the Ventura οι al., This results in smaller helium yields and consequently less helium in the cluster gas for the Ventura et al. + vields., yields. + This difference has important consequences lor the chemical evolution model. discussed further in relsec:resulls..," This difference has important consequences for the chemical evolution model, discussed further in \\ref{sec:results}." + Previously (Ixarakas2003) we compared the stellar vields from the Monash models with those from Forestini&Chnarbonnel(1997):vandenIloekGroenewegen(2001) and Lzzardetal. (2004).. for varving metallicities and find agreement for tLe for m>5M. at the level of ~3056.. with the exception of vandenΠου&Groenewegen who produce ~90% less 11ο.," Previously \citep{karakasThesis} we compared the stellar yields from the Monash models with those from \citet{forestini97,vandenhoek97,marigo01} and \citet{izzard04}, , for varying metallicities and find agreement for He for $m \ge 5\Msun$ at the level of $\sim 30$, with the exception of \citet{vandenhoek97} who produce $\sim 90$ less He." + Warakas(2003) also observed that the final surface abundance of Y in the Z=0.004 models (slightly higher but similar to the average Y. in the winds) did not monotonically increase with mass but peaked at both 2.5M. (owing to ellicient DU) and GAL. (due to hot bottom burning)., \citet{karakasThesis} also observed that the final surface abundance of $Y$ in the $Z=0.004$ models (slightly higher but similar to the average $Y$ in the winds) did not monotonically increase with mass but peaked at both $2.5\Msun$ (owing to efficient TDU) and $6\Msun$ (due to hot bottom burning). + We conclude that the relatively close agreement between helium vields [rom various studies indicates they are more robust than other species (e.g. PCC and OO)., We conclude that the relatively close agreement between helium yields from various studies indicates they are more robust than other species (e.g. C and O). + This is partly because the net result of hydrogen fusion is helium production regardless of (he rates of the various internal cycles (CNO cycle. NeNa and MgAL chains).," This is partly because the net result of hydrogen fusion is helium production regardless of the rates of the various internal cycles (CNO cycle, NeNa and MgAl chains)." + The GC chemical evolution (GCCE) model was described in detail in (2004):: here we summarize (he main features and the changes made for this study., The GC chemical evolution (GCCE) model was described in detail in \citet{fenner04}; here we summarize the main features and the changes made for this study. + We assume a lwo-slage formation model whereby (he first stageacts as a prompt initial enrichment (hat brings the cluster gas up to a metallicity of [Fe/II] = —1.4., We assume a two-stage formation model whereby the first stageacts as a prompt initial enrichment that brings the cluster gas up to a metallicity of [Fe/H] = $-1.4$ . + This first stage assumes a bimodal, This first stage assumes a bimodal +mooclel.,model. + his will be the best fitting model in the sense of minimizing the weighted sum of the deviations., This will be the 'best' fitting model in the sense of minimizing the weighted sum of the deviations. + In practise we will always have a noisev image., In practise we will always have a noisey image. + Lor example. if the noise per pixel is everywhere Gaussian with a fixed amplitude @ (this assumes the signal is not large compared to the noise) then while the other terms remain unchanged.," For example, if the noise per pixel is everywhere Gaussian with a fixed amplitude $\sigma$ (this assumes the signal is not large compared to the noise) then while the other terms remain unchanged." + N represents a Gaussian random error term with mean zero and standard deviation e., N represents a Gaussian random error term with mean zero and standard deviation $\sigma$. + As the cross-terms have an expectation value of zero equation 2 becomes where ary ds the intersection. of the spectrum. with he template., As the cross-terms have an expectation value of zero equation 2 becomes where $x_{t}$ is the intersection of the spectrum with the template. +" “Phe ""correction term. involves. only the »»rameters of the noise and the spectrum. ancl so the maximum still occurs at as=o.", The 'correction' term involves only the parameters of the noise and the spectrum and so the maximum still occurs at $\alpha_{s}=\alpha_{t}$. + As one might expect the ellects of the noise are minimised for large values of ας (large velocity widths ancl peak values)., As one might expect the effects of the noise are minimised for large values of $\alpha_{s} I_{s}^{2}$ (large velocity widths and peak values). + During the cross-correlation process we kept the intersection. ary. the same or each template so that we could compare the correlation coelficients of dillerent templates.," During the cross-correlation process we kept the intersection, $x_{t}$, the same for each template so that we could compare the correlation coefficients of different templates." + We have used Gaussian templates with full width half maximum values from 25 to 500 hin see+ at 12.5 Km see intervals., We have used Gaussian templates with full width half maximum values from 25 to 500 $km$ $sec^{-1}$ at 12.5 $km$ $sec^{-1}$ intervals. + We reject those that are not. velocity resolvec (ο<27 km s 4)., We reject those that are not velocity resolved $v<27$ $km$ $s^{-1}$ ). + The largest detected. velocity width in the sample is 337.5 Kimi s some wav below the larges template size., The largest detected velocity width in the sample is 337.5 $km$ $s^{-1}$ some way below the largest template size. + The detection process has been fully. testec on à wide range of simulated and real data., The detection process has been fully tested on a wide range of simulated and real data. + Using simulate Gaussian profiles. in real data. with central intensities of 4o we find that we can estimate profile paranmictors an LIL masses to about a factor of 3.," Using simulated Gaussian profiles, in real data, with central intensities of $\sigma$ we find that we can estimate profile parameters and HI masses to about a factor of 3." + As confirmation of this one of the galaxies in the final sample (see below) has a previous 2lem measurement., As confirmation of this one of the galaxies in the final sample (see below) has a previous 21cm measurement. + For F300-026 Matthewson arn Ford (1996) measure an HE mass of S;107 AZ. (using our derived distance of 11.3 Alpe) while the value derived from our crossecorrelation. program is 6107 AZ.., For F300-026 Matthewson and Ford (1996) measure an HI mass of $8\times10^{8}$ $M_{\odot}$ (using our derived distance of 11.3 $Mpc$ ) while the value derived from our cross-correlation program is $6\times10^{8}$ $M_{\odot}$. + We have also excluded regions in each spectra that contain known sources of noise (LILPAASS web page)., We have also excluded regions in each spectra that contain known sources of noise (HIPASS web page). + In summary the automated. LL detection process involved firstly the identification ofa te or higher value. then inding the maximum correlation coelIicient with a template of velocity width (full width at half-maximun) greater than 27 Amos the velocity resolution of the data (in practice he width of the smallest resolved? template of 37.5 Ain s +).," In summary the automated HI detection process involved firstly the identification of a $\sigma$ or higher value, then finding the maximum correlation coefficient with a template of velocity width (full width at half-maximum) greater than 27 $km$ $s^{-1}$, the velocity resolution of the data (in practice the width of the smallest 'resolved' template of 37.5 $km$ $s^{-1}$ )." +" This is what we define as our ""sample Limits’.", This is what we define as our 'sample limits'. + After carrvingIn out the template matching.ὃν we had a ist of 155 LE detections., After carrying out the template matching we had a list of 155 HI detections. + We then needed to carry out other checks to see how secure these detections were., We then needed to carry out other checks to see how secure these detections were. + The main problem is one of reliably asigning the optical and Η1 detections to the same object., The main problem is one of reliably asigning the optical and HI detections to the same object. + Pypically the galaxies in the optical sample have ciamoeters of 0.3 erc min., Typically the galaxies in the optical sample have diameters of 0.3 $arc$ $min$. + The LULL resolution is 15.5 are man., The HI resolution is 15.5 $arc$ $min$. + To overcome this problem we have used the optical Digital Sky Survey (DSS) to inspect the area around cach LIL detection., To overcome this problem we have used the optical Digital Sky Survey (DSS) to inspect the area around each HI detection. + We have also used the NASA/IPAC Extra galactic Database (NED) to find known objects within 10 ere min of the position of the LIL spectra., We have also used the NASA/IPAC Extra galactic Database (NED) to find known objects within 10 $arc$ $min$ of the position of the HI spectra. + We have removed objects from our initial list if NED has a similar redshift for another object within 10 ere min or if rere is a more prominent galaxy within the field of view., We have removed objects from our initial list if NED has a similar redshift for another object within 10 $arc$ $min$ or if there is a more prominent galaxy within the field of view. + For strong nearby signals (6<2000 Anis 1) we searche NED for 8galaxies of similar redshift at up to 1 deg4 away (bx looking at spectra at random positions around nearby ealaxies (such as NGC1365 and NGCT1291) it is clear tha rey can allect spectra up to 30 are min away from their optical centre)., For strong nearby signals $v<2000$ $km$ $s^{-1}$ ) we searched NED for galaxies of similar redshift at up to 1 $deg$ away (by looking at spectra at random positions around nearby galaxies (such as NGC1365 and NGC1291) it is clear that they can affect spectra up to 30 $arc$ $min$ away from their optical centre). + As an indication that some of our optical anc LL detections come from the same object we can compare the nieasured LIL velocities with previously determined (optical) velocities obtained from. NED. these are available for 10 galaxies in our sample (see table 1).," As an indication that some of our optical and HI detections come from the same object we can compare the measured HI velocities with previously determined (optical) velocities obtained from NED, these are available for 10 galaxies in our sample (see table 1)." + In all cases the optical and LIL velocities are in good agreement., In all cases the optical and HI velocities are in good agreement. + The above procedure resulted. in a reduction to δ4 detections. but it was clear from inspection of the images from the DSS that for the most distant objects (greater than about 6000. A75) confusion was still à problem.," The above procedure resulted in a reduction to 84 detections, but it was clear from inspection of the images from the DSS that for the most distant objects (greater than about 6000 $km/s$ ) confusion was still a problem." + The large beam size covered many faint objects not listed in NED. bu distinctly. possible sources of the LL emission.," The large beam size covered many faint objects not listed in NED, but distinctly possible sources of the HI emission." + In fact the LIL emission could. arise from the combination of a number of sources in the same group., In fact the HI emission could arise from the combination of a number of sources in the same group. + A simulation (see below) of the expected. number of sources in a set of random bears indicated that contamination of the sample was possible a a level better than about 1 in 4 for a sample limited to 5000 kms. but that this drops quickly to about 1 in 2 or worse bevond 6000 Amis.," A simulation (see below) of the expected number of sources in a set of random beams indicated that contamination of the sample was possible at a level better than about 1 in 4 for a sample limited to 5000 $km/s$, but that this drops quickly to about 1 in 2 or worse beyond 6000 $km/s$." + Given that our data is not from a set of random sight lines we should expect to do better than this and so (rather arbitrarily) we set a maximum velocity limi ol 5500 Aimfs., Given that our data is not from a set of random sight lines we should expect to do better than this and so (rather arbitrarily) we set a maximum velocity limit of 5500 $km/s$. + This fits in well with the previously measure ealaxies of table 1. which all have confirmed redshifts below this limit.," This fits in well with the previously measured galaxies of table 1, which all have confirmed redshifts below this limit." + This final sumple consists of just 26 objects. out of an initial sample of 2400. that have both a reasonably secure optical ancl LIE detection.," This final sample consists of just 26 objects, out of an initial sample of 2400, that have both a reasonably secure optical and HI detection." + Given the above discussion. and that our sample consists of relatively isolated: galaxies (see below) we believe that our detections are secure and. not due to other nearby. objects., Given the above discussion and that our sample consists of relatively isolated galaxies (see below) we believe that our detections are secure and not due to other nearby objects. + In figure 3. we have plotted the HE mass against the absolute D. banc magnitude., In figure \ref{fig:mvmhi} we have plotted the HI mass against the absolute B band magnitude. + As, As +"clumps, and its possible interaction with the forward blast wave is curious.","clumps, and its possible interaction with the forward blast wave is curious." + The nature of this knot will be discussed further in Sec. ??.., The nature of this knot will be discussed further in Sec. \ref{Sec:RK}. +" Second, the inner X-ray ring is almost perfectly superposed to the O-rich knots."," Second, the inner X-ray ring is almost perfectly superposed to the O-rich knots." +" Borkowski,Hendrick&Reynolds(2007) who observed an enhanced emission of oxygen in the X-ray spectrum at those location had already suggested it to be possibly the location of the reverse shock wave, or potentially be the consequences of a Ni-rich bubble."," \cite{Borkowski07} who observed an enhanced emission of oxygen in the X-ray spectrum at those location had already suggested it to be possibly the location of the reverse shock wave, or potentially be the consequences of a Ni-rich bubble." +" Clearly, its close association with O-rich material makes the reverse shock hypothesis the most likely one."," Clearly, its close association with O-rich material makes the reverse shock hypothesis the most likely one." +" 'Third, the knot, to the SW of the SNR center, appears not to be associated with any X-ray emission, unlike the other O-rich clumps."," Third, the knot, to the SW of the SNR center, appears not to be associated with any X-ray emission, unlike the other O-rich clumps." +" This is somewhat of a mystery, since we would expect some X-ray emission to be associated with it."," This is somewhat of a mystery, since we would expect some X-ray emission to be associated with it." + It is remotely possible that these knots are being photoionized by the diffuse X-ray field., It is remotely possible that these knots are being photoionized by the diffuse X-ray field. + 'The intensity of its emission is slightly smaller than the other O-rich clumps (see Fig. 7))., The intensity of its emission is slightly smaller than the other O-rich clumps (see Fig. \ref{fig:3dproj}) ). +" Fourth, the feature fits almost perfectlylj into a hole in the X-ray emission, This suggests that this dense cloud in the ISM lies in the foreground, and has sufficient column density to absorb the underlying diffuse X-ray emission."," Fourth, the feature fits almost perfectly into a hole in the X-ray emission, This suggests that this dense cloud in the ISM lies in the foreground, and has sufficient column density to absorb the underlying diffuse X-ray emission." +" It is delineated on part of its southern boundary by an X-ray enhancement, presumably generated by the stand-off shock associated with the cloud."," It is delineated on part of its southern boundary by an X-ray enhancement, presumably generated by the stand-off shock associated with the cloud." +" In this Section, we use the idea developed by Vogt&Dopita(2010a) to reconstruct a 3D map of the oxygen rich ejecta in SNR N132D. Assuming that N132D is still in its free expansion phase implies that there exist a linear relation in between the radial velocity v, and the distance z covered by the clumps since the explosion."," In this Section, we use the idea developed by \cite{Vogt10a} to reconstruct a 3D map of the oxygen rich ejecta in SNR N132D. Assuming that N132D is still in its free expansion phase implies that there exist a linear relation in between the radial velocity $v_r$ and the distance $z$ covered by the clumps since the explosion." +" The scale depends on two parameters: the distance D to SNR N132D, and the age of the explosion."," The scale depends on two parameters: the distance $D$ to SNR N132D, and the age of the explosion." +quantitative statements have uot been easy to make.,quantitative statements have not been easy to make. + However. MelNiunoun Stinebring (1998: 2000) have developed statistical analysis tools which should make a more meaninetul assessineut practical. and we plan to pursue this question iu a future paper (Ramachandran Rankin 2002).," However, McKinnon Stinebring (1998; 2000) have developed statistical analysis tools which should make a more meaningful assessment practical, and we plan to pursue this question in a future paper (Ramachandran Rankin 2002)." + The results of this paper can be stuuarizecl succiuctly: Conal beams have a rotating subbeam structure which also eutails displacements between he PPM aud SPM radiation iu both maguetic atitude and azimuth., The results of this paper can be summarized succinctly: Conal beams have a rotating subbeam structure which also entails displacements between the PPM and SPM radiation in both magnetic latitude and azimuth. + This results in the outer-οσο depolarization seen in conal component oürs as well as the complex (aud often ucarly complete) depolarization found im pulsar profiles hat represent an oblique sightline trajectory along he outer edge of the conal beam., This results in the outer-edge depolarization seen in conal component pairs as well as the complex (and often nearly complete) depolarization found in pulsar profiles that represent an oblique sightline trajectory along the outer edge of the conal beam. +" It also provides a new and fundamental reason why the mocal cnussion is so often statistically ""disjoiut (see Cordes 11975).", It also provides a new and fundamental reason why the modal emission is so often statistically “disjoint” (see Cordes 1978). + These characteristics of conal ciission can be identified iu ai variety of wars. and he conclusions verified by detailed models aid sinlations.," These characteristics of conal emission can be identified in a variety of ways, and the conclusions verified by detailed models and simulations." + Tt is also likely tha these effects larecly explain he frequency dependence of the fractional linear yolarization in the classic cases of conal double xofiles(we. DII33]16) first problematized bv Manchester. Tavlor ποια (1973).," It is also likely that these effects largely explain the frequency dependence of the fractional linear polarization in the classic cases of conal double profiles, B1133+16) first problematized by Manchester, Taylor Huguenin (1973)." + Mauv nore recent studies have poiuted to both the the secular decline at high frequencies and the 1uid-xud “break” point below which the agerceate ractional linear increases uo further(6.4.. Mcelkinnon 1997).," Many more recent studies have pointed to both the the secular decline at high frequencies and the mid-band “break” point below which the aggregate fractional linear increases no further, McKinnon 1997)." +" And closely associated with these profile effects are pulse-sequence pheuonmiena ranging rou the maported ""randonüziug"" of the PA at uel frecencics to distributions of polarization characteristics in subpulses.", And closely associated with these profile effects are pulse-sequence phenomena ranging from the purported “randomizing” of the PA at high frequencies to distributions of polarization characteristics in subpulses. +" If we muderstai¢ that he PPM and SPM ""Coles"" have a siguificaut displacement in magnetic colatitude at neter wavelengths. then radius-to-frequency lappine (see Paper VII) almost certainly tends to reduce this displacement at higher frequencies."," If we understand that the PPM and SPM “cones” have a significant displacement in magnetic colatitude at meter wavelengths, then radius-to-frequency mapping (see Paper VII) almost certainly tends to reduce this displacement at higher frequencies." +" Perhaps the characteristic depolarization of conal beams at ναν lieh frequencies (as well as the “random, PAs) is simply the result of modal beam overlap.", Perhaps the characteristic depolarization of conal beams at very high frequencies (as well as the “random” PAs) is simply the result of modal beam overlap. + Perhaps the “breaks” mark the frequency at which the modal beams diverge to the point that no urther depolarization occurs., Perhaps the “breaks” mark the frequency at which the modal beams diverge to the point that no further depolarization occurs. + It will be satistvine o test these ideas in future detailed studies., It will be satisfying to test these ideas in future detailed studies. +" The origin of ""orthogonal mode” emissiou has oen a topic of debate for decades.", The origin of “orthogonal mode” emission has been a topic of debate for decades. + Numerous uodels have beeu sugeestedeo wherein the two nodes are iutrinsic to the ciission niechauisui itself (c.g. Caneadhara 1997) aud. lacking stroug contrary evidence. some bias has developed iu awvor of this assmuption.," Numerous models have been suggested wherein the two modes are intrinsic to the emission mechanism itself (e.g., Gangadhara 1997) and, lacking strong contrary evidence, some bias has developed in favor of this assumption." + However. direct productiou iuples that the modes boe fully (elliptically) xolaudzed aud associates them with a basic enissiou nechanisut which is itself still uuknown [for a review. see Moelrose (1995)].," However, direct production implies that the modes be fully (elliptically) polarized and associates them with a basic emission mechanism which is itself still unknown [for a review, see Melrose (1995)]." + The possibility that disjoint orthogonal modes can arise from propagation effects was also explored very carly by several authors (Melrose 1979: Allan Melrose. 1982)., The possibility that disjoint orthogonal modes can arise from propagation effects was also explored very early by several authors (Melrose 1979; Allan Melrose 1982). + The central idea here is that the natural wave modes. beiug linearly polarizcc in two orthogonal planes. have differcut refractive indices. aud become separated im space and anele diving their propagation.," The central idea here is that the natural wave modes, being linearly polarized in two orthogonal planes, have different refractive indices, and become separated in space and angle during their propagation." + This phenomenon of refraction in the maguetosphere was explore rigorously by Barnard Arous (1986)., This phenomenon of refraction in the magnetosphere was explored rigorously by Barnard Arons (1986). + A recent work of Petrova (2001) has addresse hese issues in ereater detail., A recent work of Petrova (2001) has addressed these issues in greater detail. + According to her uodel. the primary pulsar radiation Is coniprisec of only one (ordinary) node. which is later xuwtiallv couverted iuto extraordinarv-niodoe emission.," According to her model, the primary pulsar radiation is comprised of only one (ordinary) mode, which is later partially converted into extraordinary-mode emission." + It is in this couversion that the orthoeoua volarization modes arise., It is in this conversion that the orthogonal polarization modes arise. +" Therefore. the transition roni one node to the other. as observed iu pulsar Cluission. can be understood as duc to switching )etwoeen a ""iguificaut aud “Insignificant” conversion."," Therefore, the transition from one mode to the other, as observed in pulsar emission, can be understood as due to switching between a “significant” and “insignificant” conversion." + At inv given time and pulse longitude. the disjoint inode is the sum of two superposed modes.," At any given time and pulse longitude, the disjoint mode is the sum of two superposed modes." + This nicely explains the partial polarization observed in the pulsar radiation., This nicely explains the partial polarization observed in the pulsar radiation. +" Conversion to the extraordinary mode, in Petrova’s model. is easiest for those ravs which are refracted outward. away from the magnetic axis. and such clission apparently comprises the conal beamthough her work wet gives no understanding about why there should be two distinet types of conal bemus that are both present in some cases."," Conversion to the extraordinary mode, in Petrova's model, is easiest for those rays which are refracted outward, away from the magnetic axis, and such emission apparently comprises the conal beam—though her work yet gives no understanding about why there should be two distinct types of conal beams that are both present in some cases." + It is further unclear how the ordinary or extraordinary mode would be polarized. thus how it then could be identified as a specific PPM. or SPM in a given pulsar.," It is further unclear how the ordinary or extraordinary mode would be polarized, thus how it then could be identified as a specific PPM or SPM in a given pulsar," +rate of accretion onto à given. sink is determined. only. by the local freefall time. which is in turn the same throughout the shell at any given In Figure 14.. we show the rate of sink particle formation and the cumulative number of sink particles as functions of time in the simulation.,"rate of accretion onto a given sink is determined only by the local freefall time, which is in turn the same throughout the shell at any given In Figure \ref{fig:sink_rate}, we show the rate of sink particle formation and the cumulative number of sink particles as functions of time in the simulation." + The number initially. rises strongly before beginning to tail olf around 23 Myr., The number initially rises strongly before beginning to tail off around 23 Myr. + We showed in Figure 9. that. as the first pcores become bound.," We showed in Figure \ref{fig:nclumps} that, as the first p–cores become bound," +Using the VALAL-Neiwlon and Chandra data. we have confirmed that the spectra of the central regions of M 31. obtained alter removing point sources above =3x10? erg J|. can be described by a sum of the flour spectral components: the hard component which is mainly contributed bv the photons which spill over Irom the excluded point sources. and the 0.6. 0.3 and 0.1 keV MIL components.,"Using the ${\it XMM}$ ${\it Newton}$ and ${\it Chandra}$ data, we have confirmed that the spectra of the central regions of M 31, obtained after removing point sources above $\gtrsim 3 \times 10^{35}$ erg $^{-1}$, can be described by a sum of the four spectral components: the hard component which is mainly contributed by the photons which spill over from the excluded point sources, and the 0.6, 0.3 and 0.1 keV MKL components." + The softer three thermal components have been quantified in a consistent manner by the three satellites (NALA/-Newlon. Chandra and ASCA).," The softer three thermal components have been quantified in a consistent manner by the three satellites ${\it XMM}$ ${\it Newton}$, ${\it Chandra}$ and ${\it ASCA}$ )." + All the thermal components are raclially extended to a typical seale of ~ 1.5 (0.3 kpc). in agreement wilh the repeated detections of unresolved. possibly dilluse. soft X-ray emission (CIrinchieri and Fabbiano 1991: Primini et 11993: Supper et 11997: West et 11997: Trinchieri et 11999: Dorozdin and Prieclhorsky 2000: Primini et 22000: Garcia οἱ 22000: SEAOL: Paper 1: Dosaj et 22002).," All the thermal components are radially extended to a typical scale of $\sim$ $\arcmin$ .5 (0.3 kpc), in agreement with the repeated detections of unresolved, possibly diffuse, soft X-ray emission (Trinchieri and Fabbiano 1991; Primini et 1993; Supper et 1997; West et 1997; Trinchieri et 1999; Borozdin and Priedhorsky 2000; Primini et 2000; Garcia et 2000; SEA01; Paper 1; Dosaj et 2002)." + Below. we discuss the nature of the four components.," Below, we discuss the nature of the four components." + With this analvsis. we have reconfirmed (hat (he integrated binary component dominates the spectra above ~2 keV. as already known previously (Makishima et 11989b: Trinchieri el 11999: SEAOL: Paper D).," With this analysis, we have reconfirmed that the integrated binary component dominates the spectra above $\sim 2$ keV, as already known previously (Makishima et 1989b; Trinchieri et 1999; SEA01; Paper 1)." + Using the XAZM- Neieton data. we also confirmed (hat. in the enerev band above 0.6 keV. the summed spectra of the detected point sources cannot be reproduced by the simple PL model. while the LAINB modeling is successful when adding the 2 MIXL components (5$ 3.1).," Using the ${\it XMM}$ ${\it Newton}$ data, we also confirmed that, in the energy band above 0.6 keV, the summed spectra of the detected point sources cannot be reproduced by the simple PL model, while the LMXB modeling is successful when adding the 2 MKL components $\S$ 3.1)." +J) These results agree with the main achievement of using Ginga and Paper 1 using “LSC., These results agree with the main achievement of \citet{M31_Makishima} using ${\it Ginga}$ and Paper 1 using ${\it ASCA}$. + For a further confirmation of sell-consistency. we attempted (o reproduce the summed point-source spectra over the entire 0.410 keV. (rather than in the > 0.6 keV range) by the LMXD-A3MIHEKL model. of which the MIXL temperatures were constrained at 0.6. 0.3 and 0.1 keV and the metal abunelances other than nitrogen of all the three MIXL components were fixed at 0.3 solar units.," For a further confirmation of self-consistency, we attempted to reproduce the summed point-source spectra over the entire 0.4–10 keV (rather than in the $>$ 0.6 keV range) by the LMXB+3MKL model, of which the MKL temperatures were constrained at 0.6, 0.3 and 0.1 keV and the metal abundances other than nitrogen of all the three MKL components were fixed at 0.3 solar units." + The result is moderately successful with \7/d.o.f. == 1748/1408. and the fit residuals are at most of the data.," The result is moderately successful with $\chi^{2}$ = 1748/1408, and the fit residuals are at most of the data." +" The obtained huninosities of the 3 MIL components become e3x10* eres t..7xLO eres band ~L6x10"" eres ! in the order of decreasing temperature. ancl correspond to of the integrated huminosity within 6"" of each diffuse emission (58 5)."," The obtained luminosities of the 3 MKL components become $\sim 3 \times 10^{37}$ erg $^{-1}$, $\sim 7 \times 10^{37}$ erg $^{-1}$ and $\sim 1.6 \times 10^{37}$ erg $^{-1}$ in the order of decreasing temperature, and correspond to $\sim$ of the integrated luminosity within $\arcmin$ of each diffuse emission $\S$ 5)." + This percentage is reasonable. considering that the area of the summed point-source spectra occupies ~ of the 6 radius region. and (hat the point sources concentrate around (he nucleus where (he diffuse emission is also bright.," This percentage is reasonable, considering that the event-collection area of the summed point-source spectra occupies $\sim$ of the $\arcmin$ radius region, and that the point sources concentrate around the nucleus where the diffuse emission is also bright." + This result confirms that the 3 MIXL components found in the summed point-source spectra are contaminations of the diffuse X-ray. emission., This result confirms that the 3 MKL components found in the summed point-source spectra are contaminations of the diffuse X-ray emission. +here. the sunuuation is over the five light uimima. each with its respectiveο aand Fü(fnag)),"here, the summation is over the five light minima, each with its respective, and )." +h For a eiven imodecl. the quautity exptoQJ) is proportional to the likelihood that the measured vvalues could have arisen by chance-fluctuation departures from the model.," For a given model, the quantity $\exp(-\OCstat)$ is proportional to the likelihood that the measured values could have arisen by chance-fluctuation departures from the model." + Weo use ooa downhill simplex aleorithim (Pressetal.1992) to minimizeQ.. iterated util the maxiuuu relative deviation between simplex. vertices drops below 10.!.," We use a downhill simplex algorithm \citep{Pre1992} to minimize, iterated until the maximum relative deviation between simplex vertices drops below $10^{-4}$." +" Table 2. stummarizes the coefficieuts of the linear and quadratic models,", Table \ref{tab:o-c} summarizes the coefficients $\{b_{j}\}$ of the linear and quadratic models. + As in {01} refssecuuinlvsisanndun. error bounds are doeterinined via Monte Carlo simulations.," As in \\ref{ssec:analysis-min}, error bounds are determined via Monte Carlo simulations." + Towever. rather than eeneratiug svuthetic ddata by bootstrapping. woe construct them by perturbing each wwith random deviates drawn from the appropriate PDF (cf.," However, rather than generating synthetic data by bootstrapping, we construct them by perturbing each with random deviates drawn from the appropriate PDF (cf." + Fig. 2))., Fig. \ref{fig:pdf}) ). + From the same simulations we also determine the distribution of the sstatistic. enabling us to associate the linear and quadratic fits in Fie.," From the same simulations we also determine the distribution of the statistic, enabling us to associate the linear and quadratic fits in Fig." + 3 witha Likehhood ((also specified in Tab. 2)), \ref{fig:o-c} with a likelihood (also specified in Tab. \ref{tab:o-c}) ) + that the null hypothesis is true: that is. that the deviation of the vvalues from the model arises purely due to chance fluctuations.," that the null hypothesis is true: that is, that the deviation of the values from the model arises purely due to chance fluctuations." + Table 2 indicates that the null livpothesis for the linear nunodel is unlikely (pay=0.05% ). allowing a constaut rotation period to be ruled out with a high deeree of confidence.," Table \ref{tab:o-c} indicates that the null hypothesis for the linear model is unlikely $\pnull = 0.05\%$ ), allowing a constant rotation period to be ruled out with a high degree of confidence." + However. the converse is true for the quadratic model. which fits the data extremely well.," However, the converse is true for the quadratic model, which fits the data extremely well." + Combining its cocficieuts with equs. (1)), Combining its coefficients with eqns. \ref{eqn:o-c}) ) + aud (3)) gives a revised ephemeris for the primary dlieht mininuun of ads By taking the derivative with respect to evele umber. the iustautaucous period is found as which erows linearly at à rate P=77118 por vear. (," and \ref{eqn:o-c-quadratic}) ) gives a revised ephemeris for the primary light minimum of as By taking the derivative with respect to cycle number, the instantaneous period is found as which grows linearly at a rate $\dot{P} = 77\,{\rm ms}$ per year. (" +Wo discuss the implicit asunnuption of period οτο in refsec:discuss)}.,We discuss the implicit assumption of period growth in \\ref{sec:discuss}) ). + At the reference epoch E=0. this »eriod is rather lareer than the P=119081+O!00001 reported by esseretal.(L977): however. these authors error estimate seenis overly optimistic.," At the reference epoch $\cycnum=0$, this period is rather larger than the $P=1\fd19081 \pm 0\fd00001$ reported by \citet{Hes1977}; however, these authors' error estimate seems overly optimistic." + Reimersetal.(2000) determined a period P=1H9081+Q'00001 * combining new heliu-lne data with historical neasurements from Pedersen&Thomsen(1977): their value is in good agreement with the mean period 13190833 obtained by averaging equ. (6))," \citet{Rei2000} determined a period $P = 1\fd19084 \pm +0\fd00001$ by combining new helium-line data with historical measurements from \citet{PedTho1977}; their value is in good agreement with the mean period $\overline{P} = 1\fd190833$ obtained by averaging eqn. \ref{eqn:period}) )" + over the interval spanned by the heliunu data., over the 1976--1998 interval spanned by the helium data. + Before discussing the sienificance of the measured veriod merease. we briefle review factors that may have a systematic effect on this result.," Before discussing the significance of the measured period increase, we briefly review factors that may have a systematic effect on this result." + As demonstrated by Townsend(2008).. the timing of light niuimaa is scusitive o the optical depth of the magnetospheric plasma clouds.," As demonstrated by \citet{Tow2008}, the timing of light minima is sensitive to the optical depth of the magnetospheric plasma clouds." + Iu principle. the progressive shift iu toward later times (seen iu theresiduals plot of Fig. 3))," In principle, the progressive shift in toward later times (seen in theresiduals plot of Fig. \ref{fig:o-c}) )" + could be explaimed bv the secular accumulation of dasna in the maguetosphere (see.e.g...Townsend&Owocki 2005).," could be explained by the secular accumulation of plasma in the magnetosphere \citep[see, e.g.,][]{TowOwo2005}." +. However. based on the examples eiveu w Townsend(2008.hissection2.1).. the observed shift of =O82 between the 2001 aud 2009 seasous would require a increase in the optical depth of the nagnetosplere.," However, based on the examples given by \citet[][his section~2.4]{Tow2008}, the observed shift of $\approx +0\fd02$ between the 2004 and 2009 seasons would require a increase in the optical depth of the magnetosphere." + The munima in Fie., The minima in Fig. + d. clearly do not exhibit this kiud of dramatic change., \ref{fig:minima} clearly do not exhibit this kind of dramatic change. + Indeed. although here some season-to-seasoni variations in the mimi depths (on the order of 201uuag). no monotonic trend is seen: we believe the variations are probably due o changes in the distribution of scattered ποτ fromAB.," Indeed, although there some season-to-season variations in the minima depths (on the order of $20\,{\rm mmag}$ ), no monotonic trend is seen; we believe the variations are probably due to changes in the distribution of scattered light from." +. Accordingly. we rule out the possibility that he sshift is due to plasima accumulation.," Accordingly, we rule out the possibility that the shift is due to plasma accumulation." + Similar reasoning can be addressed to «ωςτς over he change in filters. from Stromimercn « in 1977 to Johnson C in the later observations.," Similar reasoning can be addressed to concerns over the change in filters, from Strömmgren $u$ in 1977 to Johnson $U$ in the later observations." + Iu passbauds where he mmaenetosphere is more opaque. the time of primary ight wii will teud to occur later.," In passbands where the magnetosphere is more opaque, the time of primary light minimum will tend to occur later." + This ccorrelation can be clearly seen in the IEHesseretal.(1977) observations: iu the Strónuueren 4 baud (falling dueword of the Dalner jump). the time of primary ight iniuiuun is (007 later than iu the ce band (falling redward of the Balmer jump).," This correlation can be clearly seen in the \citet{Hes1977} + observations; in the Strömmgren $u$ band (falling blueward of the Balmer jump), the time of primary light minimum is $0\fd007$ later than in the $v$ band (falling redward of the Balmer jump)." + Because the £7 deid straddles the Balmer jump. the expected time lag jetween a and C should be around half of this. ~ 01003.," Because the $U$ band straddles the Balmer jump, the expected time lag between $u$ and $U$ should be around half of this, $\sim 0\fd003$ ." + Au adjustinent of this order to the 1977 »poiut. to correct for the ccorrelatiou. has a negligible effect on our results.," An adjustment of this order to the 1977 point, to correct for the correlation, has a negligible effect on our results." + A final possible issue comes from the use of paraholae ο lecasure the primayv minima times., A final possible issue comes from the use of parabolae to measure the primary minimum times. + As discussed, As discussed +"The images were bias-subtracted, flat-fielded, distortion-corrected, and combined using the standard procedures of the Suprime-Cam Deep Field Reduction (SDFRED) software (??)..","The images were bias-subtracted, flat-fielded, distortion-corrected, and combined using the standard procedures of the Suprime-Cam Deep Field Reduction (SDFRED) software \citep{2002AJ....123...66Y,2004ApJ...611..660O}." + The photometry was performed using the version of the package (?).., The photometry was performed using the version of the package \citep{1987PASP...99..191S}. +" A preliminary selection of detections with signal-to-noise ratio greater than 4 was performed with the automatic star-finding algorithm and the aperture photometry was obtained with the task using an aperture radius of 9 pixels for the images taken during the August run (fields SEI and SE2), which had the poorest seeing (see Table 1), and an aperture of 6 pixels for the others."," A preliminary selection of detections with signal-to-noise ratio greater than 4 was performed with the automatic star-finding algorithm and the aperture photometry was obtained with the task using an aperture radius of 9 pixels for the images taken during the August run (fields SE1 and SE2), which had the poorest seeing (see Table 1), and an aperture of 6 pixels for the others." + An empirical point-spread function was built with the task by selecting several isolated and bright stars in each field., An empirical point-spread function was built with the task by selecting several isolated and bright stars in each field. + Finally PSF-fitting photometry was extracted with the task (?).., Finally PSF-fitting photometry was extracted with the task \citep{1994PASP..106..250S}. +" To reduce spurious detections, the final catalogs for each field includes only objects with y?«3, and |sharp| «0.3, where y? is a parameter that indicates the quality of the fit, and sharp measures the spatial extent of a detection, being defined as the difference between the square of the width of the measure object and the square of the width of the PSF."," To reduce spurious detections, the final catalogs for each field includes only objects with $\chi^2 < 3$, and $\mid\!sharp\!\mid$ $< 0.3$, where $\chi^2$ is a parameter that indicates the quality of the fit, and $sharp$ measures the spatial extent of a detection, being defined as the difference between the square of the width of the measure object and the square of the width of the PSF." + The photometry was calibrated using data for ?) standards observed during the entire run., The photometry was calibrated using data for \citet{1992AJ....104..340L} standards observed during the entire run. + Galactic extinction corrections were derived following ?).., Galactic extinction corrections were derived following \citet{1998ApJ...500..525S}. + We applied an average correction corresponding to the extinction at the central position of each field., We applied an average correction corresponding to the extinction at the central position of each field. + The adopted values of Ay are displayed in Table 1., The adopted values of $_V$ are displayed in Table 1. + We performed artificial star tests to evaluate the completeness of our photometry., We performed artificial star tests to evaluate the completeness of our photometry. +" We added artificial stars to the original images with magnitudes in the ranges 19 mag «J 26 mag, and 19 mag «V 27 mag, with a binning step of 0.2 mag that was increased to 0.5 mag for magnitudes brighter than I = 23 mag."," We added artificial stars to the original images with magnitudes in the ranges 19 mag $< I <$ 26 mag, and 19 mag $< V <$ 27 mag, with a binning step of 0.2 mag that was increased to 0.5 mag for magnitudes brighter than I = 23 mag." + A total of 56000 stars were injected at random positions onto each image for both filters., A total of 56000 stars were injected at random positions onto each image for both filters. +" Photometry was then performed in the same way as described in the previous section, and the same selection criteria on the parameters were applied."," Photometry was then performed in the same way as described in the previous section, and the same selection criteria on the parameters were applied." +" The final detections were considered as stars if their position was within two pixels of the original list of injected sources, and their magnitude within 0.3 mag of the assigned value."," The final detections were considered as stars if their position was within two pixels of the original list of injected sources, and their magnitude within 0.3 mag of the assigned value." + Our photometric data reach the completeness level at V~25.6 mag and J~24.7 mag in all fields., Our photometric data reach the completeness level at $V \sim 25.6$ mag and $I \sim 24.7$ mag in all fields. + Figure 2 shows the CMD of the three fields in the southeastern region of the galaxy where the main complex is located (see Fig.," Figure \ref{cmdsouth} + shows the CMD of the three fields in the southeastern region of the galaxy where the main complex is located (see Fig." + 1)., 1). +" The CMDs of field SEI and SE2, which cover the two main substructures of the southeastern gaseous complex, are displayed in the andtop-right panels, respectively."," The CMDs of field SE1 and SE2, which cover the two main substructures of the southeastern gaseous complex, are displayed in the and panels, respectively." + Field SE3 maps the region between the feature and the optical disc of M33; the CMD of this area is shown in the bottom panels of the figure., Field SE3 maps the region between the feature and the optical disc of M33; the CMD of this area is shown in the bottom panels of the figure. +" To differentiate the stars at the edge of the optical disc from a more diffuse stellar component, we divided the field into two halves (SE3a, and SE3b; see Fig."," To differentiate the stars at the edge of the optical disc from a more diffuse stellar component, we divided the field into two halves (SE3a, and SE3b; see Fig." +" 1) and display the corresponding diagrams in thebottom-left andbottom-right panel of the figure, respectively."," 1) and display the corresponding diagrams in the and panel of the figure, respectively." +" The most prominent feature is the red giant branch (RGB), corresponding to stars with colours (V—I)o between 0.7 and 2 mag, and Ig«24 (see panel in Fig. 2))."," The most prominent feature is the red giant branch (RGB), corresponding to stars with colours $(V-I)_0$ between 0.7 and 2 mag, and $I_0 < 24$ (see panel in Fig. \ref{cmdsouth}) )." +" The RGB is clearly detected in all fields, although in SE2 and SE3a this feature is relatively less populated, especially in the upper end."," The RGB is clearly detected in all fields, although in SE2 and SE3a this feature is relatively less populated, especially in the upper end." + The edge of the optical disc of the galaxy is shown in panel SE3b as indicated by the redder and more populated RGB., The edge of the optical disc of the galaxy is shown in panel SE3b as indicated by the redder and more populated RGB. +" Because of the well-known age-metallicity degeneracy, different combinations of age and metal abundances are consistent with the colour of this feature."," Because of the well-known age-metallicity degeneracy, different combinations of age and metal abundances are consistent with the colour of this feature." +" This is shown in thetop-right panel where the RGB of SE2 is compared to isochrones from ?) with a common age of 10 Gyr and metallicities of [M/H]- -0.4, -0.7, -1, -1.3 (from redder to blue colours), where [M/H]= log(Z/Zo) and Zo = 0.019."," This is shown in the panel where the RGB of SE2 is compared to isochrones from \citet{2008A&A...482..883M} with a common age of 10 Gyr and metallicities of = -0.4, -0.7, -1, -1.3 (from redder to blue colours), where = $_{\odot}$ ) and $_{\odot}$ = 0.019." +" On the other hand, the width of the RGB could also be due to an age spread as the two isochrones at 1 and 10 Gyr (with [M/H]- -0.7"," On the other hand, the width of the RGB could also be due to an age spread as the two isochrones at 1 and 10 Gyr (with = -0.7" +their model of the 4U 1820-30 superburst. in which only —107erg (from a total of 4«107ergs) is radiated from the surface.,"their model of the 4U 1820-30 superburst, in which only $\approx 10^{42}\ {\rm erg}$ (from a total of $4\times 10^{43}\ {\rm ergs}$ ) is radiated from the surface." + However. the amount of neutrino emission is strongly dependent on the peak temperature. and therefore carbon fraction and ignition depth (CBO1).," However, the amount of neutrino emission is strongly dependent on the peak temperature, and therefore carbon fraction and ignition depth (CB01)." + Time-dependent models are therefore necessary to predict the superburst fluence., Time-dependent models are therefore necessary to predict the superburst fluence. + CBO! showed that for small carbon mass fractions. the carbon burns stably as the layer accumulates.," CB01 showed that for small carbon mass fractions, the carbon burns stably as the layer accumulates." +" Table 3 gives the minimum X, required for unstable ignition for each model.", Table 3 gives the minimum $X_C$ required for unstable ignition for each model. +" The range of values is Xe,= 0.08-0.2."," The range of values is $X_{C,{\rm min}}=0.08$ $0.2$." + Less carbon is required for smaller Qui. as shown by CBOI.," Less carbon is required for smaller $Q_{\rm crust}$, as shown by CB01." +" The values of Xc; given here are a little larger than those shown in CBOI’s Figure 2 because the less massive heavy element C°Fe rather than"" Ru) results in a shallower temperature gradient."," The values of $X_{C,{\rm min}}$ given here are a little larger than those shown in CB01's Figure 2 because the less massive heavy element $^{56}$ Fe rather than $^{104}$ Ru) results in a shallower temperature gradient." + The recurrence time for Χο= IS z10% lower than the recurrence time for Xc20.3.," The recurrence time for $X_C=X_{C,{\rm min}}$ is $\approx 10$ lower than the recurrence time for $X_C=0.3$." + In general. the models of Type I X-ray bursts presented in 82 give good agreement with observed recurrence times and energetics.," In general, the models of Type I X-ray bursts presented in 2 give good agreement with observed recurrence times and energetics." +" The observed 2—4h recurrence times are reproduced for a pure He companion if the time-averaged accretion rate is (M)z 7-10«107M...we!GIOkmr. or a hydrogen-poor companion if (Mjz 4-6«107?M...yr!(R/10km""."," The observed $2$ $4$ h recurrence times are reproduced for a pure He companion if the time-averaged accretion rate is $\dot{\left}\approx 7$ $10\times 10^{-9}\ M_\odot\ {\rm +yr^{-1}}\ (R/10\ {\rm km})^2$, or a hydrogen-poor companion if $\dot{\left}\approx 4$ $6\times 10^{-9}\ M_\odot\ {\rm +yr^{-1}}\ (R/10\ {\rm km})^2$." + This difference comes about because of extra heating from hot CNO burning during accumulation when hydrogen ts present. leading to earlier ignition. and requiring a lower #7 to match the observed recurrence times.," This difference comes about because of extra heating from hot CNO burning during accumulation when hydrogen is present, leading to earlier ignition, and requiring a lower $\dot +m$ to match the observed recurrence times." + For hydrogen to affect the temperature profile in the layer requires X>0.03 andZ=3x 107., For hydrogen to affect the temperature profile in the layer requires $X\gtrsim 0.03$ and $Z\gtrsim 3\times 10^{-3}$ . + If spallation reduces the metallicity in the accreted layer (Bildsten. Salpeter. Wasserman 1992). hydrogen burning will no longer play a role. in which case the accreting layer behaves like pure helium.," If spallation reduces the metallicity in the accreted layer (Bildsten, Salpeter, Wasserman 1992), hydrogen burning will no longer play a role, in which case the accreting layer behaves like pure helium." + These conclusions constrain evolutionary models. although both pure helium evolutionary models and those with hydrogen can be found that are consistent with the data.," These conclusions constrain evolutionary models, although both pure helium evolutionary models and those with hydrogen can be found that are consistent with the data." + A promising way to distinguish between different evolutionary scenarios is accurate fluence measurements as a function of #7., A promising way to distinguish between different evolutionary scenarios is accurate fluence measurements as a function of $\dot m$. + Models with hydrogen predict z10% variations in burst fluence as recurrence time varies. whereas pure helium models show a much smaller variation.," Models with hydrogen predict $\approx 10$ variations in burst fluence as recurrence time varies, whereas pure helium models show a much smaller variation." + For most models. recurrence time Is expected to vary as z|/mi. because the ignition. depth (determined by hot CNO burning or by the flux from the crust) is insensitive to accretion rate.," For most models, recurrence time is expected to vary as $\approx +1/\dot m$, because the ignition depth (determined by hot CNO burning or by the flux from the crust) is insensitive to accretion rate." + However. SAS-3 observations showed a much shallower dependence than the expected 1/71: Clark et al. (," However, SAS-3 observations showed a much shallower dependence than the expected $1/\dot m$ : Clark et al. (" +1977) observed the persistent flux increase by a factor of z5 while ἕως went from 3.4 to 2.2 hours.,"1977) observed the persistent flux increase by a factor of $\approx 5$ while $t_{\rm +recur}$ went from $3.4$ to $2.2$ hours." + Studies of timing and spectral behavior of LMXBs indicate that Ly is not necessarily well-correlated with the underlying accretion rate (e.g. van der Klis et al., Studies of timing and spectral behavior of LMXBs indicate that $L_X$ is not necessarily well-correlated with the underlying accretion rate (e.g. van der Klis et al. + 1990)., 1990). + The observed behavior then requires 77 to Increase less quickly than Ly., The observed behavior then requires $\dot m$ to increase less quickly than $L_X$. + It would be interesting to study burst properties as a function of an aceretion rate indicator (e.g. position in the color-color diagram) rather than Ly., It would be interesting to study burst properties as a function of an accretion rate indicator (e.g. position in the color-color diagram) rather than $L_X$. + Variations in heating with 7 due to thermal inertia might play some role. something that should be checked with time-dependent simulations.," Variations in heating with $\dot m$ due to thermal inertia might play some role, something that should be checked with time-dependent simulations." + Alternatively. these observations might indicate new physics. for example that the accreting material covers only part of the star at lower accretion rates. reducing the amount by which the local aceretion rate changes (a possibility suggested for hydrogen accretors by Bildsten 2000).," Alternatively, these observations might indicate new physics, for example that the accreting material covers only part of the star at lower accretion rates, reducing the amount by which the local accretion rate changes (a possibility suggested for hydrogen accretors by Bildsten 2000)." + An interesting exception to the predicted {μή behavior is for models with Xo~0.1. when the time to burn all the hydrogen is ~3 hours. in the range of observed recurrence times.," An interesting exception to the predicted $1/\dot m$ behavior is for models with $X_0\approx 0.1$, when the time to burn all the hydrogen is $\approx 3$ hours, in the range of observed recurrence times." + For Xozz0.] and fj;73 hours. the recurrence time ts predicted to increase rapidly with decreasing in. because hydrogen burning no longer occurs throughout the layer.," For $X_0\approx 0.1$ and $t_{\rm recur}>3$ hours, the recurrence time is predicted to increase rapidly with decreasing $\dot m$, because hydrogen burning no longer occurs throughout the layer." + However. this is even less consistent with the observed variations.," However, this is even less consistent with the observed variations." + The burst energy is overpredicted in. these models. in common with studies of other bursters.," The burst energy is overpredicted in these models, in common with studies of other bursters." + Galloway et al. (, Galloway et al. ( +2003) find a factor of 3—4 discrepancy for GS 1826-24. and following Bildsten (2000) propose that the accreted fuel only partially covers the neutron star surface.,"2003) find a factor of $3$ $4$ discrepancy for GS 1826-24, and following Bildsten (2000) propose that the accreted fuel only partially covers the neutron star surface." + For 4U 1636-56. Fujimoto et al. (," For 4U 1636-56, Fujimoto et al. (" +1987) proposed that vertical mixing driven by rotational shear in the incoming material led to early ignition. and reduced burst energies.,"1987) proposed that vertical mixing driven by rotational shear in the incoming material led to early ignition, and reduced burst energies." + Here. I find discrepancies of less than a factor of 2 for 4U 1820-30.," Here, I find discrepancies of less than a factor of 2 for 4U 1820-30." + This 15 easily accomodated. for example. by anisotropic burst emission (Lapidus Sunyaev 1985; Fujimoto 1988). and does not require incomplete spreading of the fuel or extra mixing.," This is easily accomodated, for example, by anisotropic burst emission (Lapidus Sunyaev 1985; Fujimoto 1988), and does not require incomplete spreading of the fuel or extra mixing." + Note however that the discrepancy increases if the neutron star radius is larger than the 10km assumed here GyXR., Note however that the discrepancy increases if the neutron star radius is larger than the $10\ {\rm km}$ assumed here $E_{\rm burst}\propto R^2$ ). + | have concentrated on the recurrence time and total burst energy. and have not discussed other properties. such as the peak luminosity or burst duration.," I have concentrated on the recurrence time and total burst energy, and have not discussed other properties, such as the peak luminosity or burst duration." + Type [ bursts from 4U 1820-30 generally show radius expansion. in which the luminosity reaches the Eddington limit.," Type I bursts from 4U 1820-30 generally show radius expansion, in which the luminosity reaches the Eddington limit." + Kuulkers et al. (, Kuulkers et al. ( +2003) recently surveyed the peak luminosity of globular cluster bursters.,2003) recently surveyed the peak luminosity of globular cluster bursters. + For 4U 1820-30. the average peak flux is 5.27+0.72«107ergem s7!. or a luminosity 3.7«1075ergsu! for a distance of 7.6 kpe.," For 4U 1820-30, the average peak flux is $5.27\pm 0.72\times 10^{-8}\ {\rm erg\ cm^{-2}\ s^{-1}}$ , or a luminosity $3.7\times 10^{38}\ {\rm erg\ s^{-1}}$ for a distance of $7.6$ kpc." + The pure helium Eddington limit is 3.545«.109eres! for M=14-2 M.. (not including general relativistic corrections).," The pure helium Eddington limit is $3.5$ $5\times 10^{38}\ +{\rm erg\ s^{-1}}$ for $M=1.4$ $2\ M_\odot$ (not including general relativistic corrections)." + When hydrogen is present. the Eddington luminosity is reduced by a factor 1-X.," When hydrogen is present, the Eddington luminosity is reduced by a factor $1+X$." + However. for small X. this change is much less than the uncertainty in the neutron star mass. and so does not allow a determination of hydrogen content.," However, for small $X$, this change is much less than the uncertainty in the neutron star mass, and so does not allow a determination of hydrogen content." + The durations of bursts from 4U 1820-30 are ~20-30 s (with exponential decay times =IO s). consistent with pure helium burning. in which the helium burns rapidly and the burst duration is set by the cooling time of the layer.," The durations of bursts from 4U 1820-30 are $\approx 20$ $30\ {\rm +s}$ (with exponential decay times $\lesssim 10\ {\rm s}$ ), consistent with pure helium burning, in which the helium burns rapidly and the burst duration is set by the cooling time of the layer." + For solar abundance of hydrogen. slow hydrogen burning via the rp process (Wallace Woosley 1981) extends the decay time to ~100s (Hanawa. Sugimoto. Hashimoto 1983: Wallace Woosley 1984: Hanawa Fujimoto 1984; Schatz et al.," For solar abundance of hydrogen, slow hydrogen burning via the rp process (Wallace Woosley 1981) extends the decay time to $\sim 100\ {\rm +s}$ (Hanawa, Sugimoto, Hashimoto 1983; Wallace Woosley 1984; Hanawa Fujimoto 1984; Schatz et al." + 1998)., 1998). + However. for X;=0.1. most of the protons are able to burn by direct capture on carbon.," However, for $X_0\lesssim 0.1$, most of the protons are able to burn by direct capture on carbon." + Therefore the small amount of hydrogen considered in this paper is not expected to substantially increase the burst duration., Therefore the small amount of hydrogen considered in this paper is not expected to substantially increase the burst duration. + This is something that could be addressed by time-dependent simulations with increasing hydrogen fractions., This is something that could be addressed by time-dependent simulations with increasing hydrogen fractions. + In $3. L used the z7/r's determined by matching the Type I burst recurrence times to calculate superburst ignition conditions.," In 3, I used the $\dot m$ 's determined by matching the Type I burst recurrence times to calculate superburst ignition conditions." +" For pure He accretion. the expected superburst recurrence times are z ]-2 years (for Qui,7 0.1-0.2 MeV per nucleon). much less than found by SBO2 (who took η= my)."," For pure He accretion, the expected superburst recurrence times are $\approx +1$ $2$ years (for $Q_{\rm crust}\approx 0.1$ $0.2$ MeV per nucleon), much less than found by SB02 (who took $\dot m=\dot m_X$ )." + If hydrogen is present.the smaller η gives recurrence times ~ 5-10 years.," If hydrogen is present,the smaller $\dot m$ gives recurrence times $\approx +5$ $10$ years." + This approach of simultaneously modelling Type I bursts and superbursts can be usefully applied to other superburst sources which exhibit regular Type I bursts., This approach of simultaneously modelling Type I bursts and superbursts can be usefully applied to other superburst sources which exhibit regular Type I bursts. + A promising candidate is KS 1731-260. for which observations of the quiescent flux," A promising candidate is KS 1731-260, for which observations of the quiescent flux" + - AOA) A= ,) = ) ) = ) = ). +The optimization proceeds as follows: There are a number of assumptions that we make in doing this optimization that may. bias the results in some manner., The optimization proceeds as follows: There are a number of assumptions that we make in doing this optimization that may bias the results in some manner. + Phey are: (1) we are applving a constant. number density with redshift using photomoetric-redshift target. pre-selection in order to ensure the most cllicient use of fibres. (2) we are optimizing for ACDAL. and (3) we are neglecting reconstruction of the acoustic peak at non-linear scales (Eisenstein οἱ al 200Gb) (i.e. assuming a non-linear power spectrum. cut-olf which evolves with redshift in the same stvle as Glazebrook Blake 2005).," They are: (1) we are applying a constant number density with redshift using photometric-redshift target pre-selection in order to ensure the most efficient use of fibres, (2) we are optimizing for $\Lambda$ CDM, and (3) we are neglecting reconstruction of the acoustic peak at non-linear scales (Eisenstein et al 2006b) (i.e. assuming a non-linear power spectrum cut-off which evolves with redshift in the same style as Glazebrook Blake 2005)." +" The assumec fiducial cosmological paranmicters are Q,,=0.3. Hl,=TOkms‘Alpe 1 Ob?=0.147. and of course wy=1 ancl ew,0."," The assumed fiducial cosmological parameters are $\Omega_m =0.3$, $H_0 = 70{\rm kms^{-1}Mpc^{-1}}$ , $\Omega_mh^2 = 0.147$, and of course $w_0=-1$ and $w_a=0$." +" We also assume a barvon fraction of 0.15. giving £2,=0.045 and a sound horizon of s=10ShtAlpe."," We also assume a baryon fraction of 0.15, giving $\Omega_b = 0.045$ and a sound horizon of $s = 108h^{-1}{\rm Mpc}$." + When optimizing a svstem. it is important to know how sensitive the optimal solution is to a slight change in the parameters.," When optimizing a system, it is important to know how sensitive the optimal solution is to a slight change in the parameters." +" We quantify this sensitivity using ""IHexibility bounds”. which are defined as the change in a survey parameter which decreases the FoM by relative to. the optimum."," We quantify this sensitivity using “flexibility bounds”, which are defined as the change in a survey parameter which decreases the FoM by relative to the optimum." + ‘Phe value of is arbitrary. based on comparisons of survey performance with other planned. experiments ancl possibilities of theoretical advancements.," The value of is arbitrary, based on comparisons of survey performance with other planned experiments and possibilities of theoretical advancements." + What this will mean for the error bars on the two parameters (uUo. we) is that. since the FoM is the square of the 1-0 error ellipse. a decrease in the FoM corresponds to a increase in the size of the error cllipse. or a zDA increase in cach error bar.," What this will mean for the error bars on the two parameters $w_0$, $w_a$ ) is that, since the FoM is the square of the $\sigma$ error ellipse, a decrease in the FoM corresponds to a increase in the size of the error ellipse, or a $\approx 5\%$ increase in each error bar." + We computed the Ilexibilitv bounds by considering the elfects of changing only one parameter. whilst keeping the other parameters at their optimal values (we do not account for correlations between parameters in their FoM dependence)," We computed the flexibility bounds by considering the effects of changing only one parameter, whilst keeping the other parameters at their optimal values (we do not account for correlations between parameters in their FoM dependence)." + We cleseribe here our mocel for converting a survey exposure time and redshift range into an observed. number density of target. galaxies lor spectroscopy., We describe here our model for converting a survey exposure time and redshift range into an observed number density of target galaxies for spectroscopy. + “Phe number counts calculator is constructed: using the observed: properties. of ] and z~3 galaxies taken [rom the literature (e.g. observed. Luminosity functions. ancl distributions of equivalent widths of emission lines)., The number counts calculator is constructed using the observed properties of $z \sim 1$ and $z \sim 3$ galaxies taken from the literature (e.g. observed luminosity functions and distributions of equivalent widths of emission lines). + We do not attempt to model observational issues such as the reliability of recshift extraction or confusion in line identifications., We do not attempt to model observational issues such as the reliability of redshift extraction or confusion in line identifications. + We consider four dillerent classes of galaxy: In ‘Table 3.. we list our assumptions for the required signal-to-noise ratio (S/N) to obtain a successful redshift for the four dillercnt galaxy classes discussed above.," We consider four different classes of galaxy: In Table \ref{tabsn}, we list our assumptions for the required signal-to-noise ratio $S/N$ ) to obtain a successful redshift for the four different galaxy classes discussed above." + These estimates are based. on previous experience. from. the literature and the 21SDSS LRG and. QSO (28LACQ) survey (Cannon ct al., These estimates are based on previous experience from the literature and the 2dF–SDSS LRG and QSO (2SLAQ) survey (Cannon et al. + 2006)., 2006). + l'or a given exposure time and redshilt. the number counts caleulator determines the Bux. limit) reachable for emission lines (OL or Lyman-a). or the apparent magnitude in the /-band reachable for continuum recdshifts. usinga full photon-counting calculation assuming the S/N values listed. in. Table 3...," For a given exposure time and redshift, the number counts calculator determines the flux limit reachable for emission lines ([OII] or $\alpha$), or the apparent magnitude in the $R$ -band reachable for continuum redshifts, usinga full photon-counting calculation assuming the $S/N$ values listed in Table \ref{tabsn}. ." + The WEALOS instrument is, The WFMOS instrument is +"where Cy=Cosfl Cy=[ee|eyLy, Where.irn is the total ummiber of clectrous per unit solid augle. equals to the number of protons im swept ISML","where $C_{1}=C_{2}\gamma_{\rm min}^{-p+1}$ $C_{2}=[\frac{\gamma_{\rm e,min}^{1-p}-\gamma_{\rm c}^{1-p}}{\gamma_{\rm c}(p-1)}+\frac{\gamma_{\rm c}^{-p}-\gamma_{\rm e,max}^{-p}}{p}]^{-1}N_{\rm e}$ Where $N_{\rm e}=\frac{1}{3}r^{3}n_{1}$ is the total number of electrons per unit solid angle, equals to the number of protons in swept ISM." +" +, is the critical electron Lorentz factor above which svuchrotron radiation is significant(Sari et al.", $\gamma_{\rm c}$ is the critical electron Lorentz factor above which synchrotron radiation is significant(Sari et al. + 1998)., 1998). +" l6epoTiu,c Semin SsYeSSSeanax“PA"," 2.For $\gamma_{\rm e,min}\leq\gamma_{\rm c}\leq\gamma_{\rm e,max}$ ." + Fig... =)Aniupillculation2 lLic1.1fop(Loat|lxος136M 56+. >t7σας36Alpc.ThA nearby κ.mumΕΕ(But⋅ the bulk 2002).Lorentz factor 3(0) keepsWe a oa i theED outflows.[m] arrive at[m] their. deceleratiou --..Fig.3 .is TereARF9," where $C_{3}=C_{4}\gamma_{\rm min}^{-p+1}$, $C_{4}=[\gamma_{\rm c}^{-1}\gamma_{\rm +e,min}^{1-p}+\frac{(1-p)\gamma_{\rm e,min}^{-p}-\gamma_{\rm +e,max}^{-p}}{p}]^{-1}N_{\rm e}$ 3.For $\gamma_{\rm c}\geq\gamma_{\rm e,max}$ where $C_{5}=\frac{p-1}{\gamma_{\rm e,min}^{1-p}-\gamma_{\rm +e,max}^{1-p}}N_{\rm e}$ We assume the bulk Lorentz factor $\gamma(\theta)$ keeps a constant before the outflows arrive at their deceleration radius $r_{\rm d}$." +71019 we choose fy = fhewhichmakes rgusing . ⋅ . Thi⋅ ≼⊳∐∪∪↴∖↴↸∖∣↗∶⋅↱⊐∙⊔⋝↸∖↸⊳⋜⋯↴∖↴↸∖∐↸∖↕∐≼↴∙⊾↕⊔∕∫−↴∕↻∪↖↖↽↸∖↥⋅↕⋜∏↖⇁∐↓≼∐∖⊼↕↴∖↴ ⋜↧↸⊳," Here we choose $k_{1}=k_{2}$ which makes $r_{\rm d}$ a constant at different $\theta$, this assumption will make calculations very simple." +∪∐↴∖↴↑⋜⋯↑⋜↧↑≼↕↕−↥↸∖↥⋅↸∖∐↑∣∣∙↑↕∐↴∖↴⋜↧↴∖↴↴∖↴∏∐∏≻⊓∪∐↖↖⇁↕∐↕⊔⋜∐↘↽↸∖ . . 1 ⋅⋅ ⋪⊔∪∏≓∙∣∙∐↴∖↴↖⇁⋪⊓↕↸∖↴∖↴↸∖↸," But notice that for different $\theta$, the time for outflows arrive at $r_{\rm d}$ is different." +∖⋯↴∖⋈↧↕↸∖⋯⋯↴∖↴∏⋪↧∙⋝∏↴∖↴⋯∐⋪∐⋅ ↸⊳⋜↧↕↸⊳∏↕⋜↧↑↕∪∐↴∖↴↖↽↸∖↥⋅⋅↖↽↴∖↴∐⊔↻↕↸∖∙↕≧∏↑∐∪↑↕∩∖↑∐⋜↧↑↕∪↥⋅≼∐↕−↥↸∖↥⋅↸∖∐↑∣∣∙ for outflows⋅ arrive⋅⋅⋅ at rq- is different. We ocalculate USthe N - ↑↕∐∖↕−⊓↕⊼↖↖↽∐↸∖," We calculate the flux when outflow reaches $r_{\rm d}$ at viewing angle $\theta_{\rm v}$, that time is: The equal arrival time surface at $\theta$ Our numerical results have been shown in Fig.1 and Fig.2." +∐⋯↕∏∪↖↖⇁↥⋅↸∖⋜↧↸⊳↕∐∖↴∖↴∣⋮≖⇂⋜↧���↖⇁↕↸∖↖↖↽↕∐∶↴∙⊾⋜⋯∶↴⋁↕↸∖∣∣∖↽∙↑∐⋜↧↑⋅ ↽is ∙∙defined surface at 0 is: may lead to ∩∙∩⊇∙↷↴⋃∶⋅↱⊐∩∩∙∣⋮≺⇂∶ ↓⋅∩∖∐∣⊓⇂≼⊳⋯⋅↙∕∟∶↕∖↕∩⇉↴↖≼⊳⋯⋅←↽≼⋅∶∩∙↕⋅←↽⊥⋟∶∩∙↕∙∣↗∶⊇∙↱⊐∙ ∕≍⋮∶⊇↕⋟∪↥⋅⋜↧∐∪∐⋯∐↕≯∪↥⋅⋯⋅↿≱↸∖↑⋜⋯≼⇂∕≍⋮∶∩↕⋟∪↥⋅⋜∐⊔∐∐↕⋟∪↥⋅⋯∪↕∐∖∙ ↕↑↴∖↴↸∖↸∖↕⊔↴∖↴↑∐⋜↧↑↕⋟∪," We choose $\theta_{\rm j}=0.1$, $\theta_{\rm c}=0.02$, $\gamma_{0}=500$, $r_{\rm d}=4.0\times 10^{16}{\rm cm}$ , $d_{\rm +L}=1\times 10^{28}{\rm cm}$, $\epsilon_{\rm e}=0.1$, $\epsilon_{\rm B}=0.1$, $p=2.5$, $k=2$ for a nonuniform jet and $k=0$ for an uniform one." +↥⋅⋜↧∐∪⋯∐∐↕⋟∪↥⋅⋯⋅↿↸∖↑∙↑↕∐∖↴∖↴⋉∖↸⊳⊓⋅⋜↧⋜↧↕∐↧ ∏∏↘↸∖↴∖↴∐↑↴⋝∪↑∐≼∶↕⊰↕≧↴∖↴⋜⋯≼↧⊸∖⊽↕⊰⋮∖↴∪↴⋝↴∖↴↸∖↥⋅↖↽⋜↧↑↕∪∐↴∖↴↕⋟⋜↧∐⋅↕⋅↖⇁," It seems that for a nonuniform jet, the spectra and fluxes fit both GRBs and XRFs observations fairly well." +↖↖⇁↸∖∐∙ ∖⊽↕↸∖↖↖⇁↸∖≺↧↕≯↥⋅∪⋯↑↕∐∖↸⊳↸∖∐↑↸∖↥⋅∙⊏↧⋝↕↴∖↴⋜∏⋝∪∏↑↕∪∩↕↘⊽↸∖∖⊽∿↕⋀∖↕↸∖∖⊽∙ and flux about is 10 Sore(0v100227sthe5 these are typical values for GRDs(o. (.," Viewed from the center, $E_{\rm p}$ is about $100{\rm KeV}\sim 1{\rm MeV}$, and flux is about $10^{-7\sim-6}{\rm erg}\cdot{\rm cm}^{-2}\cdot{\rm +s}^{-1}$, these are the typical values for GRBs(e.g." +ce. in Fie.l. the cases for =0.is 02.0.01).," in Fig.1, the cases for $\theta_{\rm v}=0,0.02,0.04$ )." +" While when viewed from off-axis. E) abo t 10KeVΊνα), fux is about 1077ας.Cl278 (e.c. in Fie.l. the cases for ος—0.0L. 0.06). thes¢ are the vpical values for NRFs."," While when viewed from off-axis, $E_{\rm p}$ is about $10{\rm KeV}-100{\rm KeV}$, flux is about $10^{-8\sim-7}{\rm erg}\cdot{\rm cm}^{-2}{\rm s}^{-1}$ (e.g. in Fig.1, the cases for $\theta_{\rm v}=0.04,0.06$ ), these are the typical values for XRFs." +" When 6,—0.0s.0.L. b is abou afew νο, the fiux secuis a little lower. but stiLB cal be ¢etected if the source distauce is lot so argo."," When $\theta_{\rm v}=0.08,0.1$, $E_{\rm +p}$ is about a few KeV, the flux seems a little lower, but still can be detected if the source distance is not so large." + But it seeuis that for an uniform jet. the fux from tli jet edge. where NRFs are thought to be fre 1uiu this inodel. are too ow.," But it seems that for an uniform jet, the flux from the jet edge, where XRFs are thought to be from in this model, are too low." + In this case the spectra pea sat TO0-100I&eV. the fluxes are about 10197.Porescm2.UN Noe. in Fig.2. the cases for (4.=0.105.0.11. 0.12).," In this case the spectra peak at 10-100KeV, the fluxes are about $10^{-13\sim -10}{\rm erg}\cdot{\rm cm}^{-2}{\rm s}^{-1}$ (e.g. in Fig.2, the cases for $\theta_{\rm v}=0.105,0.11,0.12$ )." + It can ouly explai- ΑΠΕ such as : xO.2(Yamazaki et al.," It can only explain nearby XRFs, such as $z\leq 0.2$ (Yamazaki et al." + 2002)., 2002). + (molo NRFs are more likely have cosmological orieius(IHeisezl D∙∡∡, But XRFs are more likely have cosmological origins(Heise 2002). + assume a.constant fif⋅⋅⋅ to the- most sieuificaut XN-rav flash.before ]. . our2 nonuuifornmi: jet model., Fig.3 is a fit to the most significant X-ray flash XRF971019 using our nonuniform jet model. +⋅ Here. we radius rg. L7., Here we choose $p=5.4$ because the high $\nu F_{\nu}$ power law index is about -1.7. + ⋅iil 2m : Ε ↙↾1 Ou ‘Lut lel ⋅. . case CRBOo iD980125 whosem Lnhieh-energv1 power-‘ ‘thepos⋅⋅ ↕⋜↧↖↖↽↻∐∪↑∪∐∐∐∖⊼↕↴∖↴⋅≻∙≺∖∶∶∩∙∣⋖≼∣⋜↧," This value seems a little unusual, but similar to the case of GRB980425 whose high-energy power-law photo index is $3.8\pm0.7$ (Galama et al." +↕⋜↧⊔⋜↧↸, 1998). +∖↑⋜↧↕∙↓⋂∩≺∖⋝∙⊸∖↕⊰⋮time ⋅ o ° NUM as N-rav. transients with. duration. less. than. tie is: ∎ p ⇁⊲ DAWN ↽⊥∪∩∣↴∖↴↖↖⇁↕∐↸⊳∐↕↴∖↴≼∐∖↑↸∖↸⊳↑↸∖≼↧⋝↖⇁∖↖⋮≼⋖∪∐↕≻↸∖⊔∪∺, XRF is defined as X-ray transients with duration less than $1000{\rm s}$ which is detected by WFC(on BeppoSAX) but not triggered GRBM(on BeppoSAX). +⊀≚⊸∖∏⋝∏↑∐∪↑ this definition The equal arrival time selection effects on those trausieuts (018. high power bw iudex.," Actually, this definition may lead to strong selection effects on those transients with high power law index." +" L1 2 IN We explosion has same luuinosity I Jon ⋅ ⋅ anele 0 is £,(0)=£,(0)(0/0.)2"," We assume that every explosion has same luminosity and jet shape, luminosity at center is $L_{\nu}(0)$, and at viewing angle $\theta$ is $L_{\nu}(\theta)=L_{\nu}(0)(\theta/\theta_{\rm +c})^{-2k_{1}}$." + Depending onu the viewing angle 0. a burst can be detected only at the distauce D(0): Tere £544 the threshold ofa detector.," Depending on the viewing angle $\theta$, a burst can be detected only at the distance $D(\theta)$: Here $F_{\nu,{\rm min}}$ is the threshold ofa detector." + Sothe uuubers of CBRDBsCNVonp) and NREsGNxnp.) are: mis the umber of bursts per unit volume. 04 is the critical anele. if viewing augle is larecr than it the explosion will be observed as ARFs.," Sothe numbers of $N_{\rm GRBs}$ ) and $N_{\rm XRFs}$ ) are: $n$ is the number of bursts per unit volume, $\theta_{\rm cr}$ is the critical angle, if viewing angle is larger than it the explosion will be observed as XRFs." +" We assiune the peal energy from the jet axis E, 1MeV. here we divide NRFs"," We assume the peak energy from the jet axis $E_{\rm p,c}=1{\rm MeV}$ , here we divide XRFs" +dependence on the stellar mass function and is basically the average number of mergers a galaxy experiences. per unit time.,dependence on the stellar mass function and is basically the average number of mergers a galaxy experiences per unit time. +" As such. E represents the average amount of time between mergers. and is independent of the merging scale 7, in the mocels."," As such, $\Gamma$ represents the average amount of time between mergers, and is independent of the merging time-scale $\tau_{\rm m}$ in the models." + We showresults for EL in Fig., We showresults for $\Gamma$ in Fig. +" 6. for the stellar mass ranges M,>LOM aand AL,>107M.", \ref{gamma1} for the stellar mass ranges $M_{\star} > 10^{10}$ and $M_{\star} > 10^{11}$. + 1n all the stellar mass bins we consider in the models. E is high at high redshilt. declines to à minimum at around z~1.5 and then rises again at lower redshifts for major mergers.," In all the stellar mass bins we consider in the models, $\Gamma$ is high at high redshift, declines to a minimum at around $z \sim 1.5$ and then rises again at lower redshifts for major mergers." + In other words. the predicted time between mergers at z2 is longer than it is at ~15.," In other words, the predicted time between mergers at $z>2$ is longer than it is at $z \sim 1.5$." + The predicted. E steadily increases with decreasing redshift at z<1.5. for all mass ranges and for both major and minor mergers.," The predicted $\Gamma$ steadily increases with decreasing redshift at $z<1.5$, for all mass ranges and for both major and minor mergers." + On the other hand. at -1.5. the predicted E slowly increases for major mereers. and decreases for minor mergers.," On the other hand, at $z>1.5$, the predicted $\Gamma$ slowly increases for major mergers, and decreases for minor mergers." + This is consistent with observations of massive galaxies (e.g. Conselice 20082).," This is consistent with observations of massive galaxies (e.g., \citealt{cons2008}) )." +" Phe predicted E for major mergers is about ten times larger than observed for galaxies with A,2101""AL... while it matches the observations well at low redshifts for galaxies with AJ,2Lott aat ο<2."," The predicted $\Gamma$ for major mergers is about ten times larger than observed for galaxies with $M_{\star} > 10^{10}$, while it matches the observations well at low redshifts for galaxies with $M_{\star} > 10^{11}$ at $z < 2$." +" This is a further indication that the merging history of galaxies with A4,«1044 cdo not agree in simulations and observations.", This is a further indication that the merging history of galaxies with $M_{\star} < 10^{11}$ do not agree in simulations and observations. + A common thing to try when examining the evolution of the merger fraction is to. parameterise the evolution in various ways., A common thing to try when examining the evolution of the merger fraction is to parameterise the evolution in various ways. + As discussed in Conseliceetal.(2008).. the two most popular wavs to. parameterise the merger fraction are through a power-law and through a combined exponential/power-law Press-Scheehter-like function.," As discussed in \citet{cons2008}, the two most popular ways to parameterise the merger fraction are through a power-law and through a combined exponential/power-law Press-Schechter-like function." + The power-law [fit is bv far the most common method. but. is becoming less fashionable as it appears that the observed merger [fraction turns over at. high redshifts (Conscliceetal. 2008).. while a power-law continues to increase at all redshifts.," The power-law fit is by far the most common method, but is becoming less fashionable as it appears that the observed merger fraction turns over at high redshifts \citep{cons2008}, while a power-law continues to increase at all redshifts." + Phe form of the power-law evolution is given hy: where fü(2) is the merger fraction at a given redshift. fo is the merger fraction at ο=O and m is the power-aw index for characterising the merger fraction evolution.," The form of the power-law evolution is given by: where $f_{\rm m}(z)$ is the merger fraction at a given redshift, $f_{0}$ is the merger fraction at $z = 0$ and $m$ is the power-law index for characterising the merger fraction evolution." +" Investigating how to parameterise the increase in the oedicted. merger [fraction evolution is another wav to determine how the observed and. predicted merger fractions differ,", Investigating how to parameterise the increase in the predicted merger fraction evolution is another way to determine how the observed and predicted merger fractions differ. + We find from. previous work that the index m on his power-law increase in the mereer fraction is tvpically m~2. 3. which has been found using a variety of techniques (c.g..Conscliceet.al. 2008: Conseliceetal.2009 and references therein)," We find from previous work that the index $m$ on this power-law increase in the merger fraction is typically $m \sim 2-3$ , which has been found using a variety of techniques (e.g.,\citealt{cons2008}; ; \citealt{cons2009} and references therein)." +" We find that the merger fraction in the Millennium. simulation can be characterised by a power-law index m=1.6 for z1 and m—0.99 at 1LOMi and m=3 for galaxies with masses AM,>LOM aat 2<1."," We find that the merger fraction in the Millennium simulation can be characterised by a power-law index $m = 1.6$ for $z\leq 1$ and $m=0.99$ at $1 10^{11}$, and $m = 3$ for galaxies with masses $M_{\star} > 10^{10}$ at $z < 1$." + These power lav [fits are only valid up to the merger fraction turnover at z1L5., These power law fits are only valid up to the merger fraction turnover at $z \sim 1 - 1.5$. + While the amplitude of the observed: merger fractions are higher than the simulation. theslope is fairly similar to the predictions.," While the amplitude of the observed merger fractions are higher than the simulation, theslope is fairly similar to the predictions." + Another way of characterising the merger [raction evolution. which is based on theoretical arguments that use the Press-Schechter formalism. (Carlberg.1990)... is à combined power-law exponential evolution of the form: This combined power-law/exponential description reproduces the observations better than a simple power-law (Consclice200623) and [its the merger. fraction predictions. as well as the data (c.g.. Conseliceetal.20093).," Another way of characterising the merger fraction evolution, which is based on theoretical arguments that use the Press-Schechter formalism \citep{carlberg1990}, is a combined power-law exponential evolution of the form: This combined power-law/exponential description reproduces the observations better than a simple power-law \citep{cons2006} and fits the merger fraction predictions, as well as the data (e.g., \citealt{cons2009}) )." + The behaviour of the merger fraction evolution can be interpreted as either the result. of mergers occurring later [or massive galaxies in haloes. due to the dynamical friction time-scales. or to the fact that there are not many. very massive galaxies to merge with at early times. resulting in a lowered merger fraction.," The behaviour of the merger fraction evolution can be interpreted as either the result of mergers occurring later for massive galaxies in haloes, due to the dynamical friction time-scales, or to the fact that there are not many very massive galaxies to merge with at early times, resulting in a lowered merger fraction." +" In. general. it appears that all galaxies. with the exception of the most massive ones with Al,>»10+ have a turnover in their merger fraction history and can be fit by an exponential/power-law. which is likely the correct. form. for parameterising the merger fraction history."," In general, it appears that all galaxies, with the exception of the most massive ones with $M_{\star} > 10^{11}$, have a turnover in their merger fraction history and can be fit by an exponential/power-law, which is likely the correct form for parameterising the merger fraction history." + In this Subsection we present results for the merger rate in the simulations ancl compare them to the observational data., In this Subsection we present results for the merger rate in the simulations and compare them to the observational data. + The merger rate iis currently the most uncertain merger quantity to measure in observations., The merger rate is currently the most uncertain merger quantity to measure in observations. + Estimates will likely become more straight-forward as our understanding and knowledge of galaxy number densities. merger fractions and merger time-scales improve.," Estimates will likely become more straight-forward as our understanding and knowledge of galaxy number densities, merger fractions and merger time-scales improve." + On the other hand. the merger rate is a relatively easy quantity to measure in simulations. once a proper definition has been agreed upon.," On the other hand, the merger rate is a relatively easy quantity to measure in simulations, once a proper definition has been agreed upon." + Since iis calculated by dividing the galaxy merger fraction. which scales with the time-scale. by the time-scale. the merger rate is independent of the time-scale τι used. to measure the merger fractions.," Since is calculated by dividing the galaxy merger fraction, which scales with the time-scale, by the time-scale, the merger rate is independent of the time-scale $\tau_{\rm m}$ used to measure the merger fractions." + This is true under the assumption that the merger rate slowly varies with time and can be considered approximately constant within a short time-scale., This is true under the assumption that the merger rate slowly varies with time and can be considered approximately constant within a short time-scale. + Llowever. the assumption breaks down for laree time-scales. because the merger rate itself is not intrinsically constant over large lime spans.," However, the assumption breaks down for large time-scales, because the merger rate itself is not intrinsically constant over large time spans." + The comparison of the predicted. and observed: merger rates is shown in Fig. 7.., The comparison of the predicted and observed merger rates is shown in Fig. \ref{lastfig}. +" The predicted merger rates for the o"" AL<1077 eealaxies (upper left panel) agree well with the data. despite he shortcomings due to lack of resolution in the simulation."," The predicted merger rates for the $10^{9}$ $1044 ((lower panel). agree with the observations within the error AES."," The results for the other mass bins, that is $M_{\star}> 10^{10}$ (upper right panel) and $M_{\star}> 10^{11}$ (lower panel), agree with the observations within the error bars." + The merger rates display a surprisingly good agreement otween the observations and the Millennium. simulation. which is not seen for the merger fractions of galaxies with AL«101.AL...," The merger rates display a surprisingly good agreement between the observations and the Millennium simulation, which is not seen for the merger fractions of galaxies with $M_{\star}< 10^{11}$." + Since the observed and. predieted. merger ractions agree only for the most massive galaxies. the agreement for the lower mass bins is likely coincidental.," Since the observed and predicted merger fractions agree only for the most massive galaxies, the agreement for the lower mass bins is likely coincidental." + As discussed inSubsection 2.3. the merger rate is a function of the galaxy merger fraction fai. the number density of galaxies ra and the time-scale for merging Ty.," As discussed inSubsection \ref{definition}, the merger rate is a function of the galaxy merger fraction $f_{\rm gm}$ , the number density of galaxies $n_{\rm gm}$ and the time-scale for merging $\tau_{\rm m}$ ." + Any one of these quantities can allect the measurement. of the, Any one of these quantities can affect the measurement of the +The preset understanding of cosmic structure formation relies on the observations of a Universe expanding at a rate of ff)2YOkm/s/Mpc and whose energy. budget is larecly dominated by a form of unknown ‘dark’ CDOrgv or cosmological constant. A. that. contributes ~το to the total cosmic cnerey content.,"The preset understanding of cosmic structure formation relies on the observations of a Universe expanding at a rate of $H_0\simeq\rm +70\,km/s/Mpc$ and whose energy budget is largely dominated by a form of unknown `dark' energy or cosmological constant, $\Lambda$, that contributes $\sim70\%$ to the total cosmic energy content." +" ""The residual matter contribution is roughly ~30%. but onlv a verv small fraction of ~4% consists of ordinary barvonic matter. while the rest is unknown cold. (i.e. non-relativistic) ""dark matter (DAL)."," The residual matter contribution is roughly $\sim 30\%$, but only a very small fraction of $\sim 4\%$ consists of ordinary baryonic matter, while the rest is unknown cold (i.e. non-relativistic) `dark matter' (DM)." +" Alore precisely. recent determinations suggest 0,4,=0.272. Qo,=0.728. and 044,=0.044 (?).."," More precisely, recent determinations suggest $\Omegam = 0.272$, $\Omegal = 0.728$, and $\Omegab = 0.044$ \cite[][]{Komatsu2011}." + 1n this framework. also called ACDAL model. cosmological structures can grow from gravitational instability (2) ο primordial matter Huctuations. probably originated. during the »imorcdial inflationary epoch.," In this framework, also called $\Lambda$ CDM model, cosmological structures can grow from gravitational instability \cite[][]{Jeans1902} + of primordial matter fluctuations, probably originated during the primordial inflationary epoch." + Vhese carly perturbations represent the seeds which would develop into present-cay ealaxies and stars (2). by gas cooling and condensation (?).. and they will affect. the surrounding environment through a number of mechanical. chemical and. radiative processes commonly known as feedback elfects (onthistopic.seetheextensivereviewby 7).," These early perturbations represent the seeds which would develop into present-day galaxies and stars \cite[][]{SS1953} by gas cooling and condensation \cite[][]{Spitzer1962}, and they will affect the surrounding environment through a number of mechanical, chemical and radiative processes commonly known as feedback effects \cite[on this topic, see the extensive review by][]{CiardiFerrara2005}." + Quantitatively speaking. linear. perturbation analyses are usually performed to. study the initial phases. of gravitational collapse. where a Gaussian density clistribution for the primordial matter Huüctuations is assumed.," Quantitatively speaking, linear perturbation analyses are usually performed to study the initial phases of gravitational collapse, where a Gaussian density distribution for the primordial matter fluctuations is assumed." + The linear expansion of the continuity. Euler. and energy equations can also be extended. with higher-order corrections. (e.g.??71) or non-Gaussian deviations (e.g.27077770)).. bu to studyv non-linear regimes and feedback mechanisms it ds essential to perform. numerical integrations anc use N-bodyfhyelro simulations.," The linear expansion of the continuity, Euler, and energy equations can also be extended with higher-order corrections \cite[e.g.][]{TseliakhovichHirata2010,Maio2011b,Stacy2011,Greif2011arXiv} + or non-Gaussian deviations \cite[e.g.][]{Grinstein1986,Koyama1999,Komatsu2002,Grossi2007,Desjacques2009,MaioIannuzzi2011,Maio2011arXiv,MaioKhochfar2011arXiv}, but to study non-linear regimes and feedback mechanisms it is essential to perform numerical integrations and use N-body/hydro simulations." + Indeed. to capture early eas collapse it is needed not only to follow gravity anc hivelrodyvnamics. but. also its full ehemistev. evolution auk molecule formation.," Indeed, to capture early gas collapse it is needed not only to follow gravity and hydrodynamics, but also its full chemistry evolution and molecule formation." + Since in the cosmic medium hydrogen (11) is the most abundant species with a cosmologica mass fraction of Vyx0.76 (corresponding to 0.93 in number fraction). its contribution in gas cooling is likely to play a very relevant. role. together with helium. (110).," Since in the cosmic medium hydrogen (H) is the most abundant species with a cosmological mass fraction of $X_{\rm H}\simeq 0.76 $ (corresponding to $\sim 0.93$ in number fraction), its contribution in gas cooling is likely to play a very relevant role, together with helium (He)." + llowever. LE and He collisional processes are able to cool," However, H and He collisional processes are able to cool" +Space Administration. the National Science Foundation. the U.S. Department of Energy. the Japanese Monbukagakusho. aud the Max Planck Society.,"Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society." + The SDSS is managed by the Astrophysical Researeh Consortium (ARC) for the Participating Institutions., The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. + The Participating Institutions are The University of Chicago. Fermilab. the Institute for Advanced Study. the Japan Participation Group. The Johns Hopkins University. Los Alamos National Laboratory. ihe Max-Planck-Institute for Astronomy (AIPIA). the Masx-Planeck-Institute for Astrophysics (AIPA). New Mexico State Universitv. Princeton University. the United States Naval Observatory. and the University of Washington.," The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Princeton University, the United States Naval Observatory, and the University of Washington." +through the Galactic disk.,through the Galactic disk. + The test particles are integrated for four racial oscillations periods of the dwarf galaxy orbit., The test particles are integrated for four radial oscillations periods of the dwarf galaxy orbit. + Thus the disk. feels four close pericenter passages., Thus the disk feels four close pericenter passages. + The eravitational potential of the Galaxy is not varied during the simulation. thus there is no indirect. perturbation that should have been caused by variation in the position of the center of the galaxy with respect to the center of mass frame.," The gravitational potential of the Galaxy is not varied during the simulation, thus there is no indirect perturbation that should have been caused by variation in the position of the center of the galaxy with respect to the center of mass frame." + As these are test particle simulations. the sell-gravity of the disk and response ofthe halo to the satellite are neglected.," As these are test particle simulations, the self-gravity of the disk and response of the halo to the satellite are neglected." +" We work in units of the Sun's radius from the Galactic center (Ryz8.5 kpc) and the rotational velocity for à particle in a circular orbit at Ay or eyzz 220 kms. Masses are given in units of Aly,=raha104:A4...", We work in units of the Sun's radius from the Galactic center $R_0 \approx 8.5$ kpc) and the rotational velocity for a particle in a circular orbit at $R_0$ or $v_0 \approx$ 220 km/s. Masses are given in units of $M_0 = {v_0^2 R_0 \over G} \approx 10^{11} M_\odot$. + Timescales are given in units of the rotation period. at. Ly or {νιτε 240 Myr., Timescales are given in units of the rotation period at $R_0$ or $P_0 \approx $ 240 Myr. + Initial disk particles are chosen between 0.5 and 2.5 Ry., Initial disk particles are chosen between 0.5 and 2.5 $R_0$. +" The softening length for the satellite is 0.1 Ay and that for the rotation curve is à=0.172, and within the radii of disk particles simulated.", The softening length for the satellite is 0.1 $R_0$ and that for the rotation curve is $a =0.1 R_0$ and within the radii of disk particles simulated. + The simulations are run with code described by Bagleyetal.(2000). but lacking a bar perturbation.," The simulations are run with code described by \cite{bagley09} + but lacking a bar perturbation." + To compute spatial distributions. we used 10° particles.," To compute spatial distributions, we used $10^5$ particles." +" To compute mean velocity components. mean clisk height and angular momentum and energy distributions we used simulations with 10"" particles."," To compute mean velocity components, mean disk height and angular momentum and energy distributions we used simulations with $10^6$ particles." + We used simulations of 10' disk particles to compute velocity distributions of stars in the neighborhood of a point in the disk., We used simulations of $10^7$ disk particles to compute velocity distributions of stars in the neighborhood of a point in the disk. + This allows us to search for fine structure in the velocity distribution of stars near a specific location in the disk. (like the solar neighborhood)., This allows us to search for fine structure in the velocity distribution of stars near a specific location in the disk (like the solar neighborhood). +" While the current mass of Sgr dwarf galaxy ~5107A4. is not massive enough to stronely perturb the Galactic disk. this galaxy could have been a few times LO""AL. in the past (e.g. see discussion by Lawetal.2005:Zhao 2004)) and so similar in mass to the subhalos considered by Ixazantzicisetal. (2008)."," While the current mass of Sgr dwarf galaxy $\sim 5 \times 10^8 M_\odot$ is not massive enough to strongly perturb the Galactic disk, this galaxy could have been a few times $10^9 M_\odot$ in the past (e.g., see discussion by \citealt{law05,zhao04}) ) and so similar in mass to the subhalos considered by \citet{kazantzidis08}." + In the context of a CDM hierarchical galaxy formation paradigm. Ixazantzidisetal.(2008) show that i is not uncommon for a subhalos of sizescale ~LOMAL. to merge with a Milkv Way sized galaxy.," In the context of a CDM hierarchical galaxy formation paradigm, \citet{kazantzidis08} show that it is not uncommon for a subhalos of sizescale $\sim 10^{10} M_\odot$ to merge with a Milky Way sized galaxy." + We consider satellites on tight orbits with pericenters approximately 1.342). arn masses 0.03 to 0.1 Ady (3 to 10.10AZ. )., We consider satellites on tight orbits with pericenters approximately $1.3 R_0$ and masses 0.03 to 0.1 $M_0$ $3$ to $10 \times 10^9 M_\odot$ ). + Our satellites have »ericenter and period similar to the shorter values estimatec or Ser galaxy., Our satellites have pericenter and period similar to the shorter values estimated for Sgr galaxy. + In our units the estimated peri and apocenter CGalactocentric radii of Ser ealaxy’s orbit are 1.3.2.0 anc 6.57.0 (Lawetal.2005)., In our units the estimated peri and apocenter Galactocentric radii of Sgr galaxy's orbit are 1.3–2.0 and 6.5–7.0 \citep{law05}. +. Our simulation parameters are isted. in Table 1.., Our simulation parameters are listed in Table \ref{tab:tab1}. + Phe galaxy halo potential is chosen to » mulelly oblate with q=0.95., The galaxy halo potential is chosen to be mildly oblate with $q=0.95$. + We chose a non-spherica »otential so as to allow mild. variations between pericenter ealactocentric radii., We chose a non-spherical potential so as to allow mild variations between pericenter galactocentric radii. + Variations in the orbit would have been oesent if dynamical friction were present or if the Milky Way gravitational potential were allowed to respond to the »erturbation., Variations in the orbit would have been present if dynamical friction were present or if the Milky Way gravitational potential were allowed to respond to the perturbation. + In Figure Gaa we show the morphology in the plane of the Galaxy as a [function of time from the simulation Al with parameters listed in Table 1 and satellite on a polar orbit., In Figure \ref{fig:xyh}a a we show the morphology in the plane of the Galaxy as a function of time from the simulation A1 with parameters listed in Table \ref{tab:tab1} and satellite on a polar orbit. + Images are shown separated in time by 3/4 of P. the orbital period at the Sun.," Images are shown separated in time by 3/4 of $P_0$, the orbital period at the Sun." + In Figure 6 the galaxy is oriented so that rotation is clockwise., In Figure \ref{fig:xyh} the galaxy is oriented so that rotation is clockwise. + The simulation shown in Figure 6aa has satellite orbit resembling that of Ser clwarl., The simulation shown in Figure \ref{fig:xyh}a a has satellite orbit resembling that of Sgr dwarf. + The orbit is oriented so that is it polar or lving in the jJ.2 plane.," The orbit is oriented so that is it polar or lying in the $y,z$ plane." + The first. pericenter passage is experienced 1.5 orbital periods (at the Sun) from 16 beginning of the simulation., The first pericenter passage is experienced 1.5 orbital periods (at the Sun) from the beginning of the simulation. + Phe first pericenter occurs below the Galactic plane., The first pericenter occurs below the Galactic plane. + The second. and third. pericenter passages occur closer to the Galactic plane., The second and third pericenter passages occur closer to the Galactic plane. + Phe pericenters close approaches and passages through the plane of the Galaxy induce velocity impulses in the stars in Galactic disk., The pericenters close approaches and passages through the plane of the Galaxy induce velocity impulses in the stars in Galactic disk. + Following the second pericenter spiral structure is induced in ——1e disk with structure similar to that seen in simulations of vbys CPutukov&Fedorova2006:Youngeretal.2008).," Following the second pericenter spiral structure is induced in the disk with structure similar to that seen in simulations of flybys \citep{tutukov06,younger08}." +. The isk also exhibits some LIopsidedness though not as much as isplaved by the atomic hydrogen distribution in the Milky Wav's outer clisk (Levineetal.2006a)., The disk also exhibits some lopsidedness though not as much as displayed by the atomic hydrogen distribution in the Milky Way's outer disk \citep{levine06a}. +. Alultiple close passages cause stronger spiral structure than a single Bvby., Multiple close passages cause stronger spiral structure than a single flyby. + This is not surprising as the tidal force during pericenter lasts longer when the orbit is bound rather than parabolic. and the disk. cannot completely dynamically relax between pericenters.," This is not surprising as the tidal force during pericenter lasts longer when the orbit is bound rather than parabolic, and the disk cannot completely dynamically relax between pericenters." + The disk. receives multiple perturbations from cach close approach which can aclel constructively or clestructively to particle eecentricity or inclination as the timescale between pericenters. about 3 Ly. is comparable to the orbital period at 2 Ly (or 2 11).," The disk receives multiple perturbations from each close approach which can add constructively or destructively to particle eccentricity or inclination as the timescale between pericenters, about 3 $P_0$, is comparable to the orbital period at 2 $R_0$ (or 2 $P_0$ )." + Inspection of Figure 6. shows that particle orbits can intersect. other orbits., Inspection of Figure \ref{fig:xyh} shows that particle orbits can intersect other orbits. + Stellar orbits can cross cach other but gas clouds would collide., Stellar orbits can cross each other but gas clouds would collide. + As we see orbits that intersect each other. the gas distribution may cilfer from the stellar distribution.," As we see orbits that intersect each other, the gas distribution may differ from the stellar distribution." + Lt is interesting to place this in. perspective with the outer Galaxy., It is interesting to place this in perspective with the outer Galaxy. + There is no clear structure in the 111 distribution (as seen in the maps by Levinectal.2006a)) in the Alilky Way associated with the Monoceros stream (as seen in the maps by Juricetal. 2008)) even though there is LIL gas detected in the same region., There is no clear structure in the HI distribution (as seen in the maps by \citealt{levine06a}) ) in the Milky Way associated with the Monoceros stream (as seen in the maps by \citealt{juric08}) ) even though there is HI gas detected in the same region. + Figure Ghb is similar to Figure Gaa except showing a the disk. perturbed by a satellite on a prograce inclined orbit. (simulation A2)., Figure \ref{fig:xyh}b b is similar to Figure \ref{fig:xyh}a a except showing a the disk perturbed by a satellite on a prograde inclined orbit (simulation A2). + The orbit’s spin axis is 30 from the Galactic pole., The orbit's spin axis is $^\circ$ from the Galactic pole. + We see that the perturbations on the disk are stronger for the inclined. orbit., We see that the perturbations on the disk are stronger for the inclined orbit. + The outer disk is more strongly scattered and the induced spiral structure is stronger., The outer disk is more strongly scattered and the induced spiral structure is stronger. + After the last pericenter passage. the mean height of the disk above the Galactic plane. radial and tangential velocity components (in CGalactocentrie coordinates) are shown in ligure 7. for both simulations.," After the last pericenter passage, the mean height of the disk above the Galactic plane, radial and tangential velocity components (in Galactocentric coordinates) are shown in Figure \ref{fig:sag} for both simulations." + For these plots the racial velocity component is positive in the direction away from the Galactic center., For these plots the radial velocity component is positive in the direction away from the Galactic center. + The velocity of a particle in a circular orbit ws been subtracted from the tangential velocity component., The velocity of a particle in a circular orbit has been subtracted from the tangential velocity component. + As have other works (c.g. TPutukov&Feclorova2006:Youngerctal.2008:Ixazantzidiset 2008)) we find hat the satellite induces spiral structure in the outer disk that is similar to that in Monoceros. stream.," As have other works (e.g., \citealt{tutukov06,younger08,kazantzidis08}) ) we find that the satellite induces spiral structure in the outer disk that is similar to that in Monoceros stream." + The angential velocity component. is not expected to be high (second. panels from top in Figure 7)) but there should be moderate racial velocity. variations (top panels in. Figure 7))., The tangential velocity component is not expected to be high (second panels from top in Figure \ref{fig:sag}) ) but there should be moderate radial velocity variations (top panels in Figure \ref{fig:sag}) ). + A comparison between the mean velocity components. he density. distribution and the mean height (shown in the second panels from bottom in Figure 7)) suggests that there could be correlations between these quantities in the outer Milky Way. though as we have neglected sell-eravity in the disk. we should be cautious with this implication.," A comparison between the mean velocity components, the density distribution and the mean height (shown in the second panels from bottom in Figure \ref{fig:sag}) ) suggests that there could be correlations between these quantities in the outer Milky Way, though as we have neglected self-gravity in the disk, we should be cautious with this implication." + We see from the second panel from the bottom in Figure 7 that a warp has been excited. hy the passages of the satellite., We see from the second panel from the bottom in Figure \ref{fig:sag} that a warp has been excited by the passages of the satellite. + Phe warp is complex and not well described by a, The warp is complex and not well described by a +ieluded da our simulations. aud averaging over large numbers oclusters produces reasonable results.,"included in our simulations, and averaging over large numbers of clusters produces reasonable results." + Oue effect we have not included is full selection of clusters im redshitt space., One effect we have not included is full selection of clusters in redshift space. + In the simulation. we simply «lefine a cluster in real space With a linking leneth of our choice.," In the simulation, we simply define a cluster in real space with a linking length of our choice." + Iu a survey. we select the clusters in redshift space and we iuclude some contanunating galaxies behind aud in frout of each cluster that are not members.," In a survey, we select the clusters in redshift space and we include some contaminating galaxies behind and in front of each cluster that are not members." + This would act to ierease the noise. but not by much. as they will be heavily outuuubered by cluster members.," This would act to increase the noise, but not by much, as they will be heavily outnumbered by cluster members." + A real problem would be any effect which gives a systematically positive or negative redshift for the ceutral ealaxv with respect to the other galaxies., A real problem would be any effect which gives a systematically positive or negative redshift for the central galaxy with respect to the other galaxies. + If we select cluster galaxies using a cone of coust:uit aueular size rather than a cvliuder of fixed radius. ther1 niore coutaminating ealaxies will come frou he larger volume behiud the cluster than in front. and the average redshift of the ealaxies apart from the central one will chanec.," If we select cluster galaxies using a cone of constant angular size rather than a cylinder of fixed radius, then more contaminating galaxies will come from the larger volume behind the cluster than in front, and the average redshift of the galaxies apart from the central one will change." + We have calculated the poteutial effect of this bias using the cluster-ealaxy cross-correlation function dat aot Croft (1999) to find the muuber of coutaminating galaxies., We have calculated the potential effect of this bias using the cluster-galaxy cross-correlation function data of Croft (1999) to find the number of contaminating galaxies. + We find a relative blucshift of ~1kms.! for tl1e central ealaxy., We find a relative blueshift of $\sim 1\kms$ for the central galaxy. + This C1 be avoided simply by using a evliuder to select cluster members. however.," This can be avoided simply by using a cylinder to select cluster members, however." + An additional poteutial probleui which gocs in the opposite direction is the fact that wit ha maguitude limited survey. the contaminating galaxies belind the cluster should © fewer 1n umber because they are at a greater clistance.," An additional potential problem which goes in the opposite direction is the fact that with a magnitude limited survey, the contaminating galaxies behind the cluster should be fewer in number because they are at a greater distance." + The size of this effect depends ou the steepness of the πιοτν function of galaxies., The size of this effect depends on the steepness of the luminosity function of galaxies. + It cotud also however easilv o elimiuated. by applying a local voluue ιτ in the vicinity of cach cluster. rejecting eaaxies Which would be oo faint when placed at the far edee of the cluster.," It could also however easily be eliminated by applying a local volume limit in the vicinity of each cluster, rejecting galaxies which would be too faint when placed at the far edge of the cluster." + Tu this paper we have seeu that reaistically. eravitational redshifts are an extremely siuall effec fand that looking at he most massive galaxy clusters may not help in detection vecatise the noise is wach larger thai for mall clusters.," In this paper we have seen that realistically, gravitational redshifts are an extremely small effect, and that looking at the most massive galaxy clusters may not help in detection because the noise is much larger than for small clusters." + If a detection is to be made using a eaaxy survey. it will be nuportant to carry out cross checks.," If a detection is to be made using a galaxy survey, it will be important to carry out cross checks." + For example. enough data needs to be a available that clusers can be divided by mass into more than oue bin. to make sure that the effect is largest for the Ligh mass clusters (even if the error bar is large).," For example, enough data needs to be a available that clusters can be divided by mass into more than one bin, to make sure that the effect is largest for the high mass clusters (even if the error bar is large)." + The more tracers of the €usters potential that are available. the better.," The more tracers of the clusters potential that are available, the better." + Droadlirst Scaunapieco (2000) have shown that X-ray emission from intracluster gas could be used., Broadhurst Scannapieco (2000) have shown that X-ray emission from intracluster gas could be used. + Other probes of the potential could include using redshifts of iutracluster planetary nebulae (e.g.. Feldieier 2003).," Other probes of the potential could include using redshifts of intracluster planetary nebulae (e.g., Feldmeier 2003)." + It may be mareinally possible to detect the eravitational redshift of cluster ealaxies with the data available today., It may be marginally possible to detect the gravitational redshift of cluster galaxies with the data available today. + ILowever. more survevs of ereater scope have beeu duaeined for the future.," However, more surveys of greater scope have been imagined for the future." + Someday this will provide us eunouchli information to pAseparate the gravitational redslüft effect from total redshift., Someday this will provide us enough information to separate the gravitational redshift effect from total redshift. + We thauk the anouvimous referee for useful sugeestious., We thank the anonymous referee for useful suggestions. +OO RACC ackuowledges support from the NASA-LTSA program. contract NAC5-1163L.," RACC acknowledges support from the NASA-LTSA program, contract NAG5-11634." +of NA-vav producing clectrous is equivalent to celectrou loss rate from aacceleration region. FO=Nn.,"of X-ray producing electrons is equivalent to electron loss rate from acceleration region, $F_e(t)=N_r(t)/\tau_l$." + aanalvsis of rradio data requires. therefore. Gu addition. to eclectrou injection rate and spectrum derived from RUESST) some information of ffast electron residence time at rracio source.," analysis of radio data requires, therefore, (in addition to electron injection rate and spectrum derived from ) some information of fast electron residence time at radio source." + To address ttiming. we use Phocuix-2 Gather than OOVSA) data because of its higher time resolution.," To address timing, we use Phoenix-2 (rather than OVSA) data because of its higher time resolution." +" We select ffirequency range of 3.2 to GG correspouding to ooptically thin part of rradioz spectrun and almost free of fine structures aud interference. see roffiga0iufo002,eer."," We select frequency range of 3.2 to GHz corresponding to optically thin part of radio spectrum and almost free of fine structures and interference, see \\ref{fig_30_jul_2002_over}." +" The ccrosscorrclation( theref fig,.-orr)jdisplayselearlythatthe veedioandIX Riigithie nesdenec ta tine thiosrmelons a cabledelaginthi co", cross-correlation \\ref{fig_r_z_corr}) ) displays clearly that radio and HXR light curves are very similar to each other and there is no measurable delay in radio component. +rrelationisconsistentwiththe rradiociissionpeakingo- 1301s eulier.," In fact, cross-correlation is consistent with radio emission peaking $\sim130$ ms earlier." + lack of noticeable delay between rradio auc N-rax light curves is further confirmed bv considering OOVSA Πο curves (Iss time resolution) at different optically thin frequencies., lack of noticeable delay between radio and X-ray light curves is further confirmed by considering OVSA light curves s time resolution) at different optically thin frequencies. + Therefore. nuuagueticallv trapped electron component appears to be abseut. aud iradio enuission is formed by either pprecipitating electrous or eclectrons in aacceleration region or both.," Therefore, magnetically trapped electron component appears to be absent, and radio emission is formed by either precipitating electrons or electrons in acceleration region or both." + With sspectrmu of energetic clectrous frou IIXR data. it is casy to estimate radio emission produced by pprecipitating electrou. compoucut.," With spectrum of energetic electrons from HXR data, it is easy to estimate radio emission produced by precipitating electron component." +" Taking eclectron fux. spectral index of rradio-producing electrons 6,26,|1/2. aud eclectrou lifetime at the loop £/e ttime of flight). we can vary nüuuagnetie field at source in an attempt to match sspectiuu shape and fis level."," Taking electron flux, spectral index of radio-producing electrons $\delta_r{\approx}\delta_x+1/2$, and electron lifetime at the loop $L/v$ time of flight), we can vary magnetic field at source in an attempt to match spectrum shape and flux level." + However. if we match sspectrun peak position. we strongly underestimate rradio flux. while if we nateh flux level at ppeak frequency or at an optically thin frequency. we overestimate sspectimm peak frequency: examples of such spectra are eiven iu calibrated retiiesiitthythe ddottedearces," However, if we match spectrum peak position, we strongly underestimate radio flux, while if we match flux level at peak frequency or at an optically thin frequency, we overestimate spectrum peak frequency; examples of such spectra are given in \\ref{fig:fit_tt} by dotted curves." + SV Πινdo dxsan hylapkqiatiahhed eso Divtiadivontribut iontothe , We conclude that precipitating electrons only [option (ii)] cannot make dominant contribution to observed radio spectrum. +To quantity tthird option. we have to consider further coustraiuts to estimate eelectron residence iue in nunain radio source.," To quantify third option, we have to consider further constraints to estimate electron residence time in main radio source." + On one Lh. darsftodsechhthrteri ight curve decay time. ~10 ss otherwise. ddecay. of rradio cussion would be longer than observed.," On one hand, this residence time must be shorter than radio light curve decay time, $\sim10$ s; otherwise, decay of radio emission would be longer than observed." + Ou oother haud. eextreimelv low requencv of municrowave spectrum peak miplies nunaegnetic field is well below 100 € at iradio source. Le.. much snaller than ffootpoiut uaenetie field values (——130 G€ and ~1000 (GG).," On other hand, extremely low frequency of microwave spectrum peak implies magnetic field is well below $100$ G at radio source, i.e., much smaller than footpoint magnetic field values $\sim-130$ G and $\sim+1000$ G)." + This nuplies that rresidence time in inmain radio source nmst be noticeablv larger than ttime of flight. which is ffractiou of second: otherwise. ffast electron density would be eveulv distributed over Hoop aud. gevrosvuchrotrou (CS) nücrowave cnussion would be cdominautly woduced at large feld regions. resulting iu sspectimm with uch hieher peak frequency than oobserved one (as in aalready considered case of pprecipitating electron. population).," This implies that residence time in main radio source must be noticeably larger than time of flight, which is fraction of second: otherwise, fast electron density would be evenly distributed over loop and gyrosynchrotron (GS) microwave emission would be dominantly produced at large field regions, resulting in spectrum with much higher peak frequency than observed one (as in already considered case of precipitating electron population)." + Thus. ireasonable estimate of this lifetime is somewhere vetween those two extremes. 070D ss. qquality of OOVSA data available for this event appears msufücient to perform ccomplete orward fit with all model paraimcters being free (Fleishmanetal.2009).. which would require better nuage spectroscopy data.," Thus, reasonable estimate of this lifetime is somewhere between those two extremes, $\tau_{l}\sim 3$ s. quality of OVSA data available for this event appears insufficient to perform complete forward fit with all model parameters being free \citep{Fl_etal_2009}, which would require better calibrated imaging spectroscopy data." + Iustead. we cconcludethatprecipitatii nées lido and estimate one or two remaining parameters from fit.," Instead, we have to fix as many parameters as possible \citep{Bastian_etal_2007, Altyntsev_etal_2008} + and estimate one or two remaining parameters from fit." + To do, To do +density waves into the extended disces (2).,density waves into the extended discs . + However. other mechanisms may also play a part. ?," However, other mechanisms may also play a part. ," +.. for example. suggested that an interaction between NGC 4625 and NGC 4618 acted as à Urigeer for star formation at extreme racii in NGC 4625.," for example, suggested that an interaction between NGC 4625 and NGC 4618 acted as a trigger for star formation at extreme radii in NGC 4625." + proposed a range of other mechanisms. including stellar compression and turbulence compression among others.," proposed a range of other mechanisms, including stellar compression and turbulence compression among others." + rregions in NUM clises are ideal tracers of star-formation at extreme radii. but they also encode information about the kinematics of these structures and the chemical evolution of these extreme star formation environments (??).," regions in XUV discs are ideal tracers of star-formation at extreme radii, but they also encode information about the kinematics of these structures and the chemical evolution of these extreme star formation environments ." +. Previous studies of the abuncances of NUV disc rregions have insofar been rather limited., Previous studies of the abundances of XUV disc regions have insofar been rather limited. + studied the ealaxies NGC 628. NGC 1058 and NGC 6946. but. their sample was limited to nine rregions bevond ος.," studied the galaxies NGC 628, NGC 1058 and NGC 6946, but their sample was limited to nine regions beyond $_{25}$." + More in depth studies of rregion abundances in XUV clises have focused on two galaxies in particular., More in depth studies of region abundances in XUV discs have focused on two galaxies in particular. + studied 31 rregions in the NUW clises of MS3 and NGC 4625. finding in both cases an exponential abundance gradient extending into the outer disc.," studied 31 regions in the XUV discs of M83 and NGC 4625, finding in both cases an exponential abundance gradient extending into the outer disc." + However. a deeper study of MS3 by.2.. containing 49 rregions out to 2.6 lios. found a marked. cliscontinuity in the abundance gradient at the optical edee of the galaxy. together with a Hat gradient in the NUV disc.," However, a deeper study of M83 by, containing 49 regions out to 2.6 $_{25}$, found a marked discontinuity in the abundance gradient at the optical edge of the galaxy, together with a flat gradient in the XUV disc." + NGC 4625 and MS3 have been the most studied NUM disc galaxies. parth due to their close proximity.," NGC 4625 and M83 have been the most studied XUV disc galaxies, partly due to their close proximity." + οσο galaxies possess some of the most NUV. clises known. extending out to 4 Res in both cases(??).," These galaxies possess some of the most XUV discs known, extending out to 4 $_{25}$ in both cases." +. They. share similar trends in their aand UV radial profiles. with a turnover in the pprofile near Res. vet a smooth far-UV profile extending into the NUM cise(2).," They share similar trends in their and UV radial profiles, with a turnover in the profile near $_{25}$, yet a smooth far-UV profile extending into the XUV disc." +. However. M83 displays à large number of UV knots in the XUV clise in association with structured ecemission. whilst the lower luminosity NGC 4625 has a more dilfuse UV. emission accompanving a low surface brightness optical component(?).," However, M83 displays a large number of UV knots in the XUV disc in association with structured emission, whilst the lower luminosity NGC 4625 has a more diffuse UV emission accompanying a low surface brightness optical component." +. In this paper we present a detailed chemical abundance study of the rregions in NGC 4625. including targets across the XUV disc not previously observed by GOT.," In this paper we present a detailed chemical abundance study of the regions in NGC 4625, including targets across the XUV disc not previously observed by G07." + We have sampled rregions in both the inner and outer disc out to ~2.5 lt»;. and study their oxveen abundances based. on several strong nebular emission line indicators.," We have sampled regions in both the inner and outer disc out to $\sim2.5$ $_{25}$, and study their oxygen abundances based on several strong nebular emission line indicators." + We first describe our observations and the data reduction in §2.., We first describe our observations and the data reduction in \ref{sec:obs}. + In $?? we discuss the oxygen abundances that we obtained and compare our results to those of previous datasets., In \ref{sec:nebabunds} we discuss the oxygen abundances that we obtained and compare our results to those of previous datasets. + $4 discusses the nature of rregions in the NUV disc. considering the effects. of an ageing population and stochasticity on the observed nebular line ratios.," \ref{sec:roguehii} discusses the nature of regions in the XUV disc, considering the effects of an ageing population and stochasticity on the observed nebular line ratios." + We briclly discuss our findings in the context of extragalactic star formation in 85.. before we [finally summarise our conclusions.," We briefly discuss our findings in the context of extragalactic star formation in \ref{sec:interp}, before we finally summarise our conclusions." + Throughout this paper we assume a distance to NGC 4625 of 9.5 Alpe(7)... an inclination angle /—27 and a position angle of the major axis @=150(?)..," Throughout this paper we assume a distance to NGC 4625 of 9.5 Mpc, an inclination angle $i=27^{\circ}$ and a position angle of the major axis $\theta=150^{\circ}$." + The Bos value of 66 aresec. from.?.. corresponds to 3.04 kpe.," The $_{25}$ value of 66 arcsec, from, corresponds to 3.04 kpc." + We adopt a solar metallicity value —8.69(?)., We adopt a solar metallicity value 8.69. +. Our rregion selection was based on deep limages taken using the Faint Object Camera. And Spectrograph (PFOCAS. ?)) at the Subaru telescope situated on Mauna Wea in Hawaii.," Our region selection was based on deep images taken using the Faint Object Camera And Spectrograph (FOCAS, ) at the Subaru telescope situated on Mauna Kea in Hawaii." +" Phe field of view of the instrument (6 aremin) encompasses the entire NUV clise of NGC 4625,", The field of view of the instrument (6 arcmin) encompasses the entire XUV disc of NGC 4625. + A continuume-subtracted image was constructed using a 900ss on-band image in combination with a 120ss continuum image., A continuum-subtracted image was constructed using a s on-band image in combination with a s continuum image. + We designed two multi-object slit masks. attempting to cover as wide a range in galactocentrie radius as possible. and including several rregions which were part of the spectroscopic study by GUT.," We designed two multi-object slit masks, attempting to cover as wide a range in galactocentric radius as possible, and including several regions which were part of the spectroscopic study by G07," + (>1079 Nagano&Watson2000)..," $>10^{19}$ \citep{Bhattacharjee:1998qc,Nagano:2000ve}." + >+1078Di (Nagano&Watson 2000).. ~LOY (Birdetal1993:Abbasial.2005).. (Finley&Wes," $>10^{20}$ $\sim10^{19}$ \citep{Nagano:2000ve}, $\sim10^{19}$ \citep{Bird93,Abbasi05}, \citep{Finley04,HiResIso}." +terhoff2001:Abbasictal.2001).," $>6\times10^{19}$ \citep{auger}, \citep{Fisher97,Kashti08}." +. >6«1079 2008).. (Waxaiiaun.Fishe," $>10^{19}$ $d\log N/d\log E\approx -2$ $N$ $E$ \citep{Waxman95,Bahcall03,Kashti08}." +r&Piran1997: NV £ for extra-Calactic sources. παλιο seanuna-ray bursts and active ealactic nuclei (see below). are expected to accelerate primarily protons.," \citep{Blandford87} for extra-Galactic sources, namely gamma-ray bursts and active galactic nuclei (see below), are expected to accelerate primarily protons." + Robust modelindependent considerations nuplv that UIIECR protons cau only be produced by. sources with an exceedingly high power output (Waxuman2001).. L»TeiH0eves to where Doand Je are the Loreutz factor aud characteristic velocity associated with plasma motions within thesomecet.," Robust model-independent considerations imply that UHECR protons can only be produced by sources with an exceedingly high power output \citep{Waxman_CR_rev}, $L>\Gamma^2\beta^{-1}10^{46}~{\rm erg~s^{-1}}$ , where $\Gamma$ and $\beta c$ are the Lorentz factor and characteristic velocity associated with plasma motions within the." +. Since no steady source above this power threshold is known to exist within the 100 AIpehorizon. the distance to which the propagation of ~10? eV protous is limited by their interaction with the cosmic microwave background (Caeiscn1966:Zatsepin&Ίναnin1969).. the UITECR sources are most likely transicut.," Since no steady source above this power threshold is known to exist within the 100 Mpc, the distance to which the propagation of $\sim10^{20}$ eV protons is limited by their interaction with the cosmic microwave background \citep{G66,ZK}, the UHECR sources are most likely transient." + A possible alternative is. of course. an unknown class of “dark sources”. which produce little radiation and therefore remain uudetectable by telescopes.," A possible alternative is, of course, an unknown class of ""dark sources"", which produce little radiation and therefore remain undetectable by telescopes." + Ouly two types of sources are known to satisfv the above nüninmin power requirement: active ealactic nuclei (ACN) the brightest known steady sources. and eanmnmnua-ray bursts (CRBs) the brightest kuowu transients," Only two types of sources are known to satisfy the above minimum power requirement: active galactic nuclei (AGN) – the brightest known steady sources, and gamma-ray bursts (GRBs) – the brightest known transient." +ources? The absence of ACN with L1019cres1 within the CZK horizou had. motivated Farvar&Cauzinoy(2008) to sugeest that UITECTRs may be produced by a new. vet uudetected. class of short duration ACN flares resulting from the tidal disruption of stars or accretion disk mstabilities.," The absence of AGN with $L>10^{46}~{\rm erg~s^{-1}}$ within the GZK horizon had motivated \citet{Gruzinov} to suggest that UHECRs may be produced by a new, yet undetected, class of short duration AGN flares resulting from the tidal disruption of stars or accretion disk instabilities." + We show in 5 that if electrous are accelerated together with the protous in UITECTR-produciug flares. then theirradiative losses willproduce a bright flare of N-rav and x-ray photons.," We show in \ref{sec:flares} that if electrons are accelerated together with the protons in UHECR-producing flares, then theirradiative losses willproduce a bright flare of X-ray and $\gamma$ -ray photons." + We then show in 3) that existing N-rav aud 5-ray surveys already put strinegcut constraints ou the properties of UITECR flares., We then show in \ref{sec:LFs} that existing X-ray and $\gamma$ -ray surveys already put stringent constraints on the properties of UHECR flares. + In 1 , In \ref{sec:hidden} +"It is generally accepted that the ceuter of the Faranoff-Rilev type I (ER-I) radio ealaxy AIST harbors a supermassive black hole of mass (6x0.5)\1PAL, (Gebhardt and Thomas. 2009) at a distance of 16.7 Mpc (Meietal.2007).. which js associated with a spectacular kiloparsec scale jet."," It is generally accepted that the center of the Faranoff-Riley type I (FR-I) radio galaxy M87 harbors a supermassive black hole of mass $(6\pm0.5)\times10^9 M_o$ (Gebhardt and Thomas, 2009) at a distance of 16.7 Mpc \citep{mei07}, which is associated with a spectacular kiloparsec scale jet." +" Observaious of superhuuinal motion in the jet require a jet viewing augle of 0<19 deerees and bulk Lorentz factor 5>6 at the promuneut IIST-1 jet krot. which would imply it is located 5.3«LOR, «lownstream from the core (Birettaetal. 1999).. where the Schwarzschild radius of the black hole R=bess1075 cm (Πατάσς 2010)))."," Observations of superluminal motion in the jet require a jet viewing angle of $\theta < 19$ degrees and bulk Lorentz factor $\gamma > 6$ at the prominent HST-1 jet knot, which would imply it is located $5.3\times10^5 R_s$ downstream from the core \citep{bir99}, where the Schwarzschild radius of the black hole $R_s = 1.8\times10^{15}$ cm \citep{har10}) )." + Due to its size. proximity. and orientation. M87 provides a unique opportunity for sπάν of a ceutral AGN environment. which can be probed to investigate particle enereizatiou m accretion disks. jet launching. aud other astroplivsical phenomena Occurring n these extreme situations.," Due to its size, proximity, and orientation, M87 provides a unique opportunity for study of a central AGN environment, which can be probed to investigate particle energization in accretion disks, jet launching, and other astrophysical phenomena occurring in these extreme situations." + Its spectral energy distribution (SED) suggests tha AIST ds a unisaigned BL Lac., Its spectral energy distribution (SED) suggests that M87 is a misaligned BL Lac. +" It has been observed for a inniber of vears from radio to σαι rave. ddetailed information is available from multi-vavele15oOh collaborations (AcciiuictxOs, 2010)."," It has been observed for a number of years from radio to gamma rays, and detailed information is available from multi-wavelength collaborations \citep{acc08,acc10}." +.. M87. score is variable. aud optical and x-ray beuds stow conuuion chniuges of about a factor of two. ou tinescales of mouths (Perliuau 2009).," M87's core is variable, and optical and x-ray bands show common changes of about a factor of two, on timescales of months \citep{per03,har09}." +. Very hieh energy (VIIE) observatioIs of variability. on timescales of cays CAluuoui:αιetal.2006) Suggest verv conrpact enission reeious on the order of the size of the immer accrejon disk (NeronoyandAharo-wan 2007).. and concurrent VITE. radio. aud x- campaigns have helped tie the eamuua rav cluission frou MBST. for specific events to areas close to the core (Abdoetal.2009).," Very high energy (VHE) observations of variability on timescales of days \citep{aha06} suggest very compact emission regions on the order of the size of the inner accretion disk \citep{ner07}, and concurrent VHE, radio, and x-ray campaigns have helped tie the gamma ray emission from M87, for specific events, to areas close to the core \citep{abd09}." +. A nmuuber of models have been proposed in recent decades to describe accretion disks in ACN systems with low luminosity. compared to their Eddington Lhuuinositv (the lhuuinositv Lut at," A number of models have been proposed in recent decades to describe accretion disks in AGN systems with low luminosity, compared to their Eddington luminosity (the luminosity limit at" +6.7 keV. compared to 7 photons in the 0.8 keV on either side between 5.9-6.3 ancl 6.7-7.1. a 2 sigma ‘detection.,"6.7 keV, compared to 7 photons in the 0.8 keV on either side between 5.9-6.3 and 6.7-7.1, a 2 sigma `detection'." + The distribution of the counts is consistent with the instrumental width al that energy. and their spatial distribution suggests a distribution centered towards the eastern source X-4 (although a tighter spatial selection only improves the detection significance to 2.6 sigma).," The distribution of the counts is consistent with the instrumental width at that energy, and their spatial distribution suggests a distribution centered towards the eastern source X-4 (although a tighter spatial selection only improves the detection significance to 2.6 sigma)." + If real. this line would have a luminosity of 4xI0ergs |. an equivalent width of 700 eV and a rest energy. of 6.62£0.05 keV: these may be taken as approximate upper limits to any narrow Fe Kx line.," If real, this line would have a luminosity of $4\times 10^{39}\mbox{erg s$ $}$, an equivalent width of 700 eV and a rest energy of $6.62\pm0.05$ keV; these may be taken as approximate upper limits to any narrow Fe K line." + The absorption-corrected laminosity of (he nuclear emission. including the hard halo. is L3(1—2.6)xIO!lergs |.," The absorption-corrected luminosity of the nuclear emission, including the hard halo, is $1.3 (1-2.6)\times10^{41} \mbox{erg s$ $}$." + Based on the PSF subtraction calenlations. we assign 30 percent of this to X-1. giving ~4x10Meres which is in the range of both ultra-low luminosity AGN and ultra-luninous binaries (Fabbiano 1998. Nine οἱ al.," Based on the PSF subtraction calculations, we assign 30 percent of this to X-1, giving $\sim 4\times 10^{40}\mbox{erg s$ $}$ which is in the range of both ultra-low luminosity AGN and ultra-luminous binaries (Fabbiano 1998, King et al." + 2001)., 2001). + See Table 1 for derived source positions and huminosities., See Table 1 for derived source positions and luminosities. + Could there be a further hard source al (this location. behind a much larger column?," Could there be a further hard source at this location, behind a much larger column?" + Using a canonical photon index of 1.7. we set limits of L(0.2-10 keV) = 1.4xI0Pergs for a column of L0?!em7. and 2.5x107! for a column of 5x107/em 7.," Using a canonical photon index of 1.7, we set limits of L(0.2-10 keV) = $1.4\times 10^{42}\mbox{erg s$ $}$ for a column of $10^{24} +\mbox{cm}^{-2}$, and $2.5\times 10^{44}$ for a column of $5\times +10^{24}\mbox{cm$ $}$." + However. for a column of 10%em 7. which is entirely plausible in the center of Arp 220. no useful limit can be set bv the ACIS data as even the most Iuminous quasars would have their X-ray. [Ix absorbed: one must turn to the harder X-ray limits [rom the BeppoSAX PDS of 2x1072ergs in 13-50 keV (Iwasawa et al.," However, for a column of $10^{25}\mbox{cm$ $}$, which is entirely plausible in the center of Arp 220, no useful limit can be set by the ACIS data as even the most luminous quasars would have their X-ray flux absorbed; one must turn to the harder X-ray limits from the BeppoSAX PDS of $2\times10^{42}\mbox{erg s$ $}$ in 13-50 keV (Iwasawa et al." + 2001) to eliminate this possibility., 2001) to eliminate this possibility. + In general. because of the low sensitivitv of Chandra above 6 keV. the limits we set as a function of absorbing column are weaker (han those in Figure 5 of Bbwasawa et al.," In general, because of the low sensitivity of Chandra above 6 keV, the limits we set as a function of absorbing column are weaker than those in Figure 5 of Iwasawa et al." + for the range thev study (log /N;j;224.3 and above)., for the range they study (log $N_H$ =24.3 and above). + The X-ray emission in Arp 220 is clearly divided into two parts the compact. hard nuclear emission. and the diffuse. softer extended: emission.," The X-ray emission in Arp 220 is clearly divided into two parts — the compact, hard nuclear emission, and the diffuse, softer extended emission." + This diffuse emission clearly extends right into the nucleus since the thermal component of the nuclear emission appears verv similar to the thermal emission found in the off-nuclear spectrum., This diffuse emission clearly extends right into the nucleus since the thermal component of the nuclear emission appears very similar to the thermal emission found in the off-nuclear spectrum. + The hare emission is not extended. bevond a region. 0.9$ \citep{Iwasawa96,Fab02,RN03,BR06}." +.. A similarly broad line is seen in the stacked spectra of active galactie nuclei in a long exposure of the Lockman Hole (Streblvanskaetal.2005)., A similarly broad line is seen in the stacked spectra of active galactic nuclei in a long exposure of the Lockman Hole \citep{Streb05}. +. More generally. the inlerred average radiation efficiency. of supermassive black holes suggests that (μον tend to rotate rapidly (Sollan1982:Yu&Tremaine2002:: see Marconietal.2004. [or a cliscussion of uncertainties).," More generally, the inferred average radiation efficiency of supermassive black holes suggests that they tend to rotate rapidly \citealt{Sol82,YT02}; see \citealt{marconi04} for a discussion of uncertainties)." + This is also consistent. with predictions from hierarchical merger models (e.g.. Volonterietal. 2005)).," This is also consistent with predictions from hierarchical merger models (e.g., \citealt{volonteri05}) )." + Alass ratios much less than unity may occur in some mergers. and if the masses are different enough then the kick speed can be small.," Mass ratios much less than unity may occur in some mergers, and if the masses are different enough then the kick speed can be small." + For exaniple. Bakeretal.(2007).. followed by Campanellietal. (2007b).. suggest that the spin kick component scales wilh mass ratio qemyfingX Las lis—qay)/(L+9). hence for ay=-a1 the maximum kick speed is xqU/G+q)).," For example, \citet{Baker07}, followed by \cite{Campanelli07b}, suggest that the spin kick component scales with mass ratio $q\equiv +m_1/m_2\leq 1$ as $q^2({\hat a}_2-q{\hat a}_1)/(1+q)^5$, hence for ${\hat a}_1=-{\hat a_2}=1$ the maximum kick speed is $\propto +q^2/(1+q)^4$." + For g0.1 this scales roughly as d? and hence kicks are small., For $q<0.1$ this scales roughly as $q^2$ and hence kicks are small. + However. for q>0.2 the maximum kick is within a factor ~3 of the kick possible for g=1.," However, for $q>0.2$ the maximum kick is within a factor $\sim 3$ of the kick possible for $q=1$." + An unlikely conspiracy would thus seem to be required for the masses always to be different by the required [actor of several., An unlikely conspiracy would thus seem to be required for the masses always to be different by the required factor of several. + Some tens of percent of galaxies appear to have undergone αἱ least one merger with mass ratio 20.25 within redshift 2«1 (lor recent observational results with different methods. see Belletal.2006b:Lotz2006.. aud for a recent simulation see Mallerοἱal. 2006)).," Some tens of percent of galaxies appear to have undergone at least one merger with mass ratio $>0.25$ within redshift $z<1$ (for recent observational results with different methods, see \citealt{Bell06b,Lotz06}, and for a recent simulation see \citealt{Maller06}) )." + The well-established tight correlations between central black hole mass and ealactic properties such as bulge velocity dispersion (see Ferrarese&Ford.2005 for a review) (hen suggest stronglv Chat coalescence of comparable-mass black holes should be common., The well-established tight correlations between central black hole mass and galactic properties such as bulge velocity dispersion (see \citealt{FF05} for a review) then suggest strongly that coalescence of comparable-mass black holes should be common. + The most likely solution therefore seems to be that astrophyvsical processes tend to align the spins of supermassive black holes with the orbital axis., The most likely solution therefore seems to be that astrophysical processes tend to align the spins of supermassive black holes with the orbital axis. + This astrophysical alignment is (he subject of thisLeHer., This astrophysical alignment is the subject of this. + Here we show that gas-rich mergers tend to lead (ο strong alignment. of (he spin axes with the orbital angular momentum and (hus to kick speecls much less (han the escape speeds of sizeable galaxies., Here we show that gas-rich mergers tend to lead to strong alignment of the spin axes with the orbital angular momentum and thus to kick speeds much less than the escape speeds of sizeable galaxies. + In contrast. gas-poor mergers show no net tendency for alignment.assuming an iniüallv uniform distribution of spin and orbital angular momentum vectors.," In contrast, gas-poor mergers show no net tendency for alignment,assuming an initially uniform distribution of spin and orbital angular momentum vectors." + We demonstrate (his aspect of gas-poor mergers in 2., We demonstrate this aspect of gas-poor mergers in 2. + In, In +We measure the quantity 05(3839). the difference between an individual star’s CN bandstrength and the best-fit line at the same absolute magnitude. in the plane of Figure 3.,"We measure the quantity $\delta S(3839)$, the difference between an individual star's CN bandstrength and the best-fit line at the same absolute magnitude, in the plane of Figure 3." + The eight panels of Figure 4 correspond to the panels of Figure 3. and show 6S(3839) versus S(CH) for each metallicity bin. with candidate second-generation field stars plotted as open circles and all other stars plotted as filled circles.," The eight panels of Figure 4 correspond to the panels of Figure 3, and show $\delta +S(3839)$ versus $S(CH)$ for each metallicity bin, with candidate second-generation field stars plotted as open circles and all other stars plotted as filled circles." + Because the S(CH) index has a reduced sensitivity to carbon abundance at the upper end of our metallicity range. we accept all CN-strong stars with metallicities above [Fe/H|=—1.3 as candidates. and we select only those CN-strong stars with S(CH) below the mean of the CN-normal group for stars with metallicity below |Fe/H]=-1.3.," Because the $S(CH)$ index has a reduced sensitivity to carbon abundance at the upper end of our metallicity range, we accept all CN-strong stars with metallicities above $=-1.3$ as candidates, and we select only those CN-strong stars with $S(CH)$ below the mean of the CN-normal group for stars with metallicity below $=-1.3$." + These are the same criteria as were used in MG10. and they return 16 candidate globular cluster stars. 3% of our sample.," These are the same criteria as were used in MG10, and they return $16$ candidate globular cluster stars, $3\%$ of our sample." + This is very similar to the ΜΟ10 result based on SEGUE-I stars., This is very similar to the MG10 result based on SEGUE-I stars. +" calculate heliocentric distances. D to our target stars from 1.1020 distance modulus (ro —M,).", We calculate heliocentric distances D to our target stars from the distance modulus $(r_{0}-{\rm M}_{r})$. +Errors in. distance were a by randomly sampling the error on (g —ro.then a the distance.," Errors in distance were calculated by randomly sampling the error on $(g-r)_{0}$, then recalculating the distance." + The standard deviation in. 100 of 40 realizations was then adopted as cp., The standard deviation in $100$ of these realizations was then adopted as $\sigma_{\rm D}$. +" One of the goals of * SEGUE-? survey was to observe stars at greater distances 30 were observed in SEGUE-1. and while our data set covers 20E heliocentric distance range very similar to that of ΜΟ 10.the 10 star at any fixed M, is more distant for the current data ο than for the MGIO data set."," One of the goals of the SEGUE-2 survey was to observe stars at greater distances than were observed in SEGUE-1, and while our data set covers a heliocentric distance range very similar to that of MG10, the average star at any fixed ${\rm M}_{r}$ is more distant for the current data set than for the MG10 data set." +" The upper panel of Figure 5 1 our calculated distances versus absolute M, magnitudes for the SEGUE-2 data set. with CN-normal stars drawn as small dots and CN-strong stars drawn as filled stars."," The upper panel of Figure 5 shows our calculated distances versus absolute ${\rm M}_{r}$ magnitudes for the SEGUE-2 data set, with CN-normal stars drawn as small dots and CN-strong stars drawn as filled stars." + The lower panel shows the analogous data for the MGIO data set. with only a randomly selected 25% of the MGIO CN-normal stars plotted for visual clarity.," The lower panel shows the analogous data for the MG10 data set, with only a randomly selected $25\%$ of the MG10 CN-normal stars plotted for visual clarity." + In both panels. the stars fill a band that is restricted at small distances by the SEGUE bright limit of e=14 and at large distances by our requirement that SNotue215.0.," In both panels, the stars fill a band that is restricted at small distances by the SEGUE bright limit of $g=14$ and at large distances by our requirement that $_{\rm blue} +\geq 15.0$." +" Helitocentric distances are converted geometrically to Galactocentric distances roc. using the relation Iac=D?+(8kpey—2Dcos(y) in which y is the angle on the sky between the Galactic center and the star in question,"," Heliocentric distances are converted geometrically to Galactocentric distances ${\rm r_{GC}}$, using the relation ${\rm +r_{GC}^{2}=D^{2}+(8\hbox{kpc})^{2}-2D\cos(\gamma)}$, in which $\gamma$ is the angle on the sky between the Galactic center and the star in question." +" Table 3 lists plate. MJD. and FiberID identifiers. along with our measurements of $(3839) and S(CH). our determination of astar’s CN class (normal or strong). absolute M, magnitude. heliocentric distance. Galactocentric distance. and survey name (SEGUE-1 or SEGUE-2). for the same stars as in Table I."," Table 3 lists plate, MJD, and FiberID identifiers, along with our measurements of $S(3839)$ and $S(CH)$, our determination of a star's CN class (normal or strong), absolute ${\rm M}_{r}$ magnitude, heliocentric distance, Galactocentric distance, and survey name (SEGUE-1 or SEGUE-2), for the same stars as in Table 1." + As with Table |. only the first ten rows are given in the print version of this paper. and a full version of the table is available from CDS.," As with Table 1, only the first ten rows are given in the print version of this paper, and a full version of the table is available from CDS." + Figure 6 shows ὁδ(3839) versus roc for our final data set (upper panel) and the MGIO sample (lower panel). using the same symbols as in Figure 5.," Figure 6 shows $\delta S(3839)$ versus ${\rm r_{GC}}$ for our final data set (upper panel) and the MG10 sample (lower panel), using the same symbols as in Figure 5." + The frequency of CN-strong stars appears to drop at roughly 20 kpe. with only one CN-strong star beyond rac=30 kpe.," The frequency of CN-strong stars appears to drop at roughly $20$ kpc, with only one CN-strong star beyond ${\rm r_{GC}}=30$ kpc." + To further investigate this result. we visualize. the relationship between the frequency of CN-strong stars and," To further investigate this result, we visualize the relationship between the frequency of CN-strong stars and" +llere we discuss some of the svstematics of the weak rates in the hot ancl core during the ~I0!s before core bounce.,Here we discuss some of the systematics of the weak rates in the hot and electron-degenerate core during the $\sim10^4$ s before core bounce. + Most of the nuclei with A65 present in the core will be blocked or nearly blocked to GY transitions in the zeroth order shell model picture., Most of the nuclei with $>$ 65 present in the core will be blocked or nearly blocked to $GT^+$ transitions in the zeroth order shell model picture. + Our calculation of the electron capture rates for these nuclei is based on an estimate of the CT. configuration mixing strength., Our calculation of the electron capture rates for these nuclei is based on an estimate of the $GT^+$ configuration mixing strength. + Forbidden transitions ancl transitions allowed by the thermal unblocking of strength will also contribute to the electron capture rates., Forbidden transitions and transitions allowed by the thermal unblocking of strength will also contribute to the electron capture rates. + It is useful to estimate how large the configuration mixing strength must be in order to justify (he neglect of these latter (vpes of transitions., It is useful to estimate how large the configuration mixing strength must be in order to justify the neglect of these latter types of transitions. + Thermal unblocking refers to the population of parent excited states that have zeroth order shell model configurations consistent wilh allowed (ransitions to states in the daughter., Thermal unblocking refers to the population of parent excited states that have zeroth order shell model configurations consistent with allowed transitions to states in the daughter. + Assume that these parent states comprise a fraction 0Z of the total partition. function., Assume that these parent states comprise a fraction $\delta Z$ of the total partition function. + Then. an effective thermal unblocking matrix element is Mq]?2m(0Z/Z)]Mu).," Then, an effective thermal unblocking matrix element is $|M_{\rm TU}|^2\approx (\delta Z/Z) |M_{\rm s.p.}|^2$." + Here Mis~|-- 1 a typical single particle allowed (transition matrix element.," Here $|M_{\rm +s.p.}|^2\approx 1-3$ is a typical single particle allowed transition matrix element." + An accurate estimate οἱ 9Z is very dillieult and an important open issue., An accurate estimate of $\delta Z$ is very difficult and an important open issue. + Fuller 1982 paraimetrizes Zerp(—E/T). with E* the excitation energv of the lowest parent excited state with an allowed GT transition in the zeroth order shell model picture.," Fuller 1982 parametrizes $\delta Z\approx Z +exp(-E^*/T)$ , with $E^*$ the excitation energy of the lowest parent excited state with an allowed $GT^+$ transition in the zeroth order shell model picture." + With (his schematic notation. thermal unblocking can compete with a configuration mixing strength of 0.1—1i E*/T52.," With this schematic notation, thermal unblocking can compete with a configuration mixing strength of $0.1-1$ if $E^*/T\lesssim 2$." + For a typical E*~5MeV. then. thermal unblocking can be neglected for T'<2MeV.," For a typical $E^*\sim 5\,{\rm MeV}$, then, thermal unblocking can be neglected for $T\lesssim 2{\rm \, MeV}$." + for T 2MeV the thermal population of the GP resonance states (which we do include in our calculations) also becomes important.," for $T>2{\rm\, MeV}$ the thermal population of the $GT^-$ resonance states (which we do include in our calculations) also becomes important." + Forbidden transitions become important as the electron. chemical potential increases and (he wavelength of the leptous involved in an electron capture event become small enough to probe structure in the nucleus., Forbidden transitions become important as the electron chemical potential increases and the wavelength of the leptons involved in an electron capture event become small enough to probe structure in the nucleus. +" Again following the convention of Fuller 1932. the contribution to the electron capture rate from forbidden (ranusitions can be written as Mor~Mg""σονEteQ.fhe)."," Again following the convention of Fuller 1982, the contribution to the electron capture rate from forbidden transitions can be written as $\lambda_{\rm for}\sim |M_{\rm for}|^2 f_{\rm +for}(E_{\rm for},Q, \mu_e)$." + Ilere Mi:-H!e10—20 is roughly the number of protons in the fp shell multiplied by à (vpical single particle first forbidden matrix element., Here $|M_{\rm for}|^2\sim 10-20$ is roughly the number of protons in the fp shell multiplied by a typical single particle first forbidden matrix element. +" The unique first forbidden: phase space factor fi, depends on the centroid in energy. of the forbidden strength distribution £g. the parent-daughter mass difference Q. ancl (he electron chemical potential ja."," The unique first forbidden phase space factor $f_{\rm for}$ depends on the centroid in energy of the forbidden strength distribution $E_{\rm +for}$, the parent-daughter mass difference $Q$, and the electron chemical potential $\mu_e$." +" For a typical Q=10MeV. forbidden transitions compete with a low lving configuration mixing strength of ~1/2 for ji,=31MeV if Ej,=5MeV."," For a typical $Q=10{\rm\, MeV}$, forbidden transitions compete with a low lying configuration mixing strength of $\sim 1/2$ for $\mu_e=31{\rm \, MeV}$ if $E_{\rm for}=5{\rm \, MeV}$." + If the centroid ol the forbidden strength lies instead αἱ ~10MeV. above the daughter ground state. then forbidden transitions do not become important until yt.>37MeV.," If the centroid of the forbidden strength lies instead at $\sim 10{\rm \, MeV}$ above the daughter ground state, then forbidden transitions do not become important until $\mu_e>37{\rm \, MeV}$." + With (he assumption that the high densitv electron capture rates are dominated by transitions involving low-lving configuration mixing strength. these rates are trivial finetions ol the electron Fermi energy and (he parent-daughter mass dillerence.," With the assumption that the high density electron capture rates are dominated by transitions involving low-lying configuration mixing strength, these rates are trivial functions of the electron Fermi energy and the parent-daughter mass difference." + This is shown in figure, This is shown in figure + , +proving theoretically the right auswer for the spectral type of µ. we shall be able to use it as a test of the mmuerical techniques that we shall iutroduce iu the sequel.,"proving theoretically the right answer for the spectral type of $\mu$, we shall be able to use it as a test of the numerical techniques that we shall introduce in the sequel." + We first prove a general resultProof., We first prove a general result. + Apply the halauce relation (2)) to flr}=Xpινα) the characteristic function of Bs). the ball of radius € ceutered at s (techiicallv. eq. (1)}) ," Apply the balance relation \ref{bala2})) to $f(x) = +\chi_{B_\epsilon(s)}(x)$, the characteristic function of $B_\epsilon(s)$, the ball of radius $\epsilon$ centered at $s$ (technically, eq. \ref{inva2}) )" +holds also for sunuuable fictions). to get: HBAs) Επ ο”.," holds also for summable functions), to get: (s)) = (x) ))." + If o has a bounded density. this means that the following mut exists and is equal to plo: y). the density of the measure σ at the point y: BAN) = pltaiig)t," If $\sigma$ has a bounded density, this means that the following limit exists and is equal to $\rho(\sigma;y)$ , the density of the measure $\sigma$ at the point $y$: (y)) = ;y)." +n) Using this definition. we cau now divide both sides of eq. (3))," Using this definition, we can now divide both sides of eq. \ref{ball1}) )" + by 2e and take the limit for e.»0., by $2 \epsilon$ and take the limit for $\epsilon \rightarrow 0$. + Thauks to the dominated convergence theorem the lait can be taken inside the integral at rls., Thanks to the dominated convergence theorem the limit can be taken inside the integral at r.h.s. + to obtain pnis)- ditoeyptta: IÍ, to obtain ;s) = (x) ( ). +jq9) From this last relation the thesis easily follows., From this last relation the thesis easily follows. + We now specialize the theory to thecase when o is the Lebeseuc measure. that is to say. all possible values of 3 in |1.1) are equally probable.," We now specialize the theory to thecase when $\sigma$ is the Lebesgue measure, that is to say, all possible values of $\beta$ in $[-1,1]$ are equally probable." + Let 0<6«l and let o be given by plo:3)=4D[ia]. Then. the deerant mcasire i ds absolutely continuous. with a density pipe) that às imfinitely differentiable and non-analytic.," Let $0<\delta<1$ and let $\sigma$ be given by $ + \rho(\sigma;\beta) = \frac{1}{2} \chi_{[-1,1]}(\beta). $ Then, the invariant measure $\mu$ is absolutely continuous, with a density $\rho(\mu;x)$ that is infinitely differentiable and non-analytic." +Proof.. The fact that µ has a bounded censity follows from Lemna 2.1.., The fact that $\mu$ has a bounded density follows from Lemma \ref{lem-cont}. + Furtlicrmore. inserting the value of p(o:.7) into eq. (3)).," Furthermore, inserting the value of $ + \rho(\sigma;\beta)$ into eq. \ref{dens0}) )," + we obtain pene) = asp. 22) and. taking the derivative with respect to wr. (Gia) = p(n: This equation Sascan be iterated to show the existence of derivatives of p(yτω) of all orders.," we obtain ;x) = ( ), and, taking the derivative with respect to $x$, ;x) = [; This equation can be iterated to show the existence of derivatives of $\rho(\mu;x)$ of all orders." + Furthermore. observe that. when talking.=1. both points (Lby aud (+12)D] are to the left of 1. that is. outside of the support of jr. so that all derivatives of p(p:.c) aveuull ine= 1.," Furthermore, observe that, when taking $x=-1$, both points $(\frac{-1 - \bar{\delta}}{\delta})$ and $(\frac{-1 + +\bar{\delta}}{\delta})$ are to the left of $-1$, that is, outside of the support of $\mu$ , so that all derivatives of $\rho(\mu;x)$ arenull in $x=-1$ ." + Therefore. p(y) cannot be analytic.," Therefore, $\rho(\mu;x)$ cannot be analytic." + Iu the next section. we will describe a nuuerical techuique to compute the density of this invariant nieasure.," In the next section, we will describe a numerical technique to compute the density of this invariant measure." +due to the small aspect ratio of the outer disk (1=0.03).,due to the small aspect ratio of the outer disk $h \approx 0.03$ ). + In the second case. Saturn started to accrete when Jupiter reached half its final mass (ve. vy=0.5). by which time the two planets were beyond the 2:1 MMR.," In the second case, Saturn started to accrete when Jupiter reached half its final mass (i.e., $x_J = 0.5$ ), by which time the two planets were beyond the 2:1 MMR." + The planets succeeded in breaking the 2:1 and 5:3 MMRs. became trapped in the 3:2 MMR and migrated outward only to undergo a dynamical instability putting the planets once again beyond the 2:1 MMR.," The planets succeeded in breaking the 2:1 and 5:3 MMRs, became trapped in the 3:2 MMR and migrated outward only to undergo a dynamical instability putting the planets once again beyond the 2:1 MMR." + A more detailed study of outward migration in radiative disks is underway., A more detailed study of outward migration in radiative disks is underway. + Using à simple 1-D model of an evolving Solar Nebula we showed that the disk should be optically thick at early times. then transition to optically thin from the outside-in during the late phases of its evolution.," Using a simple 1-D model of an evolving Solar Nebula we showed that the disk should be optically thick at early times, then transition to optically thin from the outside-in during the late phases of its evolution." + At the orbital distance in question (1-10 AU). the disk transitions from radiative to isothermal behavior in the last 1-2 Myr of its evolution.," At the orbital distance in question (1-10 AU), the disk transitions from radiative to isothermal behavior in the last 1-2 Myr of its evolution." + Thus. even tf we make the “pessimistic” assumption that an isothermal disk is required for outward migration of Jupiter and Saturn. the disk fulfills the criteria for long-range outward migration in its late phases.," Thus, even if we make the “pessimistic” assumption that an isothermal disk is required for outward migration of Jupiter and Saturn, the disk fulfills the criteria for long-range outward migration in its late phases." + Outward migration of Jupiter and Saturn at this time ts very likely provided the disk remains thin (7< 0.05)., Outward migration of Jupiter and Saturn at this time is very likely provided the disk remains thin $h \lesssim 0.05$ ). + Our simulations therefore show that an. inward-then-outward migration of Jupiter and Saturn is extremely likely. and that the last phase of outward migration probably coincided with the late phases of the dissipation of the Solar Nebula.," Our simulations therefore show that an inward-then-outward migration of Jupiter and Saturn is extremely likely, and that the last phase of outward migration probably coincided with the late phases of the dissipation of the Solar Nebula." + This is of particular interest because the two phase migration of Jupiter and Saturn helps resolve a long-standing problem in terrestrial planet formation., This is of particular interest because the two phase migration of Jupiter and Saturn helps resolve a long-standing problem in terrestrial planet formation. + For over 20 years. simulations of terrestrial accretion have been unable to reproduce Mars’ relatively small mass (0.11. Μι Wetherill 1978. 1991: Chambers 2001: Raymond et al.," For over 20 years, simulations of terrestrial accretion have been unable to reproduce Mars' relatively small mass $0.11$ $\mearth$; Wetherill 1978, 1991; Chambers 2001; Raymond et al." + 2009)., 2009). + This problem arises because. in a Solar Nebula that varies smoothly in orbital radius. there is a comparable or larger amount of mass in the vicinity of Mars than the Earth.," This problem arises because, in a Solar Nebula that varies smoothly in orbital radius, there is a comparable or larger amount of mass in the vicinity of Mars than the Earth." + For Mars to be so much smaller than Earth. most of the mass between roughly 1-3 AU must be removed (e.g.. Raymond et al.," For Mars to be so much smaller than Earth, most of the mass between roughly 1-3 AU must be removed (e.g., Raymond et al." + 2006. 2009; O'Brien et al.," 2006, 2009; O'Brien et al." + 2006)., 2006). + Several mechanisms have been proposed to remove this mass. including strong secular resonances (Thommes et al.," Several mechanisms have been proposed to remove this mass, including strong secular resonances (Thommes et al." + 2008. Raymond et al.," 2008, Raymond et al." + 2009) and a narrow dip in the surface density caused by a radial dependence of the disk’s viscosity (1.e.. a dead zone: Jin et al.," 2009) and a narrow dip in the surface density caused by a radial dependence of the disk's viscosity (i.e., a dead zone; Jin et al." + 2008)., 2008). + However. the problem is most easily and much better solved if the terrestrial planets did not form from a wide disk of planetary embryos but instead from a narrow annulus extending only from 0.7-1 AU (Wetherill 1978; Chambers 2001: Hansen 2009).," However, the problem is most easily and much better solved if the terrestrial planets did not form from a wide disk of planetary embryos but instead from a narrow annulus extending only from 0.7-1 AU (Wetherill 1978; Chambers 2001; Hansen 2009)." + In that case. Mars? small mass is simply an edge effect: Mars is small was built from one or perhaps a few embryos that were scattered beyond the edge of the embryo disk (this is also the case for Mercury. which was scattered inward beyond the inner edge of the embryo disk).," In that case, Mars' small mass is simply an edge effect: Mars is small was built from one or perhaps a few embryos that were scattered beyond the edge of the embryo disk (this is also the case for Mercury, which was scattered inward beyond the inner edge of the embryo disk)." + In contrast. Earth and Venus formed within the annulus anc are consequently much more massive.," In contrast, Earth and Venus formed within the annulus and are consequently much more massive." + Simulations of terrestrial planet formation can quantitatively reproduce the orbits anc masses of all four terrestrial planets as well as their radial distribution (Hansen 2009)., Simulations of terrestrial planet formation can quantitatively reproduce the orbits and masses of all four terrestrial planets as well as their radial distribution (Hansen 2009). + The flaw in simulations of terrestrial. planet. formatior in truncated. disks is that they had no justification for the truncation: the ad-hoe initial conditions were simply choser because they provided a good fit to the actual terrestrial planets (Hansen 2009)., The flaw in simulations of terrestrial planet formation in truncated disks is that they had no justification for the truncation; the ad-hoc initial conditions were simply chosen because they provided a good fit to the actual terrestrial planets (Hansen 2009). + The two phase migration of Jupiter and Saturn provides such a justification via the Grand Tack model of Walsh et al. (, The two phase migration of Jupiter and Saturn provides such a justification via the Grand Tack model of Walsh et al. ( +2011).,2011). + If Jupiter’s turnaround point was at ~1.5 AU then it would have naturally truncated the inner disk of embryos and planetesimals at about | AU — in most of our simulations Jupiter indeed tacked at roughly this distance., If Jupiter's turnaround point was at $\sim 1.5$ AU then it would have naturally truncated the inner disk of embryos and planetesimals at about 1 AU – in most of our simulations Jupiter indeed tacked at roughly this distance. + As expected. the terrestrial planets that form from this disk quantitatively reproduce the actual terrestrial planets (Walsh et al.," As expected, the terrestrial planets that form from this disk quantitatively reproduce the actual terrestrial planets (Walsh et al." + 2011)., 2011). + The Grand Tack model also provides the best explanation to date for the observed dichotomy between the inner and outer asteroid belt (Gradie Tedesco 1982)., The Grand Tack model also provides the best explanation to date for the observed dichotomy between the inner and outer asteroid belt (Gradie Tedesco 1982). + Thus. the present-day Solar System appears to bear the imprint of a two phase migration of Jupiter and Saturn.," Thus, the present-day Solar System appears to bear the imprint of a two phase migration of Jupiter and Saturn." + Our hydrodynamical simulations provide support for the Grand Tack scenario., Our hydrodynamical simulations provide support for the Grand Tack scenario. + As with any numerical study. our simulations do not fully represent reality.," As with any numerical study, our simulations do not fully represent reality." + The aspect of our simulations that is probably the least realistic is the gas accretion onto the giant planets’ cores., The aspect of our simulations that is probably the least realistic is the gas accretion onto the giant planets' cores. + In our simulations. gas aceretion onto Jupiter and Saturn is extremely fast.," In our simulations, gas accretion onto Jupiter and Saturn is extremely fast." + Once accretion starts. Jupiter and Saturn reach their final masses in only a few thousand years. whereas the Kelvin-Helmholtz time in protoplanetary disks is more like ~10° years.," Once accretion starts, Jupiter and Saturn reach their final masses in only a few thousand years, whereas the Kelvin-Helmholtz time in protoplanetary disks is more like $\sim 10^5$ years." + In addition. accretion onto growing giant planet cores requires transferring gas through circum-planetary accretion disks whose physical properties are poorly constrained (e.g.. Ward Canup 2010).," In addition, accretion onto growing giant planet cores requires transferring gas through circum-planetary accretion disks whose physical properties are poorly constrained (e.g., Ward Canup 2010)." + Once the planets reached their actual masses we artificially turned off gas accretion., Once the planets reached their actual masses we artificially turned off gas accretion. + If. during the outward migration Saturn accreted enough gas to carve a gap as deep as Jupiter's then Saturn’s outer lindblad torque would balance Jupiter's inner lindblad torque. outward migration would stop and the planets would turn back around and migrate inward.," If, during the outward migration Saturn accreted enough gas to carve a gap as deep as Jupiter's then Saturn's outer lindblad torque would balance Jupiter's inner lindblad torque, outward migration would stop and the planets would turn back around and migrate inward." + The impact of a more realistic aceretion history on Jupiter and Saturn's migration remains an open question. in particular with regards to the interplay between gas accretion and the dispersal of both the cimeumstellar and cicumplanetary disks.," The impact of a more realistic accretion history on Jupiter and Saturn's migration remains an open question, in particular with regards to the interplay between gas accretion and the dispersal of both the cimcumstellar and cicumplanetary disks." +As discussed by Gendreetal.(2008).. there are no strong differences in the afterglow properties of very distant and less distant bursts: this bias does not impact our results.,"As discussed by \citet{gen08}, there are no strong differences in the afterglow properties of very distant and less distant bursts: this bias does not impact our results." + However. a possible way to solve this bias ts to add further observations within the far infrared bands.," However, a possible way to solve this bias is to add further observations within the far infrared bands." + The difference between the fluxes of group/ and is cm 42 magnitudes one day after the burst; the optical and infrared groups are identical., The difference between the fluxes of group and is $\approx$ 3 magnitudes one day after the burst; the optical and infrared groups are identical. + This makes us confident that this clustering in luminosity is not spurious despite our small sample., This makes us confident that this clustering in luminosity is not spurious despite our small sample. + In the following. we will use the results for the optical luminosity clustering giver by Nardinietal.(2006).," In the following, we will use the results for the optical luminosity clustering given by \citet{nar06}." +. These authors reported a flux atio. between group and group of ~ 26., These authors reported a flux ratio between group and group of $\sim$ 26. + Assuming no spectral variation. between optical and hear infrared wavelengths. this translate into a difference in magnitude of 3.2. consistent. with the observed separation.," Assuming no spectral variation between optical and near infrared wavelengths, this translate into a difference in magnitude of 3.2, consistent with the observed separation." + This implies that the clustering continues towards lower wavelengths than optical bands., This implies that the clustering continues towards lower wavelengths than optical bands. +" Previous works have shown from spectral energy distributions of GRB afterelows that optical and infrared data can be fit using single power laws (seee.g.Starling2008.foroneexampleofsuch works).. or in other terms. that the injection frequency vj, is lower compared to the infrared bands."," Previous works have shown from spectral energy distributions of GRB afterglows that optical and near-infrared data can be fit using single power laws \citep[see e.g.][for one example of such works]{sta08}, or in other terms, that the injection frequency $\nu_m$ is lower compared to the infrared bands." + We thus have: with vp~2x10' Hz., We thus have: with $\nu_{IR} \sim 2 \times 10^{14}$ Hz. + In Gendreetal.(2008).. we expressed several constraints on the fireball parameters.," In \citet{gen08}, we expressed several constraints on the fireball parameters." + Using these constraints and Equation l.. we can express a constraint on the total energy of the fireball (the constants C are listed in Table 2)): Clearly. the constraint indicated in Eq.," Using these constraints and Equation \ref{eq_un}, we can express a constraint on the total energy of the fireball (the constants C are listed in Table \ref{table_constante}) ): Clearly, the constraint indicated in Eq." +" 2 is not relevant in the case of normal GRBs: even in the case of a wind environment with a very low density (says A,= 1075 for a burst of the group xI-ol. we have 1.6x1077 30$ the number roots to be determined in the eigenvalue problem represents only a small fraction of the matrix dimension (less than 10 ). + This is important for cllicient utilization of tjo d'erative Lanzeos-twpe diagonalization approaches., This is important for efficient utilization of the iterative Lanzcos-type diagonalization approaches. + The matrix diagonalization is the most consuming part of line list calcuation. boh in terms of time and memory.," The matrix diagonalization is the most consuming part of line list calculation, both in terms of time and memory." + Using these technique:s. we were abe to generate all eigenvalues and eigenvectors for values of J up to 41. suiject to t1c energy threshold of 1S000C.," Using these techniques, we were able to generate all eigenvalues and eigenvectors for values of $J$ up to 41, subject to the energy threshold of $18\,000$." +" However. only levels below .=36 were taken into the line List because higher J values did not have any ro-vibrationa states with energies below the threshold for the lower energy states in BYTe of £j, = 8000"," However, only levels below $J=36$ were taken into the line list because higher $J$ values did not have any ro-vibrational states with energies below the threshold for the lower energy states in BYTe of $E_{\rm low}$ = $8\,000$." +" As previously mentior1e. in order to conipute the eigenvalues and eigenvectors of wave emploved a new. imrove. ""specroscopic PIES. NII3-2010."," As previously mentioned, in order to compute the eigenvalues and eigenvectors of we employed a new, improved, `spectroscopic' PES, NH3-2010." + This PES was recently &eneratec through fitting to t1ο available experimental claa below J=8S., This PES was recently generated through fitting to the available experimental data below $J=8$. + Ht involved. adjustments to the analytical representation from 5).. using the refined PES [rom tlis work as a starting point.," It involved adjustments to the analytical representation from \citet{Yurchenko2005-NH3:survey}, using the refined PES from this work as a starting point." + This refinement was performec using “PROVE. which was extended: to allow suc1 fitting tasks.," This refinement was performed using TROVE, which was extended to allow such fitting tasks." + The details of the refinement. procedure and the new PES 13-2010. will be given elsewhere (Yurchenkoeta.2011)., The details of the refinement procedure and the new PES NH3-2010 will be given elsewhere \citep{PES-NH3-2010}. +. An accurate dipole nxpment surface (DATS) is a prerequisite for producing accurate line intensities., An accurate dipole moment surface (DMS) is a prerequisite for producing accurate line intensities. + Tests have shown that these are best taken direcIv from highSu qualicqvo calculations (Lynas-Gravetal.1995).., Tests have shown that these are best taken directly from high quality calculations \citep{jt156}. + lor BYTe we emploved. the ATZfle DMS of (from Yurchenkoetal.(2005). in the improvecl DAIS representation from Yurchenkoetal.(200!η. which behaves well when the molecule adopts a planar geometry.," For BYTe we employed the ATZfc DMS of from \citet{Yurchenko-NH3-DMS-2005} in the improved DMS representation from \citet{NH3-T300K-paper}, which behaves well when the molecule adopts a planar geometry." + This DAIS has been shown to provide intensities in gooc agreement with experiment (Yurchenkoetal.2005. 2009):: ib was also uscxd in producing the ‘cool’ ammonia line list (Yurchenkoctal.2009)..," This DMS has been shown to provide intensities in good agreement with experiment \citep{Yurchenko-NH3-DMS-2005,NH3-T300K-paper}; ; it was also used in producing the `cool' ammonia line list \citep{NH3-T300K-paper}." + To speed up the computation of the trarsition moments used to generate the Einstein X «'oelficients. we used the procedure. see Yurchenkoetal.(2)09).. in which only eigen-coellicients with magniude larger than 10 were selected.," To speed up the computation of the transition moments used to generate the Einstein A coefficients, we used the pre-screening procedure, see \citet{NH3-T300K-paper}, in which only eigen-coefficients with magnitude larger than $10^{-12}$ were selected." + This reduced the size of the vectorss (bv about TO-SO0%)) as wel as the computation time., This reduced the size of the vectors (by about ) as well as the computation time. + We also imposed an absorption intensity threshold 10.77 mo (1.7.107 em/molecule) at Z7—1500 Ix. for the intensities to be included in BYTe.," We also imposed an absorption intensity threshold $10^{-12}$ $/$ mol $\times 10^{-36}$ cm/molecule) at $T=1\,500$ K, for the intensities to be included in BYTe." + This threshold corresponds to abou QO75 of the maximum intensity at 7—1500 Ix 50000 cm/mol).," This threshold corresponds to about $10^{-16}$ of the maximum intensity at $T=1\,500$ K 000 $/$ mol)." + The major bottle-neck in these calcul:ULIODS Was assoclat«d with the need to read repeatedly a huge number of eigenvectors stored on the disk., The major bottle-neck in these calculations was associated with the need to read repeatedly a huge number of eigenvectors stored on the disk. + Phe large size o “these vectors. Preventce lus from keeping all of them in the virtual memory during the computational process., The large size of these vectors prevented us from keeping all of them in the virtual memory during the computational process. + We were able [0 recuce the number of readings by optimizing the computational logisics., We were able to reduce the number of readings by optimizing the computational logistics. + In intensity simulations cach transition can be independently procesedo which effectively. naturaIv. parallelizes them. distributing them between computational nodes (see Yurchenkoοἱal. (2009))).," In intensity simulations each transition can be independently processed, which effectively naturally parallelizes them, distributing them between computational nodes (see \citet{NH3-T300K-paper}) )." + The most expensive par of the intensity calculations was for J from 10 to 3)0. which accounts for approximately 75% of all transitions to be coruputed.," The most expensive part of the intensity calculations was for $J$ from $10$ to $20$, which accounts for approximately 75 of all transitions to be computed." + In Fig., In Fig. + 2 we show how the number of lines and energy. levels depend on J., \ref{f:Nlevels:Nlines} we show how the number of lines and energy levels depend on $J$. + The number of levels peaks at J=15 and the reduces gradually with higher / and eventually reaches zero due to our lower and. upper energy limits of 5000 and 15000 rrespectively.," The number of levels peaks at $J=15$ and the reduces gradually with higher $J$ and eventually reaches zero due to our lower and upper energy limits of $8\,000$ and $18\,000$ respectively." +" The BYTe NLL, {line list contains 1.138. billion lines. which are the allowed. transitions above a certain minimum. intensity. between 1.367 million ro-vibrational levels."," The BYTe $^{14}$ line list contains 1.138 billion lines, which are the allowed transitions above a certain minimum intensity, between 1.367 million ro-vibrational levels." + The structure o£ BYTe is similar to that of the D'E2 water line list (Barberetal. 2006)., The structure of BYTe is similar to that of the BT2 water line list \citep{BT2}. . +. BYTe comprises two files., BYTe comprises two files. + One. the LEnereyv file. holds the energies ancl ro-vibrational quantum numbers of all NIL; states up to Jc41 that are less than 0000 aabove the zero point energy. (our value is 7430.288276 yy," One, the Energy file, holds the energies and ro-vibrational quantum numbers of all $_3$ states up to $J\le 41$ that are less than 000 above the zero point energy (our value is 7430.288276 )." + Table 1 eives an extract [rom the [Energyfile., Table \ref{t:Energy-file} gives an extract from the Energyfile. + Apart from, Apart from +The prompt emission of gamma-ray bursts (GRB) is followed by an afterglow phase commonly attributed to the synchrotron emission of shock accelerated electrons (Mésszárros Rees 1997).,The prompt emission of gamma-ray bursts (GRB) is followed by an afterglow phase commonly attributed to the synchrotron emission of shock accelerated electrons (Mésszárros Rees 1997). + As the blast wave sweeps up matter and decelerates. the dissipated power decreases and the emission shifts to longer wavebands (e.g.. Piran 2005).," As the blast wave sweeps up matter and decelerates, the dissipated power decreases and the emission shifts to longer wavebands (e.g., Piran 2005)." +" To model this afterglow emission. one usually encodes the acceleration physics in a minimal/maximal Lorentz factor (auin/uuax dn the spectral index s of the electron spectrum. in the fraction c, of the dissipated energy that is carried by these electrons and in the fraction ερ stored in magnetic turbulence."," To model this afterglow emission, one usually encodes the acceleration physics in a minimal/maximal Lorentz factor $\gamma_{\rm + min}\,/\,\gamma_{\rm max}$ ), in the spectral index $s$ of the electron spectrum, in the fraction $\epsilon_e$ of the dissipated energy that is carried by these electrons and in the fraction $\epsilon_B$ stored in magnetic turbulence." + However. our understanding of relativistic Fermi acceleration has made significant progress in the last decade. to an extent that motivates a direct test against observational data.," However, our understanding of relativistic Fermi acceleration has made significant progress in the last decade, to an extent that motivates a direct test against observational data." + The convergence of analytical calculations and. extensive particle-in-cell (PIC) numerical calculations has led in particular to the following picture., The convergence of analytical calculations and extensive particle-in-cell (PIC) numerical calculations has led in particular to the following picture. + At (superluminal) ultra-relativistic shock waves. Fermi power-laws cannot develop because the particles get advected to the far downstream along with the magnetic tield lines to which they are tied (Begelman Kirk 1990). unless strong turbulence has been excited on scales significantly smaller than their Larmor radius (Lemoine et al.," At (superluminal) ultra-relativistic shock waves, Fermi power-laws cannot develop because the particles get advected to the far downstream along with the magnetic field lines to which they are tied (Begelman Kirk 1990), unless strong turbulence has been excited on scales significantly smaller than their Larmor radius (Lemoine et al." + 2006: Niemiec et al., 2006; Niemiec et al. + 2006: Pelletier et al., 2006; Pelletier et al. + 2009)., 2009). + In very weakly magnetized slocks. such turbulence can be excited by micro-instabilities in t18 shock precursor and therefore Fermi acceleration can develop. as confirmed by recent PIC simulations (Siront Spitkovsky οίM1).," In very weakly magnetized shocks, such turbulence can be excited by micro-instabilities in the shock precursor and therefore Fermi acceleration can develop, as confirmed by recent PIC simulations (Sironi Spitkovsky 2011)." + The critical level of magnetization below which this turbulence develops depends on the shock Lorentz factor (Lemoine Pelletier 2010. 2011) as indeed. such instabilities can grow only if their growth timescale is shorter than the timescale on which the unshocked plasma crosses the shock precursor and. the stronger the upstream background magnetization. or the larger the shock Lorentz factor. the shorter the precursor.," The critical level of magnetization below which this turbulence develops depends on the shock Lorentz factor (Lemoine Pelletier 2010, 2011) as indeed, such instabilities can grow only if their growth timescale is shorter than the timescale on which the unshocked plasma crosses the shock precursor and, the stronger the upstream background magnetization, or the larger the shock Lorentz factor, the shorter the precursor." + In practice. one may expect Fermi acceleration to proceec unhampered if the blast wave propagates ina weakly magnetizec external medium such as the interstellar medium (SM).," In practice, one may expect Fermi acceleration to proceed unhampered if the blast wave propagates in a weakly magnetized external medium such as the interstellar medium (ISM)." + In magnetized stellar winds. however. one might expect to see signatures of the above microphysics of Fermi acceleration. al the more so at early stages when the blast Lorentz factor is large.," In magnetized stellar winds, however, one might expect to see signatures of the above microphysics of Fermi acceleration, all the more so at early stages when the blast Lorentz factor is large." + Such signatures would open a window on the physies of collisionless relativistic shocks as well as on the astrophysics of GRB afterglows., Such signatures would open a window on the physics of collisionless relativistic shocks as well as on the astrophysics of GRB afterglows. +" This motivates the present study. which proposes to compute the afterglow light curve of a gamma-ray burs propagating in a magnetized stellar wind from ""ab initio"" principles regarding Fermi acceleration."," This motivates the present study, which proposes to compute the afterglow light curve of a gamma-ray burst propagating in a magnetized stellar wind from “ab initio” principles regarding Fermi acceleration." + The recent studies of Li Waxman (2006) and Li (2010) offer an interesting perspective on this problem., The recent studies of Li Waxman (2006) and Li (2010) offer an interesting perspective on this problem. +" From the observation of A-ray afterglows on sub-day scales. these authors infer a strong ower bound on the upsream magnetic field of gamma-ray bursts afterglows. £4,22004€nm7 (no the upstream density in x Li 010) actualy derives a significantly stronger bound by eonsidering on equal grounds the long lived high energy emission >»100 MeV. This implies that either micro-instabilities iive grown and excitec the magnetic field to the above values. or the pre-existing magnetic field itself satisties this bound."," From the observation of X-ray afterglows on sub-day scales, these authors infer a strong lower bound on the upstream magnetic field of gamma-ray bursts afterglows, $B_{\rm + u}\gtrsim 200\,\mu{\rm G}\, n_{\rm 0}^{5/8}$ $n_{0}$ the upstream density in $^{-3}$ ); Li (2010) actually derives a significantly stronger bound by considering on equal grounds the long lived high energy emission $>100\,$ MeV. This implies that either micro-instabilities have grown and excited the magnetic field to the above values, or the pre-existing magnetic field itself satisfies this bound." +" While he former is expected i ""the eireumburst medium is ISM like. the"," While the former is expected if the circumburst medium is ISM like, the" +can be best approximated with run (500.600.0.2). unfortunately our model does not provide results farther out for such a small Ro.,"can be best approximated with run (500,600,0.2), unfortunately our model does not provide results farther out for such a small $R_0$." + At distances above 200 AU. the run (500.600.0.5) gives a Jet width in the observed range but only after the first bump. which is intrinsic for our analytical model.," At distances above 200 AU, the run (500,600,0.5) gives a jet width in the observed range but only after the first bump, which is intrinsic for our analytical model." + Hartiganetal.(1995) give a mass of DG Tau of 0.67 M... ie. higher than in both models.," \citet{HEG95} give a mass of DG Tau of 0.67 $M_\odot$, i.e. higher than in both models." + Although this difference in mass might not be meaningful. we conclude that to be able to reproduce all jets in our sample. we need an additional effect which reduces the derived jet width.," Although this difference in mass might not be meaningful, we conclude that to be able to reproduce all jets in our sample, we need an additional effect which reduces the derived jet width." +"with the coefficient matrix and the result vector We now repeat this exercise for the strong lensing term, where Again, we isolate the non-linear terms and take them as constant during each iteration step, This yields another linear system, with the coefficient matrix for strong lensing and the result vector Also the regularisation term in Eq. (25))","with the coefficient matrix and the result vector We now repeat this exercise for the strong lensing term, where Again, we isolate the non-linear terms and take them as constant during each iteration step, This yields another linear system, with the coefficient matrix for strong lensing and the result vector Also the regularisation term in Eq. \ref{R}) )" +" has to be minimised, which contributes one additional term to the coefficient matrix and the result vector, and Finally, we collect the results to obtain the solution for Eq. [IT],"," has to be minimised, which contributes one additional term to the coefficient matrix and the result vector, and Finally, we collect the results to obtain the solution for Eq. \ref{chimin}," + given in terms of a linear system with the following coefficient matrix and the result vector, given in terms of a linear system with the following coefficient matrix and the result vector +with our analysis in 833 that optical obscuration of DALOSOSs can cause signilicant selection biases against selecting BALQSOs.,with our analysis in 3 that optical obscuration of BALQSOs can cause significant selection biases against selecting BALQSOs. +" The difference of the /—A, color difference is mainly caused by the / mag distribution difference between (he (wo populations.", The difference of the $i-K_s$ color difference is mainly caused by the $i$ mag distribution difference between the two populations. +" In the complete Jv, seauple. the [νο probability for the / mag distributions of BALQSOs and non-BALQSOs being the same is 4xLO°. while the IX-S probability for A mag distributions is 0.46."," In the complete $K_s$ sample, the K-S probability for the $i$ mag distributions of BALQSOs and non-BALQSOs being the same is $4\times10^{-6}$, while the K-S probability for $K_s$ mag distributions is 0.46." + This result is also consistent with previous studies of BALQSOs (203: T06). where BALQSOs are found to be redder in the SDSS bands.," This result is also consistent with previous studies of BALQSOs (R03; T06), where BALQSOs are found to be redder in the SDSS bands." + With only nine optically selected BALQSOs. Hall el al. (," With only nine optically selected BALQSOs, Hall et al. (" +1997) found no ciserepancy between B—A colors of BALQSOs and non-BALQSOs: however. two of their radio selected BALQSOs are particularly τος.,"1997) found no discrepancy between $B-K$ colors of BALQSOs and non-BALQSOs; however, two of their radio selected BALQSOs are particularly red." + The color differences between BALQSOs and non-BALQSOs in the 2\LASS bands are smaller and consistent will the expectation (hat (there is an extra dust. extinction in BALQSOs., The color differences between BALQSOs and non-BALQSOs in the 2MASS bands are smaller and consistent with the expectation that there is an extra dust extinction in BALQSOs. +" The median J—A, and ff—AN, colors are 1.17 and 0.64 mag for and 1.26 and 0.67 mag for BALQSOs. with color differences of 0.0940.02 and 0.03+0.02mag."," The median $J-K_s$ and $H-K_s$ colors are 1.17 and 0.64 mag for non-BALQSOs and 1.26 and 0.67 mag for BALQSOs, with color differences of $0.09\pm0.02$ and $0.03\pm0.02$mag." + These differences are broadly consistent with the R03 dust extinction fit ol .AE(D—V)=0.023 between BALQSOs and non-BALQSOs. given the observed recshilt clistvibution of the quasars.," These differences are broadly consistent with the R03 dust extinction fit of $\Delta E(B-V) =0.023$ between BALQSOs and non-BALQSOs, given the observed redshift distribution of the quasars." +" We have tested the νο probability that the near infrared color distributions of BALQSOs aud non-BALQSOs are drawn from the same sample. ancl found 0.0009 and 0.49 for the J—A, color distributions in the 221ASS sample and A, complete sample. respectively. and probabilities of 0.36 and 0.78 for the //—Ay. color distributions."," We have tested the K-S probability that the near infrared color distributions of BALQSOs and non-BALQSOs are drawn from the same sample, and found 0.0009 and 0.49 for the $J-K_s$ color distributions in the 2MASS sample and $K_s$ complete sample, respectively, and probabilities of 0.36 and 0.78 for the $H-K_s$ color distributions." + The ο test results are consistent with small 241ASS color differences between BALQSOs and non-BALQSOs., The K-S test results are consistent with small 2MASS color differences between BALQSOs and non-BALQSOs. + We performed simple simulations to model the fractions of BALQSOs in the optical and near infrared bands., We performed simple simulations to model the fractions of BALQSOs in the optical and near infrared bands. + We show that the increase of the BALQSO [Iractions with wavelength can be explained by the selection effects caused by the spectral differences between BALQSOs and non-BALQSOs including both absorption lines and dust extinction., We show that the increase of the BALQSO fractions with wavelength can be explained by the selection effects caused by the spectral differences between BALQSOs and non-BALQSOs including both absorption lines and dust extinction. + Our simulations are performed in the redshift range of 1.7<2«2.5., Our simulations are performed in the redshift range of $1.7 < z < 2.5$. +" We assumed that (he intrinsic (extinction and absorption corrected) Iuminosity functionsof DALQSOSs. 54,ini non-DALQSOs. Oyo.Εως. and total quasars. Pron BALinte share the same shape. but differ bv normalization factors. Pgari=PearPoso.μην. where [νε is the intrinsic Iraction of BALQSOs."," We assumed that the intrinsic (extinction and absorption corrected) luminosity functionsof BALQSOs, $\Phi_{BAL, intr}$, non-BALQSOs, $\Phi_{non-BAL, intr}$, and total quasars, $\Phi_{QSO, intr} = \Phi_{BAL, intr}+ \Phi_{non-BAL, intr}$ , share the same shape, but differ by normalization factors, $\Phi_{BAL, intr} = f_{BAL} \Phi_{QSO, intr}$, where $f_{BAL}$ is the intrinsic fraction of BALQSOs." + The shape of the luminosity functions are represented by a double power-law luminosity function described by (he Richards et al. (, The shape of the luminosity functions are represented by a double power-law luminosity function described by the Richards et al. ( +2005) luminosity funcüon with a bright end slope of a= —3.31. a faint end slope of ¢= —1.45. and a break al Al*(2)ΑΟ)—2.5(4z+Fasz?) with Als=0) —2L.61. hy= 139.,"2005) luminosity function with a bright end slope of $\alpha = -3.31$ , a faint end slope of $\beta=-1.45$ , and a break at $M^*(z)=M^*(0)-2.5(k_1z+k_2z^2)$ with $M^*(z=0) = -21.61$ , $k_1=1.39$ ," +ln fact. Brinkworthetal.(2000) found that the gaseous and dustv discs in SDSS J122859.98|104032.9. co-exist ab oa distance Ὁ1.24!. [rom the white iat,"In fact, \citet{bri2009} found that the gaseous and dusty discs in SDSS J122859.93+104032.9 co-exist at a distance $\la 1.2\,R_\odot$ from the white dwarf." + Although GALEN J1931|OL17 and SDSS J122859.93|104032.9 have nearly identical luminosities. the lack of a gaseous disc in the former and the dissimilarity of their NLR spectral energy distributions imply cilferent environments.," Although GALEX J1931+0117 and SDSS J122859.93+104032.9 have nearly identical luminosities, the lack of a gaseous disc in the former and the dissimilarity of their NIR spectral energy distributions imply different environments." + We identified anc analysed the properties of one of the most heavily polluted white cdwarfs known., We identified and analysed the properties of one of the most heavily polluted white dwarfs known. + The source of the material remains unknown. although the measured. NI excess may be attributed to a L5 dwarf. or to a warm debris disc.," The source of the material remains unknown, although the measured NIR excess may be attributed to a L5 dwarf or to a warm debris disc." + The measured. abundances suggest that. the material is accreted onto the atmosphere in solar proportions and favour a model involving a L chvarl companion in a close orbit., The measured abundances suggest that the material is accreted onto the atmosphere in solar proportions and favour a model involving a L dwarf companion in a close orbit. + lHlowever. the Hla. emission. notable in such systems ds absent in GALEN J1931|0117 and. the mass loss imposed on the companion appears excessive.," However, the $\alpha$ emission notable in such systems is absent in GALEX J1931+0117 and the mass loss imposed on the companion appears excessive." + NIR intermediate dispersion spectroscopy should help determine the nature of the accretion source., NIR intermediate dispersion spectroscopy should help determine the nature of the accretion source. + Xdditional optical spectra will be useful to trace putative orbital motions while Space Telescope Imaging Spectrograph high-dispersion spectra will be useful to constrain further the carbon abundance and extend the pattern to less abundant elements., Additional optical spectra will be useful to trace putative orbital motions while Space Telescope Imaging Spectrograph high-dispersion spectra will be useful to constrain further the carbon abundance and extend the pattern to less abundant elements. + S.V. and ur are by GA AV erant. numbers LAAS0003808WS and. LX:NOM‘ihn30901. respectively. and by CA CRA grant - 190:Contre0967.," S.V. and A.K. are supported by GA AV grant numbers IAA300030908 and IAA301630901, respectively, and by GA ČRR grant number P209/10/0967." +" AN. also acknowledges support from the for ""Theoretical Astrophysics (LCOGOLL).", A.K. also acknowledges support from the Centre for Theoretical Astrophysics (LC06014). + We thank the referee for useful suggestions., We thank the referee for useful suggestions. + This publication makes use of data products from the Pwo Micron All Sky Survey. which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/C'alifornia. Institute of Technology. Funded. by the National Aeronautics and Space JXdministration and the National Science Foundation.," This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation." + ↽∕∏∐∖↕≧↸∖⋯⋯≋⊀≚⊸∖⊽∪↴⋝↴∖↴↸∖↥⋅↖↽⋜↧↑↕∪∐∪↕⋟∶↴∙⊾⋜∐⊔⋯⋜⊢↥⋅⋜↧⋅↖∏∐∖↑≼↕↴↕≽⋝↽∕∏⊔∖↖↖↽∐∪↕↸∖↻↥⋅∪↸⊳↸∖↴∖∷∖↴↑⋜∐↘↽↸∖↴∖↴∿≺∖∖∐⋯∐⋅↴∖↴∙⊟≻↥⋅↴∖↴∪⊔↸∖↴∏∐∷∖↴↑↴∖↴,The BeppoSAX observation of gamma-ray burst (GRB) afterglows at X-ray wavelengths has ushered in a new era of gamma-ray burst studies. + ⋜↧↕≯↑↸∖↥⋅∶↴∙⊾↕∪↖↖⇁↴∖↴⋜↧↑⊸∖⊽≓↥⋅⋜↧⋅↖↽↖↖⇁⋜↧↖⇁↸∖↕↸∖∐∶↴⋁↑∐∖↴∐⋜↧↴∖↴∏↴∖↴∐↸∖↥⋅↸∖≼↧∐↕⋜↧∐↸∖↖↖↽↴∖↴↸∖↖↽↸∖↥⋅⋜↧↕⊺≼↙≽≼≓≽↴∖↴↖↖⇁↸∖↥⋅↸∖↴∖↴↸⊳∐↸∖≼↧∏↕↸∖≼↧∙↑⋅↖↴≻↕↸⊳⋜↕∐⋅↖⇁⋜, The breakthrough has been achieved using a conventional GRB detector in conjunction with a wide field X-ray camera and narrow field X-ray telescopes. +↧↕≯↸∖↖↖↽↽∩↓↴∖↴↕∪∐∶↴⋁∙ ↸∖↥⋅⋜↧∪↕⋟∶↴∙⊾⋜⋯∐⊔⋜⊢↥⋅⋜↧⋅↖↽↴∏∐⋅↴∖↴↑↴∖↴↑∏≼∐↸∖↴∖↴∙↽∕∏∐∖↴⋝↥⋅↸∖⋜∐↘↽↑↕∐⋅⋯↕∶↴⋁∐∐⋜↧↴∖↴∪↸⊳↸⊳↿∐⋅↥⋅↕∐∶↴⋁∿∩∙∶≩≼↧⋜↧⋅↖↽↴∖↴∙≼↧⋜↧⋅↖↽↴∖↴⋜↧∐≼↧↴∖↴↸∖↖⇁↸∖↥⋅⋜↧≼↧⋜↧⋅↖⇁↴∖↴⋜↧↕⋟↑↸∖↥⋅↑∐↸∖ ↴⋝↸∖↸∖∐⋜↧≼⊳∐↕↸∖↖↽↸∖≼↧∏↴∖↴↕∐∶↴⋁⋜↧↸⊳∪∐↖↽↸∖∐↑↕∪∐⋜↧↕≼∶↕⊰↕≧≼∐∖↑↸∖↸⊳↑∪↥⋅↕∐↕↕∐↑↕⋜↧↕∏⋅↕∶↴⋁∶↴⋁↸∖↥⋅∙⊟≻↥⋅↻∪↴∖↴↕↑↕↖↽↸∖≼∐∖↑↸∖↸⊳↑↕∪∐↴∖↴∙↑∐↸∖⊔⋮≼⊲≋⋜⋯≼↧ ↸⊳≺≻↕↕⋅↿↿↕↕↕↸⊳↑↕≺≻↕↕↖↖↽↕↑∐⋜↧↖↖↽↕≼∐∖∱∎∐∖↕≼∟∖↕↥⋅⋜↧⋅↖↽↸⊳⋜⊔⊔↸∖↥⋅⋜↧⋜⋯≼↧∐⋜∐⋅↥⋅∪↖↖⇁⋀∖∐⋮≼⊲≋∏∐↸⊳↸∖↥⋅↑⋜↧↕∐↑⋅↖⇁↥⋅⋜∥∐↕⋜∐⋅↸∖↑⋅↖⇁↻↕↸⊳⋜↧∐⋅↖↽↕∣∙⊺∪≼⋜↧↑↸∖∙↑∐↸∖↥⋅↸∖ ∐↸∖↕≼⇂⊸∖↕↥⋅⋜↧⋅↖↽↑↸∖↕↸∖↴∖↴↸⊳∪↻↸∖↴∖↴∙↽∕∏∐∖≼∶↕⊰↕≧≼∐∖↑↸∖↸⊳↑∪↥⋅↖⇁↸∖↥⋅↕∐↸∖↴∖↴↑∐↸∖∐⋜↧↖↽↸∖↴⋝↸∖↸∖∐⊔↴∖↴⋯⊳∐≼∐∖↑↸∖↸⊳↑↕∪∐↴∖↴≼∶↕⊰↕≧∩⊺∩↽∐⋖⊟∖↥⋅∪↸⊳↕↸∖↑⋜↧↕∙ ∐⋜↧⊓∐⋅↸∖∪↕⋡↑∐↸∖↴∏∐⋅↴∖↴↑⋜⋯≼↧↑∐↸∖↖↖↽↕≼∐∖∐↸∖↕≼↧↸⊳⋜↧∐∐∖↥⋅⋜↕⋜↧↸⊳↸⊳↿∐⋅⋜↧↑↸∖↕⋅↖↽↕∩∩≺∖∖⋜∪∙≼∶↕⊰↕≧∩⊺∩⊇⊇≺∖∖≺≼⊲∪↴∖↴↑⋜∏∖↑⋜↧↕∙↕∩∩⊤∶⊟⋅∪∐↸∖↥⋅⋜↕↸∖↑⋜↧↕∙ ≼∐∖↑↸∖↥⋅∐∐∐↸∖↴∖↴↕↑↴∖↴↻∪↴∖↴↕↑↕∪∐∙⋜↧∐∪↖↖⇁↕∐∶↴∙⊾⋜↧↴∖↴↿∏↑↸∖∪↕⋟↕∐∶↴∙⊾∐↕⋅↖↽↴∖↴↸∖∐↴∖↴↕↑↕↖↽↸∖∙↕∩∩≺∖∖⋝⋅≼∶↕⊰↕≧∩⊺∩∐∣⊇≺⋀∖⊽↕↸⊳⋜↧↴∖↴⊓⋅∪↸∖↑⋜↧↕∙↕∩∩≺∖∖⋜↧⋝���≼∶↕⊰↕≧∩⊤∪⋅↱↗∪≺∖∖ but uarrow field instruments. to be slewed to the burst position within a matter of hours.," The GRB detector verifies the nature of the burst and the wide field camera accurately determines its position, allowing a suite of highly sensitive, but narrow field instruments, to be slewed to the burst position within a matter of hours." + The rapid dissemination of avcaninute sized burst coordinates has resulted iu the successful detection of afterglows at other wavelengths., The rapid dissemination of arc-minute sized burst coordinates has resulted in the successful detection of afterglows at other wavelengths. + Although the data are still preliminary. we may use this new information to investieate the burst progenitor. mechamisia aud burst site.," Although the data are still preliminary, we may use this new information to investigate the burst progenitor, mechanism and burst site." + parrow feld instruments (NFI) ou the Italian- Thesatellite BeppoSAN (Boclla et al., The narrow field instruments (NFI) on the Italian-Dutch satellite BeppoSAX (Boella et al. + 19974) have 1?fields2. .view aud .include the imagine. CRBoccur dos and medium enerey concentrator spectrometers (LECS. 0.110 keV. Parmar ct al.," 1997a) have approximately $\degmark$ fields of view and include the imaging low- and medium energy concentrator spectrometers (LECS, 0.1–10 keV, Parmar et al." + 1997: and NEC'S. 10 keV. Boclla et al.," 1997; and MECS, 2--10 keV, Boella et al." + 19975)., 1997b). + The NFI are co-aligned id are normally operated simultancously., The NFI are co-aligned and are normally operated simultaneously. + Iu addition. 41ο pavload includes two wide field cameras (AVEC. | keV. Jager et al.," In addition, the payload includes two wide field cameras (WFC, 2--30 keV, Jager et al." + 1997) which observe im directious perpendicular to the ΧΕΙ aud a gauuua-ray burst monitor (GRBAL lO700 keV. Feroci et al.," 1997) which observe in directions perpendicular to the NFI and a gamma-ray burst monitor (GRBM, 40–700 keV, Feroci et al." + 1997)., 1997). + These last two mstrumneuts allow the detection of N-rav transieut phenomena aud οο... πο, These last two instruments allow the detection of X-ray transient phenomena and gamma-ray bursts. +" After a CRBAL ποσο,oo WEC data are analvzed post—facto for a sinmltaucous X-ray event aud. if oue is found. a Target of Opportunity (TOO) declared."," After a GRBM trigger, WFC data are analyzed ${post-facto}$ for a simultaneous X-ray event and, if one is found, a Target of Opportunity (TOO) declared." + The burst location is quickly derived to an accuracy of a ; ∙ ↕↸∖↖↖↽⋜∐⋅↸⊳⋯∐⋯↑↸∖↴∖↴⋜⋯≼↧↑∐↸∖⋀∖∏↴∖↴, The burst location is quickly derived to an accuracy of a few arcminutes and the NFIs slewed to this position. +↴∖↴↕↸∖↖↖⇁↸∖≼↧∪↑↕∐↴∖↴↻∪↴∖↴↕⊓∪∐∙∙ ., The whole process takes $\sim$ 8 hours. + ," For some bursts several TOOs were scheduled, typically a few $^4$ s long, occurring $\sim$ 0.3 days, days and several days after the initial trigger." +," For positive detections, the LECS and MECS uncertainty radii are typically $'$." +," To date, there have been 12 such detections – GRB970111 (Feroci et al." +," 1998a), GRB970228 (Costa et al." +, 1997; Frontera et al. +," 1998), GRB970402 (Nicastro et al." +∙∙," 1998a), GRB970508" +PMR= prety +rn).. R?= 77 + pre Fre.,"2MR^2= r_br_c(r_b +, R^2= r_b^2 + r_b r_c +." + The analvtical equasi-normal mode spectrum for the quasi-exireme 5-d5 black hole has been recently derived by Cardoso and. Lemos[0]. and reads where 7=0.1 and Vj=τί+1). for scalar ancl electromagnetic perturbations. and Vy=s;(6+2)(€—1) for gravitational perturbations.," The analytical quasi-normal mode spectrum for the quasi-extreme S-dS black hole has been recently derived by Cardoso and Lemos\cite{carlemos} and reads _n _b ) ], where $n=0,1,...\,$ , and $V_0=\kappa_b^2\ell(\ell+1)$, for scalar and electromagnetic perturbations, and $V_0=\kappa_b^2(\ell+2)(\ell-1)$ for gravitational perturbations." + Since we are considering the near extreme limit of the S-clS solution. Lor which (r.—ry)/ry<<1. ibis sultable for our purposes to write the black hole mass as AL= May t+yp= Tg," Since we are considering the near extreme limit of the S-dS solution, for which $(r_c - r_b)/r_b << 1$, it is suitable for our purposes to write the black hole mass as M = M_N + = +." +(13) Therefore. since 2=MA is [κος|l. the use of ()) and ()) leadsus to OAL Nu= 0pmorp V," Therefore, since $R=\sqrt{3/\Lambda}$ is fixed, the use of \ref{massa}) ) and \ref{raio}) ) leadsus to M = = ," +Equations (3)) and (5)) determine the heating history of the expanding plasma shell and eventually the radiation spectrum emitted by this shell.,Equations \ref{eq:nonth}) ) and \ref{eq:th}) ) determine the heating history of the expanding plasma shell and eventually the radiation spectrum emitted by this shell. + The shell itself 1s a part of the (variable) jet., The shell itself is a part of the (variable) jet. + It has the following parameters: For our calculations we use à new version of the numerical code developed by VPO9., It has the following parameters: For our calculations we use a new version of the numerical code developed by VP09. + The code is designed to model the coupled evolution of the heated outflow and the radiation it carries., The code is designed to model the coupled evolution of the heated outflow and the radiation it carries. + The evolution is tracked by solving the time-dependent kinetic equations for the particles and photons., The evolution is tracked by solving the time-dependent kinetic equations for the particles and photons. + The included interactions are Compton scattering. cyelo-synchrotron emission and absorption. photon-photon pair production and annihilation. and Coulomb collisions.," The included interactions are Compton scattering, cyclo-synchrotron emission and absorption, photon-photon pair production and annihilation, and Coulomb collisions." + We use the exact cross-sections or rates for all these processes., We use the exact cross-sections or rates for all these processes. +" The original version. of the code had one significant limitation: it used. the ""one-zone"" or ""leaking-box approximation.", The original version of the code had one significant limitation: it used the “one-zone” or “leaking-box” approximation. + This approximation pictures a uniform plasma cloud of an optical depth rp with isotropic. populations of particles and photons., This approximation pictures a uniform plasma cloud of an optical depth $\taut$ with isotropic populations of particles and photons. + It treats the loss of photons from the cloud using an escape probability instead of accurate calculations of radiation diffusion through the cloud (VPO9)., It treats the loss of photons from the cloud using an escape probability instead of accurate calculations of radiation diffusion through the cloud (VP09). + The leaking-box picture is not good for GRB jets., The leaking-box picture is not good for GRB jets. + In contrast to static sources. where radiation escapes the source on timescale ~στηο. GRB radiation remains embedded in the relativistic jet at all radit of interest.," In contrast to static sources, where radiation escapes the source on timescale $\sim\taut R/c$, GRB radiation remains embedded in the relativistic jet at all radii of interest." + It evolves with radius according to the radiative transfer equation. which is in serious conflict with the one-zone approximation.," It evolves with radius according to the radiative transfer equation, which is in serious conflict with the one-zone approximation." + For example. the true angular distribution of radiation m the jet comoving frame is far from being Isotropic. even in the subphotospheric region (BI1).," For example, the true angular distribution of radiation in the jet comoving frame is far from being isotropic, even in the subphotospheric region (B11)." + The isotropic approximation of the one-zone model becomes invalid when the optical depth 7r decreases below ~10., The isotropic approximation of the one-zone model becomes invalid when the optical depth $\taut$ decreases below $\sim 10$. + Furthermore. the large free path of photons near the photosphere leads to mixing of radiation emitted by different parts of the photospheric region with different Doppler shifts.," Furthermore, the large free path of photons near the photosphere leads to mixing of radiation emitted by different parts of the photospheric region with different Doppler shifts." + This mixing has a significant effect on the local photon spectrum and the spectrum received by a distant observer., This mixing has a significant effect on the local photon spectrum and the spectrum received by a distant observer. + For these reasons the simplified one-zone treatment has to be abandoned in favor of proper radiative transfer calculations., For these reasons the simplified one-zone treatment has to be abandoned in favor of proper radiative transfer calculations. + The kinetic equation for photons in. VPO9 is replaced by the transfer equation as described below., The kinetic equation for photons in VP09 is replaced by the transfer equation as described below. + The equation of radiative transfer m an. ultra-relativistic. matter-dominated outflow reads (BIT)," The equation of radiative transfer in an ultra-relativistic, matter-dominated outflow reads (B11)" +Due (ο its resemblance with the classical NavierStokes equations and Euler equations. we cliscretize bv (he pressurecorrection method. which is a modified form of the classical projection method (?]..[2]..[?]..,"Due to its resemblance with the classical Navier–Stokes equations and Euler equations, we discretize by the pressure–correction method, which is a modified form of the classical projection method \cite{MaTe98}, \cite{vK86}, \cite{GMS06}." + This modified form of the projection method is known to provide a better approximation of (he pressure in (he case of the NavierStokes equations and we choose to use it here. instead of the initial form of theprojection method [?].. |?]..," This modified form of the projection method is known to provide a better approximation of the pressure in the case of the Navier–Stokes equations and we choose to use it here, instead of the initial form of theprojection method \cite{Cho}, \cite{Tem69}." + The boundary conditions are different [rom those for either the NavierStokes equations or the usual Euler equations: (he pressurecorrection method has to be adapted to the svstem(2., The boundary conditions are different from those for either the Navier–Stokes equations or the usual Euler equations; the pressure–correction method has to be adapted to the system. +9).. We let A)=T/ N.vzivtr.y. FEM). and v3 represents an intermediate value between vÁ and v!. ete.," We let $\Delta t = T/K$, $\vb^k \approx \vb(x,\,y,\,k\Delta t)$ , and $\vb^{k+\frac{1}{2}}$ represents an intermediate value between $\vb^k$ and $\vb^{k+1}$, etc." + At each step. the svstem is advanced in two substeps: IIere and where nis the outer normal vector on OM’.," At each step, the system is advanced in two substeps: Here and where $\mathbf{n}$is the outer normal vector on $\partial \M'$ ." +observed in the observer's frame of reference. satisfies where Ag; is the formation mass fraction of the source progenitors.,"observed in the observer's frame of reference, satisfies where $\lambda_{GRB}$ is the formation mass fraction of the source progenitors." + Here. the division bv 1-4z accounts for time-dilatation bv cosmic expansion.," Here, the division by $1+z$ accounts for time-dilatation by cosmic expansion." + The element of comoving volume ls The GRB redshilt probability density can be written as (Cowardetal.2002) p(z)=dRepyfdsChdenidziz). Assuming that the mass fraction of GRBs progenitors is redshift independent. the scaling factor Agape is the only [ree parameter of our moclel.," The element of comoving volume is The GRB redshift probability density can be written as \citep{cow02} + $p (z) = {dR_{GRB}/dz}\left({\int_{0}^{5}dR_{GRB}/dz\,dz}\right)^{-1}.$ Assuming that the mass fraction of GRBs progenitors is redshift independent, the scaling factor $\lambda _{GRB}$ is the only free parameter of our model." +" For the flux-limited. experiments listed in Table I. we define a probability-densitv. function of detection as a function of redshift as pqz44€0)=dgufds(J;IRgetfaeiz)ο Ποιο the dependence on the Iuminosity has been integrated out in (he detected event rate Ilere. pCL) refers to the intrinsic GRBs luminosity function in the BATSE energy range 50—300 keV. The luminosity threshold as a function of redshift is given by Lj,,(2)=Επ(2)Shiny. where d, is the luminosity distance (ο a source at redshift z and where ο, denotes the sensitivitv threshold of the instrument."," For the flux-limited experiments listed in Table I we define a probability-density function of detection as a function of redshift as $p_{detect} (z) ={dR_{detect}/dz}\left({\int_{0}^{5}dR_{detect}/dz\,dz}\right)^{-1},$ where the dependence on the luminosity has been integrated out in the detected event rate \citep{bro02} + Here, $p(L)$ refers to the intrinsic GRBs luminosity function in the BATSE energy range $50 - 300$ keV. The luminosity threshold as a function of redshift is given by $L_{lim} (z) = 4\pi d_{L}^{2}(z) S_{lim}$, where $d_{L}$ is the luminosity distance to a source at redshift $z$ and where $S_{lim}$ denotes the sensitivity threshold of the instrument." + Following (Bromim&Loeb2002).. we take a threshold of BASTE of 0.2 photonem7s+.," Following \citep{bro02}, we take a flux-density threshold of BASTE of 0.2 $\mathrm{photon}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}$." + As of the time of this writing. we have 33 GRBs1 with individually measured redshilis (Table D).," As of the time of this writing, we have 33 GRBs with individually measured redshifts (Table I)." + They collectively represent a variety of past ancl current experiments., They collectively represent a variety of past and current experiments. + Due to a flux threshold in each of the instruments used. the observed GRB redshift distribution is strongly biased towards low redshifts.," Due to a flux threshold in each of the instruments used, the observed GRB redshift distribution is strongly biased towards low redshifts." + This introduces a quantitative selection effect. relative to the redshift distribution predicted by the SER. model (Fig.," This introduces a quantitative selection effect, relative to the redshift distribution predicted by the SFR model (Fig." + 1) the true distribution of representing what would be observed in the ideal case of a zero-Ilux threshokl in (he instruments., 1) – the true distribution of GRB-redshifts representing what would be observed in the ideal case of a zero-flux threshold in the instruments. + In view of (he various instruments involved. (he dependency of the observed GRB redhilt-cistribution function on the flux-Iimit is simulated in Fig.," In view of the various instruments involved, the dependency of the observed GRB redhift-distribution function on the flux-limit is simulated in Fig." + 2., 2. +superposition of groups with line-ol-sight velocity dispersions <400 km +.,superposition of groups with line-of-sight velocity dispersions $\lesssim 400$ km $^{-1}$. + According to our sensilivily plot (Figure 9)). (he svstenis in these probes should not produce a significant weak lensing signal anc we observe that they do not. in fact. produce one.," According to our sensitivity plot (Figure \ref{fig:sensitivity.ps}) ), the systems in these probes should not produce a significant weak lensing signal and we observe that they do not, in fact, produce one." + In summary. (he 6 weak lensing candidate halos with v>3.7 viekd a sample of 2 rich clusters associated with peaks 0 and 1.," In summary, the 6 weak lensing candidate halos with $\nu > 3.7$ yield a sample of 2 rich clusters associated with peaks 0 and 1." + A single svstem along the line-ol-sieht toward peak 10 may account for the lensing signal. but our error in the determination of the velocity dispersion is verv large.," A single system along the line-of-sight toward peak 10 may account for the lensing signal, but our error in the determination of the velocity dispersion is very large." + Weak lensing peak 3. and possibly 10. might result from boosting of the lensing signal by superpositions of svstems along the lime-of-sight.," Weak lensing peak 3, and possibly 10, might result from boosting of the lensing signal by superpositions of systems along the line-of-sight." + Thus the efficiency of the weak lensing map for the detection of individual massive svstemis is at best [or VIS., Thus the efficiency of the weak lensing map for the detection of individual massive systems is at best for $\nu > 3.7$. + Table 3. shows that two of the three peaks with v>4 are massive svstenis suggesting that. as expected. the efficiency may be greater at higher thresholds.," Table \ref{tbl:VDisp} shows that two of the three peaks with $\nu >4 $ are massive systems suggesting that, as expected, the efficiency may be greater at higher thresholds." + Geller et al. (, Geller et al. ( +2010) use the larger DLS field to show that the efficiency of weak lensing increases with v over the range τν<7.,2010) use the larger DLS field to show that the efficiency of weak lensing increases with $\nu$ over the range $1 < \nu < 7$. + Neither the foregrouncl redshift survey nor the galaxy counts [rom the Subaru images reveal any candidate svstems along the line-ol-sight toward weak lensing peaks 7 ancl 9., Neither the foreground redshift survey nor the galaxy counts from the Subaru images reveal any candidate systems along the line-of-sight toward weak lensing peaks 7 and 9. + The probes through the redshift survey toward these positions are similar (o (or even less than) probes toward regions where there should be no significant weak lensing signal aud none is observed., The probes through the redshift survey toward these positions are similar to (or even less well-populated than) probes toward regions where there should be no significant weak lensing signal and none is observed. + The redshift survey. provides a route to identifving candidate galaxy svstems undetected bv the weak lensing map., The redshift survey provides a route to identifying candidate galaxy systems undetected by the weak lensing map. + It thus provides some assessment of the completeness of the cluster candidate list derived from (he weak lensing map., It thus provides some assessment of the completeness of the cluster candidate list derived from the weak lensing map. + There are many approaches to identifvinsg candidate svstems in (he redshift survey., There are many approaches to identifying candidate systems in the redshift survey. + For consistency we use redshift survey. probes to identifv svstems in the same wav that we use them (ο test [or svstems along the line-of-sight toward weak lensing peaks., For consistency we use redshift survey probes to identify systems in the same way that we use them to test for systems along the line-of-sight toward weak lensing peaks. + Figure LO shows the positions of all of the Όσοι probes trough the redshift survey: (hese probes contain a well-populated redshift bin (see Section 4.1))., Figure \ref{fig:sigmamap.scaled.ps} shows the positions of all of the $\sigma_{SH}$ probes through the redshift survey; these probes contain a well-populated redshift bin (see Section \ref{sampling}) ). + Of course the bins are large enough that thev may contain a superposition of poor groups rather than a richer svstem., Of course the bins are large enough that they may contain a superposition of poor groups rather than a richer system. + We compute line-ol-sieht velocity dispersions for the peaks within each probe., We compute line-of-sight velocity dispersions for the peaks within each probe. + In addition to the clusters corresponding to weak lensing peaks 0 and 1. we find only one additional concentration in redshift space that corresponds to a massive svstem.," In addition to the clusters corresponding to weak lensing peaks 0 and 1, we find only one additional concentration in redshift space that corresponds to a massive system." +For the known extrasolar giant. planets (eCPs). the tides raised on the primary can be substantial anc can lead to significant orbital reduction during the main-sequence (?277)..,"For the known extrasolar giant planets (EGPs), the tides raised on the primary can be substantial and can lead to significant orbital reduction during the main-sequence \citep{Ibgui:2009jk, + Levrard:2009qy, Ibgui:2009fk,Spiegel:aa}." + For the same Q7. we can estimate whether a similar reduction is expected during the post-MS.," For the same $Q'_\star$, we can estimate whether a similar reduction is expected during the post-MS." +" From the previous section. we have that the tides on the primary dominate and. hence. where zn. ds the typical lifetime curing the main sequence and 7,4, is the lifetime during the ROB phase."," From the previous section, we have that the tides on the primary dominate and, hence, where $\tau_{\rm ms}$ is the typical lifetime during the main sequence and $\tau_{\rm rgb}$ is the lifetime during the RGB phase." + For the main sequence. we take a 1 Jupiter mass companion around a 1 AJ. main-sequence primary with semimajor axis ~0.05 AU.," For the main sequence, we take a 1 Jupiter mass companion around a 1 $M_\odot$ main-sequence primary with semimajor axis $\sim$ 0.05 AU." +" For the RGB phase. we assume hat the companion is orbiting at 1.8 AU. that ᾧ/*LS=Q5ss and that Ze~107/2,,. and Tn~LO2στις."," For the RGB phase, we assume that the companion is orbiting at 1.3 AU, that $Q'_{\rm \star,ms} = Q'_{\rm \star,rgb}$ and that $R_{\rm + rgb}\sim 10^2 R_{\rm ms}$ and $\tau_{\rm rgb}\sim 10^{-2} \tau_{\rm + ms}$." + Using hese parameters vields dne/Alnau.~0.063.," Using these parameters yields $\Delta {\rm ln} a_{\rm rgb} / +\Delta {\rm ln} a_{\rm ms} \sim0.063$." + Pherefore. or this system. we expect tides to be weaker on the RGB yhase than they are for EGP systems.," Therefore, for this system, we expect tides to be weaker on the RGB phase than they are for EGP systems." + This is likely to of true for low-mass primaries 1.53.) where radial expansion during the ROB is substantial (see Fig. 3)).," This is likely to be true for low-mass primaries $\lesssim +1.5 M_\odot$ ) where radial expansion during the RGB is substantial (see Fig. \ref{models}) )." + For ligher mass primaries. radial expansion is minimal during he RGB and extensive during the AGB.," For higher mass primaries, radial expansion is minimal during the RGB and extensive during the AGB." + However. tvpical AGB lifetimes are ~10710nue ," However, typical AGB lifetimes are $\sim$$10^{-2} - 10^{-3} \tau_{\rm rgb}$." +We can estimatethe οσο of tides during the AGB phase in the same wav., We can estimatethe effect of tides during the AGB phase in the same way. + Assuming Raw~200 R.. Qi.=Qiun ancl Tuan~10 n. we have that MacauΑμ710.7.," Assuming $R_{\rm agb} \sim200$ $R_\odot$, $Q'_{\rm \star,ms} = Q'_{\rm + \star,agb}$ and $\tau_{\rm agb} \sim10^{-5} \tau_{\rm ms}$ , we have that $\Delta{\rm ln} a_{\rm agb} / \Delta {\rm ln} a_{\rm ms} +\sim2.0\times10^{-3}$." + Phus in general. we expect synchronization tides on the AGB to be weaker both than those on the RGB and for typical EGPs around main sequence stars.," Thus in general, we expect synchronization tides on the AGB to be weaker both than those on the RGB and for typical EGPs around main sequence stars." + Note the steep dependence on the ratio of the stellar radii in Eq. 9., Note the steep dependence on the ratio of the stellar radii in Eq. \ref{eq:tidestrength}. +" 16 Re—24s and n,οο then Mna,4,fAlma,~1 ancl tides are approximately equal during the RGB and ACB phases."," If $R_{\rm agb}=2R_{\rm rgb}$ and $\tau_{\rm agb}=(1/30)\tau_{\rm rgb}$, then $\Delta{\rm ln} a_{\rm agb} / \Delta {\rm ln} a_{\rm rgb}\sim1$ and tides are approximately equal during the RGB and AGB phases." + Ilowever. as will be seen shortly. there is reason to expect that QL may be orders of magnitude smaller on the giant branches than on the main sequence for the same edy. with a corresponding increase inthe importance of the advanced evolutionary. phases for the orbit.," However, as will be seen shortly, there is reason to expect that $Q'_*$ may be orders of magnitude smaller on the giant branches than on the main sequence for the same $a/R_*$, with a corresponding increase inthe importance of the advanced evolutionary phases for the orbit." + lt dis worth nothing that the work of 7? and ? docs not specify a tidal dissipation mechanism., It is worth nothing that the work of \citet{Goldreich:1963nr} and \citet{Goldreich:1966qv} does not specify a tidal dissipation mechanism. + ? however. proposed a tidal theory based on turbulent viscosity.," \citet{Zahn:1966jk} however, proposed a tidal theory based on turbulent viscosity." + This theory was tested and calibrated in stellar binaries that. contain an evolved star primary (2)..., This theory was tested and calibrated in stellar binaries that contain an evolved star primary \citep{Verbunt:1995rt}. + I5volved stars are expected to possess extended convective zones. which could be erucial for tidal dissipation.," Evolved stars are expected to possess extended convective zones, which could be crucial for tidal dissipation." + In their formalism. the authors introduce a dimensionless factor f that is calibrated. via the orbital eccentricity measurements in their post-MS binary. sample.," In their formalism, the authors introduce a dimensionless factor $f$ that is calibrated via the orbital eccentricity measurements in their post-MS binary sample." + The authors argue that observational data imply that f£. isconstant and approximately unity., The authors argue that observational data imply that $f$ isconstant and approximately unity. + By setting equal the expression for the tidal torque (as a function of Q)) in ? to the expression (as a function of f) in ?.. as simplified by 2.. we have that where Aj is the mass of the convective envelope. P? is the orbital period. Tony is the convective timescale aid Tivy is the dynamical timescale.," By setting equal the expression for the tidal torque (as a function of $Q'_\star$ ) in \citet{Goldreich:1966qv} to the expression (as a function of $f$ ) in \citet{Zahn:1989lr}, as simplified by \citet{Verbunt:1995rt}, we have that where $M_{\rm env}$ is the mass of the convective envelope, $P$ is the orbital period, $\tau_{\rm conv}$ is the convective timescale and $\tau_{\rm dyn}$ is the dynamical timescale." + Lf is in fact constant. then (Q is proportional to orbital period.," If $f$ is in fact constant, then $Q'_\star$ is proportional to orbital period." + Note that the numerical prefactor in Eq. (, Note that the numerical prefactor in Eq. ( +10) (63/167) is slightly dillerent from the 225/323 that results from setting our expresion for dincdi (in Eq.,10) $63/16\pi$ ) is slightly different from the $225/32\pi$ that results from setting our expresion for $d\ln e/dt$ (in Eq. + 2) equal to the corresponding expresion in ?.., 2) equal to the corresponding expresion in \citet{Verbunt:1995rt}. + Phe difference (compared to the variation in period) is sullicicnthy small that it does not ellect our results., The difference (compared to the variation in period) is sufficiently small that it does not effect our results. + The argument for f constant anc ~1 derives. from Fie., The argument for $f$ constant and $\sim$ 1 derives from Fig. +e 4c of ?.., 4c of \cite{Verbunt:1995rt}. + The transition between circularized and. non- systenis. occurs when the abscissa is 0., The transition between circularized and non-circularized systems occurs when the abscissa is 0. + The abscissa is given by login{Mnc]/f]=logio(Ineife]logio(£3.," The abscissa is given by ${\rm log_{10} \left\{-\Delta {\rm ln \left[e\right]} / f + \right\}} = {\rm log_{10}} \left\{ {\rm ln \left[e_i / e_f \right] +}\right\} - {\rm log_{10} \left\{f\right\} }$ ." + Uf login{lncifer]} is greater than (less than) 0. the svstem is stronely (barely) circularized.," If ${\rm log_{10}} +\left\{ {\rm ln \left[e_i / e_f \right] }\right\}$ is greater than (less than) 0, the system is strongly (barely) circularized." + The transition occurs near logis{laei/e;]]=0.," The transition occurs near ${\rm log_{10}} \left\{ {\rm ln \left[e_i / e_f + \right] }\right\} = 0$." + Looking at Pig., Looking at Fig. + 4c of ?.. we see this transition happens at logio{Inοο) 0. therefore. f£.—1.," 4c of \cite{Verbunt:1995rt}, we see this transition happens at ${\rm + log_{10}} \left\{ {\rm ln \left[e_i / e_f \right] }\right\} - {\rm + log_{10} \left\{f\right\} } \sim0$ , therefore, $f\sim1$." + While this argument does. constrain f for. systems ab the sharp transition between circularization ancl non-circularization. it does not rule out a dependence of f£ on period.," While this argument does constrain $f$ for systems at the sharp transition between circularization and non-circularization, it does not rule out a dependence of $f$ on period." + In fact. the transition between circularized. and non-circularized. svstems remains at log[λος~0 if f scales as Pt7 with 1moe0 and has an appropriate normalization (see Fig. 2)).," In fact, the transition between circularized and non-circularized systems remains at $\log\left\{\Delta\ln[e]\right\} \sim 0$ if $f$ scales as $P^{1-x}$ with $1\gtrsim x\gtrsim 0$ and has an appropriate normalization (see Fig. \ref{VP_binaries}) )." + Εις corresponds to QTxP., This corresponds to $Q'_\star \propto P^x$. + lt is worth mentioning that the scaling used in Fig., It is worth mentioning that the scaling used in Fig. + 2. is one example among many that preserve the location of the transition.," \ref{VP_binaries} + is one example among many that preserve the location of the transition." + Dillerent normalizations preserve the transition for cillerent ranges ofr., Different normalizations preserve the transition for different ranges of $x$. + For example. f=(P200days)!‘ preserves the transition for 2zr0.," For example, $f =\left(P / 200\, {\rm days} \right)^{1-x}$, preserves the transition for $2\gtrsim x \gtrsim 0$." + The value (c=2 (for whieh (QxP +) has been urged by ο in the [imi DosORToae however. PTomToa [or most of the cases of interest to us.," The value $x=2$ (for which $Q'_\star\propto P^{-1}$ ) has been urged by \cite{Goldreich:1977qy} in the limit $P\ll \pi\tau_{\rm conv}$; however, $P\gtrsim\pi\tau_{\rm conv}$ for most of the cases of interest to us." + Thus. by using Eq. C10)).," Thus, by using Eq. \ref{Zahn}) )," + we are able to employ. the tidal prescription of 7. with the observational calibration of ?.., we are able to employ the tidal prescription of \citet{Zahn:1966jk} with the observational calibration of \cite{Verbunt:1995rt}. + In Section 4. we show that emploving such a formalism leads to values of Q7 between ~LO ancl LO? for post-main sequence giants.," In Section 4, we show that employing such a formalism leads to values of $Q'_\star$ between $\sim$$10^2$ and $10^3$ for post-main sequence giants." + These values are two to seven orders of magnitude lower than those twpically invoked in the contex of extra-solar giant planets (22727???) and lead to strong tidal interactions.," These values are two to seven orders of magnitude lower than those typically invoked in the context of extra-solar giant planets \citep{Goldreich:1966qv, Yoder:1981zv, + Ogilvie:2004sy, Ogilvie:2007kb, Jackson:2009bq, Ibgui:2009jk, + Ibgui:2010lr, Miller:2009lr} and lead to strong tidal interactions." + We pause to note that tidal theory is an active field of research. (227). Particularly relevant is a recent study that investigated a frequency dependence of Q’ (?)..," We pause to note that tidal theory is an active field of research \citep{Goodman:2009kx, Gu:2009yq, Arras:2009rt} Particularly relevant is a recent study that investigated a frequency dependence of $Q'$ \citep{Greenberg:2009lr}. ." + This work demonstrated that commonly used analytic approaches (which make analogy to a driven harmonic oscillator) are probably valid only for low eccentricities and inclinations., This work demonstrated that commonly used analytic approaches (which make analogy to a driven harmonic oscillator) are probably valid only for low eccentricities and inclinations. + Pheoretical and observational constraints on the tidal dissipation mechanism will help constrain the results of this work in the future., Theoretical and observational constraints on the tidal dissipation mechanism will help constrain the results of this work in the future. + For now. in light of the uncertainties in Qi. and in. f. we adopt the following form where LE=P0Pipa)al is the orbital period divided by the dynamical time. Ευ is a reference value.," For now, in light of the uncertainties in $Q'_\star$ , and in $f$ , we adopt the following form where $\Pi\equiv P/\tau_{\rm dyn} = P\left(\rho G\right)^{1/2}$ is the orbital period divided by the dynamical time, $\Pi_0$ is a reference value," +obtained at the Gemini Observatory. which is operated by the Association οἱ Universities for Research in Astronomy. Ine.. under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States). the Particle Physics ancl Astronomy Research Council (United Kingdom). the National Research Council (Canada). CONICYT (Chile). the Australian Research Council (Australia). CNPq (Brazil) and CONICET (Argentina).,"obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Particle Physics and Astronomy Research Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), CNPq (Brazil) and CONICET (Argentina)." + The NIRSPEC data presented herein were obtained at the Keck Observatory. in part via the TSIP program adiministerecl by NOAO and in part [rom telescope time allocated to NASA through the agenev's scientific partnership with the California Iistitute of Technilogy and the University of California.," The NIRSPEC data presented herein were obtained at the Keck Observatory, in part via the TSIP program administered by NOAO and in part from telescope time allocated to NASA through the agency's scientific partnership with the California Institute of Technilogy and the University of California." + The Observatory was made possible by the generous financial support of the Wiyeck Foundation., The Observatory was made possible by the generous financial support of the Keck Foundation. + The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Manna hea has always had within the indigenous Iawaiian community., The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. + We are most lortunate to have (he opportunity to conduct observations [rom this mountain.(TENES)..(NIRSPEC)..," We are most fortunate to have the opportunity to conduct observations from this mountain.,." +DLA systems and 30kms+ for LL svstems).,DLA systems and $30 \kms$ for LL systems). + μον found the cross section as a function of halo virial velocity could be fit by a power law with a slope of z1.6.," They found the cross section as a function of halo virial velocity could be fit by a power law with a slope of $\approx +1.6$ ." + However. 7. have pointed out that combining this distribution of cross-sections with the velocity. width to virial velocity relationship found by ? and in paper L is not compatible with the kinematic data.," However, \citet{pw:01} have pointed out that combining this distribution of cross-sections with the velocity width to virial velocity relationship found by \citet{hsr:98} and in paper I is not compatible with the kinematic data." + A slope of 2.5 is needed to produce he correct. distribution of velocity widths (2) which is consistent with what we found for our model in paper L. The different value found by 7. is probably due to the fact that here is effectively no feedback in their simulations leacing to much higher barvon fractions in small mass halos.," A slope of $2.5$ is needed to produce the correct distribution of velocity widths \citep{hsr:99} + which is consistent with what we found for our model in paper I. The different value found by \citeauthor{gard:01} is probably due to the fact that there is effectively no feedback in their simulations leading to much higher baryon fractions in small mass halos." + In moclels with ellicient. feedback. we would expect. the contribution rom these low mass halos to be substantially decreased., In models with efficient feedback we would expect the contribution from these low mass halos to be substantially decreased. + ? [found that none of their modelsmodel were consistent with the high-ionization state gas kinematics., \citet{wp:00b} found that none of their models were consistent with the high-ionization state gas kinematics. + They suggested. that the multiple component model might be more successful. which we now explore.," They suggested that the multiple component model might be more successful, which we now explore." + Another long-standing question pertaining to QSO absorption systems is their connection with the galaxy population identified in emission., Another long-standing question pertaining to QSO absorption systems is their connection with the galaxy population identified in emission. + At 2S1. there is compelling observational evidence that metal line and. LL absorbers are associated with galaxies (27)...," At $z\la 1$, there is compelling observational evidence that metal line and LL absorbers are associated with galaxies \citep{steid:97,clw:01}." + A theoretical model has been proposed by 2 wherein these systenis. are produced by gas clouds in the halos of galaxies., A theoretical model has been proposed by \citet{mm:96} wherein these systems are produced by gas clouds in the halos of galaxies. + At higher redshifts. it has been proposed that many of the absorbers may reside in mini-halos (?)..," At higher redshifts, it has been proposed that many of the absorbers may reside in mini-halos \citep{am:98}." + We also investigate the origin of lower column density svstems in the context of our model., We also investigate the origin of lower column density systems in the context of our model. + For our analysis we use the semi-analvtic mocdoel described in ? and ?.., For our analysis we use the semi-analytic model described in \citet{sp:99} and \citet{spf:01}. + The backbone of the model is a Monte Carlo realization of a “merger tree”. which represents the build-up of halos over time through merging and mass accretion 7..," The backbone of the model is a Monte Carlo realization of a “merger tree”, which represents the build-up of halos over time through merging and mass accretion \citet{sk:99}." + Initially. the hot gas is assumed to be distributed like the dark matter (here. a singular isothermal sphere). to be uniformly at the virial temperature of the halo. ancl not to have any substructure.," Initially, the hot gas is assumed to be distributed like the dark matter (here, a singular isothermal sphere), to be uniformly at the virial temperature of the halo, and not to have any substructure." + The cooling radius (the radius within which eas is dense enough to have cooled) is then calculated using the radiative cooling function for atomic eas in collisional equilibrium., The cooling radius (the radius within which gas is dense enough to have cooled) is then calculated using the radiative cooling function for atomic gas in collisional equilibrium. + When a halo contains more than one galaxy. gas is assumed to cool only onto the central object.," When a halo contains more than one galaxy, gas is assumed to cool only onto the central object." + Recent studies (77). suggest that this simple moclel is in good agreement with cosmological hverocdynamical simulations. at least in the absence of feedback.," Recent studies \citep{yssw:02,hell:02} suggest that this simple model is in good agreement with cosmological hydrodynamical simulations, at least in the absence of feedback." + All gas in these simplified models is labelled as either. “hot” (at the halo virial temperature) or 7cold (P103 hk)., All gas in these simplified models is labelled as either “hot” (at the halo virial temperature) or “cold” $T \la 10^4$ K). + When halos merge. the central Z-galaxy of the largest progenitor halo becomes the new central galaxy. and all other galaxies become satellites.," When halos merge, the central galaxy of the largest progenitor halo becomes the new central galaxy, and all other galaxies become satellites." + Satellites lose angular momentum cue to dynamical friction. and gradually fall towards the center of the halo. where they may eventually merge with the central object.," Satellites lose angular momentum due to dynamical friction and gradually fall towards the center of the halo, where they may eventually merge with the central object." + Cold gas is converted to stars using a simple empirical recipe. at a rate proportional to the total mass of cold gas in the galaxy.," Cold gas is converted to stars using a simple empirical recipe, at a rate proportional to the total mass of cold gas in the galaxy." + Several dillerent recipes were investigated in ? ancl 2.. but here we adopt the “collisional starburst” recipe. which was shown to produce the best agreement. with the observed. galaxy. population at z3. and with the total mass of neutral hydrogen implied by observations of DLAS (?2)..," Several different recipes were investigated in \citet{sp:99} and \citet{spf:01}, but here we adopt the “collisional starburst” recipe, which was shown to produce the best agreement with the observed galaxy population at $z\sim3$, and with the total mass of neutral hydrogen implied by observations of DLAS \citep{spf:01,pws:01}." + In this mocel. cold gas in isolated clisks is assumed to form stars with a low elliciencey. (similar to that in nearby observed. spiral galaxies). while a more cllicient starburst mode is triggered by galaxy mergers.," In this model, cold gas in isolated disks is assumed to form stars with a low efficiency (similar to that in nearby observed spiral galaxies), while a more efficient starburst mode is triggered by galaxy mergers." + Gas that has settled into a disk may be heated and removed by supernova (SN) feedback., Gas that has settled into a disk may be heated and removed by supernova (SN) feedback. + The ellicienev of the SN. feedback. is assumed to be inversely. proportional to the potential well depth of the galaxy., The efficiency of the SN feedback is assumed to be inversely proportional to the potential well depth of the galaxy. + Each generation of star formation produces a certain vield of heavy elements. which are mixed with the cold. gas or ejected by SN into the hot gas halo.," Each generation of star formation produces a certain yield of heavy elements, which are mixed with the cold gas or ejected by SN into the hot gas halo." + After reionization. cooling only takes place in dark matter halos with virial velocities v»;zz40kms11 pbecause of suppression of gas collapse ancl cooling bv. the UV background.," After reionization, cooling only takes place in dark matter halos with virial velocities $\vvir \ga 40 \kms$ because of suppression of gas collapse and cooling by the UV background." +" All of our analysis has been done assuming the currentLy favored ACDAL cosmology (e.g.72). with Oy=0,7.ο0.3.0,=0.038. 0.7. and e=1.0 ancl at a redshift of three."," All of our analysis has been done assuming the currently favored $\Lambda$ CDM cosmology \citep[e.g.][]{prim:02} with $\Omega_{\Lambda}=0.7, \Omega_{M}=0.3, \Omega_b=0.038, h=0.7$ , and $\sigma_8=1.0$ and at a redshift of three." +" Phe values of the free parameters that control the clliciency of star formation and SN feedback. the chemical vield. οσοι,"," The values of the free parameters that control the efficiency of star formation and SN feedback, the chemical yield, etc.," + are as adopted in? based on low redshift galaxy observations.," are as adopted in \citet{spf:01} + based on low redshift galaxy observations." + 3clow we describe in some detail how we incorporate a model for both the low- and high-ionization state gas in absorption svstenis into this picture., Below we describe in some detail how we incorporate a model for both the low- and high-ionization state gas in absorption systems into this picture. + X schematic illustration of the model is shown in Figure 1., A schematic illustration of the model is shown in Figure 1. +" We assume that the low-ionization state absorption is associated with the ""cold"" gas component of the galaxy ormation model.", We assume that the low-ionization state absorption is associated with the “cold” gas component of the galaxy formation model. + La paper L we explored a number of models or the distribution of cold gas in each galaxy and fou hat only bv having very extensive gas disks was it possible o produce enough. overlapping cross-section for a line of sight to a distant. quasar to pass through multiple. clisks and thus producelow-ion kinematics in agreement with he observations.," In paper I, we explored a number of models for the distribution of cold gas in each galaxy and found that only by having very extensive gas disks was it possible to produce enough overlapping cross-section for a line of sight to a distant quasar to pass through multiple disks and thus producelow-ion kinematics in agreement with the observations." +" We found that a model where the col eas was distributed such that its surface density decreases oportionallv to 4?3 until a traneation radius. £2, of column density: Vy;=4LOMTem2 7. produced. absorption. svstenis Consistent with the low ion kinematics observed by 2? as well as with the observed fV). am metallicities of DLA svstems (see paper | for more details)."," We found that a model where the cold gas was distributed such that its surface density decreases proportionally to $R^{-1}$ until a truncation radius $R_t$ of column density $N_t = 4 \times 10^{19} +\cm2$ , produced absorption systems consistent with the low ion kinematics observed by \citet{pw:97,pw:98} as well as with the observed $f(N)$ and metallicities of DLA systems (see paper I for more details)." + We take the vertical (2) distribution of the cold gas to be exponential with a scale length z; such that the disks are thin., We take the vertical $z$ ) distribution of the cold gas to be exponential with a scale length $z_s$ such that the disks are thin. + Thus the gas distribution for each galaxy is given by pideipm (pe pq).," Thus the gas distribution for each galaxy is given by (R,z)= (R < R_t)." +1) We distribute RR4Lethe cold gas in 10 clouds to properly sample the velocity field., We distribute the cold gas in 10 clouds to properly sample the velocity field. + Each cloud. is given a small. 1D random velocity. of σι=IOkms ," Each cloud is given a small, 1D random velocity of $\sigma_{low}=10 \kms$ ." +We refer tothe cold. gasas being in “disks”. and we implicitly. assume that the cold. phase is concentrated ancl rotationally supported. when implementing the star," We refer tothe cold gasas being in “disks”, and we implicitly assume that the cold phase is concentrated and rotationally supported when implementing the star" +dolls) Therefore wecan us, into the Liouville correlator. +e(p(his31)canonically conjugated pair (οexpress(he derivative with respectto theweights interms ofthe values κος)>) in agreement withthe formalarguments. us make vacuum eravimaeneltization.," It was found in \cite{zam} that logarithmic primaries in the semiclassical limit obey the following relations =A_m V(1,-m) where $A_m$ are numerical constants and D_m = ^m + d_m where $d_m$ involves the energy stress-tensor in the Liouville theory and its derivatives." + Remindconcerning thatthe surface operators correspond operators totheD2 branes fillin," The operators $\tilde{V}_{12}$ and $V_{1,-2}$ form the logarithmic pair of the operators with the same conformal dimension." +gthe (wo-dimensional sub-manifold of2! which can beconsidered from (he four-dimensional a," The natural question concerns the interpretation of the object created by the operator $\tilde{V}_{1,2}$ that is dressing of the surface operator." +sthe worldsheet of(hemagnetic string.When, Some analogy comes from the minimal string theory. + both parameters are switeliedviewpointon to some extend one can interpret this, In that case there are two types of the branes in the Liouville theory - ZZ and FZZT branes \cite{zz}. + background as €125the condensate of the magnetic strings., ZZ branes correspond to the D-instantons localized in the Liouville zero mode direction and get condensed. + Onthe gauge theory sidethe insertion ofthe surface oriented, On the other hand the FZZT branes are extended in the Liouville coordinate and correspond to the surface operators. + insome in 2!is described in the semiclassical weak fielcl limitoperatoras plane συ Zac ZEE, It was observed \cite{shih} that the instanton ZZ brane can be interpreted as the superposition of FZZT brane and anti-brane system. + J / exp The derivativeof (2)(5.34)(he partition function with the insertion, = - We can speculate that the realization of ZZ brane in terms of the pair of FZZT branes is analogous to the blowing up of the instanton. +of (hesurface operator vields in the semiclassical limit, An interesting interpretation also emerges from the Hamiltonian viewpoint. +the additional contribution A! 0«J ox Ma. coordinatez)(5.35) corresponds, The surface operators provide the degrees of freedom for the particular Hamiltonian system. + coordinate Equivalently where z towy of the D2 brane. theW hasthe interpretationthe of the twiste, One of the equivariant parameters in the $D=4$ SYM theory can be identified with the Planck constant in this Hamiltonian system \cite{ns}. +dthe superpotentialintegrableinthe worklvolume[25].. theory onD2 braneor Yang-Yang, The same interpretation can be derived in the worldvolume theory on the surface operator \cite{geras}. + functionin systems Letus turn to Vi»the Liouville side where the surfaceThe, Hence we have to differentiate the surface operator wave function with respect to the Planck constant. + operatorcontributionof correspondsthesurfaceto insertionof the primaryoperator, From the quantum mechanical viewpoint the corresponding angular momentum in $R^4$ plays the role of a kind of the R-symmetry generator. + 92. 23].. operator fieldinto eravinagnetizalion corresponds (othe insertion of the logarithmic primary, Probably such picture is related to the Parisi-Sourlas type approach to the classical dynamics where the effective R-symmetry can be naturally defined in terms of auxiliary ${\cal N}=2$ SUSY. +adio halos in galaxy. clusters are diffuse radio sources possessing large sizes and steep spectra.,Radio halos in galaxy clusters are diffuse radio sources possessing large sizes and steep spectra. + The radio emission must be produced by (he svnchrotron radiation of relativistic electrons., The radio emission must be produced by the synchrotron radiation of relativistic electrons. + Nonetheless. the sources of these relativistic electrons are still unclear.," Nonetheless, the sources of these relativistic electrons are still unclear." + In. the intracluster medium (ICM). relativistic electrons lose energy on the time scale of order~105 vears because of inverse Compton and svnehrotron losses (e.g.Ip&Axford 1999)..," In the intracluster medium (ICM), relativistic electrons lose energy on the time scale of order$\sim10^{8}$ years because of inverse Compton and synchrotron losses \citep[e.g.,][]{ip99}. ." + Decause, Because +Las tat GTOO pproviding a spectral coverage of about 58 wand 0.0282 ,1.88 $^{-1}$ at 6700 providing a spectral coverage of about 58 and 0.0282 $^{-1}$. +Different settings for the central wavceleugthi were applied on hne various nights in order to avoid um signatures in the spectrum resulting from a possible oeuproper fiatfieldiug., Different settings for the central wavelength were applied on the various nights in order to avoid any signatures in the spectrum resulting from a possible improper flatfielding. + The nain targets for the June 93 observations were some halo turnoff stars. for which he results have been presented by Suuith et al. (1998))," The main targets for the June 93 observations were some halo turnoff stars, for which the results have been presented by Smith et al. \cite +{smith98}) )" + inchiding a descriptio- of the reductious of he imaeeOo slicer observations., including a description of the reductions of the image slicer observations. + The Oct. 92 aud Feb. 95 observations have been reduced i imch tle sale wav., The Oct. 92 and Feb. 95 observations have been reduced in much the same way. + Subtraction of backeround. flat Ποια correction and extraction of spectra were performed with stanclare tasks in ΠΑΕ.," Subtraction of background, flat field correction and extraction of spectra were performed with standard tasks in IRAF." + The waveleneth calibration was base ou 28 thori lines well distributed over the wavelength reeion (6676 - GT31 A)., The wavelength calibration was based on 28 thorium lines well distributed over the wavelength region (6676 - 6734 ). + A secoud-order polynomial was adopted for the dispersion solution resulting iu a tvpica tlus deviation from the fit of 0015A., A second-order polynomial was adopted for the dispersion solution resulting in a typical rms deviation from the fit of 0.0015. + Furthermore. he EWIIM of the thormia les were measured auk ‘ound ο vary by less than along the spectrmu.," Furthermore, the FWHM of the thorium lines were measured and found to vary by less than along the spectrum." + This rear-coustaney of the iustruuen profile is important iu connection with the deterumimation of mstruneutal aux stellar ine broadening from lines near the line., This near-constancy of the instrument profile is important in connection with the determination of instrumental and stellar line broadening from lines near the line. + For the Oct. 92 and Feb. 95 observations tlie FWIIA of the Th lines corresponds to a resolution of R=105000. whereas the June 93 image sclicer spectra rave a resolution of Ro=115000.," For the Oct. 92 and Feb. 95 observations the FWHM of the Th lines corresponds to a resolution of $R = 105 \, 000$, whereas the June 93 image sclicer spectra have a resolution of $R = 115 \, 000$." + Finally. the spectra were normalized to an approximate level of 1 by fitting a fifth-order cubic spline function to the continu. aud corrected for the radial velocity shift usine the accurate wavelengths (6703.567 and ) given by Nave et al. (1995))," Finally, the spectra were normalized to an approximate level of 1 by fitting a fifth-order cubic spline function to the continuum, and corrected for the radial velocity shift using the accurate wavelengths (6703.567 and ) given by Nave et al. \cite{nave95}) )" + for the two Hines close to the the Li line., for the two lines close to the the Li line. + Table 2 lists the the uumber of observations aud exposure times as distributed over the three periods., Table 2 lists the the number of observations and exposure times as distributed over the three periods. + Note. that IIR 3575 has been observed in all three periods aud IIR S151 in two of them.," Note, that HR 3578 has been observed in all three periods and HR 8181 in two of them." + The imdividual spectra show excellent agreement aud have therefore been co-added to obtain the final spectra shown iu Fig., The individual spectra show excellent agreement and have therefore been co-added to obtain the final spectra shown in Fig. + 1 for the 6702 region., \ref{fig.1} for the 6702 – region. + These ave the spectra used for the determination of the irafio. but iu the case of IIR. 3578 we have also derived the ratio separately for cach observiug period iu order to check for possible svstematic differences.," These are the spectra used for the determination of the ratio, but in the case of HR 3578 we have also derived the ratio separately for each observing period in order to check for possible systematic differences." +Table 4)) Crowther et ((2006)) observe J-Ks colours 0.35 to mmag bluer than we do.,"Table \ref{stars_spt_mass}) ), Crowther et \cite{crowther06}) ) observe J-Ks colours 0.35 to mag bluer than we do." +" Variability as reported by Bonanos (2007)) might explain part of this discrepancy, though there might also be a systematic offset in the zeropoint calibrations of the two data sets."," Variability as reported by Bonanos \cite{bonanos07}) ) might explain part of this discrepancy, though there might also be a systematic offset in the zeropoint calibrations of the two data sets." +" For comparison to other extinction determinations, which were exclusively based on studies in the visual, we also compute the visual extinction."," For comparison to other extinction determinations, which were exclusively based on studies in the visual, we also compute the visual extinction." +" Assuming a normal extinction law with R = Ay / Eg.y = 3.1, Ακ. = mmag corresponds to Ay«10.1 mmag (Rieke Lebofsky 1985))."," Assuming a normal extinction law with R = $_{\rm V}$ / $_{\rm B-V}$ = 3.1, $_{\rm Ks}$ = mag corresponds to $_{\rm V} \approx 10.1$ mag (Rieke Lebofsky \cite{rieke85}) )." + Westerlund (1961)) derived an optical colour V-I +4.5mmag for the «80 brightest stars of the cluster., Westerlund \cite{west61}) ) derived an optical colour V–I = $+4.5$ mag for the $\approx$ 80 brightest stars of the cluster. +" By assuming an intrinsic colour of (V-IDo—0.35, which is typical for early type stars, this corresponds to E(V-I) = mmag."," By assuming an intrinsic colour of $_0 = -0.35$, which is typical for early type stars, this corresponds to E(V-I) = mag." +" If one further assumes a standard extinction law with Ay = 1.93 E(V-I) (see Rieke Lebofsky 1985)), this results in Ay « 9.4mmag."," If one further assumes a standard extinction law with $_{\rm V}$ = 1.93 E(V-I) (see Rieke Lebofsky \cite{rieke85}) ), this results in $_{\rm V}$ $\approx$ mag." + Note that Westerlund (1961)) deduced a higher Ay of 11.2 — 12mmag by assuming a ratio between total and selective absorption of 2.3+1.4 (Kron Mayall 1960))., Note that Westerlund \cite{west61}) ) deduced a higher $_{\rm V}$ of 11.2 – mag by assuming a ratio between total and selective absorption of $\pm$ 1.4 (Kron Mayall \cite{kron60}) ). + Follow-up photometric and spectroscopic observations considering about 260 cluster members yielded Αν z 9.7+0.8 mmag (Westerlund 1987))., Follow-up photometric and spectroscopic observations considering about 260 cluster members yielded $_{\rm V}$ $\approx$ $\pm$ mag (Westerlund \cite{west87}) ). +" Clark et ((2005)) estimate Ay = 11.6 to 13.6mmag, and present evidence for anomalous extinction towards ~20 OB supergiants in Wd 1."," Clark et \cite{clark05}) ) estimate $_{\rm V}$ = 11.6 to mag, and present evidence for anomalous extinction towards $\approx$ 20 OB supergiants in Wd 1." +" While for normal interstellar extinction the ratio of total to selective extinction R=3.1, R values in the range 1.7 to 5.5 have been observed in high-mass star forming regions (Patriarchi et citepatri01,, but see also Hadfield Crowther 2006 and Lamzin 2006))."," While for normal interstellar extinction the ratio of total to selective extinction ${\rm R = 3.1}$, R values in the range 1.7 to 5.5 have been observed in high-mass star forming regions (Patriarchi et \\cite{patri01}, but see also Hadfield Crowther \cite{hadfield06} and Lamzin \cite{lamzin06}) )." +" For R = 3.7, Ax1.13+0.03 mmag corresponds to Ay«12.0 mmag, iin the range of the visual extinction values determined by Clark et (2005)) towards some of the evolved stars in 11."," For R = 3.7, $_{\rm K} = 1.13 \pm 0.03$ mag corresponds to $_{\rm V} \approx 12.0$ mag, in the range of the visual extinction values determined by Clark et \cite{clark05}) ) towards some of the evolved stars in 1." +" For the age determination, we take advantage of the fact that the width and the shape of the pre-main sequence — main-sequence transition region in J-Ks varies with age."," For the age determination, we take advantage of the fact that the width and the shape of the pre-main sequence – main-sequence transition region in J–Ks varies with age." + This allows us to derive the age of the cluster by comparison with theoretical isochrones., This allows us to derive the age of the cluster by comparison with theoretical isochrones. + The best fitting Palla Stahler isochrone are for ages of 3.2 to MMyr., The best fitting Palla Stahler isochrone are for ages of 3.2 to Myr. +" Isochrones for an age of 3.0MMyr or MMyr, respectively do not fit as well, in particular when taking the adaptive optics data into account."," Isochrones for an age of Myr or Myr, respectively do not fit as well, in particular when taking the adaptive optics data into account." +" A more detailed comparison of different sets of theoretical isochrones will be presented in the second paper, which features a detailed analysis of the cluster population in the range of 0.4 to MMo."," A more detailed comparison of different sets of theoretical isochrones will be presented in the second paper, which features a detailed analysis of the cluster population in the range of 0.4 to $_\odot$." + We estimate the age of the low-mass stellar population of Wd11 since crossing the “birthline” (see Stahler 1983)) to 3.3+0.2 MMyr., We estimate the age of the low-mass stellar population of 1 since crossing the “birthline” (see Stahler \cite{stahler83}) ) to $\pm$ Myr. +" At young ages of =3 and 5.," Therefore, our results indicate a fast evolution of the stellar mass function in the short $\sim$ 1 Gyr) elapsed time between redshifts $z=3$ and 5." + As an alternative to the Schechter function. we tried a double-exponential form. in the maximum likelihood analysis.," As an alternative to the Schechter function, we tried a double-exponential form in the maximum likelihood analysis." + The two functional forms can only be distinguished in practice wren the stellar mass function is well constrained at the very bright end. (AL>M) ef., The two functional forms can only be distinguished in practice when the stellar mass function is well constrained at the very bright end $M \gg M^\ast$; cf. + Caputi et al., Caputi et al. + 2007 for a discussion in the case of luminosity functions)., 2007 for a discussion in the case of luminosity functions). + In our present analysis. we find that the maximum likelihoods obtained with either the Schechter or the double-exponential functions are consistent within 30 (the resulting stellar-mass-[unction curves are almost identical within the scollar miss range sampled in our catalogue)," In our present analysis, we find that the maximum likelihoods obtained with either the Schechter or the double-exponential functions are consistent within $\sigma$ (the resulting stellar-mass-function curves are almost identical within the stellar mass range sampled in our catalogue)." + A single power-law can be discarded. as the shape of the stellar mass function at 3.0x2«3.5 and 3.52«4.25 with 670 and 37 confidence. respectively.," A single power-law can be discarded as the shape of the stellar mass function at $3.0 \leq z < 3.5$ and $3.5 \leq z < 4.25$ with $>6\sigma$ and $>3 \sigma$ confidence, respectively." + 1nstead. we cannot exclude t10 single power-law shape at 425xz«5.0. for which the maximum likelihood is within ~2o confidence of the Schechter function case.," Instead, we cannot exclude the single power-law shape at $4.25 \leq z < 5.0$, for which the maximum likelihood is within $\sim 2 \sigma$ confidence of the Schechter function case." + It is ikely that this elfect is produced. simply because we might not be well sampling the AZ.,"1999) to derive a mean $\alpha$ luminosity of $\times$ $^{44}$ ergs $^{-1}$ based on the mean $\beta$ equivalent width of their sample, no extinction and an intrinsic ratio of 3.1 between $\alpha$ and $\beta$." + The one sigma dispersion in this value is only in their sample., The one sigma dispersion in this value is only in their sample. + Our extinction corrected Πα huninosity is then weaker thin their mean by a factor of 2.6 sugeesting the central engines are very simular., Our extinction corrected $\alpha$ luminosity is then weaker than their mean by a factor of 2.6 suggesting the central engines are very similar. + If we eo a step further and assume that the iutriusic hDuuinosities are the same. then the broad line extinction would need to be Ay =3.5 mag instead of Ay-=1.lL imag as derived above for the narrow line region.," If we go a step further and assume that the intrinsic luminosities are the same, then the broad line extinction would need to be $_V$ =3.5 mag instead of $_V$ =1.4 mag as derived above for the narrow line region." + A romainiug difference between MIRC 2025-218 and the quasars in the \fctutosh sample is the IT-baud magnitude., A remaining difference between MRC 2025-218 and the quasars in the McIntosh sample is the H-band magnitude. + MRC 2025-218 has a broad baud magnitude of T=19.1 while the mean quasaz I-baud magnitude is 15.16., MRC 2025-218 has a broad band magnitude of H=19.1 while the mean quasar H-band magnitude is 15.16. + After correcting for the different redshifts (quasar mean z=2.2) then AIRC 2025-218 is3.2 magnitudes fainter thanthe, After correcting for the different redshifts (quasar mean z=2.2) then MRC 2025-218 is3.2 magnitudes fainter thanthe +ou the Ixeck II telescope in March 2001.,on the Keck II telescope in March 2001. +" The spectra were obtained through a 0,75""«20"" slit placed along the major axis of cach galaxy with waveleneth coverage AABZINO—9500À. aud resolution of 23 kimi ! (Gaussian signua).", The spectra were obtained through a $0.75'' \times 20''$ slit placed along the major axis of each galaxy with wavelength coverage $\rm\lambda\lambda3900-9500\AA$ and resolution of 23 km $^{-1}$ (Gaussian sigma). + As shown in Table 1. the observed galaxies cover a range of cllipticitics aud three of the four are nucleated cdavarts (EN).," As shown in Table 1, the observed galaxies cover a range of ellipticities and three of the four are nucleated dwarfs (dE,N)." + These objects lie near the bright cud of the dE huninosity function and were selected to have archival WEPC2 imagine., These objects lie near the bright end of the dE luminosity function and were selected to have archival WFPC2 imaging. + Mean radial velocitics aud velocity dispersious were determined using a pixe space u nuininization scheme described iu vau der Marvel (199D., Mean radial velocities and velocity dispersions were determined using a pixel space $\chi^2$ minimization scheme described in van der Marel (1994). + The data were spatially rebinued to achieve à S/N>5 at all radii., The data were spatially rebinned to achieve a $\rm S/N > 5$ at all radii. + Velocitics are 1ieasure relative to a IOUT template star usine the bb region. AADO00—51004: an analysis of the full waveleugth region will be preseuted iu a forthcoming paper.," Velocities are measured relative to a K0III template star using the b region, $\rm\lambda\lambda5000-5400\AA$; an analysis of the full wavelength region will be presented in a forthcoming paper." + Tests show that the galaxies internal velocity dispersions are recovorec accurately down to the instrumental resolution of 23 kins |l, Tests show that the galaxies' internal velocity dispersions are recovered accurately down to the instrumental resolution of 23 km $^{-1}$. + The observed shapes and kinematics of elliptical eilaxies between 20<1''$ to avoid nuclear contamination. + The ratio μμσ 18 plotted against cllipticity in Figure 2 aud is compared o the ratio expected froin an isotropic. rotationally flattened body. (Binney Tremaine 1987).," The ratio $v_{max}/\sigma$ is plotted against ellipticity in Figure 2 and is compared to the ratio expected from an isotropic, rotationally flattened body (Binney Tremaine 1987)." +" The upper limits on 0,,,4,4/0 determined for these galaxies are 2 to 8 times snaller than expected if the observed. fattenines were due o votation.", The upper limits on $v_{max}/\sigma$ determined for these galaxies are 2 to 8 times smaller than expected if the observed flattenings were due to rotation. + Thus. we conclude that these dEs are primarily flattened by anisotropic velocity dispersious.," Thus, we conclude that these dEs are primarily flattened by anisotropic velocity dispersions." + Although the mean velocity profiles preseuted in Figure { are qualitatively simular. the velocity dispersion profiles are more heterogeneous.," Although the mean velocity profiles presented in Figure 1 are qualitatively similar, the velocity dispersion profiles are more heterogeneous." + The velocity dispersion of the uon-nucleated dE VCC 917 decreases smoothly. towards the ealaxy ceuter in contrast to the three uucleated charts. which vary more," The velocity dispersion of the non-nucleated dE VCC 917 decreases smoothly towards the galaxy center in contrast to the three nucleated dwarfs, which vary more" +produce high energy photons (Wang et al.,produce high energy photons (Wang et al. + 2010) and in fact is dependent of v., 2010) and in fact is dependent of $\nu$. + Now we confront the above theory with the observed data to constrain the unknown parameters., Now we confront the above theory with the observed data to constrain the unknown parameters. + From Abdo et al. (, From Abdo et al. ( +2009). Pandey et al. (,"2009), Pandey et al. (" +2010). we take the observed flux for LAT data at 173s. R-band optical data at 1.301008. X-ray data at 10°s and radio data at 4.67« 10°s as below: where #~0.85 is the extinction coefficient of the host galaxy in R band (Cenko et al.,"2010), we take the observed flux for LAT data at 173s, R-band optical data at $1.30\times 10^5$ s, X-ray data at $1.09\times 10^5$ s and radio data at $4.67\times 10^5$ s as below: where $\kappa \simeq 0.85$ is the extinction coefficient of the host galaxy in R band (Cenko et al." + 2010)., 2010). + The spectral regime of each frequency is given in the parentheses., The spectral regime of each frequency is given in the parentheses. + Although δι and vx belong to the same spectral regime. the X-ray flux and high-energy flux data can give two independent constraints due to two different Y. parameters.," Although $\nu_{{\rm LAT}}$ and $\nu_{{\rm X}}$ belong to the same spectral regime, the X-ray flux and high-energy flux data can give two independent constraints due to two different $Y$ parameters." + For electrons that produce the X-ray synchrotron afterglow. the inverse-Compton scattering loss is in the Thompson regime and Y~74.3¢€phase.AueAENUnDanT in the slow-cooling while for high--energy gamma-ray photons. Y parameter is small due to the KN suppression effect on the scattering cross section. as we will show later.," For electrons that produce the X-ray synchrotron afterglow, the inverse-Compton scattering loss is in the Thompson regime and $Y\sim +74.3\epsilon_{{\rm ef},-1}^{2/3}\epsilon_{{\rm Bf},-5}^{-4/9}E_{54}^{1/18}n_{-3}^{1/18}(1+z)^{1/18}T_0^{-1/18}$ in the slow-cooling phase, while for high-energy gamma-ray photons, $Y$ parameter is small due to the KN suppression effect on the scattering cross section, as we will show later." + So we obtain the constraints on the shock parameters where Y(100MeV) is the Compton parameter for the electrons whose synchrotron frequency is fi=100MeV at t= 173s. In the calculation. a typical value of p=2.2 for forward shock has been used.," So we obtain the constraints on the shock parameters where $Y(100 {\rm MeV})$ is the Compton parameter for the electrons whose synchrotron frequency is $h\nu=100{\rm MeV}$ at $t=173$ s. In the calculation, a typical value of $p=2.2$ for forward shock has been used." + Solving the above equations. we obtain For the of parameters. we obtain ¥(LOOMeV)0.03fpraboveregseteurSERnCT(oen?V)~0.06 at 173s (Wang et al.," Solving the above equations, we obtain For the above set of parameters, we obtain $Y(100 {\rm MeV})\simeq +0.03f(p)^{-5/3}\epsilon_{{\rm ef},-1}^{-2/3}\epsilon_{{\rm Bf},-5}^{-1/3}E_{54}^{1/6}n_{-3}^{1/2}T_0^{1/2}(1+z)^{1/6} +\sim 0.06 $ at $t=173$ s (Wang et al." + 2010)., 2010). + As y(lQ0Meκ|. we can just omit Y(I00MeV) in these expressions.," As $Y(\rm 100 MeV)\ll +1$, we can just omit $Y(100 {\rm MeV})$ in these expressions." + As the reverse shock propagates into the fireball ejecta. the number of shocked electrons increases. which leads to an initial rise of the reverse shock flux.," As the reverse shock propagates into the fireball ejecta, the number of shocked electrons increases, which leads to an initial rise of the reverse shock flux." + Once it has passed through the shell. no new electrons will be shocked and the flux will decrease due to adiabatic expansion of the radiating gas.," Once it has passed through the shell, no new electrons will be shocked and the flux will decrease due to adiabatic expansion of the radiating gas." + The flux of reverse shock peaks at 7;=max(Tee.To) (hereafter. we use the subseript “1 represent quantities at the peak time).," The flux of reverse shock peaks at $T_{\rm i}=\max(T_{{\rm dec}}, T_{{\rm cross}} )$ (hereafter, we use the subscript 'i' to represent quantities at the peak time)." +" Here Ty.—U/1°C1fe+2) is Selonthe shell deceleration time. where/=(E/nmyc7""j is the length and (4 is the initial Lorentz factor of the ejecta. T"," Here $T_{{\rm dec}}\equiv (l/\eta^{8/3}c)(1+z)$ is the shell deceleration time, where ${l=(E/nm_p c^2)^{1/3}}$ is the Sedov length and $\eta$ is the initial Lorentz factor of the ejecta. ," +oo. is the characteristic timescale within which the reverse shock erosses the shell. where A is the thickness of the shell (Sari Piran 1995. 1999b).," is the characteristic timescale within which the reverse shock crosses the shell, where $\Delta$ is the thickness of the shell (Sari Piran 1995, 1999b)." +" When the shell is thick so that Tony>Tyee. the reverse shock becomes relativistic early on. and we call it ""thick shell"" case. otherwise it belongs to the ""thin shell"" case."," When the shell is thick so that $T_{{\rm cross}}>T_{{\rm dec}}$, the reverse shock becomes relativistic early on, and we call it ""thick shell"" case, otherwise it belongs to the ""thin shell"" case." +" Evolution of bulk Lorentz factor. gas pressure and density of shocked electrons after crossing time follows ~77""!6, prTO anda xT6 (Sari Piran 1999a. b: Meszaros Rees 1999; Kobayashi 2000)."," Evolution of bulk Lorentz factor, gas pressure and density of shocked electrons after crossing time follows $\gamma \propto T^{-7/16}$, $p \propto +T^{-13/12}$ and $n \propto T^{-13/16}$ (Sari Piran 1999a, b; Meszaros Rees 1999; Kobayashi 2000)." + The bulk Lorentz factor of the shocked shell at the peak time is 7;I838CIE2)?SE!VN1‘pS., The bulk Lorentz factor of the shocked shell at the peak time is $\gamma_i =1838(1+z)^{3/8}E_{54}^{1/8}n_{-3}^{-1/8}T_{\rm i}^{-3/8}$. + Then we can get the Lorentz factor2 of the reverse54 shock at the peak time The mmimum random Lorentz factor of electrons is given by where e; is the fraction of thermal electrons carried by magnetic field in reverse shock. 5=PS (namely. >—12b+) and t=T/Ti.," Then we can get the Lorentz factor of the reverse shock at the peak time The minimum random Lorentz factor of electrons is given by where $\epsilon_{{\rm er}}$ is the fraction of thermal electrons carried by magnetic field in reverse shock, $b\equiv\frac{(\bar{\gamma}-1)}{\eta /\gamma}$ (namely, $\bar{\gamma}-1=b\frac{\eta}{\gamma}$ ) and $\hat t\equiv T/T_{\rm i}$." + We use this approximation for +—1 so that we can treat the calculation analytically., We use this approximation for $\bar{\gamma}-1$ so that we can treat the calculation analytically. + Usually. the value of > is taken to be 1 (Waxman Draine 2000: Kobayashi et al.," Usually, the value of $b$ is taken to be 1 (Waxman Draine 2000; Kobayashi et al." + 2007) or + (Wang et al., 2007) or $\frac{1}{2}$ (Wang et al. + 2005)., 2005). + A mildly relativistic reverse shock approximation with >—1z| is also sometimes used (see e.g. Sari Piran 19993)., A mildly relativistic reverse shock approximation with $\bar{\gamma}-1 \simeq 1$ is also sometimes used (see e.g. Sari Piran 1999a). + In this paper. we take b=4 in the calculation. as jjZ;.," In this paper, we take $b=\frac{1}{2}$ in the calculation, as $\eta\ga \gamma_i$." + For a typical value of p22.5 for the reverse shock emission. f(p)=2.," For a typical value of $p=2.5$ for the reverse shock emission, $f(p)=2$." + We get the two characteristic frequencies for the reverse shock synchrotron emission and The peak flux of the reverse shock synchrotron emission 1s Then we get the flux density at a certain frequency [fv>maxGA.14). the flux drops exponentially with time because there are no new injected electrons whose typical synchrotron frequency Hes in this regime.," We get the two characteristic frequencies for the reverse shock synchrotron emission and The peak flux of the reverse shock synchrotron emission is Then we get the flux density at a certain frequency If $\nu > \max(\nu_{{\rm mr}}, \nu_{{\rm cr}})$, the flux drops exponentially with time because there are no new injected electrons whose typical synchrotron frequency lies in this regime." + If we attribute the early optical emission at ¢~5000 s to the reverse shock synchrotron emission. we would have where #~0.85 is the extinction. coefficient of the host galaxy in R band (Cenko et al.," If we attribute the early optical emission at $t\simeq 5000$ s to the reverse shock synchrotron emission, we would have where $\kappa \simeq 0.85$ is the extinction coefficient of the host galaxy in R band (Cenko et al." + 2010)., 2010). + The reverse shock emission can produce a radio flare as has been seenin GRB 990123 (Kulkarni et al., The reverse shock emission can produce a radio flare as has been seenin GRB 990123 (Kulkarni et al. + 1999)., 1999). + Although the radio emission in GRB 090902B drops after the first detection. it shows a flattening after the second detection at 4.67« 10°s. so the," Although the radio emission in GRB 090902B drops after the first detection, it shows a flattening after the second detection at $4.67\times 10^5{\rm s}$ , so the" +Qs=1 to better than5%.,"$\Omega_{m,3}=1$ to better than." +.. Nevertheless. we have tested the matter density dependence.," Nevertheless, we have tested the matter density dependence." +" We have run three open models with n=0.7 and νο=0.45 (Q,,.5=0.75). O10=0.2 (0,5= 0.5). and μυ=0.1 (0ου=0.3) respectively. and the results of these simulations are presented in Figure 7.."," We have run three open models with $n=0.7$ and $\Omega_{m,0}=0.45$ $\Omega_{m,3}=0.75$ ), $\Omega_{m,0}=0.2$ $\Omega_{m,3}=0.5$ ), and $\Omega_{m,0}=0.1$ $\Omega_{m,3}=0.3$ ) respectively, and the results of these simulations are presented in Figure \ref{figDF}." + One can see that the recovered. linear. power spectrum does depend on the assumed. value of the density. parameter ats=2.72. even if all three models fit the observed. [ux power spectrum.," One can see that the recovered linear power spectrum does depend on the assumed value of the density parameter at $z=2.72$, even if all three models fit the observed flux power spectrum." + The dependence on the density parameter cannot be rigorously derived. analytically. but the form. found empirically can be understood approximately on the basis ob arguments from linear theory.," The dependence on the density parameter cannot be rigorously derived analytically, but the form found empirically can be understood approximately on the basis of arguments from linear theory." + The Gunn-Peterson optical depth 7 (Gunn&Peterson1965). at every spatial point is inversely. proportional to the ο along the line of sight (Lluietal.1997).. where n is the total velocity (Llubble Dow plus peculiar velocity) and we is the comoving distance.," The Gunn-Peterson optical depth $\tau$ \cite{GP65} + at every spatial point is inversely proportional to the $du/dx$ along the line of sight \cite{HGZ97}, where $u$ is the total velocity (Hubble flow plus peculiar velocity) and $x$ is the comoving distance." + In the linear regime where fodInD.fdina=Q.," In the linear regime where $f \equiv d \ln D_+ / d \ln a +\approx\Omega^{0.6}$." +" ""Phe first term in the parenthesis is the Hubble Dow. while the second one is due to peculiar velocities."," The first term in the parenthesis is the Hubble flow, while the second one is due to peculiar velocities." + In the linear regime the Llubble Low of course dominates. but at z=3 most of the Lyman-alpha forest is mildly nonlinear. with AZ—&Pr(E)/(237)~1. as can be seen [rom retfigDE..," In the linear regime the Hubble flow of course dominates, but at $z=3$ most of the Lyman-alpha forest is mildly nonlinear, with $\Delta_k^2\equiv k^3P_L(k)/(2\pi^2) \sim 1$, as can be seen from \\ref{figDF}." +" If we assume that cifferent A values are independent (which is not quite true. but good enough for our hauxd-waving arguments). we would expect that the power spectrum for the optical depth 7 is approximately inversely proportional to (1:1.f£2N,7."," If we assume that different $k$ values are independent (which is not quite true, but good enough for our hand-waving arguments), we would expect that the power spectrum for the optical depth $\tau$ is approximately inversely proportional to $(1+f\Delta_k)^2$." +" In other words. we hypothesize that the recovered. linear. power spectrum depends: on cosmological parameters in the following way: where we will call ""a(E) the ""factorized? linear power spectrum. fa is the values of f. at z= 2.72. and and thus depends on Perk)."," In other words, we hypothesize that the recovered linear power spectrum depends on cosmological parameters in the following way: where we will call $P_L^{\rm fct}(k)$ the “factorized” linear power spectrum, $f_3$ is the values of $f$ at $z=2.72$ , and and thus depends on $P_L^{\rm obs}(k)$." + 1n this form DE!(b) should be nearly independent of Figure Snow gives D(E) for the four. models shown in 7.., In this form $P_L^{\rm fct}(k)$ should be nearly independent of Figure \ref{figAL} now gives $P_L^{\rm fct}(k)$ for the four models shown in \ref{figDF}. + As one can see. the factorization (10)) does account for the main dependence of the recovered. linear power spectrum on cosmological parameters. although some dillerences remain.," As one can see, the factorization \ref{denfac}) ) does account for the main dependence of the recovered linear power spectrum on cosmological parameters, although some differences remain." + Lt is however not convenient to use in practice because it is nonlinear anc implicit [or Pere)., It is however not convenient to use in practice because it is nonlinear and implicit for $P_L^{\rm obs}(k)$. +" Jut we can notice that for. ©, substantially cülferent from 1. A, is about unity for the range of scales. where the observational error-bars are small."," But we can notice that for $\Omega_{m,3}$ substantially different from 1, $\Delta_k$ is about unity for the range of scales where the observational error-bars are small." + Ht turns out that a comparable factorization can be obtained Lowe adopt a fixed value Ay=1.4 in equation (10)). This fit is linear. so it is easier to use in joint parameter estimation. while it still recovers the density dependence to about precision.," It turns out that a comparable factorization can be obtained if we adopt a fixed value $\Delta_k=1.4$ in equation \ref{denfac}) ), This fit is linear, so it is easier to use in joint parameter estimation, while it still recovers the density dependence to about precision." + We can now summarize our results., We can now summarize our results. +" The recovered. linear power spectrum can be factorized in the following wav: where and ""nΓΙ) is independent of anvthing else (just numbers) and is shown in Ligure 9 and in Table 1 together with dts. “systematic” crror-bars."," The recovered linear power spectrum can be factorized in the following way: where and $P_L^{\rm fct}(k)$ is independent of anything else (just numbers) and is shown in Figure \ref{figAR} and in Table \ref{tabone} + together with its “systematic” error-bars." + We put the word “systematic” in quotes because we considered only a subsample of all possible cosmological models. ancl our sampling of the parameter space is by no means uniform.," We put the word “systematic” in quotes because we considered only a subsample of all possible cosmological models, and our sampling of the parameter space is by no means uniform." + We thus suggest that errors quoted by us can be considered as an estimate for the svstematic error in the Croft ct measurement. but the precise value of such an error and its covariance matrix may depend very much onthe specifies of the prior.," We thus suggest that errors quoted by us can be considered as an estimate for the systematic error in the Croft et \\shortcite{CWB01} measurement, but the precise value of such an error and its covariance matrix may depend very much onthe specifics of the prior." + The observational data (Ricottietal.2000:Schave sets the value of Qy at," The observational data \cite{RGS00,STR00,MMR01} sets the value of $Q_T$ at" +"radius, and kes is the electron scattering opacity.","radius, and $\kappa_{\rm es}$ is the electron scattering opacity." +" Here, €=nMc?/Lgqa, and for simplicity we have approximated η~ "," Here, $\ell =\eta \Mdot c^2/L_{\rm Edd}$, and for simplicity we have approximated $\eta \sim 1/r_{\rm in}$." +Using the above 1/rin.definitions the observed luminosity is where Lo=4tGMoc/kes is the Eddington luminosity for a one solar mass BH and yp is a variable that encapsulates all of the angular dependence of the radiation field., Using the above definitions the observed luminosity is where $L_0 \equiv 4\pi G \Msun c/\kappa_{\rm es}$ is the Eddington luminosity for a one solar mass BH and $\mu$ is a variable that encapsulates all of the angular dependence of the radiation field. +" In an isotropically emitting, Newtonian disk 4=cost, accounting for the inclination dependence of the disk projected area."," In an isotropically emitting, Newtonian disk $\mu = \cos i$, accounting for the inclination dependence of the disk projected area." +" In our models, two other effects are important as well: electron scattering and relativistic beaming which tend to make the disk emission more limb-darkened and limb-brightened, respectively."," In our models, two other effects are important as well: electron scattering and relativistic beaming which tend to make the disk emission more limb-darkened and limb-brightened, respectively." +" The latter depends significantly on the spin so µ can be a strong function of a, as well as i.", The latter depends significantly on the spin so $\mu$ can be a strong function of $a_*$ as well as $i$. +" Lensing by the BH can also be important, particularly for nearly edge on systems where it places a lower limit on the effective projected area of the disk."," Lensing by the BH can also be important, particularly for nearly edge on systems where it places a lower limit on the effective projected area of the disk." +" Equations (2)) and (3)) can be solved for m and έ, yielding The quantities in parentheses on the right hand side of equation (4)) are observational constraints or constants of nature."," Equations \ref{eq:tobs}) ) and \ref{eq:lobs}) ) can be solved for $m$ and $\ell$ , yielding The quantities in parentheses on the right hand side of equation \ref{eq:mass}) ) are observational constraints or constants of nature." +" Uncertainties in D enter through Lop,cD?, so we approximately have MοD-!."," Uncertainties in $D$ enter through $L_{\rm obs} \propto D^2$, so we approximately have $M \propto D^{-1}$." +" Therefore, the relatively small uncertainty in D contributes only a very modest additional uncertainty in M."," Therefore, the relatively small uncertainty in $D$ contributes only a very modest additional uncertainty in $M$." +" The remaining quantities are functions of model parameters: ri(a.), μία», i), ó(a..,i); and foot(ass£, Μ)."," The remaining quantities are functions of model parameters: $r_{\rm in}(a_*)$ , $\mu(a_*, i)$ , $\delta(a_*,i)$, and $f_{\rm col}(a_*,\ell,M)$ ." +" The dependence of rj, on a, is the primary driver of the correlation of M with a, in Figure 2..", The dependence of $r_{\rm in}$ on $a_*$ is the primary driver of the correlation of $M$ with $a_*$ in Figure \ref{f:spin}. +" As a, increases from -1 to 0.99, rin decreases from 9 to 1.45, driving corresponding increases in M."," As $a_*$ increases from -1 to 0.99, $r_{\rm in}$ decreases from 9 to 1.45, driving corresponding increases in $M$." +" This variation is strongest as a,—1, leading to the “bend” in the confidence contours at high a,."," This variation is strongest as $a_* \rightarrow 1$, leading to the “bend” in the confidence contours at high $a_*$." +" Both 6 and jf.) increase with a, and contribute to the correlation as well."," Both $\delta$ and $f_{\rm col}$ increase with $a_*$, and contribute to the correlation as well." +" The spectrumin BHSPEC is calculated directly, so there is no explicit f.o1, but we can estimate foo, by taking the best fit BHSPEC models and fitting them with the KERRBB model, for which /ζοι is a Thevariationof foo) is shown for cosi=0.5 in Figure 7.."," The spectrumin BHSPEC is calculated directly, so there is no explicit $f_{\rm col}$, but we can estimate $f_{\rm col}$ by taking the best fit BHSPEC models and fitting them with the KERRBB model, for which $f_{\rm col}$ is a Thevariationof $f_{\rm col}$ is shown for $\cos i=0.5$ in Figure \ref{f:fcol}. ." + Although fc. can vary bymorethan, Although $f_{\rm col}$ can vary bymorethan +"To conclude, each outburst is associated with a peak in the wavelet power spectrum around period 500 to 1000 days (apart from the 1958 outburst), which never appears outside of an outburst.","To conclude, each outburst is associated with a peak in the wavelet power spectrum around period 500 to 1000 days (apart from the 1958 outburst), which never appears outside of an outburst." + A detailed analysis shows that these peaks are part of the true signal and not due to the observational uncertainty., A detailed analysis shows that these peaks are part of the true signal and not due to the observational uncertainty. +" From our Bayesian analysis, using a piecewise model curve fitting for the declines from outburst, we find breakpoints in the decline at ~53, ~107 and ~143 days after the outburst."," From our Bayesian analysis, using a piecewise model curve fitting for the declines from outburst, we find breakpoints in the decline at $\sim$ 53, $\sim$ 107 and $\sim$ 143 days after the outburst." + It is not clear that these are associated with any other changes in the system’s behaviour., It is not clear that these are associated with any other changes in the system's behaviour. + The X-ray flux shows a change in the power-law of the decline at around day 70 (Bodeetal.2008;Ness2008) but there is no obvious physical reason to relate this to changes in the optical light curve.," The X-ray flux shows a change in the power-law of the decline at around day 70 \citep{Bode2008,Ness2008} but there is no obvious physical reason to relate this to changes in the optical light curve." +" The super-soft phase also settled into a reasonably stable state around day 50 (Hachisu,Kato&Luna but again this cannot be clearly associated with the optical break by any physical mechanism.", The super-soft phase also settled into a reasonably stable state around day 50 \citep{Hachisu2007} but again this cannot be clearly associated with the optical break by any physical mechanism. +" It was found that the first observed point of the 1945 outburst was ~68 days after the actual beginning of the outburst, which means that there was probably an outburst beginning at most a few days after the seasonal gap began."," It was found that the first observed point of the 1945 outburst was $\sim$ 68 days after the actual beginning of the outburst, which means that there was probably an outburst beginning at most a few days after the seasonal gap began." +" Using wavelet analysis the and post-outburst features in the light curve at this time can be distinguished, and are similar to all the other outbursts (apart from the 1958 one)."," Using wavelet analysis the pre- and post-outburst features in the light curve at this time can be distinguished, and are similar to all the other outbursts (apart from the 1958 one)." + Identifying an outburst in 1945 reduces the mean interval outburst recurrence rate from ~20 years (Starrfield2006) to ~12.5 years., Identifying an outburst in 1945 reduces the mean interval outburst recurrence rate from $\sim$ 20 years \citep{Starrfield2006} to $\sim$ 12.5 years. + This also makes the nine year interval between the 1958 and 1967 outbursts less anomalous - moving it much closer to the median interval than when the 1945 outburst is excluded (from 1.25 standard deviations to 0.7 standard deviations)., This also makes the nine year interval between the 1958 and 1967 outbursts less anomalous - moving it much closer to the median interval than when the 1945 outburst is excluded (from 1.25 standard deviations to 0.7 standard deviations). +" A more detailed look at the wavelet power for each outburst suggests that the 1945, 1985 and 2006 outbursts had similar magnitude wavelet peaks."," A more detailed look at the wavelet power for each outburst suggests that the 1945, 1985 and 2006 outbursts had similar magnitude wavelet peaks." + The 1967 outburst has an unusually strong wavelet peak while in 1958 there is no significant peak., The 1967 outburst has an unusually strong wavelet peak while in 1958 there is no significant peak. +" While we can say nothing about the outburst mechanisms from this, it does suggest some observable pre—outburst activity in most cases — with the only analysed outburst without such a peak followed by a second outburst within 9 years, still the shortest observed interval."," While we can say nothing about the outburst mechanisms from this, it does suggest some observable pre–outburst activity in most cases – with the only analysed outburst without such a peak followed by a second outburst within 9 years, still the shortest observed interval." + The only major parameter in outburst models (e.g.Yaronetal.2005) that can be varied on such short timescales is the mass accretion rate onto the WD., The only major parameter in outburst models \citep[e.g.][]{Yaron2005} that can be varied on such short timescales is the mass accretion rate onto the WD. + Variable mass transfer also seems to be the only plausible process that could generate the pre—outburst activity indicated by our wavelet analysis., Variable mass transfer also seems to be the only plausible process that could generate the pre--outburst activity indicated by our wavelet analysis. + We note that the pre—outburst signal in the power plots are similar regardless if we include or exclude the outbursts themselves in the light curve (compare Figs., We note that the pre–outburst signal in the power plots are similar regardless if we include or exclude the outbursts themselves in the light curve (compare Figs. + 4aa and 4bb)., \ref{fig-power}a a and \ref{fig-power2}b b). +" Since we know what a typical characteristic of each outburst is, then we can use it for outburst prediction."," Since we know what a typical characteristic of each outburst is, then we can use it for outburst prediction." + Even 200 days before the outburst the wavelet analysis shows this pre-outburst trend of the star., Even 200 days before the outburst the wavelet analysis shows this pre-outburst trend of the star. + For 455 days (an orbital period) this feature is less significant but in some cases (1967 and 1985 outbursts) is still recoverable., For 455 days (an orbital period) this feature is less significant but in some cases (1967 and 1985 outbursts) is still recoverable. +" Hence, we have a means to predict outbursts in this object."," Hence, we have a means to predict outbursts in this object." + Further work will extend this to similar systems., Further work will extend this to similar systems. + If it turns out to be robust then it may also have implications for the outburst mechanism as a TNR should have no pre-outburst signal., If it turns out to be robust then it may also have implications for the outburst mechanism as a TNR should have no pre-outburst signal. +" Since (almost) every analysed outburst is linked with a pre-outburst feature in the wavelet power spectrum, this can be a useful tool for outburst prediction."," Since (almost) every analysed outburst is linked with a pre-outburst feature in the wavelet power spectrum, this can be a useful tool for outburst prediction." +" To test this, wavelet analysis for the time"," To test this, wavelet analysis for the time" +likelihood distribution peaks at / = 0.72 using the standard and a f = 0.66 using the HPs approach.,likelihood distribution peaks at $h$ = 0.72 using the standard and at $h$ = 0.66 using the HPs approach. + Note the good agreement of the best fit value of / for both data with the FOL result., Note the good agreement of the best fit value of $h$ for both data with the F01 result. +" When (δημ is fixed to be 0.2. the plots shift significantly to the right. with best fi points .—1.03.1.11.1.07 and 1.03 for EF99. MME99., standarc joint analysis and HPs approach. respectively."," When $\Omega_{\rm m}$ is fixed to be 0.2, the plots shift significantly to the right, with best fit points $h= 1.03, 1.11, 1.07$ and 1.03 for EF99, MME99, standard joint analysis and HPs approach, respectively." +" We conclude that the baryon fraction data on its own canno constrain each of the two parameters. but only their combination. QA7z0.25,"," We conclude that the baryon fraction data on its own cannot constrain each of the two parameters, but only their combination, $\Omega_{\rm +m} h^{0.5} \approx 0.25$." + Therefore. although the likelihood peak is at a high value of / and a low value of £4. we should not attach much significance to the individual values.," Therefore, although the likelihood peak is at a high value of $h$ and a low value of $\Omega_{\rm m}$, we should not attach much significance to the individual values." +" To constrain the individual values of and O,, we now combine the baryon fraction data with the cepheid sample.", To constrain the individual values of $h$ and $\Omega_{\rm m}$ we now combine the baryon fraction data with the cepheid sample. + We present our results for the combined analysis in Figure 3.., We present our results for the combined analysis in Figure \ref{fig:clus_joint}. + It can be seen that the high contour regions obtained for / with the cluster data have decreased significantly., It can be seen that the high contour regions obtained for $h$ with the cluster data have decreased significantly. + The confidence regions are a lot tighter than the contidence regions of the single data seu alone. thus giving stronger constraints.," The confidence regions are a lot tighter than the confidence regions of the single data sets alone, thus giving stronger constraints." + Table 3 and Table 4 show the best fit values and 68% confidence limits of and OQ... respectively.," Table 3 and Table 4 show the best fit values and $68\%$ confidence limits of $h$ and $\Omega_{\rm m}$, respectively." + The best fit points of the parameters lie within the confidence limits. indicating that the likelihood distributions are well behaved.," The best fit points of the parameters lie within the confidence limits, indicating that the likelihood distributions are well behaved." + The dominating data sets are the cepheid-calibrated distance indicators., The dominating data sets are the cepheid-calibrated distance indicators. + This is expected. since the uncertainties on / are much larger for the cluster samples.," This is expected, since the uncertainties on $h$ are much larger for the cluster samples." + The resulting HPs of our analysis are 0.6 (EF99).. 0.1 (MME99). 1.8 (SNIa). 2.7 (TF). 0.5 CFP) and 3.3 (SBF).," The resulting HPs of our analysis are 0.6 (EF99), 0.1 (MME99), 1.8 (SNIa), 2.7 (TF), 0.5 (FP) and 3.3 (SBF)." + The HPs are actually almost identical to the HPs derived for the individual data sets in section 2 and 3., The HPs are actually almost identical to the HPs derived for the individual data sets in section 2 and 3. + We also see that the dominance of the cepheid data relative to the baryon fraction data., We also see that the dominance of the cepheid data relative to the baryon fraction data. + Since the cepheid data only constrain P. this leads to a narrower error bar for in the HPs analysis compared with the joint V (which give equal weight to each of the 6 data sets).," Since the cepheid data only constrain $h$ , this leads to a narrower error bar for $h$ in the HPs analysis compared with the joint $\chi^2$ (which give equal weight to each of the 6 data sets)." +" Since the cepheid data have no information about £,, but have higher HP values. the error bar on £O, is wider in the HPs analysis."," Since the cepheid data have no information about $\Omega_{\rm m}$ but have higher HP values, the error bar on $\Omega_{\rm m}$ is wider in the HPs analysis." + Another interesting result is that the HPs analysis probes a parameter space in good agreement with the results from 2dF Galaxy Survey and CMB anisotropy measurements., Another interesting result is that the HPs analysis probes a parameter space in good agreement with the results from 2dF Galaxy Survey and CMB anisotropy measurements. + The right panel of Figure 5. shows that our combined analysis is consistent with other measurements., The right panel of Figure \ref{fig:clus_joint} shows that our combined analysis is consistent with other measurements. + We have presented applications of a generalised procedure. Hyper-Parameters’ (HPs). for analysing a set of different measurements.," We have presented applications of a generalised procedure, `Hyper-Parameters' (HPs), for analysing a set of different measurements." + We performed a combined analysis of baryon fraction in clusters and cepheid-calibrated distances., We performed a combined analysis of baryon fraction in clusters and cepheid-calibrated distances. +" We used the HPs formalism for joint analyses of the data sets to constrain the cosmological parameters / and Ou, (assuming a flat universe) and to check the reliability of the data sets.", We used the HPs formalism for joint analyses of the data sets to constrain the cosmological parameters $h$ and $\Omega_{\rm m}$ (assuming a flat universe) and to check the reliability of the data sets. + Using the baryonmass fraction in clusters. we obtained a very," Using the baryonmass fraction in clusters, we obtained a very" +A caveat Lo this picture is that the number of non-fossils is highly sensitive to the choice of the filtering velocity.,A caveat to this picture is that the number of non-fossils is highly sensitive to the choice of the filtering velocity. +" When we raise the filtering velocity to 30 km 1, the number of non-lossils drops by a third to 60+8 from the 90+10 [or ey;=20 km !"," When we raise the filtering velocity to $30$ km $^{-1}$, the number of non-fossils drops by a third to $60\pm8$ from the $90\pm10$ for $v_{filt}=20$ km $^{-1}$." + The choice of 20 km ! assumes a constant [IGM density with Τον=10! K throughout a minihalo's evolution., The choice of $20$ km $^{-1}$ assumes a constant IGM density with $T_{IGM}=10^4$ K throughout a minihalo's evolution. +" In reality, the situation is not so simple."," In reality, the situation is not so simple." + The gas near 107? M. halos and in the filaments between may be heated to ~10°— K by AGN feedback., The gas near $10^{12}$ $_\odot$ halos and in the filaments between may be heated to $\sim 10^5-10^6$ K by AGN feedback. + The higher temperatures of this local intergalactic medium may correspond to vy;50 kpe."," In this work, we have assumed an isotropic satellite distribution at $R>50$ kpc." +" Under this assumption, the SDSS completeness correcuion for the ultra-faints 1s 3.5I."," Under this assumption, the SDSS completeness correction for the ultra-faints is $3.54$." + We briefly check if the agreement between the observed and simulated distributions is dependent on the isotropic assumption., We briefly check if the agreement between the observed and simulated distributions is dependent on the isotropic assumption. +" Recent work (22) has suggested that rather than being isotropic, the Milky Way satellites are oriented in a plane approximately perpendicular to the disk."," Recent work \citep{Metzetal:07,Metzetal:09} has suggested that rather than being isotropic, the Milky Way satellites are oriented in a plane approximately perpendicular to the disk." + We approximate this non-homogeneous satellite distribution by correcting for the SDSS sky coverage by a factor of 2.0 instead of 3.54., We approximate this non-homogeneous satellite distribution by correcting for the SDSS sky coverage by a factor of 2.0 instead of 3.54. + The number of classical fossils remains the same., The number of classical fossils remains the same. +" The dillerent correction does not change the consistency of our simulated galactocentric distribution with observations, though the lower correcton factor suggests a higher Milky Way mass."," The different correction does not change the consistency of our simulated galactocentric distribution with observations, though the lower correction factor suggests a higher Milky Way mass." +" It also does not change the bright satellite problem. in fact, the lower observational correction factor makes the overabundance of simulated Li:>10! L.. dwarfs worse by about a factor of two."," It also does not change the bright satellite problem, in fact, the lower observational correction factor makes the overabundance of simulated $L_V > 10^4$ $_\odot$ dwarfs worse by about a factor of two." + We have suggested two solutions which correct for the overabundance of bright satellites while preserving at least a fraction of the primordial fossil population., We have suggested two solutions which correct for the overabundance of bright satellites while preserving at least a fraction of the primordial fossil population. + Each presents a dillerent picture when we consider it in the context of the voids., Each presents a different picture when we consider it in the context of the voids. +" The first, and less elfecüve, solution calls for a low star lormaton efficiency."," The first, and less effective, solution calls for a low star formation efficiency." +" In this picture, the 10! M.. halos visible in current surveys will have their star formation dampened, however as we move to. 10* M. we enter the regime where stochastic feedback effects dominate over the choice of e,."," In this picture, the $10^{10}$ $_\odot$ halos visible in current surveys will have their star formation dampened, however as we move to $~10^7$ $_\odot$ we enter the regime where stochastic feedback effects dominate over the choice of $\epsilon_\ast$." + Thus. the voids would appear relatively empty. but only because we cannot yet detect the less than 10° L. fossil populations which formed in the 10* M.. halos before reionization.," Thus, the voids would appear relatively empty, but only because we cannot yet detect the less than $10^5$ $_\odot$ fossil populations which formed in the $10^7$ $_\odot$ halos before reionization." +" The dispersal of the primordial populations into ghost halos is a more eflecuve solution to the “bright satellite problem"" within 1 Mpc of the Milky Way, but leaves a conundrum in the voids."," The dispersal of the non-fossils' primordial populations into ghost halos is a more effective solution to the “bright satellite problem” within $1$ Mpc of the Milky Way, but leaves a conundrum in the voids." +" Regardless of whether the primordial population would be detectable, how do we keep the post-reionization star formation in these non-lossils low enough to prevent this later star lormation [rom producing more ή:>—16 galaxies than are currently observed?"," Regardless of whether the primordial population would be detectable, how do we keep the post-reionization star formation in these non-fossils low enough to prevent this later star formation from producing more $M_V > -16$ galaxies than are currently observed?" +" Any post-reionization star formation in the non-[ossils results in a young population which would be (1) brighter and bluer. (11) more concentrated, since enriched gas will cool faster and sink deeper into the gravitational potential, and (ii) possibly accompanied by an Ireservoir."," Any post-reionization star formation in the non-fossils results in a young population which would be (i) brighter and bluer, (ii) more concentrated, since enriched gas will cool faster and sink deeper into the gravitational potential, and (iii) possibly accompanied by an reservoir." +" Any of these properties would make the post-reionization population easier to see, and the the non-fossil harder to hide."," Any of these properties would make the post-reionization population easier to see, and the the non-fossil harder to hide." + To suppress the post-reionization baryonic evolution in the non-[ossils we examine our naive assumption that they all, To suppress the post-reionization baryonic evolution in the non-fossils we examine our naive assumption that they all +standard version o| the DIM is eiven in Fie. () ).,standard version of the DIM is given in Fig. \ref{fig:std}) ). + For conrparison we also show the case of a svstei wi ha 0.6 AL. primary., For comparison we also show the case of a system with a 0.6 $_\odot$ primary. + The effects of raciation of the dise by both the hot white cwarf aud the boundary laver has been described m detail in Ibuueurw et al. (19993).," The effects of irradiation of the disc by both the hot white dwarf and the boundary layer has been described in detail in Hameury et al. \cite{hld99}) )," + and we sunnmnarze here the most portant results., and we summarize here the most important results. + For very hot white cdwarfs (Zia> 20 000 I. the temperature in the mnernuost parts of the disc exceeds the hydrogen ionization temperature during quiescence: the viscosity is therefore high in these regions. which are thus partially depleted as first sugecstec by Ising (1997)).," For very hot white dwarfs $T_{\rm eff} >$ 20 000 K), the temperature in the innermost parts of the disc exceeds the hydrogen ionization temperature during quiescence; the viscosity is therefore high in these regions, which are thus partially depleted as first suggested by King \cite{k97}) )." + The transition region between the hot iinr dise aud the outer. cool parts is strougly destabilized by irradiation. aud the mocel predicts several sina] outysts )tween major ones.," The transition region between the hot inner disc and the outer, cool parts is strongly destabilized by irradiation, and the model predicts several small outbursts between major ones." +" Tu particular, many reflares are expected at the eud of a large outburst (sce Fig. 2))."," In particular, many reflares are expected at the end of a large outburst (see Fig. \ref{fig:ill_disc}) )." +" In certain cases, the reflares may dominate the ight c1PVC: lis depends on whether the heating froit carreach the outer edge of the disc or not."," In certain cases, the reflares may dominated the light curve; this depends on whether the heating front can reach the outer edge of the disc or not." + The reflares we «obtained do rot have the observed amplitudes but i is tempting to attribute the succession of several normal outbursts after a superoutburst in to this effect., The reflares we obtained do not have the observed amplitudes but it is tempting to attribute the succession of several normal outbursts after a superoutburst in to this effect. + Paviug with ρααλλοτος would produce a result cxrespoudiug better o the observed liehteurve xit the 1er of stich an exercise is rather dubious considering the inportaut τιicertainties of the model itself., Playing with parameters would produce a result corresponding better to the observed lightcurve but the merit of such an exercise is rather dubious considering the important uncertainties of the model itself. + Trracliation of the secondary enlaces mass trauster., Irradiation of the secondary enhances mass transfer. + ο et al. (1997)), Hameury et al. \cite{hlh97}) ) + showed that if one assumes that theeffect of nradiation is given by equation 1)). outbursts having the ecneral characteristics of superouthursts (lone duratious. fat top or expoucutial decay with au abrupt cut-off) are expected.," showed that if one assumes that theeffect of irradiation is given by equation \ref{eq:ill_sec}) ), outbursts having the general characteristics of superoutbursts (long durations, flat top or exponential decay with an abrupt cut-off) are expected." +" This model was, however. applied to a case in which the quiescent mass transfer was low enough for the disc to be stable ou the cool brauch: the iustabilitv was Óuüeeoxκα by au external perturbaion of the mass trauster froiu the secondary."," This model was, however, applied to a case in which the quiescent mass transfer was low enough for the disc to be stable on the cool branch; the instability was triggered by an external perturbation of the mass transfer from the secondary." + This was required to explain the verv lois recurrence times of svstenis such as when standard values of a are assuned., This was required to explain the very long recurrence times of systems such as when standard values of $\alpha$ are assumed. + \Lareiually unstable mass transfer rates as in Warner ct al. (1996)), Marginally unstable mass transfer rates as in Warner et al. \cite{wlt96}) ) + can give similar recurrence nues but also in this case the amount of mass accreteL during tje superoutburst requires a substantial eunliaucccut o dass transfer., can give similar recurrence times but also in this case the amount of mass accreted during the superoutburst requires a substantial enhancement of mass transfer. + Figure 3. shows the ligh curve obtained when one ieludes the secondarv racliatiou n the inodel., Figure \ref{fig:unill_m10} shows the light curve obtained when one includes the secondary irradiation in the model. + We ueelect here disc inraciation axd the «Isc is not truncated., We neglect here disc irradiation and the disc is not truncated. + We have taken > = 0.5. aud a1 other parameters are as in Fie. (1)).," We have taken $\gamma$ = 0.5, and all other parameters are as in Fig. \ref{fig:std}) )," + for à LAL. primary fic. My—3106 es 1.," for a 1 $_\odot$ primary (i.e. $\dot{M}_0 = 3 +\times 10^{16}$ g $^{-1}$ )." + The light curve is similar to those oserved i SU UMa systems: it shows several nornal outmusts separated by a large one which is sustaiue by enhanced mass trausfer from the secoudary., The light curve is similar to those observed in SU UMa systems; it shows several normal outbursts separated by a large one which is sustained by enhanced mass transfer from the secondary. +" Large οιthursts occur when the s1race deusitv at the outer edge of the dise is large enough that a cooling wave does not start muuediatelv after the heating wave has arrived: equivalently. the disc ο nust be Lueer than sole critical value. aud one therefore expects. that he recurrence tine of such large outbursts T, varies rougeily as Mo1 ."," Large outbursts occur when the surface density at the outer edge of the disc is large enough that a cooling wave does not start immediately after the heating wave has arrived; equivalently, the disc mass must be larger than some critical value, and one therefore expects that the recurrence time of such large outbursts $T_{\rm s}$ varies roughly as $\dot{M_0}^{-1}$." +Tus. however. requires that the disc lass keeps increasing despite the preseucὉ of μα] outbursts. which leans that AMyo must be large enough to refill the «Isc with more uass than is lost during such outbursts.," This, however, requires that the disc mass keeps increasing despite the presence of small outbursts, which means that $\dot{M}_0$ must be large enough to refill the disc with more mass than is lost during such outbursts." + For Aly3.10% es Ἐν which is more appropriate for short," For $\dot{M}_0 = 3 \times +10^{15}$ g $^{-1}$ , which is more appropriate for short" +warm medium works on a time-scale of 100 Myr (HY09).,warm medium works on a time-scale of 100 Myr (HY09). +" ISM phase exchange, which occurs on a time-scale of 50-100 Myr, also affects the evolution of grain size distribution (O'Donnell&Mathis 1997)."," ISM phase exchange, which occurs on a time-scale of 50–100 Myr, also affects the evolution of grain size distribution \citep{odonnell97}." +. Such longer-time-scale mechanisms could also have affected the extinction curves (grain size distributions) of those galaxies., Such longer-time-scale mechanisms could also have affected the extinction curves (grain size distributions) of those galaxies. +" The current paper, which focuses on a short-time-scale («10 Myr) grain processing, is a starting point to include other physical processes in future work."," The current paper, which focuses on a short-time-scale $<10$ Myr) grain processing, is a starting point to include other physical processes in future work." +" At z>5, it is usually assumed that the main production source of dust is SNe II whose progenitors have short lifetimes, since the cosmic age is too young for low mass stars to evolve (butetal. 2009)."," At $z>5$, it is usually assumed that the main production source of dust is SNe II whose progenitors have short lifetimes, since the cosmic age is too young for low mass stars to evolve \citep[but see][]{valiante09}." +". Thus, the extinction curves at such high z are often used to test the theory of dust production in SNe II (Maiolinoetal.2004b;Hirashita2005)."," Thus, the extinction curves at such high $z$ are often used to test the theory of dust production in SNe II \citep{maiolino04,hirashita05}." +". As a representative case of observed high-z extinction curve, we discuss the restframe UV extinction curve of ((z= 6.2) obtained by Maiolinoetal.(2004b)."," As a representative case of observed $z$ extinction curve, we discuss the restframe UV extinction curve of $z=6.2$ ) obtained by \citet{maiolino04}." +". In reffig:ext,,v, , weshowtheUV partof theextinctioncurvescalculatediyobuienddWiNhonrtheagiaimsine diktrübstion dj sinethe tiramesr veof 4637."," In \\ref{fig:ext_uv}, we show the UV part of the extinction curves calculated by our models in comparison with the observed UV extinction curve of." +.T'heextinctioncurvesarenormalizedtothevalueatA jum., The extinction curves are normalized to the value at $\lambda =0.3~\micron$ . +" We show the result for ng=1cm?, As discussed in Hirashitaetal.(2008), the initial extinction curve before shattering is too flat to explain the UV rise in the observed extinction curve because small grains are selectively destroyed in SNRs."," We show the result for $\nH =1~\mathrm{cm}^{-3}$, As discussed in \citet{hirashita08}, the initial extinction curve before shattering is too flat to explain the UV rise in the observed extinction curve because small grains are selectively destroyed in SNRs." +" However, after shattering, the extinction curve approaches the observed curve because of the production of small grains."," However, after shattering, the extinction curve approaches the observed curve because of the production of small grains." +" After 10 Myr of shattering, the observed extinction curve is reproduced."," After 10 Myr of shattering, the observed extinction curve is reproduced." +" Not only the slope but also the bump feature at 1/A~4um !, which becomes prominent after shattering3.2), may account for the behaviour of the observed extinction curve around 1/A~ 3.5-4 um"," Not only the slope but also the bump feature at $1/\lambda\sim 4~\micron^{-1}$ , which becomes prominent after shattering, may account for the behaviour of the observed extinction curve around $1/\lambda\sim 3.5$ –4 $\micron^{-1}$." +" In summary, if the metallicity is nearly solar and the age of the current episode of starburst is larger than 5 Myr, we should take the effect of shattering in turbulence into account in comparing the observed extinction curve with the theoretical one even at 5."," In summary, if the metallicity is nearly solar and the age of the current episode of starburst is larger than 5 Myr, we should take the effect of shattering in turbulence into account in comparing the observed extinction curve with the theoretical one even at $z>5$ ." +" Since quasars tend to be found in evolved stellar system whose metallicity could be nearly solar (or more than solar; 2009)), the UV rise of the extinction curve may be caused by the production of small grains by shattering."," Since quasars tend to be found in evolved stellar system whose metallicity could be nearly solar (or more than solar; \citealt{juarez09}) ), the UV rise of the extinction curve may be caused by the production of small grains by shattering." + The dependence of the extinction curve on age and metallicity may also be responsible for the variation of UV slope of the quasar spectra in the sample of Maiolinoetal.(2004a)., The dependence of the extinction curve on age and metallicity may also be responsible for the variation of UV slope of the quasar spectra in the sample of \citet{maiolino04a}. +. We have theoretically investigated the effect of shattering in We have focused on systems in which dust is predominantly produced by SNe II., We have theoretically investigated the effect of shattering in We have focused on systems in which dust is predominantly produced by SNe II. +" Although SNe II tend to eject large (a20.1 jum) grains because of (N07), shattering in WIM supplies small grains on a time-scale of several Myrcase."," Although SNe II tend to eject large $a\ga 0.1~\micron$ ) grains because of (N07), shattering in WIM supplies small grains on a time-scale of several Myr." +" Consequently, the extinction curve is steepened and the features such as the carbon bump around 1/A~4um"" and the Si bump around 1/A~7wm‘ become apparent if the metallicity is solar and the duration of shattering is longer than ~5 Myr."," Consequently, the extinction curve is steepened and the features such as the carbon bump around $1/\lambda\sim 4~\micron^{-1}$ and the Si bump around $1/\lambda\sim 7~\micron^{-1}$ become apparent if the metallicity is solar and the duration of shattering is longer than $\sim 5$ Myr." +" Therefore, when we treat a system in which the metallicity is solar and the star formation age is =5 Myr, we should take into account the effect of shattering in interstellar turbulence."," Therefore, when we treat a system in which the metallicity is solar and the star formation age is $\ga 5$ Myr, we should take into account the effect of shattering in interstellar turbulence." +" In particular, the extinction curves of high-z quasars, whose metallicity is typically (above) solar, may be affected by shattering, and theUV rise of the extinction curve as well as the bump feature at 1/A~ 3.5—4 m7! can be attributed to the small grains produced by shattering."," In particular, the extinction curves of $z$ quasars, whose metallicity is typically (above) solar, may be affected by shattering, and theUV rise of the extinction curve as well as the bump feature at $1/\lambda\sim 3.5$ –4 $\micron^{-1}$ can be attributed to the small grains produced by shattering." +observationss of a new double relic in the galaxy cluster ZwCl 0008.8+5215.,s of a new double relic in the galaxy cluster ZwCl 0008.8+5215. +is described iun a separate paper (1)..,is described in a separate paper \citep{ared}. + Poiut-spread function. (PSF) fitting has been performed in the past. see for example (Anderson& for IIST data. or the IRAE DAOPIIOT package (Stetson1987)..," Point-spread function (PSF) fitting has been performed in the past, see for example \citep{hstpsf} for HST data, or the IRAF DAOPHOT package \citep{irafpsf}." +. The approach taken here is different. deriving relatively simple. analvtical model fictions which describe the observed PSF sufficiently well.," The approach taken here is different, deriving relatively simple, analytical model functions which describe the observed PSF sufficiently well." + At the same time the muuber of free parameters needed for cach nage profile fit is kept to a mininaun by utilizing information fron πα CCD exposures to coustrail sole iuage profile model parameters., At the same time the number of free parameters needed for each image profile fit is kept to a minimum by utilizing information from many CCD exposures to constrain some image profile model parameters. + Challenges here are asvuuuetmne PSFs aud variations of he PSFs over the field of view. combined with a relatively small umber of stars per CCD frame aud the goal of ligh astrometric accuracy.," Challenges here are asymmetric PSFs and variations of the PSFs over the field of view, combined with a relatively small number of stars per CCD frame and the goal of high astrometric accuracy." +" A LOL by 1091 pixel CCD with a 9 sau pixel size was used in a single bandpass (579 to 613 nui) providing a field of view (FOV) of just over l square deerce. taking advantage of ouly a tiny fraction of the flat FOV delivered by the optical system of the Twin Astrograplis ""red lens.”"," A 4094 by 4094 pixel CCD with a 9 $\mu$ m pixel size was used in a single bandpass (579 to 643 nm) providing a field of view (FOV) of just over 1 square degree, taking advantage of only a tiny fraction of the flat FOV delivered by the optical system of the Twin Astrograph's “red lens.”" + This caniera provides bit output aud has a eain setting of 5.65 electrons (e ) per analoe-to-cdigital unit (ADU). 13 read noise. aud about 85.000 full well capacity.," This camera provides 14 bit output and has a gain setting of 5.65 electrons $^{-}$ ) per analog-to-digital unit (ADU), 13 $^{-}$ read noise, and about 85,000 $^{-}$ full well capacity." + A 2-fold overlap pattern of 85.158 fields spans the eutire sk.," A 2-fold overlap pattern of 85,158 fields spans the entire sky." + Each field was observed with a loug (about 125 s) aud a short (about 25 «) exposure., Each field was observed with a long (about 125 s) and a short (about 25 s) exposure. + The raw pixel data are stored in custom FITS differential compress (fde) format files. about 16 MD per exposure without loss of the 11 bit dynamic rauige.," The raw pixel data are stored in custom FITS differential compress (fdc) format files, about 16 MB per exposure without loss of the 14 bit dynamic range." + The detector features a poor charge transfer eficicncy (CTE) leading to asvnunetric nuages along the readout direction (Ge axis) which vary as a function of distance from the output register., The detector features a poor charge transfer efficiency (CTE) leading to asymmetric images along the readout direction $x$ axis) which vary as a function of distance from the output register. +" This leads to systematic errors iu the star positions as a function of « and the sts4 brightuess (μασOoποιο), about the worst thingC» what can happen for au astrometric iustruueut."," This leads to systematic errors in the star positions as a function of $x$ and the stars' brightness (magnitude), about the worst thing what can happen for an astrometric instrument." + The coutour plots iu Fig., The contour plots in Fig. + 1 illustrate this problem showing the chanee of image shape (from almost circular to pronounced asvuunuetric) as seen «i the left and right side of the detector. respectively.," 1 illustrate this problem showing the change of image shape (from almost circular to pronounced asymmetric) as seen on the left and right side of the detector, respectively." + The left side Cow we) is close to the readout register and also displavs the largest background noise ou the chip. likely due to a higher than average temperature there.," The left side (low $x$ ) is close to the readout register and also displays the largest background noise on the chip, likely due to a higher than average temperature there." + Initially the camera showed a 2pplogiug spot in the lower left corner.," Initially the camera showed a “glowing spot"" in the lower left corner." + The desigu was chauged to have the read amplifier powered up oulv when needed. which eliminated that problem.," The design was changed to have the read amplifier powered up only when needed, which eliminated that problem." + Iu order to nütfigate these ο and magnitude depeudeut systematic errors the detector was operated at a relatively high temperature 18C). which fled iuauy of the CTE causing traps on the silicon detector.," In order to mitigate these $x$ and magnitude dependent systematic errors the detector was operated at a relatively high temperature $-18 C$ ), which filled many of the CTE causing traps on the silicon detector." + Uufortuuatelv the warm operating temperature leads to a substautial dark current., Unfortunately the warm operating temperature leads to a substantial dark current. +" Frequent darks were taken throughout the project for each of the standard exposure times (5. LO. 20. 25, 30. 10. 100. 125. 150. 200 s)."," Frequent darks were taken throughout the project for each of the standard exposure times (5, 10, 20, 25, 30, 40, 100, 125, 150, 200 s)." + Some time iuto the project it was discovered that the darks also depend on ambicnt temperature and vacuum pressure inside the camera. which due to sinall leaks increased from about 0.1 tory to over 2 torr. when a new punipout of the camera was performed every few mouths.," Some time into the project it was discovered that the darks also depend on ambient temperature and vacuum pressure inside the camera, which due to small leaks increased from about 0.1 torr to over 2 torr, when a new pumpout of the camera was performed every few months." + The detector used for the UCAC survey has a lieh cosmetic quality with no bad coluuus aud relatively few bad pixels., The detector used for the UCAC survey has a high cosmetic quality with no bad columns and relatively few bad pixels. + Iu order to simplifv the reductions and assuming the worst case. a single list of all possible bad pixels were established spanning dark exposures taken during the cutire project.," In order to simplify the reductions and assuming the worst case, a single list of all possible bad pixels were established spanning dark exposures taken during the entire project." + Early on it was discovered that darks taken diving davtiue or iu rapid succession display differcut properties than object frames taken diving regular observing., Early on it was discovered that darks taken during daytime or in rapid succession display different properties than object frames taken during regular observing. + Most darks therefore were taken during cloudy nights with a script o obtain about 50 darks of a Ooeiven inteerationC» ine in au automated sequence., Most darks therefore were taken during cloudy nights with a script to obtain about 50 darks of a given integration time in an automated sequence. + Pauses of about a nuuute between dark exposures were introduced o closely resemble actual observing conditions., Pauses of about a minute between dark exposures were introduced to closely resemble actual observing conditions. + Using custom software these 50 FITS fles were road in parallel. block by block aud the 50 ueasures of cach pixel sorted.," Using custom software these 50 FITS files were read in parallel, block by block and the 50 measures of each pixel sorted." + The mean pixel value was calculated after rejecting about 10 of the lowest aud highest values., The mean pixel value was calculated after rejecting about 10 of the lowest and highest values. + This wav every few weeks a new combined dark was coustructed or every staudard exposure tine used during that )oriod., This way every few weeks a new combined dark was constructed for every standard exposure time used during that period. + To identify bad pixels comprehensive samples of combined darks of a given exposure tine were, To identify bad pixels comprehensive samples of combined darks of a given exposure time were +disks around main sequence stars as a possible signature of outer planet formation.,disks around main sequence stars as a possible signature of outer planet formation. + Iu this Appendix we evaluate. the total mass of CO present around 2 (Alen) and the corresponding supplving rate (Alea)., In this Appendix we evaluate the total mass of CO present around $\beta\:$ $M_{CO}$ ) and the corresponding supplying rate $\dot{M_{CO}}$ ). + We will see that this can eive an independent clue to the presence of Orbiting-Evaporatiue-Dodies., We will see that this can give an independent clue to the presence of Orbiting-Evaporating-Bodies. + The gaseous part of the ο delisk is detected through the gaseous absorptions superposed on the stellar spectruni., The gaseous part of the $\beta\:$ disk is detected through the gaseous absorptions superposed on the stellar spectrum. + These absorptious are now classified im four differeu groups (see review by Vidal-Madjar oet al., These absorptions are now classified in four different groups (see review by Vidal-Madjar et al. + 1998): the iuterstellar absorption from the local cloud at 10b a stable component at the stellar velocity (21nis +) which is considered as the gaseous counterpart of the dust disk (nevertheless the lik )otwoeen the stable Qus al the ust disk is still not established aud may even not exist): slow and rapid variable absorptious. mainly redshifted. aud well-explaincec bv the so-called Falline-Evaporatine-Boclicsc» (FEBs) which are star-erazineC»c» evaporating comets.," 1998): the interstellar absorption from the local cloud at 10; a stable component at the stellar velocity (21 ) which is considered as the gaseous counterpart of the dust disk (nevertheless the link between the stable gas and the dust disk is still not established and may even not exist); slow and rapid variable absorptions, mainly redshifted, and well-explained by the so-called Falling-Evaporating-Bodies (FEBs) which are star-grazing evaporating comets." + It is thus largelv accepted tha Idlometer-size bodies orbit about ij aid some are subject to evaporation (see also Lecavelier des Etanes e al., It is thus largely accepted that kilometer-size bodies orbit about $\beta\:$ and some are subject to evaporation (see also Lecavelier des Etangs et al. + 1997)., 1997). + Tn the FED scenario. the link between eas ux dust is faint. there is no direct connection between the presence of dust aud iufalliug material.," In the FEB scenario, the link between gas and dust is faint, there is no direct connection between the presence of dust and infalling material." + The dust produce siauultaneousle with the eas by Falliug-Evaporatiug-Dodies on eccentric orbits must be quickly expelled by radiation pressure on hyvperbolie orbits., The dust produced simultaneously with the gas by Falling-Evaporating-Bodies on eccentric orbits must be quickly expelled by radiation pressure on hyperbolic orbits. + It is likely that we are now observing two differcut phenomena which both take place in the .j ssvstem: presence of dust as around the prototypical starVeea.. aud presence of falling eus.," It is likely that we are now observing two different phenomena which both take place in the $\beta\:$ system: presence of dust as around the prototypical star, and presence of falling gas." +ons An important characteristic of the JDPictoris geascous disk is the presence of cold CO aud ((Deleuil ct al 1993. Vidal-Madjar et al.," An important characteristic of the $\beta\:$ gaseous disk is the presence of cold CO and (Deleuil et al 1993, Vidal-Madjar et al." + 1991)., 1994). + Although the CO aud aabsorptiou lines are observed at the stellar velocity as the stable component detected by the absorption lines of single ionized iousn.n.n. ete...}. there is evidence that CO and hhave a special status: - CO is cold with a typical temperature of less than 30 EK which corresponds to the temperature of C'O-evaporation: for instauce. with au albedo of 0.5. this cluperature corresponds to an evaporating body located vetween LOO and 20 AU (Lecavelier des Etaues 1996).," Although the CO and absorption lines are observed at the stellar velocity as the stable component detected by the absorption lines of single ionized ions, etc...), there is evidence that CO and have a special status: - CO is cold with a typical temperature of less than 30 K which corresponds to the temperature of CO-evaporation; for instance, with an albedo of 0.5 this temperature corresponds to an evaporating body located between 100 and 200 AU (Lecavelier des Etangs 1996)." + This temperature is also consistent with the observed -CO/PCO ratio of Ro=2045 (Jolly ct al., This temperature is also consistent with the observed $^{12}$ $^{13}$ CO ratio of $R=20\pm5$ (Jolly et al. + 1998)., 1998). + This temperature is obviously very different from the eniperature of the falling ionized eas: e.g. the triplet lines show that this eas reaches locally very. high cluperature C£;>15000 Tx. Mouillet Laerange 1995). -," This temperature is obviously very different from the temperature of the falling ionized gas: e.g., the triplet lines show that this gas reaches locally very high temperature $T_e> 15\ 000$ K, Mouillet Lagrange 1995). -" + Iu coutrary to the single ionized ious orL also observed iu the diffuse interstellar wmecdimm. CO aud aare destroved by UV interstellar photous aud have lifetime shorter than the star age (fes)~fe~200 vears).," In contrary to the single ionized ions or, also observed in the diffuse interstellar medium, CO and are destroyed by UV interstellar photons and have lifetime shorter than the star age $t_{CO}\sim t_{CI}\sim$ 200 years)." + A permanent replenishment mechanisii must exist. -, A permanent replenishment mechanism must exist. - + With the two arguments eiven above. the supplying rate of CO (and consequently. η) can be roughly estimate: and constrained.," With the two arguments given above, the supplying rate of CO (and consequently, ) can be roughly estimated and constrained." + For this estimate. Ono list assunie a cloud geometry which eives the connection between the observed coliuuu density aud the total CO mass.," For this estimate, one must assume a cloud geometry which gives the connection between the observed column density and the total CO mass." + Assunudue a disk ecometry with an opening anele «ία. to the dust disk (0=73 degrees). aud a characteristic distance eiven by the CO temperature 150450 AU). we eet a mass of CO within a factor of 5. where free is the molecular weight and Neg=22411057 7 is the column deusity of CO.," Assuming a disk geometry with an opening angle similar to the dust disk $\theta=7\pm$ 3 degrees), and a characteristic distance given by the CO temperature $r_0=150\pm50$ AU), we get a mass of CO within a factor of 5, where $\mu_{CO}$ is the molecular weight and $N_{CO}=2\pm 1 \times 10^{15}$ $^{-2}$ is the column density of CO." + Then the known photodissociation rate of CO. Tee=2.10194 + (Van Dishoeck Black. 1985) eives a relation between the total mass and supplying rate.," Then the known photodissociation rate of CO, $\tau_{CO}=2\cdot 10^{-10}$ $^{-1}$ (Van Dishoeck Black, 1988) gives a relation between the total mass and supplying rate." + We obtain We see that CO and pprobablv have a differcut origin than the other observed species and αππαν need oa permancut replenishment mechamisin., We obtain We see that CO and probably have a different origin than the other observed species and anyway need a permanent replenishment mechanism. + The most obvious mechamisiua is certainly the evaporation of cometarv-like bodies., The most obvious mechanism is certainly the evaporation of cometary-like bodies. + In that case. CO is ejectec from the evaporating )odsy. lis then produced through ιο CO dissociation (Vidal-Aladjar et al.," In that case, CO is ejected from the evaporating body, is then produced through the CO dissociation (Vidal-Madjar et al." + 1991. Jolly et al.," 1994, Jolly et al." + 1998)., 1998). + This evaporation can take place in two differeu wavs: - In Solar System. frosted bodies like comets are ejectec on very eccentric orbits inside the evaporatiou zone.," This evaporation can take place in two different ways: - In Solar System, frosted bodies like comets are ejected on very eccentric orbits inside the evaporation zone." + The evaporation is thus very rapid. these comets become exhausted in a few hundred revolutions.," The evaporation is thus very rapid, these comets become exhausted in a few hundred revolutions." + A lot of volatiles are evaporating: CO. but also CO» and TO.," A lot of volatiles are evaporating: CO, but also $_2$ and $_2$ O." +(2007. Eq.,"(2007, Eq." + 7)., 7). + Therefore. if one only considers the self-gravity acceleration. by doing the derivative with respect to z of Eq. (1))," Therefore, if one only considers the self-gravity acceleration, by doing the derivative with respect to $z$ of Eq. \ref{hydro}) )" + and assuming that the gravity is the only accelerationdependent on z. with Eqs. (2))," and assuming that the gravity is the only accelerationdependent on $z$ , with Eqs. \ref{poisson}) )" + and (3)). we get where Ky.=zm. nopKo=TiM.un ," and \ref{gravrad}) ), we get where $K_1=\frac{4\pi G}{\langle v_z^2\rangle}$, $K_2=\frac{GM_{gal}}{R^3\langle v_z^2\rangle}$." +The prime. (). stands for: the derivative with respect to z., The prime (') stands for the derivative with respect to $z$. + The differential equation (4)) may be expressed as an integral., The differential equation \ref{diffeq}) ) may be expressed as an integral. + If we set as a boundary condition that the maximum density ts reached at z=zo (o(zo0)=A. (zo)= 0). we obtain where v=ME. which ts a symmetrical distribution of (5) with respect to zo.," If we set as a boundary condition that the maximum density is reached at $z=z_0$ $\rho (z_0)=A$, $\rho '(z_0)=0$ ), we obtain where $x=\frac{A-\rho }{A}$; which is a symmetrical distribution of $\rho (z)$ with respect to $z_0$." + The half-width-half-maximum (HWHM) ts and the surface density 15 For very thin dises (p very V2K)Axhigh). the ΝΤsecond term on the right-hand side of Eq. (2))," The half-width-half-maximum (HWHM) is and the surface density is For very thin discs $\rho $ very high), the second term on the right-hand side of Eq. \ref{poisson}) )" + is negligible (K>= 0)., is negligible $K_2\approx 0$ ). + The solution to this differential equation with A>=0 is the classical squared hyperbolic secant solution (Spitzer 1942): soa=ΝΑΝΙ/ΣΞΚισ/Η.," The solution to this differential equation with $K_2=0$ is the classical squared hyperbolic secant solution (Spitzer 1942): $\rho (z)=A\ sech^2[a(z-z_0)]$ , $a=\sqrt{A K_1/2}=K_1\sigma /4$." + Since Κι and A> do not depend on 4. it is clear that the width of the disc. HWHM. is independent of ὁ. too. and only depends on the radius. so the self-gravity application does not explain the azimuthal dependence of the scaleheight.," Since $K_1$ and $K_2$ do not depend on $\phi $, it is clear that the width of the disc, HWHM, is independent of $\phi $, too, and only depends on the radius, so the self-gravity application does not explain the azimuthal dependence of the scaleheight." + We propose that the explanation for the variation in the gas disc thickness depending on @ is that the external pressure due to the aceretion of IGM onto the dise depends on 6. because the average flow falls down to the dise with an angle different to 7/2 1n general with respect to the plane (LBB).," We propose that the explanation for the variation in the gas disc thickness depending on $\phi $ is that the external pressure due to the accretion of IGM onto the disc depends on $\phi $, because the average flow falls down to the disc with an angle different to $\pi /2$ in general with respect to the plane (LBB)." + The pressure exerted over the disc would be similar to a piston mechanism. only from one side of the disc (Sánnchez-Salcedo 2006. $4.6).," The pressure exerted over the disc would be similar to a piston mechanism, only from one side of the disc (Sánnchez-Salcedo 2006, 4.6)." + The action is perhaps ram-pressure. due to the friction of clouds against the interstellar medium (Sofue Wakamatsu 1993).," The action is perhaps ram-pressure, due to the friction of clouds against the interstellar medium (Sofue Wakamatsu 1993)." + The vertical acceleration due to this pressure. d=pre. Will depend on z.," The vertical acceleration due to this pressure, $a_{z,pres}$, will depend on $z$." + There is a gradient of force in the vertical direction due the higher absorptior of linear momentum by the first layers of the dise that collide with the accreted gas., There is a gradient of force in the vertical direction due the higher absorption of linear momentum by the first layers of the disc that collide with the accreted gas. + For a very low dense. disc. as is the case of the very outer disc. the absorption of momentum is not total. because part of the gas can cross the disc completely and escape from it.," For a very low dense, disc, as is the case of the very outer disc, the absorption of momentum is not total, because part of the gas can cross the disc completely and escape from it." +" We suppose that the external pressure tis attenuated exponentially along the zaxis Pepμμioe""! where C is a cross-section per unit mass characteristic of the interaction between the accreted flow and the gas dise along the vertical axis."," We suppose that the external pressure is attenuated exponentially along the z-axis $P_{z,ext}(z)=P_{z,ext}(\pm \infty ) +e^{\pm C[\int _{\pm \infty }^z\rho (z)dz]}$, where $C$ is a cross-section per unit mass characteristic of the interaction between the accreted flow and the gas disc along the vertical axis." + Here we do not take into account the effect of the galactic rotation and the variations in the attenuation with different meident angles., Here we do not take into account the effect of the galactic rotation and the variations in the attenuation with different incident angles. + The sign + or - depends on whether the flow comes from z=eo or z=—c., The sign + or - depends on whether the flow comes from $z=\infty $ or $z=-\infty $. + The force per unit volume is -VP-(z)., The force per unit volume is $-\nabla P_z(z)$. +" Hence. where F-=P.,jCkeo) is the vertical component of the external force per unit surface (dS=RdRd&) due to accretion."," Hence, where $F_z\equiv P_{z,ext}(\pm \infty )$ is the vertical component of the external force per unit surface $dS=RdRd\phi$ ) due to accretion." + We do the derivative of Eq. (8)).," We do the derivative of Eq. \ref{azz}) )," + taking the exponential close to one in a low-density disc in the very outer disc [Co small compared to one; indeed. in $4. we will see that τουσ<~101[pptke/m7. which is smaller than one for the expected values of ps (~L077 kg/m?) although not much smaller: but we take this as a rough approximation: Given a continuous inflow of particles with density at infinite distance ps. velocity vo. and angle with respect to the plane ϐµ with azimuth óoof the direction of the inflow (so the flow comes from —4. ὁρ+7%). and Galactic mass within R of M4. the following results hold [from LBB. Eq. (," taking the exponential close to one in a low-density disc in the very outer disc $\frac{1}{2}C\sigma $ small compared to one; indeed, in \ref{.comp} we will see that $\frac{1}{2}C\sigma <\sim 10^{-13} +[\rho _b ({\rm kg/m^3})]^{-1/2}$, which is smaller than one for the expected values of $\rho _b$ $\sim 10^{-25}$ $^3$ ) although not much smaller; but we take this as a rough approximation]: Given a continuous inflow of particles with density at infinite distance $\rho _b$, velocity $v_0$, and angle with respect to the plane $\theta _0$ with azimuth $\phi _0$of the direction of the inflow (so the flow comes from $-\theta _0$, $\phi _0+\pi $ ), and Galactic mass within $R$ of $M_{gal}$, the following results hold [from LBB, Eq. (" +45): applying Eqs. (,45); applying Eqs. ( +28). (33). (34). (38) of the same Figure |. plots F7! with the parameters used by LBB: Mj=2x10! Ms. να=100 km/s. and @& is a free parameter.,"28), (33), (34), (38) of the same Figure \ref{Fig:fz} plots $F_z^{-1}$ with the parameters used by LBB: $M_{gal}=2\times 10^{11}$ $_\odot $, $v_0=100$ km/s, and $\theta _0$ is a free parameter." + F. is ~107! ke/m/s?., $F_z$ is $\sim 10^{-14}$ $^2$. +" We take @)=275°. Qj<0. the corresponding direction of the accreted flow. in order to produce the Galactic S-warp with U-warp southwards (LBB) and maximum of the S-warp at @=957.2757, as observed (Voskes 1999)."," We take $\phi _0=275^\circ $, $\theta _0<0$, the corresponding direction of the accreted flow, in order to produce the Galactic S-warp with U-warp southwards (LBB) and maximum of the S-warp at $\phi =95^\circ, 275^\circ $, as observed (Voskes 1999)." + The dependence is plotted for R=25 kpe and variable @. while other values of R give different amplitudes in the variation. but similar azimuthal dependence.," The dependence is plotted for $R=25$ kpc and variable $\phi $, while other values of $R$ give different amplitudes in the variation, but similar azimuthal dependence." + The amplitude of the variation with the azimuth ts strongly dependent on 4., The amplitude of the variation with the azimuth is strongly dependent on $\theta _0$ . +" Clearly. for any value of 60. the minimum pressure ts for ὁ=do+x95°, and the maximum is for ὁ=do 275°, "," Clearly, for any value of $\theta _0$, the minimum pressure is for $\phi =\phi _0+\pi=95^\circ $, and the maximum is for $\phi = +\phi _0=275^\circ $ ." +Nonetheless. if we took into account the rotation of the galaxy and an external pressure attenuation dependent on this and the incident angle. or the degree of clumpiness of IGM and disc. the difference in the position of the maximum and minimum would not be strictly π. and the shape of Fig.," Nonetheless, if we took into account the rotation of the galaxy and an external pressure attenuation dependent on this and the incident angle, or the degree of clumpiness of IGM and disc, the difference in the position of the maximum and minimum would not be strictly $\pi $ , and the shape of Fig." + | would vary., \ref{Fig:fz} would vary. + If we now consider that the totalacceleration Is ας=dz+ M Eq. CI.," If we now consider that the totalacceleration is $a_z=a_{z,grav}+a_{z,pres}$ in Eq. \ref{hydro}))," + assuming an immediate response of the, assuming an immediate response of the +We attempted to coustrain the mass and radius of the NS roni spectral fits o the observed thermal cussion from he NS surface.,We attempted to constrain the mass and radius of the NS from spectral fits to the observed thermal emission from the NS surface. + ? performed a simular analysis but only with the first of the observations presented here., \citet{0748:zhang10mnras} performed a similar analysis but only with the first of the observations presented here. + They ound that fitting he thermal emission with two cliffercut NS atmosphere models. audnsatmos. viclded simular results.," They found that fitting the thermal emission with two different NS atmosphere models, and, yielded similar results." + Therefore we only used the uodel in our analysis., Therefore we only used the model in our analysis. + By fitting the four observatio sinultaueouslv we were able to reduce significautlv f contours that define the mass and radius of the NS with respect o the anaysis bv ?.., By fitting the four observations simultaneously we were able to reduce significantly the contours that define the mass and radius of the NS with respect to the analysis by \citet{0748:zhang10mnras}. + ? determined an euipiriical deuse matter EoS from a heterogeicons dataset of six NSs., \citet{steiner10apj} determined an empirical dense matter EoS from a heterogeneous dataset of six NSs. + They fouud significant coustralits on the mass-racius relation for NSs. aud lieuce on the uessure-sdeusitv relation of dense matter.," They found significant constraints on the mass-radius relation for NSs, and hence on the pressure-density relation of dense matter." + For cxalple. for NSs where the photospheric radius equals tie NS radis. they ound radi of 11.0 ancl 10.6 kin for NS asses O 1.5 ane 1.5 AL... respectively.," For example, for NSs where the photospheric radius equals the NS radius, they found radii of 11.0 and 10.6 km for NS masses of 1.5 and 1.8 $\Msun$, respectively." +" For NSs where they allowed a photosshevic radius larger than the NS radius. they fouxd radii of 11.8 and |1.6 kin for a NS ass of 1.5 aud 1.5 AL... POSvectively,"," For NSs where they allowed a photospheric radius larger than the NS radius, they found radii of 11.8 and 11.6 km for a NS mass of 1.5 and 1.8 $\Msun$, respectively." + We οtain a mass of 1.78\ and a radius of J3.7 kun for a distance of 7.1 kpc aud M... and 11.5 kan for the ower nut of the distance of 5.9 kpc., We obtain a mass of $\Msun$ and a radius of 13.7 km for a distance of 7.1 kpc and of $\Msun$ and 11.8 km for the lower limit of the distance of 5.9 kpc. + Iuterestiuelv. our solution for a distance of 5.9 k20 ALLCCS VCLV WCJl with the EoS fouid by ? and would iuplv a nieciumeniss NS. in agreenent with the mass derived by comparison with the heaing curves obtained bv ? (see Sect. {1 ))," Interestingly, our solution for a distance of 5.9 kpc agrees very well with the EoS found by \citet{steiner10apj} and would imply a medium-mass NS, in agreement with the mass derived by comparison with the heating curves obtained by \citet{yakovlev04aa} (see Sect. \ref{sec:cooling}) )." + Iu contrast. οςuparing the contours iu Fig.," In contrast, comparing the contours in Fig." + with predictions for the mass to radius relation for represcutative EoSs (e.g.?).. he solution for a distance of TLkος rules out most of the EoSs derived for ai interior of nucleons aud liyperons.," \ref{fig:contours} with predictions for the mass to radius relation for representative EoSs \citep[e.g.][]{lattimer01apj}, the solution for a distance of 7.1 kpc rules out most of the EoSs derived for an interior of nucleons and hyperons." + There aro several factors which can include uncertainties in the calculation of the distance for676., There are several factors which can include uncertainties in the calculation of the distance for. +. Firstly. Hs a hieh-iuclination. dipping source. aud as such there nay be a changing partial obscuration of the NS and its expanding photosphere by the dise diving the radius expansion of the type I bursts (7)..," Firstly, is a high-inclination, dipping source, and as such there may be a changing partial obscuration of the NS and its expanding photosphere by the disc during the radius expansion of the type I bursts \citep{dist:galloway08mnras}." + The ratio of the peak. vast flux to the flux at touchdown (at the moment when the olioosphere “touches down oi to the NS) js expecte ο. crease with increasing radius of the xiotospliere. with respect to low-inclination sources. and hus the distaice could be overestimated.," The ratio of the peak burst flux to the flux at touch-down (at the moment when the photosphere 'touches down' on to the NS) is expected to increase with increasing radius of the photosphere, with respect to low-inclination sources, and thus the distance could be overestimated." + Takine this into account. ? estimated a value for the distance to oof τε 11.2 spe.," Taking this into account, \citet{dist:galloway08mnras} estimated a value for the distance to of $\pm$ 1.2 kpc." + However. the value of the distance could be smaller if the obscuration at the touch-cdow1 flux were still underestimated.," However, the value of the distance could be smaller if the obscuration at the touch-down flux were still underestimated." + We note that in an analysis of all the dipping sources observed by citepionabs:diazOGaa.. sshowed the least iouised atmosphere and a relatively cool plasina was preseut at all phases. indicating that obscuration in this source was larger than iu other dippers.," We note that in an analysis of all the dipping sources observed by \\citep{ionabs:diaz06aa}, showed the least ionised atmosphere and a relatively cool plasma was present at all phases, indicating that obscuration in this source was larger than in other dippers." + This result was confirmed by au analysis of 600 ks of high-resolution RCS spectra of 676(2).., This result was confirmed by an analysis of 600 ks of high-resolution RGS spectra of \citep{0748:vanpeet09aa}. + Secondly. the distance calculations frou type I Nay bursts assume that at touch-down. the plotosprere radius is equal to the NS. radius.," Secondly, the distance calculations from type I X-ray bursts assume that at touch-down, the photosphere radius is equal to the NS radius." + However. 7 argue that a photosphere with a radius lavecr than the NS provides iuterual consistenev di their analvsis aux thus he assumption that the phoospleric radius is equal to the NS radius Is suspect.," However, \citet{steiner10apj} argue that a photosphere with a radius larger than the NS provides internal consistency in their analysis and thus the assumption that the photospheric radius is equal to the NS radius is suspect." + Further uncertaiuties arise You variations oe1 the conposition o© the photosphere. the NS mass or variations iu he typical maxim radius reached cuius tho tv2ο I burst episodes (which affects tje eravitational redshift. and hence t16 observed Eddington ΠοΙσ) (2).," Further uncertainties arise from variations in the composition of the photosphere, the NS mass or variations in the typical maximum radius reached during the type I burst episodes (which affects the gravitational redshift, and hence the observed Eddington luminosity) \citep{dist:galloway08mnras}." + Thereore. we conclude that major uncertaüntv in the current linits oi the mass and radius of aare driven by he uncertainty in the distance estimate.," Therefore, we conclude that major uncertainty in the current limits on the mass and radius of are driven by the uncertainty in the distance estimate." + Aloreover. iu orcer to obtain consistency between the mass obtained rou f16 heating curves aud the spectral fits to the thermal component. the distance to sshould be <6 kyoc.," Moreover, in order to obtain consistency between the mass obtained from the heating curves and the spectral fits to the thermal component, the distance to should be $\approxlt$ 6 kpc." +" Alternatively. a lowfaecium mass NS, albeit wit La bacius of LL15 kan. is possible at ~7 kpe for harder EoS (e.g.T)."," Alternatively, a low/medium mass NS, albeit with a radius of 14–15 km, is possible at $\sim$ 7 kpc for harder EoS \citep[e.g.][]{lattimer07pr}." +" All curreut distance estimates to aare based in the analysis of thermmclear {vpe-I) ταν mrsts (722222),"," All current distance estimates to are based in the analysis of thermonuclear (type-I) X-ray bursts \citep[][]{dist:jonker04mnras,0748:wolff05apj,0748:ozel06nat,dist:galloway08apjs,dist:galloway08mnras}." + This method asses that he peal fiux oy very bright bursts reaches the Ecdington uunositv at je surface of the NS. at which poiut the outward radiation xessure equals or exceeds the eravitational force binding ιο outer lavers of accreter materia to the sar.," This method assumes that the peak flux for very bright bursts reaches the Eddington luminosity at the surface of the NS, at which point the outward radiation pressure equals or exceeds the gravitational force binding the outer layers of accreted material to the star." + Ouce the Eddineton flux is reached. the spectral evoution durus je first seconds shows a uaximuinun in blackbody radius simultaneous with a uaa in coor temperature. while 1e fux remains coustant. indicatiic that the photosphere expands aud the effective eniperature decreases in order ο lnaintalji the ον]τσ” at t1ο Eddington linüt.," Once the Eddington flux is reached, the spectral evolution during the first seconds shows a maximum in blackbody radius simultaneous with a minimum in color temperature, while the flux remains constant, indicating that the photosphere expands and the effective temperature decreases in order to maintain the luminosity at the Eddington limit." + A arge unceratv iu the theoretical Eddington lunuinositv arises frou variatious iu the plhotospheric composition., A large uncertainty in the theoretical Eddington luminosity arises from variations in the photospheric composition. + second large uncertainty arises fro uthe fact that dittereit nusts οκιάüt different peak fluxes., A second large uncertainty arises from the fact that different bursts exhibit different peak fluxes. + These differences ) caused bv variable obscuration (e.g.?7).., These differences may be caused by variable obscuration \citep[e.g.][]{dist:galloway03apj}. + Tf this rue. the uwcertainty will be significantly larger for high-inclination sources. such as676.. for which strong absorption along the line of sight is conunon.," If this is true, the uncertainty will be significantly larger for high-inclination sources, such as, for which strong absorption along the line of sight is common." + Iudeed. ? found that the burst profiles of iiu the soft cucrev band are lighly affected by the presence of a photo-ionised plasina. whose ionisation degree changes larecly bw the strong X-rav nmradiation of the burst.," Indeed, \citet{0748:asai06pasj} found that the burst profiles of in the soft energy band are highly affected by the presence of a photo-ionised plasma, whose ionisation degree changes largely by the strong X-ray irradiation of the burst." + Since absorption along the line of sight reduces the observed flux. bursts with higher fix will be more reliable," Since absorption along the line of sight reduces the observed flux, bursts with higher flux will be more reliable" +presented in Table 1.,presented in Table 1. +" A scanning Fabry-Perot spectrophotometer (the Wisconsin MMapper, known as WHAM) study was conducted by Madsenetal.(2006) with a ddiameter field and a spectral resolution of 12!,, measuring the [O III] 5007A,, Hel 5876A,, 66563A,, [N IT] 6583A,, and [S IT] 6716 llines."," A scanning Fabry-Perot spectrophotometer (the Wisconsin Mapper, known as WHAM) study was conducted by \citet{mad06} with a diameter field and a spectral resolution of 12, measuring the [O III] 5007, HeI 5876, 6563, [N II] 6583, and [S II] 6716 lines." + The ssurface brightness of position 1 was 86.3+0.1 Rayleighs and for position 2 it was 228.140.2 Rayleighs., The surface brightness of position 1 was $\pm$ 0.1 Rayleighs and for position 2 it was $\pm$ 0.2 Rayleighs. + The relative fluxes are given in Table 1., The relative fluxes are given in Table 1. + New spectroscopic observations were made with the Cerro Tololo Interamerican Observatory 1.5 m-telescope operated in cooperation with the SMARTS consortium., New spectroscopic observations were made with the Cerro Tololo Interamerican Observatory 1.5 m-telescope operated in cooperation with the SMARTS consortium. + The instrument was the Boller and Chivens spectrograph., The instrument was the Boller and Chivens spectrograph. + Observations were made on 2008 November 24 with Grating G58 using the Loral 1K CCD detector., Observations were made on 2008 November 24 with Grating G58 using the Loral 1K CCD detector. + A GG395 glass filter was used to prevent second order flux from contaminating the first order flux that was targeted., A GG395 glass filter was used to prevent second order flux from contaminating the first order flux that was targeted. +" One pixel projected 1733 along the llong slit, while the slit width was 27115."," One pixel projected 3 along the long slit, while the slit width was 15." + The measured full width at half maximum intensity of the nebular lines were 6A., The measured full width at half maximum intensity of the nebular lines were 6. +. The CTIO spectrophotometric standard star Feige 15 was observed nine times and the results were used to calibrate the nebular observations into energy units., The CTIO spectrophotometric standard star Feige 15 was observed nine times and the results were used to calibrate the nebular observations into energy units. + The positions of the slit setting is shown in Figure 1 in addition to the position used for determining the background sky brightness., The positions of the slit setting is shown in Figure 1 in addition to the position used for determining the background sky brightness. +" The sample was 6°007 from the Trapezium stars that containC,, the earliest spectral type star in the Orion Belt and Sword region."," The sample was 07 from the Trapezium stars that contain, the earliest spectral type star in the Orion Belt and Sword region." +in mind that ντ»=254. one can see that al a given frequency v different parts of the nanoshot and the neighboring nanoshots are scattered to somewhat different 74. leading to a slight drift of the scattered bands toward higher frequencies. just as is really observed.,"in mind that $\nu\theta^2/2=2\nu_1$, one can see that at a given frequency $\nu$ different parts of the nanoshot and the neighboring nanoshots are scattered to somewhat different $\nu_1$, leading to a slight drift of the scattered bands toward higher frequencies, just as is really observed." + Thus. the peculiar temporal aud Lrequency structure of the eiant IPs can indeed be explained in terms of induced scattering of the giant IPs.," Thus, the peculiar temporal and frequency structure of the giant IPs can indeed be explained in terms of induced scattering of the giant MPs." + The pulsar D1322-09 is known to exhibit a peculiar mode changing behavior: In the bright mode. its profile contains a strong precursor and a weak IP. whereas in the weak mode the IP is strong and the precursor is almost absent (Fowleretal.Giletal. 1994).," The pulsar B1822-09 is known to exhibit a peculiar mode changing behavior: In the bright mode, its profile contains a strong precursor and a weak IP, whereas in the weak mode the IP is strong and the precursor is almost absent \citep{f81,f82,g94}." +. Within the framework of our model. (his can be interpreted as a competition between (he processes of induced scattering of the AIP in the longitudinal and transverse regimes.," Within the framework of our model, this can be interpreted as a competition between the processes of induced scattering of the MP in the longitudinal and transverse regimes." + The variations of the scattering efficiencies can naturally be attributed to the [Iuctuations of the number density of the scattering particles., The variations of the scattering efficiencies can naturally be attributed to the fluctuations of the number density of the scattering particles. + Furthermore. the fhictuations of the plasma umber density lead to changes in the emission altitude of (he MP radiation. which may affect the applicability of the longitudinal scattering regime.," Furthermore, the fluctuations of the plasma number density lead to changes in the emission altitude of the MP radiation, which may affect the applicability of the longitudinal scattering regime." + Larger multiplicities of the plasma. &. imply lareer emission altitucdes for a given frequency. in which case the gvrolrequency appears low enough to preclude the longitudinal scattering even in the vicinitv of the emission region.," Larger multiplicities of the plasma, $\kappa$, imply larger emission altitudes for a given frequency, in which case the gyrofrequency appears low enough to preclude the longitudinal scattering even in the vicinity of the emission region." + At the same time. larger & favor stronger (ransverse scaltering.," At the same time, larger $\kappa$ favor stronger transverse scattering." + As a result. the precursor component is not formed. whereas the intensity transfer to the IP is so efficient that the MP is markedly suppressed.," As a result, the precursor component is not formed, whereas the intensity transfer to the IP is so efficient that the MP is markedly suppressed." + As (he intensity is transferred from higher to lower [requencies. rj=v0?/4. and the radio beam originally has a decreasing spectrum. the IP remains weak as compared to the MP at (he same frequency.," As the intensity is transferred from higher to lower frequencies, $\nu_1=\nu\theta^2/4$, and the radio beam originally has a decreasing spectrum, the IP remains weak as compared to the MP at the same frequency." + Thus. (he weak mode is characterized by larger plasma multiplicities and. correspondingly. by an efficient intensity transfer [rom higher to lower Ireeuencies. in which case (he total intensity of the pulse profile markedly decreases.," Thus, the weak mode is characterized by larger plasma multiplicities and, correspondingly, by an efficient intensity transfer from higher to lower frequencies, in which case the total intensity of the pulse profile markedly decreases." + In the bright mode. the plasma number density. is smaller. (he emission altitude lower. and the longitudinal scattering holds in addition to the transverse one.," In the bright mode, the plasma number density is smaller, the emission altitude lower, and the longitudinal scattering holds in addition to the transverse one." + The longitudinal scaltering gives rise to the precursor in the pulse profile. whereas the transverse scattering. being less efficient. because of lower &. forms a weaker IP.," The longitudinal scattering gives rise to the precursor in the pulse profile, whereas the transverse scattering, being less efficient because of lower $\kappa$, forms a weaker IP." +" As is evident from equation (14). the (ransverse scattering may be much more efficient in taking the intensitv [rom the AIP at a given frequency,"," As is evident from equation (14), the transverse scattering may be much more efficient in taking the intensity from the MP at a given frequency." + At the seme time. if one compare the intensity growth of the precursor and the IP at a given lrequency. it is necessary {ο keep in münd (hat these components are fed by the AIP intensity at substantially different. Irecquencies. pn=p>?>v and ↗∣∕⊬⋟∕∕∕∔≪↗∣∕⋅∖∖↕⊔↥⊔∐↲≼⇂≼↲≺∢↕⋅≼↲≀↧↪∖⊽∐↥≸≟⋟∖⊽↕↽≻≼↲≺∢∏⋅∏∐↓∪↓↕↽≻∏↥⋟∖⊽≀↧↴↕⋅," At the same time, if one compare the intensity growth of the precursor and the IP at a given frequency, it is necessary to keep in mind that these components are fed by the MP intensity at substantially different frequencies, $\nu_1^{(\rm Pr)}=\nu\theta^2\gamma^2\gg\nu$ and $\nu_1^{(\rm +IP)}=\nu\theta^2/4\ll\nu$." +↕⋅≀↧↴≼∐≀↧↴⊔∪∐⋅⊔∐⋟∖⊽∐∐↕↽≻∐≼↲⋟∖⊽∐↓∏≺∢∐↥≀↕↴↕⋅≸↽↔↴≼↲↕⋅(LP)9 . ⋅ ⋅⋅ ⋅⋅ ⋅↗∣∕↓∶," With the decreasing spectrum of pulsar radiation, this implies much larger" +is ils summation.,is its summation. +" Since the NPS defined in Eq.(2)) can be either positive or negative. we look instead at ils root mean square ""E)."," Since the XPS defined in \ref{prac}) ) can be either positive or negative, we look instead at its root mean square $\sqrt{ \langle (\xl^{jj'})^2 \rangle}$." + Due to equal partiution on both perpendicular directions of complex plane. it can be written: the right hand side of which is closely related (o a two-dimensional random walk.," Due to equal partiution on both perpendicular directions of complex plane, it can be written: the right hand side of which is closely related to a two-dimensional random walk." + Random walk statistics is emploved as a Gaussianitw test on CMD (Naselskyet&Coles 2005).," Random walk statistics is employed as a Gaussianity test on CMB \citep{naselsky,coles}." +". Recall that the celebrated Pearson's random walk is a 2D isotropic random walk withequal step-length. expressed in the complex plane r=7,|d;|exp(o;) where ια=d."," Recall that the celebrated Pearson's random walk is a 2D isotropic random walk with step-length, expressed in the complex plane ${\bi r}=\sum_k |{\bi d}_k| \exp(i\phi_k)$ where $|{\bi d}_k|=d$." + The pdf of the resultant displacement +=|r| after (steps has the form from which (72)=(P., The pdf of the resultant displacement $r\equiv |{\bi r}|$ after $\l$ steps has the form from which $\langle r^2\rangle=\l d^2$. + Pearson's walk can be generalized to unequal step-length and it can be shown (Pearson1905;Ravleieh1905) Chat when (£15 large and (he mean-square step length is known: (0)!Yld;? mo. the pdf lor the displacement has the same form as Eq.(5)) (Ilughes.1995)..," Pearson's walk can be generalized to unequal step-length and it can be shown \citep{pearson,rayleigh} that when $\l$ is large and the mean-square step length is known: $(\l)^{-1}\sum^\l |{\bi d}_k|^2=d^2$ , the pdf for the displacement has the same form as \ref{pearson}) ) \citep{hughes}." +" For unequal step length |d;=[emερ the ensembled-average square step length is then (Jou4|?JL,I)=JiJI. so the mean square displacement of the spectrum)/.∙- −⋅ ↕⋅≼↲⊳∖"," For unequal step length $|{\bi d}_k|=|j_\lm||j'_\lm|$, the ensembled-average square step length is then $ \langle |j_\lm|^2|j'_\lm|^2 \rangle =J_\l J'_\l$, so the mean square displacement of the random walk $\langle| \sum_{m=-\l}^\l |j_\lm||j'_\lm| \exp(i \Delta \phi_\lm)|^2\rangle = (2\l+1)J_\l J'_\l $." +⊽∏∐∖∖↽≼↲∪↕∐⋡∖↽≀↧↪∖⊽⊳∖⊽∏∐∐↲⋮∫⋮≀↧↴∐≺⇂⋮∫⋮∣≀↧↴↕⋅≼↲∁≀↧↴∏⊳∖⋱∖⊽↕≀↧↴∐⋅⊳∖⇁∪⊔∐↲∡∖↽≺∢≀↧↴∐∣↽≻≼↲≼↲↕⊔∐↲↕⋅∖∖⊽∐∐≼↲∐∪↕⊳∖⇁≼↲≼⋝∖∖↽↕⊔↥∐≀↧↴↥ power or others whose power spectrum has scale dependence.," Note that in driving the result we only assume $j$ and $j'$ are Gaussian, so they can be either white noise (with flat power spectrum) or others whose power spectrum has scale dependence." +" Ii any case. we can wrile The decreasing of the ""junk"" is inversely. proportional to the square root of the number of random walk. and it can be further decreased by L/V/LN with binning L=Af multipole nunmbers and averaging from .V sets of APS."," In any case, we can write The decreasing of the “junk” is inversely proportional to the square root of the number of random walk, and it can be further decreased by $1/\sqrt{LN}$ with binning $L\equiv \Delta \l$ multipole numbers and averaging from $N$ sets of XPS." + We demonstrate Eq.(6)) in Fig.l by plotting Ay trom two white-noise maps., We demonstrate \ref{result}) ) in \ref{demo} by plotting $X_\l$ from two white-noise maps. + One can see the the decreasing of the power specirum proportional to (2J+1/2)1, One can see the the decreasing of the power spectrum proportional to $(2\sqrt{\l+1/2})^{-1}$. + Note that X; is jumping either postively or negatively and onlv positive points are plotted., Note that $X_\l$ is jumping either postively or negatively and only positive points are plotted. + Knowing the residual of the junk from APS. we can estimate ils capability in extracting CAMB.," Knowing the residual of the junk from XPS, we can estimate its capability in extracting CMB." +" In crossing NV pairs of maps containing CMD with the same noise level. we assume the CAMB power spectrum is C,eAC7? and the instrument noise level isNV,=2A where"," In crossing $N$ pairs of maps containing CMB with the same noise level, we assume the CMB power spectrum is $C_\l \simeq A\l^{-2}$ and the instrument noise level is$N_\l=RA$ where" +This work was partially supported by the project Pronex/FINEP (No.,This work was partially supported by the project Pronex/FINEP (No. + 41.96.0008.00) and Conselho Nacional de Desenvolvimento Científlico ο Teenológeico - CNPq (Brazilian Research Agency)., 41.96.0908.00) and Conselho Nacional de Desenvolvimento fico e Tecnológgico - CNPq (Brazilian Research Agency). +"where Τ parameterizes the ""shape"" of (he power spectrum and the overall normalization is determined by σε. the standard deviation of density f[Iuctuations on a scale of 8h! Mpe.","where $\Gamma$ parameterizes the “shape” of the power spectrum and the overall normalization is determined by $\sigma_8$, the standard deviation of density fluctuations on a scale of $8h^{-1}$ Mpc." + The constant C is determined via the direct relation between ox and the power spectrum., The constant $C$ is determined via the direct relation between $\sigma_8$ and the power spectrum. +" For models where the total density parameter Q=1. (he shape parameter is related to the density of matter. [=Q,,f: however. we typically choose to ignore this relationship ancl (reat D' as a free parameter which we vary independently."," For models where the total density parameter $\Omega=1$, the shape parameter is related to the density of matter, $\Gamma = \Omega_m h$; however, we typically choose to ignore this relationship and treat $\Gamma$ as a free parameter which we vary independently." +" Since we are interested in reducing the sensitivity of the data (o the [ull range of nonlinear scales. we take /2,(/) to be constant in the range of interest. 2,;(4)=2, lor hy;ckck"," Since we are interested in reducing the sensitivity of the data to the full range of nonlinear scales, we take $P_{nl}(k)$ to be constant in the range of interest, $P_{nl}(k)= P_{o}$ for $k_{nl}$ 2, separated by the redshift desert within which ground-based surveys cannot effectively obtain redshifts due to the lack of galaxies emitting in the optical wavelengths." +" “Phe terminology. ‘low’ and ""high! has is meaning throughout.", The terminology `low' and `high' has this meaning throughout. + The survey parameters are limited by some constraints. listed. in. Table 2..," The survey parameters are limited by some constraints, listed in Table \ref{constraintparameters}." + These are the same as in POT. with re exception of the limits on the redshift. bins. (auia. tax). which have been relaxed as we now include a more reasonable mocel of the efficiency/response of the WIEMOS spectrograph to light at dillerent wavelengths.," These are the same as in P07, with the exception of the limits on the redshift bins $z_{\rm min}$, $z_{\rm max}$ ), which have been relaxed as we now include a more reasonable model of the efficiency/response of the WFMOS spectrograph to light at different wavelengths." + The details of us wavelength throughput are not public. but can be taken to be very similar to that of the Sloan Digital Sky Survey (SDSS) Having established the details of the survey. we compute the total number of galaxies that will be measured.," The details of this wavelength throughput are not public, but can be taken to be very similar to that of the Sloan Digital Sky Survey (SDSS) Having established the details of the survey, we compute the total number of galaxies that will be measured." + Me asstune a pre-existing source catalogue of photometrically selected. galaxies. from. which we can ellectively target," We assume a pre-existing source catalogue of photometrically selected galaxies, from which we can effectively target" +he luminosity distance (See Appendix A).,the luminosity distance (See Appendix A). +" The accuracy of this relation is inportaut to quantity 55 opacity constraints (Litlwick&Savi2001:Der-ner2OOL) applied o GRD pulses as measured with the CRB monitor aux Larec Arca Detector ouGLAST"". as well as O lnake estimates of yhotomeson production iu GRB blast Waves (Waxinau&Balicall1997)."," The accuracy of this relation is important to quantify $\gamma\gamma$ opacity constraints \citep{ls01,der04} applied to GRB pulses as measured with the GRB monitor and Large Area Detector on, as well as to make estimates of photomeson production in GRB blast waves \citep{wb97}." +". Tf curvature effects donunate the late-time cluission in GRD pulses. then a unique relation is found whereby the value of the r£, peak fux f.,(u ces units of eres ? 1) at peak photon cucrey εν, decays iu proportion to κ6e"," If curvature effects dominate the late-time emission in GRB pulses, then a unique relation is found whereby the value of the $\nu F_\nu$ peak flux $f_{\epk}$ (in cgs units of ergs $^{-2}$ $^{-1}$ ) at peak photon energy $\e_{pk}$ decays in proportion to $\propto\e_{pk}^3$." +" This relation is geucrallv uot observed in long. sinoothi CRB pulses studied bx Borgonovo&Ryde (2001).. who fud power-law decayvs f,XED. with 0.G5¢=<-3."," This relation is generally not observed in long, smooth GRB pulses studied by \citet{br01}, who find power-law decays $f_{\epk}\propto \epk^\zeta$, with $0.6 \lesssim +\zeta \lesssim 3$." + Remarkably. values of ¢ MELfor different pulses within the same GRB are confined to a rather narrow band of values.," Remarkably, values of $\zeta$ for different pulses within the same GRB are confined to a rather narrow band of values." + The wide range of values of ¢ are found not ouly in imulti-peakec GRBs. but also iu single-peaked GRBs that displav smooth fast-rise. slow-decaylight curves (Boreonovo&Ryde2001:Pet-rosiau 2002).," The wide range of values of $\zeta$ are found not only in multi-peaked GRBs, but also in single-peaked GRBs that display smooth fast-rise, slow-decaylight curves \citep{br01,rp02}." +. The inooth sinele peak CRBs could arise from curvature effects (Fenimore.Madras.Navakshin 1996).. or to external shocks (Derier.Bottcher.&Chiang 1999).," The smooth single peak GRBs could arise from curvature effects \citep{fmn96}, or to external shocks \citep{dbc99}." +. For GRB pulses that could be produced by spherically svunuetric shell collisions. discrepancy with observations sugecst a vreakdown of our assuniptions.," For GRB pulses that could be produced by spherically symmetric shell collisions, discrepancy with observations suggest a breakdown of our assumptions." + Iu the next section. the kinematic model is oxesented.," In the next section, the kinematic model is presented." + Calculations based on this model are oesented in Section 3., Calculations based on this model are presented in Section 3. + Iu Section L. we discuss the vossibility that radiative-cooliug effects produce he power-law relation. nuplviug a prediction hat can be tested withSwift?.," In Section 4, we discuss the possibility that radiative-cooling effects produce the power-law relation, implying a prediction that can be tested with." +. Alternately. the uniforiii spherical shell assuniptiou could break down. or the basic model of colliding shells could ο in error.," Alternately, the uniform spherical shell assumption could break down, or the basic model of colliding shells could be in error." +" The Appendices give derivations of siuple. widely-used approximations related to his study. a derivation of the curvature relation ""S as well as anu analytic form for the ine-depenudenut2 pulse profile. leadiug to a simple expression for the lieht curve of a pulse in the curvature limit."," The Appendices give derivations of simple, widely-used approximations related to this study, a derivation of the curvature relation $f_{\epk} \propto \e_{pk}^3$, as well as an analytic form for the time-dependent pulse profile, leading to a simple expression for the light curve of a pulse in the curvature limit." + A brief sunuuary is given iu Section 5., A brief summary is given in Section 5. + A simple kinematic model for the received flux from the illumination of a spherically svunuetric shell resulting from shell collisious is studied., A simple kinematic model for the received flux from the illumination of a spherically symmetric shell resulting from shell collisions is studied. + A shell with finite width is assmmed to be uuiforuilv ilunünated throughout its volume for a fixed duration during which the shell travels with constant speed from he explosion ceuter., A shell with finite width is assumed to be uniformly illuminated throughout its volume for a fixed duration during which the shell travels with constant speed from the explosion center. + Light-travel time aud Doppler effects are treated without regard to details of the cnereization aud cooling of the radiating particles., Light-travel time and Doppler effects are treated without regard to details of the energization and cooling of the radiating particles. + This approach gives kinematic expectations of curvature effects in a GRB colliding shell svsteu., This approach gives kinematic expectations of curvature effects in a GRB colliding shell system. +" The vF,, flux uneasured at dimensionless photou energy e=hrfimeD and timeH f isH given- by where primes refer to comoving quautities. the integration is over volume in the stationary (explosion) fraane. the Doppler factor peVl{η ια, LD)e/Ó (κου απο.Piran.&Sari(1999).. noting the correction of a (1|D) factor in the relation between the enütted and received plotou frequencies)."," The $\nu F_\nu$ flux measured at dimensionless photon energy $\e = +h\nu/m_ec^2$ and time $t$ is given by where primes refer to comoving quantities, the integration is over volume in the stationary (explosion) frame, the Doppler factor $\beta = \sqrt{1-1/\Gamma^{2}}$ , and $\ep= (1+z)\e/\delta$ (see \citet{gps99}, noting the correction of a $(1+z)$ factor in the relation between the emitted and received photon frequencies)." +" The chussivity ειν0.))=dEAVedtd.de3?(e. OY. where Q=O, is the directional vector Ceo). pl=duyAju). and οὐo."," The emissivity $j_*(\e_*,\Omega_* ) = dE_*/dV_*dt_*d\Omega_* d\e_* = +\delta^2 j^\prime(\e^\prime,\Omega^\prime)$ , where $\Omega=\Omega_*$ is the directional vector $(\mu,\phi)$, $\mu^\prime = +(\mu-\beta)/(1-\beta\mu)$, and $\phi^\prime = \phi$." + We use a notation where asterisks refer to quantities iu the stationary frame (though we have cropped asterisks for the spatial variables + aud O). and unuscripted quautities refer to the observer frame.," We use a notation where asterisks refer to quantities in the stationary frame (though we have dropped asterisks for the spatial variables $r$ and $\Omega$ ), and unscripted quantities refer to the observer frame." + The blast wave is assumed to enit isotropically in the comoving frame. which could apply to svuchrotron aud svuchrotron sclfCompton processes with raudomly-orcdered magnetic fields aud electron pitel-anele distributions. but not to external Compton processes.," The blast wave is assumed to emit isotropically in the comoving frame, which could apply to synchrotron and synchrotron self-Compton processes with randomly-ordered magnetic fields and electron pitch-angle distributions, but not to external Compton processes." + Moreover. the observer is asstuued to belocated along the azimuthal svuuuetry axis of the jet. or is viewing a uniform jet with opening angle 0;ον 1/T.," Moreover, the observer is assumed to belocated along the azimuthal symmetry axis of the jet, or is viewing a uniform jet with opening angle $\theta_j +\gg 1/\Gamma$ ." + Theretore, Therefore +Using the integrated magnitudes computed from individual photometry of cluster members available in theASCC-2.5.. we found that the sample of 648 clusters drawn from this catalogue is complete for apparent integrated magnitudes brighter than 8 mag. with 440 clusters above this completeness limit.,"Using the integrated magnitudes computed from individual photometry of cluster members available in the, we found that the sample of 648 clusters drawn from this catalogue is complete for apparent integrated magnitudes brighter than 8 mag, with 440 clusters above this completeness limit." + The corresponding completeness distances depending on the brightness of clusters are typically between | and 3 kpe. although some prominent clusters can be seen up to distances of 10 kpe and more.," The corresponding completeness distances depending on the brightness of clusters are typically between 1 and 3 kpc, although some prominent clusters can be seen up to distances of 10 kpc and more." +" The CPDLF constructed on the basis of the complete sample is observed in the range of yy,=|-10.—0.5| mag. Le. about 5 magnitudes deeper than observable in nearby galaxies."," The CPDLF constructed on the basis of the complete sample is observed in the range of $I_{M_V}= [-10,\,-0.5]$ mag, i.e. about 5 magnitudes deeper than observable in nearby galaxies." +" It increases from the brightest limit to a turnover at about Ty,9—2.5 and slowly falls down towards fainter magnitudes.", It increases from the brightest limit to a turnover at about $I_{M_V}\approx-2.5$ and slowly falls down towards fainter magnitudes. + We consider the turnover to be a real feature reflecting the behaviour of Galactic open clusters., We consider the turnover to be a real feature reflecting the behaviour of Galactic open clusters. + At magnitudes brighter than the turnover position. the CPDLF is linear with a slope ¢=40.01 (ora=2.02+ 0.02). which is in perfect agreement with the observed slopes of cluster luminosity functions in nearby spiral galaxies. although these show a higher star formation activity.," At magnitudes brighter than the turnover position, the CPDLF is linear with a slope $a=0.41\pm0.01$ (or $\alpha=2.02\pm0.02$ ), which is in perfect agreement with the observed slopes of cluster luminosity functions in nearby spiral galaxies, although these show a higher star formation activity." + The masses of Galactic open clusters cover a range from several tens to hundreds of thousands of solar masses., The masses of Galactic open clusters cover a range from several tens to hundreds of thousands of solar masses. + The CPDMF mimics the general behaviour of the CPDLF: it shows a linear part at high masses (logM.> 2.5). a broad maximum between logM.=1.5 and 2.5. and a slow decline towards lower masses.," The CPDMF mimics the general behaviour of the CPDLF: it shows a linear part at high masses $\log M_c > 2.5$ ), a broad maximum between $\log M_c=1.5$ and 2.5, and a slow decline towards lower masses." + In spite of the present-day observations only allowing for a comparison of the CPDMF data of extragalactic open clusters drawn from model mass-luminosity relations. the agreement with published values is impressive.," In spite of the present-day observations only allowing for a comparison of the CPDMF data of extragalactic open clusters drawn from model mass-luminosity relations, the agreement with published values is impressive." + We find that for logM.>2.5 the CPDMF ean by fitted with high confidence by a power law with a slope y=1.01+0.04., We find that for $\log M_c >2.5$ the CPDMF can by fitted with high confidence by a power law with a slope $\chi=1.01\pm0.04$. + We regard the observed coincidence of cluster mass function parameters derived for the Galactic and extragalactic clusters with different methods as indirect evidence that both methods of estimating cluster masses are calibrated consistently and give correct and reliable results., We regard the observed coincidence of cluster mass function parameters derived for the Galactic and extragalactic clusters with different methods as indirect evidence that both methods of estimating cluster masses are calibrated consistently and give correct and reliable results. + Inspection of cluster samples with different upper limits for age indicates that cluster mass spectra change with time., Inspection of cluster samples with different upper limits for age indicates that cluster mass spectra change with time. + At every age the cluster mass function keeps the basic features of the CPDMF. r.e.. a quasi-linear high-mass portion. and a non-linear portion at lower masses.," At every age the cluster mass function keeps the basic features of the CPDMF, i.e., a quasi-linear high-mass portion, and a non-linear portion at lower masses." + With time. the slope of the linear portion increases from y=0.66+0.14 at logs<6.9 to y=1.13£0.08 at logr< 8.5.," With time, the slope of the linear portion increases from $\chi=0.66\pm0.14$ at $\log t\leqslant6.9$ to $\chi=1.13\pm0.08$ at $\log t\leqslant8.5$ ." + Then the steepening of the CPDMF slows down and arrives at y=1.17+0.07 for logr€ 9.5., Then the steepening of the CPDMF slows down and arrives at $\chi=1.17\pm0.07$ for $\log t\leqslant9.5$ . + The low-mass portion changes from an approximately flat distribution at logr=6.9 to a clearly non-linear behaviour displaying a broad maximum with a peak at about 100 M..., The low-mass portion changes from an approximately flat distribution at $\log t=6.9$ to a clearly non-linear behaviour displaying a broad maximum with a peak at about 100 $M_\odot$. + We construct the CIMF from the data of a subsample of the 49 youngest clusters with logr€6.9.," We construct the CIMF from the data of a subsample of the 49 youngest clusters with $\log t +\leqslant6.9$." + The CIMF has a segmented structure with two power-law segments: the power-law slopes are «=1.66+0.14 for logM.=3.37...4.93 and a=0.82+0.14 for logM.=1.7...3.37., The CIMF has a segmented structure with two power-law segments: the power-law slopes are $\alpha=1.66\pm0.14$ for $\log M_c=3.37\dots4.93$ and $\alpha=0.82\pm0.14$ for $\log M_c=1.7\dots3.37$. + The luminosity function of open clusters does not show the same systematic steepening with age as does the mass function., The luminosity function of open clusters does not show the same systematic steepening with age as does the mass function. + It evolves via parallel-shifting along the ordinate without changing the slope., It evolves via parallel-shifting along the ordinate without changing the slope. + Only the faintest segment of the CLF seems to depend on age and spreads towards the fainter magnitudes with age., Only the faintest segment of the CLF seems to depend on age and spreads towards the fainter magnitudes with age. + The weak dependence on age and the presence of a mixture of clusters with different masses in every magnitude bin makes it difficult to determine the CIMF from the CLF., The weak dependence on age and the presence of a mixture of clusters with different masses in every magnitude bin makes it difficult to determine the CIMF from the CLF. +" When comparing the average mass of the newly formed. youngest clusters —OMIM,mod-5.10:M. with. the average cluster mass from. the whole sample (M,P.q for the dense gas and toward P«Poq for distributions centered at typical densities of the warm and the unstable gas."," In particular, the mean pressure in a given density interval drifts away from the thermal equilibrium value $P_{\rm eq}$ as $M$ is increased, moving toward $P > P_{\rm eq}$ for the dense gas and toward $P < P_{\rm eq}$ for distributions centered at typical densities of the warm and the unstable gas." + Flatter spectra in high M simulations could thus be produced by the weakening of pressure forces in diffuse gas., Flatter spectra in high $M$ simulations could thus be produced by the weakening of pressure forces in diffuse gas. +" In the simulations presented here there are then three physical ingredients contributing to the flattening of the density power spectrum: density fluctuations produced by turbulence, density fluctuations produced by TI, and ’enhanced’ density fluctuations produced by the interactions between turbulence and TI."," In the simulations presented here there are then three physical ingredients contributing to the flattening of the density power spectrum: density fluctuations produced by turbulence, density fluctuations produced by TI, and 'enhanced' density fluctuations produced by the interactions between turbulence and TI." +" Direct comparison of the spectral indexes we obtain for P, with observations of the density power spectrum show that they only agree with values reported by Deshpande et al. (", Direct comparison of the spectral indexes we obtain for $P_{\rho}$ with observations of the density power spectrum show that they only agree with values reported by Deshpande et al. ( +2000) and with those obtained by Dutta et al. (,2000) and with those obtained by Dutta et al. ( +2009) for nearby dwarf galaxies.,2009) for nearby dwarf galaxies. + We recall that values in Table 4 should be multiplied by a factor k? in order to be comparable with observational data (see 8??))., We recall that values in Table \ref{tab:indices} should be multiplied by a factor $k^{-2}$ in order to be comparable with observational data (see \ref{sec:esp_notation}) ). + Note that Dutta et al. (, Note that Dutta et al. ( +"2009) find that, for all the galaxies in their sample, the power-law slope remains constant as the channel thickness is increased, suggesting that the fluctuations in the HI intensity are only due to density fluctuations, or that the slope of the velocity structure function is =0.","2009) find that, for all the galaxies in their sample, the power-law slope remains constant as the channel thickness is increased, suggesting that the fluctuations in the HI intensity are only due to density fluctuations, or that the slope of the velocity structure function is $\approx 0$." +" Theoretical predictions by Lazarian and Pogosyan (2000) can be used to further compare our results with observational results, in particular with works reporting only spectral slopes from individual channel maps or averaged values over distinct velocity channels."," Theoretical predictions by Lazarian and Pogosyan (2000) can be used to further compare our results with observational results, in particular with works reporting only spectral slopes from individual channel maps or averaged values over distinct velocity channels." + The VCA method consists on gradually increase the velocity thickness of the sampling region until the slope of the observed two dimensional spectrum gets stabilized., The VCA method consists on gradually increase the velocity thickness of the sampling region until the slope of the observed two dimensional spectrum gets stabilized. +" For the thickest slices, the velocity information is averaged out and the power-law index of the"," For the thickest slices, the velocity information is averaged out and the power-law index of the" +"with Santosetal.(2008) at z—10, but at the lower redshift in Figure 3 the simulated Ag; is flat over a wider range of k than the theoretical one is, and they typically differ by ~30%.","with \citet{santos} at $z=10$, but at the lower redshift in Figure \ref{f:test3} the simulated $\Delta_{21}$ is flat over a wider range of $k$ than the theoretical one is, and they typically differ by $\sim 30\%$." +" In the comparison, in order to try to match the assumptions in the simulations as closely as possible, in the first two comparisons we assumed in the model that the ionizing emission rate from each halo is proportional to its mass."," In the comparison, in order to try to match the assumptions in the simulations as closely as possible, in the first two comparisons we assumed in the model that the ionizing emission rate from each halo is proportional to its mass." +" In test #33, we instead assumed that the emission rate is proportional to the gas infall rate into each halo; this is a more natural assumption within the context of the analytical model, and we use it in all of our model calculations below."," In test 3, we instead assumed that the emission rate is proportional to the gas infall rate into each halo; this is a more natural assumption within the context of the analytical model, and we use it in all of our model calculations below." +" In any case, the difference between these two assumptions has a minor effect on the 21-cm power spectrum (for a fixed value of z)."," In any case, the difference between these two assumptions has a minor effect on the 21-cm power spectrum (for a fixed value of $\bar{x}^i$ )." +" We note that while the analytical model accounts for the restriction of z to a value of 0 or 1, and includes a complex dependence of x’ on 6, it neglects the non-linear growth of 6."," We note that while the analytical model accounts for the restriction of $x^i$ to a value of 0 or 1, and includes a complex dependence of $x^i$ on $\del$, it neglects the non-linear growth of $\del$." + The latter becomes important only on smaller scales than those accessible to the first-generation 21-cm experiments., The latter becomes important only on smaller scales than those accessible to the first-generation 21-cm experiments. +" For example, k~1h/Mpc corresponds to a scale R~9 comoving Mpc, which at redshift 8 has a root-mean-square fluctuation of 0.14 (on an observed angular scale of 3’)."," For example, $k \sim 1 h/Mpc$ corresponds to a scale $R \sim 9$ comoving Mpc, which at redshift 8 has a root-mean-square fluctuation of 0.14 (on an observed angular scale of $3^\prime$ )." +" Also, the model does not include the small gas fraction in leftover neutral clumps within the ionized bubbles, which is important towards the end of reionization."," Also, the model does not include the small gas fraction in leftover neutral clumps within the ionized bubbles, which is important towards the end of reionization." +" The simulations do include some of the leftover neutral gas, but the limited resolution limits the ability to accurately track these small-scale, non-linear clumps."," The simulations do include some of the leftover neutral gas, but the limited resolution limits the ability to accurately track these small-scale, non-linear clumps." + From these comparisons we can conclude that the analytical model generally captures the evolution of the 21-cm power spectrum during reionization as seen in the simulations., From these comparisons we can conclude that the analytical model generally captures the evolution of the 21-cm power spectrum during reionization as seen in the simulations. +" It is difficult to make a more quantitative assessment, since the varying results in the comparison to the different simulations suggest that the simulations"," It is difficult to make a more quantitative assessment, since the varying results in the comparison to the different simulations suggest that the simulations" +proposed. for the purposes of estimating Ny. using the value of A that minimized where Ni is an estimate of Ny from a bootstrap resampling of (he original data.,"proposed, for the purposes of estimating $N_T$, using the value of $h$ that minimized where $\hat{N}_T^*$ is an estimate of $N_T$ from a bootstrap resampling of the original data." + Unfortunately. we found. as Tremblay&Merritt(1995). did. that DMISE(() returns badly oversmoothed estimates of Ny.," Unfortunately, we found, as \citet{tm95} did, that ${\rm BMISE} (h)$ returns badly oversmoothed estimates of $N_T$." + Thus. we fell back on using our subjective impressions of the smoothness of Nip. and ended bv taking the value of h given by equation (10)) and multiplving bv a factor of 1.5.," Thus, we fell back on using our subjective impressions of the smoothness of $\hat{N}_T$ , and ended by taking the value of $h$ given by equation \ref{eq:hwidth}) ) and multiplying by a factor of 1.5." + To perform the inversion and find the estimated distribution of 5. we assumed that all ealaxies have (he same (riaxialilv Z7.," To perform the inversion and find the estimated distribution of $\gamma$, we assumed that all galaxies have the same triaxiality $T$." + If (his assumption is incorrect. (hen the inversion of equation (14)) may result in Np<0 for some range of 5. which is physically impossible.," If this assumption is incorrect, then the inversion of equation \ref{eq:matrix}) ) may result in $\hat{N}_T < 0$ for some range of $\gamma$, which is physically impossible." + To exclude our hypothesis (that all galaxies have (rianialilv 2) al some fixed. statistical confidence level. we can repeat the inversion for a large number of bootstrap resamplines of the original data set.," To exclude our hypothesis (that all galaxies have triaxiality $T$ ) at some fixed statistical confidence level, we can repeat the inversion for a large number of bootstrap resamplings of the original data set." + In practice. we did 1000 resamplings. and used them to place confidence intervals on Ny.," In practice, we did 1000 resamplings, and used them to place confidence intervals on $\hat{N}_T$." + If the confidence interval falls below zero [or some valus of +. then the hypothesized value of T can be rejected at the (one-sided) confidence level.," If the confidence interval falls below zero for some valus of $\gamma$, then the hypothesized value of $T$ can be rejected at the (one-sided) confidence level." + Figure 5 shows the distribution of intrinsic shapes for ‘cle’ galaxies (fracDeV>0.9). when the adaptive moments axis ratio qa is used as the estimator of (he apparent shape.," Figure \ref{fig:de_adapt} shows the distribution of intrinsic shapes for `de' galaxies $\texttt{fracDeV} > 0.9$ ), when the adaptive moments axis ratio $q_{\rm am}$ is used as the estimator of the apparent shape." +" The heavy line is the distribution for the bright ‘de’ galaxies (V,< —21.3) and the light line is the distribution lor the fainter 4ο galaxies."," The heavy line is the distribution for the bright `de' galaxies $M_r \leq +-21.8$ ) and the light line is the distribution for the fainter `de' galaxies." + The assumed value of Tis shown in each panel. ranging [rom purely oblate shapes. wilh 2=0. in the upper left corner to purely prolate shapes. with 7= 1. in the lower right corner.," The assumed value of $T$ is shown in each panel, ranging from purely oblate shapes, with $T=0$, in the upper left corner to purely prolate shapes, with $T = 1$ in the lower right corner." + An evecatehing featureof Figure 5 is the oscillatory nature of Np in the triaxial cases., An eyecatching featureof Figure \ref{fig:de_adapt} is the oscillatory nature of $\hat{N}_T$ in the triaxial cases. + The multiple peaks in Np at high 5 result [rom the shape of the conditional probability function {δρ} for highly triaxial galaxies., The multiple peaks in $\hat{N}_T$ at high $\gamma$ result from the shape of the conditional probability function $P_T (q | \gamma )$ for highly triaxial galaxies. + When galaxies are axisymmetric (7=0 or 1). the conditional probability peaks at 4=5. the minimum possible apparent axis ratio.," When galaxies are axisymmetric $T = 0$ or $1$ ), the conditional probability peaks at $q = \gamma$, the minimum possible apparent axis ratio." + For (riaxial galaxies. however. the conditional probability has one or more local maxima al q>5.," For triaxial galaxies, however, the conditional probability has one or more local maxima at $q > \gamma$." + To see whythis can result in oscillatory solutions consider Ny For faint ide galaxies when T— 0.8: this is shown by (he lisht line in the lower left panel of Figure 5.., To see whythis can result in oscillatory solutions consider $\hat{N}_T$ for faint `de' galaxies when $T = 0.8$ ; this is shown by the light line in the lower left panel of Figure \ref{fig:de_adapt}. . + The distribution Ny has a local maximum at 5=0.42., The distribution $\hat{N}_T$ has a local maximum at $\gamma = 0.42$. + For T'= 0.8. the conditional probability Pr(q|5=0.42) peaks at q= 0.57.," For $T = 0.8$ , the conditional probability $P_T (q | \gamma = 0.42)$ peaks at $q = 0.57$ ." + Thus. the large number of +x0.42 galaxies result in many galaxies wilh an apparentaxis ralio q80.57: so many. in fact. that Ay must be made very small inthe range 0.42«40.57 in order to avoid overproducing q220.57 galaxies.," Thus, the large number of $\gamma \approx 0.42$ galaxies result in many galaxies with an apparentaxis ratio $q \approx 0.57$; so many, in fact, that $\hat{N}_T$ must be made very small inthe range $0.42 < \gamma +< 0.57$ in order to avoid overproducing $q \approx 0.57$ galaxies." + Ii [act. as seen in Figure 5... Ny has a local minimum at 5= 0.54. at which Ay fallsslightly belowzero.," In fact, as seen in Figure \ref{fig:de_adapt},, $\hat{N}_T$ has a local minimum at $\gamma = 0.54$ , at which $\hat{N}_T$ fallsslightly belowzero." + SincePr(q|5=0.54)peaks at gq= 0.65. this produces a deficit of q20.65 galaxies. which," Since$P_T (q | \gamma = 0.54)$peaks at $q = 0.65$ , this produces a deficit of $q \approx 0.65$ galaxies, which" +"The Maxwell's equations for the ER metric in terms of physical fields. EB.J are as follows: The current J is written in terms of Huid quantities as: lere. Πριν are the electronic and. protonic number densities which are assumed to be equal to the lowest. order. ic no=n,=n.","The Maxwell's equations for the FRW metric in terms of physical fields, $\mathbf{E,B,J}$ are as follows: The current $\mathbf{J}$ is written in terms of fluid quantities as: Here, $n_{e,p}$ are the electronic and protonic number densities which are assumed to be equal to the lowest order i.e ${\bar{n}}_{e}={\bar{n}}_{ p}=n$." + From Eq. (B1)), From Eq. \ref{curl_b}) ) + it follows that V.J=0 if the second term can be neglected. which is the case here (see e.g. Parker 1979).," it follows that ${\bf \nabla.J} = 0$ if the second term can be neglected, which is the case here (see e.g. Parker 1979)." + Eq. (5)), Eq. \ref{cont_eq}) ) + along with Eq. (B5)), along with Eq. \ref{curre}) ) + then shows that: in the linear theory., then shows that: in the linear theory. + One of us (SINS) would like to thank Ix. Subramanian and A. Beisenegger for many useful discussions., One of us (SKS) would like to thank K. Subramanian and A. Reisenegger for many useful discussions. +Abell 2219 and ACLI4 (Allen 1997. in. preparation),"Abell 2219 and AC114 (Allen 1997, in preparation)." + With the column clensities fixed at nominal Galactic values (Dickey Lockman 1990) the measured temperatures were somewhat higher: AY=1L0 ο. 13.8 52. 12465 and OSitt keV for Abell 2744. Abell 2163. Abell 2219 and ACIIA. respectively.," With the column densities fixed at nominal Galactic values (Dickey Lockman 1990) the measured temperatures were somewhat higher; $kT = 11.0^{+0.8}_{-0.7}$ , $13.8^{+0.8}_{-0.7}$ , $12.4^{+0.8}_{-0.7}$ and $9.8^{+1.0}_{-0.9}$ keV for Abell 2744, Abell 2163, Abell 2219 and AC114, respectively." + Phe corresponding X-ray masses within the arc radii are then 4.1Lol for Abell 2744. 2.3.1077 for Abell 2163. 3.1lo and 5.5«107 for the N and L zwes of Abell 2219. and 1.7«1055 for ACLIE.," The corresponding X-ray masses within the arc radii are then $4.1 \times 10^{13}$ for Abell 2744, $2.3 \times 10^{13}$ for Abell 2163, $3.1 \times 10^{13}$ and $5.5 +\times 10^{13}$ for the N and L arcs of Abell 2219, and $1.7 \times 10^{13}$ for AC114." + The ratios ofthe strong lensing to X-ray. masses are reduced to 2.8 (2.2) for Abell 2744. 1.9 for Abell 2163. 1.7 (1.4) and L.S (1.6) for the N and L ares in Abell 2219. and 1.8 for Ας14.," The ratios of the strong lensing to X-ray masses are reduced to 2.8 (2.2) for Abell 2744, 1.9 for Abell 2163, 1.7 (1.4) and 1.8 (1.6) for the N and L arcs in Abell 2219, and 1.8 for AC114." + Although the temperature results are therefore sensitive. in detail. to the modelling of the absorbing column density. the differences are not enough to account for the discrepancies between the strong lensing and. X-ray mass measurements for the non-cooling Low clusters.," Although the temperature results are therefore sensitive, in detail, to the modelling of the absorbing column density, the differences are not enough to account for the discrepancies between the strong lensing and X-ray mass measurements for the non-cooling flow clusters." + Several of the clusters discussed. in this paper are well-studied lensing svstems., Several of the clusters discussed in this paper are well-studied lensing systems. + From their detailed study of Abell 3915. Ixncib (1995) demonstrated that the observed arc(let) configuration implies a mass clistribution consisting of two clumps centred. on the two brightest galaxies.," From their detailed study of Abell 2218, Kneib (1995) demonstrated that the observed arc(let) configuration implies a mass distribution consisting of two clumps centred on the two brightest galaxies." + The orientation ane cllipticitics of the projected. potentials due to these chumps trace the external isophotes of brightest ellipticals. , The orientation and ellipticities of the projected potentials due to these clumps trace the external isophotes of brightest ellipticals. [ +Similar results on the orientation. of the dark matter potentials relative to the isophotes of the dominant cluster galaxies were obtained. from the lensing studies of AIS2137.3-2353 and. Abell 370 by Mellier. Fort. παρ (1993) and Ixneib. (1993).,"Similar results on the orientation of the dark matter potentials relative to the isophotes of the dominant cluster galaxies were obtained from the lensing studies of MS2137.3-2353 and Abell 370 by Mellier, Fort Kneib (1993) and Kneib (1993)." + These results may. be compared to similar findings based on the galaxian and X-rav gas distributions in other clusters Porter. Schneider Lloessel (1991). Allen (1995).]," These results may be compared to similar findings based on the galaxian and X-ray gas distributions in other clusters Porter, Schneider Hoessel (1991), Allen (1995).]" + The lensing results on Abell 2218. and comparison toa ROSAT LIE X-ray image of he cluster (from a shorter 11.5 ks exposure) lead Ixneib (1995) to suggest that Abell 2218 is undergoing a subcluster merger event. which may have shocked the central X-ray gas and caused it to deviate from byelrostatic equilibrium.," The lensing results on Abell 2218, and comparison to a ROSAT HRI X-ray image of the cluster (from a shorter 11.5 ks exposure) lead Kneib (1995) to suggest that Abell 2218 is undergoing a subcluster merger event, which may have shocked the central X-ray gas and caused it to deviate from hydrostatic equilibrium." + From heir modelling. Ixneib (1995) determine a mass within he ellipse traced. by are #884 o£ 6.11017AL... similar o the value of 5.7«101. inferred. from the simple spherical model.," From their modelling, Kneib (1995) determine a mass within the ellipse traced by arc $\#384$ of $6.1 \times 10^{13}$, similar to the value of $5.7 \times 10^{13}$ inferred from the simple spherical model." + Miralda-IEscudé Babul (1995). showed hat the application of a multi-component lensing moclel. which can account for the positions of the brightest. arcs in Abell 2218. predicts a lensing mass within the circular aperture defined. by arc 36359 of ~ST per cent of the value inferred from the simple spherical model.," Miralda-Escudé Babul (1995) showed that the application of a multi-component lensing model, which can account for the positions of the brightest arcs in Abell 2218, predicts a lensing mass within the circular aperture defined by arc $\#359$ of $\sim 87$ per cent of the value inferred from the simple spherical model." +" Ες implies AbauwfAdxX=.2ST—(0,45€(20 OPS which. is. againoO. similar. to the result listed. in ‘Table 4. ("," This implies $M_{\rm arc}/M_{\rm X} = 2.87^{+0.30}_{-0.20}$ , which is again similar to the result listed in Table 4. (" +Reeall that the errors. quoted on the AbaefAdx values denote the largest ancl smallest. values consistent with the joint confidence limits on the X-ray masses and lensing results).,Recall that the errors quoted on the $M_{\rm arc}/M_{\rm X}$ values denote the largest and smallest values consistent with the joint confidence limits on the X-ray masses and lensing results). + From their detailed lensing analvsis of the cooling-IHow cluster MS2137.3-2353. Mellier (1993) determined a mass within the external critical padius. of Aa.=3⋅-7.10713M..," From their detailed lensing analysis of the cooling-flow cluster MS2137.3-2353, Mellier (1993) determined a mass within the external critical radius of $M_{\rm arc} = 3-7 \times 10^{13}$." +. woThis is consistent. with. the value determined from the ciecalarlv-svmaimetrie mocel and is in excellent agreement with the X-rav-determined mass measurement of⋅ Ady—5.2−⊥⇁∣⋅ον107⊥⇁ (implying: Aliveλεν=0.96 2m)., This is consistent with the value determined from the circularly-symmetric model and is in excellent agreement with the X-ray-determined mass measurement of $M_{\rm X} = 5.2^{+1.9}_{-0.6} \times 10^{13}$ (implying $M_{\rm arc}/M_{\rm X} = 0.96^{+0.56}_{-0.54}$ ). + Alellier (1993) also concluded that the core radius of the lensing potential in. MS2131.3-2353 is small (50 kpe). in good agreement with the X-ray result reported here (sec also Section 4.6).," Mellier (1993) also concluded that the core radius of the lensing potential in MS2137.3-2353 is small $\sim 50$ kpc), in good agreement with the X-ray result reported here (see also Section 4.6)." + For Abell 1689. Miralda-Escudé Babul (1995) showed hat the application of a mass mocel consisting of (at least) wo clumps is required to reproduce the positions of the xiehtest ares.," For Abell 1689, Miralda-Escudé Babul (1995) showed that the application of a mass model consisting of (at least) two clumps is required to reproduce the positions of the brightest arcs." + Phe mass within the circular aperture defined w the dominant arc. determined with their mocel. is slightly arecr (104 per cent) than the value inferred from the simple spherical model. and gives Mj/Alx=2.00425 (L80. (11).," The mass within the circular aperture defined by the dominant arc, determined with their model, is slightly larger (104 per cent) than the value inferred from the simple spherical model, and gives $M_{\rm arc}/M_{\rm X} = 2.00^{+0.22}_{-0.23}$ $1.80^{+0.19}_{-0.21}$ )." + Small (L995a) present results from a. detailed ensing analysis of Abell 2219 using a multi-component mass model., Smail (1995a) present results from a detailed lensing analysis of Abell 2219 using a multi-component mass model. + “Phese authors determine a projected. mass within 100 kpe of the cluster centre of 1.1200:2«107 AL. in reasonable agreement (although slightly larger than)the valuessuggested by the simple sphericallv-symmoetrie mocel (Table 4).," These authors determine a projected mass within 100 kpc of the cluster centre of $1.1 \pm 0.2 \times +10^{14}$ , in reasonable agreement (although slightly larger than)the valuessuggested by the simple spherically-symmetric model (Table 4)." + The N-rav-determined mass withinthis projected radius: is HEN3.54ES4755Loe?13AL... implying. a strong-lensing/X-. mass ratio of AMMx=3.11 LIS ," The X-ray-determined mass withinthis projected radius is $3.54^{+0.38}_{-0.51} \times 10^{13}$, implying a strong-lensing/X-ray mass ratio of $M_{\rm arc}/M_{\rm X} = 3.11^{+1.18}_{-0.81}$ ." +Small(1995a), Smail(1995a) + (?)..," \citep{Fizeau1868}. \citep{1920ApJ....51..257M}," + (?).. (2) , \citep{1975ApJ...196L..71L} +the LSD Stokes profiles derived from a tota iuteeratiou of 36008 obtained on 12 March 2007.,the LSD Stokes profiles derived from a total integration of 3600s obtained on 12 March 2007. + The Sokes { LSD profile casily resolves the two compoucuts. he Aa star corresponding to the sharp line.," The Stokes $I$ LSD profile easily resolves the two components, the Am star corresponding to the sharp line." + In both tre Stokes V aud null polarizatio iN profiles. a simall signa is visible at the RV of the Au star. and the LSD statistics gives a false alum probability sinaller than 5m," In both the Stokes $V$ and null polarization $N$ profiles, a small signal is visible at the RV of the Am star, and the LSD statistics gives a false alarm probability smaller than $^{-3}$." + Since this detection is obtained also. even noro strongly.M on the uull polarization N profile. it is suspocted to be spurious.," Since this detection is obtained also, even more strongly, on the null polarization $N$ profile, it is suspected to be spurious." + However weak maguctic fields in subelant stars have been detected iu tre course of another magnetic sirvey with NARVAL (Απο ο al., However weak magnetic fields in subgiant stars have been detected in the course of another magnetic survey with NARVAL (Aurièrre et al. + 2009b)., 2009b). + We| therefore observed 32 Vir again 1i the same conditions on 13 Mich 2007 aud on 02 April 2XS. aud eot the same result: a weak signal was again visible on Stokes V. aud IN. profiles.," We therefore observed 32 Vir again in the same conditions on 13 March 2007 and on 02 April 2008, and got the same result: a weak signal was again visible on Stokes $V$ and $N$ profiles." + Now 32 Vir is both a binary star aud a pulsatiue star (Lampens Bofhin 2000)., Now 32 Vir is both a binary star and a pulsating star (Lampens Boffin 2000). +" Bertiau (1957) derived an orjt with a period of 38.32 days and a semi amplitude of Ls lans 5|,", Bertiau (1957) derived an orbit with a period of 38.3 days and a semi amplitude of 48 km $^{-1}$. + Asad istar. 32 Vir has a period of abou 0.07 day (Bartolini .," As a $\delta$ Scuti star, 32 Vir has a period of about 0.07 day (Bartolini et al." + 1985. Wurtz et al.," 1983, Kurtz et al." + 1976)., 1976). + The RV züuplitude variation to pulsations is uukuownu. but couId be simular to that observed for p Puppis itself. ic. 8.6 xli ? (Mathias et ," The RV amplitude variation due to pulsations is unknown, but could be similar to that observed for $\rho$ Puppis itself, i.e. 8.6 km $^{-1}$ (Mathias et al." +1997)., 1997). + These rapid RV. variations die to the binary pulsatiug status of the star are expected to induce ts in RV between t1ο LSD profes of the four (900 l-exposures of up ο about 1 km/s. Such large. AV. ts were actually measured on οἱw data. which can to detection of spurious polarizaion signals (Donati ," These rapid $RV$ variations due to the binary and pulsating status of the star are expected to induce shifts in $RV$ between the LSD profiles of the four (900 s) sub-exposures of up to about 1 km/s. Such large $RV$ shifts were actually measured on our data, which can lead to detection of spurious polarization signals (Donati et al." +1997)., 1997). + Decause of the differeu time-lags between σοιüuatious of su)ονrostizes used. for getting NV and Stokes V. profiles. the spurious signal is expected to be strouecr on the forucr than on the latter profiles.," Because of the different time-lags between combinations of sub-exposures used for getting $N$ and Stokes $V$ profiles, the spurious signal is expected to be stronger on the former than on the latter profiles." +" This process is probably the reason for the signal observed on the 3 dates,", This process is probably the reason for the signal observed on the 3 dates. + A Vir: This sar ds ao ποπιο double lined spectroscopic Aims ünarv: both stars are very similar i chemical abundances but the primary compoucut is broac-lined iud the secondary is sharp-lined (Zhao ct al., $\lambda$ Vir: This star is a well-known double lined spectroscopic Am binary: both stars are very similar in chemical abundances but the primary component is broad-lined and the secondary is sharp-lined (Zhao et al. + 2007)., 2007). + Our NARVAL observations enabled us to resolve the two components ou our LSD Stokes V. profiles. as already. presented 1w Shorlin et al. (," Our NARVAL observations enabled us to resolve the two components on our LSD Stokes $V$ profiles, as already presented by Shorlin et al. (" +2002).,2002). +" In Table 1 we show that neither of the two componcuts iudicaος a Zeenan detection and we have included individual £D, πιrelents for czich ofthe two compoucuts.", In Table 1 we show that neither of the two components indicates a Zeeman detection and we have included individual $B_\ell$ measurements for each of the two components. + 22 Boo: 22 Doo is considered to be an Am star which has aready left the nian sequence (Dursrt et al., 22 Boo: 22 Boo is considered to be an Am star which has already left the main sequence (Burkart et al. + 1980. Berte L990).," 1980, Bertet 1990)." + This is n paricularly interesting object for a lnaenetic survey since a dvnsno drive1 iuienetic field may appear during the subeiant phase (Auricirve et al., This is a particularly interesting object for a magnetic survey since a dynamo driven magnetic field may appear during the subgiant phase (Aurièrre et al. + 20091)., 2009b). + However no Zeeianu detection occur at a level of g=2.18 G for D., However no Zeeman detection occur at a level of $\sigma = 2.18$ G for $B_\ell$. + The HegMa stars are generally considered as having the most stable atinospheres among intermediate mass stars (Vauclair Vauclair. 1982).," The HgMn stars are generally considered as having the most stable atmospheres among intermediate mass stars (Vauclair Vauclair, 1982)." + However. some binary HegMu stars have con shown to display spectroscopic variations (Acehuan ct al.," However, some binary HgMn stars have been shown to display spectroscopic variations (Adelman et al." + 2002. Kochukhov ct al.," 2002, Kochukhov et al." + 2005. ITubris et al.," 2005, Hubrig et al." + 2006a. Briquet et al.," 2006a, Briquet et al." + 2010)., 2010). + The nou-uuiforii surface abuudances iuvoked to explain these variations appear to CVOIVO with tine (lochukhov et al., The non-uniform surface abundances invoked to explain these variations appear to evolve with time (Kochukhov et al. + 2007)., 2007). + It has been proyosecL tvat they could host strong magnetic fields of peculiar toxlogv. (IIubig et al., It has been proposed that they could host strong magnetic fields of peculiar topology (Hubrig et al. + 2006b. 2008). aud that SUC1 fields could be responsible for the surface structures.," 2006b, 2008), and that such fields could be responsible for the surface structures." + Wade et al. (, Wade et al. ( +2006) performed a scusitive magnetic study of he brightest HeMa stir. 6 And. and placed a 36 upper Πιτ of about 100 GC on the possible presence of ay undetected pure dipolar. quadrupolar or octupolar surace miaenetic ficlds.,"2006) performed a sensitive magnetic study of the brightest HgMn star, $\alpha$ And, and placed a $\sigma$ upper limit of about 100 G on the possible presence of any undetected pure dipolar, quadrupolar or octupolar surface magnetic fields." + Because of the rather large esin? (52 kan 1j the lo error bars reached 6 Ceo at the sunallest. even wih ESPaDOuS. We have observed. here wit1 NARVAL 3 of the brightest of the TeXn stars having esimn5t ues sinaller than a Aud.," Because of the rather large $v \sin i$ (52 km $^{-1}$ ), the $\sigma$ error bars reached 6 G at the smallest, even with ESPaDOnS. We have observed here with NARVAL 3 of the brightest of the HgMn stars having $v \sin i$ 5 times smaller than $\alpha$ And." +" The resultiug uncertainties of B, are finally 2 to L times smaler than those obained for a Aud.", The resulting uncertainties of $B_\ell$ are finally 2 to 4 times smaller than those obtained for $\alpha$ And. + H Cue: For this classical HeMu star (Zócchliug Afuthnsiun. 1987). our nou detection with a 1 6 error of 3 C for the longitudinal magnetic field coufixiis the result of Shorli ret al.," $\kappa$ Cnc: For this classical HgMn star (Zöcchling Muthsam, 1987), our non detection with a 1 $\sigma$ error of 3 G for the longitudinal magnetic field confirms the result of Shorlin et al." + 2002. that a strong surface maeuetic field. aS SIOOeeested ]x older observations. is not present.," 2002, that a strong surface magnetic field, as suggested by older observations, is not present." + i ¢1.72.rb: Observatious of this star with the Ciecko specroeraph attache to the Cauacda-Frauce-IEsvaii Telescope lave resolved the two components of the specroscopic binary (Dubaj et al., $\iota$ CrB: Observations of this star with the Gecko spectrograph attached to the Canada-France-Hawaii Telescope have resolved the two components of the spectroscopic binary (Dubaj et al. + 2005)., 2005). + The esiu/ of the Πσλίαι component was measured to be οilv about ] kin i. Shorlin et al. (, The $v \sin i$ of the HgMn component was measured to be only about 1 km $^{-1}$; Shorlin et al. ( +2002) were ouly able to fiud allpperlimit of eiui < 10 lau |.,2002) were only able to find an upperlimit of $v \sin i$ $<$ 10 km $^{-1}$. + Our measurement of this star has the best precisiou obtained for he IIeMu stars of our sale. about 1 C. Figure 3 shows he Stokes V and Stokes £ LSD profiles for + CrB. > Her: This star is a spectroscopic binary which has yoceitly been resolved (Zavala et al.," Our measurement of this star has the best precision obtained for the HgMn stars of our sample, about 1 G. Figure 3 shows the Stokes $V$ and Stokes $I$ LSD profiles for $\iota$ CrB. $\phi$ Her: This star is a spectroscopic binary which has recently been resolved (Zavala et al." + 2007) aud for which the nass of the CP star has been refined (Torres 2007)., 2007) and for which the mass of the CP star has been refined (Torres 2007). + No field is detected. with an loueitucinal field uncertaiuty of about 2 Ci. No Zeciuan detecjon was obtained for anv of the 15 stars of our sauuple. although we have achieved a precisiou oeprovenment of more than one order of mmaenitude with respec to the work of Shorliu et al. (," No field is detected, with an longitudinal field uncertainty of about 2 G. No Zeeman detection was obtained for any of the 15 stars of our sample, although we have achieved a precision improvement of more than one order of magnitude with respect to the work of Shorlin et al. (" +2002).,2002). + Although we have otained oulv one observation for the majority of the SESS ο our sanuple. the non-detection of sienificant Stokes V signatures is asrong negative result because maguctic confietvations culi produce detectable V. signatures throug ithe line profile eve1 for zero longitudinal maguetic field.," Although we have obtained only one observation for the majority of the stars of our sample, the non-detection of significant Stokes $V$ signatures is a strong negative result because magnetic configurations can produce detectable $V$ signatures through the line profile even for zero longitudinal magnetic field." + The observation of the crossover effect requires non- rotational Doppler broadenic (Alatlivs 1995). but it could be observed ta the case of TIN) Aud (esis 2knes Lo oAuróne et al.," The observation of the crossover effect requires non-negligible rotational Doppler broadening (Mathys 1995), but it could be observed in the case of HN And $vsini$ = 2 km $^{-1}$ , Aurièrre et al." + 2007). and therefore could," 2007), and therefore could" +"obtained from the AGN and Galaxy Evolution Survey (AGES: C. Kochanek et al.,","obtained from the AGN and Galaxy Evolution Survey (AGES: C. Kochanek et al.," + in prep)., in prep). +" In total, 78 sources from our sample have been observed spectroscopically."," In total, 78 sources from our sample have been observed spectroscopically." +" Of these, redshifts could not be determined for 12 sources due to optical faintness or a lack of useful lines."," Of these, redshifts could not be determined for 12 sources due to optical faintness or a lack of useful lines." + Two of the spectroscopically confirmed sources areSpitzer MIPS 244m sources at 2—4.230 and 3.675 , Two of the spectroscopically confirmed sources are MIPS $\mu$ m sources at $z$ =4.230 and 3.675 \citep{desai08}. +"The former is a narrow-line AGN exhibiting CIV and (?)..Hell, and the latter is a broad-line QSO."," The former is a narrow-line AGN exhibiting CIV and HeII, and the latter is a broad-line QSO." +" Additionally, three sources have been identified as QSOs from our DEIMOS spectra 4.230, 4.050), and one source is a Galactic star."," Additionally, three sources have been identified as QSOs from our DEIMOS spectra $z$ =3.835, 4.230, 4.050), and one source is a Galactic star." +" The (z=3.835,total number of confirmed interlopers (i.e., those other than star-forming galaxies at z~ 3.7) is 5 AGN and 1 star."," The total number of confirmed interlopers (i.e., those other than star-forming galaxies at $z\sim3.7$ ) is 5 AGN and 1 star." +" Hence, the rate of contamination ranges from (if all 12 unidentified sources are at high redshift: to all 12 sources are at low redshift: (6+12)/78)."," Hence, the rate of contamination ranges from (if all 12 unidentified sources are at high redshift: 6/78) to (if all 12 sources are at low redshift: (6+12)/78)." +"6/78) In Figure(if 1 right), we show the two redshift distributions of our spectroscopic samples, one for the full sample including the MIPS sources, and the other showing only I>22.5 galaxies without MIPS detections."," In Figure \ref{plot_redshift} ), we show the two redshift distributions of our spectroscopic samples, one for the full sample including the MIPS sources, and the other showing only $I\ge 22.5$ galaxies without MIPS detections." + We further note that the MIPS 24 jm sources are fairly bright (IS 22.5) compared to the majority of our candidates., We further note that the MIPS 24 $\mu$ m sources are fairly bright $I\lesssim 22.5$ ) compared to the majority of our candidates. +" Hence, we adopt the latter as the representative redshift distribution N (z), as the majority of our sample is fainter than J= 22.5."," Hence, we adopt the latter as the representative redshift distribution $N(z)$ , as the majority of our sample is fainter than $I=22.5$ ." +" Thus, the redshift distribution is well described by the mean (z)=3.7 and the standard deviation of 0.4."," Thus, the redshift distribution is well described by the mean $\langle z\rangle=3.7$ and the standard deviation of $0.4$." +" To further validate the adopted redshift distribution, we carried out photometric simulations to estimate the expected redshift distribution of our dropout sample based on the broad-band color selection."," To further validate the adopted redshift distribution, we carried out photometric simulations to estimate the expected redshift distribution of our dropout sample based on the broad-band color selection." +" The simulation consists of 1) creating artificial star-forming galaxies over a range of redshifts, UV luminosity, spectral slope, morphology, and size, 2) inserting them in the real images, 3) color-selecting in an identical manner in which the real galaxies were selected."," The simulation consists of 1) creating artificial star-forming galaxies over a range of redshifts, UV luminosity, spectral slope, morphology, and size, 2) inserting them in the real images, 3) color-selecting in an identical manner in which the real galaxies were selected." + We refer interested readers to ? and ? for more details., We refer interested readers to \citet{ferguson04} and \citet{lee06} for more details. +" The expected redshift distribution is shown in Figure 1right; dashed line), in good agreement with the observed(bottom one."," The expected redshift distribution is shown in Figure \ref{plot_redshift} ; dashed line), in good agreement with the observed one." +" We investigate the average SED properties of the UV-selected star-forming galaxies by stacking our imaging in the BwRIJH Ks[3.6]|4.5]|5.8][8.0] passbands on the positions of the 1,913 galaxies in our sample."," We investigate the average SED properties of the UV-selected star-forming galaxies by stacking our imaging in the $B_WRIJHK_S$ [3.6][4.5][5.8][8.0] passbands on the positions of the 1,913 galaxies in our sample." +" For a galaxy at z—3.7 — the median redshift of the sample — these bands probe the rest-frame wavelength range 0.1— 2um. In order to investigate whether their UV brightness (a proxy for star formation rate) is correlated with other galaxy properties such as stellar mass or extinction, we define six subsamples ordered by their J- band magnitudes."," For a galaxy at $z=3.7$ – the median redshift of the sample – these bands probe the rest-frame wavelength range $ 0.1-2 \mu$ m. In order to investigate whether their UV brightness (a proxy for star formation rate) is correlated with other galaxy properties such as stellar mass or extinction, we define six subsamples ordered by their $I$ -band magnitudes." +" In Table 1, we summarize the details of each subsample."," In Table 1, we summarize the details of each subsample." +" Given the relatively narrow redshift distribution (z=3.7+ 0.4), the I-band flux provides a fairly accurate representation of the observed UV luminosity measured at the rest-frame 1700A."," Given the relatively narrow redshift distribution $z=3.7\pm0.4$ ), the $I$ -band flux provides a fairly accurate representation of the observed UV luminosity measured at the rest-frame 1700." +". At a fixed I-band flux, the UV luminosity of a source at z=3.7 will be higher (lower) than that at z=3.3 (4.1) by &:0.08 dex (assuming that the UV spectrum has the form fyoc A-1955)."," At a fixed $I$ -band flux, the UV luminosity of a source at $z=3.7$ will be higher (lower) than that at $z=3.3$ (4.1) by $\approx 0.08$ dex (assuming that the UV spectrum has the form $f_\lambda \propto \lambda^{-1.45}$ )." +" In order to create average SEDs of galaxies within each luminosity bin, we first constructed stacked two dimensional images for each band."," In order to create average SEDs of galaxies within each luminosity bin, we first constructed stacked two dimensional images for each band." +" To create clean stacked images in each band, unbiased by outliers and Sky subtraction uncertainties, we adopted the following procedure. "," To create clean stacked images in each band, unbiased by outliers and sky subtraction uncertainties, we adopted the following procedure. (" +We first convolved all the images in agivenband to a common(1) PSF. (,1) We first convolved all the images in agivenband to a common PSF. ( +"2) Then, from these convolved images, we extracted 1'x1' iimage cutouts centered on each candidate. (","2) Then, from these convolved images, we extracted $\times$ image cutouts centered on each candidate. (" +"3) Next,","3) Next," +Observations iun 7— provide circumstantial evidence relating gas inflow to the starburst and therefore to the interaction.,Observations in \cite{kewley06b} provide circumstantial evidence relating gas inflow to the starburst and therefore to the interaction. + Galaxy mergers with ereater starburst streneth have lower unclear metallicity., Galaxy mergers with greater starburst strength have lower nuclear metallicity. + This effect is expected to be due to the iufall of pristine eas from the outer disk which dilutes the concentration of metals iu the nucleus., This effect is expected to be due to the infall of pristine gas from the outer disk which dilutes the concentration of metals in the nucleus. + We have measured the time of gas depletion at radii from 1 to 10 kpc., We have measured the time of gas depletion at radii from 1 to 10 kpc. + The results coustrain the net iufall velocity., The results constrain the net infall velocity. + Table 2. lists the time elapsed since the star formation rate or. equivalenuth. the gas surface density dropped abruptly.," Table \ref{tab:posdep} lists the time elapsed since the star formation rate or, equivalently, the gas surface density dropped abruptly." + The time elapsed since peak star formation activity is typically 100 to 300 Alyy at 5 to 10 kpc falling to less than 50 Myr within 5 ispc., The time elapsed since peak star formation activity is typically 100 to 300 Myr at 5 to 10 kpc falling to less than 50 Myr within 5 kpc. + These timescales indicate the nüniumiu tine for eas inflow since the eas need only flow iward. not necessarily all the way to the center of the merecr.," These timescales indicate the minimum time for gas inflow since the gas need only flow inward, not necessarily all the way to the center of the merger." + Iu observations by ?.. the dyuanical mass for objects included in our study (IRASIT208|0011. IRAS20057-0308. IRAS 23365|3601) are measured as similar to the Milkv. Way mass.," In observations by \cite{colina05}, the dynamical mass for objects included in our study (IRAS17208+0014, IRAS20087-0308, IRAS 23365+3604) are measured as similar to the Milky Way mass." + The representation that we give for the orbital velocities may be reparameterized by substituting iu distances and orbital velocities for other ealaxies. as well as changing the deusitv values used iu the freefall calculation.," The representation that we give for the orbital velocities may be reparameterized by substituting in distances and orbital velocities for other galaxies, as well as changing the density values used in the freefall calculation." + Observations (7). have indicated that ULIRGs are major mergers between galaxies with an average dass ratio of L.5:1. indicating that the orbital velocities in each component are of tle same order.," Observations \citep{dasyra06} have indicated that ULIRGs are major mergers between galaxies with an average mass ratio of 1.5:1, indicating that the orbital velocities in each component are of the same order." + This information allows us to choose the Milky Wav dinass value as the fiducial mass scale: aud we estimate iuaxinuun inflow speeds of οτε.GSkins(R/Tkpc)(ες100 My)., This information allows us to choose the Milky Way mass value as the fiducial mass scale; and we estimate maximum inflow speeds of order $v_{inflow} \sim 68~{\rm km\ s^{-1}} (R/ 7 ~{\rm kpc}) / (t_* / 100~{\rm Myr})$ . + We compare this to two timescales in ULIRGs: (1) the free fall timescale at a eiven radius iu an isothermal sphere aud (2) the orbital period., We compare this to two timescales in ULIRGs: (1) the free fall timescale at a given radius in an isothermal sphere and (2) the orbital period. + Both of these timescales duerease linearly with radius., Both of these timescales increase linearly with radius. + To deteruiune the freefall timescale we calculate the average deusity within particular radii usiug a profile of the fori py(η) with py=1.3deusity«10*AL.kpe? the local halo mass density7? (2).., To determine the freefall timescale we calculate the average density within particular radii using a density profile of the form $\rho_0\ (r/r_0)^{-2} $ with $\rho_0 = 1.3 \times 10^7~{\rm M_\odot~kpc^{-3}} $ the local halo mass density \citep{gates95}. + The average density of the Ahlkv iuterior to a radius of & is Ls10*WayM.EkpeP eivine the free fall timescale rp¢(7)10MyVP por)., The average density of the Milky Way interior to a radius of 8 is $\rho_{MW} \approx 4 \times 10^7 ~{\rm M_\odot~kpc^{-3}}$ giving the free fall timescale $\tau_{ff}(r) \approx 40~{\rm Myr}~\sqrt{\rho_{MW}/\rho(r)}$ . +" The orbital period is z,54€8)cx220Myr(R/Skpc)/(o/220kins 1j "," The orbital period is $\tau_{orb}(R) +\approx 220 ~{\rm Myr}~ (R/8~{\rm kpc}) / (v / 220 ~{\rm km~ s^{-1}})$ ." +In Figure &.. we show the truncation timescale as a function of distance from the ceuter of the merecr.," In Figure \ref{fig:pos_age}, we show the truncation timescale as a function of distance from the center of the merger." + The scatter iu values does not distinguish between freefall aud orbital time scales., The scatter in values does not distinguish between freefall and orbital time scales. + They do rule out the much longer time scales associated with diffusion and leud eupirical support to the timescales asstuced in simulations (77)..," They do rule out the much longer time scales associated with diffusion and lend empirical support to the timescales assumed in simulations \citep{hopkins08,hopkins09}." + Cas nügratiou toward the ceuter slows down star formation in the outer radii., Gas migration toward the center slows down star formation in the outer radii. + The paucity of massive stars allows tto grow., The paucity of massive stars allows to grow. + Regious closer to the nucleus are fed infalling eas from exterior regions. prolouging star formation aud allowing tto remain low longer.," Regions closer to the nucleus are fed infalling gas from exterior regions, prolonging star formation and allowing to remain low longer." + As the mereer advances. the cessation of star formation trails imward.," As the merger advances, the cessation of star formation trails inward." + All 25 ULIRGs have star formation iu thei center. iucdicating the eas surface deusity there remains above the threshold density.," All 25 ULIRGs have star formation in their center, indicating the gas surface density there remains above the threshold density." + As discussed in Section 3.L.. the higher nuclear Hin the merecr and post-merger objects mav indicate the ceutral star formation rate is declining by this stage.," As discussed in Section \ref{sect:nuc}, the higher nuclear in the merger and post-merger objects may indicate the central star formation rate is declining by this stage." + This result provides observational evidence that the ceutral eas deusitv starts dechuineg ouce the uuclei have merged., This result provides observational evidence that the central gas density starts declining once the nuclei have merged. + The plivsical processes regulatiug the rate of eas imfall diving mergers is muportaut because it influences the age and inctallicity eradieuts in the merecr renimnant as well as the streneth of supernova aud ACN feedback., The physical processes regulating the rate of gas infall during mergers is important because it influences the age and metallicity gradients in the merger remnant as well as the strength of supernova and AGN feedback. + By exanuning the positional dependence of stellar spectral indices in ESI long slit spectra. we determined the recent star formation history across galaxy 9 galaxy icrecrs.," By examining the positional dependence of stellar spectral indices in ESI long slit spectra, we determined the recent star formation history across galaxy – galaxy mergers." + Strong aabsorptiou indicates a diminished star formation rate over the past few hundred Myr. which should be accompanied by au increase in D1000. while hwdrosenu Bahuer emission indicates the presence of massive stars from more recent star formation.," Strong absorption indicates a diminished star formation rate over the past few hundred Myr, which should be accompanied by an increase in D4000, while hydrogen Balmer emission indicates the presence of massive stars from more recent star formation." + We find the measured Hucreases with radius iu the sample of spatially resolved objects., We find the measured increases with radius in the sample of spatially resolved objects. + We attribute the large to a rapid decrease in star formation activity over 100 Myr ago at radii greater than 5 kpc., We attribute the large to a rapid decrease in star formation activity over 100 Myr ago at radii greater than 5 kpc. + At radii of a few kpc. the activity appears to have decreased. just 50 to 100 Myr ago based on the slightly lower. but still," At radii of a few kpc, the activity appears to have decreased just 50 to 100 Myr ago based on the slightly lower, but still" +Despite our efforts to reduce the effects of absorption by neutral hydrogen. this absorption still affects the observe backeround photon counts measurably.,"Despite our efforts to reduce the effects of absorption by neutral hydrogen, this absorption still affects the observed background photon counts measurably." +" Tιο fields iun our sunuple cover a wide range of galactic Nyy values. TOM 1.13«107 7? to 7.06«1079 2,"," The fields in our sample cover a wide range of galactic $N_H$ values, from $1.13\times10^{20}$ $^{-2}$ to $7.06\times10^{20}$ $^{-2}$." + We correcte the observed photon counts to a coluun density of ZOro., We corrected the observed photon counts to a column density of zero. + Creclon factors were obtained 1sine the mos receut aud estimates of the cosnüc x-rav backerotud (CXRD) spectrum: a power-law with a xhoton index of 1.12 and an intensity o10 keV lokoV t superimposed ou a Ravinond-Siith hermal plasna enuüttiug at a tfem]xvature of 0.112. keV with au emissiou measure of I5.5 in NSPEC/ENSAS units )or steracian (Mivaji et al. 1998..," Correction factors were obtained using the most recent and estimates of the cosmic x-ray background (CXRB) spectrum: a power-law with a photon index of 1.42 and an intensity of 10.0 keV $^{-1}$ $^{-2}$ $^{-1}$ $^{-1}$ superimposed on a Raymond-Smith thermal plasma emitting at a temperature of 0.142 keV with an emission measure of 18.8 in XSPEC/EXSAS units per steradian (Miyaji et al. \cite{miyaji}," + hereafter Mi98)., hereafter Mi98). + The owoer-tenrature thermal plasma ¢onponeunt (fz57 eV) prodiced by the local hot bubbe did not affect our nodel spectra due to its negieible Hux iu the observed photon e1CLeV bau., The lower-temperature thermal plasma component $T\approx57$ eV) produced by the local hot bubble did not affect our model spectra due to its negligible flux in the observed photon energy band. +" The model Sspectruni was then »ojected hrough a laver of neutra wdrogen absorption COrresponicling to the Ny, value for cach quasar. and the resulting yactioual flux decrease due to absorption wa added bac. ziuto the raw backeroun yhotou count of cach field to |xoduce the corrected backernud counts elven iu κ. "," The model spectrum was then projected through a layer of neutral hydrogen absorption corresponding to the $N_H$ value for each quasar, and the resulting fractional flux decrease due to absorption was added back into the raw background photon count of each field to produce the corrected background counts given in Tab. \ref{tab:1}." +Nyy values were taken frou alsorption line ποιος when avalable (Lockman Savage 1 995: Murphex ot al. citemu xev).," $N_H$ values were taken from absorption line studies when available (Lockman Savage \cite{lockman}; ; Murphey et al. \\cite{murphey}) )," + otherwise they were calculated from the published IIT maps of Dickey Lockman (1990))., otherwise they were calculated from the published HI maps of Dickey Lockman \cite{dickey}) ). + Taking the background photons as ideutified by the SIM. we used the spectral analysis packages to create spectra of the x-ray backgrouud iu cach feld.," Taking the background photons as identified by the SIM, we used the spectral analysis packages to create spectra of the x-ray background in each field." + We first attempted to fit tje resulting spectyiun to the spectrum of Mis described above., We first attempted to fit the resulting spectrum to the spectrum of Mi98 described above. + The gooducoft was checked use a Q test.," The goodness-of-fit was checked using a $ +\chi^2$ test." + T. ⋅≻⋅⋅ ↑↕∐∖↥⋅↸∖≼↧⋯⊳↸∖≺↧∖−∐↕≼∐↸⊳⋜↧↑↸∖≼↧⋜↧↻∪∪↥⋅∏↑∙ ⋅ we calouated a best-fit spectrum «« ≻∐↴∖↴↕↴∖↴↑↕∐∶↴⋁∪↕≯↖⇁⋜∐⋅↕⋜∏⋝↕↸∖ thermal and power-law components.," If the reduced $\chi^2$ indicated a poor fit, we calculated a best-fit spectrum consisting of variable thermal and power-law components." + Example specva are plotted i Fig. 2.., Example spectra are plotted in Fig. \ref{fig:spec}. + The top specrun. of the diffuse x-ray background surrouxdiug the radio-loud quasar176.. is ft well bv t15 Mi98. backeround spectra (solid line}.," The top spectrum, of the diffuse x-ray background surrounding the radio-loud quasar, is fit well by the Mi98 background spectrum (solid line)." + The lower specruni ds of the diffuse x-ray backeround sumrouxdiug33., The lower spectrum is of the diffuse x-ray background surrounding. + The \QO9s svectra. sliown as a dasliec] liuc. clearly ¢loes not fit the «ata.," The Mi98 spectrum, shown as a dashed line, clearly does not fit the data." + Thne best-fting spectrum. jiowii as a solid line. xcultec in the sane power-law COLL»ouenut aud thermal pas onixraure as G98. oulv le enibssion iueasure of the 0.112 keV hermal paslua Was Increased.," The best-fitting spectrum, shown as a solid line, resulted in the same power-law component and thermal plasma temperature as Mi98, only the emission measure of the 0.142 keV thermal plasma was increased." + Iu fact. In virualls οὓςty background s)octiuni a reasonable f was achiever by varviug this ejdssion measure.," In fact, in virtually every background spectrum a reasonable fit was achieved by varying this emission measure." + The leπα ClussiOl ueasures varied from 15.01.7 NSPEC 1nits per stcπαπα for to 5s.534E2.[| NSPEC units per steradian for (Recall the Mi98 spectruni hac an endsson measure of 1διδ NSPEC units per steracdia1)., The best-fit emission measures varied from $15.9 \pm 1.7$ XSPEC units per steradian for to $58.5 \pm 2.4$ XSPEC units per steradian for (Recall the Mi98 spectrum had an emission measure of 18.8 XSPEC units per steradian). + This suggests that the variations in diffuse backerouud levels amoug the fields are due ο Variations in he hot thermal component of he CXRD. presunie| bv may ο Orlelna cin the galactic alo (e.g. Cendreauc tal. 1995..," This suggests that the variations in diffuse background levels among the fields are due to variations in the hot thermal component of the CXRB, presumed by many to originate in the galactic halo (e.g. Gendreau et al. \cite{gendreau}," + Nousek e al. 1982))., Nousek et al. \cite{nousek}) ). + This also suggests that all variationsla in the diffuse backgrounds or the fields we examnünued canrot be exaned. as DSII xopose. bv emission from clustcys of galaxies. whose x-ray cluperatures typically jo arouid a few keV rather than he 0.112 keV nocdeled here (see. for example. David ct al. 1993)).," This also suggests that all variations in the diffuse backgrounds for the fields we examined cannot be explained, as BSH propose, by emission from clusters of galaxies, whose x-ray temperatures typically lie around a few keV rather than the 0.142 keV modeled here (see, for example, David et al. \cite{david}) )." + The power-aw cOnrponeut to the s)ectziun fits all of he observed. fields rather well., The power-law component to the spectrum fits all of the observed fields rather well. + This agrees with the conclusions of Tsliüsaki (19973). who found that. within svsteniaic errors. the hieher-eucrey diffuse x-ravbackground is fat on angular scales of ~17 The distribution of diffuse x-rav backeround counts for our saniple is shown in Fig. 3..," This agrees with the conclusions of Ishisaki \cite{ishisaki}) ), who found that, within systematic errors, the higher-energy diffuse x-raybackground is flat on angular scales of $\sim 1\degr$ The distribution of diffuse x-ray background counts for our sample is shown in Fig. \ref{fig:ncts}. ." + The eutire sample has a meanof 2606.0+296.6 counts for the LO ksec exposure.," The entire sample has a meanof $2606.0 \pm 296.6$ counts for the 10 ksec exposure," +and earlier) is 0.2 whereas for the late tvpes (Sc and later) 145/2.2]e2.2.,and earlier) is 0.2 whereas for the late types (Sc and later) $[15/2.2] \approx 2.2$. + Figure LL shows the Dale sample in the same fashion., Figure \ref{DAL-15k-vs-7k} shows the Dale sample in the same fashion. + The sample covers a wide range of morphological types. but it is evident that barred galaxies are plentiful and especially galaxies which have been attached: with a peculiar Cp) morphology in addition to a regular Llubble type.," The sample covers a wide range of morphological types, but it is evident that barred galaxies are plentiful and especially galaxies which have been attached with a peculiar (`p') morphology in addition to a regular Hubble type." + The trend seen in the Roussel ancl Boselli samples is not clear at all., The trend seen in the Roussel and Boselli samples is not clear at all. + The whole sample groups strongly towards the Sc-mocel colour. including the morphological carly tvpe galaxies.," The whole sample groups strongly towards the Sc-model colour, including the morphological early type galaxies." + The peculiars Cp. ancl purely ος) and irregulars tend to have highest. MIIU/NLIB. ratios., The peculiars ('p' and purely `Pec') and irregulars tend to have highest MIR/NIR ratios. + The Dale sample also has many more galaxies with significantly lower 6.7/15] compared to the Roussel/Bosclli sample., The Dale sample also has many more galaxies with significantly lower $[6.7/15]$ compared to the Roussel/Boselli sample. + The dillerenee mainly comes from galaxies with hieh AIRYNIR: ratios., The difference mainly comes from galaxies with high MIR/NIR ratios. + This is true regardless of the ~40 per cent ciscrepaney in the photometry mentioned earlier., This is true regardless of the $\sim 40$ per cent discrepancy in the photometry mentioned earlier. + The Boselli ancl Roussel galaxies on the other hand are stronely concentrated along the one-to-one correlation line where 6.7/15]z1. where the galaxies are. supposedly dominated by quicscent ISM.," The Boselli and Roussel galaxies on the other hand are strongly concentrated along the one-to-one correlation line where $[6.7/15] \approx 1$, where the galaxies are supposedly dominated by quiescent ISM." + We will return to this point in Section 4.2.2.., We will return to this point in Section \ref{clues}. + As can be seen in Figs., As can be seen in Figs. + LO and 11... we have divided the diagram into four regions with the dotted. lines: the areas roughly correspond to Iow-redshift earlv-tvpes. Sab spirals. Sed's. anc “AGN? (the latter class includes several types of active sources QSOs. Sevíert nuclei. ULIRGSs. strong starbursts).," \ref{ROUBOS-15k-vs-7k} and \ref{DAL-15k-vs-7k}, we have divided the diagram into four regions with the dotted lines: the areas roughly correspond to low-redshift early-types, Sab spirals, Scd's, and 'AGN' (the latter class includes several types of active sources QSOs, Seyfert nuclei, ULIRGs, strong starbursts)." + The dividing lines in the figures can be obtained from log15/2.2]2.6.7/2.2]|b where is b—1.0.0.3. ancl 1.67 starting from the lower Left. respectively.," The dividing lines in the figures can be obtained from $\log [15/2.2] = +-\log [6.7/2.2] + b$ where is $b= -1.0, 0.3$, and 1.67 starting from the lower left, respectively." + The Roussel and Boselli galaxies fall very well into their areas., The Roussel and Boselli galaxies fall very well into their areas. +" Disregarding DCDs. there are only 6 galaxies out of 34 in a ""wrong area. and of these. 5 are very close to the border-"," Disregarding BCDs, there are only 6 galaxies out of 34 in a `wrong' area, and of these, 5 are very close to the border-lines." + his classification does not work as well for the Dale sample though., This classification does not work as well for the Dale sample though. + We conclude that according to the nearby comparison sample the NIBMILI two-colour diagrams clo discriminate between types of normal galaxies. especially those which have 6.7/15]z1.," We conclude that according to the nearby comparison sample the NIR/MIR two-colour diagrams do discriminate between types of normal galaxies, especially those which have $[6.7/15] \approx 1$." + Where are our ELAIS ealaxics in this classification?, Where are our ELAIS galaxies in this classification? + The ELALS sample as a whole clearly. groups towards the late Hubble types., The ELAIS sample as a whole clearly groups towards the late Hubble types. + However. as seen above. ΛΙMIT flux ratio may not be a good indication of morphological type for those galaxies with low 6.715].," However, as seen above, NIR/MIR flux ratio may not be a good indication of morphological type for those galaxies with low $[6.7/15]$." + Nevertheless. of the 29 ealaxies in Table 2 (see Fie. 6))," Nevertheless, of the 29 galaxies in Table 2 (see Fig. \ref{15k-vs-7k}) )" + there are 21 galaxies in the Sed-region and 5 in the Sab-region., there are 21 galaxies in the Scd-region and 5 in the Sab-region. + Two are found in the upper-most region in the [ar right — in Section 4.3. they are shown to be potential AGN., Two are found in the upper-most region in the far right – in Section \ref{qsos} they are shown to be potential AGN. + Onlv one galaxy seems to be an carly type. though it does have excess L5pun Lux.," Only one galaxy seems to be an early type, though it does have excess $15 \umu$ m flux." + Indeed. early-type galaxies have been shown to have widely dilfering amounts of cust (see Madden. Vigroux Sauvage 1999. and references therein).," Indeed, early-type galaxies have been shown to have widely differing amounts of dust (see Madden, Vigroux Sauvage 1999, and references therein)." +" ""Eraditional. ellipticals. with no significant. LSAL presence. would not have been seen at all by the ΓΑΛΛΟ filter in the ELAIS survey."," `Traditional' ellipticals, with no significant ISM presence, would not have been seen at all by the LW3 filter in the ELAIS survey." + As shown in the inset of Fig. 2..," As shown in the inset of Fig. \ref{relstar_matches1}," + there are several probable cllipticals which are detected only in LW2., there are several probable ellipticals which are detected only in LW2. + All the Largest. galaxies which show clear morphology in our data (Fig. l..," All the largest galaxies which show clear morphology in our data (Fig. \ref{nir-early}," + those labeled in Fig. 6)), those labeled in Fig. \ref{15k-vs-7k}) ) + are in consistent classification areas: “AC is the carly type galaxy and the rest are spirals., are in consistent classification areas: 'A' is the early type galaxy and the rest are spirals. + Object. I2 is a disk galaxy with a very bright compact nucleus., Object E is a disk galaxy with a very bright compact nucleus. + Lt has the lowest 6.7/15] ratio of these five bright galaxies. indicating star-formation. as will be discussed next.," It has the lowest $[6.7/15]$ ratio of these five bright galaxies, indicating star-formation, as will be discussed next." + Aluch cliscussecl tracers of star-formation include the La emission of a galaxy. the UV-continuum. and total Lar-IR. DIuminosity.," Much discussed tracers of star-formation include the $\alpha$ emission of a galaxy, the UV-continuum, and total far-IR luminosity." + I0 is also well-known that star-formation in galaxies occurs in two very distinct. places: in the disks of spirals and in compact circumnuclear regions (for a comprehensive review. see Wennicutt 1998).," It is also well-known that star-formation in galaxies occurs in two very distinct places: in the disks of spirals and in compact circumnuclear regions (for a comprehensive review, see Kennicutt 1998)." + In. principle the mid-LHt could help in solving some of the uncertainties related. to. the mentioned. diagnostics: mmnid-Llt is certainly less prone to extinction than UV and Ho studies: it could also help in determining the heating source of LR emission. which alfects the accuracy of the Ες diagnostic.," In principle the mid-IR could help in solving some of the uncertainties related to the mentioned diagnostics: mid-IR is certainly less prone to extinction than UV and $\alpha$ studies; it could also help in determining the heating source of IR emission, which affects the accuracy of the FIR diagnostic." + The FUR tracer is known to work well for. cireumnuclear, The FIR tracer is known to work well for circumnuclear +where g=ΠΗΓΗΣ. and cj. ον. cs. us well as eto. dy. do. and «s are constants depending on the core composition of the companion star.,"where $q\equiv m_1/m_2$, and $c_1$ , $c_2$, $c_3$ as well as $a_0$, $a_1$, $a_2$, and $a_3$ are constants depending on the core composition of the companion star." + The parameter y governs the strength of magnetic braking (c.f., The parameter $\gamma$ governs the strength of magnetic braking (c.f. + eq. (, eq. ( +36) in Rappaport. Verbunt Joss 1983).,"36) in Rappaport, Verbunt Joss 1983)." + The additional quantities are defined by (Johannsen et al., The additional quantities are defined by (Johannsen et al. +" 2009) Here. P is the orbitaldq period.g B ts 2l+qthe fraction of qmatter that is accreted by the black hole. £y 1s the adiabatic index of the companion star. and A, is the specific angular momentum in units of 27a7/P that is lost through the stellar wind. which carries away angular momentum J at a rate (Will Zaglauer 1989) In this expression. A, is the angular momentum loss due to stellar wind. 7, and 75 are the masses of the black hole and the companion star. respectively. siz; and si their time derivatives. and q=ni,ΓΗ. is the mass ratio."," 2009) Here, $P$ is the orbital period, $\beta$ is the fraction of matter that is accreted by the black hole, $\xi_{{\rm ad}}$ is the adiabatic index of the companion star, and $j_{\rm w}$ is the specific angular momentum in units of $2\pi a^2/P$ that is lost through the stellar wind, which carries away angular momentum $J$ at a rate (Will Zaglauer 1989) In this expression, $\dot{J}_{\rm w}$ is the angular momentum loss due to stellar wind, $m_1$ and $m_2$ are the masses of the black hole and the companion star, respectively, $\dot{m}_1$ and $\dot{m}_2$ their time derivatives, and $q=m_1/m_2$ is the mass ratio." + Observations of the system A0620-00 have been used previously in conjunction with the above theoretical prediction to constrain the asymptotic curvature radius to a value of Lx161um (Johannsen et al., Observations of the system A0620-00 have been used previously in conjunction with the above theoretical prediction to constrain the asymptotic curvature radius to a value of $L\leq161~{\rm\mu m}$ (Johannsen et al. + 2009)., 2009). + In the following. I apply the formalism above to the system XTE J1118+480.," In the following, I apply the formalism above to the system XTE J1118+480." + In order to obtain a constraint oi the asymptotic. curvature radius L of the extra dimension. It is essential to select a black-hole binary with an unevolved companion star.," In order to obtain a constraint on the asymptotic curvature radius $L$ of the extra dimension, it is essential to select a black-hole binary with an unevolved companion star." + In that case. the evolution term in equation (2)) can be neglected. and the binary can be used to constrain the AdS radius as long as the magnetic braking term is negligible compared to the evaporation term.," In that case, the evolution term in equation \ref{final}) ) can be neglected, and the binary can be used to constrain the AdS radius as long as the magnetic braking term is negligible compared to the evaporation term." + In the following I argue that this approach can be applied to the black-hole binary J1118--480. and I use previous measurements of its orbital period to place a bound on the rate of change of its orbital period.," In the following I argue that this approach can be applied to the black-hole binary J1118+480, and I use previous measurements of its orbital period to place a bound on the rate of change of its orbital period." + The system J11184-480 has been monitored for more than a decade (Remillard MeClintock 2006)., The system J1118+480 has been monitored for more than a decade (Remillard McClintock 2006). + The companion star of the black hole resembles a late-type main-sequence star of spectral type K7 V — MO V (Wagner et al., The companion star of the black hole resembles a late-type main-sequence star of spectral type K7 V – M0 V (Wagner et al. + 2001)., 2001). + In addition. the mean density is only ~50% higher than for a usual main-sequence MO star (MeClintock et al.," In addition, the mean density is only $\sim$ higher than for a usual main-sequence M0 star (McClintock et al." + 2001). and the mass ts only ~50% lower than that of such a star (see Charles Coe 20006).," 2001), and the mass is only $\sim$ lower than that of such a star (see Charles Coe 2006)." + It is important to note that this is not simply a normal star., It is important to note that this is not simply a normal star. + It has emerged out of an exeptional evolutionary history (see de Kool et al., It has emerged out of an exeptional evolutionary history (see de Kool et al. + 1986 for an example). and it does not evolve on a nuclear timescale.," 1986 for an example), and it does not evolve on a nuclear timescale." + For my analysis. however. it is sufficient that the secondary only behaves like a main-sequence star.," For my analysis, however, it is sufficient that the secondary only behaves like a main-sequence star." + Then the evolution term in equation (2)) is negligible., Then the evolution term in equation \ref{final}) ) is negligible. + Considering only the evaporatiot term and the magnetic braking term in equation (2)). I plot in Figure | the rate of change of the orbital period. versus the asymptotic curvature radius L in the extra dimension for the binary systems J1118-480 and A0620-00.," Considering only the evaporation term and the magnetic braking term in equation \ref{final}) ), I plot in Figure 1 the rate of change of the orbital period versus the asymptotic curvature radius $L$ in the extra dimension for the binary systems J1118+480 and A0620-00." + The parameters used in this plot are ἅμ= 08.p=OW fy=0. and y=0.," The parameters used in this plot are $\xi_{{\rm ad}}=0.8$, $\beta=0$, $j_{\rm w}=0$, and $\gamma=0$." + For values of the asymptotic curvature radius greater than L=35jm the evaporation term dominates the evolution of the orbital period in the case of JI118+480., For values of the asymptotic curvature radius greater than $L\simeq35~{\rm\mu m}$ the evaporation term dominates the evolution of the orbital period in the case of J1118+480. + Below thatvalue.the magnetic braking is predominant.," Below thatvalue,the magnetic braking is predominant." + For the binary A0620-00 the transition occurs at L=20yam (Johannsen et al., For the binary A0620-00 the transition occurs at $L\simeq20~{\rm\mu m}$ (Johannsen et al. + 2009)., 2009). +" Consequently. these sources are similar in constraining the asymptotic curvature radius of the extra dimension,"," Consequently, these sources are similar in constraining the asymptotic curvature radius of the extra dimension." +observing them would constitute a clear consistency check with the theory.,observing them would constitute a clear consistency check with the theory. + The Poisson peak height Te measures the average number density of galaxies and thus depends mainly on the minimum mass of galactic halos., The Poisson peak height $T_{\rm peak}^{\rm un-\delta}$ measures the average number density of galaxies and thus depends mainly on the minimum mass of galactic halos. +" We note that if significant X-ray heating happened to occur simultaneously with the coupling transition, then similar fluctuations in the X-ray flux from galaxies would generate 21-cm fluctuations that are even somewhat larger (Pritchard&Furlanetto2007);; while not included in previous studies, the X-ray fluctuations should similarly be enhanced by scattering and should also show cutoff at the H II bubble scale."," We note that if significant X-ray heating happened to occur simultaneously with the coupling transition, then similar fluctuations in the X-ray flux from galaxies would generate 21-cm fluctuations that are even somewhat larger \citep{Jonathan07}; while not included in previous studies, the X-ray fluctuations should similarly be enhanced by scattering and should also show a cutoff at the H II bubble scale." +" While X-ray heating could apossibly occur early, heating is insignificant except after the coupling fully saturates (Chen& Miralda-Escudé 2004)."," While X-ray heating could possibly occur early, heating is insignificant except after the coupling fully saturates \citep{Miralda}." +". 'The five quantitative characteristics we have focused on typically occur at relatively large scales — a fraction of a Mpc, or 10 arcseconds at z—20 — and correspond to relatively large (but still linear) fluctuations: 1-10 mK on a mean background of T;~—100 mK. Thus, the predictions are theoretically robust, and require observational capabilities only somewhat beyond those of the radio arrays being currently constructed."," The five quantitative characteristics we have focused on typically occur at relatively large scales – a fraction of a Mpc, or $\sim10$ arcseconds at $z=20$ – and correspond to relatively large (but still linear) fluctuations: 1–10 mK on a mean background of $\bar{T}_b \sim +-100$ mK. Thus, the predictions are theoretically robust, and require observational capabilities only somewhat beyond those of the radio arrays being currently constructed." +" Given current capabilities, 21-cm cosmology is the most promising method for firmly detecting and studying the properties of some of the earliest galaxies that ever formed."," Given current capabilities, 21-cm cosmology is the most promising method for firmly detecting and studying the properties of some of the earliest galaxies that ever formed." + We acknowledge support by Israel Science Foundation grant 629/05 and U.S. - Israel Binational Science Foundation grant 2004386., We acknowledge support by Israel Science Foundation grant 629/05 and U.S. - Israel Binational Science Foundation grant 2004386. +order of magnitude higher in the Type 1 AGN - including 38123. compared with MkEn3.,"order of magnitude higher in the Type 1 AGN - including 2M23, compared with Mkn3." + In considering a common origin for the soft. N-rav emission. we surmise that the ionised outflow seen in à Tvpe 2 AGN is cut olf from direct view at some minimum radius r by the same obscuring matter that hides the BLR. while ina Type E AGN the full extent of the outllow is visible.," In considering a common origin for the soft X-ray emission, we surmise that the ionised outflow seen in a Type 2 AGN is cut off from direct view at some minimum radius $r$ by the same obscuring matter that hides the BLR, while in a Type 1 AGN the full extent of the outflow is visible." + With the simplest assumption of a constant velocity. racial outllow. mass conservation vields afofed emission measure of ionised gas which increases as &.1.," With the simplest assumption of a constant velocity, radial outflow, mass conservation yields a emission measure of ionised gas which increases as $r^{-1}$." + That would require the ionisecL gas to extend. inward to ως where rer is the minimum radius observed. directly in Type 2 AGN.," That would require the ionised gas to extend inward to $r_{cut}$, where $r_{cut}$ is the minimum radius observed directly in Type 2 AGN." +" Taking Pea As intermediate between the BLIt and. NLR. and a discriminating Keplerian velocity of 2«107 Kms. I. ju; is then 101r. where r, is the gravitational radius."," Taking $r_{cut}$ as intermediate between the BLR and NLR, and a discriminating Keplerian velocity of $2\times10^{3}$ km $^{-1}$, $r_{cut}$ is then $\sim$$ 10^{4}$$r_{g}$, where $r_{g}$ is the gravitational radius." + To obtain a 10-fold increase in the integrated soft X-rav emission then iniplies the ionised flow in 2M23 to extend inward to 1077., To obtain a 10-fold increase in the integrated soft X-ray emission then implies the ionised flow in 2M23 to extend inward to $\sim$$10^{3}$$r_{g}$. + Is that consistent with observation?, Is that consistent with observation? + The escape velocity of gas at ~10%ry is —10! kin, The escape velocity of gas at $\sim$$10^{3}$$r_{g}$ is $\sim$$10^{4}$ km $^{-1}$. + ‘Turbulence in such gas would result in very broad wings to the X-ray absorption lines. apparently at odds with reported aand eerating spectra of BLAGN which are an order of magnitude narrower (e.g. Steenbrugge 22003. Ixaspi 22002).," Turbulence in such gas would result in very broad wings to the X-ray absorption lines, apparently at odds with reported and grating spectra of BLAGN which are an order of magnitude narrower (e.g. Steenbrugge 2003, Kaspi 2002)." + Llowever. those high dispersion. instruments are notably insensitive to broad features ancl broad wines could well remain undetected.," However, those high dispersion instruments are notably insensitive to broad features and broad wings could well remain undetected." + A similar - but more extreme - scenario was envisaged by Cierlinski and. Done (1994) in suggesting low energy absorption in highly turbulent matter as an explanation of the common form of the soft. X-ray spectra in many AGN., A similar - but more extreme - scenario was envisaged by Gierlinski and Done (1994) in suggesting low energy absorption in highly turbulent matter as an explanation of the common form of the soft X-ray spectra in many AGN. + In our proposed interpretation of the soft. excess in 2M23 we would expect the energy absorbed from the power law continuum by line-of-sight matter to be related. to the luminosity of an optically thin ionised gas by the the covering factor., In our proposed interpretation of the soft excess in 2M23 we would expect the energy absorbed from the power law continuum by line-of-sight matter to be related to the luminosity of an optically thin ionised gas by the the covering factor. + The values we find. of ~S-17 are consistent with the tvpical solid angle of ~1 srobserved in the biconical outflows of Tvpe 2 ACN.," The values we find, of $\sim$, are consistent with the typical solid angle of $\sim$ 1 sr in the biconical outflows of Type 2 AGN." + The ELEPIC spectrum of the Type 1. OSO iis unusual in showing low energy absorption a a level that allows a soft X-ray emission component to be resolved., The EPIC spectrum of the Type 1 QSO is unusual in showing low energy absorption at a level that allows a soft X-ray emission component to be resolved. + Modelling of the absorption and emission with the ASTAR code allows the form and strength of the soft. X-ray emission to be determined and shown to be consistent with the integrated: emission from a warm. photoionised. gas., Modelling of the absorption and emission with the XSTAR code allows the form and strength of the soft X-ray emission to be determined and shown to be consistent with the integrated emission from a warm photoionised gas. + A plausibility argument is given which suggests this enhanced soft. N-rav emission. (which should be a common feature in Type 1 AGN) arises from an inward. extension of the outllow responsible for the soft. X-ray emission in Sevfert 2 galaxies., A plausibility argument is given which suggests this enhanced soft X-ray emission (which should be a common feature in Type 1 AGN) arises from an inward extension of the outflow responsible for the soft X-ray emission in Seyfert 2 galaxies. + This is important in the context of the energy content. emission measure and origin of such outllows. since current. high resolution spectra are not. well-matehecl to the detection of broad spectral features that might arise in turbulent gas at the smaller raclii implied by our analysis.," This is important in the context of the energy content, emission measure and origin of such outflows, since current high resolution spectra are not well-matched to the detection of broad spectral features that might arise in turbulent gas at the smaller radii implied by our analysis." + The results. reported here are based on observations obtained withΤΟ an ESA science mission with instruments ancl contributions directly funded by LSA Alember States and the USA (NASA).," The results reported here are based on observations obtained with, an ESA science mission with instruments and contributions directly funded by ESA Member States and the USA (NASA)." + The authors wish to thank the SOC and SSC teams for organising the oobservations and initial data reduction., The authors wish to thank the SOC and SSC teams for organising the observations and initial data reduction. + KAD is pleased to acknowledge a Leverhulme Trust. Emeritus Fellowship ane WLP funding from PPARC., KAP is pleased to acknowledge a Leverhulme Trust Emeritus Fellowship and KLP funding from PPARC. + BIW is grateful for the financial support of GGÓO erant: NNCGOLGD2TG., BJW is grateful for the financial support of GO grant: NNG04GD27G. +briefly discussed 1- refs:conclude For a black hole accretion flow. persistent emission above the Eddington Limit is even more prohibitive thau sav for example. a star.,"briefly discussed in \\ref{s: conclude} + For a black hole accretion flow, persistent emission above the Eddington Limit is even more prohibitive than say for example, a star." + The Eddiugton Limit results from the condition of hvdrostatic equilibrium i| the limiting case where the gravitational acceleration =Vo is balanced eutirely by the radiatiou force. proportional to the radiative flux F aud opacity H.," The Eddington Limit results from the condition of hydrostatic equilibrium in the limiting case where the gravitational acceleration $=\bnabla\phi$ is balanced entirely by the radiation force, proportional to the radiative flux ${\bf F}$ and opacity $\kappa$." + The expression above can be transformed into the Eddington Lint Here. the opacity: is taken to be a constant over the Gaussian surface OV. which bounds the volume V. of the flow.," The expression above can be transformed into the Eddington Limit = Here, the opacity is taken to be a constant over the Gaussian surface $\partial V$, which bounds the volume $V$ of the flow." +" The mass of the disk is taken to be insignificant in comparison to the mass of the black hole so that Af,=AL. (sce SIL of Alramowie ct al.", The mass of the disk is taken to be insignificant in comparison to the mass of the black hole so that $M_{\bullet}=M_{_{\rm enc}}$ (see II of Abramowicz et al. + 1980)., 1980). + Note that the ecometry of the surface GV can be quite arbitrary. nuplvine that the Eddington Limit is applicable for a disk. rather than just for an object with spherical sviuuetry.," Note that the geometry of the surface $\partial V$ can be quite arbitrary, implying that the Eddington Limit is applicable for a disk, rather than just for an object with spherical symmetry." +" Given the mass of the black hole. A. [μι is specified by the opacitv. where # is set equal to the Thomson electrou-scatteriug opacity 8,4."," Given the mass of the black hole $M_{\bullet}$, $L_{_{\rm Edd}}$ is specified by the opacity, where $\kappa$ is set equal to the Thomson electron-scattering opacity $\kappa_{es}$." +" Iu addition. once the accretion power exceeds Eddington. then steady radiatively efficicut accretion is also hindered bv the coucition of radiative οαυτπα,"," In addition, once the accretion power exceeds Eddington, then steady radiatively efficient accretion is also hindered by the condition of radiative equilibrium." + For standard (thin or simi) a-disk accretion (Shakura Suuvaev 1973: Abriunowiez et al., For standard (thin or slim) $\alpha$ -disk accretion (Shakura Sunyaev 1973; Abramowicz et al. + 1988). the condition is eiven bv-," 1988), the condition is given by." +- The viscous dissipation rate is balanced by a conibination of radiative cooling Q5perpendicular to the midplaue aud the mweud advection of heat. quantified by SD6G ," The viscous dissipation rate $Q^+_{\rm vis}$ is balanced by a combination of radiative cooling perpendicular to the midplane and the inward advection of heat, quantified by $Q^-_{\rm adv}$." +"(Qanote that the radius at which the heat generated by viscous dissipation is advected iuto the hole. rather than lost by radiative cdiffusiou mediated. bv. the Thomson opacity &;4; — ie. the trapping radius Πες for values of the accretion: rate above ιο.M is given by where R,—GM,Cds the eravitatioual radius aud His the accretion rate in units of L,,,/02."," SD06 note that the radius at which the heat generated by viscous dissipation is advected into the hole, rather than lost by radiative diffusion – mediated by the Thomson opacity $\kappa_{es}$ – i.e., the trapping radius $R_{tr}$ , for values of the accretion rate above $L_{_{\rm Edd}}/c^2$, is given by where $R_g=GM_{\bullet}/c^2$ is the gravitational radius and $\dot m$ is the accretion rate in units of $L_{_{\rm Edd}}/c^2$." + For a flow with radiative efficiency. €. the ISCO is located at ηΠε.," For a flow with radiative efficiency $\epsilon$, the ISCO is located at $R_{in}\sim R_g/\epsilon$ ." +" Tt follows that as Σρι then Ry,>Ri."," It follows that as $L\rightarrow L_{_{\rm Edd}}$ , then $R_{tr}\rightarrow R_{in}$." + At the Eddinegtou Lit. the flow mareimally maintains a lieh level of radiative efficiency.," At the Eddington Limit, the flow marginally maintains a high level of radiative efficiency." +" Since Re,Xmi the not radiative cficiencey decreases in proportion a:1 and the huninosity is pinned to the Eddington value a result of the fact that gravitational power is xL/R."," Since $R_{tr}\propto\dot{m}$, the net radiative efficiency decreases in proportion $\dot{m}^{-1}$ and the luminosity is pinned to the Eddington value – a result of the fact that gravitational power is $\propto 1/R$." + Without addressing auv deep theoretical mechanisuis (turbulence. magnetic fields. reconnection. otc.)," Without addressing any deep theoretical mechanisms (turbulence, magnetic fields, reconnection, etc.,)," + it is possible to determine the necesmuw plysical requirenieuts for a black hole accretion flow to —maintain a high level of radiative cficieucy in the event that it persistently cits above the Eddington value., it is possible to determine the necessary physical requirements for a black hole accretion flow to maintain a high level of radiative efficiency in the event that it persistently emits above the Eddington value. + Tn order to cireiunvent the “trapping problem.” SD6 realized that there must be a form of vertical energv transport that separates binding energy from the mass of its origin. faster than radiative diffusion.," In order to circumvent the “trapping problem,” SD06 realized that there must be a form of vertical energy transport that separates binding energy from the mass of its origin, faster than radiative diffusion." + Au examination of eq., An examination of eq. + 7 reveals that the characteristic velocity at which thermal energy can be transported iu the vertical direction by diffusion mediated by electron scattering is Cain~efT. Where 7 is the Thomson optical depth of the flow.," \ref{e: rad_eq} reveals that the characteristic velocity at which thermal energy can be transported in the vertical direction by diffusion mediated by electron scattering is $v_{\rm diff}\sim c/\tau$, where $\tau$ is the Thomson optical depth of the flow." + By construction. a is a region that possesses relatively siall amounts of binding cucrey. but is the recipient of a disproportionate amount of it per unit time.," By construction, a is a region that possesses relatively small amounts of binding energy, but is the recipient of a disproportionate amount of it per unit time." + As a result. the corona is heated to a temperature above the photospheric temperature of the optically thick binding enerev reservolr.," As a result, the corona is heated to a temperature above the photospheric temperature of the optically thick binding energy reservoir." + If the trapping problem establishes the need for a corona. the departure from bydrostatic balance inferred from eq. 1.. ," If the trapping problem establishes the need for a corona, the departure from hydrostatic balance inferred from eq. \ref{e: hydro_stat}," +constrains its optical depth 7z.., constrains its optical depth $\tau_c$. + In the absence of other forces. the photosphere of the accretion flow cannot be iu hydrostatic equilibrium aud a radiatiou-driven wind is lunched frou the corona.," In the absence of other forces, the photosphere of the accretion flow cannot be in hydrostatic equilibrium and a radiation-driven wind is launched from the corona." + In order to avoid the couversion of photon enerev iuto outeoiug mechanical power of the wind. the optical depth of corona τ~1 (SDUG).," In order to avoid the conversion of photon energy into outgoing mechanical power of the wind, the optical depth of corona $\tau_c\sim 1$ (SD06)." + If r.2 a few. photous becomes red-shifted as a result of adiabatic losses as they trausfer their enerev to matter.," If $\tau_c\gtrsim$ a few, photons becomes red-shifted as a result of adiabatic losses as they transfer their energy to matter." + Iu such an eveut. the photon Iuninosity observed at infinitv cau be vaulshinglv small.," In such an event, the photon luminosity observed at infinity can be vanishingly small." + Powerful coronae universally appear in the spectral enerev distribution of sub-Eddineton accreting stellar and supermassive black holes., Powerful coronae universally appear in the spectral energy distribution of sub-Eddington accreting stellar and super-massive black holes. + Though binding euergv is stored in the ionic disk compouenut. upon dissipation in the corona gravitationalpower is transferred to the electrons.," Though binding energy is stored in the ionic disk component, upon dissipation in the corona gravitationalpower is transferred to the electrons." +Comptouization bv seed photous results in a power Luv distribution of X-ray photons. indicative of a,"Comptonization by seed photons results in a power law distribution of X-ray photons, indicative of a" +the kappasigma-clipped mean of pixel values in the other lniaeges.,the kappa-sigma-clipped mean of pixel values in the other images. + Special care has to be taken for the flatfüelding. since internal reflectious between the focal reducer optics and the Fabry-Perot etalon cau give rise to stravlight contributions iu the central area of the flatBelds. thus leading to a iucorrect flux calibration of the FP data.," Special care has to be taken for the flatfielding, since internal reflections between the focal reducer optics and the Fabry-Perot etalon can give rise to straylight contributions in the central area of the flatfields, thus leading to a incorrect flux calibration of the FP data." + Iu order to overcome this problem. fiat field exposures are taken through a regularly spaced multihole mask. allowing to measure the instrument transmission without noticeable stravlight contribution.," In order to overcome this problem, flat field exposures are taken through a regularly spaced multi-hole mask, allowing to measure the instrument transmission without noticeable straylight contribution." + After overlaving all images to the same world coordinae system the iniages for cach waveleugth setting aud filter are then added wp.," After overlaying all images to the same world coordinate system, the images for each wavelength setting and filter are then added up." + For eac το these suni frames he object search cugine SExtractor (ραπ Arnouts. 1996) is applied. with thresholds adjusted to their seeimg ancl exposure dcpth.," For each of these sum frames the object search engine SExtractor (Bertin Arnouts, 1996) is applied, with thresholds adjusted to their seeing and exposure depth." + The object posilous are corrected for he distortiou o ‘the camera optics. axd the object lists are nerecd to a MASTER table with averaged positious.," The object positions are corrected for the distortion of the camera optics, and the object lists are merged to a MASTER table with averaged positions." + For ucreius all objects are considered o be identical which ‘all into a common error circle of rradius., For merging all objects are considered to be identical which fall into a common error circle of radius. + The ποtology pariuneters of an object are determined on the suu frame where the object shows the highest S/N ratio. using the photometry package AIPIAPIOT ΜΕ Rosser. 1995).," The morphology parameters of an object are determined on the sum frame where the object shows the highest S/N ratio, using the photometry package MPIAPHOT (Meisenheimer Rösser, 1993)." + The photometry is performed on cach individual frame. bv inteerating the photons at the ceutroid object positions. with a Gaussian weight distribution. the width of which is determined such that the couvoltion of the seciug PSF with the weight function results iu a «απο PSF for all. funes.," The photometry is performed on each individual frame, by integrating the photons at the centroid object positions, with a Gaussian weight distribution, the width of which is determined such that the convolution of the seeing PSF with the weight function results in a common PSF for all frames." + The obtained flux Is then calibrated by tertiary spectroscopic standard sars established in cach CADIS field., The obtained flux is then calibrated by tertiary spectroscopic standard stars established in each CADIS field. + Finally. the single frame flux values are S/Naveight averaged with errors cleqjved from the counting statistics.," Finally, the single frame flux values are S/N-weight averaged with errors derived from the counting statistics." + Since the photomeIV weielit functiou is normalized to eive correct fluxes for stellar objects. the fluxes of extended objects are underesiniated aud need a correction according to their morphological parameters.," Since the photometry weight function is normalized to give correct fluxes for stellar objects, the fluxes of extended objects are underestimated and need a correction according to their morphological parameters." + The pre-selection of enussiou ine galaxies is based ou the fluxes in the FP imagesOo aud in the pre-filter mace., The pre-selection of emission line galaxies is based on the fluxes in the FP images and in the pre-filter image. +Oo Candidates have to fulfill two criteria: (1) For at least oue FP wavelength. the signal das to be larecr than the upper lint of the noise distributiym. typically located near 5o. (," Candidates have to fulfill two criteria: (1) For at least one FP wavelength, the signal has to be larger than the upper limit of the noise distribution, typically located near $\sigma$. (" +2) The signa-to-noise ratio of tlie Tuje feature in the FP scans above he pre-filter fiX Is ueher than 2.5. equivalent to abot t241020 >rere we Choose a very low threshok 1 order to be ος1uplee za ΙΟ stricter selection is possible ou the basis of the liιο fits described below).,"2) The signal-to-noise ratio of the line feature in the FP scans above the pre-filter flux is higher than 2.5, equivalent to about $2\times 10^{-20}$ $^{-2}$ (here we choose a very low threshold in order to be complete; a much stricter selection is possible on the basis of the line fits described below)." + This pre-selection viclds a few|nucred of emission lue galaxy candidates per field aid wavecheth window., This pre-selection yields a few hundred of emission line galaxy candidates per field and wavelength window. + Due to reflections wihin the FallV-Perot etalons emiploved. in CADIS. bright objects. uostlv stars. are accompanied by feaures about 6 lagiutides fünuter thaw the father object. axd appear at à fixed. offse position CI17)) away frou it.," Due to reflections within the Fabry-Perot etalons employed in CADIS, bright objects, mostly stars, are accompanied by features about 6 magnitudes fainter than the father object, and appear at a fixed offset position ) away from it." + Since i the pre-filter ages uo object should be seen at the same positions. these ghosts cau he easily sorted out aud rejected from je candiates List.," Since in the pre-filter images no object should be seen at the same positions, these ghosts can be easily sorted out and rejected from the candidates list." + Another type of ghosts on the suele FP funes Is produced by reflections of bright objects in]ICween FP etalon auc pre-filter., Another type of ghosts on the single FP frames is produced by reflections of bright objects in between FP etalon and pre-filter. + These ghosts :ypear gv11netrically to the optical axes and. due to clithering. fjiev show up at different positions in every frame.," These ghosts appear symmetrically to the optical axes and, due to dithering, they show up at different positions in every frame." + Tls these are casily identifiable aud already strougvy suppressed. by the correction for cosmic ravs in the standard data reduction., Thus these are easily identifiable and already strongly suppressed by the correction for cosmic rays in the standard data reduction. + Spurious objects were found to occur intjo wings of bright objects. due to variations in the extended wines of," Spurious objects were found to occur in the wings of bright objects, due to variations in the extended wings of" +"The discovery. using imfrared telescopes. of stars orbiting within an aresecoud of the ceutral object in our galaxy, together with accurate determinations of their orbits. has provided strong evidence for the existence there of a massive black hole (ALDII) of around 3.6«109AY, (sec Alexaider(2005) for a review).","The discovery, using infrared telescopes, of stars orbiting within an arcsecond of the central object $^*$ in our galaxy, together with accurate determinations of their orbits, has provided strong evidence for the existence there of a massive black hole (MBH) of around $3.6 \times 10^6 \,M_\odot$ (see \cite{alexander05} for a review)." + Ii addition to openiug a window ou the innermost region of the eaactic ceuter. the discovery of these stars has ma(e it possible to contemplate using orbial dynamics to probe the curved spacetime of a rotating lack. hole.," In addition to opening a window on the innermost region of the galactic center, the discovery of these stars has made it possible to contemplate using orbital dynamics to probe the curved spacetime of a rotating black hole." + The orbital periods o| these stars are on the scale of tens of vears. and thus most relativistic effects. such as the advance of the periceuter. are too sinall to be observed at present (sec. however Zuckeretal. (2006))," The orbital periods of these stars are on the scale of tens of years, and thus most relativistic effects, such as the advance of the pericenter, are too small to be observed at present (see, however \cite{zucker}) )." +") Nevertheless, there seems to be every expectation that. with iuproved observing capabilities. a population of stars siguificautly closer to the hole will eveutually be discovered. making orbital relativistic effects detectable2007)."," Nevertheless, there seems to be every expectation that, with improved observing capabilities, a population of stars significantly closer to the hole will eventually be discovered, making orbital relativistic effects detectable." +. Furthermore. plaus are cine developed to achieve infrared astrometry ou such objects at the level of LO) paresecouds (Eisenhaueretal.," Furthermore, plans are being developed to achieve infrared astrometry on such objects at the level of 10 $\mu$ arcseconds \citep{eisenhauer}." +2008).. Iigli-precision Doppler 1jeasurements may also be possible (Zuckeretal. 06).., High-precision Doppler measurements may also be possible \citep{zucker}. +". This makes it possibe to consider doing more man inerely detect relaivistic effects; but rather o provide the first testt «of the black hole ""no-id or uniqueness theorenis of ecucral relativity."," This makes it possible to consider doing more than merely detect relativistic effects, but rather to provide the first test of the black hole ``no-hair'' or uniqueness theorems of general relativity." + According to those tlCorelnus. c electrically jeutral black hole js οςupletely characterized. woits mass A and aneslar momentum J.," According to those theorems, an electrically neutral black hole is completely characterized by its mass $M$ and angular momentum $J$." + As a consequence. all the naItipole mmomeuts of its external spacetime are huctilonis of AL aud J. specifically. the cnadrupole nxue Qo=3AL (in units where Go=«= 1).," As a consequence, all the multipole moments of its external spacetime are functions of $M$ and $J$ , specifically, the quadrupole moment $Q_2 = -J^2/M$ (in units where $G=c=1$ )." + If the black hole were norotaπιο (J 0). then its οςerior metric Wold he that of Schavarzschild. axd the most imporali relativistic effect would be the advance ο the poriceuter.," If the black hole were non-rotating $J=0$ ), then its exterior metric would be that of Schwarzschild, and the most important relativistic effect would be the advance of the pericenter." + Tf it is rotating. then two new phenoniena occur. the drvageineao of inertial frames a1xd the effects of the holes quadrupolemoment. cading not onlv to," If it is rotating, then two new phenomena occur, the dragging of inertial frames and the effects of the hole's quadrupolemoment, leading not only to" +welghts are slowly varying. the post-correlation canceller ts equivalent to the dual-reference MK2b canceller.,"weights are slowly varying, the post-correlation canceller is equivalent to the dual-reference MK2b canceller." + Another way in which the MK2b and post-correlation canceller techniques can differ is in their instabilities at low INR levels., Another way in which the MK2b and post-correlation canceller techniques can differ is in their instabilities at low INR levels. + Equations (12)) and (16)) have denominators that become zero-mean noise when there is no correlated RFI signal. which can lead to numerical errors.," Equations \ref{mk2 pre +corr weights}) ) and \ref{CORRECTION SPECTRUM MK2}) ) have denominators that become zero-mean noise when there is no correlated RFI signal, which can lead to numerical errors." + The coefficients of the single-reference techniques go to zero when the RFI becomes weak and the cancellers automatically turn. off., The coefficients of the single-reference techniques go to zero when the RFI becomes weak and the cancellers automatically turn off. + These issues are discussed next., These issues are discussed next. +" Equations (12)) and (16)) show that the dual-reference cancellers can have stability problems when (VA,«1.", Equations \ref{mk2 pre corr weights}) ) and \ref{CORRECTION SPECTRUM MK2}) ) show that the dual-reference cancellers can have stability problems when $\it{INR}_r\ll 1$. + In frequency channels where the correlated interference Is zero or very small. (12)) and (16)) are noise dominated and can result in a division by zero (or very close to zero).," In frequency channels where the correlated interference is zero or very small, \ref{mk2 pre corr weights}) ) and \ref{CORRECTION SPECTRUM +MK2}) ) are noise dominated and can result in a division by zero (or very close to zero)." + This cannot occur in the MKI cancellers since (6)) goes to zeroas [>0 and they turn off.," This cannot occur in the MK1 cancellers since \ref{mk1 pre corr +weights b}) ) goes to zero as $I\rightarrow0$ and they turn off." + A modified post-correlation canceller has been suggested by Briggsetal.(2000) 1n which an extra term is added to the denominator of (16)):, A modified post-correlation canceller has been suggested by \citet{Briggs2000} in which an extra term is added to the denominator of \ref{CORRECTION SPECTRUM MK2}) ): +day period.,day period. + The uuuber of photous detected by a 50 ksec observation of such à source is ~LOO. consistent with the supposed IRS 13 source secu bv Dasanuotff (1999).," The number of photons detected by a 50 ksec observation of such a source is $\sim 100$, consistent with the supposed IRS 13 source seen by Baganoff (1999)." + Note that the mua observations of IRS 13E2 xobablv do not correspond to the WTIs companion but rather to the exteuded cinission due to the the ejected nebula frou the WRs LBV phase., Note that the mm observations of IRS 13E2 probably do not correspond to the WR's companion but rather to the extended emission due to the the ejected nebula from the WR's LBV phase. + Thus he binary separation is not constrained to match that of the resolve Lui sources., Thus the binary separation is not constrained to match that of the resolved mm sources. + Another possible interpretation of IRS 13 which would explain the observation ollows from the sugecstion bv Gerhard (2000) that the QC Tel cluster is the remains of a disrupted cluster tha formed tens of parsecs from Ser A*., Another possible interpretation of IRS 13 which would explain the observation follows from the suggestion by Gerhard (2000) that the GC HeI cluster is the remains of a disrupted cluster that formed tens of parsecs from Sgr A*. + Tf true. a massive binary svstei may uot have survived the imtfall.," If true, a massive binary system may not have survived the infall." + This raises the possibility that IRS 13E2 hides a compact object. such ax a ~10AL: black-hole. which is accreting the wind from IRS 19101.," This raises the possibility that IRS 13E2 hides a compact object, such as a $\sim 10~\mathrm{M}_{\sun}$ black-hole, which is accreting the wind from IRS 13E1." + That is. IRS 13E may be an extended N-ray system.," That is, IRS 13E may be an extended X-ray system." + This ix particularly applicable in GC since dvuamical friction over the lifetime of the Galaxy is likely to result iu a highdeusitv of LOAL: black-holes in the central parsec (sec. ce... Morris 1993).," This is particularly applicable in GC since dynamical friction over the lifetime of the Galaxy is likely to result in a highdensity of $\sim 10~\mathrm{M}_{\sun}$ black-holes in the central parsec (see, e.g., Morris 1993)." + One can estimate the X-ray Iuuinosity of such a system using where e is the accretion efficiency (taken as 0.1). AL is the mass of the black-hole. ο is the relative velocity of the black-hole to the wind. aud D is the distauce between the WR star and the black-hole.," One can estimate the X-ray luminosity of such a system using where $\epsilon$ is the accretion efficiency (taken as 0.1), $M$ is the mass of the black-hole, $v$ is the relative velocity of the black-hole to the wind, and $D$ is the distance between the WR star and the black-hole." +" If Af=10M. e—1000 km ὃν and D=h00 AU. then L,~O1L:."," If $M = 10~\mathrm{M}_{\sun}$, $v = 1000$ km $^{-1}$, and $D = 500$ AU, then $L_x \sim 0.1~\mathrm{L}_{\sun}$." + The spectrum. as shown in Fig. 3..," The spectrum, as shown in Fig. \ref{fig:WRBH}," + would be shifted to slightly higher cuerey. the fix would be less attenuated x the hieh column aud thus the ~15 detected photons would be cousisteut with the IRS 13 detection of Daganoff (1999).," would be shifted to slightly higher energy, the flux would be less attenuated by the high column and thus the $\sim 45$ detected photons would be consistent with the IRS 13 detection of Baganoff (1999)." + Note that. if the ~10 mas | relative uuu xoper motions (Zhao Goss 1999) are ασ indication. he system may be unbound. making IRS 13E a unique ransicut N-rav source.," Note that, if the $\sim 10$ mas $^{-1}$ relative mm proper motions (Zhao Goss 1999) are any indication, the system may be unbound, making IRS 13E a unique transient X-ray source." + Iu summary. whilst a single massive star of unusually Hel N-rav luminosity cannot be discounted we believe a colliding winds binary system best fits the various observations.," In summary, whilst a single massive star of unusually high X-ray luminosity cannot be discounted, we believe a colliding winds binary system best fits the various observations." + A DII svsteui also has some difficulties with reconciling the resolved nuu sources (uuless the second source is unassociated)., A BH system also has some difficulties with reconciling the resolved mm sources (unless the second source is unassociated). + Long texu monitoring at nun waveleneths as well as a long-iuteeration observation would help determine precisely what type of object lurks in IRS 13E., Long term monitoring at mm wavelengths as well as a long-integration observation would help determine precisely what type of object lurks in IRS 13E. + (Ixuutsou (Alonsoctal.2009a:Suellen2009).. (ebbetal.2009).. (ebbetal.2010)... (Bargeetal.2008).. (Alonsoetal.2008).," \citep{knutson08, machalek, christiansen, +todorov}, \citep{charb05, deming05}. \citep{alonso09a, snellen09}. \citep{hebb09}, \citep{hebb10}, \citep{barge}, \citep{alonso08}." +. janjan (Cillou.etal.2010).. (Demingetal.2007) 3.6- jan. μαι ," $\mu$$\mu$ \citep{gillon10}, \citep{deming07} $3.6$ $\mu$ $\mu$ " +shows a high velocity red wing. more promiucut than that observed iun line profile (1)ottoni paucl of Fie. D).,"shows a high velocity red wing, more prominent than that observed in line profile (bottom panel of Fig. \ref{Fespec}) )." + Five SO» lines were detected with the SALA in its compact configuration (Table 23)., Five $_2$ lines were detected with the SMA in its compact configuration (Table \ref{Tlowspec}) ). + All of them show nuresolved chussion at the origm ofthe thermal radio jet. which coimcides with the AIO (sub)nüllimoeter continuum source (Fig. 7))," All of them show unresolved emission at the origin of the thermal radio jet, which coincides with the MM1 (sub)millimeter continuum source (Fig. \ref{Fposter}) )." + aud were also detected by the SALA in its very extended configuration., and were also detected by the SMA in its very extended configuration. + The other SO» lines were uudetected due to their low intensity. their (probably) partially resolved nature aud the lower scusitivity of the ligh augular resolution data.," The other $_2$ lines were undetected due to their low intensity, their (probably) partially resolved nature and the lower sensitivity of the high angular resolution data." + The panels a) aud b) of Fie., The panels a) and b) of Fig. + S show the velocity chamnel cubes of the aud lues (nuages of the combined data with robust 0.3)., \ref{Fcubos} show the velocity channel cubes of the and lines (images of the combined data with robust 0.3). + The molecular structure at the position of NMI appears at the to velocity channels. while the peak velocity is c1340 (seo Table 21).," The molecular structure at the position of MM1 appears at the to velocity channels, while the peak velocity is $\simeq 13.0$ (see Table \ref{Tlowspec}) )." + The peak. velocity of the molecular structure is therefore redshitted with respect to the large scale dense core velocity by ~1.21..., The peak velocity of the molecular structure is therefore redshifted with respect to the large scale dense core velocity by $\sim1.2$. + The bluesbifted chanucls (8.7 to 1)) are seen to the east. while the redshifted channels (ELE and 1)) are secu to the west with respect to the thermal radio jet aud the l.l nuu continui peak position.," The blueshifted channels (8.7 to ) are seen to the east, while the redshifted channels (14.4 and ) are seen to the west with respect to the thermal radio jet and the 1.4 mm continuum peak position." + The left panels of Fig., The left panels of Fig. +" show the zero order moment (i.c.. iuteerated cussion) 9.and first order moment (16.. integrated. velocity weighted by the intensity) tages built wp from the 1654,2ud lieh augular resolution cubes."," \ref{Fmoms} show the zero order moment (i.e., integrated emission) and first order moment (i.e., integrated velocity weighted by the intensity) images built up from the and high angular resolution cubes." +2 The molecular structure toward MALL is compact and its peak coincides with the deconvolvedposition of the thermal radio ordenjet within (072., The molecular structure toward MM1 is compact and its peak coincides with the position of the thermal radio jet within $0\farcs2$. + The sizes of the zero momceut images of and are presented in Table 3.., The deconvolved sizes of the zero order moment images of and are presented in Table \ref{Tmdyn}. + Assmuiug a distance of 1.7 kpc to20Ls8.. the equivalent radius of the emission VET aém) 1s less thaw about 850 AU for both lines.," Assuming a distance of 1.7 kpc to, the equivalent radius of the emission $\sqrt{Area/\pi}$ ) is less than about 850 AU for both lines." + The first order moment nuages clearly show the southeastnortlwvest velocity eradieut ucarly perpendicular to the radio jet dshifteaxis., The first order moment images clearly show the southeast–northwest velocity gradient nearly perpendicular to the radio jet axis. + In fact. the position anglebetween the most red aud blucshitted ehiaunels are about ~1107 aud ~1307 for the aud lines. respectively.," In fact, the position angle between the most redshifted and blueshifted channels are about $\sim110\degr$ and $\sim130\degr$ for the and lines, respectively." + Iu section 85.1 woe argue that the SO» οπήκο arises from a disk/riug rotating structure., In section 5.1 we argue that the $_2$ emission arises from a disk/ring rotating structure. + Iu this section we estimate the plivysical characteristics of the MMI «disk. such as. volume density aid temperature by mcaus of RADEN inodeling.," In this section we estimate the physical characteristics of the MM1 disk, such as volume density and temperature by means of RADEX modeling." + We used RADEN to simulate the line iuteusities of the five observed SO» transitions (Fie. 10))., We used RADEX to simulate the line intensities of the five observed $_2$ transitions (Fig. \ref{Fspec_so2}) ). + The RADEN code is a non-LTE molecular radiative trausfer code which asses an isothermal homogeneous medium (2))., The RADEX code is a non-LTE molecular radiative transfer code which assumes an isothermal homogeneous medium \citealt{2007VanderTak}) ). + This assiunaiption is reasonable as à first approach to constraiu the physical properties of the eas traced by the SO» since the observed ues are optically thick (see below)., This assumption is reasonable as a first approach to constrain the physical properties of the gas traced by the $_2$ since the observed lines are optically thick (see below). + We explored a range of values between 50 and 300 I& in the kinetic teniperature. between LOT and Lott iin the volume density. (Πο). and between 1055 aud LOM iin the SOs. colunu deusitv. AN(SOS)," We explored a range of values between 50 and 300 K in the kinetic temperature, between $10^7$ and $10^{11}$ in the volume density, $n$ $_2$ ), and between $10^{14}$ and $10^{19}$ in the $_2$ column density, $N$ $_2$ )." + Iu order to constrain the plivsical properties of the SO. cimitting reeion the next sclieme was followed:, In order to constrain the physical properties of the $_2$ emitting region the next scheme was followed: +for the wind: and whether to allow the X-ray volume filling factor to vary with radius (as parameterized by 4 in fxxrἝν where the filling factor. fx. contributes to the emissivity. 7 sec Owocki&Cohen (2001))).,"for the wind; and whether to allow the X-ray volume filling factor to vary with radius (as parameterized by $q$ in $f_{\rm X} +\propto r^{-q}$, where the filling factor, $f_{\rm X}$, contributes to the emissivity, $\eta$ – see \citet{oc2001}) )." + We will very brielle describe those factors that we found. to be unimportant. and cliscuss in more detail those that did make a dilference.," We will very briefly describe those factors that we found to be unimportant, and discuss in more detail those that did make a difference." + Ehe baseline model fitting we describe here is the modelling described in the previous subsection for the 15.014 line. except that we fit only the MEG. data (so that we may evaluate the effect of including the LEC data).," The baseline model fitting we describe here is the modelling described in the previous subsection for the 15.014 line, except that we fit only the MEG data (so that we may evaluate the effect of including the HEG data)." + We examined the default. background: spectra. which were very weak. and also experimented with fitting the 15.014 line with and without the background spectrum subtracted and found almost no cdillerence in the [it quality or fit parameters.," We examined the default background spectra, which were very weak, and also experimented with fitting the 15.014 line with and without the background spectrum subtracted and found almost no difference in the fit quality or fit parameters." + We therefore opt to neglect. the background when fitting each of the lines in the spectrum., We therefore opt to neglect the background when fitting each of the lines in the spectrum. + The sensitivity to the continuum fit is a little greater. but. still. nearly negligible.," The sensitivity to the continuum fit is a little greater, but still nearly negligible." + When we changed the continuum level by a factor oftwo which is larger than the formal uncertainty on the continuum level none of the parameter. values. changed bv more than ten percent., When we changed the continuum level by a factor of two – which is larger than the formal uncertainty on the continuum level – none of the parameter values changed by more than ten percent. + Some lines in the spectrum are blended: with weaker lines., Some lines in the spectrum are blended with weaker lines. + The cleanest way to handle this situation is to exclude the contaminated bins from the modelling., The cleanest way to handle this situation is to exclude the contaminated bins from the modelling. + To test the ellects of this. we eliminated 0.03 from the red wing of the 15.014 line and refit the data.," To test the effects of this, we eliminated 0.03 from the red wing of the 15.014 line and refit the data." + We then repeated this experiment liminating 0.07 - leaving only about two-thirds of the data., We then repeated this experiment eliminating 0.07 - leaving only about two-thirds of the data. + Even in is second. extreme case. the fit parameters varied by less than ten percent and the confidence regions only expanded slightIv.," Even in this second, extreme case, the fit parameters varied by less than ten percent and the confidence regions only expanded slightly." + For most lines. the LEC data is significantly weaker than the MEC data.," For most lines, the HEG data is significantly weaker than the MEG data." + We find for the 15.014 line that including the LEG data changes the best-fitting model parameters by. at most. a few percent. but it does tighten the confidence limits somewhat.," We find for the 15.014 line that including the HEG data changes the best-fitting model parameters by, at most, a few percent, but it does tighten the confidence limits somewhat." + The cllect of including the σι cata is more significant. for the shorter wavelength lines. where the effective area of the LEC is larger relative to the MEG.," The effect of including the HEG data is more significant for the shorter wavelength lines, where the effective area of the HEG is larger relative to the MEG." + Phere is very little penalty for including the LEG data. so we do so for all lines shortwarel of 16A.," There is very little penalty for including the HEG data, so we do so for all lines shortward of 16." +.. We also fit the MEG and HEC data separately for the 15.014 line to verify that there are not svstematic elfects between these two spectra: and. there are not., We also fit the MEG and HEG data separately for the 15.014 line to verify that there are not systematic effects between these two spectra; and there are not. + The separate fits eive results that are very similar to each other. with significantly overlapping GS percent. confidence limits or all parameters.," The separate fits give results that are very similar to each other, with significantly overlapping 68 percent confidence limits for all parameters." + The original Owocki&Cohen(2001) line profile mocel allows for à racially varving filling factor of X-ray emitting plasma. parameterized as a power law function of radius.," The original \citet{oc2001} line profile model allows for a radially varying filling factor of X-ray emitting plasma, parameterized as a power law function of radius." + Values of the power-law index. q. wt diller significantly. rom zero (no racial variation) can cause changes in the line xoliles that are not insignificant. ellectively weighting the emission from parts of the wind according to their velocity (via the beta-velocity law relationship between velocity ancl radius).," Values of the power-law index, $q$, that differ significantly from zero (no radial variation) can cause changes in the line profiles that are not insignificant, effectively weighting the emission from parts of the wind according to their velocity (via the beta-velocity law relationship between velocity and radius)." + Llowever. we find that when we allow q to be a free xvwameter the best-litting value is generally. very close to zero.," However, we find that when we allow $q$ to be a free parameter the best-fitting value is generally very close to zero." + For the representative 15.014 linc. itisq=0.09. and q=0 is included in the 68 percent confidence range.," For the representative 15.014 line, it is $q=-0.09$, and $q=0$ is included in the 68 percent confidence range." + Ehe general result is consistent with that found for this and other stars (Ixramoeretal.2003:Cohenetal. 2006).," The general result is consistent with that found for this and other stars \citep{kco2003,Cohen2006}." +. Thus. to keep the number of free parameters manageable. we fix q=0.," Thus, to keep the number of free parameters manageable, we fix $q=0$." + The factors discussed above have a very minor inluence on the results of the line fitting., The factors discussed above have a very minor influence on the results of the line fitting. + However. the remaining factors can have a significant ellect.," However, the remaining factors can have a significant effect." + The velocitv-Iaw exponent. 2. allects line profiles for two reasons: (1) the velocity law alfects the mapping between radius ancl Doppler shifted: wavelength. and so alfects the emission. profile: and (2) via the continuity equation. it allects the density ancl so allects the level of both the emission and the absorption.," The velocity-law exponent, $\beta$, affects line profiles for two reasons: (1) the velocity law affects the mapping between radius and Doppler shifted wavelength, and so affects the emission profile; and (2) via the continuity equation, it affects the density and so affects the level of both the emission and the absorption." + Indeed. for our representative emission line. when we change the value of 3 from 1 to 0.8. both and change hy LO to 20 percent.," Indeed, for our representative emission line, when we change the value of $\beta$ from 1 to 0.8, both and change by 10 to 20 percent." + Phe determinations οἱ for vary [rom at least 0.9 to 1.15. and so using a value of 3=1 scons reasonable. especially as it speeds the calculation of the line profile model by allowing the optical depth integral to be done analytically. so we use that value for all the moclel fitting results reported.here.," The determinations of $\beta$ for vary from at least 0.9 to 1.15, and so using a value of $\beta = 1$ seems reasonable, especially as it speeds the calculation of the line profile model by allowing the optical depth integral to be done analytically, so we use that value for all the model fitting results reportedhere." + Lin the future. a new ane more accurate determination of 3 is mace. and it clilfers significantly from 3= 1. then the results reported. in this," If, in the future, a new and more accurate determination of $\beta$ is made, and it differs significantly from $\beta=1$ , then the results reported in this" +raw uunbers reflect the differences in the space deusities measurements outlined in Table 5 and highlight that a vast majoritv of the new EDCCIL systems are of lower richness (in the EDCCII catalogue).,raw numbers reflect the differences in the space densities measurements outlined in Table \ref{space} and highlight that a vast majority of the new EDCCII systems are of lower richness (in the EDCCII catalogue). +" Although. we do note that 113 of the 227 R,,©100 svsteius (6354)) axe not in the Abell catalogue Ovhich correspouds to RC20 systems)."," Although, we do note that $143$ of the $227$ $R_m\ge100$ systems ) are not in the Abell catalogue (which corresponds to ${\rm RC\ge0}$ systems)." + Again. these findines agree with the original EDCC cluster catalogue where almost of EDCC clusters were new compared to the Abell catalogue.," Again, these findings agree with the original EDCC cluster catalogue where almost of EDCC clusters were new compared to the Abell catalogue." + These two survevs therefore lend credence to the idea (already stated by Abell 1958 aud Abell et al., These two surveys therefore lend credence to the idea (already stated by Abell 1958 and Abell et al. + 1989) that the Abell catalogue should not be used for statistical studies., 1989) that the Abell catalogue should not be used for statistical studies. + The authors would like to thaul Brad Holden. Lori Lubin. Mare Postinan and Wath Romer for their assistance caving the course of this work.," The authors would like to thank Brad Holden, Lori Lubin, Marc Postman and Kath Romer for their assistance during the course of this work." + We also thank Chris Collins. Stuart Lunden. Luigi Guzzo and Harvey MacCallivvay for allowing us free access to the EDSGC data.," We also thank Chris Collins, Stuart Lumsden, Luigi Guzzo and Harvey MacGillivray for allowing us free access to the EDSGC data." + This project was funded through NASA eraut NAG5-3202 (RON) aud two CMU Sununuer Cudereraduate Research Crants (DAD)., This project was funded through NASA grant NAG5-3202 (RCN) and two CMU Summer Undergraduate Research Grants (DAB). +" Abell. C. O.. 1958. ApJS. 3. Abell. C. O.. Corwin. H. €. Jr. Olowin. B. P.. 1989. ApJS. 70. Dalicall. N. A.. Soucira. B. AL. 1983. ApJ. 270. Dalicall. N. Ανν Fan. N.. Cen. R.. 1997. ApJ. I85L. Bower. BR. C... Castauder. EF. J.. Ellis. R. S. Couch. W. J.. Boehringer. 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R., Guzzo, L., 1997, MNRAS, 290," +where the values of a; are given in Table 2..,where the values of $a_j$ are given in Table \ref{jhtable}. + In Fig., In Fig. + 8(a) we plotted our data together with these polynomials., \ref{j-h-a} we plotted our data together with these polynomials. +" The polynomials based on the D05 models overestimate OUT Umodet Values (rms σ= 0.412), while those from the E96 models provide much better fit for all SNe except SN 2004et (rms σ=0.301, but c=0.178 without the data of SN 2004et)."," The polynomials based on the \citeauthor{dessart2005a} models overestimate our $v_{model}$ values (rms $\sigma=0.412$ ), while those from the E96 models provide much better fit for all SNe except SN 2004et (rms $\sigma=0.301$, but $\sigma=0.178$ without the data of SN 2004et)." +" We fitted Eq.(1)) to our data (Fig. 8(a),"," We fitted \ref{eq1}) ) to our data (Fig. \ref{j-h-a}," +", black curve).", black curve). + The resulting a; coefficients are in Table 2.., The resulting $a_j$ coefficients are in Table \ref{jhtable}. +" Our fit resulted in a much lower rms scatter, o=0.276."," Our fit resulted in a much lower rms scatter, $\sigma=0.276$." +" Repeating the fitting while omitting the data of SN 2004et, the result became very similar to that from the E96 models."," Repeating the fitting while omitting the data of SN 2004et, the result became very similar to that from the E96 models." +" Since ure is thought to be a better representative of the velocity at the photosphere than ugg, it is expected that Umodel can be predicted with better accuracy by measuring Ure."," Since $v_{Fe}$ is thought to be a better representative of the velocity at the photosphere than $v_{H\beta}$, it is expected that $v_{model}$ can be predicted with better accuracy by measuring $v_{Fe}$ ." +" Indeed, Fig."," Indeed, Fig." +" 7 suggests that the vre/v;oaer ratio is almost the same from SN to SN, unlike the ΌΗΡ/υπιοάεί ratio that can be quite different for different SNe."," \ref{allsn} suggests that the $v_{Fe}/v_{model}$ ratio is almost the same from SN to SN, unlike the $v_{H\beta}/v_{model}$ ratio that can be quite different for different SNe." +" Thus, we repeated the fitting of Eq.(1)) using ure instead of vizg (Fig. 8(b)))."," Thus, we repeated the fitting of \ref{eq1}) ) using $v_{Fe}$ instead of $v_{H\beta}$ (Fig. \ref{j-h-b}) )." +" We found the rms scatter of c=0.111, which is much lower than in the previous cases.", We found the rms scatter of $\sigma=0.111$ which is much lower than in the previous cases. + Thea; coefficients of this fitting are also included in Table 2.., The$a_j$ coefficients of this fitting are also included in Table \ref{jhtable}. + The tight relation between vre and vmoae in Fig., The tight relation between $v_{Fe}$ and $v_{model}$ in Fig. + 8(b) suggests a possibility to estimate Όπιοαει from the measured ure values., \ref{j-h-b} suggests a possibility to $v_{model}$ from the measured $v_{Fe}$ values. +" However, it is emphasized that SN-specific differences in the expansion velocities may exist, thus, model building for a particular SN, whenever possible, should always be preferred."," However, it is emphasized that SN-specific differences in the expansion velocities may exist, thus, model building for a particular SN, whenever possible, should always be preferred." + Nugentetal.(2006) found that ur. evolves as where c=—0.464+0.017., \citet{nugent06} found that $v_{Fe}$ evolves as where $c=-0.464 \pm 0.017$. +" After repeating the fitting of Eq.(2)) to our data, we found the exponent to be c=—0.663+ 0.01."," After repeating the fitting of \ref{eq2}) ) to our data, we found the exponent to be $c=-0.663 \pm 0.01$ ." +" Then, since the data of SN 2005cs are very different from the rest of the sample, we omitted the velocities of SN 2005cs and repeated the fitting."," Then, since the data of SN 2005cs are very different from the rest of the sample, we omitted the velocities of SN 2005cs and repeated the fitting." + This resulted in ο=—0.546+0.01 (Fig. 9(a)))., This resulted in $c= -0.546 \pm 0.01$ (Fig. \ref{nug-a}) ). + These two exponents marginally differ (at ~ 1o) from the value given by Nugentetal.(2006)., These two exponents marginally differ (at $\sim 1 \sigma$ ) from the value given by \citet{nugent06}. +". A possible source of this difference (beside the different velocity measurement techniques applied) may be that our sample covers the phases between +13 and +104 days, while the data by Nugentetal.(2006) are between +9 and +75 days."," A possible source of this difference (beside the different velocity measurement techniques applied) may be that our sample covers the phases between +13 and +104 days, while the data by \citet{nugent06} are between +9 and +75 days." + We alsoexamined how theSYNOW model velocities evolve in time., We alsoexamined how the model velocities evolve in time. +" Combining Eq.(1)) and Eq.(2)), the following relation has be derived (again, excluding SN 2005cs from the sample): where bo=0.467+0.15, b1=0.327+0.23 and bo0.174+ 0.11."," Combining \ref{eq1}) ) and \ref{eq2}) ), the following relation has be derived (again, excluding SN 2005cs from the sample): where $b_0=0.467 \pm 0.15$, $b_1=0.327 \pm 0.23$ and $b_2=0.174 \pm 0.11$ ." + The rms scatter is o=0.148 (Fig. 9(b)))., The rms scatter is $\sigma=0.148$ (Fig. \ref{nug-b}) ). +" As was mentioned in §??,, using SDSS data Poznanskial.(2010) examined the correlation between velocities measured from the absorption minima of HG and 45169 lines (see Fig. 10))."," As was mentioned in \ref{sec_pcyg}, using SDSS data \citet{poznanski} examined the correlation between velocities measured from the absorption minima of $\beta$ and $\lambda 5169$ lines (see Fig. \ref{pozn}) )." +" They found that there is a linearrelation given by vre(50d)=a- vgg(50d),where a=0.84+ 0.05."," They found that there is a linearrelation given by $v_{Fe}(50\rmn{d})=a \cdot v_{H\beta}(50\rmn{d})$ ,where $a=0.84 \pm 0.05$ ." + Using our sample we repeatedtheir fitting., Using our sample we repeatedtheir fitting. +" First, we used all epochs where both vga and ure were measured."," First, we used all epochs where both $v_{H\beta}$ and $v_{Fe}$ were measured." + The slope of the fitted line was a=0.791+0.012 (σ= 0.146)., The slope of the fitted line was $a=0.791 \pm 0.012$ $\sigma=0.146$ ). +" Then, we kept only the velocitiesobtained before day 40 2010).."," Then, we kept only the velocitiesobtained before day 40 \citep[similar to][]{poznanski}. ." + This resulted in, This resulted in +average after LO million vears and so older populations may oe attenuated less by dust. than vounger populations and herefore dominate the observed spectrum.,average after 10 million years and so older populations may be attenuated less by dust than younger populations and therefore dominate the observed spectrum. + The theoretical model spectra in their raw state represent a population in which all the stars are static. ving at precisely the same redshift or recession velocity. and makes no account for the velocity dispersion. of stars within the observed galaxies.," The theoretical model spectra in their raw state represent a population in which all the stars are static, lying at precisely the same redshift or recession velocity, and makes no account for the velocity dispersion of stars within the observed galaxies." +" To account for broadening due o the velocity. dispersion. of stars within a tvpical star-galaxy (=100kknmiss "" 7). we convolve our final. spectra with a boxcar function of widthLA."," To account for broadening due to the velocity dispersion of stars within a typical star-burstinggalaxy $\la 100$ $^{-1}$ ), we convolve our final spectra with a boxcar function of width." + For strongly star-forming galaxies at higher redshifts a higher. velocity dispersion might be appropriate., For strongly star-forming galaxies at higher redshifts a higher velocity dispersion might be appropriate. + Any new mocel must be tested against observations., Any new model must be tested against observations. + Here we compare our mocels to three dilferent sets of observations on sites of star-formation expected to have WR. stars present., Here we compare our models to three different sets of observations on sites of star-formation expected to have WR stars present. + Defore we compare our models to distant. galaxies dU is sensible to compare them to nearby unresolved. stellar populations., Before we compare our models to distant galaxies it is sensible to compare them to nearby unresolved stellar populations. + Therefore we compare our models to a large set of observations of voung massive star clusters compiled ov(1999)., Therefore we compare our models to a large set of observations of young massive star clusters compiled by. +. They observed a number of star clusters in nearby spiral galaxies. with broad-band ohoetometry., They observed a number of star clusters in nearby spiral galaxies with broad-band photometry. +" Since the host galaxies were spiral we assume he metallicity of the clusters is broadly solar ancl compare he observations to colours from our mocdels for a cluster with a mass of 10""M..."," Since the host galaxies were spiral we assume the metallicity of the clusters is broadly solar and compare the observations to colours from our models for a cluster with a mass of $10^5 \, {\rm M}_{\odot}$." + For comparison we have created a similar track from with the same total stellar mass and initial mass distribution., For comparison we have created a similar track from with the same total stellar mass and initial mass distribution. +" This track was calculated using ""Starburst90 for Windows! using the same AIF and total mass as for our models. the standard Geneva solar metallicity stellar evolution tracks. the Lejeune stellar atmosphere models ancl the remaining options at their default values."," This track was calculated using `Starburst99 for Windows' using the same IMF and total mass as for our models, the standard Geneva solar metallicity stellar evolution tracks, the Lejeune stellar atmosphere models and the remaining options at their default values." + We plot the results in Figure 1.., We plot the results in Figure \ref{ymclusters}. + Our tracks are shorter than the results as we terminate our simulations at 40 Myrs since we do not currently include stars with initial masses below 5M. which become important at times later than this.," Our tracks are shorter than the results as we terminate our simulations at 40 Myrs since we do not currently include stars with initial masses below $5 \, {\rm M}_{\odot}$ which become important at times later than this." + From Figure 1. we see that the evolution of colours is broadly consistent between models. ancl observations., From Figure \ref{ymclusters} we see that the evolution of colours is broadly consistent between models and observations. + Llowever there are a number of important. dilferences between the model tracks., However there are a number of important differences between the model tracks. + These cdillerences are. primarily due to the dillerent stellar models emploved hy and the models presented here., These differences are primarily due to the different stellar models employed by and the models presented here. + Our model tracks tend to pass through regions of the diagram that contain more observed. clusters although the observations have a large scatter. similar to the random error of the observations.," Our model tracks tend to pass through regions of the diagram that contain more observed clusters although the observations have a large scatter, similar to the random error of the observations." + In B-V the models tend to have redder colours than our models at around. LO Myrs., In B-V the models tend to have redder colours than our models at around 10 Myrs. + However we see the greatest dillerences between the different model tracks in V-I. Our single star population tracks extend much further into the red than our binary models because binary models reduce the number of red supergiants ancl therefore reduce their contribution in the L band., However we see the greatest differences between the different model tracks in V-I. Our single star population tracks extend much further into the red than our binary models because binary models reduce the number of red supergiants and therefore reduce their contribution in the I band. + However. the overproduction of red. supergiants is a feature of all models containing only single stars (with the main cillerence being how those supergiants are characterised in the model population) aud emphasises the need for binary population mocels.," However, the overproduction of red supergiants is a feature of all models containing only single stars (with the main difference being how those supergiants are characterised in the model population) and emphasises the need for binary population models." + Our binary mocels also tend to be bluer in B-V than our single star models. this is due to the increase in the number of main-sequence stars at late times due to secondaries accreting mass in binary interactions.," Our binary models also tend to be bluer in B-V than our single star models, this is due to the increase in the number of main-sequence stars at late times due to secondaries accreting mass in binary interactions." + We note that all the models. plotted. those presented. in this paper and similar models [rom sferburst09.. deviate from the locus of observed. clusters in the D-V. vs U-D colour plane at early times (<5 MMyzr). most. likely clue to variations in the metallicity of the clusters away [rom the Solar composition of our tracks.," We note that all the models plotted, those presented in this paper and similar models from, deviate from the locus of observed clusters in the B-V vs U-B colour plane at early times $<5$ Myr), most likely due to variations in the metallicity of the clusters away from the Solar composition of our tracks." + This deviation may also be due to relatively simple approximations for the strong nebular continuum contribution at these times., This deviation may also be due to relatively simple approximations for the strong nebular continuum contribution at these times. + Models omitting this nebular contribution. while unphysical. can provide a better fit to the data in this region. suggesting that more detailed mocdelling of the nebular emission may be necessary.," Models omitting this nebular contribution, while unphysical, can provide a better fit to the data in this region, suggesting that more detailed modelling of the nebular emission may be necessary." + There ace a number of factors that we have not included in our model tracks presented here., There are a number of factors that we have not included in our model tracks presented here. + For example we have not attempted to fit absorption [rom dust in the LILLE region model., For example we have not attempted to fit absorption from dust in the HII region model. + This is because the model track does not include dust. only nebula continuum emission.," This is because the model track does not include dust, only nebula continuum emission." + In cach of the panels we indicate the reddening direction for an cl. of 0.5., In each of the panels we indicate the reddening direction for an $A_{\rm v}$ of 0.5. + We see that in some of the scatter of the observations could be explained by line of sight dust., We see that in some of the scatter of the observations could be explained by line of sight dust. + Given these caveats. we nonetheless find that binary populations have very different colours to a single star population at certain ages. and that the observational data ab these points is offen more consistent with the binary models with few sources showing V-L colours. lor example. as extreme as those precictecl for single star populations.," Given these caveats, we nonetheless find that binary populations have very different colours to a single star population at certain ages, and that the observational data at these points is often more consistent with the binary models with few sources showing V-I colours, for example, as extreme as those predicted for single star populations." + To achieve this difference between the single and binary models. binaries with orbital separations between 100 to 10001. must be included.," To achieve this difference between the single and binary models, binaries with orbital separations between $100$ to $1000 \, {\rm R}_{\odot}$ must be included." + Wider binaries do not interact so produce results little clifferent from those from single stars., Wider binaries do not interact so produce results little different from those from single stars. + Viehter binaries tend to experience mergers ancl so. while evolving as binaries for some of their lives. they eventually become single stars.," Tighter binaries tend to experience mergers and so, while evolving as binaries for some of their lives, they eventually become single stars." + recently. presented a study of a selection of SDSS galaxies showing evidence [or ongoing massive star formation., recently presented a study of a selection of SDSS galaxies showing evidence for ongoing massive star formation. +" ""They searched: the SDSS DRG archival spectra to identify those with Wolf-Ravet features in the optical.", They searched the SDSS DR6 archival spectra to identify those with Wolf-Rayet features in the optical. + The two features used for identification are known as the blue and. red. Woll-Ravet bumps at approximately aanclSSOOA., The two features used for identification are known as the blue and red Wolf-Rayet bumps at approximately and. +. These star-formüng galaxies host massive stellar populations similar to those incorporated in our models. and hence provide à good experimental verification of the predictive power of our models.," These star-forming galaxies host massive stellar populations similar to those incorporated in our models, and hence provide a good experimental verification of the predictive power of our models." + In order to construct an appropriate stellar population in our synthetic spectrum. we assume an instantaneous burst of star formation and consider its evolution with time!.," In order to construct an appropriate stellar population in our synthetic spectrum, we assume an instantaneous burst of star formation and consider its evolution with ." +. We calculate the strength of Woll-Ravet features both without and with a nebula, We calculate the strength of Wolf-Rayet features both without and with a nebula +spectroscopy to confirm the stellar nature of the majority of sources. cleterumue spectral types and distances aud conrpare our sample with other stellar N-rav survevs.,"spectroscopy to confirm the stellar nature of the majority of sources, determine spectral types and distances and compare our sample with other stellar X-ray surveys." + Iu Section 3 we analyze the coronal properties of these sources in the context of other stellar coronal studies., In Section 3 we analyze the coronal properties of these sources in the context of other stellar coronal studies. + The X-ray observations presented here are from the COSMOS Survey (7?) that has imaged au area of ~0.9 dee? of the COSMOS field using the iuager (2?) on hoardthe X-ray Observatory (?).., The X-ray observations presented here are from the COSMOS Survey \citep{elvi09} that has imaged an area of $\sim$ 0.9 $^2$ of the COSMOS field using the imager \citep{garm03} on boardthe X-ray Observatory \citep{weis02}. + The survey uses a exid of 36 overlapping poiutiugs to give a lightly uniform exposure of ~160 ks over the ceutral 0.5 dee? and ~S80 ks over au outer reeiou of 0.1 deg?., The survey uses a grid of 36 overlapping pointings to give a highly uniform exposure of $\sim$ 160 ks over the central 0.5 $^2$ and $\sim$ 80 ks over an outer region of 0.4 $^2$. + A detailed source detection procedure (7) resulted in a catalog of 1761 sources detected in oue or more XN-raw bands. with well-defined seusitivities aud completeness fractions as a function of both X-ray band and survey area.," A detailed source detection procedure \citep{pucc09} resulted in a catalog of 1761 sources detected in one or more X-ray bands, with well-defined sensitivities and completeness fractions as a function of both X-ray band and survey area." + 7) used optical and uear-IR observations of the COSMOS field to make identifications for 1750 of the L7GL sources. includiug 61 stars.," \citet{civa10} used optical and near-IR observations of the COSMOS field to make identifications for 1750 of the 1761 sources, including 61 stars."