diff --git "a/batch_s000005.csv" "b/batch_s000005.csv" new file mode 100644--- /dev/null +++ "b/batch_s000005.csv" @@ -0,0 +1,10320 @@ +source,target +2008) measurecl rotational velocities of he primary stars in the classical Aleols.,2008) measured rotational velocities of the primary stars in the classical Algols. + At least seven systems out of 23 binaries rotate faster which cüller from svnchronize rotation by more han a [actor of two., At least seven systems out of 23 binaries rotate faster which differ from synchronize rotation by more than a factor of two. + Egeleton (2000) discussed. evolution of Aleol type systems and concluded that they could not o* evolved. to their present. status without having lost substantial mass and angular momentum., Eggleton (2000) discussed evolution of Algol type systems and concluded that they could not be evolved to their present status without having lost substantial mass and angular momentum. +Phe fundamental xwameters of well-observed. detached: ancl semi-detached Algols are compiled and analvsed by. Ibanogllu et al. (,The fundamental parameters of well-observed detached and semi-detached Algols are compiled and analysed by Ibanoğllu et al. ( +2006) ο reveal some possible implications for their nuclear and angular momentum evolution.,2006) to reveal some possible implications for their nuclear and angular momentum evolution. + They arrived at a result that he mass-ratio of detached. Algols is larger than unity., They arrived at a result that the mass-ratio of detached Algols is larger than unity. + As he system evolved-olf from the main-sequence mass transfer, As the system evolved-off from the main-sequence mass transfer +for all Z.,for all $Z$. + This equation means that the absolute value of D4(Z) should be chosen to be at most of order of 1/E? for all Z., This equation means that the absolute value of $D_{1}(Z)$ should be chosen to be at most of order of $1/E^{2}$ for all $Z$ . +" In fact. if |[D4|291/E? for some Z. we can easily see that equation (53)) breaks down in the range L/E?«i?<|D,)."," In fact, if $|D_{1}|\gg 1/E^{2}$ for some $Z$, we can easily see that equation \ref{sol3}) ) breaks down in the range $1/E^{2}\ll \y^2 \ll + |D_{1}|$ ." +" Hence. we can discuss the increase of AM?~f/f, iv the range 7>L/P under the choice of D4=0. namely. according to the following equation It is now clear that we have M?~£P in therange l/E«at<1. and the outflows can pass through the fast-inagnetosonic point (i.e.. AP=1/E?) located on the radius RO,cEV,"," Hence, we can discuss the increase of $\mm^{2}\simeq + E_{k}/E_{m}$ in the range $\y \gg 1/E$ under the choice of $D_{1}=0$, namely, according to the following equation It is now clear that we have $\mm^{2}\simeq \y$ in therange $1/E \ll \y \ll 1$, and the outflows can pass through the fast-magnetosonic point (i.e., $\mm^{2}=1/E^{2/3}$ ) located on the radius $R\Omega_{F}\simeq E^{1/3}$." +" D the outflows can arrive at the radius £1.4. the equipartition Ej=E,, between magnetic and kinetic energies is realized."," If the outflows can arrive at the radius $\y \simeq 1.4$, the equipartition $E_{k}=E_{m}$ between magnetic and kinetic energies is realized." + In the asymptotic region à1 we can confirm the logarithmic increase of AP given by APsIn(272/AL) toward the complete conversion of magnetic to kinetic enerev., In the asymptotic region $\y \gg 1$ we can confirm the logarithmic increase of $\mm^{2}$ given by $\mm^{2}\simeq\ln(2\y^{2}/\mm^{2})$ toward the complete conversion of magnetic to kinetic energy. +" The numerical solution of equation (54)) is shown in Figure baa. The corresponding poloidal velocity αρ) and Lorentz [actor 5C75) are also shown in Figure 5bb. where the Lorentz factor is given by 5=E—u,/(£M7)."," The numerical solution of equation \ref{model}) ) is shown in Figure \ref{fig:gs-mm}a a. The corresponding poloidal velocity $u_p(\y)$ and Lorentz factor $\gamma(\y)$ are also shown in Figure \ref{fig:gs-mm}b b, where the Lorentz factor is given by $\gamma = E - u_p/(\xi \mm^2)$." + In this case. we obtain ελ ty. )," \ref{fig:gs-mm} may be incorrect because of our approximations, but we can expect correct features at least near and outside the fast magnetosonic point, $\y \geq \y_{\rm F}$ . )" + Next. we discuss the field configuration given by equation (52)).," Next, we discuss the field configuration given by equation \ref{sol2}) )." + Thejet flows may be confined by an external pressure (see. e.g.. Li 1993: Degelman Li 1994: Fendt 1997).," Thejet flows may be confined by an external pressure (see, e.g., Li 1993; Begelman Li 1994; Fendt 1997)." +" If the shape ZQ),=ICE) of the last (lux surface Y=Wp is determined by the outer boundary condition. the fnuction o(Z) in equation (52)) is fixed."," If the shape $Z\Omega_{F}=H(\y)$ of the last flux surface $\Psi=\Psi_{0}$ is determined by the outer boundary condition, the function $D_{2}(Z)$ in equation \ref{sol2}) ) is fixed." +" For example. let us consider the racial last {lux surface al an angle 2=0, wilh the pole axis direction. ("," For example, let us consider the radial last flux surface at an angle $R/Z \equiv \theta_{0}$ with the pole axis direction. (" +"Because the solution can be applied only (ο jets with small opening angles. we must require thal 0, is al mostof order of 1/ E.)","Because the solution can be applied only to jets with small opening angles, we must require that $\theta_{0}$ is at mostof order of $1/E$ .)" + Using the function AP=a) derived [rom equation (54)). we obtain alonga [lux ποπο.VOR.Z)= constant. where 7= ZOL/E.," Using the function $\mm^2=\mm^2(\y)$ derived from equation \ref{model}) ), we obtain alonga flux function$\Psi(R,Z)=$ constant, where $\z \equiv + Z\Omega_F/E$ ." +" Note that lor the value of M?(8,2) in equation (55)) we use the [unctionM?= AM?(P). where the variable ? should be replaced to 052."," Note that for the value of $\mm^2(\theta_0 \z)$ in equation \ref{eq:d_Z}) ) we use the function$\mm^2=\mm^2(\y)$ , where the variable $\y$ should be replaced to $\theta_0 \z$ ." +" Then. in the range 70,/2« lof Z. equations (52)) ancl (55)) leads"," Then, in the range $\theta_{0}Z\Omega_{F}/E \ll 1$ of $Z$ , equations \ref{sol2}) ) and \ref{eq:d_Z}) ) leads" +other hand. a measured anisotropy. larger than the 2356 we obtained for D0656--14 would be. from and(43).. an indication of the existence of an even vounger. nearby source. aa longer lifetime { of the PWN.,"other hand, a measured anisotropy larger than the $\approx$ we obtained for B0656+14 would be, from and, an indication of the existence of an even younger, nearby source, a longer lifetime $T$ of the PWN." + We also note that the predicted Πας from PSR. D0656--14 appears (o overpredict the observed flux above GGeV. This implies more severe constraints on the pulsar output. whereas Geminga's parameters are not that severely constrained by CR. positron observations.," We also note that the predicted flux from PSR B0656+14 appears to overpredict the observed flux above GeV. This implies more severe constraints on the pulsar output, whereas Geminga's parameters are not that severely constrained by CR positron observations." + We remark that Galactic CR. including electrons and. positrons. are subjected to solar modulation at energies below 210 GGeV. The encounter of (hese particles with the solar wind and imbedcded magnetic field causes a heliospheric anisotropy. (hat is primarily determined bv the combined modulation effects of convection. diffusion. and drilts - all solar cevcle dependent.," We remark that Galactic CR, including electrons and positrons, are subjected to solar modulation at energies below $\approx$ GeV. The encounter of these particles with the solar wind and imbedded magnetic field causes a heliospheric anisotropy that is primarily determined by the combined modulation effects of convection, diffusion, and drifts - all solar cycle dependent." + Drifts will cause (his anisotropy to have a 22-vear cvele., Drifts will cause this anisotropy to have a 22-year cycle. + CR electrons. ancl positrons al GGeV. at Earth may. therelore exhibit a heliospheric anisotropy. of up to a few percent. assuming (hat thev enter the heliosphere isotropically 2004)..," CR electrons and positrons at GeV at Earth may therefore exhibit a heliospheric anisotropy of up to a few percent, assuming that they enter the heliosphere isotropically \citep{2004ApJ...602..993P}." + It will be an interesting exercise to determine how this anisotropy will change if the LIS is anisotropic., It will be an interesting exercise to determine how this anisotropy will change if the LIS is anisotropic. + However. the anisotropy that we predict here is the largest above GGeV. an energv range αἱ which only the PAMELA mission (Doezioetal.2004) mav be," However, the anisotropy that we predict here is the largest above GeV, an energy range at which only the PAMELA mission \citep{2004NuPhS.134...39B} may be" +"of the background to the total flux from the stars is low for both observations, from to depending on the image.","of the background to the total flux from the stars is low for both observations, from to depending on the image." +" Therefore, photometric errors are not dominated by fluctuations in the background."," Therefore, photometric errors are not dominated by fluctuations in the background." +" We used a sliding median filter to select and trim outliers in flux and position greater than 50, representing and of the data for the first and second visits, respectively."," We used a sliding median filter to select and trim outliers in flux and position greater than $\sigma$, representing and of the data for the first and second visits, respectively." +" We also discarded the first half-hour's worth of observations, which is affected by significant telescope jitter before stabilization."," We also discarded the first half-hour's worth of observations, which is affected by significant telescope jitter before stabilization." + The final number of photometric measurements used is 7277 and 7362., The final number of photometric measurements used is 7277 and 7362. + The raw time series are presented in the top panel of Figure 1.., The raw time series are presented in the top panel of Figure \ref{fig:spitzerlightcurves}. +" We find that the point-to-point scatter in the photometry gives a typical signal-to-noise ratio (S/N) of 280 per image, which corresponds to of the theoretical signal-to-noise."," We find that the point-to-point scatter in the photometry gives a typical signal-to-noise ratio (S/N) of 280 per image, which corresponds to of the theoretical signal-to-noise." +" T'herefore, the noise is dominated by Poisson statistics."," Therefore, the noise is dominated by Poisson statistics." +" In order to determine the transit parameters and associated uncertainties from the ttime series we used a transit light curve model multiplied by instrumental decorrelation functions, as described by Désertetal.(2011a)."," In order to determine the transit parameters and associated uncertainties from the time series we used a transit light curve model multiplied by instrumental decorrelation functions, as described by \cite{desert11a}." +. The transit light curves were computed with the IDL transit routine from Mandel&Agol(2002)., The transit light curves were computed with the IDL transit routine from \cite{mandel02}. +" For the present case we allowed for a single free parameter in the model, which is the planet-to-star radius ratio equivalently, the depth, in the absence of limb R,/R,darkening)."," For the present case we allowed for a single free parameter in the model, which is the planet-to-star radius ratio $R_p/R_\star$ (or equivalently, the depth, in the absence of limb darkening)." +"(or The normalized orbital semi-major axis (system scale) a/R,, the impact parameter b, the period P, and the time of mid transit T, were held fixed at the values derived from the light curve, as reported by Batalhaetal.(2011) and summarized below in Sect. 7.."," The normalized orbital semi-major axis (system scale) $a/R_\star$, the impact parameter $b$, the period $P$, and the time of mid transit $T_c$ were held fixed at the values derived from the light curve, as reported by \cite{Batalha:11} and summarized below in Sect. \ref{sec:discussion}." +" Limb darkening is small atmicron,, but was nevertheless included in our modeling using the 4-parameter law by Claret(2000) and theoretical coefficients published by Sing(2010)."," Limb darkening is small at, but was nevertheless included in our modeling using the 4-parameter law by \cite{Claret:00} and theoretical coefficients published by \cite{Sing:10}." +". The Spitzer//IRAC photometry is known to be systematically affected by the so-called “pixel-phase effect"" (see,e.g.,Charbonneauetal.2005;Knutsonetal.2008)."," The /IRAC photometry is known to be systematically affected by the so-called “pixel-phase effect” \citep[see, +e.g.,][]{charbonneau05,knutson08}." +. This effect is seen as oscillations in the measured fluxes with a period corresponding to that of the telescope pointing jitter., This effect is seen as oscillations in the measured fluxes with a period corresponding to that of the telescope pointing jitter. +" For the first visit this period was 70 min, and the amplitude of the oscillations was approximately peak-to-peak; for the second visit the period was 35 min, and the amplitude about196.."," For the first visit this period was 70 min, and the amplitude of the oscillations was approximately peak-to-peak; for the second visit the period was 35 min, and the amplitude about." + We decorrelated our signal in each channel using a linear function of time for the baseline (two parameters) and a quadratic function of the PSF position (four parameters) to correct the data for each channel., We decorrelated our signal in each channel using a linear function of time for the baseline (two parameters) and a quadratic function of the PSF position (four parameters) to correct the data for each channel. + We performed a simultaneous Levenberg-Marquardt least-squares fit to the data (Markwardt2009) to determine the transit and instrumental model parameters (7 in total).," We performed a simultaneous Levenberg-Marquardt least-squares fit to the data \citep{markwardt09} + to determine the transit and instrumental model parameters (7 in total)." +" The errors on each photometric point were assumed to be identical, and were set to the rms residual of the initial best fit."," The errors on each photometric point were assumed to be identical, and were set to the rms residual of the initial best fit." +" To obtain an estimate of the correlated and systematic errors in our measurements etal.2006) we used the residual permutation bootstrap(Pont technique, or “Prayer Bead” method, as described by Désertetal.(2009)."," To obtain an estimate of the correlated and systematic errors in our measurements \citep{pont06} we used the residual permutation bootstrap technique, or “Prayer Bead” method, as described by \citet{desert09}." +". In this method the residuals of the initial fit are shifted systematically and sequentially by one frame, and then added to the transit light curve model before fitting again."," In this method the residuals of the initial fit are shifted systematically and sequentially by one frame, and then added to the transit light curve model before fitting again." +" We considered asymmetric error bars spanning of the points above and below the median of the distributions to derive the lo uncertainties for each parameter, as described by Désertetal.(2011b)."," We considered asymmetric error bars spanning of the points above and below the median of the distributions to derive the $1\sigma$ uncertainties for each parameter, as described by \citet{desert11b}." +". 'The bottom panel of Figure 1 shows the best-fit model superimposed on the observations from the two visits combined, with the data binned in 36mmin bins for clarity (295 points per bin)."," The bottom panel of Figure \ref{fig:spitzerlightcurves} shows the best-fit model superimposed on the observations from the two visits combined, with the data binned in min bins for clarity (295 points per bin)." +" The transit depths at ((after removing limb-darkening effects) are 353*112 ppm for the first visit and 339777, for the second, which are in good agreement with each other."," The transit depths at (after removing limb-darkening effects) are $353^{+115}_{-133}$ ppm for the first visit and $339^{+85}_{-110}$ for the second, which are in good agreement with each other." +" The weighted average depth of 344+85 is consistent with the non-limb-darkened value of 376+9 ppm derived from the light curve (Batalhaetal. well within the lo errors, strongly suggesting the 2011)transit is achromatic, as expected for a planet."," The weighted average depth of $344 \pm 85$ is consistent with the non-limb-darkened value of $376 \pm 9$ ppm derived from the light curve \citep{Batalha:11} well within the $\sigma$ errors, strongly suggesting the transit is achromatic, as expected for a planet." + 'The above oobservations provide a useful constraint on the kinds of false positives (blends) that may be mimicking the ssignal., The above observations provide a useful constraint on the kinds of false positives (blends) that may be mimicking the signal. +" For example, if Kepler-10 were blended with a faint unresolved background eclipsing binary of much later spectral type that manages to reproduce the transit depth in the ppassband, the predicted depth at mmay be expected to be larger because of the higher flux of the contaminating binary at longer wavelengths compared to Kepler-10."," For example, if Kepler-10 were blended with a faint unresolved background eclipsing binary of much later spectral type that manages to reproduce the transit depth in the passband, the predicted depth at may be expected to be larger because of the higher flux of the contaminating binary at longer wavelengths compared to Kepler-10." +" Since the transit depth we measure in the near infrared is about the same as in the optical, this argues against blends composed of stars"," Since the transit depth we measure in the near infrared is about the same as in the optical, this argues against blends composed of stars" +erowtli coutinues as dark matter halo mergers proceed to low redshifts.,growth continues as dark matter halo mergers proceed to low redshifts. + Gas accretion is thought to play a critical role in fucling the early stages of black hole erowth (???).. and this may explain the tightness of the AIpy0 relation (22777)..," Gas accretion is thought to play a critical role in fueling the early stages of black hole growth \citep{david:1987:eag, +kauffmann:2000:ume, merloni:2004:ags}, and this may explain the tightness of the $_{\rm BH}-\sigma$ relation \citep{Burkert:2001:smbh, +haehnelt:2000:cbh, Dimatteo:2005, Kaz:2005:msigma, +Robertson:2006:msigma}." + Since high redshift galaxies are thought to be especially eas-rich. each merecr brings a fresh supply of gas to the ceuter of the galaxy. aud new fuel to the erowine supermassive black hole (??)..," Since high redshift galaxies are thought to be especially gas-rich, each merger brings a fresh supply of gas to the center of the galaxy, and new fuel to the growing supermassive black hole \citep{Mihos:1994:gasmerger, Dimatteo:2003:bhgrowth}." + From a combination of gas accretion and binary black hole coalesceuce. it is thought that these Pop IIT-seuerated seeds may form the SMDITS we observe today (?)..," From a combination of gas accretion and binary black hole coalescence, it is thought that these Pop III-generated seeds may form the SMBHs we observe today \citep{Soltan:1982:smbh, Schneider:02topheavy}." + During a galaxw merger. cach black hole sinks to the center of the new ealaxy potential due to ανασα] friction aud eveutually becomes bound as a binary (??)..," During a galaxy merger, each black hole sinks to the center of the new galaxy potential due to dynamical friction and eventually becomes bound as a binary \citep{Kaz:2005:msigma, Escala:2005:gas}." + Dynamical friction then coutiuues to shriuk the orbit until the binary is lard (ie. the separation between each black hole. appr. is such that the svstem tends to lose energv curing stellar encounters) (?)..," Dynamical friction then continues to shrink the orbit until the binary is hard (i.e, the separation between each black hole, $_{\rm BBH}$, is such that the system tends to lose energy during stellar encounters) \citep{heggie:07}." + Thereatter. further decay is mediated by 3-body scattering with the züubieut stellar backeround uutil the binary becomes so close that the orbit can lose energv via eravitational radiation.," Thereafter, further decay is mediated by 3-body scattering with the ambient stellar background until the binary becomes so close that the orbit can lose energy via gravitational radiation." + Iu studies of static. spherical potentials. it nav be difficult for stellar eucouuters aloue to cause the αν to transition between the 3-body scattering phase and the gravitational radiation reguue (7).," In studies of static, spherical potentials, it may be difficult for stellar encounters alone to cause the binary to transition between the 3-body scattering phase and the gravitational radiation regime \citep{milos:2003:lem}." + However. in gasrich or non-splherical svstenis. the binary rapidly judeus and coalesces iuto one black hole. οιτας copious gravitational radiation iu the process (???77)..," However, in gas-rich or non-spherical systems, the binary rapidly hardens and coalesces into one black hole, emitting copious gravitational radiation in the process \citep{Mayer:2007:smbh, Kaz:2005:msigma, berczik:2006:emb, sigurdsson:03, KHB:2006fl}." +" Iu our previous work. we calculated the cosinological ucrger rate for black holes between 200 - 3&10*AL, roni redshift 19-0 022.(hereafter.MOT)).."," In our previous work, we calculated the cosmological merger rate for black holes between 200 - $3 \times 10^7 \Msun$ from redshift 49-0 \citep[][(hereafter, M07)]{KHB:2007bhgrowth, KHB:2008bhgrowth}." + Our approach combined high-resolution. snall-volume cosmological N-xlv smuulations with analytic prescriptions for the dynamics of nereius black holes below our resolution iuit: this allowed us to explore differeut black hole erowtl mechanisms and seed formation scenarios while also accurately simulating the rich aud varied merecr ustory of the host dark matter halos.," Our approach combined high-resolution, small-volume cosmological N-body simulations with analytic prescriptions for the dynamics of merging black holes below our resolution limit; this allowed us to explore different black hole growth mechanisms and seed formation scenarios while also accurately simulating the rich and varied merger history of the host dark matter halos." + Iu this paper. we calculate the eravitational wave sienal from the black hole mergers involved in asseiibling a supermassive black hole at the center of the Mille Wav analogue our simulation volume.," In this paper, we calculate the gravitational wave signal from the black hole mergers involved in assembling a supermassive black hole at the center of the Milky Way analogue our simulation volume." + The volume is designed to provide one possible evolutionary path for a region like our Local Group. aud as such. it should contain supernassive black holes ou the light cud of the supermassive black hole mass spectrum the sweet spot oe1 SMIBIT mass for LISA observations.," The volume is designed to provide one possible evolutionary path for a region like our Local Group, and as such, it should contain supermassive black holes on the light end of the supermassive black hole mass spectrum – the sweet spot in SMBH mass for LISA observations." + We inchide all 1ο niereers that have occurred from redshift 19 to the xeseut epoch within a 1000 Ape? volune of the Universe iat represeuts a Local Croup type of environment., We include all the mergers that have occurred from redshift 49 to the present epoch within a 1000 $^3$ volume of the Universe that represents a Local Group type of environment. + We found that the exavitational wave sources revealed oei this volume are from much ligher mass ratio merecrs iat the mergers predicted to be involved iu assenibliug je luost massive SMDIIS., We found that the gravitational wave sources revealed in this volume are from much higher mass ratio mergers that the mergers predicted to be involved in assembling the most massive SMBHs. +" Most of the LISA) scicuce and data analysis community las been auticipating nore equal mass mergers. aud have developed extcusive eravitational wave templates aud paramcter extraction echuiques based on the asswuption that the black hole ünaries are order unitv mass ratio svstenis (7.οι),"," Most of the LISA science and data analysis community has been anticipating more equal mass mergers, and have developed extensive gravitational wave templates and parameter extraction techniques based on the assumption that the black hole binaries are order unity mass ratio systems \citep[][e.g.]{Babak:2008}." + While this may be true for the most massive SAIBIIs. we find that the black holes in our volume experieuce uergeers with mass ratios as high as Mo/M4=10000: l.," While this may be true for the most massive SMBHs, we find that the black holes in our volume experience mergers with mass ratios as high as ${\rm M}_2/{\rm M}_1= 10000:1$ ." + These high mass ratio mergers certainly generate a different eravitational wave signal: they may even deserve a different source classification to separate it from the classical equal ass merger or extreme mass ratioral., These high mass ratio mergers certainly generate a different gravitational wave signal; they may even deserve a different source classification to separate it from the classical equal mass merger or extreme mass ratio. +. We use the rates found in our volune to extrapolate this eravitational wave signal over the IIubble Volume., We use the rates found in our volume to extrapolate this gravitational wave signal over the Hubble Volume. + Naturally. this is highly seusitive to cosmic variance. and ten runs selected from an initial huger volume are planned to mitigate cosmic variance i our merecr rate estimates.," Naturally, this is highly sensitive to cosmic variance, and ten runs selected from an initial larger volume are planned to mitigate cosmic variance in our merger rate estimates." + Towever. these s11all vole cosmological simulations are extremely nonlinear. auc as such. are computationally expensive.," However, these small volume cosmological simulations are extremely nonlinear, and as such, are computationally expensive." +" We are publishing the preliminary results frou, our first. smaller scale. siuulation i order to draw the attention of the conunuunitv to the interesting possibility. that the asseniblv of the lowest mass SMDBIIS may involve these lieh mass ratio mergers aud be a significant contributor to the LISA detectable event rate."," We are publishing the preliminary results from our first, smaller scale, simulation in order to draw the attention of the community to the interesting possibility that the assembly of the lowest mass SMBHs may involve these high mass ratio mergers and be a significant contributor to the LISA detectable event rate." + We review the details of our simulation iu section 2 and in section 3. we describe how to caleulate the eravitational wave signal from two mereie black holes.," We review the details of our simulation in section 2 and in section 3, we describe how to calculate the gravitational wave signal from two merging black holes." + We discuss our results aud implications in section [., We discuss our results and implications in section 4. + In 7. we performed a ligh-+vesolutiou “Zzoom-i cosmological N-body simulation of a comoving section of a ACDAM universe (Q\;=0.3. O4 20.7. 040.9 and hi-0.7) from z=19 to z=0.," In \citet{KHB:2008bhgrowth}, , we performed a high-resolution 'zoom-in' cosmological N-body simulation of a comoving section of a $\Lambda$ CDM universe $\Omega_{\rm M}$ =0.3, $\Omega_{\Lambda}$ =0.7, $\sigma_8$ =0.9 and h=0.7) from $=49$ to $=0$." + The high resolution region was a box 10 5h! Mpe on each side. for a total comoving volume of 1000 5.7 Mpc?.," The high resolution region was a box 10 $h^{-1}$ Mpc on each side, for a total comoving volume of 1000 $h^{-3}$ $^3$." + The vole is designed to provide oue possible evolutionary path for a region like our Local Croup. aud as such. it should contain supermassive black holes ou the light end of the supermassive black hole uass Spectruni.," The volume is designed to provide one possible evolutionary path for a region like our Local Group, and as such, it should contain supermassive black holes on the light end of the supermassive black hole mass spectrum." + Our mass resolution is 8.85«10M... and our spatial resolution is 2 kpc.," Our mass resolution is $8.85 \times 10^5 \, {\rm M}_\odot$, and our spatial resolution is 2 kpc." + After the simulation is complete. we identified alos with at least 32 particles using P-Croupfiuder (2) and seed black holes those halos in the appropriate mass and redshift range to lost Pop III stars.," After the simulation is complete, we identified halos with at least 32 particles using P-Groupfinder \citep{pgroupfinder} and seed black holes those halos in the appropriate mass and redshift range to host Pop III stars." + Note that we are using WALAPS (7) cosinological parameters in this study to compare with our previous work: however. at the time of this papers submission. zoonriu sinulations of several small volumes are underway with WALAPS parameters to better explore cosmic variance.," Note that we are using WMAP3 \citep{spergel:07} cosmological parameters in this study to compare with our previous work; however, at the time of this paper's submission, 'zoom-in' simulations of several small volumes are underway with WMAP5 parameters to better explore cosmic variance." + This will allow us to better pin down the rate of these uew eravitational wave SOULCOS., This will allow us to better pin down the rate of these new gravitational wave sources. + Iu our hvbrid method. we combine the dark matter halo merger trees obtained m muuerical simulations witli an analytical treatinent of the plhisical processes that arise m the dvnamics of galaxy aud black hole merecrs.," In our hybrid method, we combine the dark matter halo merger trees obtained in numerical simulations with an analytical treatment of the physical processes that arise in the dynamics of galaxy and black hole mergers." + Since some of the processes are ill-constrained. we probe the effect of different black hole erowth recipes on the final black hole mass function.," Since some of the processes are ill-constrained, we probe the effect of different black hole growth recipes on the final black hole mass function." + Du general. we asune cach dark matter halo is described bv au NEW profile (?).. aud include the effects of dviauical friction aud merecr- eas accretion. outo the SMDITL. as wellas the SMIDIT σος itself.," In general, we assume each dark matter halo is described by an NFW profile \citep{nfw:97}, and include the effects of dynamical friction and merger-induced gas accretion onto the SMBH, as wellas the SMBH merger itself." + This hiybrid approach generates. for cach recipe. a census of the number aud mass ratio of the niergers in our volume at cach redshift.," This hybrid approach generates, for each recipe, a census of the number and mass ratio of the mergers in our volume at each redshift." +General relativity. a cornerstone of physics. is arguably one of our greatest intellectual achievements.,"General relativity, a cornerstone of physics, is arguably one of our greatest intellectual achievements." + Lt is not only elegant ancl physically motivated. but it makes a whole host of predictions including gravitational waves. the anomalous precession of Mercury and the dellection of light.all of which have been verified.," It is not only elegant and physically motivated, but it makes a whole host of predictions including gravitational waves, the anomalous precession of Mercury and the deflection of light–all of which have been verified." + Further still. clue to its weak vet accumulative nature. gravitation is a force of the large scale.," Further still, due to its weak yet accumulative nature, gravitation is a force of the large scale." + And so cosmology. being the study of the Universe. is a field performed. within the formalism of this theory.," And so cosmology, being the study of the Universe, is a field performed within the formalism of this theory." + Lt is in this way that Cosmology, It is in this way that Cosmology +"is constrained primarily by the πας data, with a small contribution from the Integrated Sachs-Wolfe (ISW) effect in the CMB.","is constrained primarily by the $f_{\rm gas}$ data, with a small contribution from the Integrated Sachs-Wolfe (ISW) effect in the CMB." + A simple exercise provides further insight into how the CMB data help in constraining dark energy., A simple exercise provides further insight into how the CMB data help in constraining dark energy. +" For this, we re-examine the constraints in the wo—wa plane obtained from the fgas+CMB data; the 68 and 95 per cent confidence contours for the default model with 5 per cent allowances are shown (dashed curves) in Figure 6.."," For this, we re-examine the constraints in the $w_{\rm 0}-w_{\rm a}$ plane obtained from the $f_{\rm gas}$ +CMB data; the 68 and 95 per cent confidence contours for the default model with 5 per cent allowances are shown (dashed curves) in Figure \ref{fig:cmbede}. ." +" The combination of feas+CMB data provides tight constraints on QyA?, Qanh? and J, (driven primarily by the CMB data), and on A (driven by the combination of both data sets)."," The combination of $f_{\rm gas}$ +CMB data provides tight constraints on $\Omega_{\rm b}h^2$, $\Omega_{\rm + dm}h^2$ and $l_{\rm a}$ (driven primarily by the CMB data), and on $h$ (driven by the combination of both data sets)." +" Using these constraints as priors, we examine the constraints in the Wo—Wa plane that can be obtained from the fas data alone; the results are shown as the red, solid curves in Figure 6.."," Using these constraints as priors, we examine the constraints in the $w_{\rm + 0}-w_{\rm a}$ plane that can be obtained from the $f_{\rm gas}$ data alone; the results are shown as the red, solid curves in Figure \ref{fig:cmbede}." +" We see that the priors encompass some of the CMB constraining power, in particular in defining the characteristic upper boundary in the two—wa plane."," We see that the priors encompass some of the CMB constraining power, in particular in defining the characteristic upper boundary in the $w_{\rm 0}-w_{\rm a}$ plane." +" However, they do not contain the full information on, e.g., the covariance of Qy?, Qa,h? and h which is also important in constraining dark energy at later times."," However, they do not contain the full information on, e.g., the covariance of $\Omega_{\rm b}h^2$, $\Omega_{\rm dm}h^2$ and $h$ which is also important in constraining dark energy at later times." + We note that the prior on /4 provides a tight constraint on the curvature., We note that the prior on $l_{\rm a}$ provides a tight constraint on the curvature. +" The blue dotted curves in Figure 6 show the constraints obtained from the fas data alone, using only the priors on Q,h? and h and assuming flatness."," The blue dotted curves in Figure \ref{fig:cmbede} show the constraints obtained from the $f_{\rm gas}$ data alone, using only the priors on $\Omega_{\rm b}h^2$ and $h$ and assuming flatness." + The XSZ technique provides a complementary and independent experiment to measure dark energy., The XSZ technique provides a complementary and independent experiment to measure dark energy. +" Although the inclusion of constraints from the XSZ experiment leads to only modest formal improvements in the FoM with respect to the results for the fz4,4-CMB data (Table 4;; as can be expected given the relatively weak dependence on dark energy in equation 21), it is important to note that the XSZ experiment relies on different assumptions and has different systematic uncertainties."," Although the inclusion of constraints from the XSZ experiment leads to only modest formal improvements in the FoM with respect to the results for the $f_{\rm gas}+$ CMB data (Table \ref{tab:models}; as can be expected given the relatively weak dependence on dark energy in equation 21), it is important to note that the XSZ experiment relies on different assumptions and has different systematic uncertainties." +" In particular, the XSZ experiment is independent of assumptions regarding hydrostatic equilibrium, the depletion factor, and the stellar mass fraction."," In particular, the XSZ experiment is independent of assumptions regarding hydrostatic equilibrium, the depletion factor, and the stellar mass fraction." +" Thus, the combination of data from the fas and XSZ techniques can help to ensure robustness in the results."," Thus, the combination of data from the $f_{\rm gas}$ and XSZ techniques can help to ensure robustness in the results." +" In principle, the inclusion of XSZ data can also allow some of the priors in the [κας experiment to be relaxed."," In principle, the inclusion of XSZ data can also allow some of the priors in the $f_{\rm gas}$ experiment to be relaxed." +" We have examined the ability of a future X-ray observatory, with capabilities similar to those planned for Constellation-X, to constrain dark energy via the [κας experiment."," We have examined the ability of a future X-ray observatory, with capabilities similar to those planned for Constellation-X, to constrain dark energy via the $f_{\rm gas}$ experiment." +" We find that feas measurements for a sample of 500 hot (kT25002 5keV), X-ray bright, dynamically relaxed clusters, with a precision of ~5 per cent, can be used to constrain dark energy with a FoM of 15—40."," We find that $f_{\rm gas}$ measurements for a sample of 500 hot $kT_{2500}\gsim5$ keV), X-ray bright, dynamically relaxed clusters, with a precision of $\sim 5$ per cent, can be used to constrain dark energy with a FoM of $15-40$." +" These constraints are comparable to those predicted by the DETF for other leading, planned (DETF Stage IV) dark energy experiments."," These constraints are comparable to those predicted by the DETF for other leading, planned (DETF Stage IV) dark energy experiments." +" We also find that, for the fea; experiment, the FoM can be boosted up by at least ~40 per cent by selecting an optimal redshift distribution of suitable clusters on which to carry out the fgas observations."," We also find that, for the $f_{\rm gas}$ experiment, the FoM can be boosted up by at least $\sim 40$ per cent by selecting an optimal redshift distribution of suitable clusters on which to carry out the $f_{\rm gas}$ observations." +" Interestingly, the optimal redshift distribution of feas measurments appears to be shifted towards low redshifts."," Interestingly, the optimal redshift distribution of $f_{\rm gas}$ measurments appears to be shifted towards low redshifts." +" As discussed in the text, a future [κας experiment will need to be preceded by a large X-ray or SZ clustersurvey that will find hot, X-ray luminous clusters out to high redshifts."," As discussed in the text, a future $f_{\rm gas}$ experiment will need to be preceded by a large X-ray or SZ clustersurvey that will find hot, X-ray luminous clusters out to high redshifts." + A survey such as that planned with the Spectrum- mission should find several thousand of such clusters., A survey such as that planned with the Spectrum-RG/eROSITA mission should find several thousand of such clusters. + Short ‘snapshot’ follow-up observations of the, Short `snapshot' follow-up observations of the +In order to constrain the dvnamical model. it is crucial to have a good estimate of the radius of the companion stu.,"In order to constrain the dynamical model, it is crucial to have a good estimate of the radius of the companion star." + However. customary methods of determining (this radius fail because (he Cvenus N-1 svstem does not exhibit eclipses nor does the companion star fill its Roche equipotential lobe.," However, customary methods of determining this radius fail because the Cygnus X-1 system does not exhibit eclipses nor does the companion star fill its Roche equipotential lobe." + We obtain the required estimate of the stellar radius as we have done previously in our study of LMC. X-1 (Oroszetal.2009)., We obtain the required estimate of the stellar radius as we have done previously in our study of LMC X-1 \citep{oro+2009}. +. The radius. which critically depends on distance. additionally. depends on the apparent magnitude of the O-(vpe star and interstellar extinction. ancl also on the effective stellar temperature ancl corresponding bolometrie correction.," The radius, which critically depends on distance, additionally depends on the apparent magnitude of the O-type star and interstellar extinction, and also on the effective stellar temperature and corresponding bolometric correction." +" The absolute magnitude of (he star is Ma,=A 0.11.1,. where A is the apparent A-band magnitude. BC, is the bolometric correction lor the A-band. D is the distance. and Ay is the extinction in the V-baud."," The absolute magnitude of the star is $M_{\rm +abs}=K+BC_K(T_{\rm eff},g)-(5\log D-5) - 0.11A_V$ , where $K$ is the apparent $K$ -band magnitude, $BC_K$ is the bolometric correction for the $K$ -band, $D$ is the distance, and $A_V$ is the extinction in the $V$ -band." + The luminosity and radius of the star in solar units are L=10MMos15D and Tay). respectively.," The luminosity and radius of the star in solar units are $L=10^{-0.4(M_{\rm abs}-4.71)}$ and $R=\sqrt{L(5770/T_{\rm eff})^4}$ , respectively." + In computing these quantities. we use D=1.86um kpc (Reid and à A-band apparent magnitude of ἐν=6.502:0.02 (Skrutskieetal.2006).. which minimizes the effects of interstellar extinction.," In computing these quantities, we use $D = 1.86_{-0.11}^{+0.12}$ kpc \citep{rei+2010} and a $K$ -band apparent magnitude of $K=6.50\pm 0.02$ \citep{skr+2006}, which minimizes the effects of interstellar extinction." + For the A-band extinction. we adopt LE(B—V)-lllz.03and Ry=3.0240.03 (e.g.Ay=3.35.Caballero-Nievesetal.2009) and use the standard extinction law (Cardelliοἱal.1939).," For the $K$ -band extinction, we adopt $E(B-V)=1.11\pm 0.03$ and $R_V=3.02\pm 0.03$ \citep[e.g.\ $A_V=3.35$,][]{cab+2009} and use the standard extinction law \citep{car+1989}." +. The bolometrie corrections for the {ρα were computed using the OSTAR2002 grid of models with solar metallicity 2003)., The bolometric corrections for the $K$ -band were computed using the OSTAR2002 grid of models with solar metallicity \citep{lan+2003}. +. We note that the A-band bolometric corrections for the solar metallicity models ancl (he models for hall-solar metallicity differ only by 0.02 dex LLanz private communication). so our results are nol sensitive (o the metallicity.," We note that the $K$ -band bolometric corrections for the solar metallicity models and the models for half-solar metallicity differ only by 0.02 dex Lanz private communication), so our results are not sensitive to the metallicity." + Figure 1. shows the derived radius and luminosity of the star as à function of its assumec temperature in the range28.0007 @ 3:in all cases., The ISM density was set to $10^{-24}$ g $^{-3}$ in all cases. + The resulting AM density. profiles at the time of SN explosion are shown in ligure 2.., The resulting AM density profiles at the time of SN explosion are shown in figure \ref{fig-3}. + The interaction of the wind ejected by the progenitor svstem aud (he surrounding ISM follows a mechanism very similar to that at work in SNI: high speed ejecta flow into a uniform. stationarv mediun and push it away resulting in a doublv-shocked structure with a contact discontinuitv between the wind ancl the ISM.," The interaction of the wind ejected by the progenitor system and the surrounding ISM follows a mechanism very similar to that at work in SNR: high speed ejecta flow into a uniform, stationary medium and push it away resulting in a doubly-shocked structure with a contact discontinuity between the wind and the ISM." + A forward shock (prominent in all the profiles shown in figure 2)) propagates into the ISM. heating. compressing and accelerating it. while a reverse shock propagates inward. heating. compressing aud decelerating the inner windmaterial.," A forward shock (prominent in all the profiles shown in figure \ref{fig-3}) ) propagates into the ISM, heating, compressing and accelerating it, while a reverse shock propagates inward, heating, compressing and decelerating the inner windmaterial." + The kinetic energies involved. however. are four to," The kinetic energies involved, however, are four to" +scheduling.,scheduling. + Thev have contributed 3 new millisecond pulsars and 1G slow ones to the total number of the drif(-sean survey discoveries quoted above., They have contributed 3 new millisecond pulsars and 16 slow ones to the total number of the drift-scan survey discoveries quoted above. + The millisecond pulsars P5R J1640--2224 and PSR JI713--074T have been svstematically monitored at Arecibo since the time of their discovery., The millisecond pulsars PSR J1640+2224 and PSR J1713+0747 have been systematically monitored at Arecibo since the time of their discovery. + The Uiming models for these objects have been published by Wolszezan et al. (, The timing models for these objects have been published by Wolszczan et al. ( +2000) and Camilo. Foster and Wolszezan (1994). respectively.,"2000) and Camilo, Foster and Wolszczan (1994), respectively." + Our continuing observations discussed in this paper have established an accurate üming model for the third millisecond pulsar. PSR J110942313. positively verified (wo of the four unconfirmed slow pulsar candidates included in Foster et al. (," Our continuing observations discussed in this paper have established an accurate timing model for the third millisecond pulsar, PSR J1709+2313, positively verified two of the four unconfirmed slow pulsar candidates included in Foster et al. (" +1995). PSR J2151+2315 and PSR 21554-2813. and discovered two acditional slow pulsars. PSI. 18132-1322 and PSR J1908+2351.,"1995), PSR J2151+2315 and PSR 2155+2813, and discovered two additional slow pulsars, PSR 1813+1822 and PSR J1908+2351." + Two of our seeminelv original discoveries. PSR J15494-21 and PSR J19064-16. have proven to be pulsars detected by other searches (Lorimer. private communication: Camilo 1995).," Two of our seemingly original discoveries, PSR J1549+21 and PSR J1906+16, have proven to be pulsars detected by other searches (Lorimer, private communication; Camilo 1995)." + Finally. the slow pulsar candidates. PSR D18402-13 and PSR D22084-18. and the millisecond pulsar candidate. PSR. D17354-13. have not been confirmed.," Finally, the slow pulsar candidates, PSR B1840+13 and PSR B2208+18, and the millisecond pulsar candidate, PSR B1735+13, have not been confirmed." + In (his paper. we present refined timing models for the millisecond pulsar PSR J11094-23. the pulsar PSI. J05384-2817 in the supernova remnant S147. and the sixteen confirmed slow pulsars discovered by (the Penn Stale/NRL surveys since 1991.," In this paper, we present refined timing models for the millisecond pulsar PSR J1709+23, the pulsar PSR J0538+2817 in the supernova remnant S147, and the sixteen confirmed slow pulsars discovered by the Penn State/NRL surveys since 1991." + The model for PSR J1709+2313 includes a significant proper motion measurement., The model for PSR J1709+2313 includes a significant proper motion measurement. + For all pulsars listed in Foster et al. (, For all pulsars listed in Foster et al. ( +1995). both the spin parameters and the (imine positions have been significantly improved.,"1995), both the spin parameters and the timing positions have been significantly improved." + Dining parameters for the (wo new slow pulsars are published here for the first lime., Timing parameters for the two new slow pulsars are published here for the first time. + We also present the results of single pulse observations of the brightest objects in the sample., We also present the results of single pulse observations of the brightest objects in the sample. +" These include (he unusual ""bursting pulsar. PSR J175242-2359. two new drifting subpulse pulsars. PSR. J1649+2533 and PSR J2155+2813. and a new mode changing pulsar. PSR J17464-2540."," These include the unusual “bursting” pulsar, PSR J1752+2359, two new drifting subpulse pulsars, PSR J1649+2533 and PSR J2155+2813, and a new mode changing pulsar, PSR J1746+2540." + Our observations and cata analysis are described in Section 2., Our observations and data analysis are described in Section 2. + In Section 3. we give the details of the new timing models for the millisecond. pulsar PSR J17094-2313.. PSR JO538+2817. the pulsar located inside the supernova remnant 5147. and [or the 16 slow pulsars.," In Section 3, we give the details of the new timing models for the millisecond pulsar PSR J1709+2313, PSR J0538+2817, the pulsar located inside the supernova remnant S147, and for the 16 slow pulsars." + Section 4 is devoted to the single pulse analvsis of three pulsars from this sample and our conclusions are given in Section 5., Section 4 is devoted to the single pulse analysis of three pulsars from this sample and our conclusions are given in Section 5. + The pulse timing and the single pulse observations discussed in (his paper have been made with the 305-m Arecibo radiotelescope using the cdualcirenlar polarization receiving svstems al 430 MIIz and 1400 MIIz and the Penn State Pulsar Machine (PSPAI)., The pulse timing and the single pulse observations discussed in this paper have been made with the 305-m Arecibo radiotelescope using the dual-circular polarization receiving systems at 430 MHz and 1400 MHz and the Penn State Pulsar Machine (PSPM). + Timing observations made at Arecibo before 1995 with the 40 MlIIz correlation spectrometer as a pulsar backend are discussed in Foster οἱ al. (, Timing observations made at Arecibo before 1995 with the 40 MHz correlation spectrometer as a pulsar backend are discussed in Foster et al. ( +1995) ancl Cacwell (1997).,1995) and Cadwell (1997). +Variability was very carly established as a trade mark of Active Galactic Nuclei (AGN).,Variability was very early established as a trade mark of Active Galactic Nuclei (AGN). + Variability has also been used. as à key tool to derive physical properties of AGN: characteristic time scales were used to infer sizes of the emitting regions. lags between the ionising continuum and the line response have been used to determine Black Hole masses (A). multi-wavelength light. curves have been used to study the ecometrical and physical connections between the different regions around the central engine.," Variability has also been used as a key tool to derive physical properties of AGN: characteristic time scales were used to infer sizes of the emitting regions, lags between the ionising continuum and the line response have been used to determine Black Hole masses $M$ ), multi-wavelength light curves have been used to study the geometrical and physical connections between the different regions around the central engine." + The scenario accepted. until recently for the interplay of the emitting regions is that variability is driven by the emission from the X-rav corona located close to the central Black Hole (c.g. Collin-Soulfrin. 1991: Ixrolik et 11991: Clavel et al.," The scenario accepted until recently for the interplay of the emitting regions is that variability is driven by the emission from the X-ray corona located close to the central Black Hole (e.g., Collin-Souffrin, 1991; Krolik et 1991; Clavel et al.," + 1992: Collier et 11999: Cackett et 22007)., 1992; Collier et 1999; Cackett et 2007). + The negligible optical inter-band lags was carly evidence that pointed. towards reprocessing of high-energy photons bv the accretion disc. where the characteristic distances between the cilferent emitting regions correspond to the ight travelling time (Collin-Soullrin.. 1991: WKerolik ct 11991: Clavel et aL.," The negligible optical inter-band lags was early evidence that pointed towards reprocessing of high-energy photons by the accretion disc, where the characteristic distances between the different emitting regions correspond to the light travelling time (Collin-Souffrin, 1991; Krolik et 1991; Clavel et al.," + 1992)., 1992). + Later on. the measurement of short lags between the X-ray. emission and the optical. anc he leading of the X-ravs whenever significant lags were determined (es. IEdelson et al..," Later on, the measurement of short lags between the X-ray emission and the optical, and the leading of the X-rays whenever significant lags were determined (e.g., Edelson et al.," +. 1996: Wanders et al.," 1996; Wanders et al.," + 1997: Shemumer et al..," 1997; Shemmer et al.," + 2001: Desroches ct al..," 2001; Desroches et al.," + 2006). lent support o this picture (see also Nandra et al..," 2006), lent support to this picture (see also Nandra et al.," +. 2000 for evidence supporting reprocessing from the correlation between the UV flux and the spectral shape of the X-ray emission). since or intrinsic cise variability shorter wavelengths should. lag onger wavelength. emission by long (viscous) time-scales.," 2000 for evidence supporting reprocessing from the correlation between the UV flux and the spectral shape of the X-ray emission), since for intrinsic disc variability shorter wavelengths should lag longer wavelength emission by long (viscous) time-scales." + Also. light curves showed that the amplitude of the X-ray variations was much larger than that seen in the optical. which can be explained by the damping of the signal during the disc reprocessing.," Also, light curves showed that the amplitude of the X-ray variations was much larger than that seen in the optical, which can be explained by the damping of the signal during the disc reprocessing." + However. a full picture of the interplay between the X-ray corona and the disc might. not be complete just vet. as new evidence seems to suggest that long termi optical variability is. driven by accretion," However, a full picture of the interplay between the X-ray corona and the disc might not be complete just yet, as new evidence seems to suggest that long term optical variability is driven by accretion" +The interesting transition hinting for an instability was reported by Homanetal.(2001).,The interesting transition hinting for an instability was reported by \cite{homan01}. +" In the MJD 51,254 observation, when the source was still very bright, the luminosity suddenly increased without a change in the color."," In the MJD 51,254 observation, when the source was still very bright, the luminosity suddenly increased without a change in the color." +" Whether indeed this single transition hints for the radiation pressure instability or not, the source likley defines the lower limit for the radiation pressure instability to operate."," Whether indeed this single transition hints for the radiation pressure instability or not, the source likley defines the lower limit for the radiation pressure instability to operate." + In Table 1 we do not see sources which have very large Eddington ratio and are stable against the radiation pressure instability., In Table \ref{tab:binaries} we do not see sources which have very large Eddington ratio and are stable against the radiation pressure instability. +" As we mentioned above, GRS 1915--105 is a good example of showing outbursts even at Eddington ratio close to 1 so it seems we have no upper limit for the Eddington ratio in the case of radiation pressure instability."," As we mentioned above, GRS 1915+105 is a good example of showing outbursts even at Eddington ratio close to 1 so it seems we have no upper limit for the Eddington ratio in the case of radiation pressure instability." +" Thus, observationally, the radiation pressure instability should operate between the Eddington ratio 0.15 up to 1 or more."," Thus, observationally, the radiation pressure instability should operate between the Eddington ratio 0.15 up to 1 or more." + Comparing this with the several theoretical possibilities plotted in Fig., Comparing this with the several theoretical possibilities plotted in Fig. + 1 we can draw certain conclusions., \ref{fig:topo} we can draw certain conclusions. +" First, only the viscosity prescription a\/PeasProt is consistent with the lower limit for the radiation pressure instability, as the unstable region then extends from the Eddington 0.16 up."," First, only the viscosity prescription $\alpha \sqrt{P_{\rm gas}P_{\rm tot}}$ is consistent with the lower limit for the radiation pressure instability, as the unstable region then extends from the Eddington 0.16 up." + The prescription aPiot would allow instability to operate at too low luminosity., The prescription $\alpha P_{\rm tot}$ would allow instability to operate at too low luminosity. +" Second, too efficient cooling by the jet is also ruled out."," Second, too efficient cooling by the jet is also ruled out." + The cooling operates similarly in both cases of viscosity parameterization and stabilize the disc., The cooling operates similarly in both cases of viscosity parameterization and stabilize the disc. +" For the adopted values of the jet efficiency parameter, the disc is stable for Eddington ratio above 0.22, which is clrearly inconsistent with observations."," For the adopted values of the jet efficiency parameter, the disc is stable for Eddington ratio above 0.22, which is clrearly inconsistent with observations." +" Therefore, the parameter A is Eq.1 of the disk-jet coupling must be significantly lower than this exemplary value of A—25."," Therefore, the parameter $A$ is \ref{eq:jet} of the disk-jet coupling must be significantly lower than this exemplary value of $A=25$." +" However the jet is by no means excluded and still can carry a substantial energy, because in the case of equipartition between the disk and jet radiation, for the Eddington accretion rate m=1 the jet coupling constant equal to A=1 would be enough."," However the jet is by no means excluded and still can carry a substantial energy, because in the case of equipartition between the disk and jet radiation, for the Eddington accretion rate $\dot m =1$ the jet coupling constant equal to $A=1$ would be enough." +" The parameterization a,/PsasPio has an additional advantage of reducing the outburst amplitude in comparison to aPiot.", The parameterization $\alpha \sqrt{P_{\rm gas}P_{\rm tot}}$ has an additional advantage of reducing the outburst amplitude in comparison to $\alpha P_{\rm tot}$. +" Most of the candidate sources for radiation pressure instability show rather low to moderate amplitudes, from factor 2 to 20."," Most of the candidate sources for radiation pressure instability show rather low to moderate amplitudes, from factor 2 to 20." +" Only one source - GS 2023+338 - shows huge outbursts, with the factor of 500 brightenings in timescales of 60 seconds."," Only one source - GS 2023+338 - shows huge outbursts, with the factor of 500 brightenings in timescales of 60 seconds." + in’tZandetal.(1992) interpreted this short timescale variability as caused by variable absorption., \cite{zand92} interpreted this short timescale variability as caused by variable absorption. + The behaviour of this source is exceptional and puzzling., The behaviour of this source is exceptional and puzzling. +" When studying the instabilities in the supermassive black hole environment, we usually cannot directly observe a duty cycle of a one single object, since the black hole masses are large and the expected timescales are very long."," When studying the instabilities in the supermassive black hole environment, we usually cannot directly observe a duty cycle of a one single object, since the black hole masses are large and the expected timescales are very long." +" Instead, the statistical studies are useful here and we can find an evidence for the source episodic activity (e.g. Czernyetal. (2009)))."," Instead, the statistical studies are useful here and we can find an evidence for the source episodic activity (e.g. \cite{czerny09}) )." +" However, the exceptional object is NGC 4395, with the black hole mass of 3.6x10° (Petersonetal. (2005)))."," However, the exceptional object is NGC 4395, with the black hole mass of $3.6 \times 10^{5} M_{\odot}$ \cite{peterson05}) )." +" In this source, in principle, we Mocould observe the variability due to radiation pressure instability."," In this source, in principle, we could observe the variability due to radiation pressure instability." +" As was shown by Czernyetal.(2009),, the outbursts for the central black hole of the mass 10""Mo, should last below 100 years, so for a mass 30 times smaller, the outbursts should last ~3 years!"," As was shown by \cite{czerny09}, the outbursts for the central black hole of the mass $10^{7} M_{\odot}$, should last below 100 years, so for a mass 30 times smaller, the outbursts should last $\sim 3$ years!" + No such outbursts are observed., No such outbursts are observed. +" However, this fact is actually consistent with our expectations, since the Eddington ratio in this source is only 1.2x103."," However, this fact is actually consistent with our expectations, since the Eddington ratio in this source is only $1.2\times 10^{-3}$." +" The source is thus stable with both aP,o¢ and ay/PeasPtot mechanisms and provides no useful constraints for the parameterization of the viscous torque.", The source is thus stable with both $\alpha P_{\rm tot}$ and $\alpha \sqrt{P_{\rm gas}P_{\rm tot}}$ mechanisms and provides no useful constraints for the parameterization of the viscous torque. + Significant constraints can be obtained from radio galaxies., Significant constraints can be obtained from radio galaxies. +" In case of the accretion discs in radio galaxies, the Eddington ratios can be estimated e.g. through the correlation with the broad line luminosities (2007)))."," In case of the accretion discs in radio galaxies, the Eddington ratios can be estimated e.g. through the correlation with the broad line luminosities \cite{dai07}) )." +" The FR I and FR II sources in this sample have low Eddington ratios, of 0.00975 and 0.0096, for FR I and FR II sources, respectively."," The FR I and FR II sources in this sample have low Eddington ratios, of 0.00975 and 0.0096, for FR I and FR II sources, respectively." + Observations clearly show that these sources are stable against the radiation pressure instability since they form very large scale radio structures., Observations clearly show that these sources are stable against the radiation pressure instability since they form very large scale radio structures. +" In particular, the central engine of FR II galaxies must be operating in a continuous way for millions of years."," In particular, the central engine of FR II galaxies must be operating in a continuous way for millions of years." + Fig., Fig. + 1 shows that their stability is consistent with theory if the heating is given by o4/Pza;Pi«., \ref{fig:topo} shows that their stability is consistent with theory if the heating is given by $\alpha \sqrt{P_{\rm gas}P_{\rm tot}}$. +" On the other hand, the FSRQ sources with compact radio structures tend to have larger Eddington ratios."," On the other hand, the FSRQ sources with compact radio structures tend to have larger Eddington ratios." +" These sources may in fact exhibit episodic activity and the small size of the structure is indicating a new episode, as proposed by Czernyetal. (2009)."," These sources may in fact exhibit episodic activity and the small size of the structure is indicating a new episode, as proposed by \cite{czerny09}." +". Therefore, it seems that the assumption of the ay/PeasPtot can accomodate the observational constraints both for Galactic sources and AGN."," Therefore, it seems that the assumption of the $\alpha \sqrt{P_{\rm gas}P_{\rm tot}}$ can accomodate the observational constraints both for Galactic sources and AGN." + A typical value of the Eddington ratio found in the SDSS sample of quasars by Kellyetal.(2010) is 0.05 with a scatter of 0.4 dex., A typical value of the Eddington ratio found in the SDSS sample of quasars by \cite{kelly10} is 0.05 with a scatter of 0.4 dex. + This is also large enough for the episodic activity caused by the radiation pressure instability., This is also large enough for the episodic activity caused by the radiation pressure instability. +" Possibly, the selection effect is in fact the reason why we detect only the sources in the active state: most of the sources in the quiescent state are too dim to be detectable."," Possibly, the selection effect is in fact the reason why we detect only the sources in the active state: most of the sources in the quiescent state are too dim to be detectable." +" There is also a possibility that active galaxies at high Eddington ratios, close to 1, are actually stable due to the stabilizing power of jet/outflow."," There is also a possibility that active galaxies at high Eddington ratios, close to 1, are actually stable due to the stabilizing power of jet/outflow." + This mechanism seems not to work efficiently in Galactic sources but the relative jet power in accreting sources rises with the black hole mass:, This mechanism seems not to work efficiently in Galactic sources but the relative jet power in accreting sources rises with the black hole mass: +"of the work in this letter is for an observer located outside the initial jet opening. 0,My.","of the work in this letter is for an observer located outside the initial jet opening, $\theta_{\rm obs}>\theta_0$." + We have considered three different Jet models of increasing sophistication: the simplest being a point source moving along the jet axis ($22.1). and the most sophisticated is 2D hydrodynamical simulation ($22.3).," We have considered three different jet models of increasing sophistication; the simplest being a point source moving along the jet axis 2.1), and the most sophisticated is 2D hydrodynamical simulation 2.3)." +" The basic qualitative features of the light-curves are similar in all three models. for 0,),.704."," The basic qualitative features of the light-curves are similar in all three models, for $\theta_{\rm obs}>\theta_0$." + Moreover. the uniform jet model (model 2. 822.2) is in rough quantitative agreement with the hydro-model.," Moreover, the uniform jet model (model 2, 2.2) is in rough quantitative agreement with the hydro-model." +" We find that ""orphan"" optical afterglows associated with axis Jets can be observed up to a constant 0,5. rather than a constant 0,1,/( as suggested by Dalal et al. ("," We find that ""orphan"" optical afterglows associated with off-axis jets can be observed up to a constant $\theta_{\rm obs}$ rather than a constant $\theta_{\rm obs}/\theta_0$ as suggested by Dalal et al. (" +2002). if one assumes a constant energy in the jet. rather than a constant flux at the time of the jet break for an on-axis observer.,"2002), if one assumes a constant energy in the jet, rather than a constant flux at the time of the jet break for an on-axis observer." + This implies that future surveys for orphan afterelows may provide valuable data for the the distribution of jet opening angles (; and the true event rate of GRBs., This implies that future surveys for orphan afterglows may provide valuable data for the the distribution of jet opening angles $\theta_0$ and the true event rate of GRBs. + The orphan optical events discussed here can be identified from the initial rise during which the spectral slope is typically ο>0. followed by a decay. on a time scale of ~130 days. and may show a large degree of linear polarization (xz.1054).," The orphan optical events discussed here can be identified from the initial rise during which the spectral slope is typically $\beta > 0$, followed by a decay, on a time scale of $\sim 1-30$ days, and may show a large degree of linear polarization $\lesssim 40\%$ )." + The detection of such orphan afterelows may provide a new line of evidence in favor of jetted outflows in GRBs., The detection of such orphan afterglows may provide a new line of evidence in favor of jetted outflows in GRBs. + Recently Huang. Dai and Lu (2001) have considered another scenario (failed GRBs) for producing orphan afterglows: this would increase the detection rate of orphan afterglows.," Recently Huang, Dai and Lu (2001) have considered another scenario (failed GRBs) for producing orphan afterglows; this would increase the detection rate of orphan afterglows." +" A good monitoring ofoptical transients may help distinguish failed GRBs from jets seen at 0,>(y. and improve our understanding of them."," A good monitoring of optical transients may help distinguish failed GRBs from jets seen at $\theta_{\rm obs} > \theta_0$, and improve our understanding of them." + We thank Mark Miller for generating the data for model 3, We thank Mark Miller for generating the data for model 3. + This research was supported by grants NSF PHY 99-79985 and MCA93S025 (computational support). NSF grant PHY- (JG).Lyman Spitzer. Jr. Fellowship (AP). NAGS-8128 and MIT-292701 (SW).," This research was supported by grants NSF PHY 99-79985 and MCA93S025 (computational support), NSF grant PHY-0070928 (JG),Lyman Spitzer, Jr. Fellowship (AP), NAG5-8128 and MIT-292701 (SW)." +"acerete during this time. but at much reduced accretion rates of 210"" M. yr5 for the 3=0.001 calculation and 110 ""M. vr|! for the 3=0.005 calculation (measured between 20 and SO years after stellar core formation: Fig. 149.","accrete during this time, but at much reduced accretion rates of $2\times 10^{-5}$ $_\odot$ $^{-1}$ for the $\beta=0.001$ calculation and $1\times 10^{-5}$ $_\odot$ $^{-1}$ for the $\beta=0.005$ calculation (measured between 20 and 50 years after stellar core formation; Fig. \ref{convergence}) )." + Although the rate of convergence with increasing resolution is relatively slow. strong outflows are launched in all cases (see Appendix A).," Although the rate of convergence with increasing resolution is relatively slow, strong outflows are launched in all cases (see Appendix A)." + The slow convergence is due to the strong interplay between the energy released by the formation of the stellar core. and the launching of the outflow which decreases accretion and. thus. reduces the energy that is released.," The slow convergence is due to the strong interplay between the energy released by the formation of the stellar core, and the launching of the outflow which decreases accretion and, thus, reduces the energy that is released." + If the resolution is poor. the stellar core accretes more material before the energy released feeds back and manages to stop the accretion. whereas with higher resolution. the accretion of a small amount of mass can feed thermal energy into the infalling material more quickly and. thus. inhibit further accretion.," If the resolution is poor, the stellar core accretes more material before the energy released feeds back and manages to stop the accretion, whereas with higher resolution, the accretion of a small amount of mass can feed thermal energy into the infalling material more quickly and, thus, inhibit further accretion." + As mentioned in Section 3.2.. the introduction of radiative transfer and a realistic equation of state increases the lifetimes of the first core phase compared to that obtained using our barotropic equation of state by factors of 1.5—3 (Fig. 5).," As mentioned in Section \ref{rapidly_rotating}, the introduction of radiative transfer and a realistic equation of state increases the lifetimes of the first core phase compared to that obtained using our barotropic equation of state by factors of 1.5–3 (Fig. \ref{first_core_time}) )." + This is important. because the longer the first core phase lasts. the more easy it will be to observe.," This is important, because the longer the first core phase lasts, the more easy it will be to observe." + Thelifetimes obtained using radiative transfer range from es400 years (with no rotation) to =3000 years (for 3= 0.01). whereas using the barotropic equation of state they ranged from zz100 to z1500 years.," Thelifetimes obtained using radiative transfer range from $\approx 400$ years (with no rotation) to $\approx 3000$ years (for $\beta=0.01$ ), whereas using the barotropic equation of state they ranged from $\approx 100$ to $\approx 1500$ years." + As discussed above. the difference is due to the higher temperatures Cand thus higher pressures) that are obtained using the realistic physics rather than the barotropic equation of state. which slows the evolution towards the second collapse phase.," As discussed above, the difference is due to the higher temperatures (and thus higher pressures) that are obtained using the realistic physics rather than the barotropic equation of state, which slows the evolution towards the second collapse phase." + This lengthening of the lifetimes with radiation hydrodynamics compared to barotropic calculations was also seen by ?.., This lengthening of the lifetimes with radiation hydrodynamics compared to barotropic calculations was also seen by \cite{Tomidaetal2010a}. . + The lengthening occurs for both the non-rotating first cores.," The lengthening occurs for both the non-rotating first cores," +by the computed model light curve.,by the computed model light curve. + However. the theoretical light curve fit becomes worse for later phases.," However, the theoretical light curve fit becomes worse for later phases." + The luminosity of the model light curve seems to rise again at around day 25 after the explosion., The luminosity of the model light curve seems to rise again at around day 25 after the explosion. + Up to day 45. the model light curve has à second bump. which ts not observed in the light curves of SN 1999ee and SN 2002bo.," Up to day 45, the model light curve has a second bump, which is not observed in the light curves of SN 1999ee and SN 2002bo." + In the infrared I band. the decline after the maximum phase is missing. as shown in Fig. 16..," In the infrared I band, the decline after the maximum phase is missing, as shown in Fig. \ref{fig:lc_i}." + As in the R band. the rise in the beginning and maximum are well represented in the model light curve.," As in the R band, the rise in the beginning and maximum are well represented in the model light curve." + However. at maximum. the luminosity of the SN la model light curve rises further. which is not seen in the observed light curves of SN 2002bo and 1999ee.," However, at maximum, the luminosity of the SN Ia model light curve rises further, which is not seen in the observed light curves of SN 2002bo and 1999ee." + Around day 30. the difference between model and observed light curve in the I band are about | mag.," Around day 30, the difference between model and observed light curve in the I band are about 1 mag." + Up to day 50. the model light curve declines. while the observed light curves show their second maximum around 40 days after explosion.," Up to day 50, the model light curve declines, while the observed light curves show their second maximum around 40 days after explosion." + In Fig. 17..," In Fig. \ref{fig:lc_u-b}," + we compared the relation U-B of the theoretical and observed light curves., we compared the relation U-B of the theoretical and observed light curves. + The same comparision for the B-V relation is shownin Fig. 18.., The same comparision for the B-V relation is shownin Fig. \ref{fig:lc_b-v}. . +Fig.,Fig. + 9 (top panel) the CO fractional abundance is ~1077. high enough to lead a significant destruction ofN4H.," \ref{modelfigs}~ (top panel) the CO fractional abundance is $\sim10^{-4}$, high enough to lead a significant destruction of." +. Contrary to the case of aandHCO the increase of the ffractional abundance is slow. which indicates that gas phase chemistry dominates over pure evaporation.," Contrary to the case of and, the increase of the fractional abundance is slow, which indicates that gas phase chemistry dominates over pure evaporation." + This is simply a consequence of the fact that most of the ammonia is still locked in water ice: in fact. as shown by the experiments by Collings et al. (," This is simply a consequence of the fact that most of the ammonia is still locked in water ice; in fact, as shown by the experiments by Collings et al. (" +2004). ammonia is released back into the gas phase only if temperatures of ~ 100-120 K are reached (Viti et al.,"2004), ammonia is released back into the gas phase only if temperatures of $\sim$ 100-120 K are reached (Viti et al." + 2004)., 2004). + The maximum value. of 4.11075 (or N(NH3))3.2x10? 2). is reached at /~1.3xIO? yr. and then it drops until it reaches à constant abundance of 1x10? (or a column density of ~8.2x10 em).," The maximum value, of $\times10^{-8}$ (or $\simeq3.2\times10^{15}$ ), is reached at $t\simeq1.3\times10^5$ yr, and then it drops until it reaches a constant abundance of $\times10^{-9}$ (or a column density of $\sim8.2\times10^{13}$ )." + This behavior. tthe decrease in the ffractional abundance. takes place through reactions of the mmolecule with the ions C andHCO™.," This behavior, the decrease in the fractional abundance, takes place through reactions of the molecule with the ions $^+$ and." +. In this situation. the C fractional abundance increases at late stages. while the fractional abundance of iis More or less constant. which is consistent with the fact that iis produced from the destruction of ((see above) and destroyed through reactions withs.," In this situation, the $^+$ fractional abundance increases at late stages, while the fractional abundance of is more or less constant, which is consistent with the fact that is produced from the destruction of (see above) and destroyed through reactions with." +. Regarding the western and eastern cores. which were modeled assuming the same core size (~0.04 pc) and same temperature (the maximum temperature is 25 K). we found that the fractional abundance of increases moderately with time. while the fractional abundances of CO.N»..N2H7.. and rise considerably during the initial stages due to desorption effects. similar to the case of the the central core model.," Regarding the western and eastern cores, which were modeled assuming the same core size $\sim0.04$ pc) and same temperature (the maximum temperature is 25 K), we found that the fractional abundance of increases moderately with time, while the fractional abundances of CO, and rise considerably during the initial stages due to desorption effects, similar to the case of the the central core model." + At rx4x10° yr. παπά hhave constant abundance. around ~2x107!° (N(N2H7))=4x107 emp and ~1.8x107? (N(HCO53.6x10 oor »z9x10!!cm. assuming 240) for aandHCO.. respectively. while the ffractional abundance increases. up to ~5.2x107% (N(NH3)=[x10% em)» at £=~13x10° yr and then it remains roughly constant too.," At $t\simeq4\times10^3$ yr, and have constant abundance, around $\sim2\times10^{-10}$ $\simeq4\times10^{12}$ ) and $\sim1.8\times10^{-9}$ $\simeq3.6\times10^{13}$ or $\times10^{11}$, assuming ]=40) for and, respectively, while the fractional abundance increases, up to $\sim5.2\times10^{-8}$ $\simeq1\times10^{15}$ ) at $t\simeq1.3\times10^{5}$ yr, and then it remains roughly constant too." + For these cores. the values obtained from the chemical modeling are in agreement (within a factor of 2 in the case ofN>H™.. and a factor of 4 in the case of NH3)) with the column densities reported from the observational data.," For these cores, the values obtained from the chemical modeling are in agreement (within a factor of 2 in the case of, and a factor of 4 in the case of ) with the column densities reported from the observational data." + Finally. the CO fractional abundance in the western/eastern cores is ~107. significantly lower than the CO fractional abundance of the central core. indicating that the relatively low CO abundance in the western/eastern cores does not lead to a substantial destruction ofNoH7.," Finally, the CO fractional abundance in the western/eastern cores is $\sim10^{-5}$, significantly lower than the CO fractional abundance of the central core, indicating that the relatively low CO abundance in the western/eastern cores does not lead to a substantial destruction of." +. Therefore. the fraction of CO that will evaporate from grain mantles plays an important role in determining the fractional abundance ofN3H.. and hence the aabundance ratio.," Therefore, the fraction of CO that will evaporate from grain mantles plays an important role in determining the fractional abundance of, and hence the abundance ratio." + In Table 5 we show the values of the aand ccolumn densities. together with the aabundanceο” ratio for the two models that are in agreement with the observed values.," In Table \ref{tableres} we show the values of the and column densities, together with the abundance ratio for the two models that are in agreement with the observed values." + In Fig., In Fig. + 9. (bottom right panel) we present the aabundance ratio as a function of time for the central core and the western/eastern core obtained during phase II., \ref{modelfigs}~ (bottom right panel) we present the abundance ratio as a function of time for the central core and the western/eastern core obtained during phase II. + The aabundance ratio. observed. toward the central core. around -400-1000. can be reproduced by our chemical model for times ¢=~[0 yr and ¢=(4.5-5.3)x10° yr.," The abundance ratio observed toward the central core, around $\sim$ 400–1000, can be reproduced by our chemical model for times $t\simeq10^4$ yr and $t=$ $\times10^5$ yr." + For the time range r= 1074.5x10° yr the model produces a higher aabundance ratio. ~4000. slightly above the observed values for the central core.," For the time range $t\simeq10^4$ $4.5\times10^5$ yr the model produces a higher abundance ratio, $\sim4000$, slightly above the observed values for the central core." + However we adopted the longer age as It is more realistic., However we adopted the longer age as it is more realistic. + Forthe western/eastern cores. the abundance ratio initially shows high values. then it decreases due to desorption effects and finally reaches a constant value ~200 for typical ages of low-mass YSOs. at around f=10°— yr.," Forthe western/eastern cores, the abundance ratio initially shows high values, then it decreases due to desorption effects and finally reaches a constant value $\sim200$ for typical ages of low-mass YSOs, at around $t\simeq10^{5}-10^{6}$ yr." + In addition. in Fig.," In addition, in Fig." + 9 (bottom panel) we also show the temperature as a function of time., \ref{modelfigs} (bottom panel) we also show the temperature as a function of time. + For the central core. when the temperature ts low. the rratio is high (> 107).," For the central core, when the temperature is low, the ratio is high $>10^4$ )." + Around Τ~21 K there is a clear drop of the rratio due to desorption effects., Around $T\simeq21$ K there is a clear drop of the ratio due to desorption effects. + As temperature increases. the rrises until it reaches a constant value. ~10°. at around T.— K. For the western and eastern cores the temperature varies from 12 to 25 K. producing small variations on the ratio. and only for times in the range 10°-10' yr the rratio changes significantly. similar to the case of the central core.," As temperature increases, the rises until it reaches a constant value, $\sim10^3$, at around $T\simeq45$ K. For the western and eastern cores the temperature varies from 12 to 25 K, producing small variations on the ratio, and only for times in the range $10^3$ $10^4$ yr the ratio changes significantly, similar to the case of the central core." + It i5 worth noting that in the model for the central core the visual extinction is Ay=40. but typically the visual extinction in hot cores eembedded in the central core) is around ~100 or even higher.," It is worth noting that in the model for the central core the visual extinction is $A_{\mathrm{V}}\simeq40$, but typically the visual extinction in hot cores embedded in the central core) is around $\sim100$ or even higher." +" In order to evaluate the error in the aabundance introduced by this difference we performed an additional model with a higher density. which gives a visual extinction of A,= 100."," In order to evaluate the error in the abundance introduced by this difference we performed an additional model with a higher density, which gives a visual extinction of $A_{\mathrm{v}}\simeq100$ ." + In this situation. the rratio is affected by a difference of ~4 3-25 We also note that," In this situation, the ratio is affected by a difference of $\sim3$ –25 .We also note that" +the 6.511 Magellan Daade telescope with the £/2 camera.,the 6.5m Magellan Baade telescope with the f/2 camera. + All spectra cover a wavelcneth ranee of 1000-0000. With a dispersion of pper pixel and were reduced withCOSALOS. the standard data reduction package for INLAC'S spectra.," All spectra cover a wavelength range of 4000-9000 with a dispersion of per pixel and were reduced with, the standard data reduction package for IMACS spectra." + To obtain redshifts. we use the IRAF task to cross-correlate spectra with template spectra of four ealaxv types giant elliptical. spiral. E|A. aud eiissiou iue galaxy.," To obtain redshifts, we use the IRAF task to cross-correlate spectra with template spectra of four galaxy types – giant elliptical, spiral, E+A, and emission line galaxy." + Of the 1122 spectra. we recover redshitts or S57 galaxies. of which 362 are designated cluster uenibers based on a caustic analysis of the cluster iufall region (Gonzalez et al.," Of the 1122 spectra, we recover redshifts for 857 galaxies, of which 362 are designated cluster members based on a caustic analysis of the cluster infall region (Gonzalez et al." + in prep). snülu to the echuique emploved by Diaferioetal.(2005).," in prep), similar to the technique employed by \citet{diaferio2005}." +. To our catalog of 362 confirmed members. we add another LL ucibers from Barrenaetal. (2002)..," To our catalog of 362 confirmed members, we add another 44 members from \citet{barrena2002}. ." + Figure 1. shows the distribution of spectroscopic redshifts. with the cluster uembers hiehliehted iu red.," Figure \ref{fig:veldisp} shows the distribution of spectroscopic redshifts, with the cluster members highlighted in red." + In addition to the Bullet Cluster. we find two prominent redshift peaks at 20.21 and 2~0.35. contaiuiug roughly 90 members each.," In addition to the Bullet Cluster, we find two prominent redshift peaks at $z\sim0.21$ and $z\sim0.35$, containing roughly 90 members each." + TheObservatory far-intrared and. sub-nuu properties of the backerouncd eroup are studied iu relation to the Bullet Cluster by Rawle et al (2010. in press).," The far-infrared and sub-mm properties of the background group are studied in relation to the Bullet Cluster by Rawle et al (2010, in press)." + To quantify the total star formation rate of the Bullet Cluster as traced by Ihuninositv. we first identify the MIPS sources that are likely to be cluster members.," To quantify the total star formation rate of the Bullet Cluster as traced by luminosity, we first identify the MIPS sources that are likely to be cluster members." + We use WEI aud IRAC nuages to exclude galaxies whose colors are indicative of either backerouncd galaxies or active galactic uuclci (ACN)., We use WFI and IRAC images to exclude galaxies whose colors are indicative of either background galaxies or active galactic nuclei (AGN). + We then refined our sample by spectroscopically tarecting AIIPS sources that are candidate cluster members., We then refined our sample by spectroscopically targeting MIPS sources that are candidate cluster members. + We start with an initial MIPS catalog of [18 sources down to a flux of [μὴν , We start with an initial MIPS catalog of 418 sources down to a flux of $43\mu$ Jy. +We match the WFI (BYR) and IRAC catalogs and then crossauateh with the MIPS catalog., We match the WFI (BVR) and IRAC catalogs and then cross-match with the MIPS catalog. + Figure 2. shows the R-[L5] versus D-R colors for all MIPS sources with optical and IRAC counterparts., Figure \ref{fig:select} shows the R-[4.5] versus B-R colors for all MIPS sources with optical and IRAC counterparts. + Spectroscopically confirmed members from the 2005. 2006. and first part of 2009 INLACS campaigns demonstrated that the star-forming cluster menibers form a tight diagonal locus iu the R-|1.5| vs B-R space.," Spectroscopically confirmed members from the 2005, 2006, and first part of 2009 IMACS campaigns demonstrated that the star-forming cluster members form a tight diagonal locus in the R-[4.5] vs B-R space." + We define our cluster candidate sample as galaxies within the two solid diagonal lines shown in Figure 2.. and blueward of B-R=3.," We define our cluster candidate sample as galaxies within the two solid diagonal lines shown in Figure \ref{fig:select}, and blueward of B-R=3." + We then use IRAC colors to ideutiftv AGN via the “AGN ποσο (Lacyctal.2001:Sternet2005).. as shown in Figure 3..," We then use IRAC colors to identify AGN via the “AGN wedge” \citep{lacy2004,stern2005}, as shown in Figure \ref{fig:irac_colors}. ." + We exclude all galaxies within the AGN wedee from further analyses because their mid-infrared. Iuuinosityv may be dominated by ACN activity rather than bv star formation., We exclude all galaxies within the AGN wedge from further analyses because their mid-infrared luminosity may be dominated by AGN activity rather than by star formation. +" We also exclude X-ray AGN using a catalog of 115 X-ray point sources extracted from Chandra data that cover the central ~20& 207, overlapping the entire MIPS ΕΟΝ."," We also exclude X-ray AGN using a catalog of 145 X-ray point sources extracted from Chandra data that cover the central $\sim20\arcmin\times 20\arcmin$ , overlapping the entire MIPS FOV." +" The catalog contains N-ray sources down to a flux of 2.5«1016 eves au? + in the 0.5-2 keV. band. which is a luninosity of L,.=ς10% eres s tat the redshitt of the Bullet Cluster."," The catalog contains X-ray sources down to a flux of $2.5\times10^{-16}$ ergs $^{-2}$ $^{-1}$ in the 0.5-2 keV band, which is a luminosity of $L_{x}=7\times10^{40}$ ergs $^{-1}$ at the redshift of the Bullet Cluster." +" Áimong the MIPS confirmed cluster members and candidates. we exclude all X-ray point. sources with an N-ray luminosity of £,>10H cress |. Iu addition to IRAC aud N-rav selection of ACN. we also utilize our optical spectroscopy to construct Baldwin-Philips-Terlevich diagrams (BPT:Baldwinctal.1951) as illustrated in Figure L."," Among the MIPS confirmed cluster members and candidates, we exclude all X-ray point sources with an X-ray luminosity of $L_{x}\geq10^{41}$ ergs $^{-1}$ In addition to IRAC and X-ray selection of AGN, we also utilize our optical spectroscopy to construct Baldwin-Phillips-Terlevich diagrams \cite[BPT;][]{baldwin1981} as illustrated in Figure \ref{fig:BPT}." + The dotted aud dashed lines indicate the boundaries from Ἱνοπ]ονetal.(2006) that separate purely star forming galaxies from Sevferts and LINERS., The dotted and dashed lines indicate the boundaries from \citet{kewley2006} that separate purely star forming galaxies from Seyferts and LINERs. + Note that many of the MIPS sources are nisse in Figure Lo because one or more of the four required eiission lines could not be measured. often due to a promineut skv cussion line that appears at the same waveleugth as IL) at the Bullet Cluster redshift.," Note that many of the MIPS sources are missing in Figure \ref{fig:BPT} because one or more of the four required emission lines could not be measured, often due to a prominent sky emission line that appears at the same wavelength as $\beta$ at the Bullet Cluster redshift." + Figure | reveals ouly two MIPS sources classified as a Sevtert or LINER that have not been ideutified as ACN using either IRAC colors or X-ray e1iission., Figure \ref{fig:BPT} reveals only two MIPS sources classified as a Seyfert or LINER that have not been identified as AGN using either IRAC colors or X-ray emission. + One of these is à. ULIRG (star sviubol). which appears close to the Seyfert/LINER boundary wheu using the /Tlo ratio. and is classified as a LINER using the Πα ratio.," One of these is a ULIRG (star symbol), which appears close to the Seyfert/LINER boundary when using the $\alpha$ ratio, and is classified as a LINER using the $\alpha$ ratio." + The two confirmed MIPS sources in [OTthe IRAC AGN wedge (Figure 3)) are not shown ou the BPT diagram )ecause they lack the necessary euussion nes., The two confirmed MIPS sources in the IRAC AGN wedge (Figure \ref{fig:irac_colors}) ) are not shown on the BPT diagram because they lack the necessary emission lines. + However. of the 10 confirmed IRAC. AGN wedge sources that are rot MIPS iuciubers (or bevoud the MIPS FOV). two are Xotted in Figure [. with one classified as à LINER. aud he other as an II dominated galaxy.," However, of the 10 confirmed IRAC AGN wedge sources that are not MIPS members (or beyond the MIPS FOV), two are plotted in Figure \ref{fig:BPT}, with one classified as a LINER, and the other as an HII dominated galaxy." + Of the three X-rav point sources in Figure 3.. one is illustrated in Figure L asa large square aud appears close o the boundary of III dominated galaxies aud Sevferts.," Of the three X-ray point sources in Figure \ref{fig:irac_colors}, one is illustrated in Figure \ref{fig:BPT} as a large square and appears close to the boundary of HII dominated galaxies and Seyferts." + Iu total. there are S AGN identified amone the confirmed MIPS sample. using the three methods TRAC colors. N-rav enission. aud optical enission Lue ratios.," In total, there are 8 AGN identified among the confirmed MIPS sample, using the three methods – IRAC colors, X-ray emission, and optical emission line ratios." + Of these cight. two are identified solely from the BPT diagnostic. one classified as à LINER and the other a Sevtert.," Of these eight, two are identified solely from the BPT diagnostic, one classified as a LINER and the other a Seyfert." + The LINER is included iu our sample. asstuuine that of its IR fux is powered by star formation (see ULIRC OG).," The LINER is included in our sample, assuming that of its IR flux is powered by star formation (see \\ref{sec:ULIRG}) )." + The Sevtert. which is excluded from our siuuple. would contribute a neglible fraction to the global SFR.," The Seyfert, which is excluded from our sample, would contribute a neglible fraction to the global SFR." + Iu addition to isolating the AGN population. Figure 3 also illustrates that our selection of cluster candidates based on R-[1.5] and B-R colors is au effective way to cull interlopers.," In addition to isolating the AGN population, Figure \ref{fig:irac_colors} also illustrates that our selection of cluster candidates based on R-[4.5] and B-R colors is an effective way to cull interlopers." + The left aud right panels of Figure 3) show the IRAC color distribution before aud after we apply the aud B-R color selection. respectively.," The left and right panels of Figure \ref{fig:irac_colors} show the IRAC color distribution before and after we apply the R-[4.5] and B-R color selection, respectively." + We show the R-|1.5]model colors ofM82 (a local starburst galaxy) at 2=0.0.3.0.5. and 1 (Devriendtctal.1999:Steru2005) to illustrate that our color selection is effective im removing ealaxies whose IRAC colors are consistent with those of a Ligh redshift starburst (open red circles near οσο1 to 2).," We show the model colors ofM82 (a local starburst galaxy) at z=0,0.3,0.5, and 1 \citep{devriendt1999,stern2005} to illustrate that our color selection is effective in removing galaxies whose IRAC colors are consistent with those of a high redshift starburst (open red circles near $z\sim1$ to $2$ )." + The right panel of Figure 3. highlights the AGN sources among the MIPS sample. includiug four galaxies iu the IRAC AGN wedge. three N-vay point sources. outside the AGN wedge. aud one Sevfert identified fro the BPT diagram. which is sciui-hidden behind the ULIRG svinbol.," The right panel of Figure \ref{fig:irac_colors} highlights the AGN sources among the MIPS sample, including four galaxies in the IRAC AGN wedge, three X-ray point sources outside the AGN wedge, and one Seyfert identified from the BPT diagram, which is semi-hidden behind the ULIRG symbol." + Among the mou-ACN MIPS. cluster ποσα». there are two outliers. both of which do not ft in the diagonal star forming sequence (roughly outlined by the LIRCGs and ULIRG shownas star sviubols) nor the locus of passive carly type galaxies near [6|-|L.5|50.2. aud [5.8|-[8.0]~0.2.One outlier has a color of « 0. due toa blending of sources iu theaud Dbauds.," Among the non-AGN MIPS cluster members, there are two outliers, both of which do not fit in the diagonal star forming sequence (roughly outlined by the LIRGs and ULIRG shownas star symbols) nor the locus of passive early type galaxies near $\sim$0.2 and $\sim$ 0.2.One outlier has a color of $<0$ , due to a blending of sources in theand bands." + It is unclear why the second. outlier has IRAC, It is unclear why the second outlier has IRAC +colours are 1.0«(BG.RR)1.5 which we will use to compare the B band observations of the previous section with the R band observations ciscussed here.,colours are $1.0<(B-R)<1.5$ which we will use to compare the B band observations of the previous section with the R band observations discussed here. + To test the procedure described in the previous section we have added simulated ares to the raw data (each image is mace up of 5 separate LO min exposures) and then processed the frame as before., To test the procedure described in the previous section we have added simulated arcs to the raw data (each image is made up of 5 separate 10 min exposures) and then processed the frame as before. + Below we will show that an are of surface brightness 27.5 Rye (28.5-29 Byr) is easily. detectable., Below we will show that an arc of surface brightness 27.5 $\mu$ (28.5-29 $\mu$ ) is easily detectable. + This is 0.5 to 1.0 magnitudes deeper than the observations described in the previous section., This is 0.5 to 1.0 magnitudes deeper than the observations described in the previous section. + In Fig., In Fig. + 3 we show the data frame (before smoothing) and the distribution of angles that low surface brightness pixels make with the origin., 3 we show the data frame (before smoothing) and the distribution of angles that low surface brightness pixels make with the origin. + Looking carefully. the simulated. stream can just be mace out as à diagonal line across the CCD from bottom left to top right.," Looking carefully, the simulated stream can just be made out as a diagonal line across the CCD from bottom left to top right." + ln the histogram an arc at an angle of 45 degrees is clearly seen at SN=4.4., In the histogram an arc at an angle of 45 degrees is clearly seen at $SN = 4.4$. + Lt is quite clear that ares at this surface brightness level are not removed by the data processing., It is quite clear that arcs at this surface brightness level are not removed by the data processing. + Given the strong signallein] obtained for an are at a surface brightness of 27.55 Ry we are confident that our procedure is capable of detecting ares in this data set to an equivalent level of 29 Dj., Given the strong signal obtained for an arc at a surface brightness of 27.5 $\mu$ we are confident that our procedure is capable of detecting arcs in this data set to an equivalent level of 29 $\mu$. + We have applied the above procedure to the 7 galaxies in our sample., We have applied the above procedure to the 7 galaxies in our sample. + None of the galaxies have a detection at SUVo3: one has 2«SN3., None of the galaxies have a detection at $SN>3$; one has $2 (TG53B1e8) in which the field grows from |B]~3x107? to ~0.02 at radius 0.65@, by runs end.",amplitude case (TG53B1e8) in which the field grows from $|B| \sim 3\times10^{-5}$ to $\sim 0.02$ at radius $\varpi_E$ by runs end. +" A confirmation of the convergence of these results is provided by the high-resolution run TG53B100HR which falls between the B10 and B500 results, and tracks closely the corresponding energy and field amplitudes at lower resolution."," A confirmation of the convergence of these results is provided by the high-resolution run TG53B100HR which falls between the B10 and B500 results, and tracks closely the corresponding energy and field amplitudes at lower resolution." +" The only difference between the high and lower resolution curves is the growth phase in the high resolution case is triggered about one dynamical time earlier (approximately a shift in time), but saturates at the same mean field amplitude."," The only difference between the high and lower resolution curves is the growth phase in the high resolution case is triggered about one dynamical time earlier (approximately a shift in time), but saturates at the same mean field amplitude." + The exponential growth of the magnetic energy around a time t~11 suggests the onset of a powerful magnetic field amplification mechanism., The exponential growth of the magnetic energy around a time $t \sim 11$ suggests the onset of a powerful magnetic field amplification mechanism. + The delayed onset and steep exponential growth particularly favor axisymmetric modes of the MRI., The delayed onset and steep exponential growth particularly favor axisymmetric modes of the MRI. +" These modes have the shortest growth times, but require a poloidal field component to act upon."," These modes have the shortest growth times, but require a poloidal field component to act upon." +" For the initially toroidal configurations, significant poloidal fields are not present until the bar mode begins redistributing material within the star, explaining the delayed onset."," For the initially toroidal configurations, significant poloidal fields are not present until the bar mode begins redistributing material within the star, explaining the delayed onset." +" Furthermore, it is clear from Figures 4 and 5 that the magnetic field saturates"," Furthermore, it is clear from Figures \ref{fig:fieldenergy} and \ref{fig:shellamp} that the magnetic field saturates" +"In order to test the ability of our elliptical shapelet pipeline to deal with inaccurate input catalogs, we biased the input ellipticity by 2096 toward circular objects, and measured the residual bias left in the recovered ellipticity 7°.","In order to test the ability of our elliptical shapelet pipeline to deal with inaccurate input catalogs, we biased the input ellipticity by $20\%$ toward circular objects, and measured the residual bias left in the recovered ellipticity $\tilde{\gamma}^{(el)}$." +" As shown by Fig. 4,,"," As shown by Fig. \ref{fig:elliptical-nmax}," +" this test produced conceptually similar results as with circular shapelets: for small Sérrsic indices, we could recover the true ellipticity without any significant bias, while the estimates degrade significantly as we approach n; 4."," this test produced conceptually similar results as with circular shapelets: for small Sérrsic indices, we could recover the true ellipticity without any significant bias, while the estimates degrade significantly as we approach $n_s = 4$ ." +" The situation is improved when 7,4; is raised, because the transformations done during the focusing step take all available orders into account, in contrast to the simpler description underlying the construction of 5? in(14).."," The situation is improved when $n_{max}$ is raised, because the transformations done during the focusing step take all available orders into account, in contrast to the simpler description underlying the construction of $\tilde\gamma^{(n2)}$ in." +" With n4,=12 (bottom panel of Fig. 4)),"," With $n_{max}=12$ (bottom panel of Fig. \ref{fig:elliptical-nmax}) )," +" galaxies with n,=0.5 and 1 have shear estimates without bias.", galaxies with $n_s=0.5$ and 1 have shear estimates without bias. +" When raising n, beyond that, the bias is at first positive before it becomes negative."," When raising $n_s$ beyond that, the bias is at first positive before it becomes negative." +" Investigating this feature more closely, we find this estimator to have an oscillatory tendency once the bias sets in."," Investigating this feature more closely, we find this estimator to have an oscillatory tendency once the bias sets in." +" In summary, it appears that the pipeline is unable to fully correct inaccuracies in the SExtractor catalog for galaxies showing a profile close to the De Vaucouleurs one."," In summary, it appears that the pipeline is unable to fully correct inaccuracies in the SExtractor catalog for galaxies showing a profile close to the De Vaucouleurs one." +" In more realistic simulations or observational data, the galactic shapes are recorded after convolution with the PSF, pixelation by the CCD, and degraded by pixel noise."," In more realistic simulations or observational data, the galactic shapes are recorded after convolution with the PSF, pixelation by the CCD, and degraded by pixel noise." + We now discuss the impact of these effects on shear estimation with shapelets., We now discuss the impact of these effects on shear estimation with shapelets. +" Clearly, a convolution creates shallower profiles which can be better described by shapelet models."," Clearly, a convolution creates shallower profiles which can be better described by shapelet models." +" Therefore, the typical goodness-of-fit values, in particular for steeper profiles, are considerable lower than in the unconvolved case."," Therefore, the typical goodness-of-fit values, in particular for steeper profiles, are considerable lower than in the unconvolved case." +" If the PSF shape is perfectly described by its shapelet model, one can exactly undo a convolution in shapelet space."," If the PSF shape is perfectly described by its shapelet model, one can exactly undo a convolution in shapelet space." +" In such a case, the shape obtained by deconvolving a PSF-convolved galaxy model must approximate the true, unconvolved shape G’ better than its direct model G."," In such a case, the shape obtained by deconvolving a PSF-convolved galaxy model must approximate the true, unconvolved shape $G^\prime$ better than its direct model $\tilde{G}^\prime$." +" To verify this new hypothesis, we convolved Sérrsic-type galaxies in pixel space with PSF shapes P obtained from shapeletmodels*,, For circular shapelets, C is modeled with shapelets and explicitly deconvolved from P in shapelet space, while for the elliptical shapelets we obtain the unconvolved shape by convolving the model with the PSF and fitting the outcome to the image data."," To verify this new hypothesis, we convolved Sérrsic-type galaxies in pixel space with PSF shapes $P$ obtained from shapelet, For circular shapelets, $C$ is modeled with shapelets and explicitly deconvolved from $\tilde{P}$ in shapelet space, while for the elliptical shapelets we obtain the unconvolved shape by convolving the model with the PSF and fitting the outcome to the image data." + In Fig., In Fig. + 5 we compare the bias of the shear estimates from unconvolved galaxies images and from the same set of galaxies after convolution with a Gaussian PSF with a FWHM of 5, \ref{fig:bias-convolution} we compare the bias of the shear estimates from unconvolved galaxies images and from the same set of galaxies after convolution with a Gaussian PSF with a FWHM of 5 +"The stars in our normalization sample are selected from the CNS4 by their absolute visual magnitudes. according to the distribution of absolute magnitudes of the CADIS disk stars (6.5$ confidence level. + The presence of these two molecules is required to obtain a reasonable fit to the available data., The presence of these two molecules is required to obtain a reasonable fit to the available data. +" In addition, we find insignificant confidence levels (i.e. <95%)) when we increase the complexity of the model by adding CO, CH, or a combination of the two to the simple model containing H», He, H30 and CO»."," In addition, we find insignificant confidence levels (i.e. $<$ ) when we increase the complexity of the model by adding CO, $_4$ or a combination of the two to the simple model containing $_{2}$, He, $_{2}$ O and $_{2}$." +" In other words, CO and CH, provide negligible enhancements to the fitting quality and are not required to fit the dayside emission measurements to within the stated error bars (although upper limits on these species can certainly be derived)."," In other words, CO and $_{4}$ provide negligible enhancements to the fitting quality and are not required to fit the dayside emission measurements to within the stated error bars (although upper limits on these species can certainly be derived)." +" Additionally, we consider the implications of Gibsonetal. (2011), who claimed larger uncertainties on the HST/NICMOS data by re-processing its transmission spectrum (Swainetal. 2008)."," Additionally, we consider the implications of \citet{gib11}, who claimed larger uncertainties on the $HST$ /NICMOS data by re-processing its transmission spectrum \citep{swa08}." +". If the same conclusions are applicable to the secondary eclipse emission spectrum, then we must similarly increase the measurement error on the NICMOS data by a factor of five."," If the same conclusions are applicable to the secondary eclipse emission spectrum, then we must similarly increase the measurement error on the NICMOS data by a factor of five." +" This leads to even smaller confidence levels on the more complex models, and the solutions are found to be even more degenerate."," This leads to even smaller confidence levels on the more complex models, and the solutions are found to be even more degenerate." +" In this case, evaluating the F-test significance using a variety of models still suggests that both H2O and CO» are required to reproduce the dayside emission spectra (799.2946 confidence), but makes the presence of CO and CH, even more uncertain."," In this case, evaluating the $F$ –test significance using a variety of models still suggests that both $_{2}$ O and $_{2}$ are required to reproduce the dayside emission spectra $>$ confidence), but makes the presence of CO and $_4$ even more uncertain." +" We therefore conclude that, irrespective of the uncertainties on the H ST/NICMOS data, current datasets are unable to provide detections of CO and CH, on the dayside of HD 189733b with any sort of statistical certainty."," We therefore conclude that, irrespective of the uncertainties on the $HST$ /NICMOS data, current datasets are unable to provide detections of CO and $_4$ on the dayside of HD 189733b with any sort of statistical certainty." +" Nevertheless, upper limits on the abundances of these molecules can be obtained (see Section 5), and all four molecules will be included in our subsequent study."," Nevertheless, upper limits on the abundances of these molecules can be obtained (see Section 5), and all four molecules will be included in our subsequent study." +" Using the NEMESIS algorithm, we retrieve the best-fitting dayside spectrum of HD 189733b, incorporating both the Spitzer and HST observations as stated in Section 3."," Using the NEMESIS algorithm, we retrieve the best-fitting dayside spectrum of HD 189733b, incorporating both the $Spitzer$ and $HST$ observations as stated in Section 3." + Fig., Fig. +" 1 demonstrates the best-fitting spectrum to these measurements, and the retrieved atmospheric P-T profile and molecular abundances for H2O, CO», CO, and CHa."," \ref{f1} demonstrates the best-fitting spectrum to these measurements, and the retrieved atmospheric $P$ $T$ profile and molecular abundances for $_{2}$ O, $_{2}$ , CO, and $_{4}$ ." + Each panel will be described below., Each panel will be described below. + Fig., Fig. + 2 shows the contributions from the four main gases included in our model., \ref{f2} shows the contributions from the four main gases included in our model. + This figure also shows the wavelength ranges where the molecular contributions are distributed by, This figure also shows the wavelength ranges where the molecular contributions are distributed by +"Observatory gave the first clues of a potential liuk between crystalline material in protoplanetary disks aud conmets,", gave the first clues of a potential link between crystalline material in protoplanetary disks and comets. + A ercat similarity was noted between the spectra of the disk around the Ierbig star IID 100516 aud that of comet IIale-Dopp (Crovisieretal.1997:Malfüitct1998).," A great similarity was noted between the spectra of the disk around the Herbig star HD 100546 and that of comet Hale-Bopp \citep{CR97,MA98}." +. More recently. the InfraRed Spectrograph (IRS. 5 38 qun. THoucketal. 20013) on-board theTelescope allowed an wuprecedcuted combination of high sensitivity aud the ability to observe large uunibers of disks. down to the brown dwiurf limit.," More recently, the InfraRed Spectrograph (IRS, 5 – 38 $\mu$ m, \citealt{HO04}) ) on-board the allowed an unprecedented combination of high sensitivity and the ability to observe large numbers of disks, down to the brown dwarf limit." + The shape of the silicate features probed by the IRS spectra at 10 and 20 san is affected by the composition. size and structure of its cimitting dust.," The shape of the silicate features probed by the IRS spectra at 10 and 20 $\mu$ m is affected by the composition, size and structure of its emitting dust." + Amorplous silicates show broad smooth uid-IR features. while the opacities of crystalline graius show sharp features duc to their larec-scale lattice arrangcuient. such that even small fractious of crystalline erains produce additional structure in the silicate features (Ainctal.2005:Bouwiuanal.2008:πιάot2009:Olofssonet 2010).," Amorphous silicates show broad smooth mid-IR features, while the opacities of crystalline grains show sharp features due to their large-scale lattice arrangement, such that even small fractions of crystalline grains produce additional structure in the silicate features \citep{MI05,BO08,JU09,OF10}." +. Because inmost protoplauctary disks are optically thick at optical and IR wavelengths. the silicate features observed iu the mid-IR are generally emitted by dust in the optically thin disk surface oulv.," Because most protoplanetary disks are optically thick at optical and IR wavelengths, the silicate features observed in the mid-IR are generally emitted by dust in the optically thin disk surface only." + To probe the disk iidplaue. observations at longer waveleueths are recessary.," To probe the disk midplane, observations at longer wavelengths are necessary." + Additionally. the ciission at 10 and 20 jan as been shown to arise frou differeut erain populations. xobius differeut radii (IXessler-Silaccietal.2006:Olofssonetal.2009.Re] 2010)..," Additionally, the emission at 10 and 20 $\mu$ m has been shown to arise from different grain populations, probing different radii \citep{KE06,OF09,OF10}. ." + While the 10 san feature probes a warluer dust population. at < 1 AU for T Tauri stars. he dust cinitting at 20 gan is colder. further out and deeper iuto the disk (vessler-Silaceietal.2007).," While the 10 $\mu$ m feature probes a warmer dust population, at $\leq$ 1 AU for T Tauri stars, the dust emitting at 20 $\mu$ m is colder, further out and deeper into the disk \citep{KE07}." +. Two incthods lave been proposed to explain the orlation of crystal erains: thermal annealing of amorphous erains or vaporization followed by gas-phase condensation., Two methods have been proposed to explain the formation of crystal grains: thermal annealing of amorphous grains or vaporization followed by gas-phase condensation. + Both methods require high temperatures (above ~LOOO Is. Fabianetal.2000:ένα 20013) which is Inconsistent with outer disk temperatures.," Both methods require high temperatures (above $\sim$ 1000 K, \citealt{FA00,GA04}) ) which is inconsistent with outer disk temperatures." + However. crystalline eraius have been observed iu outer. as well as dmn inner disks (vauBockeletal.2001).," However, crystalline grains have been observed in outer, as well as in inner disks \citep{VB04}." +. Large-scale radial mixing has been invoked to explain the presence of crystals at low temperatures iu the outer disk (Bockeléc-Alorviuetal.2000:Cail2001:Ciesla 2009)..," Large-scale radial mixing has been invoked to explain the presence of crystals at low temperatures in the outer disk \citep{BM00,GA04,CI09}. ." + Α third proposed formation mechanisin for crystal formation is that shock waves could locally heat amorphous silicates and crystallize thei (Desch&Connolly2002:IkerDesch 2002).," A third proposed formation mechanism for crystal formation is that shock waves could locally heat amorphous silicates and crystallize them \citep{DC02,HD02}." +. Frou protoplanetary disks to comets. several autlors have attempted to infer the dust composition from IRS spectra aud laboratory data on amorphous and crystalline silicate dust. using a variety of analysis techniques.," From protoplanetary disks to comets, several authors have attempted to infer the dust composition from IRS spectra and laboratory data on amorphous and crystalline silicate dust, using a variety of analysis techniques." + Whether for individual objects etal 2008).. for mixed disk suples (Bowmanctal. 2010).. or systematic studies of the disk population of a given star-forming region (Sicilia-Agnilayctal.2009:Watsonctal.2009:Sargeutet 2009).. it has heen shown that a significant mass fraction of the dust in those disks waist be iun crystalline form.," Whether for individual objects \citep{FO04,ME07,PI08,BY08}, for mixed disk samples \citep{BO01,AP05,VB05,BO08,OF09,OF10,JU10}, or systematic studies of the disk population of a given star-forming region \citep{SI09,WA09,ST09}, it has been shown that a significant mass fraction of the dust in those disks must be in crystalline form." + However. the many studies dealing with the uuneralogical composition of dust to date focus ou a specific region or object. füling to investigate the hypothesis that the crystallinity fraction Is a 1ucasure of the evolutionary stage of a region.," However, the many studies dealing with the mineralogical composition of dust to date focus on a specific region or object, failing to investigate the hypothesis that the crystallinity fraction is a measure of the evolutionary stage of a region." + That is. uo study in the literature has vet investigated au mcerease of crystallinity fraction with cluster age.," That is, no study in the literature has yet investigated an increase of crystallinity fraction with cluster age." + Mineralogical studies of Solar Systei bodies show a range of crystallinity fractious., Mineralogical studies of Solar System bodies show a range of crystallinity fractions. +" Evidence frou, primitive chondrites shows that the abundance of crystalline silicate imaterial varies from nearly nothing wp to 20 S0 (em. Acter 091 aud ALTT7307. Poutoppidan&Brearley2010 and references therein)."," Evidence from primitive chondrites shows that the abundance of crystalline silicate material varies from nearly nothing up to 20 – 30 (e.g. Acfer 094 and ALH77307, \citealt{PB10} + and references therein)." + Oort cloud colucts. with long periods and large distances from the Sun. have interred crystallinity fractious up to 6 SO (e.@. TWale-Bopp. Woodenetal.1999.2007)). -Jupiter-zu.," Oort cloud comets, with long periods and large distances from the Sun, have inferred crystallinity fractions up to 60 – 80 (e.g. Hale-Bopp, \citealt{WO99,WO07}) ). Jupiter-family," + or short period comets. have lower fractions. up ο 735 (e.g. OP/Tempel 1. Warkeretal.2007:: 81P/Wild 2. Zoleuskyctal.2006)).," or short period comets, have lower fractions, up to $\sim$ 35 (e.g. 9P/Tempel 1, \citealt{HA07}; 81P/Wild 2, \citealt{ZO06}) )." + This discrepancy dmi fractions ntfs to the existence of a radial dependence iu crystallinity fraction in the protoplanetary disk around he vouug Sun (Warkeretal.2005)., This discrepancy in fractions points to the existence of a radial dependence in crystallinity fraction in the protoplanetary disk around the young Sun \citep{HA05}. +. It is important to rote that those values are model dependent. aud the use of large amorphous erains (10 /— 100 jun) can lead ο systematically lower ervstalline. fractious (Ibarkeral.2002).," It is important to note that those values are model dependent, and the use of large amorphous grains (10 – 100 $\mu$ m) can lead to systematically lower crystalline fractions \citep{HA02}." +. This is evident for Hale-Dopp. where Miuotal.(2005). find a πιο lower fraction (7.5 %)) than other authors. using a distribution of amorphous erain sizes up to 100 yan. What is clear is that even within the discrepancies. the crystallinity fractions derived for Solar System bodies are appreciably higher than those derived for the ISM dust (<<2C. Isemperetal.2001).," This is evident for Hale-Bopp, where \citet{MI05a} find a much lower fraction $\sim$ 7.5 ) than other authors, using a distribution of amorphous grain sizes up to 100 $\mu$ m. What is clear is that even within the discrepancies, the crystallinity fractions derived for Solar System bodies are appreciably higher than those derived for the ISM dust $< 2 \%$, \citealt{KE04}) )." + RecentSpitzer data indicate further similarities between crystalline silicate features seen dm comets or asteroids with those seen iu some debris disks around solar mass stars (Beichmanetal.2006:Lisse2007.2008).," Recent data indicate further similarities between crystalline silicate features seen in comets or asteroids with those seen in some debris disks around solar mass stars \citep{BE06,LI07,LI08}." +. One proposed explanation is that the observed spectral eatures m the disk result from the catastrophic break-up of a single huge bodv (a super comet) which creates the small dust particles needed. for detection., One proposed explanation is that the observed spectral features in the disk result from the catastrophic break-up of a single large body (a `super comet') which creates the small dust particles needed for detection. + At the even emlier protoplauetarv disk stage. there is iuüted observational evidence for radial gradients iu crystallinity from mid-infrared interferometry data; with Heher crystallinity fractious found closer to the voune stars (vanBockelctal.2001:Schegereret2008).," At the even earlier protoplanetary disk stage, there is limited observational evidence for radial gradients in crystallinity from mid-infrared interferometry data, with higher crystallinity fractions found closer to the young stars \citep{VB04,SC08}." +. All of this suggests that the crystallization occurs carly in he disk evolution aud is then incorporated iuto larger solid bodies., All of this suggests that the crystallization occurs early in the disk evolution and is then incorporated into larger solid bodies. + Besides dust composition. the evolution of grain sizes ds an essential indicator of disk evolution.," Besides dust composition, the evolution of grain sizes is an essential indicator of disk evolution." + The initially sub-jun size ISAL grains unust grow astounding LL15 orders of mnaguitude in diuneter if they are o form planets., The initially $\mu$ m size ISM grains must grow astounding 14–15 orders of magnitude in diameter if they are to form planets. + If grains were to grow orderly aud steadily. theoretical calculations predict disks to have ‘lly dissipated their small eraius within ~10° years (Weideuschilling1980:Diullemoud&Domini2005).," If grains were to grow orderly and steadily, theoretical calculations predict disks to have fully dissipated their small grains within $\sim$ $^5$ years \citep{WE80,DD05}." +. The fact that many disks a few Myv. old. are observed o have sinall erains (Hernandezetal.2008) poses a serious problem for the paradigni that eran erowth is a steady. monotonie process in disk evolution aud planotcorlmation.," The fact that many disks a few Myr old are observed to have small grains \citep{HE08} poses a serious problem for the paradigm that grain growth is a steady, monotonic process in disk evolution and planetformation." + Additionally. s2all dust has been observed ii jesurface lavers of disks in clusters of different ages aud euvironnieuts for hundreds of svsteiis.," Additionally, small dust has been observed in thesurface layers of disks in clusters of different ages and environments for hundreds of systems." + The implications. as discussed inost receutlv by Oliveiraetal.(2010) xl Olofssonetal. (2010)... is that sinall erains must be replenished by fragmentation of σος. grains. aud that 1equilibrium between eran growth aud fragmentation is established.," The implications, as discussed most recently by \citet{OL10} and \citet{OF10}, , is that small grains must be replenished by fragmentation of bigger grains, and that anequilibrium between grain growth and fragmentation is established." + Oliveiraetal.(2010). have shown that this," \citet{OL10} + have shown that this" +"was strongly modified (new opacities. new nuclear reaction rates, new equation of state. etc.).","was strongly modified (new opacities, new nuclear reaction rates, new equation of state, etc.)." + The new model is different from that given in Bazot et al. (2005))., The new model is different from that given in Bazot et al. \cite{bazot05}) ). + Apart from the constraint on the Y value. the basic reason is that in this previous paper the comparisons were only based on the stellar luminosity. which was misleading due to the Hipparcos parallax. which was later modified.," Apart from the constraint on the Y value, the basic reason is that in this previous paper the comparisons were only based on the stellar luminosity, which was misleading due to the Hipparcos parallax, which was later modified." + Also the method used at that time was not as precise as the one we now use., Also the method used at that time was not as precise as the one we now use. + Note that the scaling of parameters may lead to wrong results for stars in which the seismic modes cannot be precisely identified., Note that the scaling of parameters may lead to wrong results for stars in which the seismic modes cannot be precisely identified. + This is the case for example for the mass proposed by Kallinger et al. RO , This is the case for example for the mass proposed by Kallinger et al. \cite{kallinger08}) ) +for the star ze Arae. which is much too large (1.23 ," for the star $\mu$ Arae, which is much too large (1.23 )." +We also ο. an analysis of the size of the mixed core by testing the implications of overshooting on the mode frequencies., We also performed an analysis of the size of the mixed core by testing the implications of overshooting on the mode frequencies. + We found a strong constraint on the possibility of core overshooting. treated as an extension of convection: the size of this extension must be less than 0.5 of the pressure scale height (overshooting parameter).," We found a strong constraint on the possibility of core overshooting, treated as an extension of convection: the size of this extension must be less than 0.5 of the pressure scale height (overshooting parameter)." + This does not exclude other kinds of mild boundary effects at the edge of the core. provided that they do not lead to strong mixing.," This does not exclude other kinds of mild boundary effects at the edge of the core, provided that they do not lead to strong mixing." + At the present time. we were able to perform this deep seismic analysis on two solar type stars hosting planets. both with a large metallicity (about twice solar): t Hor (Vauclair et al 2008)) and µ Arae (this paper).," At the present time, we were able to perform this deep seismic analysis on two solar type stars hosting planets, both with a large metallicity (about twice solar): $\iota$ Hor (Vauclair et al \cite{vauclair08}) ) and $\mu$ Arae (this paper)." + In both cases. precise stellar parameters could be obtained.," In both cases, precise stellar parameters could be obtained." + We found however an important difference between these two overmetallie stars., We found however an important difference between these two overmetallic stars. + In ¢ Hor. the helium abundance ts low. even lower than the solar value. in accordance with the helium value determined for the Hyades stellar cluster.," In $\iota$ Hor, the helium abundance is low, even lower than the solar value, in accordance with the helium value determined for the Hyades stellar cluster." + As other observational parameters also coincide. we concluded that¢ Hor is an ejected member of the Hyades.," As other observational parameters also coincide, we concluded that $\iota$ Hor is an ejected member of the Hyades." + The reason why the helium abundance is so low in these stars while the metallicity is high ts still a mystery. although it certainly depends on the mass of the stars that polluted the original nebula.," The reason why the helium abundance is so low in these stars while the metallicity is high is still a mystery, although it certainly depends on the mass of the stars that polluted the original nebula." + In i Arae. on the other hand. the helium abundance is large. as expected from the usual laws for the chemical evolution of galaxies (Isotov Thuan 2004)).," In $\mu$ Arae, on the other hand, the helium abundance is large, as expected from the usual laws for the chemical evolution of galaxies (Isotov Thuan \cite{isotov04}) )." + This star was formed in a nebula which suffered normal pollution from stars with proportional yields of helium and metals., This star was formed in a nebula which suffered normal pollution from stars with proportional yields of helium and metals. + Seismology can lead to precise values of helium abundances in solar type stars. where helium cannot be directly derived from spectroscopy.," Seismology can lead to precise values of helium abundances in solar type stars, where helium cannot be directly derived from spectroscopy." + This represents a success. quite apart from all other results and constraints. and will be of importance for the study of the chemical evolution of our Galaxy.," This represents a success, quite apart from all other results and constraints, and will be of importance for the study of the chemical evolution of our Galaxy." +"he 2676 and 251 clusters using e,.=1000kms.+ for the galactic winds CTH-SW runs).",the g676 and g51 clusters using $v_w=1000 \vel$ for the galactic winds (TH-SW runs). + However. while the effect of the stronger eedback is that of decreasing the number of galaxies. (see also Sect.," However, while the effect of the stronger feedback is that of decreasing the number of galaxies, (see also Sect." + 4.4. below). it leaves their metal content. and. therefore. the ugh CMR normalization. almost unchanged.," \ref{s:lf} below), it leaves their metal content, and, therefore, the high CMR normalization, almost unchanged." + Although a Salpeter IMF fares rather well as for the CMR. we note that all the BCGs (big filled circles in Fig.2)) are much bluer. by about 0.5 magnitude. than expected from the red sequence.," Although a Salpeter IMF fares rather well as for the CMR, we note that all the BCGs (big filled circles in \ref{fi:cmr_z0}) ) are much bluer, by about 0.5 magnitude, than expected from the red sequence." + Such a blue excess of the colors of the BGCs. which takes place despite heir high metallicity. finds its origin in the large star formation rate. associated to overeooling. which takes place in the central cluster regions.," Such a blue excess of the colors of the BGCs, which takes place despite their high metallicity, finds its origin in the large star formation rate, associated to overcooling, which takes place in the central cluster regions." +" Typical values for the star formation rate of the BCG in our simulations are in range 600—1000 3. /vr for the most massive clusters Mou,1077AIAE. rand ~1004. /yr for the least massive ones (Alou)c1071ΑΗ. 1."," Typical values for the star formation rate of the BCG in our simulations are in range 600–1000 $M_\odot$ /yr for the most massive clusters $M_{200}\simeq 10^{15}\msun$ ) and $\sim +100 M_\odot$ /yr for the least massive ones $M_{200}\simeq +10^{14}\msun$ )." + Although observations indicate the presence of some ongoing star formation in some BCGs located at the center of cool core clusters. they are always at a much lower level and consistent with a star formation rate of 10-1004. /yr for clusters of comparable richness andreferences therein).," Although observations indicate the presence of some ongoing star formation in some BCGs located at the center of cool core clusters, they are always at a much lower level and consistent with a star formation rate of $\sim 10$ $100 M_\odot$ /yr for clusters of comparable richness \citep[e.g., ][and references +therein]{1987MNRAS.224...75J,2006astro.ph..2323B,2006astro.ph..4044M}." + The effect of recent star formation on the CMR is explicitely shown in Figure 3.., The effect of recent star formation on the CMR is explicitely shown in Figure \ref{fi:cmr_z1}. + We show here the case in which all star particles. formed at redshift 2 <1 are excluded from the computation of the galaxy luminosities.," We show here the case in which all star particles, formed at redshift $z<1$ are excluded from the computation of the galaxy luminosities." + This is equivalent to assume that we completely quench star formation since 2=1., This is equivalent to assume that we completely quench star formation since $z=1$. + Neglecting recent star formation has the twofold effect of reducing the scatter in the CMR and of making BCG colors signiticantly redder. although they still fall slightly below the observed relation.," Neglecting recent star formation has the twofold effect of reducing the scatter in the CMR and of making BCG colors significantly redder, although they still fall slightly below the observed relation." + A numberobservational analyses have established that the mass—to-light ratioof in clusters generally increases with the cluster mass. AM/LxM with 2 0.2-0.4. over a fairly large dynamic range. from poor groups to rich clusters (e.g.2222227222).," A number of observational analyses have established that the mass--to--light ratio in clusters generally increases with the cluster mass, $M/L\propto M^\gamma$ with $\gamma \simeq 0.2$ –0.4, over a fairly large dynamic range, from poor groups to rich clusters \citep[e.g., +][]{1998A&A...331..493A,2000ApJ...530...62G,2002ApJ...569..720G,2002ApJ...565L...5B,2003ApJ...591..749L,2004ApJ...610..745L,2004AJ....128.1078R,2004AJ....128.2022R,2005A&A...433..431P}." + A likely explanation for this trend is the reduced cooling efficiency within more massive. hotter halos (e.g...2)... which reduces star formation within richer clusters.," A likely explanation for this trend is the reduced cooling efficiency within more massive, hotter halos \citep[e.g., +][]{2003MNRAS.339..312S}, which reduces star formation within richer clusters." + In fact. an increasing trend of AML with cluster mass is naturally predicted by semi-analytical models of galaxy formation (e.g...2)..," In fact, an increasing trend of $M/L$ with cluster mass is naturally predicted by semi–analytical models of galaxy formation \citep[e.g., ][]{1999MNRAS.303..188K}." + In Figure 4. we compare the relation between mass and luminosity within rou for our simulated clusters. and compare it to the ;-band results by ?. and to the A—band results by ?..," In Figure \ref{fi:ml} we compare the relation between mass and luminosity within $r_{500}$ for our simulated clusters, and compare it to the $i$ –band results by \cite{2005A&A...433..431P} and to the $K$ –band results by \cite{2004ApJ...610..745L}." + In general. we find that the A//2 from simulations is rather close to the observed one in the / band. also with a comparably small scatter.," In general, we find that the $M/L$ from simulations is rather close to the observed one in the $i$ band, also with a comparably small scatter." + In the A band. a Salpeter IMF still agrees with observations within the statistical uncertainties. while the top-heavy IMFproduces too red galaxies. thus consistent with the results of the CMR. as shown in Fig.2..," In the $K$ band, a Salpeter IMF still agrees with observations within the statistical uncertainties, while the top–heavy IMFproduces too red galaxies, thus consistent with the results of the CMR, as shown in \ref{fi:cmr_z0}." +" We fit our mass—luminosity relation with a power-law——————)'.. we find (0.3);=(0.74.0.92) and (a.3),=(0.76.3.2) in the 7 and ἐν band. respectively. for the runs with Salpeter IMF. while (a.:7);=(0.70.0.91) and (a),=(0.74.4.7) or the top-heavy IMF."," We fit our mass–luminosity relation with a power–law, we find $(\alpha,\beta)_i=(0.74,0.92)$ and $(\alpha,\beta)_K=(0.76,3.2)$ in the $i$ and $K$ band, respectively, for the runs with Salpeter IMF, while $(\alpha,\beta)_i=(0.70,0.91)$ and $(\alpha,\beta)_K=(0.74,4.7)$ for the top–heavy IMF." + Therefore. our simulations agree with qe observational trend for an increasing mass-to-light ratio with cluster mass. independent of the IMF and luminosity band.," Therefore, our simulations agree with the observational trend for an increasing mass-to-light ratio with cluster mass, independent of the IMF and luminosity band." + Using qe stronger feedback for the top-heavy IMF turns into a sizeable ραuppression of the luminosity. especially for 51.," Using the stronger feedback for the top–heavy IMF turns into a sizeable suppression of the luminosity, especially for g51." + The reasonable level of agreement between the observed and je simulated AZ/£L may suggest that our simulations produces a realistic population of galaxies., The reasonable level of agreement between the observed and the simulated $M/L$ may suggest that our simulations produces a realistic population of galaxies. + However. as demonstrated in Figure 5.. this is not the case.," However, as demonstrated in Figure \ref{fi:ngal}, , this is not the case." + In this figure. we compare the simulated and observed number of cluster galaxies. brighter than a given luminosity limit. both in ¢ and in the A bands.," In this figure, we compare the simulated and observed number of cluster galaxies, brighter than a given luminosity limit, both in $i$ and in the $K$ bands." + Clearly. simulations underpredict such a number. by a factor ~ 2—3.," Clearly, simulations underpredict such a number, by a factor $\sim 2$ –3." + This result is at variance with respect to that from semi-analytical models of galaxy formation. which instead predict the correct number of cluster members (e.g.. 22Y.. ," This result is at variance with respect to that from semi–analytical models of galaxy formation, which instead predict the correct number of cluster members \citep[e.g.,][]{2004MNRAS.349.1101D,2005MNRAS.361..369L}. ." +However. semi-analytical models are generally successfulin producing the correct LF.," However, semi–analytical models are generally successfulin producing the correct LF." + They employ a suitable technique to track galaxies. based on the," They employ a suitable technique to track galaxies, based on the" +We have analysed the properties of pairs of galaxies in high ensitv environments corresponding to eroups and. clusters X ealaxies with virial masses 1077105734...,We have analysed the properties of pairs of galaxies in high density environments corresponding to groups and clusters of galaxies with virial masses $10^{13} - 10 ^{15} M_{\odot}$. + We stress the unact that the analysis discussed in this paper is based on —16 comparison between two galaxy. samples which cdilfered between cach otherο on the [act that one of sample 'omprises galaxies with close companions. and the other. o not.," We stress the fact that the analysis discussed in this paper is based on the comparison between two galaxy samples which differed between each other on the fact that one of sample comprises galaxies with close companions, and the other, do not." + llence. we are always estimating the statistical ilferences in the properties of galaxies introduced by the presence of a companion.," Hence, we are always estimating the statistical differences in the properties of galaxies introduced by the presence of a companion." + The main conclusions can be summarized as follow:, The main conclusions can be summarized as follow: +"the dust continuum emission is detected at ""mm and al 10n (IIughes et 22007: Ratzka et 22007).",the dust continuum emission is detected at 7mm and at $10\micron$ (Hughes et 2007; Ratzka et 2007). +" such a dust distribution could be interpreted as a result of grainMN (Strom et 11939: Dullemond Dominik 2005). (Clarke et-- ""22001: Alexander et 22006: Gorti ILollenbach 2009: OwenphotevaporatIon et 22010). or a gap an orbiting giant planet (e.g.. Marsh Mahoney. 1992: Calvet et 22002: Rice et 22003: Quillen et 2004: Calvet et 22005)."," Such a dust distribution could be interpreted as a result of grain growth (Strom et 1989; Dullemond Dominik 2005), photoevaporation (Clarke et 2001; Alexander et 2006; Gorti Hollenbach 2009; Owen et 2010), or a gap opened by an orbiting giant planet (e.g., Marsh Mahoney 1992; Calvet et 2002; Rice et 2003; Quillen et 2004; Calvet et 2005)." + These scenarios could potentially be distinguished by examining properties other than the SED. since the scenarios make different predictions for e stellar accretion rate. disk mass. and radial distribution of gas in the disk (Najita et 22007a: Alexander Armitage 2007).," These scenarios could potentially be distinguished by examining properties other than the SED, since the scenarios make different predictions for the stellar accretion rate, disk mass, and radial distribution of gas in the disk (Najita et 2007a; Alexander Armitage 2007)." +" The first two diagnostics (stellar aceretion rates and disk masses) were used by Najita et ((2007a)"" to probe (he nature of transition objects in the Taurus star forming region.", The first two diagnostics (stellar accretion rates and disk masses) were used by Najita et (2007a) to probe the nature of transition objects in the Taurus star forming region. + They found Taurus transition objects have higher than average disk masses as well as stellar accretion rates that are ~10 times lower (han non-transition objects., They found that Taurus transition objects have higher than average disk masses as well as stellar accretion rates that are $\sim 10$ times lower than non-transition objects. + These properties are roughly consistent with the predictions of theories of giant planet formation (e.g.. Lubow οἱ 11999: Lubow D'Angelo 2006).," These properties are roughly consistent with the predictions of theories of giant planet formation (e.g., Lubow et 1999; Lubow D'Angelo 2006)." +" The high disk mass of TW Ilva (>0.06.: Calvet el 22002) and its comparatively low stellar accretion rate (~10.9M,vr.ts e.g. Herczeg οἱ 22004: Muzerolle et 22000: Alenear Dasri 2000) place it in a similar region of the M Maik plane as (he Taurus transition objects."," The high disk mass of TW Hya $> 0.06\Msun$; Calvet et 2002) and its comparatively low stellar accretion rate $\sim 10^{-9}\Msunperyr$; e.g., Herczeg et 2004; Muzerolle et 2000; Alencar Basri 2000) place it in a similar region of the $\Mdot$ $\Mdisk$ plane as the Taurus transition objects." + sS(udies of line emission Irom the gaseous component of (rausition disks. like that presented. here. offer (he opportunity (to complement studies of stellar accretion rates ancl disk mass. bv probing Che radialdistribution of gas in the disk and therefore the evolutionary state of the svstem.," Studies of line emission from the gaseous component of transition disks, like that presented here, offer the opportunity to complement studies of stellar accretion rates and disk mass, by probing the radial distribution of gas in the disk and therefore the evolutionary state of the system." +" As described byNajita et ((2007a. 2008): (1) In the grain growth: ancl planetesimal formation scenario. (he inner disk is rendered oplically thin in the continuum. but the gaseous component is unaltered and would fill the region within 25,4."," As described by Najita et (2007a, 2008): (1) In the grain growth and planetesimal formation scenario, the inner disk is rendered optically thin in the continuum, but the gaseous component is unaltered and would fill the region within $R_{\rm hole}$." + Emission Irom gas witliin yo. would produce bright emission because of the lack of continuum emission [rom same region of the disk. (, Emission from gas within $R_{\rm hole}$ would produce bright emission because of the lack of continuum emission from same region of the disk. ( +2) La planet has formed with a mass sullicient to open a gap (~ 11). gas will be cleared in the vieinity of its orbit. bul gap-crossing streams. from (he outer disk to the planet. and from the planet to the inner disk. can allow continued accretion onto both the planet and the star. the latter via (he replenishimment of theinner disk n uae€Bye ie.g.. Lubow et 11999: Ixlev 1999: Bryden et 11999: D'Angelo et no22003: shBate et ni22003: Lubow D'Angelo 2006).,"2) If a planet has formed with a mass sufficient to open a gap $\sim 1 M_J$ ), gas will be cleared in the vicinity of its orbit, but gap-crossing streams, from the outer disk to the planet, and from the planet to the inner disk, can allow continued accretion onto both the planet and the star, the latter via the replenishment of the inner disk within $R_{\rm inner} < R_{\rm hole}$ (e.g., Lubow et 1999; Kley 1999; Bryden et 1999; D'Angelo et 2003; Bate et 2003; Lubow D'Angelo 2006)." + While the ihen guüseotts enission lines. the low surlace filling [actor of gas in the region of the gap would produce weak to negligible emission because of the small. projected emitting area of the accretion," While the might then produce gaseous emission lines, the low surface filling factor of gas in the region of the gap would produce weak to negligible emission because of the small projected emitting area of the accretion" +(53. atl o describe the planets and planetary svstenis emerging roii the| Eta-EarthEta-Ear Progra.,$\sim$ $\sim$ to describe the planets and planetary systems emerging from the Eta-Earth Program. +OCT: Thle statisticstatith off plananetf occi:occur-o hfroii thee EtaEta-EarEarth Survey will offer⋅ important constraints ou compctine heories∖⊳⋠∖⊳⋅∢⋅ of planct formation (77777)...2999)," The statistics of planet occurance from the Eta-Earth Survey will offer important constraints on competing theories of planet formation \citep{Ida04a,Kenyon06,Alibert05,Mordasini07,Ida_Lin08_iv}." +" Thi↴* modηςIs differ in assuniptious about the erowth rate of dust iuto ο”.B we DUB otB n i. M . anc t o the snow Bue qm the ME the cflicacy o te ectsDea the MEM ot ent aud “Ter. aud te ""nrelevance of plauet-planct mteractions."," These models differ in assumptions about the growth rate of dust into planetesimals, the viscosity of the disk, the location and effects of the snow line in the disk, the efficacy of inward migration, the accretion of gas and water, and the relevance of planet-planet interactions." + lY Gut consistent with detections and measurements of joviau gas glauuts (og.TT).," They are consistent with detections and measurements of jovian gas giants \citep[e.g.][]{Marcy_Japan_05,Udry2003}." +" However. these theories predict hat planets of mass are rare within AAU. forming a ""planet desert? of super-Earths (Mj sinis nearthe)) aud Neptune-mass planets."," However, these theories predict that planets of mass are rare within AU, forming a “planet desert” of super-Earths $M_{\mathrm{pl}}$ $i$ $\le$ ) and Neptune-mass planets." +" All models predict hat Type I inigration quickly (7 ~ 110 vr) causes the rocky planets to spiral iuxvard. destined to be lost in hestar""."," All models predict that Type I migration quickly $\tau$ $\sim$ $^5$ yr) causes the rocky planets to spiral inward, destined to be lost in the." + Moeamwhile. the more massive rocky cores (AL LII incarthe)yucerctegasquicklg.becomingict Or(gus giantsD," Meanwhile, the more massive rocky cores $M$ $>$ ) accrete gas quickly, becoming ice- or gas-giants." +E heresultingdistributionof planctargsystemsisdepletedof pl iicarthwithinl AAG, The resulting distribution of planetary systems is depleted of planets in the mass range within AU. +", If the prediction of a low-niass desert is contradicted wea statistically: well-definedd sample oft stars (such as the Eta-Earth Survey).⊲⋅ then planet formation. theory must )o Siguificauthy modified with new phvses."," If the prediction of a low-mass desert is contradicted by a statistically well-defined sample of stars (such as the Eta-Earth Survey), then planet formation theory must be significantly modified with new physics." + The planet desert has indeed∙ been challenged. bv?E who estimate: hataM ο ofD GI&paTp- dwiufs. have rocky or Noeptuneauass- anets miwud of 50dd orbits., The planet desert has indeed been challenged by \citet{Mayor09} who estimate that $\pm$ of GK dwarfs have rocky or Neptune-mass planets inward of d orbits. + Thisclaim is based in wart on detections. bv the Swiss». Peroup. of. three Neptune--sizeH planets orbitingtat 660830⋅⋅∖∙ Li (23.. two oft three plaucts," Thisclaim is based in part on detections by the Swiss group of three Neptune-size planets orbiting 69830 \citep{Lovis2006}, , two of three planets" +suggests strongly for high-order atmospheric gravity waves and they can be excited by turbulent stresses in the convection zone.,suggests strongly for high-order atmospheric gravity waves and they can be excited by turbulent stresses in the convection zone. + We can summarize the main results derived from the analysis of 1600 A continuum observations are as follows: (1) The uv bright points. uv network elements and uv background regions will exhibit a fluctuations with a smaller period in their intensity oscillations. (," We can summarize the main results derived from the analysis of 1600 $\AA$ continuum observations are as follows: (i) The uv bright points, uv network elements and uv background regions will exhibit a fluctuations with a smaller period in their intensity oscillations. (" +11) We find evidence from the power spectrum analysis for a longer period of oscillations: the uv bright points are associated with around 5.5 hours. the uv network elements exhibit around 4.6 hours and whereas the background regions show around 3.4 hours. (,"ii) We find evidence from the power spectrum analysis for a longer period of oscillations: the uv bright points are associated with around 5.5 hours, the uv network elements exhibit around 4.6 hours and whereas the background regions show around 3.4 hours. (" +11) It is noted that the different,iii) It is noted that the different +Eclipsiug Binaries (hereafter EBs) are excelleut objects for determining the physical properties of stars and detecting additional components iu them.,Eclipsing Binaries (hereafter EBs) are excellent objects for determining the physical properties of stars and detecting additional components in them. + The loug-time behavior of the period of au ED could reveal the presence of another component orbiting with the ED arouud the conuimion center of nass;, The long-time behavior of the period of an EB could reveal the presence of another component orbiting with the EB around the common center of mass. + Photometric observations of EBs soluctimes cover more than a ceutury. therefore it is possible to detect the third bodies with a similar period.," Photometric observations of EBs sometimes cover more than a century, therefore it is possible to detect the third bodies with a similar period." + The motion around the barvcenter causes apparent changes of the observed. binary’s period with a period corresponding to the orbital one of the third body. called he LiIeht-Time Effect (or light-travel time’. hereafter LITE).," The motion around the barycenter causes apparent changes of the observed binary's period with a period corresponding to the orbital one of the third body, called the LIght-Time Effect (or 'light-travel time', hereafter LITE)." + Lewin(1959). nuproved the method developed w Woltjer(1922) for analyzing the long-term variation of the times of ruininia caused by a third body orbiting he eclipsing pair., \cite{Irwin1959} improved the method developed by \cite{Woltjer1922} for analyzing the long-term variation of the times of minima caused by a third body orbiting the eclipsing pair. + Useful conmucuts and limitations were discussed. bv Fricboes-Coude&Terczee(1973) aud w Maver(010990)., Useful comments and limitations were discussed by \cite{FCH73} and by \cite{Mayer1990}. +.. Nowadays there are more than one mudred EBs showing LITE. where the effect is certainly preseuted or supposed (see e.g. Borkovits&Ilegedüs (1996).. Albavraketal. (1999).. Wolfetal. (2001).. Ποιαetal. (2006).. 0te.).," Nowadays there are more than one hundred EBs showing LITE, where the effect is certainly presented or supposed (see e.g. \cite{BorkovitsHegedus}, \cite{Albayrak1999}, \cite{Wolf2004}, , \cite{Hoffman2006}, , etc.)." + See the catalogue of the οC diagrauis by Kreineretal.(2001).. where the apparent orbital period. changes im many EBs are preseuted.," See the catalogue of the $O-C$ diagrams by \cite{Kreiner2001}, where the apparent orbital period changes in many EBs are presented." + The look of OC diagrams in the present study was adopted to be the same as in this catalogue., The look of $O-C$ diagrams in the present study was adopted to be the same as in this catalogue. + In our figures to 8 the full circles represent the primary and the open 1.circles the secondary times of minima. the bigger the point. the bigecr the weight.," In our figures \ref{FigWZAnd1} to \ref{FigAHTau} the full circles represent the primary and the open circles the secondary times of minima, the bigger the point, the bigger the weight." + For the Iunitatious auc consequences of the O6 diagram analysis. see e.g. Sterken(2005).," For the limitations and consequences of the $O-C$ diagram analysis, see e.g. \cite{Sterken2005}." +" The computation of the paramcters of the third-body orbit is a classical inverse problem with 5 parameters to be fouud pe du ow. 63. which indicate the period of the third body. the periastrou passage. the seimu-auuplitude of the light-time effect. the argunoeut of periastron and the ουσΙΤ, respectively (for a detailed description see e.g. Mawer 19903)."," The computation of the parameters of the third-body orbit is a classical inverse problem with 5 parameters to be found – $p_3$, $T_0$, $A$, $\omega$, $e_3$, which indicate the period of the third body, the periastron passage, the semi-amplitude of the light-time effect, the argument of periastron and the eccentricity, respectively (for a detailed description see e.g. \citealt{Mayer1990}) )." +" The ephemerides for the individual svstems (D, aud P for the linear one and 4 for the quadratic ono) have to be calculated together with the parnueters of LITE.", The ephemerides for the individual systems $JD_0$ and $P$ for the linear one and $q$ for the quadratic one) have to be calculated together with the parameters of LITE. +" The amass function Ελ} and the minimal massof the thirdcomponent ALji,=Ms;-:snu/sy (for"," The mass function $f(M_3)$ and the minimal massof the thirdcomponent $M_{3,min} = M_3 \cdot \sin i_3$ (for" +for the formation of a detonation.,for the formation of a detonation. + As the expected helium layer is located exactly in the region where the merger ts most violent and the hot-spots form. it may facilitate a detonation at even lower densities in our scenario.," As the expected helium layer is located exactly in the region where the merger is most violent and the hot-spots form, it may facilitate a detonation at even lower densities in our scenario." + In summary. there are reasons to believe that detonations may form for even a wider range of conditions than the ones we have assumed here.," In summary, there are reasons to believe that detonations may form for even a wider range of conditions than the ones we have assumed here." + The violent merger scenario can only be realized frequently enough to account for a significant fraction of all type la supernovae if it also works for moderate mass differences between the two white dwarfs., The violent merger scenario can only be realized frequently enough to account for a significant fraction of all type Ia supernovae if it also works for moderate mass differences between the two white dwarfs. + Thus. we have to check how changing the mass ratio for binary systems with a fixed primary white dwarf mass affects the conditions during the merger.," Thus, we have to check how changing the mass ratio for binary systems with a fixed primary white dwarf mass affects the conditions during the merger." + Only if mergers with a reasonable range also lead to the formation of a detonation. the scenario will be more than an exotic possibility.," Only if mergers with a reasonable range also lead to the formation of a detonation, the scenario will be more than an exotic possibility." + To test this. we compare four different mergers.," To test this, we compare four different mergers." +" All have the same primary mass of 0.9Μ... but different secondary masses of 0.89 M... 0.81M... 0.76Mo. and 0.7Μα which give mass ratios of 0.99, 0.9. 0.84 and 0.78."," All have the same primary mass of $0.9\, \mathrm{M_\odot}$, but different secondary masses of $0.89\, \mathrm{M_\odot}$ , $0.81\, \mathrm{M_\odot}$, $0.76\, \mathrm{M_\odot}$ and $0.7\, + \mathrm{M_\odot}$ which give mass ratios of $0.99$, $0.9$, $0.84$ and $0.78$." + In our simulations. they are set up with initial periods of 258. 33s. 305. and 40s. respectively.," In our simulations, they are set up with initial periods of $25\,\mathrm{s}$, $33\,\mathrm{s}$, $36\,\mathrm{s}$, and $40\,\mathrm{s}$, respectively." + Figure 4. shows densities and temperatures of all particles of these simulations at the time when the conditions are most favorable for a detonation as well as temperature slices through the centers of the binaries., Figure \ref{fig:qtest09} shows densities and temperatures of all particles of these simulations at the time when the conditions are most favorable for a detonation as well as temperature slices through the centers of the binaries. + Obviously. there are considerable differences between these three systems.," Obviously, there are considerable differences between these three systems." + Firstly. with decreasing mass ratio. the merger becomes less violent.," Firstly, with decreasing mass ratio, the merger becomes less violent." +" While the mergers with mass ratios of 0.99, 0.9 and 0.84 produce several hot particles that ignite carbon and reach temperatures above 2-K.IO? this is not the case for the merger with the smallest mass ratio."," While the mergers with mass ratios of $0.99$, $0.9$ and $0.84$ produce several hot particles that ignite carbon and reach temperatures above $2 \cdot 10^9 + \mathrm{K}$, this is not the case for the merger with the smallest mass ratio." + It is still possible that resolving the interaction region better will also show hotter particles., It is still possible that resolving the interaction region better will also show hotter particles. + However. at the moment it seems more likely that below a certain mass ratio the merger is just not violent enough to ignite a detonation.," However, at the moment it seems more likely that below a certain mass ratio the merger is just not violent enough to ignite a detonation." + This suggests a limiting mass ratio for the violent merger scenario of around 0.8., This suggests a limiting mass ratio for the violent merger scenario of around $0.8$. + Another difference is the dynamical effect of the merger on the primary white dwarf., Another difference is the dynamical effect of the merger on the primary white dwarf. + In a nearly equal mass merger the primary star is heavily distorted. very similar to the equal mass merger described in ?..," In a nearly equal mass merger the primary star is heavily distorted, very similar to the equal mass merger described in \citet{pakmor2010a}." + For a mass ratio of 0.9. the primary white dwarf remains unaffected in the center. but its surface Is distorted.," For a mass ratio of $0.9$, the primary white dwarf remains unaffected in the center, but its surface is distorted." + For the smaller mass ratios. 1t stays completely intact and cool and is surrounded by the material of the disrupted less massive companion.," For the smaller mass ratios, it stays completely intact and cool and is surrounded by the material of the disrupted less massive companion." + The etfect of the merger on the primary white dwarf can also be seer in the right panels of Figure 4.., The effect of the merger on the primary white dwarf can also be seen in the right panels of Figure \ref{fig:qtest09}. + In the q=0.99 merger the central density of the remaining white dwarf is lower than in the other cases.," In the $\mathrm{q} = + 0.99$ merger the central density of the remaining white dwarf is lower than in the other cases." + As for these mergers the amount of *°Ni produced depends sensitively on the central density of the remaining white dwarf. this leads to smaller °°Ni masses in mergers with higher mass ratios.," As for these mergers the amount of $^{56}\mathrm{Ni}$ produced depends sensitively on the central density of the remaining white dwarf, this leads to smaller $^{56}\mathrm{Ni}$ masses in mergers with higher mass ratios." + While this does not change the scenario fundamentally. it breaks the relation between mass of the primary white dwarf and the final °°Ni mass of the explosion for dim explosions.," While this does not change the scenario fundamentally, it breaks the relation between mass of the primary white dwarf and the final $^{56}\mathrm{Ni}$ mass of the explosion for dim explosions." +" For explosions of mergers of more massive white dwarfs. however. where most of the ""Ni is produced in nuclear statistical equilibrium. this will be a minor effect only."," For explosions of mergers of more massive white dwarfs, however, where most of the $^{56}\mathrm{Ni}$ is produced in nuclear statistical equilibrium, this will be a minor effect only." + As shown in Figure 4.. with decreasing mass ratio the merger becomes less violent and the density m the hot spots drops.," As shown in Figure \ref{fig:qtest09}, with decreasing mass ratio the merger becomes less violent and the density in the hot spots drops." + This may make the formation of a detonation more dificult for smaller mass ratios., This may make the formation of a detonation more difficult for smaller mass ratios. + For the smallest mass ratio no violent merger occurs and we see the onset of a different merger regime in which an accretion disk forms around primary white dwarf., For the smallest mass ratio no violent merger occurs and we see the onset of a different merger regime in which an accretion disk forms around primary white dwarf. + Figure 5. shows the ejecta composition of the thermonuclear explosion of the merger of two 0.859M.. as described in ?.. which is close to the merger with a mass ratio of 0.99 described above.," Figure \ref{fig:comp} shows the ejecta composition of the thermonuclear explosion of the merger of two $0.89\, \mathrm{M_\odot}$ as described in \citet{pakmor2010a}, which is close to the merger with a mass ratio of $0.99$ described above." + The final composition contains 0.03M.« of carbon. 0.54M. of oxygen. 1.05M. of intermediate-mass elements and 0.1M. of iron group elements.," The final composition contains $0.03 \, \mathrm{M_\odot}$ of carbon, $0.54 \, \mathrm{M_\odot}$ of oxygen, $1.05 \, \mathrm{M_\odot}$ of intermediate-mass elements and $0.1 \, \mathrm{M_\odot}$ of iron group elements." + As the densities at the time the explosion happens do not exceed 2x10’gem™. nuclear burning does not reach uclear statistical equilibrium anywhere in the object.," As the densities at the time the explosion happens do not exceed $2 \times 10^7 \mathrm{g\ cm^{-3}}$, nuclear burning does not reach nuclear statistical equilibrium anywhere in the object." + Instead. iron group elements are only produced by incomplete silicon burning.," Instead, iron group elements are only produced by incomplete silicon burning." + As the nuclear burning in the detonation takes place at low densities. electron captures are not efficient.," As the nuclear burning in the detonation takes place at low densities, electron captures are not efficient." +" Therefore the initial electron fraction Y, of the unburned material 15 conserved throughout the nuclear burning.", Therefore the initial electron fraction $Y_e$ of the unburned material is conserved throughout the nuclear burning. +" In case of Y,=0.5 the iron group elements consist of almost pure ??Ni.", In case of $Y_e = 0.5$ the iron group elements consist of almost pure $^{56}\mathrm{Ni}$. + A lower initial Y; is equivalent to more neutron-rich material in the pre-explosion composition (i.e. more Ne resulting from the He burning phase)., A lower initial $Y_e$ is equivalent to more neutron-rich material in the pre-explosion composition (i.e. more $^{22}$ Ne resulting from the He burning phase). + It leads to the production of some amount of stable iron replacing some of the ~°Ni., It leads to the production of some amount of stable iron replacing some of the $^{56}\mathrm{Ni}$. + In total. however. the fraction of stable iron group elements produced is very small.," In total, however, the fraction of stable iron group elements produced is very small." + As shown in Figure 5.. iron group elements are located at the center only. surrounded by intermediate-mass elements which are mixed with oxygen.," As shown in Figure \ref{fig:comp}, iron group elements are located at the center only, surrounded by intermediate-mass elements which are mixed with oxygen." + Most carbon is found in the outermost parts. but there is some mixing with intermediate-mass elements.," Most carbon is found in the outermost parts, but there is some mixing with intermediate-mass elements." + It is important to note that both. carbon and oxygen. are at different locations than the iron. group elements. i.e. there is no mixing of unburned material with iron group elements.," It is important to note that both, carbon and oxygen, are at different locations than the iron group elements, i.e. there is no mixing of unburned material with iron group elements." + There is also a clear difference between the distribution in the x—v--plane. which is the plane of rotation. and the distribution along the z--axis.," There is also a clear difference between the distribution in the -plane, which is the plane of rotation, and the distribution along the -axis." + Along the c--axis. the iron group elements are spread out much more. which means that in this direction there are iron group elements at higher velocities than within the 1-v--plane.," Along the -axis, the iron group elements are spread out much more, which means that in this direction there are iron group elements at higher velocities than within the -plane." + The opposite trend is observed for oxygen and intermediate mass elements. which reachfurther out in the plane of rotation than perpendicular to it.," The opposite trend is observed for oxygen and intermediate mass elements, which reachfurther out in the plane of rotation than perpendicular to it." + This is a result of the density structure of the merged object through which the detonation propagates., This is a result of the density structure of the merged object through which the detonation propagates. + Consequently. lightcurves and spectra of this explosion are expected to show considerable viewing angle dependence ?)..," Consequently, lightcurves and spectra of this explosion are expected to show considerable viewing angle dependence \citep[for viewing + angle dependent lightcurves see][]{pakmor2010a}. ." +"Thus, where the second term of equation (42)) dominates the convective flux.","Thus, where the second term of equation \ref{eqn:qconv}) ) dominates the convective flux." + Figure 6 shows these two heat fluxes normalized to the initial fiducial heat flux., Figure \ref{fig:A2-heatflux} shows these two heat fluxes normalized to the initial fiducial heat flux. +" The mass advection heat flux is enhanced due to the inability of the dark matter profile to adjust to changes in the ICM structure, so it is not a physically important quantity."," The mass advection heat flux is enhanced due to the inability of the dark matter profile to adjust to changes in the ICM structure, so it is not a physically important quantity." +" What is interesting, however, is that the convective heat flux is quite small."," What is interesting, however, is that the convective heat flux is quite small." +" In fact, it is roughly four orders of magnitude smaller than the conductive heat flux."," In fact, it is roughly four orders of magnitude smaller than the conductive heat flux." + The small convective heat flux seems to result from two principal causes., The small convective heat flux seems to result from two principal causes. +" First, unlike in solar convection, there is a second channel open for energy flow, namely directly through conduction which is quite efficient."," First, unlike in solar convection, there is a second channel open for energy flow, namely directly through conduction which is quite efficient." +" Second, as the magnetic fields become more radial, the buoyant driving is significantly reduced, reducing the baseline convective motions."," Second, as the magnetic fields become more radial, the buoyant driving is significantly reduced, reducing the baseline convective motions." + At this point it is also appropriate to discuss run A8., At this point it is also appropriate to discuss run A8. +" Run Αδ is chosen to be initialized at the MTI stability boundary for strong magnetic fields, namely kvA~Omax, for wavenumbers corresponding to scales slightly smaller than the cluster radius."," Run A8 is chosen to be initialized at the MTI stability boundary for strong magnetic fields, namely $kv_A \sim \sigma_{\textrm{max}}$, for wavenumbers corresponding to scales slightly smaller than the cluster radius." +" In this limit, all but the largest scale modes are suppressed entirely by magnetic tension."," In this limit, all but the largest scale modes are suppressed entirely by magnetic tension." + There is both theoretical motivation and numerical evidence that the conductive flux increases as the initial magnetic field increases., There is both theoretical motivation and numerical evidence that the conductive flux increases as the initial magnetic field increases. +" We do indeed find that for run A8, the convective flux is within an order of magnitude of the conductive flux; however, this phase lasts only a very short time (less than 500 Myr) and the net convective flux never is larger than 0.035Q."," We do indeed find that for run A8, the convective flux is within an order of magnitude of the conductive flux; however, this phase lasts only a very short time (less than 500 Myr) and the net convective flux never is larger than $0.035 \,\widetilde{Q}$." +" In addition, for this run, the total heat flux carried is considerably smaller than the other runs."," In addition, for this run, the total heat flux carried is considerably smaller than the other runs." +" Thus, we conclude that conduction is the dominant heat transport mechanism and that convective heat transport can never be larger than a small fraction of the Spitzer conductivity for MTI-driven turbulence in galaxy clusters."," Thus, we conclude that conduction is the dominant heat transport mechanism and that convective heat transport can never be larger than a small fraction of the Spitzer conductivity for MTI-driven turbulence in galaxy clusters." +" In order to emphasize the nature of the MTI as a truly convective instability, we have performed simulations with purely isotropic conductivity."," In order to emphasize the nature of the MTI as a truly convective instability, we have performed simulations with purely isotropic conductivity." + A long-favored approach to understanding thermal conduction in galaxy clusters has been to assume a tangled magnetic field geometry passively determined by hydrodynamic turbulence., A long-favored approach to understanding thermal conduction in galaxy clusters has been to assume a tangled magnetic field geometry passively determined by hydrodynamic turbulence. + This tangled geometry then provides an effective thermal conductivity that is a specified fraction of Spitzer (???)..," This tangled geometry then provides an effective thermal conductivity that is a specified fraction of Spitzer \citep{rr78, cc98, nm01}." +" A major point of this paper is that such an approach is incorrect since thermal conduction along the magnetic field self-consistently modifies the magnetic field geometry, resulting in an that evolves with time and is not consistent with these fgpitzertheories."," A major point of this paper is that such an approach is incorrect since thermal conduction along the magnetic field self-consistently modifies the magnetic field geometry, resulting in an $f_{\textrm{Spitzer}}$ that evolves with time and is not consistent with these theories." +" Thus, here we present simulations I1 and I2 which have a thermal diffusivity fixed at or of the Spitzer value, respectively, for comparison purposes."," Thus, here we present simulations I1 and I2 which have a thermal diffusivity fixed at or of the Spitzer value, respectively, for comparison purposes." +" The temperature profiles of these two runs evolve in ways quite similar to that of run A2 and A3, reaching fairly isothermal in 5-7 Gyr."," The temperature profiles of these two runs evolve in ways quite similar to that of run A2 and A3, reaching fairly isothermal in 5-7 Gyr." + A much more illustrative difference is found by considering the time evolution of the two runs., A much more illustrative difference is found by considering the time evolution of the two runs. +" The runs are initialized with a Mach 0.01 velocity perturbation that decays in time quite quickly, peaking at 1 Gyr or less, as opposed to 7 Gyr for run A2."," The runs are initialized with a Mach 0.01 velocity perturbation that decays in time quite quickly, peaking at 1 Gyr or less, as opposed to 7 Gyr for run A2." +" Without the MTI, the magnetic field is barely amplified at all, 6(B2)zx1.3 for both cases."," Without the MTI, the magnetic field is barely amplified at all, $\delta\langle B^2\rangle \approx 1.3$ for both cases." +" Finally, the magnetic field geometry is somewhat rearranged by the cluster motions, but does not even reach a geometrically isotropic state, with reaching à maximum of 0.19."," Finally, the magnetic field geometry is somewhat rearranged by the cluster motions, but does not even reach a geometrically isotropic state, with reaching a maximum of 0.19." +" Of course, we started in à state of pure azimuthal fields, so the key message here is that a field that started isotropically distributed would remain isotropically distributed—there is no force here pushing the field to be radially biased as with the MTI."," Of course, we started in a state of pure azimuthal fields, so the key message here is that a field that started isotropically distributed would remain isotropically distributed—there is no force here pushing the field to be radially biased as with the MTI." +" Clearly the comparison between these isotropic conduction calculations and the preceeding anisotropic heat conduction calculation shows that the MTI plays a significant role in setting a self-consistent solution for magnetic field amplification, convective velocities, and for the magnetic field geometry of a cluster."," Clearly, the comparison between these isotropic conduction calculations and the preceeding anisotropic heat conduction calculation shows that the MTI plays a significant role in setting a self-consistent solution for magnetic field amplification, convective velocities, and for the magnetic field geometry of a cluster." +" We now turn to the case of tangled magnetic fields, examined in run A3."," We now turn to the case of tangled magnetic fields, examined in run A3." +" This run has the exact same set-up as the previously discussed runs, except the intial magnetic field is a turbulent magnetic field distributed according to the Kolmogorov scaling law."," This run has the exact same set-up as the previously discussed runs, except the intial magnetic field is a turbulent magnetic field distributed according to the Kolmogorov scaling law." +" Thus, in this initial case, there is a zeroth order anisotropic heat flux that exists independent of the MTT's evolution."," Thus, in this initial case, there is a zeroth order anisotropic heat flux that exists independent of the MTI's evolution." +" Figure 7 shows the fairly rapid evolution of the temperature profile for the tangled field, reflecting this zeroth order"," Figure \ref{fig:A3-temp} + shows the fairly rapid evolution of the temperature profile for the tangled field, reflecting this zeroth order" +As far as the exercise in this paper is concerned. it is more important to emphasise. again. the discrepancy between lines in Fie. 6.,"As far as the exercise in this paper is concerned, it is more important to emphasise, again, the discrepancy between lines in Fig. \ref{tz}," + which calls into question how well the evolution in specific star formation rates hasreally boon captured by surveys thus far., which calls into question how well the evolution in specific star formation rates has been captured by surveys thus far. + Very cilferent trends of stellar mass to star formation rate have been attributed. to the same observational sample2010)., Very different trends of stellar mass to star formation rate have been attributed to the same observational sample. +. In this paper. we have carried out a more rigorous investigation into the origin of these two key estimated. physical quantities.," In this paper, we have carried out a more rigorous investigation into the origin of these two key estimated physical quantities." + A simple argument. based. on. hierarchical galaxy formation theory. was presented to understand why a strong trend might exist between these two quantities. anc that such a relationship can result from the self-similar nature of galaxy assembly. independently: of star. formation or [cedback processes.," A simple argument, based on hierarchical galaxy formation theory, was presented to understand why a strong trend might exist between these two quantities, and that such a relationship can result from the self-similar nature of galaxy assembly, independently of star formation or feedback processes." + Using a mocel galaxy population as a guide. we have shown that. due to the combined. clleets of selection bias and physical scatter in the relations between observable and physical properties. this underlving trend can be easily nusrepresented.," Using a model galaxy population as a guide, we have shown that, due to the combined effects of selection bias and physical scatter in the relations between observable and physical properties, this underlying trend can be easily misrepresented." +" ""There can also be a large discrepancy between inferred and true parameter values.", There can also be a large discrepancy between inferred and true parameter values. + These results highlight the importance of using realistic. physical galaxy formation models to guide the interpretation of high-redshift surveys.," These results highlight the importance of using realistic, physical galaxy formation models to guide the interpretation of high-redshift surveys." + By subjecting mocdel-sgenerated galaxy populations to the same analysis as the real data. observation can be compared with competing theories on an even footing.," By subjecting model-generated galaxy populations to the same analysis as the real data, observation can be compared with competing theories on an even footing." + In this wav. new surveys can Lead to more incisive quantitative conclusions about the true underlving galaxy population.," In this way, new surveys can lead to more incisive quantitative conclusions about the true underlying galaxy population." + The authors would like to. thank Andrew Benson and Claudia Lagos for their helpful comments., The authors would like to thank Andrew Benson and Claudia Lagos for their helpful comments. + CSE acknowledges a Roval Society Wolfson Research Merit Award and SAIC acknowledges the support of the Leverhulme Trust. Research Fellowship., CSF acknowledges a Royal Society Wolfson Research Merit Award and SMC acknowledges the support of the Leverhulme Trust Research Fellowship. + DPS acknowledges support from an STEC postdoctoral research fellowship., DPS acknowledges support from an STFC postdoctoral research fellowship. + This work was supported by an STEC rolling grant to the Institute for Computational Cosmology., This work was supported by an STFC rolling grant to the Institute for Computational Cosmology. + The mock galaxy population in the figures in this article was generated using a version of the semi-analvtic model which is currenth under development., The mock galaxy population in the figures in this article was generated using a version of the semi-analytic model which is currently under development. + The goal of this new version is to combine the most realistic aspects of the two previously published versions2006).. whilst achieving a better match. than either of these. to current observational constraints.," The goal of this new version is to combine the most realistic aspects of the two previously published versions, whilst achieving a better match, than either of these, to current observational constraints." + The development model is most closely related to the model published by(2006).. but uses parameters [or star. formation and feedback.et that are more realistic: closer to those favoured by(2005).," The development model is most closely related to the model published by, but uses parameters for star formation and feedback that are more realistic; closer to those favoured by." +. A list of parameter changes appears in table Al., A list of parameter changes appears in table \ref{parameters}. +" The parameters 7, and a, apply to star formation rate c. as follows: These. and all other parameters. are as defined in(2006)... and references therein."," The parameters $\tau_\star$ and $\alpha_\star$ apply to star formation rate $\psi$, as follows: = These, and all other parameters, are as defined in, and references therein." + Other changes are the distribution of. orbital parameters. which has been updated to. follow(2005).. and the treatment of the cooling of hot halo gas. which now follows(2010).," Other changes are the distribution of orbital parameters, which has been updated to follow, and the treatment of the cooling of hot halo gas, which now follows." +. Full details of this version will appear in Lacey et al. (, Full details of this version will appear in Lacey et al. ( +2011. in prep.),"2011, in prep.)." + To explore this relationship. we return to the moclel galaxy population that was shown in Fig. 2..," To explore this relationship, we return to the model galaxy population that was shown in Fig. \ref{hist}." + Consider. first. their star formation rate vs. rest-[rame UV magnitude. which is shown in the left main panel of Fig. Bl.," Consider, first, their star formation rate vs. rest-frame UV magnitude, which is shown in the left main panel of Fig. \ref{comp}." + The relation assumed. in observational analysis is shown in the, The relation assumed in observational analysis is shown in the +The acceleration during the planar phase. ie.. before a shell doubles its radius. follows (Johnson&Melee1971:PanSari200G)::where / is the lab frame time (not to be confused with observer time) measured since breakout.,"The acceleration during the planar phase, i.e., before a shell doubles its radius, follows \citep{Johnson71,Pan06}:where $t$ is the lab frame time (not to be confused with observer time) measured since breakout." + If the shell is optically thick at the end of acceleration aud acceleration ends during the planar phase then (he final Lorentz [actor is This relation is general as it does not depend on the exact densitv. profile. as long as there is a large energy reservoir behind the accelerating shell.," If the shell is optically thick at the end of acceleration and acceleration ends during the planar phase then the final Lorentz factor is This relation is general as it does not depend on the exact density profile, as long as there is a large energy reservoir behind the accelerating shell." + The acceleration ends al Thus. more massive shells end their acceleration at earlier times and lower Lorentz factors.," The acceleration ends at Thus, more massive shells end their acceleration at earlier times and lower Lorentz factors." +" In (his paper we restrict our treatment (o cases where the shell ends its acceleration dung the planar phase. ie. /pj«/, where is the lab Iranmie time of transition between the planar and spherical phases."," In this paper we restrict our treatment to cases where the shell ends its acceleration during the planar phase, i.e., $t_{f,0} E_{\ell=0}$ ." +" Nevertheless, 77,4 presents still à minimum value for modes between two consecutive radial ones showing a somewhat regular pattern."," Nevertheless, $E_{\ell=1}$ presents still a minimum value for modes between two consecutive radial ones showing a somewhat regular pattern." +" Even if the F value is larger than that corresponding to radial modes we can still consider those modes, based on the value of E, as observable ""p-modes""."," Even if the $E$ value is larger than that corresponding to radial modes we can still consider those modes, based on the value of $E$, as observable “p-modes”." +" For (=2 modes, the coupling between the g- and p-cavities is smaller than for (=1 and hence the trapping more efficient."," For $\ell=2$ modes, the coupling between the g- and p-cavities is smaller than for $\ell=1$ and hence the trapping more efficient." +" Therefore, independently of the central condensation of the model, à spectrum of regularly spaced /=2 ""p-modes"" with yo.zzFy) 1s expected."," Therefore, independently of the central condensation of the model, a spectrum of regularly spaced $\ell=2$ “p-modes” with $E_{\ell=2}\approx E_{\ell=0}$ is expected." +" Finally, note that the turning points for acoustic modes (/p, defined as the point where μις= 5,) are inside the convective envelope for the RGB model and in the radiative region for the He-B one."," Finally, note that the turning points for acoustic modes $tp_\ell$ defined as the point where $\nu_{\rm max}=S_{\ell}$ ) are inside the convective envelope for the RGB model and in the radiative region for the He-B one." +Quantities related to the How are unchanged by the averaging procedure since the superlluid How velocity is independent of whether vortices are pinned or not.,Quantities related to the flow are unchanged by the averaging procedure since the superfluid flow velocity is independent of whether vortices are pinned or not. + The factors of f; in eq. (49)), The factors of $f_v$ in eq. \ref{fave}) ) + account for the fact that only the motion of the translating vortex segments contributes to the mutual frietion (see. also. 2)).," account for the fact that only the motion of the translating vortex segments contributes to the mutual friction (see, also, \citealt{jahanmiri06}) )." + The value of f is unimportant for the following estimates., The value of $f_v$ is unimportant for the following estimates. + The force of eq. (47)).," The force of eq. \ref{fagain}) )," + which is appropriate for vortex creep. must equal the average force (f/f). giving the following relationships: We now use estimates of oyαυ to obtain the ratio 3/a.," which is appropriate for vortex creep, must equal the average force $\langle{\fbf_0}/\rho\rangle$, giving the following relationships: We now use estimates of $\beta_0/\alpha_0$ to obtain the ratio $\beta/\alpha$." + The dominant drag process on unpinned vortex segments considered so far arises from the excitation of Kelvin modes as the vortex moves past nuclei., The dominant drag process on unpinned vortex segments considered so far arises from the excitation of Kelvin modes as the vortex moves past nuclei. + Calculations of dissipation bv Ixelvin phonon production on a long vortex with periodic »oundary conditions for ey~LO geive typical values of ο=0.1 and ag~1 (2).," Calculations of dissipation by Kelvin phonon production on a long vortex with periodic boundary conditions for $v_0\sim 10^7$ give typical values of $\beta_0/\alpha_0= 0.1$ and $\alpha_0\sim +1$ \citep{eb92}." + Pinning occurs [or eg107.Land «οαυ is likely to be significantly smallerin this velocity regime due to strong suppression of Ixelvin phonon production (?)..," Pinning occurs for $v_0\lap 10^5$, and $\beta_0/\alpha_0$ is likely to be significantly smaller in this velocity regime due to strong suppression of Kelvin phonon production \citep{jones92}." + Vortex ereep is therefore a low-clrag »ocess if Ixelvin phonon production is the dominant dissipative mechanism., Vortex creep is therefore a low-drag process if Kelvin phonon production is the dominant dissipative mechanism. + We fix τα=0.1 for illustration in the following. which we consider to be an upper limit: we expect tvpical values to be smaller.," We fix $\beta/\alpha=0.1$ for illustration in the following, which we consider to be an upper limit; we expect typical values to be smaller." + We nowestimate 3., We nowestimate $\beta$. + We adopt polar coordinates (7.0.2). with the unperturbecl vorticity along ὁ and the unperturbed low vy along ὦ. and take the unperturbed flow and vortex velocity field. to be axisvmmoetric.," We adopt polar coordinates $(r,\phi,z)$, with the unperturbed vorticity along $\hat{z}$ and the unperturbed flow $\vbf_0$ along $\hat{\phi}$, and take the unperturbed flow and vortex velocity field to be axisymmetric." + In the rotating frame. the unperturbed vortex velocity from eq. (19))," In the rotating frame, the unperturbed vortex velocity from eq. \ref{vv0}) )" + is where 5 is the average direction of vortex motion., is where $\hat{n}$ is the average direction of vortex motion. + For steady spin down of the star. the inner crust superfIuid and the crust are spinning down atthe same rate for a local differential velocity ey.," For steady spin down of the star, the inner crust superfluid and the crust are spinning down atthe same rate for a local differential velocity $v_0$." + Phe creep velocity in this steady state is related to the spin-down rate by (72) where © is the spin rate of the supertluicl. Oy is the observed spin downrate of the crust. and rr is approximately the stellar racius 7.," The creep velocity in this steady state is related to the spin-down rate by \citep{alpar_etal84,leb93} where $\Omega$ is the spin rate of the superfluid, $\dot{\Omega}_0$ is the observed spin downrate of the crust, and $r$ is approximately the stellar radius $R$." + We arrive at the estimate where QcQy is assumed. and fase=Qu/2|Qu| is spin-down age.," We arrive at the estimate where $\Omega\simeq\Omega_0$ is assumed, and $t_{\rm age}\equiv +\Omega_0/2\vert\dot{\Omega}_0\vert$ is the spin-down age." + Eq. (53)).," Eq. \ref{ss}) )," + with 3= θα. gives the fiducial value 121074.," with $\beta=0.1\alpha$ , gives the fiducial value $\alpha\beta=10^{-21}$." + For this value. we deduce fo~(odfoagdu)?7be10)1 that is. most of the vortex length is pinned at any instant.," For this value, we deduce $f_v\sim (\alpha\beta/\alpha_0\beta_0)^{1/2}\sim 10^{-11}$, that is, most of the vortex length is pinned at any instant." + The unperturbed vortex creep speed. from eq. (513).," The unperturbed vortex creep speed, from eq. \ref{vv0again}) )," + is ~ary107 ivo. justifving the neglect of Or.Οἱ compared to vy in the stability analysis.," is $\sim\alpha\, v_0\sim 10^{-5}$ $<>k_c$ , the growth rate from eq. \ref{highk}) )" + is The hydrodynamic treatment is restricted to keg<<ο., is The hydrodynamic treatment is restricted to $kc_T<<\Omega$. + To est high the growth mue could be. we consider a maximum wavenumber defined by ομως=0.10. where erc10imate1(0/100.pwrads1957.1.," To estimate how high the growth rate could be, we consider a maximum wavenumber defined by $c_Tk_{\rm max}=0.1\,\Omega$, where $c_T\simeq 10^{-1}\, (\Omega/100\mbox{ \rads})^{1/2}$." + The growth rate at this waventunber. from eq. (43)).," The growth rate at this wavenumber, from eq. \ref{highk}) )," + is For ο=100 rad J|. the corresponding wavenumber is Aac100 1," is For $\Omega=100$ rad $^{-1}$, the corresponding wavenumber is $k_{\rm max}\simeq 100$ $^{-1}$." + Ίσα. (56)), Eq. \ref{highsigma}) ) + does not represent a physical limit. but only the restrictions of the hydrodynamic treatment: the instability could continue to exist also for wavenumbers in the regime ker> Q.," does not represent a physical limit, but only the restrictions of the hydrodynamic treatment; the instability could continue to exist also for wavenumbers in the regime $kc_T>\Omega$ ." + If vortex creep is in the strongly-clamiped regime 7 a. contrary to the estimateshere. there is still abroad. window for instability.," If vortex creep is in the strongly-damped regime $\beta>>\alpha$ , contrary to the estimateshere, there is still abroad window for instability." + RequiringAe«Aue gives and the star will be unstable at some wavenumber that is consistent with the hvdrodyvnamic regime hep<< ο., Requiring$k_c0 and e>0 defined as is a second order accurate variance stabilization transform. with asviuptotic wit variance.," Using a local homogeneity assumption, i.e. $\lambda_{i-j}=\lambda$ for all $j$ within the support of $h$, it has been shown that for a non-negative filter $h$, the transform $Z = b \sqrt{Y + c}$ with $b > 0$ and $c >0$ defined as c = - b = is a second order accurate variance stabilization transform, with asymptotic unit variance." +" By second-order accurate, we mean that the error term in the variance of the stabilized variableZ decreases rapidly as O(A3], From(1).."," By second-order accurate, we mean that the error term in the variance of the stabilized variable$Z$ decreases rapidly as $O(\lambda^{-2})$." + if is obvious that when h=à. we obtain the classical Anscombe VST paramcters 5=2 and ο=3/8.," From, it is obvious that when $h=\delta$ , we obtain the classical Anscombe VST parameters $b=2$ and $c=3/8$ ." + The authors in lave also proved that Z is asvinptotically distributed as a Gaussian variate with mean byf7A and unit variance., The authors in have also proved that $Z$ is asymptotically distributed as a Gaussian variate with mean $b \sqrt{\tau_1\lambda}$ and unit variance. + A non-positive 5 with a negative c could also be considered: see for more details., A non-positive $h$ with a negative $c$ could also be considered; see for more details. + Fig.2 shows the estimates of obtained from 9:10 Poisson noise realizatious of X. plotted as a function of the intensity A for both Auscombe (clashed-dotted). Ilaar-Fisz and our VST with the 2D Bs-Spline filter as a low-pass filter / (solid).," \ref{fig_msvst} shows the estimates of obtained from $2 \cdot 10^5$ Poisson noise realizations of $\fX$, plotted as a function of the intensity $\lambda$ for both Anscombe (dashed-dotted), Haar-Fisz and our VST with the 2D $B_3$ -Spline filter as a low-pass filter $h$ (solid)." + The axviiptotie bounds (dots) (i.e. 1 for the variance aud VAfor the expectation) are also shown., The asymptotic bounds (dots) (i.e. $1$ for the variance and $\sqrt{\lambda}$for the expectation) are also shown. + It can be secu hat for increasing iutensity. E|Z| aud Var|Z] approach he theoretical bounds at different rates depenudiug ou the VST used.," It can be seen that for increasing intensity, $\bE[Z]$ and $\var{Z}$ approach the theoretical bounds at different rates depending on the VST used." + Quantitatively. Poisson. variables trausformed using the Anscombe VST can )o reasonably considered to τὸ unbiased and stabilized for Az10. using Ibuu-Fisz for Az l. and using out (after low-pass filtering with he chosen 7) for Az0.1.," Quantitatively, Poisson variables transformed using the Anscombe VST can be reasonably considered to be unbiased and stabilized for $\lambda \gtrapprox 10$, using Haar-Fisz for $\lambda \gtrapprox 1$ , and using out (after low-pass filtering with the chosen $h$ ) for $\lambda \gtrapprox 0.1$." + The uudeciaated: wavelet transform (UWT) uses au analysis filter bauk (5.9) to decompose a signal ay iuto a cocficient set Woo={dy.....γα]. where dj is the wavelet (detail) coefficients. at scale jj and d; is the approximation cocficicuts at the coarsest resolution J.," The undecimated wavelet transform (UWT) uses an analysis filter bank $(h,g)$ to decompose a signal $a_0$ into a coefficient set $W = \{d_1, \dots, d_J, a_J\}$, where $d_j$ is the wavelet (detail) coefficients at scale $j$ and $a_J$ is the approximation coefficients at the coarsest resolution $J$." +" The passage from one resolution to the next one is obtained using the ""à trous” algorithin where Εξhl]if !/2/c Z aud ϐ otherwise. Alf}= h|Ff. aud ""« denotes discrete circular convolution."," The passage from one resolution to the next one is obtained using the “à trous” algorithm where $h^{\uparrow j}[l] = h[l]$if $l / 2^j \in \bZ$ and $0$ otherwise, $\bar{h}[l] = h[-l]$ , and $\star$ ” denotes discrete circular convolution." + The reconstruction ds eiven by ZH=$[Mwayal|(ghtxej3d ., The reconstruction is given by $a_{j}[l] = \frac{1}{2}\left[ (\tilde{h}^{\uparrow j} \star a_{j+1})[l] + (\tilde{g}^{\uparrow j} \star w_{j+1})[l] \right]$ . + The filterbank (fry.h.g) needs to satisfv the so-called exact reconstruction condition (?7).," The filterbank $(h,g,\tilde{h},\tilde{g})$ needs to satisfy the so-called exact reconstruction condition ." +. The Isotropic UWT (IUWT) uses the <er bank (hy=àh.h-byà) wherefi is typically a sviunietric low-pass filter such as the B3-Splinefilter.," The Isotropic UWT (IUWT) uses the filter bank $(h,g=\delta-h,\tilde{h}=\delta,\tilde{g}=\delta)$ where$h$ is typically a symmetric low-pass filter such as the $B_3$ -Splinefilter." + The, The +on scales smaller than this separation around the quasars we examine.,on scales smaller than this separation around the quasars we examine. +" At slightly larger radii we find no evidence for photometric objects being systematically excluded for spectroscopic follow-up, so we expect our analysis to be complete beyond this radius."," At slightly larger radii we find no evidence for photometric objects being systematically excluded for spectroscopic follow-up, so we expect our analysis to be complete beyond this radius." +" In addition to this photometric incompleteness, our analysis may also be limited by the spectroscopic resolution of the data."," In addition to this photometric incompleteness, our analysis may also be limited by the spectroscopic resolution of the data." +" The galaxy redshifts in the DEEP2 catalogue have a typical lo precision of o,=1.3x107* which corresponds a physical scale of ~400 h7'kpc for matter in the Hubble flow at z=1.", The galaxy redshifts in the DEEP2 catalogue have a typical $\sigma$ precision of $\sigma_{z}$ $\times10^{-4}$ which corresponds a physical scale of $\sim$ 400 $^{-1}$ kpc for matter in the Hubble flow at z=1. +" As such, detections of galaxies and absorbers that are physically associated at the same redshift may still have measured separations on the order of this limiting resolution."," As such, detections of galaxies and absorbers that are physically associated at the same redshift may still have measured separations on the order of this limiting resolution." +" To investigate any possible incompleteness in the data, we re-examined the spectra of all quasars with a projected separation of «200 h! kpc from DEEP2 galaxies."," To investigate any possible incompleteness in the data, we re-examined the spectra of all quasars with a projected separation of $<$ 200 $^{-1}$ kpc from DEEP2 galaxies." +" Stacking each of these 63 spectra in the rest-frame of the nearby galaxy revealed a 2c cumulative detection ofII, which grew in significance as we reduced the maximum projected separation allowed."," Stacking each of these 63 spectra in the rest-frame of the nearby galaxy revealed a $\sigma$ cumulative detection of, which grew in significance as we reduced the maximum projected separation allowed." +" After examining the individual spectra contributing to the stack, we determined that no absorbers with >3o significance were undetected by the automated algorithm."," After examining the individual spectra contributing to the stack, we determined that no absorbers with $>$ $\sigma$ significance were undetected by the automated algorithm." +" We also found that the bulk of the contribution to the absorption signal in the stacked spectrum could be attributed to the single, strong absorber with a 37 h! kpc separation from a DEEP2 galaxy (ID 16 in Table 1), which has been thoroughly discussed in Section 5."," We also found that the bulk of the contribution to the absorption signal in the stacked spectrum could be attributed to the single, strong absorber with a 37 $^{-1}$ kpc separation from a DEEP2 galaxy (ID 16 in Table 1), which has been thoroughly discussed in Section 5." +" The bias we measure for absorbers is consistent with that of the DEEP2 galaxies, although the measurement error is substantial due to the small size of the sample."," The bias we measure for absorbers is consistent with that of the DEEP2 galaxies, although the measurement error is substantial due to the small size of the sample." + This basic agreement suggests that strong absorbers at z~1 reside in similar environments to those of the galaxies in the DEEP2 survey., This basic agreement suggests that strong absorbers at $\sim$ 1 reside in similar environments to those of the galaxies in the DEEP2 survey. +" Furthermore, the average halo mass we estimate, 1.5642:0.11x10? is consistent with observations at lower redshift."," Furthermore, the average halo mass we estimate, $\pm$ $\times10^{12}\Msun$ , is consistent with observations at lower redshift." +" LundgrenMo,etal.(2009) measured a typical halo mass of 1.812x101?h-!Mo for absorbers with W??798 at z=0.6, in agreement with Bouchéetal.(2006) and Gauthieretal. (2009)."," \citet{L09} measured a typical halo mass of $\pm^{4.2}_{1.6}\times10^{12}h^{-1}\Msun$ for absorbers with $_{r}^{\lambda2796}$ at z=0.6, in agreement with \citet{B06} and \citet{Gauthier09}." +". The consistency with our measurement at higher redshift suggests that the halo masses of absorbers evolve very little from z=1, though the errors remain large."," The consistency with our measurement at higher redshift suggests that the halo masses of absorbers evolve very little from z=1, though the errors remain large." +" It is also worth noting that the luminosity function of z~0.65 galaxies selected by absorption in nearby quasar sightlines has been shown to peak at Mpg--20 (Steideletal.1994),, which is consistent with the mean luminosity of the DEEP2 galaxies."," It is also worth noting that the luminosity function of $\sim$ 0.65 galaxies selected by absorption in nearby quasar sightlines has been shown to peak at $M_{B}$ =-20 \citep{Steideletal94}, which is consistent with the mean luminosity of the DEEP2 galaxies." +" While we have not analysed statistical sample of MgII-selected galaxies, it seems likelya that the z~1 absorbers not only trace the same environments as the DEEP2 galaxy sample but also similar types of galaxies (~ L5)."," While we have not analysed a statistical sample of -selected galaxies, it seems likely that the $\sim$ 1 absorbers not only trace the same environments as the DEEP2 galaxy sample but also similar types of galaxies $\sim L_{B}^{*}$ )." +" As measurements of the bias of have never been reported at this redshift, we can provide the first constraints on theoretical models describing the evolution of absorbers and their respective haloes."," As measurements of the bias of have never been reported at this redshift, we can provide the first constraints on theoretical models describing the evolution of absorbers and their respective haloes." +" Tinker&Chen(2008) produced a model for the halo occupation distribution of cold gas at z=0.6, where the bias ofII has been precisely measured from cross-correlations with LRGs."," \citet{TC08} produced a model for the halo occupation distribution of cold gas at z=0.6, where the bias of has been precisely measured from cross-correlations with LRGs." +" With this model, Tinker&Chen(2008) predict the probability of finding an absorber with an equivalent width W;. in a halo of mass Μη."," With this model, \citet{TC08} predict the probability of finding an absorber with an equivalent width $_{r}$ in a halo of mass $_{h}$." +" In doing so, they demonstrate that the observed anti-correlation of and bias at z=0.6 may be reproduced by the absence of high density cold gas in the hot haloes of the most massive (and most biased) galaxies."," In doing so, they demonstrate that the observed anti-correlation of and bias at z=0.6 may be reproduced by the absence of high density cold gas in the hot haloes of the most massive (and most biased) galaxies." +" Tinker&Chen(2010) built on the Tinker&Chen(2008) model to incorporate the observed redshift evolution of the number density, thus enabling predictions of the absorber halo occupation distribution as a function of redshift."," \citet{TC10} built on the \citet{TC08} model to incorporate the observed redshift evolution of the number density, thus enabling predictions of the absorber halo occupation distribution as a function of redshift." + The number density of absorbers in the SDSS has been shown to be roughly constant with redshift (Nestoretal.2005;Prochter2006a;Lundgren 2009).," The number density of absorbers in the SDSS has been shown to be roughly constant with redshift \citep{Nestor05,Prochter06,L09}." +". Reconciling this non-evolving number density within the context of hierarchical growth, which produces fewer haloes at a fixed mass at higher redshifts, requires evolution in the distribution of cold gas in haloes."," Reconciling this non-evolving number density within the context of hierarchical growth, which produces fewer haloes at a fixed mass at higher redshifts, requires evolution in the distribution of cold gas in haloes." + One can achieve this effect by varying either the effective gas radius of the haloes or the typical absorber halo mass., One can achieve this effect by varying either the effective gas radius of the haloes or the typical absorber halo mass. +" As detailed in Tinker&Chen (2010), the observational outcomes of these two scenarios are degenerate in number density, but they diverge in predicted bias over a range in redshift."," As detailed in \citet{TC10}, the observational outcomes of these two scenarios are degenerate in number density, but they diverge in predicted bias over a range in redshift." + In Figure 5 we overlay theMgII bias measurement from this work onto the curves of projected bias evolution calculated separately for models of evolving gas radius and halo mass from Tinker&Chen(2010)., In Figure 5 we overlay the bias measurement from this work onto the curves of projected bias evolution calculated separately for models of evolving gas radius and halo mass from \citet{TC10}. +" The bias measurement at z~1 suggests a preference for the model of gas radius evolution, though the error on our measurement is still too large to rule out the mass evolution model."," The bias measurement at $\sim$ 1 suggests a preference for the model of gas radius evolution, though the error on our measurement is still too large to rule out the mass evolution model." +"It is importantto note that the model curves of Tinker&Chen have been calculated for an absorber sample with W,»1À , whereas our data extends to a lower equivalent","It is importantto note that the model curves of \citet{TC10} have been calculated for an absorber sample with $_{r}>$ , whereas our data extends to a lower equivalent" +differences in its statistical quality. may be applied to deseribe the data.,"differences in its statistical quality, may be applied to describe the data." + All errors derived in spectral fitting are statistical errors given by their Additional uncertainties may arise from errors in the atomic data and instrumental calibration. which are not explicitly accounted for.," All errors derived in spectral fitting are statistical errors given by their Additional uncertainties may arise from errors in the atomic data and instrumental calibration, which are not explicitly accounted for." + We investigated the X-ray properties of Altair by analyzing its light curves. spectra and emission lines and present our results obtained from different analysis methods in the respective physical context.," We investigated the X-ray properties of Altair by analyzing its light curves, spectra and emission lines and present our results obtained from different analysis methods in the respective physical context." + To search for short-term vartability on timescales of hours to days. we investigated the temporal behavior of Altair's X-ray brightness during our 2x2 exposures. that are separated by 14 days and cover in total roughly hh of observation time.," To search for short-term variability on timescales of hours to days, we investigated the temporal behavior of Altair's X-ray brightness during our 2x2 exposures, that are separated by 14 days and cover in total roughly h of observation time." + In refle we show the count rate in the 0.222.0 keV band as measured by the EPIC. i.e. summed PN and MOS. instrument in time-steps of half an hour.," In \\ref{lc} we show the count rate in the 2.0 keV band as measured by the EPIC, i.e. summed PN and MOS, instrument in time-steps of half an hour." + While clearly no strong flares are present. significant variability of Altair’s X-ray brightness at a level of roughly in all individual exposures and over the total observation time.," While clearly no strong flares are present, significant variability of Altair's X-ray brightness at a level of roughly in all individual exposures and over the total observation time." + This variability could in. principle be due to rotational modulation or caused by intrinsic variability of the X-ray emitting features: e.g. microflaring or emergence/decay of weakly active regions., This variability could in principle be due to rotational modulation or caused by intrinsic variability of the X-ray emitting features; e.g. microflaring or emergence/decay of weakly active regions. + These possible scenarios can in principle be distinguished by studying the periodicity of the light curve or the spectral changes related to the changes in brightness., These possible scenarios can in principle be distinguished by studying the periodicity of the light curve or the spectral changes related to the changes in X-ray brightness. + Due to Altair’s inclination of about ..only those features being sufficiently close to the surface and being located at equatorial up to intermediate latitudes would induce a rotational modulation: in contrast. emission from high and polar latitudes or very extended regions would be always visible.," Due to Altair's inclination of about ,only those features being sufficiently close to the surface and being located at equatorial up to intermediate latitudes would induce a rotational modulation; in contrast, emission from high and polar latitudes or very extended regions would be always visible." + Spectral variations are expected to be rather minor in the case of rotational modulation and for the emergence/decay of weakly active regions. in contrast flaring should be accompanied by a spectral hardening.," Spectral variations are expected to be rather minor in the case of rotational modulation and for the emergence/decay of weakly active regions, in contrast flaring should be accompanied by a spectral hardening." + Rotational modulation can be studied with our X-ray data that covers in total three to four stellar rotations., Rotational modulation can be studied with our X-ray data that covers in total three to four stellar rotations. + However. the uncertainties in the relevant stellar parameters (Vsini.ἐς R) allow a range of rotation periods with values around 9.5+1 h. Further. our data is not continuous. and especially the data gap of two weeks between both observations leads to large phase uncertainties.," However, the uncertainties in the relevant stellar parameters $Vsini, i, R$ ) allow a range of rotation periods with values around $9.5\pm 1$ h. Further, our data is not continuous, and especially the data gap of two weeks between both observations leads to large phase uncertainties." + Additionally. some restructuring of X-ray emitting surface features might have occurred over times of several days.," Additionally, some restructuring of X-ray emitting surface features might have occurred over times of several days." + To investigate periodicity of the obtained X-ray light curves. that might be related to rotational modulation. we tested periods in the range of 113 h for both observations separately. resulting in à minimum of ten time bin pairs per period and observation.," To investigate periodicity of the obtained X-ray light curves, that might be related to rotational modulation, we tested periods in the range of 13 h for both observations separately, resulting in a minimum of ten time bin pairs per period and observation." + We then calculated the variation of the folded light curve. weighted with the mean deviation. for each period.," We then calculated the variation of the folded light curve, weighted with the mean deviation, for each period." +" As shown in the upper panel of refpha,r..amininuan. particularly pronounced forthe firstobservation. is This indicates. that rotational modulation is indeed present and points to a distribution of active regions that persists at least over a stellar rotation."," As shown in the upper panel of \\ref{pha_hr}, a minimum, particularly pronounced for the first observation, is obtained for periods around $10\pm 1$ h. This indicates, that rotational modulation is indeed present and points to a distribution of active regions that persists at least over a stellar rotation." + The X-ray period is fully consistent with the range of rotation periods derived above and particularly favors values the longer periods., The X-ray period is fully consistent with the range of rotation periods derived above and particularly favors values the longer periods. + Neglecting possible differential rotation. that might even be anti-solar. our periods correspondingly suggest values in the lower range for Vsini or in the upper range for the radius.," Neglecting possible differential rotation, that might even be anti-solar, our periods correspondingly suggest values in the lower range for $Vsini$ or in the upper range for the radius." + A period of around IOhh provides very good self-similarity of the data obtained from the first observation within errors. ie. over roughly two rotations.," A period of around h provides very good self-similarity of the data obtained from the first observation within errors, i.e. over roughly two rotations." + Likewise 1t deseribes the second observation best. however here the scatter is much larger and the X-ray light curve appears rather irregular.," Likewise it describes the second observation best, however here the scatter is much larger and the X-ray light curve appears rather irregular." + We suspect that short-term variability. emergence and decay of quiescent coronal features or coronal restructuring are very likely responsible for this behavior.," We suspect that short-term variability, emergence and decay of quiescent coronal features or coronal restructuring are very likely responsible for this behavior." + The here derived X-ray period ts in the same range. but slightly larger than a low-frequency period (P 99.3hh) found in the pulsation study of ? and the periods derived from modeling of interferometric data. for example P 2299.3hh (?) and P==88.9hh (?).," The here derived X-ray period is in the same range, but slightly larger than a low-frequency period $P$ h) found in the pulsation study of \cite{buz05} and the periods derived from modeling of interferometric data, for example $P$ h \citep{sou05} and $P$ h \citep{pet06}." +" If the differences have to be attributed to systematic and measurement errors or indicate different ""physical periods remains uncertain. yet the derived periods of Altair are close to each other. supporting that rotational modulated X-ray emission is indeed present during the observation."," If the differences have to be attributed to systematic and measurement errors or indicate different `physical' periods remains uncertain, yet the derived periods of Altair are close to each other, supporting that rotational modulated X-ray emission is indeed present during the observation." + The absence of larger or even moderate flares. which are commonly observed in more active stars. may be a chance effect. but indicates the rareness of such events In stars with shallow convection zones.," The absence of larger or even moderate flares, which are commonly observed in more active stars, may be a chance effect, but indicates the rareness of such events in stars with shallow convection zones." + The overall X-ray brightness remained fairly constant (mean net count rate of 0.23 cts/s vs. 0.2] ets/s) between both observations. Le. over two weeks. corresponding to more than 30 stellar rotations.," The overall X-ray brightness remained fairly constant (mean net count rate of 0.23 cts/s vs. 0.21 cts/s) between both observations, i.e. over two weeks, corresponding to more than 30 stellar rotations." + Further. the brightness only varies by about These findings indicate. that the. X-ray emitting features are," Further, the X-ray brightness only varies by about These findings indicate, that the X-ray emitting features are" +increasing dependence on micro turbulence in cooler stars.,increasing dependence on micro turbulence in cooler stars. + An increase in temperature causes an increase 1n surface gravity and our values are 0.15 dex higher compared to the literature values., An increase in temperature causes an increase in surface gravity and our values are 0.15 dex higher compared to the literature values. + The comparison between the mean metallicity of our total sample of giant stars and giant stars with announced companions reveals that the companion hosting stars have a 0.13 + 0.03 dex higher metallicity than the mean metallicity of our total sample., The comparison between the mean metallicity of our total sample of giant stars and giant stars with announced companions reveals that the companion hosting stars have a 0.13 $\pm$ 0.03 dex higher metallicity than the mean metallicity of our total sample. + This is in agreement with the enhanced metallicity of companion hosting dwarf stars. but is based or low number statistics.," This is in agreement with the enhanced metallicity of companion hosting dwarf stars, but is based on low number statistics." + Rotational velocities are determined using the method described by ?.., Rotational velocities are determined using the method described by \citet{fekel1997}. + Stars in common between our sample and that observed by ? are used to convert FWHM of moderate lines ATI to total line broadening |kms! J., Stars in common between our sample and that observed by \citet{gray1989} are used to convert FWHM of moderate lines ] to total line broadening $^{-1}$ ]. + We used a log g vs. Tar correlation to determine the luminosity class of the stars., We used a $\log$ g vs. $_{\rm{eff}}$ correlation to determine the luminosity class of the stars. + This lummosity class was subsequently used to calculate the macro turbulence. which has a different relation with temperature for different classes.," This luminosity class was subsequently used to calculate the macro turbulence, which has a different relation with temperature for different classes." + Our data are in agreement with those obtained by ?.. but are on average larger than the values obtained by ?..," Our data are in agreement with those obtained by \citet{gray1989}, but are on average larger than the values obtained by \citet{demedeiros1999}." + This is due to the different diagnosties used to determine esinf. , This is due to the different diagnostics used to determine $\varv \sin i$ +"In these Appendices, a number of instructional cases are considered for the polarized line profiles shapes from a Keplerian disk when the illuminating star is treated as a point source.","In these Appendices, a number of instructional cases are considered for the polarized line profiles shapes from a Keplerian disk when the illuminating star is treated as a point source." + This means that both stellar occultation and the finite star depolarization factor are ignored., This means that both stellar occultation and the finite star depolarization factor are ignored. + A consequence of this approximation is that a non-zero pprofile canonly result from the Hanle effect., A consequence of this approximation is that a non-zero profile can result from the Hanle effect. +" Before considering polarized line profiles, Stokes-I profile shapes are derived for the case of isotropic scattering."," Before considering polarized line profiles, Stokes-I profile shapes are derived for the case of isotropic scattering." + These solutions form the base emissivity function from which the polarized lines are constructed., These solutions form the base emissivity function from which the polarized lines are constructed. +" Isotropic scattering corresponds to E,=0, and it means there is no polarization from resonance line scattering."," Isotropic scattering corresponds to $E_1=0$, and it means there is no polarization from resonance line scattering." +" Of course, that also means there is no Hanle effect, regardless of the field strength."," Of course, that also means there is no Hanle effect, regardless of the field strength." +" Even though there is no Hanle effect, the isotropic case is useful to explore as a reference for the production of the Stokes-I line shape."," Even though there is no Hanle effect, the isotropic case is useful to explore as a reference for the production of the Stokes-I line shape." + The integrand for the line emission as a function of velocity shift in the observed line represents the contributions by the disk density and the Sobolev effect for the profile shape., The integrand for the line emission as a function of velocity shift in the observed line represents the contributions by the disk density and the Sobolev effect for the profile shape. + Allowing for ΕΙ#0 and the Hanle effect simply represents new weighting functions for non-isotropic scattering that multiply the integrand from the isotropic case., Allowing for $E_1 \neq 0$ and the Hanle effect simply represents new weighting functions for non-isotropic scattering that multiply the integrand from the isotropic case. + The flux of line emission at normalizedDoppler shift t; is where the factor of 2 arises from the back-front symmetry of the integration along the isovelocity zone., The flux of line emission at normalizedDoppler shift $\wz$ is where the factor of 2 arises from the back-front symmetry of the integration along the isovelocity zone. +" As a reminder, t=σ΄} and to=w?."," As a reminder, $t=\varpi^{-1}$ and $t_0=\wzz$." + Again the preceding expression is only valid in the point star approximation., Again the preceding expression is only valid in the point star approximation. + The power law exponent m is from the surface density distribution that is assumed to be a power law of the form X=ρα.," The power law exponent $m$ is from the surface density distribution that is assumed to be a power law of the form $\Sigma = \Sigma_0\, \varpi^{\rm -m}$." + This formulation leads to symmetric double-peaked line profile shapes for m> 2., This formulation leads to symmetric double-peaked line profile shapes for $m>2$ . + Larger values of m result in, Larger values of $m$ result in +"As another comparison. the last four columns in Table 1 give analytically computed results of w, and A, for Riemann $-tvpe ellipsoids having the specified axes ratios b/a and e/o. as well as the ratio between numerical and analytical results (only models with a«5be have been computed).","As another comparison, the last four columns in Table \ref{n0} give analytically computed results of $\omega_{a}$ and $\lambda_{a}$ for Riemann S-type ellipsoids having the specified axes ratios $b/a$ and $c/a$, as well as the ratio between numerical and analytical results (only models with $a < b < c$ have been computed)." + To obtain these analvlical results. we used standard incomplete elliptic integrals to evaluate (he potential field of a homogeneous ellipsoid 1987.seetheirTable 2-2)..," To obtain these analytical results, we used standard incomplete elliptic integrals to evaluate the potential field of a homogeneous ellipsoid \cite[see their Table 2-2]{BT87}. ." + In virtually all cases. the error in w is < a few percent.," In virtually all cases, the error in $\omega$ is $\lesssim$ a few percent." + On the other hand. for the direct configurations the fractional error in A can be as large as5056 the error is largest [or models whose A almost vanishes.," On the other hand, for the direct configurations the fractional error in $\lambda$ can be as large as; the error is largest for models whose $\lambda$ almost vanishes." + This is understandable because a small variation in (he magnitude of A will result in a large percentage cdillerence when A is approaching zero., This is understandable because a small variation in the magnitude of $\lambda$ will result in a large percentage difference when $\lambda$ is approaching zero. + Also some mismatch between numerical and analvtical results may arise because the discrete nature of our grids makes it difficult [or us to define an exact axis ratio for our moclels., Also some mismatch between numerical and analytical results may arise because the discrete nature of our grids makes it difficult for us to define an exact axis ratio for our models. + For compressible equations of state. we can compare our results with those presented bv LaiRasio&Shapiro(1993).. who used an energy variational method (ο. determine approximate equilibrium configurations for ellipsoidal sell-gravitating svstems.," For compressible equations of state, we can compare our results with those presented by \cite{LRS93}, who used an energy variational method to determine approximate equilibrium configurations for ellipsoidal self-gravitating systems." + Lai.Rasio&Shapiro(1993) assumed that the iso-densitv contours of each configuration are concentric ellipses. which as we have already. emphasized is not the case.," \cite{LRS93} assumed that the iso-density contours of each configuration are self-similar concentric ellipses, which as we have already emphasized is not the case." + In (heir Table 4. for compressible analogues of Jacobi ellipsoids. a configuration with b/a=0.75 and cfa=0.4983 has T'/|W|=0.1407: the closest match among our 7=0.5 models (see Table 2)) with b/a=0.74 and c/a=0.487 has 177Wy=0.135.," In their Table 4, for compressible analogues of Jacobi ellipsoids, a configuration with $b/a=0.75$ and $c/a=0.4983$ has $T/|W|=0.1407$; the closest match among our $n=0.5$ models (see Table \ref{n05}) ) with $b/a=0.74$ and $c/a=0.487$ has $T/|W|=0.135$." + Other quantities also match well. alter a proper normalization is applied as prescribed by their equation (3.27).," Other quantities also match well, after a proper normalization is applied as prescribed by their equation (3.27)." +B We omit more comparisons here and leave the rest to interested readers., We omit more comparisons here and leave the rest to interested readers. + Other models (hat are of interest are the /——2 inrotational sequence 1993)., Other models that are of interest are the $f=-2$ irrotational sequence \citep{UE98}. +. It turns out that the / parameter is very sensitive to (he axis ratios. so we could not build models that are very close to the irrotational sequence due to the discrete nature of our computational erids.," It turns out that the $f$ parameter is very sensitive to the axis ratios, so we could not build models that are very close to the irrotational sequence due to the discrete nature of our computational grids." + Our model that comes closest has f.=—1.9: it is a direct configuration with n=0.5 ancl its other parameters are listed in Table 2.., Our model that comes closest has $f=-1.9$; it is a direct configuration with $n=0.5$ and its other parameters are listed in Table \ref{n05}. + We have presented a new method to construct 3D models for Riemann S-tvpe ellipsoids (n= 0). and the method has been extended (o construct compressible counterparts (hat share the same velocity. field as that of Riemann S-tvpe ellipsoids.," We have presented a new method to construct 3D models for Riemann S-type ellipsoids $n=0$ ), and the method has been extended to construct compressible counterparts that share the same velocity field as that of Riemann S-type ellipsoids." + With this method. we have been able to build 3D models (hat cover almost (he entire parameterspace of Riemann 5-Lvpe ellipsoids.," With this method, we have been able to build 3D models that cover almost the entire parameterspace of Riemann S-type ellipsoids." + Our results are in good agreement will previous studies., Our results are in good agreement with previous studies. + We expect (hat this method can also be straightforwardly extended to the construction of Roche-Riemann, We expect that this method can also be straightforwardly extended to the construction of Roche-Riemann +2007).,. +. This must be related to the decreasing star formation activity over the same period (e.g..LeFlochetal. 2005).. aud the production of such quiesceut ealaxies through the truncation of star formation (6.9..Faberetal.2007:Bellct 2007): the color scatter among quiescent galaxies aud its evolution are in precise agreement with such a scenario (Ruhlancdetal.2009).," This must be related to the decreasing star formation activity over the same period \citep[e.g.,][]{lefloch05}, and the production of such quiescent galaxies through the truncation of star formation \citep[e.g.,][]{faber07, bell07}; the color scatter among quiescent galaxies and its evolution are in precise agreement with such a scenario \citep{ruhland09}." +. There ares however. quiesceut galaxies at all redshifts 2S13 that are more massive than the most massive star-forming ealaxics.," There are, however, quiescent galaxies at all redshifts $z\lesssim 1.3$ that are more massive than the most massive star-forming galaxies." + This imiplics that star formation in the most massive galaxies was truucated even earlier. and/or that merecrs play an inportaut role in producing assive ealaxies.," This implies that star formation in the most massive galaxies was truncated even earlier, and/or that mergers play an important role in producing massive galaxies." + Evidence for the carly formation of massive galaxies is provided by their old stellar populations., Evidence for the early formation of massive galaxies is provided by their old stellar populations. +" Ποπονα, we need to bear in πιά that there can be a large difference between the age of the stellaz population aud the assembly age. especially if mergers are miportant. as is the case in a hierarchical framework for galaxy formation (DeLuciaetal.2007)."," However, we need to bear in mind that there can be a large difference between the age of the stellar population and the assembly age, especially if mergers are important, as is the case in a hierarchical framework for galaxy formation \citep{delucia07}." +. Hence. the muuber density evolution of galaxies is iniportant iu constraining their assembly history.," Hence, the number density evolution of galaxies is important in constraining their assembly history." + Measure this is cifficult because of its seusitivity to the luminosity evolution correction. especially for massive galaxies at the exponential cut-off of the mass function.," Measuring this is difficult because of its sensitivity to the luminosity evolution correction, especially for massive galaxies at the exponential cut-off of the mass function." + As a result. there is no conseusus among the currently available measurements (Cimattietal. 2008).," As a result, there is no consensus among the currently available measurements \citep{cimatti06, wake06, brown07, + cool08}." +. Given these difficulties. other observations have beeu used. to either directly or inclirectly coustrain the assembly of galaxies.," Given these difficulties, other observations have been used to either directly or indirectly constrain the assembly of galaxies." + Merging activity amone the massive ealaxv population is observed (c.e..vanDoldctal. 2008)... and has been shown to produce a color-magnitude relation that is iu agreement with observations (Skeltouetal. 2009).," Merging activity among the massive galaxy population is observed \citep[e.g.,][]{vandokkum99, vandokkum05, bell06a, bell06b, lin08}, and has been shown to produce a color-magnitude relation that is in agreement with observations \citep{skelton09}." + Tlowever. its cosnological relevance has always been difficult to determine. given the nucertaimtics iu converting observed iuereer fractions to merger rates and the associated growth in mass.," However, its cosmological relevance has always been difficult to determine, given the uncertainties in converting observed merger fractions to merger rates and the associated growth in mass." + An independent and indirect indication that massive ealaxies undergo continuous evolution is provided by the recent result that ligh-+vedshift quicscent sealaxies are substantially smaller than local galaxies with the sale nns (see.vanderWeletal.2008.audrefer-ences therein).," An independent and indirect indication that massive galaxies undergo continuous evolution is provided by the recent result that high-redshift quiescent galaxies are substantially smaller than local galaxies with the same mass \citep[see,][and references therein]{vanderwel08c}." + This strongly suggests that mergers are nmuportant (sec.e.g.vanderWeletal.2009).. and that the assembly of massive galaxies is contiuuius up uutil the preseut dav.," This strongly suggests that mergers are important \citep[see, +e.g.,][]{vanderwel09a}, and that the assembly of massive galaxies is continuing up until the present day." + Another indirect. vet powerful. constraint is provided by the evolution iu the clustering and halo occupation distribution of red galaxies (Whiteetal.2007:ConroyBrown 2008):: the evolution in the clustering strength of red salaxies is slower than expected in the absence of mereine.," Another indirect, yet powerful, constraint is provided by the evolution in the clustering and halo occupation distribution of red galaxies \citep{white07, conroy07, + brown08}: the evolution in the clustering strength of red galaxies is slower than expected in the absence of merging." + Iu this Letter we address the question whether major moreie is the dominant mechauisu for the production of verv massive. quicscent galaxies.," In this Letter we address the question whether major merging is the dominant mechanism for the production of very massive, quiescent galaxies." + The aremuent that we invoke is simply that major mereie ecucrally leads to roundoer galaxies., The argument that we invoke is simply that major merging generally leads to rounder galaxies. +" Au analysis ofthe shape distribution of quiescent ealaxies can therefore coustrain the importance of ποσο,", An analysis of the shape distribution of quiescent galaxies can therefore constrain the importance of merging. + Since niereiug among galaxies with mass ratios of =3 is the onlv known mechanisia to produce round galaxies (see Section 3 for further discussiou). this is a powerful test.," Since merging among galaxies with mass ratios of $\lesssim 3$ is the only known mechanism to produce round galaxies (see Section 3 for further discussion), this is a powerful test." + The disadvantage of this method. compared to those mentioned above. is that no information about the time scale and epoch of galaxy assembly can be ferred.," The disadvantage of this method, compared to those mentioned above, is that no information about the time scale and epoch of galaxy assembly can be inferred." + Vincent&Ryden(2005) and Paclilla&Strauss(2008) were the first to systematically study the axial ratio distribution. p(b/a). of a laree ΙΟ of galaxies. selected fron the Sloan Digital Sky Survey (SDSS).," \citet{vincent05} and \citet{padilla08} were the first to systematically study the axial ratio distribution, $p(b/a)$, of a large number of galaxies, selected from the Sloan Digital Sky Survey (SDSS)." + Through a detailed analysis. they inter the intrinsic shape distribution and the effect of extinction.," Through a detailed analysis, they infer the intrinsic shape distribution and the effect of extinction." +" Both divide the sample iuto ""elliptical aud ‘spiral’ galaxies. and coufimed that luminous elliptical galaxies arc. on average. rounder and triaxial. compared to low-huninosity “ellipticals”. which are more elongated ancl oblate (Daviesctal.1983:Frauxet1991).. and display disky isophotes (Jorgensen&Fraux1991)."," Both divide the sample into 'elliptical' and 'spiral' galaxies, and confirmed that luminous 'elliptical' galaxies are, on average, rounder and tri-axial, compared to low-luminosity 'ellipticals', which are more elongated and oblate \citep{davies83, franx91}, and display disky isophotes \citep{jorgensen94}." +. This phenomenon is not recent: Toldenetal.(2009) showed that this trend persists at least out to :~1.," This phenomenon is not recent: \citet{holden09a} + showed that this trend persists at least out to $z\sim 1$." + Tere we preseut a complementary. modified analysis. focusing 6i ο) as a function of stellar mass for quiescent. Le. non-star-foriumng. galaxies.," Here we present a complementary, modified analysis, focusing on $p(b/a)$ as a function of stellar mass for quiescent, i.e., non-star-forming, galaxies." + Because mas-to-liehlt ratios are well coustrained bv broad-baud colors for mescent galaxies. stellar iüass estimates are robust.," Because mass-to-light ratios are well constrained by broad-band colors for quiescent galaxies, stellar mass estimates are robust." + This is essential for our purposes. as we are interested in the most massive objects; Le.. those that populate the exponential tail of the mass function.," This is essential for our purposes, as we are interested in the most massive objects, i.e., those that populate the exponential tail of the mass function." + Furthermore. as opposed to previous studies. we pre-select ealaxies independent of their photometric properties.," Furthermore, as opposed to previous studies, we pre-select galaxies independent of their photometric properties." + Our sliape-independent. spectroscopic selection criteria circumvent the biases that are poteutially introduced by selecting ealaxies by their morphological’ properties. or sone surface brightness profile.," Our shape-independent, spectroscopic selection criteria circumvent the biases that are potentially introduced by selecting galaxies by their 'morphological' properties, or some pre-defined surface brightness profile." + With this sample. for which we have determined wial ratios from our own fits to two-dimensional light istributious. we address the following specific questions.," With this sample, for which we have determined axial ratios from our own fits to two-dimensional light distributions, we address the following specific questions." + Are hiel-ass. quiescent ealaxies rounder than low-lass quiescent galaxies?," Are high-mass, quiescent galaxies rounder than low-mass quiescent galaxies?" + Tf so. is there a mass Ht at which p(b/a) distinctly changes. aud above which disk-dominated are completely absent?," If so, is there a mass limit at which $p(b/a)$ distinctly changes, and above which disk-dominated are completely absent?" + Such evidence would nuply that the only evolutionary path to such masses is a cisk-destroving mechanisui. L6. major mereiug.," Such evidence would imply that the only evolutionary path to such masses is a disk-destroying mechanism, i.e., major merging." + We select a sample of 17.180 quiesceut galaxies from Data Release 6 of the SDSS (Adchnan-\leCart2008).," We select a sample of 17,480 quiescent galaxies from Data Release 6 of the SDSS \citep{adelman08}." +. Our sample iucludes galaxies at redshifts 0.01 = 2340.7 (see Table 2)).," The hard photon index is broadly distributed in our sample ranging from $\sim$ 1.3 to very steep values such as $\sim$ 3.6, with a mean value $<$$\Gamma_{20-100 keV}$$>$ $=$ $\pm$ 0.7 (see Table \ref{table=hard}) )." + This value is consistent within errors with the one previously found. in a smaller sample of tive NLSy1 (κοςtoon = 2.60.3.Alalizia ct al.," This value is consistent within errors with the one previously found in a smaller sample of five NLSy1 $<$$\Gamma_{20-100 keV}$$>$ $=$ $\pm$ 0.3,Malizia et al." + 2008)., 2008). + Phe BLSy1 mean hard photon index «VouLOUbYut = 2040.2) is only slightlv [latter and consistent with the Αν] «Lejgoopevc as dndeced a Ixolmogorov-Smirnov. (Ix-8) test (probability P= of a ranclom result) indicates. that the distributions are not significantly dilleren.," The BLSy1 mean hard photon index $<$$\Gamma_{20-100 keV}$$>$ $=$ $\pm$ 0.2) is only slightly flatter and consistent with the NLSy1 $<$$\Gamma_{20-100 keV}$$>$, as indeed a Kolmogorov-Smirnov (K-S) test (probability $P = 0.030$ of a random result) indicates that the distributions are not significantly different." + Phis is also in agreement with estimates. [rom tvpe 1 Sevlert spectra. from οBAT (Loulookey 5 2-28+0.11. Ajello et al.," This is also in agreement with estimates from type 1 Seyfert spectra from /BAT $<$$\Gamma_{20-100 keV}$$>$ $=$ $\pm$ 0.11, Ajello et al." + 2008)., 2008). + From this analysis. the average photon index of NLSy1 at hard X-rays appears not to be steeper than in BLSw however. we should consider that faint steep spectrum sources1. may be missed by hard X-ray surveys.," From this analysis, the average photon index of NLSy1 at hard X-rays appears not to be steeper than in BLSy1, however, we should consider that faint steep spectrum sources may be missed by hard X-ray surveys." + ὃν fitting the 0.8-100 keV. broad-band spectrum (as in ‘Table 6 and including data from literature for NGC 4051. Ark 783 and NGC 5506). the resulting photon index varies rom ~ 1.5 to — 2.6 with a mean of «Lusi005Vv = 2.0zE0.3. consistent with the typical values found. for this class of sources (e... Leighlv 1999).," By fitting the 0.3-100 keV broad-band spectrum (as in Table \ref{table=best} and including data from literature for NGC 4051, Mrk 783 and NGC 5506), the resulting photon index varies from $\sim$ 1.5 to $\sim$ 2.6 with a mean of $<$$\Gamma_{0.3-100 keV}$$>$ $=$ $\pm$ 0.3, consistent with the typical values found for this class of sources (e.g., Leighly 1999)." + We should note that the 3-100 keV. spectral fit parameters are more representative of the spectra below LO keV. for the larger statistics. especially when data are used.," We should note that the 0.3-100 keV spectral fit parameters are more representative of the spectra below 10 keV, for the larger statistics, especially when data are used." + In a complete nud X-ray selected sample of BLSv1. Molina et al. (," In a complete hard X-ray selected sample of BLSy1, Molina et al. (" +2009) ound a Blatter mean value «Leopounce 1.3 (a = 0.3). confirming the evidence that NLSy1 tend to have steeper hoton indeces. as also confirmed in Bianchi et al. (,"2009) found a flatter mean value $<$$\Gamma_{20-100 keV}$$>$ $\sim$ 1.7 $\sigma$ $=$ 0.2), confirming the evidence that NLSy1 tend to have steeper photon indeces, as also confirmed in Bianchi et al. (" +20092). or an X-ray selected sample.,"2009a), for an X-ray selected sample." + Pherefore. no clear separation tween NLSy1I and BLSy average hard X-ray photon index is found. as instead: observed.1 for the broad-band photon inclex.," Therefore, no clear separation between NLSy1 and BLSy1 average hard X-ray photon index is found as instead observed for the broad-band photon index." + In Figure 4 (right panel) we plot the hard X-ray versus the 0.3-100. keV. broad. band X-ray photon index., In Figure \ref{figure=foton} (right panel) we plot the hard X-ray versus the 0.3-100 keV broad band X-ray photon index. + The one-to-one regression line is also drawn., The one-to-one regression line is also drawn. + The steeper hard. X-ray. photon indeces are also clear from this. plot sugeesting the possible presence of a high energy. cut-oll., The steeper hard X-ray photon indeces are also clear from this plot suggesting the possible presence of a high energy cut-off. + Llowever. with the present data we were able to constrain this parameter only in Swift J2127.415654 (eaapp = 49.D keV). in agreement with our previous estimate (Malizia et al.," However, with the present data we were able to constrain this parameter only in Swift J2127.4+5654 $_{cut-off}$ $=$ $^{+49}_{-17}$ keV), in agreement with our previous estimate (Malizia et al." + 2008) and with the PLN measurement. (Miniutti et al., 2008) and with the PIN measurement (Miniutti et al. + 2000)., 2009). + A very steep hard. rav photon index is measured in Ark 766 (E — 2.9) and indeed. a spectral decrease is evident at ~ 50 keV from the PIN data (Yurner ct al.," A very steep hard X-ray photon index is measured in Mrk 766 $\Gamma$ $\sim$ 2.9) and indeed, a spectral decrease is evident at $\sim$ 50 keV from the PIN data (Turner et al." + 2007)., 2007). + In. AIrk 783. LRAS 15091-2107 and in Lk. 16385-2057 the hard. X-ray photon index is much steeper than the SRP and one.," In Mrk 783, IRAS 15091-2107 and in IGR J16385-2057 the hard X-ray photon index is much steeper than the XRT and one," +on the apparent scatter in the broad-band spectra.,on the apparent scatter in the broad-band spectra. + These errors are included in all tables and figures., These errors are included in all tables and figures. +" For analysis, we grouped our data into “epochs”, with observations included in a given epoch separated by no more than three days."," For analysis, we grouped our data into “epochs”, with observations included in a given epoch separated by no more than three days." + Tables 1 and 2 list the flux densities at each epoch., Tables \ref{srcTab1} and \ref{srcTab2} list the flux densities at each epoch. +" On days 40.6 and 61.4, we obtained observations of wwith the Swift satellite etal. of duration 3.0 and 5.5 ks."," On days 40.6 and 61.4, we obtained observations of with the satellite \citep{Gehrels04} of duration 3.0 and 5.5 ks." + Each observation(Gehrels resulted2004) in an exposure with the X-ray telescope (XRT) and an image with the Ultraviolet Optical Telescope (UVOT)., Each observation resulted in an exposure with the X-ray telescope (XRT) and an image with the Ultraviolet Optical Telescope (UVOT). + We used theSwift data analysis routines in HEASoft version 6.10 throughout our analysis., We used the data analysis routines in HEASoft version 6.10 throughout our analysis. +" The UVOT images were both obtained with the UVW1 filter, which has a central wavelength of 2600 and a FWHM of 693 etal. 2008)."," The UVOT images were both obtained with the UVW1 filter, which has a central wavelength of 2600 and a FWHM of 693 \citep{Poole08}." +. wwas not detected in either UVOT image with a limiting UVWI magnitude of 20.36 (20.65) in the first (second) observation., was not detected in either UVOT image with a limiting UVW1 magnitude of 20.36 (20.65) in the first (second) observation. + The XRT was operated in photon counting mode during both observations., The XRT was operated in photon counting mode during both observations. +" We produced cleaned level 2 event files by running the XRT reduction pipeline on the level 1 event files, retaining events with grades 0-12."," We produced cleaned level 2 event files by running the XRT reduction pipeline on the level 1 event files, retaining events with grades 0–12." + We then used XSelect v2.4 to create spectra for each dataset., We then used XSelect v2.4 to create spectra for each dataset. +" Source counts were extracted from 30""--radius circular region centered onAql; background counts were extracted from a 95""--radius source free region.", Source counts were extracted from -radius circular region centered on; background counts were extracted from a -radius source free region. +" The ancilliary response files (ARF) were generated using the taskxrtmkarf, and were corrected for hot pixels and dead columns using an exposure map of each observation."," The ancilliary response files (ARF) were generated using the task, and were corrected for hot pixels and dead columns using an exposure map of each observation." +" Finally, we used the most recent response matrix file (RMF) appropriate for PC mode and event grades 0-12 from theSwift calibration database."," Finally, we used the most recent response matrix file (RMF) appropriate for PC mode and event grades 0–12 from the calibration database." +" Aql’ss light curves are characterized by an initial steep rise until around day 50 (S,ο.1?? at 32.1 GHz), at which point there is a turnover and rapid decay at the lower frequencies (1-9 GHz) and flattening at 19 GHz and higher "," s light curves are characterized by an initial steep rise until around day 50 $S_{\nu} \propto t^{3.3}$ at 32.1 GHz), at which point there is a turnover and rapid decay at the lower frequencies (1–9 GHz) and flattening at 19 GHz and higher (Figure \ref{lcPlot}) )." +"In order to characterize the radio spectra, we fit (Figuresimple 1)).power-law models to each epoch's 4-37 GHz spectrum; the spectra, along with fits and residuals, are shown in Figure 2.."," In order to characterize the radio spectra, we fit simple power-law models to each epoch's 4–37 GHz spectrum; the spectra, along with fits and residuals, are shown in Figure \ref{specPlot}." +" The fit residuals in some epochs suggest the presence of a spectral break, so we performed separate power-law fits to the lower (1—9 GHz) and higher (19-37 GHz) frequencies as well."," The fit residuals in some epochs suggest the presence of a spectral break, so we performed separate power-law fits to the lower (1--9 GHz) and higher (19–37 GHz) frequencies as well." +" In order to determine whether any improvement in fit was statistically significant, we performed F-tests for each epoch."," In order to determine whether any improvement in fit was statistically significant, we performed F-tests for each epoch." +" The addition of a second power-law is favored at less than 3o significance, so we use the results from the single power-law fits in our discussion ofAql."," The addition of a second power-law is favored at less than $3\sigma$ significance, so we use the results from the single power-law fits in our discussion of." +". We also plot this spectral index a (S,ος v%) in the lower panel of Figure 1,, showing that the rise portion of the light curve is accompanied by flattening of the spectrum, which then steepens again witha the turnover in low-frequency flux."," We also plot this spectral index $\alpha$ $S_{\nu} \propto \nu^{\alpha}$ ) in the lower panel of Figure \ref{lcPlot}, showing that the rise portion of the light curve is accompanied by a flattening of the spectrum, which then steepens again with the turnover in low-frequency flux." + We report the results of our spectral fitting in Table 3.. TheSwift, We report the results of our spectral fitting in Table \ref{radFits}. + XRT detected 25 (47) events at the position of oonday 41 (61)., The XRT detected 25 (47) events at the position of onday 41 (61). +" We estimate 2 (4) background counts, resulting in count rates of 7.6+1.6 (7.8+ 1.2) x107? c s-!."," We estimate 2 (4) background counts, resulting in count rates of $7.6\pm1.6$ $7.8\pm1.2$ ) $\times \,10^{-3}$ c $^{-1}$ ." +" We fit the unbinned, non-background subtracted X-ray datawith absorbed power-law and"," We fit the unbinned, non-background subtracted X-ray datawith absorbed power-law and" +By several new images of Hlt 7329 X and D obtained with HIS'T/NICMOS and. VLE/NACO with Ll ves epoch dillerence. we could reject (2Pla) the background hypothesis. that LER 7329 D would have been a non-moving background object unrelated to LU 7329 A. Hence. HV 7329 A and D form a common proper motion pair.,"By several new images of HR 7329 A and B obtained with HST/NICMOS and VLT/NACO with 11 yrs epoch difference, we could reject $\ge 21 \sigma$ ) the background hypothesis, that HR 7329 B would have been a non-moving background object unrelated to HR 7329 A. Hence, HR 7329 A and B form a common proper motion pair." + Phe possible detection of a small linear. change in separation (but no change in PA) is consistent with an on-skv 2D orbit of D around A. which is eccentric and/or inclined.," The possible detection of a small linear change in separation (but no change in PA) is consistent with an on-sky 2D orbit of B around A, which is eccentric and/or inclined." + Curvature in orbital motion as acceleration or deceleration would be a final proof for being gravitational bound. but is not vet detected. as in all other sub-stellar companions detected. by direct imaging. except PZ Tel B (Mugrauer et al.," Curvature in orbital motion as acceleration or deceleration would be a final proof for being gravitational bound, but is not yet detected, as in all other sub-stellar companions detected by direct imaging, except PZ Tel B (Mugrauer et al." + 2010)., 2010). + The magnitude dillerence between HI 7329 A and D is All = 6.7520.10 mag and AWK. = 6.620.1 mag (Lable 1). with DMXE0.033 mag for Ht. 7329 A|D (281ASS). we eet Wo=11.640.1p mag for HX 7329 D: we obtain L=11.1+0.2 mage for IL D (from Table 1 with L=5.0 mag for Lh 7329 as AO-tvpe star with J—II-Ix-L-5.0 mag): from the magnitude cdillerence between LER. 7329 A and D in the LIST I110NV filter CFable 1): we get J = 12.0630.19 mae forHi 7329 DB. calibrated with the M9.5 dwarf BAI Boo21-02 from Persson ct al. (," The magnitude difference between HR 7329 A and B is $\Delta$ H = $6.75 \pm 0.10$ mag and $\Delta$ $_{\rm s}$ = $6.6 \pm 0.1$ mag (Table 1), with $5.008 \pm 0.033$ mag for HR 7329 A+B (2MASS), we get $_{\rm s}$ $11.6 \pm 0.1$ mag for HR 7329 B; we obtain $11.1 \pm 0.2$ mag for HR 7329 B (from Table 1 with L=5.0 mag for HR 7329 as A0-type star with J=H=K=L=5.0 mag); from the magnitude difference between HR 7329 A and B in the HST F110W filter (Table 1); we get J = $12.06 \pm 0.19$ mag for HR 7329 B, calibrated with the M9.5 dwarf BRI B0021-02 from Persson et al. (" +1998) and the NIC web site.,1998) and the NIC web site. + Those JL colors are Consistent with spectral type. MY-8 for LU 7320 D. With a bolometric correction of D.C.=3.10+0.05 mag (for M7-8. Golimowski ct al.," Those JHKL colors are consistent with spectral type M7-8 for HR 7329 B. With a bolometric correction of $_{\rm K} = 3.10 \pm 0.05$ mag (for M7-8, Golimowski et al." +" 2004). and the distance towards 7329 A. we get a luminosity of 2.627£pn""0.087 for Lh » 1. For = 2500-2800 Ix (for nedM7-8. Golimowskl et al."," 2004), and the distance towards HR 7329 A, we get a luminosity of $\log (L_{\rm bol}/L_{\odot}) = -2.627 \pm 0.087$ for HR 7329 B. For $_{\rm eff}$ = 2500-2800 K (for M7-8, Golimowski et al." + 2004 and Luhmann 1999 scale) at ~12 Alves. we then derive the mass of LR 7329. D from evolutionary tracks to be 20 to 50 Jup masses (Burrows ct al.," 2004 and Luhmann 1999 intermediate scale) at $\sim 12$ Myrs, we then derive the mass of HR 7329 B from evolutionary tracks to be 20 to 50 Jup masses (Burrows et al." + 1997 Chabrier ct al.," 1997, Chabrier et al." + 2000. Daralle et al.," 2000, Baraffe et al." + 2002)., 2002). + LHence. IIR 7329 D is indeed a brown dwarf.," Hence, HR 7329 B is indeed a brown dwarf." +" No additional companion candidates were detected. up to <9"".", No additional companion candidates were detected up to $\le 9 ^{\prime \prime}$. + Phe LR 7329 LID 181327 svstem is therefore a triple svstem. with two stars with debris disks (Hllt. 7329 and its wide companion LID 181327. Jackman Paresce 1993. Smith et al.," The HR 7329 / HD 181327 system is therefore a triple system with two stars with debris disks (HR 7329 and its wide companion HD 181327, Backman Paresce 1993, Smith et al." + 2009. Schneider et al.," 2009, Schneider et al." + 2006) plus one brown cwarf (LR M 13)., 2006) plus one brown dwarf (HR 7329 B). + With 3 Pie (Smith Terrile 1984. Lagrange et al.," With $\beta$ Pic (Smith Terrile 1984, Lagrange et al." +2 ων.)and PZ Vol (Smith et al., 2010) and PZ Tel (Smith et al. + 2009. Biller ct al.," 2009, Biller et al." + 201C). el al.," 2010, Mugrauer et al." + POLO) there are two more members of the ? Pic moving eroup. which have both a debris disk ancd a sub-stcllar companion. indicating quite a large fraction and motivating further searches.," 2010) there are two more members of the $\beta$ Pic moving group, which have both a debris disk and a sub-stellar companion, indicating quite a large fraction and motivating further searches." + We thank the ESO Paranal Team and ESO Users Support eroup., We thank the ESO Paranal Team and ESO Users Support group. + RN. CG. anc POBS wish to acknowledge Deutsche l'orschungsgemeinschaft (DEC) for grant. NE 515 / 30-1.," RN, CG, and TOBS wish to acknowledge Deutsche Forschungsgemeinschaft (DFG) for grant NE 515 / 30-1." + We used Simbad. ancl Vizier and. archival data from the ESO. LUST. and 2ALASS.," We used Simbad and Vizier and archival data from the ESO, HST, and 2MASS." + We thank Andreas Seifahrt for his PSI subtraction routine written in LOL., We thank Andreas Seifahrt for his PSF subtraction routine written in IDL. + LIST data were obtained from the cata archive at. the. Space Telescope. Institute. which is operated. by the association of Universities. for Research in Astronomy. Inc. under the NASA contract NAS 5-26555.," HST data were obtained from the data archive at the Space Telescope Institute, which is operated by the association of Universities for Research in Astronomy, Inc. under the NASA contract NAS 5-26555." + We would also like to thank Alexander Ixrivov and Nina Vetzlalf for valueable discussion about cebris disks and runaway stars. respectively.," We would also like to thank Alexander Krivov and Nina Tetzlaff for valueable discussion about debris disks and runaway stars, respectively." +period reported by Schwarz et al (2004) in our data.,period reported by Schwarz et al (2004) in our data. + We would like to thank Gary. ΟΠΗ for use of his Fourier analvsis progranis., We would like to thank Gary Schmidt for use of his Fourier analysis programs. + We would also like to thank (he anonvanous referee for their many useful. comments which helped to improve this paper., We would also like to thank the anonymous referee for their many useful comments which helped to improve this paper. +view. old galaxies with a given σ teud to be metal poor. whereas vounecr galaxies with the same σ are metal rich (c.g. Worthev 1991: Trager et al.,"view, old galaxies with a given $\sigma$ tend to be metal poor, whereas younger galaxies with the same $\sigma$ are metal rich (e.g. Worthey 1994; Trager et al." + 20005)., 2000b). + Thus. recent work suggests that residuals from the color-magnitude relation are age indicators. whereas studies of chemical abundances sugeest that velocity dispersion is a colubination of both age and metallicity.," Thus, recent work suggests that residuals from the color-magnitude relation are age indicators, whereas studies of chemical abundances suggest that velocity dispersion is a combination of both age and metallicity." + One. of the goals of the preseut work is to see if these couclusions are consistent with ouc-another., One of the goals of the present work is to see if these conclusions are consistent with one-another. + We do this bv studyiug the joint distribution of color. huuiuositv aud velocity dispersion iu a suuple of 39320 early-type galaxies drawu from the Sloan Digital ον Survey (York et al.," We do this by studying the joint distribution of color, luminosity and velocity dispersion in a sample of 39320 early-type galaxies drawn from the Sloan Digital Sky Survey (York et al." + 2000: Stoughton et al, 2000; Stoughton et al. + 2002: Abazajian et al., 2002; Abazajian et al. + 2003) database (hereafter SDSS)., 2003) database (hereafter SDSS). + Section ?? describes our sample., Section \ref{sample} describes our sample. + Section ον preseuts the color-magnitude aud color-7 relations. aud demonstrates that color-o aud maguitude-7 are the primary correlations.," Section \ref{cms} presents the color-magnitude and $\sigma$ relations, and demonstrates that $\sigma$ and $\sigma$ are the primary correlations." + A simple model is introduced which illustrates clearly what our measurements duply for the relations between age. moetalliityv aud velocity dispersion.," A simple model is introduced which illustrates clearly what our measurements imply for the relations between age, metallicity and velocity dispersion." + The mathematics associated with this model is in Appendix D.., The mathematics associated with this model is in Appendix \ref{algebra}. + Section ?? uses the model to derive a umber of consequences of the observed coloranagnitude-o relations. and summarizes our findings.," Section \ref{discuss} uses the model to derive a number of consequences of the observed $\sigma$ relations, and summarizes our findings." + Throughout. we assimue that {10= rülans + Mpe+ in a universe with Qy=0.3 which is spatially flat.," Throughout, we assume that $H_0=70$ km $^{-1}$ $^{-1}$ in a universe with $\Omega_0=0.3$ which is spatially flat." + For our analysis we used galaxies selected from the Sloan Dieital Sky Survey (SDSS) database., For our analysis we used galaxies selected from the Sloan Digital Sky Survey (SDSS) database. + See York et al. (, See York et al. ( +2000) for a technical παν of the SDSS project: Stoughton et al. (,2000) for a technical summary of the SDSS project; Stoughton et al. ( +2002) for a description of the Early Data Release: Abazajian et al. (,2002) for a description of the Early Data Release; Abazajian et al. ( +2003) ct al.,2003) et al. + for a description of DRI. the First Data Release: Comm et al. (," for a description of DR1, the First Data Release; Gunn et al. (" +1998) for details about the camera: Fukueita et al. (,1998) for details about the camera; Fukugita et al. ( +1996). Ποσο et al. (,"1996), Hogg et al. (" +2001) ancl Suuüth et al. (,2001) and Smith et al. ( +2002) for details of the plotometric svstem and calibration: Lupton et al. (,2002) for details of the photometric system and calibration; Lupton et al. ( +20H) for a discussion of the photometric data reduction pipcline: Picr et al. (,2001) for a discussion of the photometric data reduction pipeline; Pier et al. ( +2003) for the astrometric calibrations: Banton et al. (,2003) for the astrometric calibrations; Blanton et al. ( +2003) for details of the tilius aleorithim: Strauss et al. (,2003) for details of the tiling algorithm; Strauss et al. ( +2002) aud Eisenstein et al. (,2002) and Eisenstein et al. ( +2001) for details of the target selection.,2001) for details of the target selection. + Our earh-tvpe galaxy sainple is selected similarly to that of Bernardi et al. (, Our early-type galaxy sample is selected similarly to that of Bernardi et al. ( +20032). with some minor changes: We selected. all objecs targeted as galaxies aud haviug de-reddened Petrosian appareut magnitude 115 10).," From this subsample, we finally chose those objects for which the spectroscopic pipeline had measured velocity dispersions (meaning that the signal-to-noise ratio in pixels between the restframe wavelengths and is S/N $>10$ )." + These selection criteria produced a sample of 39320 objects with photometric paramcters output by version V5.4 of the SDSS photometric pipeline aud V.23 reductions of the spectroscopic pipeline (6. v4_10_2 of idlspec2d aud v5.9.4 of spectrold)., These selection criteria produced a sample of 39320 objects with photometric parameters output by version ${\tt V5.4}$ of the SDSS photometric pipeline and ${\tt V.23}$ reductions of the spectroscopic pipeline (i.e. ${\tt v4\_10\_2}$ of ${\tt idlspec2d}$ and ${\tt v5\_9\_4}$ of ${\tt spectro1d}$ ). + The main quantities we use in this paper are naguitudes. sizes. colors. redshifts aud velocity dispersious: the first three are output from the SDSS photometric pipeline. aud the final two from the SDSS spectroscopic pipeline.," The main quantities we use in this paper are magnitudes, sizes, colors, redshifts and velocity dispersions; the first three are output from the SDSS photometric pipeline, and the final two from the SDSS spectroscopic pipeline." + The, The +in both raw aud foreground template corrected forms (Bennettetal.2003a.b) and three heavily processed maps derived to minimize the foreground coutibutio- la rempinte incdependeut wav (WILC Bennett2003b:aL 2003)).LILC — Eriksenetal.20015: TOII — Teguuuket ,"in both raw and foreground template corrected forms \citep{bennett:2003a,bennett:2003b} + and three heavily processed maps derived to minimize the foreground contribution in a template independent way (WILC – \citealt{bennett:2003b}; ; LILC – \citealt{eriksen:2004b}; TOH – \citealt{tegmark:2003}) )." +"For the three ILC-like maps we consider the full sky in the analvsis. whereas the Isp2 or Kpopt masks(Bennettetal.90020) are imposed otherwise,"," For the three ILC-like maps we consider the full sky in the analysis, whereas the Kp2 or Kp0 masks \citep{bennett:2003b} are imposed otherwise." + A are smoothed to a conuuon resolition of 5.5°of FWIIA and downeraded to a resolution Node=32 corresponding to larimonics up to (=GL., All are smoothed to a common resolution of $5.5\degr$ FWHM and downgraded to a resolution of $N_{\textrm{side}}=32$ corresponding to harmonics up to $\ell=64$. + Such processing does not compromise the analysis since the Bianchi models exhibit little power outside of this (- range., Such processing does not compromise the analysis since the Bianchi models exhibit little power outside of this $\ell$ -range. + To assess the statistical significance of the fits we colmpare our results to an ensemble of 100000 LILC siuulations. produced using the pipeline described by Eviksenctal.(200L)..," To assess the statistical significance of the fits we compare our results to an ensemble of 000 LILC simulations, produced using the pipeline described by \citet{eriksen:2004b}." + The Biauchi model templates are constructed sine formalis of Barrowetal.(1985)., The Bianchi model templates are constructed using the formalism of \citet{barrow:1985}. +. These models re parameterized by Qy. 1=vh(1.94) (where / is 1ο scale ou Which basis vectors change orientation). aud haudeduess.," These models are parameterized by $\Omega_0$, $ x = +\sqrt{h/(1-\Omega_0)} $ (where $h$ is the scale on which basis vectors change orientation), and a handedness." + These models have a preferedaxis along which the expansion rate is different. aud about which 1e basis vectors themselves rotate.," These models have a preferedaxis along which the expansion rate is different, and about which the basis vectors themselves rotate." + The smaller the wr. i6 more rotation in a elven distance traversed along ecodesic. and therefore the tighter the observed spiral xittern of induced temperature anisotropies.," The smaller the $x$, the more rotation in a given distance traversed along a geodesic, and therefore the tighter the observed spiral pattern of induced temperature anisotropies." + The sinaller re Oy. the larger is the asviuuetry along the axis aud 1ο mnore focused is the structure in only oue direction.," The smaller the $\Omega_0$, the larger is the asymmetry along the axis and the more focused is the structure in only one direction." + Iu this analysis. we consider the range 0.1x6<10 and (175% ol the time) at 4.8 GlIIz was found in 28 of the 62 sources. of which 12 are galaxies.," Inspection of the information on EVPA given in Table 2 shows that longterm stability $\ge 75 \%$ of the time) at 4.8 GHz was found in 28 of the 62 sources, of which 12 are galaxies." + In contrast. at 14.5 Gllz only 7 sources show a statistically significant preferred. EVPA >75% of the time: however. several sources show preferred EVPAs [for more than a third ol the time.," In contrast, at 14.5 GHz only 7 sources show a statistically significant preferred EVPA $\ge 75 \%$ of the time; however, several sources show preferred EVPAs for more than a third of the time." + Of these 7 objects with longterm. stable EVPAs. 5 are variable QSOs. one is a variable DL Lac ancl only one is a steep-spectrum. quiescent. lobe-dominated galaxy.," Of these 7 objects with longterm, stable EVPAs, 5 are variable QSOs, one is a variable BL Lac and only one is a steep-spectrum, quiescent, lobe-dominated galaxy." + For the hiehly variable sources. in particular the BL Lacs. we had attributed the lack of long-term preferred EVPA at 14.5 GllIz to the fact that the integrated polarization is dominated. by contributions from evolving source components near. or in. the core (Allerοἱal.1999).," For the highly variable sources, in particular the BL Lacs, we had attributed the lack of long-term preferred EVPA at 14.5 GHz to the fact that the integrated polarization is dominated by contributions from evolving source components near, or in, the core \citep{all99}." + llowever. we find here that even among the BL Lacs. long-term preferred ΕΟΝΡΑΣ do exist over significant portions of the time window. and over Gime periods which include several events.," However, we find here that even among the BL Lacs, long-term preferred EVPAs do exist over significant portions of the time window, and over time periods which include several events." + This suggests that the magnetic field may have a ‘memory. in the central regions. and that subsequent outbursts in a source may exhibit (he same or a related magnetic [field structure. or. alternatively. that there is a persistent standing shock in the “Core.," This suggests that the magnetic field may have a `memory', in the central radio-band regions, and that subsequent outbursts in a source may exhibit the same or a related magnetic field structure, or, alternatively, that there is a persistent standing shock in the `core'." + Figure 14. showing the data lor QSO 0212-138. illustrates another behavior we [ind in some AGNs: a preferred EVPA which changes abruptly to a second longterm preferred EVPA.," Figure 14, showing the data for QSO 0212+738, illustrates another behavior we find in some AGNs: a preferred EVPA which changes abruptly to a second longterm preferred EVPA." + Such behavior has previously been identified in non-sample members 13084-326 1999) and 3C 279 (Aller.Aller.andIIughes.1996).," Such behavior has previously been identified in non-sample members 1308+326 \citep{all99} + and 3C 279 \citep{all96}." +. In 0212+738 we lind a longterm preferred EVPA at 4.8 GlIz which is maintained in spite of the nearly continuous activity in the source., In 0212+738 we find a longterm preferred EVPA at 4.8 GHz which is maintained in spite of the nearly continuous activity in the source. + The average centimeter-band spectral index is very flat: a=0.03., The average centimeter-band spectral index is very flat: $\alpha=0.03$. + At 14.5 Gllz. however. we find (wo preferred orientations: a first near to the value preferred at 4.5 Gz until 1995. followed by a rotation. and a second. relatively stable orientation nearly," At 14.5 GHz, however, we find two preferred orientations: a first near to the value preferred at 4.8 GHz until 1995, followed by a rotation, and a second relatively stable orientation nearly" +about of which is in excess to the positrons expected [rom secondary production in cosmic-ray interactions.,about of which is in excess to the positrons expected from secondary production in cosmic-ray interactions. + The total electron spectrum has not been determined with PAMELA vel. but we may use the excellent Fermi-LAT data that between 20 GeV and | TeV are well represented by a single power law (Abdoetal.2009) Combining Eqs.," The total electron spectrum has not been determined with PAMELA yet, but we may use the excellent Fermi-LAT data that between 20 GeV and 1 TeV are well represented by a single power law \citep{lat-dat} + Combining Eqs." + 4 and 5 we find the positron density al 82 GeV as The positron excess over ordinary secondary production is measured (ο be only about 0.03 at 1T GeV. thus indicating that the excess component has a spectrum nol significantly softer than E7.," \ref{eq3} and \ref{eq4} we find the positron density at 82 GeV as The positron excess over ordinary secondary production is measured to be only about 0.03 at 17 GeV, thus indicating that the excess component has a spectrum not significantly softer than $E^{-2}$." + Equation 1 indicates that this requires the injection of electron and positrons will a (vpical energv above 80 GeV. For simplicitv we assume the injection of monoenergetic electrons. where FEX.900 GeV. to avoid a spectral feature in the total electron. spectrum. which would be in conflict with the power-law fit to the Fermi data.," Equation \ref{eq1} indicates that this requires the injection of electron and positrons with a typical energy above 80 GeV. For simplicity we assume the injection of monoenergetic electrons, where $E_{\rm max}\lesssim 500$ GeV to avoid a spectral feature in the total electron spectrum, which would be in conflict with the power-law fit to the Fermi data." + We shall see that the s-rav limits ealeulated below provide much tighter constraints on £4; , We shall see that the $\gamma$ -ray limits calculated below provide much tighter constraints on $E_{\rm max}$. +Assuming an equal nunmber of excess electrons aud positrons. we therefore estimate the total differential density ol electrons/positrons that may come from cark-matter decay as In Figure 1 we demonstrate that the sum of this modeled dark-anatler decay component and (he expected contribution of secondary. positron. production provides a good fit to the PAMELA data.," Assuming an equal number of excess electrons and positrons, we therefore estimate the total differential density of electrons/positrons that may come from dark-matter decay as In Figure \ref{fig2} we demonstrate that the sum of this modeled dark-matter decay component and the expected contribution of secondary positron production provides a good fit to the PAMELA data." + For comparison. the figure also displavs the positron fraction lor the case of a Mat injection spectrum. which mar result [rom the decay of an intermediate particle with high kinetic energy.," For comparison, the figure also displays the positron fraction for the case of a flat injection spectrum, which may result from the decay of an intermediate particle with high kinetic energy." +"metallicity it is necessary to remove the T,;; and log y dependence.",metallicity it is necessary to remove the $_{eff}$ and log $g$ dependence. +" Armandroff&DaCosta and Olszewskietal.(1991). demonstrated Chat the cluster stars deline a sequence in the XC'« plane. using lunminositwv measures [rom indicators like M, or ug)."," \citet{adc91} and \citet{ol91} demonstrated that the cluster stars define a sequence in the $\Sigma Ca$ plane, using luminosity measures from indicators like $_I$ or $_{HB}$ )." + These sequences are separated as a Iunction of the cluster metallicity., These sequences are separated as a function of the cluster metallicity. +" The theoretical explanation of (his can be found in Pontetal.(2004).. using Jorgensenetal.(1992) models. which describe the behaviour of the CaT Ines as a function of T,jj. log g and metallicity,"," The theoretical explanation of this can be found in \citet{pont04}, using \citet{jcj92} models, which describe the behaviour of the CaT lines as a function of $_{eff}$, log $g$ and metallicity." + It is necessary to study the morphology. of the sequence defined by each cluster in the “Ca plane., It is necessary to study the morphology of the sequence defined by each cluster in the $\Sigma Ca$ plane. +" From a theoretical point of view. the increment of luminosity along the RGB comes with a drop in T,;; and log g that decreases ancl increases the strength of the lines. respectively,"," From a theoretical point of view, the increment of luminosity along the RGB comes with a drop in $_{eff}$ and log $g$ that decreases and increases the strength of the lines, respectively." +" The result is a modest increment in “Ce with Iuminosity (0OMCaf0M,; ~0.5)."," The result is a modest increment in $\Sigma Ca$ with luminosity $\delta\Sigma Ca/\delta +M_I\sim$ 0.5)." + Moreover. the models predict that Ca increases more rapidly with Inminosity in the upper part of the RGB (above the HB) than in the lower part.," Moreover, the models predict that $\Sigma Ca$ increases more rapidly with luminosity in the upper part of the RGB (above the HB) than in the lower part." + In other words. the sequence defined by each cluster might not be linear and might be best described adding a quadratic component.," In other words, the sequence defined by each cluster might not be linear and might be best described adding a quadratic component." + The Jorgensenetal.(1992) models also predict that “Ca increases more rapidly when log g decreases. or when (he Iuminositv increases. for (the more nelal-rich clusters than for the more metal-poor ones.," The \citet{jcj92} models also predict that $\Sigma Ca$ increases more rapidly when log $g$ decreases, or when the luminosity increases, for the more metal-rich clusters than for the more metal-poor ones." + Therefore. the linear ancl quaclratic terms. which characterize the sequence defimed for each cluster in the XC'« plane. increase wilh metallicity. as can be seen in Figure 15 of Pontetal.(2004)..," Therefore, the linear and quadratic terms, which characterize the sequence defined for each cluster in the $\Sigma Ca$ plane, increase with metallicity, as can be seen in Figure 15 of \citet{pont04}." + Observationallv. the variation in XCa with metallicity has traditionally been studied rom (V-Vjg5). which removes any dependence on distance and reddening (e.g.ArmanclrollCosta1991:Rutledgeetal.1997a:Cole 2004).," Observationally, the variation in $\Sigma Ca$ with metallicity has traditionally been studied from $_{HB}$ ), which removes any dependence on distance and reddening \citep[e.g.][]{adc91,r97a,c04}." +. In this context. it is found that clusters define linear sequences in the (V-Vjj5) “Ca plane. where the reduced equivalent width. W. is defined as Ca= ον) μη). Rutledg," In this context, it is found that clusters define linear sequences in the $_{HB}$ $\Sigma Ca$ plane, where the reduced equivalent width, $W'$, is defined as $\Sigma +Ca=W'_{HB}$ $\beta$ $_{HB}$ )." +eetal.(19972). found that the slopes ol these sequences were the same for all clusters in (heir sample. independently of (heir metallicity.," \citet{r97a} found that the slopes of these sequences were the same for all clusters in their sample, independently of their metallicity." +" Therefore only W7,5 changes from one cluster to another. and its variation is directly related to metallicity."," Therefore only $W'_{HB}$ changes from one cluster to another, and its variation is directly related to metallicity." + Other studies have reached (he same conclusion using open and globular clusters (e.g.Olszewskietal.1991)., Other studies have reached the same conclusion using open and globular clusters \citep[e.g.][]{ol91}. +. Pontetal.(2004). (seealso&DaCosta1991). have demonstrated that this also occius in the λοςa ancl Mj-MC'a planes.," \citet{pont04} \citep[see +also][]{adc91} have demonstrated that this also occurs in the $_V$ $\Sigma Ca$ and $_I$ $\Sigma Ca$ planes." + However. no studies have observed the theoretical predictions that cluster sequences are not exactly linear with huninositw. or that their shape depends on metallicity.," However, no studies have observed the theoretical predictions that cluster sequences are not exactly linear with luminosity, or that their shape depends on metallicity." + The main objective of this study is to apply the relationships obtained to derive metallicities of individual stars in Local Group galaxies. which in general have had multiple star formation epochs and do not always have a well defined IIB (e.g. LMC: Carrera et al.," The main objective of this study is to apply the relationships obtained to derive metallicities of individual stars in Local Group galaxies, which in general have had multiple star formation epochs and do not always have a well defined HB (e.g. LMC: Carrera et al." + 2007: SAIC: Noell et al., 2007; SMC: Noëll et al. + 2007: Leo A: Cole et al., 2007; Leo A: Cole et al. + 2007)., 2007). + For example. the \lagellanie Clouds do not have a measurable ILD in the CMD. and in studies which deline the reduced equivalent width as a function of (V—Vays) ((e.g.Coleetal. 2005))). the IIB position has been taken as that of," For example, the Magellanic Clouds do not have a measurable HB in the CMD, and in studies which define the reduced equivalent width as a function of $(V-V_{HB})$ \citep[e.g.][]{c05}) ), the HB position has been taken as that of" +long-term radioactive nuclei are also included.,long-term radioactive nuclei are also included. +" Together with the consideration of recoiling target particles, this leads to a significant broadening of the lines."," Together with the consideration of recoiling target particles, this leads to a significant broadening of the lines." +" Although some nonthermal emission is associated with the forward shock, recent studies showed that electron acceleration to multi-TeV energies is likely to take place mainly at the reverse shock within the supernova ejecta (?),, making Cas A to a unique object for studying particle acceleration at the reverse-shock side."," Although some nonthermal emission is associated with the forward shock, recent studies showed that electron acceleration to multi-TeV energies is likely to take place mainly at the reverse shock within the supernova ejecta \citep{Helder2008}, making Cas A to a unique object for studying particle acceleration at the reverse-shock side." + The resulting spectrum is depicted in Fig., The resulting spectrum is depicted in Fig. + [I] and agrees well with the approximate calculation above., \ref{fig:1} and agrees well with the approximate calculation above. +" As can be seen in Fig. [I],"," As can be seen in Fig. \ref{fig:1}," + the adopted acceleration scenario for cosmic rays in Cas A leads to a flux of nuclear lines that would be clearly detectable by a gamma- telescope with enhanced sensitivity as sucessor to the COMPTEL mission (e.g.theproposedGRIPSmissionby?)..," the adopted acceleration scenario for cosmic rays in Cas A leads to a flux of nuclear de-excitation lines that would be clearly detectable by a gamma-ray telescope with enhanced sensitivity as sucessor to the COMPTEL mission \citep[e.g. the proposed GRIPS mission +by][]{Greiner2009}." + The line emissivity is additionally boosted because the thermal target gas reflects the heavily enriched abundances of the Wolf-Rayet progenitor star., The line emissivity is additionally boosted because the thermal target gas reflects the heavily enriched abundances of the Wolf-Rayet progenitor star. +" Though the detailed line characteristics always depend on the precise knowledge of the supernova ejecta's composition, the natural process of element synthesis in the progenitor star and the supernova explosion mechanisms lead to peculiar properties in the gamma-ray spectrum."," Though the detailed line characteristics always depend on the precise knowledge of the supernova ejecta's composition, the natural process of element synthesis in the progenitor star and the supernova explosion mechanisms lead to peculiar properties in the gamma-ray spectrum." + A unique feature arises because the C and O lines in the 4—6MeV band dominate the line flux from the Ne-Fe group in the 1—3MeV band.," A unique feature arises because the C and O lines in the $4-6\, \mathrm{MeV}$ band dominate the line flux from the Ne-Fe group in the $1-3\, \mathrm{MeV}$ band." +" Of course, the reasonability of extrapolating the proton spectrum obtained from high-energy measurements"," Of course, the reasonability of extrapolating the proton spectrum obtained from high-energy measurements" +In the end. the observations presented here represent another test passed byACDM.. and place the Local Group firmly in the cosmological context of the local universe.,"In the end, the observations presented here represent another test passed by, and place the Local Group firmly in the cosmological context of the local universe." + They do. however. beg some questions.," They do, however, beg some questions." + First. at what scale. if any. do the standard abundance matching assumptions break down?," First, at what scale, if any, do the standard abundance matching assumptions break down?" + This work shows that it is successful for eas=95laus '. while the results of ? suggest problems with MW satellites for e~50Xm+.," This work shows that it is successful for $v_{\rm max} \gtrsim 95 \; \kms$ , while the results of \citet{bk11toobigtofail} suggest problems with MW satellites for $v_{\rm max} \sim 50 \; \kms$." + This implies there may be a break down scalesomewhere in the range 50.2.16: Pentericci et 11997): 02001015 (2= 3: Jarvis et al.," All the radio-loud objects with two-dimensional $\alpha$ images showing substantial asymmetries of whichwe are aware are, in order of increasing distance: 3C 294 $z = 1.82$; McCarthy et 1990); 3C 326.1 $z = 1.82$; McCarthy et 1987); $-$ 262 $z=2.16$; Pentericci et 1997); $+$ 015 $z=2.23$ ; Jarvis et al." + 2003) 52) 124: (2=PAT: Gopal-Ixrishna. ct 11995): D3 J2330| 3927 (2=3.09: Pérrez-Vorres et 22006): AIRC 257 (s=3.19: Venemans ct 22005): 6€ | 39 (2=3.22: Eales ct 11993): | 036 (2=3.57: van Oijk et 11996): 4€ 41.17 (2=3.80: Chambers. Miley van Dreugel 1990): and SC | 635 (2=4.26: Spinrad. Dev Graham 1995).," 2003) $+$ 124; $z=2.47$; Gopal-Krishna et 1995); B3 $+$ 3927 $z=3.09$; Pérrez-Torres et 2006); MRC $-$ 257 $z=3.13$; Venemans et 2005); 6C $+$ 39 $z=3.22$; Eales et 1993); $+$ 036 $z=3.57$; van Oijk et 1996); 4C 41.17 $z=3.80$; Chambers, Miley van Breugel 1990); and 8C $+$ 635 $z=4.26$; Spinrad, Dey Graham 1995)." + For six of the seven RGs from this list for which the orientation of the radio lobes can be determined. he Lye asvmnmetry is in the sense that stronger emission is seen from the side of the approaching lobe.," For six of the seven RGs from this list for which the orientation of the radio lobes can be determined, the $\alpha$ asymmetry is in the sense that stronger emission is seen from the side of the approaching lobe." + Thus. the most ikely explanation is that the Lye photons coming from the zwther side of the active nucleus are being obscurecl by a arge eas disk around the parent galaxy. (CNW00).," Thus, the most likely explanation is that the $\alpha$ photons coming from the farther side of the active nucleus are being obscured by a large gas disk around the parent galaxy (GKW00)." + Levine CGnedin (2005) have recently. modelled: expansion of hot thermal wind outllowing from an AGN., Levine Gnedin (2005) have recently modelled expansion of hot thermal wind outflowing from an AGN. + In this scenario they combine cosmological simulations with an AGN luminosity funetion ancl place the AGN at local LAL density. peaks., In this scenario they combine cosmological simulations with an AGN luminosity function and place the AGN at local IGM density peaks. + “Phev find that large portions of the LAL can be filled with such outllows unless kinetic luminosities are «LOM of the bolometric luminosities., They find that large portions of the IGM can be filled with such outflows unless kinetic luminosities are $< 10\%$ of the bolometric luminosities. + This remarkable conclusion is similar to that reached by. Furlanetto Loeb (2001) for similar spherical outllows and by Copal-Ixrishna Wiita (2001) anc Ixronberg et. ((2001) [or outllows in the form of relativistic jets BBarai Wiita 2007)., This remarkable conclusion is similar to that reached by Furlanetto Loeb (2001) for similar spherical outflows and by Gopal-Krishna Wiita (2001) and Kronberg et (2001) for outflows in the form of relativistic jets Barai Wiita 2007). + Therefore. the impact of AGNs on the formation of structure in the universe may be quite significant. bv trigecring/accelerating global star formation in a multiphase intergalactic medium (e.g. De Young 1989: Rees 1950: Choskhi 1997: Gopal-Ixrishna Wiita 2001: Gopal-IExrishna. Wiita Osterman 2003: Silk 2005: Barai Wiita 2006. 2007) or inhibiting it in the case ofa single-phase IM («NTIn] Rawlings Jarvis 2004: Scannapieco. Silk DBouwens 20)5)," Therefore, the impact of AGNs on the formation of structure in the universe may be quite significant, by triggering/accelerating global star formation in a multiphase intergalactic medium (e.g., De Young 1989; Rees 1989; Choskhi 1997; Gopal-Krishna Wiita 2001; Gopal-Krishna, Wiita Osterman 2003; Silk 2005; Barai Wiita 2006, 2007) or inhibiting it in the case of a single-phase IGM (e.g., Rawlings Jarvis 2004; Scannapieco, Silk Bouwens 2005)." + The role of large radio lobes in spreading magnetic fields (Ixronberg et 22001: Ciopal-INrishna Wiita 2001: Gopal-Ixrishna et 22003: Barai et 22004) and in distributing metals (Ciopal-Ixrishna Wiita 2003: Gopal-Ixrishna. Wiita Barai 2004) through the IGM may also be very significant.," The role of large radio lobes in spreading magnetic fields (Kronberg et 2001; Gopal-Krishna Wiita 2001; Gopal-Krishna et 2003; Barai et 2004) and in distributing metals (Gopal-Krishna Wiita 2003; Gopal-Krishna, Wiita Barai 2004) through the IGM may also be very significant." + The Levine Cnedin (2005. hereafter LO) mocel builds upon that of Scannapieco Oh (2004. hereafter SO) and we shall employ. results from cach of these papers in the following.," The Levine Gnedin (2005, hereafter LG) model builds upon that of Scannapieco Oh (2004, hereafter SO) and we shall employ results from each of these papers in the following." +" Assume that the AGN injects thermal wind with kinetic energv f,ταις Where bylcoLi4) is the kinetic luminosity. z ds the time the AGN is active in this mode anc Lia. the bolometric luminosity. is a measure of the acerction power."," Assume that the AGN injects thermal wind with kinetic energy $E_w = L_w \tau_{\rm act}$, where $L_w (\equiv \epsilon_w L_{bol})$ is the kinetic luminosity, $\tau_{\rm act}$ is the time the AGN is active in this mode and $L_{\rm bol}$, the bolometric luminosity, is a measure of the accretion power." +" Then. if 9,, is the mean relative overdensity in the environment in which the ACN is situated (assumed to be constant over the relevant volume) then the racius of the (spherical) bubble inflated. for a time §>Tye will be (LO) where Lago=LyflO’ere. 2 is the redshift and. /o is the time since the active phase began. in units of Car."," Then, if $\delta_m$ is the mean relative overdensity in the environment in which the AGN is situated (assumed to be constant over the relevant volume) then the radius of the (spherical) bubble inflated, for a time $t > \tau_{\rm act}$ will be (LG) where $E_{w,60} = E_w/10^{60}{\rm erg}$, $z$ is the redshift and $t_{9}$ is the time since the active phase began, in units of Gyr." +" The bubble should. grow according to ((1) until it reaches pressure equilibrium with the ambient environment. at which point the size of the bubble would be (LC) where the external thermal pressure due to the LAL. P=(1|0,JanketT: hore its mean barvon density. ni=33.10(1)z)*em. . and the tvpical IGM temperature. which is taken to be constant with epoch. is Z21.5.loth (LO)."," The bubble should grow according to (1) until it reaches pressure equilibrium with the ambient environment, at which point the size of the bubble would be (LG) where the external thermal pressure due to the IGM, $P = (1+\delta_m) n_b k_B T$; here its mean baryon density, $n_b = +3.3\times 10^{-7}(1+z)^3~{\rm cm}^{-3}$ , and the typical IGM temperature, which is taken to be constant with epoch, is $T \simeq 1.5 \times 10^4$ K (LG)." + We note that it might be more appropriate to allow for the average LGAL temperature to increase as 2 decreases (Cen Ostriker 1909). but including this ellect does not make significant changes in our argument. whereas considering expansion into à much hotter and significantly denser ICM would do so. in that the radii out to which the bubbles would expand. supersonically would be much smaller (e.g. Sternberg et 22007).," We note that it might be more appropriate to allow for the average IGM temperature to increase as $z$ decreases (Cen Ostriker 1999), but including this effect does not make significant changes in our argument, whereas considering expansion into a much hotter and significantly denser ICM would do so, in that the radii out to which the bubbles would expand supersonically would be much smaller (e.g., Sternberg et 2007)." + Attimes after the wind energy has been completely injected. the velocity of the bubbles expansion is given by (SO) where Rsate is Ws in units of Alpe.," Attimes after the wind energy has been completely injected, the velocity of the bubble's expansion is given by (SO) where $R_{S,{\rm Mpc}}$ is $R_S$ in units of Mpc." + This result assumes that za is short compared the cooling time for the hot gas in the bubble so that radiative losses can be ignored: in addition. 2dV work and the work done against the galaxys gravity can also be ignored (SO. LC).," This result assumes that $\tau_{\rm act}$ is short compared the cooling time for the hot gas in the bubble so that radiative losses can be ignored; in addition, $PdV$ work and the work done against the galaxy's gravity can also be ignored (SO, LG)." + These are all plausible approximations (e.g.. Purlanetto Loeb 2001).," These are all plausible approximations (e.g., Furlanetto Loeb 2001)." + The final approximation involved in these formulae is that the inertia of the displaced. galactic LSAT is less than that of the IGM. which will be reasonable once Ls exceeds about 10 kpe.," The final approximation involved in these formulae is that the inertia of the displaced galactic ISM is less than that of the IGM, which will be reasonable once $R_S$ exceeds about 10 kpc." +" We find that the corresponding equation for earlier limes. f>1."," In the present work, we propose to explore in detail the generalization of this type of instability to the ultra-relativistic regime $\Gamma_{\rm sh}\,\gg\,1$." + One crucial difference with the previous works on the streaming instability is that we consider the most natural ease of superluminal shock waves (with a magnetic field perpendicular to the shock normal in the shock front frame)., One crucial difference with the previous works on the streaming instability is that we consider the most natural case of superluminal shock waves (with a magnetic field perpendicular to the shock normal in the shock front frame). + This case is more generic than the parallel configuration studied previously because the transverse component of the magnetic field is boosted by the shock Lorentz factor when going to the shock frame., This case is more generic than the parallel configuration studied previously because the transverse component of the magnetic field is boosted by the shock Lorentz factor when going to the shock frame. + Another important difference is that we bring to light a new type of instability. of a compressive nature.," Another important difference is that we bring to light a new type of instability, of a compressive nature." + Finally. in contrast with most particle-in-cell simulations performed to date. our study focusses on magnetized shock waves. for which there exists a coherent upstream magnetic field (whose dynamical influence on the shock jump conditions can be neglected however).," Finally, in contrast with most particle-in-cell simulations performed to date, our study focusses on magnetized shock waves, for which there exists a coherent upstream magnetic field (whose dynamical influence on the shock jump conditions can be neglected however)." + Nevertheless there exist pioneering PIC simulations in the moderately relativistic regime. which include both a mean field and a significant mass ratio between electrons and ions. see Hededal Nishikawa (2005). Dieckmann. Shukla. Drury (2008).," Nevertheless there exist pioneering PIC simulations in the moderately relativistic regime, which include both a mean field and a significant mass ratio between electrons and ions, see Hededal Nishikawa (2005), Dieckmann, Shukla, Drury (2008)." +" We adopt a simplitied description in which the cosmic-ray ""istribution is modeled as a step function out to some distance f and we neglect the cosmic-ray response to the disturbance.", We adopt a simplified description in which the cosmic-ray distribution is modeled as a step function out to some distance $\ell_{\rm cr}$ and we neglect the cosmic-ray response to the disturbance. + This latter assumption is justified by the fact that the instability is maximal on the shortest spatial scales. orders of magnitude below the typical Larmor radius of accelerated particles.," This latter assumption is justified by the fact that the instability is maximal on the shortest spatial scales, orders of magnitude below the typical Larmor radius of accelerated particles." + The paper is organized as follows., The paper is organized as follows. + In Section ??.. we introduce the main scales of the problem. most notably the diffusion scale of the cosmie rays: we then calculate the level of amplification that is necessary to make Fermi acceleration operative.," In Section \ref{sec:general}, we introduce the main scales of the problem, most notably the diffusion scale of the cosmic rays; we then calculate the level of amplification that is necessary to make Fermi acceleration operative." + Section ?? is devoted to the investigation of the instabilities under. the condition that some cosmic-rays have undergone a first Fermi cycle., Section \ref{sec:instab} is devoted to the investigation of the instabilities under the condition that some cosmic-rays have undergone a first Fermi cycle. + Section ?? summarizes out results and provides some outlook., Section \ref{sec:conc} summarizes out results and provides some outlook. + Details of the ealeulations are provided in Appendix ??.., Details of the calculations are provided in Appendix \ref{sec:appperp}. + We carry out most of the discussion in the shock front rest frame. hence unless otherwise noted. all quantities are evaluated in this frame.," We carry out most of the discussion in the shock front rest frame, hence unless otherwise noted, all quantities are evaluated in this frame." + We use the subscripts jy or jy to tag quantities measured in the upstream or in the downstream rest frame respectively., We use the subscripts $_{\rm\vert u}$ or $_{\rm\vert d}$ to tag quantities measured in the upstream or in the downstream rest frame respectively. +" In the upstream rest frame. cosmic rays can never stream too far ahead of a relativistic shock wave since this latter propagates towards upstream with velocity ry=Byec [the shock Lorentz factor Py,=(1—B)Ux»1]."," In the upstream rest frame, cosmic rays can never stream too far ahead of a relativistic shock wave since this latter propagates towards upstream with velocity $v_{\rm sh}=\beta_{\rm sh}c\approx c$ [the shock Lorentz factor $\Gamma_{\rm sh} \equiv (1-\beta_{\rm + sh}^2)^{-1/2}\,\gg\,1$ ]." +" Cosmic rays scatter on magnetic turbulence upstream before they are caught back by the shock wave when their pitch angle 4,Εν (Gallant Achterberg 1999, Achterberg 2001)."," Cosmic rays scatter on magnetic turbulence upstream before they are caught back by the shock wave when their pitch angle $\theta_{\rm\vert u} \sim 1/\Gamma_{\rm sh}$ (Gallant Achterberg 1999, Achterberg 2001)." +" Consequently. they can travel a distance Coy. Which may take the following values depending on the ratio of the Larmor radius rij, to the coherence length of the upstream magnetic field vty (Milosavljevic Nakar 2006): Both regimes. short or large scale turbulence can be expected at some point. insofar as the excitation of the upstream magnetic field on short spatial scales is due to the streaming of the non- particle population in the shock precursor."," Consequently, they can travel a distance $\ell_{\rm cr\vert + u}$, which may take the following values depending on the ratio of the Larmor radius $r_{\rm L\vert u}$ to the coherence length of the upstream magnetic field $\lambda_{\rm c\vert u}$ (Milosavljević Nakar 2006): Both regimes, short or large scale turbulence can be expected at some point, insofar as the excitation of the upstream magnetic field on short spatial scales is due to the streaming of the non-thermal particle population in the shock precursor." + Indeed. cosmic rays of the first generation are to interact with a turbulent magnetic field ordered on large scales.," Indeed, cosmic rays of the first generation are to interact with a turbulent magnetic field ordered on large scales." + However. provided the instability that they trigger grows fast enough. cosmic rays of the next generation will propagate in short scale turbulence.," However, provided the instability that they trigger grows fast enough, cosmic rays of the next generation will propagate in short scale turbulence." + In reality. the situation is likely to be more complex as the process of particle propagation upstream and magnetic field generation are closely intertwined.," In reality, the situation is likely to be more complex as the process of particle propagation upstream and magnetic field generation are closely intertwined." + The fact that the non-thermal population contains particles of ditferent energies. which can stream at ditferent distances from the shock front. should also play a significant role.," The fact that the non-thermal population contains particles of different energies, which can stream at different distances from the shock front, should also play a significant role." + In this respect. Keshet (2008) have observed that the upstream magnetic field is atfected to greater distances as time goes on.," In this respect, Keshet (2008) have observed that the upstream magnetic field is affected to greater distances as time goes on." + This strongly suggests that higher energy cosmic rays are produced as time goes on. and that. by travelling farther in the upstream medium. they excite the turbulence at larger distances from the shock front.," This strongly suggests that higher energy cosmic rays are produced as time goes on, and that, by travelling farther in the upstream medium, they excite the turbulence at larger distances from the shock front." + In the discussion that follows. we estimate the growth of unstable modes in both the limits of small or large scale turbulence in order to remain as general as possible.," In the discussion that follows, we estimate the growth of unstable modes in both the limits of small or large scale turbulence in order to remain as general as possible." + Certainly the limit of large scale turbulence is more restrictive with respect to the growth of the instability. since the distance travelled upstream is significantly reduced with respect to that in small scale turbulence.," Certainly the limit of large scale turbulence is more restrictive with respect to the growth of the instability, since the distance travelled upstream is significantly reduced with respect to that in small scale turbulence." + Whichever limit prevails depends on the ratio of the short scale turbulent to the large scale (coherent) magnetic field strength. as discussed in Section ??..," Whichever limit prevails depends on the ratio of the short scale turbulent to the large scale (coherent) magnetic field strength, as discussed in Section \ref{sec:fermi}." + We also discuss the effect of higher energy cosmic rays on the growth rate., We also discuss the effect of higher energy cosmic rays on the growth rate. +" It is important to emphasize that the distance that controls the growth ofthe instability is that between the shock front and the position of theparticle. which is smaller than fay by a factor O-BaQr)"" "," It is important to emphasize that the distance that controls the growth ofthe instability is that between the shock front and the position of theparticle, which is smaller than $\ell_{\rm cr\vert u}$ by a factor $(1-\beta_{\rm sh})\sim \left(2\Gamma_{\rm + sh}^2\right)^{-1}$." +In the following. we will need the expression for Copy (also noted £4). Le. the length scale of the cosmic-ray distribution as measured in the shock front rest frame.," In the following, we will need the expression for $\ell_{\rm cr\vert sh}$ (also noted $\ell_{\rm cr}$ ), i.e. the length scale of the cosmic-ray distribution as measured in the shock front rest frame." +" It can be calculated by transforming the upstream residence time Cay/c in the shock front frame £44,=fy/Pyy. and then by rewriting in the expression obtained the upstream Larmor radius and coherence length in terms of their shock frame equivalent."," It can be calculated by transforming the upstream residence time $t_{\rm r\vert u}\,\simeq\,\ell_{\rm cr\vert u}/c$ in the shock front frame $t_{\rm r\vert sh}=t_{\rm r\vert u}/\Gamma_{\rm + sh}$, and then by rewriting in the expression obtained the upstream Larmor radius and coherence length in terms of their shock frame equivalent." + In the perpendicular tor superluminal and ultra-relativistic) configuration of interest. ria5 ΕΠ. AaD das," In the perpendicular (or superluminal and ultra-relativistic) configuration of interest, $r_{\rm L\vert + sh}\,\simeq\, \Gamma_{\rm sh}^{-2} r_{\rm L\vert u}$ , $\lambda_{\rm + c\vert sh}\,\simeq\, \Gamma_{\rm sh}^{-1} \lambda_{\rm c\vert + u}$ ." + This boost of the coherence length is valid for wavenumber modes that are parallel, This boost of the coherence length is valid for wavenumber modes that are parallel +code (Nenkovaetal.1999). adopting optical constants from Ordaletal.(LOSS) for metallic iron. Draine for amorphous silicates. DBegemannctal.(1997) for amorphous alumina and Henningetal.(1995) for FeO. We assume the dust consists of solid spheres. whileerain size populations follow the distribution of Mathisetal. (1971).,"code \citep{NIE99}, adopting optical constants from \citet{OBA+88} for metallic iron, \citet{DL84} for amorphous silicates, \citet{BDH+97} for amorphous alumina and \citet{HBMD95} for FeO. We assume the dust consists of solid spheres, whilegrain size populations follow the distribution of \citet{MRN77}." +. We further assume that. since the optical depth is low. the wind density follows s numerical solution for racliativelv-driven winds (density type = 3).," We further assume that, since the optical depth is low, the wind density follows 's numerical solution for radiatively-driven winds (density type = 3)." + X stellar atmosphere model was used for the underlving photosphere., A stellar atmosphere model was used for the underlying photosphere. + This was interpolatecl from the grid. used bv MvVLD using 10 temperature ancl metallicity listed in Table 1.., This was interpolated from the grid used by MvLD using the temperature and metallicity listed in Table \ref{SourcesTable}. + Dillerences exist between the absolute flux calibration of the photometry in the literature (including IILACZMIDPS 24-/m fluxes from AIVLD) and the HUS spectra., Differences exist between the absolute flux calibration of the photometry in the literature (including IRAC/MIPS $\mu$ m fluxes from MvLD) and the IRS spectra. + In eeneral. the IRS spectra are brighter than the IRACYAILPS photometry.," In general, the IRS spectra are brighter than the IRAC/MIPS photometry." + This can occur duc to source blending. and hence light from other sources entering rw IRS gmodule. or from. intrinsic. luminosity variations such as stellar. pulsation.," This can occur due to source blending, and hence light from other sources entering the IRS module, or from intrinsic luminosity variations such as stellar pulsation." + In the latter case. phase-corrected photomoetry can be used to eliminate this problem. but this cannot be done for irregular variables and/or those with unknown infrared. pulsation amplitudes without contemporaneous infrared. photometry.," In the latter case, phase-corrected photometry can be used to eliminate this problem, but this cannot be done for irregular variables and/or those with unknown infrared pulsation amplitudes without contemporaneous infrared photometry." + Ehese mean that it can be dillicult to determine whether an infrared. excess is attributable to dust. or is an artifact.," These mean that it can be difficult to determine whether an infrared excess is attributable to dust, or is an artifact." + Source blending can usually be identified by an olfset between the SL anc LL components of the spectra. which observe different angular areas.," Source blending can usually be identified by an offset between the SL and LL components of the spectra, which observe different angular areas." + The clillerence between the SL and LL fluxes can be used to approximate the photometric uncertainty: tvpically54... and <17% in all cases.," The difference between the SL and LL fluxes can be used to approximate the photometric uncertainty: typically, and $\lesssim$ in all cases." + Stellar pulsation. however. is more dillieult to remove. especially in cases where pulsation periods are uncertain and/or variable.," Stellar pulsation, however, is more difficult to remove, especially in cases where pulsation periods are uncertain and/or variable." + While the typical cllect on infrared photometry may only be a few percent. strongly pulsating stars can vary by several tens of percent (sec. o.g.. re[V6Sect)). rendering the existence of an apparent small Sym excess dn the sinele-epoch photometry meaningless.," While the typical effect on infrared photometry may only be a few percent, strongly pulsating stars can vary by several tens of percent (see, e.g., ), rendering the existence of an apparent small $\mu$ m excess in the single-epoch photometry meaningless." + To complicate matters further. absorption or emission rom the extended molecular atmosphere can also increase à star's infrared πας.," To complicate matters further, absorption or emission from the extended molecular atmosphere can also increase a star's infrared flux." + The ollending molecules in this case are wedominantly. H2O0 and SiO. SiO produces an absorption ixd at S fim. which is included in the mocels. but he modelled. equivalent width may. vary from those of the stars themselves.," The offending molecules in this case are predominantly $_2$ O and SiO. SiO produces an absorption band at 8 $\mu$ m, which is included in the models, but the modelled equivalent width may vary from those of the stars themselves." + We expect this may alter the S-jm {lux in he region of £24 (a similar amplitude to the photometric error). but will have negligible cllect on the continuum xdacement or the determination of the dust. fraction.," We expect this may alter the $\mu$ m flux in the region of $\pm$ (a similar amplitude to the photometric error), but will have negligible effect on the continuum placement or the determination of the dust fraction." + Conversely. H2O can provide absorption or emission hroughout the spectrum and may allect. to some ceeree. he continuum placement and hence the amount and composition of dust.," Conversely, $_2$ O can provide absorption or emission throughout the spectrum and may affect, to some degree, the continuum placement and hence the amount and composition of dust." + I£ this water [aver is optically thick at infrared wavelengths. this emission will tend to approximate a single blackbocdy.," If this water layer is optically thick at infrared wavelengths, this emission will tend to approximate a single blackbody." + This will multiplicativelvy. increase the RavieighJeans tail of the stellar. spectrum. resulting in an infrared. spectrum that has a roughly constant value of ME. but is above that expeeted ofthe stars photospheric emission.," This will multiplicatively increase the Rayleigh–Jeans tail of the stellar spectrum, resulting in an infrared spectrum that has a roughly constant value of $\lambda^2 F_\nu$, but is above that expected of the star's photospheric emission." + When this extended envelope expands and. forms opticallv-thin dust at larger radii. however. it will show a spectrum where ATE. increases with A.," When this extended envelope expands and forms optically-thin dust at larger radii, however, it will show a spectrum where $\lambda^2 F_\nu$ increases with $\lambda$." + This criterion can be used to identify cireumstellar dust. in more ambiguous Cases. and we only model stars where such a trend is clearly present.," This criterion can be used to identify circumstellar dust in more ambiguous cases, and we only model stars where such a trend is clearly present." + In the stars with weak metallic iron emission. there is thus a degencracy between emission. from. circumstellar water and emission from the metallic iron dust.," In the stars with weak metallic iron emission, there is thus a degeneracy between emission from circumstellar water and emission from the metallic iron dust." + We estimate this may alfeet our cust. production rates by a few 10.1 AL [LL, We estimate this may affect our dust production rates by a few $\times 10^{-11}$ $_\odot$ $^{-1}$. + Of the 14 targets observed. only LELD 33062. (V6) and 35250 (V17) show 10- and. I8-/n silicate dust. features (weakly in the latter: V6Sect)).," Of the 14 targets observed, only LEID 33062 (V6) and 35250 (V17) show 10- and $\mu$ m silicate dust features (weakly in the latter; \\ref{V6Sect}) )." + Several spectra vary as ἐν(X £70. suggesting," Several spectra vary as $F_\nu \propto \nu^{2}$ , suggesting" +this case. à density wave. which is the only mode in a 2D disc. is intluencecl by self-gravity and thus can become unstable. as the local dispersion relation for the latter clearly demonstrates (7?),"this case, a density wave, which is the only mode in a 2D disc, is influenced by self-gravity and thus can become unstable, as the local dispersion relation for the latter clearly demonstrates \citep{GT78,BT87,Bertetal89}." + Stability analysis in. a more realistic case of sel-eravitating three-cimensional (3D) clises ds. more complicated., Stability analysis in a more realistic case of self-gravitating three-dimensional (3D) discs is more complicated. + The disc is vertically stratified due to both its own self-eravity ancl the vertical component of. the eravity of a central object., The disc is vertically stratified due to both its own self-gravity and the vertical component of the gravity of a central object. + Depending on the nature of the stratification. there exists a whole new set of. various vertical modes in the system (see below). some of which can become unstable cue to sell-gravitv on horizonta length. scales comparable to the disc thickness.," Depending on the nature of the stratification, there exists a whole new set of various vertical modes in the system (see below), some of which can become unstable due to self-gravity on horizontal length scales comparable to the disc thickness." + Ln this situation. the vertical variation of perturbations is importan and for a correct characterization of the eravitationa instability it is necessary to introduce another parameter not involving height-cdependent variables. such as the sounc speed in Toomre's parameter.," In this situation, the vertical variation of perturbations is important and for a correct characterization of the gravitational instability it is necessary to introduce another parameter not involving height-dependent variables, such as the sound speed in Toomre's parameter." + Furthermore. not all tvpes of stratification permit two-dimensional modes. that is. modes with no vertical motions commonly occurring in the 2L treatment.," Furthermore, not all types of stratification permit two-dimensional modes, that is, modes with no vertical motions commonly occurring in the 2D treatment." + For example. in non-sell-gravitating discs with polvtropic vertical structure. there are no 2D modes (?77) implving that the dynamies does not always reduce to that of the 2D. case.," For example, in non-self-gravitating discs with polytropic vertical structure, there are no 2D modes \citep{LPS90,LP93a,KP95} implying that the dynamics does not always reduce to that of the 2D case." + Pherefore. a more accurate stability analysis of selil-gravitating clises should necessarily be three-dimensional.," Therefore, a more accurate stability analysis of self-gravitating discs should necessarily be three-dimensional." + Obviously. before studying the gravitational instability ol stratified. discs. one must first classify ancl characterize vertical normal modes of perturbations in the simplified case of no sell-gravitv.," Obviously, before studying the gravitational instability of stratified discs, one must first classify and characterize vertical normal modes of perturbations in the simplified case of no self-gravity." + Analysis of the modal structure of stratified. polvtropic. compressible. non-scll-eravitating clises has beendone in several papers: ?.hereafter.RPL.. 7.hereafter IKP.. ?..," Analysis of the modal structure of stratified, polytropic, compressible, non-self-gravitating discs has beendone in several papers: \citet[][hereafter RPL]{RPL88}, \citet[][hereafter KP]{KP95}, \citet{Og98}." + In convectively stable discs. ic. with subacdiabatic vertical stratification. four principal tvpes of vertical modes. can be distinguished.," In convectively stable discs, i.e., with subadiabatic vertical stratification, four principal types of vertical modes can be distinguished." + These. modes: are: acoustic p-modes. surface gravity. [-modes.. buovancy g-nmicdes and. inertial r-mocdes.," These modes are: acoustic p-modes, surface gravity f-modes, buoyancy g-modes and inertial r-modes." + “Phe modes are named. after heir corresponding restoring forces. which can be well identified for each mode at horizontal wavelengths smaller han the disc height and are provided. by one of the ollowing: compressibilitv/pressure. displacements of. [ree surfaces of a disc. buovancy due to vertical stratification and inertial forces due to disc rotation. respectively. for he p-. É. g- and r-modes.," The modes are named after their corresponding restoring forces, which can be well identified for each mode at horizontal wavelengths smaller than the disc height and are provided by one of the following: compressibility/pressure, displacements of free surfaces of a disc, buoyancy due to vertical stratification and inertial forces due to disc rotation, respectively, for the p-, f-, g- and r-modes." + In the case of superacdiabatic stratification. the r- and e-modes merge and appear as a single mode. which becomes convectively unstable [or iorizontal wavenumbers larger than a certain value (RPL): he p- and f-modes remain qualitatively unchanged.," In the case of superadiabatic stratification, the r- and g-modes merge and appear as a single mode, which becomes convectively unstable for horizontal wavenumbers larger than a certain value (RPL); the p- and f-modes remain qualitatively unchanged." + For neutral/adiabatic stratification. buovancy is absent and the e-mode disappears.," For neutral/adiabatic stratification, buoyancy is absent and the g-mode disappears." + So. the mode dynamics in the 3D case can appear more complex than that in the 2D one. where only the density wave mode can be subject to gravitational instability.," So, the mode dynamics in the 3D case can appear more complex than that in the 2D one, where only the density wave mode can be subject to gravitational instability." + Previously. 7.hereafterGLB considered. gravitational instability in a uniformly. rotating gaseous slab with an adiabatic vertical stratification. thereby leaving out all modes associated with buovanev.," Previously, \citet[][hereafter GLB]{GLB65a} considered gravitational instability in a uniformly rotating gaseous slab with an adiabatic vertical stratification, thereby leaving out all modes associated with buoyancy." + Other studies also considered. the gravitational instability of 3D ealactic disces. however. the analysis was essentially 2D. finite-thickness ellects were only taken into account by means of various reduction factors in. 2D dispersion relations οον.," Other studies also considered the gravitational instability of 3D galactic discs, however, the analysis was essentially 2D, finite-thickness effects were only taken into account by means of various reduction factors in 2D dispersion relations \citep{Shu68,Rom92,Rom94}." + In all these studies. as in GLB. the main focus was on finding the criterion flor the onset of gravitational instability. so that a Lull analysis of various types of vertical normal miocles existing in stratified self-eravitating cliscs was not carried out.," In all these studies, as in GLB, the main focus was on finding the criterion for the onset of gravitational instability, so that a full analysis of various types of vertical normal modes existing in stratified self-gravitating discs was not carried out." + Actually. we generalize the study of GLB to. subadiabatic ancl superadiabatic stratifications having cillercnt mocal structure.," Actually, we generalize the study of GLB to subadiabatic and superadiabatic stratifications having different modal structure." + Another motivation for our study is that the. [-mode is thought to plav an important dvnamical. role in self-egravitating discs., Another motivation for our study is that the f-mode is thought to play an important dynamical role in self-gravitating discs. + The non-linear. behaviour of 3D perturbations involving large surface distortions. as seen in numerical simulations. has been attributed to the surface eravity [mode (?). l," The non-linear behaviour of 3D perturbations involving large surface distortions, as seen in numerical simulations, has been attributed to the surface gravity f-mode \citep{Petal00}." +LHlowever. this was done without analvsing the behaviour of other vertical modes under eravity.," However, this was done without analysing the behaviour of other vertical modes under self-gravity." + Lt was shown that the [-moce leads to a large energy issipation in the vicinity of the disc surface. which may facilitate clise cooling. because the energy. is deposited at gamaller optical depth where it can be raciatecl away more uickly (seee...2?)..," It was shown that the f-mode leads to a large energy dissipation in the vicinity of the disc surface, which may facilitate disc cooling, because the energy is deposited at smaller optical depth where it can be radiated away more quickly \citep[see +e.g.,][]{JG03,Betal06}." + Later it was realized that in fact the non-linear vertical motions in self-gravitating discs can be much more complex than just the f-mode and can have a gajoCck character (shockbores.?)..," Later it was realized that in fact the non-linear vertical motions in self-gravitating discs can be much more complex than just the f-mode and can have a shock character \citep[shock bores,][]{BD06}." + Thus. in the 3D case. the cdvnanmies of self-gravitating discs is much richer and diverse than that of idealized 2D ones and requires farther study.," Thus, in the 3D case, the dynamics of self-gravitating discs is much richer and diverse than that of idealized 2D ones and requires further study." + To fully understand. the origin of such three-dimensional ellects. and. what tvpe of instability they are associated with. one should start with a rigorous linear study of the characteristic properties of all the tvpes of vertical normal modes mentioned above. not only the [-mocdoe. in the presence of sel(-eravityv.," To fully understand the origin of such three-dimensional effects and what type of instability they are associated with, one should start with a rigorous linear study of the characteristic properties of all the types of vertical normal modes mentioned above, not only the f-mode, in the presence of self-gravity." + The present work is just a first step in this direction., The present work is just a first step in this direction. + Numerical simulations of self-gravitating discs are often in the context. of global disces (e.g...2?7?7??777?7)— and. therefore. are not. always. able to well resolve vertical motions. which. as shown in the present. study. inevitably arise during the development of the gravitational instability associated with intrinsically three-climensional modes.," Numerical simulations of self-gravitating discs are often in the context of global discs \citep[e.g.,][]{Petal00,Petal03,Riceetal03,RLA05,LR04,LR05,Betal06,Bol09} + and, therefore, are not always able to well resolve vertical motions, which, as shown in the present study, inevitably arise during the development of the gravitational instability associated with intrinsically three-dimensional modes." + So. hese simulations mav not quite accurately capture all he subtleties of the gravitational instability in 3D clises.," So, these simulations may not quite accurately capture all the subtleties of the gravitational instability in 3D discs." + 1n this connection. we should mention the work by ? hat extensively discusses the issue of vertical resolution ancl its importance in the outcome of the gravitational instability in numerical simulations of scll-eravitation clises.," In this connection, we should mention the work by \citet{N06} that extensively discusses the issue of vertical resolution and its importance in the outcome of the gravitational instability in numerical simulations of self-gravitation discs." + tesolving and analysing vertical motions are also crucial or properly understanding cooling processes in cliscs and. particularly. whether convection is able to. provide sulliciently effective cooling for disc fragmentation to occur. which is still a matter for debate in the literature (72?7?)..," Resolving and analysing vertical motions are also crucial for properly understanding cooling processes in discs and, particularly, whether convection is able to provide sufficiently effective cooling for disc fragmentation to occur, which is still a matter for debate in the literature \citep{B04,Mayeretal07,Betal06,Betal07,Raf07}." +" In addition. these studies. for simplicity. use the criterion for gravitational instability based. on the two-dimensional '""Toomre's parameter. which. as we will demonstrate. cannot always be uniquely mapped. into an analogous threc- stability parameter ancl give a precise criterion for the onset of gravitational instability."," In addition, these studies, for simplicity, use the criterion for gravitational instability based on the two-dimensional Toomre's parameter, which, as we will demonstrate, cannot always be uniquely mapped into an analogous three-dimensional stability parameter and give a precise criterion for the onset of gravitational instability." + In this paper. following other works in a similar vein: ?.hereafter.LP... KP. 2.hereafter. LOOs.. we adopt the shearing box approximation and consider the linear dyvnamies of vertical normal modes of perturbations in a compressible. stratified. self-gravitating gaseous disc with," In this paper, following other works in a similar vein: \citet[][hereafter LP]{LP93a}, KP, \citet[][hereafter LO98]{LO98}, , we adopt the shearing box approximation and consider the linear dynamics of vertical normal modes of perturbations in a compressible, stratified, self-gravitating gaseous disc with" +jiostlv iuflowiug°.,mostly inflowing. +. The best fit found for N-ray bright ETGs is also shown in the left pauel (O'Sullivan ct al., The best fit found for X-ray bright ETGs is also shown in the left panel (O'Sullivan et al. + 2003). and gives a good represcutation of the distribution of observed T's down to a ranee of low teniperatures and gas contents never explored before.," 2003), and gives a good representation of the distribution of observed $T$ 's down to a range of low temperatures and gas contents never explored before." +" The slope of the ft (Pox of!) and that of the T,x602 relation. are sinular. with the fit beme shallower: this could be due to the fact that uot all heating sources depeud on 62. see. e... the portant SNIa’s contribution iu 75,;. that produces a mnch flatter run of T;,; with σι (Fig. 2))."," The slope of the fit $T\propto +\sigma_c^{1.79}$ ) and that of the $T_{\sigma }\propto \sigma_c^2$ relation are similar, with the fit being shallower; this could be due to the fact that not all heating sources depend on $\sigma_c^2$, see, e.g., the important SNIa's contribution in $T_{inj}$, that produces a much flatter run of $T_{inj}$ with $\sigma_c$ (Fig. \ref{f2}) )." +" The fit was mostly based on eas-rich ETCGs. whose 77s show a trend with o, closer to that of T5 (an aspect further addressed below iu Sects."," The fit was mostly based on gas-rich ETGs, whose $T$ 's show a trend with $\sigma_c$ closer to that of $T_{\sigma}$ (an aspect further addressed below in Sects." + 77. and ?7?7)). while gas-poor LICs depart most from it. since their 7s change little for largely. varving σι. (asx found by BIKE: see Sect.," \ref{gravhea} + and \ref{temp}) ), while gas-poor ETGs depart most from it, since their $T$ 's change little for largely varying $\sigma_c $ (as found by BKF; see Sect." + below)., \ref{reduc} below). + The right panel of Fig., The right panel of Fig. +" 2 shows the stellar temperature XOT.>. the injection temperature <—Tj,j;>. the escape temperature $, the injection temperature $$, the escape temperature $$ and the characteristic temperature for slowly outflowing gas $$ , calculated for a set of representative galaxy mass models (Sect. \ref{mass}) )." +" At any fixed o, aud Sérrsie iudex ». «T. and are larger for larger galaxy hass CR). and mass concentration (smaller 35."," At any fixed $\sigma _c$ and Sérrsic index $n$, $$, $$ and $$ are larger for larger galaxy mass ${\cal R}$ ), and mass concentration (smaller $\beta$." +" The dashed lines represent a reasonable upper limit to the values of cach of the characteristic temperatures. since hey correspond to the most massive model ETGs,. with he most concentrated dark matter allowed for by receut studies (Sect. ?7))."," The dashed lines represent a reasonable upper limit to the values of each of the characteristic temperatures, since they correspond to the most massive model ETGs, with the most concentrated dark matter allowed for by recent studies (Sect. \ref{mass}) )." +" The «T4.> curves lie below the shuple approximation of the escape temperature given NOI =LeaT.>. for Ro=3. aud c5,2«T. for the three cases with R=5."," The $$ curves lie below the simple approximation of the escape temperature given by $4T_{\sigma}$ ; $=4.8$, for ${\cal R}=3$, and $\simeq 5.2$, for the three cases with ${\cal R}=5$." +" As expected. all the <7.> curves lie below 7,5. hat overestimates the kinetic cuerev associated with he stellar random motions (Sect. 7273)."," As expected, all the $$ curves lie below $T_{\sigma}$, that overestimates the kinetic energy associated with the stellar random motions (Sect. \ref{inj}) )." + Note that. from he virial theorem. $ is independent of orbital anisotropy, that just redistributes differently the stellar heating within a galaxy; the presence of ordered rotation in the stellar motions, instead, requires a more careful consideration." + For auv fixed galaxy mass model. this rotation would leave the total stellar heating uuchanecd lower it. depending ou whether the whole stellar streaming motion is couverted into leat. or just a fraction of it (Ciotti Pellegrini 1996).," For any fixed galaxy mass model, this rotation would leave the total stellar heating unchanged or lower it, depending on whether the whole stellar streaming motion is converted into heat, or just a fraction of it (Ciotti Pellegrini 1996)." + For the worst case that the stellar rotational motion is not thermalized at all. and the ealaxy is a flat isotropic rotator. <7.> in Fig.," For the worst case that the stellar rotational motion is not thermalized at all, and the galaxy is a flat isotropic rotator, $$ in Fig." + 2 should be an overestimate of ~30% of the temperature corresponding to the stellar heating (Ciotti Peclleerini 1996): the possible reduction of «T.7 to be cousidered should be lower than this. as far as the massive ETCis in Fig.," \ref{f2} + should be an overestimate of $\sim 30$ of the temperature corresponding to the stellar heating (Ciotti Pellegrini 1996); the possible reduction of $$ to be considered should be lower than this, as far as the massive ETGs in Fig." + 2 are less flattened and more pressure supported systenis (0.0.Eausellemi et al.," \ref{f2} are less flattened and more pressure supported systems (e.g., Emsellem et al." + 2011)., 2011). + All observed 77s are located above : thus. additional heating with respect to the thermalization of the stellar kinetic enerev is needed. asnoticed previously using Z5 (c.g. Davis White 1996. DNE).," All observed $T$ 's are located above $$; thus, additional heating with respect to the thermalization of the stellar kinetic energy is needed, asnoticed previously using $T_{\sigma}$ (e.g., Davis White 1996, BKF)." + The eas could retain mienmorv of its injection temperature. and have the additional infall heating. as examined in Sects.," The gas could retain memory of its injection temperature, and have the additional infall heating, as examined in Sects." + ο and low.," \ref{gravhea} + and \ref{sna} below." + Finally. the values of <Τμ)> tor f=0.85 avo by far the largest temperatures of Fie. 2.," Finally, the values of $$ for $f=0.85$ are by far the largest temperatures of Fig. \ref{f2}," +" lager than «T,,,7ebay up toa. ~250 kan 1. herefore. SNIas should. cause the escape of the gas for all ETCis up to this o... since the eas at every tine is injected with au cnerev larecr thu required to leave the galaxy potential."," larger than $$ up to $\sigma_c\sim 250$ km $^{-1}$; therefore, SNIa's should cause the escape of the gas for all ETGs up to this $\sigma_c$, since the gas at every time is injected with an energy larger than required to leave the galaxy potential." +" This expectation is fulfilled by: all ETGs with σσος kins |: their Nora properties (a low Ly. and T's of the order of ) agree well with what expected if outflows are important iu them."," This expectation is fulfilled by all ETGs with $\sigma_c +\lsim 200$ km $^{-1}$: their X-ray properties (a low $L_X$, and $T$ 's of the order of $$ ) agree well with what expected if outflows are important in them." + This result had been suggested previously based ou the low observed Ly: now for the first time it can he confiiued based on the observed F values., This result had been suggested previously based on the low observed $L_X$; now for the first time it can be confirmed based on the observed $T$ values. +" At o,>200 lan +. instead. ETCs mav have Ly far larger than expected for outflows (black sxaubols). aud most ETCs where likely outflows are important (1iagenta or «ναι ο have T nmch lower than : these fiucines are discussed iu Sect."," At $\sigma_c > 200$ km $^{-1}$, instead, ETGs may have $L_X$ far larger than expected for outflows (black symbols), and most ETGs where likely outflows are important (magenta or cyan symbols) have $T$ much lower than $$; these findings are discussed in Sect." + 2? below., \ref{reduc} below. + We coxamine here the possibility that the additional jeatiug with respect to the thermalization of the stellar sinetic energy is provided bv iufall heating aud SNIa‘s., We examine here the possibility that the additional heating with respect to the thermalization of the stellar kinetic energy is provided by infall heating and SNIa's. +" Davis White (1996) assumed that in all ETCs the tot eas is inflowine. and suggested that the observed eniperatures are larger than Z5i just due to the Iuniuous warts of ETCs beige embed in dark matter halos dvuamically hotter than the stars: Le. a form of ""gravitational potential’ way for the eas heating was invoked."," Davis White (1996) assumed that in all ETGs the hot gas is inflowing, and suggested that the observed temperatures are larger than $T_{\sigma}$ just due to the luminous parts of ETGs being embedded in dark matter halos dynamically hotter than the stars; i.e., a form of “gravitational potential” way for the gas heating was invoked." +" This wav cau consist of an effect of the dark ido on the stellar motions. that are then thermalized. or directly on the eas during iufall (¢.¢.. via £,duae j"," This way can consist of an effect of the dark halo on the stellar motions, that are then thermalized, or directly on the gas during infall (e.g., via $E_{\rm grav}^+$ )." + The first possibility is excluded by the $ curves in Fig. \ref{f2}," + that are always lower than Z5. audthat. through he Jeans equations. include the effect of Massive dark halo consistent with the current kuowledee of the ETCGs structure.," that are always lower than $T_{\sigma}$, andthat, through the Jeans equations, include the effect of a massive dark halo consistent with the current knowledge of the ETGs' structure." + In the secouc possibility of heating Yon gas tufall. £L... is indeed potentially an important source of heating. that increases with the amount aud concentration of thedark matter.," In the second possibility of heating from gas infall, $E_{\rm grav}^+$ is indeed potentially an important source of heating, that increases with the amount and concentration of thedark matter." + This can be judged roni Fig. 2..," This can be judged from Fig. \ref{f2}," + after cousiderig that «Ty.275Ti>. and that the teniperature possibly attainable from iufall was estimated to be Tigi (oud of Sect. 224).," after considering that $\sim +5$, and that the temperature possibly attainable from infall was estimated to be $T_{infl}\lsim $ (end of Sect. \ref{esc}) )." +" Note that Tj,j; (if it behaves as <τοις >) could be x62. a trend close to that shown by the T's of eas-rich ETCs (BKE: see also Sect."," Note that $T_{infl}$ (if it behaves as $$ ) could be $\propto \sigma_c^2$, a trend close to that shown by the $T$ 's of gas-rich ETGs (BKF; see also Sect." + 7? below).," \ref{temp} + below)." + Iufjowiug ETGscau also benefit of the SNIa's energy input: for the unit mass of injected eas. this is written as EV=Πανον AL.," Inflowing ETGscan also benefit of the SNIa's energy input; for the unit mass of injected gas, this is written as $E_{SN}^{tot}=R_{SN}E_{SN}/ \dot M_*$ ." +" Both El. and EGY the- contribute to the required additional thermal energy witli respect to that gained from the stellar random notions. Lo. to ALY,=3CT. Ρα."," Both $E_{\rm grav}^+$ and $E_{SN}^{tot}$ then contribute to the required additional thermal energy with respect to that gained from the stellar random motions, i.e., to $\Delta E_{th}=3k(T-)/2\mu m_p$ ." + aud EG can be in large part radiated in σαςΊσα ETCs.but theyποσο to far exceed the required AZ.," $E_{\rm grav}^+$ and $E_{SN}^{tot}$ can be in large part radiated in gas-rich ETGs,but theyseem to far exceed the required $\Delta E_{th}$ ." + For example. for," For example, for" +ionization parameter (όν) and a larger column. density CNINI107€m 7).,"ionization parameter $\xi_{\rm v}$ ) and a larger column density $N_{\rm W}^{\rm v}\simeq +1\times 10^{23}$ )." + Bt imposes an absorption [eature above 1 keV and peaked around 1.5 keV in the quiescent state while it has almost disappeared in the active phase due to high ionization (£.2480 yy," It imposes an absorption feature above 1 keV and peaked around 1.5 keV in the quiescent state while it has almost disappeared in the active phase due to high ionization $\xi_{\rm +v}\geq 480$ )." + Phe change in £i is mareinally consistent with the change in luminosity of the continuum source which has shown a factor of 23 variations during the active phase., The change in $\xi_{\rm v}$ is marginally consistent with the change in luminosity of the continuum source which has shown a factor of 2–3 variations during the active phase. + Phe multi-laver warm: absorber model makes excess cold absorption marginally recuired at the 90 per cent significant level =2.8il]O07em 7).," The multi-layer warm absorber model makes excess cold absorption marginally required at the 90 per cent significant level $ = +2.8^{+2.1}_{-2.8}\times 10^{21}$ )." + The 0.52 keV fluxes for the quiescent and. active states estimate [rom this model are 2.0.10.Perg aand 6.2o.10Mere3+. respectively.," The 0.5–2 keV fluxes for the quiescent and active states estimatd from this model are $2.0\times 10^{-13}$ and $6.2\times 10^{-13}$, respectively." +. Lf the covering. factor of the absorbing gas is high. emissin-lines [rom the ionized eas in the absorber are expected.," If the covering factor of the absorbing gas is high, emissin-lines from the ionized gas in the absorber are expected." + “Phere is an emission-line like feature at 1.4 keV seen in the active state spectrum. which can be identified with ΜΟΙ.," There is an emission-line like feature at 1.4 keV seen in the active state spectrum, which can be identified with MgXI." + The 210 keV ASCAX spectrum. is well described by a power-law of Pox1.72 modified by cold. absorption of 23.107e6m7.," The 2–10 keV ASCA spectrum is well described by a power-law of $\Gamma\simeq 1.72$ modified by cold absorption of $\simeq 2.3\times +10^{22}$." + This cold absorption model however does not explain the soft N-rav. spectrum (see Fig., This cold absorption model however does not explain the soft X-ray spectrum (see Fig. + SN), 8). + A variability study revealed that emission in the 12 keV band is more variable than in the higher enerev band (Fig., A variability study revealed that emission in the 1–2 keV band is more variable than in the higher energy band (Fig. + 4)., 4). + Phe variation above 2 keV is directly attributed to the intrinsic Ilux change in the primary source., The variation above 2 keV is directly attributed to the intrinsic flux change in the primary source. + A plausible explanation for the excess variability in the 12 keV. band is a change in a warn absorber., A plausible explanation for the excess variability in the 1–2 keV band is a change in a warm absorber. + Although Moran. ct al (1999). speculatec about the presence of a warm absorber through spectral analysis of the IOSAT PSPC data. the properties of the N-rav. absorption in NGC4395 appear to be more complex than they assumed.," Although Moran et al (1999) speculated about the presence of a warm absorber through spectral analysis of the ROSAT PSPC data, the properties of the X-ray absorption in NGC4395 appear to be more complex than they assumed." + As shown by the ASCA spectrum. the ROSAT energy range is dominated by absorption. which makes the use of the PSPC spectrum to assess the primary continuum cdillicult.," As shown by the ASCA spectrum, the ROSAT energy range is dominated by absorption, which makes the use of the PSPC spectrum to assess the primary continuum difficult." + A spectral fit to the ASCA data from the quiescent and active states can be explained by the presence of a constant and a variable warm absorber., A spectral fit to the ASCA data from the quiescent and active states can be explained by the presence of a constant and a variable warm absorber. +" The physical condition of the constant absorber is similar to that seen in many higher luminosity Seyfert 1: galaxies (Revnolds 1997: George et al 1998) while the variable absorber is found to have higher ionization parameter. which leacs absorption features to be imprinted around 2 keV due to highlv ionized O. Ne. Mg. Si. 5 and Fe-L. Evidence for multi-zone warm absorber has also been found in Sevfort 1 nuclei like MC6-30-15 (Otani et al 1996: Morales. Fabian Itevnolds 1999) Using the formulae in Otani ο al. (1996) for the warm absorber in. ALCG6-30-15.. the receombination time scale for highly ionized gas can be approximated by ἐςc200»,71""CZ/Zo)b s or lccm20088LloLITREZIZo) es where density+ isH 1020Ln7. temperature is 10775 Is. ionization paranieter is 100£5 . the luminosity. of the irradiating source is 107LoLay the distance of the warm absorber from e itracliating source is 10.18| pc. and Z is the atomic number (Zo=S for oxvgen)."," The physical condition of the constant absorber is similar to that seen in many higher luminosity Seyfert 1 galaxies (Reynolds 1997; George et al 1998) while the variable absorber is found to have higher ionization parameter, which leads absorption features to be imprinted around 2 keV due to highly ionized O, Ne, Mg, Si, S and Fe-L. Evidence for multi-zone warm absorber has also been found in Seyfert 1 nuclei like MCG–6-30-15 (Otani et al 1996; Morales, Fabian Reynolds 1999) Using the formulae in Otani et al (1996) for the warm absorber in MCG–6-30-15, the receombination time scale for highly ionized gas can be approximated by $t_{\rm rec}\simeq 200n_9^{-1}T_5^{0.7}(Z/Z_{\rm O})^{-1}$ s, or $t_{\rm rec}\simeq 200\xi_2L_{40}^{-1}T_5^{0.7}R_{-4}^2(Z/Z_{\rm O})^{-1}$ s, where density is $10^{9}n_{9}$, temperature is $10^5T_5$ K, ionization parameter is $100\xi_2$ $^{-1}$, the luminosity of the irradiating source is $10^{40}L_{\rm 40}$, the distance of the warm absorber from the irradiating source is $10^{-4}R_{-4}$ pc, and $Z$ is the atomic number $Z_{\rm O} = 8$ for oxygen)." + The luminosity of the continuum source during the active state is about 110!erg aab the source distance of 2.6 Alpe. when the power-law is integrated over 13.6 eV to 20 keV. Ifthe constant absorber. which is dominated by oxygen orplion. is indeed. constant during the active state for Y1 s the recombination⋠⋠ time. scale is. then 7.2Lot s. This locates the absorber at the distance οc1.3)3PhyOSesde02055 pe from. the central source and Constrains. the lensityM to be n.xEM2.«107spbem ..," The luminosity of the continuum source during the active state is about $1\times 10^{40}$ at the source distance of 2.6 Mpc, when the power-law is integrated over 13.6 eV to 20 keV. If the constant absorber, which is dominated by oxygen absorption, is indeed constant during the active state for $10^4$ s, the recombination time scale is then $t^{\rm c}_{\rm rec}\geq 10^4$ s. This locates the absorber at the distance $R_{\rm c}\geq 1.3\times 10^{-3}L_{40}^{0.5}T_5^{-0.35}$ pc from the central source and constrains the density to be $n_{\rm c}\leq 2\times 10^7T_5^{0.7}$ ." + On comparing. with. 1e model for the nuclear emission-line region derived. [ron 10 photoionization calculation based. on the optical/UV woperties by [Ixraemer. et al (1999). ἐν is just. outside rw BLE (note that the size of the cmiussion-line regions erived by Kraemer et al 1999 becomes larger if the ionizing uminosity obtained from our work is used).," On comparing with the model for the nuclear emission-line region derived from the photoionization calculation based on the optical/UV properties by Kraemer et al (1999), $R_{\rm c}$ is just outside the BLR (note that the size of the emission-line regions derived by Kraemer et al 1999 becomes larger if the ionizing luminosity obtained from our work is used)." + Phe absorption eatures seen across the CIV line profile presented in Ixraemoer et al (1999) could be due to this warm absorber. as 10 Ionizalion parameter (£30 13) is consistent =vith CIV.," The absorption features seen across the CIV line profile presented in Kraemer et al (1999) could be due to this warm absorber, as the ionization parameter $\xi\sim 30$ ) is consistent with CIV." + The duration of the individual [ares in the active state is about 1000. s. Since the spectral softening in the absorption banc appears to occur at the peaks of those laves (Fig., The duration of the individual flares in the active state is about 1000 s. Since the spectral softening in the absorption band appears to occur at the peaks of those flares (Fig. +" 6). the recombination time scale of the variable absorber is probably less than the duration of the individual laves. Le.. f1000 s. This gives constraints on density and distance of the absorber: ay27I0777(CZ/Zo)tem7. and 2,1.510""LSd5PE pe. when the emperature of the absorber is i=Loess; Ix. As highly ionized Ne. Mg. Si and S as well as O are major elements or absorption. (Z/Zo)z 12."," 6), the recombination time scale of the variable absorber is probably less than the duration of the individual flares, i.e., $t_{\rm rec}^{\rm v}\leq 1000$ s. This gives constraints on density and distance of the absorber: $n_{\rm v}\geq 10^9T_6^{0.7}(Z/Z_{\rm O})^{-1}$, and $R_{\rm v}\leq 4.5\times 10^{-5}L_{40}^{0.5}T_6^{-0.35}(Z/Z_{\rm O})^{0.5}$ pc, when the temperature of the absorber is $T_{\rm v}=10^6T_6$ K. As highly ionized Ne, Mg, Si and S as well as O are major elements for absorption, $(Z/Z_{\rm O})\simeq $ 1–2." + The filling factor is described as (NAR=ENWwR/Lm3s10TENyokLal. where he distance of the absorber is //=10ΤΗs pc and the column density is Nw=bo107Αννατις W," The filling factor is described as $\Delta R/R= \xi N_{\rm W}R/L \simeq 3\times 10^{-2}\xi_2N_{\rm W23}R_{-5}L^{-1}_{40}$, where the distance of the absorber is $R = 10^{-5}R_{-5}$ pc and the column density is $N_{\rm W} = 1\times 10^{23}N_{\rm W23}$." +"hen &=500 aand 2.=110 pe are assumed. the filling factor and the density are AR/R~0.15 and ηνc2«107""em.7."," When $\xi_{\rm v} = 500$ and $R_{\rm v} = 1\times 10^{-5}$ pc are assumed, the filling factor and the density are $\Delta R/R\simeq 0.15$ and $n_{\rm v}\simeq 2\times 10^{10}$." + If the absorbing matter is space filling às suggested by the above argument. significant emission from the same matter is also expected.," If the absorbing matter is space filling as suggested by the above argument, significant emission from the same matter is also expected." + This is consistent with the detection of MgXNI at. 1.4 keV. Although the quality of our data is not sullicient to investigate weaker line emission. the emission could. mask some absorption features which mav cause a supuriouslv high ionization parameter.," This is consistent with the detection of MgXI at 1.4 keV. Although the quality of our data is not sufficient to investigate weaker line emission, the emission could mask some absorption features which may cause a supuriously high ionization parameter." + ]t has been pointed out by Moran et al (1999. and. also see Lira ct al 1999) that the spectral energy. clistribution (SED) ofΝας205 diverses from. either a typical one. of Sevfert/radio quiet quasars or of dwarl ΑΣ.," It has been pointed out by Moran et al (1999, and also see Lira et al 1999) that the spectral energy distribution (SED) ofNGC4395 diverses from either a typical one of Seyfert/radio quiet quasars or of dwarf AGNs." + In particular.," In particular," +9.—NawAf21). depends on the munber of actuators across the diameter of the primary (7?)..,"$\theta_{c} = N_{act}\lambda/2D$, depends on the number of actuators across the diameter of the primary \citep{sivar01}." + For Mt. Wilson. (his area extends out to 8A/D so a design with an IWD of closer to 4A;D or less would be ideal.," For Mt. Wilson, this area extends out to $8\lambda/D$ so a design with an IWD of closer to $4\lambda/D$ or less would be ideal." + Ground based observations are also limited by the contrast ratio of the uncorrected halo to the core (25444)., Ground based observations are also limited by the contrast ratio of the uncorrected halo to the core $z_{\mbox{halo}}$ ). + Phe FWILM of the halo is approximately the uncorrected seeing. which tvpically is ο.," The FWHM of the halo is approximately the uncorrected seeing, which typically is $> \theta_c$." + In Chat case a good estimate of the best contrast achievable is simply the ratio of (he peak intensity of the uncorrected halo to the peak intensity of the corrected image core (?):: where 9 is (he Strehl Ratio. rj is the Fried Parameter of alinospheric turbulence. ancl D is the cliameter of the telescope.," In that case a good estimate of the best contrast achievable is simply the ratio of the peak intensity of the uncorrected halo to the peak intensity of the corrected image core \citep{hardy}: where $S$ is the Strehl Ratio, $r_o$ is the Fried Parameter of atmospheric turbulence, and $D$ is the diameter of the telescope." +" ? has reported S values of ~.2 for the AEOS telescope in the visible (.55 pam) for an r,~12 cm. giving an approximate contrast of 7."," \citet{roberts02} has reported $S$ values of $\sim$ .2 for the AEOS telescope in the visible (.55 $\mu m$ ) for an $r_o\sim12$ cm, giving an approximate contrast of $^{-3}$." + In this case. arger telescopes gain an advantage in contrast given the same seeing conditions and ability fo allain a certain Strehl ratio.," In this case, larger telescopes gain an advantage in contrast given the same seeing conditions and ability to attain a certain Strehl ratio." + Higher order adaptive optics will need (o correct (o. very vigh levels (Se .9) to successfully achieve a high contrast with a GAPM., Higher order adaptive optics will need to correct to very high levels $\sim.9$ ) to successfully achieve a high contrast with a GAPM. + Llowever. using a nore modest a with a more modest level of high contrast may present a usebul alternative io a coronagraph for geroundbased searches with AO. lor example in relatively dense voung clusters or for faint companion searches to white clwarls.," However, using a more modest $\alpha$ with a more modest level of high contrast may present a useful alternative to a coronagraph for groundbased searches with AO, for example in relatively dense young clusters or for faint companion searches to white dwarfs." + We have performed several simulations. lab tests. and telescope observations with GAPAIs in order (o better understand the interplay between theory and the reality of observations.," We have performed several simulations, lab tests, and telescope observations with GAPMs in order to better understand the interplay between theory and the reality of observations." + GAPMSs alone provide an improvement over a simple circular aperture for quick high contrast imaging., GAPMs alone provide an improvement over a simple circular aperture for quick high contrast imaging. + Thev are very sensitive (o an accurate reproduction of shape ancl (hus need accuracies that require nanolabrication techniques such as e-beam lithography. similar to what has been used [or noteh-liller masks (?)..," They are very sensitive to an accurate reproduction of shape and thus need accuracies that require nanofabrication techniques such as e-beam lithography, similar to what has been used for notch-filter masks \citep{debes04}." + We have commissioned some precise GAPAMs with accuracies on the order of .25 jan which should lead to a more accurate shape reproduction and a minimüzation of errors., We have commissioned some precise GAPMs with accuracies on the order of .25 $\micron$ which should lead to a more accurate shape reproduction and a minimization of errors. + Precisely fabricating these masks can potentially improve performance (o the ideal limit for a mask provided it is above the scattered light limit of the telescope. bringing it in line with Lyot coronagraphs of comparable throughput.," Precisely fabricating these masks can potentially improve performance to the ideal limit for a mask provided it is above the scattered light limit of the telescope, bringing it in line with Lyot coronagraphs of comparable throughput." + Demonstration of (hese masks in conjunction with an adaptive optics svstem could present a workable example of a quick wav (o survev for faint companions without needing to incur the overhead cost of precise alignment behind a coronagraphic image mask., Demonstration of these masks in conjunction with an adaptive optics system could present a workable example of a quick way to survey for faint companions without needing to incur the overhead cost of precise alignment behind a coronagraphic image mask. +does not have time to build up observable signatures in the density distribution of debris disks.,does not have time to build up observable signatures in the density distribution of debris disks. +" In addition, the particles do not have the time to drift inside since they are destroyed before PR drag and the ISM drag force them to migrate inside."," In addition, the particles do not have the time to drift inside since they are destroyed before PR drag and the ISM drag force them to migrate inside." + If a gap is present in the inside regions of the disk this will not be filled up by the grain migration., If a gap is present in the inside regions of the disk this will not be filled up by the grain migration. + Significantly different is the situation when 7 is as low as 10:56 (Fig.5 bottom plot): particles in the disk have time to move along the Stark cycle., Significantly different is the situation when $\tau$ is as low as $10^{-6}$ \ref{f5} bottom plot): particles in the disk have time to move along the Stark cycle. + This is not interrupted by collisions since the collisional lifetime is longer than Titarx and the particles can build up large orbital eccentricities and inclinations., This is not interrupted by collisions since the collisional lifetime is longer than $T_{stark}$ and the particles can build up large orbital eccentricities and inclinations. +" In this scenario, the only mechanism able to halt the Stark cycling is the fast inward drift due to the large eccentricity."," In this scenario, the only mechanism able to halt the Stark cycling is the fast inward drift due to the large eccentricity." + The particles migrate inside driven by the PR and ISM drag forces ending either onto the star or sublimating or impacting onto a planet., The particles migrate inside driven by the PR and ISM drag forces ending either onto the star or sublimating or impacting onto a planet. +" This sink mechanism is more effective for smaller values of 4rsj; since the maximum eccentricity e€maz that can be achieved by the particles decreases for increasing irs, according to the Stark general problem."," This sink mechanism is more effective for smaller values of $i_{ISM}$ since the maximum eccentricity $e_{max}$ that can be achieved by the particles decreases for increasing $i_{ISM}$, according to the Stark general problem." + In Fig.6 we show the evolution of the eccentricity and inclination for increasing values of isa., In \ref{f6} we show the evolution of the eccentricity and inclination for increasing values of $i_{ISM}$. +" Their values are strongly correlated, as predicted by the theory of Belyaev&Rafikov(2010) (the theoretical curves are plotted as continuous lines in the figures)."," Their values are strongly correlated, as predicted by the theory of \cite{bera} (the theoretical curves are plotted as continuous lines in the figures)." + Two interesting features come out from Fig.6.., Two interesting features come out from \ref{f6}. + First of all the drag forces tend to reduce the eccentricity detaching the numerical data from the theoretical curve even if the difference is not very marked., First of all the drag forces tend to reduce the eccentricity detaching the numerical data from the theoretical curve even if the difference is not very marked. +" In addition, when the maximum eccentricity is lower, for higher irs, the particles move farther within the Stark cycle because their drift time is longer."," In addition, when the maximum eccentricity is lower, for higher $i_{ISM}$, the particles move farther within the Stark cycle because their drift time is longer." +" When irsm=90° the particles complete a full cycle and some start a new one, even if they do not complete more than two cycles before drifting inside 20 AU."," When $i_{ISM} = 90^o$ the particles complete a full cycle and some start a new one, even if they do not complete more than two cycles before drifting inside 20 AU." + Additional features related to the dynamics of the dust particles under the action of the ISM flow and PR drag can be seen in the density plots shown in Fig.7.., Additional features related to the dynamics of the dust particles under the action of the ISM flow and PR drag can be seen in the density plots shown in \ref{f7}. + In the parent body plane the density distribution appears very asymmetric., In the parent body plane the density distribution appears very asymmetric. +" In the case where irs;=20? (Fig.7 top plots) it is still possible to recognize the two elliptical structures produced by the evolution in the (e,w) plane but their shape is blurred due to the inclination distribution."," In the case where $i_{ISM} = 20^o$ \ref{f7} top plots) it is still possible to recognize the two elliptical structures produced by the evolution in the $(e,\omega)$ plane but their shape is blurred due to the inclination distribution." +" However, when irsw=60° the double-elliptical structure has fully disappeared and the inclination distribution determines the density distribution also in the parent body plane."," However, when $i_{ISM} = 60^o$ the double–elliptical structure has fully disappeared and the inclination distribution determines the density distribution also in the parent body plane." +" As it can be argued from Fig.6 middle plots, the orbital inclination is concentrated around i~50? and, in addition, when the inclination is higher, the node longitude is clustered around"," As it can be argued from \ref{f6} middle plots, the orbital inclination is concentrated around $i \sim 50^o$ and, in addition, when the inclination is higher, the node longitude is clustered around" +ig). placing Ho within the BGD-a sequence. suggesting it has a similar metallicity of Fe/1l] ~ 0.8.,"), placing it within the RGB-a sequence, suggesting it has a similar metallicity of [Fe/H] $\sim$ –0.8." + Comparison with spectra of stars from more metal-rich &lobular clusters μοι VISSEig:: spectra from MeDonald.&vanLoon 2007)) indicates that V42's spectrum is similar to those of the most-evolved stars in 47 Tuc. (ο) = 0.7)., Comparison with spectra of stars from more metal-rich globular clusters \\ref{UVESFig}; ; spectra from \citealt{MvL07}) ) indicates that V42's spectrum is similar to those of the most-evolved stars in 47 Tuc ([Fe/H] = –0.7). + The other comparison star in τοVESEig (NGC 362. VIG) has similar pulsation properties and shows a similar infra-red spectrum to V42 (both in terms of dust. composition and. amount of excess: Sloanetal. 2010)). and is likely at a similar evolutionary stage.," The other comparison star in \\ref{UVESFig} (NGC 362 V16) has similar pulsation properties and shows a similar infra-red spectrum to V42 (both in terms of dust composition and amount of excess; \citealt{SMM+10}) ), and is likely at a similar evolutionary stage." + VIG. however. is a factor of ~3 more metal-poor at οΗ] ~ 1.2.," V16, however, is a factor of $\sim$ 3 more metal-poor at [Fe/H] $\sim$ –1.2." + As the most evolved star in NGC 362. V16 should be at à similar. or more-evolved. evolutionary stage compared to V42.," As the most evolved star in NGC 362, V16 should be at a similar, or more-evolved, evolutionary stage compared to V42." + Despite this. reUVESFie shows NGC 362 V16 is clearly warmer than V42. with much less opaque TiO anc VO bands. suggesting V42 has a metallicity more in line with 47 Tucs Γο/Η] = O.7.," Despite this, \\ref{UVESFig} shows NGC 362 V16 is clearly warmer than V42, with much less opaque TiO and VO bands, suggesting V42 has a metallicity more in line with 47 Tuc's [Fe/H] = –0.7." + As an additional test. we compared. V42's spectrum with the synthetic spectral library provided by Coelho et al. (," As an additional test, we compared V42's spectrum with the synthetic spectral library provided by Coelho et al. (" +2005).,2005). + We investigated the parameter space Zi; = 3500 Ix and Κοη = 2.5 to |0.5. in 0.5En dex increments.," We investigated the parameter space $T_{\rm eff}$ = 3500 K and [Fe/H] = –2.5 to +0.5, in 0.5 dex increments." + A general ack of spectral models below 35OO Ix makes an accurate metallicity determination dillieult., A general lack of spectral models below 3500 K makes an accurate metallicity determination difficult. + From these comparisons. jowever. we concluded that V42 likely lies between οΗ] land Le/ll]- 0.," From these comparisons, however, we concluded that V42 likely lies between [Fe/H] = –1 and [Fe/H] = 0." + lt would. appear.facie. that V42. belongs to he anomalous RGB. at Fe/1] z 0.8.," It would appear, that V42 belongs to the anomalous RGB, at [Fe/H] $\approx$ –0.8." + However. while we consider it unlikely. we cannot rule out at the present stage hat it may come from w Cen's metalintermediate (Fe/1] = 1.5.5. 1.2. 1.0) populations (Johnson&Pilachowski2010).," However, while we consider it unlikely, we cannot rule out at the present stage that it may come from $\omega$ Cen's metal-intermediate ([Fe/H] = –1.5, –1.2, –1.0) populations \citep{JP10}." +. This determination decreases the derived mass-Ioss rate and increases the terminal wind velocity compared to a star with average metallicity. (Fe/l1l] = 1.63) bv a factor of vielding the values Listed in Table 3..," This determination decreases the derived mass-loss rate and increases the terminal wind velocity compared to a star with average metallicity ([Fe/H] = –1.62) by a factor of $\times$ ,yielding the values listed in Table \ref{DustyTable}. ." +(Krieketal.2007).. and potentially even higher AGN fractions in massive galaxies at 3«τσ4 (Marchesinietal.2010).,"\citep{kriek2007}, and potentially even higher AGN fractions in massive galaxies at $3=3.5.," The availability of -IRAC data in the 3.6, 4.5, 5.8, and $\mu$ m channels allows us to robustly estimate the LFs and LDs in the rest-frame $J$ and $H$ bands with a minimum dependence on the SED templates up to $z=3.5$." + Ours is the first measurement of the //-band LF at 2>0 to-date., Ours is the first measurement of the rest-frame $H$ -band LF at $z>0$ to-date. + We determined the LF with three independent methods. namely the 1/Vinas. the SWML .and the STYML methods. finding that they agree well with each other.," We determined the LF with three independent methods, namely the $1/V_{\rm max}$, the SWML ,and the STYML methods, finding that they agree well with each other." + Uncertainties introduced by the cosmic variance were estimated using two distinct methods. one by Mosteretal.(2010). and the other by Driver&Robotham(2010).," Uncertainties introduced by the cosmic variance were estimated using two distinct methods, one by \citet{moster2010} and the other by \citet{driver2010}." +. We find that. for our data. the two approaches broadly agree.," We find that, for our data, the two approaches broadly agree." +" Our rest-frame /-band LF is consistent with previous determination by Saraccoetal.(2006)... although the recovered Schechter parameters AJ"" and o are consistent only at the 20 level."," Our rest-frame $J$ -band LF is consistent with previous determination by \citet{saracco2006}, although the recovered Schechter parameters $M^*$ and $\alpha$ are consistent only at the $\sigma$ level." + This might be due to the limited range in rest-frame magnitudes probed by the sample in Saraecoetal.(2006) and by large errors due to cosmic variance given their small surveyed area., This might be due to the limited range in rest-frame magnitudes probed by the sample in \citet{saracco2006} and by large errors due to cosmic variance given their small surveyed area. + Our J-band LF is consistent also with the LF measured by Pozzetti ata~1.5., Our $J$ -band LF is consistent also with the LF measured by \citet{pozzetti2003} at $z\sim1.5$. + We analyzed the evolution with redshift of the Schechter function parameters. making full use of the data available from the literature.," We analyzed the evolution with redshift of the Schechter function parameters, making full use of the data available from the literature." +" We found that the faint end slope à of the LF is nearly constant over the whole redshift range. witha,=—1.05+0.03 andag=1.1540.02 in the J and // bands. respectively."," We found that the faint end slope $\alpha$ of the LF is nearly constant over the whole redshift range, with $\alpha_J=-1.05\pm0.03$ and $\alpha_H=-1.15\pm0.02$ in the $J$ and $H$ bands, respectively." + The characteristic density O° decreases by a factor of zz6 from z~0 tos= 1.75. and by a factor of zz3 from ς—1.75 to z=3.25.," The characteristic density $\phi^*$ decreases by a factor of $\approx 6$ from $z\sim0$ to $z=1.75$ , and by a factor of $\approx 3$ from $z\sim 1.75$ to $z=3.25$." + We introduced a parameterization based on an exponential form for the evolution of 6° as a function of z., We introduced a parameterization based on an exponential form for the evolution of $\phi^*$ as a function of $z$ . + The fit of this function to the available data shows good agreement. especially for the rest-frame J band. where more data from the literature are available in the redshift range z¢0.1]. complementing our measurements at SIl5.," The fit of this function to the available data shows good agreement, especially for the rest-frame $J$ band, where more data from the literature are available in the redshift range $z \in[0, 1]$, complementing our measurements at $z>1.5$." + The characteristic magnitude A is found to brighten from 2o— 0toz~ 2by ~OS mag. whereas AJ” gets fainter with increasing redshift at =—2.," The characteristic magnitude $M^*$ is found to brighten from $z=0$ to $z\sim2$ by $\sim0.8$ mag, whereas $M^*$ gets fainter with increasing redshift at $z \gtrsim 2$." + We adopted a Schechter (1976)--like expression for its description. resulting in a good representation of the observed evolution.," We adopted a \cite{schechter1976}- -like expression for its description, resulting in a good representation of the observed evolution." + We computed the LD in the rest-frame ./ and // bands. using the Schechter parameters previously determined.," We computed the LD in the rest-frame $J$ and $H$ bands, using the Schechter parameters previously determined." + The LD is nearly constant up to z1 and decreases as a power-law by a factor of zz6 from z1 to z=3.25., The LD is nearly constant up to $z\approx 1$ and decreases as a power-law by a factor of $\approx 6$ from $z\approx1$ to $z=3.25$. + We compared the evolution with redshift of the LFs and LDs in the rest-frame ./ and A bands., We compared the evolution with redshift of the LFs and LDs in the rest-frame $J$ and $K$ bands. + The Schechter parameters ó* and Α/Τ in the rest-frame A band show different evolutions with redshift with respect to the ./ band. although these differences are only marginally signiticant at the 2-0 level.," The Schechter parameters $\phi^*$ and $M^*$ in the rest-frame $K$ band show different evolutions with redshift with respect to the $J$ band, although these differences are only marginally significant at the $\sigma$ level." + Specitically. the decrease of the characteristic density with redshift appears faster in the A than in the ./ band at -1.5.," Specifically, the decrease of the characteristic density with redshift appears faster in the $K$ than in the $J$ band at $z \gtrsim 1.5$." + The characteristic magnitude in the rest-frame ἐν band brightens with redshift over the whole redshift interval 0~2. and then slowly gets fainter out to >=3.5 although a constant value of Aj at zc1.5 is consistent within the uncertainties}.," The characteristic magnitude in the rest-frame $K$ band brightens with redshift over the whole redshift interval $01.5$ is consistent within the uncertainties)." + Most of these differences cancel out when computing the LDs. with similar evolutions with redshift of the rest-frame ./- and A -band LDs out to >—2.5.," Most of these differences cancel out when computing the LDs, with similar evolutions with redshift of the rest-frame $J$ - and $K$ -band LDs out to $z\sim2.5$." + Evidence for a faster decrease with increasing redshift of the rest-frame A-band LD at >2.5 seems present., Evidence for a faster decrease with increasing redshift of the rest-frame $K$ -band LD at $z\gtrsim2.5$ seems present. + However. these differences are significant only to a level (2 0).," However, these differences are significant only to a level (2 $\sigma$ )." + Large errors at 2— in both the JJ and ἐν bands prevent to firmly assess differences between the evolution with redshift of the /- and A-band LFs and LDs., Large errors at $z>2$ in both the $J$ and $K$ bands prevent to firmly assess differences between the evolution with redshift of the $J$ - and $K$ -band LFs and LDs. + In order to further constrain the rest-frame ./- and //-band LFs. a larger area is needed to better probe the bright end and reduce the impact of tield-to-field variations and low number statistics.," In order to further constrain the rest-frame $J$ - and $H$ -band LFs, a larger area is needed to better probe the bright end and reduce the impact of field-to-field variations and low number statistics." + Better photometric redshift estimates are also needed to improve the LF measurements at the bright end. by. e.g.. reducing the impact of catastrophic outliers.," Better photometric redshift estimates are also needed to improve the LF measurements at the bright end, by, e.g., reducing the impact of catastrophic outliers." + The recently publicly released NEWFIRM Medium-Band Survey (Whitakeretal.2011) will provide the dataset to significantly improve on all of these aspects., The recently publicly released NEWFIRM Medium-Band Survey \citep{whitaker2011} will provide the dataset to significantly improve on all of these aspects. +" Ongoing very deep ground-based surveys. such as the Ultra-VISTAsurvey"". and space-based surveys with WFC3 on theTelescope.. such as the CANDELS (Groginetal.2011:Koeke-al.2011) and 3D-HST (Brammer et al."," Ongoing very deep ground-based surveys, such as the Ultra-VISTA, and space-based surveys with WFC3 on the, such as the CANDELS \citep{grogin2011,koekemoer2011} and 3D-HST (Brammer et al." + 2011. in prep.)," 2011, in prep.)" + surveys. Will allow for much improved constraints of the faint end of the rest-frame NIR LF and of the contribution of low-luminosity galaxies to the total NIR LD.," surveys, will allow for much improved constraints of the faint end of the rest-frame NIR LF and of the contribution of low-luminosity galaxies to the total NIR LD." + We thank all the members of the FIRES. FIREWORKS. and MUSYC collaborations for their contribution to this research.," We thank all the members of the FIRES, FIREWORKS, and MUSYC collaborations for their contribution to this research." + We thank A. Fernandez-Soto and P. Saracco for useful comments and constructive discussions., We thank A. Fernandez-Soto and P. Saracco for useful comments and constructive discussions. + MUSYC has greatly benetited from the support of Fundacion Andes and the Yale Astronomy Department., MUSYC has greatly benefited from the support of Fundacion Andes and the Yale Astronomy Department. + This work is based on observations with the Spitzer Space Telescope. which is operated by the Jet Propulsion Laboratory JPL). California Institute of Technology under NASA contract 07: based on observations with the NASA/ESA Hubble Space Telescope. obtained at the Space Telescope Science Institute. which isoperated by AURA. Inc.. under NASA contractNASS- based on observations collected at the European Southern Observatories. Chile (ESO Programme LP164.0-0612. 168.A- .170.A-0788. 074.A-0709.. 275.A-5060. and. 171.A-30455: based on observations obtained at the Cerro Tololo Inter-American Observatory. a division of the National Optical Astronomy Observatories. which is operated by the Association of Universities for Research in Astronomy. Inc.. under cooperative agreement with the National Science Foundation.," This work is based on observations with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory (JPL), California Institute of Technology under NASA contract 1407; based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which isoperated by AURA, Inc., under NASA contractNAS5-26555; based on observations collected at the European Southern Observatories, Chile (ESO Programme LP164.O-0612, 168.A-0485, 170.A-0788, 074.A-0709, 275.A-5060, and 171.A-3045); based on observations obtained at the Cerro Tololo Inter-American Observatory, a division of the National Optical Astronomy Observatories, which is operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation." +the dillerent background features to a consistency of approximately 0.02 magnitudes.,the different background features to a consistency of approximately 0.03 magnitudes. +difference iu the final wuuber of ideutifications aud in the associated reliability (see below) has been foc.,difference in the final number of identifications and in the associated reliability (see below) has been found. +" As probabilitv distribution of positional errors we adopted a Gaussian distribution with standard deviation. c. which takes iuto account the combined effect of the radio aud the optical positional uucertaiuties: For cach source the value of σ used is the average value between σι—ν΄|opae aud 9,=vPEE where Crop 18 the error on the optical position (we. assumed a value of 0.5 aresec). while 6;, and os are the radio positional errors iu RA aud DEC reported in Table 1."," As probability distribution of positional errors we adopted a Gaussian distribution with standard deviation, $\sigma$, which takes into account the combined effect of the radio and the optical positional uncertainties: For each source the value of $\sigma$ used is the average value between $\sigma_x = \sqrt{er_{op}^2+\sigma_{\alpha}^2}$ and $\sigma_y = \sqrt{er_{op}^2+\sigma_{\delta}^2}$, where $er_{op}$ is the error on the optical position (we assumed a value of 0.5 arcsec), while $\sigma_{\alpha}$ and $\sigma_{\delta}$ are the radio positional errors in RA and DEC reported in Table 1." + Uaving determined the values of ΓΗ). sudnf. we computed the £R value for all the optical sources within a clistance of 5 arcsec from the radio position.," Having determined the values of , and, we computed the $LR$ value for all the optical sources within a distance of 5 arcsec from the radio position." + Once hat the LR values have been computed for all the optical candidates. one has to choose he best threshold value or LR (La) to discriminate between spurious and real identifications.," Once that the $LR$ values have been computed for all the optical candidates, one has to choose the best threshold value for $LR$ $L_{\rm th}$ ) to discriminate between spurious and real identifications." +" The choice of £44, depends on two ‘actors: first. if should be small enough to avoid missing uaznyv veal identifications aud having a rather incomplete siuuple."," The choice of $L_{\rm th}$ depends on two factors: first, it should be small enough to avoid missing many real identifications and having a rather incomplete sample." +" Secondly. £4, should be large enough to keep the ΠΗΛΟ of spurious ideutifications as low as possible aud ο Iucrease the reliabilitv."," Secondly, $L_{\rm th}$ should be large enough to keep the number of spurious identifications as low as possible and to increase the reliability." +" As ER threshold we adopted L4,20.2.", As $LR$ threshold we adopted $L_{\rm th}$ =0.2. + With this value. according to Eq. (," With this value, according to Eq. (" +"7) aud cousidering that our estimate ‘or Q is OS. all the optical counterparts of radio sources with ouly one identification (the majority iu our sample) and LR>ERy, have a reliability ereater than 0.5.","7) and considering that our estimate for Q is 0.8, all the optical counterparts of radio sources with only one identification (the majority in our sample) and $LR>LR_{\rm th}$ have a reliability greater than 0.5." + This choice also approximately maximizes the stun of sample reliability aud completeness., This choice also approximately maximizes the sum of sample reliability and completeness. +" With this threshold value we fud 56 radio sources with a likely identification (three of which have two optical caudidates with L4,20.20 for a total of 59 optical candidates with £4,70.20).", With this threshold value we find 56 radio sources with a likely identification (three of which have two optical candidates with $L_{\rm th}>$ 0.20 for a total of 59 optical candidates with $L_{\rm th}>$ 0.20). + The relabihtv (Rel) of cach of these optical identifications (see Eq., The reliability (Rel) of each of these optical identifications (see Eq. +" T) is always high (295 per cout for most of the sources). except for the few cases where more than one optical candidate with £4,20.20 is preseut for the same radio source."," 7) is always high $>$ 95 per cent for most of the sources), except for the few cases where more than one optical candidate with $L_{\rm th}>$ 0.20 is present for the same radio source." +" The ummber of expected real identifications (obtained adding the reliability of all the objects with Ly,20.20) is about 53 he we expect that about 3 of the 56 proposed. radio-optical associations nav be spurious positional coincidences.", The number of expected real identifications (obtained adding the reliability of all the objects with $L_{\rm th}>$ 0.20) is about 53 $i.e$ we expect that about 3 of the 56 proposed radio-optical associations may be spurious positional coincidences. + Similar results are obtained using the catalogue in the V band., Similar results are obtained using the catalogue in the V band. + The results of the optical identificationi are sunnuulzed iu Table 3., The results of the optical identification are summarized in Table 3. + For each raclio source we report all the optical counterparts within 3 aresec aud with a magnitude Iz21.5 plus two jects which. haviug I221.5 mae. are too faint for a reliable deteriuination of their likelihood. ratio. but we however cousidered as likely identification because of them small distance (lower than 0.6 aresec) from the radio position (LOCK4105158|573330. and 660111105259|573226).," For each radio source we report all the optical counterparts within 3 arcsec and with a magnitude $\leq$ 24.5 plus two objects which, having $>$ 24.5 mag, are too faint for a reliable determination of their likelihood ratio, but we however considered as likely identification because of their small distance (lower than 0.6 arcsec) from the radio position J105158+573330 and 105259+573226)." + Tn the three cases in which more than one optical object with LR>Lh have been found associated to the same radio source. we assinned the object with the lughest Likelihood Ratio value as the counterpart of this radio source.," In the three cases in which more than one optical object with $LR>LR_{\rm th}$ have been found associated to the same radio source, we assumed the object with the highest Likelihood Ratio value as the counterpart of this radio source." + As said above. the K baud data cover the 6 cu field in a nonuniform fashion.," As said above, the $^{\prime}$ band data cover the 6 cm field in a non-uniform fashion." + For 12 of the 63 radio sources I’ baud data are not available., For 12 of the 63 radio sources $^{\prime}$ band data are not available. + Siuce all the 51 radio sources with available K baud data do have an optical ideutification iu the I baud. we looked for I counterparts une a naximmnu distauce of 1.0 arcsec from the optical position.," Since all the 51 radio sources with available $^{\prime}$ band data do have an optical identification in the I band, we looked for $^{\prime}$ counterparts using a maximum distance of 1.0 arcsec from the optical position." + We found a IN! counterpart for 19 of the 51 radio sources., We found a $^{\prime}$ counterpart for 49 of the 51 radio sources. + The same results is obtained using a search radius of 2 arcsec., The same results is obtained using a search radius of 2 arcsec. + A «μα of the results of our identifications is eiveu in Table 3., A summary of the results of our identifications is given in Table 3. + For each radio source. we eive the V. I and I maeuitude (when available). the total distance aud the distance in RA iux DEC vetween the radio aud the optical »o»xtiou and the Likelihood Ratio aud reliability values obtained using the I baud catalogue.," For each radio source, we give the V, I and $^{\prime}$ magnitude (when available), the total distance and the distance in RA and DEC between the radio and the optical position and the Likelihood Ratio and reliability values obtained using the I band catalogue." + For the radio sources with more than one optical counterpart we assumed as he real identification the optical source with the highest reliability., For the radio sources with more than one optical counterpart we assumed as the real identification the optical source with the highest reliability. + A blank Πο]ε in theK maenitude cohuuu ueans no data available., A blank field in the$^{\prime}$ magnitude column means no data available. + Iu sununary. considering as good identifications also he two sources fainter than I—21.5 mag. we have a," In summary, considering as good identifications also the two sources fainter than $\sim$ 24.5 mag, we have a" +approximately parallel to the major axis of the apparent nebular ellipse. shows that the northern end of the nebula is rec-shiftecl with respect to the south indicating that the nebular inclination is such that the northern. side of the nebula is pointed away from the observer ancl the south towards.,"approximately parallel to the major axis of the apparent nebular ellipse, shows that the northern end of the nebula is red-shifted with respect to the south indicating that the nebular inclination is such that the northern side of the nebula is pointed away from the observer and the south towards." + The Slit 3 cehellogram also shows two separate emission regions [rom the near and far sides of the nebular shell (ic. no closed. velocity ellipse). suggesting that the nebula is open at both ends of this svnunuetry axis.," The Slit 3 echellogram also shows two separate emission regions from the near and far sides of the nebular shell (i.e. no closed velocity ellipse), suggesting that the nebula is open at both ends of this symmetry axis." + This is supported by the emission. profile from. the slit’ perpendicular to Slit 3. Slit 5 Figure 3((0)].. which shows a partial velocity. ellipse.," This is supported by the emission profile from, the slit perpendicular to Slit 3, Slit 5 [Figure \ref{fig:pvarrays}( (e)], which shows a partial velocity ellipse." + “Phe ellipse is not. closed as a result of both the open ended. ancl inclined. nature of the nebular shell. meaning that the slit cuts across a region where only the blue-shiltecd side. of the nebula is present.," The ellipse is not closed as a result of both the open ended and inclined nature of the nebular shell, meaning that the slit cuts across a region where only the blue-shifted side of the nebula is present." + However. projection effects. surface brightness aud shell thickness variations could produce an apparently open velocity. ellipse from. a closed. shell. due to the sensitivity limits of the observations.," However, projection effects, surface brightness and shell thickness variations could produce an apparently open velocity ellipse from a closed shell, due to the sensitivity limits of the observations." + The intrinsic nebular structure and variation in brightness across the nebula are cliscussecl further in Sections 3.2 and 3.4.., The intrinsic nebular structure and variation in brightness across the nebula are discussed further in Sections \ref{sec:modelling} and \ref{sec:ism}. + A spatio-kinematical model. corresponding to the simplest three-dimensional structure consistent with the large-scale nebular cemission features. has been derived for A 41.," A spatio-kinematical model, corresponding to the simplest three-dimensional structure consistent with the large-scale nebular emission features, has been derived for A 41." + cemission was selected rather than cemission due to its lower thermal broadening and its shell-like distribution (as discussed in section 3.1))., emission was selected rather than emission due to its lower thermal broadening and its shell-like distribution (as discussed in section \ref{sec:ionisationstructure}) ). + Phe modelling was performed in order to confirm. the bipolar nature of the nebular shell anc to constrain the inclination angle of this shell. for comparison with the inclination of the central binary (MT. Ser).," The modelling was performed in order to confirm the bipolar nature of the nebular shell and to constrain the inclination angle of this shell, for comparison with the inclination of the central binary (MT Ser)." + Phe model was developed: using (7) and bv assuming a LHlubble-tvpe Low. where expansion velocity is racial and proportional to the distance from the centre of the nebula.," The model was developed using \citep{steffen06} and by assuming a Hubble-type flow, where expansion velocity is radial and proportional to the distance from the centre of the nebula." + “Phe model parameters (dimensions. shape. expansion scale velocity and inclination) were manually varied over a wide range of values ancl the results compared by eve to both spectral observations and imagine. until a best-fit was found.," The model parameters (dimensions, shape, expansion scale velocity and inclination) were manually varied over a wide range of values and the results compared by eye to both spectral observations and imaging, until a best-fit was found." + This best Π moclel comprises a bipolar shell waisted. by an equatorial ring with an expansion velocity. of ~40, This best fit model comprises a bipolar shell waisted by an equatorial ring with an expansion velocity of $\sim$. + The model nebula is slightly asvmmetric in that the northern lobe is shortened byδι. has a narrower opening angle anc has a slight shear with respect to its southern counterpart.," The model nebula is slightly asymmetric in that the northern lobe is shortened by, has a narrower opening angle and has a slight shear with respect to its southern counterpart." + No symmetric model could be found to reproduce the observed PV arravs., No symmetric model could be found to reproduce the observed PV arrays. + The nebular inclination. angle. as defined. by the ün-sheared southern lobe. is determined to be 66°+5° (in excellent agreement with the value determined. by 2.. 7.. by deprojecting the nebular ring).," The nebular inclination angle, as defined by the un-sheared southern lobe, is determined to be $66\degr \pm 5\degr$ (in excellent agreement with the value determined by \citeauthor{pollacco97}, \citeyear{pollacco97}, by deprojecting the nebular ring)." + The mocel nebula is shown at the observed. orientation in Figure 5 and at an inclination of to highlight the asymmetry. in. Figure 6..," The model nebula is shown at the observed orientation in Figure \ref{fig:modelimage} and at an inclination of, to highlight the asymmetry, in Figure \ref{fig:modelsideon}." + The svnthetic PV arrays are shown. along with their observed counterparts. in Figure 3..," The synthetic PV arrays are shown, along with their observed counterparts, in Figure \ref{fig:pvarrays}." + ]t is not unheard of for bipolar nebulae {ο show asvnunetry between the opposing lobes. both in the extension of the lobes (e.g. NGC 6881: ?)) and their opening angles (c.g. OLI231.8|4.2: 2)).," It is not unheard of for bipolar nebulae to show asymmetry between the opposing lobes, both in the extension of the lobes (e.g. NGC 6881: \citealp{ramos-larios08}) ) and their opening angles (e.g. OH231.8+4.2: \citealp{sanchezcontreras04}) )." + In. comparison. the level of asymmetry shown by A 41 is very low.," In comparison, the level of asymmetry shown by A 41 is very low." + One possible explanation for the asvmimetry is discussed in Section 3.4.., One possible explanation for the asymmetry is discussed in Section \ref{sec:ism}. + Also of note. the equatorial expansion velocity. of ~40 Lods unusually large for a bipolar nebula. though not exceptionally so (?.. 2)).," Also of note, the equatorial expansion velocity, of $\sim$, is unusually large for a bipolar nebula, though not exceptionally so \citealt{solf84}, \citealt{weinberger89}) )." + Comparison of svnthetic model spectra to their observed counterparts provides an unambiguous measure of the nebular svstemic heliocentric radial velocity ο). unallected. for example. by brightness variations or nebular asvmmetry (?)..," Comparison of synthetic model spectra to their observed counterparts provides an unambiguous measure of the nebular systemic heliocentric radial velocity $V_{sys}$ ), unaffected, for example, by brightness variations or nebular asymmetry \citep{jones10}." +" Using the best-fit model. described. in Section 3.2... V, is determined to be 30 2 5 iin good agreement with the value of 30. ddetermined by ον,"," Using the best-fit model described in Section \ref{sec:modelling}, $V_{sys}$ is determined to be 30 $\pm$ 5 in good agreement with the value of 30 determined by \citet{beaulieu99}." + Similarly. the nebular expansion velocity. determined by the kinematical modelling. can be used to calculate a kinematical age for the nebula.," Similarly, the nebular expansion velocity, determined by the kinematical modelling, can be used to calculate a kinematical age for the nebula." + This. however. requires the distance to the nebula to be known.," This, however, requires the distance to the nebula to be known." + The distance to A 41 is a matter of some debate with values in the literature ranging from 1 kpe (7) up to 9.0 + 0.4 kpe (?).. this probably results from the notorious variation in results from different methods of distance determination (see e.g... 2)).," The distance to A 41 is a matter of some debate with values in the literature ranging from $\sim$ 1 kpc \citep{grauer83} up to 9.0 $\pm$ 0.4 kpc \citep{shimanskii08}, this probably results from the notorious variation in results from different methods of distance determination (see e.g., \citealp{gurzadyan97}) )." + Therefore. rather than favour one particular distance estimate over another we quote a kinematical age per kiloparsee of ~SOO vears ," Therefore, rather than favour one particular distance estimate over another we quote a kinematical age per kiloparsec of $\sim800$ years $^{-1}$." +The asvnimetries in both brightness ancl shape (discussed in Sections 3.1. and 3.2)) could be thought of as strong evidence for interaction with the interstellar medium (18M)., The asymmetries in both brightness and shape (discussed in Sections \ref{sec:ionisationstructure} and \ref{sec:modelling}) ) could be thought of as strong evidence for interaction with the interstellar medium (ISM). + Consider. if the nebula were moving through the ISM with the northern lobe at the leacing edge. it would be reasonable to expect to see this lobe brightened (through shock excitation) and less extended (due to the greater drag) with respect to its relatively unimpeded southern counterpart.," Consider, if the nebula were moving through the ISM with the northern lobe at the leading edge, it would be reasonable to expect to see this lobe brightened (through shock excitation) and less extended (due to the greater drag) with respect to its relatively unimpeded southern counterpart." + This brightening ancl lesser extension is precisely what is, This brightening and lesser extension is precisely what is +Kinetic power and timescales to those invoked in the context of massive black hole accretion in? and ?..,kinetic power and timescales to those invoked in the context of massive black hole accretion in \citet{bloom11} and \citet{burrows11}. + The phenomenology of the resulting emission depends largely on the properties of the jet and thus should in many ways be independent of the central nature of the engine. complicating the interpretation of The localization of to near the center of its host galaxy is highly suggestive of AGN activity. but it is also not unreasonable to suspect that a stellar explosion might occur in the galactic nucleus. perhaps associated with circumnuclear star formation.," The phenomenology of the resulting emission depends largely on the properties of the jet and thus should in many ways be independent of the central nature of the engine, complicating the interpretation of The localization of to near the center of its host galaxy is highly suggestive of AGN activity, but it is also not unreasonable to suspect that a stellar explosion might occur in the galactic nucleus, perhaps associated with circumnuclear star formation." + Long-duration GRBs have a tendency to appear in the brightest star forming regions of a galaxy (2)... which in this case coincides with the center.," Long-duration GRBs have a tendency to appear in the brightest star forming regions of a galaxy \citep{fruchter06}, which in this case coincides with the center." + The offset distributions for GRBs constructed by ? indicate a ~10% probability of tinding a GRB within the radius allowed by observations of (he.. within ~20% of the galaxy half light radius)," The offset distributions for GRBs constructed by \cite{bloom02} indicate a $\sim 10\%$ probability of finding a GRB within the radius allowed by observations of (i.e., within $\sim 20\%$ of the galaxy half light radius)." + GRB 021004. for example. was located similarly close (<119 pe) to its host galaxy center (2)..," GRB 021004, for example, was located similarly close $< 119$ pc) to its host galaxy center \citep{fynbo05}." + In some ways. did not show the expected signatures of a tidal disruption event.," In some ways, did not show the expected signatures of a tidal disruption event." + In the usual picture. the allback of bound material forms a disk near the tidal disruption radius and radiates primarily in the ultraviolet/optical (2)..," In the usual picture, the fallback of bound material forms a disk near the tidal disruption radius and radiates primarily in the ultraviolet/optical \citep{ulmer99}." + For systems with super-Eddington fallback rates. which are probably he most likely to power relativistic jets. a particularly bright optical ransient is expected associated with outflows driven by radiation oressure. (2): there are indeed several recent tidal disruption candidates selected on such optical emission ¢??)..," For systems with super-Eddington fallback rates, which are probably the most likely to power relativistic jets, a particularly bright optical transient is expected associated with outflows driven by radiation pressure \citep{strubbe09}; there are indeed several recent tidal disruption candidates selected on such optical emission \citep{farrar11, cenko11}." +" The fact that no such optical transient was seen for could be he result of significant dust extinction (A,~10 mag) in the vost galaxy nucleus. which ? argue is consistent with the high ivdrogen column density determined from the x-ray spectrum."," The fact that no such optical transient was seen for could be the result of significant dust extinction $A_v \sim 10$ mag) in the host galaxy nucleus, which \citet{levan11} argue is consistent with the high hydrogen column density determined from the x-ray spectrum." + In he magnetar GRB model. high dust extinction would likely also need to be invoked to explain the non-detection of a supernova.," In the magnetar GRB model, high dust extinction would likely also need to be invoked to explain the non-detection of a supernova." + On he other hand. in the RSG collapse model the absence of a bright optical transient is to be expected given the failure (or extreme weakness) of the su»ernova explosion.," On the other hand, in the RSG collapse model the absence of a bright optical transient is to be expected given the failure (or extreme weakness) of the supernova explosion." + Continued motnitoring of should help clarify its origin., Continued monitoring of should help clarify its origin. + A prolonged phase of relatively constant x-ray luminosity becomes. at some point. ditficult to reconcile with a tidal disruption model.," A prolonged phase of relatively constant x-ray luminosity becomes, at some point, difficult to reconcile with a tidal disruption model." +" Rather. one expects to see the power decline on the fallback imeseale. which is £j,~20€Mgg/10M7(ΑηΑΛ.ymin for a solar type star (where Aj; is the black hole mass and A, is the xribothron distance of the stellar orbit. scaled to 3 Schwarzschild radii)."," Rather, one expects to see the power decline on the fallback timescale, which is $t_{fb} \sim 20 \, (M_{BH}/10^6 M_\odot)^{5/2} \, (R_p/ 3 R_s)^3 \, {\rm min}$ for a solar type star (where $M_{BH}$ is the black hole mass and $R_p$ is the peribothron distance of the stellar orbit, scaled to 3 Schwarzschild radii)." +" For a 10*(107)Az; black hole. £j,€7(20) days unless the disrupted star is a giant with a large radius."," For a $10^6 \, (10^7) \, M_\odot$ black hole, $t_{fb} \lesssim 7 \, (20)$ days unless the disrupted star is a giant with a large radius." + For ¢>{μι the jet yower should decrease in time. which is not readily apparent in he recent data for (though the interpretation is complicated by the dithculty of relating the luminosity in the bandpass to the bolometric luminosity. let alone to the jet yower or accretion rate).," For $t \gtrsim t_{fb}$, the jet power should decrease in time, which is not readily apparent in the recent data for (though the interpretation is complicated by the difficulty of relating the luminosity in the bandpass to the bolometric luminosity, let alone to the jet power or accretion rate)." + In the magnetar model. the jet power will remain roughly constant for the initial spindown timescale of the neutron star.," In the magnetar model, the jet power will remain roughly constant for the initial spindown timescale of the neutron star." + Depending on the jet collimation and efficiency. the requisite power can be maintained for significantly longer than a month while still satisfying the energy constraints of a maximally spinning neutron star ($2.1).," Depending on the jet collimation and efficiency, the requisite power can be maintained for significantly longer than a month while still satisfying the energy constraints of a maximally spinning neutron star \ref{sec:energy}) )." + The RSG collapse model predicts a nearly constant jet power for up to 1060 days. followed by a rapid drop off (see $2.2. and Fig. 19.," The RSG collapse model predicts a nearly constant jet power for up to $\sim 100$ days, followed by a rapid drop off (see \ref{sec:jet} and Fig. \ref{fig:edot}) )." + If was in fact of stellar origin. one might ask why its properties were so discontinuous compared to any other GRB observed to date.," If was in fact of stellar origin, one might ask why its properties were so discontinuous compared to any other GRB observed to date." + The magnetar model provides no obvious explanation — presumably a continuous range of magnetic field strengths. and hence spin down rates. could be realized.," The magnetar model provides no obvious explanation – presumably a continuous range of magnetic field strengths, and hence spin down rates, could be realized." + In the supergiant collapse ease. on the the other hand. the discontinuity reflects the bimodality of progenitor radii depending on whether or not a massive star retains its hydrogen envelope.," In the supergiant collapse case, on the the other hand, the discontinuity reflects the bimodality of progenitor radii depending on whether or not a massive star retains its hydrogen envelope." + Figure | ?. (e.g.22) (2)..," Figure \ref{fig:edot} \cite{woosley02} \citep[e.g.,][]{quimby07,miller09} \citep{kasen10}." +" (2). (2)... GEκ10°"" (???).. (2)."," \citep{quimby09} \citep{hamuy03}, \citep[$E < 10^{50}$ \citep{kulkarni07,thompson09,bond09}. \citep{prieto08}." +"Neilletal.(2002). found. P,=5.796+0.036 hb for A5 V101 from band photometry.",\citet{neill02} found $P_{\mathrm{orb}} = 5.796\pm0.036$ h for M5 V101 from -band photometry. + They saw two peaks in he orbital modulation in the τοσο band light curve and only one peak per orbit in the V-band. leading them to interpret one of the modulations as being associated: with he secondary. which. at IX5.MO (which they estimated from heir (V1) colour. & 2.2). would be much fainter in the V-band.," They saw two peaks in the orbital modulation in the redder -band light curve and only one peak per orbit in the -band, leading them to interpret one of the modulations as being associated with the secondary, which, at K5–M0 (which they estimated from their $(V-I)$ colour, $\simeq 2.2$ ), would be much fainter in the -band." + Our INT H-band light curve for the night. of.1990 April 1 (Fig., Our INT -band light curve for the night of1990 April 1 (Fig. + Ll (a)) exhibits a 0.3-mag modulation at the orbital period of Neilletal.(2002)., \ref{fig:lcint}~ (a)) exhibits a 0.3-mag modulation at the orbital period of \cite{neill02}. +.. Phe modulation does not appear as strongly in the June data (Fig., The modulation does not appear as strongly in the June data (Fig. + LL (b))., \ref{fig:lcint}~ (b)). + Some Lickering of the object was observed at this time., Some flickering of the object was observed at this time. + We superimposed the sume model (Equation 2)) used by. Neillet al... on our folded light curves for comparison: the resulting plots are shown in Fig. 11..," We superimposed the same model (Equation \ref{eq:model}) ) used by \citeauthor{neill02}, on our folded light curves for comparison: the resulting plots are shown in Fig. \ref{fig:lcint}." + The main peak we observe in the orbital light curve is probably due to the hotspot (the region where the accretion stream from the secondary impacts the accretion disc) rotating into view while the absence of any eclipse suggests the inclination is not high. (Neilletal. estimated the inclination to be between 60°)., The main peak we observe in the orbital light curve is probably due to the hotspot (the region where the accretion stream from the secondary impacts the accretion disc) rotating into view while the absence of any eclipse suggests the inclination is not high \citeauthor{neill02} estimated the inclination to be between $\degr$ ). + We find reasonable agreement with the results of Neillct abe: our {ρα data show an intermediate situation between what, We find reasonable agreement with the results of \citeauthor{neill02}: : our -band data show an intermediate situation between what +Fig.23 shows the period-Iuminosity diagram lor our sample of RIA Lyraes.,\ref{RRLyrPV} shows the period-luminosity diagram for our sample of RR Lyraes. + Those that lie in the S\IC are easily distinguishable5 from those that lie in the Galactic Halo Guarked with a 1I)., Those that lie in the SMC are easily distinguishable from those that lie in the Galactic Halo (marked with a H). + The long-period AUB RR. Lyraes are also identified., The long-period AHB1 RR Lyraes are also identified. + The average V. magnitude ol the SAIC stars lies at V—19.682:0.24., The average V magnitude of the SMC stars lies at $\pm$ 0.24. + The mean V absolute magnitude of RR. Lvraes in the SAIC is My (RRjJ=0.75. as assumed by Graham(1975).. and also used by Ixaluzny and includes correction for metallicity effects.," The mean V absolute magnitude of RR Lyraes in the SMC is $_{V}$ (RR)=0.75, as assumed by \citet{Grah75}, and also used by \citet{Kal98} and includes correction for metallicity effects." + It therefore follows that the SAIC! distance modulus (m-M)y: from our sample of RR Lyvraes is 18.9340.24 or 61.45z 1.0 Kpe., It therefore follows that the SMC distance modulus $_V$ from our sample of RR Lyraes is $\pm$ 0.24 or $\pm$ 7.0 Kpc. + The large errorbar is due to the relatively small sample size., The large errorbar is due to the relatively small sample size. + The average magnitude ol each of the RR Lyrae stars was found. by integrating across the lighteurve. and then the phase of the variability amplitude at the time of the CMD dataset was used to determine the actual apparent magnitude at this same (ime.," The average magnitude of each of the RR Lyrae stars was found, by integrating across the lightcurve, and then the phase of the variability amplitude at the time of the CMD dataset was used to determine the actual apparent magnitude at this same time." + The dillerence between (his and the mean magnitude was then measured., The difference between this and the mean magnitude was then measured. + The error in this measurement as plotted on Fig.23 was taken as (he residual scatter in (he pliase-wrapped lishteurve points at this Gime., The error in this measurement as plotted on \ref{RRLyrPV} was taken as the residual scatter in the phase-wrapped lightcurve points at this time. + This method allows us to account for the variability amplitude when finding the V. magnitudes of our stars. and hence a more accurate measure of (he SAIC distance.," This method allows us to account for the variability amplitude when finding the V magnitudes of our stars, and hence a more accurate measure of the SMC distance." + Our result compares favourably with that of 18.8940.10 presented by Harries.Hilditeh.&Howarth(2003)., Our result compares favourably with that of $\pm$ 0.10 presented by \citet{Harries03}. +.. A larger sample size would help to indicate more conclusively if the SAIC is extended in the radial dimension towards the direction of 47 Tuc., A larger sample size would help to indicate more conclusively if the SMC is extended in the radial dimension towards the direction of 47 Tuc. +" The Blazhko Effect is a little understood feature of some RR. Lyrae stars. in which the amplitude of variation itself varies will a certain perioclicily,"," The Blazhko Effect is a little understood feature of some RR Lyrae stars, in which the amplitude of variation itself varies with a certain periodicity." +" One popular theory (o explain (his erratic behaviour is that il is related {ο (he presence of a strong photospheric magnetic field (Cousens1983).. vel recently Chaclicl,Wade.Shorlin.&Lanclstveet(2004) has ruled oul a magnetic field [ον the brightest Blazhko (DL) star - RR Lyrae itself. the prototype of the class."," One popular theory to explain this erratic behaviour is that it is related to the presence of a strong photospheric magnetic field \citep{Cous83}, yet recently \citet{Chad2004} has ruled out a magnetic field for the brightest Blazhko (BL) star - RR Lyrae itself, the prototype of the class." + Neither this. nor the rotating resonant pulsator model (Dziembowski1999) explain observed BL star properties.," Neither this, nor the rotating resonant pulsator model \citep{Dziem99} explain observed BL star properties." + The frequency of such BL stars seems to be dependent on the metallicity of the environment in which thev occur.," The frequency of such BL stars seems to be dependent on the metallicity of the environment in which they occur," +Historically. OLR emission. from low mass X-ray binaries (LAINBs) during outburst is known to originate in the outer regions of the accretion disc. mostly due to the reprocessing of UVX-ray. photons 2006).,"Historically, OIR emission from low mass X-ray binaries (LMXBs) during outburst is known to originate in the outer regions of the accretion disc, mostly due to the reprocessing of UV/X-ray photons ." +. Non-thermal emission. or thermal evelosvnchrotron in the OLR regime has also been reported since the 1980s but only recentIy has its origin been identified as most likely svnehrotron emission from a compact jet. an outflow and not an inflow. due to its spectral energy. distribution high brightness temperature ancl rapid variability which is correlated with X-ray. variability in a complex manner 2010).. long-term (anti-) correlations with X-ray [lux and. linear polarization 2008:: for a review see 20103).," Non-thermal emission, or thermal cyclosynchrotron in the OIR regime has also been reported since the 1980s but only recently has its origin been identified as most likely synchrotron emission from a compact jet, an outflow and not an inflow, due to its spectral energy distribution high brightness temperature and rapid variability which is correlated with X-ray variability in a complex manner , long-term (anti-) correlations with X-ray flux and linear polarization ; for a review see )." + If one wishes to study the disc. or the jet. at. OLR wavelengths it is usually necessary to isolate the desired component. since contamination from the other can allect the observed spectrum. variability properties (c.g. fractional rms) and correlations with other wavelengths.," If one wishes to study the disc, or the jet, at OIR wavelengths it is usually necessary to isolate the desired component, since contamination from the other can affect the observed spectrum, variability properties (e.g. fractional rms) and correlations with other wavelengths." + H£ the jet is to make a contribution in quiescence this will allect estimates of black hole or neutron star mass. since these rely on the successful isolation of the companion," If the jet is to make a contribution in quiescence this will affect estimates of black hole or neutron star mass, since these rely on the successful isolation of the companion" +of the local sound speed.,of the local sound speed. + Using the SE ghost. cavity. we estimate a evcle time of approximately ἐν107 yr (2«107 vr) if the cavities rose at 0.5 times (1 times) the local sound speed. roughly consistent with our estimate from the shock features.," Using the SE ghost cavity, we estimate a cycle time of approximately $4 \times 10^7$ yr $2 \times 10^7$ yr) if the cavities rose at 0.5 times (1 times) the local sound speed, roughly consistent with our estimate from the shock features." +" Fitting a cooling flow model Guchicdine Galactic absorption aud an extra thermal APEC model to account for overlving gas) to the cluster spectra within a radius of 137""= 95 spe yields a mass deposition rate of AT=M vy2.", Fitting a cooling flow model (including Galactic absorption and an extra thermal APEC model to account for overlying gas) to the cluster spectra within a radius of $\arcsec$ = 95 kpc yields a mass deposition rate of $\dot{M}=55\pm4~ M_{\odot}$ $^{-1}$. + This corresponds to a cooling huninosity δες10P eres +., This corresponds to a cooling luminosity of $5.4\times10^{43}$ erg $^{-1}$. + Heating from the central ACN cau cole the form of shock heating as well as buovantly risingnbubbles inflated by the radio lobes., Heating from the central AGN can come in the form of shock heating as well as buoyantly rising bubbles inflated by the radio lobes. + If the density juup features represeut shocks. we may calculate the shock heating per unit volume using where P is the pre-shock pressure. 5=5/3. and 2afw is the time interval between shocks (Al¢eNamara Nulseu 2007).," If the density jump features represent shocks, we may calculate the shock heating per unit volume using where P is the pre-shock pressure, $\gamma=5/3$, and $2\pi/\omega$ is the time interval between shocks (McNamara Nulsen 2007)." +" For the inner shock. using the pre-shock pressure of1.0«10.29 dar ein7. aud the expected pressure jp of a factor of 1.55. we find I,Lo2:810*EUT7 organ ?sD | or an cherev input rate of EUpbs Cresyes ! within the spherical volume interior to the immer shock using the evele fiue. calculated fom the potential shock feature separation of 1.5«10 vr."," For the inner shock, using the pre-shock pressure of $1.0 \times 10^{-10}$ dyn $^{-2}$, and the expected pressure jump of a factor of 1.55, we find $\Pi_{s}=2.8 \times 10^{-27}$ erg $^{-3}$ $^{-1}$, or an energy input rate of $1.0\times10^{43}$ erg $^{-1}$ within the spherical volume interior to the inner shock using the cycle time calculated from the potential shock feature separation of $1.5\times10^7$ yr." + Therefore. energy iuput from the shocks may coutribute to heating. but falls short by a factor of approximately five of offsetting the cooling.," Therefore, energy input from the shocks may contribute to heating, but falls short by a factor of approximately five of offsetting the cooling." + We may: uso estimate the cherey input from buovantlv rising bubldes., We may also estimate the energy input from buoyantly rising bubbles. + Here. the heat inpit comes from the work done iu wating the bubbles aud the energv conuteut of any eas within the bubbles. E=2j1PV (Chnurazov “ 22002). uxiug 5=5/3.," Here, the heat input comes from the work done in inflating the bubbles and the energy content of any gas within the bubbles, $E = (5/2)PV$ (Churazov et 2002), using $\gamma=5/3$." +" Usiie the pressure in the bubble unus of P=1]«101"" dvi an7. computing the N and S bubble voluues usiic a bubble radius of 105onter = 7.2 Kye aud using the evcle time inferred from the |nibble positions of L<10* yr (2410* yr). we fiud au energy input rate of 2.0.10"" eres 1 (L0«107 ere 1)"," Using the pressure in the bubble rims of $P = 1.1 \times 10^{-10}$ dyn $^{-2}$, computing the N and S bubble volumes using a bubble radius of $10\farcs5$ = 7.2 kpc, and using the cycle time inferred from the outer bubble positions of $4 \times 10^7$ yr $2\times10^7$ yr), we find an energy input rate of $2.0\times10^{43}$ erg $^{-1}$ $4.0\times10^{43}$ erg $^{-1}$ )." +" Tf we assume that the bubbles are filled with relativistic plasma (>3) then £=LPVSlightly (Chinazoyv et 22002) aud the energy Input rate Is higher, 32«107 orgs 1 (Ls107 eres 1)."," If we assume that the bubbles are filled with relativistic plasma $\gamma=4/3$ ) then $E = 4PV$ (Churazov et 2002) and the energy input rate is slightly higher, $3.2\times10^{43}$ erg $^{-1}$ $6.4\times10^{43}$ erg $^{-1}$ )." + The combination of direct shock heating aud energy input from buovautly rising bubbles can then offset the cooling of the gas iu the ceuter of A2052., The combination of direct shock heating and energy input from buoyantly rising bubbles can then offset the cooling of the gas in the center of A2052. + We thank the aunonyinous referee for comments which sienificautly improved this paper., We thank the anonymous referee for comments which significantly improved this paper. + We acknowledge helpful discussions with Christine Jones aud Paul Nulseu., We acknowledge helpful discussions with Christine Jones and Paul Nulsen. + Support for this work was provided by the National Aeronauties and Space Aduinistration. through Award Nuber (QO5-G13TN. ELD was partially supported bv a Clare Boothe Luce Professorship.," Support for this work was provided by the National Aeronautics and Space Administration, through Award Number GO5-6137X. ELB was partially supported by a Clare Boothe Luce Professorship." + |Basic research in radio at the Naval Research Laboratory is ... N 6.1 Base finding., Basic research in radio astronomy at the Naval Research Laboratory is supported by 6.1 Base funding. + SWR was supported |supporter.)o» the Chandra N-rav Center through NASA contract NASs-03060., SWR was supported by the Chandra X-ray Center through NASA contract NAS8-03060. +The similarity between Eqs.,The similarity between Eqs. + Ὁ and 7/ indicates that direction-dependent gains can be incorporated as part of the deconvolution iterations by using an efficient algorithm for the forward and backward calculations., \ref{GRIDDED_ME} and \ref{ME_M} indicates that direction-dependent gains can be incorporated as part of the deconvolution iterations by using an efficient algorithm for the forward and backward calculations. + We have chosen to use a technique similar to that used in the algorithm to correct for the effects of non co-planar baselines (2)., We have chosen to use a technique similar to that used in the algorithm to correct for the effects of non co-planar baselines \citep{W_PROJECTION}. + As discussed in section 4.1.. an approximately unitary operator Ei can be constructed asthe Fourier transform of Eq. 4..," As discussed in section \ref{SEC_JONES}, an approximately unitary operator $\E{ij}{}{}$ can be constructed asthe Fourier transform of Eq. \ref{MUELLER}." + For our purpose. using Ei as the interpolation operator for gridding the visibilities on a regular grid and using FFT to mvert the gridded visibilities would suffice.," For our purpose, using $\E{ij}{^\dag}{}$ as the interpolation operator for gridding the visibilities on a regular grid and using FFT to invert the gridded visibilities would suffice." + The accuracy of the forward calculation is proportional to the accuracy of which can. in principle. be arbitrarily precise (e.g. by accurateFi measurement of the antenna voltage pattern).," The accuracy of the forward calculation is proportional to the accuracy of $\E{ij}{}{}$ which can, in principle, be arbitrarily precise (e.g. by accurate measurement of the antenna voltage pattern)." + An iterative deconvolution scheme using such transforms should ultimately drive the residual image to be noise-like. although it would seem desirable to limit the number of free parameters introduced in the process.," An iterative deconvolution scheme using such transforms should ultimately drive the residual image to be noise-like, although it would seem desirable to limit the number of free parameters introduced in the process." + Note that since the final model image ts iteratively built using accurate computations only in one direction. the intermediate residual dirty images have no physical meaning as ts usually the case.," Note that since the final model image is iteratively built using accurate computations only in one direction, the intermediate residual dirty images have no physical meaning as is usually the case." + JSY affects the measurements as described by Eq. Ι.., $\JS{}{Sky}{}$ affects the measurements as described by Eq. \ref{ME}. + The forward and backward transforms discussed above crucially depend on being at least approximately unitary., The forward and backward transforms discussed above crucially depend on $\E{ij}{}{}$ being at least approximately unitary. + Since Me is an outer Fiproduct of antenna based Jones matrices (Eq. 3)), Since $\MS{ij}{Sky}{}$ is an outer product of antenna based Jones matrices (Eq. \ref{JONES}) ) + and Fi- where 777 represents the element-by-element Fourier ΤΤΙΜΙtransform of its argument. for our purpose it is. sufficient- to ensure that the J’Sky* is- approximately.," and $\E{ij}{}{} = +\mathcal{FT}(\MS{ij}{Sky}{})$ where $\mathcal{FT}$ represents the element-by-element Fourier transform of its argument, for our purpose it is sufficient to ensure that the $\JS{i}{Sky}{}$ is approximately." +"unitary-.. The diagonal terms of Jp (of the form ο,-J Jm correspond to the ideal (un-squinted) power patterns and are nearly equal to each other."," The diagonal terms of $\JS{i}{Sky^\dag}{}\JS{i}{Sky}{}$ (of the form $\JS{i}{p}{}\JS{i}{p^{\textstyle *}}+\JS{i}{pq^{\textstyle +*}}{}\JS{i}{pq}{}$ ) correspond to the ideal (un-squinted) power patterns and are nearly equal to each other." + Fig., Fig. + 3 shows the real and imaginary parts of the off-diagonal term normalized by det(JP)., \ref{Ji01} shows the real and imaginary parts of the off-diagonal term normalized by $det \left(\JS{i}{Sky}{}\right)$. + The peak amplitude is about two orders of magnitude lower than the diagonal term making J; approximately unitary., The peak amplitude is about two orders of magnitude lower than the diagonal term making $\JS{i}{}{}$ approximately unitary. + Image plane corrections therefore can be incorporated as part of the image deconvolution procedure by using =TTMUI and E; as part of the forward and reverseE; transforms between the visibility and image domains for baseline /- j., Image plane corrections therefore can be incorporated as part of the image deconvolution procedure by using $\E{ij}{}{}=\mathcal{FT}\left[\MS{ij}{Sky}{}\right]$ and $\E{ij}{\dag}{}$ as part of the forward and reverse transforms between the visibility and image domains for baseline $i$ $j$ . + Our deconvolution algorithm proceeds as follows:, Our deconvolution algorithm proceeds as follows: +"in the other XDINSs, would imply an anomalously large optical emission efficiency, ~1000 times larger than that of rotation-powered pulsars (Zharikov et al.","in the other XDINSs, would imply an anomalously large optical emission efficiency, $\sim 1000$ times larger than that of rotation-powered pulsars (Zharikov et al." + 2006)., 2006). +" Alternatively, on the basis of a detection in one band only and lacking a deep upper limit in the R band, we suggested that non-thermal optical emission could be powered by the presumably large neutron star magnetic field (z1014 G; Zane et al."," Alternatively, on the basis of a detection in one band only and lacking a deep upper limit in the R band, we suggested that non-thermal optical emission could be powered by the presumably large neutron star magnetic field $\approx 10^{14}$ G; Zane et al." +" 2005), as it has been proposed for the magnetars, whose optical/IR emission efficiency is also a factor of z1000 larger than that of the radio pulsars (Mignani et al."," 2005), as it has been proposed for the magnetars, whose optical/IR emission efficiency is also a factor of $\approx 1000$ larger than that of the radio pulsars (Mignani et al." + 2007a)., 2007a). +" However, in the few cases where multi-band photometry is available, magnetar optical spectra are consistent with PLs with spectral index a&0, again very much different from our limit for1774."," However, in the few cases where multi-band photometry is available, magnetar optical spectra are consistent with PLs with spectral index $\alpha \ga 0$, again very much different from our limit for." +. The R-band upper limit is consistent with a R-J spectrum which passes through the B-band flux., The R-band upper limit is consistent with a R-J spectrum which passes through the B-band flux. +" A linear function connecting the BB-band point and the R-band upper limit has a slope ~ —1.26, and the R-band upper limit lies only ~25% above the extrapolation of the R-J spectrum that passes through the central value of the measured B-band flux."," A linear function connecting the B-band point and the R-band upper limit has a slope $\sim -1.26$ , and the R-band upper limit lies only $\sim 25\%$ above the extrapolation of the R-J spectrum that passes through the central value of the measured B-band flux." +" This is well compatible with both the B and R-band fluxes being on the same R-J spectrum, conceivably emitted by a region of the star surface which is colder than that responsible for the X-ray emission."," This is well compatible with both the B and R-band fluxes being on the same R-J spectrum, conceivably emitted by a region of the star surface which is colder than that responsible for the X-ray emission." + As in Zane et al. (, As in Zane et al. ( +"2008), we consider a picture in which the optical emission originates from a colder fraction of the neutron star surface, which emits a blackbody spectrum at a temperature To (Braje Romani 2002; Pons et al.","2008), we consider a picture in which the optical emission originates from a colder fraction of the neutron star surface, which emits a blackbody spectrum at a temperature $T_O$ (Braje Romani 2002; Pons et al." + 2002; Kaplan et al., 2002; Kaplan et al. + 2003; Trümmper et al., 2003; Trümmper et al. + 2004)., 2004). +" In the R-J tail, the ratio between the optical and X-ray fluxes scales as zràTo/r&Tx=f, where ro is the size of the optically emitting region (which, of course, cannot exceed the value of the neutron star radius), while rx and Tx are the radius and temperature of the X-ray emitting region, as inferred from X-ray spectroscopy, Tx—104 eV, rx km."," In the R-J tail, the ratio between the optical and X-ray fluxes scales as $\approx r_O^2 T_O/r_X^2 T_X \equiv f $, where $r_O$ is the size of the optically emitting region (which, of course, cannot exceed the value of the neutron star radius), while $r_X$ and $T_X$ are the radius and temperature of the X-ray emitting region, as inferred from X-ray spectroscopy, $T_X=104$ eV, $r_X = 2 (d/300 \, {\rm pc})$ km." +" Since the ddistance is unknown, we iterated our computations over several values of d and ro and derived the value of To that corresponds to a given value of the optical excess, f (as computed from the B-band flux)."," Since the distance is unknown, we iterated our computations over several values of $d$ and $r_O$ and derived the value of $T_O$ that corresponds to a given value of the optical excess, $f$ (as computed from the B-band flux)." + Since no contribution from such a cold component is observed in the 0.1-1 keV, Since no contribution from such a cold component is observed in the 0.1-1 keV +where we have introduced the norinalized: Stokes paralucters Q=QI aud ©=U/TI.,where we have introduced the normalized Stokes parameters $\bar{Q}=Q/I$ and $\bar{U}=U/I$. + The above relations can be easily inverted to vield: Finally. the circular poluization deeree. not discussed in this paper. is sunply P.=V—Vi.," The above relations can be easily inverted to yield: Finally, the circular polarization degree, not discussed in this paper, is simply $P_c=\bar{V}\equiv V/I$." + For the sake of clarity. we will set V —0 and neglect all circular polarization effects throughout the paper.," For the sake of clarity, we will set $V$ =0 and neglect all circular polarization effects throughout the paper." + The ideal iuieasureinenut svstem for linear polarization is composed of ao halfwave retarder plate CUWP) followed bv the analyzer. which is a Wollastou prisin AVP) producing two beams with orthogonal polarization directions.," The ideal measurement system for linear polarization is composed of a half-wave retarder plate (HWP) followed by the analyzer, which is a Wollaston prism (WP) producing two beams with orthogonal polarization directions." + In ecueral. each of these elements cau be treated as a mathematical operator that acts on the iuput Stokes vector 5 (seeforexampleShurcliff1962:Cold-stein 2003).," In general, each of these elements can be treated as a mathematical operator that acts on the input Stokes vector $\vec{S}$ \cite[see for example][]{shurcliff,goldstein}." +. What one measures ou the detector is the iutensifios in the ordinary aud extraordinary beams at a eiven LIP angle 0;. which are related to the Stokes parameters by: If the observations are carried out using VW positions for the ΗΝΤΟ. the whole problem of computing Z. iud C reduces to the solution of the 2.N lincar equations svsteuni eiven by Eqs. LL.," What one measures on the detector is the intensities in the ordinary and extraordinary beams at a given $HWP$ angle $\theta_i$, which are related to the Stokes parameters by: If the observations are carried out using $N$ positions for the HWP, the whole problem of computing $I,Q$ and $U$ reduces to the solution of the $N$ linear equations system given by Eqs. \ref{eq:ord}." + It is clear that. having three unkuownus G.Q and C). at least N=2 TWP position augles have to be usec.," It is clear that, having three unknowns $I,Q$ and $U$ ), at least $N$ =2 HWP position angles have to be used." + Iutroduciug the normalized fiux differences F; and notius that fo;|frg;=£. Eqs.," Introducing the normalized flux differences $F_i$ and noting that $f_{O,i}+f_{E,i}=I$, Eqs." + b reduce to the following No equations: We note that cach F parameter is totally determined by a single observation. aud it is therefore iudepenudoenut from sky conditions changes.," \ref{eq:ord} reduce to the following $N$ equations: We note that each $F$ parameter is totally determined by a single observation, and it is therefore independent from sky conditions changes." + It is also worth mentioniue that alternative approaches to the normalized flux ratios exist., It is also worth mentioning that alternative approaches to the normalized flux ratios exist. + One example can be found in Miller.RobinsonGoodrich (1987)., One example can be found in \cite{miller}. +. Iu principle. oue can use auv set of TAWP angles to solve the problem. but is is casy to show that adopting a coustaut step Ad=a/s is the optimal choice.," In principle, one can use any set of HWP angles to solve the problem, but is is easy to show that adopting a constant step $\Delta +\theta$ $\pi/8$ is the optimal choice." + Ii fact. besides miniinizing the errors of the Stokes parameters. this choice makes the solution of Eqs.," In fact, besides minimizing the errors of the Stokes parameters, this choice makes the solution of Eqs." +" 6 trivial: Finally. it preveuts the ""power leakage"" (sec.forin-stance.Pressetal.1999) when oue is to perform a Fourier analysis (see below)."," \ref{eq:system} trivial: Finally, it prevents the “power leakage” \cite[see, for instance,][]{numrep} + when one is to perform a Fourier analysis (see below)." + Tn the ideal case. the normalized flux. differences FP; obey Eq. 6..," In the ideal case, the normalized flux differences $F_i$ obey Eq. \ref{eq:system}," + which is a pure cosinusoid., which is a pure cosinusoid. + Since all possible effects iutroduced. by the TWP aust reproduce after a full revolution. it is natural to consider them as harmonics of a fundamental function. whose period is 25.," Since all possible effects introduced by the HWP must reproduce after a full revolution, it is natural to consider them as harmonics of a fundamental function, whose period is $2\pi$." +" ""Therefore. if 0;=zif8. Eq."," Therefore, if $\theta_i=\pi i/8$, Eq." + 6 cau be rewritten as the following Fourier series: where the Fourier coefficieuts are given by which are valid for Vo=14.8.12.16.," \ref{eq:system} can be rewritten as the following Fourier series: where the Fourier coefficients are given by which are valid for $N=4,8,12,16$." + Comparing Eqs., Comparing Eqs. + with Eq. 6..," \ref{eq:fourcoeff} + with Eq. \ref{eq:system}," + it is clear that the polarization signal is carried bv the &=NIE harmonic., it is clear that the polarization signal is carried by the $k=N/4$ harmonic. +" In a quasi-iceal case. all Fourier cocfiicieuts are expected to be small compared with ey;, and by; and deviatious frou this behaviour could arise from a umber of effects;"," In a quasi-ideal case, all Fourier coefficients are expected to be small compared with $a_{N/4}$ and $b_{N/4}$ and deviations from this behaviour could arise from a number of effects." + For such an approach to the error analysis aud for the meauius of the various harmouics. the reader is referred to Feudtotal. (1996).," For such an approach to the error analysis and for the meaning of the various harmonics, the reader is referred to \cite{fendt}." +. Tlere we just notice that the ay term. which should be vigorously null in the ideal case. is related to the deviations of the WP from the ideal behaviour (see Sec. 1)).," Here we just notice that the $a_0$ term, which should be rigorously null in the ideal case, is related to the deviations of the WP from the ideal behaviour (see Sec. \ref{sec:wollaston}) )." + Tn general. a Fourier analysis is meaningful when AN —16. and can reveal possible problems directly related to the TWP quality (cf," In general, a Fourier analysis is meaningful when $N$ =16, and can reveal possible problems directly related to the HWP quality (cf." + Sec. 8))., Sec. \ref{sec:HWP}) ). + Iu most cases. though. due to practical reasons. one typically uses W= Laud. iu that circumstance. a differeut error treatinent is required.," In most cases, though, due to practical reasons, one typically uses $N$ =4 and, in that circumstance, a different error treatment is required." + Under the assmuptiou that all relevant quantities are cistributed according ο Caussian laws. one can analytically derive simple expressions for the corresponding errors of the final results.," Under the assumption that all relevant quantities are distributed according to Gaussian laws, one can analytically derive simple expressions for the corresponding errors of the final results." + As we will see in the next section. this assumption is not always correct and. when this happens. a ummerical treatineut is required in order to test the analytical results and their range of validity.," As we will see in the next section, this assumption is not always correct and, when this happens, a numerical treatment is required in order to test the analytical results and their range of validity." + Asstunine that the background level is the same in the ordinary and extraordinary beans aud that the reac out noise cau be neglected. the analytical expression for the absolute error of P can be readily derived," Assuming that the background level is the same in the ordinary and extraordinary beams and that the read out noise can be neglected, the analytical expression for the absolute error of $P$ can be readily derived" +with the NSE on behalf of the Gemini. partnership: the National Science. Foundation (United States). the Science ancl Technology. Facilities Council (United. Ixingdom). the National Research Council (Canada). CONICYT. (Chile)da the Australian Research Council (Australia). Ministérrio Cionncia ο Tecnologia. (Brazil) and Ministerio de Ciencia. 'Tecnologtaa e Innovaciónn Productiva (Argentina).,"with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Science and Technology Facilities Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministérrio da Ciênncia e Tecnologia (Brazil) and Ministerio de Ciencia, Tecnologíaa e Innovaciónn Productiva (Argentina)." +We are grateful to the anonymous referee for his/her comments and corrections which helped to improve the content of this paper.,We are grateful to the anonymous referee for his/her comments and corrections which helped to improve the content of this paper. + A.S.C. and G.R. warmly thank to Nidia Morrell for her help with the reduction of echelle spectra., A.S.C. and G.R. warmly thank to Nidia Morrell for her help with the reduction of echelle spectra. + A.S.C. and E.E. acknowdlege finantial support from Agencia de Promociónn Cientiftica v Tecnológgica of Argentina (BID AR PICT 2010-0410 and BID AR PICT 2007-883)., A.S.C. and F.F. acknowdlege finantial support from Agencia de Promociónn Científfica y Tecnológgica of Argentina (BID AR PICT 2010-0410 and BID AR PICT 2007-885). + T.R. acknowledges financial support from the Chilean Center for Astrophysics. FONDAP Nr.," T.R. acknowledges financial support from the Chilean Center for Astrophysics, FONDAP Nr." + 15010003. from FONDECYT project Nr.," 15010003, from FONDECYT project Nr." + 1100620. and from the BASAL Centro de Astrofíssica y Tecnologiaas Atines (CATA) PFB-06/2007.," 1100620, and from the BASAL Centro de Astrofíssica y Tecnologíaas Afines (CATA) PFB-06/2007." + G.R. was supported by ALMA/Conicyt (grant 31070021) and ESO/comite mixto., G.R. was supported by ALMA/Conicyt (grant 31070021) and ESO/comite mixto. + This work was also funded with grants from Consejo Nacional de Investigaciones Científficas y Técenicas de la Repübblica Argentina. Agencia Nacional de Promociónn Científfica y Tecnologgica and Universidad Nacional de La Plata (Argentina).," This work was also funded with grants from Consejo Nacional de Investigaciones ficas y Téccnicas de la Repúbblica Argentina, Agencia Nacional de Promociónn fica y Tecnológgica and Universidad Nacional de La Plata (Argentina)." + Part of the data used in this paper were obtained under GEMINI programs GS-2008A-Q-56. GS-2009A-Q-25 and GS-2010A-Q-31.," Part of the data used in this paper were obtained under GEMINI programs GS-2008A-Q-56, GS-2009A-Q-25 and GS-2010A-Q-21." +aud MHD effects in the initial phase of solar flares.,and MHD effects in the initial phase of solar flares. +(emission) and interstellar (absorption) components of the DLA ealaxies is crucial for a complete understanding of hese objects.,(emission) and interstellar (absorption) components of the DLA galaxies is crucial for a complete understanding of these objects. + At present. there is much debate about he nature of the DLA galaxies: on the basis of the velocity structure in metal absorption lines. Prochaska Wolfe. (1997). argue. that DLA absorbers are the fully-ormed gaseous disks of present-clay spiral galaxies. while llaehnelt et al. (," At present, there is much debate about the nature of the DLA galaxies: on the basis of the velocity structure in metal absorption lines, Prochaska Wolfe (1997) argue that DLA absorbers are the fully-formed gaseous disks of present-day spiral galaxies, while Haehnelt et al. (" +1998) demonstrate that the same data can ος interpreted equally well as the signatures of merging otogalactie clumps.,1998) demonstrate that the same data can be interpreted equally well as the signatures of merging protogalactic clumps. + Helping to resolve such issues is the motivation for the imaging campaign described here., Helping to resolve such issues is the motivation for the imaging campaign described here. + In this paper we are concerned with DLA absorbers at high-recdshift. z1.75. (, In this paper we are concerned with DLA absorbers at high-redshift $z>1.75$. ( +The best imaging study of Iow-redshift DLA absorbers is by Le Brun et al 1997.),The best imaging study of low-redshift DLA absorbers is by Le Brun et al 1997.) + Attempts to image high-redshift DLA absorbers [rom the ground have mostly been unsuccessful., Attempts to image high-redshift DLA absorbers from the ground have mostly been unsuccessful. + Moller and Warren (1998) and IEvnbo. Moller. and Warren (1999) provide a summary of the observations and the conclusions that can be drawn [rom hem.," ller and Warren (1998) and Fynbo, ller, and Warren (1999) provide a summary of the observations and the conclusions that can be drawn from them." + The measured. impact. parameters of the handful of . . ∠⇂∢⋅⊓⋅≼∙∣↓∪⊔⊳∖⋜⊔⋅∢⋅↓⊔↿↓↥⋖⋅↓⋅⋜⋯⋏∙≟⋖⋅∪⋅≤⋗↿∪−≻⋅≤⋗⋡⋜⊔∐⇂⊔↓⋜↧⋏∙≟⊔↓⊓⊔⇂∢⋅⊳∖⋜⊔⋅⋖⊾ ∕∕⋅∕∕ ⋠ − ⊀ ⋅," The measured impact parameters of the handful of detections are in the range $0.9\arcsec$ to $2.9\arcsec$, and magnitudes are $V\sim 25$ . (" +"⋅∕∕ ∖∿−≽⋅↱≻⊳↿∖⇀∖↿∶∶−≽⋅⋅↱≻⋜⋯↓⊔↓↓≻⋯↛↿↓≻⋜⊔⋅⋜⋯↓⋖⊾∩⊾↓⋅∪⇂↓≼↛∪↓⋅↓⋅∢⋅≱∖↓≻∪⊔∠⇂⋡∖ n. . ⋅ ∪⇀∫≻⋅≤⋗∣∣↓∡↓≻≼⇍↓≻↓↥∙∖⇁⊳∖⊔⇍⋜↧↓⊳∖∢⊾↓≻⋜⊔⋅⋜∐↓∪⊔⇂∪↓⋅≤≥⋯∶↓⋅∪⊳≤≥↽∖∶∪⋅∪⋡ and to 5.7h+ kpe for ©,=0.3. O4=0.7. where f=141 100.)","At $z=2.5$ an impact parameter of corresponds to $3.9h^{-1}$ kpc physical separation for $\Omega_m=1.0$, $\Omega_\Lambda=0.0$, and to $5.7h^{-1}$ kpc for $\Omega_m=0.3$, $\Omega_\Lambda=0.7$, where $h=H_{\circ}/100$ .)" + One may reasonably suppose that the absorbers hat have escaped detection have similar impact parameters. rut are fainter. or have smaller impact. parameters.," One may reasonably suppose that the absorbers that have escaped detection have similar impact parameters, but are fainter, or have smaller impact parameters." + In either case the clear choice of telescope for a new imaging campaign is the Hubble Space Telescope. for the unrivaled depth and spatial resolution.," In either case the clear choice of telescope for a new imaging campaign is the Hubble Space Telescope, for the unrivaled depth and spatial resolution." +. We are engaged in a programme of imaging with the STIS and NICAIOS (NIC?) instruments aboard HIST. to search for the galaxy counterparts of LS high-recshift 1.75 DLA absorption lines seen in the spectra of 16 target quasars.," We are engaged in a programme of imaging with the STIS and NICMOS (NIC2) instruments aboard HST, to search for the galaxy counterparts of 18 high-redshift $z>1.75$ DLA absorption lines seen in the spectra of 16 target quasars." + This paper presents the results of the imaging campaign with the NIC2 camera., This paper presents the results of the imaging campaign with the NIC2 camera. + The STIS images reach about 2.5 AD mae., The STIS images reach about 2.5 AB mag. + deeper than the NICMOS images. and have twice the resolution. anc therefore are expected to be the most useful in terms of proportion of detections.," deeper than the NICMOS images, and have twice the resolution, and therefore are expected to be the most useful in terms of proportion of detections." + The NICAIOS observations complement the STIS observations. providing colours. as well as luminosity profiles in the restframe optical.," The NICMOS observations complement the STIS observations, providing colours, as well as luminosity profiles in the restframe optical." + Also the NICMOS frames will be more sensitive for any galaxy counterparts that are. particularly red., Also the NICMOS frames will be more sensitive for any galaxy counterparts that are particularly red. + In Section. 2 we tabulate the target. quasars. and the details of the observations. and describe the steps Followed. in reducing the data and combining in mosaics.," In Section 2 we tabulate the target quasars, and the details of the observations, and describe the steps followed in reducing the data and combining in mosaics." + We describe the methods used for subtracting the image of the quasar in each field. and for constructing error frames that include the svstematic errors associated with the point spread function (psf) subtraction.," We describe the methods used for subtracting the image of the quasar in each field, and for constructing error frames that include the systematic errors associated with the point spread function (psf) subtraction." + Section 3 includes a description of the detection algorithm and catalogues the candidate galaxy counterparts found in each field. together with details of their shapes. sizes. and. luminosity profiles. where measurable.," Section 3 includes a description of the detection algorithm and catalogues the candidate galaxy counterparts found in each field, together with details of their shapes, sizes, and luminosity profiles, where measurable." + The detection limits as a function. of angular separation from the quasar are also provided. for cach field., The detection limits as a function of angular separation from the quasar are also provided for each field. + In a recent preprint Kulkarni et al. (, In a recent preprint Kulkarni et al. ( +"2000). present similar NICMOS observations of a single quasar field. where they detect à candidate DLA absorber counterpart at small inipact parameter. 0.25"".","2000) present similar NICMOS observations of a single quasar field, where they detect a candidate DLA absorber counterpart at small impact parameter, $0.25\arcsec$." +" ""heir method of psf subtraction is different from. ours.", Their method of psf subtraction is different from ours. + Their preprint appeared. after we had completed this work. and the techniques were developed independently.," Their preprint appeared after we had completed this work, and the techniques were developed independently." + We compare their method of psf subtraction with ours. and discuss their detection in the light of the detections reported here.," We compare their method of psf subtraction with ours, and discuss their detection in the light of the detections reported here." + The target absorbers were selected with a view to covering a wide range of column densities in order to be able to investigate any correlation between column density and. for example. impact parameter.," The target absorbers were selected with a view to covering a wide range of column densities in order to be able to investigate any correlation between column density and, for example, impact parameter." + We wished also to cover a broad redshift interval. to quantify any evolution in the properties of the absorbing galaxies.," We wished also to cover a broad redshift interval, to quantify any evolution in the properties of the absorbing galaxies." +" A lower redshift limit z,5;=1.75 was imposed as this corresponds to the wavelength at which Lye enters the range observable from the ground.", A lower redshift limit $z_{abs}=1.75$ was imposed as this corresponds to the wavelength at which $\alpha$ enters the range observable from the ground. + In fac many of the nearly 100. DLA absorbers so far cataloguec lio within quite a narrow range of redshifts LS2\times 10^{20}$ $^{-2}$, and otherwise as LLS, standing for Lyman-limit system." + There are LS absorbers classified DLA. 5 classified LLS. and one candidate hieh-column clensity svstem that remains to be confirmed.," There are 18 absorbers classified DLA, 5 classified LLS, and one candidate high-column density system that remains to be confirmed." + These are the absorbers for which we aim to detect the counterpart ealaxies., These are the absorbers for which we aim to detect the counterpart galaxies. + In. Fig., In Fig. + Lo we plot column density against redshift for the 23 absorbers in Table 1 that have been confirmed with high-resolution spectroscopy., 1 we plot column density against redshift for the 23 absorbers in Table 1 that have been confirmed with high-resolution spectroscopy. + Weused the NICD camera with the FIGOW (ic. 11 band) filter to observe the fields around these 16 quasars. at various dates Commencing 23 April 1998 and ending 12 Sep," Weused the NIC2 camera with the F160W (i.e. H band) filter to observe the fields around these 16 quasars, at various dates commencing 23 April 1998 and ending 12 Sep" +numerical domain extends from the photosphere to R. = 20 Rs radially.,numerical domain extends from the photosphere to R = 20 Rs radially. + The spacial resolution is 25 km at the surface and increasing with radius., The spacial resolution is 25 km at the surface and increasing with radius. +" The horizonal length is 3,000 km at the photosphere with spacial resolution of ~ 100 km."," The horizonal length is 3,000 km at the photosphere with spacial resolution of $\sim$ 100 km." + Total grid points in our simulation are 8198 in radial direction and 32 in horizontal direction., Total grid points in our simulation are 8198 in radial direction and 32 in horizontal direction. + 'The turbulent heating rate is estimated by dimensional analysis since viscosity and resistivity are not included explicitly in our basic equations., The turbulent heating rate is estimated by dimensional analysis since viscosity and resistivity are not included explicitly in our basic equations. +" First, we derive the Fourier component, 66, of the Alfvénnic disturbance (vo) as follows."," First, we derive the Fourier component, $\hat{v}_\theta$, of the Alfvénnic disturbance $v_\theta$ ) as follows." +" Then, energy spectral density, E(r,ko), becomes where A@ indicates the angular system size in ϕ direction."," Then, energy spectral density, $E(r,k_\phi)$, becomes where $\Delta \phi$ indicates the angular system size in $\phi$ direction." +" By using kg and E(r,kg), we can estimate the energy exchanging rate, e(r, for a certain wave number, kg, with neighboring Fourier kg),modes."," By using $k_\phi$ and $E(r,k_\phi)$ we can estimate the energy exchanging rate, $\epsilon (r,k_\phi)$, for a certain wave number, $k_\phi$, with neighboring Fourier modes." +" Then e(r,kg) becomes where p denotes the mean density averaged over time and ¢ direction."," Then $\epsilon(r,k_\phi)$ becomes where $\bar{\rho}$ denotes the mean density averaged over time and $\phi$ direction." +" As a turbulent heating rate, we use e(r, whose wave number is larger than critical wave numberko) that is determined by numerical aresolution."," As a turbulent heating rate, we use $\epsilon(r,k_\phi)$ whose wave number is larger than a critical wave number that is determined by numerical resolution." + We choose kgrAg/2m=4 as the critical wave number that corresponds to the spatial resolution covering one wave length by 8 grid points in our simulation., We choose $k_\phi r \Delta \phi / 2\pi = 4$ as the critical wave number that corresponds to the spatial resolution covering one wave length by 8 grid points in our simulation. +" The coupling between the magnetic field and the surface convection excites upward propagating Alfvénn wave (Steineretal. and it could be an efficient energy carrier in the 1998),,solar atmosphere."," The coupling between the magnetic field and the surface convection excites upward propagating Alfvénn wave \citep{steiner98}, and it could be an efficient energy carrier in the solar atmosphere." +" Considering such scenario, we performed 2.5 D MHD simulations covering regions directly from the photosphere to the interplanetary space."," Considering such scenario, we performed 2.5 D MHD simulations covering regions directly from the photosphere to the interplanetary space." +" Once the Alfvénn wave is forced to excite, the numerical system attains quasi-steady state within 1,800 minutes."," Once the Alfvénn wave is forced to excite, the numerical system attains quasi-steady state within 1,800 minutes." +" Due to the dissipation of the Alfvénn wave, the initially static and isothermal (104 K) atmospheres eventually develops a hot corona K) and a high-speed (> 500 km s-!) solar wind (109(Figs."," Due to the dissipation of the Alfvénn wave, the initially static and isothermal $^4$ K) atmospheres eventually develops a hot corona $^6$ K) and a high-speed $\gtrsim$ 500 km $^{-1}$ ) solar wind (Figs." + 1 and 2)., 1 and 2). +" The radial profiles of velocity, temperature, and density are quite consistent with the spectroscopic and interplanetary scintillation observations (Fig."," The radial profiles of velocity, temperature, and density are quite consistent with the spectroscopic and interplanetary scintillation observations (Fig." + , 2). +"Even though previous one dimensional simulations (Suzuki2).&Inutsuka2005,2006) show similar radial variations, the coronal heating and solar wind acceleration mechanism in our two dimensional simulation is essentially different from the previous ones."," Even though previous one dimensional simulations \citep{suzu05,suzu06} show similar radial variations, the coronal heating and solar wind acceleration mechanism in our two dimensional simulation is essentially different from the previous ones." +" The energy losses such as radiative cooling, thermal conduction, and adiabatic cooling due to the solar wind are the main cooling processes in the solar atmosphere."," The energy losses such as radiative cooling, thermal conduction, and adiabatic cooling due to the solar wind are the main cooling processes in the solar atmosphere." +" In order to maintain the solar corona,heating processes are necessary to balance the cooling processes."," In order to maintain the solar corona,heating processes are necessary to balance the cooling processes." + As shown in the, As shown in the +be dissipated by the (large) resistivity.,be dissipated by the (large) resistivity. + Downstream of the shock. the deuse pseudodisk collapses horizontally. nearly perpeudieular to the (poloidal) field lines.," Downstream of the shock, the dense pseudodisk collapses horizontally, nearly perpendicular to the (poloidal) field lines." + At the relatively late time shown in Figure 7.. the field lines inside the pseudodisk are nearly held fixed in space. with the ward advection due to infalling material balance by the outward resistivityv-driven diffusion.," At the relatively late time shown in Figure \ref{ER20}, the field lines inside the pseudodisk are nearly held fixed in space, with the inward advection due to infalling material balanced by the outward resistivity-driven diffusion." + The role of resistivity in enabling disk formation can be seen clearly in Figure 11l.. where the vertica conrponeut of the magnetic field on the equator. D.. is plotted as a function of tine for all three moclels with different cuhanced resistivities.," The role of resistivity in enabling disk formation can be seen clearly in Figure \ref{Bz_all}, where the vertical component of the magnetic field on the equator, $B_z$, is plotted as a function of time for all three models with different enhanced resistivities." + The equatorial iufal in the pseudodisk teuds to compress the poloidal fiek ines. leading to a sharp increase in the poloidal fick streneth at small radii.," The equatorial infall in the pseudodisk tends to compress the poloidal field lines, leading to a sharp increase in the poloidal field strength at small radii." + Resistivity. on the other haud. ends to smooth out the feld distribution.," Resistivity, on the other hand, tends to smooth out the field distribution." + The uct effect is that the poloidal field streugth at sinall radii depends stronely ou the magnitude of the resistivity. cine larger for smaller resistivities.," The net effect is that the poloidal field strength at small radii depends strongly on the magnitude of the resistivity, being larger for smaller resistivities." + Since most of the uaenetie braking occurs at relatively πα] radi. where he infalling material attempts to spin up the fastest to conserve aueular moment. the stronger poloidal fields in the two less resistive cases (110dels ERIS and ERIT9) xoduce a stronger braking. which is enough to suppress he formation of a rotationally supported disk.," Since most of the magnetic braking occurs at relatively small radii, where the infalling material attempts to spin up the fastest to conserve angular momentum, the stronger poloidal fields in the two less resistive cases (models ER18 and ER19) produce a stronger braking, which is enough to suppress the formation of a rotationally supported disk." + The most resistive case (model ER20) has the weakest poloida field at small radii (where maeuetic braking matters uost in the model) which. together with a laree slippage οσοι the field) lines and matter in the azuuutha direction (which males it hard to generate a toroida field). makes the magnetic braking ineffective and disk ormation possible.," The most resistive case (model ER20) has the weakest poloidal field at small radii (where magnetic braking matters most in the model) which, together with a large slippage between the field lines and matter in the azimuthal direction (which makes it hard to generate a toroidal field), makes the magnetic braking ineffective and disk formation possible." + That the disk im model ER20 forms as a result of enhanced resistivity rather than munaerica diffusion is supported by the fact that a nearly ideutica disk is formed in the lower resolution run (sce Figure 8))., That the disk in model ER20 forms as a result of enhanced resistivity rather than numerical diffusion is supported by the fact that a nearly identical disk is formed in the lower resolution run (see Figure \ref{ER20r}) ). + One can roughly estimate the size of the resistivityenabled disk- as follows., One can roughly estimate the size of the resistivity-enabled disk as follows. + Iu order for the formes rotationally supported disk to survive agaimst magnetic braking. the disk rotation must not twist up the poloida magnetic field that threads the disk too strongly.," In order for the formed rotationally supported disk to survive against magnetic braking, the disk rotation must not twist up the poloidal magnetic field that threads the disk too strongly." + This is satisfied when the magnetic diffusion speed becomes comparable to the Keplerian speed. which leads to the condition 4egif. where FH is the vertical scale leneth over Which the toroidal magnetic field varies.," This is satisfied when the magnetic diffusion speed becomes comparable to the Keplerian speed, which leads to the condition $\eta\sim v_K H$, where $H$ is the vertical scale length over which the toroidal magnetic field varies." + If we take II to he the disk pressure scale height (ignoring possible magnetic compression of the disk). aud use the standard result for à thiu-disk ff/r~ef£cegy (Gvhere p ds the radius and e is the isothermal sound speed). then are or pocajacBBsIOSAU (for y=1070s! aud a—2«qO0lens P).," If we take $H$ to be the disk pressure scale height (ignoring possible magnetic compression of the disk), and use the standard result for a thin-disk $H/r \sim a/v_K$ (where $r$ is the radius and $a$ is the isothermal sound speed), then $\eta \sim +r a$ or $r \sim \eta/a \sim 3.3\times 10^2\au$ (for $\eta=10^{20}\etaunit$ and $a=2\times +10^4\cms$ )." + This is about a factor of two larger than the disk radius that we found uuucericallv iu Figure 7.., This is about a factor of two larger than the disk radius that we found numerically in Figure \ref{ER20}. + We should cautiou the reader that the above estimate did not take iuto account the detailed magnetic ecolctry and braking cficiency. which depends on the field strength (see below).," We should caution the reader that the above estimate did not take into account the detailed magnetic geometry and braking efficiency, which depends on the field strength (see below)." + For a weal. enough field. a disk Ce‘an form independent of the magnitude of the resistivity.," For a weak enough field, a disk can form independent of the magnitude of the resistivity." + Besides the three representative iuodels discussed above. we have carried out two additional simulations with 7=3<1025 (Model ERIS.5) and ὃς102eni?τ (Model. ER19.5).," Besides the three representative models discussed above, we have carried out two additional simulations with $\eta=3\times 10^{18}$ (Model ER18.5) and $3\times 10^{19}\etaunit$ (Model ER19.5)." + As one would expect based on the results for Models ERIS aud ERI9. uo rotationally supported disk forms in Model ER18.5.," As one would expect based on the results for Models ER18 and ER19, no rotationally supported disk forms in Model ER18.5." + There is a sinall (~LOAT in radius) rotationally supported disk in the more resistive Model ER19.5 at the fiducial time t=lol’s., There is a small $\sim 40\au$ in radius) rotationally supported disk in the more resistive Model ER19.5 at the fiducial time $t=10^{12}\second$. + The disk shrinks with time. however.," The disk shrinks with time, however." + By t=2«10M?s. its radius decreases to 25AU: it may disappear altogether at a later time.," By $t=2\times 10^{12}\second$, its radius decreases to $\sim 25\au$; it may disappear altogether at a later time." + The troeud indicates that7=3<10anesfis probably close to the critical resistivity 5j. needed for disk formation., The trend indicates that$\eta=3\times 10^{19}\etaunit$ is probably close to the critical resistivity $\eta_c$ needed for disk formation. + The value for the critical resistivity jj. depends ou the initial feld strveneth By., The value for the critical resistivity $\eta_c$ depends on the initial field strength $B_0$. + This is to be expected since. in the lint of infinitely weak field. rotationally supported disks can form without auv (enhaucecl) resistivity at all (Le. ay.=0).," This is to be expected since, in the limit of infinitely weak field, rotationally supported disks can form without any (enhanced) resistivity at all (i.e., $\eta_c=0$ )." + For a moderately magnetized deuse core of By=10.0eC. we find that the transition between the formation of a rotationally support disk and its suppression occurs between 4j=102775 (Model ERISw) aud 3.«108cues! (Model ERIS.Pw).," For a moderately magnetized dense core of $B_0=10.6\muG$, we find that the transition between the formation of a rotationally support disk and its suppression occurs between $\eta=10^{18}$ (Model ER18w) and $3\times 10^{18}\etaunit$ (Model ER18.5w)." + This value of By is probably close to the lower limit to the field strenetl in dense cores. jucdeie from the fact that the median field streneth for the more diffuse. cold neutral medi (CNM) of atomic gas is 6Ce (IIoiles&Trolaud2005) and that the directly measured line-of-sight componcut of the magnetic fields iu a number of deuse cores is of this order or higher (Crutcher&Troland2008): the full streneth of the core maeuetic field is likely significantly lnieher.," This value of $B_0$ is probably close to the lower limit to the field strength in dense cores, judging from the fact that the median field strength for the more diffuse, cold neutral medium (CNM) of atomic gas is $\sim 6\muG$ \citep{ht05} + and that the directly measured line-of-sight component of the magnetic fields in a number of dense cores is of this order or higher \citep{ct08}; the full strength of the core magnetic field is likely significantly higher." + It is therefore reasonable to expect the critical value 44 for disk formation in cloud cores magnetized. to a realistic level to lie somewhat between i.~3<10475 and ~3&101?u?81.," It is therefore reasonable to expect the critical value $\eta_c$ for disk formation in cloud cores magnetized to a realistic level to lie somewhat between $\eta_c \sim +3\times 10^{18}$ and $\sim 3\times 10^{19}\etaunit$." + In what follows. we will take Wo=10)02st as the characteristic critical value. with the understanding that it depeuds somewhat ou the field streneth. and cau be uncertain by a factor of 3 in either direction.," In what follows, we will take $\eta_c=10^{19}\etaunit$ as the characteristic critical value, with the understanding that it depends somewhat on the field strength, and can be uncertain by a factor of $\sim 3$ in either direction." + Our most important result is that classical resistivity alone appears unable to weaken maguetic braking euougl to allow a rotationally supported disk to form for a realistic level of core magnetization. aud that au cnhhanced resistivity of order i).=10219cues1 is needed.," Our most important result is that classical resistivity alone appears unable to weaken magnetic braking enough to allow a rotationally supported disk to form for a realistic level of core magnetization, and that an enhanced resistivity of order $\eta_c=10^{19}\etaunit$ is needed." + A Lunge. enhanced resistivity (of order 2«1079cm?s 1) was advocated by Shuctal.(2006) to solve the so-called “magnetic flux problem” iu star formation.," A large, enhanced resistivity (of order $2\times 10^{20}\etaunit$ ) was advocated by \citet{sglc06} to solve the so-called “magnetic flux problem” in star formation." + They introduced the concept of the Oli sphere. with a radius: where M. is the central stellar mass.," They introduced the concept of the Ohm sphere, with a radius: where $M_*$ is the central stellar mass." + It can be obtained bv settiug the characteristic maguetic diffusion speed eamafr equal to the free-fall speed egΛΙ5., It can be obtained by setting the characteristic magnetic diffusion speed $v_{\rm d}=\eta/r$ equal to the free-fall speed $v_{\rm ff}= (2 G M_*/r)^{1/2}$. + Tn the lanit of a weak imaeuetic field (so that the magnetic forces do not affect the accretion αναΙσ) and zero rotation. Shuetal.(2006). showed that the magnetic field becomes more or less uniforii inside the Olun sphere: the sphere may be thus regarded as the reeion of complete magnetic decoupling.," In the limit of a weak magnetic field (so that the magnetic forces do not affect the accretion dynamics) and zero rotation, \citet{sglc06} showed that the magnetic field becomes more or less uniform inside the Ohm sphere; the sphere may be thus regarded as the region of complete magnetic decoupling." + Ifa rotationally supported disk were to form inside the Olu sphere. it would be protected against strong braking by the decoupling.," If a rotationally supported disk were to form inside the Ohm sphere, it would be protected against strong braking by the decoupling." + If the Oluu sphere 1iust be larecr than the rotationally supported disk. then to form a disk of 10?AU in radius around a half-solar ass star. the resistivity inst be tyΕΕ~L530, if a black hole is present."," Thus, for radial velocities in M 15, $g_*=0.07$ at best, and we would expect to see $N_{\rm M15}^L=0.1$ stars, moving with a relative radial velocity $\ge +3\sigma_0$ if a black hole is present." + That no such star has been seen is. therefore. unsurprising and uninformative.," That no such star has been seen is, therefore, unsurprising and uninformative." + Combining the entire dozen most-likely clusters vields perhaps one or two fast-moving stars., Combining the entire dozen most-likely clusters yields perhaps one or two fast-moving stars. + VU);=0.004 stars., $N_{\rm M15}^H=0.004$ stars. + The nunmber expected is effectively zero., The number expected is effectively zero. + A futher problem with using radial velocities to detect the fast-moving stars lies in (heir racial distribution as given by the integrands in equations (8)) aud (9)) after an appropriate coordinate transformation., A further problem with using radial velocities to detect the fast-moving stars lies in their radial distribution as given by the integrands in equations \ref{E:I1})) and \ref{E:I2}) ) after an appropriate coordinate transformation. + We compare (these in Figure 1. lor /=3 and the three values of D., We compare these in Figure \ref{F:x} for $k=3$ and the three values of $D$. + In all three cases. the fast-moving stars are concentrated well within ij.," In all three cases, the fast-moving stars are concentrated well within $r_h$." +" The break point al 0.80, is (he result of the break in σε at this radius.", The break point at $0.4r_h$ is the result of the break in $\sigma_\bullet$ at this radius. + Note the very different expected radial distributions for the fast-moving stars depending on whether (solid) or not (dolled) (here is a black hole., Note the very different expected radial distributions for the fast-moving stars depending on whether ) or not ) there is a black hole. + If there is a black hole. the fast-moving stars should be concentrated in the center ol the cluster. with a maximum inside 0.175.," If there is a black hole, the fast-moving stars should be concentrated in the center of the cluster, with a maximum inside $0.1 r_h$." + For radial velocities. the high-velocity stars are confined within about 0.15rj or 073 for the nearer clusters.," For radial velocities, the high-velocity stars are confined within about $0.15r_h$ or 3 for the nearer clusters." + For the higher-dimensional velocities. (he detection region is somewhat broader.," For the higher-dimensional velocities, the detection region is somewhat broader." + Clearly. radial velocities are unlikely to prove the question one wav or another.," Clearly, radial velocities are unlikely to prove the question one way or another." + For proper motions. the situation is much better. at least lor nearby. clusters for which such observations are feasible.," For proper motions, the situation is much better, at least for nearby clusters for which such observations are feasible." +" In the case of NGC 6752. Rubenstein&Bailvn(1997) measure 153 stars brighter (han V; within r,=276 of the cluster center."," In the case of NGC 6752, \cite{rb97} measure 153 stars brighter than $V_d$ within $r_h=2\farcs6$ of the cluster center." + To the same radius. (2003).. measure the proper motions of 15 stars.," To the same radius, \citet{dbvg}, measure the proper motions of 15 stars." + Their detection region only covers about a third of (he area within rj due to gaps in their 1999 data., Their detection region only covers about a third of the area within $r_h$ due to gaps in their 1999 data. + These gaps. unfortunately. covers much of the very. center of the cluster. so it is difficult to estimate Che detection rate within about 0.375 where we expect to find most of the [ast-moving stus.," These gaps, unfortunately, covers much of the very center of the cluster, so it is difficult to estimate the detection rate within about $0.3r_h$ where we expect to find most of the fast-moving stars." + Crowcding is bound to be a problem in this region. even for UST.," Crowding is bound to be a problem in this region, even for ." + Extrapolating from the most crowded regions studied by Drukieretal.(2003). and taking into account the gapsin their coverage. we," Extrapolating from the most crowded regions studied by \citet{dbvg} and taking into account the gapsin their coverage, we" +of both stars in the heating of the wall should be calculated for a particular configuration before comparison with the observed SED.,of both stars in the heating of the wall should be calculated for a particular configuration before comparison with the observed SED. + This paper has several goals., This paper has several goals. + The first is to find a simplilied structure of the inner edee of the CD disk around the Cok Tau/4 binary svstem that consistently reproduces the observed spectral energy. distribution (SED)., The first is to find a simplified structure of the inner edge of the CB disk around the CoKU Tau/4 binary system that consistently reproduces the observed spectral energy distribution (SED). + The second is to determine the properties of the dust particles of that edge., The second is to determine the properties of the dust particles of that edge. + Spitzer observations probe mostiv the upper lavers of ihe inner 10-20 AU regions of typical disks (D'Alessioetal.2006).. while at the present resolution of subamillimeter and millimeter interferometers. (he main contribution comes from the midplane at larger distances.," Spitzer observations probe mostly the upper layers of the inner 10-20 AU regions of typical disks \citep{Dalessio3}, while at the present resolution of submillimeter and millimeter interferometers, the main contribution comes from the midplane at larger distances." + In contrast. circumbinary. ancl (ransitional disks are truncated at a certain radius. making them a natural laboratory (ο study the dist near the midplane in the inner disk region. inaccessible bv other means.," In contrast, circumbinary and transitional disks are truncated at a certain radius, making them a natural laboratory to study the dust near the midplane in the inner disk region, inaccessible by other means." + In 2 we describe the physies of the models. and in 3. we present the fiducial model adopted as a reference for later comparisons; in 4 we study (he effects of changing parameters in the SED ofthe fiducial model: in 5 we apply our methods to the case of Colxu Tau/4. aud in 6 we discuss our results and give conclusions.," In \ref{sec-description} we describe the physics of the models, and in \ref{sec-fiducial} we present the fiducial model adopted as a reference for later comparisons; in \ref{sec-var-param} we study the effects of changing parameters in the SED ofthe fiducial model; in \ref{sec-results} we apply our methods to the case of CoKu Tau/4, and in \ref{sec-conclusions} we discuss our results and give conclusions." + Our basic model consists of a CD disk. from whieh only its inner wall contributes to theSED in the mxl-IR. spectral range (5— 40jan). surrounding (vo stars that contribute mainlv (o the near-IR flux.," Our basic model consists of a CB disk, from which only its inner wall contributes to theSED in the mid-IR spectral range $5-40\mu$ m), surrounding two stars that contribute mainly to the near-IR flux." + The main dillerence between the present model aud the one described in D05 is that here the inner wall is irradiated bv (wo stars and each of them has a clifferent distance to anv surface element of the wall since neither of the stars is located at the geometrical center of the CD disk., The main difference between the present model and the one described in D05 is that here the inner wall is irradiated by two stars and each of them has a different distance to any surface element of the wall since neither of the stars is located at the geometrical center of the CB disk. + Moreover. since the stars are moving in their orbits. their distance to each portion of the inner wall changes with time.," Moreover, since the stars are moving in their orbits, their distance to each portion of the inner wall changes with time." + Asstuning that the wall reaches thermal equilibrium in a timescale shorter (han the orbital timescale of the binary svstem (see the Appendix for the evaluation of this assumption). the temperature of each portion of the wall and the resulting SED are periodically variable with its orbital timescale.," Assuming that the wall reaches thermal equilibrium in a timescale shorter than the orbital timescale of the binary system (see the Appendix for the evaluation of this assumption), the temperature of each portion of the wall and the resulting SED are periodically variable with its orbital timescale." + The fact that we are describing a CD disk implies that a whole set of new parameters should be included into the model. in comparison to the model proposed by 005.," The fact that we are describing a CB disk implies that a whole set of new parameters should be included into the model, in comparison to the model proposed by D05." + At first sight. it might look like (his increasing degree of freedom makes (he problem degenerate.," At first sight, it might look like this increasing degree of freedom makes the problem degenerate." + llowever. new restrictions allow one to break part of this degeneracy. as we will see in the following sections.," However, new restrictions allow one to break part of this degeneracy, as we will see in the following sections." + Figure 16. shows the geometrical parameters that describe the spatial configuration of the svstem. namely. the semi-major axis a. eccentricity € and the angle ©. that locates one," Figure \ref{fig-configuracion} shows the geometrical parameters that describe the spatial configuration of the system, namely, the semi-major axis $a$ , eccentricity $e$ and the angle $\phi$ , that locates one" + , +the probability of a detection.,the probability of a detection. + Even in the presence of a null result. a more sensitive survey will allow the derivation oftighter limits on the planet abundance.," Even in the presence of a null result, a more sensitive survey will allow the derivation of tighter limits on the planet abundance." + The calculations presented in this work were done using IDL programs and the CONDOR distributed computing software., The calculations presented in this work were done using IDL programs and the CONDOR distributed computing software. +" IDL is provided. under license. by Research Systems Inc. DMB is grateful to PPARC for the provision of a PhD studentship whilst at St. Andrews University and post-doctoral support at LIMU. the latter as part of the ""RoboNet-1.0"" project."," IDL is provided, under license, by Research Systems Inc. DMB is grateful to PPARC for the provision of a PhD studentship whilst at St. Andrews University and post-doctoral support at LJMU, the latter as part of the “RoboNet-1.0” project." +mass-loss rate of individual stars and the optical thickness of their envelope (??)..,"mass-loss rate of individual stars and the optical thickness of their envelope \citep{2008AIPC.1001..331M,2006A&A...448..181G}." + We display the mid-IR SEDs between 3.6 and 24 im Figures 5 and 6., We display the mid-IR SEDs between 3.6 and 24 in Figures 5 and 6. +" In Figure 5 we select all sources where AF, varies by less than one order of magnitude between 5.8 and 8. While sources with larger differences are plotted in Figure 6."," In Figure 5 we select all sources where $\lambda F_\lambda$ varies by less than one order of magnitude between 5.8 and 8, while sources with larger differences are plotted in Figure 6." + Notice that all sources in Figure 6 have a dip at 4.5 (seealso?) except s17. which is the source with the lowest Ha’ flux.," Notice that all sources in Figure \ref{fig:irac2} + have a dip at 4.5 \citep[see also][]{2007A&A...476.1161V} except s17, which is the source with the lowest $\alpha$ flux." + Sources are ordered according to the SED slope between 8 and 24 wwith s5 being the source with the largest gradient and s14 the source with the smallest one., Sources are ordered according to the SED slope between 8 and 24 with s5 being the source with the largest gradient and s14 the source with the smallest one. + For all sources in Figure 6 we detect CO emission., For all sources in Figure \ref{fig:irac2} we detect CO emission. + Sources in Figure 5. instead have either weak or no CO emission and no dip at 4.5jim., Sources in Figure \ref{fig:irac1} instead have either weak or no CO emission and no dip at 4.5. +.. We have identified s].s?.s3. and s20 as regions containing evolved variable stars.," We have identified s1,s2,s3, and s20 as regions containing evolved variable stars." + It has been shown that the MIR SED of YSOs and HII regions have steeper slopes than evolved stars (??).. in agreement with our finding.," It has been shown that the MIR SED of YSOs and HII regions have steeper slopes than evolved stars \citep{2009AJ....138.1597B,2009ApJS..184..172G}, in agreement with our finding." + This is because the SED of star forming regions in the mid-infrared peaks at wavelenghts longer than 24 (e.g.2.)., This is because the SED of star forming regions in the mid-infrared peaks at wavelenghts longer than 24 \citep[e.g.][ ]{2010ApJ...716..453L}. + The CO emission associated with sources in Figure 5.. is weak or under our detection limit.," The CO emission associated with sources in Figure \ref{fig:irac1}, is weak or under our detection limit." + The ? catalogue does not extend as far as sd. which might be a variable associated with M33 or with our Galaxy.," The \citet{2007ApJ...664..850M} catalogue does not extend as far as s4, which might be a variable associated with M33 or with our Galaxy." + The only HII region where no CO has been detected 1s s16. likely an evolved HII region.," The only HII region where no CO has been detected is s16, likely an evolved HII region." + Evolved stars and evolved HII regions show a shallow slope in the IRAC bands., Evolved stars and evolved HII regions show a shallow slope in the IRAC bands. + The dip at 4.5 is present in the SEDs of HII regions even though some star forming site (517 for example). might not have it.," The dip at 4.5 is present in the SEDs of HII regions even though some star forming site (s17 for example), might not have it." + Some YSO SEDs show that the dip is common but not always present (??).. ," Some YSO SEDs show that the dip is common but not always present \citep{2009ApJS..184..172G,2007ApJ...669..327S}. ." +Results from ISO spectroscopy around massive protostars have shown that CO and CO» absorption bands are present in the j.5 bband (?).., Results from ISO spectroscopy around massive protostars have shown that CO and $_2$ absorption bands are present in the 4.5 band \citep{2004ARA&A..42..119V}. + These features can explain the dip mostly present in the SED of star forming regions., These features can explain the dip mostly present in the SED of star forming regions. + The CO» absorption line and a time dependent CO absorption feature can also be present in the spectra of AGB stars (??) but their strengths are not sufficient to affect notably the flux in our sample.," The $_2$ absorption line and a time dependent CO absorption feature can also be present in the spectra of AGB stars \citep{2010ApJ...709..120M,2004A&A...417..625J} but their strengths are not sufficient to affect notably the flux in our sample." + Fig., Fig. + 7. shows all long period. variables catalogued by ? which have been detected at 3.6. 4.5 and 8.0 in the [3.6]-[8.0]/|3.6]-[4.5] and [4.5]-[$.0]/[3.6]-[4.5] color-color diagrams.," \ref{fig:col1} shows all long period variables catalogued by \citet{2007ApJ...664..850M} which have been detected at 3.6, 4.5 and 8.0 in the [3.6]-[8.0]/[3.6]-[4.5] and [4.5]-[8.0]/[3.6]-[4.5] color-color diagrams." + In the same figure we plot sources in the catalogue of ? with H« emission. and hence are likely to be young star forming regions. and do not have anylong-term variable coincident with the extent of the 24 eemission.," In the same figure we plot sources in the catalogue of \citet{2007A&A...476.1161V} + with $\alpha$ emission, and hence are likely to be young star forming regions, and do not have anylong-term variable coincident with the extent of the 24 emission." + As we can see. variable stars occupy a well defined," As we can see, variable stars occupy a well defined" + anaxles cover a vast Faiee of types aud properties.,t} Galaxies cover a vast range of types and properties. + The by far most [requent type of galaxy are cw:ul galaxies. Le.. galaxies with low mass. low luminosity. low metallicity. aud suall in size.," The by far most frequent type of galaxy are dwarf galaxies, i.e., galaxies with low mass, low luminosity, low metallicity, and small in size." + The terminological disiuction between dwarl galixles and. “normal” or glant galaxies is poorly defined and is used in cdierent ways by different auhors., The terminological distinction between dwarf galaxies and “normal” or giant galaxies is poorly defined and is used in different ways by different authors. + For the pu‘pose of this paper we shall use the absolute V-band uaguitude as a simple clistiuguishing criterion aud consider al galaxies fainter thau AA—]15 nag as dwarf galaxies., For the purpose of this paper we shall use the absolute $V$ -band magnitude as a simple distinguishing criterion and consider all galaxies fainter than $M_V = -18$ mag as dwarf galaxies. + A |j»otentially more ueaulngful criterion would be mass ralrer than Ltmiiosity since dwarf galaxies lave a range of «il'erent. mass-to-ligjit ratios., A potentially more meaningful criterion would be mass rather than luminosity since dwarf galaxies have a range of different mass-to-light ratios. + Such a definition wotIn Or instance. cousider all οἱdaxies with masses of 1/10 or 1/100 0 AM as dwarf [n]oOalaxies.," Such a definition would, for instance, consider all galaxies with masses of 1/10 or 1/100 of $M^*$ as dwarf galaxies." + However. sincemasses are unktiown for most dwaT galaxies while hminosities are a irecty Beasrable observable. we will use tie luminosity criterion lere.," However, since are unknown for most dwarf galaxies while luminosities are a directly measurable observable, we will use the luminosity criterion here." + m jierarchica structure formation sceuarios dwarf galaxies (or more geue‘alyi stuall dark 1jatter halos) are important building blocss of nore Inassive galaxies aud 510ulc L1ave been even iore nuimerous 1 the early Universe., In hierarchical structure formation scenarios dwarf galaxies (or more generally: small dark matter halos) are important building blocks of more massive galaxies and should have been even more numerous in the early Universe. + Accordingly. the dwarfs we observe today are considered survivors of an iiitially much. richer popuation.," Accordingly, the dwarfs we observe today are considered survivors of an initially much richer population." + Iuterestiuglv. at the low-Lass end we observe fewer «warl galaxies today than the uumber of predicted surviving dark iater halos (e.g.. Whypin et 1999).," Interestingly, at the low-mass end we observe fewer dwarf galaxies today than the number of predicted surviving dark matter halos (e.g., Klypin et 1999)." + This may imply that we are either missing a large fraction of low-Luass galaxies. tliat these halos do not have optically detectabe counterparts. or that the scenariOs are wroOlig.," This may imply that we are either missing a large fraction of low-mass galaxies, that these halos do not have optically detectable counterparts, or that the scenarios are wrong." +(han those accounting for (he majority of the Lixich stars.,than those accounting for the majority of the Li-rich stars. + For example. ILD 39853 in Table 2 is a Li-rich IX giant but with log L/L. =2.7 is probably a post- early AGB candidate where. as cliseussecl by Charbonnel&Balachandran(2000).. Li-production by the Cameron-Fowler mechanism has occurred by a variant of ils operation in bump stars (see below).," For example, HD 39853 \citep{gratton1989} in Table 2 is a Li-rich K giant but with log $_{\odot}$ =2.7 is probably a post-clump early AGB candidate where, as discussed by \citet{charbonnel2000}, Li-production by the Cameron-Fowler mechanism has occurred by a variant of its operation in bump stars (see below)." + In contrast. the high Iuminosity. warm (Zr=51501.) Li-vich star IID 21018 is. as suggested by Charbonnel&Balachandran(2000)... caught prior to dilution of lithium by the convective envelope. ie.. il is a Li-normal star exhibiGne a Li abundance close to ils in initial abundance.," In contrast, the high luminosity warm $T_{\rm eff}=5150$ K) Li-rich star HD 21018 is, as suggested by \citet{charbonnel2000}, caught prior to dilution of lithium by the convective envelope, i.e., it is a Li-normal star exhibiting a Li abundance close to its in initial abundance." + We focus here on the Litvich giants at bump auc clump ]uminosities., We focus here on the Li-rich giants at bump and clump luminosities. + since the Li-riceh Ix giants are concentrated within a narrow Iuminositv range. one may suppose a significant event must be associated directly or indirectly with this range.," Since the Li-rich K giants are concentrated within a narrow luminosity range, one may suppose a significant event must be associated directly or indirectly with this range." + One suspects that the significant event is either (he bump on the first ascent of the RGB and/or associated with (he red clump formed of IHe-core burning giants that have experienced the lIle-core flash at the tip of the RGB., One suspects that the significant event is either the bump on the first ascent of the RGB and/or associated with the red clump formed of He-core burning giants that have experienced the He-core flash at the tip of the RGB. + The observed luminosity range is crossed by first. ascent RGB stars in which the shell passes into the region that previously was the maxinnuu extent reached by the convective envelope., The observed luminosity range is crossed by first ascent RGB stars in which the H-burning shell passes into the region that previously was the maximum extent reached by the convective envelope. + When (he oulward moving IH-burning shell. as a result of increasing lle-core mass. first encounters this region. a star reacts to the increased availability of Η by lowering the surface huninosity.," When the outward moving H-burning shell, as a result of increasing He-core mass, first encounters this region, a star reacts to the increased availability of H by lowering the surface luminosity." + After a while. the giant continues its ascent of the RGB.," After a while, the giant continues its ascent of the RGB." + This creates a kink on the evolutionary (racks [or stars of masses up to 2AL. ancl a bump in the Iuminositv finetion along the RGB.," This creates a kink on the evolutionary tracks for stars of masses up to $_{\odot}$ \citep{iben1968,bertelli2008} and a bump in the luminosity function along the RGB." + As shown in Fie., As shown in Fig. + 2. (he kink on the evolutionary (racks (Bertellietal.2008) is visible only up to 2M. for solar metallicity stars.," 2, the kink on the evolutionary tracks \citep{bertelli2008} + is visible only up to $_{\odot}$ for solar metallicity stars." + Internally. the kink is associated with an inversion in the run of mean molecular weight with distance [rom the stellar center.," Internally, the kink is associated with an inversion in the run of mean molecular weight with distance from the stellar center." +" This inversion is linked to destruction of ""Ile by the reaction “Le@He.2p)'lle which lowers the mean molecular weight. and the homogenization of the composition within (he convective enevelope."," This inversion is linked to destruction of $^3$ He by the reaction $^3$ $^3$ $p$ $^4$ He which lowers the mean molecular weight, and the homogenization of the composition within the convective enevelope." + Eeeletonetal.(2008) show that this inversion leads to ‘compulsory mixing ancl changes to (he surface abundances of C.N. and ο isotopic abundances. i.e. the PC/MC ratio is lowered relative to its value before the bump.," \citet{eggleton2008} show that this inversion leads to `compulsory' mixing and changes to the surface abundances of C,N, and O isotopic abundances, i.e., the $^{12}$ $^{13}$ C ratio is lowered relative to its value before the bump." + Charbonnel&Lagarde(2010) recognize too that mixing occurs as a result of the molecular weight inversion but include the effects of rotationallv-induced mixing to drive the mixing.," \citet{charbonnel2010} + recognize too that mixing occurs as a result of the molecular weight inversion but include the effects of rotationally-induced mixing to drive the mixing." + This mixing referred (o as 0jiemixing by Egeletonetal.(2008) or thermohaline mixing by Charbonnel&Lagarde(2010) is observationally confirmed by measurements of the 2C 06, This mixing referred to as $\delta\mu$ -mixing by \citet{eggleton2008} or thermohaline mixing by \citet{charbonnel2010} is observationally confirmed by measurements of the $^{12}$ $^{13}$ C +that disk galaxies naturally forma iu a cosmological contest in simulations such as those studied here. aud have sizes that place them ou the Lhaud TullyFisher relation (TF. e.g. Cüovanellietal.1997:AleGaueh2005: 20063).,"that disk galaxies naturally form in a cosmological context in simulations such as those studied here, and have sizes that place them on the I-band Tully–Fisher relation (TF, e.g. \citealp{Giovanelli1997,Mcgaugh2005, + Geha2006}) )." +" Brooksetal.(2007) used a set of GASOLINE simulations Guchiding MW1) to show that ealaxies with total += 0 halo masses in the range 23.1«109AZ.—X/dof for the best fits are as follows for the ASM A. B and C bands. the 15 GHz Ryle data and the 2.25 and 8.30 GHz GBI data. respectively.," The values of the statistic $\chi^2_\nu= \chi^2/\mbox{dof}$ for the best fits are as follows for the ASM A, B and C bands, the 15 GHz Ryle data and the 2.25 and 8.30 GHz GBI data, respectively." + For the model (X: X2=(S/IT. H7. 13707. 10707. L7. 20/073. (0o: (8/16. LI/16. 1H/16. 10/16. 11/16. 17/163. (tcx: (9/16. 11/16. 13/16. 11/16. 12/16. 22/16). cdi: (8/16. 11/16. 14/16. 10/16. 11/16. 17/16).," For the model (a): $\chi^2_\nu =(8/17$, 11/17, 14/17, 10/17, 11/17, 21/17), (b): (8/16, 11/16, 14/16, 10/16, 11/16, 17/16), (c): (9/16, 11/16, 13/16, 11/16, 12/16, 22/16), (d): (8/16, 11/16, 14/16, 10/16, 11/16, 17/16)." + Thus. we see that we cannot distinguish between the models based on the fit quality.," Thus, we see that we cannot distinguish between the models based on the fit quality." + For the model (c). we use L'=1.7 (the average X-ray index of the hard state of Cyg X-1) for the ASM data. and of Cyg X-I in the hard state. Fenderetal. 20005) for the Ryle data.," For the model (c), we use $\Gamma=1.7$ (the average X-ray power-law index of the hard state of Cyg X-1) for the ASM data, and $\Gamma=1$ (corresponding to the observed 2.2–220 GHz radio emission of Cyg X-1 in the hard state, \citealt{f00}) ) for the Ryle data." + In the latter case. we do not include emission of the counter jet.," In the latter case, we do not include emission of the counter jet." + The results for those two cases are consistent with a coronal outflow üt 20.3 explaining the X-ray Compton reflection strength (Malzac.Beloborodov&Poutanen2001)... and the inferred radio jet velocity of :J2 0.5—0.7 in Cyg X-1 (Stirlingetal.2001:Gleiss-neretal. 2004).. respectively.," The results for those two cases are consistent with a coronal outflow at $\beta \simeq 0.3$ explaining the X-ray Compton reflection strength \citep*{mbp01}, and the inferred radio jet velocity of $\beta\simeq 0.5$ –0.7 in Cyg X-1 \citep{st01,gl04}, respectively." + The model (ο) fitted to the Ryle data superorbital phase diagram is shown in reff:sophase((b)., The model (c) fitted to the Ryle data superorbital phase diagram is shown in \\ref{f:sophase}( (b). + We point out that the jet in Cyg X-1I is embedded in the stellar wind from the companion. which causes the orbital modulation of the radio emission via free-free absorption (Szostek&Zdziarski 2007).," We point out that the jet in Cyg X-1 is embedded in the stellar wind from the companion, which causes the orbital modulation of the radio emission via free-free absorption \citep{sz07}." +". Thus. a jet precession, which changes the path of the jet during the course of the orbital motion. will also change the average optical depth in the wind along the line of sight."," Thus, a jet precession, which changes the path of the jet during the course of the orbital motion, will also change the average optical depth in the wind along the line of sight." + This will give rise to a superorbital modulation in addition to that caused by the jet beaming., This will give rise to a superorbital modulation in addition to that caused by the jet beaming. + The dominant radiative process giving rise to X-rays in the hard state of Cyg Χ-{ is. most likely. Comptonization of some soft seed photons by predominantly thermal electrons at the temperature of 750-100 keV (Gierlifiskietal.1997:Poutanen1998:DiSalvoetal.2002:Ibragimov 2005).," The dominant radiative process giving rise to X-rays in the hard state of Cyg X-1 is, most likely, Comptonization of some soft seed photons by predominantly thermal electrons at the temperature of $\sim$ 50–100 keV \citep{gier97,p98,d01,f01,z02,mc02,i05}." +.. This is evidenced mostly by the characteristic form of its high-energy cutoff. present also in other black-hole binaries in the hard state (e.g.Groveetal.&Gierlinski 2004).," This is evidenced mostly by the characteristic form of its high-energy cutoff, present also in other black-hole binaries in the hard state \citep[e.g.][]{g98,zpm98,w02,zg04}." +. The location of the thermally Comptonizing plasma is either a hot inner accretion flow Yuanetal.2007) or a coronal outflow (Beloborodov1999: 2001).," The location of the thermally Comptonizing plasma is either a hot inner accretion flow \citep*[e.g.][]{pkr97,e98,p98,z02,yuan07} or a coronal outflow \citep{b99,mbp01}." + Thus. we fit such a model to a representative hard-state spectrum of Cyg X-I.," Thus, we fit such a model to a representative hard-state spectrum of Cyg X-1." + We choose the observation. 10238-01-03-00 together with the CGRO//OSSE observation VP.612.5 (spectrum 6 of Ibragimovetal. 2005). which gives us a broad-band energy coverage of 73-1000. keV. Our detailed model consists of the main component due to thermal Comptonization in a slab geometry calculated using the iterative," We choose the observation 10238-01-03-00 together with the /OSSE observation VP612.5 (spectrum 6 of \citealt{i05}) ), which gives us a broad-band energy coverage of $\sim$ 3–1000 keV. Our detailed model consists of the main component due to thermal Comptonization in a slab geometry calculated using the iterative" +particle can be written as In the Newtonian case. the gravitational force obeys the inverse square law.,"particle can be written as In the Newtonian case, the gravitational force obeys the inverse square law." + “Lhe gravitational force on the test particle can therefore be written as €/ —Cv1s Newton's constant. dV. denotes a volume element inside the shell. and the integration is carried out over the entire volume of the shell.," The gravitational force on the test particle can therefore be written as where $G=G_N$ is Newton's constant, $dV$ denotes a volume element inside the shell, and the integration is carried out over the entire volume of the shell." + Phe volume clement can be expressed using coordinates as Beeause of spherical symmetry. components of F perpendicular to the line connecting the test. particle and the center of the shell vanish.," The volume element can be expressed using coordinates as Because of spherical symmetry, components of $\vec{F}$ perpendicular to the line connecting the test particle and the center of the shell vanish." + Lhe component parallel to this line. whieh we denote with £05. can be caleulateck using the projection coellicient (rcos@—z)/4: ‘This integral evaluates to In the weak-field approximation. the ALOG acceleration law can be written as Newton's law of gravity with an cllective eravitational constant that incorporates a repulsive Yukawatern: where à controls the strength of the Yukawa contribution. and ye is a range parameter.," The component parallel to this line, which we denote with $F_0$, can be calculated using the projection coefficient $(r\cos{\theta}-z)/l$: This integral evaluates to In the weak-field approximation, the MOG acceleration law can be written as Newton's law of gravity with an effective gravitational constant that incorporates a repulsive Yukawa: where $\alpha$ controls the strength of the Yukawa contribution, and $\mu$ is a range parameter." + In the following we use only this weak field approximation., In the following we use only this weak field approximation. + Therefore. our conclusions may be applicable to theories other than MOC;. so long as in the weak field approximation. they also vield a Yukawa-like mocification of gravity.," Therefore, our conclusions may be applicable to theories other than MOG, so long as in the weak field approximation, they also yield a Yukawa-like modification of gravity." + In the cosmological context. the coefficient jr ds set to the reciprocal of the horizon scale e/o. where e is the speed of light and {1ο is Llubble’s constant: which vields good. agreement with key cosmological observations (?)..," In the cosmological context, the coefficient $\mu$ is set to the reciprocal of the horizon scale $c/H_0$, where $c$ is the speed of light and $H_0$ is Hubble's constant: which yields good agreement with key cosmological observations \citep{Moffat2007c}." +" In the case of a spherical volume of uniform mass density and radius A. alter evaluating (2). the gravitational force in the interior and the exterior. denoted by £j and. £5. respectively. are written as The gravitational force inside. within. and outside a spherical shell of inner radius #2, and outer radius A can be written às In particular. (ονο)FE.2) is nonvanishing: the net force in the interior of a spherically svmmetric shell is not zero."," In the case of a spherical volume of uniform mass density and radius $R$, after evaluating $\ref{eq:F}$ ), the gravitational force in the interior and the exterior, denoted by $F_1$ and $F_2$, respectively, are written as The gravitational force inside, within, and outside a spherical shell of inner radius $R_1$ and outer radius $R_2$ can be written as In particular, $F_1(R_2,z)-F_1(R_1,z)$ is nonvanishing; the net force in the interior of a spherically symmetric shell is not zero." + For an infinitesimally thin shell. we can write: Or We imagine a test particle that is surrounded by an infinite series of infinitesimally thin concentric shells of matter.," For an infinitesimally thin shell, we can write: or We imagine a test particle that is surrounded by an infinite series of infinitesimally thin concentric shells of matter." + Located at the center of the shells. the test. particle experiences no net force.," Located at the center of the shells, the test particle experiences no net force." + We now bring the particle into motion with velocity ce. and the shells ave dragged. along.," We now bring the particle into motion with velocity $v$, and the shells are dragged along." + Llowever. because of the finite propagation velocity of the eravitational interaction. the shells will no longer appear concentric as viewed from the vantage point of the moving particle.," However, because of the finite propagation velocity of the gravitational interaction, the shells will no longer appear concentric as viewed from the vantage point of the moving particle." + Therefore. a force will act on the particle.," Therefore, a force will act on the particle." + This force can be caleulatecl by integrating the displacement of the particle relative to cach of the concentric shells while taking into account the particle's motion: This expression allows us to caleulate the displacement z associated with velocity e at which forces are in equilibrium and the net force acting on the particle is zero. by solving the equation for z.," This force can be calculated by integrating the displacement of the particle relative to each of the concentric shells while taking into account the particle's motion: This expression allows us to calculate the displacement $z$ associated with velocity $v$ at which forces are in equilibrium and the net force acting on the particle is zero, by solving the equation for $z$ ." + This equation is dillicult to solve exactly. but for nonrelativistic velocities. it vields Dillerentiating this equation with respect to / gives The value dzfdl is a velocity. specifically thevelocity," This equation is difficult to solve exactly, but for nonrelativistic velocities, it yields Differentiating this equation with respect to $t$ gives The value $dz/dt$ is a velocity, specifically thevelocity" +The details of how massive stars form are poorly understood.,The details of how massive stars form are poorly understood. + Ligh-mass voung stellar objects (YSOs) evolve. rapidly and are intrinsically rare (due to the declining initial DASS funetion). whiehhich οgenerallyIL: impliespl large.lage distancesdist (2500 pe).," High-mass young stellar objects (YSOs) evolve rapidly and are intrinsically rare (due to the declining initial mass function), which generally implies large distances $\gtrsim500$ pc)." + Furthermore. they form deeply. embedded. in croweled regions wiere high extinction prevents observations in the optical arid infrared.," Furthermore, they form deeply embedded in crowded regions where high extinction prevents observations in the optical and infrared." + Lacking firm observational support. models o| high-mass star formation have remained controversial. with three dilferent scenarios active in the recent literature: (1) monolithie collapse and cise accretion2003): (2) competitive accreion in protoclusters2004).. aux similar theories in which protostellar dynamics greatly allect the ongoing accretion2010): and (3)2 scellar collisions and. mergers2005).. although this path is likely only viable in the most extreme clustered environments2011).," Lacking firm observational support, models of high-mass star formation have remained controversial, with three different scenarios active in the recent literature: (1) monolithic collapse and disc accretion; (2) competitive accretion in protoclusters, and similar theories in which protostellar dynamics greatly affect the ongoing accretion; and (3) stellar collisions and mergers, although this path is likely only viable in the most extreme clustered environments." +. As originally formulated. the last) two models. are based on the evidence that most massive stars. form in dense protostellar clusters2003).. where the stellar densities may be so high that dynamical interactions (including close passages or collisions and. mergers). are naturally expected anc may be common in the very carly stages of massive cluster evolution.," As originally formulated, the last two models are based on the evidence that most massive stars form in dense protostellar clusters, where the stellar densities may be so high that dynamical interactions (including close passages or collisions and mergers) are naturally expected and may be common in the very early stages of massive cluster evolution." + In. contrast. the first scenario envisions a scaled-up version of low-mass star formation. where dises ancl outllows are invoked to reduce the effect of radiation pressure from massive protostars and enable ongoing accretion: disces concentrate. the infalling material into small solid. angles and collimate the radiation Ποια. preferentiallv in the polar direction. where stellar photons can escape along the cavity of lower density eas excavated by outllows," In contrast, the first scenario envisions a scaled-up version of low-mass star formation, where discs and outflows are invoked to reduce the effect of radiation pressure from massive protostars and enable ongoing accretion; discs concentrate the infalling material into small solid angles and collimate the radiation field preferentially in the polar direction, where stellar photons can escape along the cavity of lower density gas excavated by outflows" +"temperature structure of the clouds and the progress of star formation within them, it is useful to examine how the dominant heating and cooling process vary with density within an atomic cloud and a molecular cloud.","temperature structure of the clouds and the progress of star formation within them, it is useful to examine how the dominant heating and cooling process vary with density within an atomic cloud and a molecular cloud." + We have therefore calculated the median heating/cooling rate as a function of density for each process included in our thermal model for runs B and D2 at a time just before the onset of star formation., We have therefore calculated the median heating/cooling rate as a function of density for each process included in our thermal model for runs B and D2 at a time just before the onset of star formation. + The results are plotted in Figure 7 (for run B) and Figure 8 (for run D2)., The results are plotted in Figure \ref{heatcool_atom} (for run B) and Figure \ref{heatcool_mol} (for run D2). + Values are plotted only for the most important processes; minor contributions to the cooling from HH* recombination or the collisional ionization of atomic hydrogen are omitted., Values are plotted only for the most important processes; minor contributions to the cooling from $^{+}$ recombination or the collisional ionization of atomic hydrogen are omitted. +" We have chosen to plot the median values rather than the mean values because the latter are strongly influenced by dissipation in shocks, which occupy a relatively small fraction of the simulation volume but dissipate a significant amount of energy within the shocked regions (seee.g.Pan& 2009)."," We have chosen to plot the median values rather than the mean values because the latter are strongly influenced by dissipation in shocks, which occupy a relatively small fraction of the simulation volume but dissipate a significant amount of energy within the shocked regions \citep[see e.g.][]{pp09}." +. The median values give a fairer picture of the balance of heating and cooling rates in the bulk of the gas., The median values give a fairer picture of the balance of heating and cooling rates in the bulk of the gas. +" Figure 7 demonstrates that in the atomic cloud, there are three main regimes."," Figure \ref{heatcool_atom} demonstrates that in the atomic cloud, there are three main regimes." +" At densities τι«2000οπι the heating of the gas is dominated by photoelectric emission?, from dust grains, and the cooling is dominated by fine structure emission from C*."," At densities $n < 2000 \: {\rm cm^{-3}}$, the heating of the gas is dominated by photoelectric emission from dust grains, and the cooling is dominated by fine structure emission from $^{+}$." +" Between n~2000cm? and nc2x10*cm Ct remains the main coolant, but photoelectric heating?, becomes much less effective, owing to the increasing visual extinction of the cloud at these densities."," Between $n \sim 2000 \: {\rm cm^{-3}}$ and $n \sim 2 \times 10^{4} \: {\rm cm^{-3}}$, $^{+}$ remains the main coolant, but photoelectric heating becomes much less effective, owing to the increasing visual extinction of the cloud at these densities." +" In this density range, adiabatic compression of the gas (indicated in the plot as the pdV term), dissipation of turbulent kinetic energy in shocks, and cosmic ray ionization heating are all significant sources of heat."," In this density range, adiabatic compression of the gas (indicated in the plot as the pdV term), dissipation of turbulent kinetic energy in shocks, and cosmic ray ionization heating are all significant sources of heat." +" Finally, at densities greater than n~2x10*cm?, the timescale for energy transfer between gas and dust becomes short enough to couple the gas and dust temperatures together, at which point this (followed by thermal emission from the dust grains) becomes the most important cooling process."," Finally, at densities greater than $n \sim 2 \times 10^{4} \: {\rm cm^{-3}}$, the timescale for energy transfer between gas and dust becomes short enough to couple the gas and dust temperatures together, at which point this (followed by thermal emission from the dust grains) becomes the most important cooling process." +" Weak shocks and adiabatic compressions together dominate the heating of the gas in this regime, each contributing close to half of the total heating rate."," Weak shocks and adiabatic compressions together dominate the heating of the gas in this regime, each contributing close to half of the total heating rate." +" Figure 8 shows that in the molecular cloud, a number of additional processes come into play: Hz and CO provide additional cooling channels through their rotational line emission, but the presences of H» also introduces additional heating processes such asHz photodissocation heating (Black&Dalgarno1977),, or heating due to the pumping of highly excited vibrational levels of Ho by UV photons (Burton,Hollenbach&Tielens1990)."," Figure \ref{heatcool_mol} shows that in the molecular cloud, a number of additional processes come into play: $_{2}$ and CO provide additional cooling channels through their rotational line emission, but the presences of $_{2}$ also introduces additional heating processes such as$_{2}$ photodissocation heating \citep{bd77}, or heating due to the pumping of highly excited vibrational levels of $_{2}$ by UV photons \citep{bht90}." +". Nevertheless, despite the additional complexity, we can again identify three main regimes marked out by different dominant processes."," Nevertheless, despite the additional complexity, we can again identify three main regimes marked out by different dominant processes." +" At n«1000cm?, the behaviour is very similar to that in the atomic run: Ct is the dominant coolant, while most of the heating comes from photoelectric emission from dust."," At $n < 1000 \: {\rm cm^{-3}}$, the behaviour is very similar to that in the atomic run: $^{+}$ is the dominant coolant, while most of the heating comes from photoelectric emission from dust." +" Above n=1000cm?, C* quickly gives way to CO as the dominant coolant, reflecting the fact that the gas becomes CO-dominated at around this density (see Figure 5)), and the photoelectric heating rate also begins to fall off with increasing density."," Above $n = 1000 \: {\rm cm^{-3}}$, $^{+}$ quickly gives way to CO as the dominant coolant, reflecting the fact that the gas becomes CO-dominated at around this density (see Figure \ref{rhoco}) ), and the photoelectric heating rate also begins to fall off with increasing density." +" The fact that these changes occur at a very similar density is no coincidence: the photoelectric heating rate and the CO photodissociation rate have a very similar dependence on the visual extinction of the gas, and so both become unimportant at roughly the same point."," The fact that these changes occur at a very similar density is no coincidence: the photoelectric heating rate and the CO photodissociation rate have a very similar dependence on the visual extinction of the gas, and so both become unimportant at roughly the same point." +" CO remains the dominant coolant between n=1000cm and n10?cm~3, but photoelectric heating quickly becomes? irrelevant, and dissipation in shocks becomes the main source of heat."," CO remains the dominant coolant between $n = 1000 \: {\rm cm^{-3}}$ and $n \sim 10^{5} \: {\rm cm^{-3}}$, but photoelectric heating quickly becomes irrelevant, and dissipation in shocks becomes the main source of heat." +" Finally, at n>105cm-?, dust takes over from CO as the most important coolant, and pdV heating becomes almost as important as shock heating."," Finally, at $n > 10^{5} \: {\rm cm^{-3}}$ dust takes over from CO as the most important coolant, and pdV heating becomes almost as important as shock heating." +" Figure 8 also illustrates that cooling by H» is never particularly important: at best, it contributes only a few percent of the total cooling rate, and at most densities contributes far less than this."," Figure \ref{heatcool_mol} also illustrates that cooling by $_{2}$ is never particularly important: at best, it contributes only a few percent of the total cooling rate, and at most densities contributes far less than this." +" In addition, it demonstrates that He formation heating is unimportant in run D2, which is unsurprising given the fully molecular initial conditions used for this run."," In addition, it demonstrates that $_{2}$ formation heating is unimportant in run D2, which is unsurprising given the fully molecular initial conditions used for this run." + A similar plot for run D1 would show a much larger contribution from H» formation heating at densities between n=10?cm? and n=10* cm?., A similar plot for run D1 would show a much larger contribution from $_{2}$ formation heating at densities between $n = 10^{3} \: {\rm cm^{-3}}$ and $n = 10^{4} \: {\rm cm^{-3}}$ . +" If we compare Figures 7 and 8,,we can see why the presence of Hz and CO appears to have such a limited effect"," If we compare Figures \ref{heatcool_atom} and \ref{heatcool_mol}, ,we can see why the presence of $_{2}$ and CO appears to have such a limited effect" +of the opacity in material containing both hvedrogen and C/O excesses. that is. al points inside the triangle of Fig. 1..,"of the opacity in material containing both hydrogen and C/O excesses, that is, at points inside the triangle of Fig. \ref{fig:opac}." + In interpolating within the set of tables represented in Fie. 1..," In interpolating within the set of tables represented in Fig. \ref{fig:opac}," + we distinguish between (hree cases: Case l|No CO excesses., we distinguish between three cases: Case I—No CO excesses. + Interpolation is performed only within the 7 r-axis (hydrogen) tables., Interpolation is performed only within the 7 $x$ -axis (hydrogen) tables. + Within each table we use cubic Hermite splines to interpolate in log£2 aud log1. in order to obtain log& and its 7 ancl H derivatives.," Within each table we use cubic Hermite splines to interpolate in $\log R$ and $\log T$ , in order to obtain $\log\kappa$ and its $T$ and $R$ derivatives." + Among the seven resulting values of log&. we then interpolate in order to obtain the final opacity value. together with ils ΑΧ derivative. for the required hydrogen mass fraction.," Among the seven resulting values of $\log\kappa$, we then interpolate in order to obtain the final opacity value, together with its $X$ derivative, for the required hydrogen mass fraction." + Similar interpolations among the seven T derivatives. and among the seven /2 derivatives. vield the To and & derivatives for the required X. (," Similar interpolations among the seven $T$ derivatives, and among the seven $R$ derivatives, yield the $T$ and $R$ derivatives for the required $X\,$. (" +Since 2=p/T;. the p derivative is simply related to the T and 2 derivatives.),"Since $R=\rho/T_6^3\,$, the $\rho$ derivative is simply related to the $T$ and $R$ derivatives.)" + Case Ηno hvedrogeninterpolation within v-axis tables (where for each Neg value there are (vo tables. the excess being completely in C for one. and completely in O for the second).," Case II—no hydrogen—interpolation within y-axis tables (where for each $X_{CO}$ value there are two tables, the excess being completely in C for one, and completely in O for the second)." + We begin as in case IL. by interpolating first among the ‘excess all carbon! tables. and then among the ‘excess all oxveen’ tables.," We begin as in case I, by interpolating first among the `excess all carbon' tables, and then among the `excess all oxygen' tables." +" The final value of log& is then obtained by linear interpolation: logre.&o denotüng the opacities as obtained separately from Cables for which excesses are all in C andl and [rom tables for which excesses are all in O. respectively,"," The final value of $\log\kappa$ is then obtained by linear interpolation: $\log\kappa_C,\ \log\kappa_O$ denoting the opacities as obtained separately from tables for which excesses are all in C and and from tables for which excesses are all in O, respectively." + Composition derivatives of the opacity. with respect to Ne. or wilh respect to Ne. are then obtained [rom (he last Formula.," Composition derivatives of the opacity, with respect to $X_C$, or with respect to $X_O$, are then obtained from the last formula." + The final Z7 and 2 derivatives are obtained by similar. linear interpolations.," The final $T$ and $R$ derivatives are obtained by similar, linear interpolations." + In comparing logrw obtained by this method with the one returned by Boothrovd’s interpolation (which has its own uncertainties). we found deviations of no more than a few percent.," In comparing $\log\kappa$ obtained by this method with the one returned by Boothroyd's interpolation (which has its own uncertainties), we found deviations of no more than a few percent." + And the largest of these were at fairly low temperatures. ~5.5 LOW (RRavmond. Cox Smith 1976).," The combined energy equation of ions and electrons is: where $\Lambda(T)$ is the radiative cooling function for a low-density, optically thin gas of cosmic abundances in the temperature range of $10^4-10^8$ K and is taken to be the Bremsstrahlung radiation function for $T>10^8$ K (Raymond, Cox Smith 1976)." + Note (that the last terms in the right side of Eq.(1)). Eq.(4)). and Eq.(6)) are the fLuring terms (Mever Mever-IlofBineister 1994).," Note that the last terms in the right side of \ref{continuity}) ), \ref{ionenergy}) ), and \ref{energy}) ) are the flaring terms (Meyer Meyer-Hofmeister 1994)." +" The pressure Z in these equations is no longer the gas pressure but the total pressure. so the sound speed (P/p) has an additional factor 1+(1/3) compared with the sound speed without the magnetic pressure (72,/p) (where jm/D,, is the ratio of gas pressure to magnetic pressure)."," The pressure $P$ in these equations is no longer the gas pressure but the total pressure, so the sound speed $P/\rho$ ) has an additional factor $1+(1/\beta)$ compared with the sound speed without the magnetic pressure $P_g/\rho$ ) (where $\beta\equiv P_g/P_m$ is the ratio of gas pressure to magnetic pressure)." + The ratio of specific heals 5 also changes with 2. with the relation +=(534-3)/(324-6) (eL.," The ratio of specific heats $\gamma$ also changes with $\beta$, with the relation $\gamma= (5\beta + +8)/ (3\beta+6)$ (cf." + Appendix A of Esin 1997. but note that the definition of 9 is different there).," Appendix A of Esin 1997, but note that the definition of $\beta$ is different there)." +" Both 3 and 5s affect the lower boundary conditions in the corona. which are ( Meyer 2006) whereÀ=ΑΓπαρ isthe fraction of the standard value (Spitzer value αρ=LO""gemsth 77) of the heat conduction coefficient (Alever-Lofineister Alever 2006)."," Both $\beta$ and $\kappa$ affect the lower boundary conditions in the corona, which are ( Meyer-Hofmeister Meyer 2006) where$\lambda\equiv \kappa/\kappa_{\rm Sp}$ isthe fraction of the standard value (Spitzer value $\kappa_{\rm Sp}=10^{-6} + g\ cm\ s^{-3}K^{-7/2}$ ) of the heat conduction coefficient (Meyer-Hofmeister Meyer 2006)." + We integrate Eq. (1)), We integrate Eq. \ref{continuity}) ) + to Eq.(6)) until the upper boundary conditions, to \ref{energy}) ) until the upper boundary conditions +uushocked jet iu the transverse direction aud that of the COCOOLL.,unshocked jet in the transverse direction and that of the cocoon. + The energy stored in the cocoon is roughly E.~Lj(frée) when the sub-relativistic jet reaches radius r after a time f., The energy stored in the cocoon is roughly $E_c\simeq L_j (t-r/c)$ when the sub-relativistic jet reaches radius $r$ after a time $t$. +" The voluue of the cocoon is V.=ayαμ, where ry=cyt is the transverse size of the cocoon (Matzuer 2003)."," The volume of the cocoon is $V_c=\frac{\pi}{3}r_{\bot}^2r$, where $r_{\bot}=v_{\bot}t$ is the transverse size of the cocoon (Matzner 2003)." + Since the cocoon pressure is niuch larger than that of the stellar material. the transverse expausion velocity ¢ of the cocoon is given by the balance between the cocoou pressure p. and the ram pressure of the stellar material. Lee=(pu/p)7.," Since the cocoon pressure is much larger than that of the stellar material, the transverse expansion velocity $v_{\bot}$ of the cocoon is given by the balance between the cocoon pressure $p_c$ and the ram pressure of the stellar material, i.e. $v_{\bot}=(p_c/\rho)^{1/2}$." +" Frou p.=E./3V.. we eet The pressure in the unshocked relativistic jet iu the transverse direction. frou the relativistic Bernoulli equation. d8 pjLL;(2217),"," From $p_c=E_c/3V_c$, we get The pressure in the unshocked relativistic jet in the transverse direction, from the relativistic Bernoulli equation, is $p_{j,\bot}=\frac{1}{3}L_j/(2\pi r^2 \theta_j^2 c\Gamma_j^2)$." + As the internal energv ects converted iuto the kineOFDuΠο enerev of thefactor jet. increases.," As the internal energy gets converted into the kinetic energy of the jet, $\Gamma_j$ increases." + ou whether the adsjet Lorentz D;has saturated or Dependingnotbefore the evolutionjetbre out of the star. there are two cases for the of Pj: one is the high yecase (case D). in schich D;x(00;)—<4) all along the path (see the left panel of Votrf£roy0;/09)Fie ," Depending on whether the jet Lorentz factor has saturated or not before the jet breaks out of the star, there are two cases for the evolution of $\Gamma_j$: one is the high $\eta$ case (case I), in which $\Gamma_j\propto +(r\theta_j)=\Gamma_0 (r/r_0)(\theta_j/\theta_0)<\eta$ all along the path (see the left panel of Fig." +| 1).aud the other is the low y case (case IT) ta which P; las reached its saturation value jg at some radius inside the star (see the right paucl of Fig.," 1), and the other is the low $\eta$ case (case II) in which $\Gamma_j$ has reached its saturation value $\eta$ at some radius inside the star (see the right panel of Fig." + 1)., 1). + The latter case is more casily satisfied when 4 is lower or when the initial injection radius ry is sinaller., The latter case is more easily satisfied when $\eta$ is lower or when the initial injection radius $r_0$ is smaller. +" The jet pressure is differcut in the two cases. being given by. respectively. From pjij=pe we get the opening angle for the two cases respectively, For case with the parameters J)=1. l. ry=WemL aud the stellar deusity profile 100n)Pecan >. the opening angle is while for case II. Note that these values of the opening angles are the ones at the jet breakout time. which are not the final values that we expect in the internal shock phase or in the afterglow."," The jet pressure is different in the two cases, being given by, respectively, From $p_{j,\bot}=p_c$, we get the opening angle for the two cases respectively, For case I, with the parameters $\theta_0=1$, $\Gamma_0=1$ , $r_0=10^7 {\rm cm}$ and the stellar density profile $\rho=1 +(r/10^{11}{\rm cm})^{-3} \,{\rm g cm^{-3}}$ , the opening angle is while for case II, Note that these values of the opening angles are the ones at the jet breakout time, which are not the final values that we expect in the internal shock phase or in the afterglow." + After exiting the star. the hot jet is expected to expand freely to an openius augle comparable to 1Γι~0.1. where Ey is the Loreutz factor of the jet at thebreakout time.," After exiting the star, the hot jet is expected to expand freely to an opening angle comparable to $1/\Gamma_{\rm br}\sim 0.1$, where $\Gamma_{\rm br}$ is the Lorentz factor of the jet at the breakout time." + With the above values of the opening augles. we can )btaiu the jet breakout time from Eq.(1) for the two cases. Tere α is the inteeratiug factor over r in Eq.(1).," With the above values of the opening angles, we can obtain the jet breakout time from Eq.(4) for the two cases, Here $\alpha$ is the integrating factor over $r$ in Eq.(4)." + In case L since powor7 starts roughly above s=LO?cu. below which the free fall deusitv profile pxor3%? aay apply Rees 2001). a—4Indr/LOPcm)~£ for 10Hen.," In case I, since $\rho\propto r^{-3}$ starts roughly above $r=10^9{\rm cm}$, below which the free fall density profile $\rho\propto r^{-3/2}$ may apply Rees 2001), $\alpha=_1{\rm ln}(r/10^9{\rm cm})\simeq 4$ for $r=10^{11}{\rm +cm}$." + Tn case Π. the integration over r in Eq.{1) eives a2=3/2.," In case II, the integration over $r$ in Eq.(4) gives $\alpha_2=3/2$." + We cau see that a low-huninosityv. weals jet takes a longer time to break out of the star. cousisteut with recent fiudiues byWoosley Zhang (2007) from the munerical bydrodvuamuc simulation of the jet propagation.," We can see that a low-luminosity, weak jet takes a longer time to break out of the star, consistent with recent findings byWoosley Zhang (2007) from the numerical hydrodynamic simulation of the jet propagation." +" The dependence of the breakout time fj, on the Iuninositv is illustrated in the inset plot of the left panel of Fig.1", The dependence of the breakout time $t_{\rm br}$ on the luminosity is illustrated in the inset plot of the left panel of Fig.1. +" Requiring that the breakout time fj, is less than the duration of the prectrsor T,,~10s, we get. for case 1. The asvinptotic Lorentz factor 7 in this case is required to be larger thau Dy,=Dotr6;/roo)215. from the high ip asstunption of case L For case IT. the breakout time is seusitive to jj. more than to the jet luminosity. aud we eet by requiring the breakout time to be shorter than LOs (see the inset plot of the right panelof Fie.1)."," Requiring that the breakout time $t_{\rm br}$ is less than the duration of the precursor $T_p\simeq 10 \,{\rm s}$, we get, for case I, The asymptotic Lorentz factor $\eta$ in this case is required to be larger than $\Gamma_{\rm br}=\Gamma_0(r\theta_j/r_0\theta_0) +\simeq 15$, from the high $\eta$ assumption of case I. For case II, the breakout time is sensitive to $\eta$, more than to the jet luminosity, and we get by requiring the breakout time to be shorter than $T_p\simeq10 +{\rm s}$ (see the inset plot of the right panel of Fig.1)." + Therefore we see that iu both cases. it is only when 5=10 that the jet breakout time can be <10 seconds. for a Iuuinositv of the order of L;—LOMeres1.," Therefore we see that in both cases, it is only when $\eta\ga10$ that the jet breakout time can be $\la 10$ seconds, for a luminosity of the order of $L_j\sim10^{49}{\rm erg s^{-1}}$." + This reflects the fact that a lower Lorentz factor jet is less penetrating and needs a longer time to break out of the stellar progenitor., This reflects the fact that a lower Lorentz factor jet is less penetrating and needs a longer time to break out of the stellar progenitor. + This shows that even the precursor jet should have a relatively laugh Loreutz factor. although it need not be as laree as =LOO as in the case of the main burst.," This shows that even the precursor jet should have a relatively high Lorentz factor, although it need not be as large as $\ga100$ as in the case of the main burst." + After the weak jet breaks out. the cocoon material escapes.," After the weak jet breaks out, the cocoon material escapes." + There is now a wide funucl opened bw the weak jet aud its accoiipauviug cocoon along its path., There is now a wide funnel opened by the weak jet and its accompanying cocoon along its path. + As evidencedby GRBOSOS20A. (Cenko et al., As evidenced by GRB050820A (Cenko et al. + 2006). a burst with precur«x. the main burst jet is collimated to 0—0.1. ike other typical loug bursts without precursors.," 2006), a burst with precursor, the main burst jet is collimated to $\theta\sim0.1$, like other typical long bursts without precursors." + Since a closed. chanucl is a necessary condition for the main jet | be collimated. one may ask whether the initial chauuel. nade by the precursor jet. will have had time to close again x the time that the main jet starts to make its way out. »LOO seconds later.," Since a closed channel is a necessary condition for the main jet to be collimated, one may ask whether the initial channel, made by the precursor jet, will have had time to close again by the time that the main jet starts to make its way out, $\sim100$ seconds later." + As the weak jet propagates outward. the cocoon pushes he stellar material sideways.," As the weak jet propagates outward, the cocoon pushes the stellar material sideways." + The opening augle of the cocoon. Which is also the fuunel opening anele after the cocoon flows out. is approximately given by where the last equality is obtained with the help of the second line of Eq.(10).," The opening angle of the cocoon, which is also the funnel opening angle after the cocoon flows out, is approximately given by where the last equality is obtained with the help of the second line of Eq.(10)." +" For Ej,2:10. the cocoon opening angle is about teus of degrees."," For $\Gamma_{\rm br}\simeq10$, the cocoon opening angle is about tens of degrees." +" The cocoon can drive a trausverse shock iuto the stellar material aloug its passage. heating it up. so the pressure of the shocked. stellar material (p.~ pei) Is conrparable to that of the cocoon. ic. p,z p.."," The cocoon can drive a transverse shock into the stellar material along its passage, heating it up, so the pressure of the shocked stellar material $p_e\sim \rho v_{\bot}^2$ ) is comparable to that of the cocoon, i.e. $p_e\simeq p_c$ ." + After the cocoon flows out. this external stellar material will re-expaud back iuto the funnel at a speed of sound. given by," After the cocoon flows out, this external stellar material will re-expand back into the funnel at a speed of sound given by" +One of. the successes of. the Infrared. Space Observatory (£50) mission.. have been the new extragalactic. source counts in. the mid-infrared.... extracted. from.⋅ both. deep (Oliver. et al.,"One of the successes of the Infrared Space Observatory ) mission have been the new extragalactic source counts in the mid-infrared, extracted from both deep (Oliver et al." + 1997. Elbaz et al.," 1997, Elbaz et al." + 1999) and wide field (Serjeant et al., 1999) and wide field (Serjeant et al. + 2000) surveys., 2000) surveys. + These counts are important in planning effective observing. strategies ⊀⋅for the next. generation. of space-borne lli missions. theSLATE (Fanson et al.," These counts are important in planning effective observing strategies for the next generation of space-borne IR missions, the (Fanson et al." + 1998) andTRO-F (Pearson et al., 1998) and (Pearson et al. + 2000). particularly. with respect to expected source densitiesu and confusion.," 2000), particularly with respect to expected source densities and confusion." +uM Confusion⊲⋅⊀ is. usually defined. as the Ποιαλος. of⋅ the mackerounc sky brightness below which sources cannot ο detected: individually these Luctuations are caused ⊽⊀∙⊀⊀intrinsicalls ⊽⊀∙discrete extragalacticvl. SOUrCeS. [WO do not confusionDp. due⋅⊀ to Galactic cirrus∢⊀ in .this work)., Confusion is usually defined as the fluctuations of the background sky brightness below which sources cannot be detected individually – these fluctuations are caused by intrinsically discrete extragalactic sources (we do not consider confusion due to Galactic cirrus in this work). +"--- Thus developed. he fluctuations.. or MENnoise. come from"" the same sources. one wishes to study."," Thus the fluctuations, or noise, come from the same sources one wishes to study." + Confusion sets an important. and fundamental limit o astronomical observations., Confusion sets an important and fundamental limit to astronomical observations. + Lor a given wavelength and resolution. it will not. be productive to extend the exposure time indefinitely since a Εαν density limit will be reached bevond which no additional discrete sources can be extracted.," For a given wavelength and resolution, it will not be productive to extend the exposure time indefinitely since a flux density limit will be reached beyond which no additional discrete sources can be extracted." + This ...is the limit.. usually referred⋅ to as thelm., This is the limit usually referred to as the. + ⊲⋅⋠Confusion cannot be avoided. even with. arbitrarily. high resolution because of the finite sizes of sources on the sky., Confusion cannot be avoided even with arbitrarily high resolution because of the finite sizes of sources on the sky. + ↼∣⊔⊳∖⇂⋜↧⊳∖⊔⋖⋅∖∖⋎⊳∖⊔⋡−⊔↓⊔↓∠⇂⋜⊔⋜↧⋜↧↓↓⋖≱∖∖⋎⋖⊾∠⇂⊥≧↓⋜↧↕↓↥⊳↓∖⋰↓⊳∖∪⊔⊾∖↽ Small (1998) to set observational limits on source confusion at those wavelengths. we are now able to estimate more accurately the confusion at mid-infrared. wavelengths using deep psgalaxv counts from. data.," Just as new sub-mm data allowed Blain, Ivison Smail (1998) to set observational limits on source confusion at those wavelengths, we are now able to estimate more accurately the confusion at mid-infrared wavelengths using deep galaxy counts from data." + Confusion in. mid-LHi has been discussed in connection. with the individual deep surveys Oliver. LOOT_ for the50 HIDE. survey), Confusion in mid-IR has been discussed in connection with the individual deep surveys Oliver 1997 for the HDF survey). + AC useful theoretical definition of confusion was by. Scheuer (1957) ancl followed up in numerous consider other works., A useful theoretical definition of confusion was developed by Scheuer (1957) and followed up in numerous other works. + More recently. essentially. the same formalism. has been used to predict.: confusione. in. observations. done at radio Franceschini 1950. Wall 1982. Condon 1974). sub-mm Clollolatti 998). and Χαν (Darcons 1992. Scheuer 1974) wavelengths.," More recently, essentially the same formalism has been used to predict confusion in observations done at radio Franceschini 1989, Wall 1982, Condon 1974), sub-mm (Toffolatti 1998), and X-ray (Barcons 1992, Scheuer 1974) wavelengths." + Ht turns out that sources at the flux density level where the surface density is approximately 1 source per beam produce the bulk of the confusion noise., It turns out that sources at the flux density level where the surface density is approximately 1 source per beam produce the bulk of the confusion noise. + This is easy, This is easy +"from the beginning of star formation), we show that our best models — a series of uniform models with same Mi; f, WH,He; Amw, €, d but different n and suitable ¢ — can well reproduce the spread in the observations.","from the beginning of star formation), we show that our best models – a series of uniform models with same $M_{inf}$ , $w_{\rm H,He}$ , $\lambda_{mw}$, $\epsilon$, $d$ but different $n$ and suitable $t$ – can well reproduce the spread in the observations." +" DLAs could be the progenitors of dwarf irregular galaxies, as already suggested by Matteuccietal.(1997) and Caluraetal.(2003)."," DLAs could be the progenitors of dwarf irregular galaxies, as already suggested by \cite{Matteucci97} and \cite{Calura03}." +" In our best models, we adopted a fixed duration for each burst with the purpose of changing the parameters as less as possible."," In our best models, we adopted a fixed duration for each burst with the purpose of changing the parameters as less as possible." +" The evolutionary tracks of our best models pass through the DLA data, but could not explain the scatter."," The evolutionary tracks of our best models pass through the DLA data, but could not explain the scatter." +" However, if we reduce the duration of the first SF burst to d—0.01~0.1 Gyr, by taking model M9b3 as an example, the models can explain the scatter in the abundance ratiosof DLAsmuch better (see Fig."," However, if we reduce the duration of the first SF burst to $d=0.01\sim0.1$ Gyr, by taking model M9b3 as an example, the models can explain the scatter in the abundance ratiosof DLAsmuch better (see Fig." + 17 and Table 3 for details," \ref{Fig:DLAabund} + and Table \ref{Tab:best} for details" +"opacities. a major improvement in the stellar astrophysies. various studies have suggested a modest amount of OS; that is. OS =~0.2H,,.. where H,is the pressure scale height (Stothers 1991: Demarque. Sarajedini. Guo 1994; Kozhurina-Platais et al.","opacities, a major improvement in the stellar astrophysics, various studies have suggested a modest amount of OS; that is, OS $\approx 0.2$, where is the pressure scale height (Stothers 1991; Demarque, Sarajedini, Guo 1994; Kozhurina-Platais et al." + 1997)., 1997). + OS has many effects on stellar evolution. but the most notable ones are its effects on the shape of the MSTO and on the luminosity function.," OS has many effects on stellar evolution, but the most notable ones are its effects on the shape of the MSTO and on the luminosity function." +" As shown in Figure 5. inclusior of a modest amount of OS causes a longer stretch of the MS before the blueward motion because it induces a larger supply of hydrogen fuel from the overshooting (""overmixing"") regior into the core."," As shown in Figure 5, inclusion of a modest amount of OS causes a longer stretch of the MS before the blueward motion because it induces a larger supply of hydrogen fuel from the overshooting (“overmixing”) region into the core." + As a result. stars with OS (20.2 ) stay longer in the core hydrogen burning stage. but in the MS rather than ii the RGB.," As a result, stars with OS $= 0.2$ ) stay longer in the core hydrogen burning stage, but in the MS rather than in the RGB." + The table in Figure 5 lists the lifetime in the hydroger burning phase and in the RGB. both in Myr.," The table in Figure 5 lists the lifetime in the hydrogen burning phase and in the RGB, both in Myr." + OS also causes stars to leave the RGB earlier., OS also causes stars to leave the RGB earlier. + Thediamonds in Figure 5 are the locations of the RGB tips when OS is included. while are for the no-OS case.," The in Figure 5 are the locations of the RGB tips when OS is included, while are for the no-OS case." + This directly affects isochrones. as shown in Figure 6.," This directly affects isochrones, as shown in Figure 6." + The RGB tips in the isochrones reach farther without OS., The RGB tips in the isochrones reach farther without OS. + Because most of the visible flux comes from red giants. a decrease in the RGB lifetime results in a lower visible flux.," Because most of the visible flux comes from red giants, a decrease in the RGB lifetime results in a lower visible flux." + Figure 7 shows the integrated spectra with and without OS., Figure 7 shows the integrated spectra with and without OS. + One can see the impact of OS on the normalized integrated spectra of | Gyr models and thus on the age estimates., One can see the impact of OS on the normalized integrated spectra of 1 Gyr models and thus on the age estimates. + When the isochrones with OS are used in the population synthesis. the same observed integrated spectrum indicates a larger age. especially when the age is as small as 1 Gyr.," When the isochrones with OS are used in the population synthesis, the same observed integrated spectrum indicates a larger age, especially when the age is as small as 1 Gyr." + Most of the previous age estimates of 553W091 were based on the single abundance population models. typically for solar composition.," Most of the previous age estimates of 53W091 were based on the single abundance population models, typically for solar composition." + The solar abundance approximation has been popular for decades because reliable spectral libraries were available only for solar compositions., The solar abundance approximation has been popular for decades because reliable spectral libraries were available only for solar compositions. + The first obvious problem in this approximation ts that there is little justification in the choice of solar composition in modeling giant elliptical galaxies., The first obvious problem in this approximation is that there is little justification in the choice of solar composition in modeling giant elliptical galaxies. + Observers have long believed that the majority of stars in giant elliptical galaxies are metal-rich (approximately twice solar) because of their extremely red colors and strong, Observers have long believed that the majority of stars in giant elliptical galaxies are metal-rich (approximately twice solar) because of their extremely red colors and strong +NGC 5253 (Turner 11999) are near enough and have observations with high enough resolution that the radio imaging can directly. constrain the sizes of the emitting regions without recourse to model assumptions.,NGC 5253 (Turner 1999) are near enough and have observations with high enough resolution that the radio imaging can directly constrain the sizes of the emitting regions without recourse to model assumptions. + In both cases. our simple homogeneous spherical models described above produce size esliniates in excellent agreement with the hieh-resolution radio maps.," In both cases, our simple homogeneous spherical models described above produce size estimates in excellent agreement with the high-resolution radio maps." + The deconvolved diameters of the radio sources in NGC: 253 are 2-4 pc. in excellent agreement will the models shown in Figure 6..," The deconvolved diameters of the radio sources in NGC 253 are 2-4 pc, in excellent agreement with the best-fitting models shown in Figure \ref{N253.plot}." + In NGC: 5253. the single rraclio source has a deconvolved diameter of 1-2 pe (Turner.Deck.&Ho2000).. consistent wilh (he expectations of the simple model predictions based on the observed radio Iuminosities of Turner ((1993).," In NGC 5253, the single radio source has a deconvolved diameter of 1-2 pc \citep{turner00}, consistent with the expectations of the simple model predictions based on the observed radio luminosities of Turner (1998)." + As further support for our simple models. recently Mohan.Anantharamaiah.&Goss(2001) have made slightly more sophisticated multi-densitv models for radio recombination line observations of He 2-10 and and NGC! 5253: their results are in excellent agreement with the results we find with our simple mocels.," As further support for our simple models, recently \citet{mohan01} have made slightly more sophisticated multi-density models for radio recombination line observations of He 2-10 and and NGC 5253; their results are in excellent agreement with the results we find with our simple models." + Given the agreement in these (wo nearby cases. we believe (hat the simple Gwo-parameter models are sufficiently instructive to make meaningful inferences about the sizes and densities of UDILIIs based on radio continuum Iuminosities.," Given the agreement in these two nearby cases, we believe that the simple two-parameter models are sufficiently instructive to make meaningful inferences about the sizes and densities of s based on radio continuum luminosities." + More realistic models would include an arbitrary number of rregions within each each wilh its own density. profile. ancl an mmecdium wilh a specified density profile ancl temperature distribution.," More realistic models would include an arbitrary number of regions within each each with its own density profile, and an medium with a specified density profile and temperature distribution." + ILowever. relaxing the simple (wo-parameter approach results in (he number of [ree parameters and computational complexitv growing rapidly.," However, relaxing the simple two-parameter approach results in the number of free parameters and computational complexity growing rapidly." + The production rate of Lyman continuum photons. and. thus. the stellar content of each rregion can be estimated [rom the thermal radio luninosity following Concon(1992).. since (he non-thermal component becomes weaker al higher [requencies. for each of the Hs in this sample we use the luminositwv measured at the highest frequency in each," The production rate of Lyman continuum photons, and, thus, the stellar content of each region can be estimated from the thermal radio luminosity following \citet{condon92}, Since the non-thermal component becomes weaker at higher frequencies, for each of the s in this sample we use the luminosity measured at the highest frequency in each" +the constancy. to within a few percent. of our galaxy source counts for identified galaxies in the PSC'z as a function of Ii.,"the constancy, to within a few percent, of our galaxy source counts for identified galaxies in the PSCz as a function of $I_{100}$." + Overall. differential source densities across the sky due to incompleteness. Malmequist cllects and sensitivity variations are not believed to be greater than a few percent anvwhere at high latitudes for z«0.1.," Overall, differential source densities across the sky due to incompleteness, Malmquist effects and sensitivity variations are not believed to be greater than a few percent anywhere at high latitudes for $z<0.1$." + Tacos (1999) found an upper limit to the rms amplitude of large scale. high Latitude spherical harmonic components to the density Lickel of the PSCz of:," Tadros (1999) found an upper limit to the rms amplitude of large scale, high latitude spherical harmonic components to the density field of the PSCz of." + Since this is close to the expected. variations due to clustering. the variations due to non-uniformity in the catalogue must be smaller than this.," Since this is close to the expected variations due to clustering, the variations due to non-uniformity in the catalogue must be smaller than this." + At lower latitucles. variations are estimated to be no greater than for z« 0.05.," At lower latitudes, variations are estimated to be no greater than for $z<0.05$ ." + The 12v survey of 5500 LIGAS galaxies (Fisher 1995) used. looser colour criteria than the PSCz. and as such acts as a valuable check on the ellicacy of our selection procedure from the PSC.," The $1.2\Jy$ survey of 5500 IRAS galaxies (Fisher 1995) used looser colour criteria than the PSCz, and as such acts as a valuable check on the efficacy of our selection procedure from the PSC." + We find that the L24Jy. survey contains 11 galaxies that have been excluded by our selection criteria., We find that the $1.2\Jy$ survey contains 11 galaxies that have been excluded by our selection criteria. + 10 contains a further 5κ ealaxies that satisfy the PSC criteria. but. ave not included:k due to. programming ancl editing errors. either curing construction of the QIGC survey or its various extensions and supplements to form the DPSCz.," It contains a further 5 galaxies that satisfy the PSCz criteria, but are not included due to programming and editing errors, either during construction of the QIGC survey or its various extensions and supplements to form the PSCz." + Extrapolating these numbers to lower fluxes. we can expect that about 50 PSC ealaxies are missing altogether from the catalogue.," Extrapolating these numbers to lower fluxes, we can expect that about 50 PSC galaxies are missing altogether from the catalogue." + Conversely. the conservative selection criteria for the 1.2J. survey lec to much greater. levels of contamination bv cirrus and other Galactic sources than in the PSC'z.," Conversely, the conservative selection criteria for the $1.2\Jy$ survey led to much greater levels of contamination by cirrus and other Galactic sources than in the PSCz." + In the 1.2.Jw survey. these were eliminated: by visual. inspection of sky survey. plates: inevitably real galaxies occasionally eot thrown out by mistake. especially at low latitudes.," In the $1.2\Jy$ survey, these were eliminated by visual inspection of sky survey plates; inevitably real galaxies occasionally got thrown out by mistake, especially at low latitudes." + We wave found. within the PSCz area. 110. galaxies which are misclassificcd as Galactic in the 1.2Jy. survey. and we have obtained redshifts for 67 of them.," We have found, within the PSCz area, 110 galaxies which are misclassified as Galactic in the $1.2\Jy$ survey, and we have obtained redshifts for 67 of them." +" Most of the remainder are inter than our b;=19.5"" eutolÉ", Most of the remainder are fainter than our $b_J=19.5^m$ cutoff. + There are also known o be to date a Further 117 galaxies classified as Galactic in he L.2Jy survey outside the PSCz area., There are also known to be to date a further 117 galaxies classified as Galactic in the $1.2\Jy$ survey outside the PSCz area. +" These were found as part of the ongoing ""Dehind the Plane’ extension of the ""SC to lower Latitudes clescribect in more detail in Saunders (1999).", These were found as part of the ongoing `Behind the Plane' extension of the PSCz to lower latitudes described in more detail in Saunders (1999). + Along with the PSC) data. the catalogue also contains the following information: POSS/SRC plate ancl position on that plate: the RAL. offset. diameters and. magnitude of the best match from the cligitised sky survey plates: name. magnitude and diameters from UGC/ZIESO/MCCCCGG. DOC name. de Vaucouleurs type ancl HE widths where available: most accurate available recshift and our own redshift measurement: classification as galaxy/cirrus/etc: estimated diag and extinction: adcscan [ux ane width when treated as an extended: source. ancl point source filtered acddsean Lux.," Along with the PSC data, the catalogue also contains the following information: POSS/SRC plate and position on that plate; the $\delta$, offset, diameters and magnitude of the best match from the digitised sky survey plates; name, magnitude and diameters from UGC/ESO/MCG, PGC name, de Vaucouleurs type and HI widths where available; most accurate available redshift and our own redshift measurement; classification as galaxy/cirrus/etc; estimated $I_{100}$ and extinction; addscan flux and width when treated as an extended source, and point source filtered addscan flux." + The cata is available from. the CDS catalogue. service (http:/fecsweb.urstrasbefr/Cats.btml)., The data is available from the CDS catalogue service (http://cdsweb.u-strasbg.fr/Cats.html). + Pull ancl short versions of the catalogue. maskfiles. description files. format statements and. notes. are also available via the PSCz web site /wwwe-astro.phivsies.ox.ac.uk/wjs/pscz.html). or by anonymous {tp [rom fip://ftp-astro.physics.ox.ac.uk/pub/users{ws/pscz ," Full and short versions of the catalogue, maskfiles, description files, format statements and notes, are also available via the PSCz web site $\sim$ wjs/pscz.html), or by anonymous ftp from ftp://ftp-astro.physics.ox.ac.uk/pub/users/wjs/pscz/ ." +The PSC-z survey has only been possible because of the &enerous assistance from many people in the astronomical community., The PSC-z survey has only been possible because of the generous assistance from many people in the astronomical community. + We are particularly erateful to John Lluchra. ‘Tony Fairall. Iarl Fisher. Michael Strauss. Marc. Davis. ltaj Visvanathan. Luis DaCosta. Riccardo Ciovanelli. Nanvao Lu. Carmen Pantoja. Taclafumi Takata. Ixouichiro," We are particularly grateful to John Huchra, Tony Fairall, Karl Fisher, Michael Strauss, Marc Davis, Raj Visvanathan, Luis DaCosta, Riccardo Giovanelli, Nanyao Lu, Carmen Pantoja, Tadafumi Takata, Kouichiro" +cloud) seales have a vastly lower density (han the mean (e.g.. Elmegreen 1997). (,"cloud) scales have a vastly lower density than the mean (e.g., Elmegreen 1997). (" +c) Models with the same global parameters(74... D. a. g). but differing in (he placement ol the dense clumps relative to the central star. show strong variations in even the averaged [Iuxes.,"c) Models with the same global parameters, $D$ , $a$, $g$ ), but differing in the placement of the dense clumps relative to the central star, show strong variations in even the averaged fluxes." + There are significant dillerences between hierarchical models in which the str happens to lie within a dense clump of dust. in contrast to those in which it falls within a void (or if there is a central hole).," There are significant differences between hierarchical models in which the star happens to lie within a dense clump of dust, in contrast to those in which it falls within a void (or if there is a central hole)." + IF (he star happens to lie within a void. there are liehtlv. reddenecl paths Chat reach from the star to the edge of the sphere.," If the star happens to lie within a void, there are lightly reddened paths that reach from the star to the edge of the sphere." + If the star is almost unattenuated as seen [rom a particular direction. the nebula would be interpreted as having the star in Iron of the dust. except that there can be a significant amount of scattered light that would not be there if the star were truly [oreground.," If the star is almost unattenuated as seen from a particular direction, the nebula would be interpreted as having the star in front of the dust, except that there can be a significant amount of scattered light that would not be there if the star were truly foreground." + In these cases. the albedo derived [rom uniform models would be >1.," In these cases, the albedo derived from uniform models would be $>1$." + The power law index. ». of the projected density. distribution of our is ~ 00. reflecting the fact that their projected. density is non-hierarchical.," The power law index, $\beta$, of the projected density distribution of our is $\sim$ 0, reflecting the fact that their projected density is non-hierarchical." +" The always provide a smaller range in 7,4((0. 60) (about 40.12) than the hierarchical. but (heir spread in is comparable to hierarchical models at low (S2)."," The always provide a smaller range in $\theta, \phi$ ) (about $\pm$ 0.12) than the hierarchical, but their spread in is comparable to hierarchical models at low $\lesssim2$ )." + The spread at large decreases because the interclump medium becomes opaque.so that in (he ultraviolet (UV) make a prediction of e that is rather independent of viewing angle.," The spread at large decreases because the interclump medium becomes opaque,so that in the ultraviolet (UV) make a prediction of $a$ that is rather independent of viewing angle." + Figure 1. shows plotted againstΤον. for the case = 2. D = 2.6. a = 0.6. g = 0.6 for a hierarchical distribution of chuups wil an initial seed for the density distribution (hat provides a tvpical (defined below) placement with respect to the star.," Figure \ref{fig1} shows plotted against, for the case = 2, $D$ = 2.6, $a$ = 0.6, $g$ = 0.6 for a hierarchical distribution of clumps with an initial seed for the density distribution that provides a typical (defined below) placement with respect to the star." + Each point represents a particular viewing direction., Each point represents a particular viewing direction. + One sees a large spread in the values of7:4., One sees a large spread in the values of. +. The values for Lor Chis model range up to 6.8. and to 2.4.," The values for for this model range up to 6.8, and to 2.4." + Thus. this one model of cbumpy dust can produce a wide range of stellar fluxes and scattered light.," Thus, this one model of clumpy dust can produce a wide range of stellar fluxes and scattered light." +" We represent the direction-averaged escaping flux (not mean optical depth) by(text). defined by where Ny, is the number of bins we are using (=18x 36). all of equal solid angle."," We represent the direction-averaged escaping flux (not mean optical depth) by, defined by where $N_{\theta,\phi}$ is the number of bins we are using $= 18\times36$ ), all of equal solid angle." + I the star is embedded within a clump. the uniform dust component is of reduced importance because scattering occurs within the clump.," If the star is embedded within a clump, the uniform dust component is of reduced importance because scattering occurs within the clump." + Similarly. represents the angle-averaged scattered radiation. with replacing in the above relation.," Similarly, represents the angle-averaged scattered radiation, with replacing in the above relation." + The filled square in Figure | shows aand(Thea). Which are useful for contrasting the results of models with the same value of but different initial seeds.," The filled square in Figure \ref{fig1} shows and, which are useful for contrasting the results of models with the same value of but different initial seeds." + As the figure shows. the((r.4).. ἔτι) point is of very. limited valuein guessing what actual optical depths a given nebula might show if it were viewed," As the figure shows, the, ) point is of very limited valuein guessing what actual optical depths a given nebula might show if it were viewed" +be tentatively considered as D-class with some confidence.,be tentatively considered as B-class with some confidence. + For each object. the second central momen about the B V.V. Rand VI maeuitudesOo from the typical colors for cach taxonondc class are computed. aud the class with nininimna seco ceutral moment is assigned as the objects class.," For each object, the second central moment about the $B-V$ , $V-R$ and $V-I$ magnitudes from the typical colors for each taxonomic class are computed, and the class with minimum second central moment is assigned as the object's class." + Iu some cases. the error range of the colors have covered more than one class and/or the secouc ceutral moment of several classes are very close. so iultiple classes are assigned to this object with the first class being most probable.," In some cases, the error range of the colors have covered more than one class and/or the second central moment of several classes are very close, so multiple classes are assigned to this object with the first class being most probable." + Ta two cases (13732) Woodall aud (228717) 2002 VIS]. only a very crude classification (0N-like or S-like) can be mace due to low-quality observations (see Section [.3 for details).," In two cases [(13732) Woodall and (228747) 2002 VH3], only a very crude classification (C/X-like or S-like) can be made due to low-quality observations (see Section 4.3 for details)." + When the secoud ceutral moment of the most probable class for a particular object is large (~ 0.003). a αλ (uncertain) is appended to indicate hat this classification may be uucertaiu.," When the second central moment of the most probable class for a particular object is large $\sim>0.003$ ), a $(u)$ ” (uncertain) is appended to indicate that this classification may be uncertain." +" The colors aud the classiicatious for the observe NEAs/high eccentrieitv (inclination) asteroids and paired-asteroid candidates observed in this study are shown in Table 5. aud Table 6 respectively,", The colors and the classifications for the observed NEAs/high eccentricity (inclination) asteroids and paired-asteroid candidates observed in this study are shown in Table \ref{tbl-5} and Table \ref{tbl-6} respectively. + Classification audor albedo measurement frou previous work is also given if available., Classification and/or albedo measurement from previous work is also given if available. + We note the a total of four objects were observed iu different nights. color measurements across these welts with different calibration stars are found to be consistent.," We note that a total of four objects were observed in different nights, color measurements across these nights with different calibration stars are found to be consistent." + Moeasureineuts from cach night are liste separately illustrate the accuracy and consisteucyv of our work., Measurements from each night are listed separately illustrate the accuracy and consistency of our work. +" Following the procedure described im Section 2 and 3. we have derived color iudices and classifications for 35 NEÀs. iuchiding 17 Αλλοι, 13 Apollos aud 5 Atens."," Following the procedure described in Section 2 and 3, we have derived color indices and classifications for 35 NEAs, including 17 Amors, 13 Apollos and 5 Atens." + Amone the sample. a total of cight NEAs were reportedly classified by previous surveys: it has been found that our classifications are generally cousisteut with then.," Among the sample, a total of eight NEAs were reportedly classified by previous surveys; it has been found that our classifications are generally consistent with them." + Iu addition. we note that a total of six NEAs in our sanuple were also observed bw receutly-conducted λαΤζο prograun (Trillinectal. 2010).. with uucertaimties around a factor of 2 unless otherwise specified (see Section 5.3.1 of their paper).," In addition, we note that a total of six NEAs in our sample were also observed by recently-conducted Warm-Spitzer program \citep{tri10}, with uncertainties around a factor of 2 unless otherwise specified (see Section 5.3.4 of their paper)." + Although: Wiunur-Spitzer derives albedo of the NEAs aud does not classify them directly. its observation can be a good addition to broad-band photometiv. expecially when the classification is ambienous.," Although Warm-Spitzer derives albedo of the NEAs and does not classify them directly, its observation can be a good addition to broad-band photometry, especially when the classification is ambiguous." + Each case of these cross-observed NEAs is discussed below., Each case of these cross-observed NEAs is discussed below. +" The V.Rand VI colors measured from our observation suggested V-. O-. C- or R-type classification. with V-type to be most likely,"," The $V-R$ and $V-I$ colors measured from our observation suggested V-, Q-, C- or R-type classification, with V-type to be most likely." + This is consistent with the classification made by Diuzeletal.(2001) iun spectroscopy., This is consistent with the classification made by \citet{bin04} in spectroscopy. + Alhedo moeasureineut by Delbdéetal.(2003). aud Narnr-Spitzer observation (Trillingetal.2010) also sugeestOO a high albedo that support a V-type classification., Albedo measurement by \citet{del03} and Warm-Spitzer observation \citep{tri10} also suggest a high albedo that support a V-type classification. + The S- aud Sq-type classification suggested bv Dandy et ab, The S- and Sq-type classification suggested by Dandy et al. + and deLeónctal.(2010) are consistent with the S-type classification suggested by our observation., and \citet{del10} are consistent with the S-type classification suggested by our observation. + de Leónn et al., de Leónn et al. + sugeestedOO a SLtype classification which is consistent with the S-type classification sugeested by our observation., suggested a Sl-type classification which is consistent with the S-type classification suggested by our observation. + Winu-Spitzer reported an albedo of 0.37 for this object., Warm-Spitzer reported an albedo of 0.37 for this object. + This is a rough match to our R-type classification according to the debiased mean albedo estimates for BR-tvpoe NEAs given by Stuart&Binzel(200L).. which is 0.310.," This is a rough match to our R-type classification according to the debiased mean albedo estimates for R-type NEAs given by \citet{stu04}, which is 0.340." + ITowever. we need to point out that Stuart Diuzel was actually using the average albedo of imiuadn-belt asteroids derived from the work of Tedescoetal.(2002).. as no albedo measurements of auv R-type NEAs had been reported (See Section 1.1. Paragraph 3 aud Footnote 1 in their oper for details). hence this comparison cau be uisleacding.," However, we need to point out that Stuart Binzel was actually using the average albedo of main-belt asteroids derived from the work of \citet{ted02}, as no albedo measurements of any R-type NEAs had been reported (See Section 1.4, Paragraph 3 and Footnote 1 in their paper for details), hence this comparison can be misleading." + Nou-iufraved spectroscopy * Lazzannuctal.(2005) reported (41789) 2001 AIZi to be au X-conmplex asteroid while BVRI yhotometry by Betzlerctal.(2010). sueecsted CHype classification., Near-infrared spectroscopy by \citet{laz05} reported (54789) 2001 MZ7 to be an X-complex asteroid while $BVRI$ photometry by \citet{bet10} suggested G-type classification. + These two results are cousistet with the N-type classification made im this study. sincethe degenerate N-type includes the C and € vpes.," These two results are consistent with the X-type classification made in this study, sincethe degenerate X-type includes the C and G types." + The color indices we measured also match with Betzler et al, The color indices we measured also match with Betzler et al. +s within 0.03 mae.,'s within 0.03 mag. +The original paper by ? formulated the RIME in terms of 4x matrices (2)..,The original paper by \citet{ME1} formulated the RIME in terms of $4\times4$ matrices \citep{Muller}. + This is mathematically fully equivalent to the 2x form introduced by ? in the fourth paper. and has since been adopted by many authors (????)..," This is mathematically fully equivalent to the $2\times2$ form introduced by \citet{ME4} in the fourth paper, and has since been adopted by many authors \citep{JEN:note185,tms,SB:imageplane,Rau:DDEs}." + In my view. this is somewhat unfortunate. as the 2x formulation is both simpler and more elegant. and has far more intuitive appeal. especially for understanding calibration problems.," In my view, this is somewhat unfortunate, as the $2\times2$ formulation is both simpler and more elegant, and has far more intuitive appeal, especially for understanding calibration problems." + For completeness. I will make an explicit link to the 4x form here.," For completeness, I will make an explicit link to the $4\times4$ form here." +" Instead of taking the matrix product of two voltage vectors v, and v, and getting a 2x2 visibility matrix. as in Eq. (49)."," Instead of taking the matrix product of two voltage vectors $\vec v_p$ and $\vec v_q$ and getting a $2\times2$ visibility matrix, as in Eq. \ref{eq:coherency}) )," + we can take the of the two to get the Vg! Combining this with Eq. (2)).," we can take the of the two to get the $v_{pq}$ : Combining this with Eq. \ref{eq:e-voltage}) )," + we get which then gives us the 4x form of Eq. (8)):, we get which then gives us the $4\times4$ form of Eq. \ref{eq:me0}) ): +" Here. Spy=Jp@Jy SIis a 4x4 matrix describing the combined effect of the signal paths to antennas p and q. { is à column vector of the Stokes parameters (7.Q.U.V). and S is a conversion matrix that turns the Stokes vector into the brightness vectorο: The equivalent of the ""onion"" form of Eq. (9))"," Here, ${\cal J}_{pq}=\jones{J}{p} \otimes \jones{J}{q}$ is a $4\times4$ matrix describing the combined effect of the signal paths to antennas $p$ and $q$, $\jones{I}{}$ is a column vector of the Stokes parameters $(I,Q,U,V)$, and $\jones{S}{}$ is a conversion matrix that turns the Stokes vector into the brightness vector: The equivalent of the “onion” form of Eq. \ref{eq:me0-onion}) )" + is then: Likewise. the full-skv RIME of Eq. (18))," is then: Likewise, the full-sky RIME of Eq. \ref{eq:me-allsky}) )" + can be written in the 4x form as: This form of the RIME ts particularly favoured when describing imaging problems (?2)..," can be written in the $4\times4$ form as: This form of the RIME is particularly favoured when describing imaging problems \citep{SB:imageplane,Rau:DDEs}." +" It emphasizes that an interferometer performs a linear. operation on the sky distribution Z(J.a), via the linear operators G4. 65,0.n. and the Fourier Transform 7. while eliding the internal structure of G and &."," It emphasizes that an interferometer performs a linear operation on the sky distribution $\jones{I}{}(l,m)$, via the linear operators ${\cal G}_{pq}$, ${\cal E}_{pq}(l,m)$, and the Fourier Transform $\cal F$, while eliding the internal structure of ${\cal G}$ and ${\cal E}$." + On the other hand. if we're interested 1n the underlying physics of signal propagation (as is often the case for calibration problems). then the 4x form of the RIME becomes extremely opaque.," On the other hand, if we're interested in the underlying physics of signal propagation (as is often the case for calibration problems), then the $4\times4$ form of the RIME becomes extremely opaque." + When considering any specific set of propagation effects (and its corresponding Jones chain). the outer product operation turns simple-looking 2x Jones matrices into an intractable sea of indices: see ?.Eq.4 and ?. for typical examples.," When considering any specific set of propagation effects (and its corresponding Jones chain), the outer product operation turns simple-looking $2\times2$ Jones matrices into an intractable sea of indices; see \citet[Eq. 4]{SB:imageplane} and \citet[Appendix A]{ME1} for typical examples." + The 2x form provides a more transparent description of calibration problems. and for this reason is also far better suited to teaching the RIME.," The $2\times2$ form provides a more transparent description of calibration problems, and for this reason is also far better suited to teaching the RIME." + An excellent example of this transparency is given in Paper II (?.Sect.2.2.2).. where I consider the effect of differential Faraday rotation.," An excellent example of this transparency is given in Paper II \citep[Sect.~2.2.2]{RRIME2}, where I consider the effect of differential Faraday rotation." + There are also potential computational issues raised by the [Lx4 formalism., There are also potential computational issues raised by the $4\times4$ formalism. + A naive implementation of. e.g.. Eq. (26) ," A naive implementation of, e.g., Eq. \ref{eq:me:mueller-onion}) )" +ncurs à series of 4x matrix multiplications for each interferometer and time/frequency point., incurs a series of $4\times4$ matrix multiplications for each interferometer and time/frequency point. + Multiplication of two 3x4 matrices costs 112 floating-point operations (flops). and the outer product operation another 16.," Multiplication of two $4\times4$ matrices costs 112 floating-point operations (flops), and the outer product operation another 16." + Therefore. each pair of Jones terms in the chain incurs 128 flops.," Therefore, each pair of Jones terms in the chain incurs 128 flops." + The same equation in 2x form invokes 12 floating-point operations (Hops) per matrix multiplication. or 24 per each pair of Jones terms.," The same equation in $2\times2$ form invokes 12 floating-point operations (flops) per matrix multiplication, or 24 per each pair of Jones terms." + This is roughly 5 times fewer than the 4x case., This is roughly 5 times fewer than the $4\times4$ case. + Often. the true computational bottleneck lies elsewhere. i.e. in solving (for calibration) or gridding (for imaging). in which case these considerations are irrelevant.," Often, the true computational bottleneck lies elsewhere, i.e. in solving (for calibration) or gridding (for imaging), in which case these considerations are irrelevant." + However. when running massive simulations (that is. using the RIME to predict visibilities). my profiling of MeqTrees has often shown matrix multiplication to be the major consumer of CPU time.," However, when running massive simulations (that is, using the RIME to predict visibilities), my profiling of MeqTrees has often shown matrix multiplication to be the major consumer of CPU time." + In this case. implementing calculations using the 2x2 form represents a significant optimization.," In this case, implementing calculations using the $2\times2$ form represents a significant optimization." + Formulations of the RIME such às Eqs. (18)), Formulations of the RIME such as Eqs. \ref{eq:me-allsky}) ) + or (16)) are entirely general and non-specific. in the sense that they allow for any combination of propagation effects to be inserted in place of the G and E terms.," or \ref{eq:me-nps-ge}) ) are entirely general and non-specific, in the sense that they allow for any combination of propagation effects to be inserted in place of the $\jones{G}{}$ and $\jones{E}{}$ terms." + A specific formulation may be obtained by inserting a particular sequence of Jones matrices., A specific formulation may be obtained by inserting a particular sequence of Jones matrices. + The first RIME paper (?) already suggested a specific Jones chain., The first RIME paper \citep{ME1} already suggested a specific Jones chain. + This was further elaborated on by ?.. and eventually implemented in AIPS++. which subsequently became CASA.," This was further elaborated on by \citet{JEN:note185}, and eventually implemented in AIPS++, which subsequently became CASA." +" The Jones chain used by current versions of CASA is described by ?.AppendixΕ.7; The Jones matrices given here correspond to particular effects in the signal chain. with specific parameterizations (e.g. B, is a frequency-variable bandpass. G, is time-variable receiver gain. etc.)"," The Jones chain used by current versions of CASA is described by \citet[Appendix E.1]{CASA:UserRef}: The Jones matrices given here correspond to particular effects in the signal chain, with specific parameterizations (e.g. $\jones{B}{p}$ is a frequency-variable bandpass, $\jones{G}{p}$ is time-variable receiver gain, etc.)" + Other authors (?) suggest variations on this theme., Other authors \citep{Rau:DDEs} suggest variations on this theme. +" Such a ""Jones-specific"" approach has considerable merit. in that it shows how different real-life propagation effects fit together. and gives us specific to be thought about and implemented in software."," Such a “Jones-specific” approach has considerable merit, in that it shows how different real-life propagation effects fit together, and gives us specific to be thought about and implemented in software." + It does have a few pitfalls which should be pointed out., It does have a few pitfalls which should be pointed out. + The first pitfall of this approach ts that it tends to place the trees firmly before the forest., The first pitfall of this approach is that it tends to place the trees firmly before the forest. + A majorvirtue of the RIME is its elegance and simplicity. but this gets obscured às soon às elaborate chains of Jones matrices are written out.," A majorvirtue of the RIME is its elegance and simplicity, but this gets obscured as soon as elaborate chains of Jones matrices are written out." + I submit that the RIME's slow acceptance among astronomers at large is. insome part. due to the literature being full of equations similar to," I submit that the RIME's slow acceptance among astronomers at large is, insome part, due to the literature being full of equations similar to" +astronomical community.,astronomical community. + About of the observed spectra have been fitted with a x?<3 and we consider fits with such values to be reliable., About of the observed spectra have been fitted with a $\chi^2 \leq 3$ and we consider fits with such values to be reliable. +" For higher values, a visual inspection is recommended to asses the reliability of the spectral fit."," For higher values, a visual inspection is recommended to asses the reliability of the spectral fit." +" For each spectrum that has been analyzed we give the following: Whenever one of the above listed quantities is not available, this is flagged with a 99.99."," For each spectrum that has been analyzed we give the following: Whenever one of the above listed quantities is not available, this is flagged with a 99.99." + All the data and physical quantities described in this paper will be available by querying the ddatabase at the following webh, All the data and physical quantities described in this paper will be available by querying the database at the following web. +"ttp://web.oapd.inaf.it/wings/.. In Table 2 we give an example of how the full set of information will look like, reporting data for 5 galaxies of the sample."," In Table \ref{tab:sfh} we give an example of how the full set of information will look like, reporting data for 5 galaxies of the sample." +" A description of each item, together with their units, can be foundin table 3.."," A description of each item, together with their units, can be foundin table \ref{tab:header}." +compare our velocity distribution to those of other authors (see Section 3)),compare our velocity distribution to those of other authors (see Section\ref{distribution}) ). + Having fixed the stellar sample. we can now proceed with the analysis.," Having fixed the stellar sample, we can now proceed with the analysis." + Llipparcos parallaxes ancl proper motions. together with the radial velocities from the Hipparcos Input Catalogue. have been used. to compute the stellar space velocities relative to the Sun.," Hipparcos parallaxes and proper motions, together with the radial velocities from the Hipparcos Input Catalogue, have been used to compute the stellar space velocities relative to the Sun." + The rie¢ht-hanclecl coordinate system has been used. with the .X-axis pointing towards the ealactic centre. Y-axis in the direction of galactic rotation (clockwise. when seen from the north galactic pole). and Z-axis towards the north galactie pole.," The right-handed coordinate system has been used, with the $X$ -axis pointing towards the galactic centre, $Y$ -axis in the direction of galactic rotation (clockwise, when seen from the north galactic pole), and $Z$ -axis towards the north galactic pole." + Corresponding velocitycomponents are C. V and VW respectively.," Corresponding velocitycomponents are $U$, $V$ and $W$ respectively." + X typical error-bar in. cach velocity. component is. close to 1kmsL. with about NO per cent of stars having their. velocity uncertainties less than 2kms as shown in Fig. 3..," A typical error-bar in each velocity component is close to $1\ \kms$, with about 80 per cent of stars having their velocity uncertainties less than $2\ \kms$, as shown in Fig. \ref{uvwsig}." + The error propagation has been treated taking into account the [ull correlation matrix between the Lipparcos astrometric parameters., The error propagation has been treated taking into account the full correlation matrix between the Hipparcos astrometric parameters. + In order to estimate the probability density function εςV From the observed data. we use here anmethod Lor more details see Silverman 1986).," In order to estimate the probability density function $f(U,V)$ from the observed data, we use here an (for more details see Silverman 1986)." + The basic idea of this method. is to apply a smooth weight function (called. theΑΟ function) to estimate the probability density at any given. point. using a number of neighbouring data points.," The basic idea of this method is to apply a smooth weight function (called the function) to estimate the probability density at any given point, using a number of neighbouring data points." +" The term ""adaptive. here means that the kernel width depends on the actual density. so that the smoothing is done over a larger area if the density is smaller."," The term `adaptive' here means that the kernel width depends on the actual density, so that the smoothing is done over a larger area if the density is smaller." + We use the following definition of the adaptive kernel estimator (see page LOL of Silverman 1986).defined at an arbitrary point £=(U.V): where A(rF)is the kernel function. A; are the local bandwidth factors (climensionless numbers controlling the overall kernel width at cachdata point). and fr is a gencral smoothing factor.," We use the following definition of the adaptive kernel estimator (see page 101 of Silverman 1986),defined at an arbitrary point $\vec\xi=(U,V)$: where $K(\vec r)$ is the kernel function, $\lambda_i$ are the local bandwidth factors (dimensionless numbers controlling the overall kernel width at eachdata point), and $h$ is a general smoothing factor." + We assume also that there are n data points £=(CU;V;)," We assume also that there are $n$ data points $\vec\xi_i=(U_i,V_i)$." + Our function A(PF) is a 2-D racdially svnunetric version of thebieeighl kernel (Fig. 4)).," Our function $K(\vec r)$ is a 2-D radially symmetric version of the kernel (Fig. \ref{kernel}) )," + and is defined by: so that [{νά=] (a condition that anv kernel must satisfy in order to produce an estimate f as a proper probability density. function).Vhe local bandwidth factors A; needed for the computation of f(£) are defined by: where g is the geometric mean of the f(£;): and à is àparemcelcr. which we fix at à=0.5- (a typical value for the two-dimensional case).," and is defined by: so that $\int K(\vec r)d\vec r=1$ (a condition that any kernel must satisfy in order to produce an estimate $\hat f$ as a proper probability density function).The local bandwidth factors $\lambda_i$ needed for the computation of $\hat f(\vec\xi)$ are defined by: where $g$ is the geometric mean of the $\hat f(\vec\xi_i)$: and $\alpha$ is a, which we fix at $\alpha=0.5$ (a typical value for the two-dimensional case)." + Note that in order to compute A; we need the distribution estimate f which. in turn. can be computed only when all A; are known.," Note that in order to compute $\lambda_i$ we need the distribution estimate $\hat f$ which, in turn, can be computed only when all $\lambda_i$ are known." + This problem. however. can be solved iteratively. by starting with an approximate distribution (a fixed kernel estimate. [or example). and then improving the function as well as the A; lactors in a couple of subsequent iterations.," This problem, however, can be solved iteratively, by starting with an approximate distribution (a fixed kernel estimate, for example), and then improving the function as well as the $\lambda_i$ factors in a couple of subsequent iterations." + Finally. an optimal value for the smoothing parameter h is determined. using the least-squares cross-validation method. by minimizing the score function: where [frDn can be computed. numerically. and f(61) is the density estimate at £. constructed. Crom all data points erecpí £.," Finally, an optimal value for the smoothing parameter $h$ is determined using the least-squares cross-validation method, by minimizing the score function: where $\int\!\!\hat f^2$ can be computed numerically, and $\hat f_{-i}(\vec\xi_i)$ is the density estimate at $\vec\xi_i$ , constructed from all data points $\vec\xi_i$ ." +" lt can be shown that minimizing M,(h) is equivalent (in terms of mathematical expectation) to minimizing the integrated square crror |(fo for. so that"," It can be shown that minimizing $M_o(h)$ is (in terms of mathematical expectation) to minimizing the integrated square error $\int(\hat f-f)^2$ , so that" +We report the analysis of long-slit spectroscopic observations of J0927+2943.,We report the analysis of long-slit spectroscopic observations of $+$ 2943. + Comparing our extracted 1D spectrum with the SDSS spectrum. obtained 4 years before. we place a 3c constraint on the acceleration between the red and blue component to be less than 32 'yr|.," Comparing our extracted 1D spectrum with the SDSS spectrum, obtained 4 years before, we place a $\sigma$ constraint on the acceleration between the red and blue component to be less than 32 $^{-1}$." + This is a factor 3 smaller than the one expected for the binary black hole model (?).., This is a factor 3 smaller than the one expected for the binary black hole model \citep{Bogdanovic09}. + However. this alone could not rule out the binary black hole model but rather tightens the constraints on the orbital parameters (see2)..," However, this alone could not rule out the binary black hole model but rather tightens the constraints on the orbital parameters \citep[see][]{Shields09a}." + Moreoverone of the directly testable predictions of this model is the compact sizes (sub-parsec scale) of the emitting regions (?).., Moreover one of the directly testable predictions of this model is the compact sizes (sub-parsec scale) of the emitting regions \citep{Dotti09}. + Here we show that the imi]] emission from the red component originates from an extended region of size ~ Skkpc., Here we show that the ] emission from the red component originates from an extended region of size $\sim$ kpc. +" This observation probably rules out the binary black hole model for JO927+2944,", This observation probably rules out the binary black hole model for $+$ 2944. + In the frame work of recoil model with maximally spinning holes we expect the maximum possible kick of ~4000 !(2).., In the frame work of recoil model with maximally spinning holes we expect the maximum possible kick of $\sim$ 4000 \citep{Campanelli07a}. + The extended emission from the red component can be understood in this model as an effect of photoionisation by the accretion dise emission associated with the recoiling black hole., The extended emission from the red component can be understood in this model as an effect of photoionisation by the accretion disc emission associated with the recoiling black hole. + Off centred emissions are also expected in these models (see???)..," Off centred emissions are also expected in these models \citep[see][]{Haehnelt06, Loeb07, Guedes09}." + Thus extended [Om] emission from the red component or the sligh ottset we found for this emission with respect to the QSO trace alone can not rule out the recoiling black hole scenario., Thus extended ] emission from the red component or the slight offset we found for this emission with respect to the QSO trace alone can not rule out the recoiling black hole scenario. + ? proposed that 7092742943 could be a high redshif analog of 11275., \citet{Heckman09} proposed that $+$ 2943 could be a high redshift analog of 1275. + Based on a simple model of in-falling gas photoionised by the QSO continuum. ? suggested that the observec emission lines could be produced by a gas of density 300 ? a a distance of 8 kpe from the QSO with a projected area of 12 kpe-.," Based on a simple model of in-falling gas photoionised by the QSO continuum, \citeauthor{Heckman09} suggested that the observed emission lines could be produced by a gas of density 300 $^{-3}$ at a distance of 8 kpc from the QSO with a projected area of 12 $^2$ ." + The extent of the gas we tind (~8 Kpo) for the red component is consistent with ?'s simple picture., The extent of the gas we find $\sim 8$ kpc) for the red component is consistent with \citeauthor{Heckman09}' 's simple picture. + However we wish to point ou that in the case of NGC 1275. 21-em and X-ray absorption is seen at the higher redshift suggesting the in-falling gas is in between us and the continuum source (2).," However we wish to point out that in the case of NGC 1275, 21-cm and X-ray absorption is seen at the higher redshift suggesting the in-falling gas is in between us and the continuum source \citep{DeYoung73}." + In their calculation. ? consider NOCH) that will be optically thick to Lyman continuum radiation.," In their calculation, \citeauthor{Heckman09} consider $N$ (H) that will be optically thick to Lyman continuum radiation." + Such gas is also expected to produce absorption if the in-falling gas is well aligned with the QSO., Such gas is also expected to produce absorption if the in-falling gas is well aligned with the QSO. + In the SDSS spectrum we do not detect any absorption., In the SDSS spectrum we do not detect any absorption. + However. detailed photoionisation modelling is needed to rule out the in falling gas model based on the absence of absorption.," However, detailed photoionisation modelling is needed to rule out the in falling gas model based on the absence of absorption." + Our observations confirm the 150086 from = 0.7028 reported by ?.., Our observations confirm the $\lambda$ 5008 from = 0.7028 reported by \citet{Shields09a}. + To explain the three redshifted emission lines. ? proposed a hypothesis in which different emission components originate from a chance alignment of galaxies that are part of a massive cluster.," To explain the three redshifted emission lines, \citet{Shields09a} proposed a hypothesis in which different emission components originate from a chance alignment of galaxies that are part of a massive cluster." + However there is no clear indication of J0927+2943 residing in the centre of a galaxy cluster (see?).., However there is no clear indication of $+$ 2943 residing in the centre of a galaxy cluster \citep[see][]{Decarli09}. + In the recoil models this third emission line component has to come from the unbound gas that got kicked also with the black hole., In the recoil models this third emission line component has to come from the unbound gas that got kicked also with the black hole. + Future deep observations under better seeing conditions are needed to provide a strong constraint on the spatialextent of the third system., Future deep observations under better seeing conditions are needed to provide a strong constraint on the spatialextent of the third system. +"during 1984—1985, when the very different light curve features in the millimetre and radio domains cannot be correctly described by the 1983.4 flare alone.","during 1984–1985, when the very different light curve features in the millimetre and radio domains cannot be correctly described by the 1983.4 flare alone." + The obtained evolution of the parameters with frequency for the typical outburst is shown in Fig. 3.., The obtained evolution of the parameters with frequency for the typical outburst is shown in Fig. \ref{param}. + The amplitude A(v) of the light curve has a maximum at ~45 GGHz., The amplitude $A(\nu)$ of the light curve has a maximum at $\sim\!45$ GHz. + Both the rise time trise(v) and the e-folding decay time tgn(v) increase monotonically with wavelength., Both the rise time $t\dmrm{rise}(\nu)$ and the $\mrm{e}$ -folding decay time $t\dmrm{fall}(\nu)$ increase monotonically with wavelength. +" If we extrapolate the cubic spline to low frequency, it is striking to see that both trise(V) and tran(v) tend to very high values of the order of 10 years at GGHz, while the amplitude of the outburst would still be significant (A(1GHz)z 1JJy)."," If we extrapolate the cubic spline to low frequency, it is striking to see that both $t\dmrm{rise}(\nu)$ and $t\dmrm{fall}(\nu)$ tend to very high values of the order of 10 years at GHz, while the amplitude of the outburst would still be significant $A(\mbox{1\,GHz})\!\approx\!1$ Jy)." +" Due to the lack of submillimetre observations before 1981, the amplitude Ao(v) is not constrained at frequencies above ~300 GGHz."," Due to the lack of submillimetre observations before 1981, the amplitude $A_0(\nu)$ is not constrained at frequencies above $\sim\!300$ GHz." +" The increase of Αο(ν) at these frequencies — due to the spline is probably not real, but does notaffect the fit because the corresponding decay time is short (£g(1000GHz)e1 year)."," The increase of $A_0(\nu)$ at these frequencies – due to the spline -- is probably not real, but does notaffect the fit because the corresponding decay time is short $t\dmrm{fall}(\mbox{1000\,GHz})\!\approx\!1$ year)." + The two exponents p(v) and ó(v) which describe the shape of the outburst's light curve are both higher at radio frequencies than in the mm/submm domain., The two exponents $\rho(\nu)$ and $\phi(\nu)$ which describe the shape of the outburst's light curve are both higher at radio frequencies than in the mm/submm domain. +" As a consequence, the light curves at higher frequencies have a steeper rise just after the start of the outburst and a steeper decay just after the peak (see Figs."," As a consequence, the light curves at higher frequencies have a steeper rise just after the start of the outburst and a steeper decay just after the peak (see Figs." + 1 and 7aa)., \ref{func} and \ref{complc}a a). +" The five parameters A(v), trise(v), ttan(v), p(v) and @(v) define the typical outburst that can be represented in three dimensions in the (logS,logv, t)-space as shown in Fig."," The five parameters $A(\nu)$, $t\dmrm{rise}(\nu)$ , $t\dmrm{fall}(\nu)$, $\rho(\nu)$ and $\phi(\nu)$ define the typical outburst that can be represented in three dimensions in the $(\log{S},\log{\nu},\log{t})$ -space as shown in Fig." + 4dd. The three other panels of Fig., \ref{evo1}d d. The three other panels of Fig. + 4 show the three Cartesian projections of this surface., \ref{evo1} show the three Cartesian projections of this surface. +" The frequency and time axes cover the same logarithmical range of ddex, so that the dotted diagonal in Fig."," The frequency and time axes cover the same logarithmical range of dex, so that the dotted diagonal in Fig." + 4cc corresponds to v«t~!., \ref{evo1}c c corresponds to $\nu\!\propto\!t^{-1}$. +" At least at low frequencies, both the maximum of the spectra and of the light curves follow quite well this diagonal."," At least at low frequencies, both the maximum of the spectra and of the light curves follow quite well this diagonal." + The outburst’s evolution is thus amazingly symmetric in Figs., The outburst's evolution is thus amazingly symmetric in Figs. + 4aa and 4bb. The maximum amplitude of the typical outburst is of ~16 JJy and is reached after ~7.5 months at a frequency of ~45 GGHz., \ref{evo1}a a and \ref{evo1}b b. The maximum amplitude of the typical outburst is of $\sim\!16$ Jy and is reached after $\sim\!7.5$ months at a frequency of $\sim\!45$ GHz. +" The frequency r4, of the spectrum’s maximum is steadily decreasing with time (Fig.", The frequency $\nu\dmrm{m}$ of the spectrum's maximum is steadily decreasing with time (Fig. + 4cc)., \ref{evo1}c c). +" The corresponding flux density Syn is first increasing with decreasing frequency r4, according to S,,οςv5, whereas it decreases as S,«xvil during the final decline of the outburst (Fig."," The corresponding flux density $S\dmrm{m}$ is first increasing with decreasing frequency $\nu\dmrm{m}$ according to $S\dmrm{m}\!\propto\!\nu\dmrm{m}^{-0.7}$, whereas it decreases as $S\dmrm{m}\!\propto\!\nu\dmrm{m}^{+1.0}$ during the final decline of the outburst (Fig." + 4bb)., \ref{evo1}b b). + This behaviour corresponds qualitatively to what is expected by shock models (e.g. MG85)., This behaviour corresponds qualitatively to what is expected by shock models (e.g. MG85). +" At frequencies above the spectral turnover (v>> v), the spectral index a is first of ~—0.5 and steepens very slightly to ~—0.7 at the maximum development of the outburst."," At frequencies above the spectral turnover $\nu\gg \nu\dmrm{m}$ ), the spectral index $\alpha$ is first of $\sim\!-0.5$ and steepens very slightly to $\sim\!-0.7$ at the maximum development of the outburst." + The somewhat chaotic behaviour during the final declining phase — due to the abrupt change in the parameter (v) — does not enable us to define a reasonable spectral index during this last stage., The somewhat chaotic behaviour during the final declining phase – due to the abrupt change in the parameter $\phi(\nu)$ �� does not enable us to define a reasonable spectral index during this last stage. +" At frequencies below the spectral turnover (v< v), the spectral index o is smoothly steepening with time from ~1.8 to ~ 2.5."," At frequencies below the spectral turnover $\nu\ll \nu\dmrm{m}$ ), the spectral index $\alpha$ is smoothly steepening with time from $\sim\!1.8$ to $\sim\!2.5$ ." + This is what is expected from a synchrotron source that starts inhomogeneous and progressively becomes homogeneous (e.g. Marscher 1977))., This is what is expected from a synchrotron source that starts inhomogeneous and progressively becomes homogeneous (e.g. Marscher \cite{M77}) ). + The twelve individual outbursts have different amplitudes ranging from5JJy up to 32JJy for the 1983.0 flare studied, The twelve individual outbursts have different amplitudes ranging fromJy up to Jy for the 1983.0 flare studied +the very high-exeitation forbidden. lines. of FeN]A6375. JeNI]A7892 anc FeNIV]A5303.,"the very high-excitation forbidden lines of $\lambda 6375$ $\lambda +7892$ and $\lambda 5303$." + These are the so-called iron coronal lines., These are the so-called iron coronal lines. + Previous studies of the coronal lines in Sevífert ealaxies have found them to have line widths intermediate oetween that of the lower-cxcitation forbidden narrow lines (such as ΟΠΗ) and the permitted broad. lines. (Grandi 1978)., Previous studies of the coronal lines in Seyfert galaxies have found them to have line widths intermediate between that of the lower-excitation forbidden narrow lines (such as [OIII]) and the permitted broad lines (Grandi 1978). + These studies have also found the coronal lines to »e slightly blueshifted with respect to the narrow forbidden ines., These studies have also found the coronal lines to be slightly blueshifted with respect to the narrow forbidden lines. + As shown in Table 2. the coronal lines in 6- follow exactly these trends.," As shown in Table 2, the coronal lines in $-$ 6-30-15 follow exactly these trends." + Note that the true width and Dux of the FeNIV]A5303 line may be less than that xesented in Table 2 due to blending with CaV]A5309., Note that the true width and flux of the $\lambda 5303$ line may be less than that presented in Table 2 due to blending with $\lambda 5309$. + Oliva et al. (, Oliva et al. ( +1994) have examined various mocels for the coronal ine enission.,1994) have examined various models for the coronal line emission. + Such observations have led to the discussion. of the coronal line region (CLAIR) which is distinct from the BLR or NLR., Such observations have led to the discussion of the coronal line region (CLR) which is distinct from the BLR or NLR. + Here we address the possibility that the CLR in 6-30-15 can be identified. with the outer warm absorber., Here we address the possibility that the CLR in $-$ 6-30-15 can be identified with the outer warm absorber. + The collision strengths for these transitions are poorly known (Osterbrock Fulbright 1996: Oliva 1996)., The collision strengths for these transitions are poorly known (Osterbrock Fulbright 1996; Oliva 1996). + Any calculations of line strengths that we perform will be tainted by this basic uncertainty in the atomic physics., Any calculations of line strengths that we perform will be tainted by this basic uncertainty in the atomic physics. + Despite these uncertainties. we have used to examine the coronal line emission [rom the inner and outer warm absorber.," Despite these uncertainties, we have used to examine the coronal line emission from the inner and outer warm absorber." + ‘Table 3 reports the predicted coronal line [Buxes as a fraction of the observed line Dux., Table 3 reports the predicted coronal line fluxes as a fraction of the observed line flux. + These predicted fluxes assume an optically-thin. ποσοο spherical shell with total covering fraction f..," These predicted fluxes assume an optically-thin, unobscured spherical shell with total covering fraction $f_{\rm c}$." + Lt is clear from Table 3 that the inner warm. absorber cannot contribute much to. the observed. coronal line emission., It is clear from Table 3 that the inner warm absorber cannot contribute much to the observed coronal line emission. +" ""This is primarily due to the fact. that iron is too highly ionized. although collisional de-excitation is also relevant in suppressing the coronal line emission."," This is primarily due to the fact that iron is too highly ionized, although collisional de-excitation is also relevant in suppressing the coronal line emission." + On the other hand. the outer warn. absorber can produce significantcoronal emission.," On the other hand, the outer warm absorber can produce significantcoronal emission." + I£ we hypothesize that all of the Fex]A6375 and. FeNIV]A5303 emission originates [rom the outer warm. absorber. we deduce that fos0.03.," If we hypothesize that all of the $\lambda 6375$ and $\lambda 5303$ emission originates from the outer warm absorber, we deduce that $f_{\rm +c}\approx 0.04$." + However. half of the optical emission from this region may well be blocked by very. optically-thick material (c.g. the molecular torus).," However, half of the optical emission from this region may well be blocked by very optically-thick material (e.g. the molecular torus)." + This is suggested by the fact that. in some other Seyfert nuclei. even infrared coronal lines are observed to be blueshifted with respect to the low-ionization narrow lines implving that any redshiftecl coronal emission must be heavily extinguished.," This is suggested by the fact that, in some other Seyfert nuclei, even infrared coronal lines are observed to be blueshifted with respect to the low-ionization narrow lines implying that any redshifted coronal emission must be heavily extinguished." + I this is the case. the true obscuration-correeted coronal line flux. maybe twice that observed Leading to a revised covering fraction of foz0.08.," If this is the case, the true obscuration-corrected coronal line flux maybe twice that observed leading to a revised covering fraction of $f_{\rm c}\approx 0.08$." + This compares well with the estimate of the covering fraction of the outer warm. absorber. fies~OL. based on the analvsis of data for a sample of Sevfert. galaxies tevnolds 1997).," This compares well with the estimate of the covering fraction of the outer warm absorber, $f_{\rm owa}\sim 0.1$, based on the analysis of data for a sample of Seyfert galaxies (Reynolds 1997)." + According to our caleulations. the observed FeXUATS92 emission cannot. be explained. as originating from the same material as the other coronal lines.," According to our calculations, the observed $\lambda +7892$ emission cannot be explained as originating from the same material as the other coronal lines." + Within our hypothesis. three possibilities present themselves.," Within our hypothesis, three possibilities present themselves." + First. the observed. FeNIJATSO2 may have its origins elsewhere.," First, the observed $\lambda 7892$ may have its origins elsewhere." + Any separate coronal line emitting component would then be heavily constrained by the fact that it. could. not over-procduce FeN]A6375 and FeNIV]A5303., Any separate coronal line emitting component would then be heavily constrained by the fact that it could not over-produce $\lambda 6375$ and $\lambda 5303$. + Secondly. the uncertainties in the atomic physics may lead: to grossly underestimate the FeNI[ATS92. flux. and. this. line may. in [act. originate within the same material as the other coronal lines.," Secondly, the uncertainties in the atomic physics may lead to grossly underestimate the $\lambda 7892$ flux and this line may, in fact, originate within the same material as the other coronal lines." + Thirdly. the uncertainties in the atomic ohvsics may have lec to grossly overestimate the FexX]A6375 and FeXIV]A5303 emission from the outer warm absorber.," Thirdly, the uncertainties in the atomic physics may have led to grossly overestimate the $\lambda 6375$ and $\lambda 5303$ emission from the outer warm absorber." + In this case. either the warm absorber covering raction is large (f.zz0.1) or the coronal lines are emitted rom a completely distinct (and as vet unidentified) region.," In this case, either the warm absorber covering fraction is large $f_{\rm c}\approxgt 0.1$ ) or the coronal lines are emitted from a completely distinct (and as yet unidentified) region." + Further progress in this area clearly. requires better atomic xwameters for these transitions. such as those which will be oovided by the project (LLumamoer ct al.," Further progress in this area clearly requires better atomic parameters for these transitions, such as those which will be provided by the project (Hummer et al." + 1993)., 1993). + Several authors have noted a high degree of polarization in the optical/LR spectrum of 6-30-15 (e.g. Fhompson Martin 1988: Brindle et al., Several authors have noted a high degree of polarization in the optical/IR spectrum of $-$ 6-30-15 (e.g. Thompson Martin 1988; Brindle et al. + 1990)., 1990). + Polarization fractions of 46 per cent have been observed. with a slight tendency towards increasing polarization with decreasing wavelength.," Polarization fractions of 4–6 per cent have been observed, with a slight tendency towards increasing polarization with decreasing wavelength." + This is a significantly larger polarization than is typically [ound in Sevfert nuclei., This is a significantly larger polarization than is typically found in Seyfert nuclei. + The polarization is found to be aligned with the major axis of the host galaxy., The polarization is found to be aligned with the major axis of the host galaxy. + There are two possible causes for this polarization (see ]xartje 1995 for à recent review of polarization mechanisms in AGN)., There are two possible causes for this polarization (see Kartje 1995 for a recent review of polarization mechanisms in AGN). + First. a large. scale. alignment of dust. grains along the line of sight to the central source can produce polarization via dichroic extinction (i.e. one polarization is preferentially scattered. out of. the line. of. sight by the dust grains).," First, a large scale alignment of dust grains along the line of sight to the central source can produce polarization via dichroic extinction (i.e. one polarization is preferentially scattered out of the line of sight by the dust grains)." + Secondly. scattering of flux. into the observers line of sight by dust. or free electrons will naturally produce polarization.," Secondly, scattering of flux into the observers line of sight by dust or free electrons will naturally produce polarization." + La 6-30-15 we have independent. evidence for both scattering ancl the presence of line-of-sight dust., In $-$ 6-30-15 we have independent evidence for both scattering and the presence of line-of-sight dust. + Thus. both of these mechanisms may be relevant — careful spectropolarimetry and detailed modeling will be needed to disentangle these effects.," Thus, both of these mechanisms may be relevant – careful spectropolarimetry and detailed modeling will be needed to disentangle these effects." + We note that ΕκΛΑ 13349|2438. the other good custy-warm absorber candidate. also clisplavs a very high degree of polarization (about S per cent).," We note that IRAS 13349+2438, the other good dusty-warm absorber candidate, also displays a very high degree of polarization (about 8 per cent)." + Wills et al. (, Wills et al. ( +1992) have found that the spectrum of the polarized light is typical of an aunrecdened ACXGN. thereby suggesting that the polarization is primarily due to scattering of the flux along a relatively dust-[ree path into the observers line-of-sight.,"1992) have found that the spectrum of the polarized light is typical of an unreddened AGN, thereby suggesting that the polarization is primarily due to scattering of the flux along a relatively dust-free path into the observers line-of-sight." + Using the estimated unreddened spectrum. we can address the issue of the energy distribution/Ilow in this source.," Using the estimated unreddened spectrum, we can address the issue of the energy distribution/flow in this source." + Here.we shall assume a reddening of L(V)= 0.61. leading to the unreddened spectrum sketched in Fig.," Here,we shall assume a reddening of $E(B-V)=0.61$ , leading to the unreddened spectrum sketched in Fig." + 4., 4. + Phe (isotropic) luminosity in the kkeV. band is then, The (isotropic) luminosity in the keV band is then +"The results and analysis of the total intensity distributions have been presented in Fengetal.(2006),, where spectral fits to some of the components and radiative mechanism are investigated in detail.","The results and analysis of the total intensity distributions have been presented in \citet{fen06}, where spectral fits to some of the components and radiative mechanism are investigated in detail." +" Here, we reproduce the intensity distributions at all the 5 frequencies as contour profiles in the left panel of each map in Figures 1 and 2,, with antenna gains calibrated to those antennas of unreasonable magnitude by checking amplitude versus distance plots at all but 43 GHz before imaging this time (e.g. Zavala&Taylor 2004))."," Here, we reproduce the intensity distributions at all the 5 frequencies as contour profiles in the left panel of each map in Figures \ref{fig1} + and \ref{fig2}, with antenna gains calibrated to those antennas of unreasonable magnitude by checking amplitude versus distance plots at all but 43 GHz before imaging this time (e.g. \citealt{zav04}) )." + This gives rise to small differences in the resultant components’ amplitude in model fitting., This gives rise to small differences in the resultant components' amplitude in model fitting. +" In terms of the recovered proportion of total flux density on pc scale, the current results is more consistent in comparison to that shown in MOJAVE data archive (http://www.physics.purdue.edu/astro/mojave)."," In terms of the recovered proportion of total flux density on pc scale, the current results is more consistent in comparison to that shown in MOJAVE data archive (http://www.physics.purdue.edu/astro/mojave)." + The total intensity distributions show that the detectable emission region decreases rapidly with frequency., The total intensity distributions show that the detectable emission region decreases rapidly with frequency. +" This is mainly due to large changes in resolution, and the sensitivity difference at different frequencies may also have contribution to it."," This is mainly due to large changes in resolution, and the sensitivity difference at different frequencies may also have contribution to it." + Model fitting is done using the MODELFIT program in the DIFMAP package., Model fitting is done using the MODELFIT program in the DIFMAP package. +" Since a model fit to total intensity distribution is not necessarily unique (Listeretal.2009),, we tried not to introduce any artificial estimate into the process of model fitting to keep the same components as presented in Fengetal.(2006)."," Since a model fit to total intensity distribution is not necessarily unique \citep{lis09}, we tried not to introduce any artificial estimate into the process of model fitting to keep the same components as presented in \citet{fen06}." +. We started with a Gaussian component to model the Stokes structure., We started with a Gaussian component to model the Stokes structure. +" When the reduced Chi-square no longer decreases and there are still sufficient bright feature(s) present in the residual image, a new Gaussian component is added into the residual image for further fitting."," When the reduced Chi-square no longer decreases and there are still sufficient bright feature(s) present in the residual image, a new Gaussian component is added into the residual image for further fitting." + The process was repeated until no apparently bright feature could be found in the residual image., The process was repeated until no apparently bright feature could be found in the residual image. +" The linear polarization is fitted using the same components as derived from the total intensity fits with the only parameter flux left free to estimate the Stokes and flux density, and the corresponding linear polarized flux and positional angle were obtained by using P=4/Q?--U? and x=0.5arctanU/Q, respectively."," The linear polarization is fitted using the same components as derived from the total intensity fits with the only parameter flux left free to estimate the Stokes and flux density, and the corresponding linear polarized flux and positional angle were obtained by using $P = +\sqrt{Q^2 + U^2}$ and $\chi = 0.5\arctan{U/Q}$, respectively." +" The fitting results of the southmost component and the component at phase tracking center (hereafter central component) (see the right bottom panel of Figure 2) are shown in Table 2,, where flux density (f,), fractional polarization (m), EVPA, major axis (Qmaj), axial ratio (65,45 /05,i;4) and the derived brightness temperature (Tg) in the source frame for both components are listed in the corresponding columns."," The fitting results of the southmost component and the component at phase tracking center (hereafter central component) (see the right bottom panel of Figure 2) are shown in Table \ref{tb2}, where flux density $f_\nu$ ), fractional polarization $m$ ), EVPA, major axis $\theta_{maj}$ ), axial ratio $\theta_{maj}/\theta_{min}$ ) and the derived brightness temperature $T_B$ ) in the source frame for both components are listed in the corresponding columns." +" The Tz is estimated by using the following expression (Ghisellinietal.1993),, where f, is flux density at frequency v, θα is angular size θά=\/Omaj9min With 05,45; and Omin being major and minor axis, respectively."," The $T_B$ is estimated by using the following expression \citep{ghi93}, where $f_\nu$ is flux density at frequency $\nu$, $\theta_d$ is angular size $\theta_d = \sqrt{\theta_{maj}\theta_{min}}$ with $\theta_{maj}$ and $\theta_{min}$ being major and minor axis, respectively." +" Due to large difference in resolutions, we cannot separate the southmost component at lower frequencies 5 and 8 GHz, the central component at the two frequencies therefore probably contains a larger emission region in comparison to that at higher frequencies, and will be investigated separately from the other frequencies below."," Due to large difference in resolutions, we cannot separate the southmost component at lower frequencies 5 and 8 GHz, the central component at the two frequencies therefore probably contains a larger emission region in comparison to that at higher frequencies, and will be investigated separately from the other frequencies below." + The total intensity distributions show a typical core- structure with jet roughly extending to north., The total intensity distributions show a typical core-jet structure with jet roughly extending to north. +" Small fluctuations of jet orientation occurs down the jet, which can be more clearly seen by comparing radio structures at different frequencies."," Small fluctuations of jet orientation occurs down the jet, which can be more clearly seen by comparing radio structures at different frequencies." +" One can find in Table 2 that the component lies in the extreme end of the radio structure, and has relatively high brightness temperature in comparison to the componentB,, although its flux density is relatively low."," One can find in Table \ref{tb2} that the component lies in the extreme end of the radio structure, and has relatively high brightness temperature in comparison to the component, although its flux density is relatively low." + This may imply that it is the component that represents the radio core of the source., This may imply that it is the component that represents the radio core of the source. +" To have more evidence for the hypothesis, we fitted power law spectra to both components from 15 GHz to 43 GHz, which is shown in Figure 3.."," To have more evidence for the hypothesis, we fitted power law spectra to both components from 15 GHz to 43 GHz, which is shown in Figure \ref{fig3}." +" The spectral indices for component and are estimated to be 0.08+0.11 and —0.52+0.03, respectively."," The spectral indices for component and are estimated to be $0.08\pm0.11$ and $-0.52\pm0.03$, respectively." +" Obviously, the power-law spectrum for componentis fitted badly, but surely harder, while the component Aexhibits a spectrum of quite a good power-law form, which argues for the core hypothesis of the component A,, as suggested in Jorstadetal.(2001) and Fengetal. (2006).."," Obviously, the power-law spectrum for componentis fitted badly, but surely harder, while the component exhibits a spectrum of quite a good power-law form, which argues for the core hypothesis of the component , as suggested in \citet{jos01} and \citet{fen06}. ." +consider the case where the combined mass exceeds. Aog. and by analogy identify the likely merger products as the maenetars.,"consider the case where the combined mass exceeds $M_{\rm Ch}$, and by analogy identify the likely merger products as the magnetars." + We summarize our conclusions in Section 4., We summarize our conclusions in Section 4. + Since the outcome of a CO white dwarf merger is cilficult to predict theoretically. we start from a case where the answer is clear. namely when the total binary mass M. is slightly smaller than AMcgy.," Since the outcome of a CO white dwarf merger is difficult to predict theoretically, we start from a case where the answer is clear, namely when the total binary mass $M$ is slightly smaller than $M_{\rm +Ch}$." + A supernova is unlikely (but see Section 3 below). so there must be a remnant à massive white chvarl.," A supernova is unlikely (but see Section 3 below), so there must be a remnant – a massive white dwarf." + Indeed. Livio. Pringle Saller (1992) suggested that a significant fraction of massive white cbwarfs are the result of mergers.," Indeed Livio, Pringle Saffer (1992) suggested that a significant fraction of massive white dwarfs are the result of mergers." + Furthermore the white dwarf is spun up to rapid rotation by accretion from a disc. and is likely to be highly magnetic because of the winding up of magnetic fields in this clisc.," Furthermore the white dwarf is spun up to rapid rotation by accretion from a disc, and is likely to be highly magnetic because of the winding up of magnetic fields in this disc." + Statistical evidence supports this picture., Statistical evidence supports this picture. + I is now well established that the mass distribution of isolated white dwarfs has. in addition to the dominant peak at 0.57 M... a second peak near 1.2 AL. with a tail which extends. up to Alou.," It is now well established that the mass distribution of isolated white dwarfs has, in addition to the dominant peak at 0.57 $\msun$, a second peak near 1.2 $\msun$ with a tail which extends up to $M_{\rm +Ch}$." + Wickramasinghe Ferrario (2000) show that a large proportion (about 25 per cent) of the white dwarls in this high mass group are strongly magnetic. while for the white dwarf sample as a whole. only 5 per cent are magnetic.," Wickramasinghe Ferrario (2000) show that a large proportion (about 25 per cent) of the white dwarfs in this high mass group are strongly magnetic, while for the white dwarf sample as a whole, only 5 per cent are magnetic." + However it is unlikely thata££ high mass magnetic white chvarls result. from mergers. since some rotate very slowly (periods z-100 vr).," However it is unlikely that high mass magnetic white dwarfs result from mergers, since some rotate very slowly (periods $>100$ yr)." + These must arise from single star evolution (see Wickramasinghe and Ferrario 2000)., These must arise from single star evolution (see Wickramasinghe and Ferrario 2000). + We should next ask lor a specific example of such a merecr remnant., We should next ask for a specific example of such a merger remnant. + The best studied massive magnetic white ανα is RE J0317853. which has mass AMwp=1.35M.. magnetic field By in the range 3.5«10>8107 C. and spin period £4=725 s (see Wickramasinghe Ferrario 2000 and references therein).," The best studied massive magnetic white dwarf is RE J0317–853, which has mass $M_{\rm WD} =1.35\msun$, magnetic field $B_0$ in the range $3.5\times 10^8 - 8\times 10^8$ G, and spin period $P_0 = 725$ s (see Wickramasinghe Ferrario 2000 and references therein)." + This looks remarkably like a white chwarf merger product which missed. Alou by a narrow margin., This looks remarkably like a white dwarf merger product which missed $M_{\rm Ch}$ by a narrow margin. + However before accepting this important conclusion we should examine other possibilities., However before accepting this important conclusion we should examine other possibilities. + RE J0317853 could in principle have formed in the normal course of singlestar evolution as the degenerate core of à giant., RE J0317–853 could in principle have formed in the normal course of single–star evolution as the degenerate core of a giant. + Hs mass ΛίνοςMey implies that the latter star must have had a mass close to the maximum that will give a white dwarf rather than a neutron star or black hole. ic. about SM...," Its mass $M_{\rm WD} \la M_{\rm Ch}$ implies that the latter star must have had a mass close to the maximum that will give a white dwarf rather than a neutron star or black hole, i.e. about $8\msun$." +" Livio Pringle (1998) argue that clynamegenerated magnetic fields at the coreenvelope interface will make the core of such a star rotate with angular. velocity QmOQ,6.6«10σος 4 at the end of the giant phase.", Livio Pringle (1998) argue that dynamo--generated magnetic fields at the core–envelope interface will make the core of such a star rotate with angular velocity $\Omega_c \simeq 6.6\times 10^{-11}$ $^{-1}$ at the end of the giant phase. +" The inner 1.35M.. of this core has radius 0.215.: collapsing this to the likely racius fy~310 em of RE J0317.853 and assiiiine angular Momentun conservation procdtiuces a spin period of about 4.10 s. This is probably an unclerestimate. as the white dwarl magnetic field implied by Livio Pringle's calculations is much smaller than the observed By2358.10 G: the core field at the end of the giant hase is B,0210.το. and Dux conservation increases his only to ~50 €i for the white ναι,"," The inner $1.35\msun$ of this core has radius $0.2\rsun$: collapsing this to the likely radius $R_0 \sim 3\times +10^8$ cm of RE J0317–853 and assuming angular momentum conservation produces a spin period of about $4\times 10^7$ s. This is probably an underestimate, as the white dwarf magnetic field implied by Livio Pringle's calculations is much smaller than the observed $B_0 = +3.5-8\times 10^8$ G: the core field at the end of the giant phase is $B_c \simeq 2\times 10^{-2}$ G, and flux conservation increases this only to $\sim 50$ G for the white dwarf." + Spruit Phinney (1998) predict somewhat longer white chvarl spin periods 10° s. as in their calculations the degenerate core is close Oo corotation with the giant envelope.," Spruit Phinney (1998) predict somewhat longer white dwarf spin periods $\sim 10^8$ s, as in their calculations the degenerate core is close to corotation with the giant envelope." +" We conclude. that the .J0317853's observed spin period. £4,2725 s cannot be explained if it is the result of singlestar evolution.", We conclude that RE J0317–853's observed spin period $P_0 = 725$ s cannot be explained if it is the result of single–star evolution. + Further. his evolution olfers no obvious reason why the observed magnetic field should be so strong.," Further, this evolution offers no obvious reason why the observed magnetic field should be so strong." + Descent from an interacting binary olfers a clear avenue for explaining the rapid spin of It JO317.853. (, Descent from an interacting binary offers a clear avenue for explaining the rapid spin of RE J0317–853. ( +a) The most straightforward idea is that RE JO3L7853 night represent some endpoint of cataclysmic variable (CV) evolution. in which a white dwarl accretes from a lowmass companion.,"a) The most straightforward idea is that RE J0317–853 might represent some endpoint of cataclysmic variable (CV) evolution, in which a white dwarf accretes from a low–mass companion." + RE J03178S53's strong field would make it an extreme member of the AM. Lerculis subgroup (in fact its Ποια is stronger than any known member of this class)., RE J0317–853's strong field would make it an extreme member of the AM Herculis subgroup (in fact its field is stronger than any known member of this class). + In the conventional picture of AAT Herculis evolution. the strong field of the white dwarf keeps the spin of this star locked to the orbital motion.," In the conventional picture of AM Herculis evolution, the strong field of the white dwarf keeps the spin of this star locked to the orbital motion." +" RE J0317853 cannot descend. [rom this evolution. as the minimum orbital period for any. CV is about SO minutes. far above the observed. £7,=725 s. (b)evolution In a recent. paper. Meyer Meyer.Llolmeister (1999) argue that XM Που systems may lose svnchronism at very short orbital periods. when the secondary becomes so cool that the conductivity of its envelope drops catastrophically."," RE J0317–853 cannot descend from this evolution, as the minimum orbital period for any CV is about 80 minutes, far above the observed $P_0 = 725$ s. (b) In a recent paper, Meyer Meyer–Hofmeister (1999) argue that AM Her systems may lose synchronism at very short orbital periods, when the secondary becomes so cool that the conductivity of its envelope drops catastrophically." + In this case the white cwarl could. indeed spin up to much shorter periods. and the companion star would be disrupted on à short timescale as the binary separation shrinks because of the draining of orbital angular momentum to the white dwarl spin.," In this case the white dwarf could indeed spin up to much shorter periods, and the companion star would be disrupted on a short timescale as the binary separation shrinks because of the draining of orbital angular momentum to the white dwarf spin." + At first sight this looks like an attractive idea for explaining the properties of RE JO317853., At first sight this looks like an attractive idea for explaining the properties of RE J0317–853. + However since the deeper lavers of the companion must remain ijonized. we would expect this star to retain a strong enough clipole moment to remain svnchronous.," However since the deeper layers of the companion must remain ionized, we would expect this star to retain a strong enough dipole moment to remain synchronous." + Even leaving this aside. this idea olfers no explanations for the unusually high mass anc magnetic field of WE 0317.853.," Even leaving this aside, this idea offers no explanations for the unusually high mass and magnetic field of RE J0317–853." + We conclude that RE JO0317.853 is not likely to be be explained as an endproduct of these other tvpes of evolution., We conclude that RE J0317–853 is not likely to be be explained as an end–product of these other types of evolution. + On the other hand. as we suggested. above. i arises quite naturally as the result of a CO white dwarf merger. with at least one of the white chvarls being milely. magnetic.," On the other hand, as we suggested above, it arises quite naturally as the result of a CO white dwarf merger, with at least one of the white dwarfs being mildly magnetic." + A variant of this idea is to invoke coalescence of sucha CO white dwarl with the fairly massive core of a gian companion through commonenvelope evolution., A variant of this idea is to invoke coalescence of such a CO white dwarf with the fairly massive core of a giant companion through common–envelope evolution. + For many purposes these two possibilities are extremely similar., For many purposes these two possibilities are extremely similar. + We concluded. above that the massive white dwacrl RE 10211853 is the result of a white dwarl merger with AL , We concluded above that the massive white dwarf RE J0317–853 is the result of a white dwarf merger with $M$ +The thermal gas. that is the dominant component in the Inter-Galactic-Medium (GM). is mixed with magnetic. fields and relativistic particles. as proven by radio observations which detected Mpe-sized diffuse radio emission from the IGM. in ye form of radio halos and relics (e.g.22).,"The thermal gas, that is the dominant component in the Inter-Galactic-Medium (IGM), is mixed with magnetic fields and relativistic particles, as proven by radio observations which detected Mpc-sized diffuse radio emission from the IGM, in the form of radio halos and relics \citep[e.g.][]{2003astro.ph..1576F,2008SSRv..134...93F}." + These Mpe-scale radio sources are found in a fraction of massive clusters with complex dynamics. which suggests a connection between non-jermal emission and cluster mergers (e.g.222) Cluster mergers are the most energetic events in the universe and a fraction of je energy dissipated during these mergers may be channelled into the amplification of the magnetic fields (e.g.22?) and into qe acceleration of relativistic. primary. electrons and protons via Relativistic protons in the IGM have long life-times and remain confined within galaxy clusters for a Hubble time (e.g.??)..," These Mpc-scale radio sources are found in a fraction of massive clusters with complex dynamics, which suggests a connection between non-thermal emission and cluster mergers \citep[e.g.][]{2001ApJ...553L..15B,2008A&A...484..327V,2009A&A...507..661B} + Cluster mergers are the most energetic events in the universe and a fraction of the energy dissipated during these mergers may be channelled into the amplification of the magnetic fields \citep[e.g.][]{2002A&A...387..383D,2006MNRAS.366.1437S,2008Sci...320..909R} + and into the acceleration of relativistic, primary, electrons and protons via shocks and turbulence \citep[e.g.][]{1998A&A...332..395E,1999astro.ph.11439S,2001MNRAS.320..365B, +2004MNRAS.350.1174B,2001ApJ...557..560P,2003ApJ...583..695G,2003ApJ...593..599R, +2005MNRAS.357.1313C,2006MNRAS.367..113P,2007MNRAS.378..245B,2009A&A...504...33V} + Relativistic protons in the IGM have long life-times and remain confined within galaxy clusters for a Hubble time \citep[e.g.][]{1996SSRv...75..279V,1997ApJ...487..529B}." + Asuconsequence they are expected to be the dominant non-thermal particle component., As a consequence they are expected to be the dominant non-thermal particle component. + Collisions between these relativistic protons and the thermal protons in the IGM generate secondary particles hat combined with the primary relativistic particles are expected o producea complex emission spectrum from radio to -rays ?2)..," Collisions between these relativistic protons and the thermal protons in the IGM generate secondary particles that combined with the primary relativistic particles are expected to producea complex emission spectrum from radio to $\gamma$ -rays \citep[e.g.][]{2001APh....15..223B,2009A&A...507..661B}." + Only upper limits to the ~-ray emission from galaxy clusters iive been obtained so far (22222). however the FERMI Gamma-ray telescope will shortly allow a step forward. having a chance o obtain first detections of galaxy clusters or to put stringent constraints on the energy density of the relativistic protons.," Only upper limits to the $\gamma$ -ray emission from galaxy clusters have been obtained so far \citep[][]{2003ApJ...588..155R,2006ApJ...644..148P, +2009A&A...495...27A,2009A&A...502..437A,2009arXiv0909.3267T} however the FERMI Gamma-ray telescope will shortly allow a step forward, having a chance to obtain first detections of galaxy clusters or to put stringent constraints on the energy density of the relativistic protons." + Most importantly. in a few years the Low Frequency Array C(LOFAR) and he Long Wavelength Array (LWA) will observe galaxy clusters at ow radio frequencies with the potential to discover the bulk of the cluster-scale synchrotron emission in the Universe (e.g.222)..," Most importantly, in a few years the Low Frequency Array (LOFAR) and the Long Wavelength Array (LWA) will observe galaxy clusters at low radio frequencies with the potential to discover the bulk of the cluster-scale synchrotron emission in the Universe \citep[e.g.][]{2002A&A...396...83E,2009arXiv0910.2025C,2006MNRAS.369.1577C}." + The emerging theoretical picture is very complex and modern numerical simulations provide an efficient way to obtain detailed models of non thermal emission from galaxy clusters to compare with present and future observations., The emerging theoretical picture is very complex and modern numerical simulations provide an efficient way to obtain detailed models of non thermal emission from galaxy clusters to compare with present and future observations. + Advances in this respect have been recently obtained by including aspects of cosmic-ray physics into cosmological Lagrangian simulations mostly focussing on the acceleration of relativistic particles at shocks and on the relative production of secondary electrons (e.g. ?).., Advances in this respect have been recently obtained by including aspects of cosmic-ray physics into cosmological Lagrangian simulations mostly focussing on the acceleration of relativistic particles at shocks and on the relative production of secondary electrons \citep[e.g.][]{2008MNRAS.385.1211P}. . + In this work we investigate the non-thermal emission from secondary particles in galaxy clusters extracted from Lagrangian, In this work we investigate the non-thermal emission from secondary particles in galaxy clusters extracted from Lagrangian +"If an observed microlensing (or occultation) event of a uniform source has a maximum depth given by 855,4. and if the function is known. then the measured depth can be fit by any Αι=ES=OHinaRI~.","If an observed microlensing (or occultation) event of a uniform source has a maximum depth given by $\delta \mu_{max}$, and if the limb-darkening function is known, then the measured depth can be fit by any $R_L=\left[2R_E^2-\delta\mu_{max}R_*^2\right]^{1/2}$." + However. the lighteurve near the edge of the source depends differently on Ry and Αι.," However, the lightcurve near the edge of the source depends differently on $R_E$ and $R_L$." +" In Figure 4. we show lightcurves near the edge computed from equation which have the same ομως but have different ratios of Ry/R. and R,/R..."," In Figure 4, we show lightcurves near the edge computed from equation which have the same $\delta\mu_{max}$ , but have different ratios of $R_E/R_*$ and $R_L/R_*$." + The cases with larger Einstein radii have a larger magnification and dip near the edge than the pure occultation case., The cases with larger Einstein radii have a larger magnification and dip near the edge than the pure occultation case. + The peak in ὃμ corresponds to the point at which the image outside of the Einstein radius ts first occulted. at which point z—7.27j—H/ry for rj>1.," The peak in $\delta\mu$ corresponds to the point at which the image outside of the Einstein radius is first occulted, at which point $z-r_*=r_L-1/r_L$ for $r_L>1$." + At this point. the magnification is In the limit that r.3»rp21. this reduces to 6peqe=4rp. which becomes small rapidly.," At this point, the magnification is In the limit that $r_* \gg r_L \gg 1$, this reduces to $\delta \mu_{peak}=4^{-1}r_*^{-2}r_L^{-2}$, which becomes small rapidly." + In principle this can be used to break the degeneracy between Ry and Αι since the maximum magnfication has a different dependence on these quantitities., In principle this can be used to break the degeneracy between $R_E$ and $R_L$ since the maximum magnfication has a different dependence on these quantitities. + When limb-darkening is included using the parameterization KR)=1—1(1—40—2»(1740) and jj=[1-R7]7. the magnification outside of eclipse is decreased slightly due to the darker limb. while the dip within the eclipse disappears since the dip becomes larger as the lens covers the brighter regions of the star (Figure 4).," When limb-darkening is included using the parameterization $I(R)=1-\gamma_1(1-\mu)-\gamma_2(1-\mu)^2$ and $\mu=[1-R^2]^{1/2}$, the magnification outside of eclipse is decreased slightly due to the darker limb, while the dip within the eclipse disappears since the dip becomes larger as the lens covers the brighter regions of the star (Figure 4)." + These deviations may be useful for distinguishing a brown dwarf from a planetary transit. or a close white dwarf from a terrestrial planet.," These deviations may be useful for distinguishing a brown dwarf from a planetary transit, or a close white dwarf from a terrestrial planet." + In the case of a limb-darkened star. we must integrate the magnification for a uniform source over the limb-darkened profile of the star.," In the case of a limb-darkened star, we must integrate the magnification for a uniform source over the limb-darkened profile of the star." + The magnification of a limb-darkened source ts approximately where Fo=22[ή@RRICR) is the total flux of the source star and Óp(R)2ju(R)-ΞξλίνRYO(R/Ry—z).," The magnification of a limb-darkened source is approximately where $F_0=2\pi\int_0^{R_*} dR R I(R)$ is the total flux of the source star and $\delta \mu_e(R) = \mu_e(R)-1 +=2(R_E/R)^2\Theta(R/R_E-z)$." + Since dpR7 Is simply proportional to the step function. its derivative is the delta function.," Since $\delta \mu_e R^2$ is simply proportional to the step function, its derivative is the delta function." + Integrating over this delta function picks out the surface brightness at the position of the lens., Integrating over this delta function picks out the surface brightness at the position of the lens. + We finally find that where (P5=Fy/(7R2) and we have added in occultation by the foreground star., We finally find that where $\langle I \rangle = F_0/(\pi R_*^2)$ and we have added in occultation by the foreground star. + It is remarkable that although the magnification involves integrating over the surface of the entire star. it ends up depending only on the surface brightness underneath the lens!," It is remarkable that although the magnification involves integrating over the surface of the entire star, it ends up depending only on the surface brightness underneath the lens!" + This results from the fact that the microlensing amplification of a point source becomes infinite for an exactly aligned source. which may be approximated as a delta function.," This results from the fact that the microlensing amplification of a point source becomes infinite for an exactly aligned source, which may be approximated as a delta function." + Figure 5 shows a comparison of this approximation with exact lighteurves., Figure 5 shows a comparison of this approximation with exact lightcurves. + The agreement between the approximate lightcurves and exact lighteurvesaway from the edges is astoundingly good. especially considering that the analytic approximation involves a," The agreement between the approximate lightcurves and exact lightcurvesaway from the edges is astoundingly good, especially considering that the analytic approximation involves a" +"Iu adaitiou. we also define The latitude offsets (.e.. 9, 0.) though interesting cau not be directly related to observations preseutlv available.","In addition, we also define The latitude offsets (i.e., $\hat{\theta_r} -\theta_r$ ) though interesting can not be directly related to observations presently available." + We therefore concentrate ouly on the longitude offsets Ay., We therefore concentrate only on the longitude offsets $\Delta \varphi$. + Using Eq., Using Eq. + 15 we have calculated the offsets Ay over the range of co-rotatiou velocity for various values of à., \ref{dp} we have calculated the offsets $\Delta \varphi$ over the range of co-rotation velocity for various values of $\alpha$. + Fies., Figs. + l-1 show these plots for a values as labelled., 1-4 show these plots for $\alpha$ values as labelled. +As of today. there are 77 extrasolar planets listed in the California Carnegie Planet Search. home page http://exoplanets.org/almanac.himl.,"As of today, there are 77 extrasolar planets listed in the California Carnegie Planet Search home page http://exoplanets.org/almanac.html." + Almost all of the 57 planets with, Almost all of the 57 planets with +Doradi (ID 33262).,Doradi (HD 33262). + Obviously. anv bint of a systematic dependence of £? on 4A disappears if these are valid points.," Obviously, any hint of a systematic dependence of $\xi^2$ on $A$ disappears if these are valid points." + However. it appears that thev lie well outside the distribution of £? values lor stars wilh similar values of cosA.," However, it appears that they lie well outside the distribution of $\xi^2$ values for stars with similar values of $\cos A$." + There is basis for suspecting that the line widths might be affected by blends of (wo or more components. thus inflating a single component fit to the line.," There is basis for suspecting that the line widths might be affected by blends of two or more components, thus inflating a single component fit to the line." + For this reason. Alkaid and ¢ Dor may be provisionally considered outliers.," For this reason, Alkaid and $\zeta$ Dor may be provisionally considered outliers." + In the analvses which follow. we have considered. the complete data set of 53J) absorption measurements. as well as an edited subset in which Alkaid and & Doradi are removed.," In the analyses which follow, we have considered the complete data set of 53 absorption measurements, as well as an edited subset in which Alkaid and $\zeta$ Doradi are removed." + Figure 2 does not present a strong case for anisotropy. clefined as close adherence of the data to (he expression given in Equation (3).," Figure 2 does not present a strong case for anisotropy, defined as close adherence of the data to the expression given in Equation (3)." + ILowever. it is possible that an anisotropy of the sort we are seeking is present. but obscured by star-to-staàr variations of another. unknown nature.," However, it is possible that an anisotropy of the sort we are seeking is present, but obscured by star-to-star variations of another, unknown nature." + To detect anisotropy in (his case. il is necessary lo average measurements for several stars.," To detect anisotropy in this case, it is necessary to average measurements for several stars." + Furthermore. we need a means of extracting from the data a quantitative upper limit to the anisotropy. parameter e.," Furthermore, we need a means of extracting from the data a quantitative upper limit to the anisotropy parameter $\epsilon$." + A simple wav of addressing both of these points is to average the data over intervals in cos;l., A simple way of addressing both of these points is to average the data over intervals in $\cos A$. + For these purposes. we consiler (he star-(o-s(ar variations as noise superposed to a (rue signal of the form in Equation (3).," For these purposes, we consider the star-to-star variations as noise superposed to a true signal of the form in Equation (3)." + If anisotropy is present. (he average value οἱ e for all lines of sight with ο 0.3$ were allowed to have disks with lifetimes in the range $\tau_\star$ to $\tau_{max}$. + Stars with ACEI) below thisthreshold were evolved with stellar winds only., Stars with $\Delta$ (I-K) below this threshold were evolved with stellar winds only. + For the stars with no IR data of the sariple) (lisks were raucoiily saliplecd from the range 0 to Ty»., For the stars with no IR data of the sample) disks were randomly sampled from the range 0 to $\tau_{max}$. + For 81 the stars used in this study. ad excess It enisou.," For 81 the stars used in this study, had excess IR emission." + The resulting expected ONC clistribttion for 7445=6 Myr Was COnistet wit1 tlie Pleiades by νο test., The resulting expected ONC distribution for $\tau_{max} = 6$ Myr was consistent with the Pleiades by K-S test. + For our salupe of ONC sta‘s. the two period distributions of sta* above and below the IR limit are st:1istically ixcistinguishable by Ix-8 test. altlioeh the mean perioc is slightly smaller for stars below ihe IR limit.," For our sample of ONC stars, the two period distributions of stars above and below the IR limit are statistically indistinguishable by K-S test, although the mean period is slightly smaller for stars below the IR limit." + Figure 6 shows the cumulative distributionsi for stars above aud below the IR excess li1il.it., Figure 6 shows the cumulative distributions for stars above and below the IR excess limit. + Tje similarity o “these two distributions slshows that οw prescription of assigniug disks to stars rega‘cdless of IR data did not bias our resulS., The similarity of these two distributions shows that our prescription of assigning disks to stars regardless of IR data did not bias our results. +It is impossible to rule oul a cosmological evolution of the host (GRB environment or ealaxv) column density that follows the values found by ancl reaches Ny~1075 7.,It is impossible to rule out a cosmological evolution of the host (GRB environment or galaxy) column density that follows the values found by and reaches $N_H \sim 10^{23}$ $^{-2}$. + On the other hand. at high redshift it is reasonable to assume that the contribution of the host galaxy to the opacity al 0.5 keV is small because of the recdshilt effect and the photo-ionization cross-section energy dependence e(E)eE.2? discussed above.," On the other hand, at high redshift it is reasonable to assume that the contribution of the host galaxy to the opacity at 0.5 keV is small because of the redshift effect and the photo-ionization cross-section energy dependence $\sigma (E) \sim E^{-2.5}$ discussed above." + At low redshilt (he opacity of the host certainly is dominant. but suffers from a large spread as is seen in Fig. &..," At low redshift the opacity of the host certainly is dominant, but suffers from a large spread as is seen in Fig. \ref{fig:tau}," + see also(2010)., see also. +. This spread impedes any concrete conclusions regarding (he hosts based only on their aabsorption properües., This spread impedes any concrete conclusions regarding the hosts based only on their absorption properties. + Such a spread is expected from the variety of host galaxies. GRB environments. GRB locations within the galaxies. and lines of sights.," Such a spread is expected from the variety of host galaxies, GRB environments, GRB locations within the galaxies, and lines of sights." + In Fig., In Fig. +" 10 we include a (high) mean host absorber of Vy,=3x10?!em 7. whose contribution to 7(0.5 keV) is significant al low redshift. but becomes less important than the IGM at 2~1.5."," \ref{fig:igm} we include a (high) mean host absorber of $N_H = 3\times 10^{21}$ $^{-2}$, whose contribution to $\tau$ (0.5 keV) is significant at low redshift, but becomes less important than the IGM at $z \sim 1.5$." + At high z. where the host contribution eradually becomes negligible. the spread in opacity values indeed becomes smaller. ancl (he theoretical IGM opacity curve. thus. well describes the observed values.," At high $z$, where the host contribution gradually becomes negligible, the spread in opacity values indeed becomes smaller, and the theoretical IGM opacity curve, thus, well describes the observed values." + Since even for hieh-z sources. much of the IGM opacity is due to the gas up to z«2 (see Eq. 3)).," Since even for $z$ sources, much of the IGM opacity is due to the gas up to $z < 2$ (see Eq. \ref{tauIGM}) )," + a clumpy IGM can also cause a spread in opacily ab high z., a clumpy IGM can also cause a spread in opacity at high $z$. + We wish to further explore whether soft. aabsorption of hish-z GRBs is due to the peculiar environment of the GRBs. or whether there is à significant intervening [GAM contribution.," We wish to further explore whether soft absorption of $z$ GRBs is due to the peculiar environment of the GRBs, or whether there is a significant intervening IGM contribution." + A natural place to check for IGM absorption is with high-z steady N-ray sources. namely quasars.," A natural place to check for IGM absorption is with $z$ steady X-ray sources, namely quasars." + For (his. we searched the aarchive for all quasars wilh z>2 for which the ccamera recorded more Chan 5000 source photons. to ensure high S/N. We found the 13 quasars listed in Table 1.. most of which were already individually reported in (he literature.," For this, we searched the archive for all quasars with $z > 2$ for which the camera recorded more than 5000 source photons, to ensure high S/N. We found the 13 quasars listed in Table \ref{tab:RLQ}, most of which were already individually reported in the literature." + We used the standard ppipeline products and fitted all the quasar spectra in the exact same manner as the GRB speclva. namely with a host (2) absorber.," We used the standard pipeline products and fitted all the quasar spectra in the exact same manner as the GRB spectra, namely with a host $z$ ) absorber." + The column densitv Nyy(2) obtained from this nmeasurenient was (hen translated into the optical dept 7(0.5 keV) according to Eq. 1.., The column density $N_H(z)$ obtained from this measurement was then translated into the optical depth $\tau$ (0.5 keV) according to Eq. \ref{tau*}. + No abundance correction was needed (Eq. 2)), No abundance correction was needed (Eq. \ref{tau}) ) + as we used the abundanees of for both the Galactic and host absorbers., as we used the abundances of for both the Galactic and host absorbers. + The best-fit 7(0.5 keV) values are listed in Table and plotted in Fig., The best-fit $\tau$ (0.5 keV) values are listed in Table \ref{tab:RLQ} and plotted in Fig. + 10. and can be seen to compare well with (he mean GRB opacities., \ref{fig:igm} and can be seen to compare well with the mean GRB opacities. + Quoted and plotted. errors correspond to the confidence limits., Quoted and plotted errors correspond to the confidence limits. + When more than one, When more than one +rather complicated [function as a non-trivial test. of several features of the code that are critical to ils success on data modeling problems.,rather complicated function as a non-trivial test of several features of the code that are critical to its success on data modeling problems. + Specifically. we test the ability of the code to work efficiently in verv high-dimensional parameter spaces. to avoid being trapped bv nunmerous local minima. and to hunction as a solution class-finder by distributing solutions over a [imite-volumed optimal region.," Specifically, we test the ability of the code to work efficiently in very high-dimensional parameter spaces, to avoid being trapped by numerous local minima, and to function as a solution class-finder by distributing solutions over a finite-volumed optimal region." + Furthermore. our test problem has a simple solution. but cannot be solved by any caleulus-based numerical approach because the gradient is zero evervwhere. except at discontinuities.," Furthermore, our test problem has a simple solution, but cannot be solved by any calculus-based numerical approach because the gradient is zero everywhere, except at discontinuities." +" The funcüon f, is a discontinuous funcüon with a long. flat-bottomed spiral whose minimun has thickness 2:rj anc repeats wilh radial wavelength Ay in the Cry..r2) subspace."," The function $f_1$ is a discontinuous function with a long, flat-bottomed spiral whose minimum has thickness $2*r_0$ and repeats with radial wavelength $\lambda_1$ in the $(x_1, x_2)$ subspace." + In this finite domain. fj breaks up into 9 disünct minima of equal depth.," In this finite domain, $f_1$ breaks up into 9 distinct minima of equal depth." + The function fo is another discontünuous function designed to generate many local minima. spaced by wavelength As. and a single global minimum of width As centred al cj.," The function $f_2$ is another discontinuous function designed to generate many local minima, spaced by wavelength $\lambda_2$, and a single global minimum of width $\lambda_2$ centred at $x_0$ ." + We chose Vo—20. vy—5. and a range of —10xe;<10 for all parameters.," We chose $N=20$ , $x_0=5$, and a range of $-10 \le x_i \le 10$ for all parameters." + Figure 2aa shows one term of f». where À»=| and. over the same range as above.," Figure \ref{fig:test}a a shows one term of $f_2$, where $\lambda_2=1$ and, over the same range as above." + Figure 2bb shows the sum over anv two terms. where we have zoomed in to the region near (he global minimum at (5.5).," Figure \ref{fig:test}b b shows the sum over any two terms, where we have zoomed in to the region near the global minimum at (5,5)." + On our chosen range.e each term of f5 ALSgenerates 19 local minima. includinge a singleex exglobal mininunm.," On our chosen range, each term of $f_2$ generates 19 local minima, including a single global minimum." + The summation over V—2 (terms results in 19.7? minima., The summation over $N-2$ terms results in $19^{N-2}$ minima. + Multiplving bv the 9 minima in fy. we find that the combined function f/ has 9x19.7=9.410?* isolated. linite-volumed minima. of which only 9 are global minima.," Multiplying by the 9 minima in $f_1$, we find that the combined function $f$ has $9\times 19^{N-2} = 9.4 \times 10^{23}$ isolated, finite-volumed minima, of which only 9 are global minima." + Our goal is (o map out the 9 elobal minima while evading all other local minima. which should reveal the spiral structure of fi in the Cry.-re) projection. ancl look like a 1x square box centred on (5.5) in any projection that does not include wry or vrs.," Our goal is to map out the 9 global minima while evading all other local minima, which should reveal the spiral structure of $f_1$ in the $(x_1, x_2)$ projection, and look like a $1 \times 1$ square box centred on (5,5) in any projection that does not include $x_1$ or $x_2$." + We ran (he code using a population size of 1000 for 500 generations. and performed several (vials.," We ran the code using a population size of 1000 for 500 generations, and performed several trials." + In. each (rial. all global minima were found and covered with points in less (han 100 generations.," In each trial, all global minima were found and covered with points in less than 100 generations." + Subsequent generations increased (he density of points aud improved the resolution of the boundaries., Subsequent generations increased the density of points and improved the resolution of the boundaries. + Figure 206 shows the projection of the solution set in the Gra.ο) stbspace. and Figure 2dd shows an example of another projection.," Figure \ref{fig:test}c c shows the projection of the solution set in the $(x_1, x_2)$ subspace, and Figure \ref{fig:test}d d shows an example of another projection." + All subspaces that do not include i or i look like Figure 2dd. This problem is more difficult (hat the parameter searches required to model (he cloud because our astrophyvsical models have fewer (6-8) parameters. and lew local minima. other than the globalminimum.," All subspaces that do not include $x_1$ or $x_2$ look like Figure \ref{fig:test}d d. This problem is more difficult that the parameter searches required to model the G11.11-0.12 cloud because our astrophysical models have fewer (6-8) parameters, and few local minima, other than the globalminimum." + We conclude that our code succeeded on this test problem. and should be adecquate for themodeling conducted later in (his paper.," We conclude that our code succeeded on this test problem, and should be adequate for themodeling conducted later in this paper." + ↑↸∖∐∏⋉∖↥⋅⋜↧⊓∐⋅↸∖↕⊔⋜↧↴∖↴↴∖↴∙⊺⇀↸⋀∐∙↥⋅↸∖↕⋜↧↑↕∪∐⋜⋯≼↧↑↕∐∖↕∏∐∐∐∪↴∖↴↕↑⋅↖↽ (Heurv&Arnaud1991:2001).. eclationiswidelguscdbgimeangoftheseauth," $M$ \citep{HA91,WEF93,Eke96,VL96,VL99,Henry97,Henry00,Borgani01,Pierpaoli01, +Seljak02,Pierpaoli03,Viana03,Allen03,Henry04}." +orstoconstrainth particularlyductohowelusteriniassisestinated(¢ IaavtsovYepes2000:ise dempto. Tenry200L AMarkevitch1998:Nue&Wir2000).," $-M$ $\sigma_8$ $-M$ \citealt{HMS99}) $\sigma_8$ \citealt{Henry04} \citep{EdS91,WJF97,AlF98,Mar98,XuW00}." +. if the only source of heating was via eravitational infall (Isaiscr1986)., if the only source of heating was via gravitational infall \citep{Kaiser86}. +" This makes the problem more dificult o investigate theoretically, although it allows studies of cluster scaling relations to reveal more information on he physics eovermime the structure of the iutracluster ued."," This makes the problem more difficult to investigate theoretically, although it allows studies of cluster scaling relations to reveal more information on the physics governing the structure of the intracluster medium." + The departure from selfsimilarity can be attributed to an Increase in theentropy of the eas that particularly affects low-mass systems (Evrard&Teury1991:Kaiser1999:Voit&Bryan2001:etal.2002. 2003).," The departure from self-similarity can be attributed to an increase in the of the gas that particularly affects low-mass systems \citep{EH91,Kaiser91,Bower97,TN01,PCN99,VB01,Voit02,Voit03}." +". Muy theoretical studies have been performed to investigate the oletMUR[ 9 ydg Tru]pisi5a. ross bbs DnRT PAYWasingthepa the ὁ ""Ot the eas. based on models 1wolviiue heating ns(MefelonyidoliLoctvensteniosly;Tan""fh . radiative cooling (I&uight.&Pomman1997:PearceDavé.Ikatz&Weinberg2002:WuXue. 2002).. aud a comibination of the two (Muaiuvoueetal...2002:Nav.Carthyetal. 2001)."," Many theoretical studies have been performed to investigate the effects of various physical processes that can raise the entropy of the gas, based on models involving heating \citep{ME94,Balogh99,KY00,Low00,WFN00,Bower01,Borgani02} , radiative cooling \citep{KP97,Pearce00,Bryan00,Muanwong01,Muanwong02,DKW02,WX02}, and a combination of the two \citep{Muanwong02,KTT03,Tornatore03,Valdarnini03,Borgani04,Kay04,McCarthy04}." +. Measurements of how cluster scaling relations evolve with redshift allow even tighter coustraiuts to be placed on cosiwological parameters (and cutropy generation models). and observations of cluster properties at high redshift are now starting to become available. owing primarily to the hieh sensitivity of audNewton.," Measurements of how cluster scaling relations evolve with redshift allow even tighter constraints to be placed on cosmological parameters (and entropy generation models), and observations of cluster properties at high redshift are now starting to become available, owing primarily to the high sensitivity of and." +" Frou, a theoretical point of view. this isau excitingpliase aswe can now filly exploit the availability of our simulated distant clusters aud compare their N-rav"," From a theoretical point of view, this isan excitingphase aswe can now fully exploit the availability of our simulated distant clusters and compare their X-ray" +paper we present the results and analysis of our polarimetric. photometric and spectroscopic observations of this system.,"paper we present the results and analysis of our polarimetric, photometric and spectroscopic observations of this system." + hoto-polarimetric observations were made at the NOT (Nordic Optical Telescope. La Palma) using the “Purpol-hoto-polarimeter. in October anc November 1997. (see able 1 for the log of observations).," Photo-polarimetric observations were made at the NOT (Nordic Optical Telescope, La Palma) using the Turpol-photo-polarimeter in October and November 1997 (see table 1 for the log of observations)." + Observations were also made on December 1997 and January 1998. with the 2.15 m CASLEO-tclescope (Argentina) using the Turin-photo-»xolerimeter., Observations were also made on December 1997 and January 1998 with the 2.15 m CASLEO-telescope (Argentina) using the Turin-photo-polarimeter. + This instrument at CASLEEO is almost identical ο 1e Turpol at the NOT., This instrument at CASLEO is almost identical to the Turpol at the NOT. + The polarimetors have four cichroic filters. splitting he light into CDVA2 bands.," The polarimeters have four dichroic filters, splitting the light into $UBVRI$ bands." + The time resolution [ου shotometric data is 24 sec., The time resolution for photometric data is 24 sec. + One polarization measurement consistsof eight integrations and takes ~3 minutes., One polarization measurement consistsof eight integrations and takes $\sim$ 3 minutes. + In the simultaneous circular linear mode with the A/4retarder he ellicienev. for circular polarization is about TO per cent and for linear polarization about 50 per cent., In the simultaneous circular linear mode with the $\lambda$ /4–retarder the efficiency for circular polarization is about 70 per cent and for linear polarization about 50 per cent. + With the A/2retarder 100 percent cllicieney for linear. polarization 1s achieved., With the $\lambda$ /2--retarder $\sim$ 100 percent efficiency for linear polarization is achieved. + Ehe seeing was between 0.6 and 1.5 aresee during all the nights at the NOT and the 7.5-aresee diaphragm was used., The seeing was between 0.6 and 1.5 arcsec during all the nights at the NOT and the 7.5-arcsec diaphragm was used. + At the CASLEQO. average seeing was between 2 and 3 aresce and the diaphragm 11 aresee.," At the CASLEO, average seeing was between 2 and 3 arcsec and the diaphragm 11 arcsec." + Sky background polarization was eliminated by using a calcite plate as a beam splitter., Sky background polarization was eliminated by using a calcite plate as a beam splitter. + Sky intensity was measured at 15 30 min intervals., Sky intensity was measured at 15 – 30 min intervals. + Instrumental polarization ancl he zero-point of position angle were determined from. observations of standard. stars 3273739. LD 204827. 64° 106. LIDI61056. and 11D155197. (Schmidt.ElstonLupie 1992).," Instrumental polarization and the zero-point of position angle were determined from observations of standard stars $^{\circ}$ 3739, HD 204827, $^{\circ}$ 106, HD161056, and HD155197 \cite{b32}." +. Photometric UBYRI standard stars 02282. 04242. 97351. 110340. ancl 114750 (Landolt1992) were used o calibrate the photometry.," Photometric UBVRI standard stars 92282, 94242, 97351, 110340, and 114750 \cite{b20} were used to calibrate the photometry." + Spectroscopic observations of V1300. Ori were carried out on 3 nights. starting on 25 Dec 1908. using the ANU (Australian National University) 2.3 m telescope at. Siding Spring Observatory (SSO). Australia.," Spectroscopic observations of V1309 Ori were carried out on 3 nights, starting on 25 Dec 1998, using the ANU (Australian National University) 2.3 m telescope at Siding Spring Observatory (SSO), Australia." + Spectra were obtained with the double beam spectrograph using GOO lines/muam eratings., Spectra were obtained with the double beam spectrograph using 600 lines/mm gratings. + Phe ellective wavelength: coverage was 3800.5000 A and 62007500 A in the blue and red arms of the spectrograph. respectively.," The effective wavelength coverage was 3800–5000 ${\rm \AA}$ and 6200–7500 ${\rm \AA}$ in the blue and red arms of the spectrograph, respectively." + The conditions were photometric throughout the observations. and the cllective resolution as measured from the FWIIM. of the are lines was 2.1A.," The conditions were photometric throughout the observations, and the effective resolution as measured from the FWHM of the arc lines was 2.1." + Phe exposure time was 300 sec for both blue and. red spectra., The exposure time was 300 sec for both blue and red spectra. + Wavelength calibration of the Hat-Fielded ancl bias-subtracted two dimensional images was performed using Ar arc spectra taken at various points during the night., Wavelength calibration of the flat-fielded and bias-subtracted two dimensional images was performed using He-Ar arc spectra taken at various points during the night. + The photometric ephemeris of Staude. Schwope Schwarz (2001). (their equation (1)) is used to phase the data throughout the paper.," The photometric ephemeris of Staude, Schwope Schwarz \shortcite{b42} (their equation (1)) is used to phase the data throughout the paper." + During our observations V1300 Ori was in a high accretion state (V —16). as found. also in earlier photometric studies (Garnavich et al.," During our observations V1309 Ori was in a high accretion state $V$ =16), as found also in earlier photometric studies (Garnavich et al." + 1994: Shafter et al., 1994; Shafter et al. + 1995)., 1995). + In Figure 1. we esent simultaneous CDVRE lieht curves covering nearly he full orbital evele. obtained on November 24/25. 1997. at he NOV.," In Figure \ref{ubvri} we present simultaneous $UBVRI$ light curves covering nearly the full orbital cycle, obtained on November 24/25, 1997, at the NOT." + Our observations made in October (NOT) 1997 and in January 1998 (CASLIZO) do not cover the complete orbital evele (and are not shown here) show that V1309 Ori was in the same brightness level (V—16) as in November 1997., Our observations made in October (NOT) 1997 and in January 1998 (CASLEO) do not cover the complete orbital cycle (and are not shown here) show that V1309 Ori was in the same brightness level (V=16) as in November 1997. + We show the circular polarisation data in Figure 2 and the linear polarisation data in Figure 3.., We show the circular polarisation data in Figure \ref{circpol} and the linear polarisation data in Figure \ref{linpol}. + The most distinctive feature of the intensity curves (Figure 1)) is the well known deep. eclipse which has a duration of ~O.1 orbital phase ancl also a strong colour ependence (up to 4 mag in C. and less than 1 mag in I).," The most distinctive feature of the intensity curves (Figure \ref{ubvri}) ) is the well known deep eclipse which has a duration of $\sim$ 0.1 orbital phase and also a strong colour dependence (up to $\sim$ 4 mag in $U$, and less than 1 mag in $I$ )." + Flux variations outside the eclipse are about 1.5 mag in the C. and about one magnitude in the DYRL bands.," Flux variations outside the eclipse are about 1.5 mag in the $U$, and about one magnitude in the $BVRI$ bands." + Light curves show two local brightness maxima. at orbital phases b=0.2 and 9=0.7.," Light curves show two local brightness maxima, at orbital phases $\Phi=0.2$ and $\Phi=0.7$." + There is a clear asymmetry. between jese two maximae in the C-band the first peak near 9=0.2 is about 0.5 mag brighter than observed at 9= 0.7. whereas in the B- and V -bands this dillerence is about 0.3 mag ancl in the Z-band tvpically about 0.2 mag.," There is a clear asymmetry between these two maxima: in the $U$ -band the first peak near $\Phi=0.2$ is about 0.5 mag brighter than observed at $\Phi=0.7$ , whereas in the $B$ - and $V$ -bands this difference is about 0.3 mag and in the $I$ -band typically about 0.2 mag." + The colour indices in Figure 4. show V1309 Ori bier after the eclipse. where the system. is also brighter than," The colour indices in Figure \ref{colour} show V1309 Ori $bluer$ after the eclipse, where the system is also brighter than" +citeptomerl0.. although there it was kinematically resolved (19004150 vversus 2300 1)).,", although there it was kinematically resolved $\pm$ 150 versus –2300 )." + The oxvgen and nitrogen lines of component 3 are narrow and thus suspect of having a local origin., The oxygen and nitrogen lines of component 3 are narrow and thus suspect of having a local origin. +" These lines require eq, — 100 = 170 !)). which is less than equ, = 300|. which is used for higher ionization."," These lines require $v_\mathrm{turb}$ = 100 = 170 ), which is less than $v_\mathrm{turb}$ = 300, which is used for higher ionization." + This narrow width is consistent with local. ionizecl ISAT aabsorption lines along this line of sight (Ixraemerοἱal.2002).," This narrow width is consistent with local, ionized ISM absorption lines along this line of sight \citep{kraemer02}." +. There are a few additional reasons to favor the local component scenario lor O and N. First. they form at lower ionization parameters of log£~0—2. while most of component 3 is primarily comprised of hieh ionization species.," There are a few additional reasons to favor the local component scenario for O and N. First, they form at lower ionization parameters of $\log \xi \sim 0-2$, while most of component 3 is primarily comprised of high ionization species." + In Fe. we do not detect any. M-Shell ions. and not even ! in this component.," In Fe, we do not detect any M-Shell ions, and not even $^{+16}$ in this component." + Even though we can not conclusively determine whether (he oxvgen and nitrogen absorption comes from outflow component 3.2 or has a local origin. we tend to favor the local origin scenario. because such a component is often observed.," Even though we can not conclusively determine whether the oxygen and nitrogen absorption comes from outflow component 3, or has a local origin, we tend to favor the local origin scenario, because such a component is often observed." + The (presumably) local component column densiües are shown in Table 7.., The (presumably) local component column densities are shown in Table \ref{tab:local}. + The low charge states are clue to the Galactic disce and halo. and likely not associated with the higher ionizalion states that are due to the hot phase of the Galactic halo or the Local group.," The low charge states are due to the Galactic disc and halo, and likely not associated with the higher ionization states that are due to the hot phase of the Galactic halo or the Local group." +" The oxvgen ionic column densities are all in the range of several LOM7.. which implies a neutral hydrogen column density of a few 107""7. using 49x10. ! for the O to II ratio (Asplundetal.2009) ancl a fractional ionic abundance of 0.5."," The oxygen ionic column densities are all in the range of several $^{16}$, which implies a neutral hydrogen column density of a few $^{20}$, using $\times$ $^{-4}$ for the O to H ratio \citep{asplund09} and a fractional ionic abundance of 0.5." +" This value is consistent with the Galactic absorption of Vy = 3.23xI0?"" citepdickev1990..", This value is consistent with the Galactic absorption of $N_H$ = $\times10^{20}$ \\citep{dickey1990}. + Using the same caleulations lor N° gives a slightly higher neutral hydrogen column density of the order of ~ 107!7., Using the same calculations for $^{+6}$ gives a slightly higher neutral hydrogen column density of the order of $\sim$ $^{21}$. + Note that most species of component 3 are likely not local since their ionization and column densities are too high., Note that most species of component 3 are likely not local since their ionization and column densities are too high. + lons such as 7)7. K-shell S and Si. (see Table 4)) are usually not observed in the local ionizecl ISAT.," Ions such as $^{+23 - +25}$, K-shell S and Si, (see Table \ref{tab2}) ) are usually not observed in the local ionized ISM." + Moreover. the high column density measured in (his component of Ng~1075 iis bv far higher than (vpical local ISAL columns.," Moreover, the high column density measured in this component of $_{H} \sim 10^{23}$ is by far higher than typical local ISM columns." + The observation of 2006 caught iin à much higher stale than the 2001 observation. as can be seen in Fig. 2..," The observation of 2006 caught in a much higher state than the 2001 observation, as can be seen in Fig. \ref{spectra_01,06}." + So [ar. the analvsis in (his paper focused on the 2006 observation.," So far, the analysis in this paper focused on the 2006 observation." + We now want to use the two flux states to study the differences between the (vo., We now want to use the two flux states to study the differences between the two. + Several explanations lor the flux and spectral variability of ccan be found in the literature., Several explanations for the flux and spectral variability of can be found in the literature. + Netzerοἱal.(2002). reported a slow. monotonic decay in," \citet{netzer02} reported a slow, monotonic decay in" +The rate. D;. depends on the extinction. 21... measured inward from the surface of the cloud in units of visual magnitudes.,"The rate, $\Gamma_i$, depends on the extinction, $A_v$, measured inward from the surface of the cloud in units of visual magnitudes." + Here 0;(À) is (the waveleneth dependent. cross section for the process of interest. and (he integration runs from Ay=91.2nm to the threshold wavelength: A; for the process of interest.," Here $\sigma_i(\lambda)$ is the wavelength dependent cross section for the process of interest, and the integration runs from $\lambda_H=91.2\,$ nm to the threshold wavelength $\lambda_i$ for the process of interest." +" The quantity οκτν} is the mean intensity of radiation at depth A, in photons 7s | tum !.", The quantity $J_{\lambda}(A_v)$ is the mean intensity of radiation at depth $A_v$ in photons $^{-2}$ $^{-1}$ $^{-1}$ $^{-1}$. +" ROL used the spherical harmonics method to solve numerically the radiative transfer equation for J4(4,) for clouds of and 100mag."," R91 used the spherical harmonics method to solve numerically the radiative transfer equation for $J_{\lambda}(A_v)$ for clouds of $A_v^{tot}=1,10$ and $100\,$ mag." +" The solution for J4(.1.) allowed R91 to calculate the photodestruction rates for a large number of species al various depths A, into each of their model clouds Ce=1.10 and 100 mag)."," The solution for $J_{\lambda}(A_v)$ allowed R91 to calculate the photodestruction rates for a large number of species at various depths $A_v$ into each of their model clouds $A_v^{tot}=1,10$ and $100\,$ mag)." + In addition. ROL found that a bi-exponential function. of the form provided a reasonable fit to (heir munerical results. where C; is the unattenmuated photodestruction rate and a; and 5j; are fit parameters. lor a given species 7.," In addition, R91 found that a bi-exponential function, of the form provided a reasonable fit to their numerical results, where $C_i$ is the unattenuated photodestruction rate and $\alpha_i$ and $\beta_i$ are fit parameters, for a given species $i$." + A point P in the interior of an R91 plane-parallel slab is ilbuminated by radiation coming from many directions., A point $P$ in the interior of an R91 plane-parallel slab is illuminated by radiation coming from many directions. + If we consider a slab with sl.= 100. we can assume that near one surface of the slab. essentially all photodissociating radiation originates at the nearer surface.," If we consider a slab with $A_v=100$ , we can assume that near one surface of the slab, essentially all photodissociating radiation originates at the nearer surface." +" Under such conditions. the point J? “sees” rays diminished by an ""effective visual extinction. AV=Acos9 coming from a direction 9. where the angle is measured from the normal to the slab and A, is the depth measured from the surface of the cloud to the point J? along the normal ray."," Under such conditions, the point $P$ “sees” rays diminished by an “effective visual extinction”, $A_v^{\prime} =A_v/\cos \theta$ coming from a direction $\theta$, where the angle is measured from the normal to the slab and $A_v$ is the depth measured from the surface of the cloud to the point $P$ along the normal ray." + In order to calculate photodissociation rates valid for a point Q interior (o a sphere. we realized that we should decompose the photoclissociating radiation arriving al point P inside a slab into constituent ravs coming [rom a direction 0.," In order to calculate photodissociation rates valid for a point $Q$ interior to a sphere, we realized that we should decompose the photodissociating radiation arriving at point $P$ inside a slab into constituent rays coming from a direction $\theta$." + This would give us the photodissociation rate due to a single rav., This would give us the photodissociation rate due to a single ray. + Then. we can use the result for a single rav io integrate over all ravs arriving al (he point Q in the interior of the sphere.," Then, we can use the result for a single ray to integrate over all rays arriving at the point $Q$ in the interior of the sphere." +" Such a point (J ""sees? rays diminished by a different. ""effective visual extinction”. AY=06.1,./sin9."," Such a point $Q$ “sees” rays diminished by a different “effective visual extinction”, $A_v^{\prime\prime}=\theta A_v/\sin \theta$." + We can then integrate over all ravs arriving al point Q. to determine the total photodissociation rate for a point internal to a sphere.," We can then integrate over all rays arriving at point $Q$, to determine the total photodissociation rate for a point internal to a sphere." +" So. given a formula for the photodissociation rate I""=Cyexp(—al4,—jJ""A?) in a plane-parallel slab. we should be able to find best fit valuesfor the parameters ay and 27 subject to the condition that for all vl, of interest. where"," So, given a formula for the photodissociation rate $\Gamma_i^{pp}=C_i \exp(-\alpha_i^{pp} A_v - \beta_i^{pp} A_v^2)$ in a plane-parallel slab, we should be able to find best fit valuesfor the parameters $\alpha_i^{r}$ and $\beta_i^{r}$ subject to the condition that for all $A_v$ of interest, where" +point in the * ὢ plane corresponding to the provisional solution found above (/=82.67 and €?= 0.76) and the routine was run at each point on the grid.,point in the $i-Q$ plane corresponding to the provisional solution found above $i=82.6^{\circ}$ and $Q=0.76$ ) and the routine was run at each point on the grid. + For these fits. the values of / and Q were fixed at the values corresponding to he erid location. leaving only the two surface potentials as ree parameters.," For these fits, the values of $i$ and $Q$ were fixed at the values corresponding to the grid location, leaving only the two surface potentials as free parameters." + The grid search. routine was then used to optimize the Qs. Figure 5 shows a contour map of the 4? values., The grid search routine was then used to optimize the $\Omega$ s. Figure 5 shows a contour map of the $\chi^2$ values. +" We found the minimum X7. value of A24,04:54 or LOO data points occurred. at the point 7=80.0% and Q=1.15. relatively far from our provisional fit found above."," We found the minimum $\chi^2$ value of $\chi^2_{\rm min}=94.84$ for 100 data points occurred at the point $i=89.0^{\circ}$ and $Q=1.15$, relatively far from our provisional fit found above." + The standard deviation of the residuals tthe data minus he model fit) is 0.002 mag. which is comparable to the statistical errors of the points in the binned light curve.," The standard deviation of the residuals the data minus the model fit) is 0.002 mag, which is comparable to the statistical errors of the points in the binned light curve." +" Our values of ὃς89.0"" and Q=1.15 are significantly different from the values of ¢=78.05+0.50"" and Qo=0.87£0.15 found by WOW.", Our values of $i=89.0^{\circ}$ and $Q=1.15$ are significantly different from the values of $i=78.05\pm 0.50^{\circ}$ and $Q=0.87\pm 0.15$ found by KOW. + We believe our present results are more reliable than those of KOW for two reasons., We believe our present results are more reliable than those of KOW for two reasons. + First. we have z36.6 hours of CCD observations from a 2.1m telescope (of which zz8.2 hours was spent reading out the CCD). compared to 7.9 hours of observations obtained. by IXOW using a high-speed. photometer on a 2.1m telescope.," First, we have $\approx 36.6$ hours of CCD observations from a 2.1m telescope (of which $\approx 8.2$ hours was spent reading out the CCD), compared to 7.9 hours of observations obtained by KOW using a high-speed photometer on a 2.1m telescope." + llence our statistics will be better., Hence our statistics will be better. + Second. our CCL) data are more reliable since we were able to identify and remove the extra 7.8 hour modulation.," Second, our CCD data are more reliable since we were able to identify and remove the extra 7.8 hour modulation." + LOW were unaware of the extra 7.8 hour modulation. and as a result their folded. 0 and D light curves are likely to be biased and not accurately representative of the true ellipsoidal light curves.," KOW were unaware of the extra 7.8 hour modulation, and as a result their folded $U$ and $B$ light curves are likely to be biased and not accurately representative of the true ellipsoidal light curves." + We used a Monte Carlo procedure to compute confidence limits on the fitted and derived. parameters., We used a Monte Carlo procedure to compute confidence limits on the fitted and derived parameters. +" At cach point in the i-( plane shown in Figure 5 we have fitted: values of ,45 and Op and a us of the fit. (", At each point in the $i$ $Q$ plane shown in Figure 5 we have fitted values of $\Omega_{\rm sdB}$ and $\Omega_{\rm WD}$ and a $\chi^2$ of the fit. ( +Lhe fitted: values of the Os are basically independent. of the inclination and hence are only a function of the mass ration €9 larger values of Q result in larger values for both Qo and Op.),The fitted values of the $\Omega$ s are basically independent of the inclination and hence are only a function of the mass ration $Q$ –larger values of $Q$ result in larger values for both $\Omega_{\rm sdB}$ and $\Omega_{\rm WD}$ .) +" One can define a region in the plane corresponding to a certain confidence limit based on the change in the 4? values. tthe 68 per cent confidence region is defined bv 47=«Zu,|2-34."," One can define a region in the plane corresponding to a certain confidence limit based on the change in the $\chi^2$ values, the 68 per cent confidence region is defined by $\chi^2=\chi^2_{\rm min}+2.34$." +" We divided up the plane into 50 regions with region l corresponding to confidence limits between O and 2 per cent (AZ,EXX72za| 0.041). region 2 corresponding to confidence limits between 2 anc i4 per cent (\inin|Q.041 1, and 1/Ajj, otherwise, where Aj; is the ratio of the areas under the profile at velocities lower (S;) and higher (5η) than the central velocity (V,,): where V, and V; represent the low and high velocities measured at intensity level withrespect to the peak."," We employ an areal asymmetry index to quantify profile lopsidedness, namely the integrated flux density ratio $A_{flux~ratio}$ (e.g. \citealt{1998AJ....115...62H}, \citealt{2001AJ....121.1358K}) ), defined as $A_{flux~ratio}= A_{l/h}$, if $A_{l/h}$ $>$ 1, and $1/A_{l/h}$ otherwise, where $A_{l/h}$ is the ratio of the areas under the profile at velocities lower $_l$ ) and higher $_h$ ) than the central velocity $V_m$ ): $A_{l/h}=\frac{S_{l}}{S_{h}}=\frac{\int\limits_{V_l}^{V_m}S_{v}dv}{\int\limits^{V_h}_{V_{m}}S_{v}dv}$, where $V_l$ and $V_h$ represent the low and high velocities measured at intensity level withrespect to the peak." +" η is calculated as the mean velocity at the same level,(V,+V))/2."," $V_{m}$ is calculated as the mean velocity at the same level,." +" Note that Ayj,ratio 1s invariant to the sense of rotation of the galaxy.", Note that $A_{flux~ratio}$ is invariant to the sense of rotation of the galaxy. + We use this parameter since it is the most common asymmetry index that can be found in the literature and allows us to compare our results with other samples of galaxies(see Sect. /4-2))., We use this parameter since it is the most common asymmetry index that can be found in the literature and allows us to compare our results with other samples of galaxies(see Sect. \ref{sub:samples}) ). +" Equivalent definitions are found in the bibliography and can be easily converted to Afiuxratio, as e.g.: A= (3) and El=10x(1—1/Ariratio) (?).."," Equivalent definitions are found in the bibliography and can be easily converted to $A_{flux~ratio}$, as e.g.: $ A=\frac{S_{l}-S_{h}}{S_{l}+S_{h}}$ \citep{1998AJ....116.1169M} and $E1 = 10 \times (1~-~1/A_{flux~ratio})$ \citep{2005A&A...438..507B}." +" We indicate the mAΑΓ]ratio values in Figure 2}, B], and] for the examples of pprofiles visually classified as symmetric, CIG 226, slightly asymmetric, CIG 421, and strongly asymmetric, CIG361, which are characterized by Afiyxratio = 1.05, 1.15, and 1.51, respectively."," We indicate the $A_{flux~ratio}$ values in Figure \ref{fig:HIProfilesLopsidednessSample1}, \ref{fig:HIProfilesLopsidednessSample2}, and \ref{fig:HIProfilesLopsidednessSample3} for the examples of profiles visually classified as symmetric, CIG 226, slightly asymmetric, CIG 421, and strongly asymmetric, CIG361, which are characterized by $A_{flux~ratio}$ = 1.05, 1.15, and 1.51, respectively." +" We estimate the uncertainty of the asymmetry index, AArixratio, by taking into account a) the per channel, b) the uncertainty in the calculation of thevelocity, and c) the observationaloffsets:: We added these sources of uncertainty in quadrature to estimate the net uncertainty in Afiux ratio, AAflux ratio-"," We estimate the uncertainty of the asymmetry index, $\Delta A_{flux~ratio}$, by taking into account $a)$ the per channel, $b)$ the uncertainty in the calculation of the, and $c)$ the observational: We added these sources of uncertainty in quadrature to estimate the net uncertainty in $A_{flux~ratio}$ , $\Delta A_{flux~ratio}$ ." +" In addition to these sources of uncertainty, there are other effects that can induce an artificial asymmetry on the"," In addition to these sources of uncertainty, there are other effects that can induce an artificial asymmetry on the" +In this paper. we will report the fine spectroscopy οἱ Ark 564.,"In this paper, we will report the fine spectroscopy of Ark 564." + Section 2 describes the details of the observations ancl data reduction., Section 2 describes the details of the observations and data reduction. + Ii 833. (he analysis of power spectral density is performed.," In 3, the analysis of power spectral density is performed." + 844 contains the spectral analvsis., 4 contains the spectral analysis. + We detected many absorption lines. but no prominent narrow eniission line around 1 keV is detected.," We detected many absorption lines, but no prominent narrow emission line around 1 keV is detected." + Ii 855. we discuss the inferred photoionization model and the location of warm absorber.," In 5, we discuss the inferred photoionization model and the location of warm absorber." + We also find that the | keV enission line feature appears (to be an artifact of the warm absorber., We also find that the 1 keV emission line feature appears to be an artifact of the warm absorber. + Finally. we summarize the results in 866.," Finally, we summarize the results in 6." + We carried out an observation of Ark 564 with the HETGS on 2000 June 17 06:5021:05., We carried out an observation of Ark 564 with the HETGS on 2000 June 17 06:50–21:05. + The detector was the Advanced CCD Imaging Spectrometer (ACIS)., The detector was the Advanced CCD Imaging Spectrometer (ACIS). + Our observation was 50 ks in duration and continuous., Our observation was 50 ks in duration and continuous. + We analvzed ihe most recent standard processed level 2 data (revision 3) using the CIAO version 2.2.0. CALDB version 2.9. and IIEAsoft version 5.1.," We analyzed the most recent standard processed level 2 data (revision 3) using the CIAO version 2.2.0, CALDB version 2.9, and HEAsoft version 5.1." +" The peak of the zeroth order image is located at. R.À.—.2242?39,3:5. and 297433176 (equinox 2000.0) in good agreement with the optical position of A.—2221239345°, Decl.— 29*43'31'31 (Clements 1981) with the spatial resolution (0.49 arcsec/pixel)."," The peak of the zeroth order image is located at $={\rm 22^h 42^m 39.33^s}$ and $=29^\circ 43' 31\rlap{$ $}.6$ (equinox 2000.0) in good agreement with the optical position of $={\rm 22^h 42^m 39.345^s}$, $=29^\circ 43' 31\rlap{$ $}.31$ (Clements 1981) with the spatial resolution (0.49 arcsec/pixel)." + since (he HETGS response matrices are subject to the extension of the source. we checked whether or not the source is point-like.," Since the HETGS response matrices are subject to the extension of the source, we checked whether or not the source is point-like." + At first. we looked at the zeroth order image.," At first, we looked at the zeroth order image." + We [ound the image is circular in shape. (hus asvnunelry possibly associated will extended enission is ruled oul.," We found the image is circular in shape, thus asymmetry possibly associated with extended emission is ruled out." + Next. we tried (to investigate point spread function. but it is difficult with the zeroth order image. since the central and adjacent pixels suffer significant pile-up.," Next, we tried to investigate point spread function, but it is difficult with the zeroth order image, since the central and adjacent pixels suffer significant pile-up." + Then. we examined the first order data in spatial direction and found that 67 of photons lie within +1 pixel and 37 Πο within +2 pixels.," Then, we examined the first order data in spatial direction and found that 67 of photons lie within $\pm$ 1 pixel and 87 lie within $\pm$ 2 pixels." + The encircled power radii of 50 and 80 are 0.418 and 0.685 arcsec (0.85 and 1.4 in the unit of pixel).respectivelv!.," The encircled power radii of 50 and 80 are 0.418 and 0.685 arcsec (0.85 and 1.4 in the unit of pixel),." +. Therefore. the core of (he X-ray emission is not extended. and we used the response matrices for a point source in the spectral analyses.," Therefore, the core of the X-ray emission is not extended, and we used the response matrices for a point source in the spectral analyses." + Fig., Fig. + l shows the lighteurve from the HETGS., \ref{fig:lc} shows the lightcurve from the HETGS. + We use data only [rom the MEG and WEG £1 orders., We use data only from the MEG and HEG $\pm1$ orders. + The count rate is somewhat higher during, The count rate is somewhat higher during +arge scales. rising to SO% on small scales) while halos with blue central galaxies show a weaker one which is very similar to that for all blue galaxies (7 5%).,"large scales, rising to $\sim\!80\%$ on small scales) while halos with blue central galaxies show a weaker one which is very similar to that for all blue galaxies $\sim\!5\%$ )." + The strong cllect or red central galaxies reflects the fact that such objects are ound primarily in two very specilic tvpes of halo: massive ialos where cooling and star-formation have been curtailed w AGN feedback: ancl lower mass halos which have just yassed through a more massive system. thereby losing their i00 gas atmospheres ancl so their source of [uel for star ormation.," The strong effect for red central galaxies reflects the fact that such objects are found primarily in two very specific types of halo: massive halos where cooling and star-formation have been curtailed by AGN feedback; and lower mass halos which have just passed through a more massive system, thereby losing their hot gas atmospheres and so their source of fuel for star formation." + Both cases are associated with a massive halo. renee the high clustering amplitude.," Both cases are associated with a massive halo, hence the high clustering amplitude." + The great majority of central. galaxies are associated: with more isolated: and/or ower mass halos and have ongoing star formation: these objects are blue., The great majority of central galaxies are associated with more isolated and/or lower mass halos and have ongoing star formation; these objects are blue. + We now generalise the above results including all galaxics which are well resolved. by the formation model regardless of their subhalo mass at z=0., We now generalise the above results including all galaxies which are well resolved by the formation model regardless of their subhalo mass at $z\!=\!0$. + Fig., Fig. + 2. shows the relative bias between the shulllecl and the original galaxy populations as a function of both colour luminosity., \ref{fig2} shows the relative bias between the shuffled and the original galaxy populations as a function of both colour luminosity. + On scales kc23h!Mpe. I-balo terms do. not. contribute to the correlations and the relative bias is approximately constant for all samples we have considered., On scales $r \simgt 3h^{-1}{\rm Mpc}$ 1-halo terms do not contribute to the correlations and the relative bias is approximately constant for all samples we have considered. + For simplicity we therefore average the relative bias measurements. for each of our 10 shullled catalogues over the separation range G12h!Mpe and we characterise the result by the mean and le scatter of these values., For simplicity we therefore average the relative bias measurements for each of our 10 shuffled catalogues over the separation range $6\!-\!12h^{-1}{\rm Mpc}$ and we characterise the result by the mean and $1\sigma$ scatter of these values. + In the following we refer to his quantity as the as it measures the bias induced by the environmental dependence of halo assembly ustory at [fixed halo mass., In the following we refer to this quantity as the as it measures the bias induced by the environmental dependence of halo assembly history at fixed halo mass. + The top panel of Fig., The top panel of Fig. + 2. shows this assembly. bias or absolute magnitude limited subsamples of galaxies as à unction of their magnitude limit., \ref{fig2} shows this assembly bias for absolute magnitude limited subsamples of galaxies as a function of their magnitude limit. + Again we plot results for ealaxies of all colours (solid line) and for blue (dot-dashed ine) and red (long-dashed line) galaxies separately., Again we plot results for galaxies of all colours (solid line) and for blue (dot-dashed line) and red (long-dashed line) galaxies separately. + The xÀttom. panel shows an identical analysis but. for samples restricted to central. galaxies., The bottom panel shows an identical analysis but for samples restricted to central galaxies. + Note that selecting galaxy subsamples by limiting stellar mass rather than luminosity xoduces similar behaviour to that. presented below., Note that selecting galaxy subsamples by limiting stellar mass rather than luminosity produces similar behaviour to that presented below. + Εις is expected given that the scatter in log(ML) for the galaxies is typically small in comparison with the magnitude range over which the assembly bias changes., This is expected given that the scatter in $\log({\rm M}/\rm{L})$ for the galaxies is typically small in comparison with the magnitude range over which the assembly bias changes. + If we focus first on the upper panel of Fig. 2..," If we focus first on the upper panel of Fig. \ref{fig2}," + we see that correlations between assembly historv and environment at fixed halo mass can either enhance (for faint galaxies) or clilute (for bright galaxies) the strength of galaxy clustering. with a transition near the characteristic luminosity L. of the galaxy luminosity function.," we see that correlations between assembly history and environment at fixed halo mass can either enhance (for faint galaxies) or dilute (for bright galaxies) the strength of galaxy clustering, with a transition near the characteristic luminosity $L_*$ of the galaxy luminosity function." + Painter than νι5logh~20.5 bias values for the red and blue subpopulations are svnunetrically olfset from the curve for the population as a whole by about5%., Fainter than $M_{\rm b_J}\!-5\log h \sim -20.5$ bias values for the red and blue subpopulations are symmetrically offset from the curve for the population as a whole by about. +. Brighter than this. the bias for the population as a whole approaches that for the red subpopulation. reflecting the fact that there are low blue galaxies at these magnitudes.," Brighter than this, the bias for the population as a whole approaches that for the red subpopulation, reflecting the fact that there are few blue galaxies at these magnitudes." +" At AM,5logh~20 blue galaxies have an assembly bias of about 0.9. showing that they oceupy halos with significantly lower density environments than randomlv selected halos of the same mass."," At $M_{\rm b_J} \!-5\log h \sim -20$ blue galaxies have an assembly bias of about 0.9, showing that they occupy halos with significantly lower density environments than randomly selected halos of the same mass." + In the bottom panel of Fig., In the bottom panel of Fig. + 2 we show the assembly bias for absolute magnitude Limited samples ofας ealaxies (i.e. For samples of halos defined by the Luminosity ancl colour of their. central galaxies)., \ref{fig2} we show the assembly bias for absolute magnitude limited samples of galaxies (i.e. for samples of halos defined by the luminosity and colour of their central galaxies). + A notable dillerence. from. the central galaxy samples studied in the bottom panel of Fig., A notable difference from the central galaxy samples studied in the bottom panel of Fig. + (which were defined by the of their halos) is that the assembly bias cilfers from unity not only for the red and blue subsamples but also for samples without colour selection., \ref{fig1} (which were defined by the of their halos) is that the assembly bias differs from unity not only for the red and blue subsamples but also for samples without colour selection. +" μις cilference is caused by scatter in the relation between halo mass and central galaxy luminosity which correlates with halo environment in a way that is cüllerent for halos with faint (L« L,) and with bright (L7 £L.) central galaxies.", This difference is caused by scatter in the relation between halo mass and central galaxy luminosity which correlates with halo environment in a way that is different for halos with faint $L\!<\!L_*$ ) and with bright $L\!>\!L_*$ ) central galaxies. + Low-mass halos with brighter than average central galaxies are in denser than average environments. while the opposite is true for higher mass halos.," Low-mass halos with brighter than average central galaxies are in denser than average environments, while the opposite is true for higher mass halos." + At all magnitudes blue central ealaxies inhabit halos with lower density environments than red central galaxies., At all magnitudes blue central galaxies inhabit halos with lower density environments than red central galaxies. + TFhis is in part because at given absolute magnitude blue central galaxies tend to have lower mass halos than red ones., This is in part because at given absolute magnitude blue central galaxies tend to have lower mass halos than red ones. + From Fig., From Fig. + we see that assembly. bias is strongest. [or faint red central 2.galaxies., \ref{fig2} we see that assembly bias is strongest for faint red central galaxies. + Phese galaxies reside at the centres of low-mass (~ 107137.) dark matter halos and have a b value of about 1.4. which translates to an autocorrelation amplitude about twice that which would have been found," These galaxies reside at the centres of low-mass $\sim\!10^{11}M_{\odot}$ ) dark matter halos and have a $b$ value of about 1.4, which translates to an autocorrelation amplitude about twice that which would have been found" + asstining. as discussed above. that $=0.,"conditions of high free-free optical depth and low density, we find assuming, as discussed above, that $S = 0$." + These conditions are not uncommon aud exceptionally high emission measures are not required to achieve bieh optical depth at 1.1 GHz., These conditions are not uncommon and exceptionally high emission measures are not required to achieve high optical depth at 1.1 GHz. + In the case of M 12 the optical depth at 1.1 GHz is 1.2 aud the beam cilutecd line strength would be about { mils. versus a coutinuum antenua temperature of ~ [00 Ix. The metastable 254;5 state of hydrogen is likely overpopulated in HII regious.," In the case of M 42 the optical depth at 1.1 GHz is 1.2 and the beam diluted line strength would be about 4 mK, versus a continuum antenna temperature of $\approx$ 400 K. The metastable $2s_{1/2}$ state of hydrogen is likely overpopulated in HII regions." + Lyimau-a o»uupiug of the 2p states is expected to be uegligible due to absorption of Lyimanu-a radiation yy dust., $\alpha$ pumping of the $2p$ states is expected to be negligible due to absorption of $\alpha$ radiation by dust. +" Thus. the 25(;51/2—2p4;5aya transitions (0.9 GHz) are predicted to appear in absorption aud he 254,542py/o transitions (1.1 GHz) in stimulated emission."," Thus, the $2s_{1/2}\rightarrow 2p_{3/2}$ transitions (9.9 GHz) are predicted to appear in absorption and the $2s_{1/2}\rightarrow 2p_{1/2}$ transitions (1.1 GHz) in stimulated emission." + Because of the short lifetime of the inal 2p states. the width of the lines is dominated completely by intrinsic line width.," Because of the short lifetime of the final $2p$ states, the width of the lines is dominated completely by intrinsic line width." + Iu ellect. then. he power is distributed over zz100 MHz of line width resulting in very weak lines.," In effect, then, the power is distributed over $\approx 100$ MHz of line width resulting in very weak lines." + In addition. the yower 15 distributed over three strougly. blended hyperfiue lines in each multiplet.," In addition, the power is distributed over three strongly blended hyperfine lines in each multiplet." + Searching for the 0.9 GHz lines in high emission iueasure HIT regious olfers the best prospects or detection., Searching for the 9.9 GHz lines in high emission measure HII regions offers the best prospects for detection. + Iu the optically thin limit. the line strength varies as the square of the free-free optical depth.," In the optically thin limit, the line strength varies as the square of the free-free optical depth." + Precdicted lIine-to-coutinuum ratios (in absorptiou) rauge up to several tentlis of a percent in W58AÀ. including the effects of line blendiug.," Predicted line-to-continuum ratios (in absorption) range up to several tenths of a percent in W58A, including the effects of line blending." +" With the Creeu Bank Telescope. the predicted peak absorption line streugtli may reach AT,zz—1T0 imd in this case. allowing for the redistribution of line streneth over the three livperfiue lines."," With the Green Bank Telescope, the predicted peak absorption line strength may reach $\Delta T_a\approx -170$ mK in this case, allowing for the redistribution of line strength over the three hyperfine lines." + Other high emission HII regions are expected to slow somewhat weaker 9.0 GHz lines. for example. with line-to-continuunm ratios of about 0.1. percent auc line streugths of teus of us with the Green Bank Telescope.," Other high emission HII regions are expected to show somewhat weaker 9.9 GHz lines, for example, with line-to-continuum ratios of about 0.1 percent and line strengths of tens of mK with the Green Bank Telescope." + These precictious are uucertaiu. however. owing to biases inherent in estimating emission measures as well as selection effects in various interferometric surveys of compact HII regions.," These predictions are uncertain, however, owing to biases inherent in estimating emission measures as well as selection effects in various interferometric surveys of compact HII regions." + These coi‘lusions apply to thermal sources., These conclusions apply to thermal sources. + An important extension of this work would consider the broad liue regions of active galactic uuclel aud quasars in which a stroug uonutliermal microwave radiation field could influence the populatious of the 2s and 2p levels. as well as provide a background for line absorption or stimulated emission.," An important extension of this work would consider the broad line regions of active galactic nuclei and quasars in which a strong nonthermal microwave radiation field could influence the populations of the $2s$ and $2p$ levels, as well as provide a background for line absorption or stimulated emission." + Iu general. detection of the fine structure lines of hydrogen will be challenging due to the extraordinary liue width and bleuded structure.," In general, detection of the fine structure lines of hydrogen will be challenging due to the extraordinary line width and blended structure." + The observatious will require meticulous baseline calibration and subtraction., The observations will require meticulous baseline calibration and subtraction. + We thank Drs., We thank Drs. + R. Brown aud J. Simonetti [or useful discussions. aud Dr. A. Ershov for bringing his work to our attention.," R. Brown and J. Simonetti for useful discussions, and Dr. A. Ershov for bringing his work to our attention." + Portions of this work were completed while oue of the authors (B.D.) was a Visiting Scientist at the National Radio Astronomy Observatory (NRAQO) in Green Bank.," Portions of this work were completed while one of the authors (B.D.) was a Visiting Scientist at the National Radio Astronomy Observatory (NRAO) in Green Bank," +vyary on both the spin and the ovd cycles. and that the variations are compatible with a model in which the accreion [low Uips from one magneAic pole to the other over the beat evele the hallmark οἱ cliscless accretion in an asynchronous magnetic cataclysmic variable.,"vary on both the spin and the beat cycles, and that the variations are compatible with a model in which the accretion flow flips from one magnetic pole to the other over the beat cycle — the hallmark of discless accretion in an asynchronous magnetic cataclysmic variable." + We have [oun that a simple model of this xhaviour. in which a stream falls to the magnetosphere anc then fecds the nearest Ποια ine. reproduces the observed. line-profile changes over the sin and beat eveles.," We have found that a simple model of this behaviour, in which a stream falls to the magnetosphere and then feeds the nearest field line, reproduces the observed line-profile changes over the spin and beat cycles." + However. i should be noted. that the line-profile variations involve ony 5 per cent of the line emission. and that the bulk of the emission shows no etectable variation.," However, it should be noted that the line-profile variations involve only 5 per cent of the line emission, and that the bulk of the emission shows no detectable variation." + As a reult of this. the variations over the orbital evele ave hareler tointerpre," As a result of this, the variations over the orbital cycle are harder to interpret." + Mea opt an inclination of10.. since js is the minimum necessary to reproduce the line-profile variations over the sin evele (Section 7).," We adopt an inclination of, since this is the minimum necessary to reproduce the line-profile variations over the spin cycle (Section 7)." + However. if all jo eniission came from a collimated. infalling stream. this inclination would lead to an orbital modulation of hundreds ofLo whereas {vw observed. value is only 5.8 ((Seetion 5rA," However, if all the emission came from a collimated, infalling stream, this inclination would lead to an orbital modulation of hundreds of, whereas the observed value is only 5.8 (Section 5)." + This implies that the bulk of the emitting material is not in the infalline stream. but is instead SVNUCLLic about the white εναν.," This implies that the bulk of the emitting material is not in the infalling stream, but is instead symmetric about the white dwarf." + ‘This interoetation is supported by X-ray data. in which the heat-evele modulation is only 25 per cent deep.," This interpretation is supported by X-ray data, in which the beat-cycle modulation is only 25 per cent deep." + Given that the svstem is a so low an inclination that we only ever see the upper »ole. this suggests that only a minorivof the accreting material [ios [rom pole to pole. and that there is a continual Dow to both poles irrespective of beat-cycle phase.," Given that the system is at so low an inclination that we only ever see the upper pole, this suggests that only a minority of the accreting material flips from pole to pole, and that there is a continual flow to both poles irrespective of beat-cycle phase." + What is the haure of this Low?, What is the nature of this flow? + One possibility might be a conventional accretion disc., One possibility might be a conventional accretion disc. + This coud feed. field lines from its inrjer edge. forming ‘accretion curains of material in the usual manner or an LP.," This could feed field lines from its inner edge, forming `accretion curtains' of material in the usual manner for an IP." + However. why. then. do we see no X-ray spin pulse?," However, why, then, do we see no X-ray spin pulse?" + Given that the inclination and cipole olfset are sullicient to produce obvious spin-evele variations in the emission lines. we would expect. the aspect. of the accretion sites to vary with spin phase. and thus absortion and scattering of XN-ravs in the accretion. curtain would produce a sxn pulse (this is best documented in AO Pse: Lellior. Creypper AlMason 1f991: Lellier 11996: SCO αso the moclel of Kim BBeucrmann 1995).," Given that the inclination and dipole offset are sufficient to produce obvious spin-cycle variations in the emission lines, we would expect the aspect of the accretion sites to vary with spin phase, and thus absorption and scattering of X-rays in the accretion curtain would produce a spin pulse (this is best documented in AO Psc; Hellier, Cropper Mason 1991; Hellier 1996; see also the model of Kim Beuermann 1995)." + Another issue is how the stream coexists with the disc. since. having dillerent velocities. they couldn't bot 1occupy the orbital plane.," Another issue is how the stream coexists with the disc, since, having different velocities, they couldn't both occupy the orbital plane." + One plausible answer is that the stream could overllow the disc (see Armitage LLivio 1998 for theoretical simulations of this)., One plausible answer is that the stream could overflow the disc (see Armitage Livio 1998 for theoretical simulations of this). + This idea has been invok«d to explain the LPs showing both spin and beat pulses in the X-ray lighteurves 1οτος 1991)., This idea has been invoked to explain the IPs showing both spin and beat pulses in the X-ray lightcurves Hellier 1991). + However. again. a 5xn-cevele pulsation is nearly always seen. and. taking the example of FO Aqr. the beat-evele modulation is alwavs weaker or even absent (Norton 11992: Helier 1993b: Bearclmore 11998).," However, again, a spin-cycle pulsation is nearly always seen, and, taking the example of FO Aqr, the beat-cycle modulation is always weaker or even absent (Norton 1992; Hellier 1993b; Beardmore 1998)." + 1n view of the cdilliculties in invoking a disc. we turn instead to he idea of magnetically threaded accretion Lows. developed w Wine (1993) and Wynn IxIxing (10595).," In view of the difficulties in invoking a disc, we turn instead to the idea of magnetically threaded accretion flows, developed by King (1993) and Wynn King (1995)." + This model treats the Low as diamagnetic blobs. which are divertecl from a ballistic trajectory hy the magnetic drag produced. by. their crossing field. lines.," This model treats the flow as diamagnetic blobs, which are diverted from a ballistic trajectory by the magnetic drag produced by their crossing field lines." + The resulting trajectories depend on bob size and. density., The resulting trajectories depend on blob size and density. + Simulations by Wine WWvnn (1999) suggest. that it is posible for less-dense matter to be easily threaded. and. conrolled by field. lines (which would then act as in our simulations). while cdenser blobs cross field lines ancl circulate arouncd the white chwarl.," Simulations by King Wynn (1999) suggest that it is possible for less-dense matter to be easily threaded and controlled by field lines (which would then act as in our simulations), while denser blobs cross field lines and circulate around the white dwarf." + “Phese blobs would lose knowledge of orbital phase. ancl eventually be. cestroved by maenetohvcrocynamic," These blobs would lose knowledge of orbital phase, and eventually be destroyed by magnetohydrodynamic" +"cut Myyy—M,=4.25.",cut $M_{NUV} - M_{r} = 4.25$. +" Because of our rest-frame B—band luminosity selection, we do not find a significant population of red (Μνυν—M,z 4), dusty SF (M,—M;z 1) galaxies (i.e., they are faint due to the dust extinction)."," Because of our rest-frame $B-$ band luminosity selection, we do not find a significant population of red $M_{NUV} - M_{r} \gtrsim 4$ ), dusty SF $M_{r} - M_{J} \gtrsim 1$ ) galaxies (i.e., they are faint due to the dust extinction)." +" In contrast, this population appears in NIR-selected samples, as those from or?."," In contrast, this population appears in NIR-selected samples, as those from or." +". To explore in more details the nature of red and blue sources, we use the spectro-photometric types (S types) of the galaxies."," To explore in more details the nature of red and blue sources, we use the spectro-photometric types $S_{\rm types}$ ) of the galaxies." +" These spectro-photometric types were obtained by fitting 62 templates, that include ellipticals and SO's (Stype= 13), early-type spirals (Stype=14— 29), late-type spirals (Stype=30— 43), and irregulars and starburst (Stype=44—62; see?,, for details)."," These spectro-photometric types were obtained by fitting 62 templates, that include ellipticals and S0's $S_{\rm type} = 1-13$ ), early-type spirals $S_{\rm type} = 14-29$ ), late-type spirals $S_{\rm type} = 30-43$ ), and irregulars and starburst $S_{\rm type} = 44-62$; see, for details)." +" In Fig. 6,,"," In Fig. \ref{nuvrjtotfig}," +" we also show thenumber density contours of M*,<—20 galaxies when we split them into early (Stypes€ 8) and late (Stypes> 8) types.", we also show thenumber density contours of $M_B^{\rm e} \leq -20$ galaxies when we split them into early $S_{\rm types} \leq 8$ ) and late $S_{\rm types} > 8$ ) types. +" We show that, as expected, red sequence galaxies are mainly (~ 90%)) early types, while blue cloud is populated (~ 95%)) by later types?)."," We show that, as expected, red sequence galaxies are mainly $\sim 90$ ) early types, while blue cloud is populated $\sim 95$ ) by later types." +". Because of this, and for simplicity, we define red, quiescent galaxies as those with Myuy—M,>4.25, and blue, star-forming galaxies as those with Myyy—M,<4.25."," Because of this, and for simplicity, we define red, quiescent galaxies as those with $M_{NUV} - M_{r} \geq 4.25$, and blue, star-forming galaxies as those with $M_{NUV} - M_{r} < 4.25$." +" We note that the trends and main results in this section remain the same if we either vary the blue-red limit by +0.25 mag or use spectro-photometric types to define an early (i.e., red) and a late (i.e., blue) population."," We note that the trends and main results in this section remain the same if we either vary the blue–red limit by $\pm0.25$ mag or use spectro-photometric types to define an early (i.e., red) and a late (i.e., blue) population." +" With the previous definitions, the principal sample comprises 268 red and 743 blue sources."," With the previous definitions, the principal sample comprises 268 red and 743 blue sources." +" We look for nec100! kpc close companions, regardless of their colour, to ensure good statistics."," We look for $r_{\rm p}^{\rm max} = 100h^{-1}$ kpc close companions, regardless of their colour, to ensure good statistics." +" As was mentioned in the previous section, the trends obtained with this search radius are representative to trends observed at smaller separation."," As was mentioned in the previous section, the trends obtained with this search radius are representative to trends observed at smaller separation." +" We find that: The fraction of principal galaxies that have a companion and are blue, foue=Np ΝΟ, does not depend on p at z 0.8, folue,1~70%."," We find that: The fraction of principal galaxies that have a companion and are blue, $f_{\rm blue,1} = N_{\rm p}^{\rm blue}/N_{\rm p}$ , does not depend on $\mu$ at $z = 0.8$ , $f_{\rm blue,1} \sim 70$." +". On the other hand, fpiue,1 increases when ju decreases at z=0.5, varying from Άγιοι~50% atu>1/10 to foe.~40% atu>1/4, in contrast with ~70% at z=0.8."," On the other hand, $f_{\rm blue,1}$ increases when $\mu$ decreases at $z = 0.5$, varying from $f_{\rm blue,1} \sim 50$ at $\mu \geq 1/10$ to $f_{\rm blue,1} \sim 40$ at $\mu \geq 1/4$, in contrast with $\sim 70$ at $z = 0.8$." +" The fraction of principal galaxies that have a companion and are red is fiai=ΝΕ/N,—1—μοι."," The fraction of principal galaxies that have a companion and are red is $f_{\rm red,1} = N_{\rm p}^{\rm red}/N_{\rm p} = 1 - f_{\rm blue,1}$." +" We find that the fraction of companions that are blue is Sowe20.8, regardless either of the colour of the principal or μ."," We find that the fraction of companions that are blue is $f_{\rm blue,2} \sim 0.8$, regardless either of the colour of the principal or $\mu$ ." +" This means that red—red (dry), red—blue or blue—red (mixed), and blue-blue (wet) pairs account for ~10%//40%//50%of the pairs with a minor companion in all the redshift range"," This means that red–red (dry), red–blue or blue–red (mixed), and blue–blue (wet) pairs account for $\sim$of the pairs with a minor companion in all the redshift range" +(Masset.etal.2006a}.,\citep{masset06a}. +. There is still nucertaiutv about this estimate of the weration time., There is still uncertainty about this estimate of the migration time. + Iudeed. the distribution consistent with observations of exoplauets cau be reproduced ouly if the timescale of the type I unieration is at least an order of maenitude lounger than that derived from the linear analysis (Ida&Lin2008).," Indeed, the distribution consistent with observations of exoplanets can be reproduced only if the timescale of the type I migration is at least an order of magnitude longer than that derived from the linear analysis \citep{ida_lin08}." +. We should also investigate the streneth of such σταο for the survival of cores of eas giant planets in our future work., We should also investigate the strength of such migration for the survival of cores of gas giant planets in our future work. + Tn this paper. we investigate the erowth of planetary enibrvos by talking muto account. among others. two effects that are of major miportance.," In this paper, we investigate the growth of planetary embryos by taking into account, among others, two effects that are of major importance." + One of them is collisional fragmentation of planetesimals. which is induced by their gravitational interaction with plauctary cores.," One of them is collisional fragmentation of planetesimals, which is induced by their gravitational interaction with planetary cores." + Another effect is an enliauceiment of collisional cross section of a erowine enibrvo by a tenuous atinosphere of uebular gas. which becomes substantial when an embryo has reached about a Mars ass.," Another effect is an enhancement of collisional cross section of a growing embryo by a tenuous atmosphere of nebular gas, which becomes substantial when an embryo has reached about a Mars mass." + The main results are sumunarized as follows., The main results are summarized as follows. + , +The formation time of Iris is most consistent with the late-lorming echondrules in CR chondrites.,The formation time of Iris is most consistent with the late-forming chondrules in CR chondrites. +" Chondrules from CB chonclrites also formed. relatively late (as determined by 2"" ΟΡ measurements). likely by a giant impact in the early solar system 2005)."," Chondrules from CB chondrites also formed relatively late (as determined by $^{207}$ $^{206}$ Pb measurements), likely by a giant impact in the early solar system \citep{kro05}." + The parent bodies of both CR and CB chonclrites were scarcely heated 2006).. similar to Wild 2 (Brownleeetal.2006).," The parent bodies of both CR and CB chondrites were scarcely heated \citep{sco06}, similar to Wild 2 \citep{bro06}." +. However. tvpe H chondrules like Iris (and similar Stardust [raements) are very rare in CR and CD meteorites: «176 of all chondrules (Weisbergοἱal.1993:Ixrotetal...2002).," However, type II chondrules like Iris (and similar Stardust fragments) are very rare in CR and CB meteorites: $<$ of all chondrules \citep{wei93,kro02}." +. The Iris mesostasis is Fe-poor and Na-rich compared to mesostasis in tvpe II ehondrules in unequilibrated CTI chondrules. and the Iris olivine is Ca- and Al-rich relative (ο olivine in Ch. tvpe II chondrules 2011).," The Iris mesostasis is Fe-poor and Na-rich compared to mesostasis in type II chondrules in unequilibrated CR chondrules, and the Iris olivine is Ca- and Al-rich relative to olivine in CR type II chondrules \citep{ber11}." +. Although Iris is similar to chondrules from CR and CB meteorites in that it formed relatively late. Iris and similar Stardust fragments are unlikely to have originated from the CR- or CBD-chondrite-forming region.," Although Iris is similar to chondrules from CR and CB meteorites in that it formed relatively late, Iris and similar Stardust fragments are unlikely to have originated from the CR- or CB-chondrite-forming region." + The Fe-rich olivines in Iris must have formed in an environment with oxvgen fugacitv hieher than the typical redox conditions of the steady-state solar nebula (Ixrotetal.2000).., The Fe-rich olivines in Iris must have formed in an environment with oxygen fugacity higher than the typical redox conditions of the steady-state solar nebula \citep{kro00}. . + Shocks in the outer solar nebula. bevond the water-snow line ad &5 AU (Cyretal.1998).. were rich in water vapor (Cieslaοἱal...2003) which could have formed a chondrule like Iris near (he current orbit of Jupiter.," Shocks in the outer solar nebula, beyond the water-snow line at $\sim$ 5 AU \citep{cyr98}, were rich in water vapor \citep{cie03} which could have formed a chondrule like Iris near the current orbit of Jupiter." + However. the predicted composition of chondrule olivine in such a shock is strongly. peaked between Foz; and Foxy. Foz; olivine and lower is predicted to be ~3% (Fedkin.Ciesla.&Grossman2008) of all chondrule olivine generated in the shock.," However, the predicted composition of chondrule olivine in such a shock is strongly peaked between $_{76}$ and $_{89}$, $_{70}$ olivine and lower is predicted to be $\sim$ \citep{fed08} of all chondrule olivine generated in the shock." + Therefore we conclude that Iris was probably not created in an outer-nebula shock. but likely formed in (he inner solar nebula. from material with relatively high Fe/Mg or in a region of high oxvgen fugacitv (Jones1990).. more than 3 Myr after CAIs.," Therefore we conclude that Iris was probably not created in an outer-nebula shock, but likely formed in the inner solar nebula, from material with relatively high Fe/Mg or in a region of high oxygen fugacity \citep{jon90}, more than 3 Myr after CAIs." + Recent measurements of oxvgen isotope variations in the rim of a CAI trom the CV3 chondrite Allende (Simonetal.—2011) indicate that these early objects experienced circulation in the solar nebula., Recent measurements of oxygen isotope variations in the rim of a CAI from the CV3 chondrite Allende \citep{sim11} indicate that these early objects experienced circulation in the solar nebula. + A Type C CAI found in the Starcust samples was constrained to have ervstallized at least 1.7 Myr after the onset of CAI formation Cassuming a homogeneous nebular reservoir of canonical CAI/7* AD)4). though it likely experienced a complex history (Matzeletal.2010).," A Type C CAI found in the Stardust samples was constrained to have crystallized at least 1.7 Myr after the onset of CAI formation (assuming a homogeneous nebular reservoir of canonical $^{26}$ $^{27}$ $_0$ ), though it likely experienced a complex history \citep{mat10}." +. Additionally. high-temperature components (CAIs and ehondrules) do not appear (o be scarce in the Stardust samples.," Additionally, high-temperature components (CAIs and chondrules) do not appear to be scarce in the Stardust samples." + These observations provide strong evidence of a clinic early solar svstem transporting material between the inner and outer nebula., These observations provide strong evidence of a dynamic early solar system transporting material between the inner and outer nebula. + The formation of Iris in the inner nebula requires it (ο be (transported to the scattered disk al 735 AU (Duneanetal.2004:Tirpák2009) where it was incorporated into comet Wild 2.," The formation of Iris in the inner nebula requires it to be transported to the scattered disk at $\sim$ 35 AU \citep{dun04,tir09} where it was incorporated into comet Wild 2." + This transport could have occurred outside the plane of the disk (e.g. Ciesla(2007 ))). by diffusion (e.g. Cuzzi.Davis.&Dobrovolskis (2003))).aerocvnaamic lofting and radial dift (e.g. Ciesla (2008))). or outward advective Lows (e.g. Ighes&Armitage (2011))).," This transport could have occurred outside the plane of the disk (e.g. \citet{cie07}) ), by diffusion (e.g. \citet{cuz03}) ),aerodynamic lofting and radial drift (e.g. \citet{cie08}) ), or outward advective flows (e.g. \citet{hug11}) )." + Jupiter's erowing embryo would open a gap in the disk (Dateοἱal.2003). which. would prohibit, Jupiter's growing embryo would open a gap in the disk \citep{bat03} which would prohibit +[act that we use a mass ratio of unity. may. explain this conclusion. (,"fact that we use a mass ratio of unity, may explain this conclusion. (" +4) Concerning mass accretion rates. although we could not reach a definite conclusion due to the long time required to attain à steady state. we observe that the ratio between the mass aceretion and mass injection rates is about 0.5 to 0.6.,"4) Concerning mass accretion rates, although we could not reach a definite conclusion due to the long time required to attain a steady state, we observe that the ratio between the mass accretion and mass injection rates is about 0.5 to 0.6." + This is however very dependent on the numerical viscosity and the inner boundary. condition., This is however very dependent on the numerical viscosity and the inner boundary condition. +he best fit of the multi-band spectra of 3€273 give a high inclination of about 607 (Ixrissetal.1999).,the best fit of the multi-band spectra of 3C273 give a high inclination of about $60^{\circ}$ \cite{kriss}. +. There are astrophysical reasons to relate the short- N-ray variability in AGNs with the accretion rate., There are astrophysical reasons to relate the short-time X-ray variability in AGNs with the accretion rate. + For example. high variability can be introduced. by some increased instability in high aceretion rate objects.," For example, high variability can be introduced by some increased instability in high accretion rate objects." +" Llowever, here are still no reliable estimation for the accretion rate of AGNs."," However, there are still no reliable estimation for the accretion rate of AGNs." + For example. the accretion rate of NGC4258. one of he best studied object. is still in controversy.," For example, the accretion rate of NGC4258, one of the best studied object, is still in controversy." + Hs estimated values dilfer more than one order of magnitude: (Neufeld&Maloney.1995:CGamnmie.," Its estimated values differ more than one order of magnitude \cite{nm95,gnb}." +NaravanBlanelford 1999). There are separate large amplitude Iares in the light curves of many objects. especially in some NLSI possibly. with high accretion rates: what's more. there exists some [lare events in the light. curves of some NLSIs (e.g. PINSO0558-504) which a very large raciative ellicienev. (Ciliozzi et al.," There are separate large amplitude flares in the light curves of many objects, especially in some NLS1 possibly with high accretion rates; what's more, there exists some flare events in the light curves of some NLS1s (e.g. PKS0558-504) which require a very large radiative efficiency (Gliozzi et al." + 2000 and requirereferences therein)., 2000 and references therein). + Therefore. the short-time X-ray variability may be more complicated than expected. and it may also depend on some other parameters.," Therefore, the short-time X-ray variability may be more complicated than expected, and it may also depend on some other parameters." + X solid conclusion could be drawn by the current broad band: X-ray mission like Chandra and NMM-Néeston., A solid conclusion could be drawn by the current broad band X-ray mission like Chandra and XMM-Newton. +" To summarize. we have found. a significant anti-correlation between the ""excess variance” in X-ray band and the centra black hole mass for a composite sample of Sevfert 1 galaxies. QSOs and LLAGNs."," To summarize, we have found a significant anti-correlation between the “excess variance” in X-ray band and the central black hole mass for a composite sample of Seyfert 1 galaxies, QSOs and LLAGNs." + Some simple global coherent variations in the X-ray emission region. which scales with the size of the central black hole. can lead to such a relation.," Some simple global coherent variations in the X-ray emission region, which scales with the size of the central black hole, can lead to such a relation." + Basec on our finding. the fact that NLSI ancl high redshift QSOs show enhanced excess X-ray. variability than broad line loca AGNs at a given luminosity can be explained by that they harbor smaller black holes than the normal local AGNs.," Based on our finding, the fact that NLS1 and high redshift QSOs show enhanced excess X-ray variability than broad line local AGNs at a given luminosity can be explained by that they harbor smaller black holes than the normal local AGNs." + These results highlight the significance of pursuing a large-sample X-rav. variability investigation. which can shed light into the physical mechanism of AGNs and its evolution.," These results highlight the significance of pursuing a large-sample X-ray variability investigation, which can shed light into the physical mechanism of AGNs and its evolution." + We thank an anonymous referee for helpful comments and suggestions and Dr S. P. Oh for a careful reading of the manuscript., We thank an anonymous referee for helpful comments and suggestions and Dr S. P. Oh for a careful reading of the manuscript. + YL acknowledges the hospitality of the Department of Astrophysical Sciences. Princeton University.," YL acknowledges the hospitality of the Department of Astrophysical Sciences, Princeton University." + This rescarch has made use of data obtained through the Ligh Enerev Astrophysics Science Archive Research Center Online Service. provided. by the NASA/CGodedarcl Space Flight Center.," This research has made use of data obtained through the High Energy Astrophysics Science Archive Research Center Online Service, provided by the NASA/Goddard Space Flight Center." +rendering it a difficult population to iclentify let alone classify as il is mixed) with the RC and RG populations.,rendering it a difficult population to identify let alone classify as it is mixed with the RC and RG populations. +Iu most cases the main purpose was the determination of the correlation leneth. ry. aud the power iudex. 5. of the function: for recent studies we refer to Sutherland (1955). Efstathiou (1992). Dalton (1992). aud Croft (1997).,"In most cases the main purpose was the determination of the correlation length, $r_0$, and the power index, $\gamma$, of the function; for recent studies we refer to Sutherland (1988), Efstathiou (1992), Dalton (1992), and Croft (1997)." + These authors have shown that the correlation leneth for APAL clusters is simaller than that for Abell clusters., These authors have shown that the correlation length for APM clusters is smaller than that for Abell clusters. + This can be explained in part by the overlapping of Abell clusters in superclusters: a sinall intrinsic difference is also possible., This can be explained in part by the overlapping of Abell clusters in superclusters; a small intrinsic difference is also possible. + As shown by real data aud uunuerical Sa.uulations. the cluster correlation function depends o- cluster richuess (Balicall West 1992. Dalicall Cen 1992. Frisch 1995).," As shown by real data and numerical simulations, the cluster correlation function depends on cluster richness (Bahcall West 1992, Bahcall Cen 1992, Frisch 1995)." + We also find a wea difference of the cluster correlation length for Abell iuxPm APAI samples., We also find a weak difference of the cluster correlation length for Abell and APM samples. + A πιο stronecr dependence exists fo clusters located in different enviromneuts: the correlatio leugth for clusters in rich and very rich superclusters i: much ligher than for all clusters (E97b. Paper IT).," A much stronger dependence exists for clusters located in different environments: the correlation length for clusters in rich and very rich superclusters is much higher than for all clusters (E97b, Paper II)." + Thi:4. effect is due to variable deusitv threshold in the definitio- of clusters ina differcut euvironmeut. for iui analysis of this effect see Einasto (1999b).," This effect is due to variable density threshold in the definition of clusters in a different environment, for an analysis of this effect see Einasto (1999b)." + In the preseut study we confirm this result (see Table 1):cnveirommoent., In the present study we confirm this result (see Table 1):. + Iu the preseut study we lave conceutrated on the study of cluster correlations at large separations., In the present study we have concentrated on the study of cluster correlations at large separations. + For sanall separations the correlation fuuction characterizes the distribution of clusters iu superclusters. aud for large separations the distribution of superclusters themselves. ic. properties of the supercluster-void network (E970).," For small separations the correlation function characterizes the distribution of clusters in superclusters, and for large separations the distribution of superclusters themselves, i.e. properties of the supercluster-void network (E97c)." + The present study has coufirmed earlier fiudiugs of E97b. that on large scales the Abell cluster correlation function is oscillating. ic. it consists of alternating secondary maxima and muna.," The present study has confirmed earlier findings of E97b, that on large scales the Abell cluster correlation function is oscillating, i.e. it consists of alternating secondary maxima and minima." + Oscillations are clearly detected if we use suuples of clusters in very rich superclusters., Oscillations are clearly detected if we use samples of clusters in very rich superclusters. + There is mactically uo difference between the oscillatory behavior of samples of all clusters and clusters with measured redshifts. ACO.AS and ACO.Bs. respectively.," There is practically no difference between the oscillatory behavior of samples of all clusters and clusters with measured redshifts, ACO.A8 and ACO.R8, respectively." + We find a iod of oscillations of 116420Mpce. very close o the value found earlier.," We find a period of oscillations of $116 \pm 20$, very close to the value found earlier." + The APA cluster sample also shows signs of oscillations with the same period. if we use all clusters (sample APALAS).," The APM cluster sample also shows signs of oscillations with the same period, if we use all clusters (sample APM.A8)." + If we use clusters with ueasured redshifts ouly (sample APALRs). we see again a strong secondary maxima. but at wach larger separation correspouding to the mutual distance of two dominating superchisters in the sample. the ΠονοιοσΠοσαι aud the Sculptor superchisters (sec Figure 6).," If we use clusters with measured redshifts only (sample APM.R8), we see again a strong secondary maximum, but at much larger separation corresponding to the mutual distance of two dominating superclusters in the sample, the Horologium-Reticulum and the Sculptor superclusters (see Figure 6)." + This is the main difference between Abell aud APM samples of clusters., This is the main difference between Abell and APM samples of clusters. + We continue the discussion of this difference in the next Section., We continue the discussion of this difference in the next Section. +" The principal statistic to characterize the distribution of matter on large scales has been the power spectrum of clusters of galaxies,", The principal statistic to characterize the distribution of matter on large scales has been the power spectrum of clusters of galaxies. + Our study confirms previous evidence (E97a. R98. aud TOs) for the existence of a real differeuces between power spectra of Abell and APM cluster samples.," Our study confirms previous evidence (E97a, R98, and T98) for the existence of a real differences between power spectra of Abell and APM cluster samples." + The power spectrum of the Abell sample has a peak on à scale of z120Mpc., The power spectrum of the Abell sample has a peak on a scale of $\approx 120$. + A peaked power spectrum corresponds to an oscillating correlation function (E97Ta) with a period of 120Mpe., A peaked power spectrum corresponds to an oscillating correlation function (E97a) with a period of 120. +. The APA cluster sauple as analyzed by TOs has uo feature ou this scale., The APM cluster sample as analyzed by T98 has no feature on this scale. + It has been areued that the APM cluster sample is free of the projection and selection biases kuown to affect the Abell cluster sample CT98)., It has been argued that the APM cluster sample is free of the projection and selection biases known to affect the Abell cluster sample (T98). + For this reason the reality of the feature seen in the Abell sample has beeu questioned (Postman L998}., For this reason the reality of the feature seen in the Abell sample has been questioned (Postman 1998). + This brings us to the ceutral problem of our study: How well do the Abell and APM cluster samples trace the structure of the Universe ou large scales?, This brings us to the central problem of our study: How well do the Abell and APM cluster samples trace the structure of the Universe on large scales? + Oi study has shown that selectiou effects are more colplicated than assumed previously., Our study has shown that selection effects are more complicated than assumed previously. + In particular. the selection function in distance depends on four cdiffereut effects: the diticulty to detect clusters at large aud. siuall distances. the deficiency of clusters at laree distance due to random errors in estimated redshifts used for the selection of clusters. aud the selection caused by observing prograiis of cluster redshifts.," In particular, the selection function in distance depends on four different effects: the difficulty to detect clusters at large and small distances, the deficiency of clusters at large distance due to random errors in estimated redshifts used for the selection of clusters, and the selection caused by observing programs of cluster redshifts." + Our analysis has shown that the sample of all Abell clusters. (ACO.AL) is affected by. cistamce-dependent selection effects only on very huge distances: this sclection effect iav be reduced if the sample is cut at a redshift of 2=0.13., Our analysis has shown that the sample of all Abell clusters (ACO.A1) is affected by distance-dependent selection effects only on very large distances; this selection effect may be reduced if the sample is cut at a redshift of $z=0.13$. + In contrast. the APAL sample with measured redshifts CAPNLERI) is affected by several distauce-depeudeut selection effects within the range of distances of interest for the prescut study.," In contrast, the APM sample with measured redshifts (APM.R1) is affected by several distance-dependent selection effects within the range of distances of interest for the present study." + T98 has compcusated distance-dependeut selection effects using weights for clusters inversely proportional— to the mean spatial density of the cluster sample at its respective distance. following the prescription by Feldman. Ἱναίκο Peacock (1991. hereafter FISP).," T98 has compensated distance-dependent selection effects using weights for clusters inversely proportional to the mean spatial density of the cluster sample at its respective distance, following the prescription by Feldman, Kaiser Peacock (1994, hereafter FKP)." +" TOs has also applied truucation of the sample at large distances. rjj,=GOO and 100Ape."," T98 has also applied truncation of the sample at large distances, $r_{lim}=600$ and 400." + The resulting estimates of the spectrmm are simular. but the scatter of the power spectruni is sinaller when cutting the sample at smaller distance.," The resulting estimates of the spectrum are similar, but the scatter of the power spectrum is smaller when cutting the sample at smaller distance." + T98 argue that the pAsample of APM clusters with measured redshifts is representative for a volume of depth 400Mpc., T98 argue that the sample of APM clusters with measured redshifts is representative for a volume of depth 400. +. The Figure 3 shows that the spatial density of the APM salple is very low at huge distances., The Figure 3 shows that the spatial density of the APM sample is very low at large distances. + The same effect cau (0 seen also in Figure 1 of TOS (note that T98 do not Not the spatial deusitv. but the number of clusters iu respective bins).," The same effect can be seen also in Figure 1 of T98 (note that T98 do not plot the spatial density, but the number of clusters in respective bins)." + The comparison of the spatial densities of the Abell and APM samples in Figure 3 deimoustrates wat the APA sample with measured redshifts becomes very sparse or diluted at distances kr>300Ape: in 16 Abell sample dilution becomes strong only at distances pom400\Ipe., The comparison of the spatial densities of the Abell and APM samples in Figure 3 demonstrates that the APM sample with measured redshifts becomes very sparse or diluted at distances $r > 300$; in the Abell sample dilution becomes strong only at distances $r > 400$. +. The question is: Is tlhe use of weights sufficient to compensate for the strong dilution observed iu 10 APM sample at large distance?, The question is: Is the use of weights sufficient to compensate for the strong dilution observed in the APM sample at large distance? + FKDP areuc that statistical properties of large scale structures can be fixed by using sparse samples if deusity orturbations are Caussian., FKP argue that statistical properties of large scale structures can be fixed by using sparse samples if density perturbations are Gaussian. + The Gaussian character of sinall-scale perturbations has been checked by the analysis of FIP., The Gaussian character of small-scale perturbations has been checked by the analysis of FKP. + Ou large scales the problems is unsolved., On large scales the problem is unsolved. + Szalav (1998) has demoustrated that the distribution of large structures (superchister-void network eeucrated by Voronoi tessellation) may be destroved completely by raudonmizatiou of the phases of perturbations without changing the power spectrum., Szalay (1998) has demonstrated that the distribution of large structures (supercluster-void network generated by Voronoi tessellation) may be destroyed completely by randomization of the phases of perturbations without changing the power spectrum. + A sparse sample cannot distiueuish between a regular superchister-void network aud random distribution of hieh-deusitv regions., A sparse sample cannot distinguish between a regular supercluster-void network and random distribution of high-density regions. + This simple example shows verv clearly that a very sparse sample is not suitable to describe the real superchister-void network., This simple example shows very clearly that a very sparse sample is not suitable to describe the real supercluster-void network. + Qur experience has shown (Einasto 1991. Frisch 1995. E97c) that dilution is uot dangerous to locate hiehl-density regions. as long as the main structural elements are uot destroved.," Our experience has shown (Einasto 1991, Frisch 1995, E97c) that dilution is not dangerous to locate high-density regions, as long as the main structural elements are not destroyed." + The distribution of matter on large scales is, The distribution of matter on large scales is +"In Figure 3, we show the images of the distributions of four very torsionally/vibrationally highly excited lines, CH30H(743-64,3) A (vj22), CH30H(743-643) A (viz), HC3N(37-36)(v7=1), and S$O2(2120-211,21)02=1), and the 870 um continuum, overlaid on the moderate excitation CH3CN (125-113) line toward the core of the Orion KL region.","In Figure 3, we show the images of the distributions of four very torsionally/vibrationally highly excited lines, $_3$ $_{4,3}$ $_{4,3}$ ) $^-$ $\nu_t$ =2), $_3$ $_{4,3}$ $_{4,3}$ ) $^-$ $\nu_t$ =1), $_3$ $\nu_7$ =1), and $_2$ $_{2,20}$ $_{1,21}$ $\nu_2$ =1), and the 870 $\mu$ m continuum, overlaid on the moderate excitation $_3$ CN $12_3-11_3$ ) line toward the core of the Orion KL region." + These four lines have energies up to 943 K and thus trace the hottest molecular material., These four lines have energies up to 943 K and thus trace the hottest molecular material. +" The continuum emission arises from only three compact sources that were already reported at millimeter wavelengths by???;; namely the Hot Core -> SMM3, the Northwest Clump -> SMM2, and the Compact Ridge -> SMMI."," The continuum emission arises from only three compact sources that were already reported at millimeter wavelengths by; namely the Hot Core $>$ SMM3, the Northwest Clump $>$ SMM2, and the Compact Ridge $>$ SMM1." +" In Table 2, we list their observational parameters."," In Table 2, we list their observational parameters." +" The source SMMI is further resolved into three compact sources: SMA 1, Hot Core, and Source(?)."," The source SMM1 is further resolved into three compact sources: SMA 1, Hot Core, and Source." +. The 1300 um continuum emission is quite similar to that at 870 uum so that we do not show a map of this wavelength., The 1300 $\mu$ m continuum emission is quite similar to that at 870 $\mu$ m so that we do not show a map of this wavelength. + The torsionally/vibrationally highly excited emission is seen to be compact and located exclusively on the northeast side of the heart-shaped structure as traced by the emission of CH3CN(123-113)., The torsionally/vibrationally highly excited emission is seen to be compact and located exclusively on the northeast side of the heart-shaped structure as traced by the emission of $_3$ $_3$ $_3$ ). + We list the observational and physical parameters of these lines in Table 1., We list the observational and physical parameters of these lines in Table 1. +" Clearly this CH3OH and HC3N emission shows pronounced extensions or tails toward the northeast part of the , oriented in the direction of the Extended Ridge."," Clearly this $_3$ OH and $_3$ N emission shows pronounced extensions or tails toward the northeast part of the , oriented in the direction of the Extended Ridge." + Such a tail or extension is also observed in CH3CN(123-113) as already mentioned in the previous section., Such a tail or extension is also observed in $_3$ $_3$ $_3$ ) as already mentioned in the previous section. +" The HC3N(37-36)(v7=1) and CH30H(743-643) A (v,22) line emissions seem to surround the submillimeter source SMM3 like part of a shell, and both lines peak between that submillimeter source and the origin of the explosion."," The $_3$ $\nu_7$ =1) and $_3$ $_{4,3}$ $_{4,3}$ ) $^-$ $\nu_t$ =2) line emissions seem to surround the submillimeter source SMM3 like part of a shell, and both lines peak between that submillimeter source and the origin of the explosion." + The morphology of the HC3N(37-36)(v7=1) emission even appears to point toward this origin., The morphology of the $_3$ $\nu_7$ =1) emission even appears to point toward this origin. +" The vibrationally excited SO, emission, with an energy of the lower state of almost 1000 K (see Table 1), is very compact and peaks at the same position as does HC3N(37-36)(v7=1) emission."," The vibrationally excited $_2$ emission, with an energy of the lower state of almost 1000 K (see Table 1), is very compact and peaks at the same position as does $_3$ $\nu_7$ =1) emission." + It is important to note that the vibrationally/torsionally excited lines are not associated with any radio or submillimeter continuum sources and always fall well outside or on the edge of the heart-shaped structure as traced by CH3CN(123-113); see Figure 3., It is important to note that the vibrationally/torsionally excited lines are not associated with any radio or submillimeter continuum sources and always fall well outside or on the edge of the heart-shaped structure as traced by $_3$ $_3$ $_3$ ); see Figure 3. + This suggests that the heating source of the Hot Core is external as proposed by and?., This suggests that the heating source of the Hot Core is external as proposed by and. +". However, here we refer ""external heating"" to the input of mechanical energy from the explosive disintegration to the dusty core rather than the input of radiative energy from an external stellar source located at a certain distance."," However, here we refer “external heating” to the input of mechanical energy from the explosive disintegration to the dusty core rather than the input of radiative energy from an external stellar source located at a certain distance." +" If the heating of the Orion KL Hot Core were internal one might expect the hot molecular gas to be centered on a strong compact continuum source located within the core, butthis is not the case."," If the heating of the Orion KL Hot Core were internal one might expect the hot molecular gas to be centered on a strong compact continuum source located within the core, butthis is not the case." + The fact that both HC3N(37-36)(v7=1), The fact that both $_3$ $\nu_7$ =1) +Two heatinge sources are taken into consideration: the viscous dissipation and the irradiation of the central star.,Two heating sources are taken into consideration: the viscous dissipation and the irradiation of the central star. +" Balancing the heating sources and the radiative cooling. the equilibrium temperature is obtained: where qi is (he heating rate by the viscous dissipation. ge. is the heating rate bv the irradiation of the central star. αν is the extinction coellicient. c, is the single scattering albedo. J,(Q) is the diffuse radiation field in the disk (intensity. without including the direct radiation ουν the central star). and D,(7) is the Planck function."," Balancing the heating sources and the radiative cooling, the equilibrium temperature is obtained: where $q_{\mathrm{vis}} $ is the heating rate by the viscous dissipation, $q_{\mathrm{irr}}$ is the heating rate by the irradiation of the central star, $\kappa_{\nu}$ is the extinction coefficient, $\varpi_{\nu}$ is the single scattering albedo, $I_{\nu}(\bm{\Omega})$ is the diffuse radiation field in the disk (intensity without including the direct radiation from the central star), and $B_{\nu}(T)$ is the Planck function." + Quantities with subscript v are a function of the frequency v., Quantities with subscript $\nu$ are a function of the frequency $\nu$. + The integral $dQ on the left hand side of eq. (A2)), The integral $\oint d\Omega$ on the left hand side of eq. \ref{eq:radiative_equilibrium}) ) + represents the integral over the entire solid angle., represents the integral over the entire solid angle. + The viscous heating rate qui; is et al.," The viscous heating rate $q_{\mathrm{vis}}$ is given by (e.g., D'Alessio et al." + 1998). qi;29=paeivenbv(e.g..D'Alessio Og.," 1998), $ %\begin{equation} + q_{\mathrm{vis}} = \frac{9}{4}\rho\nu_{t}\Omega_{ ." +" The dilfuse component of the intensity Z,,,((3) and qui; ave obtained by solving the radiative transfer."," The diffuse component of the intensity $I_{\mu,\nu}(\bm{\Omega})$ and $q_{\mathrm{irr}}$ are obtained by solving the radiative transfer." +" Assuming a plane-parallel structure along the Z-direction. the radiative transfer equation is wrillen as where ji ids the cosine of the propagation direction of radiation and 5$, is the source funelion."," Assuming a plane-parallel structure along the $Z$ -direction, the radiative transfer equation is written as where $\mu$ is the cosine of the propagation direction of radiation and $S_{\nu}$ is the source function." +" The source Iunction 5, is given by where Fij,CZ) is the radiation energy flux from the central star."," The source function $S_{\nu}$ is given by where $F_{\mathrm{irr},\nu}(Z)$ is the radiation energy flux from the central star." + Therein. (he isotropic scattering is assumed.," Therein, the isotropic scattering is assumed." +" The energy [lux Fi,,0(Z) "," The energy flux $F_{\mathrm{irr},\nu}(Z)$ " +figure 3aa. These isochrones clearly confirm the presence of a metallicity spread within the Sculptor RGB stars.,figure \ref{isochrones}a a. These isochrones clearly confirm the presence of a metallicity spread within the Sculptor RGB stars. + The colour magnitude diagrams can also be compare directly to globular cluster observations., The colour magnitude diagrams can also be compared directly to globular cluster observations. + Ferraroetal.(2000) and Savianeetal.(2000). provide fiducial lines for the RGB of Galactic globular clusters for a wide range of metallicity. in the (V.J.Ix) and (VoL) photometric systems.," \cite{FER00} and \cite{SAV00} provide fiducial lines for the RGB of Galactic globular clusters for a wide range of metallicity, in the (V,J,K) and (V,I) photometric systems." +" Figure 4 shows the fiducials of Ferraroctal.(2000). elobular clusters on the (V-Ix..4x,). colour-magnitude ciagram of Sculptor.", Figure \ref{ferraro} shows the fiducials of \cite{FER00} globular clusters on the $_s$ $_s$ ) colour-magnitude diagram of Sculptor. + The transformation. from absolute to. relative magnituces is the same as the one applied for the theoretica isochrones., The transformation from absolute to relative magnitudes is the same as the one applied for the theoretical isochrones. + However the V. and Ix. magnitudes are not on the same photometric svstemi as ours. leading to expectet photometric dillerences of the order of 0.1 mag.," However the V and K magnitudes are not on the same photometric system as ours, leading to expected photometric differences of the order of 0.1 mag." + Considering that globular clusters tend to have alpha-enhanced elemen ratios. whereas the Sculptor stars do not. we indicate their elobal metallicities as defined by Ferraro et al. (," Considering that globular clusters tend to have alpha-enhanced element ratios, whereas the Sculptor stars do not, we indicate their global metallicities as defined by Ferraro et al. (" +1999).,1999). + The definition of this global metallicity scale and how it can be translated into Fe/11] for Seulptor is discussed in section 4., The definition of this global metallicity scale and how it can be translated into [Fe/H] for Sculptor is discussed in section 4. + Here again a metallicity spread. is confirmed. as. being consistent with the width of the Sculptor RGB., Here again a metallicity spread is confirmed as being consistent with the width of the Sculptor RGB. + Figure 4 illustrates that all stars in Sculptor are more metal-poor than ξ-1.0., Figure \ref{ferraro} illustrates that all stars in Sculptor are more metal-poor than $=-1.0$. +" The spread. of the ROB in the (ιν νι) and (V-LL) CAIDs is smaller ancl more sensitive to photometric errors than in (V-Ix,.Ix,)."," The spread of the RGB in the $_s$ $_s$ ) and (V-I,I) CMDs is smaller and more sensitive to photometric errors than in $_s$ $_s$ )." + According to Savianeetal.(2000).. a variation of metallicity from 2.0 to 1.5 dex results in a difference in V-L of 0.04 mag at 2 (one magnitucle brighter than the RGB bump). while according to Ferraroetal. (2000).. the same variation of metallicity at 3 results in a variation of 0.2 mag in. V-Ix. Considering the relative photometric errors in V. EF and Wo. this means that V-Ix. ds 1.7 times as sensitive to metallicity as is V-L. Me will therefore use preferentially the (V-Ixi.Ix;) €CMD in the Following to derive photometric metallicity indicators.," According to \cite{SAV00}, a variation of metallicity from $-2.0$ to $-1.5$ dex results in a difference in V-I of 0.04 mag at $-2$ (one magnitude brighter than the RGB bump), while according to \cite{FER00}, the same variation of metallicity at $-3$ results in a variation of 0.2 mag in V-K. Considering the relative photometric errors in V, I and $_s$, this means that $_s$ is 1.7 times as sensitive to metallicity as is V-I. We will therefore use preferentially the $_s$ $_s$ ) CMD in the following to derive photometric metallicity indicators." + Local maxima are observed in the luminosity function. of the giant branch of old metal-poor stellar populations., Local maxima are observed in the luminosity function of the giant branch of old metal-poor stellar populations. + These 1GDB and AGB bumps are well known features of the magnitude clagrams of globular clusters (e.g. Ferraroet 1999))., These RGB and AGB bumps are well known features of the colour-magnitude diagrams of globular clusters (e.g. \citealt{FER99}) ). + hose two bumps are detected in all our visible and near-infrared bands (table 2)). as illustrated in figure 5. for the V and Ix; bands.," Those two bumps are detected in all our visible and near-infrared bands (table \ref{bumptab}) ), as illustrated in figure \ref{bump} for the V and $_s$ bands." + To allow us to compare the absolute magnitudes of these features in Sculptor with other studies. the ESO WEL V and L photometry was converted into the standard Johnson photometry using the Cirardietal.(2002) isochrones in those two filter svstems.," To allow us to compare the absolute magnitudes of these features in Sculptor with other studies, the ESO WFI V and I photometry was converted into the standard Johnson photometry using the \cite{GIR02} isochrones in those two filter systems." +" At the location of the bumps. (V1);=0.96. a given simulated star of the isochrones present the colours V;lis;=0.06 and 4jJive,=00."," At the location of the bumps, $(V-I)_{J}=0.96$, a given simulated star of the isochrones present the colours $V_J-V_{WFI}=-0.06$ and $I_J-I_{WFI}=0.1$." + Xs previously. the conversion to absolute magnitudes assumes a distance modulus of 19.54 mag and E(D-V)-0.02.," As previously, the conversion to absolute magnitudes assumes a distance modulus of 19.54 mag and E(B-V)=0.02." + Errors in the determination of the imp location are of about 0.1 mag., Errors in the determination of the bump location are of about 0.1 mag. + Alajewskietal.(1999). also detected those two bumps within the central10... but associated the second one with he RGB bump of a more metal-poor population.," \cite{MAJ99} also detected those two bumps within the central, but associated the second one with the RGB bump of a more metal-poor population." + Indeed. he AGB bump of a population of metallicity Fe/ll]z—1.5 is located at the same position on the CMD as is the RGB imp of a population of metallicity Fe/Il]2.," Indeed, the AGB bump of a population of metallicity $\simeq -1.5$ is located at the same position on the CMD as is the RGB bump of a population of metallicity $\simeq -2$." + The V magnitude of the second bump is consistent with the value of AdGABbump)=0.8+0.1 used. by Ferraroct (1999)., The V magnitude of the second bump is consistent with the value of $M_V(AGBbump) = -0.3 \pm 0.1$ used by \cite{FER99}. + Its clear detection can be explained by the fact that he luminosity level of the AGB bump stays fairly constant with the cluster metallicity (e.g. Castellanietal. 1991))., Its clear detection can be explained by the fact that the luminosity level of the AGB bump stays fairly constant with the cluster metallicity (e.g. \citealt{CAS91}) ). + Phe AGB bump being always bluce than the RGB. it explains the detection of this second bump on the blue side of the KGB bv Majewskietal. (1999)..," The AGB bump being always bluer than the RGB, it explains the detection of this second bump on the blue side of the RGB by \cite{MAJ99}. ." + Using. as they did. a division," Using, as they did, a division" +"Our results present a picture where the star formation on sub-kpc scales in AGN host galaxies traces the BHAR in a somewhat sub-linear fashion, while star formation on larger scales only weakly traces the BHAR.","Our results present a picture where the star formation on sub-kpc scales in AGN host galaxies traces the BHAR in a somewhat sub-linear fashion, while star formation on larger scales only weakly traces the BHAR." +" Recently, argued that host galaxy star formation only shows a clear dependence on AGN luminosity for high-luminosity sources (Lagn>1035 erg s! or Mgg>0.1 Mo yr, see their Figure 6), but our results show that this relationship persists towards lower AGN"," Recently, argued that host galaxy star formation only shows a clear dependence on AGN luminosity for high-luminosity sources $L_{AGN}>10^{45}$ erg $^{-1}$ or $\dot{M}_{BH}>0.1$ $_{\odot}$ $^{-1}$, see their Figure 6), but our results show that this relationship persists towards lower AGN" +for hydrogen (Lindgren&Virtamo1979:ChenGold-man1992).,"for hydrogen \citep{lindgren79, chenz92}." + Also. the secoucl condition is relevaut ouly to the inner orbitals which are not iuportaut for N-rav spectroscopy since their binding eucreies are high (2 10 keV).," Also, the second condition is relevant only to the inner orbitals which are not important for X-ray spectroscopy since their binding energies are high $>$ 10 keV)." + Iu the presence of a magnetic field. the collective motion of an atom ancl its internal degrees of freedom are coupled. and this coupling modifes the electronics structure of the atom (Pavlov&Moeszaros1993:Potekhin1991).," In the presence of a magnetic field, the collective motion of an atom and its internal degrees of freedom are coupled, and this coupling modifies the electronics structure of the atom \citep{pavlov93, potekhin94}." +. Consequences of this coupling iuclude distortion of the wavefunetions. violation of some dipole selection rules and line broadening.," Consequences of this coupling include distortion of the wavefunctions, violation of some dipole selection rules and line broadening." + Most work ou these finite unclear mass effects has been performed on hydrogen atoms (Laiidakisetal.1996:Potekhiu1998) aud hwdrogenic ious Dezehastuovetal.1998).," Most work on these finite nuclear mass effects has been performed on hydrogen atoms \citep{lai92, pavlov93, potekhin94, kopidakis96, potekhin98-2} and hydrogenic ions \citep{bezchastnov98}." +. The inuuediate impact on our work is that the ΟΠΟΙΟΥ. levels aud oscillator streueths are affected by rese collective effects., The immediate impact on our work is that the energy levels and oscillator strengths are affected by these collective effects. + Tn this section we briefly review ie collective motion and the theoretical framework for addressing it., In this section we briefly review the collective motion and the theoretical framework for addressing it. + In this paper we do not relax the assuuption of an infinite nuclear mass in the Uamiltoniau., In this paper we do not relax the assumption of an infinite nuclear mass in the Hamiltonian. +" This ‘acilitates direct mmuuerie comparison of our AICPID approach with other approaches for solvine the strong naenetic field Παιονία, since they also assumed infinite nuclear mass."," This facilitates direct numeric comparison of our $^3$ approach with other approaches for solving the strong magnetic field Hamiltonian, since they also assumed infinite nuclear mass." + We do explain. iu light of previous work on lydrogcnic svstenis. how we will incorporate he collective motion into the MCPIP technique in a subsequent paper.," We do explain, in light of previous work on hydrogenic systems, how we will incorporate the collective motion into the $^3$ technique in a subsequent paper." + Iu the case of the bound-bound ransitions of interest to us we describe the straightforward Incorporation of finite nuclear nass into the oscillator streneth calculation., In the case of the bound-bound transitions of interest to us we describe the straightforward incorporation of finite nuclear mass into the oscillator strength calculation. + This is appropriate since previous ivdrogeu work also included the effects of the finite nuclear nass on the oscillator streugtlis., This is appropriate since previous hydrogen work also included the effects of the finite nuclear mass on the oscillator strengths. + The finite nuclear mass treatment is quite complicated in hydrogen aud las not really be dealt with previously for ueher Z atoms., The finite nuclear mass treatment is quite complicated in hydrogen and has not really be dealt with previously for higher $Z$ atoms. + We outline in this section how substautial siuplificatious of this problem arise when considering voth the specifics of higher Z systems iu general aud he requirements of N-ray spectroscopic modeling iu articular., We outline in this section how substantial simplifications of this problem arise when considering both the specifics of higher $Z$ systems in general and the requirements of X-ray spectroscopic modeling in particular. +" When the nuclear mass is uot assumed to be iufiuite the Hamiltonian. imceludius a term for nuclear motion. can be separated iuto center-of-mass (CAD) aud relative coordinates by a canonical transformation. vieldiug where Z£., aud {νε are the Tamiltonian for the CAL motion and the internal part."," When the nuclear mass is not assumed to be infinite the Hamiltonian, including a term for nuclear motion, can be separated into center-of-mass (CM) and relative coordinates by a canonical transformation, yielding where $H_{cm}$ and $H_{int}$ are the Hamiltonian for the CM motion and the internal part." + There is a scaling law for If; from the infinite nuclear mass case (corresponding to the ILuuitoniau in equation (2))) to the finite mass case (Pavlov-Verevikin&Zhilinskii1980:Beckeuetal. 1999).," There is a scaling law for $H_{int}$ from the infinite nuclear mass case (corresponding to the Hamiltonian in equation \ref{5.1}) )) to the finite mass case \citep{pavlov-verevkin80-1, becken99}." +. Even when there is no trauslation motion of the atom. there is an additional term mhQp (i is the τ-conrponeut of angular 1iomienutum and 05 is the evclotrou frequency of the nucleus) arising from the evelotrou motion of the uucleus (hereafter we call this terii as the nuclear evelotron term).," Even when there is no translation motion of the atom, there is an additional term $m\hbar\Omega_B$ $m$ is the $z$ -component of angular momentum and $\Omega_B$ is the cyclotron frequency of the nucleus) arising from the cyclotron motion of the nucleus (hereafter we call this term as the nuclear cyclotron term)." + Due to the nuclear cvclotron term. the large m) states are autoionized (Ixopidakisetal.1996).," Due to the nuclear cyclotron term, the large $m$ states are autoionized \citep{kopidakis96}." +". Since this term conuuutes with the ILbEuniltonian. it is easv to jmplement as an additive term im T;,;"," Since this term commutes with the Hamiltonian, it is easy to implement as an additive term in $H_{int}$." + Less straightforward to handle is the coupling term Lf..., Less straightforward to handle is the coupling term $H_c$. + This term arises because the motion of the CAL through the magnetic field iuduces an clectric field the so-called motional Stark effect., This term arises because the motion of the CM through the magnetic field induces an electric field – the so-called motional Stark effect. + The motional Stark field acts as a dipole clectric field which increases the separation between electron and nucleus aud therefore decreases the binding cherey compared to the infinite nuclear mass case., The motional Stark field acts as a dipole electric field which increases the separation between electron and nucleus and therefore decreases the binding energy compared to the infinite nuclear mass case. + Z7. can be expressed as: where M is the nuclear mass aud οὐ is the relativo coordinate between the uucleus aud the electron., $H_c$ can be expressed as: where $M$ is the nuclear mass and $\vec{r}$ is the relative coordinate between the nucleus and the electron. + A—&cQsr)feisthe pscudomomentum where 72ροές represents the kinetic momentum.," $\vec{K} = \vec{\pi} - e(\vec{B}\times\vec{r})/c$ is the pseudomomentum, where $\vec{\pi} = \vec{p}+e\vec{A}/c$ represents the kinetic momentum." + The pseudomonmoenutuu conuuutes with the ILuniltonmian aud therefore ds a constant of inotioun., The pseudomomentum commutes with the Hamiltonian and therefore is a constant of motion. + The pseudomeomentium defues a separation between the euiding ceuters of the nucleus aud the electrou: 7UNNB)., The pseudomomentum defines a separation between the guiding centers of the nucleus and the electron; $\vec{r}_c = \case{c}{eB^2}(\vec{K} \times\vec{B})$. + The components of the pseudomonmoentuni conuuute for neutral atoms. while they do not commute for a charged system (Bave&Vincke1990).," The components of the pseudomomentum commute for neutral atoms, while they do not commute for a charged system \citep{baye90}." +. The iuotfionid Stark field) breaks the cevlindiical svinmnetry which is present by the central Coulomb) field in the infinite nuclear mass case., The motional Stark field breaks the cylindrical symmetry which is present by the central Coulomb field in the infinite nuclear mass case. + As a result the system observables eeucrallv depend ou Jv. the transverse component of the pseudonmonenutuu.," As a result the system observables generally depend on $K_{\perp}$ , the transverse component of the pseudomomentum." + For mstance. we express the binding οποίος of au electron in an orbital Gn.Up) as €jpotIa).," For instance, we express the binding energy of an electron in an orbital $(m,\nu)$ as $\epsilon_{m\nu}(K_{\perp})$." +" States can be classified according o the relative size of A, compared to a critical »eudomonoentunm A,~(2Me,,,00))!3 and €o(0) Is the iudiug energv of the electron iu a nonauovius atom."," States can be classified according to the relative size of $K_{\perp}$ compared to a critical pseudomomentum $K_c +\sim (2M\epsilon_{m\nu}(0))^{1/2}$ and $\epsilon_{m\nu}(0)$ is the binding energy of the electron in a non-moving atom." +" When A,«A. the ceutral Coulomb field. exceeds he Stark field: this is called a centered state.", When $K_{\perp}I. the Stark field dominates and it separates the electron frou its equilibria (Coulomb) position arouud he nucleus: this is a deceutered state., When $K_{\perp} > K_c$ the Stark field dominates and it separates the electron from its equilibrium (Coulomb) position around the nucleus; this is a decentered state. + Treatment of collective effects in the Παποαι epeuds on whether a state is centered or deceutered., Treatment of collective effects in the Hamiltonian depends on whether a state is centered or decentered. + For decentered states a coordinate system ο=£F6 is useful because the coupling term 1. becomes zero in the transformed Wamiltonian ΠΠ.," For decentered states a coordinate system $\vec{r}\,' = \vec{r}-\vec{r}_c$ is useful because the coupling term $H_c$ becomes zero in the transformed Hamiltonian $H'$." + Instead the nuclear Coulomb term is shifted by ιν requiring evaluation of matrix clemenuts at each A.," Instead the nuclear Coulomb term is shifted by $\vec{r}_c$, requiring evaluation of matrix elements at each $K_{\perp}$." + For nearly centered states the motional Stark effect can be treated by considering the coupling term 1. as a perturbation to theinfinite nuclear mass solution (Pavlov&Meszaros1993)., For nearly centered states the motional Stark effect can be treated by considering the coupling term $H_c$ as a perturbation to theinfinite nuclear mass solution \citep{pavlov93}. +. Iu the perturbation method binding energy is given by. ALL is the transverse mass; which can be obtained by the 2ud order perturbation. since the bound states are non-," In the perturbation method binding energy is given by, $M^{\perp}_{m\nu}$ is the transverse mass, which can be obtained by the 2nd order perturbation, since the bound states are non-degenerate." + The transverse mass islarger than the atomic mass M (nass anisotropy]., The transverse mass islarger than the atomic mass $M$ (mass anisotropy). + Non-perturbative calculation was first studied by Viucke (1992).., Non-perturbative calculation was first studied by \citet{vincke92}. . + Potekhin(1991). studied binding cucreics. oscillator streneths and size of mowviug bydrogen ato bv the imulti-coufigurational method.," \citet{potekhin94} studied binding energies, oscillator strengths and size of moving hydrogen atom by the multi-configurational method." + Potekhin(1998) ," \citet{potekhin98-2} + " +As discussed. above. discs have higher mass at earlier evolutionary stages.,"As discussed above, discs have higher mass at earlier evolutionary stages." + At Class LL. the fraction. of objects hosting 2-25 MMSN is around Is in the reeime of Jupiter-building models. and also matching the 15 of gas-giant planet πω... inferred. around mature stars (Cummingetal.2008)..," At Class I, the fraction of objects hosting 2-25 MMSN is around 18, in the regime of Jupiter-building models, and also matching the 18 of gas-giant planet systems inferred around mature stars \citep{cumming}." + However. if planetary cores can erow this early on which could indeed occur if migration were to accelerate the core growth as noted above — then in principle the process coud even start in the Class 0 protostar phase. within the first OL Myr.," However, if planetary cores can grow this early on – which could indeed occur if migration were to accelerate the core growth as noted above – then in principle the process could even start in the Class 0 protostar phase, within the first 0.1 Myr." + At this time the central objec is only partly. acereted. and much of the mass of the svstem is sti Lina circumstellar envelope.," At this time the central object is only partly accreted, and much of the mass of the system is still in a circumstellar envelope." + Alillimetre photometry will be dominated by the envelope Ilux. but many of he Class 0 objects have now been studied with millimere-wavelength interferometry.," Millimetre photometry will be dominated by the envelope flux, but many of the Class 0 objects have now been studied with millimetre-wavelength interferometry." + This resolves out the large-scale. envelope emission. leaving in most cases a compact or point-like signal attributed to à very voung disc.," This resolves out the large-scale envelope emission, leaving in most cases a compact or point-like signal attributed to a very young disc." + ‘Table 3 ists these interferomoetry-based results. in order of increasing disc mass.," Table 3 lists these interferometry-based results, in order of increasing disc mass." + The mass estimates were mace with cdillerent methods ancl assumed. temperatures and emissivities. and may be lower limits at z1 mm if the inner disc has non-negligible opacity. so only rough comparisons may be made.," The mass estimates were made with different methods and assumed temperatures and emissivities, and may be lower limits at $\approx 1$ mm if the inner disc has non-negligible opacity, so only rough comparisons may be made." + However. among these. 19 Class 0 objects. half now host upwards of 2 ALAISN. increased three-fold over the equivalent population within Class L This continues the trend. of finding more substantial dises at each earlier phase studied. and is very promising for forming many luture. planetary. systems.," However, among these 19 Class 0 objects, half now host upwards of 2 MMSN, increased three-fold over the equivalent population within Class I. This continues the trend of finding more substantial discs at each earlier phase studied, and is very promising for forming many future planetary systems." + In addition. as the protostar is largely assembled in the Class O phase. it must for part of this period have much less than its final mass.," In addition, as the protostar is largely assembled in the Class 0 phase, it must for part of this period have much less than its final mass." +" Therefore. as the disces are mostly substantial. AM;/Mausu, can be high. raising the possibility of forming planets. by the alternative mechanism: where gravitational instability. leads. to disc fragmentation."," Therefore, as the discs are mostly substantial, $M_{disc}/M_{star}$ can be high, raising the possibility of forming planets by the alternative mechanism where gravitational instability leads to disc fragmentation." + To attempt to quantify this. we estimate masses for the protostars assuming that the bolometric luminositv is supplied by the energy. released. in infall.," To attempt to quantify this, we estimate masses for the protostars assuming that the bolometric luminosity is supplied by the energy released in infall." + The accretion rate is taken to be LO7 M. [| ie. building most. of an~|M. star in about 0.1. Myr (evansetal.2009).," The accretion rate is taken to be $10^{-5}$ $_{\odot}$ $^{-1}$ , i,e, building most of an $\sim 1~M_{\odot}$ star in about 0.1 Myr \citep{evans}." +". The mass of the protostar Als. is then derived. from big=(611dALfdiRoa. taking Row, to be zSR. alter André&Alontmerle(1994)..."," The mass of the protostar $M_{star}$ is then derived from $L_{bol} = (G M_{star} dM/dt) / R_{star}$, taking $R_{star}$ to be $\approx 5 R_{\odot}$ after \citet{am}." + “Phe protostellar racii have not been measured but for pre-main-sequence phases should be moderately independent of mass (Whitneyetal., The protostellar radii have not been measured but for pre-main-sequence phases should be moderately independent of mass \citep{whitney04}. + 2004).. ALMaus values may be uncertain by factors up to à few. as dise opacities. stellar radii and aceretion rates are not known for individual svstenis.," $M_{disc}/M_{star}$ values may be uncertain by factors up to a few, as disc opacities, stellar radii and accretion rates are not known for individual systems." + The estimates in Table 3 suggest that halfo “the dises should be unstable to fragmentation. with AL;Matar οἱ roughly 0.3 or more.," The estimates in Table 3 suggest that half of the discs should be unstable to fragmentation, with $M_{disc}/M_{star}$ of roughly 0.3 or more." + In four cases. the disc appears to actualy oul-weigh the star. as in some mocels of άσσο&Cuillo(2005):Riceetal.," In four cases, the disc appears to actually out-weigh the star, as in some models of \citet{hg05,rma}." + (2009).. The stellar masses are low. as expected if the stars are not vet.fully ilt.," The stellar masses are low, as expected if the stars are not yetfully built." + The protostars estimated to be the most massive also tend to, The protostars estimated to be the most massive also tend to +l)Ów.,. + For logarithmic grids. the same condition reads: ποο”...re1 where Fu—ulE is the οσαας increment of the photon exid.," For logarithmic grids, the same condition reads: $\omega_{\rm{max}}/\omega_{\rm{min}} > r_\omega^{n-1} $ where $r_\omega=\omega^{i+1}/\omega^{i} $ is the logarithmic increment of the photon grid." +" By denoting R, the number of bius per decade cucrey. ic. the resolution of the photou erid. and ep,=1067lH.1 he condition for the integral approach to be valid reads: When the resolution is huge enough: ej,7δη 1}."," By denoting $R_\omega$ the number of bins per decade energy, i.e. the resolution of the photon grid, and $\epsilon_{\rm{I,\omega}}=10^{(n-1)/R_\omega}-1$, the condition for the integral approach to be valid reads: When the resolution is large enough: $\epsilon_{\rm{I},\omega} \approx 2 (n-1)/R_\omega$ ." +" Ποπονα, as à ds typically of several. (οDAR can be larger than unity for low resolution runs aud the exact relation must be used."," However, as $n$ is typically of several, $(n-1)/R_\omega$ can be larger than unity for low resolution runs and the exact relation must be used." +" The condition 16 Is satisfied in a well defined region of the (p.w) space,"," The condition \ref{eq_bdr_I_photons} is satisfied in a well defined region of the $(p,\omega)$ space." + Usiug Eq., Using Eq. + 19 and 20 to compute the scattered distribution width. one can write an equation in w for the boundary of this region.," \ref{bdr1} and \ref{bdr2} to compute the scattered distribution width, one can write an equation in $\omega$ for the boundary of this region." + It is the solution of a 2ud order polvuoimial aud the direct nunuerical iuteeration is found to be accurate for all photon aud particle energieserccept iu the region where: with The inverse equation pr(z) for this boundary would be more practical since it would be mono-valued. and could be used directly in the combined approach (see hereafter)., It is the solution of a 2nd order polynomial and the direct numerical integration is found to be accurate for all photon and particle energies in the region where: with The inverse equation $p_{\rm I}(\omega)$ for this boundary would be more practical since it would be mono-valued and could be used directly in the combined approach (see hereafter). + It is the solution of a high order polvuonmial aud is most easily found unuuerically., It is the solution of a high order polynomial and is most easily found numerically. + Bouudarics for the integral approach are shown in Fie., Boundaries for the integral approach are shown in Fig. + 5 for Ryoc0200.930.97.13.3.8.2.0.1.3 aud s=b.," \ref{fig_photons} for $R_\omega \approx 9200,930,97,13,3.8,2.0,1.3$ and $n=5$." + For comparison typical ruus have a resolution. Ry.=1 30., For comparison typical runs have a resolution $R_\omega=1-30$ . + In the case πω=19. oulv the scatterius of low euerev photous (fv«200 keV) off subaclativistic particles (p« 0.2) is inaccuratelv described by the inteeral approach.," In the case $R_\omega=13$, only the scattering of low energy photons $h\nu < 200$ keV) off sub-relativistic particles $p < 0.2$ ) is inaccurately described by the integral approach." + Although it is not general. the inteeral method for the photon equation can thus be used to address many of astrophysical situations. such as those involving high euerev particles.," Although it is not general, the integral method for the photon equation can thus be used to address many of astrophysical situations, such as those involving high energy particles." + Ideuticallhv. the integral approach for particles is valid when the width of the scattered distribution is larger than theparticle biu size.," Identically, the integral approach for particles is valid when the width of the scattered distribution is larger than theparticle bin size." +" For logarithmic erids this condition 1s: μμμία7rm* where Πο=VIEDuoμμμμ]ld are the largest and smallest momenta of the scattered particle distribution aud +),=pillyy pois the logarithiuic increment of the particle eric.", For logarithmic grids this condition is: $p_{\rm{max}}/p_{\rm{min}} > r_p^{n-1} $ where $p_{\rm{max/min}}=\sqrt{(\gamma+\omega-\omega_{\rm{min/max}})^2-1}$ are the largest and smallest momenta of the scattered particle distribution and $r_p=p^{i+1}/p^i$ is the logarithmic increment of the particle grid. +" By defining 72, aud εν as for the photons. it vields: Contrary to the photon case. there is no simple equation for the boundary defining this region aud the iupliit equation 51 must be solved uumerically."," By defining $R_p$ and $\epsilon_{{\rm I},p}$ as for the photons, it yields: Contrary to the photon case, there is no simple equation for the boundary defining this region and the implicit equation \ref{eq_I_particles} must be solved numerically." + The boundary ον] is computed easilv since there is ouly oue positive solution to the equation on w and it happens to be always siiller than wy)(y}., The boundary $\omega_{\rm I}(p)$ is computed easily since there is only one positive solution to the equation on $\omega$ and it happens to be always smaller than $\omega_0^*(p)$ . + A simple approximation for this boundary. accurate in all regimes to better than 30%. is: When the resolution is good enough (2.=>1. εν<>1$, $\epsilon_{{\rm I},p} << 1$ ), condition \ref{eq_I_particles} reduces to that used in Eq." +" 78 of Vir&Poutanen(2009) or electron down-scattermeg: w>ey,/(105) for relativistic particles."," 78 of \citet{Poutanen08} for electron down-scattering: $\omega > \epsilon_{{\rm I},p}/(4\gamma)$ for relativistic particles." + Fie., Fig. +" 6 shows this boundary for various resolutions (GIU,=9200.930.97.10.2,8.2.0.1.3 and à—5)."," \ref{fig_bdr_part} shows this boundary for various resolutions $R_p \approx 9200,930,97,13,3.8,2.0,1.3$ and $n=5$ )." + Contrary to the equation for photons. solving the evolution equation for particles with a simple uumuerical integration requires very high resolutiou to guarantee a correct accuracy.," Contrary to the equation for photons, solving the evolution equation for particles with a simple numerical integration requires very high resolution to guarantee a correct accuracy." +" For example. soft photons of energv w=E107a scattering. offJ highB euergv particlesH (5=107)D are accuratelv described by the integral approach ouly if R,>900. which is far ονομα current desktop computer capabilities arc the constraint is even more severe when wuldly relativistic particles are involved."," For example, soft photons of energy $\omega=10^{-5}$ scattering off high energy particles $\gamma=10^2$ ) are accurately described by the integral approach only if $R_p > 900$, which is far beyond current desktop computer capabilities and the constraint is even more severe when mildly relativistic particles are involved." + If conditions 16 aud 5j ire not satisfie OVer the chtire sinulation domain. nuuerical computation of the Compton scattering iav lead to macceuracy.," If conditions \ref{eq_bdr_I_photons} and \ref{eq_I_particles} are not satisfied over the entire simulation domain, numerical computation of the Compton scattering may lead to inaccuracy." + Iu particular. energv ds not couserved when logarithiiic grids are used (as explained before). and its measure provides a good way fo estimate muuerical," In particular, energy is not conserved when logarithmic grids are used (as explained before), and its measure provides a good way to estimate numerical." +, Fig. +"errors”, Fie. 7 shows the error on energv when soft monoe-cucrectic photos are upeseattered bv lieh αιαον particles.", \ref{int_prec} shows the error on energy when soft mono-energetic photons are up-scattered by high energy particles. + The nuucerical conputatioun was performed with the code presented. iu Dehuonutetal.(2008).. on a single time step. using anu explicit scheme on logarithuuc euergv erids. aud turning off all processes/iujection/escape but Compton scatteriug.," The numerical computation was performed with the code presented in \citet{Belmont08}, on a single time step, using an explicit scheme on logarithmic energy grids, and turning off all processes/injection/escape but Compton scattering." + The contribution of Compton scattering was forced to be colmputed by the inteeral approach for the equation on yarticles., The contribution of Compton scattering was forced to be computed by the integral approach for the equation on particles. + The contribution to the equation on photons was also computed with the integral approach but eiven the energv range and the erid resolution considered here. this nethod is accurate in this case.," The contribution to the equation on photons was also computed with the integral approach but given the energy range and the grid resolution considered here, this method is accurate in this case." + Both initial distributions were set to zero except in one euerev biu. and they were rorlualised to unitv toseep the number of scattering events coustant as the photon energy is varied.," Both initial distributions were set to zero except in one energy bin, and they were normalised to unity tokeep the number of scattering events constant as the photon energy is varied." +" The error was measured by computing the total enerev lost by yarticles HE, aud comparing it to the cuerey gained by photons QR E.", The error was measured by computing the total energy lost by particles $\partial_t E_p$ and comparing it to the energy gained by photons $\partial_t E_\omega$ . + For low cucrey photous. the scattering takes place far low the boundarym the (pew) plane of Fie. 6..," For low energy photons, the scattering takes place far below the boundaryin the $(p,\omega)$ plane of Fig. \ref{fig_bdr_part}. ." + The, The +obtained using the distribution of cluster galaxies. gravitationally lensed images (??) and the X-ray emission from the intra-cluster plasma (?)..,"obtained using the distribution of cluster galaxies, gravitationally lensed images \citep{Clowe+06,MilvangJensen+08} and the X-ray emission from the intra-cluster plasma \citep{Johnson+06}." +" In. the spherically-symmetric.— Jeans analysis. our observables are the galaxy number density profile N(R,) and the los velocity dispersion profile oyj,,(R,)."," In the spherically-symmetric Jeans analysis, our observables are the galaxy number density profile $N(R_n)$ and the los velocity dispersion profile $\sigma_{los}(R_n)$." +" N(R,). 1s uniquely related to the 3-dimensional (3-d) galaxy number density profile v(7,) via the Abel inversion equation. where r,=r/roog 1s the 3-d clustercentric radius in normalized units."," $N(R_n)$ is uniquely related to the 3-dimensional (3-d) galaxy number density profile $\nu(r_n)$ via the Abel inversion equation, where $r_n \equiv r/r_{200}$ is the 3-d clustercentric radius in normalized units." +" The other observable. c;,,(R,) is related to the cluster mass profile. M(r,). and the cluster velocity anisotropy profile. where «νι». «ντ» are the mean squared tangential and radial velocity components. which reduce to c7 and oc respectively. in the absence of bulk motions and net rotation."," The other observable, $\sigma_{los}(R_n)$ is related to the cluster mass profile, $M(r_n)$ , and the cluster velocity anisotropy profile, where $\rm{<} v_t^2 \rm{>}$, $\rm{<} v_r^2 \rm{>}$ are the mean squared tangential and radial velocity components, which reduce to $\sigma_t^2$ and $\sigma_r^2$ respectively, in the absence of bulk motions and net rotation." +" Given Mtr) and BGr,). the observable cj,(R,) follows through (2) and (3) where G is the gravitational constant."," Given $M(r_n)$ and $\beta(r_n)$, the observable $\sigma_{los}(R_n)$ follows through \citep{vanderMarel94} + and \citep{BM82} + where $G$ is the gravitational constant." + Note that in practice the upper limit of the integrals in the above equations is set to à finite radius (typically 20 in the integration units). large enough às to ensure that the result of the integration does not change significantly by pushing the limit to larger values.," Note that in practice the upper limit of the integrals in the above equations is set to a finite radius (typically $20$ in the integration units), large enough as to ensure that the result of the integration does not change significantly by pushing the limit to larger values." +" It is therefore possible to adopt parameterized model representations of Λο) and f(r,) and determine the best-fit parameters by comparing the observed co,,(R,,) profile with the predicted one. using the y statistics and the uncertainties on the observed profile."," It is therefore possible to adopt parameterized model representations of $M(r_n)$ and $\beta(r_n)$ and determine the best-fit parameters by comparing the observed $\sigma_{los}(R_n)$ profile with the predicted one, using the $\chi^2$ statistics and the uncertainties on the observed profile." + From the eqs., From the eqs. +" above it is however clear that different combinations of the mass and anisotropy profiles can produce the same los velocity dispersion profile. the so-called “mass—anisotropy"" degeneracy."," above it is however clear that different combinations of the mass and anisotropy profiles can produce the same los velocity dispersion profile, the so-called ``mass--anisotropy'' degeneracy." + Different methods exist to solve this degeneracy (see.e.g..2222)..," Different methods exist to solve this degeneracy \citep[see, + e.g.,][]{Merritt87,vanderMarel+00,LM03,WT06}." + These methods are effective for data-sets of ~1000 tracers of the gravitational potential., These methods are effective for data-sets of $\sim 1000$ tracers of the gravitational potential. + Given the smaller size of our distant clusters data-set we here adopt another method. recently suggested by ? for application to the case of dwarf galaxies.," Given the smaller size of our distant clusters data-set we here adopt another method, recently suggested by \citet{Battaglia+08} + for application to the case of dwarf galaxies." +" The method of ? consists in considering not one. but two different tracers of the cluster gravitational potential. so that there are two observables (the los velocity dispersion profiles of the two tracers) to solve for the two unknowns. M(r,) and BU)."," The method of \citet{Battaglia+08} consists in considering not one, but two different tracers of the cluster gravitational potential, so that there are two observables (the los velocity dispersion profiles of the two tracers) to solve for the two unknowns, $M(r_n)$ and $\beta(r_n)$." +" Since M(r,) must be the same for both tracers. but B(r,) can in principle be different. the degeneracy is only partially broken. however the constraints on the dynamics of the system are significantly stronger than with a sigle tracer."," Since $M(r_n)$ must be the same for both tracers, but $\beta(r_n)$ can in principle be different, the degeneracy is only partially broken, however the constraints on the dynamics of the system are significantly stronger than with a single tracer." + Of course. this method works only if the two tracers have different projected phase-space distributions.," Of course, this method works only if the two tracers have different projected phase-space distributions." + This is the case of cluster nELGs and ELGs. which we therefore adopt as our two populations of tracers.," This is the case of cluster nELGs and ELGs, which we therefore adopt as our two populations of tracers." +" In practice. we adopt parameterized models for MG;,) and BG). solve eqs.(1)). (3)). and (4)) separately for nELGs and ELGs in each of the two stacked clusters. and jointly compare the solutions to the observed c,,(R,) of the two galaxy populations."," In practice, we adopt parameterized models for $M(r_n)$ and $\beta(r_n)$, solve \ref{eq:abel}) ), \ref{eq:sigmar}) ), and \ref{eq:sigmalos}) ) separately for nELGs and ELGs in each of the two stacked clusters, and jointly compare the solutions to the observed $\sigma_{los}(R_n)$ of the two galaxy populations." +" Say c7,5,; and Coder; the observed and predicted σι of a given population of tracers (nELG or ELG). in the ;-th of ; radial bins. and say 6; the corresponding c uncertainty on c,5,;."," Say $\sigma_{obs,i}$ and $\sigma_{model,i}$ the observed and predicted $\sigma_{los}$ of a given population of tracers (nELG or ELG), in the $i$ -th of $m$ radial bins, and say $\delta_i$ the corresponding $\sigma$ uncertainty on $\sigma_{obs,i}$." +" We find the best-fit parameter of the model representing M(r,) and its uncertainties by minimizing with Since M(r,) must be unique for the two populations. we then adopt the joint best-fit solution for M(r,) and solve again eqs.(3)) and (4)) separately for nELGs and ELGs to determine thebest-fit parameters (and uncertainties) of their £-profiles through the y minimization. eq.(6)). i.e. we marginalize over Mr) to constrain the two £(r,) solutions."," We find the best-fit parameter of the model representing $M(r_n)$ and its uncertainties by minimizing with Since $M(r_n)$ must be unique for the two populations, we then adopt the joint best-fit solution for $M(r_n)$ and solve again \ref{eq:sigmar}) ) and \ref{eq:sigmalos}) ) separately for nELGs and ELGs to determine thebest-fit parameters (and uncertainties) of their $\beta$ -profiles through the $\chi^2$ minimization, \ref{eq:chi2}) ), i.e. we marginalize over $M(r_n)$ to constrain the two $\beta(r_n)$ solutions." + The choice of the models cannot be too generic nor too restrictive., The choice of the models cannot be too generic nor too restrictive. + [f it i$ too restrictive. we might find it difficult to find," If it is too restrictive, we might find it difficult to find" +The observational data for the cluster 77006. used to apply our method. were obtained with the Telescope at SAO RAS equipped with the k-5s5 CCD-detector in B.V.R. Johuson - Cousins passbauds (Crerashchenko. 2007).,"The observational data for the cluster 7006, used to apply our method, were obtained with the Zeis-1000 Telescope at SAO RAS equipped with the K-585 CCD-detector in $B, V, R_c$ Johnson - Cousins passbands (Gerashchenko, 2007)." + T7006 is a cluster of intermediate metallicity: its values. determined by various methods. vary within broad limits (see Table 2).," 7006 is a cluster of intermediate metallicity; its values, determined by various methods, vary within broad limits (see Table 2)." + After rejection of several extreme values. the average [F'e/I7] = 11.59.," After rejection of several extreme values, the average $[Fe/H]$ = 1.59." + luteuse studies of 77006 carried out by Sandage and Wildev (1967) showed that its ITB morphology does not correspond to its inetallicitv., Intense studies of 7006 carried out by Sandage and Wildey (1967) showed that its HB morphology does not correspond to its metallicity. + Later ou. au eutire eroup of intermeciatc-uetallicity clusters was found. in which TB appears to be redder than it should be for a given metallicity: this discrepaucy. known as the xobleim of the second parameter. has still not explained.," Later on, an entire group of intermediate-metallicity clusters was found, in which HB appears to be redder than it should be for a given metallicity; this discrepancy, known as ""the problem of the second parameter"", has still not explained." + At the beginning of the 90-ies. in the study of Duouauno et al.1991) it was assumed that the WB color teuds o be bluer with a decrease in the distance from the cluster center.," At the beginning of the 90-ies, in the study of Buonanno et al.(1991) it was assumed that the HB color tends to be bluer with a decrease in the distance from the cluster center." +" In our study (Cerashchenko. 2007). it was sroved for distances from the center of a cluster up to r215”,"," In our study (Gerashchenko, 2007), it was proved for distances from the center of a cluster up to $r\geq15^{\prime\prime}$." + Iu addition to that. in the above study. using the relations obtained in the study of Ferraro ct al.(1999) )etwoeen metallicity and CB parameters derived frou the Wes.(Okms~!, generally has |Z|>5 kpe."," The Halo I sub-population with $\feh \sim -1.3$ and $\Vrot > 0 \kmprs$, generally has $|Z| > 5$ kpc." +" Since it is well accepted that the edge of the thick disk is at about 5.5 kpc above the Galactic plane as suggested by Majewski (1994), and since we have measured scale height for the thick disk of |Z|=1.2+0.3 kpc, awe suggest this sub-population, Halo I, really corresponds to the halo."," Since it is well accepted that the edge of the thick disk is at about 5.5 kpc above the Galactic plane as suggested by Majewski (1994), and since we have measured a scale height for the thick disk of $|Z|=1.2\pm 0.3$ kpc, we suggest this sub-population, Halo I, really corresponds to the halo." +" In connection with the halo population, our result confirms with the existence of the inner and the outer halo sub-population in the R - diagram."," In connection with the halo population, our result confirms with the existence of the inner and the outer halo sub-population in the $R$ - $|Z|$ diagram." +" From the [Fe/H] - |Z| diagram, it hints that |Z|the inner halo shows a metallicity gradient while the outer halo does not."," From the $\feh$ - $|Z|$ diagram, it hints that the inner halo shows a metallicity gradient while the outer halo does not." +" From our data, we cannot detect any sign of stellar streams reported before due to the selection effect of the spectroscopic survey of the SDSS project and the star number in our sample is too small for detecting any overdensity produced by stellar streams."," From our data, we cannot detect any sign of stellar streams reported before due to the selection effect of the spectroscopic survey of the SDSS project and the star number in our sample is too small for detecting any overdensity produced by stellar streams." +" Based on photometric and spectral data, a group of RHB stars have been selected from the SDSS survey, whose distances can be estimated by using the calibrations from Chen et "," Based on photometric and spectral data, a group of RHB stars have been selected from the SDSS survey, whose distances can be estimated by using the calibrations from Chen et (2009)." +"Combining with available proper motions from the ((2009).USNO survey and radial velocities from the SDSS survey, the space velocities (U,V,W) have been calculated for a sample of 5391 RHB stars, and their metallicities and kinematical gradients have been investigated in order to trace the evolution of the Galaxy."," Combining with available proper motions from the USNO survey and radial velocities from the SDSS survey, the space velocities (U,V,W) have been calculated for a sample of 5391 RHB stars, and their metallicities and kinematical gradients have been investigated in order to trace the evolution of the Galaxy." + The main results are as follows. (, The main results are as follows. ( +"1) There are two peaks in the metallicity distributions of RHB stars with a division at [Fe/H]~—0.9. Stars with [Fe/H]> —0.9, centered at [Fe/H]~—0.6, correspond to the thick-disk population, while stars with [Fe/H]<—0.9, peaking at [Fe/H]~—1.3, have generally halo kinematics in the Toomre diagram.","1) There are two peaks in the metallicity distributions of RHB stars with a division at $\feh \sim -0.9$ Stars with $\feh > -0.9$, centered at $\feh \sim -0.6$, correspond to the thick-disk population, while stars with $\feh < -0.9$, peaking at $\feh \sim -1.3$, have generally halo kinematics in the Toomre diagram." + The metallicity gradient for thick disk stars with —0.9<[Fe/H]—0.3 is significant with [Fe/H]=—0.255|Z|+0.02., The metallicity gradient for thick disk stars with $-0.9 < \feh < -0.3$ is significant with $\feh = -0.255|Z|+0.02$. +" RHB stars from the thick disk with |Z|<5 kpc have a peak metallicity of [Fe/H]~—0.6 dex, a peak rotation velocity of Veot~170kms-!, and a vertical scale height of |Z|~1.2 kpe. ("," RHB stars from the thick disk with $|Z|<5$ kpc have a peak metallicity of $\feh \sim -0.6$ dex, a peak rotation velocity of $\Vrot \sim 170\,\kmprs$, and a vertical scale height of $|Z| \sim 1.2$ kpc. (" +"2) The division between the thick disk and the halo seems to be quite clear in the [Fe/H] versus |Z| diagram as clearly shown in Figure 8, where the edge of the thick disk could be as high as |Z|~8 kpc at [Fe/H]~—0.6 and reduces to |Z|~2 kpc at [Fe/H]~ -—1.5.Meanwhile, there is a detectable rotational gradient in the thick disk and a nearly constant","2) The division between the thick disk and the halo seems to be quite clear in the $\feh$ versus $|Z|$ diagram as clearly shown in Figure 8, where the edge of the thick disk could be as high as $|Z| \sim 8$ kpc at $\feh \sim +-0.6$ and reduces to $|Z| \sim 2$ kpc at $\feh \sim -1.5$ .Meanwhile, there is a detectable rotational gradient in the thick disk and a nearly constant" +a galaxy remains asvmumetric is 2504 of the total mereer time-scale. but this is a verv unlikely scenario (Lotz ct al.,"a galaxy remains asymmetric is $>$ of the total merger time-scale, but this is a very unlikely scenario (Lotz et al." + 30051., 2008). + We also carrey out a Monte. Carlo. simulation to determine how much influence a small (L0%)) fraction of galaxies in our sample with long CAS time-scales (710 Cyr) would allect our results. finding no sienilicant increase in the measured. time-scale.," We also carry out a Monte Carlo simulation to determine how much influence a small ) fraction of galaxies in our sample with long CAS time-scales $> 10$ Gyr) would affect our results, finding no significant increase in the measured time-scale." + However. simulations suggest that the range of time-scales dillers bv only a factor of 2-3. and a wide time-scale distribution is an unlikely scenario.," However, simulations suggest that the range of time-scales differs by only a factor of 2-3, and a wide time-scale distribution is an unlikely scenario." + We however know that massive galaxies at ο«1.2 still undergo some merging (e.e.. Conselice et al.," We however know that massive galaxies at $z < 1.2$ still undergo some merging (e.g., Conselice et al." + 2008: Bluck et al., 2008; Bluck et al. + 2009). even between two close redshifts.," 2009), even between two close redshifts." + H£ we denote the fraction of galaxies which have begun to undergo a merger between σι and zo as fos then the time-scale τι can be measured as. where the value of. foe needs to. be. determined independently of the change of merger fraction between σι and zo.," If we denote the fraction of galaxies which have begun to undergo a merger between $z_1$ and $z_2$ as $f_{\rm 2,new}$ then the time-scale $\tau_{\rm m}$ can be measured as, where the value of $f_{\rm 2,new}$ needs to be determined independently of the change of merger fraction between $z_1$ and $z_2$." + We explore possible values for f.new. although the value is unlikely to be higher than a few at.<0.7.," We explore possible values for $f_{\rm 2,new}$, although the value is unlikely to be higher than a few at $z < 0.7$." +" TDhis approach can be generalised. by the fact that the value of fouce depends on the merger rate. or the inverse merger rate per galaxy. D. which is measured as EL—zi/fia. anel the evolution of E can be parameterised. as a function of redshift, (Conselice et al."," This approach can be generalised by the fact that the value of $f_{\rm 2,new}$ depends on the merger rate, or the inverse merger rate per galaxy, $\Gamma$, which is measured as $\Gamma = \tau_{\rm m}/f_{\rm gm}$, and the evolution of $\Gamma$ can be parameterised as a function of redshift (Conselice et al." + 2008: Bluck et al., 2008; Bluck et al. + 2008)., 2008). +" lU we measure P in units of 1 Gyr. such that P— ). then by considering the fraction of new mergers. (ewhich is fos=04 /E. then the time-scale 7, is: where the value of Pyays is measured. using a time-scale of 1 Gyr."," If we measure $\Gamma$ in units of 1 Gyr, such that $\Gamma = \Gamma_{\rm 1 gyr} \left(\frac{\tau_{\rm m}}{\rm 1\, Gyr}\right)$ , then by considering the fraction of new mergers, which is $f_{\rm 2,new} = \delta t/\Gamma$ , then the time-scale $\tau_{\rm m}$ is: where the value of $\Gamma_{1\, {\rm gyr}}$ is measured using a time-scale of 1 Gyr." + The values of Poin this paper are measured. in a slightly cifferent way than previously. as the time between successive mergers.," The values of $\Gamma$ in this paper are measured, in a slightly different way than previously, as the time between successive mergers." + Phe value of P we use in equation (7) is based on the merger fractions from Conselice ct al. (, The value of $\Gamma$ we use in equation (7) is based on the merger fractions from Conselice et al. ( +2009b) ($3).,2009b) 3). + The data we use for this paper originates from the study of merger fractions at 2«1.2. published by Consclice et al. (," The data we use for this paper originates from the study of merger fractions at $ z < 1.2$, published by Conselice et al. (" +2009b).,2009b). + Conselice et al. (, Conselice et al. ( +2009b) find that the merger fraction drops steadily at z«1.2. although the most rapid drop is seen at z«0.7.,"2009b) find that the merger fraction drops steadily at $z < 1.2$, although the most rapid drop is seen at $z < 0.7$." + This decline is found in both the Extended ποια Strip (IG) and the Cosmic Evolution Survey (COSMOS)., This decline is found in both the Extended Groth Strip (EGS) and the Cosmic Evolution Survey (COSMOS). + This evolution is shown in detail in Figure 7 ofConselice et al. (, This evolution is shown in detail in Figure 7 of Conselice et al. ( +2009b). in which paper the values we use are also tabulated.,"2009b), in which paper the values we use are also tabulated." + In this paper. we use the individually: measured merger fractions in both the COSMOS and EGS surveys. as well as the combination of the two surveys. to measure the merger. fraction.," In this paper, we use the individually measured merger fractions in both the COSMOS and EGS surveys, as well as the combination of the two surveys, to measure the merger fraction." + We do not. discuss the details. of the caleulation of the merger. fraction. although this. is described in great. detail in Conselice (2003). Conselice et al. (," We do not discuss the details of the calculation of the merger fraction, although this is described in great detail in Conselice (2003), Conselice et al. (" +2008a) and Consclice et al. (,2008a) and Conselice et al. ( +2009a.b).,"2009a,b)." + An important aspect concerning our use of merger fractions within this paper is that they are measured within the same rest-frame wavelength. and in the same way. at different redshilts.," An important aspect concerning our use of merger fractions within this paper is that they are measured within the same rest-frame wavelength, and in the same way, at different redshifts." + Our analysis first consists of examining how eq. (, Our analysis first consists of examining how eq. ( +5) gives an upper limit on the merger time-scale.,5) gives an upper limit on the merger time-scale. + We later we utilise eq. (, We later we utilise eq. ( +7) to measure the merger time-scale for our sample while accounting for any additional mergers that have occurred between τι and co.,7) to measure the merger time-scale for our sample while accounting for any additional mergers that have occurred between $z_1$ and $z_2$. + We carry out our analyses by applying these two equations to various redshift bins of sizes ὃς = OL., We carry out our analyses by applying these two equations to various redshift bins of sizes $\delta z$ = 0.1. + Our resulting time-scales are the average values we find. while the error is the average error on these measurements. elven uncertainties in the measured merger fractions.," Our resulting time-scales are the average values we find, while the error is the average error on these measurements, given uncertainties in the measured merger fractions." + We also describe the scatter in these values at dillerent redshilts., We also describe the scatter in these values at different redshifts. +" When we apply equation (5) to our data the maximum time-scale is my,=L1c0.3 Cir.", When we apply equation (5) to our data the maximum time-scale is $\tau_{\rm m} = 1.1\pm0.3$ Gyr. + That. is. the maximunr time for à CAS asymmetry to last is roughly ~ 1 Gyr.," That is, the maximum time for a CAS asymmetry to last is roughly $\sim$ 1 Gyr." + This is similar to the maximum time-scale found for CAS mergers in N-bocky mocdels by Lotz et al. (, This is similar to the maximum time-scale found for CAS mergers in N-body models by Lotz et al. ( +2008).,2008). + Vhis reveals that any claims that the merger time-scale for CAS assumed to date (c.g.. Conselice 2006a: Lotz et al.," This reveals that any claims that the merger time-scale for CAS assumed to date (e.g., Conselice 2006a; Lotz et al." + 2008) are uncderestimated » more than a factor of 2-3 cannot be correct., 2008) are underestimated by more than a factor of 2-3 cannot be correct. + We now utilize the fact that even when the merger raction is declining there are still ongoing mergers between different redshifts. which will raise the merger fraction. and hus result in an overestimated merger time-scale using eq. (," We now utilize the fact that even when the merger fraction is declining there are still ongoing mergers between different redshifts, which will raise the merger fraction, and thus result in an overestimated merger time-scale using eq. (" +5).,5). + We use equation (7) to caleulate the likely true merger ime-scale. through an examination of the merger rate per galaxy. or the time between mergers. given by D.," We use equation (7) to calculate the likely true merger time-scale, through an examination of the merger rate per galaxy, or the time between mergers, given by $\Gamma$." +" Using equation. (7) the computed. merger. time-scale ranges between O.3+0.3 ον and. 0.90.3. Civr.. with an average value of mj,=0.6£0.3."," Using equation (7) the computed merger time-scale ranges between $\pm0.3$ Gyr and $\pm$ 0.3 Gyr, with an average value of $\tau_{\rm m} = 0.6\pm0.3$." + In general. we find that the computed. merger time-scale is lower at lower redshifts between 2=0.7 and 2=0.2 within the combined. EGS and COSMOS samples.," In general, we find that the computed merger time-scale is lower at lower redshifts between $z = 0.7$ and $z = 0.2$ within the combined EGS and COSMOS samples." + The values we calculate are roughly similar to what N-body models of the merger process find is the time-scale for CAS sensitivity (ο. Conselice 2006a: Lotz et al.," The values we calculate are roughly similar to what N-body models of the merger process find is the time-scale for CAS sensitivity (e.g., Conselice 2006a; Lotz et al." + 2008)., 2008). + Our measurement of merger times is thus likely correct. given the consisteney of independent methods.," Our measurement of merger times is thus likely correct, given the consistency of independent methods." + Our merger time-scale measurement is smaller by roughly a factor of two compared to the results of Ixitzbichler White (2008). who calculate. merger time-scales for pairs based on semi-analytical simulations.," Our merger time-scale measurement is smaller by roughly a factor of two compared to the results of Kitzbichler White (2008), who calculate merger time-scales for pairs based on semi-analytical simulations." + Our merger time-scale is also shorter than other predictions based on semi-analytical models of merging dark matter halos (e.e.. DBovlan-Ixolchin. Ma Quatacrt 2008). suggesting that the implementations of merging time-scales in these models are olf by at least a factor of two (see also e.g.. Conroy et. al.," Our merger time-scale is also shorter than other predictions based on semi-analytical models of merging dark matter halos (e.g., Boylan-Kolchin, Ma Quataert 2008), suggesting that the implementations of merging time-scales in these models are off by at least a factor of two (see also e.g., Conroy et al." + 2007: Bertone Conselice 2009)., 2007; Bertone Conselice 2009). + One important caveat about this measurement of the merger time-scale is that we cannot assume that it applies at earlier times. particularly in the carly universe at z2 when galaxies were more gas rich than they are today.," One important caveat about this measurement of the merger time-scale is that we cannot assume that it applies at earlier times, particularly in the early universe at $z > 2$ when galaxies were more gas rich than they are today." + I principle. the method used in this paper can be applied at higher redshifts. but will require more accurate nieasures of the merger fraction than that provided by the available data (c.g. Conselice ct al.2008).," In principle, the method used in this paper can be applied at higher redshifts, but will require more accurate measures of the merger fraction than that provided by the available data (e.g., Conselice et al.2008)." + Future [large surveys with WECS on Hubble will potentially allow this measurement to be made at z> 1., Future large surveys with WFC3 on Hubble will potentially allow this measurement to be made at $z > 1$ . +Kauthnann Charlot (1998)) argued that the cumulative redshift distribution iu the A-baud eui be used as a test or the scenarios of galaxy formation.,Kauffmann Charlot \cite{kauff}) ) argued that the cumulative redshift distribution in the $K$ -band can be used as a test for the scenarios of galaxy formation. + In Fig., In Fig. + G6 we have compared our data with the theoretical expectations given o Rauffiuaun Charlot (1998)). in the case of monolithic (PLE) and uerarchical galaxy formation scenarios.," \ref{nzcum} we have compared our data with the theoretical expectations given by Kauffmann Charlot \cite{kauff}) ), in the case of monolithic (PLE) and hierarchical galaxy formation scenarios." + The original A- vaudmagnitude bins have been shifted by ~2 maguitudes o match the AB maenitudes used here., The original $K$ -band magnitude bins have been shifted by $\sim 2$ magnitudes to match the AB magnitudes used here. + The fraction of galaxies at high redshifts is much larger in the case of the PLE models than in the hierarchical scenario., The fraction of galaxies at high redshifts is much larger in the case of the PLE models than in the hierarchical scenario. + The observed ITDEs. ciunulative redshift distribution lie between the two inodels aud. iu auv case. it is always below the predictions ofthe PLE models.," The observed HDFs cumulative redshift distribution lie between the two models and, in any case, it is always below the predictions of the PLE models." + This result was already pointed out by RKauffiiuun Charlot (1998)). when comparing their predictions with the results fouud with the Songaila et (6199 19) and Cowie et (019963) ~@uples. in the two brightest maeitucle bins.," This result was already pointed out by Kauffmann Charlot \cite{kauff}) ), when comparing their predictions with the results found with the Songaila et \cite{songaila}) ) and Cowie et \cite{cowie2}) ) samples, in the two brightest magnitude bins." + The preseut results ou the WDFs extend this trend towards the faintest magnitude bins., The present results on the HDFs extend this trend towards the faintest magnitude bins. + ILowever. this results nimmst be considered with caution. mainly because of the small size of the," However, this results must be considered with caution, mainly because of the small size of the" + 'The rate at which 5galaxies convert 5eas into stars (the star formation rate. SER) determines (heir evolution ancl a wide range of their observable properties.," The rate at which galaxies convert gas into stars (the star formation rate, SFR) determines their evolution and a wide range of their observable properties." + Schmidt (1959) suggested the existence of a relation between (he volume density of the SFR and the gas volume density., Schmidt (1959) suggested the existence of a relation between the volume density of the SFR and the gas volume density. +" ]ennieutt. (1989) derived the surface densitv of the SFR (Marg)en| from Ha measurements and combined it with total gas surface density. (X,) measurements using HT and CO lines observations in what is now commonly referred to as the IXennicutt-Schmidti (INS) relation VeenXM5.", Kennicutt (1989) derived the surface density of the SFR $\Sigma_{SFR}$ ) from $\alpha$ measurements and combined it with total gas surface density $\Sigma_{g}$ ) measurements using HI and CO lines observations in what is now commonly referred to as the Kennicutt-Schmidt (KS) relation $\Sigma_{SFR} \propto \Sigma_{g}^{n}$. + Determining the value of 7 has been the subject of intense efforts., Determining the value of $n$ has been the subject of intense efforts. + In. high surface clensitv reeions in which massive star formation is present. Kennicutt (1989) found n—1.32:0.3.," In high surface density regions in which massive star formation is present, Kennicutt (1989) found $n=1.3 \pm 0.3$." + Duat et al. (, Buat et al. ( +1989) used the UV emission at 2000 1 of 28 late-tvpe galaxies as à (racer of their recent star formation and found à»=1.65220.16.,1989) used the UV emission at 2000 $\AA$ of 28 late-type galaxies as a tracer of their recent star formation and found $n=1.65 \pm 0.16$. + IXennieutt (1998) included on the same ligure data points for normal galaxies and starburst galaxies ancl obtained n—1440.15., Kennicutt (1998) included on the same figure data points for normal galaxies and starburst galaxies and obtained $n=1.4 \pm 0.15$. + Murgia et al (2002) used radio continuum luminosities as a proxy for the SER for a sample of 130 galaxies⋅ and obtained⋅ τομExΣα2La-u.' where τμ.DP is the molecular hvdrogen surface density.," Murgia et al (2002) used radio continuum luminosities as a proxy for the SFR for a sample of 180 galaxies and obtained $\Sigma_{SFR} \propto \Sigma_{H_{2}}^{1.3 \pm 0.1}$, where $\Sigma_{H_{2}}$ is the molecular hydrogen surface density." + Martin IXenniceutt (2001). IXomugi et al. (," Martin Kennicutt (2001), Komugi et al. (" +2005). and Schuster et al. (,"2005), and Schuster et al. (" +"2007) studied (he dependence of the racially averaged X5,45, on the gas density. profiles in ealaxies and found values o£» in the range 1.5220.3. while a few other studies found larger or smaller values (πο et al.","2007) studied the dependence of the radially averaged $\Sigma_{SFR}$ on the gas density profiles in galaxies and found values of $n$ in the range $\sim 1.5 \pm 0.3$, while a few other studies found larger or smaller values (Kuno et al." + 1995: Boissier et al., 1995; Boissier et al. + 2003)., 2003). + Ilever et al. (, Heyer et al. ( +"2004) found that in M33. (he star formation law follows ΣΣ.» butπι. also. that XsjgxοX177""5, ","2004) found that in M33, the star formation law follows $\Sigma_{SFR} \propto \Sigma_{g}^{3.3 \pm 0.07}$ but also that $\Sigma_{SFR} \propto \Sigma_{H_{2}}^{1.36 \pm 0.08}$." +Zhang7-. οἱ al. (, Zhang et al. ( +"2001) analysed the region-by-region dependence of the X75 on X, in the Antennae and found a~ 1.4. and Kennicutt et al. (","2001) analysed the region-by-region dependence of the $\Sigma_{SFR}$ on $\Sigma_{g}$ in the Antennae and found $n \sim {1.4}$ , and Kennicutt et al. (" +2007) found similar results in M51.,2007) found similar results in M51. +" Other studies have found linear relations between X554; and Xj, or the surface density of molecules that trace higher density gas such as LICN (e.g.. Rownd Young 1999: Wong Blitz 2002: Gao Solomon 2004)."," Other studies have found linear relations between $\Sigma_{SFR}$ and $\Sigma_{H_{2}}$ or the surface density of molecules that trace higher density gas such as HCN (e.g., Rownd Young 1999; Wong Blitz 2002; Gao Solomon 2004)." + Aside from the data of IxXennicutt (1998) which included high surface density starburst galaxies. most of the other studies explored surface density ranges extending from," Aside from the data of Kennicutt (1998) which included high surface density starburst galaxies, most of the other studies explored surface density ranges extending from" + , +objects were classified as stars based on their near-infrared colours.,objects were classified as stars based on their near-infrared colours. +" The near-infrared colours of bright stars were examined in the colour-magnitude diagrams of the 7 observed fields, and the following colour-selection criteria were designed to separate stars from galaxies."," The near-infrared colours of bright stars were examined in the colour-magnitude diagrams of the 7 observed fields, and the following colour-selection criteria were designed to separate stars from galaxies." + Stars were defined as objects which obey all of the following conditions: These criteria were tested using the Pickles stellar library., Stars were defined as objects which obey all of the following conditions: These criteria were tested using the Pickles stellar library. +" All stars are selected by this criteria, except for very red stars such as L- or early T-type dwarfs, but the density of such stars is very low."," All stars are selected by this criteria, except for very red stars such as L- or early T-type dwarfs, but the density of such stars is very low." + We identify stars in both the control fields and the HzRG fields using the same colour criteria so the results presented in this work are not sensitive to moderate changes in these criteria., We identify stars in both the control fields and the HzRG fields using the same colour criteria so the results presented in this work are not sensitive to moderate changes in these criteria. + Changing these colour cuts by up to mmag does not affect our conclusions., Changing these colour cuts by up to mag does not affect our conclusions. + Differential K-band galaxy number counts were measured from the HzRG fields and the control field (CF) and are compared to galaxy counts from the literature in reffig:nc.., Differential $K$ -band galaxy number counts were measured from the HzRG fields and the control field (CF) and are compared to galaxy counts from the literature in \\ref{fig:nc}. +" The galaxy number counts were not corrected for completeness, and no attempt was made to correct for the difference in the filter bandpasses."," The galaxy number counts were not corrected for completeness, and no attempt was made to correct for the difference in the filter bandpasses." + The observed number counts are fully consistent with literature counts up to the completion limit of the images: there is no large galaxy excess in any HzRG field compared to the control field or the literature., The observed number counts are fully consistent with literature counts up to the completion limit of the images: there is no large galaxy excess in any HzRG field compared to the control field or the literature. + Any protocluster structure associated with the HzRGs may only contribute a small fraction of the galaxies in the observed field., Any protocluster structure associated with the HzRGs may only contribute a small fraction of the galaxies in the observed field. + The wide-field HAWK-I images contain a large contribution of foreground and background objects which dominate over any structure associated with the radio galaxy., The wide-field HAWK-I images contain a large contribution of foreground and background objects which dominate over any structure associated with the radio galaxy. +" Additionally, cosmic variance of these galaxies may hide a protocluster, or make a region appear overdense through chance superposition."," Additionally, cosmic variance of these galaxies may hide a protocluster, or make a region appear overdense through chance superposition." + It is therefore necessary to remove as many interloping galaxies as possible before searching for structures around the HzRGs., It is therefore necessary to remove as many interloping galaxies as possible before searching for structures around the HzRGs. + To identify galaxy overdensities near the HzRGs we attempt to isolate galaxies at 2.2«z2.7., To identify galaxy overdensities near the HzRGs we attempt to isolate galaxies at $2.2 10%) do not allow us to reject the model indicating that the flattening is not particularly significant., The K-S probability $>10\%$ ) do not allow us to reject the model indicating that the flattening is not particularly significant. + However the best-fit value of the slope is significantly sub-euclidean. in contrast to BeppoSAX and ASCA findings. indicating that probably the Log(N)-Log(S) flattens at faint The 5-10 keV Log(N)-Log(S) is in agreement. within the errors. with both Lockman Hole data (Hasingeretal. 2001).. which is a subsample of ours. andBeppoSAX HELLAS survey (Fioreetal.2001b).," However the best-fit value of the slope is significantly sub-euclidean, in contrast to BeppoSAX and ASCA findings, indicating that probably the Log(N)-Log(S) flattens at faint The 5-10 keV Log(N)-Log(S) is in agreement, within the errors, with both Lockman Hole data \citep{has01}, which is a subsample of ours, and HELLAS survey \citep{fio01b}." +. Our Log(N)-Log(S) connects deep observations with shallowerBeppoSAX ones., Our Log(N)-Log(S) connects deep observations with shallower ones. + The sample selected in this band (100 sources) is currently smaller than the BeppoSAX HELLAS sample (about 150 sources)., The sample selected in this band (100 sources) is currently smaller than the HELLAS sample (about 150 sources). + However. we go deeper by an order of magnitude than the HELLAS survey and the error circle we can use in the optical follow up (conservatively we are assuming 3”)is considerably smaller than BeppoSAX(about 1). making the optical identification far A maximum likelihood fit of the5-10 keV Log(N)-Log(S) with a single power-law model gives a value of a=I.54023m and a normalization K=175.2$3.," However, we go deeper by an order of magnitude than the HELLAS survey and the error circle we can use in the optical follow up (conservatively we are assuming $3^{\prime\prime}$ ) is considerably smaller than (about $1^\prime$ ), making the optical identification far A maximum likelihood fit of the 5-10 keV Log(N)-Log(S) with a single power-law model gives a value of $\alpha=1.54^{+0.25}_{-0.19}$ and a normalization $K=175.2^{+56.3}_{-36.2}$." + As in the 2-10 keV band. the single power-law model is found to give an acceptable description of the data (the K-S probability 1s larger than 20%) In each panel of Figure 2.. the cyan dashed line represents the expected Log(N)-Log(S) from the improved (1995) XRB synthesis model (seeComastrietal.2001.fordetails)...," As in the 2-10 keV band, the single power-law model is found to give an acceptable description of the data (the K-S probability is larger than $20\%$ In each panel of Figure \ref{logn}, the cyan dashed line represents the expected Log(N)-Log(S) from the improved \citet{com95} XRB synthesis model \citep[see][for details]{com01}." + In the 0.5-2 keV band. the counts overestimates the model predictions at bright fluxes. because of the contribution from clusters and stars to the soft Log(N)-Log(S).," In the 0.5-2 keV band, the counts overestimates the model predictions at bright fluxes, because of the contribution from clusters and stars to the soft Log(N)-Log(S)." + At fainter fluxes. where the AGN are the dominant. contributors. the agreement is quite good.," At fainter fluxes, where the AGN are the dominant contributors, the agreement is quite good." + In the 2-10 keV band the agreement between XRB model predictions and our Log(N)-Log(S) is good at brighter fluxes. becoming marginal towards fainter fluxes.," In the 2-10 keV band the agreement between XRB model predictions and our Log(N)-Log(S) is good at brighter fluxes, becoming marginal towards fainter fluxes." + However. by varying the normalization of the model of ~20%. the predicted Log(N)-Log(S) agrees well with both our data and CDFS data.," However, by varying the normalization of the model of $\sim20\%$, the predicted Log(N)-Log(S) agrees well with both our data and CDFS data." + In the 5-10 keV band the model predictions are in agreement within the errors with our Log(S) and the Lockman Hole and HELLAS surveys., In the 5-10 keV band the model predictions are in agreement within the errors with our Log(N)-Log(S) and the Lockman Hole and HELLAS surveys. + It is worth noting that we do not make any correction for confusion or Eddington biases., It is worth noting that we do not make any correction for confusion or Eddington biases. + Nevertheless. the agreement between our source counts and andROSAT data. in the 0.5-2 keV band. indicates that source confusion is. still negligible at these fluxes.," Nevertheless, the agreement between our source counts and and data, in the 0.5-2 keV band, indicates that source confusion is still negligible at these fluxes." + We have carried out a serendipitous survey., We have carried out a serendipitous survey. + We cover nearly three square degrees in 15 fields observed during satellite calibration and performance verification phase., We cover nearly three square degrees in 15 fields observed during satellite calibration and performance verification phase. + This is. to date. the survey with the largest solid The present sample ts one of the largest available in the 0.5-2 keV band and ts surely the largest in the 2-10 keV band at these fluxes.," This is, to date, the survey with the largest solid The present sample is one of the largest available in the 0.5-2 keV band and is surely the largest in the 2-10 keV band at these fluxes." + In the 4.5-10 keV band we currently have a smaller sample than the HELLAS survey., In the 4.5-10 keV band we currently have a smaller sample than the HELLAS survey. + However. the flux limit ts a factor about 10 deeper than HELLAS and the opticalfollow up of our survey is easier because of XMM-Newton better positional We computed the Log(N)-Log(S) curves in the 0.5-2 keV. 2-10 keV and 5-10 keV bands.," However, the flux limit is a factor about 10 deeper than HELLAS and the opticalfollow up of our survey is easier because of XMM-Newton better positional We computed the Log(N)-Log(S) curves in the 0.5-2 keV, 2-10 keV and 5-10 keV bands." + Our measurements are Ἡ agreement with previous determinations by other satellites and itself (Hasingeretal.1998;Ueda1999;Hasingeretal.2001) and with the predictions of the improvec Comastrietal.(1995) XRB synthesis In the hard bands. we sample an intermediate flux range: deeper than andBeppoSAX and shallower than anc deep pencil-beam surveys.," Our measurements are in agreement with previous determinations by other satellites and itself \citep{has98,ued99,cag98,gio00,gia01,has01} and with the predictions of the improved \citet{com95} XRB synthesis In the hard bands, we sample an intermediate flux range: deeper than and and shallower than and deep pencil-beam surveys." + It is worth to note that our approach is complementary to the latters: we probe large areas. at fluxes bright enough to allow. at least. a coarse spectral characterization of them.," It is worth to note that our approach is complementary to the latters: we probe large areas, at fluxes bright enough to allow, at least, a coarse spectral characterization of them." + One of our main goals is in fact to find a good number of those rare objects (like type-2 QSOs) which are supposed to contribute significantly to the extragalactic hard X-ray In the soft band. the Log(N)-Log(S)distribution showsa flattening around 5«107 erg em s.," One of our main goals is in fact to find a good number of those rare objects (like type-2 QSOs) which are supposed to contribute significantly to the extragalactic hard X-ray In the soft band, the Log(N)-Log(S)distribution showsa flattening around $5\times10^{-15}$ erg $^{-2}$ $^{-1}$." + A similar result was also found from the ROSAT data (Hasingeretal. 1998).., A similar result was also found from the data \citep{has98}. . + A broken power-law fit gives a differential slope index »j , A broken power-law fit gives a differential slope index $\beta_2$ +The lighteurves from August 9 are shown in Fig. 3..,The lightcurves from August 9 are shown in Fig. \ref{VLTLCFig}. + The source is clearly considerably fainter in X-rays. but considerable variability is still present (r.m.s.," The source is clearly considerably fainter in X-rays, but considerable variability is still present (r.m.s." + 15 ppercent on timescales longer than Iss), $\sim15$ percent on timescales longer than s). + It is hard to directly compare these with the July optical observations due to the very different characteristics of the data., It is hard to directly compare these with the July optical observations due to the very different characteristics of the data. + Both slow and rapid optical variations do appear to be present. however. as in the previous datasets.," Both slow and rapid optical variations do appear to be present, however, as in the previous datasets." + To better characterise the temporal properties at each epoch we have calculated power density spectra (PDS) of each RXTE//PCA lighteurve and show them in Fig. 4.., To better characterise the temporal properties at each epoch we have calculated power density spectra (PDS) of each /PCA lightcurve and show them in Fig. \ref{PDSFig}. + The general form of each PDS is band-limited noise. resembling a broken power-law. characteristic of the hard state.," The general form of each PDS is band-limited noise, resembling a broken power-law, characteristic of the hard state." + The data from July additionally includes a strong low-frequency quasi-periodic oscillation close to HHz., The data from July additionally includes a strong low-frequency quasi-periodic oscillation close to Hz. + We fit these PDS with a multi-Lorentzian decomposition following Bellonietal.(2002).., We fit these PDS with a multi-Lorentzian decomposition following \citet{Belloni:2002a}. +. The band-limited noise is represented by a zero-centred Lorentzian oone with zero centroid frequency) and the QPO by a peaked one oone with non-zero centroid frequency)., The band-limited noise is represented by a zero-centred Lorentzian one with zero centroid frequency) and the QPO by a peaked one one with non-zero centroid frequency). + Even when white noise is included. we find pronounced residuals at a few Hz. so include a second broader QPO.," Even when white noise is included, we find pronounced residuals at a few Hz, so include a second broader QPO." + This is a similar model to that adopted by except that we allow the third Lorentzian to be a peaked QPO rather than a band-limited noise component., This is a similar model to that adopted by except that we allow the third Lorentzian to be a peaked QPO rather than a band-limited noise component. + With these components. good fits can be obtained for all three nights: we summarize the characteristic frequency and amplitude of each component in Table. L..," With these components, good fits can be obtained for all three nights; we summarize the characteristic frequency and amplitude of each component in Table. \ref{PDSFitTable}." + The QPOs were less pronounced, The QPOs were less pronounced +disk systems.,disk systems. + It should be uoted. however. that it is difficult to positively identily a unique planetary companion without temporal information showing the changes iu disk structure over tlie course of a planetary orbit.," It should be noted, however, that it is difficult to positively identify a unique planetary companion without temporal information showing the changes in disk structure over the course of a planetary orbit." + The authors wish to thanks Hal Levisou for useful discussions about RAIVS3 and Dave Wilner [or providing an unpublished 350 iinage., The authors wish to thanks Hal Levison for useful discussions about RMVS3 and Dave Wilner for providing an unpublished 350 image. + We also thank the anonymous referee for providing useful feedback aud suggestions., We also thank the anonymous referee for providing useful feedback and suggestions. + AD was supported by a Stunmer Vacation Scholarship from the Swinburne Centre for Astrophysics aud Supercomputing., AD was supported by a Summer Vacation Scholarship from the Swinburne Centre for Astrophysics and Supercomputing. +Ü. SeAll simulations: were run on the Swinburne1., All simulations were run on the Swinburne. +supercomputers. Our svuthetic debris disk catalogue is available ouline, Our synthetic debris disk catalogue is available online +the rotational and diffusion velocities. it is possible to ensure that (he “right” abundances are established in the 9MZ in à short enough time bv increasing the accretion rate sulliciently.,"the rotational and diffusion velocities, it is possible to ensure that the “right” abundances are established in the SMZ in a short enough time by increasing the accretion rate sufficiently." + In all the cases shown in Fig. 1..," In all the cases shown in Fig. \ref{fig:fig1}," + the net {his in the SMZ is still dominated by accretion because the flux at the surface is larger than the [lux at the base of the SMZ [Al> v))suz]. even when diffusion and circulations overwhelm the accretion [low that the base of the SMZ.," the net flux in the SMZ is still dominated by accretion because the flux at the surface is larger than the flux at the base of the SMZ $\dot{M} > 4\pi(\rho r^2 +(v_{acc}-v))_{SMZ}$ ], even when diffusion and circulations overwhelm the accretion flow that the base of the SMZ." + In those cases however. tje limescales become too long to expect the necessary abundances anomalies to form reasonably early in the stars life.," In those cases however, the timescales become too long to expect the necessary abundances anomalies to form reasonably early in the star's life." + In the eases of C. N. O. and 5. it is genera]v assumed. as we do here. that their abundance is normal in the accreted matter.," In the cases of C, N, O, and S, it is generally assumed, as we do here, that their abundance is normal in the accreted matter." + As these elements are not significantly supported by radiative pressure. their abundance will remain 1ormad in sslars provided that the accretion rate is large erough to compensate (he eravitational seltling at the base of the SAIZ.," As these elements are not significantly supported by radiative pressure, their abundance will remain normal in stars provided that the accretion rate is large enough to compensate the gravitational settling at the base of the SMZ." + This is easily sadisfied in the models and so they do not provide significant constraints on the accretion rates and particle transport processes., This is easily satisfied in the models and so they do not provide significant constraints on the accretion rates and particle transport processes. + lt has been shown that indications of deep mixing in F. A and D stars can have a significant effect on the accretion/ditfasion model for sslars. leading to larger predicted. accretion rates or longer (imnescales for the formation of (he requisite surface composition.," It has been shown that indications of deep mixing in F, A and B stars \citep{RMT00} + can have a significant effect on the accretion/diffusion model for stars, leading to larger predicted accretion rates or longer timescales for the formation of the requisite surface composition." + This asstunes (hat the mixing in slowly rotating stars is similarly active in faster rotators., This assumes that the mixing in slowly rotating stars is similarly active in faster rotators. + Such a1 exirapolation. as is done here. is still founded on ciremustantial evidence and is subject to confirmation.," Such an extrapolation, as is done here, is still founded on circumstantial evidence and is subject to confirmation." + Nevertheless. deep mixing in sslars raises intriguing possibilities regarding the few but important points of contention between the standard accretion/cdiffusion model (TurcotteandCharbonneau1993) and the observations (Solanoetal.2001:Leiter2002).," Nevertheless, deep mixing in stars raises intriguing possibilities regarding the few but important points of contention between the standard accretion/diffusion model \citep{TC93} and the observations \citep{Solanoetal01,Heiteretal02}." +. One of the most difficult problem Lacing (he accretion model is the existence of old sstars., One of the most difficult problem facing the accretion model is the existence of old stars. + In A (vpe stars. cireumstellar disks are not expected (o persist more than a couple ol hundred Myrs (MeverandBeckwith2000) which is far less than the oldestDootis.," In A type stars, circumstellar disks are not expected to persist more than a couple of hundred Myrs \citep{MeyerBeckwith00} which is far less than the oldest." +. If one assumes that sstars are mixed to a depth of LO° in fractional mass. as argued here. and that the accretion rate was high enough early on to ensure the observed abunclances reflect those of the accreted matter. then the larger timescale for the evolution of the surface abundance might provide a wav lo explain older sslars.," If one assumes that stars are mixed to a depth of $10^{-6}$ in fractional mass, as argued here, and that the accretion rate was high enough early on to ensure the observed abundances reflect those of the accreted matter, then the larger timescale for the evolution of the surface abundance might provide a way to explain older stars." +impedances and the cavity formed with the sample holder. it is possible to directly impedance match the LEKID to free space (Doyleetal. 2009)).,"impedances and the cavity formed with the sample holder, it is possible to directly impedance match the LEKID to free space \cite{doyle:156}) )." + Alternatively. a lens and antenna structure can be used to adapt the resonator to free space.," Alternatively, a lens and antenna structure can be used to adapt the resonator to free space." + Due to the increased geometric complexity. it has proven more difficult to achieve satisfactory device performance with antenna structures than with direct absorbtion LEKIDs.," Due to the increased geometric complexity, it has proven more difficult to achieve satisfactory device performance with antenna structures than with direct absorbtion LEKIDs." + Despite this drawback. antenna-coupled KIDs remain a very active area of research due to their frequency selectivity (Schlaerthetal. 2008)).," Despite this drawback, antenna-coupled KIDs remain a very active area of research due to their frequency selectivity \cite{Schlaerth2008}) )." + For both LEKIDs and antenna-coupled KIDs. detection is achieved in the same manner once the incident radiation has been absorbed.," For both LEKIDs and antenna-coupled KIDs, detection is achieved in the same manner once the incident radiation has been absorbed." + In a superconductor. the conduction electrons are condensed into charge carrying Cooper pairs.," In a superconductor, the conduction electrons are condensed into charge carrying Cooper pairs." + Mediated by lattice vibrations. superconductivity results in an energy gap in the carrier density of states.," Mediated by lattice vibrations, superconductivity results in an energy gap in the carrier density of states." + Incident photons with an energy exceeding the gap energy can break a Cooper pair. producing two quasiparticles and a concurrent change in the complex impedance.," Incident photons with an energy exceeding the gap energy can break a Cooper pair, producing two quasiparticles and a concurrent change in the complex impedance." + The result is a shift in the KID resonance frequency which can be read out by the measurement electronics., The result is a shift in the KID resonance frequency which can be read out by the measurement electronics. + We are currently developing a fully-integrated measurement system based on KIDs known as the Néeel IRAM KIDs Array (NIKA)., We are currently developing a fully-integrated measurement system based on KIDs known as the Néeel IRAM KIDs Array (NIKA). + The two primary goals of NIKA are to asses the viability of KIDs for terrestrial astronomy and to develop a filled-array. dual-band resident instrument for the Institute for Millimetric Radio Astronomy (IRAM) 30-meter telescope at Pico Veleta. Spain.," The two primary goals of NIKA are to asses the viability of KIDs for terrestrial astronomy and to develop a filled-array, dual-band resident instrument for the Institute for Millimetric Radio Astronomy (IRAM) 30-meter telescope at Pico Veleta, Spain." + Based on a custom-designed dilution eryostat with a base temperature of ~70 nK (Benoitetal. 2008)). a first generation single-band NIKA prototype was previously tested at the Pico Veleta telescope in October 2009 (Monfardinietal. 20100).," Based on a custom-designed dilution cryostat with a base temperature of $\sim$ 70 mK \cite{benoit:702009}) ), a first generation single-band NIKA prototype was previously tested at the Pico Veleta telescope in October 2009 \cite{Monfardini:29}) )." + This successful neasurement was the first to directly compare the performance of LEKID and antenna-coupled KID designs., This successful measurement was the first to directly compare the performance of LEKID and antenna-coupled KID designs. + Leveraging the experience gained from the first generation ΙΚΑ. an improved instrument has been designed and tested at the IRAM 30-meter telescope in October 2010.," Leveraging the experience gained from the first generation NIKA, an improved instrument has been designed and tested at the IRAM 30-meter telescope in October 2010." + This second generation system includes a large number of enhancements., This second generation system includes a large number of enhancements. + Dual-band optics. integrating a polarization-sensitive splitter and anew baffling structure. allow simultaneous imaging at 190 GHz and 220 GHz.," Dual-band optics, integrating a polarization-sensitive splitter and a new baffling structure, allow simultaneous imaging at 150 GHz and 220 GHz." + Resonator desigi modifications resulted in improved single-pixel sensitivity., Resonator design modifications resulted in improved single-pixel sensitivity. + Faster digital-signal-processing electronics enable synchronous measurement of up to 112 pixels for each measurement band., Faster digital-signal-processing electronics enable synchronous measurement of up to 112 pixels for each measurement band. + Fabrication of a sky simulator to replicate typical measurement conditions at the telescope facilitated improved array testing and quality control., Fabrication of a sky simulator to replicate typical measurement conditions at the telescope facilitated improved array testing and quality control. + Along with a detailed discussior of these system upgrades. we present here the results of the October 2010 neasurement campaign.," Along with a detailed discussion of these system upgrades, we present here the results of the October 2010 measurement campaign." + This includes a discussion of the limiting. noise sources. an analysis of the system performance determined using calibration sources such as planets. and an estimate of the improved full-system sensitivity.," This includes a discussion of the limiting noise sources, an analysis of the system performance determined using calibration sources such as planets, and an estimate of the improved full-system sensitivity." + Finally we present astronomically-relevant observations of a number of faint and extended sources in both measurement bands which were previously unattainable with the less sensitive first generation NIKA., Finally we present astronomically-relevant observations of a number of faint and extended sources in both measurement bands which were previously unattainable with the less sensitive first generation NIKA. + The new dual-band NIKA is engineered to fit the receiver cabin of the IRAM telescope in Pico Veleta. Spain.," The new dual-band NIKA is engineered to fit the receiver cabin of the IRAM telescope in Pico Veleta, Spain." + The 30-meter primary mirror (MI) and the hyperbolic secondary (M2. D=2m) are installed directly on a large alt-azimuth mounting.," The 30-meter primary mirror (M1) and the hyperbolic secondary (M2, D=2m) are installed directly on a large alt-azimuth mounting." + The incident beam ts directed into the receiver cabir through a hole in MI using a standard Cassegrain configuration., The incident beam is directed into the receiver cabin through a hole in M1 using a standard Cassegrain configuration. + A rotating tertiary (M3) provides a fixed focal plane (asmyth focus)., A rotating tertiary (M3) provides a fixed focal plane (Nasmyth focus). + The optical axis. in order to conform to the dimensions of the cabin. is deviated by two flat mirrors (M4 and M5).," The optical axis, in order to conform to the dimensions of the cabin, is deviated by two flat mirrors (M4 and M5)." + M4 can rotate between two fixed positions. selecting either heterodyne or continuum instruments.," M4 can rotate between two fixed positions, selecting either heterodyne or continuum instruments." + NIKA re-images the large telescope focal plane onto the small sensitive area covered by the KIDs., NIKA re-images the large telescope focal plane onto the small sensitive area covered by the KIDs. + The demagnification factor is around 6.6. achieving a well-adapted scale of 5 areseconds/mm on the detector plane.," The demagnification factor is around 6.6, achieving a well-adapted scale of 5 arcseconds/mm on the detector plane." + This is accomplished using two flat mirrors (M6. M7). one bi-conical mirror (M8) and three high-density polyethylene (HDPE) corrugated lenses (LI. L2. L3).," This is accomplished using two flat mirrors (M6, M7), one bi-conical mirror (M8) and three high-density polyethylene (HDPE) corrugated lenses (L1, L2, L3)." + The lens corrugatior consists of machined concentric grooves. providing a soft transition between vacuum (n=l) and HDPE (nz1.56) to reduce reflective losses.," The lens corrugation consists of machined concentric grooves, providing a soft transition between vacuum (n=1) and HDPE (n=1.56) to reduce reflective losses." + The size of the grooves is 0.4 mm x 0.4 mm in depth and width. while the width of the ridges is 0.4 mm.," The size of the grooves is 0.4 mm $\times$ 0.4 mm in depth and width, while the width of the ridges is 0.4 mm." + LI is located at room temperature and coincides with the cryostat vacuum isolation window., L1 is located at room temperature and coincides with the cryostat vacuum isolation window. + L2 is mounted on the screen at 4 K. while the final L3 lenses (one per array) are installec at the coldest stage just in front of the arrays (~70 mK).," L2 is mounted on the screen at 4 K, while the final L3 lenses (one per array) are installed at the coldest stage just in front of the arrays $\sim$ 70 mK)." + A simple grid polarizer with a grid pitch of 4 ym was inserted at 45 degrees with respect to the main optical axis before the final L3 lenses., A simple grid polarizer with a grid pitch of 4 ${\mu}$ m was inserted at 45 degrees with respect to the main optical axis before the final L3 lenses. + Since all KID designs currently employed in NIKA are sensitive to a single, Since all KID designs currently employed in NIKA are sensitive to a single + (e.g..," \citep[e.g.,][]{Zuckerman+Evans:1974,Larson_1981-turbulence_MC,Myers_1983-subsonic_turbulence}." +" 10""em™. (Goodmanetal.1998).. (seealsoCasellietal.2002).. (Pinedaetal.2010.2011).."," $10^{4}~{\rm cm^{-3}}$ \citep{Goodman_1998-coherence}. \citep[see also][]{Caselli:2002-n2h+_maps}. \citep{Pineda_2010-transition_coherence,Pineda_2011-GBT_Maps}." + Pinedaetal.(2010) 30” between the coherent section of the B5 dense core and the more turbulent dense gas outside it (seealsoPinedaetal.2011.forresultsontheotherregions surveyed).., \cite{Pineda_2010-transition_coherence} $30\arcsec$ between the coherent section of the B5 dense core and the more turbulent dense gas outside it \citep[see also][for results on the other regions surveyed]{Pineda_2011-GBT_Maps}. + However. the angular resolution of these observations did not allow us to study in great detail the spatial variations of the velocity dispersion or column density.," However, the angular resolution of these observations did not allow us to study in great detail the spatial variations of the velocity dispersion or column density." + In this letter. we present new ((1.1) observations of B5 obtained with the Expanded Very Large Array (EVLA) through the Open Shared Risk Observing (OSRO) program. see Perleyetal.(2011) for a deseription of the EVLA project.," In this letter, we present new (1,1) observations of B5 obtained with the Expanded Very Large Array (EVLA) through the Open Shared Risk Observing (OSRO) program, see \cite{Perley_2011-EVLA_description} for a description of the EVLA project." + These data are combined with previous observations from the GBT to study the dense gas traced by at high angular and spectral resolution., These data are combined with previous observations from the GBT to study the dense gas traced by at high angular and spectral resolution. + Here. we present results from the combined EVLA and GBT observations that enable us to analyze the kinematic properties of the dense gas traced by ((1.1) and also to study the radial profile of new filamentary structure found within this core.," Here, we present results from the combined EVLA and GBT observations that enable us to analyze the kinematic properties of the dense gas traced by (1,1) and also to study the radial profile of new filamentary structure found within this core." + Observations were carried out with the EVLA of the National Radio Astronomy Observatory on Μαν 16th. 2010 (project IOA-181).," Observations were carried out with the EVLA of the National Radio Astronomy Observatory on May 16th, 2010 (project 10A-181)." + We used the high-frequency K-band receiver and configured the WIDAR correlator to observe à 1MMHz window around the ((1.1) rest frequency GGHz).," We used the high-frequency K-band receiver and configured the WIDAR correlator to observe a MHz window around the (1,1) rest frequency GHz)." + The correlator generated 256 channels across the window. giving a 3.90625 kHz channel separation. equivalent to 0.049kms! at the observed frequency.," The correlator generated 256 channels across the window, giving a 3.90625 kHz channel separation, equivalent to $0.049~\kms$ at the observed frequency." + This configuration covers the main hyperfine component and also one of the inner pair of satellite lines for ((1.1).," This configuration covers the main hyperfine component and also one of the inner pair of satellite lines for (1,1)." +" At this frequency the primary beam of the array is about 1.9""", At this frequency the primary beam of the array is about $1.9\arcmin$. + The array was in the compact (D) configuration. which covers baselines from 35 meters up to | km. and included 26 antennas.," The array was in the compact (D) configuration, which covers baselines from 35 meters up to 1 km, and included 26 antennas." + The observations covered the entire region of interest using 27 pointings., The observations covered the entire region of interest using 27 pointings. +" The observations were carried out under fair weather (7>GH,=0.0689 nepers) for 7 hours.", The observations were carried out under fair weather $\tau_{\rm 22GHz}=0.0689$ nepers) for 7 hours. + The bandpass and absolute flux calibrator was the quasar 448.whilethe phase and amplitude calibrator. quasar J033643218. was observed every 15 minutes.," The bandpass and absolute flux calibrator was the quasar 48,whilethe phase and amplitude calibrator, quasar J0336+3218, was observed every 15 minutes." + The X-band, The $X$ -band +the side). while the dashed. is computed from the output of a single. PAL simulation of 256° particles in a box of 512h!Mpe on the side.,"the side), while the dashed is computed from the output of a single PM simulation of $256^3$ particles in a box of $512\hmpc$ on the side." + The le error-hars attached to the PZ curve are estimated using the bootstrap method as follows., The $1\sigma$ error-bars attached to the PZ curve are estimated using the bootstrap method as follows. + We generate 500 sets of simulations where each set contains 60 simulations picked randomly out of the 60 original simulations (i.e. some of these simulations could be selected more than once)., We generate 500 sets of simulations where each set contains 60 simulations picked randomly out of the 60 original simulations (i.e. some of these simulations could be selected more than once). + For each set we compute the mean correlation and the errors are estimated. as the standard deviations between the mean correlations of the 500 sets., For each set we compute the mean correlation and the errors are estimated as the standard deviations between the mean correlations of the 500 sets. + The bump in £(r) in figure (2)) at scales smaller than 2h*\Ipe (also visible in figure 3)) is due to the finite resolution in the simulations., The bump in $\xi(r)$ in figure \ref{fig:corr_func}) ) at scales smaller than $2\hmpc$ (also visible in figure \ref{fig:sets_corr_func}) ) is due to the finite resolution in the simulations. + Therefore. we will base our conclusion on correlations on scales larger than 2hMpe Objects (7halos) in a PZ simulation are point-like and are identified using different criteria than halos in full N-bocly simulations.," Therefore, we will base our conclusion on correlations on scales larger than $2\hmpc$ Objects (“halos”) in a PZ simulation are point-like and are identified using different criteria than halos in full N-body simulations." + Therefore. we expect. only a rough agreement between the mass functions of halos (number density versus mass) computed from PZ simulations and full dynamics.," Therefore, we expect only a rough agreement between the mass functions of halos (number density versus mass) computed from PZ simulations and full dynamics." + We compared the abundance of objects versus mass in the PZ runs with the analytic predictions of Sheth Tormen (2002) and Press Sehechter (1974) for the halo mass function., We compared the abundance of objects versus mass in the PZ runs with the analytic predictions of Sheth Tormen (2002) and Press Schechter (1974) for the halo mass function. + Phe transfer function used in these predictions is taken from Barcleen (1986) with a slope ol n=1 for the primordial power spectrum., The transfer function used in these predictions is taken from Bardeen (1986) with a slope of $n=1$ for the primordial power spectrum. + Overall. there is only à qualitative agreement between PZ and the analytic expressions.," Overall, there is only a qualitative agreement between PZ and the analytic expressions." + For masses —4310155ΑΙ. the PZ simulation agrees with PS and ST., For masses $~4.3 \times 10^{11}h^{-1}M_\odot$ the PZ simulation agrees with PS and ST. + Llowever. for more massive haloes. the PZ overestimates abundance up to a factor of two for masses 1075.TAL.," However, for more massive haloes, the PZ overestimates abundance up to a factor of two for masses $~10^{13}h^{-1}M_\odot$." + The difference is reduced as we go to higher masses until it disappears at. 6ο+ALL., The difference is reduced as we go to higher masses until it disappears at $6 \times 10^{13}h^{-1}M_\odot$. + At higher masses. PZ [alls short of the analytic expressions by a factor which increases with mass.," At higher masses, PZ falls short of the analytic expressions by a factor which increases with mass." + The merging. history of an object (7halo) in our implementation of the PZ approximation is readily provided., The merging history of an object (“halo”) in our implementation of the PZ approximation is readily provided. + We consider only halos containing more than LOO particles (4.3«loth TAL.) at the final time (2=0) and. define the formation time of a halo as the redshift at which it has acquired of halfits final mass (Gao. Springel White 2005).," We consider only halos containing more than 100 particles $4.3\times 10^{11}h^{-1}M_\odot$ ) at the final time $(z=0)$ and define the formation time of a halo as the redshift at which it has acquired half of its final mass (Gao, Springel White 2005)." + We use the correlation functions to probe the clustering properties of halos., We use the correlation functions to probe the clustering properties of halos. + In figure 8 we plot the correlation functions. (μη) as à function of separation. .r. for halos in three mass ranges in the left. middle ancl right. columns. respectively.," In figure \ref{fig:sets_corr_func} we plot the correlation functions, $\xi(x)$, as a function of separation, $x$, for halos in three mass ranges in the left, middle and right columns, respectively." + The dashed. (dotted) lines in the top. mide and bottom panels. respectively. correspond to104... anc oldest (voungest) halos.," The dashed (dotted) lines in the top, middle and bottom panels, respectively, correspond to, and oldest (youngest) halos." + Phe solid lines in all panels are identical ancl represent the correlation function of the mass densitw field., The solid lines in all panels are identical and represent the correlation function of the mass density field. + In. cach panel the halo correlations are shown by two curves representing de deviations computed using the bootstrap method. as outlined in refsecisimu..," In each panel the halo correlations are shown by two curves representing $\pm\sigma$ deviations computed using the bootstrap method, as outlined in \\ref{sec:simu}." + Ehe dependence of the correlation function on the formation time is clear for all mass ranges shown in the figure., The dependence of the correlation function on the formation time is clear for all mass ranges shown in the figure. + The bias persists even between the voungest and oldest halos., The bias persists even between the youngest and oldest halos. + We use the difference between the correlation functions of old. and voung halos to quantify the assembly bias at various separations., We use the difference between the correlation functions of old and young halos to quantify the assembly bias at various separations. + We determine the bias parameter b in separation range Grr|Aw) by minimizing the quantity (Gao White 2007) Figure (4)) shows the bias as a function of halo mass. for various separations.," We determine the bias parameter $b$ in separation range $(x,x+\Delta x)$ by minimizing the quantity (Gao White 2007) Figure \ref{fig:sets_bias}) ) shows the bias as a function of halo mass, for various separations." + For masses Z2.3LOYAL. the bias is about 1.7 and is similar for all separations considered here.," For masses $\ltsim 2-3\times 10^{12}M_\odot$, the bias is about $1.7$ and is similar for all separations considered here." + The error-bars are large at separations >»LohL“Alpe and we cannot detect an increase in the bias as claimed. by Cao. Springel White (2005).," The error-bars are large at separations $>10\hmpc$ and we cannot detect an increase in the bias as claimed by Gao, Springel White (2005)." + The bias weakens with increasing halo mass. but remains statistically significant only for the old/voung halos. at separations z;Sh.1Mpe.," The bias weakens with increasing halo mass, but remains statistically significant only for the old/young halos, at separations $\ltsim 8\hmpc$." + Lhe ligure shows that the mass scale 23LOMA. marks a mass threshold. above which assembly bias weakens. for all separations.," The figure shows that the mass scale $2-3\times 10^{12}M_\odot$ marks a mass threshold above which assembly bias weakens, for all separations." +" Εις threshold. is close to the non-linear mass scale AJ, defined as the mass scale over which the ros of density [Luctuations is 1.69.", This threshold is close to the non-linear mass scale $M_\star$ defined as the mass scale over which the rms of density fluctuations is $1.69$. +" For our initial conditions M,m54075tal...", For our initial conditions $M_\star \approx 5\times 10^{12}h^{-1}M_\odot$. + Assembly bias may be caused by dillerent environments of old. and. voung halos., Assembly bias may be caused by different environments of old and young halos. + We have experimented with cross correlating the bias with several statistical measure of the environment., We have experimented with cross correlating the bias with several statistical measure of the environment. +" The most relevant measure that we find is the ""dimensionalitv of the density. [ield in regions near halo particles at the initial time."," The most relevant measure that we find is the “dimensionality"" of the density field in regions near halo particles at the initial time." + This parameter is an indicator of the geometry. of the structure developing at later times in those regions., This parameter is an indicator of the geometry of the structure developing at later times in those regions. +" We show here that halo ages are strongly correlated with the ""dimensionalitv of initial [Iuctuation Ποιά as defined by where A; are the eigenvalues of the tensor 00;fOqi,."," We show here that halo ages are strongly correlated with the “dimensionality"" of initial fluctuation field as defined by where $\lambda_i$ are the eigenvalues of the tensor $\partial \theta_l/\partial q_m$." + A the centers of spherical. evlindrical and planar perturbations η obtains the values ap=V3. 2 and η=1. respectively.," At the centers of spherical, cylindrical and planar perturbations $\eta$ obtains the values $\eta=\sqrt{3}$, $\sqrt{2}$ and $\eta=1$, respectively." + We have computed the mean value a as a function. of distance from particles making up voung ancl old. halos., We have computed the mean value $\eta$ as a function of distance from particles making up young and old halos. + The results are plotted in figure Fig. 5.., The results are plotted in figure Fig. \ref{fig:dimm}. + Solid ancl dottec lines. respectively. show a for old and voung halos (two lines representing de deviations from the mean. caleulatec as explained in 833).," Solid and dotted lines, respectively, show $\eta$ for old and young halos (two lines representing $\pm\sigma$ deviations from the mean, calculated as explained in 3)." + This figure shows clearly that voung haloes have an average higher dimensionality than old ones., This figure shows clearly that young haloes have an average higher dimensionality than old ones. + We have shown that assembly. bias of halos persists even in a simplified. description of gravitational dynamics. like the punctuated Zeldovich. (PZ) approximation., We have shown that assembly bias of halos persists even in a simplified description of gravitational dynamics like the punctuated Zel'dovich (PZ) approximation. + The PZ approximation prevents the coasting away of particles in multi-streaming regions by coalescing objects that have come within a critical distance of cach other., The PZ approximation prevents the coasting away of particles in multi-streaming regions by coalescing objects that have come within a critical distance of each other. + The PZ is fast. simple to implement. ancl readily. provides object merging trees.," The PZ is fast, simple to implement, and readily provides object merging trees." + This allows us to study. assembly bias in a large number of simulations (60 simulations. cach of 512? particles in a (128hIxMpe)? cubic box).," This allows us to study assembly bias in a large number of simulations (60 simulations, each of $512^3$ particles in a $(128h^{-1}{\rm Mpc})^3$ cubic box)." + Phe magnitude of the bias is comparable to that found in full simulations., The magnitude of the bias is comparable to that found in full simulations. + This implies that hiehly non-linear cllects such as mass loss from halos in the vicinity of larger mass concentrations. may not be the dominant driver for assembly bias.," This implies that highly non-linear effects such as mass loss from halos in the vicinity of larger mass concentrations, may not be the dominant driver for assembly bias." + We intend. to apply the PZ scheme to the initial conditions used in the millennium simulation. (Springel, We intend to apply the PZ scheme to the initial conditions used in the millennium simulation (Springel +Low aud iuteriuediate mass stars (M zc tha - δ M.) pass through the post-asviuptotic giaut brauch (post-AGB) phase of evolution. on their wav to becoming planetary nebulae (PNe).,Low and intermediate mass stars (M $\simeq$ 0.8 - 8 $_{\odot}$ ) pass through the post-asymptotic giant branch (post-AGB) phase of evolution on their way to becoming planetary nebulae (PNe). + From an analysis of the Infrared Astronomical Satellite Point Source Catalog (IRAS PSC} cooler post-ACB stars having ΕΔΑ. supereiant like character were first identified (Parthasarathy Pottasch 1956. Lamers et al.," From an analysis of the Infrared Astronomical Satellite Point Source Catalog (IRAS PSC) cooler post-AGB stars having G,F,A supergiant like character were first identified (Parthasarathy Pottasch 1986, Lamers et al." + 1986. Pottasch Parthasaratlv 1988a. Ihrivnak et al.," 1986, Pottasch Parthasarathy 1988a, Hrivnak et al." + 1989)., 1989). + These stars were found to have cireumistellar dust shells with far-IR colors aud fiux distributious similar to the dust shells of PNe., These stars were found to have circumstellar dust shells with far-IR colors and flux distributions similar to the dust shells of PNe. + Later. from an analysis of IRAS data. Parthasarathy Pottasch (1989) found a few hot (OB spectral types) post-ACGD candidates.," Later, from an analysis of IRAS data, Parthasarathy Pottasch (1989) found a few hot (OB spectral types) post-AGB candidates." + Their supergiaut like character. the presence of cold detached. dust. shells. far-IR colors simülu to PNe aud lieh ealactic latitudes sugeested that hey may be dn a post-ACGD phase of evolution.," Their supergiant like character, the presence of cold detached dust shells, far-IR colors similar to PNe and high galactic latitudes suggested that they may be in a post-AGB phase of evolution." + Thus. there seenis to be an evolutionary sequence ranging from the cooler CLE.À supergiaut-like stars to hotter O-B types. evolving from the tip of the ACD towards voung PN stage (Parthasaratliy. 1993€).," Thus, there seems to be an evolutionary sequence ranging from the cooler G,F,A supergiant-like stars to hotter O-B types, evolving from the tip of the AGB towards young PN stage (Parthasarathy, 1993c)." + Pottasch et al. (, Pottasch et al. ( +1988b) and van der Veen IIabiug (1055) identified a regiou of the IRAS color-color diagram. (F(1259 /F(255) « 0.35 and F(254/) /F(6059/) 2 0.3) which was inainly populated by stars in transition from the ACB to the PN phase.,1988b) and van der Veen Habing (1988) identified a region of the IRAS color-color diagram $\mu$ $\mu$ ) $<$ 0.35 and $\mu$ $\mu$ ) $>$ 0.3) which was mainly populated by stars in transition from the AGB to the PN phase. + Based on their far-IR colors uid low resolution optical spectra. several hot post-AGB candidates were identified (Parthasarathy Pottasch 1989. Parthasarathy 199348. 1993¢. Parthasarathy et al.," Based on their far-IR colors and low resolution optical spectra, several hot post-AGB candidates were identified (Parthasarathy Pottasch 1989, Parthasarathy 1993a, 1993c, Parthasarathy et al.," + 2000a)., 2000a). + The optical spectra of these objects show strong Bahuer cussion lines and iu some cases low excitation nebular enissiou lines such as [NII| aud |SIT] superposed on the OD stellar contiuuun., The optical spectra of these objects show strong Balmer emission lines and in some cases low excitation nebular emission lines such as [NII] and [SII] superposed on the OB stellar continuum. + The absence of |OIII| lue and the presence of low excitation nebular CUSSION lues indicate that photoioulsation las just started., The absence of [OIII] line and the presence of low excitation nebular emission lines indicate that photoionisation has just started. + It is important to study these stars in the UV to obtain better estimates of their temperatures aud to look for signatures of circtuustcllay reddening. mass-loss and stellar winds.," It is important to study these stars in the UV to obtain better estimates of their temperatures and to look for signatures of circumstellar reddening, mass-loss and stellar winds." + The UV(IUE) spectra of some hot post-AGB stars (ee., The UV(IUE) spectra of some hot post-AGB stars (eg. + Hou3-1357. Parthasarathy ct al.," Hen3-1357, Parthasarathy et al." +" L993), 1995. Feibelinan. 1995) have revealed violet shifted stellar wind P-Cveui profiles of CIV. SIV and NV. indicating hot and fast stellar wind. post-ACD mass-loss aud rapid evolution."," 1993b, 1995, Feibelman, 1995) have revealed violet shifted stellar wind P-Cygni profiles of CIV, SiIV and NV, indicating hot and fast stellar wind, post-AGB mass-loss and rapid evolution." + In this paper we have analvsec the UV(IUE) spectra of 15 hot post-ACD candidates., In this paper we have analysed the UV(IUE) spectra of 15 hot post-AGB candidates. + The hot post-ACGD candidates in this paper (Table 1) were ideutifed on the basis of their IRAS colors (F(12;)/F(25p) < 0.35 and F(25j)0/F(G0j/) > 0.3). high ealactic latitudes and OD-giaut or supereiant spectra iu the optical (Parthasarathy et al.," The hot post-AGB candidates in this paper (Table 1), were identified on the basis of their IRAS colors $\mu$ $\mu$ ) $<$ 0.35 and $\mu$ $\mu$ ) $>$ 0.3), high galactic latitudes and OB-giant or supergiant spectra in the optical (Parthasarathy et al.," + 2000a) with Balmer lines in enission., 2000a) with Balmer lines in emission. + Young massive OB supergiauts are not expected at ligh ealactic latitudes and also they are not expected to have detached cold circtiustellar cust shells., Young massive OB supergiants are not expected at high galactic latitudes and also they are not expected to have detached cold circumstellar dust shells. +" Wiech ealactic latitude OB supereiauts with detached dust shells aud far-IR colors similar to PNe were found to be in the post-AGB phase of evolution (Parthasarathy, 10006, Parthasarathy et al.."," High galactic latitude OB supergiants with detached dust shells and far-IR colors similar to PNe were found to be in the post-AGB phase of evolution (Parthasarathy, 1993c, Parthasarathy et al.," + 2000a)., 2000a). + Low vesolution (~ 6 7A). huge aperture. UV(IUE) cAvectra of the hot post-ACB candidates from {ο were extracted from the Multinission Archive at STScI (Table 2).," Low resolution $\sim$ 6 $-$ ), large aperture, UV(IUE) spectra of the hot post-AGB candidates from to were extracted from the Multimission Archive at STScI (Table 2)." + The spectra obtained by centering the stars in the LOUN 23”apertuve were processed using the IUE NEWSIPS (new spectral damage processing svsteni) pipeline which applies the signal weighted extraction technique (SWET) as well as the latest fis calibration and close-out camera sensitivity corrections., The spectra obtained by centering the stars in the X aperture were processed using the IUE NEWSIPS (new spectral image processing system) pipeline which applies the signal weighted extraction technique (SWET) as well as the latest flux calibration and close-out camera sensitivity corrections. + &u increased signal-to-noise (S/N) ratio of has been demonstrated for low dispersion IUE spectra reprocessed with the NEWSIPS software (Nichols Linsky. 1996).," An increased signal-to-noise (S/N) ratio of $-$ has been demonstrated for low dispersion IUE spectra reprocessed with the NEWSIPS software (Nichols Linsky, 1996)." + Well exposed IUE NEWSIPS spectra have S/N of ~ 50 while weak. high-backerounc. uuder-exposed spectra have S/N of ~ 20 (Nichols et al..," Well exposed IUE NEWSIPS spectra have S/N of $\sim$ 50 while weak, high-background, under-exposed spectra have S/N of $\sim$ 20 (Nichols et al.," + 1991. Nichols Linsky. 1996).," 1994, Nichols Linsky, 1996)." +" Frou, our sample. IRASII331-6135 (Iecus-1013). IRAST707I-1815. (ITo2-1317). IRAS17203- IRAS15023-3109 (LSS 163D). TRASLS379-1707 (LSS"," From our sample, IRAS14331-6435 (Hen3-1013), IRAS17074-1845 (Hen3-1347), IRAS17203-1534, IRAS18023-3409 (LSS 4634), IRAS18379-1707 (LSS" +magnetic energies can be advected with the accretion flow into the black hole. producing no effeclive increase ooverall effidency.,"magnetic energies can be advected with the accretion flow into the black hole, producing no effective increase overall efficiency." + This point is closely related to (he issue of advected energv discussed in 3.4..., This point is closely related to the issue of advected energy discussed in \ref{sec:extrap}. + Framed in the context of predictions for real accretion flows in Nature. these «questions emphasize the importance of realistic dissipation and radiation physics for obtaining more accurate accounts of radiation associated with accretion.," Framed in the context of predictions for real accretion flows in Nature, these questions emphasize the importance of realistic dissipation and radiation physics for obtaining more accurate accounts of radiation associated with accretion." + In the vicinity of the ISCO. where 1e energy. available for release is largest. one cannol sav wilh confidence that in general the dissipation and cooling mes are shorter than the inflow time.," In the vicinity of the ISCO, where the energy available for release is largest, one cannot say with confidence that in general the dissipation and cooling times are shorter than the inflow time." + Moreover. both processes are likely to depend on the detailed circumstances pertaining to anv particular accreting black hole. so that there max not be a single efficiency number applicable to all black holes of a given spin.," Moreover, both processes are likely to depend on the detailed circumstances pertaining to any particular accreting black hole, so that there may not be a single efficiency number applicable to all black holes of a given spin." + In sum. we have shown (hat by use of a tov-moclel opticallv-thin cooling function. it is possible both to control the thickness of the accretion flow and to Cally (approximately) the rate at which radiation can be produced bv dissipation in the flow.," In sum, we have shown that by use of a toy-model optically-thin cooling function, it is possible both to control the thickness of the accretion flow and to tally (approximately) the rate at which radiation can be produced by dissipation in the flow." + At relatively large racii. where the inflow (nme is long compared to the cooling Gime. ouransatz of substituting eridscale dissipation lor genuine microphDvsies aud radiating the heat so generated at an arbitrarily chosen rate is capable of capturing the global energetics of accretion reasonably well.," At relatively large radii, where the inflow time is long compared to the cooling time, our of substituting gridscale dissipation for genuine microphysics and radiating the heat so generated at an arbitrarily chosen rate is capable of capturing the global energetics of accretion reasonably well." + However. at smaller raci (parlicularly near and inside the ISCO). where the inflow lime can be comparable to the cooling time. use of realistic dissipation and radiation rates can be more important.," However, at smaller radii (particularly near and inside the ISCO), where the inflow time can be comparable to the cooling time, use of realistic dissipation and radiation rates can be more important." + llaving demonstrated the technical feasibilitw of (his approach. we will next. emplov it (o explore more fully how accretion onto black holes depends on disk thickness aud on black hole rotation rate.," Having demonstrated the technical feasibility of this approach, we will next employ it to explore more fully how accretion onto black holes depends on disk thickness and on black hole rotation rate." + In this context. we point out that although there is a stanclard notation [or describing black hole rotation (the spin parameter αλ). there are several extant definitions of the scale-height. differing [rom one another by factors of order unitv.," In this context, we point out that although there is a standard notation for describing black hole rotation (the spin parameter $a/M$ ), there are several extant definitions of the scale-height, differing from one another by factors of order unity." + We use the vertical density moment: standardization of this definition would be of benefit so (hat different calculations can be compared quantitatively without confusion., We use the vertical density moment; standardization of this definition would be of benefit so that different calculations can be compared quantitatively without confusion. + Lastly. we remark that in (his paper we have set aside the fact that photons are not the only form in which energy can be sent to infinitv [rom the vieinity of black holes.," Lastly, we remark that in this paper we have set aside the fact that photons are not the only form in which energy can be sent to infinity from the vicinity of black holes." + Accreting black holes are also capable of driving mass motions. often relativistic. (hat can carry significant. power in Povnüng flux.," Accreting black holes are also capable of driving mass motions, often relativistic, that can carry significant power in Poynting flux." + Simulational work exploring the associated huninosity has already. begun (2277)...," Simulational work exploring the associated luminosity has already begun \citep{2004ApJ...611..977M, +2006ApJ...641..103H,2008ApJ...678.1180B}." +Globular clusters are made up of a very large number of stars with varying mass but ideutical age. Composition. aud distance.,"Globular clusters are made up of a very large number of stars with varying mass but identical age, composition, and distance." + This makes them a rich aud productive application of the theory of stellar structure aud evolution., This makes them a rich and productive application of the theory of stellar structure and evolution. +" Detailed stellar evolution calculatious are done ununerically. using computer programms which incorporate previously calculated unclear reaction rates aud opacities. approximatious to Complex, phenomena such as convection. aud assumptions about the chemical"," Detailed stellar evolution calculations are done numerically using computer programs which incorporate previously calculated nuclear reaction rates and opacities, approximations to complex phenomena such as convection, and assumptions about the chemical" +sensitivity. ancl the larger areal coverage does not make up lor that loss.,"sensitivity, and the larger areal coverage does not make up for that loss." + An albskv. moderately deep. mid-infrared survev must be undertaken (o find large numbers of easilv-recoverable. cool brown dwarls.," An all-sky, moderately deep, mid-infrared survey must be undertaken to find large numbers of easily-recoverable, cool brown dwarfs." + This twpe of survey offers the prospect ol finding hundreds of nearby. extremely cool brown clwarls.," This type of survey offers the prospect of finding hundreds of nearby, extremely cool brown dwarfs." + The Wide-field Infrared Survey Explorer (WISE) (Wright.Eisenhardt.&WISEScienceTeam2004) is one such mission that has already been proposed. surveving the entire skv at 3.5. 4.7. 12 and 23 yam. WISE makes use of the extremely red 3.5jm. 4.7;an color of very. cool dwarls to distinguish them from other sources.," The Wide-field Infrared Survey Explorer (WISE) \citep{wright} is one such mission that has already been proposed, surveying the entire sky at 3.5, 4.7, 12 and 23 $\mu$ m. WISE makes use of the extremely red $\mu$ $\mu$ m color of very cool dwarfs to distinguish them from other sources." + The predicted 7j sensitivity will be similar to the SWIRE Spitzer Legacy survev. but. will cover (he entire sky. not just TO square degrees.," The predicted $\mu$ m sensitivity will be similar to the SWIRE Spitzer Legacy survey, but will cover the entire sky, not just 70 square degrees." + Overall. WISE will detect over 270.000 P. dwarfs and. 40.000 cooler objects. including hundreds within 20-30 parsecs of the Sun.," Overall, WISE will detect over 270,000 T dwarfs and 40,000 cooler objects, including hundreds within 20-30 parsecs of the Sun." + In the near future upcoming ground based [aciliies will provide the capability of detecting significant nunbers of T and cooler objects., In the near future upcoming ground based facilities will provide the capability of detecting significant numbers of T and cooler objects. + For example. the VISTA collaboration will have a wide-field near-inlrared imager behind a 4m class telescope in Chile within 2 vears.," For example, the VISTA collaboration will have a wide-field near-infrared imager behind a 4m class telescope in Chile within 2 years." + Much of the time (757)) will be allocated to survevs., Much of the time ) will be allocated to surveys. + This instrument will probe 5-6 magnitudes deeper than 2\TASS or DENIS. which enables the compilation of a larger sample of late-T cdwarfs aud the possible detection of cooler objects.," This instrument will probe 5-6 magnitudes deeper than 2MASS or DENIS, which enables the compilation of a larger sample of late-T dwarfs and the possible detection of cooler objects." + In the interim. the conjunction of the completed 2\LASS survey and the ongoing SDSS provide the best prospects for further understanding of the substellar mass function.," In the interim, the conjunction of the completed 2MASS survey and the ongoing SDSS provide the best prospects for further understanding of the substellar mass function." + While SDSS does not cover the whole skv as 2MAÀS5 does. it supplies eritical color information that allows easier extraction of late-L and early-T dwirfs.," While SDSS does not cover the whole sky as 2MASS does, it supplies critical color information that allows easier extraction of late-L and early-T dwarfs." + The 2\LASS colors of late-L and dwarls fall into a very crowded area of the color-magnitude ciagram., The 2MASS colors of late-L and early-T dwarfs fall into a very crowded area of the color-magnitude diagram. + Selection criteria [or early-T dwarls become much cleaner with the addition of short wavelength SDSS photometry (Figure 15))., Selection criteria for early-T dwarfs become much cleaner with the addition of short wavelength SDSS photometry (Figure \ref{fig:cmd}) ). + In this way. we obtain preliminary space densities for late L and T dwarls before a definitive project. like WISE. is carried out.," In this way, we obtain preliminary space densities for late L and T dwarfs before a definitive project, like WISE, is carried out." + This paper produces new models of the luminosity function. of field brown dwartls., This paper produces new models of the luminosity function of field brown dwarfs. + Through these models. we explore the role of the rapid evolution of brown dwarls on the Iuninositv and {νε distributions. and find that those distributions are surprisingly insensitive to changes in Che underlving age distribution.," Through these models, we explore the role of the rapid evolution of brown dwarfs on the luminosity and $T_{eff}$ distributions, and find that those distributions are surprisingly insensitive to changes in the underlying age distribution." + Our main goal is to use our Davesian statistical method to constrain the field substellar mass function using data on late-M. L. and T dwarls (INC'AD).," Our main goal is to use our Bayesian statistical method to constrain the field substellar mass function using data on late-M, L, and T dwarfs (KCAB)." + We present results that demonstrate the extant dala provide modest constraints on, We present results that demonstrate the extant data provide modest constraints on +C/O ratios to be higher (han for the diffuse sishtlines.,C/O ratios to be higher than for the diffuse sightlines. + This is the case for these four sightlines (hat have a weighted average C/O = 0.68d:0.08 compared to the dilfuse cloud weighted average of 0.47250.05., This is the case for these four sightlines that have a weighted average C/O = $0.68 \pm 0.08$ compared to the diffuse cloud weighted average of $0.47 \pm 0.05$. + The hieh C/O ratios in these translucent sightlines contrast ihe measurement in (he translucent sightline toward WD 24534 where C/O = 0.28+0.09 (Soliaοἱal.1993:Snowet1993).," The high C/O ratios in these translucent sightlines contrast the measurement in the translucent sightline toward HD 24534 where C/O = $0.28 \pm 0.09$ \citep{sfm98,sno98}." +. One must keep in mind (hat the noise structure discussed in 822 could affect some of our measurements in the direction of increasing C/O. The sightline toward HD 152590 has a measured C/I that is well above any other interstellar measurement. and above anv standard abundances used (o represent the total interstellar C abundance.," One must keep in mind that the noise structure discussed in 2 could affect some of our measurements in the direction of increasing C/O. The sightline toward HD 152590 has a measured C/H that is well above any other interstellar measurement, and above any standard abundances used to represent the total interstellar C abundance." + The C uj and O absorption features for this sightline (see Figure 1) ook very similar with the profiles showing only a slight deviation toward the lone-waveleneth sile of the features., The C ] and O absorption features for this sightline (see Figure 1) look very similar with the profiles showing only a slight deviation toward the long-wavelength side of the features. + One possibility. is that. structured. noise is particularly strong in the absorption feature and the C abundance is highly overestimated., One possibility is that structured noise is particularly strong in the absorption feature and the C abundance is highly overestimated. + Another explanation. that would also explain the similarity of the 2 absorption profiles. is (hat (he sighüline is passing through an atypical region of the interstellar medium with unusual abundances.," Another explanation, that would also explain the similarity of the 2 absorption profiles, is that the sightline is passing through an atypical region of the interstellar medium with unusual abundances." + This seems unlikely since (he O/II ratio toward the star is not atvpical (Cartledgeοἱal.2003)., This seems unlikely since the O/H ratio toward the star is not atypical \citep{cml03}. +. This star was reported (o have an enhanced depletion of O compared to diffuse siehtlines by Cartledgeetal.(2001)., This star was reported to have an enhanced depletion of O compared to diffuse sightlines by \citet{car01}. +. That determination was based on the O/Ixr ratio. however a recent measurement of the IL abundance from FUSE data shows that the apparent depletion enhancement was (he result of a high Ixr/II (Carclelli&Mever1997) rather (han a low Ο/Η (Cartledgeοἱal.2003).," That determination was based on the O/Kr ratio, however a recent measurement of the H abundance from $FUSE$ data shows that the apparent depletion enhancement was the result of a high Kr/H \citep{cm97} rather than a low O/H \citep{cml03}." +. While only a 2o result. the apparent higher (han average Ixr/1l ratio toward (he star leaves open the possibilitv that the sie¢htline may possess unusual abundances.," While only a $\sigma$ result, the apparent higher than average Kr/H ratio toward the star leaves open the possibility that the sightline may possess unusual abundances." + The IID 27778 sightline has a well-determined lower limit on its carbon column density wl gives a carbon-to-hvdrogen ratio of < 108 C atoms per million Il in the gas., The HD 27778 sightline has a well-determined lower limit on its carbon column density that gives a carbon-to-hydrogen ratio of $\leq$ 108 C atoms per million H in the gas. + This abundance suggests a substantial enhancement in the depletion of C as compared to diffuse V.iehtlines., This abundance suggests a substantial enhancement in the depletion of C as compared to diffuse sightlines. + Wilh a gas-phase C/O ratio of «0.37. it also implies (hat C is more substantially Mthancecd in depletion than O. Looking at the standard parameters used to determine V.ightline characteristics in Table 1. there is no obvious reason why the IID 27778 sightline V.10uld have such a low carbon abundance as compared to the others.," With a gas-phase C/O ratio of $<0.37$, it also implies that C is more substantially enhanced in depletion than O. Looking at the standard parameters used to determine sightline characteristics in Table 1, there is no obvious reason why the HD 27778 sightline should have such a low carbon abundance as compared to the others." + In fact. it has an à iab ds closer to the Galactic mean (han any other in our sample (i.e.. ils extinction curve is lose to the Galactic average: (he extinction curve is shown in Josephetal. (1986))). it has 1e lowest IL column density. and its «n(ILI)2 is a very typical value.," In fact, it has an $R_{V}$ that is closer to the Galactic mean than any other in our sample (i.e., its extinction curve is close to the Galactic average; the extinction curve is shown in \citet{jos86}) ), it has the lowest H column density, and its $<$ $>$ is a very typical value." + The sightline is relatively V.rort (225 pe: Perrvinan οἱ al., The sightline is relatively short (225 pc; Perryman et al. + 1997). so we would not expect anv metallicity gradients to xe affecting the abundance.," 1997), so we would not expect any metallicity gradients to be affecting the abundance." + The only extreme interstellar characteristic shown in Table I is wal. of the sample. the WD 27778 sightline has the hiehest fraction of its Hin the form of IIs.," The only extreme interstellar characteristic shown in Table 1 is that, of the sample, the HD 27778 sightline has the highest fraction of its H in the form of $_{2}$." + This fraction. however. is not unusual with the translucent sightline toward ILD 24534 (Snowοἱal.1998) and the diffuse sightlines toward ¢ Per and ¢ Oph having substantially," This fraction, however, is not unusual with the translucent sightline toward HD 24534 \citep{sno98} and the diffuse sightlines toward $\zeta$ Per and $\zeta$ Oph having substantially" +The derived abundances can also be compared to the predictions of evolutionary models.,The derived abundances can also be compared to the predictions of evolutionary models. + These abundances are very useful to constrain the physics included in the code., These abundances are very useful to constrain the physics included in the code. + For F stars. the models calculated by Turcotteetal.(1998) include radiative diffusion and gravitational settling for 28 chemical elements (Z < 28).," For F stars, the models calculated by \cite{1998ApJ...504..559T} include radiative diffusion and gravitational settling for 28 chemical elements (Z $\leq$ 28)." + At the age of the Pleiades cluster (100 Myr). these models predict slight underabundances of carbon and oxygen for stars with Zy>6500 K which are confirmed in our data.," At the age of the Pleiades cluster (100 Myr), these models predict slight underabundances of carbon and oxygen for stars with $T_{\rm{eff}} > 6500$ K which are confirmed in our data." + However the predicted underabundances of Mg. Si and Ca are not found in our analysis.," However the predicted underabundances of Mg, Si and Ca are not found in our analysis." + The predicted slight overabundances for Cr. Fe and Ni are indeed observed for the five F stars analysed.," The predicted slight overabundances for Cr, Fe and Ni are indeed observed for the five F stars analysed." + The overall trend for F stars. slight underabundances of light elements and overabundances of iron-peak elements agree well with the predictions of the models (except for a few elements) suggesting that the appropriate physics is included in the code for F For A stars. we can compare our results to the predictions of the Richer et al. (," The overall trend for F stars, slight underabundances of light elements and overabundances of iron-peak elements agree well with the predictions of the models (except for a few elements) suggesting that the appropriate physics is included in the code for F For A stars, we can compare our results to the predictions of the Richer et al. (" +2000) models which include turbulent diffusion in addition to radiative diffusion.,2000) models which include turbulent diffusion in addition to radiative diffusion. + Inspection of their figures 10 and 11 reveals that at the age of the Pleiades. C and O should be slightly underabundant by about —0.1 dex and the iron peak elements be slightly overabundant from about 0.1 to 0.4 dex.," Inspection of their figures 10 and 11 reveals that at the age of the Pleiades, C and O should be slightly underabundant by about $-$ 0.1 dex and the iron peak elements be slightly overabundant from about 0.1 to 0.4 dex." + The derived abundances respectively for C. O and iron peak elements in this analysis agree well with these levels of deficiency and The star-to-star scatter of abundances among the 16 A stars analysed here was already previously found in other open clusters and in a few field A stars.," The derived abundances respectively for C, O and iron peak elements in this analysis agree well with these levels of deficiency and The star-to-star scatter of abundances among the 16 A stars analysed here was already previously found in other open clusters and in a few field A stars." + It appears to be a characteristic property of dwarf A and F stars and strongly suggests that hydrodynamical processes competing with radiative and turbulent diffusion must be at work m the radiative zones of these stars (see a review in Zahn 2009)., It appears to be a characteristic property of dwarf A and F stars and strongly suggests that hydrodynamical processes competing with radiative and turbulent diffusion must be at work in the radiative zones of these stars (see a review in Zahn 2005). + In order to fully characterize this scatter. spectroscopy of the remaining A and F stars in the Pleiades 1s foreseen in the near future.," In order to fully characterize this scatter, spectroscopy of the remaining A and F stars in the Pleiades is foreseen in the near future." + Also non-LTE analysis should be performed to yield more accurate abundances for C. Mg and Ba as most of the lines analysed here for these elements are prone to non-LTE effects.," Also non-LTE analysis should be performed to yield more accurate abundances for C, Mg and Ba as most of the lines analysed here for these elements are prone to non-LTE effects." +"survev are all bright (2;<23.7 magnitudes) compared to the limiting magnitude of many ol the survev fields Gn,=25.7 magnitudes).",survey are all bright $m_{R}<23.7$ magnitudes) compared to the limiting magnitude of many of the survey fields $m_{R}=25.7$ magnitudes). +" A roll-over in the Neptune Trojan CLF is apparent around m,=23.5£0.3.", A roll-over in the Neptune Trojan CLF is apparent around $m_{R}=23.5\pm0.3$. +" For the Neptune Trojans the best fit to the CLF lor mgc23.5 mag isa —0.840.2 and my,=24.45c0.4."," For the Neptune Trojans the best fit to the CLF for $m_{R} < 23.5$ mag is $\alpha = 0.8 \pm 0.2$ and $m_{o} = 24.45 +\pm 0.4$." + The points in a CLF are heavily correlated with one another. tendinge to exgive excess weieht to the faint end of the distribution.," The points in a CLF are heavily correlated with one another, tending to give excess weight to the faint end of the distribution." + The Differential Luminosity Function (DLE) does 100 suffer from this problem., The Differential Luminosity Function (DLF) does not suffer from this problem. + We plot the DLE using a bin size of 0.5 mae for all Neptune Trojans detected in our survey (Figure 3))., We plot the DLF using a bin size of 0.5 mag for all Neptune Trojans detected in our survey (Figure \ref{fig:diffTrojans}) ). + The roll-over in the number of fainter objects is shown more dramatically through the DLE. and is insensitive to bin size choice.," The roll-over in the number of fainter objects is shown more dramatically through the DLF, and is insensitive to bin size choice." +" If the ainter (smaller) objects continued to follow the q=5 size distribution slope of the brighter larger) objects we would have expected to discover 80+10 Neptune Trojans between the roll-over point at my,23.5 magnitudes (r~45 km) and our survey limit of mge25.7 nagnitudes (716 km).", If the fainter (smaller) objects continued to follow the $q=5$ size distribution slope of the brighter (larger) objects we would have expected to discover $80\pm 10$ Neptune Trojans between the roll-over point at $m_{R}\sim 23.5$ magnitudes $r\sim 45$ km) and our survey limit of $m_{R}\sim 25.7$ magnitudes $r\sim 16 $ km). + Though we found hundreds of Kuiper Bell objects with my>24 nagnitudes we found zero Neptune Trojans of this faintness. which gives about an 36 resull that the smaller Neptune Trojans have a shallower power-law slope than the larger Neptune Trojans.," Though we found hundreds of Kuiper Belt objects with $m_{R} > 24$ magnitudes we found zero Neptune Trojans of this faintness, which gives about an $8\sigma$ result that the smaller Neptune Trojans have a shallower power-law slope than the larger Neptune Trojans." + Thus like the other known stable small body reservoirs. the CLE of the Neptune Trojans is best fit bv a broken power law that breaks from a steep slope for the largest objects to a shallow distribution for the smaller objects.," Thus like the other known stable small body reservoirs, the CLF of the Neptune Trojans is best fit by a broken power law that breaks from a steep slope for the largest objects to a shallow distribution for the smaller objects." + The data at the faintest end for the Neptune Trojans ave within about 26 of the shallow slope found for faint ος (Figure 2))., The data at the faintest end for the Neptune Trojans are within about $2\sigma$ of the shallow slope found for faint KBOs (Figure \ref{fig:cumTrojans}) ). + Further dala are required to determine a reliable slope lor the Neptune Trojans at the faint. end of the CLE., Further data are required to determine a reliable slope for the Neptune Trojans at the faint end of the CLF. + Though we cannot completely rule oul the possibilitw that the Neptune Trojans have a single verv shallow power law il seems unlikelv since we cannot fit a single power law to all the points to within lo and the best fit power law to all the data would be the shallowest observed (q 2.5) [ον such relatively large objects in (he solar svstem., Though we cannot completely rule out the possibility that the Neptune Trojans have a single very shallow power law it seems unlikely since we cannot fit a single power law to all the points to within $1\sigma$ and the best fit power law to all the data would be the shallowest observed $q\sim 2.5$ ) for such relatively large objects in the solar system. + This slope would also be much shallower Chan the Dohnanyi slope of 3.5 Chat is expected if the objects were in a state of collisional equilibrium (OBrien Greenberg 2003)., This slope would also be much shallower than the Dohnanyi slope of 3.5 that is expected if the objects were in a state of collisional equilibrium (O'Brien Greenberg 2003). + One of the main wavs to constrain the formation and collisional history of an ensemble ol objects such as the Neptune Trojans is to determine their size distribution., One of the main ways to constrain the formation and collisional history of an ensemble of objects such as the Neptune Trojans is to determine their size distribution. + The size distribution is an indicator of how the accretion process worked and is related to the CLE., The size distribution is an indicator of how the accretion process worked and is related to the CLF. + If we assume the Neptune Trojans all have similar albedos to the Jupiter Trojans (0.05. Fernandez et al.," If we assume the Neptune Trojans all have similar albedos to the Jupiter Trojans (0.05, Fernandez et al." + 2003) and are at a distance of 30 AU we can determine the size distribution (Figure 4)) of the Neptune Trojans from the CLF., 2003) and are at a distance of 30 AU we can determine the size distribution (Figure \ref{fig:sizeTrojans}) ) of the Neptune Trojans from the CLF. + A slope of q=541 is found for the large, A slope of $q=5\pm1$ is found for the large +We have performed magnetohydrodynamic (MHD) simulations of the collapse of molecular cloud cores. some with initial ny=2 density perturbations. and others that were homogenous.,"We have performed magnetohydrodynamic (MHD) simulations of the collapse of molecular cloud cores, some with initial $m=2$ density perturbations, and others that were homogenous." + In terms of the effect of magnetic fields on the fragmentation of perturbed molecular clouds. we have two main conclusions.," In terms of the effect of magnetic fields on the fragmentation of perturbed molecular clouds, we have two main conclusions." + First. we tind that wide binaries can be readily obtained from perturbed molecular cloud cores even with mass-to-flux ratios as low as AL/D=23.," First, we find that wide binaries can be readily obtained from perturbed molecular cloud cores even with mass-to-flux ratios as low as $M/\Phi = 2-3$." + Since most molecular cloud cores are observed to be strongly aspherical.suggested.," Since most molecular cloud cores are observed to be strongly aspherical,." + Second. in agreement with past studies. we find that magnetic tields act to suppress fragmentation.," Second, in agreement with past studies, we find that magnetic fields act to suppress fragmentation." + However. contrary to past studies that have emphasized the importance of magnetic tension forces and magnetic braking in suppressing fragmentation. we tind thatfragmentation.," However, contrary to past studies that have emphasized the importance of magnetic tension forces and magnetic braking in suppressing fragmentation, we find that." + For all calculations. we find that stronger magnetic fields result in longer delays to the collapse due to the increased support provided by the field above that provided by thermal pressure alone.," For all calculations, we find that stronger magnetic fields result in longer delays to the collapse due to the increased support provided by the field above that provided by thermal pressure alone." + The delaying of the collapse has a potentially crucial effect on protostellar disces that form around protostars., The delaying of the collapse has a potentially crucial effect on protostellar discs that form around protostars. + Because the infall rate of mass onto the dise from the envelope is reduced. the disces are less prone to gravitational instabilities.," Because the infall rate of mass onto the disc from the envelope is reduced, the discs are less prone to gravitational instabilities." + This may have at least three important effects., This may have at least three important effects. + First. high infall rates on to dises have been shown in the past to be responsible for driving gravitational instabilities that are strong enough to result in dise fragmentation and the production of binary and multiple systems.," First, high infall rates on to discs have been shown in the past to be responsible for driving gravitational instabilities that are strong enough to result in disc fragmentation and the production of binary and multiple systems." + Thus. we conclude that magnetic fields tend to inhibit dise fragmentation.," Thus, we conclude that magnetic fields tend to inhibit disc fragmentation." + Second. even for initial conditions that in the absence of magnetic fields give infall rates insufficient to cause disc fragmentation. the discs frequently generate spiral density waves hat efficiently transport angular momentum.," Second, even for initial conditions that in the absence of magnetic fields give infall rates insufficient to cause disc fragmentation, the discs frequently generate spiral density waves that efficiently transport angular momentum." + With magnetic fields. he lowering of the infall rate on to the dise decreases the strength and importance of these instabilities.," With magnetic fields, the lowering of the infall rate on to the disc decreases the strength and importance of these instabilities." + Third. spiral density waves iive been suggested as a possible mechanism for producing high enough concentrations of metre-sized planetesimals to produce kilometre-sized planetesimals via gravitational instability.," Third, spiral density waves have been suggested as a possible mechanism for producing high enough concentrations of metre-sized planetesimals to produce kilometre-sized planetesimals via gravitational instability." + Since we tind that magnetic tields decrease the strength of the spiral density waves in protostellar discs. magnetic fields may also decrease the ikelihood of forming planetary systems by such a mechanism.," Since we find that magnetic fields decrease the strength of the spiral density waves in protostellar discs, magnetic fields may also decrease the likelihood of forming planetary systems by such a mechanism." + We thank the referee. Ant. Whitworth. for asking questions that led to a significant improvement in the paper.," We thank the referee, Ant Whitworth, for asking questions that led to a significant improvement in the paper." + DJP is supported by a UK PPARC postdoctoral research fellowship., DJP is supported by a UK PPARC postdoctoral research fellowship. + MRB is grateful for the support of a Philip Leverhulme Prize and a EURYI Award., MRB is grateful for the support of a Philip Leverhulme Prize and a EURYI Award. + Calculations were performed using the School of Physics iMac cluster at the University of Exeter and on the United Kingdom Astrophysical Fluids Facility (UKAFF)., Calculations were performed using the School of Physics iMac cluster at the University of Exeter and on the United Kingdom Astrophysical Fluids Facility (UKAFF). +. We thank Charles Williams in particular for support on the iMac cluster., We thank Charles Williams in particular for support on the iMac cluster. + Visualisations made use of SPLASH/SUPERSPHPLOT. a visualisation tool for SPH that is publicly available at http:/Avww.astro.exacuk/people/dprice/splash.," Visualisations made use of SPLASH/SUPERSPHPLOT, a visualisation tool for SPH that is publicly available at http://www.astro.ex.ac.uk/people/dprice/splash." +" This work. conducted as part of the award ""The formation of stars and planets: Radiation hydrodynamical and magnetohydrodynamical simulations” made under the European Heads of Research Councils and European Science Foundation EURYT (European Young Investigator) Awards scheme. was supported by funds from the Participating Organisations of EURYT and the EC Sixth Framework Programme."," This work, conducted as part of the award “The formation of stars and planets: Radiation hydrodynamical and magnetohydrodynamical simulations"" made under the European Heads of Research Councils and European Science Foundation EURYI (European Young Investigator) Awards scheme, was supported by funds from the Participating Organisations of EURYI and the EC Sixth Framework Programme." +The term of the change of the energy density by the radiation is therefore given by Another change of the energy density is due to the work W done by the adiabatic expansion of the SN Ia atmosphere.,The term of the change of the energy density by the radiation is therefore given by Another change of the energy density is due to the work $W$ done by the adiabatic expansion of the SN Ia atmosphere. + For à discrete step this work is given by The expansion is assumed to be homologous., For a discrete step this work is given by The expansion is assumed to be homologous. + Since we solve the energy equation for the matter. we do not include the radiation pressure work.," Since we solve the energy equation for the matter, we do not include the radiation pressure work." + Since the system is radiation dominated there is the possibility of numerical inaccuracies in coupling the matter and radiation only by Q., Since the system is radiation dominated there is the possibility of numerical inaccuracies in coupling the matter and radiation only by $Q$. + For the calculation of the new radii and densities as well as a discussion about the accuracy of this assumption see ?.., For the calculation of the new radii and densities as well as a discussion about the accuracy of this assumption see \citet{jack09}. +" Including all energy changing effects. the new energy density of the material e» after a discrete time step Ar is explicitly given by where e, Is the old energy density."," Including all energy changing effects, the new energy density of the material $e_{2}$ after a discrete time step $\Delta t$ is explicitly given by where $e_{1}$ is the old energy density." + To obtain all the needed quantities we have to solve the spherically symmetric special relativistic radiative transfer equation., To obtain all the needed quantities we have to solve the spherically symmetric special relativistic radiative transfer equation. + The advantage of our new approach is that we do not have to iterate for each time step., The advantage of our new approach is that we do not have to iterate for each time step. + In our previous paper the calculation of each time step involved an iteration. process to obtain the new matter temperature., In our previous paper the calculation of each time step involved an iteration process to obtain the new matter temperature. + With the new approach we can calculate the new temperature for the next time step directly from all the known quantities., With the new approach we can calculate the new temperature for the next time step directly from all the known quantities. + The translational energy density of the material is given by with the mean molecular weigh 4| and the universal gas constant R., The translational energy density of the material is given by with the mean molecular weigh $\mu$ and the universal gas constant $R$. + The gas pressure Is represented by p and the density by p., The gas pressure is represented by $p$ and the density by $\rho$. + 7 stands for the temperature of the material., $T$ stands for the temperature of the material. + This equation of the energy density is now used to determine the new temperature after the next time step., This equation of the energy density is now used to determine the new temperature after the next time step. + During the first phase of the SN Ia envelope evolution. the material of the atmosphere is hot and. therefore. highly ionized.," During the first phase of the SN Ia envelope evolution, the material of the atmosphere is hot and, therefore, highly ionized." + The energy change due to ionization and exeitation changes of the atoms present in the SN Ia atmosphere cannot be neglected., The energy change due to ionization and excitation changes of the atoms present in the SN Ia atmosphere cannot be neglected. + aalready solves the equation of state (EOS). where all the excitation. and ionization stages of the present atoms and molecules are included.," already solves the equation of state (EOS), where all the excitation and ionization stages of the present atoms and molecules are included." +" Using the EOS. we obtain the overall energy density of the material by the sum of the ionization energy ej, and the translational energy ej; Hence. the energy density change of the material goes into a change of the translational energy and the ionization energy. Which both depend on the temperature."," Using the EOS, we obtain the overall energy density of the material by the sum of the ionization energy $e_{ions}$ and the translational energy $e_{trans}$ Hence, the energy density change of the material goes into a change of the translational energy and the ionization energy, which both depend on the temperature." + Therefore. we obtain the new temperature by an iteration scheme.," Therefore, we obtain the new temperature by an iteration scheme." + The matter density at the next point in time is determined by homologous expansion., The matter density at the next point in time is determined by homologous expansion. + A first temperature guess is used. and the EOS is solved to obtain the ionization energy density.," A first temperature guess is used, and the EOS is solved to obtain the ionization energy density." + Combined with the translational energy density. the overall energy density 15 computed.," Combined with the translational energy density, the overall energy density is computed." + This is checked against the target energy density. which we obtained equation 6..," This is checked against the target energy density, which we obtained equation \ref{eq:newenergy}." + If the obtained energy density Is Incorrect. à new temperature guess is made.," If the obtained energy density is incorrect, a new temperature guess is made." + This new temperature guess is obtained by assuming a linear dependence of the energy density and temperature., This new temperature guess is obtained by assuming a linear dependence of the energy density and temperature. + The current temperature guess Is iterated to the target energy density., The current temperature guess is iterated to the target energy density. + It takes about 5 - 10 iteration steps to determine the new temperature., It takes about 5 - 10 iteration steps to determine the new temperature. + If the EOS delivers the correct target energy density. the new temperature of the next time step has been found.," If the EOS delivers the correct target energy density, the new temperature of the next time step has been found." + The accuracy relative of the energy density in this iteration process is set to 1015., The accuracy relative of the energy density in this iteration process is set to $10^{-5}$. + The maximum of the light curve of an SN Ia event is observed around 20 days after explosion., The maximum of the light curve of an SN Ia event is observed around 20 days after explosion. +" Causing this later maximum of the light curve of an SN Ia event is the energy release into the envelope caused by the radioactive decay of *°Ni and its also radioactive decay product ""Co. Therefore. this energy deposition has a strong influence on the energy change of the SN Ia envelope structure."," Causing this later maximum of the light curve of an SN Ia event is the energy release into the envelope caused by the radioactive decay of $^{56}$ Ni and its also radioactive decay product $^{56}$ Co. Therefore, this energy deposition has a strong influence on the energy change of the SN Ia envelope structure." + Hence. the energy deposition due to radioactive decay has to be taken into account for the calculation of the SN Ia envelope evolution.," Hence, the energy deposition due to radioactive decay has to be taken into account for the calculation of the SN Ia envelope evolution." + The energy deposition due to the y-rays emitted by radioactive isotopes needs to be computed by a radiative transfer solver for the y-rays., The energy deposition due to the $\gamma$ -rays emitted by radioactive isotopes needs to be computed by a radiative transfer solver for the $\gamma$ -rays. + In this work. we solve the y- deposition with the assumption of a gray atmosphere for the y-rays.," In this work, we solve the $\gamma$ -ray deposition with the assumption of a gray atmosphere for the $\gamma$ -rays." + ? did a detailed study of the y-ray deposition and pointed out that this is an adequate approach to calculate y- deposition in SN Ia atmospheres., \citet{jeffery98} did a detailed study of the $\gamma$ -ray deposition and pointed out that this is an adequate approach to calculate $\gamma$ -ray deposition in SN Ia atmospheres. +" In the decay of a ~°Ni nucleus. a y-photon is emitted with an energy of 2.136 MeV. The “Co nucleus decays to an “Fe nucleus and emits a y- which has an energy of 4.566 MeV. In the decay of ""Co about of the energy is released by positrons."," In the decay of a $^{56}$ Ni nucleus, a $\gamma$ -photon is emitted with an energy of 2.136 MeV. The $^{56}$ Co nucleus decays to an $^{56}$ Fe nucleus and emits a $\gamma$ -photon, which has an energy of 4.566 MeV. In the decay of $^{56}$ Co about of the energy is released by positrons." + The positrons are assumed to be locally trapped., The positrons are assumed to be locally trapped. + They annihilate by emitting two photons each with an energy of 512 keV. which has to be taken into account for the energy deposition calculation.," They annihilate by emitting two photons each with an energy of 512 keV, which has to be taken into account for the energy deposition calculation." + The opacity is considered to be constant and a pure absorption opacity. meaning that no scattering is assumed.," The opacity is considered to be constant and a pure absorption opacity, meaning that no scattering is assumed." + As in ?.. ky=0.06«Z/A>emg! was chosen as the opacity.," As in \citet{jeffery98}, $\kappa_{\gamma}=0.06 {\rm cm}^{2} {\rm + g}^{-1}$ was chosen as the opacity." + «Z/A> is the proton fraction. which is counts both bound and free electrons. since the electron binding energy i5 small compared to the energy of gamma rays.," $$ is the proton fraction, which is counts both bound and free electrons, since the electron binding energy is small compared to the energy of gamma rays." + The energy deposition into the atmosphere per unit time is given by where / is the mean intensity. which has been obtained by solving the gray radiative transfer for the y-rays.," The energy deposition into the atmosphere per unit time is given by where $J$ is the mean intensity, which has been obtained by solving the gray radiative transfer for the $\gamma$ -rays." + This obtained energy deposition has to be taken into account for the calculation of the overall energy change., This obtained energy deposition has to be taken into account for the calculation of the overall energy change. + The timescale for energy changes in the SN Ia envelope will change during the evolution of the light curve., The timescale for energy changes in the SN Ia envelope will change during the evolution of the light curve. + In order to save computation time. the light curves have to be calculated," In order to save computation time, the light curves have to be calculated" +Gtruein,6truein +The initial spectrum of the host ealaxv of CRB 980703. obtained at the Neck telescope on 7 July L998 UT. when the OT was still contributingoO about one third of the observed continu.,"The initial spectrum of the host galaxy of GRB 980703, obtained at the Keck telescope on 7 July 1998 UT, when the OT was still contributing about one third of the observed continuum." + The spectra was smoothed with a eaussian with ao =5À.. roughly corresponding to the instrmuental resolution.," The spectrum was smoothed with a gaussian with a $\sigma = 5$, roughly corresponding to the instrumental resolution." + Promincut emission aud absorption lines are labeled., Prominent emission and absorption lines are labeled. + The far-ed spectrmm of the lost ealaxy of CRB 980703. obtained at the I&eck telescope ou. 19 July 1998 UT.," The far-red spectrum of the host galaxy of GRB 980703, obtained at the Keck telescope on 19 July 1998 UT." + The spectrum was sinvothed with a gaussian with ao =2À.. roughly correspoudiug to the instrumental resolution.," The spectrum was smoothed with a gaussian with a $\sigma = 2$, roughly corresponding to the instrumental resolution." + Prominent cussion lines are labeled., Prominent emission lines are labeled. + The contribution of the OT to the spectrum was negligible at this point., The contribution of the OT to the spectrum was negligible at this point. +sample.,sample. +" Note, the X-ray data in the KFC06 sample are taken in the 1-10 keV band."," Note, the X-ray data in the KFC06 sample are taken in the 1-10 keV band." + As the NGC 7213 data points are in the 2-10 keV band we assume a photon index of [=1.8 and add a correction factor to the NGC 7213 data points to make them comparable., As the NGC 7213 data points are in the 2-10 keV band we assume a photon index of $\Gamma$ =1.8 and add a correction factor to the NGC 7213 data points to make them comparable. + We apply a similar correction to the BHXRB sample., We apply a similar correction to the BHXRB sample. + From this plot it is clear that the NGC 7213 data points are positioned slightly above the best fit line., From this plot it is clear that the NGC 7213 data points are positioned slightly above the best fit line. +" Considering the postion of NGC 7213 on the fundamental plane with respect to other LLAGN (see figure 6), we calculate its radio loudness parameter to assess the differentiation."," Considering the postion of NGC 7213 on the fundamental plane with respect to other LLAGN (see figure 6), we calculate its radio loudness parameter to assess the differentiation." +" We calculate the radio loudness parameter R=Leéem/Lp (where Lecm and Lg are the radio and optical luminosities); we use a B band magnitude of 16.3, and find the optical flux $55; using B= —2.5logSop—48.6 (Halpern&Filippenko 1984):: giving R = 134.8."," We calculate the radio loudness parameter $R = L_{6cm}/L_{B}$ (where $L_{6cm}$ and $L_{B}$ are the radio and optical luminosities); we use a $B$ band magnitude of 16.3, and find the optical flux $S_{opt}$ using $B = -2.5$ $S_{opt}-48.6$ \citep{Einstein_1}: giving $R$ = 134.8." +" In this scheme radio- sources are typically defined as having an R parameter > 10, while radio-quite range between 0.1-1 (Kellermannet 1989)."," In this scheme radio-loud sources are typically defined as having an $R$ parameter $>$ 10, while radio-quite range between 0.1-1 \citep{Kellermann}." +" Using the alternative radio loudness parameter of Terashima&Wilson(2003) which utilises the X-ray instead of optical luminosity, Rx=Léem/L2-10kev, we find logRx= -3.28."," Using the alternative radio loudness parameter of \cite{R_xray} which utilises the X-ray instead of optical luminosity, $R_{X} = L_{6cm}/L_{2-10 keV}$, we find $R_{X} = $ -3.28." + Panessaetal.(2007) show that for a sample of low-luminosity Seyfert Galaxies logRx=—3.64+0.16 while for a sample of low-luminosity radio Galaxies (LLRGs) logRx=—1.40+0.11., \cite{Panessa} show that for a sample of low-luminosity Seyfert Galaxies $R_{X} = -3.64 \pm 0.16$ while for a sample of low-luminosity radio Galaxies (LLRGs) $R_{X} = -1.40 \pm 0.11$. +" Therefore, with respect to the X-ray radio loudness, NGC 7213 is only slightly higher than that of a sample of low-luminosity Seyfert Galaxies; while under the standard definition of radio loudness it is indeed radio loud."," Therefore, with respect to the X-ray radio loudness, NGC 7213 is only slightly higher than that of a sample of low-luminosity Seyfert Galaxies; while under the standard definition of radio loudness it is indeed radio loud." + These results are consistent with the position of NGC 7213 on figure 6.., These results are consistent with the position of NGC 7213 on figure \ref{KFC}. + As was discussed earlier in this paper there is an apparent time lag between events in the X-ray and radio., As was discussed earlier in this paper there is an apparent time lag between events in the X-ray and radio. + Therefore comparing the fitting parameters found from the NGC 7213 data with the MHdMO03 relationship without correcting for the lag might give rise to errors as we are not matching the correct data points., Therefore comparing the fitting parameters found from the NGC 7213 data with the MHdM03 relationship without correcting for the lag might give rise to errors as we are not matching the correct data points. + The width in the cross-correlation peaks shows that the time lag is variable., The width in the cross-correlation peaks shows that the time lag is variable. +" Thus, for example, the two radio flares could have different lag times associated with them."," Thus, for example, the two radio flares could have different lag times associated with them." + Therefore shifting the entire radio light curve back by a set amount to match the X- could still give a scatter., Therefore shifting the entire radio light curve back by a set amount to match the X-ray could still give a scatter. + To simplify this problem we separated out the data for the first flare only because we have a more accurate measurement of the lag in this specific case., To simplify this problem we separated out the data for the first flare only because we have a more accurate measurement of the lag in this specific case. + We then shifted the radio data -35 days which was the time lag measured for this singular flare using the DCF at 4.8 GHz (see table 1))., We then shifted the radio data -35 days which was the time lag measured for this singular flare using the DCF at 4.8 GHz (see table \ref{lag_table}) ). + The top panel of figure 7 shows the uncorrected data on the MHdMO03 plot while the middle panel shows the corrected data; for completeness the bottom panel shows all radio data points shifted back., The top panel of figure \ref{shifted} shows the uncorrected data on the MHdM03 plot while the middle panel shows the corrected data; for completeness the bottom panel shows all radio data points shifted back. + For the first flare correcting the data appears to reduce the scatter and increase the gradient more in line with the MHdM03 best fit., For the first flare correcting the data appears to reduce the scatter and increase the gradient more in line with the MHdM03 best fit. + It is now described by Lg=(0.587314) log Lx+8.572., It is now described by $L_{R} = (0.58^{+0.14}_{-0.14})$ log $L_{X}+8.5^{+7.6}_{-7.6}$. + To check the statistical significance of this we measured the gradient for a variety of shifts., To check the statistical significance of this we measured the gradient for a variety of shifts. + From 0-25 days the gradient gradually steepens until it gets close to 1 (giving a coefficient of ~ 0.6)., From 0-25 days the gradient gradually steepens until it gets close to 1 (giving a coefficient of $\sim$ 0.6). + From 30-50 days it plateaus ~ 1 and from 50 days the gradient decreases towards 0., From 30-50 days it plateaus $\sim$ 1 and from 50 days the gradient decreases towards 0. + Thus it does appear that moving the flare back by the amount given from the DCF function does seem to better represent the data with respect to the MHdM03 fit., Thus it does appear that moving the flare back by the amount given from the DCF function does seem to better represent the data with respect to the MHdM03 fit. +" However, it should be noted that as this is a log/log plot, measuring gradients from such a small range of values should be treated with care."," However, it should be noted that as this is a log/log plot, measuring gradients from such a small range of values should be treated with care." +" It would, however, be interesting in future studies to assess the importance of this parameter."," It would, however, be interesting in future studies to assess the importance of this parameter." + We have used the Australian Telescope Compact Array and the Rossi X-ray Timing Explorer to conduct a long term study of AGN variability in the LLAGN NGC 7213., We have used the Australian Telescope Compact Array and the Rossi X-ray Timing Explorer to conduct a long term study of AGN variability in the LLAGN NGC 7213. + We have used the cross-correlation function to show that a complex and weakly significant correlated behaviour exists between the X-ray and radio emitting regions., We have used the cross-correlation function to show that a complex and weakly significant correlated behaviour exists between the X-ray and radio emitting regions. + Although the statistics, Although the statistics +instability fingers began to grow.,instability fingers began to grow. + Figure 2. shows that the Rayleigh-Taylor instability had far more time to develop in the solar composition models than primordial composition models., Figure \ref{stability} shows that the Rayleigh-Taylor instability had far more time to develop in the solar composition models than primordial composition models. +" The zero-metallicity models, particularly Model z15D, were far more compact than their solar metallicity counterparts."," The zero-metallicity models, particularly Model z15D, were far more compact than their solar metallicity counterparts." +" The reverse shock took only 2100 seconds to reach the center of Model z15D, leaving very little time for the Rayleigh-Taylor instability to grow."," The reverse shock took only $\approx$ 100 seconds to reach the center of Model z15D, leaving very little time for the Rayleigh-Taylor instability to grow." +" This is reflected in the low degree of mixing seen in Figure 4,, which shows the final distribution of isotopes as a function of mass for all stars."," This is reflected in the low degree of mixing seen in Figure \ref{compare_el_prof_flash}, which shows the final distribution of isotopes as a function of mass for all stars." + The original structure of these stars can be seen in Figure 3.., The original structure of these stars can be seen in Figure \ref{compare_el_prof_orig}. +" Two-dimensional snapshots of mixing are shown in Figure 5,, which shows the density structure of the entire star, and Figure 9,, which shows the isotopic composition of the mixed region at the center of the model."," Two-dimensional snapshots of mixing are shown in Figure \ref{z15D_dens}, which shows the density structure of the entire star, and Figure \ref{z15D_all}, which shows the isotopic composition of the mixed region at the center of the model." +" In Model z25D, the reverse shock took longer, about 10? seconds, to reach the center of the star, allowing the RT instability to grow for a longer period of time."," In Model z25D, the reverse shock took longer, about $^3$ seconds, to reach the center of the star, allowing the RT instability to grow for a longer period of time." +" Figure 2 shows an unstable band between the He/!?C-160 shell boundary, and that was indeed the place we saw mixing in these models."," Figure \ref{stability} shows an unstable band between the $^4$ $^{12}$ $^{16}$ O shell boundary, and that was indeed the place we saw mixing in these models." +" More mixing in z25D than z15D can be seen in Figures 4,, 6,, and 10.."," More mixing in z25D than z15D can be seen in Figures \ref{compare_el_prof_flash}, \ref{z25D_dens}, and \ref{z25D_all}." +" Solar composition models were about 50 times larger in radius than their primordial composition counterparts, and correspondingly less dense."," Solar composition models were about 50 times larger in radius than their primordial composition counterparts, and correspondingly less dense." +" The reverse shock took longer to form and 10° and 2x10? seconds to propagate back to the mass-coordinate origin for Models s15A and 825A, respectively."," The reverse shock took longer to form and $^5$ and $2\times10^5$ seconds to propagate back to the mass-coordinate origin for Models s15A and s25A, respectively." +" This was about 100 times longer than for Model z25D, giving the Rayleigh-Taylor instability more time to develop."," This was about 100 times longer than for Model z25D, giving the Rayleigh-Taylor instability more time to develop." +" Additionally, a wider range of regions between and including the aand Si+S shells were unstable than in the zero metallicity counterparts."," Additionally, a wider range of regions between and including the and Si+S shells were unstable than in the zero metallicity counterparts." + Figure 2 implies that the solar metallicity stars were mixed to a greater degree than stars of zero metal initial composition., Figure \ref{stability} implies that the solar metallicity stars were mixed to a greater degree than stars of zero metal initial composition. + Figures 7 and 8 show that about half the, Figures \ref{s15A_dens} and \ref{s25A_dens} show that about half the +a channel separation ofkuns.,a channel separation of. +. A rectaugular grid of positions was selected. centred ou the uucleus of the galaxy. (see Table 1)). aud with offsets parallel or orthogonal to the major axis at PA=13°.," A rectangular grid of positions was selected, centred on the nucleus of the galaxy (see Table \ref{TAB.INT.PROPERTIES}) ), and with offsets parallel or orthogonal to the major axis at $PA = 43\degr$." +" The spectra were obtaiec at iutervals of 10"" along the major and minor axes, auc ” olsewhere."," The spectra were obtained at intervals of $''$ along the major and minor axes, and $''$ elsewhere." +" Iu total. LOL positions were sampled with offsets from the uucleus that rauged TOlu 370” to |360"" parallel to the major axis. ancl from 60"" to 160 perpendicular to it."," In total, 404 positions were sampled with offsets from the nucleus that ranged from $-370''$ to $+360''$ parallel to the major axis, and from $-60''$ to $+60''$ perpendicular to it." + All spectra were obtained using a dual beam-switchine uode (switching frequency ITITz). with a beam throw of 11/7.," All spectra were obtained using a dual beam-switching mode (switching frequency Hz), with a beam throw of 7." + The iuteerationu time was Επ per position ancl. averaging seven contieuous channels (channel spacing: zaus)). the rius noise ranged between 20 and nuuk on aly sscale.," The integration time was min per position and, averaging seven contiguous channels (channel spacing: ), the rms noise ranged between 20 and mK on a scale." +" A set of three spectra was preceded bv a short calibration observation of a black body ""paddle which provided an intensity couversion toT3.", A set of three spectra was preceded by a short calibration observation of a black body `paddle' which provided an intensity conversion to. +. Periodic continui observations of the suall-diameter nucleus of 16 radio source AA at GGIIz provided antenna »»mÓtius corrections., Periodic continuum observations of the small-diameter nucleus of the radio source A at GHz provided antenna pointing corrections. + The pointing was also nssessed wo regularlv re-observius the profile shape of the CO spectrin at the central position of 15., The pointing was also assessed by regularly re-observing the profile shape of the CO spectrum at the central position of 4945. +" These ueasuremieuts inter absolute positional uncertainties <8 it aud relative positional errors <5"",", These measurements infer absolute positional uncertainties $<$ $''$ and relative positional errors $<$ $''$. + The data were processed with the CLASS package of he Groupe d'Astroplivsique cde Cwenoble., The data were processed with the CLASS package of the Groupe d'Astrophysique de Grenoble. + To facilitate a conrarison of CO withΠΠ. the CO spectra were ranstormed iuto a data cube and transferred to the AIPS software.," To facilitate a comparison of CO with, the CO spectra were transformed into a data cube and transferred to the AIPS software." + The distributions of 1.LGGIIZ continmnun enission. integrated emission. aud iutegrated eenission are shown in refFIC.AIAPS.. superimposed on an optical image from the UI Scliuidt SRC (Science Research Council) survey.," The distributions of GHz continuum emission, integrated emission, and integrated emission are shown in \\ref{FIG.MAPS}, superimposed on an optical image from the UK Schmidt SRC (Science Research Council) survey." +" The position offsets are relative to a(2000) = 198 053 27721. A(2000) = 19° 2s' 05”,"," The position offsets are relative to $\alpha(2000)$ = $^{\rm h}$ $^{\rm m}$ 4, $\delta(2000)$ = $\degr$ $'$ $''$." + The coutimmun cussion MA rOefFIC shows a bright small-diameter nucleus superimposed on an elongated distribution of enission., The continuum emission \\ref{FIG.MAPS}a a) shows a bright small-diameter nucleus superimposed on an elongated distribution of emission. + The map is iu reasonable agreement with the 1.1GCIIz nuage of Elnouttie et al. (, The map is in reasonable agreement with the GHz image of Elmouttie et al. ( +1997) but shows additional details.,1997) but shows additional details. +" The )eak flux deusitv of the ceutral source is 1240.1 aat (2000)=135059 2753, 62000)--10728'07"" (the position agrees to within 2"" with those given by Whiteoak Bunton (1985) and Ehuouttie et al. ("," The peak flux density of the central source is $\pm0.1$ at $\alpha(2000) = 13^{\rm h} 05^{\rm m}$ 3, $\delta(2000) = -49\degr 28' 07''$ (the position agrees to within $2''$ with those given by Whiteoak Bunton (1985) and Elmouttie et al. (" +1997)).,1997)). + The fiux density inteerated over the ceutral source is 00.1 JJy., The flux density integrated over the central source is $\pm$ Jy. +" The eiission extends over LLG"" < Yd with the major axis at a position angle PA~15°", The emission extends over $'$ $\times$ $'$ with the major axis at a position angle $PA\sim45\degr$. +" Northeast of the nucleus a ridge-line ruus above the major axis and veers to the east at Π ον 210"",", Northeast of the nucleus a ridge-line runs above the major axis and veers to the east at $R$ $\sim$ $''$. +" Soutlives of the nucleus the ridge appears to run low the major axis. turuing to the west at R~ 300""."," Southwest of the nucleus the ridge appears to run below the major axis, turning to the west at $R$ $\sim$ $''$." +" Faint (σπιν) curved structures extendine out of the disk at R — 200"" are residual sidelobes caused by the relatively bright. emission a the nucleus (cf", Faint mJy) curved structures extending out of the disk at $R$ $\sim$ $''$ are residual sidelobes caused by the relatively bright emission at the nucleus (cf. + 22.1)., 2.1). + Iu our contour map of the distribution refFIC.ALAPShbb) the central region ids donünated by absorption against the strong contiuuuni cluussion of he nucleus., In our contour map of the distribution \\ref{FIG.MAPS}b b) the central region is dominated by absorption against the strong continuum emission of the nucleus. + However. uo absorption was observed agaiust the exteucded continui outside this coutral region.," However, no absorption was observed against the extended continuum outside this central region." + Because of the influence of the absorption. the otal iuteerated flux deusitv discussed in 22.1 is not representative of the total conteut.," Because of the influence of the absorption, the total integrated flux density discussed in 2.1 is not representative of the total content." + Iu he figure. the »eak value of the iutegrated enission dis —JN | (at R — 2207).," In the figure, the peak value of the integrated emission is $\sim3.8$ $^{-1}$ (at $R$ $\sim$ $''$ )." + The emission extends over 93! Vo (13 « kkpe). showing a stretched S-structure.," The emission extends over $\sim$ $'$ $\times$ $'$ (43 $\times$ kpc), showing a stretched `S'-structure." + Within this. a ridge of enüssion extends 13 across the nucleus at PA~13°. whereas the major axis as defined w the iutensity levelisat PA ~ 507.," Within this, a ridge of emission extends $13'$ across the nucleus at $PA\sim 43^{\circ}$, whereas the major axis as defined by the intensity level is at $PA$ $\sim$ $^\circ$." + At the southavestern cud of the distribution there is a moderately xieht concentration that is extending to the north., At the south-western end of the distribution there is a moderately bright concentration that is extending to the north. + At he opposite cud of the galaxy the distribution exteuds o the south., At the opposite end of the galaxy the distribution extends to the south. + ΤΟΤΕULINTSPECaa shows the average spectra or the eutire galaxy., \\ref{FIG.HI.INTSPEC}a a shows the average spectrum for the entire galaxy. + The velocity relative to the Local Standard of Rest (LSB) extends from 310 to aand the cussion peaks at LOO and., The velocity relative to the Local Standard of Rest (LSR) extends from 340 to and the emission peaks at 400 and. +zaus.. The xvsteuic velocity. as eiven by the average of the extreme aud peak velocities. is V7 555 andzaus.. respectively (cf.," The systemic velocity, as given by the average of the extreme and peak velocities, is $\sim$ 555 and, respectively (cf." + Table 1))., Table \ref{TAB.INT.PROPERTIES}) ). + The deep asviuuetnic central depression reflects the presence of absorptiou against the nucleus., The deep asymmetric central depression reflects the presence of absorption against the nucleus. + The shape of the spectrum is simular o that obtained with the Parkes telescope directed owards the centre of the galaxy. (Whiteoak Carducr 1971)., The shape of the spectrum is similar to that obtained with the Parkes telescope directed towards the centre of the galaxy (Whiteoak Gardner 1977). + ULCENABSaa shows our spectrum with +23” resolution towards the position of the uuclear continua source., \\ref{FIG.HI.CENABS}a a shows our spectrum with $\sim$ $''$ resolution towards the position of the nuclear continuum source. + is preseut in absorption against the «οΕΠΙ chussion at velocities of 350 laus. be.svnunuetricallv offset up to ~210 fromVà.," is present in absorption against the continuum emission at velocities of 350 –, i.e. symmetrically offset up to $\sim$ from." + The profile is asyiunetüc and appears to be composed of several componueuts., The profile is asymmetric and appears to be composed of several components. + A peak absorption flix density of, A peak absorption flux density of +161000 high-quality spectra in the 2dEGIU. constituting a arge-scale environmentallv-unbiased study of E|A systems in the local Universe.,"161000 high-quality spectra in the 2dFGRS, constituting a large-scale environmentally-unbiased study of E+A systems in the local Universe." + We used. two. dilferent selection echniques: the first utilizing three Balmer absorption lines (119. Lis. LL?) together with the OLI] 3727A feature. and he second technique emploving solely the 115 and OL] ines.," We used two different selection techniques: the first utilizing three Balmer absorption lines $\delta$ , $\gamma$, $\beta$ ) together with the [OII] $3727 \ang$ feature, and the second technique employing solely the $\delta$ and [OII] lines." + Phese methocls resulted in the selection of 56 and 243 galaxies. respectively.," These methods resulted in the selection of 56 and 243 galaxies, respectively." + We inspected the morphologies of the LE|A) galaxies using images drawn from the Supercosmos Sky Survey (SSS). linding that: The individual catalogues resulting from the two E|A selection techniques contain a dilferent distribution of galaxy populations.," We inspected the morphologies of the E+A galaxies using images drawn from the Supercosmos Sky Survey (SSS), finding that: The individual catalogues resulting from the two E+A selection techniques contain a different distribution of galaxy populations." + Less than 104 of average-Dalmoer E|X galaxies vield any detection of Ho emission. with the highest deduced star-formation rate being 0.17AL. +.," Less than $10\%$ of average-Balmer E+A galaxies yield any detection of $\alpha$ emission, with the highest deduced star-formation rate being $0.17 \, M_\odot$ $^{-1}$." + In contrast. GO% of spectra selected by strong H8 absorption (and no OL) emission) contain a measurable Hla line (although only rarely does the inferred. star-formation rate exceed. 1A. 1 ].," In contrast, $60\%$ of spectra selected by strong $\delta$ absorption (and no [OII] emission) contain a measurable $\alpha$ line (although only rarely does the inferred star-formation rate exceed $1 \, M_\odot$ $^{-1}$ )." + These samples permitted a statistical investigation of the environments ancl luminosities of low-redshift LE|A galaxies., These samples permitted a statistical investigation of the environments and luminosities of low-redshift E+A galaxies. + We compared. the two LE|A catalogues to both the entire δα database anc a sub-population of 2dPCRS cellipticals'. the latter selected. using the spectral classification parameter η.," We compared the two E+A catalogues to both the entire 2dFGRS database and a sub-population of 2dFGRS `ellipticals', the latter selected using the spectral classification parameter $\eta$." + With regard to the environments of ILX galaxies. we found that: Concerning the luminosity function of IE[X galaxies: What can we conclude from these results?," With regard to the environments of E+A galaxies, we found that: Concerning the luminosity function of E+A galaxies: What can we conclude from these results?" + Considering inst the average-Balmer I5|A catalogue: the preference for spheroidal morphologies. the incidence of identifiable merger remnants. and the match of the luminosity distribution o that of elliptical galaxies is all consistent with being an important formation process for hese galaxies.," Considering first the average-Balmer E+A catalogue: the preference for spheroidal morphologies, the incidence of identifiable merger remnants, and the match of the luminosity distribution to that of elliptical galaxies is all consistent with being an important formation process for these galaxies." + Indeed. this model has proven successlu in theoretical simulations (Bekki ct 22001).," Indeed, this model has proven successful in theoretical simulations (Bekki et 2001)." + Thus it is interesting that the distribution of local environments. of hese I5| Asvstems matches that of the ensemble of galaxics: or example. there is no correlation with the properties of galaxy groups.," Thus it is interesting that the distribution of local environments of these E+A systems matches that of the ensemble of galaxies; for example, there is no correlation with the properties of galaxy groups." + This in part rellects the fact that at low redshift the merger probability is enhanced in the field with respect to clusters., This in part reflects the fact that at low redshift the merger probability is enhanced in the field with respect to clusters. + Elliptical galaxies forming today do no follow the classic morphology-cdensity relation. because the relative velocities of galaxies in denser environments is too high to permit mergers: cluster sub-structure has become cdvnamucally relaxed.," Elliptical galaxies forming today do not follow the classic morphology-density relation, because the relative velocities of galaxies in denser environments is too high to permit mergers: cluster sub-structure has become dynamically relaxed." + The impressive manner in which the distribution of local environments of LE|A svstems traces that of the ensemble of 2dORS galaxies implies that the I2|A galaxy formation mechanism is driven by very local encounters. without reference to the wider group environment.," The impressive manner in which the distribution of local environments of E+A systems traces that of the ensemble of 2dFGRS galaxies implies that the E+A galaxy formation mechanism is driven by very local encounters, without reference to the wider group environment." + “Pheorctical simulations indicate that an LE)A spectrum marks a late stage of a merger. when the cores of the merging systems have coalesced and the merging companion is no longer identifiable (Bekki et 22001): we would. not. expect a surplus of close companions.," Theoretical simulations indicate that an E+A spectrum marks a late stage of a merger, when the cores of the merging systems have coalesced and the merging companion is no longer identifiable (Bekki et 2001): we would not expect a surplus of close companions." + Furthermore. we note a consistency of our findings with the dependence. of star formation upon environment BBalogh οἱ 22004).," Furthermore, we note a consistency of our findings with the dependence of star formation upon environment Balogh et 2004)." + Ln such studies. the only environmentally-sclectecl population at low redshift to show enhancements of star formation are close galaxy. pairs. which are no longer distinguishable atthe onset of the I5|A phase.," In such studies, the only environmentally-selected population at low redshift to show enhancements of star formation are close galaxy pairs, which are no longer distinguishable atthe onset of the E+A phase." + ‘Turning now to galaxies selected. by 15 absorption, Turning now to galaxies selected by $\delta$ absorption +where au overline indicates the mean value. where for the quadrupole ο|i0=2.,"where an overline indicates the mean value, where for the quadrupole $n+m=2$." + We mia redefine the surface brightuecss. IG.gy) to any other function of flux without a loss of eeneralitv in the above expression.," We may redefine the surface brightness, $I(x,y)$ to any other function of flux without a loss of generality in the above expression." + The quadrupole moments are ecucrally trauslated iuto a complex ellipticitv via one of the relations: Or The expectation value of the couples ollipticities around a circular auuulus gives au estimate of the combination of parameters: where g is known as the reduced shear., The quadrupole moments are generally translated into a complex ellipticity via one of the relations: or The expectation value of the complex ellipticities around a circular annulus gives an estimate of the combination of parameters: where $g$ is known as the reduced shear. + This expression iniplies a degeneracy between values of the shear aud convergence., This expression implies a degeneracy between values of the shear and convergence. + It should also be noted that these relations hold oulv iu the lait of small variance in the intrinsic ellipricitv distribution and for small values of g., It should also be noted that these relations hold only in the limit of small variance in the intrinsic ellipticity distribution and for small values of $g$. + Strictly speaking. these approximations are invalid iu the strong leusiug regine characterized by the dramatic arcs aud multiple images.," Strictly speaking, these approximations are invalid in the strong lensing regime characterized by the dramatic arcs and multiple images." + Iu this section. we address the issue of analysis of higher order moments of the elt distribution.," In this section, we address the issue of analysis of higher order moments of the light distribution." + Iu particular. we show that. even in the weak lensing limit iu which oue would strictly uot expect to be able to detect gravitational arcs. an arc-like signature cau be fouud from the octopole momeuts of the ealaxy light distribution.," In particular, we show that, even in the weak lensing limit in which one would strictly not expect to be able to detect gravitational arcs, an arc-like signature can be found from the octopole moments of the galaxy light distribution." + Iu order to simplify this discussion somewhat. we assume a radially svanmetric poteutial throughout. aud for a fiducial ealaxv we further choose the coordinate system with a configuration such that it lios along the positive x-axis.," In order to simplify this discussion somewhat, we assume a radially symmetric potential throughout, and for a fiducial galaxy we further choose the coordinate system with a configuration such that it lies along the positive x-axis." + This is cutirely equivalent to defining a radial aud tangential component., This is entirely equivalent to defining a radial and tangential component. + However. for practical reasons. we chose to do all calculations in Cartesian coordinates.," However, for practical reasons, we chose to do all calculations in Cartesian coordinates." + Under these assumptions. using only lincar theory. the lensed (subscript 0) aud uuleused (subscript 0) ποιοτς cau be related in a very straightforward wav since the Jacobian is diagonal.," Under these assumptions, using only linear theory, the lensed (subscript $\theta$ ) and unlensed (subscript $\beta$ ) moments can be related in a very straightforward way since the Jacobian is diagonal." + Thus. Application of this transform to the quadrupole terius in the weak leusiug limit. vields the complex ellipticity transformations above.," Thus, Application of this transform to the quadrupole terms in the weak lensing limit, yields the complex ellipticity transformations above." + If galaxies are raudonly orieuted. as is assumed (however. see Crittenden et al.," If galaxies are randomly oriented, as is assumed (however, see Crittenden et al." + 2001 for au estimate of the degree of expected intrinsic aliguiieutz). then the expectation value of any of the intrinsic octopole moments (aud hence the lensed octopole moments in a circularly svuuuctric potential) will necessarily. vanish.," 2001 for an estimate of the degree of expected intrinsic alignments), then the expectation value of any of the intrinsic octopole moments (and hence the lensed octopole moments in a circularly symmetric potential) will necessarily vanish." + However. even in the absence of an intrinsic octopole moment. the second order Tavlor expansion of the lensing equation can eive rise to octopole moments.," However, even in the absence of an intrinsic octopole moment, the second order Taylor expansion of the lensing equation can give rise to octopole moments." + Consider the Πα when the source nage has a small but finite size. the lensed field iav be approxinated as: By inspection. the following sviunetries: Ay.)=Ajj aud ijj=hij hold.," Consider the limit when the source image has a small but finite size, the lensed field may be approximated as: By inspection, the following symmetries: $A_{ik,j}=A_{ij,k}$ and $A_{ji,k}=A_{ij,k}$, hold." +" The corresponding teris (expressible as local derivatives of the shear iud convergence field) ave: 5 =05δν,the racial derivative of the shear field."," The corresponding terms (expressible as local derivatives of the shear and convergence field) are: where $\gamma'=\partial \gamma/\partial r$, the radial derivative of the shear field." + Since the potential. aud thus the surface deusity of the lous. X(0). as circularly svuuuetric. aud the ceuter of the leus lies on the x-axis. κο=0.," Since the potential, and thus the surface density of the lens, $\Sigma(\vec{\theta})$, is circularly symmetric, and the center of the lens lies on the x-axis, $\kappa_{,2}=0$." + Likewise. since evervwhere on the x-axis. 59=0. 594=0.," Likewise, since everywhere on the x-axis, $\gamma_2=0$, $\gamma_{2,1}=0$." + In addition. we haveused the relation derived by Iaiser (1995): Finally. it can be shown that συ:hlIWw9," In addition, we haveused the relation derived by Kaiser (1995): Finally, it can be shown that $\gamma_{2,2}=2\gamma/r$ ." +and metallicity of ISM gas.,and metallicity of ISM gas. +" For these parameters of SNe and ambient ISM, once Mswept and 7(a,a’) for each dust species are calculated, the time evolution of dust mass and size distribution can be followed in a consistent way with the star formation activity in galaxies as described in Section 3.."," For these parameters of SNe and ambient ISM, once $M_{\rm swept}$ and $\eta(a,a^{\prime})$ for each dust species are calculated, the time evolution of dust mass and size distribution can be followed in a consistent way with the star formation activity in galaxies as described in Section \ref{sec:galmodel}." +" The calculations of n(a,a’) and Mswept are performed byusing the method developed by Nozawaetal.(2006) as follows; the efficiency of dust destruction increases with increasing the explosion energy and/or increasing ngn but is almost independent of the progenitor mass as long as the explosion energy is the same (Nozawaetal. 2006)."," The calculations of $\eta(a,a^{\prime})$ and $M_{\rm swept}$ are performed byusing the method developed by \citet{Noz06} as follows; the efficiency of dust destruction increases with increasing the explosion energy and/or increasing $n_{\rm SN}$ but is almost independent of the progenitor mass as long as the explosion energy is the same \citep{Noz06}." +. We assume that SNe driving high- shock in ISM are represented by Type II SN with the progenitor mass of 20Mo and the explosion energy of 10°!erg., We assume that SNe driving high-velocity shock in ISM are represented by Type II SN with the progenitor mass of $20\ M_{\odot}$ and the explosion energy of $10^{51}\ {\rm erg}$. +" The ISM surrounding the SN is considered to be uniform with hydrogen number densities ngn=0.03, 0.1, 0.3, 1.0, 3.0 and 10cm-?."," The ISM surrounding the SN is considered to be uniform with hydrogen number densities $n_{\rm SN}=0.03$, $0.1$, $0.3$ , $1.0$, $3.0$ and $10\ {\rm cm}^{-3}$." +" By distributing dust grains with radius a’ uniformly in ISM, the conversion efficiency n(a,a’) is evaluated for each grain species by calculating the erosion of dust by sputtering until the truncation time t;, which is defined as a time when the shock velocity is decelerated below 100kms! (seeNozawaetal.2006,forthe details)."," By distributing dust grains with radius $a^{\prime}$ uniformly in ISM, the conversion efficiency $\eta(a,a^{\prime})$ is evaluated for each grain species by calculating the erosion of dust by sputtering until the truncation time $t_{\rm tr}$ which is defined as a time when the shock velocity is decelerated below $100\ {\rm km}\ {\rm s}^{-1}$ \citep[see][for the details]{Noz06}." +" In the calculations, the radii of grains in the ISM range from 0.00013 to 6.3wm for each grain species."," In the calculations, the radii of grains in the ISM range from $0.00013$ to $6.3\ {\rm \mu m}$ for each grain species." +" In Figure 4,, we present the changes in the dust size distributions due to the shock-processing for different ISM-densities, where the initial mass distribution of dust is set to be aMaj(a)=1 for clarity."," In Figure \ref{fig:dest}, , we present the changes in the dust size distributions due to the shock-processing for different ISM-densities, where the initial mass distribution of dust is set to be $a{\cal M}_{{\rm d},j}(a)=1$ for clarity." +" As can be seen from the figure, small-size grains are destroyed significantly due to the erosion by sputtering, and more dust grains are processed for a higher ISM density."," As can be seen from the figure, small-size grains are destroyed significantly due to the erosion by sputtering, and more dust grains are processed for a higher ISM density." +" The mass of gas swept up by the forward shock until the truncation time ti, Mswept, depends on not only the ISM density but also the initial metallicity of the gas in the ISM."," The mass of gas swept up by the forward shock until the truncation time $t_{\rm tr}$, $M_{\rm swept}$, depends on not only the ISM density but also the initial metallicity of the gas in the ISM." +" As the line cooling by heavy elements becomes more efficient for a higher gas metallicity, the forward shock is decelerated more quickly, resulting in a smaller Mswept-"," As the line cooling by heavy elements becomes more efficient for a higher gas metallicity, the forward shock is decelerated more quickly, resulting in a smaller $M_{\rm swept}$." +" By fitting Mswept calculated for different ngn and Z, we derived the following approximation formula, whose fitting accuracy is within 1696 for 0.03cm?€ngw30cm""? and for 1074«Z/Zs€ 1.0."," By fitting $M_{\rm swept}$ calculated for different $n_{\rm SN}$ and $Z$, we derived the following approximation formula, whose fitting accuracy is within $16\%$ for $0.03\ {\rm cm}^{-3}\le n_{\rm SN}\le 30\ {\rm cm}^{-3}$ and for $10^{-4}\le Z/Z_{\odot}\le1.0$ ." +" In terms of the conversion efficiency describing the processing of dust by sputtering, here we formulate the timeevolution of the mass of j-th dust grains with radii between a and a4-Aa in our model galaxies, AMa,;(a,t)=4203p;f;(a. t)Aa, as where Migm(t) is the total mass of gas and"," In terms of the conversion efficiency describing the processing of dust by sputtering, here we formulate the timeevolution of the mass of$j$ -th dust grains with radii between $a$ and $a+\Delta a$ in our model galaxies, $\Delta M_{{\rm d},j}(a,t)=\frac{4\pi}{3}a^{3}\rho_{j}f_{j}(a,t)\Delta a$ , as where $M_{\rm ISM}(t)$ is the total mass of gas and" +where V is the volume and γω is the volume enclosed by a single pixel.,where $V$ is the volume and $V_{pixel}$ is the volume enclosed by a single pixel. + To obtain a final image to be compared with observational data we follow the conceptual steps shown in Fig. 2.., To obtain a final image to be compared with observational data we follow the conceptual steps shown in Fig. \ref{Schema}. + We first compute the emission along each strand in a given line., We first compute the emission along each strand in a given line. + The strand emissions can be put in the form of a 1-D image consisting of a strip of pixels on an appropriate grey scale., The strand emissions can be put in the form of a 1-D image consisting of a strip of pixels on an appropriate grey scale. + We obtain 2000 pixel strips., We obtain 2000 pixel strips. + We then put them side by side and obtain a 1024x2000 pixel image., We then put them side by side and obtain a $1024 \times 2000$ pixel image. +" We have chosen to rebin our images by summing over bundles of 65 strands, so to obtain a collection of about 30 parallel loops."," We have chosen to rebin our images by summing over bundles of $65$ strands, so to obtain a collection of about $30$ parallel loops." +" The evolution of nanoflaring plasma confined in coronal loop is well known from previous works (?????) and is similar to that of proper flaring loops, although on a smaller scale (c.g., ???))."," The evolution of nanoflaring plasma confined in coronal loop is well known from previous works \citep{Peres_al_1993_inproc,Warren_al_2002,Warren_al_2003,Patsourakos_Klimchuk_2005,Testa_al_2005} and is similar to that of proper flaring loops, although on a smaller scale (e.g., \cite{Nagai_1980,Peres_1982,Reale_Peres_1995}) )." + We show the evolution of the density and temperature along a single strand in Fig. 3.., We show the evolution of the density and temperature along a single strand in Fig. \ref{time_profile}. +" The temperature soon settles to about 10 MK along most of the strand, due to the strong heat pulse: then it slowly decreases as expected with an e-folding time scale given by τι«500Lo/VT,x s (Reale 2007, 2009) where T, and Ly are the maximum temperature and the length ofthe strand measured in units of 10° K (MK) and 10? em respectively."," The temperature soon settles to about 10 MK along most of the strand, due to the strong heat pulse; then it slowly decreases as expected with an e-folding time scale given by $\tau_s \approx 500 ~ L_9/\sqrt{T_6} \approx 500$ s (Reale 2007, 2009) where $T_6$ and $L_9$ are the maximum temperature and the length ofthe strand measured in units of $10^6$ K (MK) and $10^9$ cm respectively." + At ¢=2000 s the strand has cooled below the temperature it had before the heat pulse., At $t = 2000$ s the strand has cooled below the temperature it had before the heat pulse. + At ¢=20 s the density plot clearly shows a strong evaporation front coming up from the chromosphere (the density of the front jumps by more than a factor 10)., At $t = 20$ s the density plot clearly shows a strong evaporation front coming up from the chromosphere (the density of the front jumps by more than a factor 10). + At t=100 s the front has filled the whole strand with some extra accumulation in the apex region., At $t= 100$ s the front has filled the whole strand with some extra accumulation in the apex region. +" At £=400 s the density distribution has a shape similar to the initial equilibrium one, but settled around a maximum value of ~10! em."," At $t = 400$ s the density distribution has a shape similar to the initial equilibrium one, but settled around a maximum value of $\sim 10^{10}$ $^{-3}$." +" Then the density begins to decrease and at the final time computed it is lower, by a factor ~5 than the maximum, still much higher than the initial value."," Then the density begins to decrease and at the final time computed it is lower, by a factor $\sim 5$ than the maximum, still much higher than the initial value." +" As described in Sec. 2.,"," As described in Sec. \ref{sec:model}, ," +" this evolution is replicated in all strands with different relative timing,"," this evolution is replicated in all strands with different relative timing," +to where Tog is the effective temperature of the annulus.,to where $T_{\rm eff}$ is the effective temperature of the annulus. +" Note that the right hand side terms, and therefore are independent of height with this assumption."," Note that the right hand side terms, and therefore $dF/dm$ are independent of height with this assumption." + We dF/dmcannot use the stress prescription to specify a local viscous-like dissipation as this is proportional to some combination of radiation and gas pressure., We cannot use the stress prescription to specify a local viscous-like dissipation as this is proportional to some combination of radiation and gas pressure. +" 'These pressures are largest at the disk midplane due to hydrostatic equilibrium, so the dissipation is also largest there, and the resulting temperatures are so high as to lead to the disk becoming Rayleigh-Taylor unstable."," These pressures are largest at the disk midplane due to hydrostatic equilibrium, so the dissipation is also largest there, and the resulting temperatures are so high as to lead to the disk becoming Rayleigh-Taylor unstable." +" This would lead to convection, presumably driving the disk structure towards the marginally stable condition where the dissipation is proportional to density."," This would lead to convection, presumably driving the disk structure towards the marginally stable condition where the dissipation is proportional to density." + Time and horizontal averages of shearing box simulations indicate that a somewhat(Turner greater fraction of the dissipation occurs at low column near the surface., Time and horizontal averages of shearing box simulations indicate that a somewhat greater fraction of the dissipation occurs at low column near the surface. + We use vertically integrated disk model to determine the above aparameters for each annulus., We use a vertically integrated disk model to determine the above parameters for each annulus. +" The tidal gravity is specified by the choice of spacetime and radius, while the radiative flux at the surface is independent of stress prescription for a thin disk1973)."," The tidal gravity is specified by the choice of spacetime and radius, while the radiative flux at the surface is independent of stress prescription for a thin disk." +". Therefore, we only require(see a stress prescription to determine the surface density in this model. ("," Therefore, we only require a stress prescription to determine the surface density in this model. (" +"Note, however, that the theoretical arguments which motivate the stress prescription may also require modifications to the dissipation profile, a point we will discuss further in refdiscus..)","Note, however, that the theoretical arguments which motivate the stress prescription may also require modifications to the dissipation profile, a point we will discuss further in \\ref{discus}. .)" +" The surface density may be determined by enforcing angular momentum conservation n where 7,5 is the accretion stress, M is the accretion rate, and Q is the Keplerian frequency."," The surface density may be determined by enforcing angular momentum conservation dz = where $\tau_{r\phi}$ is the accretion stress, $\mdot$ is the accretion rate, and $\Omega$ is the Keplerian frequency." + The functions A(r) and D(r) (both —1 for radii much larger than the last stable orbit) defined in incorporate the no-torque (stress inner boundary condition and parameterize the free)deviation of general relativistic disk structure from the Newtonian limit., The functions $A(r)$ and $D(r)$ (both $\to 1$ for radii much larger than the last stable orbit) defined in incorporate the no–torque (stress free) inner boundary condition and parameterize the deviation of general relativistic disk structure from the Newtonian limit. + The integral in eq. (2)), The integral in eq. \ref{eq:coa}) ) +" presents a computational difficulty since depends on local variable such as temperature and r,,density for the stress prescriptions considered here.", presents a computational difficulty since $\tau_{r\phi}$ depends on local variable such as temperature and density for the stress prescriptions considered here. +" Therefore, the exact computation requires the full vertical structure which, in turn, requires a choice of X."," Therefore, the exact computation requires the full vertical structure which, in turn, requires a choice of $\Sigma$." +" Therefore, an exact solution can only be computed via iteration provided an initial guess for 2)2005).."," Therefore, an exact solution can only be computed via iteration provided an initial guess for $\Sigma$." +" Given the approximations inherent in our stress prescriptions, we instead solve for X using moderately crude vertical averages to replace fT, with 2H"," Given the approximations inherent in our stress prescriptions, we instead solve for $\Sigma$ using moderately crude vertical averages to replace $\int\tau_{r\phi} dz$ with $2 +H\langle\tau_{r\phi}\rangle$." +" Here H is an approximate vertical scale odheight for the (7,-¢).disk determined via the equation of hydrostatic equilibrium", Here $H$ is an approximate vertical scale height for the disk determined via the equation of hydrostatic equilibrium +where jj is the spherical Bessel function of the first kind of order 1.,where $j_1$ is the spherical Bessel function of the first kind of order 1. + Note (hat this window is the Fourier transform of MW(r)., Note that this window is the Fourier transform of $W(r)$. +" In our case of WC) given by (25)). the Fourier-space window reads 559 of ?2)) where Syi, and Lyi, are as above."," In our case of $W(r)$ given by \ref{eq:Psi_r}) ), the Fourier-space window reads 59 of \citealt{CCBCC}) ) where $S_\mathrm{min}$ and $L_\mathrm{min}$ are as above." +" The window i is a function of both the wavenumber / and the minimum flux 5,454, (hence the subscript s).", The window $\tilde{w}_s$ is a function of both the wavenumber $k$ and the minimum flux $S_\mathrm{min}$ (hence the subscript $s$ ). + On the other hand. it does depend on the distance. as the latter is integrated out. together with absolute luminosities (with the use of the luminosity function).," On the other hand, it does depend on the distance, as the latter is integrated out, together with absolute luminosities (with the use of the luminosity function)." + This means that when comparing observations to theoretical expectations. we never use (he effective distance (17)) for the caleulations of the conditional velocity ο (18)) and its variance c (23)).," This means that when comparing observations to theoretical expectations, we never use the effective distance \ref{eq:r_eff}) ) for the calculations of the conditional velocity $v_\mrc$ \ref{eq:v_cond}) ) and its variance $\sigma_\mrc$ \ref{eq:sigma_cond}) )." +" Our observable is (he minimum flux of (he sample. related to maximum maenitude Via S44,=SyLO""Hs,"," Our observable is the minimum flux of the sample, related to maximum magnitude via $S_\mathrm{min}=S_0\,10^{-0.4K_\mathrm{max}}$." + For clarity however. in the relevant plots weprefer to show the results in terms of a linear scaling in the effective distance.," For clarity however, in the relevant plots weprefer to show the results in terms of a linear scaling in the effective distance." +" In Figuree 5 we plot the 2MAÀSS flux-limited window with A4,;-—mas13.5 mage and compare it with (wo top-hat windows for distance-Himited survevs: one with. Aya,=296Mpe/h and (he other with yay=105Mpc/h. which are respectively the effective distances of galaxies at the limit of the PATASS and 2MBRS A4;=11.25 mag sample."," In Figure \ref{Fig:windows} we plot the 2MASS flux-limited window with $K_\mathrm{max}=13.5$ mag and compare it with two top-hat windows for distance-limited surveys: one with $R_\mathrm{max}=296\Mpch$ and the other with $R_\mathrm{max}=105\Mpch$, which are respectively the effective distances of galaxies at the limit of the 2MASS and 2MRS $K_\mathrm{max}=11.25$ mag sample." + The Fourier form of the top-hat window is (?) with jj=sinc/ being the spherical Bessel function of the first kind of order 0.," The Fourier form of the top-hat window is \citep{JVW} + with $j_0\equiv\sin x\slash x$ being the spherical Bessel function of the first kind of order 0." + The oscillating behavior of this window in the Fourier space is a result of the rapid trunceation in the real space., The oscillating behavior of this window in the Fourier space is a result of the rapid truncation in the real space. +" As we can see. (he top-hat window with ya,=296Mpc/h. which asvmptotically behaves in (he same wav as the 2\TASS one with Au,=13.5 mag. passes clearly more large-scale signal (&<0.025 /Mpc)."," As we can see, the top-hat window with $R_\mathrm{max}=296\Mpch$, which asymptotically behaves in the same way as the 2MASS one with $K_\mathrm{max}=13.5$ mag, passes clearly more large-scale signal $k\lesssim0.02\hMpc$ )." + This will result in much faster convergence of the dipole measured through the top-hat window than through the 2MASS [fIux-weighted one (see below)., This will result in much faster convergence of the dipole measured through the top-hat window than through the 2MASS flux-weighted one (see below). + On the other hand. the top-hat window with a cut-off equivalent to the limit of 244AS at 105Mpc/h blocks almost all the signal already. for lh<0.01 h/Mpe. as expected.," On the other hand, the top-hat window with a cut-off equivalent to the limit of 2MRS at $105\Mpch$ blocks almost all the signal already for $k\lesssim0.01\hMpc$ , as expected." +The Hhumninosity is incdepencdent(~—0.02) of RC luminosity. and is almost equally determined by FIR and CO huninosity.,"The luminosity is $\sim -0.02$ ) of RC luminosity, and is almost equally determined by FIR and CO luminosity." + The FIR luminosity from a model fit to the IICN. RC. and CO (theIRCLyex..Lic. Lco)) model). however. vields Tlerve. aand sseem to be roughly comparably important though RC appears to have more weight than HCN.," The FIR luminosity from a model fit to the HCN, RC, and CO (the, ) model), however, yields Here, and seem to be roughly comparably important though RC appears to have more weight than HCN." + This is much more extreme (han the (hrvee-parameter f[it (IICNACO [or FIR) given in Equation (3) of GS04a. and CO indeed contributes nothing to FIR when both ICN and RC are used in the fit.," This is much more extreme than the three-parameter fit (HCN+CO for FIR) given in Equation (3) of GS04a, and CO indeed contributes nothing to FIR when both HCN and RC are used in the fit." + In other words. adding CO does not have anv elfect on predicting FIR once both WON and RC are involved.," In other words, adding CO does not have any effect on predicting FIR once both HCN and RC are involved." + Finally. we show the CO luminosity [rom a model fit of the ION. RC. and FIR (theCO(Lyox..Lee. Ligg)) model). which vields The Hwninosity is independent (70.06) of FIR luminosity. and is mainly determined by (0.51) and marginally by (0.21).," Finally, we show the CO luminosity from a model fit of the HCN, RC, and FIR (the, ) model), which yields The luminosity is independent $-0.06$ ) of FIR luminosity, and is mainly determined by (0.51) and marginally by (0.21)." + This is essentially verv similar to Equation (5) in G504a. ie. CO is mainly determined by ICN with little contribution from FIR.," This is essentially very similar to Equation (5) in GS04a, i.e., CO is mainly determined by HCN with little contribution from FIR." + Adding an additional parameter RC only affects the overall fit slehtly and makes FIR useless in predicting CO trom HCN., Adding an additional parameter RC only affects the overall fit slightly and makes FIR useless in predicting CO from HCN. + Although it is mareinal. this might suggest that RC is slightly more important than FUR in predicting CO.," Although it is marginal, this might suggest that RC is slightly more important than FIR in predicting CO." + In summary. FIR-IICN. and FIR-RC correlations are the strongest ones among: all.," In summary, FIR-HCN and FIR-RC correlations are the strongest ones among all." + Despite a ight RC-CO correlation. the RC-IICN correlation is much tighter in comparison.," Despite a tight RC-CO correlation, the RC-HCN correlation is much tighter in comparison." + Nonetheless. it appears that the RC-IICN correlation might be a direct consequence of the combinational result [rom the two lightest RC-FIR. and EFIR-IICN correlations.," Nonetheless, it appears that the RC-HCN correlation might be a direct consequence of the combinational result from the two tightest RC-FIR and FIR-HCN correlations." + The [it models further support these resulis and reveal the difference between LCN, The multi-parameter fit models further support these results and reveal the difference between HCN +It is a challenge to identify massive young stellar objects during their early evolution.,It is a challenge to identify massive young stellar objects during their early evolution. + The youngest protostars form deeply embedded in their cold (T ~ 10-20 K) parental clouds (Pudritz 2002)., The youngest protostars form deeply embedded in their cold (T $\sim$ 10-20 K) parental clouds (Pudritz 2002). + The association with dense ambient material makes such objects best detectable às cold condensations at far-infrared and (sub)millimeter wavelengths., The association with dense ambient material makes such objects best detectable as cold condensations at far-infrared and (sub)millimeter wavelengths. + The short evolutionary timescales (Palla Stahler 1993) and low spatial density of massive objects require large scale surveys for their identification., The short evolutionary timescales (Palla Stahler 1993) and low spatial density of massive objects require large scale surveys for their identification. + Many of the known intermediate- and high-mass protostellar candidates have therefore been discovered by follow-up studies towards IRAS sources (eg., Many of the known intermediate- and high-mass protostellar candidates have therefore been discovered by follow-up studies towards IRAS sources (eg. + Shepherd et al., Shepherd et al. + 2000. Cesaroni et al.," 2000, Cesaroni et al." + 1997. Molinari et al.," 1997, Molinari et al." + 1998. Beuther et.," 1998, Beuther et." +" al 2002). which were selected on the basis of color and flux density criteria (e.g. by Wood Churchwell 1989, Palla et al."," al 2002), which were selected on the basis of color and flux density criteria (e.g. by Wood Churchwell 1989, Palla et al." + 1991) The earliest stages of massive star formation are characterized by the initial conditions of their parental cloud cores with spectral energy distributions peaking beyond 100 gm (Evans et al., 1991) The earliest stages of massive star formation are characterized by the initial conditions of their parental cloud cores with spectral energy distributions peaking beyond 100 $\mu$ m (Evans et al. + 2002)., 2002). + In order to unveil such young objects we are using the ISOPHOT (Lemke et al., In order to unveil such young objects we are using the ISOPHOT (Lemke et al. + 1996) 170 jim Serendipity Survey (15055) (Bogun et al., 1996) 170 $\mu$ m Serendipity Survey (ISOSS) (Bogun et al. + 1996). which is the largest high spatial resolution survey performed beyond the IRAS 100 ;;m band.," 1996), which is the largest high spatial resolution survey performed beyond the IRAS 100 $\mu$ m band." + We selected bright and compact sources detected by ISOSS and IRAS with a flux ratio [F170;mmyVF1004/m] > 2. implying a low dust temperature T 18 K and a large mass of the cold ISM in these objects.," We selected bright and compact sources detected by ISOSS and IRAS with a flux ratio $\mu$ $\mu$ m] $>$ 2, implying a low dust temperature T $<$ 18 K and a large mass of the cold ISM in these objects." + Since the clustered mode of massive star formation commonly involves young stellar objects of different evolutionary stages. we require the presence of embedded sources with thermal infrared excess as indicated by the 2MASS (Cutri et al.," Since the clustered mode of massive star formation commonly involves young stellar objects of different evolutionary stages, we require the presence of embedded sources with thermal infrared excess as indicated by the 2MASS (Cutri et al." + 2000) and MSX (Price et al., 2000) and MSX (Price et al. + 2001) infrared surveys., 2001) infrared surveys. + The latter criterium also avoids confusion with cold interstellar cirrus., The latter criterium also avoids confusion with cold interstellar cirrus. + Here. we present the results of follow-up observations of the cold star forming region ISOSS J 2029843559 and show evidence for its early evolutionary stage.," Here, we present the results of follow-up observations of the cold star forming region ISOSS J 20298+3559 and show evidence for its early evolutionary stage." + 170 jim data covering the region around ISOSS J 2029843559 have been extracted from the ISOPHOT Serendipity Survey., 170 $\mu$ m data covering the region around ISOSS J 20298+3559 have been extracted from the ISOPHOT Serendipity Survey. + The scans performed with the C200 2x2 pixel detector array of stressed Ge:Ga with a pixel size of 89.4 aresec provide a spatial resolution of 1.8 aremin FWHM., The scans performed with the C200 2x2 pixel detector array of stressed Ge:Ga with a pixel size of 89.4 arcsec provide a spatial resolution of 1.8 arcmin FWHM. + A flatfield correction for the individual scans was derived from redundant measurements at scan crossings., A flatfield correction for the individual scans was derived from redundant measurements at scan crossings. + The calibration accuracy Is estimated to be + 30 (Stickel et al., The calibration accuracy is estimated to be $\pm$ 30 (Stickel et al. + 2000) Submillimeter jiggle maps at 450;:m and 850; were obtained with the SCUBA bolometer array (Holland et al., 2000) Submillimeter jiggle maps at $\mu$ m and $\mu$ m were obtained with the SCUBA bolometer array (Holland et al. + 1999) at the JCMT from Mauna Kea (Hawaii) on July 28. 2001 under excellent and stable sky conditions (Τάση = 0.185 + 0.01).," 1999) at the JCMT from Mauna Kea (Hawaii) on July 28, 2001 under excellent and stable sky conditions $\tau_{850 \mu m}$ = 0.185 $\pm$ 0.01)." + The observing time was 30 min., The observing time was 30 min. + The atmospheric transmission. was determined from sky dips and water radiometer data (at JCMT and CSO)., The atmospheric transmission was determined from sky dips and water radiometer data (at JCMT and CSO). + Mars. Uranus and CRL 618 served as calibrators.," Mars, Uranus and CRL 618 served as calibrators." + The data were reduced using the SCUBA User Reduction Facility (SURF) includingσι identification of noisy bolometer pixels and removal of sky noise., The data were reduced using the SCUBA User Reduction Facility (SURF) including identification of noisy bolometer pixels and removal of sky noise. + The photometric accuracy derived from the calibration observations is 25 at 450 jm and 20 at 850 jm. The measured HPBW is 7.9 arcsec at µην and 14.9 aresec at jm (derived from observations of CRL618)., The photometric accuracy derived from the calibration observations is 25 at 450 $\mu$ m and 20 at 850 $\mu$ m. The measured HPBW is 7.9 arcsec at $\mu$ m and 14.9 arcsec at $\mu$ m (derived from observations of CRL618). + In order to remove the error beam of the telescope. which contributes significantly to the 450 jim data. the SCUBA maps were deconvolved with a beam map of Uranus using the SCLEAN algorithm (Keel 1991) and finally restored to the initial spatial resolution.," In order to remove the error beam of the telescope, which contributes significantly to the 450 $\mu$ m data, the SCUBA maps were deconvolved with a beam map of Uranus using the SCLEAN algorithm (Keel 1991) and finally restored to the initial spatial resolution." + We know that the maps may be distorted by chopping into ambient cloud emission., We know that the maps may be distorted by chopping into ambient cloud emission. +" This will affect the 450 gm flux more than the 850 jm flux. because the error lobe is larger at 450 jm. The 450 j/mm map was therefore finally corrected by adding a constant level of 5 of the peak value to the map. before convolving it to the final resolution,"," This will affect the 450 $\mu$ m flux more than the 850 $\mu$ m flux, because the error lobe is larger at 450 $\mu$ m. The 450 $\mu$ m map was therefore finally corrected by adding a constant level of 5 of the peak value to the map, before convolving it to the final resolution." +broadly following their initial classification. showing a goocl separation between N and J stars.,"broadly following their initial classification, showing a good separation between N and J stars." + Lt is clear that using two measures gives a better isolation of the J stars than can be achieved with just one axis (or spectral feature)., It is clear that using two measures gives a better isolation of the J stars than can be achieved with just one axis (or spectral feature). + It should also be noted that the Co-weak stars lie to the right-hand edge of the main body of non-J) stars showing that they can be distinguished from the typical cool N stars through the shape of the CN bands in the wavelength range., It should also be noted that the $_2$ -weak stars lie to the right-hand edge of the main body of non-J stars showing that they can be distinguished from the typical cool N stars through the shape of the CN bands in the wavelength range. + Lhe dominant cause of the overlap between the two types is the simplistic nature of the initial classification., The dominant cause of the overlap between the two types is the simplistic nature of the initial classification. + The few stars which are seen in the border area between the J stars and the rest were checked inclividually and classified accordingly., The few stars which are seen in the border area between the J stars and the rest were checked individually and classified accordingly. + The presence of stars in that arca. is mainly due to greater noise in their spectra., The presence of stars in that area is mainly due to greater noise in their spectra. + Phe set of open circles represents the sample of J stars used in this paper., The set of open circles represents the sample of J stars used in this paper. + AX seb of stars associated with the main boc of stars in Fig., A set of stars associated with the main body of stars in Fig. + 3. was chosen to represent non-J stars for use as a comparison with the J stars., \ref{jfind_b} was chosen to represent non-J stars for use as a comparison with the J stars. + A pseucdo-continuum was defined as two linear segments between maxima at5722... andG620A.," A pseudo-continuum was defined as two linear segments between maxima at, and." +. These are points where Cs and CN banc absorption is weakest., These are points where $_2$ and CN band absorption is weakest. + Ideally. a point at would be used. (see Westerlund et al. (1991)))," Ideally, a point at would be used (see Westerlund et al. \shortcite{westerlund91}) )" + but the 2dE μαvectra do not extend. this far into the red., but the 2dF spectra do not extend this far into the red. + For some stars. the maximum at was ereater than the one at so the pseudo-continuum was defined by that point instead.," For some stars, the maximum at was greater than the one at, so the pseudo-continuum was defined by that point instead." + Minima associated. with the principal lines ancl bancds were then measured. as were maxima each side of these minima.," Minima associated with the principal lines and bands were then measured, as were maxima each side of these minima." + Dand strengths were calculated with respect to the pseudo-continuum and also to a local continuum cefined by the nearby maxima., Band strengths were calculated with respect to the pseudo-continuum and also to a local continuum defined by the nearby maxima. + ALL this was done after applying a slight smoothing to the spectra using a 3-pixel box which is equivalent to the instrumental resolution., All this was done after applying a slight smoothing to the spectra using a 3-pixel box which is equivalent to the instrumental resolution. + Three important maxima [ie immediately to the red of the heads of the (0.22) and (1.33) *7€47C° bands and the (0.22) CIC band. atG202A.. and. respectively.," Three important maxima lie immediately to the red of the heads of the 2) and 3) $^{12}{\rmn C}^{12}{\rmn C}$ bands and the 2) $^{13}{\rmn C}^{12}{\rmn C}$ band, at, and respectively." + These are marked by arrows on Fig. 1.., These are marked by arrows on Fig. \ref{plex}. + Fig., Fig. + 4 shows the relationship between two spectral slopes relating these maxima. Φ(A6202/A6134) and 9(46202/AGISO). after normalizing to a Lat pseudo-continuum.," \ref{slopes} shows the relationship between two spectral slopes relating these maxima, $\Phi\,(\lambda6202/\lambda6134)$ and $\Phi\,(\lambda6202/\lambda6180)$, after normalizing to a flat pseudo-continuum." + This normalisation is particularly useful here in order to remove instrumental fects in the 2dE. spectra. due to errors in the CCD Lat fielding and calibration procedures. and to chromatic effects inherent in the 2dbE opties (see Lewis et al.," This normalisation is particularly useful here in order to remove instrumental effects in the 2dF spectra, due to errors in the CCD flat fielding and calibration procedures, and to chromatic effects inherent in the 2dF optics (see Lewis et al." + (2002) for details)., \shortcite{lewis02} for details). + Llowever. the corrections were relatively small here since the carbon star spectra are in the red spectral region and cover only a limited wavelength range.," However, the corrections were relatively small here since the carbon star spectra are in the red spectral region and cover only a limited wavelength range." +fully established. (see Paper 1I).,fully established (see Paper II). + Our models use 200000 particles.," Our models use $200\,000$ particles." + Twenty-six simulations were performed simultaneously using a serial version of the code on single 1 GIIz Pentium 111 processors of the Parallel Computing Facility of the American Museum of Natural History (AMNID., Twenty-six simulations were performed simultaneously using a serial version of the code on single 1 GHz Pentium III processors of the Parallel Computing Facility of the American Museum of Natural History (AMNH). + Each computation took about 6 months., Each computation took about 6 months. + Figure | and Figure 2 show the density distribution of the gas., Figure \ref{fig_sinkdis1} and Figure \ref{fig_sinkdis2} show the density distribution of the gas. + To make the figures. a 256° grid was filled with densities properly computed from the SPIL kernel. and the result is displaved in (hree-climensional projection row)) and in a slice through maxiniun density one lree-lall Gime alter sell-gravitv is turned on lor selected 5 and both driving wavenunbers.," To make the figures, a $^3$ grid was filled with densities properly computed from the SPH kernel, and the result is displayed in three-dimensional projection ) and in a slice through maximum density one free-fall time after self-gravity is turned on for selected $\gamma$ and both driving wavenumbers." + As found in previous studies citealimm99)). the driving wavenumber strongly influences the densitv distribution.," As found in previous studies \\citealt{mm99}) ), the driving wavenumber strongly influences the density distribution." + Driving with /=1 2 produces strong filaanentary structure. while the density distribution for /—7 remains more uniform at large scale.," Driving with $k=1$ –2 produces strong filamentary structure, while the density distribution for $k=7$ --8 remains more uniform at large scale." + We find that the value of 5 is as important as the driving in determining collapse behavior., We find that the value of $\gamma$ is as important as the driving in determining collapse behavior. + As > increases. the number of collapsed cores replaced by sink particles decreases. and the cores cluster less.," As $\gamma$ increases, the number of collapsed cores replaced by sink particles decreases, and the cores cluster less." + For the same 5. driving with &=1 2 produces both far more. and more clustered dense cores than driving with /=7 8.," For the same $\gamma$, driving with $k=1$ –2 produces both far more, and more clustered dense cores than driving with $k=7$ –8." + The dense cores tend to collapse predominantly in filaments or at intersections of filaments., The dense cores tend to collapse predominantly in filaments or at intersections of filaments. + At >1.1. no fragmentation occurs bv the time shown lor driving with f= 78.," At $\gamma \geq 1.1$, no fragmentation occurs by the time shown for driving with $k=7$ –8." + The isothermal case. 5;=1.0. agrees well with previous results in Papers II and ΠΠ.," The isothermal case, $\gamma=1.0$, agrees well with previous results in Papers II and III." + Our current investieation agrees wilh (he results in Paper I.HI. that collapse tends to form clusters with high efliciency in regions with weak turbulence. while in regions with strong (turbulence. sparse. slow collapse occurs.," Our current investigation agrees with the results in Paper I–III, that collapse tends to form clusters with high efficiency in regions with weak turbulence, while in regions with strong turbulence, sparse, slow collapse occurs." + We now add the additional criterion that collapse and fragmentation depends strongly on 3., We now add the additional criterion that collapse and fragmentation depends strongly on $\gamma$. +" In regions with 5«1. fragmentation occurs earlier and more Irequenilv. while in regions where 5>1, fragmentation is retarded and less frequent."," In regions with $\gamma < 1$, fragmentation occurs earlier and more frequently, while in regions where $\gamma > 1$, fragmentation is retarded and less frequent." + Fieure 3. compares the number of collapsed cores at different 5 for models with different diving wavenumbers., Figure \ref{fig_sinknum} compares the number of collapsed cores at different $\gamma$ for models with different driving wavenumbers. + The rate al which new protostellar cores form differs [ον different ., The rate at which new protostellar cores form differs for different $\gamma$. + Alodels with low 5 form cores quickly. while models with large 5 form new cores more rarely.," Models with low $\gamma$ form cores quickly, while models with large $\gamma$ form new cores more rarely." + Again we see more cores for driving with &= 12 than for / =78. Rou, Again we see more cores for driving with $k=1$ –2 than for $k=7$ –8. +leau&Bastien(1990). found an empirical scaling relation A.x5? of the critical," \citet{rb90} found an empirical scaling relation $J_c +\propto \gamma^2$ of the critical" +"the two radio relics, although at low SNR.","the two radio relics, although at low SNR." + For relic RW the polarization fraction is around 5—10% (reportedpolariza-tionfractionsarecorrectedforRiceanbias; ?)..," For relic RW the polarization fraction is around $5-10\%$ \citep[reported polarization fractions are +corrected for Ricean bias;][]{1974ApJ...194..249W}." +" For RE the polarization fraction varies, with a maximum of ~25%."," For RE the polarization fraction varies, with a maximum of $\sim 25\%$." +" For the fainter parts of the relics no polarized emission is detected, but this is expected if the relics are polarized at the level or less."," For the fainter parts of the relics no polarized emission is detected, but this is expected if the relics are polarized at the level or less." + Most polarization E-vectors are aligned perpendicular to the major axis of the two relics (for the parts where polarized emission was detected)., Most polarization E-vectors are aligned perpendicular to the major axis of the two relics (for the parts where polarized emission was detected). + Spectral index and polarization properties for the compact sources are discussed in Sect. 1.., Spectral index and polarization properties for the compact sources are discussed in Sect. \ref{sec:agn}. + The cluster hosts several interesting tailed radio sources., The cluster hosts several interesting tailed radio sources. + Radio overlays on optical images are shown in Figs., Radio overlays on optical images are shown in Figs. + 10 to 14.., \ref{fig:SA} to \ref{fig:SEF}. + Sources are referred to as in Fig. 7.., Sources are referred to as in Fig. \ref{fig:gmrt610_labels}. +" The morphology of these radio sources is as expected for a system undergoing a merger, with high galaxy velocities with respect to the ICM."," The morphology of these radio sources is as expected for a system undergoing a merger, with high galaxy velocities with respect to the ICM." +" The radio powers reported for the sources in Table 3,, are consistent with them being sources (?) located in the cluster (e.g.,???).. S"," The radio powers reported for the sources in Table \ref{tab:relicflux}, are consistent with them being sources \citep{1974MNRAS.167P..31F} located in the cluster \citep[e.g.,][]{1991MNRAS.249..164O, 1994ASPC...54..319O,1995ApJ...451...88B}." +ource A is a “head-tail” source belonging to the elliptical galaxyJ0012032045234132., Source A is a “head-tail” source belonging to the elliptical galaxy. +". The spectral index steepens along the tail, from —0.6 to —2.1 to the west."," The spectral index steepens along the tail, from $-0.6$ to $-2.1$ to the west." + The, The +significant in Mrk 766(2).,significant in Mrk 766(2). + In this instance. this may simply be due to poor statistics in the case of Mrk 766(2).," In this instance, this may simply be due to poor statistics in the case of Mrk 766(2)." + We have presented the rms variability spectra of a sample of 15 observations of I+ Seyfert galaxies observed byXMM-Newton.. concentrating on their iron Ka line variability.," We have presented the rms variability spectra of a sample of 18 observations of 14 Seyfert galaxies observed by, concentrating on their iron $\alpha$ line variability." + Perhaps the most striking result of our study is the extraordinary. diversity in the rms spectra., Perhaps the most striking result of our study is the extraordinary diversity in the rms spectra. + Different objects clearly display different variability properties around the iron line., Different objects clearly display different variability properties around the iron line. + The rms spectrum is typically also different to the time-averaged spectrum. sometimes showing suppressed variability around the iron line. and enhanced variability in other sources.," The rms spectrum is typically also different to the time-averaged spectrum, sometimes showing suppressed variability around the iron line, and enhanced variability in other sources." + Finally. objects observed at more than one epoch show changes in their rms spectra. indicating different variability modes at different times. even in the same object.," Finally, objects observed at more than one epoch show changes in their rms spectra, indicating different variability modes at different times, even in the same object." + The diversity in he rms variability at the iron line throughout the sample shows that is unlikely that there is a universal line formation mechanism., The diversity in the rms variability at the iron line throughout the sample shows that it is unlikely that there is a universal line formation mechanism. + Indeed our results are extremely difficult to explain in any single jeoretical framework., Indeed our results are extremely difficult to explain in any single theoretical framework. + One robust and easily-interpreted result of our study is that. in all observations. we find a lack of variability at the neutral iron ine energy of 6.4 keV. Nearly all of the objects were found by NO7 © contain a narrow line at this energy.," One robust and easily-interpreted result of our study is that, in all observations, we find a lack of variability at the neutral iron line energy of 6.4 keV. Nearly all of the objects were found by N07 to contain a narrow line at this energy." + The lack of variability of he line core in the rms spectra supports the interpretation that it arises from material far from the central black hole. for example in he molecular torus.," The lack of variability of the line core in the rms spectra supports the interpretation that it arises from material far from the central black hole, for example in the molecular torus." + The core is expected to be constant because variations in the power-law continuum will be averaged out over he light crossing time of the torus and therefore emission from the orus should not have any effect on the rms., The core is expected to be constant because variations in the power-law continuum will be averaged out over the light crossing time of the torus and therefore emission from the torus should not have any effect on the rms. + The broad iron line emission and its variability are far more ouzzling., The broad iron line emission and its variability are far more puzzling. + The simple disk interpretation for the broad line is that variations should follow those in the continuum. as the line emitting region is close to the production site of the power-law continuum. he corona.," The simple disk interpretation for the broad line is that variations should follow those in the continuum, as the line emitting region is close to the production site of the power-law continuum, the corona." + This would result in an rms spectrum that shows a variable broad line that matches the time-averaged spectrum., This would result in an rms spectrum that shows a variable broad line that matches the time-averaged spectrum. + This is seen only in a very few objects., This is seen only in a very few objects. + Variability in the broad emission is not uncommon in the sample. however. being present in 6/18 observations.," Variability in the broad emission is not uncommon in the sample, however, being present in 6/18 observations." + This includes at least two observations where variations in the red wing exceed those of the continuum. indicative hat in these objects. beaming. light bending or other relativistic effects may be in play.," This includes at least two observations where variations in the red wing exceed those of the continuum, indicative that in these objects, beaming, light bending or other relativistic effects may be in play." + Some of the objeets that display broad iron line variability jive been suggested to possess absorption layers that can mimic he red wing e.g. MCG 6-30-15¢1) (Miller et al., Some of the objects that display broad iron line variability have been suggested to possess absorption layers that can mimic the red wing e.g. MCG 6-30-15(1) (Miller et al. + 2008)., 2008). + A partial covering absorber. when combined with distant reflection. can oroduee a hump in the spectrum between 3-7 keV. which is hen taken to be an emission feature.," A partial covering absorber, when combined with distant reflection, can produce a hump in the spectrum between 3-7 keV, which is then taken to be an emission feature." +" This requires no relativistic component as the absorption zones are >1007, from the black 10le and the weak narrow iron line arises completely from the distant torus.", This requires no relativistic component as the absorption zones are $>100 r_g$ from the black hole and the weak narrow iron line arises completely from the distant torus. + Another example is NGC 3783. where there has been some controversy over whether or not a broad red wing is present.," Another example is NGC 3783, where there has been some controversy over whether or not a broad red wing is present." + Reeves et al. (, Reeves et al. ( +2004) suggested that much of the broad red wing may be an artefact of a warm absorber adding curvature to the continuum. although they and NO7 both concluded that some disk reflection was also present.,"2004) suggested that much of the broad red wing may be an artefact of a warm absorber adding curvature to the continuum, although they and N07 both concluded that some disk reflection was also present." + None the less the spectrum is very complex. with two zones of ionized gas. a strong H-like emission line and a blurred Compton reflection component.," None the less the spectrum is very complex, with two zones of ionized gas, a strong H-like emission line and a blurred Compton reflection component." + The effect of absorption on the rms is not completely clear but if the red wing is a product of partial covering absorption or distant scattered components. then the rms variability of the red wing cannot be larger than that of the continuum.," The effect of absorption on the rms is not completely clear but if the red wing is a product of partial covering absorption or distant scattered components, then the rms variability of the red wing cannot be larger than that of the continuum." + This is compatible with NGC 3783. but disagrees with the suggestion that thick warm absorbers can mimic the red wing in NGC 3516¢2) (Turner et al.," This is compatible with NGC 3783, but disagrees with the suggestion that thick warm absorbers can mimic the red wing in NGC 3516(2) (Turner et al." + 2005) as the variability of the iron line is much stronger than the continuum., 2005) as the variability of the iron line is much stronger than the continuum. + The rms spectrum is thus better explained with the blurred reflection model (NO7) if relativistic effects are enhancing the variability of he red wing., The rms spectrum is thus better explained with the blurred reflection model (N07) if relativistic effects are enhancing the variability of the red wing. + A similar argument can be applied to the observations where complex absorption has been suggested to solely cause spectral curvature in the red wing (e.g. Reeves et al., A similar argument can be applied to the observations where complex absorption has been suggested to solely cause spectral curvature in the red wing (e.g. Reeves et al. + 2004) but a flat rms spectrum reveals a non-variable broad line and constant disk reflection., 2004) but a flat rms spectrum reveals a non-variable broad line and constant disk reflection. + For example. Schurch et al. (," For example, Schurch et al. (" +2003) have suggested hat the red wing in NGC 4151¢3) might be accounted for purely by complex absorption.,2003) have suggested that the red wing in NGC 4151(3) might be accounted for purely by complex absorption. + In this case the excess photons seen in our ime-averaged spectrum between 4-6 keV are continuum photons. which should naturally show the same variability as the remainder of the 4-6 keV continuum. over which the red wing is seen.," In this case the excess photons seen in our time-averaged spectrum between 4-6 keV are continuum photons, which should naturally show the same variability as the remainder of the 4-6 keV continuum, over which the red wing is seen." + We are able to reject this possibility using the flat rms spectrum for NGC 4151¢3) and conclude that when invariant. the broad red wing must therefore be a distinet additional component. almost certainly from reflection.," We are able to reject this possibility using the flat rms spectrum for NGC 4151(3) and conclude that when invariant, the broad red wing must therefore be a distinct additional component, almost certainly from reflection." + A flat rms spectrum corresponds to a fractional (i.e. normalised) variance spectrum with a dip and has been found oeviously in. e.g.. MCG-6-30-15 (Vaughan Fabian 2004).," A flat rms spectrum corresponds to a fractional (i.e. normalised) variance spectrum with a dip and has been found previously in, e.g., MCG-6-30-15 (Vaughan Fabian 2004)." + This ws been taken as evidence of a decoupling between the continuum and line., This has been taken as evidence of a decoupling between the continuum and line. + With MCG-6-30-15. the peak of the reflected emission corms close to the black hole. so for the reflection component to not be strongly associated with the direct power-law component. he intrinsic X-ray emission must be anisotropic.," With MCG-6-30-15, the peak of the reflected emission forms close to the black hole, so for the reflection component to not be strongly associated with the direct power-law component, the intrinsic X-ray emission must be anisotropic." + Gravitational light bending has been proposed to explain this as the anisotropy can result from the gravitational field of the black hole bending power-aw photons away from the observer and towards the disk., Gravitational light bending has been proposed to explain this as the anisotropy can result from the gravitational field of the black hole bending power-law photons away from the observer and towards the disk. + This ight bending is most severe when the height of the corona over the disk is small., This light bending is most severe when the height of the corona over the disk is small. + Instead of reaching us. the continuum photons will be reflected off the disk which can enhance the disk component.," Instead of reaching us, the continuum photons will be reflected off the disk which can enhance the disk component." + As the coronal height increases. less photons are deflected onto he disk and so more reach us directly.," As the coronal height increases, less photons are deflected onto the disk and so more reach us directly." + Miniutti Fabian (2004) iive calculated how the intensities of the direct and reflection components may vary with the corona height ina simple toy model., Miniutti Fabian (2004) have calculated how the intensities of the direct and reflection components may vary with the corona height in a simple toy model. + They find that at a low coronal height. both vary together which would give an rms spectrum with an excess that matches the time-averaged iron line profile e.g. MCG-6-30-15¢1).," They find that at a low coronal height, both vary together which would give an rms spectrum with an excess that matches the time-averaged iron line profile e.g. MCG-6-30-15(1)." + As the height increases further. another regime is reached where the direct flux varies by a factor of 3 or 4. but the reflection component changes by less than10¢c.," As the height increases further, another regime is reached where the direct flux varies by a factor of 3 or 4, but the reflection component changes by less than." +. Thus this could correspond to flat rms spectra such as that of MCG-6-30-15(2)., Thus this could correspond to flat rms spectra such as that of MCG-6-30-15(2). + As the two observations of MCG-6-30-15 are separated by a year. the light bending interpretation suggests that there is a large change in the coronal height within a relatively small amount of time.," As the two observations of MCG-6-30-15 are separated by a year, the light bending interpretation suggests that there is a large change in the coronal height within a relatively small amount of time." + The observations where the variability excess is stronger than the red wing of the time-averaged iron line could also be explained by gravitational light bending if relativistic effects such as relativistic beaming enhance the variability of the disk reflection component., The observations where the variability excess is stronger than the red wing of the time-averaged iron line could also be explained by gravitational light bending if relativistic effects such as relativistic beaming enhance the variability of the disk reflection component. + However. NGC 4151¢2) and NGC 55480) have the strong excesses but do not have iron lines that are relativistically broadened as would be expected if this interpretation is correct.," However, NGC 4151(2) and NGC 5548(2) have the strong excesses but do not have iron lines that are relativistically broadened as would be expected if this interpretation is correct." +" Along with MCG-6-30-15, the other three objects with multiple observations. NGC 4151. Mrk 766 and NGC 5506 show a change in the variability at the iron line between their two observations."," Along with MCG-6-30-15, the other three objects with multiple observations, NGC 4151, Mrk 766 and NGC 5506 show a change in the variability at the iron line between their two observations." + This demonstrates the complexity of variability in Seyfert [s as there is not only a range of behaviour found between objects. but also within objects themselves.," This demonstrates the complexity of variability in Seyfert 1s as there is not only a range of behaviour found between objects, but also within objects themselves." + The implication is that the inner accretion flow is highly unstable and chaotic. with ehanges in illumination and/or geometry occurring," The implication is that the inner accretion flow is highly unstable and chaotic, with changes in illumination and/or geometry occurring" +where Gt.tyre.ry) is the Creeu's function where Jy is the Bessel function of zeroth order.,"where $G(t,t_0;x,x_0)$ is the Green's function where $J_0$ is the Bessel function of zeroth order." + From linear perturbation. it i possible to predict that the mass fiux scales with ALG. since the source terii is the second order of perturbation.," From linear perturbation, it is possible to predict that the mass flux scales with $M_{\rm p}^2$, since the source term is the second order of perturbation." + Later in this paper. we compare this result with wmuerical calculations to understand how much mass flix is excited by the planet.," Later in this paper, we compare this result with numerical calculations to understand how much mass flux is excited by the planet." + We now consider the model in which the source terii is giveu by where Sy20 and ic;>0 are positive constants. aud àpCGe) denotes the Dirac's delta fiction.," We now consider the model in which the source term is given by where $S_0>0$ and $x_s>0$ are positive constants, and $\delta_D(x)$ denotes the Dirac's delta function." + We later see that the source term is positive in the region .c20. and negative for «©«0.," We later see that the source term is positive in the region $x>0$, and negative for $x<0$." + This form of the source terii is the simplest case where we can obtain an analytic solution for the mass flux., This form of the source term is the simplest case where we can obtain an analytic solution for the mass flux. + Changing the integration variable from (τρις) to (7.0) via equation can be rewritten to Iu order to see the mass flux ouly in the vicinity of the planet. we assinae 0«eory.," Changing the integration variable from $(t_0,x_0)$ to $(r,\theta)$ via equation can be rewritten to In order to see the mass flux only in the vicinity of the planet, we assume $0»oc.," Substituting equation , and integrate over $r$ , we obtain We take the limit $t\to\infty$." + Then. we can approximate cosMITou)ct]~7/2.," Then, we can approximate $\cos^{-1}[(x \pm x_s)/ct]\sim\pi/2$." + Using the formula (Abramowitz and Steeun 1970) where e>0. the integration over 0 cau be performed to obtain where Ay is the modified. Bessel fuuctiou of the zeroth order.," Using the formula (Abramowitz and Stegun 1970) where $a>0$, the integration over $\theta$ can be performed to obtain where $K_0$ is the modified Bessel function of the zeroth order." + Iu the vicinity of the planet...«ary. the mass fiux changes with Fa;xc. which iudicates that the eap opeus up.," In the vicinity of the planet, $x \ll x_s$, the mass flux changes with $\mathcal{F}_M\propto x$, which indicates that the gap opens up." +" We note that divergence at 1=dc, is the artefact of our simplification where we have used delta function as a source term.", We note that divergence at $x= \pm x_s$ is the artefact of our simplification where we have used delta function as a source term. + We have secu that if there is a source of specific vorticity. mass flux appears in the vicinity of the planet. aud it leads to the change of surface deusitv to open a eap.," We have seen that if there is a source of specific vorticity, mass flux appears in the vicinity of the planet, and it leads to the change of surface density to open a gap." + We now briefly diseuss how this eap opening process eucds., We now briefly discuss how this gap opening process ends. + Au inviscid disk with a rapid surface density variation is prone to a linear instability. which is referred to as Rossby wave instability (Li et al.," An inviscid disk with a rapid surface density variation is prone to a linear instability, which is referred to as Rossby wave instability (Li et al." + 2000. de Val-Borro et al.," 2000, de Val-Borro et al." + 2007)., 2007). + In Appendix D.. we show a brief outline of the lincar stability analyses for a disk with a gap. aud derive the necessary. conditions for the instability.," In Appendix \ref{app:RWI}, we show a brief outline of the linear stability analyses for a disk with a gap, and derive the necessary conditions for the instability." + Cap induced by a planet in the disk naturally excites the variation of specific vorticity. aud gap edees are likely places where such instability occurs.," Gap induced by a planet in the disk naturally excites the variation of specific vorticity, and gap edges are likely places where such instability occurs." + Rossby wave instability may stop the eap-opening processes described iu previous subsections., Rossby wave instability may stop the gap-opening processes described in previous subsections. + We do not expect that the instability leads to the complete closing of the gap. since the plauet always try to repel the fiuid clement by the excitation of the density wave.," We do not expect that the instability leads to the complete closing of the gap, since the planet always try to repel the fluid element by the excitation of the density wave." +" There may be at least ""unuderdeuse region around theplanetaryorbit. which may be called a ""gap."," There may be at least “underdense region” around theplanetaryorbit, which may be called a “gap”." +The HAT-P-13 system is unusual in that a transiting hot Jupiter and its host star are accompanied by a clearly-detected third component on a wider orbit.,The HAT-P-13 system is unusual in that a transiting hot Jupiter and its host star are accompanied by a clearly-detected third component on a wider orbit. + Such a configuration should result in 13ec inducing TTVs within the AA.b system. which may be detectable within a comparatively short time period.," Such a configuration should result in c inducing TTVs within the A,b system, which may be detectable within a comparatively short time period." + This yossibility has generated substantial interest. resulting in a large body of photometric observations covering many transits of the star by the inner planet.," This possibility has generated substantial interest, resulting in a large body of photometric observations covering many transits of the star by the inner planet." + We have assembled the available transit timing measurements and shown that they are most easily explained by a inear ephemeris. albeit with a small number of values which occur ater than expected.," We have assembled the available transit timing measurements and shown that they are most easily explained by a linear ephemeris, albeit with a small number of values which occur later than expected." + The diserepant measurements are not clumped ogether. so could only be explained via highly complex functional 'orms.," The discrepant measurements are not clumped together, so could only be explained via highly complex functional forms." + Previous claims of TTVs can be attributed to small-number statistics. although continued photometric monitoring has a good chance of turning up something interesting in the future.," Previous claims of TTVs can be attributed to small-number statistics, although continued photometric monitoring has a good chance of turning up something interesting in the future." + We have presented new observations of four transits. obtained using telescope defocussing techniques.," We have presented new observations of four transits, obtained using telescope defocussing techniques." + Including previously published data. we have ten good sets of transit light curves.," Including previously published data, we have ten good sets of transit light curves." + These were each analysed within the context of our project (Southworth2008.2009.2010.2011). and a good agreement between the results was found.," These were each analysed within the context of our project \citep{Me08mn,Me09mn,Me10mn,Me11mn}, and a good agreement between the results was found." + We combined them with the measured spectroscopic properties of the host star and several sets of theoretical stellar model predictions to find the physical properties of the system., We combined them with the measured spectroscopic properties of the host star and several sets of theoretical stellar model predictions to find the physical properties of the system. + HAT-P-13 is now well-characterised. although additional photometric and spectroscopic measurements would allow further improvement.," HAT-P-13 is now well-characterised, although additional photometric and spectroscopic measurements would allow further improvement." + We have included it in the TEPCat of the physical properties of transiting planetary systems., We have included it in the TEPCat of the physical properties of transiting planetary systems. + We find a signiticantly different set of physical properties compared to previous studies. which had access to only two of the ten photometric datasets used here.," We find a significantly different set of physical properties compared to previous studies, which had access to only two of the ten photometric datasets used here." + The star is more massive. larger and more evolved.," The star is more massive, larger and more evolved." + The planet. whose properties are measured relative to its host star. is similarly heavier and bigger.," The planet, whose properties are measured relative to its host star, is similarly heavier and bigger." + Its lower density and higher equilibrium temperature place it tirmly in the ‘pM? class advocated by Fortneyetal.(008)..., Its lower density and higher equilibrium temperature place it firmly in the `pM' class advocated by \citet{Fortney+08apj}. + Its radius is too large to match the values predicted by the models of Fortneyetal.(2007) or Baraffeetal., Its radius is too large to match the values predicted by the models of \citet{Fortney++07apj} or \citet{Baraffe++08aa}. +(2008). Laughlinetal.(2011)> found that the radius anomaly (the measured radius of a TEP versus that predicted by theoretical models) is correlated with equilibrium temperature. and possibly inversely correlated with host star.," \citet{Laughlin++11apj} found that the radius anomaly (the measured radius of a TEP versus that predicted by theoretical models) is correlated with equilibrium temperature, and possibly inversely correlated with host star." +. The large radius anomaly and high equilibrium temperature of[4] bb corroborate the former observation. but the highly metal-rich nature of the parent star [E]=0.41+ 0.08) is contrary to the latter suggestion.," The large radius anomaly and high equilibrium temperature of b corroborate the former observation, but the highly metal-rich nature of the parent star $\FeH = 0.41 \pm 0.08$ ) is contrary to the latter suggestion." + The reduced light curves presented in this work will be made available at the CDS and at., The reduced light curves presented in this work will be made available at the CDS ) and at. + This observational campaign has been possible thanks to the generous allocation of telescope time by the TAC of the Bologna Observatory and to the invaluable help of the technical staff., This observational campaign has been possible thanks to the generous allocation of telescope time by the TAC of the Bologna Observatory and to the invaluable help of the technical staff. + TS acknowledges financial support from STFC in the form of an Advanced Fellowship., JS acknowledges financial support from STFC in the form of an Advanced Fellowship. + We thank Andras Pall for supplying photometric data and the anonymous referee for insightful comments., We thank Andras Páll for supplying photometric data and the anonymous referee for insightful comments. + The following internet-based resources were used in research for this paper: the ESO Digitized Sky Survey: the NASA Astrophysics Data System: the SIMBAD database operated at CDS. Strasbourg. France: and the aryiv scientific paper preprint service operated by Cornell University.," The following internet-based resources were used in research for this paper: the ESO Digitized Sky Survey; the NASA Astrophysics Data System; the SIMBAD database operated at CDS, Strasbourg, France; and the $\chi$ iv scientific paper preprint service operated by Cornell University." + Fabian&Twasawa1999)). ~75% (Nyy> 1072 2: Risalitictal.1999)). zz1. (el (Treisteretal.2001).. Alartinez-, \citealp{fabian99a}) $\sim$ $N_H$$>$ $^{23}$ $^{-2}$ \citealp{risaliti99}) $z$$\gtrsim$ $>$ \citep{treister04}. \citealp{martinez06}) +Sansiereetal.20063). (οσα 7) Ly> Lott 21057L.. (ivasawa2009) (Bauerctal.2010)., $N_H$$>$ $^{24}$ $^{-2}$ $_{IR}$$>$ $^{11}$ $>$ $^{12}$ $_\odot$ \citep{iwasawa09} \citep{bauer10}. +". N-rav observations performed using the NADENewtou 2005)(οιο,, Braitoetal.2003. 20013). Chandra (Teneetal. and Suzaku (Tengetal.2009) observatories have shown that most ULIRGs are intrinsically faint N-ray sources, most Likely due to the effects of obscuration. while their X-ray spectra show combined signatures of starburst and ACN activity."," X-ray observations performed using the XMM-Newton (e.g., \citealp{braito03,braito04}) ), Chandra \citep{teng05} and Suzaku \citep{teng09} observatories have shown that most ULIRGs are intrinsically faint X-ray sources, most likely due to the effects of obscuration, while their X-ray spectra show combined signatures of starburst and AGN activity." +" The key features observed in the A-vav spectra of ULIRGs are a soft thermal colmpoucnt. typically associated with star formation. a reavily-obsemved (Nyp~ 1074 2) power-law associated with the ACN direct ciission. aud a promincut emission ine at ~6.1 keV. identified with fluorescence enissiou roni ion iu the I&,, ionization level. originating either iu he accretion disk or iu the surroundiug material (Mattetal. 1991)."," The key features observed in the X-ray spectra of ULIRGs are a soft thermal component, typically associated with star formation, a heavily-obscured $_H$$\sim$ $^{24}$ $^{-2}$ ) power-law associated with the AGN direct emission, and a prominent emission line at $\sim$ 6.4 keV, identified with fluorescence emission from iron in the $_\alpha$ ionization level, originating either in the accretion disk or in the surrounding material \citep{matt91}." + The presence of leavily-obscured ACN among the nost extreme ULIRGs at τσ] has recently been established from deep Spitzer observations (Dacddictal.2007:xFioreetal.2008:Treister 2009b).," The presence of heavily-obscured AGN among the most extreme ULIRGs at $z$$\simeq$ 1-2 has recently been established from deep Spitzer observations \citep{daddi07,fiore08,treister09c}." +. Most of these sources have very high. quasar-like. iutriusic Iuniuosities. aud hence most likely do not coustitute the bulk of the heavily-obscured ACN population (Treisteretal. 2010).," Most of these sources have very high, quasar-like, intrinsic luminosities, and hence most likely do not constitute the bulk of the heavily-obscured AGN population \citep{treister10}." +. Establishing the fraction of (U)LIBCs thathost a lower hnuninositv ACN is a iore challeugiue task., Establishing the fraction of (U)LIRGs thathost a lower luminosity AGN is a more challenging task. + Recent works based on N-rav stacking 20090) and using τμ selected sources (INartaltepeetal.2010). report a steep decrease in the fraction of ACN with decreasing IR luminosity. eoing from ~100% at 1ο L.. to «104 at Lpg τοῦ L..," Recent works based on X-ray stacking \citep{fiore09} and using $\mu$ m selected sources \citep{kartaltepe10} report a steep decrease in the fraction of AGN with decreasing IR luminosity, going from $\sim$ at $_\textnormal{IR}$ $^{13}$ $_\odot$ to $<$ at $_\textnormal{IR}$ $^{10}$ $_\odot$ ." + Tn the local LggpUniverse. Schawinskietal.(2010a) found that the incicence of low-Inunünositv. Sevfert-AGN as a function of stelhuümass is more coniplicated. aud is iufluenced. by other paraimcters.," In the local Universe, \citet{schawinski10} found that the incidence of low-luminosity, Seyfert-like,AGN as a function of stellarmass is more complicated, and is influenced by other parameters." + For, For +of particles turning around at the same time (Bertschinger1985))) or. equivalentLy. here is no apocentre-crossing of. particle orbits during virialisaion.,"of particles turning around at the same time \citep{Ber85}) ) or, equivalently, there is no apocentre-crossing of particle orbits during virialisation." + This result was extended in SVMS to non-radial DA., This result was extended in SVMS to non-radial PA. + An important consequence of tus result was that the spherically averaged densiy profile Cei(r) for a virialised halo does not allow one to tell whether or no ith as sullered major, An important consequence of this result was that the spherically averaged density profile $\srho(r)$ for a virialised halo does not allow one to tell whether or not it has suffered major. +"she reason for this is that. given a virialised halo with any arbitrary agerceaion history. we can always think about one peak with appropriate clensity profile (or equivalentby. the spherical energy. distribution £,0CA)). leading by A to à virialise object with idenical spherically averaged density. profile."," The reason for this is that, given a virialised halo with any arbitrary aggregation history, we can always think about one peak with appropriate density profile (or equivalently, the spherical energy distribution ${\cal + E}\p(M)$ ), leading by PA to a virialised object with identical spherically averaged density profile." + Such a putative accreting seed of t1e halo really exists: it is the |ocak tracing the current evolution by smooth accretion of the halo according to he peak formalism., Such a putative accreting seed of the halo really exists; it is the peak tracing the current evolution by smooth accretion of the halo according to the peak formalism. +" Thus. i is à nornial peaκ contributing to he peak number density just as the halo associated with it is a normal halo contributing to the halo mass ""unction."," Thus, it is a normal peak contributing to the peak number density just as the halo associated with it is a normal halo contributing to the halo mass function." + Phereforc. the halo is incdistinguishable from one evolved by PA. regardless of its rea agerceation history.," Therefore, the halo is indistinguishable from one evolved by PA, regardless of its real aggregation history." + ut what about t16 shape and. kinematics of wloes?, But what about the shape and kinematics of haloes? + Do they allow one to tell between objects forme by PA and having sullered major mergers?, Do they allow one to tell between objects formed by PA and having suffered major mergers? + The answer is always the same: major mergers go unnoticed in these properties as well., The answer is always the same: major mergers go unnoticed in these properties as well. + The proof is similar to that carried out in SVMS for the density profile., The proof is similar to that carried out in SVMS for the density profile. + Using the one-to-one relations inferred in Section1?? thanks to the results of SMVS. given a halo with any arbitrary aggregation history. one can always think about one peaκ not only with the appropriate density. profile.peak. leading by. PA to the spherica[ly averaged profile of the halo (SVMS). but also with a shape also leading to its shape and kinematics.," Using the one-to-one relations inferred in Section \ref{eccentricity} thanks to the results of SMVS, given a halo with any arbitrary aggregation history, one can always think about one peak not only with the appropriate density profile, leading by PA to the spherically averaged profile of the halo (SVMS), but also with a shape also leading to its shape and kinematics." + The shape of this putative accreting seed. coincides. by continuity. with that of the peak tracing the halo in the peak formalism (see SVMS) and is hus a normal peak contribuing to the peak number density.," The shape of this putative accreting seed, coincides, by continuity, with that of the peak tracing the halo in the peak formalism (see SVMS) and is thus a normal peak contributing to the peak number density." + As a consecuence. the halo is indistinguishable from the one that would grow bv PA from that seed not only regarding the spherically averaged density profile. but also the shape and kinematics.," As a consequence, the halo is indistinguishable from the one that would grow by PA from that seed not only regarding the spherically averaged density profile, but also the shape and kinematics." + Εις result can be stunmarised by saving that major mergers σοιinnoticed in virialised objects regarding all those properles., This result can be summarised by saying that major mergers go unnoticed in virialised objects regarding all those properties. + As 6iscussed in SVAIS. the previous conclusion relects the fact that virialisation is a real relaxation process vielding the Menoryv loss of the halo past history.," As discussed in SVMS, the previous conclusion reflects the fact that virialisation is a real relaxation process yielding the memory loss of the halo past history." + “Phis obviously afects not only the inner structure but also the shape and kinematics of virialised objects., This obviously affects not only the inner structure but also the shape and kinematics of virialised objects. + Certainly. the one-to-one corresporncence between virialised haloes and their seeds in PA implies that there is no ful memory loss in PA due to virialisation. in agreement with the results of simulations (c.g. Vera-C'ircyetal.2011)).," Certainly, the one-to-one correspondence between virialised haloes and their seeds in PA implies that there is no full memory loss in PA due to virialisation, in agreement with the results of simulations (e.g. \citealt{VCea11}) )." + Ilowever. the fact that it is impossible O peconstLuc the seed of any simulated: virialised halo by running he simulation backwards is evidence of the existence « La time arrow indicating the direction of virialisation.," However, the fact that it is impossible to reconstruct the seed of any simulated virialised halo by running the simulation backwards is evidence of the existence of a time arrow indicating the direction of virialisation." + What makes both aspects consistent is the fact that. as just mentioned. the properties of virialised haloes do not allow one to tell wheher they have sullered major mergers or they have evoved by PA.," What makes both aspects consistent is the fact that, as just mentioned, the properties of virialised haloes do not allow one to tell whether they have suffered major mergers or they have evolved by PA." + ‘Pherclore. we cannot unambiguously determine their initial conclitions.," Therefore, we cannot unambiguously determine their initial conditions." + In other words. we can reconstruct their putative accreting seeds. but these may or may not be their real (possialy multinode) seeds.," In other words, we can reconstruct their putative accreting seeds, but these may or may not be their real (possibly multinode) seeds." + An important corollary of this resul is that the present nioclel for the shape and kinematics of virialised objects formed by PA also holds for objects having sulfered major mergers., An important corollary of this result is that the present model for the shape and kinematics of virialised objects formed by PA also holds for objects having suffered major mergers. + One must simply infer the properties of the virialised object from those of its putative acercting seed. that is the peak tracing its current evolution by smooth accretion.," One must simply infer the properties of the virialised object from those of its putative accreting seed, that is the peak tracing its current evolution by smooth accretion." + The model developed in SVMS for he inner structure (spherically averaged density profile) of virialised haloes has been extended to deal with their triaxial shape (eccentricity profiles) ancl kinematics (velocity dispersion and anisotropy profiles)., The model developed in SVMS for the inner structure (spherically averaged density profile) of virialised haloes has been extended to deal with their triaxial shape (eccentricity profiles) and kinematics (velocity dispersion and anisotropy profiles). + To do this we have considered the simple scenario of haloes evolving by pure accretion., To do this we have considered the simple scenario of haloes evolving by pure accretion. + Under this assumption we have derived he shape and kinematies of the final ojects from the shape of their seeds., Under this assumption we have derived the shape and kinematics of the final objects from the shape of their seeds. + “Phe reason why dealing with the case of pure accretion is sufficient is hat all virialisecl halos. even those having undergone major mergers. can be seen to arise in this wav from the peak which. according to the peak formalism. traces their current evolution.," The reason why dealing with the case of pure accretion is sufficient is that all virialised halos, even those having undergone major mergers, can be seen to arise in this way from the peak which, according to the peak formalism, traces their current evolution." + Ehe fact that in pure accretion he final objects keeps the memory. of he initial conditions is a consequence of virialisation being achieved. in this case. hrough shell-crossing with no crossing ¢E particle apocentres.," The fact that in pure accretion the final objects keeps the memory of the initial conditions is a consequence of virialisation being achieved, in this case, through shell-crossing with no crossing of particle apocentres." + Εις is not contradictory with the idea that virialisation is à real relaxation process., This is not contradictory with the idea that virialisation is a real relaxation process. + € )ntjo COonlrarv. the fact that major mergers do not leave any particular imprint in the shape and kinematics of virialised οjocs implies 1mt one cannot be sure about the real aggregation history or. equivalently. about the real seed of any given virialised object.," On the contrary, the fact that major mergers do not leave any particular imprint in the shape and kinematics of virialised objects implies that one cannot be sure about the real aggregation history or, equivalently, about the real seed of any given virialised object." + Applied to virialisecl haoes in hierarchical cosmologies. the model allows one to make the link between the typical (mean) shape and kinematies of these objects and the power-spectrum of random CGaussian density perturbations.," Applied to virialised haloes in hierarchical cosmologies, the model allows one to make the link between the typical (mean) shape and kinematics of these objects and the power-spectrum of random Gaussian density perturbations." + Following a simpler comprehensive approximate approach. we have shown that the overall shape and kinematies predicted by the mocel are consistent with the resuls of simulations of CDM cosmologies.," Following a simpler comprehensive approximate approach, we have shown that the overall shape and kinematics predicted by the model are consistent with the results of simulations of CDM cosmologies." + In. particular. the theoretical anisotropy profile has the same universal form as empirically found. with a substantial scatter due to the variety of peak (halo) shapes.," In particular, the theoretical anisotropy profile has the same universal form as empirically found, with a substantial scatter due to the variety of peak (halo) shapes." + Likewise. the," Likewise, the" +of Sw 1644457 within the context of black hole accretion. a RSG must have undergone the weakest of explosions. or none at all.,"of Sw 1644+57 within the context of black hole accretion, a RSG must have undergone the weakest of explosions, or none at all." + Standard long-duration GRBs have durations ~| minute and are associated with Type Ibe supernovae (2).., Standard long-duration GRBs have durations $\sim 1$ minute and are associated with Type Ibc supernovae \citep{wb06}. + These two facts are not unrelated: the compact stripped progenitors associated with Type Ibe supernovae are the only progenitors in which a jet can escape its host star on a timescale comparable to the duration of the GRB itself (2)., These two facts are not unrelated: the compact stripped progenitors associated with Type Ibc supernovae are the only progenitors in which a jet can escape its host star on a timescale comparable to the duration of the GRB itself \citep{matzner03}. +.We now consider the same reasoning but applied to much ower power jets., We now consider the same reasoning but applied to much lower power jets. + A jet with a momentum flux P; has an associated kinetic ;»ower of L;=Pv; where v; is the velocity of the jet material.," A jet with a momentum flux $\dot P_j$ has an associated kinetic power of $L_j = \dot P_j \, v_j$, where $v_j$ is the velocity of the jet material." +" If he jet interacts with an ambient medium of density p. the speed of he head of the jet through the ambient medium v; can be estimated by considering the balance between the momentum flux of the jet and the ram pressure of the ambient medium p,AS (22)... where Aj is the surface area of the head of the jet and 4; is the jet's openingnu angle."," If the jet interacts with an ambient medium of density $\rho_a$, the speed of the head of the jet through the ambient medium $v_h$ can be estimated by considering the balance between the momentum flux of the jet and the ram pressure of the ambient medium $\rho_a A_j v_h^2$ \citep{bc89, matzner03}, where $A_j \sim \pi \, \theta_j^2 r^2$ is the surface area of the head of the jet and $\theta_j$ is the jet's opening angle." + This yields: ME where L;5 is the isotropic equivalent kinetic power in the jet and in the 3.10:second equality we have assumed that the jet is relativistic., This yields: v_h v_j c where $L_{i} \simeq 4 L_j/\theta_j^2$ is the isotropic equivalent kinetic power in the jet and in the second equality we have assumed that the jet is relativistic. +" Equation 4. implies +,~0.007ANMyURNο where £; is scaled to 10ergs!'. which is appropriate for eres band 8;~3—10 deg."," Equation \ref{eq:vh} implies $v_h \sim 0.007 \, +L_{i,48}^{1/2} \, M_{10}^{-1/2} \, R_{14}^{1/2} \, c$ where $L_{i}$ is scaled to $10^{48} \ergs$, which is appropriate for $L_j \sim 10^{45-46} \ergs$ and $\theta_j \sim 3-10$ deg." + As the head of the jet propagates through the star (and/or supernova ejecta). a cocoon of shocked stellar and jet material forms around the jet.," As the head of the jet propagates through the star (and/or supernova ejecta), a cocoon of shocked stellar and jet material forms around the jet." + This cocoon in turn drives a lateral shock into the ambient medium., This cocoon in turn drives a lateral shock into the ambient medium. + The speed of this lateral shock 1 can be estimated by balancing the pressure in the cocoon with the ram pressure of the lateral shock., The speed of this lateral shock $v_l$ can be estimated by balancing the pressure in the cocoon with the ram pressure of the lateral shock. + Since the jet produced by a central magnetar and/or black hole accretion disk is very likely to be magnetized. the same applies to the cocoon.," Since the jet produced by a central magnetar and/or black hole accretion disk is very likely to be magnetized, the same applies to the cocoon." + The toroida magnetic field in the cocoon in turn creates an asymmetric pressure distribution. with the pressure being much larger near the je axis than at large cylindrical radii (2)...," The toroidal magnetic field in the cocoon in turn creates an asymmetric pressure distribution, with the pressure being much larger near the jet axis than at large cylindrical radii \citep{bl92}." + This reduces the latera expansion speed of the cocoon., This reduces the lateral expansion speed of the cocoon. + To account for this. we estimate the pressure in the cocoon that drives the lateral expansion as p.=FEfRGV) where Eis the total energy supplied by the centra engine up to the time of interest. V is the volume of the cocoon. and the factor f«| accounts for the pinching ettect of the toroida magnetic field.," To account for this, we estimate the pressure in the cocoon that drives the lateral expansion as $p_c \simeq f E/(3 V)$ where $E$is the total energy supplied by the central engine up to the time of interest, $V$ is the volume of the cocoon, and the factor $f < 1$ accounts for the pinching effect of the toroidal magnetic field." +" The speed of the lateral shock driven by the cocoon is thus v;2v,/'talο "," The speed of the lateral shock driven by the cocoon is thus $v_l \simeq v_h \, f^{1/4} \, \theta_j^{1/2} \, (c/v_h)^{1/4}$." +We now consider the limit in which the timescale for the je to escape the surrounding star is short compared to the expansion time of the stellar envelope., We now consider the limit in which the timescale for the jet to escape the surrounding star is short compared to the expansion time of the stellar envelope. + This is appropriate. e.g. for a failed supernova explosion. as in the supergiant collapse scenario considered in 32.1..," This is appropriate, e.g., for a failed supernova explosion, as in the supergiant collapse scenario considered in \ref{sec:energy}." + In this case. the time for the jet to escape the progenitor is LAOSL days(no expansion)nj The corresponding lateral speed of the cocoon-driven shock is where we have sealed the reduction factor / to a value appropriate if the magnetic energy in the cocoon is comparable to the thermal energy (e.g.. Fig.," In this case, the time for the jet to escape the progenitor is 5 no expansion) The corresponding lateral speed of the cocoon-driven shock is v_l 0.3 v_h where we have scaled the reduction factor $f$ to a value appropriate if the magnetic energy in the cocoon is comparable to the thermal energy (e.g., Fig." + 3 of 11)., 3 of \citealt{bucciantini07}) ). + Equation 6 implies that the lateral expansion time (~[ποΑΗ is a factor of ~S longer than the time it takes the jet to escape the star. even for the low power jets of interest here.," Equation \ref{eq:vlatnum} implies that the lateral expansion time $\sim [\pi/2][R/v_l]$ ) is a factor of $\sim 5$ longer than the time it takes the jet to escape the star, even for the low power jets of interest here." + It is thus plausible that the jet can escape the star before the cocoon completely envelops the stellar envelope., It is thus plausible that the jet can escape the star before the cocoon completely envelops the stellar envelope. + Once the jet escapes the star. the material in the cocoon. which has a sound speed ~οV3>>vy. will escape along with the jet. depressurizing the cocoon.," Once the jet escapes the star, the material in the cocoon, which has a sound speed $\sim c/\sqrt{3} \gg v_l$, will escape along with the jet, depressurizing the cocoon." +" After the cocoon depressurizes. the lateral shock will decelerate as it sweeps up mass. reaching a velocity of order v;ΕΛΟΤ, where E,~Lf. is the energy acquired prior to breakout."," After the cocoon depressurizes, the lateral shock will decelerate as it sweeps up mass, reaching a velocity of order $v_{\rm l,f} \sim (2 E_{\rm c}/M)^{1/2}$, where $E_{\rm c} \sim f L_j t_{\rm esc}$ is the energy acquired prior to breakout." + The timescale for the lateral shock to propagate completely around the star is The energy of the lateral shock ~μι exceeds the binding energy of the envelope of a supergiant progenitor (~107 ergs) if foeewmO4C//0.03)'L1. days. where the total jet power is scaled to 10ergsΙ!.," The timescale for the lateral shock to propagate completely around the star is The energy of the lateral shock $\sim f L_j t_{\rm esc}$ exceeds the binding energy of the envelope of a supergiant progenitor $\sim 10^{48}$ ergs) if $t_{\rm esc} \gtrsim 0.4 \, (f/0.03)^{-1} L_{j, 45}^{-1}$ days, where the total jet power is scaled to $10^{45} \ergs$." + This inequality also applies at each radia shell within a given progenitor., This inequality also applies at each radial shell within a given progenitor. +" Thus. once the head of the je reaches the radius r where {ο=0.43€/0.03)!L days. the remaining outer envelope of the star is unbound. with an energy ~Jo""LU.Mi.Ru(0,/3degY(f/0.03) ergs."," Thus, once the head of the jet reaches the radius $r$ where $t_{\rm esc}(r) \gtrsim 0.4 \, (f/0.03)^{-1} L_{j, 45}^{-1}$ days, the remaining outer envelope of the star is unbound, with an energy $\sim 10^{49} \, L_{i, 48}^{1/2} \, M_{10}^{1/2} \, R_{14}^{1/2} \, (\theta_j/3 \, {\rm deg})^2 \, (f/0.03)$ ergs." +" For our fiducia parameters, matter is unbound outside ~LO} em."," For our fiducial parameters, matter is unbound outside $\sim 10^{13}$ cm." + Matter at smaller radii can. however. continue to infall onto the central black hole.," Matter at smaller radii can, however, continue to infall onto the central black hole." + The maximum timescale over which infall can proceed withou being strongly attected by the expulsion of the envelope is 70τρις where we have used the fact that the density profile at large radii in supergiants is ptr)«xor7., The maximum timescale over which infall can proceed without being strongly affected by the expulsion of the envelope is 70 where we have used the fact that the density profile at large radii in supergiants is $\rho(r) \propto r^{-2}$. + These order of magnitude arguments suggest that the collapse of a RSG could potentially power jets for up to ~100 days., These order of magnitude arguments suggest that the collapse of a RSG could potentially power jets for up to $\sim 100$ days. +" One uncertainty in these estimates is how much of the star at small radii xLO""!! em falls directly into the black hole vs. circularizes in a disk: this matter can in principle produce large jet powers at early times x1000 sec (Fig. 1)."," One uncertainty in these estimates is how much of the star at small radii $\lesssim 10^{10-11}$ cm falls directly into the black hole vs. circularizes in a disk; this matter can in principle produce large jet powers at early times $\lesssim 1000$ sec (Fig. \ref{fig:edot}) )," + which might more readily unbind the outer stellar envelope., which might more readily unbind the outer stellar envelope. + We have assumed that most of this mass instead forms the initial black hole., We have assumed that most of this mass instead forms the initial black hole. + We now consider the case of a successful stellar explosion. in which the stellar envelope expands outwards with a velocity οs |.," We now consider the case of a successful stellar explosion, in which the stellar envelope expands outwards with a velocity $v_{ej} \sim 10,000 \kms$ ." + In this ease the head of the low power jet initially cannot keep up with the expansion induced by the stellar explosion., In this case the head of the low power jet initially cannot keep up with the expansion induced by the stellar explosion. + As the stellar density decreases due to expansion the, As the stellar density decreases due to expansion the +measured by integrating the curvature of the contour surface aud applving the Gauss-Donnet theorem. which relates (he genus number to this integral (GMD: HIIGW: M89).,"measured by integrating the curvature of the contour surface and applying the Gauss-Bonnet theorem, which relates the genus number to this integral (GMD; HGW; M89)." + It is typical {ο measure the eenus number as a function of the contour threshold. aud to parametrize the threshold level bv the fraction of volume above threshold.," It is typical to measure the genus number as a function of the contour threshold, and to parametrize the threshold level by the fraction of volume above threshold." + This vields a genus eurve (IIGW: Weinberg. Gott. Aelott 1937).," This yields a genus curve (HGW; Weinberg, Gott, Melott 1987)." + When the genus measured is for an isodensitv surface of a Gaussian random phase field. WGW show that the genus number per unit volume is G=N(IE-—22)exp(—172/2).," When the genus measured is for an isodensity surface of a Gaussian random phase field, HGW show that the genus number per unit volume is $G = N (1-\nu^2) \exp(-\nu^2/2)$." + Here v is the contour threshold in standard deviations [rom the mean densitv. aud NV depends only on the (Gvo-point correlation function of the field being studied.," Here $\nu$ is the contour threshold in standard deviations from the mean density, and $N$ depends only on the two-point correlation function of the field being studied." + The commonest astrophysical application of genus statistics has been the characterization ol density fields. usually traced by galaxies (e.g.. Gott et al 1989) and/or galaxy clusters (e.g... Rhoads. Gott Postman 1994).," The commonest astrophysical application of genus statistics has been the characterization of density fields, usually traced by galaxies (e.g., Gott et al 1989) and/or galaxy clusters (e.g., Rhoads, Gott Postman 1994)." + Additional applications of the 2D statistic have been made or proposed for microwave background maps ancl for gravitational lensing shear measurements (e.g.. Jain Matsubara 2001).," Additional applications of the 2D statistic have been made or proposed for microwave background maps and for gravitational lensing shear measurements (e.g., Jain Matsubara 2001)." + There is also a one-dimensional analog. the threshold crossing statistic. which has been applied to quasar spectra al z26 (Fan οἱ al 2002).," There is also a one-dimensional analog, the threshold crossing statistic, which has been applied to quasar spectra at $z\approx 6$ (Fan et al 2002)." + To successfully identilv the topological signature of ooverlap in a search for eenitters. a few conditions must be fulfilled.," To successfully identify the topological signature of overlap in a search for emitters, a few conditions must be fulfilled." + First. the tvpical rracdius must be large enough that à substantial fraction of flix escapes [rom eeniitters in the bubble.," First, the typical radius must be large enough that a substantial fraction of flux escapes from emitters in the bubble." +" The optical depth of ddamping wing absorption [from neutral gas outside a Us for pphotons emitted at a velocity offset Av from the svstemie velocity of a galaxy. located a physical distance r, (or comoving distance r,=(1+ z)rj) from the edge of thebubble.", The optical depth of damping wing absorption from neutral gas outside a is for photons emitted at a velocity offset $\Delta v$ from the systemic velocity of a galaxy located a physical distance $r_p$ (or comoving distance $r_c \equiv (1+z) r_p$ ) from the edge of the. +. A bubble radius of 1.2pMpec=1.2(1+z)eMpe. results in a line center optical depth 7T=1 (ee. Rhoads Malhotra 2001).," A bubble radius of $1.2 \pMpc = 1.2 (1+z) \cMpc$ results in a line center optical depth $\tau = 1$ (e.g., Rhoads Malhotra 2001)." + Bubbles of (his size or lareer will be apparent in the, Bubbles of this size or larger will be apparent in the +that the cavity leaves the field-of-view (250 Mm high) at about the same time in both wavelengths (around 07:00 UT).,that the cavity leaves the field-of-view (250 Mm high) at about the same time in both wavelengths (around 07:00 UT). +" In Fig. 3,,"," In Fig. \ref{fig:cut304}," + the time slices evidence the evolution of the cool plasma at during the eruption process: the slow rise of the cavity during 4-5 hours and then the eruption., the time slices evidence the evolution of the cool plasma at during the eruption process: the slow rise of the cavity during 4-5 hours and then the eruption. + The plasma of the cavity observed at does not reach heights above 250 Mm., The plasma of the cavity observed at does not reach heights above 250 Mm. + During the eruption process most of the plasma is drained back down along magnetic structures as highlighted in Fig. 2.., During the eruption process most of the plasma is drained back down along magnetic structures as highlighted in Fig. \ref{fig:evol_cav}. +" From Fig. 4,,"," From Fig. \ref{fig:cut171}," + we define the initial and final stages of the eruption as observed at from the asymptotic behaviour of the time slice (2) as indicated by the straight white lines., we define the initial and final stages of the eruption as observed at from the asymptotic behaviour of the time slice (2) as indicated by the straight white lines. +" At the start, the cavity is stable justifying why we started our study at 00:00 UT."," At the start, the cavity is stable justifying why we started our study at 00:00 UT." + The first phase is a slow rise of the cavity with a characteristic speed of 0.6 km-s!., The first phase is a slow rise of the cavity with a characteristic speed of 0.6 $\cdot$ $^{-1}$. + The cavity follows this trend until 03:00 UT., The cavity follows this trend until 03:00 UT. + The second phase of the eruption is the faster motion of the cavity with a characteristic speed of 25 km-s7!., The second phase of the eruption is the faster motion of the cavity with a characteristic speed of 25 $\cdot$ $^{-1}$. +" Even if this speed is far less than local Alfvénn or sound speeds, this is comparable to the speed of plasmoid ejection as reported by ?.."," Even if this speed is far less than local Alfvénn or sound speeds, this is comparable to the speed of plasmoid ejection as reported by \citet{tsu97}." + We propose to define a polar crown cavity as a density depletion at the bottom of which the polar crown filament material sits indicating the existence of a magnetohydrostatic equilibrium., We propose to define a polar crown cavity as a density depletion at the bottom of which the polar crown filament material sits indicating the existence of a magnetohydrostatic equilibrium. + The filament material is drained down along the polar crown cavity by gravity and sustained by the action of the upward-directed magnetic field curvature force., The filament material is drained down along the polar crown cavity by gravity and sustained by the action of the upward-directed magnetic field curvature force. +" This fact as well as the long, steady observations of the polar crown cavity indicate that the cavity is in a magnetohydrostatic equilibrium."," This fact as well as the long, steady observations of the polar crown cavity indicate that the cavity is in a magnetohydrostatic equilibrium." + The cold and hot coronal plasma are located at a similar location along the same field lines., The cold and hot coronal plasma are located at a similar location along the same field lines. + The observations of the cavity structure and plasma spatial distribution are consistent with the classical 2D cartoon of a cavity depicted by concentric ellipses., The observations of the cavity structure and plasma spatial distribution are consistent with the classical 2D cartoon of a cavity depicted by concentric ellipses. +" For instance, in the classicalCSHKP model (????),, the eruptive structure is composed of a twisted flux tube at the bottom of which the plasma is concentrated."," For instance, in the classical model \citep{car64,stu68,hir74,kop76}, the eruptive structure is composed of a twisted flux tube at the bottom of which the plasma is concentrated." +" Contrary to the cartoon proposed by ? placing the filament material at the centre of the cavity, the filament material is located at the bottom of the cavity which is more consistent with the model of ?.."," Contrary to the cartoon proposed by \citet{cli86} placing the filament material at the centre of the cavity, the filament material is located at the bottom of the cavity which is more consistent with the model of \citet{mar89}." +" In the observations reported here, magnetic curvature compensates gravity to create an equilibrium state in which the density is considerably increased at the bottom of the cavity."," In the observations reported here, magnetic curvature compensates gravity to create an equilibrium state in which the density is considerably increased at the bottom of the cavity." + We also show that the flows along field lines and varying from one wavelength to an other are important for the initiation, We also show that the flows along field lines and varying from one wavelength to an other are important for the initiation +G ts sheared in real-space by transforming the coordinates by means of the linearized lens equation (e.g.Bartelmann such that G’(.\”) is obtained by evaluating G at the position X.,"$G$ is sheared in real-space by transforming the coordinates by means of the linearized lens equation \citep[e.g.][]{Bartelmann01.1} + such that $G^\prime(\vec{x^\prime})$ is obtained by evaluating $G$ at the position $\vec{x}$." +" The values of y, range between 0 and 0.5: y» is set to zero.", The values of $\gamma_1$ range between 0 and 0.5; $\gamma_2$ is set to zero. + It is important to notice that G ts circular. while observed galaxies show a wide distribution of intrinsic ellipticities (Bernstein&Jarvis 2002).," It is important to notice that $G$ is circular, while observed galaxies show a wide distribution of intrinsic ellipticities \citep{Bernstein02.1}." +. Hence. G has to acquire its intrinsic ellipticity entirely from the applied shear.," Hence, $G$ has to acquire its intrinsic ellipticity entirely from the applied shear." + To obtain roughly realistic results. the applied shear is varied up to |y]=0.5 although such values cannot be generated by the cosmic large-scale structure and are even untypical for all but the innermost parts of galaxy clusters.," To obtain roughly realistic results, the applied shear is varied up to $|\vec\gamma|=0.5$ although such values cannot be generated by the cosmic large-scale structure and are even untypical for all but the innermost parts of galaxy clusters." + As an advantage of this procedure. G has elliptical isophotes. for which the axis ratio and orientation are consistent at all radii. and therefore all ellipticity measures formed from these images should agree.," As an advantage of this procedure, $G$ has elliptical isophotes, for which the axis ratio and orientation are consistent at all radii, and therefore all ellipticity measures formed from these images should agree." +" G' is sampled at the final resolution of 20R,x pixels."," $G^\prime$ is sampled at the final resolution of $20\, R_e\times 20\, R_e$ pixels." +" While R,=5 is already rather large for typical weak-lensing galaxies. we chose to simulate also even larger ones so as to mimic higher resolution images from which we can assess the impact of pixelation on the shear estimates."," While $R_e=5$ is already rather large for typical weak-lensing galaxies, we chose to simulate also even larger ones so as to mimic higher resolution images from which we can assess the impact of pixelation on the shear estimates." + Because there is no pixel noise in these test images and the resolution is veryhigh. the ellipticity € measured from quadrupole moments of the pixelated image Is always compatible with the shear y.," Because there is no pixel noise in these test images and the resolution is veryhigh, the ellipticity $\vec\epsilon$ measured from quadrupole moments of the pixelated image is always compatible with the shear $\vec\gamma$." + Additionally. the centroid position can be computed with essentially arbitrary. precision from the image.," Additionally, the centroid position can be computed with essentially arbitrary precision from the image." +" According to Refregier(2003 ).. defines the two-dimensional shapelet basis function of order Ξ(2).#2) and scale size B which is related to the dimensional Gauss-Hermite polynomial with H,, being the Hermite polynomial of order 1, "," According to \citet{Refregier03.1}, , defines the two-dimensional shapelet basis function of order $\vec{n}=(n_1,n_2)$ and scale size $\beta$ which is related to the one-dimensional Gauss-Hermite polynomial with $H_n$ being the Hermite polynomial of order $n$ ." +From the shapelet coefficients of some two-dimensional function G one can reconstruct a shapelet model The model ts found by minimizing with respect to the parameters gg., From the shapelet coefficients of some two-dimensional function $G$ one can reconstruct a shapelet model The model is found by minimizing with respect to the parameters $g_\mathbf{n}$ . + P and μι could be fixed at values chosen to be suitable to describe the galaxy ensemble well on average (Kuijken2006) or be determined from the minimization of y as well (Massey&Refregier2005;Mel-chioretal.2007).," $\beta$ and $n_{max}$ could be fixed at values chosen to be suitable to describe the galaxy ensemble well on average \citep{Kuijken06.1} or be determined from the minimization of $\chi^2$ as well \citep{Massey05.1,Melchior07.1}." +. One foreseeable problem of the shapelet decomposition stems from the Gaussian weighting function in(4)., One foreseeable problem of the shapelet decomposition stems from the Gaussian weighting function in. +. We discussed already that galaxies typically have steeper profiles than a Gaussian. which means that an optimized shapelet model requires higher orders.," We discussed already that galaxies typically have steeper profiles than a Gaussian, which means that an optimized shapelet model requires higher orders." + However. due to the polynomial in(4).. the largest oscillation amplitudes of high-order modes are located at rather large distances from the centroid.," However, due to the polynomial in, the largest oscillation amplitudes of high-order modes are located at rather large distances from the centroid." + Models which include higher orders thus allow a better description of the outer parts of a galaxy. while they still fail to reproduce correctly the central region in the case of steep profiles.," Models which include higher orders thus allow a better description of the outer parts of a galaxy, while they still fail to reproduce correctly the central region in the case of steep profiles." + Additionally. in case of noisy image data. the number of modes must be limited to avoid overfitting spurious nearby noise fluctuations.," Additionally, in case of noisy image data, the number of modes must be limited to avoid overfitting spurious nearby noise fluctuations." + Hence. galactic shapes with steeper profiles than a Gaussian are expected to be described by shapelet models with systematically shallower profiles.," Hence, galactic shapes with steeper profiles than a Gaussian are expected to be described by shapelet models with systematically shallower profiles." + Of similar concern is the circularity of the shapelet basis system., Of similar concern is the circularity of the shapelet basis system. + As the scale size for both dimensions in is the same. the zeroth-order is round.," As the scale size for both dimensions in is the same, the zeroth-order is round." + If the shape to be described ts stretched in a particular direction — as a result of its intrinsic shape or due to gravitational lensing — this elongation has to be carried by higher shapelet orders., If the shape to be described is stretched in a particular direction – as a result of its intrinsic shape or due to gravitational lensing – this elongation has to be carried by higher shapelet orders. + Again. for a limited number of basis modes we must expect an insufficient representation of the true shape by the shapelet model.," Again, for a limited number of basis modes we must expect an insufficient representation of the true shape by the shapelet model." + In particular. we have to consider an underestimation of the source elongation much more likely than an overestimation. as the basis system preferentially remains circular.," In particular, we have to consider an underestimation of the source elongation much more likely than an overestimation, as the basis system preferentially remains circular." + These shortcomings are likely but do not have to affect the estimation of a weak shear., These shortcomings are likely but do not have to affect the estimation of a weak shear. + Whether a model with limited fidelity leads to a biased shear estimate depends an the construction of the estimator., Whether a model with limited fidelity leads to a biased shear estimate depends an the construction of the estimator. + The most straightforward estimator is obtained from the complex ellipticity (e.g.Bartelmann&Schneider2001) where Q;; are the quadrupole moments measured from the shapelet model G'.," The most straightforward estimator is obtained from the complex ellipticity \citep[e.g.][]{Bartelmann01.1} + where $Q_{ij}$ are the quadrupole moments measured from the shapelet model $\tilde{G}^\prime$." + From this we obtain a direct shear estimator y'?=€ , From this we obtain a direct shear estimator $\tilde{\vec\gamma}^{(Q)} \equiv \tilde{\vec\epsilon}$. +By choosing this particular definition. we benefit from an ellipticity estimator with a perfect response to external shear. i.e. the shear responsivity R=0é/0¥ (e.g.Bernstein2002) equals unity and we do not have to correct for it.," By choosing this particular definition, we benefit from an ellipticity estimator with a perfect response to external shear, i.e. the shear responsivity $R=\partial\vec\epsilon / \partial\vec\gamma$ \citep[e.g.][]{Bernstein02.1} equals unity and we do not have to correct for it." + It is important to note that the Q;; integrate over the entire shape of G'. consequently Q;; are linear combinations of all available shapelet coeflicients of G (Bergé 2005). therefore this estimatoreritically relies ona decent shapelet model.," It is important to note that the $Q_{ij}$ integrate over the entire shape of $G^\prime$ , consequently $\tilde{Q}_{ij}$ are linear combinations of all available shapelet coefficients of $\tilde{G}^\prime$ \citep{shapelets_manual}, , therefore this estimatorcritically relies ona decent shapelet model." + For the problem of describing galactic shapes. it is often more convenient to use a polar coordinate frame (7.y)instead of the," For the problem of describing galactic shapes, it is often more convenient to use a polar coordinate frame $(r,\varphi)$instead of the" +to that of the VWSCs.,to that of the VSGs. + The fraction of the total dust mass contributed by PATL/VSCs is also fixed to a value calculated for the Alilky Way., The fraction of the total dust mass contributed by PAH/VSGs is also fixed to a value calculated for the Milky Way. + This could affect the relative streugth of the MUR and FIR enüssion., This could affect the relative strength of the MIR and FIR emission. + To nodel the appearance and SED cach galaxy we Call ater the following free parameters of the model: steHar scale leneth. stellar scale height. dust scale leneth. dust scale height. stellar luminosity. total dust nass. iuclination and the LDuuinositv of the obseured star forination coniponent.," To model the appearance and SED each galaxy we can alter the following free parameters of the model: stellar scale length, stellar scale height, dust scale length, dust scale height, stellar luminosity, total dust mass, inclination and the luminosity of the obscured star formation component." + The overall fitting process was done manually to fud tlre w of parameters that could provide adequate fits to both the optical aud the UV-FIR SED., The overall fitting process was done manually to find the set of parameters that could provide adequate fits to both the optical and the UV-FIR SED. +" Tnitial values for the fitΠιο process were taken frou. ""OIwees in the literature.", Initial values for the fitting process were taken from sources in the literature. + ? have previously investigated UC (F321 using a three dimensional Moute Carlo scattered light code ancl t11 paraiueters for a suooth steHar aud dust distribuion were adopted as initial values m this case., \citet{matthews_modeling_2001} have previously investigated UGC 7321 using a three dimensional Monte Carlo scattered light code and their parameters for a smooth stellar and dust distribution were adopted as initial values in this case. + 7 and ? have previously estimated tlre| scale leneths of 102233 and NGC 1211 respectively. by fitting an expoucutial fiction to the observed surface biiehtuess profiles.," \citet{matthews_H_2008} and \citet{fry_deep_1999} have previously estimated the scale lengths of IC2233 and NGC 4244 respectively, by fitting an exponential function to the observed surface brightness profiles." + While the functions used take no acc‘count of the effects of dust on the galaxy profiles they slic»ild provide reasonable initial estimates for the stellar distributions assunuüne that dust effects are uot severe., While the functions used take no account of the effects of dust on the galaxy profiles they should provide reasonable initial estimates for the stellar distributions assuming that dust effects are not severe. + Ficmu the work of ? on high surface brightuess. αςex--O1. ealaxies we initially adopted the relation tha the dust scale heights would be approximately half the stellar scale heights and the dust scale lengths around 1.1 times arecr than the stellar values.," From the work of \citet{xilouris_are_1999} on high surface brightness, edge-on, galaxies we initially adopted the relation that the dust scale heights would be approximately half the stellar scale heights and the dust scale lengths around $1.4$ times larger than the stellar values." + (Jue of the iain difficulties in modeling the dust distributions of LSB ealaxics is that their disks appear ο be optically thin. even when viewed οσο on.," One of the main difficulties in modeling the dust distributions of LSB galaxies is that their disks appear to be optically thin, even when viewed edge on." + When nocdeling he appearance of TSB ealaxies. the effects of the dust. distition can be quantified based on the Mesencec of a dust lane along fje ealactic mid-plane.," When modeling the appearance of HSB galaxies, the effects of the dust distribution can be quantified based on the presence of a dust lane along the galactic mid-plane." + As none of our galaxy sample shows αν sigu of a dust aue the xoblem becomes iore ¢egenerate., As none of our galaxy sample shows any sign of a dust lane the problem becomes more degenerate. + Initially we lucreased he dust mass in the adopted geometry uutil he effects of the dust became owious aud the optical xofiles of he model ealaxy no louger matched the shape of the observed data., Initially we increased the dust mass in the adopted geometry until the effects of the dust became obvious and the optical profiles of the model galaxy no longer matched the shape of the observed data. + It was found that the dust. iiass required to reprocess the sellar light aud reproduce the observed FIR cussion could not be located in an average IISD type dust disk without revealing is presence by flattening the optical profile iu the central region of the ealaxy., It was found that the dust mass required to reprocess the stellar light and reproduce the observed FIR emission could not be located in an average HSB type dust disk without revealing its presence by flattening the optical profile in the central region of the galaxy. + We fud that the optical appearance and total FIR cuuission of the LSB salaxies cau be reproduced= by removing the constraint that the dust be more COicentrated in the ealactic midplane than the stars., We find that the optical appearance and total FIR emission of the LSB galaxies can be reproduced by removing the constraint that the dust be more concentrated in the galactic midplane than the stars. + It the dust scale height is taken to be equal to the steHar scale height then it is also possible to fit the opical appearance of the ealaxy adequately., If the dust scale height is taken to be equal to the stellar scale height then it is also possible to fit the optical appearance of the galaxy adequately. +" Iu this Case. however, a significantly larger dust iass cau be accommodated within the dust disk without the apoearance of a dust lane."," In this case, however, a significantly larger dust mass can be accommodated within the dust disk without the appearance of a dust lane." + In order to reproduce the observed FIR. fiux distribution it was also necessary to lucrease the dust scale length., In order to reproduce the observed FIR flux distribution it was also necessary to increase the dust scale length. + When the dust is vertically CXended iuto a disk with a larger scale height that is we. Lanixed with the stellar population. the exact radial distiibution of the dust becomes poorly constrained from optical data alone.," When the dust is vertically extended into a disk with a larger scale height that is well mixed with the stellar population, the exact radial distribution of the dust becomes poorly constrained from optical data alone." + We have fouud the dust scale lenetl is between LS2.6 times the stellar scale length for our LSB disk galaxies., We have found the dust scale length is between $1.8-2.6$ times the stellar scale length for our LSB disk galaxies. + The best fit parazineters for our models ofcach galaxy ο found in Table 3.., The best fit parameters for our models ofeach galaxy can be found in Table \ref{fit}. +" Ry and Ry ave the radial leugths of the stars aud dust while Z; aud Z,; are the vertical scale heights.", $R_{s}$ and $R_{d}$ are the radial scale lengths of the stars and dust while $Z_{s}$ and $Z_{d}$ are the vertical scale heights. + £. is the intrinsic bolometric uinositv of the stellar population., $L_{s}$ is the intrinsic bolometric luminosity of the stellar population. +" M, represcuts the dust mass and / the inclination auele.", $M_{d}$ represents the total dust mass and $i$ the inclination angle. +" L,4,,4,4 gives ininositv enütted from the template of compactst chuission (see section ?7)).", $L_{cloud}$ gives the luminosity emitted from the template of compactdust emission (see section \ref{emission}) ). + Trace and z4 ogive the V bau facc-onaud equatorial optical dept, $\tau_{face}$ and $\tau_{eq}$ give the $V$ band face-on and equatorial optical depths. +lisxespectively?.. Figures L. 5 and 6 show a comparison of the B (or rh. JS66;0u . Span. τομ and 160712. data (left panel) aud svutheic Huages (tight panel)," Figures \ref{ugc_7321_im}, \ref{ic2233_im} and \ref{ngc4244_im} show a comparison of the $B$ (or $r$ ), $3.6\mu$ m, $8\mu$ m, $70\mu$ m and $160\mu$ m data (left panel) and synthetic images (right panel)." + In general the B (οr r) aud 2.6724 model images match the large scale luorphologv of the data reasonably well., In general the $B$ (or $r$ ) and $3.6\mu$ m model images match the large scale morphology of the data reasonably well. + Differences are. mnvever. apparent in the longer waveleugth emission at 8. τίVand 160722 that is dominated by eiissiou frou PATIs ancl dust Ooeras.," Differences are, however, apparent in the longer wavelength emission at $8$, $70$ and $160\mu$ m that is dominated by emission from PAHs and dust grains." + IC 2233 and NGC 1211 show sieuificauto structure du their S aud τομ images. suggesting that perhaps a more complex ion-axisviunietric dust distribution is needed.," IC 2233 and NGC 4244 show significant structure in their $8$ and $70\mu$ m images, suggesting that perhaps a more complex non-axisymmetric dust distribution is needed." + Ta both galaxies several small xiunt like sources iu the outer disk are pronunenut ETurces at T0jun. These are likely star forming regions as they appear brighter at shorter waveleugths aud show associated emission in GALEN far-UV aud Πο imagine., In both galaxies several small point like sources in the outer disk are prominent sources at $70\mu$ m. These are likely star forming regions as they appear brighter at shorter wavelengths and show associated emission in far-UV and $\alpha$ imaging. + The 16 yan emissiou from all three of our model galaxies shows a significant deviation from the data., The $160\mu$ m emission from all three of our model galaxies shows a significant deviation from the data. + The models Diedict a coutrally concentrated 160722 image while the data πιeecst a more diffuse distribution., The models predict a centrally concentrated $160\mu$ m image while the data suggest a more diffuse distribution. + Figures 7.. 8 and 9 show D (or r) baud intensity profiles parallel to he nmuünuor axes of the ealaxies at various poiuts while fieures 10.. 11 and 12 show the output model SEDs for he three LSB galaxies.," Figures \ref{7321_slice}, \ref{ic2233_slice} and \ref{ngc4244_slice} show $B$ (or $r$ ) band intensity profiles parallel to the minor axes of the galaxies at various points while figures \ref{7321_sed}, \ref{ic2233_sed} and \ref{ngc4244_sed} show the output model SEDs for the three LSB galaxies." + Overall the models are able to reproduce the elobal xoperties of the data., Overall the models are able to reproduce the global properties of the data. + T1ο surface brightuess slices xwallel to the uiinor axis and along the major axis slow a stuularity to the data aux eviations are likely caused w the comparison of smiocth axisvuunetric models to observations of a galaxy hat shows a clear chuupv structure (sce Figure 1)), The surface brightness slices parallel to the minor axis and along the major axis show a similarity to the data and deviations are likely caused by the comparison of smooth axisymmetric models to observations of a galaxy that shows a clear clumpy structure (see Figure \ref{HST}) ). + The main ciscrepancies found )etwoeen the surface brightress of the model aud data eenerallv occur in the ceutral rceious of the ealaxies., The main discrepancies found between the surface brightness of the model and data generally occur in the central regions of the galaxies. +" As can be ποσα in Figure 1 these are also the regious that show the ereatest nuuber o dark clouds aud bright star clusters,", As can be seen in Figure \ref{HST} these are also the regions that show the greatest number of dark clouds and bright star clusters. + Our smooth axisvuuuetric model is not able to reproduce such structures and so oulv a relatively poor fit can be achieved in the central regions., Our smooth axisymmetric model is not able to reproduce such structures and so only a relatively poor fit can be achieved in the central regions. + The short dashed line in Figure 10. shows the result of fittine the optical Πασάς of UCC 7321 using the average TSB ealaxy stellar-to-dust scaling relation of ?.., The short dashed line in Figure \ref{7321_sed} shows the result of fitting the optical imaging of UGC 7321 using the average HSB galaxy stellar-to-dust scaling relation of \citet{xilouris_are_1999}. . + Iu order to produce the required 70722 emission a large Iuuimnosity Is assigued to the obscured star formation template (see SCction 273)., In order to produce the required $70\mu$ m emission a large luminosity is assigned to the obscured star formation template (see section \ref{emission}) ). + However. this scenario uuderestimates the 160501 emission by a factor ~ 2.," However, this scenario underestimates the $160\mu$ m emission by a factor $\sim 2$ ." + Tn the SEDsthe shorter wavoleusth data from the UV through to NIR originate in the underlying stellar, In the SEDsthe shorter wavelength data from the UV through to NIR originate in the underlying stellar +surrounded by two alinost perpeudicular eiut rines.,surrounded by two almost perpendicular giant rings. + Both vine-like structures look somewhat mreeular., Both ring-like structures look somewhat irregular. + The galaxy colors (after Galactic reddening correction and A-correction for an earlv-tvpe galaxy) correspond to those of an Sb-tvpe spiral., The galaxy colors (after Galactic reddening correction and $K$ -correction for an early-type galaxy) correspond to those of an Sb-type spiral. + Fie., Fig. + | preseuts the spectral οποιον distribution (SED) for ESO 17-626., 4 presents the spectral energy distribution (SED) for ESO 474-G26. + As can be seen. although both observed aud modeled SED curves for Sh galaxies fit well the observed SED youn the £ baud to larger waveleugths. the SED for he prototype advanced lüuereer reninaut ~Atoms-for-Peace” galaxy.NGC 1252 (e.g... Sclaveizer 1982) eives a uch better approximation (see further ciscussion).," As can be seen, although both observed and modeled SED curves for Sb galaxies fit well the observed SED from the $I$ band to larger wavelengths, the SED for the prototype advanced merger remnant “Atoms-for-Peace” galaxy,NGC 7252 (e.g., Schweizer 1982) gives a much better approximation (see further discussion)." + ESO 17-C26 is a strong source of fu-infrared emission (Table 2)., ESO 474-G26 is a strong source of far-infrared emission (Table 2). + The detected far-infrared Inuimositv. converted to a star formation rate. incicates a very high rate of star formation (Table 2). as docs the laree Lgin/Lpg ratio of 1.1.," The detected far-infrared luminosity, converted to a star formation rate, indicates a very high rate of star formation (Table 2), as does the large $L_{FIR}/L_B$ ratio of 1.1." + The ratio of the IT» mass to blue huninosityv (0.18 p)) is typical of SbShe spirals (Young I&nezek 1989). as are the relative cconteut aud the IT» to rratios (Table 2).," The ratio of the $_2$ mass to blue luminosity (0.18 ) is typical of Sb–Sbc spirals (Young Knezek 1989), as are the relative content and the $_2$ to ratios (Table 2)." +" A faint backeround galaxy (with a radial velocity of about 32000 Ian ! see the PRC) is located 50"" NW of ESO 171-26 (Figs.", A faint background galaxy (with a radial velocity of about 32000 km $^{-1}$ – see the PRC) is located $''$ NW of ESO 474-G26 (Figs. + 1.3).," 1,3)." + The total apparent magnitude of the galaxy is Vr=17.140.1 and its colors are (5.V)pr= [O.52. (VRp1030. (RDT)gpz 0.0.," The total apparent magnitude of the galaxy is $V_T=17.1 \pm 0.1$ and its colors are $(B-V)_T=+0.82$ , $(V-R)_T=+0.30$, $(R-I)_T\approx0.0$ ." + Therefore. this is a giant (with an absolute maeuitude in the D bw of about |20.7) late-tvpo (from optical morphology. aux colors) spiral galaxy.," Therefore, this is a giant (with an absolute magnitude in the $B$ band of about –20.7) late-type (from optical morphology and colors) spiral galaxy." + General properties of ESO 171-626 are suuiuarized in Table 2., General properties of ESO 474-G26 are summarized in Table 2. + The central object has almost round isophotes (Fig., The central object has almost round isophotes (Fig. + 3) with apparent axial ratios in the Ro passband of h/ay=0.9140.015 within 15” of the center., 3) with apparent axial ratios in the $R$ passband of $\langle b/a \rangle$ $\pm$ 0.015 within $''$ of the center. + Photometric profiles at wo position angles are shown in Fig., Photometric profiles at two position angles are shown in Fig. + 5., 5. + At Jor 30 particles."," We select cells which have a molecular gas surface densityabove 4 $_{\odot}$ pc $^{-2}$, as used for our previous results \citep{Dobbs2007}, , and only include clouds with $>$ 30 particles." + The resolution of the simulations shown here is over twice that of previous analysis (?) with the mass of each particle approximately 40 Mo., The resolution of the simulations shown here is over twice that of previous analysis \citep{Dobbs2007} with the mass of each particle approximately 40 $_{\odot}$ . + Theminimum total mass of a cloud, Theminimum total mass of a cloud +"where 6,—4bor.d is the component of the galaxy formation field which is uncorrelated with the οσα] These equations are simply a result of applying the continuity equatio1 (Equatiou 5)) to he case of continuous star formation. rather than an mstautaneous burst. as in Equaion (6)).","where $\delta_\perp \equiv \delta_\ast - b_\ast r_\ast \delta$ is the component of the galaxy formation field which is uncorrelated with the local These equations are simply a result of applying the continuity equation (Equation \ref{continuity}) ) to the case of continuous star formation, rather than an instantaneous burst, as in Equation \ref{bandr}) )." + Figure 9shows ὃν ry(2}. aud τς} for all galaxies reconstructed froii tle properties of «nr galaxy formation fields.," Figure \ref{csstartime} shows $b_g(z)$, $r_g(z)$, and $b_g(z) r_g(z)$ for all galaxies reconstructed from the properties of our galaxy formation fields." + b4(z)r4(2) represeuts the linear regression of the galaxy deusity ou the mass desity., $b_g(z)r_g(z)$ represents the linear regression of the galaxy density on the mass density. +" Note that the reconstruction of this quautity is quite accurate: on the other haud. the reconstructions of by() aud rt) separately. which require knowledge of (84:894""). have significant errors."," Note that the reconstruction of this quantity is quite accurate; on the other hand, the reconstructions of $b_g(z)$ and $r_g(z)$ separately, which require knowledge of $\avg{\delta_\perp(z') +\delta_\perp(z'')}$, have significant errors." + These errors are mostly due o the poor time resolution of our The continuity equation will prove useful o future theoretical and observational work. as we discuss in Section 1..," These errors are mostly due to the poor time resolution of our The continuity equation will prove useful to future theoretical and observational work, as we discuss in Section \ref{conclusions}." + Tere we discuss the observational consequences of the evolution of the spatial distribution of galaxy formation., Here we discuss the observational consequences of the evolution of the spatial distribution of galaxy formation. + First. we consider observable properties of the star formation deusitv field.," First, we consider observable properties of the star formation density field." + Second. we cousider the resultingoO properties of Ooealaxy clusters.," Second, we consider the resulting properties of galaxy clusters." + We noticed in the last section that the correation coefficient between star forming ealaxies and mass should decrease considerably with tine., We noticed in the last section that the correlation coefficient between star forming galaxies and mass should decrease considerably with time. +" We caunot currently observe this decrease directly iu the real Tlowever. from Figure 9 we note that he galaxy distribution as a wholedocs correlate well with the mass, 3n the seuse that k,(2)1 at all redshifts."," We cannot currently observe this decrease directly in the real However, from Figure \ref{csstartime} we note that the galaxy distribution as a whole correlate well with the mass, in the sense that $r_g(z)\sim 1$ at all redshifts." + Therefore. we should be able to detect the evolutiou of ος} by cross-correlating galaxy. formation wih the distribution of all galaxies.," Therefore, we should be able to detect the evolution of $r_\ast(z)$ by cross-correlating galaxy formation with the distribution of all galaxies." +" Iu Figure 10. we plot ba,σ.σ giaud rvg—6Oy)7.0, between the οalaxy formation deusity field aud all galaxies as a function of redshift. a Sh| Mpe scales."," In Figure \ref{grecent} we plot $b_{\ast +g}\equiv\sigma_\ast/\sigma_g$ and $r_{\ast +g}\equiv\avg{\delta_\ast\delta_g}/\sigma_\ast\sigma_g$ between the galaxy formation density field and all galaxies as a function of redshift, at 8 $h^{-1}$ Mpc scales." + While the evolujou in δει is rather weak. the evolution in 74 is striking. and should be observable.," While the evolution in $b_{\ast +g}$ is rather weak, the evolution in $r_{\ast g}$ is striking, and should be observable." + Observationally. measuring this correlation will require mapping the density field Of in the universe. which has not vet been done.," Observationally, measuring this correlation will require mapping the density field of in the universe, which has not yet been done." + Given that the fundamental prediction «ft ealaxy formation models is the location of star formation as a function of time. such a map would be extremely useful.," Given that the fundamental prediction of galaxy formation models is the location of star formation as a function of time, such a map would be extremely useful." +" The spectral coverage' of the Las Campanas Redshitt Survey (LCRS) includes a star formation indicator (OT equivalent widths: Schectinanefef.1996: Tashimotoefal. 1998)): thus. oue c‘al nieasure this correlation at low redshift using this «ata,"," The spectral coverage of the Las Campanas Redshift Survey (LCRS) includes a star formation indicator ([OII] equivalent widths; \cite{schechtman96ap}; \cite{hashimoto98ap}) ); thus, one can measure this correlation at low redshift using this data." +" Using the LORS. Teemarl&Bromley(1998). have addressed a related question by nujieasriug the correlation between the distributions of carly aud late spectral types (as classified by Bromleyctab, 1998)): tle found r~0.1 0.7. in qualitative agreement with our fiudiues here. if one makes a correspolncence betwee1 spectral type aud star formation rate."," Using the LCRS, \cite{tegmark98b} have addressed a related question by measuring the correlation between the distributions of early and late spectral types (as classified by \cite{bromley98ap}) ); they found $r\sim 0.4$ $0.7$ , in qualitative agreement with our findings here, if one makes a correspondence between spectral type and star formation rate." + They can calculate à because, They can calculate $r$ because +value (urns out to be 0.1 mag larger than the Harris(1996).estimate.,value turns out to be 0.1 mag larger than the \citet{harris} . +.. This research is supported by the Agenzia5 Spaziale Italiana. CASI) and the Ministero dellIstruzione. dellUniversità e della Ricerca.," This research is supported by the Agenzia Spaziale Italiana (ASI) and the Ministero dell'Istruzione, dell'Università e della Ricerca." + We (hank the anonymous referee for his/her helpful comments and suggestions which sienifieantlv contributed ο improve the paper presentation., We thank the anonymous referee for his/her helpful comments and suggestions which significantly contributed to improve the paper presentation. +There is uo general solution for the motion of a particle under the influence of radiatiou aud eravitatioual forces in a system comprising a star aud one or more plauets.,There is no general solution for the motion of a particle under the influence of radiation and gravitational forces in a system comprising a star and one or more planets. + However. analytic solutions aud analytic approximations exist for particle notion in the two-body (Wyatt&Whipple aud the circularly restricted three-body (Liou&Zook1997) problems respectively.," However, analytic solutions and analytic approximations exist for particle motion in the two-body \citep{wyatt50} + and the circularly restricted three-body \citep{lz97} problems respectively." + These specilic cases cau be used to check the accuracy of the modified RALIWS3 code., These specific cases can be used to check the accuracy of the modified RMVS3 code. + To eusure that the adcditiou of radiatiou aud solar wid forces did uot ellect the normal ruuniug ol the code. we rau a series of tests in which 9 was set to zero. and compared the results to ideutical tests run using the original RMVS3.," To ensure that the addition of radiation and solar wind forces did not effect the normal running of the code, we ran a series of tests in which $\beta$ was set to zero, and compared the results to identical tests run using the original RMVS3." + The results were iudistiugulsliable in all cases., The results were indistinguishable in all cases. +" The time rate of change of a test particle's orbital elemeuts in the racliatiou-imeoclilied two body problem are given in Moro-Martiu&Malhotra(2002) (following the work of (1979))). aud are equal to where A, is the mass of the central star. and c is the speed of light."," The time rate of change of a test particle's orbital elements in the radiation-modified two body problem are given in \citet{mm02} (following the work of \citet{wyatt50,burns79}) ), and are equal to where $M_{\star}$ is the mass of the central star, and $c$ is the speed of light." +" To test the code against the two-body solutions. we ran a simulation with a single ο=0.15 fest particle placed in orbit around a solar-miass star. released from a parent body with aj=250 AAU. ρε=0.8 and iy,=7.6."," To test the code against the two–body solutions, we ran a simulation with a single $\beta=0.15$ test particle placed in orbit around a solar-mass star, released from a parent body with $a_{pb} = 250$ AU, $e_{pb} = 0.8$ and $i_{pb} = 7.6\degree$." + The particles argument of perihelion. longitude of asceuding node auc mean anomaly were selected raudomly.," The particle's argument of perihelion, longitude of ascending node and mean anomaly were selected randomly." + The analytical and numerical results plotted in Figure are in excellent agreement., The analytical and numerical results plotted in Figure \ref{fig:twobody} are in excellent agreement. + The addition of a planet greatly. complicates the motion of the test particle. but have derived expressious for the tine evolution of a particle’s orbital elements whilst in au MMR with a zero eccentricity planet.," The addition of a planet greatly complicates the motion of the test particle, but \citet{lz97} have derived expressions for the time evolution of a particle's orbital elements whilst in an MMR with a zero eccentricity planet." + These expressions are a second order approximation. valid only for low test particle eccentricities aud inclinations. aud low order resonances. aud are given by," These expressions are a second order approximation, valid only for low test particle eccentricities and inclinations, and low order resonances, and are given by" +We summarize in Tables Al and A2 the main distinctive properties of the observed. galaxy population in. the NGC 5044 group.,We summarize in Tables \ref{a2} and \ref{a3} the main distinctive properties of the observed galaxy population in the NGC 5044 group. + Column caption. for both tables is as follows:," Column caption, for both tables is as follows:" + , +RAL acknowledges the award of a PPARC PDA.,RJM acknowledges the award of a PPARC PDRA. + JSD acknowledges the enhanced. research time provided » (he award of a PPARC Senior Fellowship., JSD acknowledges the enhanced research time provided by the award of a PPARC Senior Fellowship. + The authors acknowledge Matt Jarvis for useful. discussions., The authors acknowledge Matt Jarvis for useful discussions. + Funding for the Sloan Digital Sky Survey (SDSS) has »en provided. bv the. Alfred. P. Sloan Foundation. the 'articipating lnstitutions. the National Acronautics and Space Administration. the National Science Foundation. the U.S. Department of Energy. the Japanese \lonbukagakusho. and the Max Tanck Society.," Funding for the Sloan Digital Sky Survey (SDSS) has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society." + Phe SDSS Web. site is. http:wavwesdss.ore/. “The SDSS is managed by the Astrophysical Research Consortium (ARC) for. the Participating Institutions., The SDSS Web site is http://www.sdss.org/. 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 llopkins University. Los Alamos National Laboratory. the AMas-Planek-lostitute for. Astronomy (AIPLA). the Alax-Planck-lnstitute for Astrophysics (AIPA). New Alexico State University. University of Pittsburgh. Princeton. University. the United States Naval Observatory. and the Universitv 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, University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of Washington." + is the ratio of the dust absorption efficiencies at εωthe color temperatures of the incident and reciting radiation fields.,$\epsilon_Q$ is the ratio of the dust absorption efficiencies at the color temperatures of the incident and reemiiting radiation fields. + Note that the dust temperature also depends on additional radiatiou sources. such as that of the surrounding disk(7).. which will teud to push the radius at a specific temperature outwards.," Note that the dust temperature also depends on additional radiation sources, such as that of the surrounding disk, which will tend to push the radius at a specific temperature outwards." + However. this prescription allows a direct comparison to the analysis of?.," However, this prescription allows a direct comparison to the analysis of." +. As ds seen in Figue 5.. the eas lines are indeed dominated oby eas at radi well bevoud the interferometrically measured dust sublimation radi at Τ.1000 15001. ancl consistently match dust at ΠΟΙΝΗ. Iu the lait of a disk truncated at a sharp. optically thick. immer disk rin the CO sizes correspond to dust at somewhat higher temperatures of 5001. Tt is portant to realize that some molecular gas may still extend inwards. as indicated by the best-fit iuner radii and the high velocities of emission in the line wines(?).. but the lines are not dominated by that couponeut: the astrometric sizes measure the bulk of the gas enission.," As is seen in Figure \ref{size_lum}, the gas lines are indeed dominated by gas at radii well beyond the interferometrically measured dust sublimation radii at $T$$\sim$$1000-1500\,$ K, and consistently match dust at K. In the limit of a disk truncated at a sharp, optically thick, inner disk rim, the CO sizes correspond to dust at somewhat higher temperatures of $\sim$ K. It is important to realize that some molecular gas may still extend inwards, as indicated by the best-fit inner radii and the high velocities of emission in the line wings, but the lines are not dominated by that component; the astrometric sizes measure the bulk of the gas emission." + Of particular interest. however. is that some transition disks fall ou the size-luinosity relation defined by the classical disks. specifically TW να and ΠΟ 135311B SR 21 fall somewhat above the relation.," Of particular interest, however, is that some transition disks fall on the size-luminosity relation defined by the classical disks, specifically TW Hya and HD 135344B – SR 21 falls somewhat above the relation." + This is consistent with the fiudines of?7.. and?:: that the inner disk eas of some transition di often las not been removed iu the same wav as the population of small dust erains.," This is consistent with the findings of, and; that the inner disk gas of some transition disks often has not been removed in the same way as the population of small dust grains." + For these disks. it now appears that there is not even a difference in the radii forming the CO eas cnussion. aud that the lines simply follow the expected dependence on Iuninositv.," For these disks, it now appears that there is not even a difference in the radii forming the CO gas emission, and that the lines simply follow the expected dependence on luminosity." + This can be interpreted as the removal of the small dust opacity coupoucut through the process of planetesinial formation. as this will preserve a sjenificaut column of gas in the inner evolved zoue of he disk.," This can be interpreted as the removal of the small dust opacity component through the process of planetesimal formation, as this will preserve a significant column of gas in the inner evolved zone of the disk." + The caveat is that this is a very simall sample of transition disks. aud the iuclusion of additional disks nay show a ereater degree of complexity. inchiding the operation of other mechanisms of inner disk clearing. such as photoevaporation or clearing by an unseen. but nassive. (stellar) companion. both of which would teud o move the inner edge of the eas-cisk outwards.," The caveat is that this is a very small sample of transition disks, and the inclusion of additional disks may show a greater degree of complexity, including the operation of other mechanisms of inner disk clearing, such as photoevaporation or clearing by an unseen, but massive, (stellar) companion, both of which would tend to move the inner edge of the gas-disk outwards." + It will )e Interesting to see how many transition disks. in fact. all on the relation.," It will be interesting to see how many transition disks, in fact, fall on the relation." + Spectro-astrometry suffers from oa findaieutal svinmnetry ambiguity., Spectro-astrometry suffers from a fundamental symmetry ambiguity. + —Because the line centroid offsets aro ineasured relative to the contimuun. departurcs from circular svnunetry i the continua brightuess distribution will be inpriuted in the astrometric signal.," Because the line centroid offsets are measured relative to the continuum, departures from circular symmetry in the continuum brightness distribution will be imprinted in the astrometric signal." + For instance. if the continua emission is due to a sharp inner rini in the dust disk aud the disk is viewed at some mcelination. a asviuietrv should be seen in the astrometric line spectrum when the slit is oriented along the disk müuor axis.," For instance, if the continuum emission is due to a sharp inner rim in the dust disk and the disk is viewed at some inclination, an asymmetry should be seen in the astrometric line spectrum when the slit is oriented along the disk minor axis." + However.," However," +following the method of Scovilleetal.(1986).,following the method of \citet{scoville86}. +".* For T=30 KK. the SR 21 N disk has a eas Lass Mj,728x10ONE ΝΕ... where Xceo is the CO abundance relative to Ho (Xeq=[(CO/H»s])."," For $T=30$ K, the SR 24 N disk has a gas mass $M_g \ge 2.8 \times 10^{-9} +X_{\rm{CO}}^{-1}$ $_{\odot}$, where $X_{\rm{CO}}$ is the CO abundance relative to $_2$ $X_{\rm{CO}} \equiv [ \rm{CO} / \rm{H}_2 ]$ )." +" The upper limit from tje dust aud the lower limit from the eas imply 2.8xLOUNa1< Mu (Μον10f. wlich gives a 3e lower limit on the CO abundance. Yeo>3.1x10"" jan. whee Neoism=10|."," The upper limit from the dust and the lower limit from the gas imply $2.8 \times 10^{-9} +X_{\rm{CO}}^{-1} <$ $M_{disk}$ $_{\odot}$ ) $< 9.0 \times 10^{-4}$, which gives a $\sigma$ lower limit on the CO abundance, $X_{\rm{CO}} > 3.1 \times +10^{-6} = 3.1 \times 10^{-2} X_{\rm{CO,ism}}$ , where $X_{\rm{CO,ism}} = +10^{-4}$." + For temperatures between T=20—100 IWIN. the limit on Neg varies [rom 0.02—0.26Xc6μμ. 8lowing that the CO depletion is no more than 100 in the SR 21 N disk.," For temperatures between $T = 20 - 100$ K, the limit on $X_{\rm{CO}}$ varies from $0.02 - 0.26 X_{\rm{CO,ism}}$, showing that the CO depletion is no more than 100 in the SR 24 N disk." + In fact. tlese nieasurerments are consistent with there beiug no depletion compared to the ISAL iu the SR 21 N disk.," In fact, these measurements are consistent with there being no depletion compared to the ISM in the SR 24 N disk." + This contasts with the SR 215 disk where the ratio of the CO line intensity to the continuiun flux density is more than a [actor of 100 lower and the CO depletion is ~10° (T.=30 IKIX). similar to other eireinstellar disks.," This contrasts with the SR 24 S disk where the ratio of the CO line intensity to the continuum flux density is more than a factor of 100 lower and the CO depletion is $\sim 10^3$ $T = 30$ K), similar to other circumstellar disks." + The broadband spec‘tral energy cistributions (SEDs) of SR 21 N and S. shown in Figure 2. are similar shortward of 5 in. The infrared «ala. taken [rom the work of Cireeueetal.(199[).. indicate that both components are typical Class LH sources.," The broadband spectral energy distributions (SEDs) of SR 24 N and S, shown in Figure 2, are similar shortward of $\mu$ m. The infrared data, taken from the work of \citet{greene94}, indicate that both components are typical Class II sources." + The infrared excesses out to jun coupled with the strong Ha emission lines a‘e clear judicatious that both sources harbor actively accreting disks out to radii of at least AAU., The infrared excesses out to $\mu$ m coupled with the strong $\alpha$ emission lines are clear indications that both sources harbor actively accreting disks out to radii of at least AU. + The semimajor axis of the SR 21 N binary is «=32 AAU., The semimajor axis of the SR 24 N binary is $a = 32$ AU. + Dynamical simulations cM binaries with «isks show that the individual circumstellar disks will be ‘apidly truucated at a fraction (0.2—0.1. dependiug primarily ou the orbital eccentricity) of he semimajor axis (Artvimowicz&Lubow1991).," Dynamical simulations of binaries with disks show that the individual circumstellar disks will be rapidly truncated at a fraction $\sim0.2 - 0.4$, depending primarily on the orbital eccentricity) of the semimajor axis \citep{artymowicz94}." +. In the case of SR 24 N. the truncation radius is estimated to lie between 6 and AAU.," In the case of SR 24 N, the truncation radius is estimated to lie between 6 and AU." + Asstumine radial temperature profiles of typical Class II disks (e.g.Beckwithetal.1990).. the truncated SR 21 N circumstellar disks sliould ye able to produce ther:yal excesses out to ~100pin. which is consistent with the SED.," Assuming radial temperature profiles of typical optically-thick Class II disks \citep[e.g.,][]{bscg90}, the truncated SR 24 N circumstellar disks should be able to produce thermal excesses out to $\sim$ $\mu$ m, which is consistent with the SED." +" The same cyuaimica process which truucates the ""àürcuinstellar disks iu the binary will open a arge gap in the circuiulinary disk to a raclius a [actor of 2—3x the semimajor axis [).. meaning 7-60—100AAL fo rSR 21 N. The observed CO emission. which extends to a radius of ~250AAU. --sely originates in the remnant outer portion of the SR 21 N circumbiuary disk."," The same dynamical process which truncates the circumstellar disks in the binary will open a large gap in the circumbinary disk to a radius a factor of $2-3\times$ the semimajor axis \citep{artymowicz94}, meaning $\sim$ $-$ AU for SR 24 N. The observed CO emission, which extends to a radius of $\sim$ AU, likely originates in the remnant outer portion of the SR 24 N circumbinary disk." + Dynamical theory would predict that the SR 24 N disk structure cousists of at least one circumstellar accretion E swith radius τς AAU and a cireumbinary ring which extends out from 80AAU., Dynamical theory would predict that the SR 24 N disk structure consists of at least one circumstellar accretion disk with radius $\lesssim$ AU and a circumbinary ring which extends out from $\sim$ AU. + The observatious confirm the presence of au inuer disk aud a large gas disk exteucdiug to AAU. but cannot coustralii a gap size if oue Indeed exists.," The observations confirm the presence of an inner disk and a large gas disk extending to AU, but cannot constrain a gap size if one indeed exists." + Since the average density in a disk is expected to decrease with radius. tlie €'O depletion may be less in the outer regious.," Since the average density in a disk is expected to decrease with radius, the CO depletion may be less in the outer regions." + If the CO eluission arouud SR 21 N arises in au outer cireumbiuary rine. this may explain the very different 'elative strengths of the line ancl continuum eimission iu the SR 21 N aud 5 disks.," If the CO emission around SR 24 N arises in an outer circumbinary ring, this may explain the very different relative strengths of the line and continuum emission in the SR 24 N and S disks." + Because they are ucontaminated by emissiou from au iuner disk. cireumbiuary structures like that around SR 214N uay be a good way to directly [obe pliysical couditious in the outermost regions of disks.," Because they are uncontaminated by emission from an inner disk, circumbinary structures like that around SR 24 N may be a good way to directly probe physical conditions in the outermost regions of disks." + Assumiug the SR 2 ΕΝ system has a reasonably eccentric orbit (6~ 0.1). the upper limit on he coutiuuum [μπιν density is mareinally consistent. with the simple disk + gap mocels computed," Assuming the SR 24 N system has a reasonably eccentric orbit $e \sim 0.4$ ), the upper limit on the continuum flux density is marginally consistent with the simple disk + gap models computed" +and its friends.,and its friends. + A search is then made around the galaxies linked to i., A search is then made around the galaxies linked to $i$. + This process is repeated until no further friends are found., This process is repeated until no further friends are found. + The group-candidate k is defined as a real group if it satisfies equation 14:: For the purposes of this paper Nin>3., The group-candidate $k$ is defined as a real group if it satisfies equation \ref{eq:t}: For the purposes of this paper $N_{min} \geq 3$. +" This is a reasonable assumption when dealing with LRGs, which are not common objects."," This is a reasonable assumption when dealing with LRGs, which are not common objects." +" To determine the optimum values of Ro and zo for the DFoF code, a mock galaxy catalogue that simulates the 25LAQ catalogue was produced."," To determine the optimum values of $_0$ and $_0$ for the DFoF code, a mock galaxy catalogue that simulates the 2SLAQ catalogue was produced." +" This mock catalogue contains a distribution of 7,651,076 dark matter haloes and 824,704 galaxies across an octant of the sky."," This mock catalogue contains a distribution of 7,651,076 dark matter haloes and 824,704 galaxies across an octant of the sky." + The halo catalogue was derived from the Horizon 47 simulation (??)..," The halo catalogue was derived from the Horizon $4\pi$ simulation \citep{teyssier:09,prunet:08}." +" This is a ACDM dark matter N-body simulation using WMAP 3 cosmology with a 2h! Gpc periodic box on a grid of 40,963 cells."," This is a $\Lambda$ CDM dark matter $\it{N}$ -body simulation using WMAP 3 cosmology with a $2$ $^{-1}$ Gpc periodic box on a grid of 40,963 cells." +" The 7x107° particles were evolved using the Particle Mesh scheme of the RAMSES code (?) on an adaptively refined grid (AMR) with around 1.4x10!! cells, reaching a formal resolution of 262,144 cells in each direction ( 7h kpc comoving)."," The $7 \times 10^{10}$ particles were evolved using the Particle Mesh scheme of the RAMSES code \citep{teyssier:02} on an adaptively refined grid (AMR) with around $1.4 \times 10^{11}$ cells, reaching a formal resolution of 262,144 cells in each direction $\sim$ $^{-1}$ kpc comoving)." +" The simulation covers a sufficiently large !volume to compute a full-sky dark matter distribution, while resolving Milky-Way size haloes with more than 100 particles and exploring small scales deeply into the non-linear regime."," The simulation covers a sufficiently large volume to compute a full-sky dark matter distribution, while resolving Milky-Way size haloes with more than 100 particles and exploring small scales deeply into the non-linear regime." +" The dark matter distribution in the simulation was integrated in a light cone out to redshift 1, around an observer located at the centre of the simulation box."," The dark matter distribution in the simulation was integrated in a light cone out to redshift 1, around an observer located at the centre of the simulation box." +" The underlying cosmology for WMAP 3 is: Quy = 0.24, Qa = 0.76, Ny = 0.042, n = 0.958, Ho = 73 and og = 0.77."," The underlying cosmology for WMAP 3 is: $\Omega_M$ = 0.24, $\Omega_\Lambda$ = 0.76, $\Omega_b$ = 0.042, n = 0.958, $_0$ = 73 and $\sigma_8$ = 0.77." + Gravitationally bound haloes of dark matter are selected using the spherical overdensity method of ?.., Gravitationally bound haloes of dark matter are selected using the spherical overdensity method of \citet{Eisenstein:98}. + HOP is based on a hybrid approach in which the local density field is first obtained by smoothing the density field with an SPH-like kernel using the n nearest neighbours., HOP is based on a hybrid approach in which the local density field is first obtained by smoothing the density field with an SPH-like kernel using the $n$ nearest neighbours. +" Then the particles above a given threshold are linked with their highest density neighbours until, after several “hops”, they are connected to the one particle with the highest density within the region above the threshold."," Then the particles above a given threshold are linked with their highest density neighbours until, after several “hops”, they are connected to the one particle with the highest density within the region above the threshold." + All particles linked to the local density maximum are identified as a group., All particles linked to the local density maximum are identified as a group. +" The haloes were then populated using the Halo Occupation Distribution (HOD), where the number of galaxies residingwithin each halo is drawn from a probability, P(N|M), that a dark matter halo of mass M will host N galaxies."," The haloes were then populated using the Halo Occupation Distribution (HOD), where the number of galaxies residing within each halo is drawn from a probability, $P(N |M )$, that a dark matter halo of mass $M$ will host $N$ galaxies." + The first moment of P(N|M) is the mean number of galaxies as a function of halo mass and it is usually parameterised as a sum of a central and a satellite components (?7).," The first moment of $P(N|M)$ is the mean number of galaxies as a function of halo mass and it is usually parameterised as a sum of a central and a satellite components \citep{Kravtsov:04, Tinker:07}." +. The probability that a halo contains a central galaxy is given by: and the number of satellite galaxies is obtained from a Poisson sampling of: 'The HOD model used is that of ? and includes several derived parameters that were computed at various redshifts bins between 0.4