diff --git "a/batch_s000009.csv" "b/batch_s000009.csv" new file mode 100644--- /dev/null +++ "b/batch_s000009.csv" @@ -0,0 +1,10393 @@ +source,target + Open field mes can. and likely do. trausport some angular momenti frou he star and/or disk (via winds).," Open field lines can, and likely do, transport some angular momentum from the star and/or disk (via winds)." + However. no augular uonmentun is exchanged between the star aud disk aloug open field lines.," However, no angular momentum is exchanged between the star and disk along open field lines." + Tn the preseut work. we consider oulv he torques arising in the star-disk interaction and thus weelect auv torques that may arise from open field lues.," In the present work, we consider only the torques arising in the star-disk interaction and thus neglect any torques that may arise from open field lines." + To take iuto account the opening of the field. the \IPO5 ormulation inclides a maxiuimn for the absolute value of the twist. σον," To take into account the opening of the field, the MP05 formulation includes a maximum for the absolute value of the twist, $\gamma_c$." + Iu the regions of the disk where the twist is greater than this critical value. the mocel assiues that he magnetic ficld no longer connects the star to the disk.," In the regions of the disk where the twist is greater than this critical value, the model assumes that the magnetic field no longer connects the star to the disk." + The torque on the star that would have arisen from those nagnuetic field lines is mstead taken to be zero., The torque on the star that would have arisen from those magnetic field lines is instead taken to be zero. +" MP05 showed that a value of 5,=ox represcuts the classical asstuuption of a field that remains connected at all radi in the disk.", MP05 showed that a value of $\gamma_c = \infty$ represents the classical assumption of a field that remains connected at all radii in the disk. + To show the effect of the opening of the magnetic field iu more realistic systems. a value of +.=1 is appropriate (Uzdeuskyetal.2002).," To show the effect of the opening of the magnetic field in more realistic systems, a value of $\gamma_c = 1$ is appropriate \citep{uzdensky3ea02}." +. Furthermore. \IP05 showed that there exists a mode change in the magnetic connection between the star aud disk. at a threshold value of the spin rate.," Furthermore, MP05 showed that there exists a mode change in the magnetic connection between the star and disk, at a threshold value of the spin rate." + Specifically. if where then the stellar 1nagnetic field ouly connects to a simall region near the inner edee of the disk.," Specifically, if where then the stellar magnetic field only connects to a small region near the inner edge of the disk." +" In this case. which they call ""State 1° no magnetic field connects"," In this case, which they call “State 1,” no magnetic field connects" +seven galaxies Wwath redshift coutrold «i>=0.09001+0.0007 aud velocity dispersion of 53y+200Ians ,"seven galaxies with redshift centroid $=0.0901 \pm 0.0007$ and velocity dispersion of $530 \pm 200 +\kms $." +hupact parameter range is 38.5. 117.58| kpc(h=Hifi100lans!Mpο1). gy—=yn 0.5).," Impact parameter range is $38.5$ – $117.8 \ h^{-1}$ kpc $h~=~H_0/(100 \kms \mbox{Mpc}^{-1})$, $q_0=0.5$ )." + The fact tha we observe a nuuiber of resolved lines shows that the absorptious arise in discrete clouds of cold οἱs dustead of arising iu a large sinele diffuse eas coniponent., The fact that we observe a number of resolved lines shows that the absorptions arise in discrete clouds of cold gas instead of arising in a large single diffuse gas component. + The comparison between the cross-correlation function (CF) between the eaaxies ancl absor)ers in the data with the CF correspondiug tfo a raloni case shows that tlfare is a non-randoni connection between the absorbers iud t1e Galaxies iu our data., The comparison between the cross-correlation function (CF) between the galaxies and absorbers in the data with the CF corresponding to a random case shows that there is a non-random connection between the absorbers and the galaxies in our data. + If we assume that galaxies within the real grou yor cliister are distribited in velocity space according to a gaussiau cüstribution. ao1e-to-one match )otwoeen the absorbers aud the galaxies camuot be established with the preseut cata.," If we assume that galaxies within the real group or cluster are distributed in velocity space according to a gaussian distribution, a one-to-one match between the absorbers and the galaxies cannot be established with the present data." + From these results we cau conclude the ollowiue: (1) The detection of groups of adavsortion lines implies that some oft1e OODSOTvers do actually cluster. (, From these results we can conclude the following: (1) The detection of groups of absorption lines implies that some of the absorbers do actually cluster. ( +2) The velocity spanned by the OODSOTion lines arising m eroups or custers is consistent with the velocity dispersion of tlic! corresponcdiuo oroup or cluster of ealaxies.,2) The velocity spanned by the absorption lines arising in groups or clusters is consistent with the velocity dispersion of the corresponding group or cluster of galaxies. + This imiplics that the OODSOTvers arising in those clusters occipy the same region iu space than the eaaxies themsclves. (, This implies that the absorbers arising in those clusters occupy the same region in space than the galaxies themselves. ( +3) There is no strong preference for παοςers to avoid overdense cuvirouments. (,3) There is no strong preference for absorbers to avoid overdense environments. ( +1) adavsortion eaused by galaxy groups or clusters arises m discrete clouds of COd gas. rather than iu some hypothetical smoothly distributed cold phase iu the intracluster medi.,"4) absorption caused by galaxy groups or clusters arises in discrete clouds of cold gas, rather than in some hypothetical smoothly distributed cold phase in the intracluster medium." +AN-stales of positive parity. which are forbidden in this reaction.,"$\Delta N$ -states of positive parity, which are forbidden in this reaction." + In order to exclude these states one needs to consider the A-isohar ecxitation explicitely., In order to exclude these states one needs to consider the $\Delta$ -isobar ecxitation explicitely. + Another simplest process which allows to probe fundamental properties of NN svstem is photoabsorption on (wo nucleon svstems., Another simplest process which allows to probe fundamental properties of NN system is photoabsorption on two nucleon systems. + The deuteron photocisinlegration reaction pn is wiclely used as a testing eround for different theoretical models of the NN-interaction. however. much less is known on the photoclisintegration of the diproton. 5{pp}.—pp. or the inverse process of the photoproduction pp—{pp}.>.," The deuteron photodisintegration reaction $\gamma d\to pn$ is widely used as a testing ground for different theoretical models of the NN-interaction, however, much less is known on the photodisintegration of the diproton, $\gamma \{pp\}_s\to pp$, or the inverse process of the photoproduction $pp\to \{pp\}_s\gamma$." + Whereas in the photodisinegration of the deuteron the M1 magnetic dipole transition dominates al several hundred MeV. through ihe excitation of the A(1232) isobar. in the reaction with the 4S) diproton M-odd multipoles are forbidden due to angular momentum and. parity conservation.," Whereas in the photodisinegration of the deuteron the M1 magnetic dipole transition dominates at several hundred MeV through the excitation of the $\Delta(1232)$ isobar, in the reaction with the $^1S_0$ diproton M-odd multipoles are forbidden due to angular momentum and parity conservation." + Therefore. (here is no direct. contribution of the intermediate S-wave A.V states in the reaction pp—>{pp}s.," Therefore, there is no direct contribution of the intermediate S-wave $\Delta N$ states in the reaction $pp\to \gamma \{pp\}_s$." +" Non-direct excitation of the ""59 AN state is possible via the E2 transition [0].. but. this contribution is expected to be less important than the \li-trausition."," Non-direct excitation of the $^5S_2$ $\Delta N$ state is possible via the E2 transition \cite{WNA}, but this contribution is expected to be less important than the M1-transition." + The OPE model of the reaction pp—(ppl; allows to account for the A contributions via the subprocess zp— p., The OPE model of the reaction $pp\to \{pp\}_s\gamma$ allows to account for the $\Delta$ contributions via the subprocess $\pi^0 p\to p\gamma$ . + The corresponding OPE diagram is similar to those in Fig. 2..," The corresponding OPE diagram is similar to those in Fig. \ref{fig1}," +" but with the subproscess z""p—po in the down vertex.", but with the subproscess $\pi^0 p\to p\gamma$ in the down vertex. + The result of the OPE calewlations are shown in Fig.4.., The result of the OPE calculations are shown in \ref{figgamma}. + One can see that Chis model explaines the observed in Ref., One can see that this model explaines the observed in Ref. + [4) rise of the cross section almost equantativelv.," \cite{komar08} + rise of the cross section almost quantatively." + The second bump at 1.6 GeV is caused by the energy dependence of the πρ—ps cross section [11]. andrelated to excitation of more heavy nucleon isobars., The second bump at 1.6 GeV is caused by the energy dependence of the $\pi^0 p\to p\gamma$ cross section \cite{arndt} andrelated to excitation of more heavy nucleon isobars. +Panels (a) and (c) of Fig.,Panels (a) and (c) of Fig. +" 5 show a portion of the observed penumbra as seen in the continuum intensity (att=449—300 mA)). before and after straylight removal, respectively."," 5 show a portion of the observed penumbra as seen in the continuum intensity (at $\lambda=\lambda_0 - 300$ ), before and after straylight removal, respectively." + The corresponding maps of Doppler velocity are plotted in panels (b) and (d)., The corresponding maps of Doppler velocity are plotted in panels (b) and (d). +" Obviously both bluc- and redshifts are present in the penumbra, in particular after straylight removal."," Obviously both blue- and redshifts are present in the penumbra, in particular after straylight removal." + A striking feature in Fig., A striking feature in Fig. +" 5b is the localized patches of strong blueshift, up to 3.3 ss' coinciding with the bright heads of penumbral filaments."," 5b is the localized patches of strong blueshift, up to 3.3 $^{-1}$, coinciding with the bright heads of penumbral filaments." + These bright heads are surrounded by lanes of gas nearly at rest or slightly redshifted., These bright heads are surrounded by lanes of gas nearly at rest or slightly redshifted. +" In panel (b) significant redshifts are visible only at two locations, once at the side of a filament reaching into the umbra (at x=6"" and y=1"") and once, rather weakly around the bright and strongly blueshifted head of a filament (at x=6.5"" and v=4.5"")."," In panel (b) significant redshifts are visible only at two locations, once at the side of a filament reaching into the umbra (at $x = 6\varcsec$ and $y = 1\varcsec$ ) and once, rather weakly around the bright and strongly blueshifted head of a filament (at $x = 6.5\varcsec$ and $y = 4.5\varcsec$ )." +" A number of new redshifted patches are found in the Doppler map after straylight removal (panel d), appearing dominantly at locations previously seemingly at rest in panel (b)."," A number of new redshifted patches are found in the Doppler map after straylight removal (panel d), appearing dominantly at locations previously seemingly at rest in panel (b)." +" We have grayed out areas where intensity is below 0.6 times that of the quiet Sun, because y values of the Gaussian fits to the line profiles are high in these areas since the line is very weak there and possibly blended (as suggested by the fact that we obtain mainly strong blueshifts in the umbra contrary to all previous studies based on other spectral lines)."," We have grayed out areas where intensity is below 0.6 times that of the quiet Sun, because $\chi^2$ values of the Gaussian fits to the line profiles are high in these areas since the line is very weak there and possibly blended (as suggested by the fact that we obtain mainly strong blueshifts in the umbra contrary to all previous studies based on other spectral lines)." +" Redshifts (largest value 2.0 ') show a tendency to be located in dark regions, as can be judged by considering the white contours in panel (c)."," Redshifts (largest value 2.0 $^{-1}$ ) show a tendency to be located in dark regions, as can be judged by considering the white contours in panel (c)." + These contours outline the redshift of panel (d)., These contours outline the redshift of panel (d). +" Redshifts are now found clearly around the head of multiple filaments (e.g.. atv=2"" and y=3"" and around the filaments protruding into the umbra)."," Redshifts are now found clearly around the head of multiple filaments (e.g., at $x=2\varcsec$ and $y=3\varcsec$ and around the filaments protruding into the umbra)." + Narrow redshifted areas are also found in the middle and outer penumbra beside and between bright filaments., Narrow redshifted areas are also found in the middle and outer penumbra beside and between bright filaments. +" Clearly, in the lower photosphere redshifts are present at many different locations in the penumbra."," Clearly, in the lower photosphere redshifts are present at many different locations in the penumbra." + We expect that only a part of redshifted features actually present in the penumbra has been detected., We expect that only a part of redshifted features actually present in the penumbra has been detected. + We have provided the first direct measurements of downflows (reaching 2.0 !) in the body of a penumbra., We have provided the first direct measurements of downflows (reaching 2.0 $^{-1}$ ) in the body of a penumbra. +" The studied sunspot, located at j=0.84, had only a partial penumbra, on the disk-center side of the spot, so that all well-defined filaments partially point to disk center."," The studied sunspot, located at $\mu =0.84$, had only a partial penumbra, on the disk-center side of the spot, so that all well-defined filaments partially point to disk center." +" Hence the Evershed flow contributes a blueshift, so that redshifts in Fig."," Hence the Evershed flow contributes a blueshift, so that redshifts in Fig." +" 5d must be caused by downflows (or inflow, which appears rather unlikely, however)."," 5d must be caused by downflows (or inflow, which appears rather unlikely, however)." +" The line reveals a highly structured velocity pattern, with large variations in velocity around the head"," The line reveals a highly structured velocity pattern, with large variations in velocity around the head" +Radio observations of the 21 cm hydrogen emission. line reveal that the Alilky Way (MW) contains a thin clelisk surrounded by a population of with velocities incompatible with models of galactic rotation vet apparently not part of the Hubble How either (Mulleretal (1963))).,Radio observations of the 21 cm hydrogen emission line reveal that the Milky Way (MW) contains a thin disk surrounded by a population of with velocities incompatible with models of galactic rotation yet apparently not part of the Hubble flow either \cite{mull63}) ). + The nature of these ‘high-velocity (LIVCs) remains somewhat unclear mostly because it is dillieult to determine their distances and hence infer physical o»operties., The nature of these high-velocity (HVCs) remains somewhat unclear mostly because it is difficult to determine their distances and hence infer physical properties. + Observations of stars with known distances along the ine of sight to a LIVC can be used to constrain the distance o the cloud. by testing whether or not it is detected in absorption in the stellar spectrum (see e.g. Schwarzctal (1995))).," Observations of stars with known distances along the line of sight to a HVC can be used to constrain the distance to the cloud, by testing whether or not it is detected in absorption in the stellar spectrum (see e.g. \cite{schw95}) )." + Unfortunately. such constraints. are available for only a relatively small number of LIVCs (Wakker (2001)))., Unfortunately such constraints are available for only a relatively small number of HVCs \cite{wakk01}) ). + Putmanetal.(2003) use constraints from Lie emission. and find that most LEVC's are within 40 kpe. except for hose associated with the Magellanic stream.," \cite{putm03} use constraints from $\alpha$ emission, and find that most HVCs are within $\sim 40$ kpc, except for those associated with the Magellanic stream." + Drünsctal. claim that some fraction of LIVCs display a heacl- morphology. may be a result of interaction with a clilfuse ambient. galactic wind (Quilis&Moore (2001))).," \cite{brun01} claim that some fraction of HVCs display a head-tail morphology, may be a result of interaction with a diffuse ambient galactic wind \cite{quil01}) )." + Searches Or stars associated with Ηλος have so far resulted in non-detections (e.g. Hoppetal. (2007)))., Searches for stars associated with HVCs have so far resulted in non-detections (e.g. \cite{hopp07}) ). + Metallicities have been measured for a small number of LIVCs and vary over a wide range (e.g. Gibsonetal. (2001))). suggesting that IIVCs are not a homogeneous set.," Metallicities have been measured for a small number of HVCs and vary over a wide range (e.g. \cite{gibs01}) ), suggesting that HVCs are not a homogeneous set." + Finally one can observe other galaxies to infer the nature of HIVCSs from their projected distances., Finally one can observe other galaxies to infer the nature of HVCs from their projected distances. + The Andromeda galaxy (M31) has a population of LUVCs close (50 kpe) to its disk (Westmeicr (2007)))., The Andromeda galaxy (M31) has a population of HVCs close $\le 50$ kpc) to its disk \cite{west07}) ). + Other nearby spiral galaxies also contain neutral gas (see e.g. Barbierictal. (2005)))., Other nearby spiral galaxies also contain extra-planar neutral gas (see e.g. \cite{barb05}) ). + Pisano(2007) have searched for LIVC analogues in six loose groups of galaxies. similar to the Local Group.," \cite{pisa07} have searched for HVC analogues in six loose groups of galaxies, similar to the Local Group." + Their failure to detect compact. LIVCs implies that any cclouds are near to the galaxies in this group: they are not roaming [πουν throughout the group. itself., Their failure to detect compact HVCs implies that any clouds are near to the galaxies in this group: they are not roaming freely throughout the group itself. + These observations do not unambieuously determine the nature of LEVC's. ancl several theoretical models for them have been proposed.," These observations do not unambiguously determine the nature of HVCs, and several theoretical models for them have been proposed." + Oort (1970) discusses a model where the LWCs are close to the MW. disk. ancl result. from. of a “galactic ((Shapiro&Field (1976))).," Oort (1970) discusses a model where the HVCs are close to the MW disk, and result from of a galactic \cite{shap76}) )." + Gas from the galactic disk rises buovantly after being heated by supernovae (SNe). becomes thermally unstable and cools raciatively into neutral clouds.," Gas from the galactic disk rises buoyantly after being heated by supernovae (SNe), becomes thermally unstable and cools radiatively into neutral clouds." + Once the clouds. are dense (μον. fall back ballisticallv onto the disk. and are seen as the λος.," Once the clouds are dense they fall back ballistically onto the disk, and are seen as the HVCs." + Whether SNe explosions can start a galactic fountain has been investigated both theoretically (Ixahn. (1998))) and through numerical simulations (deAvillez(1998):de&Berry (2001))).," Whether SNe explosions can start a galactic fountain has been investigated both theoretically \cite{kahn98}) ) and through numerical simulations \cite{deav98,deav01}) )." + Blitz et al. (, Blitz et al. ( +1999: see also Braun&Burton (1999))) suggest (some) LIVC's are neutral gas associated with the numerous dark matter substructures seen in simulations of haloes of galaxies and groups of galaxies.,1999; see also \cite{brau99}) ) suggest (some) HVCs are neutral gas associated with the numerous dark matter substructures seen in simulations of haloes of galaxies and groups of galaxies. + Such λος are at large clistances 40 kpe) from the galactic centre. anc," Such HVCs are at large distances $\gtrsim$ 40 kpc) from the galactic centre, and" +in the longitude range 20° at the magnetico caps of he neutron star and therefore the P?> model is. correct in SAX J1808.4-3658 and the CE model is ruled out., Thus we infer that the X-ray variability carrying the rms-flux relation originates at the magnetic caps of the neutron star and therefore the PP model is correct in SAX J1808.4-3658 and the CF model is ruled out. + For completeness. we note here the possibility that. case (i) corresponds to a more complicated PP model. where most of the aperiodic variability is produced. before. the »ulsed: variability. by perturbations propagating through a separate unpulsed emitting region (e.g. a static corona above he disk). before reaching the site of the pulsed. emission.," For completeness, we note here the possibility that case (i) corresponds to a more complicated PP model, where most of the aperiodic variability is produced before the pulsed variability by perturbations propagating through a separate unpulsed emitting region (e.g. a static corona above the disk), before reaching the site of the pulsed emission." + Llowever. given the available spectral-variability. evidence ‘or other neutron stars (Cillanov.Revnivisey& 2003).. it is simplest to assume that all the variable emission originates at or close to the neutron star surface.," However, given the available spectral-variability evidence for other neutron stars \citep{gil03}, it is simplest to assume that all the variable emission originates at or close to the neutron star surface." + We have demonstrated that the aperiodic X-ray. variations which contain the linear rnis-IHux relation in SAX J180S.4-3658 are coupled to the 401 Hz pulsation. and hence originate on or close to the magnetic caps of the neutron star.," We have demonstrated that the aperiodic X-ray variations which contain the linear rms-flux relation in SAX J1808.4-3658 are coupled to the 401 Hz pulsation, and hence originate on or close to the magnetic caps of the neutron star." + The only existing mocel which can explain this result is the PP model: specifically. the rmis-IHux relation is produced by the coupling of perturbations in the aceretion [low as they propagate inwards.," The only existing model which can explain this result is the PP model: specifically, the rms-flux relation is produced by the coupling of perturbations in the accretion flow as they propagate inwards." + When the accretion flow is channeled on to the magnetic caps of the neutron star. the energy of accretion is released and the pattern of Ductuations in the accretion How (including the rms-Iux relation) is imprinted on the resulting X-ray emission.," When the accretion flow is channeled on to the magnetic caps of the neutron star, the energy of accretion is released and the pattern of fluctuations in the accretion flow (including the rms-flux relation) is imprinted on the resulting X-ray emission." + Although we have only shown that the PP model is the most likely explanation of the rms-Iux relation in SAN JISOS.4-3658. it seems highly likely also that the PP model explains the aperiodic variability and. rmis-Hux. relation in other accreting neutron star ancl black hole svstems. (including AGN).," Although we have only shown that the PP model is the most likely explanation of the rms-flux relation in SAX J1808.4-3658, it seems highly likely also that the PP model explains the aperiodic variability and rms-flux relation in other accreting neutron star and black hole systems (including AGN)." + For example. the power spectra of broadband: noise in both black hole and neutron star NRBs (including SAN JI1808.4-3658) can be described by a simple model involving the superposition of broad. Lorentzian features (Belloni.Psaltis&vanderIxlis2002:Pottschmicltetal.2003:vanStraaten.derIxlis&Wijnands 2003)). and both neutron star and. black hole systems show similar correlations between the dillerent characteristic frequencies of these features (c.g. Wijnands&vancerExlis1999:Bel-loni.Psaltis&vanderIxlis2002:Pottschimidtetal. 2003)).," For example, the power spectra of broadband noise in both black hole and neutron star XRBs (including SAX J1808.4-3658) can be described by a simple model involving the superposition of broad Lorentzian features \citealt{bel02,pot03,str03}) ), and both neutron star and black hole systems show similar correlations between the different characteristic frequencies of these features (e.g. \citealt{wij99,bel02,pot03}) )." + The strong similarities between black hole ΧΙ variability and that of AGN. with characteristic time-scales apparentIv scaling with the black hole mass (c.g. Uttlev.MLlardy&Pa-padakis2002:Markowitzetal.2003:Al’Lares 2003)) also strongly support the idea that AGN and XItDs share the same aperiodic variability mechanism.," The strong similarities between black hole XRB variability and that of AGN, with characteristic time-scales apparently scaling with the black hole mass (e.g. \citealt{utt02,mar03,mch03}) ) also strongly support the idea that AGN and XRBs share the same aperiodic variability mechanism." + Since the light curves of all these tvpes of system. show a linear rms-Iux relation (c.g. Uttlev&M'LEbardy2001:Vaughan.FabianNandra2003:Gleissnerοἱal. 2003)). the application of Ockham's tazor would suggest that the rms-Iux relation is produces w the same mechanism in all cases and hence the aperiocdic X-ray variabilitv in neutron star and black bole NliDs aux AGN is produced by a PP mechanism. and not by corona lares.," Since the light curves of all these types of system show a linear rms-flux relation (e.g. \citealt{utt01,vau03,gle03}) ), the application of Ockham's Razor would suggest that the rms-flux relation is produced by the same mechanism in all cases and hence the aperiodic X-ray variability in neutron star and black hole XRBs and AGN is produced by a PP mechanism, and not by coronal flares." + Lt should. be restated here that the PP interpretation of he variability does not carry any implications for the existence of an X-ray emitting corona., It should be restated here that the PP interpretation of the variability does not carry any implications for the existence of an X-ray emitting corona. + This is because the aperiodic variability (and. the rms-dux. relation. imprintec in it) is produced in the accretion Low and is independen of where the X-rays are emitted. provided that. variations in the accretion [low can modulate the X-ray. emission.," This is because the aperiodic variability (and the rms-flux relation imprinted in it) is produced in the accretion flow and is independent of where the X-rays are emitted, provided that variations in the accretion flow can modulate the X-ray emission." + Thus a corona which is heated by many small reconnection events (too small to have a very strong ellect on. the variability) remains a viable source of the X-ray emission (in black hole svstems. at least).," Thus a corona which is heated by many small reconnection events (too small to have a very strong effect on the variability) remains a viable source of the X-ray emission (in black hole systems, at least)." + In fact. by invoking an extended. X-ray. emitting region (such as à corona) which »ossesses à temperature eradient. so that higher energy. ravs are prelerentially emitted closer to the black hole. PP- models naturally produce the time-dependent: delays oween energy. bands and the energy-dependent. shape of le power spectrum. which are observed in black hole ray binaries (c.g. Alisra2000:Ixotov.2001:Zvcki 2003)) and AGN (e.g. dra2003:MLlardy.ctal. 2003)).," In fact, by invoking an extended X-ray emitting region (such as a corona) which possesses a temperature gradient, so that higher energy X-rays are preferentially emitted closer to the black hole, PP-type models naturally produce the time-dependent delays between energy bands and the energy-dependent shape of the power spectrum, which are observed in black hole X-ray binaries (e.g. \citealt{mis00,kot01,zyc03}) ) and AGN (e.g. \citealt{vau03,mch03}) )." + We have recently shown τον.AlUardy&Vaughan 2003.. ancl Uttlev et al.," We have recently shown \citealt{utt03}, and Uttley et al.," + in prep.), in prep.) + that the existence of an rms-Hux relation on all time-scales leads naturally to the appearance of non-linear behaviour which is observed. over a range of time-scales in both NRBs (Alaccarone 2003)) and AGN," that the existence of an rms-flux relation on all time-scales leads naturally to the appearance of non-linear behaviour which is observed over a range of time-scales in both XRBs \citealt{mac02,gie03}) ) and AGN" +"The nullsets in the preceding section may naturally be replaced by an abstract notion of ""negligible"" sets, i.e, members of a (briefly: p.131.","The nullsets in the preceding section may naturally be replaced by an abstract notion of “negligible” sets, i.e. members of a (briefly: p.l.i." + ideal) in E. defined as follows., ideal) in $\R$ defined as follows. + A nonempty family 7C2-\[IE] is termed to be a p.Li., A nonempty family $\id\subset 2^{\R} \setminus \{\R\}$ is termed to be a p.l.i. + ideal (resp., ideal (resp. + p.l.i., p.l.i. + —ideal) provided that it is closed under finite (resp., $\sigma-$ ideal) provided that it is closed under finite (resp. +" countable) set theoretical unions, i.e. hereditary with respect to descending inclusions, i.e. and such that jointly with a given set it contains its image under any alfine transformation of the real line onto itself, i.e Clearly the family of all nullsets (sets of Lebesgue measure zero) in IE. forms a p.l.i."," countable) set theoretical unions, i.e. hereditary with respect to descending inclusions, i.e. and such that jointly with a given set it contains its image under any affine transformation of the real line onto itself, i.e Clearly the family of all nullsets (sets of Lebesgue measure zero) in $\R$ forms a p.l.i." + o-ideal., $\sigma$ -ideal. + However there are numerous other p.l.i., However there are numerous other p.l.i. + ideals: let us mention only a few of them:, ideals; let us mention only a few of them: +eemission-line flux for 26/34 (~ 75%)) galaxies in the sample.,emission-line flux for 26/34 $\sim 75$ ) galaxies in the sample. + The remaining 8 galaxies have either a too low SNR or the eemission-line is polluted by sky-line residuals., The remaining 8 galaxies have either a too low SNR or the emission-line is polluted by sky-line residuals. + A recent study (?) has shown that unveiling the presence of AGN in high-redshift galaxies is a difficult exercise., A recent study \citep{wright10} has shown that unveiling the presence of AGN in high-redshift galaxies is a difficult exercise. +" In the case of metallicity studies, in which abundances are deduced from the ratio of different emission lines of the ionised gas, it is critical to check that the intensity and width of these lines are due to star formation and not related to any non-thermal nuclear activity."," In the case of metallicity studies, in which abundances are deduced from the ratio of different emission lines of the ionised gas, it is critical to check that the intensity and width of these lines are due to star formation and not related to any non-thermal nuclear activity." +" The common way to disentangle AGN contribution from star-forming galaxies consists in comparing the relative intensity of the main nebular emission lines (mainly textsciii]]|5007, H8, Ha, and [N1]6584)) in a diagnostic diagram, so-called BPT diagram (??)."," The common way to disentangle AGN contribution from star-forming galaxies consists in comparing the relative intensity of the main nebular emission lines (mainly ]5007, $\beta$, $\alpha$, and ) in a diagnostic diagram, so-called BPT diagram \citep{bpt81, kewley01}." +" Various physical conditions in the ISM -— SFR, ionisation parameter, metallicity and/or chemical composition -— have been invoked to explain the fact that some high-z star-forming galaxies lie in the transition region of the local BPT diagram (as defined by the SDSS galaxies) between star-forming galaxies and AGN hosts."," Various physical conditions in the ISM – SFR, ionisation parameter, metallicity and/or chemical composition – have been invoked to explain the fact that some $z$ star-forming galaxies lie in the transition region of the local BPT diagram (as defined by the SDSS galaxies) between star-forming galaxies and AGN hosts." +" ? have been able -— thanks to high resolution adaptive optics observations -— to subtract the active nuclear emission in a z~1.6 galaxy (HDF-BMZ1299), and have shown that the residual extended star-forming emission was characteristic of a local SDSS star-forming galaxy, whereas the integrated emission would have placed the object in the transition region."," \citet{wright10} have been able – thanks to high resolution adaptive optics observations – to subtract the active nuclear emission in a $z\sim 1.6$ galaxy (HDF-BMZ1299), and have shown that the residual extended star-forming emission was characteristic of a local SDSS star-forming galaxy, whereas the integrated emission would have placed the object in the transition region." +" The nature of our observations did not give us simultaneous access to the set of emission lines textsciii]]5007, H8, Ha, and textscii]]6584 or 1]6717,31)) commonly used in standard diagnostic diagrams."," The nature of our observations did not give us simultaneous access to the set of emission lines ]5007, $\beta$, $\alpha$, and ]6584 or ) commonly used in standard diagnostic diagrams." +" However, for all but two objects in our sample, the emission-line ratio N2=log([N1]6584/Ho) is lower than —0.5, with a median N2 value of —0.72."," However, for all but two objects in our sample, the emission-line ratio $\mathrm{N2} = +\log(\textrm\niia{}/\textrm\ha)$ is lower than $-0.5$, with a median $\mathrm{N2}$ value of $-0.72$." + Such low values are indicative for a very low contamination by AGN in our sample (eg.?).., Such low values are indicative for a very low contamination by AGN in our sample \citep[eg.][]{bpt81}. +" For 24 galaxies of our sample we calculated, following ?,, the N2 ""concentrated ratio"", corresponding to the value in the nuclear region of the galaxy."," For 24 galaxies of our sample we calculated, following \citet{wright10}, the N2 “concentrated ratio”, corresponding to the value in the nuclear region of the galaxy." +" We defined the nuclear region as the spaxel with the highest flux along with its 8 nearest neighbours (corresponding to a 0.7"" diameter aperture, matching our mean spatial resolution of 0.65"")."," We defined the nuclear region as the spaxel with the highest flux along with its 8 nearest neighbours (corresponding to a $0.7''$ diameter aperture, matching our mean spatial resolution of $0.65''$ )." +" We assumed this aperture to be small enough to probe the inner nucleus part as objects usually span from 1"" to 2"" with SNR»2 in our observations.", We assumed this aperture to be small enough to probe the inner nucleus part as objects usually span from $1''$ to $2''$ with $SNR>2$ in our observations. + Fig., Fig. + 2 shows i) the distribution of the 24 galaxies as a function of their global and nuclear N2 ratio (left panel) and ii) the relation between the global and nuclear N2 ratios for each galaxy (right panel)., \ref{distrib} shows i) the distribution of the 24 galaxies as a function of their global and nuclear N2 ratio (left panel) and ii) the relation between the global and nuclear N2 ratios for each galaxy (right panel). + The median values of N2 for each distribution are not very different (A~ —0.07)., The median values of N2 for each distribution are not very different $\Delta\sim -0.07$ ). + The median nuclear N2 ratio is lower than the global ratio which would not be the case if a significant fraction of our sample galaxies were hosting an AGN., The median nuclear N2 ratio is lower than the global ratio which would not be the case if a significant fraction of our sample galaxies were hosting an AGN. +" When comparing the global ratio to the nucleus ratio distribution, the highest bin does not shift and contains a single object."," When comparing the global ratio to the nucleus ratio distribution, the highest bin does not shift and contains a single object." + We investigated in more detail the galaxy in this bin: VVDS140096645., We investigated in more detail the galaxy in this bin: VVDS140096645. + It shows the following high N2 ratios: N2global=--0.252 and N2nuclear= —0.294., It shows the following high N2 ratios: $N2_\textrm{global}=-0.252$ and $N2_\textrm{nuclear}=-0.294$ . +" Looking further into its integrated spectrum (global and nuclear, see 3)), we noticed that: (i) the emission lines are broad, which is a possible sign of nuclear activity, (ii) the two nitrogen lines are clearly visible, as is the sulfur doublet,"," Looking further into its integrated spectrum (global and nuclear, see ), we noticed that: (i) the emission lines are broad, which is a possible sign of nuclear activity, (ii) the two nitrogen lines are clearly visible, as is the sulfur doublet," +The binary content of a elobular cluster is important in determining the lrequency and nature of eluster stellar exotica. as well as the dvnamical evolution of the cluster.,"The binary content of a globular cluster is important in determining the frequency and nature of cluster stellar exotica, as well as the dynamical evolution of the cluster." + ]t has long been recognized that binary formation is inevitable in a sell-gravitatingsvstem!., It has long been recognized that binary formation is inevitable in a self-gravitating. +. Indeed. (he presence of binaries as a central enerev source is vital to avoid complete (Goodman πι 1989).," Indeed, the presence of binaries as a central energy source is vital to avoid complete core-collapse (Goodman Hut 1989)." + However. only more recently has it been realised that elobular clusters nist. also have formed with a sizeable binary population (see IIut et al.," However, only more recently has it been realised that globular clusters must also have formed with a sizeable binary population (see Hut et al." + 1992 [or an early review)., 1992 for an early review). + That globular clusters harbour a mixture of dvnamically [ormed and primordial binaries can be used to understand observations of their stellar content. such as (he diverse blue straggler population in 47 Tucanae (Mapelli et al.," That globular clusters harbour a mixture of dynamically formed and primordial binaries can be used to understand observations of their stellar content, such as the diverse blue straggler population in 47 Tucanae (Mapelli et al." + 2004)., 2004). + ]|xnowledge of the likely primordial binary fraction of globular clusters is essential as input to models of globular cluster evolution., Knowledge of the likely primordial binary fraction of globular clusters is essential as input to models of globular cluster evolution. + H also provides a constraint on the cluster omnation process., It also provides a constraint on the cluster formation process. + Considering (hat (he presence of binaries in (he cluster core has a pronounced effect on the core properties and cluster evolution (Hut 1996). knowledge of the central binary requency is also important.," Considering that the presence of binaries in the cluster core has a pronounced effect on the core properties and cluster evolution (Hut 1996), knowledge of the central binary frequency is also important." + Indieations are (hat this is relatively small o£ the order of (e.g. Bellazzini et al., Indications are that this is relatively small – of the order of (e.g. Bellazzini et al. + 2002) or less (e.g. Cool Bolton 2002) — when compared to the yequencies of binaries observed in the solar neighbourhood (Duquennov Mayor 1991) and open clusters such as M67 (Fan et al., 2002) or less (e.g. Cool Bolton 2002) – when compared to the frequencies of binaries observed in the solar neighbourhood (Duquennoy Mayor 1991) and open clusters such as M67 (Fan et al. + 1996) which are of the order of50%., 1996) which are of the order of. +.. It would be particularly useful to take measurements of the current binary. traction in elobular clusters whether that be in (he core or outer regions and extrapolate backwards Lo gain a reliable determination of the primordial binary content., It would be particularly useful to take measurements of the current binary fraction in globular clusters – whether that be in the core or outer regions – and extrapolate backwards to gain a reliable determination of the primordial binary content. + However. processes involved," However, processes involved" +show how the simultaneous comparison of the size and mass cistributions can reveal interesting insights on how to improve the performance of theoretical models of galaxy evolution.,show how the simultaneous comparison of the size and mass distributions can reveal interesting insights on how to improve the performance of theoretical models of galaxy evolution. + We find. in agreement with previous studies. that this hierarchical nioclel provides a poor match to the size-mass relation of local galaxies. irrespective of the exact sample we compare it with.," We find, in agreement with previous studies, that this hierarchical model provides a poor match to the size-mass relation of local galaxies, irrespective of the exact sample we compare it with." + In particular. the model tends to produce a much latter relation than the one actually observed.," In particular, the model tends to produce a much flatter relation than the one actually observed." + This Hlattening is mainly. produced by the combined effects of having. with respect to the local data. too large (3 kpc) low-mass galaxies (<10: )). and of having a non-negligible fraction of compact. galaxies (0.51 kpc) at high masses (= LOMAL.)).," This flattening is mainly produced by the combined effects of having, with respect to the local data, too large $\sim 3$ kpc) low-mass galaxies $<10^{11}$ ), and of having a non-negligible fraction of compact galaxies $\lesssim 0.5-1$ kpc) at high masses $\gtrsim 10^{11}$ )." + Such discrepancies are reflected. in. the predicted size distribution., Such discrepancies are reflected in the predicted size distribution. + Although the model. produces a size clistribution in broad agreement with the data. it tends to overproduce the number of large galaxies bevond the peak £3 kpe). and the number of very compact. galaxies (S1 kpe).," Although the model produces a size distribution in broad agreement with the data, it tends to overproduce the number of large galaxies beyond the peak $\gtrsim 3$ kpc), and the number of very compact galaxies $\lesssim 1$ kpc)." + We discussed that the former issue is present at all epochs. and it might therefore be linked to how spheroids ave formed in the first place. either. from not. properly reating initial disk instabilities and/or computing the sizes of remnants in gas-rich. mergers.," We discussed that the former issue is present at all epochs, and it might therefore be linked to how spheroids are formed in the first place, either from not properly treating initial disk instabilities and/or computing the sizes of remnants in gas-rich mergers." + Regarding the overproduction of compact ancl massive (Mio(0.51)104 )) galaxies with respect to he data. already. pointed out in the recent Literature. we ind it to be less prominent than previously claimed. and confined to only ultracompact galaxies 2.0.5 kpe) when considering only ellipticals.," Regarding the overproduction of compact and massive $\sim (0.5-1)\times 10^{11}$ ) galaxies with respect to the data, already pointed out in the recent Literature, we find it to be less prominent than previously claimed, and confined to only ultracompact galaxies $\lesssim 0.5$ kpc) when considering only ellipticals." + We discuss two possible reasons »hind the survival of such compact. galaxies until the esent epoch., We discuss two possible reasons behind the survival of such compact galaxies until the present epoch. + First. we find that mocdel early-type galaxies end to be significantly. older than those in SDSS.," First, we find that model early-type galaxies tend to be significantly older than those in SDSS." + This in urn mieht induce more compact galaxies at. fixed. stellar mass. given that galaxies formed at higher redshifts are more compact (see 2009a)).," This in turn might induce more compact galaxies at fixed stellar mass, given that galaxies formed at higher redshifts are more compact (see )." + We also find that moclel earlv-tvpe compact galaxies underwent peculiar merging histories characterized by extremely compact. progenitors. that could. prevent them to elliciently. grow their sizes.," We also find that model early-type compact galaxies underwent peculiar merging histories characterized by extremely compact progenitors, that could prevent them to efficiently grow their sizes." + ES acknowledges support from the Alexander von Humboldt Foundation anc partial support. from NASA Grant NNGOSGUTTG. MD is supported by NASA grant. LESA-NNGOGGCUIOG and NASA ADP/NNXOOADO2C. We thank CGuinevere Ixaulfmann. Ravi Sheth. Andrew Benson. Luigi Danese. Itosalind Skelton. Simon White. Qi Guo. and Volker Springel for various discussions.," FS acknowledges support from the Alexander von Humboldt Foundation and partial support from NASA Grant NNG05GH77G. MB is supported by NASA grant LTSA-NNG06GC19G and NASA ADP/NNX09AD02G. We thank Guinevere Kauffmann, Ravi Sheth, Andrew Benson, Luigi Danese, Rosalind Skelton, Simon White, Qi Guo, and Volker Springel for various discussions." + We finally thank the referee [or several useful suggestions that improved the presentation of the paper., We finally thank the referee for several useful suggestions that improved the presentation of the paper. + The filled squares in Figure Al represent the Dernardi οἱ al. (, The filled squares in Figure A1 represent the Bernardi et al. ( +2009) estimate of the ERE obtained from the VYu method for our sample of carly-type galaxies selected: with concentration C.22.86.,2009) estimate of the ERF obtained from the $V/V_{\rm max}$ method for our sample of early-type galaxies selected with concentration $C_r>2.86$. + For consistency. we here show that the V/V based ERP is consistent. within the errors. with the one obtained from the convolution of the luminosity function or velocity dispersion function with the bivariate distribution of points inthe £42. plane.," For consistency, we here show that the $V/V_{\rm max}$ -based ERF is consistent, within the errors, with the one obtained from the convolution of the luminosity function or velocity dispersion function with the bivariate distribution of points in the $L-R_e$ plane." + More specifically. following the methods outlined in 7. and ?.. we have convolved the luminosity function ®(£) with the bivariate distribution of £; and I. llere £;; is the fraction of sources in the sample with effective radius A7. and luminosity Lj. normalized to the total number of sources with luminosity L;.," More specifically, following the methods outlined in \citet{Sheth03} and \citet{Shankar04}, we have convolved the luminosity function $\Phi(L)$ with the bivariate distribution of $L_j$ and $R_e$, Here $\xi_{ij}$ is the fraction of sources in the sample with effective radius $R_e^i$ and luminosity $L_j$, normalized to the total number of sources with luminosity $L_j$." + The luminosity function (L) has been computed from the VYiuuu. method bv Bernardi ct al. (, The luminosity function $\Phi(L)$ has been computed from the $V/V_{\rm max}$ method by Bernardi et al. ( +2009) for the same sample of galaxies. and we refer the reader to that paper for analvtical fits anc detailed discussions of the sample.,"2009) for the same sample of galaxies, and we refer the reader to that paper for analytical fits and detailed discussions of the sample." + The result. of eq. CX1)), The result of Eq. \ref{eq|bivar}) ) + is shown in Figure X1 with long-dashed lines. which bracket the statistical uncertainties in the luminosity function Lit parameters.," is shown in Figure A1 with long-dashed lines, which bracket the statistical uncertainties in the luminosity function fit parameters." + We have also used the bivariate distribution in equation CX1)) applied to the velocity dispersion. function Pia). again derived. by Bernardi et al. (," We have also used the bivariate distribution in equation \ref{eq|bivar}) ) applied to the velocity dispersion function $\Phi(\sigma)$, again derived by Bernardi et al. (" +2009). for. this same sample. and with the weights £;; now computed from the distribution of sources in the 0. &. plane.,"2009) for this same sample, and with the weights $\xi_{ij}$ now computed from the distribution of sources in the $\sigma-R_e$ plane." + The result is shown with dotted lines in the same Figure. again bracketing the statistical uncertainties in the velocity dispersion function fit. parameters.," The result is shown with dotted lines in the same Figure, again bracketing the statistical uncertainties in the velocity dispersion function fit parameters." + This exercise proves that. as expected. convolutions of other statistical distributions PCr) ," This exercise proves that, as expected, convolutions of other statistical distributions $\Phi(x)$ " +synchrotron self-compton (SSC) model (e.g.2).,synchrotron self-compton (SSC) model \citep[e.g.][]{maraschi92}. + We assume a spherical. homogeneous emission region - coined blob - containing isotropically distributed non-thermal electrons and a randomly oriented magnetic field.," We assume a spherical, homogeneous emission region - coined blob - containing isotropically distributed non-thermal electrons and a randomly oriented magnetic field." + DDue to the presence of this magnetic field the electrons emit svnchrotron radiation., Due to the presence of this magnetic field the electrons emit synchrotron radiation. + The photons are then scattered off the same electron population via the inverse Compton process., The photons are then scattered off the same electron population via the inverse Compton process. + The resulting spectrum shows the typical two bump structure commonly found in blazars., The resulting spectrum shows the typical two bump structure commonly found in blazars. + In the following section the governing equations of the SSC-model are explained., In the following section the governing equations of the SSC-model are explained. + To determine the time-dependent spectral energy distribution of blazars we solve the ditterential equation for the differential photon number density. obtained from the radiative transfer equation. including the corresponding terms with respect to SSC model. In the following context the well known ó-approximation (22). is applied to describe the synchrotron radiation in à convenient way.," To determine the time-dependent spectral energy distribution of blazars we solve the differential equation for the differential photon number density, obtained from the radiative transfer equation, including the corresponding terms with respect to SSC model, In the following context the well known $\delta$ -approximation \citep{fm66, +schlick02} is applied to describe the synchrotron radiation in a convenient way." +" Thus the synchrotron photon production rate Ay is given by with the pitch angle averaged total power P, emitted by a single electron having Lorentz factor y (2???) and y, being a function of v. obtained from the pitch angle averaged critical synchrotron frequency."," Thus the synchrotron photon production rate $R_S$ is given by with the pitch angle averaged total power $P_S$ emitted by a single electron having Lorentz factor $\gamma$ \citep{rybicki79, bg70, gs69} + and $\gamma_c$ being a function of $\nu$, obtained from the pitch angle averaged critical synchrotron frequency." + In optically thick regimes the emitted synchrotron radiation is absorbed by the emitting electrons itself., In optically thick regimes the emitted synchrotron radiation is absorbed by the emitting electrons itself. + This is described by the synchrotron self absorption coethcient. which leads to the absorption rate The second main feature of the SSC model is Compton scattering of the synchrotron photons by the emitting electrons themselves.," This is described by the synchrotron self absorption coefficient, which leads to the absorption rate The second main feature of the SSC model is Compton scattering of the synchrotron photons by the emitting electrons themselves." + Here the full Klein-Nishina cross section is used to calculate the photon production rate. The formula was taken from ? with minor corrections according to ?..," Here the full Klein-Nishina cross section is used to calculate the photon production rate, The formula was taken from \citet{wax05} with minor corrections according to \citet{cb90}." + The photon energies are rewritten in terms of the electrons rest mass. so that /n*=enc? for the scattered photons and hv=eumc for the target photons.," The photon energies are rewritten in terms of the electrons rest mass, so that $h \nu = \epsilon m c^2$ for the scattered photons and $h \nu = +\epsilon_1 m c^2$ for the target photons." +" To make use of the full Klein- cross section we applied the approximate inverse Compton spectrum (2). of a single electron scattered off by a unit density photon field. where q""=eftdeyytl—e/yn and Αγ). we can write equation 13. interms of 4: Solving equation 20 we obtain where 5,0—σαν=1) is the initial Lorentz factor of the electron. just the shock. and u 18 the maximal Lorentz factor at behindV>1. which corresponds to an electron with σος>x. and ts given by The of electrons with a Lorentz factor within the interval fraction[55.54alld5,] is given by: withN(z,)d5,/n. and remains constant as these quantities evolve increasing 4."," Since $\Gamma^2\propto t^{k-3}$, we obtain that Using equation \ref{to_chi} and the relation $dt'=dt/\gamma$, we can write equation \ref{dgamma_dt} interms of $\chi$: Solving equation \ref{dgamma_dchi} we obtain where $\gamma_{e,0}\equiv\gamma_e(\chi=1)$ is the initial Lorentz factor of the electron, just behind the shock, and $\gamma_{\rm max}(\chi)$ is the maximal Lorentz factor at $\chi>1$, which corresponds to an electron with $\gamma_{e,0}\to \infty$, and is given by The fraction of electrons with a Lorentz factor within the interval $[\gamma_{e},\gamma_{e}+ d\gamma_{e}]$ is given by: $N(\gamma_{e})d\gamma_{e}/n$, and remains constant as all these quantities evolve with increasing $\chi$." + The electron distribution ts therefore given by: Where5uin(A2=Femina.\)-," The electron distribution is therefore given by: where $\gamma_{\rm min}(\chi)=\gamma_e(\gamma_{{\rm min},0},\chi)$." + We now have explicit expressions for both. the hydrodynamical quantities and the electron distribution. over all relevant space-time. and can calculate the flux density near the various break frequencies.," We now have explicit expressions for both the hydrodynamical quantities and the electron distribution, over all relevant space-time, and can calculate the flux density near the various break frequencies." +" For breaks that are in the opticallythin regime (b=2.3.9.11) one may use the equation which is a generalization of equation 13 of GPS99a. where d; and z are the Juminosity distance and cosmological redshift of the source. respectively. P7, is the radiated power per unit volume per unit frequency in the local rest frame of the fluid. and should be taken at the coordinate time ¢=f-ric. where t-=fasfCl+2). E is the energy of the blast wave. v=R/R, (e.g. GPS99a). i!=vr(l—jr)."," For breaks that are in the opticallythin regime (b=2,3,9,11) one may use the equation which is a generalization of equation 13 of GPS99a, where $d_L$ and $z$ are the luminosity distance and cosmological redshift of the source, respectively, $P'_{\nu'}$ is the radiated power per unit volume per unit frequency in the local rest frame of the fluid, and should be taken at the coordinate time $t=t_z+r\mu/c$, where $t_z\equiv t_{\rm obs}/(1+z)$, $E$ is the energy of the blast wave, $y\equiv R/R_l$ (e.g. GPS99a), $\nu'=\nu\gamma(1-\beta\mu)$." +" The Spectral emissivity of a single electron (in the fluid rest frame) ts given by where g, is the electric charge of the electron. à is the pitch angle between the direction of the electron’s velocity and the magnetic field. in the local rest frame of the fluid. and F is the standard synchrotron function (e.g. Rybicki Lightman 1979)."," The Spectral emissivity of a single electron (in the fluid rest frame) is given by where $q_e$ is the electric charge of the electron, $\alpha$ is the pitch angle between the direction of the electron's velocity and the magnetic field, in the local rest frame of the fluid, and $F$ is the standard synchrotron function (e.g. Rybicki Lightman 1979)." +" In order to obtain an expression for P7, (which appears in equation 24)) we average P7,. over o. assuming an isotropic distribution of electrons in the local rest frame. and then integrate over the electron distribution. For the remaining spectral breaks (bz1.4.5.6.7.8.10). where the system Is not always optically thin. we follow the formalism of GPS99b."," In order to obtain an expression for $P'_{\nu'}$ (which appears in equation \ref{optically_thin}) ) we average $P'_{\nu',e}$ over $\alpha$, assuming an isotropic distribution of electrons in the local rest frame, and then integrate over the electron distribution, For the remaining spectral breaks (b=1,4,5,6,7,8,10), where the system is not always optically thin, we follow the formalism of GPS99b." +" Since the emission is isotropic in the local rest frame of the fluid. the emission coefficient is simply Επ. where P7, is given by equation 29.."," Since the emission is isotropic in the local rest frame of the fluid, the emission coefficient is simply $j'_{\nu'}=P'_{\nu'}/4\pi$ , where $P'_{\nu'}$ is given by equation \ref{Pnu}. ." + The absorption coefficient is given by Since the flow ts spherically symmetric. the afterglow image is circular. with physical radius of," The absorption coefficient is given by Since the flow is spherically symmetric, the afterglow image is circular, with physical radius of" +"The recent abundance of cosinological data iu the last few decades has provided compelling evidence towards a standard concordance cosmology. in which the Universe is composed of approxtmately barvons. ‘dark’ matter and ""dark energy.","The recent abundance of cosmological data in the last few decades has provided compelling evidence towards a standard concordance cosmology, in which the Universe is composed of approximately baryons, `dark' matter and `dark' energy." + One of the main challenges of modera cosmology is to understand the nature of the iivsterious dark energy which drives the observed cosmic acceleration , One of the main challenges of modern cosmology is to understand the nature of the mysterious dark energy which drives the observed cosmic acceleration . +The Inteerated Sacls-Wolte CSW) effect ds a secondary anidsotropv οἳ the Cosmic Microwave Backeround (CAIB). which arises because of he variation with time of the cosmuc gravitational potential between ocal observers and the surface of last scattering.," The Integrated Sachs-Wolfe (ISW) effect is a secondary anisotropy of the Cosmic Microwave Background (CMB), which arises because of the variation with time of the cosmic gravitational potential between local observers and the surface of last scattering." + The oteutial can be traced by Large Scale Structure (LSS) survevs (7).. and the ISW effect is therefore a probe which inks he high redshift CAIB with the low redshift matter distribution aud cau be detected by cross-correlating the Wo.," The potential can be traced by Large Scale Structure (LSS) surveys , and the ISW effect is therefore a probe which links the high redshift CMB with the low redshift matter distribution and can be detected by cross-correlating the two." +" As a cosinological probe. the ISW effect has less statistical power than weak lensing or galaxy clustering 7). but it is directly sensitive to dark enerev. curvature or modified eravity (2?777).. such tha in universes where io0dified gravity and curvature excluded. detection of the ISW signal provides a direc sjeuature of dark οποίον,"," As a cosmological probe, the ISW effect has less statistical power than weak lensing or galaxy clustering , but it is directly sensitive to dark energy, curvature or modified gravity , such that in universes where modified gravity and curvature are excluded, detection of the ISW signal provides a direct signature of dark energy." + Ta more geucra uuverses. the ISW effect can be used to trace alternative models of eyavity.," In more general universes, the ISW effect can be used to trace alternative models of gravity." + The CAMB WMAP survey is already optimal for detecting the ISW signa (sce Sections 77. aud ?7)). ane sienificance is not expected to ierease with the arriva of Planck. unless the effect of the foreground Galactic mask can be reduced.," The CMB WMAP survey is already optimal for detecting the ISW signal (see Sections \ref{sec:theory} and \ref{sec:method}) ), and significance is not expected to increase with the arrival of Planck, unless the effect of the foreground Galactic mask can be reduced." + The amplitude of the measured ISW signal should however depend strongly on the details of the local tracer of mass., The amplitude of the measured ISW signal should however depend strongly on the details of the local tracer of mass. + Survey optuuisations show that an ideal ISW survey requires the same configuration as surveys which are optimised for weak lensing or galaxy clustering - caning that an optimal measure of the ISW signal will essentially come “for free’ with future planned weak lensing aud galaxy cblusterime surveys?)., Survey optimisations show that an ideal ISW survey requires the same configuration as surveys which are optimised for weak lensing or galaxy clustering - meaning that an optimal measure of the ISW signal will essentially come `for free' with future planned weak lensing and galaxy clustering surveys. +. In the best scenario. a lo detection is expected(?).. aud it has been shown that combined with weak lensing. galaxy correlation and other probes such as clusters. the ISW can be useful to break parameter degeneracies(?).. making it a promising probe.," In the best scenario, a $\sigma$ detection is expected, and it has been shown that combined with weak lensing, galaxy correlation and other probes such as clusters, the ISW can be useful to break parameter degeneracies, making it a promising probe." + Iuitial attempts to detect the ISW effect with COBE as the CAIB tracer were fruitless(2).. but since the arrival of WALAP data. tens of positive detections lave been made. with the highest significance reported for analyses usimg a tomographic combination of surveys (soe Sections 77 and 2? for a cletailed review of detections).," Initial attempts to detect the ISW effect with COBE as the CMB tracer were fruitless, but since the arrival of WMAP data, tens of positive detections have been made, with the highest significance reported for analyses using a tomographic combination of surveys (see Sections \ref{sec:theory} and \ref{sec:method} for a detailed review of detections)." + However. severa studies using the same tracer of LSS appear to have contradicting conclusions. some analvses do not find correlation where others do. aud as statistical methods to analyse the data evolve. the significance of the ISW signal Is sometimes reduced222).," However, several studies using the same tracer of LSS appear to have contradicting conclusions, some analyses do not find correlation where others do, and as statistical methods to analyse the data evolve, the significance of the ISW signal is sometimes reduced." + Iu Section ?7.. we describe the cause of the ISW effect and review curent detectious.," In Section \ref{sec:theory}, we describe the cause of the ISW effect and review current detections." +" Iu Section οον, we describe the methodology for detection and measuring the ISW signal and review a laree proportion of reported detections 1i the literature. as well as their advantages and disadvantages."," In Section \ref{sec:method}, we describe the methodology for detection and measuring the ISW signal, and review a large proportion of reported detections in the literature, as well as their advantages and disadvantages." + Tavine ideutified the main issues with current methods. we propose a new aud complete method in Section ??.. which capitalises ou the fact that different st:istical methods are complementary aud uses sparse inpaiutiug to solve the issue of missing data and a bootstrapping technique tomeasure the estimuitor's probability distribution function (PDF).," Having identified the main issues with current methods, we propose a new and complete method in Section \ref{sec:saclaymethod}, which capitalises on the fact that different statistical methods are complementary and uses sparse inpainting to solve the issue of missing data and a bootstrapping technique tomeasure the estimator's probability distribution function (PDF)." + Iu Section 5.. we validate our new icthod using simulations for 2\TASS and Enclid-like surveys.," In Section \ref{sec:validation}, we validate our new method using simulations for 2MASS and Euclid-like surveys." + In Section 6.. we apply our new method to WALAP 7 and the 2\LASS survey.," In Section \ref{sec:data}, we apply our new method to WMAP 7 and the 2MASS survey." + In Section 77S we present our conclusions.," In Section \ref{sec:discussion}, , we present our conclusions." +"an ""outside-in"" twpe comes from examining the individual Πειραιά anc V-band outburst light. curves in bie.",an “outside-in” type comes from examining the individual R-band and V-band outburst light curves in Fig. + ὸ and Fig., \ref{fig:rband} and Fig. + 9 respectively., \ref{fig:vband} respectively. + Lt can easily be seen that the rise to outburst eclipses are wider than the eclipses in the late stages of the outburst (sce Fig., It can easily be seen that the rise to outburst eclipses are wider than the eclipses in the late stages of the outburst (see Fig. + 2. Fig 3 and Fig.," 2, Fig 3 and Fig." + 6).Xlso. eclipse depths during the rise are much shallower than the eclipses during the decline. indicating that during mid eclipse there is more (ux observed. from either side of the secondary star during the rise phase than the decline phase of the outburst.," 6).Also, eclipse depths during the rise are much shallower than the eclipses during the decline, indicating that during mid eclipse there is more flux observed from either side of the secondary star during the rise phase than the decline phase of the outburst." + Since the outburst eclipses are extremely symmetric. we fitted them with a Gaussian to measure the curation and depth of cach eclipse.," Since the outburst eclipses are extremely symmetric, we fitted them with a Gaussian to measure the duration and depth of each eclipse." + The residuals from the Caussian [it were at the level., The residuals from the Gaussian fit were at the level. + Fable 1. lists the full width half minimum for each light curve along with the depth of each eclipse., Table \ref{tab:observation_log} lists the full width half minimum for each light curve along with the depth of each eclipse. + Lt is evident from Table 1 that the outburst eclipses increase their depth anc become narrower as the eruption progresses., It is evident from Table \ref{tab:observation_log} that the outburst eclipses increase their depth and become narrower as the eruption progresses. + I is a further indication that the outburst starts at the edge of the disc. whose luminous part is relatively large at the beginning of the outburst. and decreases in size as the outburst progresses.," It is a further indication that the outburst starts at the edge of the disc, whose luminous part is relatively large at the beginning of the outburst, and decreases in size as the outburst progresses." + Patterson(1981) observed ανα nova oscillations (DNO) during an eruption of WP Cas in LOTS., \scite{Patterson81} observed dwarf nova oscillations (DNO) during an eruption of HT Cas in 1978. + X. power spectrum of our V. and. 1t out-of-eclipse data did. not reveal any significant oscillations., A power spectrum of our V and R out-of-eclipse data did not reveal any significant oscillations. + Given that we have a relatively low temporal resolution and. also that DNOs are usually found in shorter wavelength regions. this is not very surprising.," Given that we have a relatively low temporal resolution and also that DNOs are usually found in shorter wavelength regions, this is not very surprising." + ‘Table 1. shows the mid-eclipse timines obtained during the quiescent ancl outburst. periods in 1995 and. 1997., Table \ref{tab:observation_log} shows the mid-eclipse timings obtained during the quiescent and outburst periods in 1995 and 1997. + Previous data. that were explicitly tabulated. from Patterson(1981).. Zhang.Itobinson&Nather(1986).. and Horne (1991).," Previous data, that were explicitly tabulated, from \scite{Patterson81}, \scite{Zhang86}, and Horne (1991)." + were converted from LHeliocentrie Julian Date to Barycentric Dynamical Julian Date ancl used in our calculations., were converted from Heliocentric Julian Date to Barycentric Dynamical Julian Date and used in our calculations. + Only the quiescent data were used in order to caleulate the refined ephemeris presented. here., Only the quiescent data were used in order to calculate the refined ephemeris presented here. + “Phe mid-eclipse positions were calculated by measuring the time of the white dwarl ingress and egress., The mid-eclipse positions were calculated by measuring the time of the white dwarf ingress and egress. + For the outburst data presented. here we used. a Gaussian curve fit to measure the time of minimum Lux., For the outburst data presented here we used a Gaussian curve fit to measure the time of minimum flux. + Vhe data for November 17th from Ixeele Observatory have a timing problem and they have been left out from all our calculations involving time and are not displaved on the O-C cliagram., The data for November 17th from Keele Observatory have a timing problem and they have been left out from all our calculations involving time and are not displayed on the O-C diagram. + 3elow ds our calculated. ephemeris in. Baryeentric Dynamical Julian Date with the uncertainties shown in brackets., Below is our calculated ephemeris in Barycentric Dynamical Julian Date with the uncertainties shown in brackets. + We used our derived. period to project back to the Zi quoted by Patterson(1981)., We used our derived period to project back to the $T_{0}$ quoted by \scite{Patterson81}. +. Phe residuals of our ephemeris calculations (O-C€ diagram) can be seen in Fig. 4.., The residuals of our ephemeris calculations (O-C diagram) can be seen in Fig. \ref{fig:o-c}. + The unused: outburst eclipse points are represented: as circles., The unused outburst eclipse points are represented as circles. + Woodetal.(1995). speculated that IE. Cas might have a non zero period derivative., \scite{Wood95} speculated that HT Cas might have a non zero period derivative. + Llowever. due to the large scatter of the data points in Fig.," However, due to the large scatter of the data points in Fig." + 4 we could only fit the data with a linear ephemeris., \ref{fig:o-c} we could only fit the data with a linear ephemeris. + During the outburst an anomaly of the O-C points is observed. especially during the second night of observations when the svstem is at its carly decline stages. (," During the outburst an anomaly of the O-C points is observed, especially during the second night of observations when the system is at its early decline stages. (" +see Fig. 5)),see Fig. \ref{fig:outburst_o-c}) ) + During the decline from outburst the points gradually cirift o à maximum cillerence of TO seconds from the caleulated value., During the decline from outburst the points gradually drift to a maximum difference of 79 seconds from the calculated value. + Observations of other objects on the same night show his is not à computer clock problem., Observations of other objects on the same night show this is not a computer clock problem. + The O-C points then return to their normal level the following night., The O-C points then return to their normal level the following night. + We comment on this unusual behaviour in the discussion section of the )Aper., We comment on this unusual behaviour in the discussion section of the paper. + A model that takes into account the [Lux emitted by a white dwarl encirclec by an optically thick accretion disc and a Roche-lobe filling secondary star. which is. tically locked in the frame of the binary. was mocified ancl usec for the investigation of the observed. light curves during the ITE Cas outburst.," A model that takes into account the flux emitted by a white dwarf encircled by an optically thick accretion disc and a Roche-lobe filling secondary star, which is tidally locked in the frame of the binary, was modified and used for the investigation of the observed light curves during the HT Cas outburst." + The model also accounts for the irradiation of the secondarys surface by a heating source at the centre of the disc., The model also accounts for the irradiation of the secondary's surface by a heating source at the centre of the disc. + We also incorporate approximate temperature dependent limb darkening coellicients taken from Al-Naimiv (1978)., We also incorporate approximate temperature dependent limb darkening coefficients taken from \scite{Naimiy78}. +. Descriptions of previous versions of the code can be found in Shahbaz.Navlor&Charles(1993). and Somers.Mukai&Navlor (1996a)., Descriptions of previous versions of the code can be found in \scite{Shahbaz93} and \scite{Somers96a}. +. Phe model does not include the physical size ancl shape of the white dwarf or the white dwarl’s shadow onto the aceretion disc., The model does not include the physical size and shape of the white dwarf or the white dwarf's shadow onto the accretion disc. + Also. it takes no account of a bright spot or an accretion stream.," Also, it takes no account of a bright spot or an accretion stream." +than the average spin teniperature othe eas means that the eas must have multiple phases. including a wari phase.,"than the average spin temperature of the gas means that the gas must have multiple phases, including a warm phase." + Caven the relatively good agrcomment between the and 21-0 III coluun densities aud the reasonable value of the derived kinetic teniperature of the wide componcut. we consider it hielillikely that the side component is indeed gas iu the WNA phase.," Given the relatively good agreement between the and 21-cm HI column densities and the reasonable value of the derived kinetic temperature of the wide component, we consider it highly likely that the wide component is indeed gas in the WNM phase." + Note that iu calculating the fraction of eas in the WNAL phase we have assuned that the Nyy imeasureineut is the best estimate of the total neutral-hbydrogen column clensity., Note that in calculating the fraction of gas in the WNM phase we have assumed that the $\NHI$ measurement is the best estimate of the total neutral-hydrogen column density. + As discussed in the previous section. the 21-cin absorption profile of the +0.2212 DLA is in excellent aerecment with that expected were the absorption to arise in a inulti-phase 1ieciun similar to that of the Mls Way.," As discussed in the previous section, the 21-cm absorption profile of the $z=0.2212$ DLA is in excellent agreement with that expected were the absorption to arise in a multi-phase medium similar to that of the Milky Way." + However. unlike the Calaxy. where the CNM and WNM both lads equitable contributions to the total HI colhuun density (Kulkarni&Ieiles 1988)). —75% ofthe neutral hivdroseu along this line ο [seht through the DLA umst be in the warn phase. ic. with temperature eSOOO Is. in order to account for its high estimated spin temperature.," However, unlike the Galaxy, where the CNM and WNM both make equitable contributions to the total HI column density \cite{kulkarni88}) ), $\sim 75\%$ of the neutral hydrogen along this line of sight through the DLA must be in the warm phase, i.e. with temperature $\sim 8000$ K, in order to account for its high estimated spin temperature." + The average spin teniperature for the ;=0.2212 absorber of ~900 Ik is far higher than the typical spin teirperatures of 100—200 I& found in the Galaxy and nearby spirals (Braun&Walterbos1992.Draun 1997)).," The average spin temperature for the $z = 0.2212$ absorber of $\sim 900$ K is far higher than the typical spin temperatures of $100 - 200$ K found in the Galaxy and nearby spirals \cite{braun92, braun97}) )." + Iheh spin temperatures of simular magnitude were earlier obtained by Coil et al. (, High spin temperatures of similar magnitude were earlier obtained by Carilli et al. ( +1996) in DLAs at hieh redshift.,1996) in DLAs at high redshift. + It was suggested there that the ligh Ty values at high : might be explained bv evolutionary effects., It was suggested there that the high $T_s$ values at high $z$ might be explained by evolutionary effects. + Since then. however. there has been a substantial iucrease ia the wuuber of DLAs with 21-«4uu observations (Laneetal.1998.. Cheneahw&Kaucku1999.CheugalurIauckar2000.Ianekar&Chneusalur 2001)) and. as Cheugalur Ikanekar (2000) poiut out. high spin teniperatures appear to be typical for DLAs at all redslifts.," Since then, however, there has been a substantial increase in the number of DLAs with 21-cm observations \cite{lane98}, \cite{chengalur99, chengalur00,kanekar01}) ) and, as Chengalur Kanekar (2000) point out, high spin temperatures appear to be typical for DLAs at all redshifts." + So ar. the ouly DLAs which show ow Ty values are those known to be associate with the disks of spiral galaxies.," So far, the only DLAs which show low $T_s$ values are those known to be associated with the disks of spiral galaxies." + Cheugalur IKaueku (2000) (soe also Nanckar Choeugalur 2001) sugecsted that the higlh-T; DLAs were ikely to be associatc¢ with dwarf or LSD-tvpe galaxies. where a conibination of low central pressures. low dust conteut and low metallicities result in a simaller fraction for the ϱΝΑΙ," Chengalur Kanekar (2000) (see also Kanekar Chengalur 2001) suggested that the $T_s$ DLAs were likely to be associated with dwarf or LSB-type galaxies, where a combination of low central pressures, low dust content and low metallicities result in a smaller fraction for the CNM." +", Our conchision that ~A of the gas along the ine of siglt through the +=0.2212 DLA is iu the WNM yhase is dn good agreement with the observations of Young et al. (", Our conclusion that $\sim 75\%$ of the gas along the line of sight through the $z = 0.2212$ DLA is in the WNM phase is in good agreement with the observations of Young et al. ( +2000). who find that nearby dwarf galaxies rave ονNUS of their neutral gas in the WNM phase.,"2000), who find that nearby dwarf galaxies have $\sim 80\%$ of their neutral gas in the WNM phase." + Apart from possible selection effects. the association of DLAs with dwarf galaxies is somewhat surprising. both yecause of the existing paradiem of DLAs being associated with massive rotating disks (Prochaska&Wolfe1997.Prochaska&Wolfe 1998)). aud the expectation (based ou a ceusius of the III content of +=0 optically catalogued ealaxies by Rao&Briges1993)) that the bulk of the ueutral IIT at low redshifts is im large spiral galaxies.," Apart from possible selection effects, the association of DLAs with dwarf galaxies is somewhat surprising, both because of the existing paradigm of DLAs being associated with massive rotating disks \cite{prochaska97,prochaska98}) ), and the expectation (based on a census of the HI content of $z=0$ optically catalogued galaxies by \cite{rao93}) ) that the bulk of the neutral HI at low redshifts is in large spiral galaxies." + Iloxwvever. blind searches for ΤΗ cussion at low redshift (ic. unbiased by the presence of a catalogued galaxy: Schneideretal.1998.Roseubere& 20003) also indicate that there could be substautial amounts of III in optically faint galaxies. although these results are still controversial (c.g. see Zwaan et al. (," However, blind searches for HI emission at low redshift (i.e. unbiased by the presence of a catalogued galaxy; \cite{schneider98, rosenberg00}) ) also indicate that there could be substantial amounts of HI in optically faint galaxies, although these results are still controversial (e.g. see Zwaan et al. (" +1997). for an opposing point of view).,"1997), for an opposing point of view)." + Tn this context. it is of interest that the three lowest redshift DLAs known have all con. (tentatively) identified as dwrf (or LSB) galaxies (Bowenctal.2001.Turusheketal.2001.Cohen 20011) G@vhere. followine Turushek et al.," In this context, it is of interest that the three lowest redshift DLAs known have all been (tentatively) identified as dwarf (or LSB) galaxies \cite{bowen01,turnshek01,cohen01}) ) (where, following Turnshek et al." +" 2001. we only cousider svstems to be DLAs if they amect the ""classical selection criterion for a DLA. ie. for which an observed Lyius-oe profile yields an DIE column density Nyyο2«1077 23."," 2001, we only consider systems to be DLAs if they meet the “classical” selection criterion for a DLA, i.e. for which an observed $\alpha$ profile yields an HI column density $\NHI \ge 2\times 10^{20}$ )." + Tu the case of the current absorber. Le Brun et al. (," In the case of the current absorber, Le Brun et al. (" +1997) sugeested that a galaxy at au impact parameter of G from OL 363 was likely to be the DLA lost.,1997) suggested that a galaxy at an impact parameter of $\sim 6^{''}$ from OI 363 was likely to be the DLA host. + The spectrin of this ealaxy (Cohen2001)) confirms that it is dudeed at the correct redshift to produce the damped absorpion., The spectrum of this galaxy \cite{cohen01}) ) confirms that it is indeed at the correct redshift to produce the damped absorption. + Turushek et al. (, Turnshek et al. ( +2007) present both detailed uultiwaveleusth photometry aux optical spectroscopy of lis system. aud find that its colours are cousisCl with a cdwart (L~ VIL.) early-type galaxy.,"2001) present both detailed multi-wavelength photometry and optical spectroscopy of this system, and find that its colours are consistent with a dwarf $L \sim 0.1L_*$ ) early-type galaxy." + The radial profile. jowever. indicates the presence of both a bulge aud a disk.," The radial profile, however, indicates the presence of both a bulge and a disk." + Hence. these authors suggest that this ealaxy could be he equivalent of the dwiirf spirals seen at low redshifts (Schombertetal. 19051) aud/or might have evolved from he faint blue galaxies seen at ligher redshifts.," Hence, these authors suggest that this galaxy could be the equivalent of the dwarf spirals seen at low redshifts \cite{schombert95}) ) and/or might have evolved from the faint blue galaxies seen at higher redshifts." + It should also be note that the iupact parameter (18) kpc is κοποματ large for a dwarf galaxy and it is thus also oossible that the absorption arises in an even fainter conipauiionu galaxy., It should also be noted that the impact parameter $\sim 18$ ) kpc is somewhat large for a dwarf galaxy and it is thus also possible that the absorption arises in an even fainter companion galaxy. + The preseut detection of the WNAL in he; = absorber towards OI 363 is the second case of evidence for a multi-phase iuediuni in an extragalactic system., The present detection of the WNM in the $z=0.2212$ absorber towards OI 363 is the second case of evidence for a multi-phase medium in an extragalactic system. + Lane et al. (, Lane et al. ( +2000) found that the :=0.0912 absorber towards the same quasar also has a multiphase medium. with at most ~ one-third of the eas iu the ΝΑΙ phase.,"2000) found that the $z=0.0912$ absorber towards the same quasar also has a multi-phase medium, with at most $\sim$ one-third of the gas in the CNM phase." + Interestingly. this DLA is also likely to be associated with a dwarf galaxy: Turushek ot al. (," Interestingly, this DLA is also likely to be associated with a dwarf galaxy; Turnshek et al. (" +2001) place an upper nuit of ~0.1L ouds I< baud huninosity.,2001) place an upper limit of $\sim 0.1~L_*$ on its K band luminosity. + It is possible that such svclus dominate current samples of DLAs because the obscuration for lines of sight passing through gas with both ligh inetallicity and high dust couteut nuelt well be sufficient to make medi resolution spectroscopy ofthe backgrouu quasar extremely difficult (Fall&Pei1993 ), It is possible that such systems dominate current samples of DLAs because the obscuration for lines of sight passing through gas with both high metallicity and high dust content might well be sufficient to make medium resolution spectroscopy of the background quasar extremely difficult \cite{fall93}) ). + Às conjectured earlier. the high observed spin teniperaures of DLAs thus seem to be a cousequence of their having a higher fraction of the WNM than is found for the Galaxy.," As conjectured earlier, the high observed spin temperatures of DLAs thus seem to be a consequence of their having a higher fraction of the WNM than is found for the Galaxy." + The fact that the two lowest redshift known DLAs have high ZF. uicaus that this cannot be due to evolutionary effects., The fact that the two lowest redshift known DLAs have high $T_s$ means that this cannot be due to evolutionary effects. +"to single out the effect of the stars, since that limit would remain even if the instrumental halo noise could be removed.","to single out the effect of the stars, since that limit would remain even if the instrumental halo noise could be removed." +" As an extreme example for a possible confusion error, it is worth mentioning that the orbit of the star S2 possibly was affected in 2002, during its pericenter passage, by such an event."," As an extreme example for a possible confusion error, it is worth mentioning that the orbit of the star S2 possibly was affected in 2002, during its pericenter passage, by such an event." + Both recent analyses (??) therefore treat the respective 2002 data separately; either by ignoring it or by assigning large errors to it.," Both recent analyses \citep{Ghez:2008p945,Gillessen:2009p1117} therefore treat the respective 2002 data separately; either by ignoring it or by assigning large errors to it." +" In order to assess the magnitude of the confusion noise, we simulated stellar background populations in a Monte-Carlo fashion."," In order to assess the magnitude of the confusion noise, we simulated stellar background populations in a Monte-Carlo fashion." + That needed two basic input distributions: a K-band luminosity function and the radial surface density profile., That needed two basic input distributions: a K-band luminosity function and the radial surface density profile. + We based these on the findings of ?.., We based these on the findings of \cite{Genzel:2003p151}. +" We used three radial bins for our simulations: 0""«r10.2"", 0.2""c0.8"" and r3=3.5""."," We used three radial bins for our simulations: $0''18 only main sequence stars are present., This essentially assumes that for $m_\mathrm{K}>18$ only main sequence stars are present. + Figure 13 shows the densities used., Figure \ref{f8} shows the densities used. +" Using the assumed densities per magnitude we simulated stellar fields, using Gaussian profiles with a FWHM of 30mas-42 mas(magnitudedependent, FWH Mofrealsourcesinthedeconvolvedy frames)Ogot =,cosV , and&binningof13 ο mas/pix."," Using the assumed densities per magnitude we simulated stellar fields, using Gaussian profiles with a FWHM of $30\,$ $-\,42\,$ mas (magnitude dependent, to mimic the FWHM of real sources in the deconvolved frames) and a binning of $13\,$ mas/pix." +"F oreachimage,ας. thetarg simulated images "," For each image, the target star was placed in the center of a box of 12 pixels width and background stars fainter than the target star were added." +per magnitude bin., The positional error of the target star is given by the difference between input position and the position at which it is found back by fitting the star with a Gaussian profile plus a floor. + tomimicthe, We used up to $10^5$ simulated images per magnitude bin. +"The distribution of positional differences per magnitude bin was then fit with a Gaussian, the width of which estimates the position error."," The distribution of positional differences per magnitude bin was then fit with a Gaussian, the width of which estimates the position error." + The resulting errors as a function of magnitude are shown in figure 13.., The resulting errors as a function of magnitude are shown in figure \ref{f8}. +" For the S-stars cluster (r< 0.8"") the error due to unrecognized confusion is of similar magnitude as the error due to halo noise.", For the S-stars cluster $r\lesssim0.8''$ ) the error due to unrecognized confusion is of similar magnitude as the error due to halo noise. +" For larger radii, the confusion induced error is smaller than the halo noise as the stellar densities drop rapidly with radius."," For larger radii, the confusion induced error is smaller than the halo noise as the stellar densities drop rapidly with radius." +" The increase of confusion error with stellar magnitude is well described by a power law of type Cx10°4""* (as the halo noise)."," The increase of confusion error with stellar magnitude is well described by a power law of type $C \times 10^{0.4\, m_\mathrm{K}}$ (as the halo noise)." +" Currently, relativistic effects have not yet been detected in the data of any star orbiting the GC MBH."," Currently, relativistic effects have not yet been detected in the data of any star orbiting the GC MBH." +" Actually, detecting 6? effects will be possible probably first in radial velocity measurements (?).."," Actually, detecting $\beta^2$ effects will be possible probably first in radial velocity measurements \citep{Zucker:2006p194}." + Astrometrically detectable deviations from Newton's law have not yet been seen in the GC., Astrometrically detectable deviations from Newton's law have not yet been seen in the GC. +" Vice versa, the effects can currently be neglected in the analysis."," Vice versa, the effects can currently be neglected in the analysis." +" Still, a few effects are worth discussing here."," Still, a few effects are worth discussing here." + We have analyzed a multitude of error sources that potentially influence and bias stellar positions as obtained from adaptive optics assisted imaging data in crowded, We have analyzed a multitude of error sources that potentially influence and bias stellar positions as obtained from adaptive optics assisted imaging data in crowded +"relie200 sinmlatious. respectively,","$relic200$ simulations, respectively." + We choose to ouly fit halos above this π��πά mass because at siialler scales additional plysics such as cooling not iucluded im our sinulatious would possibly stronely affect the emission., We choose to only fit halos above this minimum mass because at smaller scales additional physics such as cooling not included in our simulations would possibly strongly affect the emission. + Additionally. we do not capture smedl mass halos that are Likely moving through these small clusters possibly creating a large fraction of the total radio enission.," Additionally, we do not capture small mass halos that are likely moving through these small clusters possibly creating a large fraction of the total radio emission." + Because our simulation data does not have a measurable uncertainty for a given radio power. we have to use an alternate method of determining the error estinates of our paranueters.," Because our simulation data does not have a measurable uncertainty for a given radio power, we have to use an alternate method of determining the error estimates of our parameters." + We first fud the best fit parameters using a uniform weighting., We first find the best fit parameters using a uniform weighting. + By caleulatiug the residuals for cach point from this best-fit relation. we estimate the muiform error for cach point as the standard deviation of this residual.," By calculating the residuals for each point from this best-fit relation, we estimate the uniform error for each point as the standard deviation of this residual." + We then ft the data again using this error to obtain the uncertainty estimates in cach parameter., We then fit the data again using this error to obtain the uncertainty estimates in each parameter. + The values of these parameters are shown inTable 1.., The values of these parameters are shown inTable \ref{tab:fitpars}. . +Amendola L. D. Tocehini-Valentini. astro-ph/0111535.Phys.,"Amendola L. D. Tocchini-Valentini, astro-ph/0111535, Phys." +" Rev.D66.. 043!cVTble Amendola L.. C. Quercellini. D. Tocehini-Valentini and. A. ακοή, (2002) ph/0205097 Amendola L.. M. Gasperini. D. Tocchini-Valentini and C. Unearelli. (2002) Baccigalupi C...A. Balbi. ο, Matarrese. F. Perrotta. N. Vittorio. astro-ph/0109007. Phys."," Rev., 043528 Amendola L., C. Quercellini, D. Tocchini-Valentini and A. Pasqui, (2002) astro-ph/0205097 Amendola L., M. Gasperini, D. Tocchini-Valentini and C. Ungarelli, (2002) Baccigalupi C., A. Balbi, S. Matarrese, F. Perrotta, N. Vittorio, astro-ph/0109097, Phys." +Rev. (2002) Dahcall N. et al.,Rev. (2002) Bahcall N. et al. + 2002. Dean R. Melehiorri A.. astro-ph/0110472. Phys.," 2002, Bean R. Melchiorri A., astro-ph/0110472, Phys." +Rev. (2002) Benilez N. et al.. (,"Rev. (2002) Benitez N. et al., (" +2002) Bonanno A. M. Reuter (2002) Phys.,2002) Bonanno A. M. Reuter (2002) Phys. + Lett., Lett. + D 527. Caldwell BR... Dave R. Steinhardt DJ. (1993). Phys.," B 527, Caldwell R.R., Dave R. Steinhardt P.J. (1998), Phys." + Rev. Lett., Rev. Lett. + 80. 1582 Carvalho J.C... J.A.S. Lima. Ll. Waga. Rev.D46::2404-2407.1992 Chimento L.P.. A. $. Jakubi D. Pavon. Phys.," 80, 1582 Carvalho J.C., J.A.S. Lima, I. Waga, :2404-2407,1992 Chimento L.P., A. S. Jakubi D. Pavon, Phys." + Rev.D62.. OS (2000). Corasaniti E. Copeland. Phys.," Rev., 063508 (2000), astro-ph/0005070; Corasaniti E. Copeland, Phys." +Hev. (2002) Damour Esposito-Farese G.. Class.,"Rev. (2002) Damour Esposito-Farese G., Class." + Quantum Gray., Quantum Grav. + 9. 2093 Damour T. Nordtvedt Ix.. Plivs.," 9, 2093 Damour T. Nordtvedt K., Phys." + Rev. Lett., Rev. Lett. + 70. 2217 Damour T.. G. W. Gibbons and C. Gundlach. Phys.," 70, 2217 Damour T., G. W. Gibbons and C. Gundlach, Phys." + Rev. Lett..," Rev. Lett.," + 64. 123. Dalal N. et al..," 64, 123, Dalal N. et al.," + Phys., Phys. + Rev. Lett..," Rev. Lett.," +87.. 141802 De Bernarclis et al., 141302 De Bernardis et al. +Nature, Nature +lhuninostv iu the range 1l«1007l0Peres +.,"luminosity in the range $\rm 1\times 10^{42} < Ly\alpha < +1.5 \times 10^{43} erg \; s^{-1}$ ." + Here we assumed that the LLF docs not evolve from :—6.6 to :—7.1., Here we assumed that the LF does not evolve from $z$ =6.6 to $z$ =7.7. + Each galaxy was then assigned a raudonm redshift τε«tolg where ze andl zy correspoud to the minima and imaxiuuui wavelengths where the trausuüssion of the UND filter drops to zero., Each galaxy was then assigned a random redshift $z_{L} < z < z_{H}$ where $z_{L}$ and $z_{H}$ correspond to the minimum and maximum wavelengths where the transmission of the UNB filter drops to zero. +" Next. to each galaxy we assigned a flux F=Lis,Ind; where dp is the luminosity distance."," Next, to each galaxy we assigned a flux $\rm F=L_{Ly\alpha}/4\pi d_{L}^{2}$ where $\rm d_{L}$ is the luminosity distance." + We distribute this flux in waveleneth using an asviunietrie hue profile drawn from the +=5.7 spectra of Rhoadsetal. (2003).., We distribute this flux in wavelength using an asymmetric line profile drawn from the $z=5.7$ spectra of \citet{rho03}. . + The flux transiuitted through the UND filter was then determined as feesffxTadd (where Ty is the filter transmission and fy the fux density of the cluission line).," The flux transmitted through the UNB filter was then determined as $f_{trans} = \int f_\lambda T_\lambda +d\lambda$ (where $T_\lambda$ is the filter transmission and $f_\lambda$ the flux density of the emission line)." + This accounts for the loss of the flux that results from a filter whose width is comparable to the line width (and not much greater as would be the case for a filter)., This accounts for the loss of the flux that results from a filter whose width is comparable to the line width (and not much greater as would be the case for a filter). + We then created a histogram of magnitudes after converting the couvolved fiux to magnitudes calculated using the following relation: and with e the speed of light., We then created a histogram of magnitudes after converting the convolved flux to magnitudes calculated using the following relation: and with $c$ the speed of light. + Lastly. to include the instrumental effects. we multiplied the ΡΟ of galaxies in cach maeuitude biu bv the corresponding recovery fraction obtained frou our artificial source simulations in our UND image(sece section 2.1).," Lastly, to include the instrumental effects, we multiplied the number of galaxies in each magnitude bin by the corresponding recovery fraction obtained from our artificial source simulations in our UNB image(see section 2.4)." + We then converted cach magnitude bin to a ]huunünositv biu. and counted the nuuber of detected ealaxies iu cach hunuinositv biu.," We then converted each magnitude bin to a luminosity bin, and counted the number of detected galaxies in each luminosity bin." + We repeated this simulation teu times. aud taking au average. we found that about one eenitter should be expected im our survey.," We repeated this simulation ten times, and taking an average, we found that about one emitter should be expected in our survey." + It should be noted that we assumed a nou-evolving LLF from :26.6 to τιfadτν and that every ecnmütter has the same asviuuetrie line profile.," It should be noted that we assumed a non-evolving LF from $z$ =6.6 to $z$ =7.7, and that every emitter has the same asymmetric line profile." + While we expect about one eenuütter iun our survey there are huge uncertainties mainly due to the Poisson noise. aud field to field variation or cosmic variance.," While we expect about one emitter in our survey there are large uncertainties mainly due to the Poisson noise, and field to field variation or cosmic variance." + Tibietal.(20090) have estimated feld to field variation of οσους to be 230% for a volume and flux limited ssurvey with a survey volue ~2100Mpc?., \citet{til09} have estimated field to field variation of emitters to be $\gtrsim 30\%$ for a volume and flux limited survey with a survey volume $\rm \sim 2 \times 10^{5} \; Mpc^{3}$. + We expect a larger field to field variation for suialler survey volutes., We expect a larger field to field variation for smaller survey volumes. + We also estimated the cosmic variance expected im our survey using the cosmic variance caleulator (Trenti&Sti-avelli 20083., We also estimated the cosmic variance expected in our survey using the cosmic variance calculator \citep{tre08}. +. For our survey we should expect à cosnic variance of about 5854 assuming au intrinsic uuuber of ssourees at lo=fad in agreement with a non-evolviug LLF from :=6.6 (Iwashikawaetal.2006) to --7.7., For our survey we should expect a cosmic variance of about $58\%$ assuming an intrinsic number of sources at $z=7.7$ in agreement with a non-evolving LF from $z=6.6$ \citep{kas06} to $z=7.7$. + On the other hand our caudidate counts are quite consistent with the buninosity function at z=5.7 2004)).., On the other hand our candidate counts are quite consistent with the luminosity function at z=5.7 \citep{ouc09}. . + Using a large sample of candidates. (2008) fouud no aut evolution of LLF between : siguific Land :—5.7.," Using a large sample of candidates, \citet{ouc08} found no significant evolution of LF between $z$ =3.1 and $ z$ =5.7." + The evolution of the LLF between 2 —5.7 aud :=6.5 is not conclusive., The evolution of the LF between $z=$ 5.7 and $z=6.5$ is not conclusive. + For exaniple. Malliotra&Rhoads(2001) found no significant evolution of LLFbetween 2=5.7 aud :=6.5. while IashikawactinH.(2006) sugeest an evolution of bright cud of the LE this redshift range.," For example, \citet{mr04} found no significant evolution of LF between $z$ =5.7 and $z=6.5$, while \citet{kas06} suggest an evolution of bright end of the LF in this redshift range." + Ou the theoretical frout. several models(Thomunes&Aeiscnheiner2005:Furlanettoot9) havebeen developed to predict redshift evolutiou of the LLF.," On the theoretical front, several models \citep{tho05,fer05, del06, dij07,kob07,mcq07, day08, nag08,sam09,til09} have been developed to predict redshift evolution of the LF." + While several imiodoels (6.8.Sammictal.2009:etal.2009) predict no significant evolution of LLF at :€7. the predictions differ greatly amoug different models.," While several models \citep[e.g.][]{sam09, til09} predict no significant evolution of LF at $z\lesssim 7$, the predictions differ greatly among different models." + These differeuces among the models can be attributed to differiug input assumptions. which in turn stem from our iniperfect undoerstaudius of the physical nature of aoeealaxies. aud from the simall samples currently availableat lieh redshift.," These differences among the models can be attributed to differing input assumptions, which in turn stem from our imperfect understanding of the physical nature of galaxies, and from the small samples currently availableat high redshift." + At 2> 6.5. there are ouly a few searches for celitters.," At $z>$ 6.5, there are only a few searches for emitters." + Iveetal.(2006). found. one spectroscopically confirmed LAE at :=6.96. audcurrently there are no spectroscopically confirmed LAEs at :> ," \citet{iye06} found one spectroscopically confirmed LAE at $z$ =6.96, andcurrently there are no spectroscopically confirmed LAEs at $z>$ 7." +However. there are few photometric searches for," However, there are few photometric searches \citep{par94, wil05, cub07, hib09} for" +Observations of Active Galactic Nuclei (AGN) have revealed tha many of them are partially obscured by material in our line of sight. within the inner tens of parsecs of the central engine (e.g. ? and ? or a review).,"Observations of Active Galactic Nuclei (AGN) have revealed that many of them are partially obscured by material in our line of sight, within the inner tens of parsecs of the central engine (e.g. \citealt*{risaliti99} and \citealt*{maiolino&risaliti07} for a review)." +" This obscuring material will influence both the AG and our observations. and the study of its properties is fundamenta or an unbiased understanding o"" AGN physics."," This obscuring material will influence both the AGN and our observations, and the study of its properties is fundamental for an unbiased understanding of AGN physics." + The gas arounc he nucleus will be under the efect of the inward gravitationa orce of the supermassive black 10le and the outward pressure of he radiation emitted in the cenral region., The gas around the nucleus will be under the effect of the inward gravitational force of the supermassive black hole and the outward pressure of the radiation emitted in the central region. + By investigating the balance between these two forces. one can predict the behaviour of the gas.," By investigating the balance between these two forces, one can predict the behaviour of the gas." +" The Eddington luminosity. £p. is defined as the value at which the radiation pressure balances the gravitational force of he black hole: £=Ly. with Le=4taCimedlyfor. where G is the gravitational constant. m, the proton mass. ο the speed of ight. Mig the mass of the black hole and op the cross-section for Thomson scattering."," The Eddington luminosity, $L_{\rm E}$, is defined as the value at which the radiation pressure balances the gravitational force of the black hole: $L = L_{\rm E}$, with $L_{\rm E}=4\pi Gm_{\rm p}cM_{\rm BH}/\sigma_{\rm T}$, where G is the gravitational constant, $_{\rm p}$ the proton mass, c the speed of light, $M_{\rm BH}$ the mass of the black hole and $\sigma_{\rm T}$ the cross-section for Thomson scattering." + The Eddington ratio (A=£/ Lp). is then a measure of the balance between these two forces. for a certain AMyg.," The Eddington ratio $\lambda = L/L_{\rm E}$ ), is then a measure of the balance between these two forces, for a certain $M_{\rm BH}$." + In the presence of dust. the gas couples with the dust grains via Coulomb interactions and the cross-section for the interaction with photons is considerable enhanced.," In the presence of dust, the gas couples with the dust grains via Coulomb interactions and the cross-section for the interaction with photons is considerable enhanced." + The effective cross-section for dusty gas can be defined as 4=shor with a boost factor .1 (2.. 2.. 2).," The effective cross-section for dusty gas can be defined as $\sigma_{\rm d}=A\sigma_{\rm T}$ with a boost factor $A$ \citealt{fabiancelottierlund06}, \citealt*{fabian&vasudevan08}, \citealt{fabian09}) )." + We can then determine an effective Eddington ratio for dusty gas as a function of the classical Eddington ratio: It follows that. A= L/-Lis now the limit at which the radiation pressure from the black hole is able to expel the mass of dusty gas around it.," We can then determine an effective Eddington ratio for dusty gas as a function of the classical Eddington ratio: It follows that, $\lambda = 1/A$ is now the limit at which the radiation pressure from the black hole is able to expel the mass of dusty gas around it." + 2 and ? explored the effective Eddington limit for dusty gas by investigating the properties of AGN samples in the Deep Field South (CDF-S). Lockman Hole and in the local Universe. and found that the objects tend to lie below their effective Eddington limit. as expected.," \cite{fabian&vasudevan08} and \cite{fabian09} explored the effective Eddington limit for dusty gas by investigating the properties of AGN samples in the Deep Field South (CDF-S), Lockman Hole and in the local Universe, and found that the objects tend to lie below their effective Eddington limit, as expected." + AGN are expected to interact with the surrounding galaxy. affecting its evolution.," AGN are expected to interact with the surrounding galaxy, affecting its evolution." + In fact. there is evidence of a close," In fact, there is evidence of a close" +as a random realization of some DF. then each value calculated in this system can be considered as a random variable.,"as a random realization of some DF, then each value calculated in this system can be considered as a random variable." + Let Q; be random variable defined as the value Q calculated in piece i., Let $Q_i$ be random variable defined as the value $Q$ calculated in piece $i$. + For example. if the two systems under consideration are just two random realization of the same DF. then 4; and q»; are two samples of the random variable Q;.," For example, if the two systems under consideration are just two random realization of the same DF, then $q_{1,i}$ and $q_{2,i}$ are two samples of the random variable $Q_i$." + We can estimate the variance of this random variable., We can estimate the variance of this random variable. + Let var); and var»; be estimates of the variance of Q; calculated for the first and the second system. respectively. and let us consider the value (KenneyandKeeping.1951).. (KenneyandKeeping.1951.p.164).. (AT))," Let $var_{1,i}$ and $var_{2,i}$ be estimates of the variance of $Q_i$ calculated for the first and the second system, respectively, and let us consider the value \citep{K51}. \citep[p. 164]{K51}. \ref{eq_c})" +"Cy; (solid). c,,; (dotted). aud s (dashed).","$e_{y,z}$ (solid), $e_{y,z}$ (dotted), and $s$ (dashed)." + Note that Chu(Ng). and ον(kg). are zero. for ky because of the periodic boundaries.," Note that $e_{z,y}(k_0)$ and $e_{z,x}(k_0)$ are zero for $k_0$ because of the periodic boundaries." +" The shear term s primarily drives the variation of |B,(hy)P. fippiug sign as [B.Ahy)? goes to zero."," The shear term $s$ primarily drives the variation of $|\tilde{B}_y(k_0)|^2$, flipping sign as $|\tilde{B}_x(k_0)|^2$ goes to zero." + In contrast. ον. 1s generally negative. acting as turbulent resistivity.," In contrast, $e_{x,z}$ is generally negative, acting as turbulent resistivity." +" The ος(0) term is more crratic, frequently flipping sign over a sinele cycle. but the net effect is an overall oscillation of [D(&9)|? over ~7 orbital periods."," The $e_{y,z}(k_0)$ term is more erratic, frequently flipping sign over a single cycle, but the net effect is an overall oscillation of $|\tilde{B}_x(k_0)|^2$ over $\sim 7$ orbital periods." + Tu many respects. the behavior we see in the stratified «λατοις is simular to that observed in the uustratified. zoro-uet flux calculations of Lesur&Ogilvie(2008).," In many respects, the behavior we see in the stratified simulations is similar to that observed in the unstratified, zero-net flux calculations of \citet{lo08}." + Using au incompressible spectral code. they find dynamo evcles with a ~5 orbit periodicity.," Using an incompressible spectral code, they find dynamo cycles with a $\sim 5$ orbit periodicity." + This is similar to the oscillatious in our stratified runs where rms power on large scales is broadly distributed ou times scales ~610 orbits (see Figure 7))., This is similar to the oscillations in our stratified runs where rms power on large scales is broadly distributed on times scales $\sim 6-10$ orbits (see Figure \ref{f:kvsf}) ). + The normalized quantities plotted in Figure 17. are to them Equation (16)., The normalized quantities plotted in Figure \ref{f:emft} are to their Equation (16). + Comparison of Figure 17 with Figs, Comparison of Figure \ref{f:emft} with Figs. + [| aud 5 in their paper. show that the behavior of the EMES during oscillations are also quite simular. sugeesting that a common (or. at least. related) niechanisni iav be respousible for these oscillations.," 4 and 5 in their paper, show that the behavior of the EMFs during oscillations are also quite similar, suggesting that a common (or, at least, related) mechanism may be responsible for these oscillations." + This motivates a more detailed comparison between uustratified and stratified ruus in future work., This motivates a more detailed comparison between unstratified and stratified runs in future work. + Although it is useful to focus ou the vertical wave vectors when trving to understand properties of large scale fields. an understanding of the overall powcr spectrum beuefits from an analysis of the shell integrated quantities.," Although it is useful to focus on the vertical wave vectors when trying to understand properties of large scale fields, an understanding of the overall power spectrum benefits from an analysis of the shell integrated quantities." + We plot the time aud shell average EMES terms in Figure 18. for S32R1Z1 (black) S6LRIZL (blue). and SI28RIZLE (red).," We plot the time and shell average EMFs terms in Figure \ref{f:emf} for S32R1Z4 (black) S64R1Z4 (blue), and S128R1Z4 (red)." + As iu Figure 17.. these quantities are normalized by the shell inteerated power spectra.," As in Figure \ref{f:emft}, these quantities are normalized by the shell integrated power spectra." + Each normalized term is then time averaged frou 50-300 orbits., Each normalized term is then time averaged from 50-300 orbits. + Since the amplitudes of the maguctic energv densities ποσα to be in statistical steady states over this period. we prestune the left haud sides of (12)) and (13)) are nearly zero.," Since the amplitudes of the magnetic energy densities seem to be in statistical steady states over this period, we presume the left hand sides of \ref{eq:fourx}) ) and \ref{eq:foury}) ) are nearly zero." + Therefore the sum of the terms in each panel must be balanced by uuucerical dissipation ternis. as discussed iu previous work (Fromang&Papaloizou," Therefore the sum of the terms in each panel must be balanced by numerical dissipation terms, as discussed in previous work \citep{fp07,shb09}." +" Iu the top panel we plot the terms οςμή) (solid) and ορ) (dotted) which coutribute to evolution of D,."," In the top panel we plot the terms $e_{z,y}(k)$ (solid) and $e_{y,z}(k)$ (dotted) which contribute to evolution of $B_x$." + At the large scales. we find that the c. terii is more inrportant for Ποια ecucration and its normalized amplitude is nearly independent of resolution.," At the large scales, we find that the $e_{z,y}$ term is more important for field generation and its normalized amplitude is nearly independent of resolution." +" The «,,.- termi is simaller iu amplitude and slightly negative as large scales."," The $e_{y,z}$ term is smaller in amplitude and slightly negative as large scales." + Even though ορ. teuds to oscillates about zero over an individual dynamo cvele while ος ustially renmuus positive. the amplitude of ος 38 generally larecr. so the dominance of e; at large scales isnot sinply the result of time averaging.," Even though $e_{y,z}$ tends to oscillates about zero over an individual dynamo cycle while $e_{z,y}$ usually remains positive, the amplitude of $e_{z,y}$ is generally larger, so the dominance of $e_{z,y}$ at large scales is simply the result of time averaging." +" As one moves to smaller scales. ο Visesand eventually dominates the geucration of B,.."," As one moves to smaller scales, $e_{y,z}$ risesand eventually dominates the generation of $B_x$." + The characteristic vaveuumber at which the crossing occurs shifts to higher values as the resolution increases., The characteristic wavenumber at which the crossing occurs shifts to higher values as the resolution increases. +" The bottom. panel shows ¢..(4) (solid). ον.) (dotted) aud s (dashed). the terms which contribute growth in B,."," The bottom panel shows $e_{z,x}(k)$ (solid), $e_{x,z}(k)$ (dotted) and $s$ (dashed), the terms which contribute growth in $B_y$." +" At large scales growth of B, is dominated bv the shear term. while both 6. aud ορ. are of comparable magnitude and negative."," At large scales growth of $B_y$ is dominated by the shear term, while both $e_{z,x}$ and $e_{x,z}$ are of comparable magnitude and negative." +" At small scales. €, and ος both grow. becoming positive and dominating over the shear term."," At small scales, $e_{z,x}$ and $e_{x,z}$ both grow, becoming positive and dominating over the shear term." + Again. the wavemmuber of the crossover Hiereases with resolutio1.," Again, the wavenumber of the crossover increases with resolution." + Authors have often focused oi horizontally average properties of the flow or (equivaleutlv) the power spectral variation onlv along vertical wav| vectors (οιFromanediscussed above)..," Authors have often focused on horizontally average properties of the flow or (equivalently) the power spectral variation only along vertical wave vectors \citep[e.g][ which were discussed +above]{fp07,lo08}." + We note that the behavior of ομ.. aud exy we lave described diffCrs slenificantly frou what one would iufer if ouly verical wavevectors were considered.," We note that the behavior of $e_{y,z}$ and $e_{z,y}$ we have described differs significantly from what one would infer if only vertical wavevectors were considered." + As previously mcutiored. the svuuuetries of the periodic box force ονμή.) to be zero. and oulv Cyzv) contributes.," As previously mentioned, the symmetries of the periodic box force $e_{z,y}(k_z)$ to be zero, and only $e_{y,z}(k_z)$ contributes." + However. it is clear from Figure Ls that the vertical EMF and its toroidal variation is also esseutial for uuderstaudiug the mechanism which sustains turbulence in these simulations.," However, it is clear from Figure \ref{f:emf} that the vertical EMF and its toroidal variation is also essential for understanding the mechanism which sustains turbulence in these simulations." + The question remains as to why the addition. of stratification leads to couvergence iu the turbulent stresses and cherey densities., The question remains as to why the addition of stratification leads to convergence in the turbulent stresses and energy densities. + One possibility is that development of local toroidal field is key to sustainiug turbulence iu both stratified and wustratified domains., One possibility is that development of local toroidal field is key to sustaining turbulence in both stratified and unstratified domains. + It is possible that the strength of toroidal field is eutirely set bv the resolution in unstratified domains. while stratified domains offer a characteristic scale which is independent of resolution. duc to the action of the large scale dvnamo.," It is possible that the strength of toroidal field is entirely set by the resolution in unstratified domains, while stratified domains offer a characteristic scale which is independent of resolution, due to the action of the large scale dynamo." + Indeed. it has already been demonstrated (e.g.Hawleyetal.1995:Sinon&2009) that a elobal net toroidal field leads to enhanced turbulent enerev densitics aud stresses. aud leads to couvergeuce in the stress as resolution inereses (Caranetal. 2009)..," Indeed, it has already been demonstrated \citep[e.g.][]{hgb95,sh09} that a global net toroidal field leads to enhanced turbulent energy densities and stresses, and leads to convergence in the stress as resolution increses \citep{gua09}. ." + Furthermore. our sinmlatious show a correlation between the stress and the streugth of the mean toroidal field. both elobally in the two scale height averages (Table," Furthermore, our simulations show a correlation between the stress and the strength of the mean toroidal field, both globally in the two scale height averages (Table" +A trivial solution of equation (5)) is both .X=laud Y—Lin the meridional plane wherein the perturbing object lies (42=0). which indicates the (vertically) highest intersecting points between the outer and inmer boundaries. le.. the extension limit of the intensively perturbed region.,"A trivial solution of equation \ref{equ:mor}) ) is both $X=1$ and $Y=1$ in the meridional plane wherein the perturbing object lies $\varphi=0$ ), which indicates the (vertically) highest intersecting points between the outer and inner boundaries, i.e., the extension limit of the intensively perturbed region." + X=1 aud Y—1 staud for au ellipse aud a hyperbola. by definition. with the common foci at the location of the perturber and the mirror point about the orbital axis.," $X=1$ and $Y=1$ stand for an ellipse and a hyperbola, by definition, with the common foci at the location of the perturber and the mirror point about the orbital axis." +" However. both .X=1 aud Y=1 actually correspoud to the same formula for a hyperbola since we only consider the shape of a wake induced by a supersonic perturber (M4,>1)."," However, both $X=1$ and $Y=1$ actually correspond to the same formula for a hyperbola since we only consider the shape of a wake induced by a supersonic perturber $\mach>1$ )." +" The vertex of the hyperbola. r/ry=Mj,! correspouds to the distance of the junction between the outer aud inner arm boundaries in the orbital plane."," The vertex of the hyperbola, $r/r_p=\mach^{-1}$, corresponds to the distance of the junction between the outer and inner arm boundaries in the orbital plane." +" The extension limit of the high density ares in the vertical direction is simplified to the asyimptotes of the lyperbola. which are overlaid by black lines in Figure Lbb. This tuclicates that the angular size of the ares is 21anον—13E?, further extended with higher orbital Mach number."," The extension limit of the high density arcs in the vertical direction is simplified to the asymptotes of the hyperbola, which are overlaid by black lines in Figure \ref{fig:ptm}b b. This indicates that the angular size of the arcs is $2\tan^{-1}(\mach^2-1)^{1/2}$, further extended with higher orbital Mach number." +" This vertical stretch. however. does not depend very strougly on «τρ except for near unity (1.e.. 607-— (lor M,z 2)."," This vertical stretch, however, does not depend very strongly on $\mach$ except for near unity (i.e., – for $\mach\ge2$ )." + Iu Figure Lbb iudividual segments of the boundaries. satisfying equation (5)). appear to be circular arcs about the centers at either the object position or the mirror point.," In Figure \ref{fig:ptm}b b individual segments of the boundaries, satisfying equation \ref{equ:mor}) ), appear to be circular arcs about the centers at either the object position or the mirror point." +" In the plane of the object (422 Orr 0).the ares extended from the outer boundaries of the spiral arm in Figure laa (Le. r/ry=1. 1-222MI. b+ME,T 14+Gs MET. 1+80M, T. and 1+108PpE at z/ry 0) center around the perturbing object at. (e.2)/rg=(1.0)."," In the plane of the object $\varphi=0$ ; $x>0$ ),the arcs extended from the outer boundaries of the spiral arm in Figure \ref{fig:ptm}a a (i.e., $x/r_p=1$, $1+2\pi\mach^{-1}$, $1+4\pi\mach^{-1}$, $1+6\pi\mach^{-1}$ $1+8\pi\mach^{-1}$ , and $1+10\pi\mach^{-1}$ at $z/r_p=0$ ) center around the perturbing object at $(x,z)/r_p=(1,0)$." + These concentric arcs have endpoints on the hyperbola defined in equation (9)) (or. the asymptotes in eq. [10]]).," These concentric arcs have endpoints on the hyperbola defined in equation \ref{equ:hyp}) ) (or, the asymptotes in eq. \ref{equ:asy}] ])," +" except for the point (not visible) at the perturber position and the curve passing througl ο...25M,LO). which completes its full circle."," except for the point (not visible) at the perturber position and the curve passing through $(x,z)/r_p=(1+2\pi\mach^{-1},0)$, which completes its full circle." +" The inner :-intercept of this circle at /ry=1—23M,! actually corresponds to the inner edge of the curved Mach cone. which is cousidered as a part of the outer arm boundary (see relsec:spi)) aud. here. tliis is clarified."," The inner $x$ -intercept of this circle at $x/r_p=1-2\pi\mach^{-1}$ actually corresponds to the inner edge of the curved Mach cone, which is considered as a part of the outer arm boundary (see \\ref{sec:spi}) ) and, here, this is clarified." + Ou the other haud. the arcs crossing the inner arin boundaries on this side Gr> 0) have the center at the mirror point (e.2)/ry=(71.0). resulting in larger radii compared to the radii of the outer counterparts.," On the other hand, the arcs crossing the inner arm boundaries on this side $x>0$ ) have the center at the mirror point $(x,z)/r_p=(-1,0)$, resulting in larger radii compared to the radii of the outer counterparts." +" The outer boundaries ou the opposite side Gr« 0). Le.. the ares having intercepts at ur/ry=—1—aM,| -]1—SUME,| -1-onME, οDOM,B aud —1-—Us.ME,. are concentric about the mirror point of the object. Gr.2)/ry=(-1.0)."," The outer boundaries on the opposite side $x<0$ ), i.e., the arcs having intercepts at $x/r_p=-1-\pi\mach^{-1}$, $-1-3\pi\mach^{-1}$, $-1-5\pi\mach^{-1}$, $-1-7\pi\mach^{-1}$, and $-1-9\pi\mach^{-1}$, are concentric about the mirror point of the object, $(x,z)/r_p=(-1,0)$." + On this side Ge« 0). iustead. the center of the inner boundaries is at the objectposition. Cr.z)/ry= (1.0).," On this side $x<0$ ), instead, the center of the inner boundaries is at the objectposition, $(x,z)/r_p=(1,0)$ ." + The inner aud outer boundaries. in fact. constitute the same circles. which is better visualized in Figure 2. for the number of perturbations.," The inner and outer boundaries, in fact, constitute the same circles, which is better visualized in Figure \ref{fig:num} for the number of perturbations." + Particularly.the largest sphere about," Particularly,the largest sphere about" +"very long ""filaments? in the bottom panel of Figure 10..",very long “filaments” in the bottom panel of Figure \ref{fig:S4densityglobus}. + This cluster is a remnant οἱ cloud 1. and its mass is ~3000 solar Dlasses.," This cluster is a remnant of cloud 1, and its mass is $\sim 3000$ solar masses." + In fact most of the stars in simulations $83 and 84 belong to a cluster., In fact most of the stars in simulations S3 and S4 belong to a cluster. + This clustered mode of star formation in the fast-cooling runs is due to the gas collapsing promptly and thus forming very massive dense gas halos., This clustered mode of star formation in the fast-cooling runs is due to the gas collapsing promptly and thus forming very massive dense gas halos. + We suspect that these results would have been dillerent had. we been able to treat radiative feedback from star formation in our simulations., We suspect that these results would have been different had we been able to treat radiative feedback from star formation in our simulations. + We note that in such a dense environment. any feedback from star formation activity. such as radiation or outflows. would not have been able to escape easily and would therefore. have heated the surrounding. gas. suppressing further fragmentation and increasing the Jeans mass (??7).," We note that in such a dense environment, any feedback from star formation activity, such as radiation or outflows, would not have been able to escape easily and would therefore have heated the surrounding gas, suppressing further fragmentation and increasing the Jeans mass \citep{Nayakshin06a,KrumholzEtal07}." +. Rather than the multiple low-mass stars in a cluster we would perhaps have seen fewer but higher mass stars., Rather than the multiple low-mass stars in a cluster we would perhaps have seen fewer but higher mass stars. + The mass spectrum of stars would. probably also change if the colliding clouds had net rotation. (spin) or a turbulent structure before the collision. providing some stability against collapse.," The mass spectrum of stars would probably also change if the colliding clouds had net rotation (spin) or a turbulent structure before the collision, providing some stability against collapse." + All these effects are however minor as far as orbital motion of the stars is concerned. which is the focus of our paper.," All these effects are however minor as far as orbital motion of the stars is concerned, which is the focus of our paper." + Simulation $4 is the fast-cooling equivalent of 82., Simulation S4 is the fast-cooling equivalent of S2. + As such. the inner gaseous disc in S4 is subject to a similar intermittent infall of gas [rom larger radii.," As such, the inner gaseous disc in S4 is subject to a similar intermittent infall of gas from larger radii." + The newly arriving gas tweaks the disc orientation signilicantly. causing it to undergo midplane rotation (refer back to ?7)).," The newly arriving gas tweaks the disc orientation significantly, causing it to undergo midplane rotation (refer back to \ref{sec:s2dynamics}) )." + The cdillerence here however is that disc is fragmenting into stars whilst its orientation is changing., The difference here however is that disc is fragmenting into stars whilst its orientation is changing. + Interestingly. these stars do not follow the evolving disc orientation but rather remain in their original configuration.," Interestingly, these stars do not follow the evolving disc orientation but rather remain in their original configuration." +" This is clearly seen in Figure 11.. where the stellar. disc remembers the ""old"" orientation of the gaseous disc in which the stars were born. whereas the gaseous. disc evolves to quite a different orientation."," This is clearly seen in Figure \ref{fig:S4_inner_disk}, where the stellar disc remembers the “old” orientation of the gaseous disc in which the stars were born, whereas the gaseous disc evolves to quite a different orientation." + The possibility of this effect taking place was suggested by ?).., The possibility of this effect taking place was suggested by \cite{NC05}. + Phese authors found that stars will not follow clisc midplane changes if these occur faster than the “critical rotation time”. which is estimated to be about 500 code units lor the disc in Figure 11..," These authors found that stars will not follow disc midplane changes if these occur faster than the “critical rotation time”, which is estimated to be about 500 code units for the disc in Figure \ref{fig:S4_inner_disk}." + Our simulations are thus consistent with these predictions as the disc orientation changed on a timescale of just SO code units., Our simulations are thus consistent with these predictions as the disc orientation changed on a timescale of just $80$ code units. + As a result of a several star forming events in gaseous discs of dilferent orientations. the inner stellar disc in 84 is very much different from that found in S2. and even more so when compared to S1.," As a result of a several star forming events in gaseous discs of different orientations, the inner stellar disc in S4 is very much different from that found in S2, and even more so when compared to S1." + In the latter cases. when cooling is more gradual (io. ο)= 1). stars only form in the inner gaseous disc once it has settled into a relatively stable orientation.," In the latter cases, when cooling is more gradual (i.e. $\beta=1$ ), stars only form in the inner gaseous disc once it has settled into a relatively stable orientation." + Hence the resulting distribution of stars is corresponcingly thin (although in S2 it is significantly thicker than 81. ef," Hence the resulting distribution of stars is correspondingly thin (although in S2 it is significantly thicker than S1, cf." + Figure 6))., Figure \ref{fig:S1S2globus}) ). + Such a distribution is broacly consistent with the observed. orbits of voung massive stars in the clockwise disc in the GC (7).., Such a distribution is broadly consistent with the observed orbits of young massive stars in the clockwise disc in the GC \citep{PaumardEtal06}. + Due to gaseous disc midplane changes coupled with quicker fragmentation. then. the stellar disc in S4 is much thicker. with 7A-—I.," Due to gaseous disc midplane changes coupled with quicker fragmentation, then, the stellar disc in S4 is much thicker, with $H/R\sim 1$." + This particular simulation thus fails to account for the most prominent. feature of the observational data: namely. a thin inner stellar disc.," This particular simulation thus fails to account for the most prominent feature of the observational data; namely, a thin inner stellar disc." + Simulation S5 is somewhat distinct from all the rest due to its small impact. parameter. 6. between the gas clouds (see ‘Table 1).," Simulation S5 is somewhat distinct from all the rest due to its small impact parameter, $b$, between the gas clouds (see Table 1)." + Xs a result of this fact and the relatively laree value of 3. a higher degree of mixing is achieved.," As a result of this fact and the relatively large value of $\beta$, a higher degree of mixing is achieved." + Figure 12. shows a snapshot from this simulation. showing both gas and stars.," Figure \ref{fig:S5} shows a snapshot from this simulation, showing both gas and stars." +lensing. Sect.,"lensing, Sect." + 3. presents the adaptive contouring algorithm and Sect., \ref{sec:adaptive} presents the adaptive contouring algorithm and Sect. + + shows how to determine the magnification of an extended source star from the image contour line.," \ref{sec:area} + shows how to determine the magnification of an extended source star from the image contour line." + Sect., Sect. + 5. discusses the critical curves and caustics of a binary point-mass lens in order to derive an algorithm for finding a point inside an image stretching over a critical curve., \ref{sec:binary} discusses the critical curves and caustics of a binary point-mass lens in order to derive an algorithm for finding a point inside an image stretching over a critical curve. + Example light curves are shown in Sect., Example light curves are shown in Sect. + 6 before the paper concludes with a short summary in Sect. 7.., \ref{sec:lightcurves} before the paper concludes with a short summary in Sect. \ref{sec:summary}. +" Light received from a source object at distance Ds is bent due to the gravitational field of a thin sheet of matter at a distance 2i, with surface mass density X(£/) by the angle (2) For 8 denoting the true source position angle and @ the apparent position angle of its observed images. this implies theequation where w@=6/45. y=(DL/Ds) (9/0). and with (z)=ο0)2XGD0,2 )."," Light received from a source object at distance $D_\rmn{S}$ is bent due to the gravitational field of a thin sheet of matter at a distance $D_\rmn{L}$ with surface mass density $\Sigma({\vec \xi}')$ by the angle \citep{Schneider:theory} + For $\vec \beta$ denoting the true source position angle and $\vec \theta$ the apparent position angle of its observed images, this implies the where $\vec x = \vec \theta/\theta_0$, $\vec y = (D_\rmn{L}/D_\rmn{S})\,(\vec \beta/\theta_0)$ , and with $\kappa({\vec x}') = (D_\rmn{L}\theta_0)^2\,\Sigma(D_\rmn{L} \theta_0 +{\vec x}')$ ." + It provides a surjective mapping of the image position a to the source position g. but the lack of injectivity means that a source may have more than just one image.," It provides a surjective mapping of the image position $\vec x$ to the source position $\vec y$, but the lack of injectivity means that a source may have more than just one image." + At x. detined by two images merge. so that the number of images changes if and only if the source passes a pointy.=ylae).," At ${\vec x}_\rmn{c}$, defined by two images merge, so that the number of images changes if and only if the source passes a ${\vec y}_\rmn{c} = {\vec y}({\vec x}_\rmn{c})$." + In general. critical points and caustic points form. closed curves. known as and. unless. these degenerate into a point in special cases.," In general, critical points and caustic points form closed curves, known as and unless these degenerate into a point in special cases." + The conservation of surface brightness by gravitational lensing. It) Tyla]. /mplicsthattbetolalmagni ficationofapointsourecisgive so that it Uydiverges if the source comes to He on a caustic.," The conservation of surface brightness by gravitational lensing, $I(\vec x) = I[\vec y(\vec x)]$ , implies that the total magnification of a point source is given by so that it diverges if the source comes to lie on a caustic." + For an extended source. as a consequence of Liouville's theorem. source and lens contours of same brightness correspond.," For an extended source, as a consequence of Liouville's theorem, source and lens contours of same brightness correspond." + This means that if a source contour is described byan implicit function f(y:p)=0. with p being a parameter vector specifying the contour. then all its image contours are given by Py(a):p]= 0.," This means that if a source contour is described byan implicit function $F(\vec y; \vec p) = 0$, with $\vec p$ being a parameter vector specifying the contour, then all its image contours are given by $F[\vec y(\vec x); \vec p] = 0$ ." + Therefore. a contour plot provides image contour lines without inversion of the lens equation (2)..," Therefore, a contour plot provides image contour lines without inversion of the lens equation \citep{SK87}." + A search grid in the image plane needs to be large enough to cover all images and dense enough. so that no images or holes in the images are missed.," A search grid in the image plane needs to be large enough to cover all images and dense enough, so that no images or holes in the images are missed." + While fulfilling these two condition. the grid resolution should be kept as low as possible.," While fulfilling these two condition, the grid resolution should be kept as low as possible." + Obviouslv. an adaptive grid that just provides higher resolution in regions where this is required turns out to be superior to a fixed-resolution grid.," Obviously, an adaptive grid that just provides higher resolution in regions where this is required turns out to be superior to a fixed-resolution grid." + Such an adaptive grid can be built by hierachically nesting squares that represent parts of the image plane., Such an adaptive grid can be built by hierachically nesting squares that represent parts of the image plane. +In order to approximate the position of the contour line. a ray is shot to the corresponding image position given by the detined mapping. Eq. (5).,"In order to approximate the position of the contour line, a ray is shot to the corresponding image position given by the defined mapping, Eq. \ref{eq:lenseq}) )," + and it is noted whether the corresponding true source position falls inside or outside the source contour., and it is noted whether the corresponding true source position falls inside or outside the source contour. + In this respect. the proposed algorithm resembles the ray-shooting approach (22). but the indicator of whether the light ray hits the source is kept with the image position.," In this respect, the proposed algorithm resembles the ray-shooting approach \citep{KRS:rayshooting,SchneiWei:AGN}, but the indicator of whether the light ray hits the source is kept with the image position." + In fact. with the conservation of surface brightness. as pointed out in Sect. 2..," In fact, with the conservation of surface brightness, as pointed out in Sect. \ref{sec:gravlens}," + the image position has the nthjme relation (inside or outside) with respect to the image contour as the corresponding source position to the source contour., the image position has the same relation (inside or outside) with respect to the image contour as the corresponding source position to the source contour. + A square with the inside/outside indicators for its corners constitutes the elementary datastructure. out of which all relevant information about the image plane is constructed.," A square with the inside/outside indicators for its corners constitutes the elementary datastructure, out of which all relevant information about the image plane is constructed." + Being characterized by its four indicators. there are 24=16 types of elementary squares. shown in Fig. l..," Being characterized by its four indicators, there are $2^4 = 16$ types of elementary squares, shown in Fig. \ref{fig:square_type}." + 12 of these elementary squares. namely those of type “corner in/out’ or “half-in/half-out’. define part of the contour line. which crosses two edges of the square whose corners have different status.," 12 of these elementary squares, namely those of type 'corner in/out' or 'half-in/half-out', define part of the contour line, which crosses two edges of the square whose corners have different status." + If two opposite corners are found to be inside and the other two corners outside. the contour needs to cross all four edges. but it is not clear which edges it connects.," If two opposite corners are found to be inside and the other two corners outside, the contour needs to cross all four edges, but it is not clear which edges it connects." + Therefore. such indecisive squares need to be subdivided in order to improve the resolution (this is rule 1 below).," Therefore, such indecisive squares need to be subdivided in order to improve the resolution (this is rule 1 below)." +" The length of an edge of a square of depth & is 2)""a. where a denotes a unit size."," The length of an edge of a square of depth $k$ is $2^{-k} a$, where $a$ denotes a unit size." +" Squares are nested so that each square S$?nn of depth & either contains + subsquares of depth &|.1 each sharing a differentuc corner with ""mης or δη| does not have any subsquare."," Squares are nested so that each square $S^k_{mn}$ of depth $k$ either contains 4 subsquares of depth $k+1$ each sharing a different corner with $S^k_{mn}$, or $S^k_{mn}$ does not have any subsquare." + The minimal and initial data structure consists of a square of depth 1 with 4 subsquaresofdepth 0., The minimal and initial data structure consists of a square of depth $-1$ with 4 subsquaresofdepth 0. + The version of the adaptive contouring algorithm presented here uses just two operations on the data structure. and zxccnz. illustrated in Fig. 2.," The version of the adaptive contouring algorithm presented here uses just two operations on the data structure, and , illustrated in Fig. \ref{fig:operations}." +.While creates, .While creates +simulations provide the ideal tool to describe in detai how metals are produced. within galaxies and. distribute during the hierarchical assembly of a cluster.,simulations provide the ideal tool to describe in detail how metals are produced within galaxies and distributed during the hierarchical assembly of a cluster. + Besides semianalytical approaches (e.g. De Lucia. Waullman White 2003). attempts to include. within hyerodynamica simulations. star formation. SN energy feedback and meta enrichment. from tvpela and LL SN. have been. pursue bv dillerent. authors (Aguirre ct al.," Besides semi–analytical approaches (e.g. De Lucia, Kauffman White 2003), attempts to include, within hydrodynamical simulations, star formation, SN energy feedback and metal enrichment from type–Ia and II SN, have been pursued by different authors (Aguirre et al." + 2001: Lia. Portinari Carraro 2002: Valdarnini 2002: Kawata Gibson 2003: Ixobavashi 2003: Fissera Scannapieco 2003).," 2001; Lia, Portinari Carraro 2002; Valdarnini 2002; Kawata Gibson 2003; Kobayashi 2003; Tissera Scannapieco 2003)." +" It is however clear that such approaches rely on the capability. of the numerical codes to provide a physically. sound. description of the relevant “subgrid"" processes.", It is however clear that such approaches rely on the capability of the numerical codes to provide a physically sound description of the relevant “sub–grid” processes. + In thisLeffer we present the first. results from our hydrodynamical simulations of clusters based on the implementation of chemical enrichment in the GADGET code (Springel. Yoshida White 2001).," In this we present the first results from our hydrodynamical simulations of clusters based on the implementation of chemical enrichment in the GADGET code (Springel, Yoshida White 2001)." + Our chemo-dvnamical version of GADGET combines the rather advanced: treatment of star formation and. SN. feedback. proposed by Springel Lernquist (2003a. 81103 hereafter). to a careful description of the role of tvpela ancl LL SN in releasing metalenriched gas into the diffuse medium.," Our chemo-dynamical version of GADGET combines the rather advanced treatment of star formation and SN feedback, proposed by Springel Hernquist (2003a, SH03 hereafter), to a careful description of the role of type–Ia and II SN in releasing metal–enriched gas into the diffuse medium." + In the following. when expressing the ICM metal abundances in solar units. we assume the photospheric abundance provided by CGrevesse Sauval (1998).," In the following, when expressing the ICM metal abundances in solar units, we assume the photospheric abundance provided by Grevesse Sauval (1998)." + Our simulations are based on an evolution of. (Springel ct al., Our simulations are based on an evolution of (Springel et al. + 2001). a parallel Tree|SPILL code with fully adaptive timestepping.," 2001), a parallel Tree+SPH code with fully adaptive time–stepping." + As a starting point. we used a version. of GADGET. kindly provided by V. Springel. which includes an entropyconserving integration scheme. radiative cooling. the effect of a uniform and evolving UV background. (Llaardt Aladau 1909). star formation from a multiphase interstellar medium. and a prescription for galactic winds triggered by SN explosions (sec SIIO3 for à detailed description).," As a starting point, we used a version of GADGET, kindly provided by V. Springel, which includes an entropy–conserving integration scheme, radiative cooling, the effect of a uniform and evolving UV background (Haardt Madau 1999), star formation from a multiphase interstellar medium and a prescription for galactic winds triggered by SN explosions (see SH03 for a detailed description)." + In the original version of the code. the energev release and a global metallicity was produced. only by SNIL under the instantanousrecvcling. approximation (LRA).," In the original version of the code, the energy release and a global metallicity was produced only by SNII under the instantanous–recycling approximation (IRA)." + The GADGET code has been suitably mocified. so as to correctly include the lifetimes of dillerent. stellar populations. to follow metal production from both SNlIa and Η. while self.consistently introducing the dependence of the cooling function on metallicitv.," The GADGET code has been suitably modified, so as to correctly include the life–times of different stellar populations, to follow metal production from both SNIa and II, while self–consistently introducing the dependence of the cooling function on metallicity." + A detailed description of the implementation of these algorithms will be presented in a forthcoming paper Cl'ornatore ct al., A detailed description of the implementation of these algorithms will be presented in a forthcoming paper (Tornatore et al. + 2004. in. preparation). while we provide here à short descriptions of the most relevant. features of the code.," 2004, in preparation), while we provide here a short descriptions of the most relevant features of the code." + In order to maintain the general approach of the multiphase model by SLIIQ3. we still treat under the LRA stars with masses ον20M.. while accounting for the different life-times of stars of smaller mass (Matteucci DPadovani 1993).," In order to maintain the general approach of the multiphase model by SH03, we still treat under the IRA stars with masses $>20\,M_\odot$, while accounting for the different life-times of stars of smaller mass (Matteucci Padovani 1993)." + Within the stochastic approach to star formation (SIIQ3). each star particle is considered as a single stellar population (SSP).," Within the stochastic approach to star formation (SH03), each star particle is considered as a single stellar population (SSP)." + For each SSP we compute the number of stars turning into SNIL and la at each time-step after its creation., For each SSP we compute the number of stars turning into SNII and Ia at each time-step after its creation. + The SNla are associated to. binary svstems whose components are in the SAZ. mass range (Ciregeio venzini 1983). while SNIL arise from stars with mass SAL. (ef.," The SNIa are associated to binary systems whose components are in the $8\,M_\odot$ mass range (Greggio Renzini 1983), while SNII arise from stars with mass $>8\,M_\odot$ (cf." + also Lia et al., also Lia et al. + 2002. who adopt the lower mass hreshold of GAL. for SNIL).," 2002, who adopt the lower mass threshold of $6M_{\odot}$ for SNII)." + Besides SNe. which release energy and metals. we also account for planctary nebulae (PN).," Besides SNe, which release energy and metals, we also account for planetary nebulae (PN)." + They contribute to metal production. but not to the energv feedback. and are identified with those stars. not urning into SNla. in the mass range SM..," They contribute to metal production, but not to the energy feedback, and are identified with those stars, not turning into SNIa, in the mass range $\,M_\odot$." + We use the analvtical fitting formulas for stellar vields of SNla. SNIL ancl PNe as provided by Reechi et al. (," We use the analytical fitting formulas for stellar yields of SNIa, SNII and PNe as provided by Recchi et al. (" +2001). ancl based on he original nucleosvnthesis computations of Nomoto et al. (,"2001), and based on the original nucleosynthesis computations of Nomoto et al. (" +1997. using their W model). Woosley Weaver (1995) and Benzin Voli (1981).,"1997, using their W7 model), Woosley Weaver (1995) and Renzini Voli (1981)." + The ormulation for the SNla rate has been calculated. as in Alatteuccei Reeehi (2001)., The formulation for the SNIa rate has been calculated as in Matteucci Recchi (2001). + Besides HE and Ho. the current version of the code follows the production. of Fe. ο. ο Si Mg. S. and can be casily modified. to include other metal species.," Besides H and He, the current version of the code follows the production of Fe, O, C, Si, Mg, S, and can be easily modified to include other metal species." + Once. produced. by à star. particle. metals are spread over the same number of neighbours. 82. used [or the SPLL implementation. also using the same kernel.," Once produced by a star particle, metals are spread over the same number of neighbours, 32, used for the SPH implementation, also using the same kernel." +" In this wav. we find that 90 per cent of the metals are distributedDl withinM a gas mass of. 5.4.1075.""ΑΙ..."," In this way, we find that 90 per cent of the metals are distributed within a gas mass of $5.4\times 10^9 +h^{-1}M_\odot$." + We. have verified that using a twice as Large number of neighbors to spread metals results in a twice as large gas mass for metal mixing. while final results on the amount and distribution of metals (see below) are left almost unchanged.," We have verified that using a twice as large number of neighbors to spread metals results in a twice as large gas mass for metal mixing, while final results on the amount and distribution of metals (see below) are left almost unchanged." + As for the energy release. each SN is assumed to produce 10ergs.," As for the energy release, each SN is assumed to produce $10^{51}$ ergs." + Insteacl of assuming any specific value for the thermalization ellicieney. of the energy. released by SN. we prefer to dump all the energy to the surrounding σας particles and. leave to the simulation the computation of the radiation losses.," Instead of assuming any specific value for the thermalization efficiency of the energy released by SN, we prefer to dump all the energy to the surrounding gas particles and leave to the simulation the computation of the radiation losses." + Since the physical processes determining the actual SN Mlicieney are below the resolution scale of our simulations. 16 rationale behind our choice is to leave to the sub.grid multiphase niocel by 1109 establishing how much of this energy enters in regulating the star formation process.," Since the physical processes determining the actual SN efficiency are below the resolution scale of our simulations, the rationale behind our choice is to leave to the sub–grid multiphase model by SH03 establishing how much of this energy enters in regulating the star formation process." + We normalize the IMEs in the mass range 0.1.LOO A7..., We normalize the IMFs in the mass range 0.1–100 $M_\odot$. + Owing to the uncertainty in modelling vields for very massive stars. we take vields to be independent. of mass above 40M...," Owing to the uncertainty in modelling yields for very massive stars, we take yields to be independent of mass above $40\,M_\odot$." + While any uncertainty in the vields of such massive stars has a negligible effect for a Salpeter IML (Salpeter 1955. 855 hereafter). their accurate description (e.g. Phiclemann et al.," While any uncertainty in the yields of such massive stars has a negligible effect for a Salpeter IMF (Salpeter 1955, S55 hereafter), their accurate description (e.g. Thielemann et al." + 1996: Leger Woosley 2002) is required. when using a topheavier EME., 1996; Heger Woosley 2002) is required when using a top–heavier IMF. + We note that our scheme to distribute metals in the ICM does not include the effect. o£ dillusion., We note that our scheme to distribute metals in the ICM does not include the effect of diffusion. + Lia et al. (, Lia et al. ( +2002) included the ellect. o£ cülfusion driven by SN blast waves (see Thornton et al.,2002) included the effect of diffusion driven by SN blast waves (see Thornton et al. + 1998) in their SPILL simulations with chemical enrichment., 1998) in their SPH simulations with chemical enrichment. + Although this cllect is quite important to describe the dilfusion of metals within the interstellar medium. it is likely to play a minor role on . . ≱∖⋯↓⋖⋅≱∖⋜↧∣⋯∖⇁∢⋅↥⇂↥⋖⋅↿∙∖⇁↓≻⊔∼⋜↧↓↓⋅∢⊾⊳∖∪↓⋯↓∪⊔⊳∖⋯↓⋖⋅⊳∿↓∪∣∣↳↓≻≼⋱∪⊓↓∐⊾ 1 ⋅ cluster simulations that we are discussing here.," Although this effect is quite important to describe the diffusion of metals within the interstellar medium, it is likely to play a minor role on scales above the typical resolution scale, $\sim 10\,h^{-1}$ kpc, of the cluster simulations that we are discussing here." +zero vields negligibly dillerent results.,zero yields negligibly different results. +" For our final solution (solution 19 of Table 5) we adopt. 2,=8.5kpe (see below) and corresponding values of O7 and OF from fig 5 of PMD together with the values of i, and ον, from PMD.", For our final solution (solution 19 of Table 5) we adopt $R_{\rm o}=8.5\ {\rm kpc}$ (see below) and corresponding values of $\Theta_{\rm o}''$ and $\Theta_{\rm o}'''$ from fig 5 of PMB together with the values of $u_{\rm o}$ and $v_{\rm o}$ from PMB. +" Thus we adopt from the proper JA-—1482cz054kmsl. B=1237EO61kms3 and £2,=21.1940.87kms These results are. essentially independent of the acloptecl distance scale or of scaling the PAIB values of R.A"" and Q7 (compare solutions 15. 17 and 19 of table 5)."," Thus we adopt from the proper $ A = 14.82 \pm 0.84\ \rm km\ s^{-1}$, $ B = -12.37 \pm 0.64\ \rm km\ s^{-1}$ and $\Omega _{\rm o} = 27.19 \pm 0.87\ \rm km\ s^{-1}$ These results are essentially independent of the adopted distance scale or of scaling the PMB values of $R_{\rm o}, \Theta''_{\rm o}$ and $\Theta'''_{\rm o}$ (compare solutions 15, 17 and 19 of table 5)." + Comparison of this adopted value of; with the value from racial velocities (15.92 £0.34) leacs (via fig 5 of PAIB), Comparison of this adopted value of $A$ with the value from radial velocities $15.92 \pm 0.34$ ) leads (via fig 5 of PMB) +Vel 668826) was classified as BpSi bv. ancl was reported. as an eclipsing binary by (1995).,Vel 68826) was classified as BpSi by and was reported as an eclipsing binary by . +.. In fact it is one of the only two double-Hined eclipsing binaries with a Bpsi component known to date 2004)., In fact it is one of the only two double-lined eclipsing binaries with a BpSi component known to date . +. From light-time effect on the times of minima. deduced the presence of a third body.," From light-time effect on the times of minima, deduced the presence of a third body." + In our previous paper 2006).. using FEROS spectroscopic observations. we discovered that this system is actually a spectroscopic quadruple system: with components close to the ZAXMS.," In our previous paper , using FEROS spectroscopic observations, we discovered that this system is actually a spectroscopic quadruple system with components close to the ZAMS." + The four stars form. two close spectroscopic pairs (periods of 1.58 and 4.15 days) bound gravitationally to each other in a wide eccentric orbit with a period of vr., The four stars form two close spectroscopic pairs (periods of 1.58 and 4.15 days) bound gravitationally to each other in a wide eccentric orbit with a period of 41 yr. + In that paper we combined our radial velocity (RV) measurements41 with the available photometric data to derive orbital parameters for both binary systems and to calculate the absolute parameters of the eclipsing svstem., In that paper we combined our radial velocity ) measurements with the available photometric data to derive orbital parameters for both binary systems and to calculate the absolute parameters of the eclipsing system. + For the first time. direct determination of the radius and the mass was obtained for a Όροι star.," For the first time, direct determination of the radius and the mass was obtained for a BpSi star." + In this work we present high-resolution. high signal-to-noise UVIES spectra. which were used to perform. an abundance analysis of all four components of this multiple system.," In this work we present high-resolution, high signal-to-noise UVES spectra, which were used to perform an abundance analysis of all four components of this multiple system." + In 22 we present the observations and describe the reconstruction of the component spectra., In 2 we present the observations and describe the reconstruction of the component spectra. + In 33 we analyze the spectral characteristics of cach component and present the results of the abundance analysis., In 3 we analyze the spectral characteristics of each component and present the results of the abundance analysis. + In the last Section we discuss the main results and the occurrence of chemical peculiarities in binary ancl multiple svstenis., In the last Section we discuss the main results and the occurrence of chemical peculiarities in binary and multiple systems. + Three spectra were obtained in service mode with UVES at VLI-UT2 telescope in October 2005., Three spectra were obtained in service mode with UVES at VLT-UT2 telescope in October 2005. + The spectra have been taken with the aarcsec slit for the blue arm and the aarcsec slit for the red arm on three consecutive nights with two cdillerent clichroics to achieve the highest UVES resolution of 110.000 in the red spectral region ancl 50.000 in the blue spectral region.," The spectra have been taken with the arcsec slit for the blue arm and the arcsec slit for the red arm on three consecutive nights with two different dichroics to achieve the highest UVES resolution of 110,000 in the red spectral region and 80,000 in the blue spectral region." + We used exposure times of 20.30 min. obtaining à S/N ratio above 200 in the spectral rangeSOOOA.," We used exposure times of 20–30 min, obtaining a S/N ratio above 200 in the spectral range." +. These spectra are analyzed here along with five FEROS spectra described in the previous paper bv(2006)., These spectra are analyzed here along with five FEROS spectra described in the previous paper by. +. To calculate. separate spectra for the four components of the system and to measure their RVs. the iterative method. described by was adapted for the multiple system AO Vel.," To calculate separate spectra for the four components of the system and to measure their RVs, the iterative method described by was adapted for the multiple system AO Vel." + This algorithm computes the spectra of the individual components and the RVs iteratively., This algorithm computes the spectra of the individual components and the RVs iteratively. + In each step the computed spectra are used to remove the spectral features of all but one component from the observed spectra., In each step the computed spectra are used to remove the spectral features of all but one component from the observed spectra. + Ehe resulting single-lined spectra, The resulting single-lined spectra +secondary pair production im pulsars requires a source of photons will energies 2l1 MeV. The sources considered in conventional models are curvature enüssion and resonant Thomson scattering by primary. particles.,"Secondary pair production in pulsars requires a source of photons with energies $>1\,$ MeV. The sources considered in conventional models are curvature emission and resonant Thomson scattering by primary particles." + In an oscillating model LAE is an additional possibility., In an oscillating model LAE is an additional possibility. + For LAE to be viable as the source of secondary pairs. (wo conditions need {ο be satisfied: the photon energv must exceed an MeV. and the power in LAE must be sufficient to account for the required number of pairs.," For LAE to be viable as the source of secondary pairs, two conditions need to be satisfied: the photon energy must exceed an MeV, and the power in LAE must be sufficient to account for the required number of pairs." + Consider a model in which there is a large number of localized. transient LAEWs in the polar cap region. with the pairs in the LAEW created through LAE.," Consider a model in which there is a large number of localized, transient LAEWs in the polar cap region, with the pairs in the LAEW created through LAE." +" Let the number density of pairs be a multiplicity. AZ. times the Goldreich-Julian density. so that the lrequency of the LAEW is eascCUO,0,)!s where Q,=2z/P is (he rotation Irequency. of a pulsar with period P. and Q,=(nc?/h)uB/D.) is the evelotron frequency. with B,=44x10""T the Schwinger field."," Let the number density of pairs be a multiplicity, $M$, times the Goldreich-Julian density, so that the frequency of the LAEW is $\omega_{\rm max}\sim (M\Omega_r\Omega_c)^{1/2}\gamma_{\rm max}^{3/2}$, where $\Omega_r=2\pi/P$ is the rotation frequency of a pulsar with period $P$, and $\Omega_c=(mc^2/\hbar)(B/B_c)$ is the cyclotron frequency, with $B_c=4.4\times10^9\rm\,T$ the Schwinger field." + The threshold condition. «y27/2mech. requires110. where P is in seconds.," The threshold condition, $\omega_{\rm max}>2mc^2/\hbar$, requires, where $P$ is in seconds." + The fraction of the οποιον lost bv a LAEW as it propagates outward through the pulsar magnetosphere can be estimated by mulliplving this damping decrement by the number of oscillations before the LAEW leaves the magnetosphere., The fraction of the energy lost by a LAEW as it propagates outward through the pulsar magnetosphere can be estimated by multiplying this damping decrement by the number of oscillations before the LAEW leaves the magnetosphere. +" Assuming propagation al close to the speed of light this number is of order Q/Q,.", Assuming propagation at close to the speed of light this number is of order $\Omega/\Omega_r$. +" Hence. the fraction of the energv lost to LAE is of order (r5?/O,c)suusoALryQ,/¢=MalB/B.). where a221/137 is the line structure constant."," Hence, the fraction of the energy lost to LAE is of order $(r_0\Omega^2/\Omega_rc)\gamma_{\rm max}\sim Mr_0\Omega_c/c=M\alpha(B/B_c)$, where $\alpha\approx1/137$ is the fine structure constant." + We conclude that LAE is energetically, We conclude that LAE is energetically +optical outburst is difficult to assess.,optical outburst is difficult to assess. + While the optical outburst is naturally interpreted as an accretion outburst (with the optical luminosity due to increased luminosity of the accretion shock). why this should cause a hot plasma component to appear in the star is not clear.," While the optical outburst is naturally interpreted as an accretion outburst (with the optical luminosity due to increased luminosity of the accretion shock), why this should cause a hot plasma component to appear in the star is not clear." + Indeed. accreting YSOs in the COUP sample are statistically less X-ray luminous than non-accreting ones (Preibischetal.. 2005)) and less prone to show flares from large magnetic structures (Favataetal.. 2005)).," Indeed, accreting YSOs in the COUP sample are statistically less X-ray luminous than non-accreting ones \citealp{pkf+2005}) ) and less prone to show flares from large magnetic structures \citealp{ffr+2005}) )." +We parameterise the global densities in which individual objects are embedded by measuring their distance to notorious landmarks in the simulation.,We parameterise the global densities in which individual objects are embedded by measuring their distance to notorious landmarks in the simulation. +" Possible choices For lucdanarks inelucle galas, clusters aud voids. which correspond to rare fluetuations in the density Ποια."," Possible choices for landmarks include galaxy clusters and voids, which correspond to rare fluctuations in the density field." + Pilaments could also be selected as Iandinarks bu in these structures are located at the void walls in our niunerieal principlesimulation (Le. 0.8 ont) and we therelore do no use them in our analysis., Filaments could also be selected as landmarks but in principle these structures are located at the void walls in our numerical simulation (i.e. $0.8-1.2 r_{void}$ ) and we therefore do not use them in our analysis. + In order to illustrate the meaning of a global density parametrised this way. notice that galaxies locatec on aspherical shell centred in. lor instanee. a Cluster al galaxies could in principle be embedded in a wide range of local densities. depending on whether they are field galaxies or part of filaments or groups.," In order to illustrate the meaning of a global density parametrised this way, notice that galaxies located on a spherical shell centred in, for instance, a Cluster of galaxies could in principle be embedded in a wide range of local densities, depending on whether they are field galaxies or part of filaments or groups." + Lor a fixed global environment the local environmen can ciller significantlv., For a fixed global environment the local environment can differ significantly. + DAL haloes in the numerical simulation follow quite approximately NEW profiles. (Navarro.Prenk&White1996).. where haloes of similar concentrations ean be sealed to a single prolile Using a scale radius. reog. which eneloses an overdensity of 200 times the critical density in the aniverse.," DM haloes in the numerical simulation follow quite approximately NFW profiles \citep{nfw}, where haloes of similar concentrations can be scaled to a single profile using a scale radius, $r_{200}$, which encloses an overdensity of $200$ times the critical density in the universe." + Once this scaling is applied. the spherical shells distant by 7/rooo Irom any halo centre are characterised) by similar overdensities.," Once this scaling is applied, the spherical shells distant by $r/r_{200}$ from any halo centre are characterised by similar overdensities." + Phis approximation js also valid lor the full population of haloes whieh presents a Barrow range ol possible concentrations (σοςetal.1998]., This approximation is also valid for the full population of haloes which presents a narrow range of possible concentrations \citep{hus}. + As the latter becomes an even better approximation when the population of haloes is restricted to a narrow. range al masses. we select as Iuncdanarks lor global density estimators haloes with Abs olehTAL.. for a total of T0 selected DAL haloes.," As the latter becomes an even better approximation when the population of haloes is restricted to a narrow range of masses, we select as landmarks for global density estimators haloes with $M>10^{13}$ $^{-1}M_{\odot}$, for a total of $70$ selected DM haloes." + We then proceed ta label galaxies according to their distance. in terms of rogo. to the closest DM halo within this ," We then proceed to label galaxies according to their distance, in terms of $r_{200}$, to the closest DM halo within this sample." +"From now on. we divide galaxies in. 1 stthsamples at different. sample.distances from halo centres. which we will reler to as Ay, to ga (with limiting values at rfrouy=0.0.1.5.5.9 and 20)."," From now on, we divide galaxies in $4$ subsamples at different distances from halo centres, which we will refer to as $R_{H1}$ to $R_{H4}$ (with limiting values at $r/r_{200}=0.0,1.5,5,9$ and $20$ )." + The corresponding average DAL density around galaxies in cach stthbsample ranges Irom σε200;%¢« lo 7per where pec ds the critical mass density.," The corresponding average DM density around galaxies in each subsample ranges from $\approx 200 \rho_C$ to $\approx \rho_C$, where $\rho_C$ is the critical mass density." + A similar principle applies to voids where their density proliles can be scaled using the void radius ρα (Padilla.Ceeca-relli&Lambas 2005): the profiles approach the average densit in the Universe at ορα£1.5 (Patirietal.2006)..," A similar principle applies to voids where their density profiles can be scaled using the void radius $r_{void}$ \citep{pad}; the profiles approach the average density in the Universe at $r/r_{void} +\approx 1.5$ \citep{pat}." + The void. identification algorithin we adopt. corresponds to the one deseribed tn Padilla.Ceccarelli&Lambas(2005).. and consists of a search of underdense spheres of varving radii within the periodic simulation box. satisbving 0=pop0.9.," The void identification algorithm we adopt corresponds to the one described in \citet{pad}, and consists of a search of underdense spheres of varying radii within the periodic simulation box, satisfying $\delta=\frac{\rho-\left<\rho\right>}{\left<\rho\right>}<-0.9$." +" In the simulation x woe identify a total of TO voids"" with 7,54 lh 4Alpe. each containing in average a total of ©190 galaxies in the range ρω5USN1.2."," In the simulation box we identify a total of $70$ voids with $r_{void}>4$ $^{-1}$ Mpc, each containing in average a total of $\simeq 180$ galaxies in the range $r/r_{void}=0.8-1.2$." + We use these voids to make a second xuwaneterisation of global densities lor the semi-analytic galaxies using Pérou., We use these voids to make a second parameterisation of global densities for the semi-analytic galaxies using $r/r_{void}$. +" We define 1 distance ranges. relerred to as a4 to Haas delimitec by the values οδρ=0.0.55.0.85. 1.05 and 1,1: he average overdensity in these samples ranges [rom àΟσο: WFpet."," We define $4$ distance ranges, referred to as $R_{V1}$ to $R_{V4}$, delimited by the values $r/r_{void}=0,0.55,0.85$, $1.05$ and $1.4$; the average overdensity in these samples ranges from $\approx 0.05 \rho_C$ to $\approx \rho_C$." + The resulting distributions of normalised distances to lialocs and voids lor the seimi-analvtie galaxies in the simulation are shown in Figure 1z the vertical long-dashed lines indicate the limits between clifferent global density samples selected according to the distance to haloes (left. panel) ancl voids (right) in the simulation., The resulting distributions of normalised distances to haloes and voids for the semi-analytic galaxies in the simulation are shown in Figure \ref{fig:fig1}; the vertical long-dashed lines indicate the limits between different global density samples selected according to the distance to haloes (left panel) and voids (right) in the simulation. + Solid lines show the results lor the full sample of galaxies in the simulation. dotted lines show central galaxies (notice the lack of near the halo centres. indicating the minimum distance objectsbetween haloes in the simulation). and typicaldashed lines to satellite galaxies.," Solid lines show the results for the full sample of galaxies in the simulation, dotted lines show central galaxies (notice the lack of objects near the halo centres, indicating the typical minimum distance between haloes in the simulation), and dashed lines to satellite galaxies." + Except for the lack of central galaxies near halo. centres. the of these distributions do not change significantly with the shapesgalaxy tape.," Except for the lack of central galaxies near halo centres, the shapes of these distributions do not change significantly with the galaxy type." + ‘Lhe problem of celining a measure of the local density. aro galaxies has multiple possible solutions. depending on the relevan quantities that are to be associated to this estimate.," The problem of defining a measure of the local density around galaxies has multiple possible solutions, depending on the relevant quantities that are to be associated to this estimate." + On the one mand the standard approach of estimating a density using a fixec voltune around a galaxy eimsures a fixed seale. but the extremelh wide dynamic range of densities (228 orders of magnitude) has he drawback of procucing low signal to noise estimates [or ow densities. (dominated. by Poisson noise). ancl oversample meastrements at high cleusity values;," On the one hand the standard approach of estimating a density using a fixed volume around a galaxy ensures a fixed scale, but the extremely wide dynamic range of densities $\approx 8$ orders of magnitude) has the drawback of producing low signal to noise estimates for low densities (dominated by Poisson noise), and oversampled measurements at high density values." + Several works apply this method either by using a gaussian kernel to smooth the density distribution (e.g. Balogh et al.," Several works apply this method either by using a gaussian kernel to smooth the density distribution (e.g. Balogh et al.," + 2001a). or a more simple top-jx kernel of fixed. size (C'eccarelli:Padilla&Lambas20058).," 2004a), or a more simple top-hat kernel of fixed size \citep{cec}." +. A thoiee of local density estimate associated: to galaxv-galaxy interactions is the one taking into account the closest. neeghbors oL a galaxy by using the distance to the IN/ nearest neighbor., A choice of local density estimate associated to galaxy-galaxy interactions is the one taking into account the closest neighbors of a galaxy by using the distance to the $N^{th}$ nearest neighbor. + The advantages from using such an estimator relies in the likely relation between galaxy interactions anc the SI in galaxies., The advantages from using such an estimator relies in the likely relation between galaxy interactions and the SF in galaxies. +" Mos observational studies adopting this latter approach use adaptive projected 2D density estimators such as Ss: lor instance. Baloghetal.(2001a) compute Xz using the distance to the filth neares neighbour brighter than AZ,=20 confined to a recdshilt slice of της+ to avoid biases Irom the linger-ol-eud elect."," Most observational studies adopting this latter approach use adaptive projected 2D density estimators such as $\Sigma_5$; for instance, \citet{bal} compute $\Sigma_5$ using the distance to the fifth nearest neighbour brighter than $M_r=-20$ confined to a redshift slice of $\pm 1000km s^{-1}$ to avoid biases from the finger-of-god effect." +" ""he alternatives to these approaches. generally applied to nammerieal simulations with Full 3-dimensional information. σασί on using an smoothing length proportional to the local particle oradaptive galaxy separation. or the galaxy-galasy distance (lor Smoothed Particle Lyclrodynamies. SPI. or adaptive loca density estimates given by Voronoi Pessellations (VI. Voronoi. 1908)."," The alternatives to these approaches, generally applied to numerical simulations with full 3-dimensional information, consist on using an adaptive smoothing length proportional to the local particle or galaxy separation, or the galaxy-galaxy distance (for Smoothed Particle Hydrodynamics, SPH), or adaptive local density estimates given by Voronoi Tessellations (VT, Voronoi, 1908)." + With VI. each particle is associated to a domain volume πο that every point inside this volume is closer to the particle ad its centre than to any other particle: smoothing these density estimates with those of their immediate neighbors ean be used to obtain a reliable measure of the local density.," With VT, each particle is associated to a domain volume so that every point inside this volume is closer to the particle at its centre than to any other particle; smoothing these density estimates with those of their immediate neighbors can be used to obtain a reliable measure of the local density." + This. particular measurement method. called the Literpolated Voronoi Density VD). can be very useful Lor identification af ος objects Platen.vandeWeygaert&Jones2007:Aragon-Calvuetal.Nevrinck.Cinedin&{αμα2005:CionzálezTheuns2009). in ..PI simulations and bas beenο shown to have a better resolution jur any other adaptive density estimate including SPIL kernel smoothing techniques (Schaap&vandeWergacrt2000:Pelu-oessyCtal.," This particular measurement method called the Interpolated Voronoi Density (IVD), can be very useful for identification of bound objects \citep{platen,aragon,ney,rob} + in SPH simulations and has been shown to have a better resolution than any other adaptive density estimate including SPH kernel smoothing techniques \citep{schaap,pel}." + 2003). In the remainder of this work we adopt IVDs or our estimates of local densities in the numerical simulation., In the remainder of this work we adopt IVDs for our estimates of local densities in the numerical simulation. + The left. panel o£ Figure 2. shows the IVD distributions of galaxies ott to 207200 Lrom the cluster centres (same as in the left xuiel ofFigure 1: the right panel shows the IVD distributions of galaxies ott to ἘνCeh from the void centres (as in the right xuiel of 1)., The left panel of Figure \ref{fig:fig2} shows the IVD distributions of galaxies out to $20r_{200}$ from the cluster centres (same as in the left panel of 1); the right panel shows the IVD distributions of galaxies out to $1.4r_{void}$ from the void centres (as in the right panel of 1). + RegardlessΌσο of whether the haloes elt panel) or voids (right panel) are used as global density laucimarks. the distributions of local densities are similar since both selection criteria cover a large fraction ofthe volume ofthe simulation.," Regardless of whether the haloes (left panel) or voids (right panel) are used as global density landmarks, the distributions of local densities are similar since both selection criteria cover a large fraction of the volume of the simulation." + Phe VD distributions show a clear bimodal behaviour. where the peak at hieh densities is dominated by satellite galaxies in massive DN 1alocs (long-dashed lines). and the density distribution of centra galaxies (short-dashecl) retleets the density field around their lios raloes. characterised by masses AfL04th 1AZ..," The IVD distributions show a clear bimodal behaviour, where the peak at high densities is dominated by satellite galaxies in massive DM haloes (long-dashed lines), and the density distribution of central galaxies (short-dashed) reflects the density field around their host haloes, characterised by masses $M\gtrsim 10^{11}$ $^{-1}M_{\odot}$." + We use these density estimates tuo characterise the loca environment of the semi-analytie galaxies., We use these density estimates to characterise the local environment of the semi-analytic galaxies. +" La ραοπο, we wil separate galaxies in three local density bins. to be relerred to as the prow. pup and µε samples."," In particular, we will separate galaxies in three local density bins, to be referred to as the $\rho_{LOW}$ $\rho_{MID}$ and $\rho_{HIGH}$ samples." + Lhe first tentative cuts in stellar densities are applied at 3.16x1027h. FAL. ? ane 6:1xLlotth ΑΗ selected: so as to lave a significan number of galaxies Alpein cach subsample.," The first tentative cuts in stellar densities are applied at $3.16 \times 10^{10}$ $^{-2}M_{\odot} $ $^{-3}$ and $6.31 \times 10^{11}$ $^{-2}M_{\odot} $ $^{-3}$, selected so as to have a significant number of galaxies in each subsample." + Further restrictions in density may be needed in order to ensure a constant median IND in each sample studied., Further restrictions in density may be needed in order to ensure a constant median IVD in each sample studied. +" Por reference.the barvon density in the simulation is py=f,x2.810h. 72A. 7. with à barvon fraction fj= 0.037."," For reference,the baryon density in the simulation is $\rho_b = f_b \times 2.8 \times 10^{11}$ $^{-2}M_{\odot} $ $^{-3}$ , with a baryon fraction $f_b=0.037$ ." +"the volume of à single cell and NV,=398 is the number of ealaxies in the simulation box.",the volume of a single cell and $N_g=398$ is the number of galaxies in the simulation box. + To allow a direct comparison of the simulation results with the observational data we construct synthetic Lva spectra as described in Bruscoliat... by tracing random LOS through the box.," To allow a direct comparison of the simulation results with the observational data we construct synthetic $\alpha$ spectra as described in Bruscoli, by tracing random LOS through the box." + We then estimate the mean Lya transmitted [Dux as a function of the impact parameter Ar. computing the average on all the pixels at a distance from a galaxy in a given interval centered on Ar.," We then estimate the mean $\alpha$ transmitted flux as a function of the impact parameter $\Delta r$, computing the average on all the pixels at a distance from a galaxy in a given interval centered on $\Delta r$." + The results are plotted in Fig.3 ancl compared with the data. represented by the black points.," The results are plotted in Fig.3 and compared with the data, represented by the black points." + The three panels show the mean Lye lux computed on different samples of galaxies: all the 398 galaxies (left panel). ealaxies with mass above 2107 M. (central panel) and those with mass below 9.3107 M. (right panel).," The three panels show the mean $\alpha$ flux computed on different samples of galaxies: all the 398 galaxies (left panel), galaxies with mass above $2 \times 10^{10}$ $_\odot$ (central panel) and those with mass below $9.3 \times 10^8$ $_\odot$ (right panel)." + Solid. dotted and. dotted-dashed lines are derived from the outputs of run A. run D and from a simulation analogous to run B. but with SERs boosted.," Solid, dotted and dotted-dashed lines are derived from the outputs of run A, run B and from a simulation analogous to run B, but with SFRs boosted." +hoc. Phe dillerence between run A and run BD in the left panel is marginal: we conclude that the mean cllect of the local photoionization on the Lya transmitted [lux is negligible when all galaxies are included in the analysis., The difference between run A and run B in the left panel is marginal: we conclude that the mean effect of the local photoionization on the $\alpha$ transmitted flux is negligible when all galaxies are included in the analysis. + Massive galaxies are the best candidates for LBCs due to their high luminosity and clustering properties., Massive galaxies are the best candidates for LBGs due to their high luminosity and clustering properties. + The SET. derived for the most massive galaxies in the MSPL simulation are in the range LO30 M.vr the highes values in the simulation.," The SFR derived for the most massive galaxies in the MSPH simulation are in the range $10\div30$ $_{\odot} {\rm yr}^{-1}$, the highest values in the simulation." + Due to their high. luminosity. one would expect them to produce a strong impact on the ionization of the surrounding σας.," Due to their high luminosity, one would expect them to produce a strong impact on the ionization of the surrounding gas." + However this is no the case., However this is not the case. + Looking at the solid line in the central panel. obtained by neglecting the local emission. we note tha the hieh density characterizing the environment of massive galaxies suppresses the mean transmitted Dux with respec to the mean trend obtained. for all the galaxies in. the simulation (solid line in the left panel).," Looking at the solid line in the central panel, obtained by neglecting the local emission, we note that the high density characterizing the environment of massive galaxies suppresses the mean transmitted flux with respect to the mean trend obtained for all the galaxies in the simulation (solid line in the left panel)." + The UV radiation emitted by these galaxies. using the SER. derived from the MSPL simulation (dotted. line in central panel). is not strong enough to enhance significantly the transparency. of he surrounding ICM. because of the high recombination rale in the denser environment.," The UV radiation emitted by these galaxies, using the SFR derived from the MSPH simulation (dotted line in central panel), is not strong enough to enhance significantly the transparency of the surrounding IGM, because of the high recombination rate in the denser environment." + Higher values of SER. are necessary to produce a significant increase of the transmitted lux nearby massive galaxies., Higher values of SFR are necessary to produce a significant increase of the transmitted flux nearby massive galaxies. + This can be seen from the x)osted. case. with SER in the range 100300 M. +.," This can be seen from the boosted case, with SFR in the range $100 \div 300$ $_\odot$ $^{-1}$." + Although on the high side. the values are still plausible according to observations (Shapley.. 2001).," Although on the high side, the values are still plausible according to observations (Shapley, 2001)." + Despite he sharp increase in the mean [να transmitted. (lux. vet his simulation does not match the AOS data.," Despite the sharp increase in the mean $\alpha$ transmitted flux, yet this simulation does not match the A03 data." + This result sugeests that the mean transmissivity strongly depends on he galactic enviroment., This result suggests that the mean transmissivity strongly depends on the galactic enviroment. + The right panel shows the trend for he Lya transmitted [lax obtained. selecting galaxies with mass <=9.8.107 M.., The right panel shows the trend for the $\alpha$ transmitted flux obtained selecting galaxies with mass $ \le 9.3 \times 10^8$ $_\odot$. + In this case the transmissivity of he gas at Ar for the total energy>. budgetὃν calculated here.," However, since the BHCs are so much more radio loud then this is not significant for the total energy budget calculated here." + A [it to the power in transient optically thin ejection, A fit to the power in transient optically thin ejection +system exacerbates this elfeet.,system exacerbates this effect. + Llowever because these effects are symmetric the overall global errors remain minimal., However because these effects are symmetric the overall global errors remain minimal. + This is confirmed. by monitoring the total energv. of the svstem. Figure(4)), This is confirmed by monitoring the total energy of the system. \ref{energy}) ) +" traces the fractional variation in total enerey of the system. (£z,dyη."," traces the fractional variation in total energy of the system, $(E_t-E_{t_0})/E_{t_0}$." + Phe model is à Lowered Evans with 20000 particles. being Tree particles. and timestep df=0.05.," The model is a Lowered Evans with 20000 particles, being Tree particles, and timestep $dt=0.05$." + Enerey is conserved. in this svstem to within over a period of 50 time units., Energy is conserved in this system to within over a period of 50 time units. + As ΜΗ all expansion codes angular anc linear momentum are intrinsically not conserved exactly. due to approximations in the force calculation.," As with all expansion codes angular and linear momentum are intrinsically not conserved exactly, due to approximations in the force calculation." + We might expect i to be more pronounced in the SCETRELE case where the particles in the Tree and SCE codes do not. respond to cach other equally and: oppositely., We might expect it to be more pronounced in the SCFTREE case where the particles in the Tree and SCF codes do not respond to each other equally and oppositely. + Linear. momentun is known not to be conserved in the pure SCE case. and," Linear momentum is known not to be conserved in the pure SCF case, and" +Ay difference. total sly ditference. (21 %)). and the LOOyam intensity difference at ly: difference (9 %)). respectively.,"$A_{V}$ difference, total $A_{V}$ difference (21 ), and the $100\ \mu m$ intensity difference at $A_{V}$ difference (9 ), respectively." + On the other hand. the noise of the IRIS data is 0.03 \lJv/sr for A=60jum and 0.06 MJv/sr for A=100µη (Miville Lagache 2005).," On the other hand, the noise of the IRIS data is 0.03 MJy/sr for $\lambda = 60\ \mu m$ and 0.06 MJy/sr for $\lambda = 100\ \mu m$ (Miville Lagache 2005)." +" These values correspond to less than 1.56 for Ay and are negligiblv small compared to the differenο between ;A,: (best) and Ay (SFD98).", These values correspond to less than 1 for $A_{V}$ and are negligibly small compared to the difference between $A_{V}$ (best) and $A_{V}$ (SFD98). +" Figure 10 shows the comparison between 4) (best) and A, (slow).", Figure 10 shows the comparison between $A_{V}$ (best) and $A_{V}$ (slow). +" It can be seen that the difference is large compared to the noise of the DIRBE data points. reflecting the fact that the power of the slow case does not represent the entire correlation in the Cyenus region,"," It can be seen that the difference is large compared to the noise of the DIRBE data points, reflecting the fact that the power of the slow case does not represent the entire correlation in the Cygnus region." + Figure 11 shows (he comparison between 24\- (best) ancl “dy: (steep)., Figure 11 shows the comparison between $A_{V}$ (best) and $A_{V}$ (steep). + The difference ls 5% (1 sigma of (chy (best) — Ay (steep))/;dy (best))., The difference is 5 (1 sigma of $A_{V}$ (best) $-$ $A_{V}$ $A_{V}$ (best)). +" The difference between 1\: (steep) and A, (SEDOS) is 20 (1 sigma of (ly (steep) — ely (SED93))/Ay. (steep)).", The difference between $A_{V}$ (steep) and $A_{V}$ (SFD98) is 20 (1 sigma of $A_{V}$ (steep) $-$ $A_{V}$ $A_{V}$ (steep)). +" Thus. the dust temperature difference in the 4, difference is estimated as 18 by Equation (11)."," Thus, the dust temperature difference in the $A_{V}$ difference is estimated as 18 by Equation (11)." +" Figure 12 shows the comparison of ly (steep) and A, (single).", Figure 12 shows the comparison of $A_{V}$ (steep) and $A_{V}$ (single). + The difference. (24). (steep) — Ay (single))/.Ay. (steep)). scatters by 21 in 1 sigma.," The difference, $A_{V}$ (steep) $-$ $A_{V}$ $A_{V}$ (steep)), scatters by 21 in 1 sigma." + Ht is consistent with the hvpothesis described in Section 2 that the steep. slow. and best-fit cases are more accurate compared with (he single case.," It is consistent with the hypothesis described in Section 2 that the steep, slow, and best-fit cases are more accurate compared with the single case." + Dobashi et al. (, Dobashi et al. ( +"2005) published an jd, map within |b<40° by the star counting method using the DSS images.",2005) published an $A_{V}$ map within $\mid b \mid \ < 40^\circ$ by the star counting method using the DSS images. + The spatial resolution is 6'. similar to the present study.," The spatial resolution is $'$ , similar to the present study." + Figure 13 shows the result of the comparison of both Ay data in the Cygnus region., Figure 13 shows the result of the comparison of both $A_{V}$ data in the Cygnus region. + The 4A (DSS) data is distributed lower than 24) (best) and saturated at 4 (DSS) > 5 mag., The $A_{V}$ (DSS) data is distributed lower than $A_{V}$ (best) and saturated at $A_{V}$ (DSS) $>$ 5 mag. + This indicates that the star counting method with DSS has a limit of around Ay (DSS) ~ 5 mag., This indicates that the star counting method with DSS has a limit of around $A_{V}$ (DSS) $\sim$ 5 mag. + IU is apparent that their method is not useful for Aq > 10 mag because the optical radiation does not reach us because of heavy extinction by the dust., It is apparent that their method is not useful for $A_{V}$ $>$ 10 mag because the optical radiation does not reach us because of heavy extinction by the dust. + Dobashi (2009) applied their star counting method to the Two-Micron. All Skv Survey (2A\LASS) to reach Ay ~ 30 mag., Dobashi (2009) applied their star counting method to the Two-Micron All Sky Survey (2MASS) to reach $A_{V}$ $\sim$ 30 mag. + As shown in Section 4.1. Ay bv the best-fit ancl steep cases are more precise than that by SED9S in the Cygnus region.," As shown in Section 4.1, $A_{V}$ by the best-fit and steep cases are more precise than that by SFD98 in the Cygnus region." + But these methods would not be effective in high Galactic ]atitudes because {ο(140pone) has a lower S/N ratio in those latitudes., But these methods would not be effective in high Galactic latitudes because $I_{C}\ (140\ \mu m)$ has a lower S/N ratio in those latitudes. + Therefore. if we choose onlv one case out of the best-fit. slow. steep. the main-correlation. and the sub-correlation for the entire sky. the sub-correlation is best suitedbecause of its similarity to the steep case.," Therefore, if we choose only one case out of the best-fit, slow, steep, the main-correlation, and the sub-correlation for the entire sky, the sub-correlation is best suitedbecause of its similarity to the steep case." +"fractions, from 0 to 0.2 in the primary and satellite galaxies, and a range of orbital parameters.","fractions, from 0 to 0.2 in the primary and satellite galaxies, and a range of orbital parameters." +" As shown in ?,, minor mergers result in a redistribution of orbital into internal angular momentum, which affects all galaxy components."," As shown in \citet{quDM210a}, minor mergers result in a redistribution of orbital into internal angular momentum, which affects all galaxy components." +" In particular, old stars, i.e. those already in place before the interaction, always lose angular momentum during the merging process."," In particular, old stars, i.e. those already in place before the interaction, always lose angular momentum during the merging process." +" The decrease of the specific AM of old stars is accompanied by a redistribution of stellar orbits, as traced by the anisotropy parameter 8, which become increasingly radial."," The decrease of the specific AM of old stars is accompanied by a redistribution of stellar orbits, as traced by the anisotropy parameter $\beta$, which become increasingly radial." + In minor mergers with gas in the disk of the primary galaxy we find a similar trend of old stars losing angular momentum and as a result their orbits becoming more radially dominated., In minor mergers with gas in the disk of the primary galaxy we find a similar trend of old stars losing angular momentum and as a result their orbits becoming more radially dominated. +" However, when a new stellar component forms from gas present in the primary disk during the merger, its AM content is significantly different: the orbits tend to be more tangentially dominated, thus providing a higher rotational support."," However, when a new stellar component forms from gas present in the primary disk during the merger, its AM content is significantly different: the orbits tend to be more tangentially dominated, thus providing a higher rotational support." + This different behavior results in a final stellar disk with two different stellar populations with significantly different AM content., This different behavior results in a final stellar disk with two different stellar populations with significantly different AM content. +" In particular, old stars always show a rotational lag with respect to the young stellar component."," In particular, old stars always show a rotational lag with respect to the young stellar component." +" If one separates all stars into thin disk stars (at heights |z |x1 kpc from the galaxy midplane) and thick disk stars (at |z |>1 kpc), three different components can be found, with different dynamical properties: (1) young stars in the thin disk, which are rotationally supported and show the highest values of v;, (2) old thin disk stars lagging with respect to the new stars and (3) old thick disk stars lagging with respect to both thin disk components."," If one separates all stars into thin disk stars (at heights $\mid z\mid\le$ 1 kpc from the galaxy midplane) and thick disk stars (at $\mid z\mid >$ 1 kpc), three different components can be found, with different dynamical properties: (1) young stars in the thin disk, which are rotationally supported and show the highest values of $v_t$, (2) old thin disk stars lagging with respect to the new stars and (3) old thick disk stars lagging with respect to both thin disk components." +" For a minor 1:10 merger, with a satellite accreted on a direct orbit and with an initial primary disk gas fraction of 0.2, the old stars in the thin disk have a rotational lag of about 20 km sl, while the old stars in the thick disk have a velocity about 50 km s! lower than the young stellar component, both lag values being compatible with the estimates for the Milky Way (see ?).."," For a minor 1:10 merger, with a satellite accreted on a direct orbit and with an initial primary disk gas fraction of 0.2, the old stars in the thin disk have a rotational lag of about 20 km $^{-1}$, while the old stars in the thick disk have a velocity about 50 km $^{-1}$ lower than the young stellar component, both lag values being compatible with the estimates for the Milky Way \citep[see ][]{gilmore202}." +" Multiple mergers can further reduce the tangential velocity of the old stellar components, while leaving that of the new stars mostly unchanged, thus resulting in a further increase in rotational lag with every successive accretion episode."," Multiple mergers can further reduce the tangential velocity of the old stellar components, while leaving that of the new stars mostly unchanged, thus resulting in a further increase in rotational lag with every successive accretion episode." +" As the two populations, old stars and new stars, have different tangential velocities, in a plot of v, as function of age we expect to find a discontinuity at the time when the merger occurs."," As the two populations, old stars and new stars, have different tangential velocities, in a plot of $v_t$ as function of age we expect to find a discontinuity at the time when the merger occurs." +" Of course, the newly formed stars will evolve in time, and if no other merger takes place they will be slowly heated by secular effects."," Of course, the newly formed stars will evolve in time, and if no other merger takes place they will be slowly heated by secular effects." +" However, as we have shown in Fig. 3,,"," However, as we have shown in Fig. \ref{totAMisomer}," + secular processes are much less effective in altering stellar kinematics than minor mergers., secular processes are much less effective in altering stellar kinematics than minor mergers. +" Therefore, in our opinion, a discontinuity in the age-v; plane (or the age-G parameter) between the old and new stellar populations should still be visible, even if secular processes, and asymmetric drift in particular, contribute to the slow heating of the new stellar populations."," Therefore, in our opinion, a discontinuity in the $v_t$ plane (or the $\beta$ parameter) between the old and new stellar populations should still be visible, even if secular processes, and asymmetric drift in particular, contribute to the slow heating of the new stellar populations." +" Unfortunately, the"," Unfortunately, the" +In this paper. we report the discovery of a wide VLM binary (hereafter 4445) separated by 130 AU. 373.,"In this paper, we report the discovery of a wide VLM binary (hereafter ) separated by 130 AU, $\farcs$ 3." + The brighter primary component of was identified by ?. in the Two Micron All Sky Survey ?) and classified as an M9 dwarf on the ? red optical scheme. indicating a spectrophotometric distance of 33.142.2 pe.," The brighter primary component of was identified by \citet{Reid2008} in the Two Micron All Sky Survey \citep[2MASS;][]{Skrutskie2006} and classified as an M9 dwarf on the \citet{Kirkpatrick1999} red optical scheme, indicating a spectrophotometric distance of $\pm$ 2.2 pc." + Neither nor1. activity and age indicators. respectively. were evident in the optical spectrum.," Neither nor, activity and age indicators, respectively, were evident in the optical spectrum." + The primaryhas a proper motion of (120414. -25+20) tand a tangential velocity of 19+3 ?).," The primaryhas a proper motion of $\pm$ 14, $\pm$ 20) and a tangential velocity of $\pm$ 3 \citep{Faherty2009}." + The system is unresolved in 2MASS. and there have been no reports of a faint companion to this source in either optical survey data or follow-up observations (??)..," The system is unresolved in 2MASS, and there have been no reports of a faint companion to this source in either optical survey data or follow-up observations \citep{Reid2008, + Faherty2009}." + In our own follow-up observations of4445. we have identified a well-separated. faint L dwarf companion. indicating that this is a wide VLM binary system with a probable BD component.," In our own follow-up observations of, we have identified a well-separated, faint L dwarf companion, indicating that this is a wide VLM binary system with a probable BD component." + In Sections ?? and ??.. we describe our imaging and spectroscopic observations. respectively. and discuss the properties of the components of the resolved binary system.," In Sections \ref{Sec: NIRimaging} and \ref{Sec: NIRspectra}, we describe our imaging and spectroscopic observations, respectively, and discuss the properties of the components of the resolved binary system." + We discuss the physical association. mass. and age of the binary 4445AB in Section ?? and its implications on VLM formation and evolution scenarios in Section ??..," We discuss the physical association, mass, and age of the binary AB in Section \ref{Sec: analysis} and its implications on VLM formation and evolution scenarios in Section \ref{Sec: discussion}." + The conclusions are presented in Section ?2.., The conclusions are presented in Section \ref{Sec: summary}. + was imaged with the 3m NASA Infrared Telescope Facility (IRTF) SpeX spectrograph (?) on December 7. 2009 (UT). as part of a program to identify unresolved M/L dwarf plus T dwarf spectral binaries (e.g..?)..," was imaged with the 3m NASA Infrared Telescope Facility (IRTF) SpeX spectrograph \citep{Rayner2003} on December 7, 2009 (UT), as part of a program to identify unresolved M/L dwarf plus T dwarf spectral binaries \citep[e.g.,][]{Burgasser2008a}." + Conditions were clear but with poor seeing. 172 at A-band. due in part to the large airmass of the observation (2.34—2.37).," Conditions were clear but with poor seeing, $\farcs$ 2 at $K$ -band, due in part to the large airmass of the observation (2.34–2.37)." +" These images revealed a faint point source due east of the primary target at à separation of roughly 3"".", These images revealed a faint point source due east of the primary target at a separation of roughly $\arcsec$. + Four dithered exposures were obtained of the pair in each of the J. IT. and Jv filters. with individual exposure times of 45s. 30s. and 30s. respectively.," Four dithered exposures were obtained of the pair in each of the $J$, $H$ , and $K$ filters, with individual exposure times of 45s, 30s, and 30s, respectively." + The field rotator was aligned at a position angle of0: Le.. north up and east to the left.," The field rotator was aligned at a position angle of $\degr$; i.e., north up and east to the left." + Imaging data were reduced in à standard manner using custom IDL routines., Imaging data were reduced in a standard manner using custom IDL routines. + Raw images were mirror-flipped about the y-axis to reproduce the sky orientation. and. pair-wise subtracted to remove sky contributions., Raw images were mirror-flipped about the y-axis to reproduce the sky orientation and pair-wise subtracted to remove sky contributions. + The difference images were divided by normalized flat field frames. constructed by median-combining the imaging data for each filter after masking out the sources.," The difference images were divided by normalized flat field frames, constructed by median-combining the imaging data for each filter after masking out the sources." + Subsections of each image. 10” (83 pixels) on a side and centered on the target source. were extracted from these calibrated frames.," Subsections of each image, $\arcsec$ (83 pixels) on a side and centered on the target source, were extracted from these calibrated frames." + A final image for each filter/target pair (Figure 1)) was produced by averaging the registered subframes together. rejecting 5o pixel outhers.," A final image for each filter/target pair (Figure \ref{Fig: image}) ) was produced by averaging the registered subframes together, rejecting $\sigma$ pixel outliers." + The two sources of are well resolved along a nearly east-west axis., The two sources of are well resolved along a nearly east-west axis. + The brighter western component is hereafter referred toas 4445A and the eastern component as 4445B. Component magnitudes and the angular separation of the pair were determined through point spread function (PSF) fits to the reduced imaging data. following the prescription described in 2..," The brighter western component is hereafter referred to as A and the eastern component as B. Component magnitudes and the angular separation of the pair were determined through point spread function (PSF) fits to the reduced imaging data, following the prescription described in \citet{McElwain2006}." + The PSF models were derived from Gaussian fits to the primary component in the individual subimage frames., The PSF models were derived from Gaussian fits to the primary component in the individual subimage frames. + For each filter. four distinct PSF models were produced. each of which were fit to the individual images. resulting in a total of 16 independent measures of the relative component magnitudes and 48 independent measures of the separation and orientation. of the pair. in each of the 11 filters.," For each filter, four distinct PSF models were produced, each of which were fit to the individual images, resulting in a total of 16 independent measures of the relative component magnitudes and 48 independent measures of the separation and orientation of the pair, in each of the $JHK$ filters." + However. as the secondary was undetected in one of the four J-band images. four measures of the relative J-band flux and separation were discarded before computingmean values and standard deviations.," However, as the secondary was undetected in one of the four $J$ -band images, four measures of the relative $J$ -band flux and separation were discarded before computingmean values and standard deviations." + Separation measurements were converted. from pixels to areseconds assuming a plate scale of 01204-07002 (J. Rayner. 2005. private communication) and no distortion.," Separation measurements were converted from pixels to arcseconds assuming a plate scale of $\farcs$ $\pm$ $\farcs$ 002 $^{-1}$ (J. Rayner, 2005, private communication) and no distortion." + The position angle (set at 07) was assumed to be accurate to within 0725 (ibid.)., The position angle (set at $\degr$ ) was assumed to be accurate to within $\fdg$ 25 (ibid.). + Results are listed in Table 1.., Results are listed in Table \ref{Tab: psf}. + The angular separation of the pair was measured to be 37282-07047 at a position angle of 877343:079: r.e.. along an east-west line.," The angular separation of the pair was measured to be $\farcs$ $\pm$ $\farcs$ 047 at a position angle of $\fdg$ $\pm$ $\fdg$ 9; i.e., along an east-west line." + The secondary is both considerably fainter and significantly redder than the primary., The secondary is both considerably fainter and significantly redder than the primary. + We derived relative magnitudes of A.J= 3.11+0.06 and AA= 2.34+0.04., We derived relative magnitudes of $\Delta{J}=$ $\pm$ 0.06 and $\Delta{K}=$ $\pm$ 0.04. + Using the combined-light 2MASS photometry for thesystem?.. this translates into colors of 1.132:0.04 and 1.946 0.08 forthe primary and secondary. respectively.," Using the combined-light 2MASS photometry for the, this translates into colors of $\pm$ 0.04 and $\pm$ 0.08 forthe primary and secondary, respectively." + The two components of were observed on separate nights with the prism-dispersed mode of SpeX. the primary on December 7. 2009 (the same night as the imaging observations) and the secondary on December," The two components of were observed on separate nights with the prism-dispersed mode of SpeX, the primary on December 7, 2009 (the same night as the imaging observations) and the secondary on December" +svstem like Capella Aa.,system like Capella Aa. + This also implies that this effect would not be detectable for a slow-rotatine. niain-sequence star like our Sun.," This also implies that this effect would not be detectable for a slow-rotating, main-sequence star like our Sun." + Our modeling coufiriis this. showing a total U-I& amplitude of < 0.1 µας for a 1.0 NL... LOR. star witha rotation period of 30.0 days at 10.0 parsecs.," Our modeling confirms this, showing a total U-K amplitude of $\ll$ 0.1 $\mu$ as for a 1.0 $_{\sun}$, 1.0 $_{\sun}$ star with a rotation period of 30.0 days at 10.0 parsecs." + These conclusious ou detectabilitv are made with the assmuption that. for bright stars like these. SIM Lite can achieve its 1iicroaresecoud beuchinark.," These conclusions on detectability are made with the assumption that, for bright stars like these, SIM Lite can achieve its microarcsecond benchmark." + We show this is possible in narrow angle (NA) mode by cuploving the SIMI Differential Astrometry Performance Estimator (DAPE) (?).., We show this is possible in narrow angle (NA) mode by employing the SIM Differential Astrometry Performance Estimator (DAPE) \citep{Plummer09}. + For a target star with magnitude V—5. and a single comparison star with V=L0 located within a deeree of it on the sky. bv iutegratiug 15 seconds on the target. and 30 seconds on the refereuce. for 10 visits at 5 chop cveles cach. a final precision of EL.01 µας is achieved in only 1.01 hours of total nissiou time.," For a target star with magnitude $=$ 5, and a single comparison star with $=$ 10 located within a degree of it on the sky, by integrating 15 seconds on the target, and 30 seconds on the reference, for 10 visits at 5 chop cycles each, a final precision of $\pm$ 1.01 $\mu$ as is achieved in only 1.04 hours of total mission time." + For a fainter target with V —10. this precision is ouly reduced to #£1.32 pas iu the same amount of mission time.," For a fainter target with $V$ =10, this precision is only reduced to $\pm$ 1.32 $\mu$ as in the same amount of mission time." + Iu utilizine NA mode. one must be careful in choosing the reference star(s). to ensure that they are not stars with a substantial wavelcneth depeudant ceutroid.," In utilizing NA mode, one must be careful in choosing the reference star(s), to ensure that they are not stars with a substantial wavelength dependant centroid." + Civeu the ouly coustraiuts on reference stars are that they need to have V z 10 and are within one degree ou the sky. one could easily choose a slow-rotatiug. nmain-sequence star. determined as such via erouud-based observatious. as a waveleugth-audepeudeut astrometric reference star.," Given the only constraints on reference stars are that they need to have V $\gtrsim$ 10 and are within one degree on the sky, one could easily choose a slow-rotating, main-sequence star, determined as such via ground-based observations, as a wavelength-independent astrometric reference star." +" We also note that wide angle SIM. Lite measurements. witli a precision of —5 µας. may not detect the wavelength dependent photoceter of a system like Capella. but will have no difficulty detecting it in stars like Capella Ab or οσα,"," We also note that wide angle SIM Lite measurements, with a precision of $\sim$ 5 $\mu$ as, may not detect the wavelength dependent photoceter of a system like Capella, but will have no difficulty detecting it in stars like Capella Ab or Vega." + The effect of decreasing the eravity darkening exponent is to decrease the total amplitude of the effect in each wavelength. with shorter waveleneths affected more thu longer wavelengths.," The effect of decreasing the gravity darkening exponent is to decrease the total amplitude of the effect in each wavelength, with shorter wavelengths affected more than longer wavelengths." + Thus. the choice of gravity darkening exponent is intimately tied to the derived inclination.," Thus, the choice of gravity darkening exponent is intimately tied to the derived inclination." + If one were to model observed data with a eravity darkening exponent that was ~LO% different than the true value. they would derive au inclination that would also be ~10% ciffercut from the true inclination.," If one were to model observed data with a gravity darkening exponent that was $\sim$ different than the true value, they would derive an inclination that would also be $\sim$ different from the true inclination." + However. the," However, the" +"The parameters m these models are f,=0.5.0.1. 0.01. fifAL)=U038pCM)/8p(2«10AL...) with δρ as in ((3}). vt=136M... fop=33 Myr. and f,,=0.5. The first του of these parameters appear in combination both iu he expression for the overall streneth of the winds (x fFofav) and the metallicity (x fav).","The parameters in these models are $f_\star = 0.5, 0.1, 0.01$ , $f_w(M) += 0.3\delta_B(M)/\delta_B(2 \times 10^8 M_\odot)$ with $\delta_B$ as in \ref{eq:deltaB}) ), $\nu^{-1} = 136 M_\odot$, $t_{\rm OB}= 33$ Myr, and $f_m = 0.5.$ The first three of these parameters appear in combination both in the expression for the overall strength of the winds $\propto f_\star f_w \nu)$ and the metallicity $\propto +f_\star \nu$ )." + Ou the other haud. fop has almost no effect on our results as the relevaut nues for star formation are small compared to structure ormation times scales.," On the other hand, $t_{\rm OB}$ has almost no effect on our results as the relevant times for star formation are small compared to structure formation times scales." + Thus we can provide a conservative estimate of the model uncertainties introduced by these xuanieters by simply cousiderius a wide rauge of star ornmation efüciencies. and applying a linear shift iu the final metallicity to cstimate the effect of varvine fie.," Thus we can provide a conservative estimate of the model uncertainties introduced by these parameters by simply considering a wide range of star formation efficiencies, and applying a linear shift in the final metallicity to estimate the effect of varying $f_w$." +" Finally, while the mass loading parameter f£, las little effect on the overall filliug factor. it is Important for galaxy eedback. and we consider its impact in detail 81123."," Finally, while the mass loading parameter $f_m$ has little effect on the overall filling factor, it is important for galaxy feedback, and we consider its impact in detail 4.3." + The inmost obvious. vet perhaps most important feature of 1l is that the filliug factor is always substautially ess than unity. ranging from to at 2=3.," The most obvious, yet perhaps most important feature of 1 is that the filling factor is always substantially less than unity, ranging from to at $z=3$." +" Note hat these values axe consistent with the 20% curicliueut at 2=| fouud iu nmunuerncal simulations by Thacker. Scannapieco. Davis (2002). using a model simila to our f,=U.l case."," Note that these values are consistent with the $20\%$ enrichment at $z=4$ found in numerical simulations by Thacker, Scannapieco, Davis (2002), using a model similar to our $f_\star = 0.1$ case." +" The fact that ICAL enrichiueut is inhomogeneous even in the maximal case im which of all barvons in collapsed objects are taken to form stars. however. leads us to au important conclusion: starburst dviven outflows. while au effective source of metals in overdeuse regious (SD). are uot able to eurich the ICAL in its entirety,"," The fact that IGM enrichment is inhomogeneous even in the maximal case in which of all baryons in collapsed objects are taken to form stars, however, leads us to an important conclusion: starburst driven outflows, while an effective source of metals in overdense regions (SB), are not able to enrich the IGM in its entirety." + This is true even in the ACDM . model considered in our simulations. in which chwart ealaxics are formed at very lieh redshifts. aud the barvoulc/dark uatter ratio is relatively high. resulting in a large unmuber of stars.," This is true even in the $\Lambda$ CDM model considered in our simulations, in which dwarf galaxies are formed at very high redshifts, and the baryonic/dark matter ratio is relatively high, resulting in a large number of stars." + The details of our results depend sensitively ou the uiiminmni nass scale of the galaxies iu our simulation. iowever. Which is set by our minima virial teniperature of 104 K. Tn the central panel of this figure. we plot a series of models iu which no feedback as per ((7)) is miposed. mit instead we allow outflows only from objects above a fixed mass scale.," The details of our results depend sensitively on the minimum mass scale of the galaxies in our simulation, however, which is set by our minimum virial temperature of $10^4$ K. In the central panel of this figure, we plot a series of models in which no feedback as per \ref{eq:strip}) ) is imposed, but instead we allow outflows only from objects above a fixed mass scale." + Both the redshift at which outflows ein to become miportanut and their overall filling factor depends closely on this mass., Both the redshift at which outflows begin to become important and their overall filling factor depends closely on this mass. +" Thus. while iu the ru with f,=0.1. outflowing bubbles fill of the volume at redslift LL12 and reach a final filling factor of 16% exchiding all objects with masses below 1.1«10?A£., shifts these values to z2:S and 6% respectively."," Thus, while in the run with $f_\star = 0.1$, outflowing bubbles fill of the volume at redshift $\lsim 12$ and reach a final filling factor of $16\%$, excluding all objects with masses below $1.1 \times 10^9 M_\odot$ shifts these values to $z \approx 8$ and $6\%$ respectively." + Note that this lower resolution is similar to that adopted by Aguirre et ((2001a) and approximately equal to the mass of a sinele dark matter particle in the simulations by Cen aud Ostriker (1990)., Note that this lower resolution is similar to that adopted by Aguirre et (2001a) and approximately equal to the mass of a single dark matter particle in the simulations by Cen and Ostriker (1999). + Tn spite of the seusitivitv of metal enrichment to low-uass objects. its overall dependence ou barvouic stripping eedback is weak. as can be seen by comparing the solid ines dn which equation (7)) has been imposed with the dashed lines in which such feedback from outflows is welected.," In spite of the sensitivity of metal enrichment to low-mass objects, its overall dependence on baryonic stripping feedback is weak, as can be seen by comparing the solid lines in which equation \ref{eq:strip}) ) has been imposed with the dashed lines in which such feedback from outflows is neglected." + The shape aud fal value of the filline factor are extremely similar between such models for all values of f. )ocomine indistinguishable in niauy cases.," The shape and final value of the filling factor are extremely similar between such models for all values of $f_\star$, becoming indistinguishable in many cases." + This is because xuvonie stripping can only occur in a perturbation that is sutiicicutly nearby aud latecollapsing., This is because baryonic stripping can only occur in a perturbation that is sufficiently nearby and late–collapsing. + Then the shock velocity. Ry. is large and the overdenuse region occupies a huge solid anele. w. when the outflow reaches it.," Then the shock velocity, $\dot R_s$, is large and the overdense region occupies a large solid angle, $\omega$, when the outflow reaches it." + Thus the perturbations succtunbing to barvonic stripping correspond to lateforming galaxies in the most heavily xopulated regions of space. which have little effect ou the overall &lliug factor.," Thus the perturbations succumbing to baryonic stripping correspond to late–forming galaxies in the most heavily populated regions of space, which have little effect on the overall filling factor." + The higher bias of suppressed objects can also be secu w comparing the evolution of the filliue factor with the overall mass-averaged ICAL metallicity. plotted in the right xuels of Figure 1..," The higher bias of suppressed objects can also be seen by comparing the evolution of the filling factor with the overall mass-averaged IGM metallicity, plotted in the right panels of Figure \ref{fig:vol}." + Iu these panels. the differences between he models with and without suppression are ΙΟ more xonounced.," In these panels, the differences between the models with and without suppression are much more pronounced." +" The ditfercuce is most apparent iu the f,=4.5 case. im which the wind velocities are the highest. aux lus the suppression of ucighbors is most severe."," The difference is most apparent in the $f_\star=0.5$ case, in which the wind velocities are the highest, and thus the suppression of neighbors is most severe." + In this case at 2=3 the overall metallicities differ bv a factor of 1.5 while the difference in volume filliug factor is less than a factor of 1.15., In this case at $z = 3$ the overall metallicities differ by a factor of 1.5 while the difference in volume filling factor is less than a factor of 1.15. + Note that the mass-averaged metallicity scales alios huearly with f.. as this parameter controls the ΠΙΟ of stars formed in each galaxy. and hence the ΠΙΟ: of supernovac aud mass of ejected metals.," Note that the mass-averaged metallicity scales almost linearly with $f_\star$, as this parameter controls the number of stars formed in each galaxy, and hence the number of supernovae and mass of ejected metals." + We find tha at.=3. ZocmQf. where this relation depends on the assmnued vield (2A/.. per SN. 1/2 ejected). the gas ejected fraction (50%). and the iuinuuni mass scaleim the simulation.," We find that at $z = 3$, $Z \approx 0.1 f_\star$, where this relation depends on the assumed yield $2 M_\odot$ per SN, 1/2 ejected), the gas ejected fraction $50\%$ ), and the minimum mass scalein the simulation." +" This mass dependence.while seusitive. is more limited than that of the overall filliug factor. as cau be seen by comparing the f,=0.1 model with the series of iiodels with a threshold mass miposed. plotted in the"," This mass dependence,while sensitive, is more limited than that of the overall filling factor, as can be seen by comparing the $f_\star = 0.1$ model with the series of models with a threshold mass imposed, plotted in the" +stars are aligned (always meaning as seen from the observer with G=0)?,stars are aligned (always meaning as seen from the observer with $G=0$ )? + Should we make the recognition by calling the circular image Chwolson ring instead of Einstein ring?, Should we make the recognition by calling the circular image Chwolson ring instead of Einstein ring? + We consider a few aspects before casting an intellectually reasonable vote., We consider a few aspects before casting an intellectually reasonable vote. +same energy band.,same energy band. + The brightest region does not correspond to the region with the minimum photon energy. at odd with what we observe in the FilD cloud (Fig. 7..," The brightest region does not correspond to the region with the minimum photon energy, at odd with what we observe in the FilD cloud (Fig. \ref{fig:avgEAB}," + right panel)., right panel). + In. Paper 1. we singled out spatial regions with homogeneous physical properties and we performed a spatially resolved spectral analysis on them.," In Paper I, we singled out spatial regions with homogeneous physical properties and we performed a spatially resolved spectral analysis on them." + In order to compare the observed spectra with those synthesized from the hydrodynamic simulations. we have used the same procedure. by defining physically homogeneous regions.," In order to compare the observed spectra with those synthesized from the hydrodynamic simulations, we have used the same procedure, by defining physically homogeneous regions." + The regions are indicated in the upper right panel of Fig. 5..," The regions are indicated in the upper right panel of Fig. \ref{fig:mappeXAB}," + for setup Sphl., for setup Sph1. + In each of these regions there are limited fluctuations of mean photon energy (S1.7% m region a. €6% in region f. and €2% in region y).," In each of these regions there are limited fluctuations of mean photon energy $\la 1.7\%$ in region $\alpha$, $\la 6\%$ in region $\beta$ , and $\la 2\%$ in region $\gamma$ )." + Region « is in the bright northern part of the X-ray knot. where the emission associated to the transmitted shock dominates and the mean photon energy is low. regio P is in the brightest part of the cloud where both transmittec and reflected shocks contribute to the emission. and regior y is located on the South. where we have high values of temperature and of mean photon energy.," Region $\alpha$ is in the bright northern part of the X-ray knot, where the emission associated to the transmitted shock dominates and the mean photon energy is low, region $\beta$ is in the brightest part of the cloud where both transmitted and reflected shocks contribute to the emission, and region $\gamma$ is located on the South, where we have high values of temperature and of mean photon energy." + Part of the regions we selected for the analogous spatially. resolved spectral analysis of the data are shown in Fig. I.., Part of the regions we selected for the analogous spatially resolved spectral analysis of the data are shown in Fig. \ref{fig:XMM}. + The spectral fittings were performed simultaneously on the synthesized and the observed MOS spectra., The spectral fittings were performed simultaneously on the synthesized and the observed MOS spectra. + In agreement with the findings of Paper I. we adopted a MEKAL model of an optically-thin plasma in CIE. with two thermal components. we fixed Nj=1«10°° em. and we left the model Fe abundance free and linked the Ne abundance to it. so as to have (Ne/Nes)/(Fe/Fes)=4.4.," In agreement with the findings of Paper I, we adopted a MEKAL model of an optically-thin plasma in CIE with two thermal components, we fixed $N_{H}=1\times 10^{20}$ $^{-2}$, and we left the model Fe abundance free and linked the Ne abundance to it, so as to have $(Ne/Ne_\odot)/(Fe/Fe_\odot)=4.4$." + We added to the model an energy-independent multiplicative factor to take into account the differences in surface brightness between the synthesized and the observed spectra and the different areas of the spectral regions., We added to the model an energy-independent multiplicative factor to take into account the differences in surface brightness between the synthesized and the observed spectra and the different areas of the spectral regions. + Our results are summarized in Table 2.., Our results are summarized in Table \ref{tab:spettriAB}. + Notice that. since the observed spectra are by themselves well described by this spectral model (as shown in Paper D. the y values in Table 2. can be considered as an indication of the agreement between the observed and the synthesized spectra.," Notice that, since the observed spectra are by themselves well described by this spectral model (as shown in Paper I), the $\chi^{2}$ values in Table \ref{tab:spettriAB} can be considered as an indication of the agreement between the observed and the synthesized spectra." + As shown in the table and in the upper panel of Fig. 8..," As shown in the table and in the upper panel of Fig. \ref{fig:spettriA}," + there Is a good agreement between the spectrum synthesized in region a and those observed in the FilD regions with low mean photon energy (region 2 and region 4). but if we compare the spectra of region B and region 4 (1. e. the ones with the highest synthesized and observed surface brightness). we have significant differences (see Table 2)).," there is a good agreement between the spectrum synthesized in region $\alpha$ and those observed in the FilD regions with low mean photon energy (region 2 and region 4), but if we compare the spectra of region $\beta$ and region 4 (i. e. the ones with the highest synthesized and observed surface brightness), we have significant differences (see Table \ref{tab:spettriAB}) )." + Instead. the spectrum of region 6 has similar spectral features to the one observed in region 7. where the count rate is lower than in region 4. but the mean photon energy is higher.," Instead, the spectrum of region $\beta$ has similar spectral features to the one observed in region 7, where the count rate is lower than in region 4, but the mean photon energy is higher." + The spectrum extracted from region y. not shown in the table. is completely different and significantly harder than all the observed spectra (see the lower panel of Fig. 8)).," The spectrum extracted from region $\gamma$, not shown in the table, is completely different and significantly harder than all the observed spectra (see the lower panel of Fig. \ref{fig:spettriA}) )," + even than those extracted form the RegNE cloud. which ts the hardest X-ray emitting region in the EPIC field of view (see Paper I).," even than those extracted form the RegNE cloud, which is the hardest X-ray emitting region in the EPIC field of view (see Paper I)." + InSph2.. the post shock temperature of the cloud (1. e. the temperature behind the transmitted shock) is ~10° K (as in setup Sphl). while the cloud density is slightly higher than in setup Sphl (n.€6 em).," In, the post shock temperature of the cloud (i. e. the temperature behind the transmitted shock) is $\sim10^{6}$ K (as in setup Sph1), while the cloud density is slightly higher than in setup Sph1 $n\la 6$ $^{-3}$ )." + We synthesized the X-ray count-rate maps and focal plane spectra also for setup Sph2., We synthesized the X-ray count-rate maps and focal plane spectra also for setup Sph2. + The emission morphologies in the three energy bands (0.3—0.5 keV. 0.5—| keV. and 0.3—2 keV) are very similar to those of setup Sphl.," The emission morphologies in the three energy bands $0.3-0.5$ keV, $0.5-1$ keV, and $0.3-2$ keV) are very similar to those of setup Sph1." + Moreover. the synthesized X-ray emission presents similar spectroscopic features to setup Sphl (see Sect. 3.1)).," Moreover, the synthesized X-ray emission presents similar spectroscopic features to setup Sph1 (see Sect. \ref{A: spherical cloud}) )." + However. the global X-ray luminosity of setupSph2 ts too high (more than one order of magnitude) with respect to the observed one. therefore this setup will not be discussed in detail.," However, the global X-ray luminosity of setupSph2 is too high (more than one order of magnitude) with respect to the observed one, therefore this setup will not be discussed in detail." +for Rez21 ancl. respectively. all 2.ha,"for $\mbox{Re}~z>1$ and, respectively, all $z$." +"ve Following steps similar to those leading to (161). we have £(2)=—— that may be decomposed in integration over (0.1] and. |1.x). where""her gi(2) :)includes regularization about z2=1 made explicit in (260))(26)) by —L.=>. wherewher (he singulari(v αἱ z=1 in € can be seen (o result [rom the Prime Number Theorem in the form of οντό)—1=o(1) on the basis of the asymptotic behavior of the function 1999)."," Following steps similar to those leading to \ref{EQN_R}) ), we have $\xi(z)=\frac{\pi^\frac{z}{2}}{\Gamma\left(\frac{z}{2}\right)}\int_0^\infty x^{\frac{z}{2}-1}\phi(x) dx,$ that may be decomposed in integration over $(0,1]$ and $[1,\infty)$, where $g_1(z)$ includes regularization about $z=1$ made explicit in \ref{EQN_B0}) ) by $\frac{1}{z-1}$, where the singularity at $z=1$ in $\xi$ can be seen to result from the Prime Number Theorem in the form of $2\sqrt{x}\phi(x)-1=o(1)$ on the basis of the asymptotic behavior of the function \citep{dus99}." +. The substitution .c=€? gives (25))., The substitution $x=e^{2\lambda}$ gives \ref{EQN_R4}) ). + , $\Box$ . +In a neighborhood of 00.," In a neighborhood of $00$." + With z=a4 ib. the second term on the right haud side in the expancecl Evler’s identity (7)) satisfies whereby it is bounded in Re 2=a>5.," With $z=a+ib$ , the second term on the right hand side in the expanded Euler's identity \ref{EQN_B2}) ) satisfies whereby it is bounded in Re $z=a>\frac{1}{2}$." + Since the second (term ¢(22) in (7)) is analvGe in Rez=a> 4. it follows that g(a) as defined in Proposition 3.1 is analvtic on a>+.," Since the second term $\zeta(2z)$ in \ref{EQN_B2}) ) is analytic in Re $z=a>\frac{1}{2}$ , it follows that $g(a)$ as defined in Proposition 3.1 is analytic on $a>\frac{1}{2}$." + In view ol the analytic and finite behavior of the right hand sidein (7)). the first aud second term on the left hand side in (7)) remain balanced as à approaches 4fromthe right. giving where oli) is analvtic al à= 4.," In view of the analytic and finite behavior of the right hand sidein \ref{EQN_B2}) ), the first and second term on the left hand side in \ref{EQN_B2}) ) remain balanced as $a$ approaches $\frac{1}{2}$fromthe right, giving where $u_2(a)$ is analytic at $a=\frac{1}{2}$ ." + As à approaches 4 [rom theright. we have," As $a$ approaches $\frac{1}{2}$ from theright, we have" +"(2006).. 1£ £i""moc. the cnerev losses. and annihilation rates diller by only a factor of —10 and a substantial fraction of high energy positrons annihilate during the slow-down process.",", if $E_{\rm kin}\gg m_ec^2$, the energy losses and annihilation rates differ by only a factor of $\sim$ 10 and a substantial fraction of high energy positrons annihilate during the slow-down process." + These high energy. positrons will form a broad feature at a mean energy cm««|Lys2. while the slowed down positrons will annihilate at. much lower energies and will power a narrow 511 keV line.," These high energy positrons will form a broad feature at a mean energy $\sim +m_ec^2+E_{\rm kin}/2$, while the slowed down positrons will annihilate at much lower energies and will power a narrow 511 keV line." + Thus. a high energy (above 511 keV) component is expected. to be present in the spectrum. with the relative intensity with respect to the narrow 511 keV line depending on the initial positron energy. {μμ and the ionization state of the interstellar medium.," Thus, a high energy (above 511 keV) component is expected to be present in the spectrum, with the relative intensity with respect to the narrow 511 keV line depending on the initial positron energy $E_{\rm kin}$ and the ionization state of the interstellar medium." + The latter controls the contribution of the ionization ancl Coulomb losses to the total energy. loss rate., The latter controls the contribution of the ionization and Coulomb losses to the total energy loss rate. + Shown in Fig., Shown in Fig. + 19 is the observed. spectrum. of the julge component and the expected. in-flight annihilation for a neutral (solid) and. ionizecl (dashed) medium., \ref{fig:ia} is the observed spectrum of the Bulge component and the expected in-flight annihilation for a neutral (solid) and ionized (dashed) medium. + The clifference in normalization is due to the larger energv losses in the ionized. medium. which increases the fraction of the slowed down positrons at the expense of in-Hight annihilation.," The difference in normalization is due to the larger energy losses in the ionized medium, which increases the fraction of the slowed down positrons at the expense of in-flight annihilation." + Phe fraction of slowed down positrons annihilating via positronium formation was set to {ως=0.07., The fraction of slowed down positrons annihilating via positronium formation was set to $f_{\rm ps}=0.97$ . + The spectra shown correspond to initial positron energies of 1. 3. 5. 10. 50 ancl 100 MeV. No significant Ilux above 511 keV is observed by SPL in the Bulge component (for the two-component model described in refsecitemplates)). and in Fig.," The spectra shown correspond to initial positron energies of 1, 3, 5, 10, 50 and 100 MeV. No significant flux above 511 keV is observed by SPI in the Bulge component (for the two-component model described in \\ref{sec:templates}) ), and in Fig." + LO we show the corresponding 20 upper limits., \ref{fig:ia} we show the corresponding $\sigma$ upper limits. + IEvidently. the SPI data above 511 keV do not place tight constraints on the initial energy of positrons.," Evidently, the SPI data above 511 keV do not place tight constraints on the initial energy of positrons." +" As discussed by Beacom&Yüksel(2006):Sizun.Casse.Schanne(2006).. tighter constraints come from ςΟΛΗTEL data combined. with the SPI measurements of the 511 keV line Hus and. fi. restricting £i, to less than 37.5 MeV. depending on the ionization state of the medium (seeGCregion).."," As discussed by \citet{2006PhRvL..97g1102B,2006PhRvD..74f3514S}, tighter constraints come from COMPTEL data combined with the SPI measurements of the 511 keV line flux and $f_{\rm ps}$, restricting $E_{\rm kin}$ to less than 3–7.5 MeV, depending on the ionization state of the medium \citep[see + also][for similar calculations based on earlier measurements of the + gamma-ray flux from the GC region]{1981SvAL....7..395A}." + The limits on the Bulec Hux above 511. keV clo not stronely constrain the amount of cosmic rays in theDulge. which may produce positrons via a procluction.," The limits on the Bulge flux above 511 keV do not strongly constrain the amount of cosmic rays in theBulge, which may produce positrons via $\pi^+$ production." +" Indeed. the sae cosmic rays would also produce a comparable amount of z. which would be visible as gamma-ray emission with a peak around LOO MeV. As discussed. by c.g. Abaronian&Atovan (2000). the total gamma-ray [lux from the Inner Galaxy associated. with x"" decav does not exceed ~10photcmτςlay corresponding to a [lux ἳ withing the Dulge area (assuming a solid. angle of the Bulge of —0.1sr."," Indeed, the same cosmic rays would also produce a comparable amount of $\pi^0$, which would be visible as gamma-ray emission with a peak around 100 MeV. As discussed by e.g. \citet[][]{2000A&A...362..937A}, the total gamma-ray flux from the Inner Galaxy associated with $\pi^0$ decay does not exceed $\sim 10^{-4}~{\rm + phot~cm^{-2}~s^{-1}~sr^{-1}}$, corresponding to a flux $\lesssim + 10^{-5}~{\rm phot~cm^{-2}~s^{-1}}$ withing the Bulge area (assuming a solid angle of the Bulge of $\sim 0.1~{\rm sr}$." + This is about two orders of magnitude smaller than the observed. Bulge παν 10phots in the annihilation linc., This is about two orders of magnitude smaller than the observed Bulge flux $10^{-3}~{\rm phot~s^{-1}}$ in the annihilation line. + The curves shown in Fig., The curves shown in Fig. + 10. are scaled. by the observed rate of. positron woduction and they approximately match the SPL upper imits (for the initial energv of positrons ~LOO MeV)., \ref{fig:ia} are scaled by the observed rate of positron production and they approximately match the SPI upper limits (for the initial energy of positrons $\sim$ 100 MeV). + Therefore. the SPL upper limits on the in-flight annihilation of positrons constrain the mw production rate to be less han ~10sfl.," Therefore, the SPI upper limits on the in-flight annihilation of positrons constrain the $\pi^+$ production rate to be less than $\sim 10^{-3}~{\rm s^{-1}}$." + Since the w and x” production rates w the same cosmic ravs are comparable. it is obvious hat observations of LOO MeV. gamma-rays provide much ῃehter constraints on the amount of cosmic ravs in the E2ulge.," Since the $\pi^+$ and $\pi^0$ production rates by the same cosmic rays are comparable, it is obvious that observations of $\sim 100$ MeV gamma-rays provide much tighter constraints on the amount of cosmic rays in the Bulge." + We now proceed with spectral fitting of the 511 keV line and ortho-positronium continuum below 511 keV. The simplest possible model is a combination of a Gaussian at 511 keV to describe two-photon annihilation and the three-photon spectrum of Ore&Powell (1949).., We now proceed with spectral fitting of the 511 keV line and ortho-positronium continuum below 511 keV. The simplest possible model is a combination of a Gaussian at 511 keV to describe two-photon annihilation and the three-photon spectrum of \citet{1949PhRv...75.1696O}. . + The line normalization. energv and width and the normalization of the ortho- continuum. are free. parameters of the moclel.," The line normalization, energy and width and the normalization of the ortho-positronium continuum are free parameters of the model." + The best-fitting values of these parameters are given in Table, The best-fitting values of these parameters are given in Table +Mapping the entire disk of M31 at mic-inlrarecl wavelengths allows local aid global studies of the galaxy.,Mapping the entire disk of M31 at mid-infrared wavelengths allows local and global studies of the galaxy. + Observations with the Infrared Array. Camera (IRAC: on theTelescope simultaneously (trace the dust in the spiral arms at and the oldest stars in the disk and bulge al 3.6 and without the complicating extinction or distance effects that make such studies in the Milky Way difficult., Observations with the Infrared Array Camera \citep[IRAC;][]{irac} on the simultaneously trace the dust in the spiral arms at and the oldest stars in the disk and bulge at 3.6 and without the complicating extinction or distance effects that make such studies in the Milky Way difficult. + IRAC observations of M31 are complemented by deep data now available al many other wavelengths., IRAC observations of M31 are complemented by deep data now available at many other wavelengths. + They also complement.Spitzer studies of other nearby galaxies., They also complement studies of other nearby galaxies. + This paper presents an initial look at the IRAC observations of. M31. focusing on the surface brightness profiles and extended: emission.," This paper presents an initial look at the IRAC observations of M31, focusing on the surface brightness profiles and extended emission." + Companion papers discuss longer-wavelength. MIPS observations of M31 (Gordonοἱal.2006).. FRAC and MIPS observations of the M31 satellite galaxy NGC 205 (Marleauetal.2006)... and the implications of the ealaxy’s morphology as seen in non-stellar emission (Blocketal.2006).," Companion papers discuss longer-wavelength MIPS observations of M31 \citep{gordon06}, IRAC and MIPS observations of the M31 satellite galaxy NGC 205 \citep{marleau06}, and the implications of the galaxy's morphology as seen in non-stellar emission \citep{block06}." +.. A distance to AI3l of 783 kpe (Stanek&Garnavich1998). is assumed throughout.," A distance to M31 of 783 kpc \citep{sg98} + is assumed throughout." + All magnitudes are on the Vega svstem. using the calibration given bv Reachetal.(2005)..," All magnitudes are on the Vega system, using the calibration given by \citet{reach05}." + The IRAC observations of M31 were taken as part ofSpitzer General Observer program 3126 in 2005 January and Fifteen Astronomical Observation Requests (AORs) were used to map a region approximately 37x176 (chosen to match the Spifzer/MIPS observations mace as part of program ID 99). with an extension to the NW to include NGC 205.," The IRAC observations of M31 were taken as part of General Observer program 3126 in 2005 January and Fifteen Astronomical Observation Requests (AORs) were used to map a region approximately $3\fdg7 \times 1\fdg6$ (chosen to match the /MIPS observations made as part of program ID 99), with an extension to the NW to include NGC 205." + The central 126x(054 was covered. by three AORs. each having two I2-second [rames per position.," The central $1\fdg6 \times 0\fdg4$ was covered by three AORs, each having two 12-second frames per position." + The outer regions were covered bv two AORs each with two clithered 30-second frames per position., The outer regions were covered by two AORs each with two dithered 30-second frames per position. + This mapping strategy ensured that observations of each position in the galaxy. were separated by at least 2.5 hours. allowing efficient asteroid rejection in data processing.," This mapping strategy ensured that observations of each position in the galaxy were separated by at least 2.5 hours, allowing efficient asteroid rejection in data processing." + The complete dataset consists of 3000 individual images in each of the IRAC channels., The complete dataset consists of 3000 individual images in each of the IRAC channels. + Data reduction began with the Basie Calibrated Data (BCD) produced by versions 11 (for the January data) or 12 (he August data) of theSpizer Science Center (SSC) Pipeline., Data reduction began with the Basic Calibrated Data (BCD) produced by versions 11 (for the January data) or 12 (the August data) of the Science Center (SSC) Pipeline. +" A ""delta. dark’ offset correction was applied to the 12-second frames to correct. for the first-lrame effect. Lollowed by use of the ‘artifact corrector. software developed by S. Carey. which attempts to remove the electronic effects caused by bright stars."," A `delta dark' offset correction was applied to the 12-second frames to correct for the first-frame effect, followed by use of the `artifact corrector' software developed by S. Carey, which attempts to remove the electronic effects caused by bright stars." + The remaining, The remaining +Chicago. Fermilab. the Institute for Advanced Study. the Japan Participation Group. The Johns Hopkins University. Los Alamos National Laboratory. the Max-Planck-Institue for Astronomy (MPIA). the Max-Planck-Institute for Astrrophysics (MPA). New Mexico State University. University of Pitsburgh. Princeton University. the United States Naval Observatory. and the University of Washington.,"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." +disk covered by individual structures.,disk covered by individual structures. + In this way. we have considered separately the evolution of large active regions and small short-lived ephemeral regions.," In this way, we have considered separately the evolution of large active regions and small short-lived ephemeral regions." + Additionally. we have considered the evolution of sunspots (umbrae and penumbrae).," Additionally, we have considered the evolution of sunspots (umbrae and penumbrae)." + The coefficients of the neural network are constrained by comparing the output of the model and measurements of the solar irradiance by instruments onboard of SORCE spacecraft., The coefficients of the neural network are constrained by comparing the output of the model and measurements of the solar irradiance by instruments onboard of SORCE spacecraft. + The generalization of the network is tested by dividing the data sets on two groups: (1) the training set; and. (2) the validation set.," The generalization of the network is tested by dividing the data sets on two groups: (1) the training set; and, (2) the validation set." + We have found that the model error is wavelength dependent., We have found that the model error is wavelength dependent. + While the model error for 24-hour forecast in the band from 115 to 180 nm is lower than, While the model error for 24-hour forecast in the band from 115 to 180 nm is lower than +"spectra from tje three observations we obtaine Lan upoor Li coufideuce) for the fiux of a line at keV dn the backeround spectimm s«—LlJ|κ* photous 97sἘν Ίνα, κτά of the cetected liιο flux.","spectra from the three observations we obtained an upper limit confidence) for the flux of a line at keV in the background spectrum $n < 4.14 \times 10^{-8}$ photons $^{-2}{\rm s^{-1}}$ , i.e. $< 1$ of the detected line flux." + The lack of a feaτιre at comparable flux or equivalent widhi n 1ο backeround data also rules out an origin of the kkeV line as a detector feature., The lack of a feature at comparable flux or equivalent width in the background data also rules out an origin of the keV line as a detector feature. + We μοι exauined each NIS independenlv. aud ound the KkeV liue to be siguiBcantlv deected iu each NIS unit independenlv. further verifviug he reality of the reported feature (Figure 6)).," We then examined each XIS independently, and found the keV line to be significantly detected in each XIS unit independently, further verifying the reality of the reported feature (Figure \ref{fig:in3xis}) )." + Regarding tle more eutative ine at kkeV: the AIS cup does include. a Mn calibration source eiuitine a line at kkeC for the purpose of calibration of the AXIS encYev scale., Regarding the more tentative line at keV: the XIS chip does include a Mn calibration source emitting a line at keV for the purpose of calibration of the XIS energy scale. + The calibratiOl sonrco Is ocated at the cu» edge aud the counts from hat source are obviously conservativelv excluled. from ay μ.ο... and bacseround extractio1 cells for scientific alalvsis., The calibration source is located at the chip edge and the counts from that source are obviously conservatively excluded from any source and background extraction cells for scientific analysis. +" Ilowever awe clo cletec fox weak Mu Ixo emission iu the backerouud προςσπα,"," However, we do detect a weak Mn $\alpha$ emission in the background spectrum." + The Mn coutanination Ina a level «10%( |: the measured ne sreneth in the AGN spectruiu., The Mn contamination is at a level $< 10\%$ of the measured line strength in the AGN spectrum. +" As the source extraction cell is further Yolu the Abu calibratio1 sonrce thaji the backeroui cell and therefore sub,ject to ess Contalatiol. Wwe ονiniate the Mu line COLLaunination frou 1C Caibration source to iIO M_{\rm lim},z)$ by integrating appropriately over $z$, that is, In order to compute the limiting mass of the survey we will make a point source approximation, that is, we will assume that each galaxy detected will be smaller than the telescope beam, and hence, all the flux it emits will contribute to a single beam." + This is likely to be à good approximation for most objects in the survey. but will break down for the closest. most massive objects.," This is likely to be a good approximation for most objects in the survey, but will break down for the closest, most massive objects." + We expect those objects which violate this assumption to be the minority if we choose the survey strategy sensibly., We expect those objects which violate this assumption to be the minority if we choose the survey strategy sensibly. + There is an empirically derived relation between the LIL chameter. gj. which is defined to be the region inside which the LIE surface density is greater than LAL.pe>. and the LLL mass of a galaxy.," There is an empirically derived relation between the HI diameter, $D_{\rm HI}$, which is defined to be the region inside which the HI surface density is greater than $1M_{\odot}\,{\rm pc}^{-2}$, and the HI mass of a galaxy." + This can be used to investigate the extent to which the point source approximation is valid., This can be used to investigate the extent to which the point source approximation is valid. + We will use (BrocilsandRhee1997:VerheijenSancisi2001) which has been converted to an angular scale using the angular diameter distance dy(2) for the range of relevant IHE masses in Fig. 1..," We will use \citep{BR,VS} + which has been converted to an angular scale using the angular diameter distance $d_{\rm A}(z)$ for the range of relevant HI masses in Fig. \ref{fig:rda}." + We note immediately that at z50.02 massive galaxies containing LOAAL. of LEE will be resolved by the FAST beam (see Fig. 1)), We note immediately that at $z\approx 0.02$ massive galaxies containing $10^{10}M_{\odot}$ of HI will be resolved by the FAST beam (see Fig. \ref{fig:rda}) ) + but we postpone more detailed discussion of the validity of the point source assumptions to later in section D. Lhe beam area increases like A7x(1|z)., but we postpone more detailed discussion of the validity of the point source assumptions to later in section B. The beam area increases like $\lambda^{2}\propto (1+z)^2$ . + As a result if an optimal survey strategy. in which one uniformly tiles the z=0 slice. is chosen then slices of the survey at higher redshift receive extra exposure due to the fact that hese slices will overlap.," As a result if an optimal survey strategy, in which one uniformly tiles the $z=0$ slice, is chosen then slices of the survey at higher redshift receive extra exposure due to the fact that these slices will overlap." + Ehe elect has been considered in ref., The effect has been considered in ref. + (AbdallaancRawlings2004) where it was shown that he Hux limit relevant toa particular redshift slice is reduced w (112)te, \citep{AR} where it was shown that the flux limit relevant to a particular redshift slice is reduced by $(1+z)^{-1}$. + Hence. the (lux limit for an observation. Spy. or à specific signal-to-noise ratio (S/N) is given by A given object is detectable if its flux density in bancwidth Av=vAVfe is ereater than Spa ," Hence, the flux limit for an observation, $S_{\rm lim}$, for a specific signal-to-noise ratio $(S/N)$ is given by A given object is detectable if its flux density in bandwidth $\Delta\nu=\nu\Delta V_o/c$ is greater than $S_{\rm lim}$." +"A simple assumption. which should vield an order of magnitude estimate of the number of objects that one might expect to fine in a survey. is that the line width ofa£ the galaxies is AV,=200kms"," A simple assumption, which should yield an order of magnitude estimate of the number of objects that one might expect to find in a survey, is that the line width of the galaxies is $\Delta V_{\rm o}=200\,{\rm km}\,s^{-1}$." + Under this assumption we have computed Αμ). anc the number of. galaxies one would expect to find in an average cay of observation as a function of La. the amount of time spent observing each beam area.," Under this assumption we have computed $M_{\rm lim}(z)$ and the number of galaxies one would expect to find in an average day of observation as a function of $t_{\rm obs}$, the amount of time spent observing each beam area." + Allowing for calibration and. telescope maintainance. we will use an on-source integration time of 15 hours to represent one day.," Allowing for calibration and telescope maintainance, we will use an on-source integration time of 18 hours to represent one day." + Ehe mass limit and number counts as a Function of redshift Gvith bin width As= 0.01) are presented in Fig., The mass limit and number counts as a function of redshift (with bin width $\Delta z=0.01$ ) are presented in Fig. + 2. for S/N=4 for ny=19., \ref{fig:simple} for $S/N=4$ for $n_{\rm B}=19$. + The probability of a spurious detection will be ο«10 assuming a Gaussian distribution for the noise.," The probability of a spurious detection will be $\sim 6\times 10^{-5}$, assuming a Gaussian distribution for the noise." +" Since an all sky survey will contain 4«10 independent. volume elements (the number of independent beam areas multipliec by the number of indepndent depth slices) this would mean ~210"" spurious detections.", Since an all sky survey will contain $\sim 4\times 10^{9}$ independent volume elements (the number of independent beam areas multiplied by the number of indepndent depth slices) this would mean $\sim 2\times 10^{5}$ spurious detections. + In such a survey. therefore. iere. will be around. I spurious detections (we will finc i around LO’ galaxies can be detected).," In such a survey, therefore, there will be around $1\%$ spurious detections (we will find that around $10^{7}$ galaxies can be detected)." + This will no gaignificantly alfect the measurement of the power spectrum iscussed in the [ater sections of this paper., This will not significantly affect the measurement of the power spectrum discussed in the later sections of this paper. + One can immediately scale the number counts cliscusse in the previous paragraph to longer integration times aux larger numbersof beams., One can immediately scale the number counts discussed in the previous paragraph to longer integration times and larger numbersof beams. + ἑμνον ds the total time ofthe survey and the focal plane array has vp beams then the number of galaxies detected at a particular signal-to-noise ratio is given by, If $t_{\rm survey}$ is the total time ofthe survey and the focal plane array has $n_{\rm B}$ beams then the number of galaxies detected at a particular signal-to-noise ratio is given by +in its spectrum.,in its spectrum. + With the lieher spatial resolution of the data. we do not resolve significaut line ciission comune from the stellar poiut source (see Figure 6.. Left).," With the higher spatial resolution of the data, we do not resolve significant line emission coming from the stellar point source (see Figure \ref{Ddetail}, Left)." + It is likely that the spectrum from resulted. from a superposition of nebular cussion lines from the region and the stellar coutimmiu frou this star., It is likely that the spectrum from resulted from a superposition of nebular emission lines from the region and the stellar continuum from this star. + The strongest evidence for a disk iu region D from our data is the apparent void of radio aud emission between the the two peaks of region D. a dark lane runing north-south through its center iu both radio aud nuages," The strongest evidence for a disk in region D from our data is the apparent void of radio and emission between the the two peaks of region D, a dark lane running north-south through its center in both radio and images." + We suggest that this dark lane represcuts a region of largely neutral gas which has been shielded from the ionizing radiation of the central star by the disk (see Figure 8))., We suggest that this dark lane represents a region of largely neutral gas which has been shielded from the ionizing radiation of the central star by the disk (see Figure \ref{Dmodel}) ). + Absent a disk. oue melt expect to see a amore continuous spherical shell of ionizatiou around the star.," Absent a disk, one might expect to see a more continuous spherical shell of ionization around the star." + Although our extinction map does not. clearly identify a peak of extinction at or around the ionizing star corresponding to this disk. this is not iuconsisteut with the preseuce of a deuse disk.," Although our extinction map does not clearly identify a peak of extinction at or around the ionizing star corresponding to this disk, this is not inconsistent with the presence of a dense disk." + We can explain the lack of significant extinction detected toward this disk if the disk. is smaall and thus uuresolved by our observations. 6 vit the disk does not occult significant ionized euission along the line of sight. in which case we would have no meeΠοτάΊο on the extinction toward the neutral gas. wcluding the disk. along the line of sight of the disk.," We can explain the lack of significant extinction detected toward this disk if the disk is small, and thus unresolved by our observations, or if the disk does not occult significant ionized emission along the line of sight, in which case we would have no information on the extinction toward the neutral gas, including the disk, along the line of sight of the disk." + An crample sightline for which this would be the case is shown in Figure 8.., An example sightline for which this would be the case is shown in Figure \ref{Dmodel}. + We concur with vat the asvuuuctry of the cluission from region D. with the blueshifted: ciission arising much closer to the ceutral star than the redshifted Cluission. is almost certainly duc to the region being embedded: in a deusitv eradient (see Figure 8)).," We concur with that the asymmetry of the emission from region D, with the blueshifted emission arising much closer to the central star than the redshifted emission, is almost certainly due to the region being embedded in a density gradient (see Figure \ref{Dmodel}) )." + The extinction measured toward the easteru peal of D is slightly lower than that measured toward the western peak. aud the cinission falls off mach more steeply ou the western edee of D. suggesting a lore steeply Increasing colunn density eradieut m that direction.," The extinction measured toward the eastern peak of D is slightly lower than that measured toward the western peak, and the emission falls off much more steeply on the western edge of D, suggesting a more steeply increasing column density gradient in that direction." + This increase in column density corresponds to the location of the deuse western ridge of the M-0.02-0.07 cloud. located between the regions aud Ser A East (see Figure 3)).," This increase in column density corresponds to the location of the dense western ridge of the M-0.02-0.07 cloud, located between the regions and Sgr A East (see Figure \ref{color}) )." + Tudeed. a comparison of the position of region D to higher resolution observations of dense gas traced by aüiunonia (1.1) enissiou in the western ridge shows that region D appears to lie on the castern edge of a dense core (see Figure 10)).," Indeed, a comparison of the position of region D to higher resolution observations of dense gas traced by ammonia (1,1) emission in the western ridge shows that region D appears to lie on the eastern edge of a dense core (see Figure \ref{nh3}) )." + Based on its extinction. region D is likely embedded in or behind this core.," Based on its extinction, region D is likely embedded in or behind this core." + A structure reminiscent of region D is also seen on the northeast edee of region A (Figure 9))., A structure reminiscent of region D is also seen on the northeast edge of region A (Figure \ref{A_lane}) ). + A protrusion of cuuission is separated from the main shell of region A bv another apparently dark huie. exhibiting a lack of cluission iu both ands.l GIIz images.," A protrusion of emission is separated from the main shell of region A by another apparently dark lane, exhibiting a lack of emission in both and 8.4 GHz images." + This protrusion of cuuission is also resolved in the Ne II spectra of7.. but appears not to have the same kinematic structure as reeion D: cussion on cach side of the dark lane appears to have the same radial velocity.," This protrusion of emission is also resolved in the Ne II spectra of, but appears not to have the same kinematic structure as region D: emission on each side of the dark lane appears to have the same radial velocity." + It is still possible that this structure. like region D. is a vouug massive disk. with the dark lane correspouding to the shadow of the disk. but either it has no collamatecdl outflows. or we are observing this svsteii closer to edgc-on.," It is still possible that this structure, like region D, is a young massive disk, with the dark lane corresponding to the shadow of the disk, but either it has no collimated outflows, or we are observing this system closer to edge-on." + Like region D. a star is visible sliehtlv. offset from the ceuter of the dark lane.," Like region D, a star is visible slightly offset from the center of the dark lane." + The star is visible in ucar-infrared images of and appears similar in color to the star m region D. though uo value for its ΗΝ color is reported.," The star is visible in near-infrared images of and appears similar in color to the star in region D, though no value for its H-K' color is reported." + To verify the presence of a disk iu regious A aud D. one could observe these regions at high spatialresolution iu the millimeter and radio regimes to search for wart dust or molecular gas in the disk. or even free-free cussion from the surface of the disk.," To verify the presence of a disk in regions A and D, one could observe these regions at high spatial-resolution in the millimeter and radio regimes to search for warm dust or molecular gas in the disk, or even free-free emission from the surface of the disk." + Ilehler resolution spectra of the stars in regions A and D could also help determine whether thei properties are consistent with extremely vouue. massive stars.," Higher resolution spectra of the stars in regions A and D could also help determine whether their properties are consistent with extremely young, massive stars." + To the southwest of region À lie three roughly linear ionized ridges with increasing separation from the opening of the region (Figures 2.. 11)).," To the southwest of region A lie three roughly linear ionized ridges with increasing separation from the opening of the region (Figures \ref{palpha}, \ref{A_fils}) )." + While it is possible that these ridges could be pre-existing structures that are being ilhuniuated as the central star of region A passes nearby. their unusual aligumieut with cach other and with the opening of region A sugeests a closer relationship.," While it is possible that these ridges could be pre-existing structures that are being illuminated as the central star of region A passes nearby, their unusual alignment with each other and with the opening of region A suggests a closer relationship." + We interpret thon as most Lisely to be the interaction between au ionized flow frou inside region A and the diffuse surrounding ISM., We interpret them as most likely to be the interaction between an ionized flow from inside region A and the diffuse surrounding ISM. + These luab-briehtened shells would propagate outward at the souud speed., These limb-brightened shells would propagate outward at the sound speed. + Tf. as sugeested by?.. region A is moving both to the east and toward us. then we should be able to see a differeuce in velocity between the racial velocitics of region A aud the expaudiug shells.," If, as suggested by, region A is moving both to the east and toward us, then we should be able to see a difference in velocity between the radial velocities of region A and the expanding shells." + However. the magnitude of such a velocity difference would be the sound speed (~ 10 kia 1) projected along the line of sight. aud for motion 20 to 30 degrees out of the plane of the sky would correspond to a velocity differcuce of ouly 3 to 5 hans +.," However, the magnitude of such a velocity difference would be the sound speed $\sim$ 10 km $^{-1}$ ) projected along the line of sight, and for motion 20 to 30 degrees out of the plane of the sky would correspond to a velocity difference of only 3 to 5 km $^{-1}$." + In Figure S (Left) of ?.. two of the ridges are seen to have radial velocities around ~50 kj 1. similar to the mean radial velocity of the region. aud of the ambient medium of the M-0.02-0.07 cloud.," In Figure 8 (Left) of , two of the ridges are seen to have radial velocities around $\sim 50$ km $^{-1}$, similar to the mean radial velocity of the region, and of the ambient medium of the M-0.02-0.07 cloud." + The data show uo evidence for a velocity difference between region A aud the ridges of ereater than 5 kin but the data lack the velocity resolution to couchisively determine whether a smaller velocity shift is present.," The data show no evidence for a velocity difference between region A and the ridges of greater than 5 km $^{-1}$, but the data lack the velocity resolution to conclusively determine whether a smaller velocity shift is present." + Alternatively. it is possible these structures could be due to an instability first proposed for the case of old planetary nebulae passing through a magnetized ISM. essentially à maguetie Ravleigh-Tavlor instability).," Alternatively, it is possible these structures could be due to an instability first proposed for the case of old planetary nebulae passing through a magnetized ISM, essentially a magnetic Rayleigh-Taylor instability." +. As post-shock material cools isothermally. it is subject to a maenetie Ravieigh-Tavlor instability. stabilized in the direction perpendicular to the maeuetic field. leaciug to a deusity pattern of ridges iu the ISAL behiud the region. parallel to the ambient maeuetic field.," As post-shock material cools isothermally, it is subject to a magnetic Rayleigh-Taylor instability, stabilized in the direction perpendicular to the magnetic field, leading to a density pattern of ridges in the ISM behind the region, parallel to the ambient magnetic field." + Although he inferred velocity of the ceutral star of region A Gs slower than the nium estimated ly for siguificant instabilities to develop (10 kia 1). the warn deuse ISM of the GC combined with the likely xeseuce of a strong pervasive maeuetie field2). ave both factors that should be conducive o the development of such instabilitics.," Although the inferred velocity of the central star of region A is slower than the minimum estimated by for significant instabilities to develop (40 km $^{-1}$ ), the warm, dense ISM of the GC combined with the likely presence of a strong pervasive magnetic field, are both factors that should be conducive to the development of such instabilities." + IIowever. it is unclear why sinular iustabilities would uot also be seeu ο be associated with regions D aud C. which are believed o be have the same stellar wind bowshock kinenmatics(?).," However, it is unclear why similar instabilities would not also be seen to be associated with regions B and C, which are believed to be have the same stellar wind bowshock kinematics." +. Iligher spectral-resolutiou observations as well as iore sensitive observatious of the faint ionized sas in these ridgelike features are necessary to determine whether the ridges of region A lave kinematics cousisteut with shells propagating outward at the sound speed., Higher spectral-resolution observations as well as more sensitive observations of the faint ionized gas in these ridgelike features are necessary to determine whether the ridges of region A have kinematics consistent with shells propagating outward at the sound speed. + Iu addition. if the iouiziug sources for these reeious were identified. measuring the radial velocities of thestars could testthe possibility that the ridges are due to a," In addition, if the ionizing sources for these regions were identified, measuring the radial velocities of thestars could testthe possibility that the ridges are due to a" +"Yo illustrate the effects. we use a sample of realistic photometric redshift probabilities [p(2,)). from Borcdoloi οἱ al. (","To illustrate the effects, we use a sample of realistic photometric redshift probabilities $\{p(z_p)\}$ from Bordoloi et al. (" +2009). which are a simulated set of redshift: probability distributions like those expected from ISuclid.,"2009), which are a simulated set of redshift probability distributions like those expected from Euclid." + We show these in Figure 1.., We show these in Figure \ref{realpz}. + We use a representative sample of 3000 redshift distributions. for computational speed. which for a surface number density of ny=35 per square arcmin represents a sample of galaxies from around. LOO square arcmin.," We use a representative sample of $3000$ redshift distributions, for computational speed, which for a surface number density of $n_0=35$ per square arcmin represents a sample of galaxies from around $100$ square arcmin." + This is low compared to the expected number of galaxies in future surveys. however we use this sample as representative for the investigation of the approximations we highlighted. in Section 2.1 in fact with low(er) number statistics we may expect a larger deviation than in reality because the error on the mean will be larger (a L/N elfect).," This is low compared to the expected number of galaxies in future surveys, however we use this sample as representative for the investigation of the approximations we highlighted in Section \ref{Including Photometric Redshifts} – in fact with low(er) number statistics we may expect a larger deviation than in reality because the error on the mean will be larger (a $1/N$ effect)." + To match the total number to the surface density we multiplv the signal covariance by an extra factor of (05/3000)? (and the noise by ny 2000)., To match the total number to the surface density we multiply the signal covariance by an extra factor of $(n_0/3000)^2$ (and the noise by $n_0/3000$ ). + We consider two Cases We show the n(2) from the sample of photometric recdshift posteriors we use in Figure 1.., We consider two cases We show the $n(z)$ from the sample of photometric redshift posteriors we use in Figure \ref{realpz}. + In Figure 2. we show the inpact on the 3D. cosmic shear power spectra., In Figure \ref{pzplot} we show the impact on the 3D cosmic shear power spectra. + The power spectra are a function of { and two physical wavenumbers. hence we show the plane (Ay.ο) for a series of£/ modes. as well as the diagonal CRCPPb.," The power spectra are a function of $\ell$ and two physical wavenumbers, hence we show the plane $(k_1,k_2)$ for a series of $\ell$ modes, as well as the diagonal $C^{3D}_{\ell}(k,k)$." + HC can be seen that using an approximation of the redshift distribution can cause significant residuals in the power spectra. with residuals of order 0.01. 1 over all scales.," It can be seen that using an approximation of the redshift distribution can cause significant residuals in the power spectra, with residuals of order $0.01$ $1$ over all scales." + Έπος residuals are. most prominent at low-f and small racial scales., These residuals are most prominent at $\ell$ and small radial scales. +" Using the Fisher matrix approach Figure 3. shows how the approximation of averaging the posteriors p(z|z,) in photometric redshift. can allect cosmological parameter errors."," Using the Fisher matrix approach Figure \ref{pzfisherplot} shows how the approximation of averaging the posteriors $\bar p(z|z_p)$ in photometric redshift, can affect cosmological parameter errors." + In. general the errors are degraded by averaging the individual galaxy posteriors pj(z|24) by a factor of 10 50%. and in some cases the parameter degeneracies are changed.," In general the errors are degraded by averaging the individual galaxy posteriors $p_g(z|z_g)$ by a factor of $10$ $50\%$, and in some cases the parameter degeneracies are changed." + This is a result of the individual ΤΕ distributions explicitly including outlving and non-Gaussian behaviour on a galaxyv-bv-galaxy basis., This is a result of the individual $p_g(z|z_g)$ distributions explicitly including outlying and non-Gaussian behaviour on a galaxy-by-galaxy basis. +" In making the approximation of p(z|z,) the best fit cosmological parameter values may. also be biased. as well as the errors being alfected."," In making the approximation of $\bar p(z|z_p)$ the best fit cosmological parameter values may also be biased, as well as the errors being affected." + La Appendix € we show how to calculate the bias in the Fisher matrix approximation for the case that the parameter dependency is in the covariance (this is a generalisation of the result. of Ixnox ct al..," In Appendix C we show how to calculate the bias in the Fisher matrix approximation for the case that the parameter dependency is in the covariance (this is a generalisation of the result of Knox et al.," +. 1905)., 1998). +" We find that the approximation made in this example introcluces a neeligible bias on all cosmological parameters: οί3.0:107). On62.5.10.Dons 10.νο 12105 (0.2«.10.1. O4710%).(1.3: 605317) and n,(2.5.104)."," We find that the approximation made in this example introduces a negligible bias on all cosmological parameters: $\Omega_m (-3.0\times 10^{-5})$, $\Omega_{de}(2.5\times 10^{-4})$, $w_0(1.3\times 10^{-4})$, $w_a(-1.2\times 10^{-4})$ , $h(5.2\times +10^{-4})$, $\Omega_b(1.1\times 10^{-6})$, $\sigma_8(7.3\times 10^{-5})$ and $n_s(2.5\times 10^{-4})$." + We note that changes in the covariance only impact cosmological parameter biases if the change induced is similar to the effect of any cosmological parameter (see or example Witching et al., We note that changes in the covariance only impact cosmological parameter biases if the change induced is similar to the effect of any cosmological parameter (see for example Kitching et al. + 2009: form filling functions)., 2009; form filling functions). + In this case the changes in the covariance are large. but he changes are not similar to the cllect of cosmological xwanmeter so the biases are small.," In this case the changes in the covariance are large, but the changes are not similar to the effect of cosmological parameter so the biases are small." + The amplitude of the jas will depend on the οχασ distribution and form of the posterior redshift distributions. here we use an example to introduce the methodology. we leave a more detailed. study or a future article.," The amplitude of the bias will depend on the exact distribution and form of the posterior redshift distributions, here we use an example to introduce the methodology, we leave a more detailed study for a future article." + Lor any ὃνgiven experiment. the exact. degradation> will be dependent on the exact galaxy survey ancl quality of photometric redshifts available.," For any given experiment, the exact degradation will be dependent on the exact galaxy survey and quality of photometric redshifts available." + Note that in Heavens ct al. (, Note that in Heavens et al. ( +"2006) we mace a further approximation by assuming that the p(s|s,)=πο where n(z,) is the number censity of galaxies as a. function of photometric redshift andl poass(2|25). is the normalised photometric redshift distribution at cach redshift which we assummed to be a Gaussian at cach redshift with a variance σε(ορ).","2006) we made a further approximation by assuming that the $\bar +p(z|z_p)=\bar n(z_p)p_{\rm Gauss}(z|z_p)$ where $\bar n(z_p)$ is the number density of galaxies as a function of photometric redshift and $p_{\rm Gauss}(z|z_p)$ is the normalised photometric redshift distribution at each redshift which we assummed to be a Gaussian at each redshift with a variance $\sigma_z(z_p)$." + We now investigate various. approximations of the 3D shear field., We now investigate various approximations of the 3D shear field. + From LoVerde Afshordi (2008) the Limber approximation can be encapsulated. in. the following substitution ). where 6? is the Dirac delta function.," From LoVerde Afshordi (2008) the Limber approximation can be encapsulated in the following substitution ), where $\delta^D$ is the Dirac delta function." + This is substituted into any integral or sum that the Bessel function appears: [or example equations (11)) and (12))., This is substituted into any integral or sum that the Bessel function appears; for example equations \ref{CGU}) ) and \ref{Gcont}) ). + We note that. this does not explicitly. convert a 3D. wavevector into a 2D wavevector.&2(yh)οGushu) Ovhich is explicit in an alternative and complementary derivation of the Limboer," We note that this does not explicitly convert a 3D wavevector into a 2D wavevector,$k=(k_x,k_y,k_z)\rightarrow (k_x,k_y)$ (which is explicit in an alternative and complementary derivation of the Limber" +by a [actor of 4 recovery between the May and October observations.,by a factor of 4 recovery between the May and October observations. + The brightest detection was the second peak. with a flix of (7.4250.8) x LO? photons ? 1," The brightest detection was the second peak, with a flux of $\pm$ 0.8) $\times$ $^{-5}$ photons $^{-2}$ $^{-1}$." + The source [aded by at least a factor of eight in the 55 days alter (he second peak., The source faded by at least a factor of eight in the 55 days after the second peak. + The 3o [lux upper limit [or the 2004-December-05 observation (9x10. * ph ? !) vields an e-folding decay time after the second peak of «1 month., The $\sigma$ flux upper limit for the 2004-December-05 observation $\times$ $^{-6}$ ph $^{-2}$ $^{-1}$ ) yields an $e$ -folding decay time after the second peak of $<$ 1 month. + Π the 2o detection of (62:3) x ? phem ?s ! in the 2004-December-05 observation is real. then the e-folding decay time was ~2? davs.," If the $\sigma$ detection of $\pm$ $)\times$ $^{-6}$ ph $^{-2}$ $^{-1}$ in the 2004-December-05 observation is real, then the $e$ -folding decay time was $\sim$ 22 days." + This decav was [faster (hanChat observed. after the first peak. where (he flux decaved by a [actor of 2.8 in 55 clavs. exhibiting an e-folding decay time of 7254 davs.," This decay was faster thanthat observed after the first peak, where the flux decayed by a factor of 2.8 in 55 days, exhibiting an $e$ -folding decay time of $\sim$ 54 days." + Although r3-127 was 9' ofl-axis. the images provided a precise source position.," Although r3-127 was $'$ off-axis, the images provided a precise source position." + We measured (he position in the (wo brightest detections., We measured the position in the two brightest detections. + Table 3. shows the significant sources ol error in this measurement., Table \ref{xpos} shows the significant sources of error in this measurement. + These were the alignment errors. determined byπαν. and (he position errors. determined byncentroid.," These were the alignment errors, determined by, and the position errors, determined by." + We added these errors in quadrature for each measurement., We added these errors in quadrature for each measurement. + Then we took the weighted mean R.A. and Dee. to obtain our final position ancl position error of (he source in the LGS coordinate svstem. which we used to plot the 1o error ellipses shown in Figure 1..," Then we took the weighted mean R.A. and Dec. to obtain our final position and position error of the source in the LGS coordinate system, which we used to plot the $\sigma$ error ellipses shown in Figure \ref{ims}." +" The final X-ray position aud errors were R.A = 0:43:09.940 + 0.65"" and Dec. = 41:23:32.49 + 0.66"".", The final X-ray position and errors were R.A = 0:43:09.940 $\pm$ $''$ and Dec. = 41:23:32.49 $\pm$ $''$. + At the distance of M31 (780 kpe). (he semi-major axis of the error ellipse is 2.5 pe.," At the distance of M31 (780 kpc), the semi-major axis of the error ellipse is 2.5 pc." + The (wo brightest detections contained sufficient counts to perform [fits to the X-ray spectrum of 13-127., The two brightest detections contained sufficient counts to perform fits to the X-ray spectrum of r3-127. + The results of the fits are given in Table 4.., The results of the fits are given in Table \ref{spectab}. +" Thev show that. while the spectrum was well-fitted bv both the absorbed disk blackbody aud the absorbed power-law models. it was better fitted by (the absorbed disk blackbody wilh an absorption-corrected keV luminosity of ~L.1< 10"" erg J| at the time of the brightest detection."," They show that, while the spectrum was well-fitted by both the absorbed disk blackbody and the absorbed power-law models, it was better fitted by the absorbed disk blackbody with an absorption-corrected 0.3--7 keV luminosity of $\sim$ $\times$ $^{37}$ erg $^{-1}$ at the time of the brightest detection." + The spectrum was soft. and it may have become softer during the decay.," The spectrum was soft, and it may have become softer during the decay." + This softening can be seen in the hardness ratios. as HRI declined from 0.62:0.2 at the first detection to 0.02:0.4 during the decay.," This softening can be seen in the hardness ratios, as HR1 declined from $\pm$ 0.2 at the first detection to $\pm$ 0.4 during the decay." + There is also a hint that Che second peak may have been softer than the first in both (he hardness ratios and the spectral fits (see Tables 2 and 4))., There is also a hint that the second peak may have been softer than the first in both the hardness ratios and the spectral fits (see Tables \ref{flux} and \ref{spectab}) ). + These soft spectra are (vpical of Galactic LMXDs. especially those svstems (hat contain a black hole primary (e.g. 20041).," These soft spectra are typical of Galactic LMXBs, especially those systems that contain a black hole primary (e.g. \citealp{tanaka1995,church2001,mcclintock2004}) )." + Conciselv. the X-ray lighteurve of 13-127 was complex. having at least (wo peaks.," Concisely, the X-ray lightcurve of r3-127 was complex, having at least two peaks." +" The position was measured [from the images with 0.7"" precision. and the spectral fits provided an estimate of the peak absorption-corrected 0.3.7 keV luminosity reached on of —1.1x10* erg s..."," The position was measured from the images with $''$ precision, and the spectral fits provided an estimate of the peak absorption-corrected 0.3–7 keV luminosity reached on 04-Oct-2004 of $\sim$ $\times$ $^{37}$ erg $^{-1}$ ." +Alicrolensing can also be used to. probe the mass distribution. in the lensing galaxy.,Microlensing can also be used to probe the mass distribution in the lensing galaxy. + Initial stuclies of quasar microlensing indicated. that microlensing was not significantly. dependent. within certain constraints. on the mass spectrum within the lens (e.g.Wambsganss1992:Lewis&Lrwin 1995). in particular how much mass. is in compact objects ancl how much is in smooth matter.," Initial studies of quasar microlensing indicated that microlensing was not significantly dependent, within certain constraints, on the mass spectrum within the lens \citep[e.g.][]{wambsganss1992,lewis1995b}, in particular how much mass is in compact objects and how much is in smooth matter." + Llowever. during investigations of anomalous (lux ratios in the lensecl quasar MG. 0414]0534 (Schechter&Wanihs-eanss 2002).. evidence against this view was found. and numerical modelling presented by Schechter.Wambsganss.&Lewis(2004) showed that it must be false.," However, during investigations of anomalous flux ratios in the lensed quasar MG 0414+0534 \citep{schechter2002}, evidence against this view was found, and numerical modelling presented by \citet{schechter2004} showed that it must be false." + Beginning with a laree number of solar-mass (1M.) stars for the lens galaxy. they replaced a substantial fraction of these with smooth matter. keeping the total mass the same. and found that the microlensing variability was enhanced.," Beginning with a large number of solar-mass $_\odot$ ) stars for the lens galaxy, they replaced a substantial fraction of these with smooth matter, keeping the total mass the same, and found that the microlensing variability was enhanced." + This also introduced the “bi-mocal” mass distribution into computational microlensing. where two very distinct. mass components in the lens are modelled (e.g.Pooleyοἱal. 2010).," This also introduced the “bi-modal” mass distribution into computational microlensing, where two very distinct mass components in the lens are modelled \citep[e.g.][]{pooley2011}." +. Lewis&Gil-Merino(2006). replaced the smooth matter with many compact objects. all of the same mass. aud significantly. less than LAL...," \citet{lewis2006b} replaced the smooth matter with many compact objects, all of the same mass, and significantly less than $_\odot$." + The objects produced. simall-scale microlensing variability that was not present when smooth matter was used. as expected.," The objects produced small-scale microlensing variability that was not present when smooth matter was used, as expected." + However. it was found that the variability produced. by the small objects could. be smioothecl out enough so that they could not be distinguished. from. smooth matter. if the source size was over a threshold.," However, it was found that the variability produced by the small objects could be smoothed out enough so that they could not be distinguished from smooth matter, if the source size was over a threshold." + It was also found that. if source size was taken into account. the amplitude of these variations was an indicator of the mass of the objects in the lens.," It was also found that, if source size was taken into account, the amplitude of these variations was an indicator of the mass of the objects in the lens." + IHecently. Chen&Ixoushiappas(2010) conducted similar mocelling. expanding the bi-mocdal distribution by using a (1955) mass distribution for the stars and a Navarro.Frenk.&White(1997) power-law distribution for the compact objects. considering these as potential dark matter candidates.," Recently, \citet{chen2010} conducted similar modelling, expanding the bi-modal distribution by using a \citet{salpeter1955} mass distribution for the stars and a \citet{nfw1997} power-law distribution for the compact objects, considering these as potential dark matter candidates." +" Phev conclude that their small compact objects will acid detectable small microlensing events (nanolensing"" events) to a microlensing light curve of no more than about kl mag over a time scale smaller than a vear.", They conclude that their small compact objects will add detectable small microlensing events (“nanolensing” events) to a microlensing light curve of no more than about 0.1 mag over a time scale smaller than a year. + Chen&Ixoushiappas(2010) were less interested in source size and row this cdiminishes the detectability of nanolensing events. out. did confirm that larger sources would smooth out the ight curves and make nanolensing harder to detect.," \citet{chen2010} were less interested in source size and how this diminishes the detectability of nanolensing events, but did confirm that larger sources would smooth out the light curves and make nanolensing harder to detect." + The term 7nanolensing'. used. previously by Lewis(2008) and Schechter.Wanbseanss.&Lewis (2004).. is gaining in usage and refers to light dellections on much smaller scales than microlensing. due to planctary-size objects or possible dark matter objects (Zakharov2009).," The term “nanolensing”, used previously by \citet{walker2003} and \citet{schechter2004}, is gaining in usage and refers to light deflections on much smaller scales than microlensing, due to planetary-size objects or possible dark matter objects \citep{zakharov2009}." +. The work of Walker&Lewis(2003) involved the detection of cosmological planetary masses by the nanolensing of eamma rav bursts (Walker&Lewis2003).. and. nanolensing is also referred to in exoplanet searches (Zakharovetal.2010).," The work of \citet{walker2003} involved the detection of cosmological planetary masses by the nanolensing of gamma ray bursts \citep{walker2003}, and nanolensing is also referred to in exoplanet searches \citep{zakharov2010}." +.. We use it here to refer to lensing variability produced by objects in a lens with masses far below that of LAL. stars. e.g. the low-mass objects in a bi-mocal mass distribution.," We use it here to refer to lensing variability produced by objects in a lens with masses far below that of $_\odot$ stars, e.g. the low-mass objects in a bi-modal mass distribution." + This paper expands on the work of Lewis&Gil-Moerino (2006).. Lewis(2008) and Chen&WKoushiappas(2010) in investigating nanolensing events due to small masses. and their interaction with source size.," This paper expands on the work of \citet{lewis2006b}, \citet{lewis2008} and \citet{chen2010} in investigating nanolensing events due to small masses, and their interaction with source size." +" Using bi-mocdal mass distributions. we use several mass values down to 2.5r10 ""M. for the size of the small objects. while increasing wir number to over a billion far more than has been modelled in the past."," Using bi-modal mass distributions, we use several mass values down to $2.5\times 10^{-5}$ $_\odot$ for the size of the small objects, while increasing their number to over a billion – far more than has been modelled in the past." + We use a mock lensed quasar system alt has been modelled by Schechter&Wambsganss(2002) and Chen&Ixoushiappas(2010).. similar to the lensed uasar ALG O414|0534.," We use a mock lensed quasar system that has been modelled by \citet{schechter2002} and \citet{chen2010}, similar to the lensed quasar MG 0414+0534." + M. 041410534. has not been used in this ancl past works due to the high magnification of the source quasar. produced by à very large number of objects in 16 lens galaxy. which are dillieult to deal with in numerical models.," MG 0414+0534 has not been used in this and past works due to the high magnification of the source quasar, produced by a very large number of objects in the lens galaxy, which are difficult to deal with in numerical models." + Simple statistics allow us to use the amplitude of nanolensing events to infer small objects in a lens. based on a range of source sizes.," Simple statistics allow us to use the amplitude of nanolensing events to infer small objects in a lens, based on a range of source sizes." + We then follow this with an investigation into the duration of the nanolensing events and the source sizes needed to resolve them — something has not not been done in past studies., We then follow this with an investigation into the duration of the nanolensing events and the source sizes needed to resolve them – something has not not been done in past studies. + We show that there are two time and source scales involved in these events ad indicate how they may be observed., We show that there are two time and source scales involved in these events and indicate how they may be observed. + We discuss how our investigations provide direction to further work that can be conducted in this area., We discuss how our investigations provide direction to further work that can be conducted in this area. + The structure of the paper is as follows: In Section 2. we introduce numerical modelling of microlensing. and the lensing model and parameters used for this study. in Section 3. we present the results of nanolensing of bi-modal mass distributions with cilferent. source sizes. including event amplitudes and curations.," The structure of the paper is as follows: In Section \ref{method} we introduce numerical modelling of microlensing, and the lensing model and parameters used for this study, in Section \ref{results} we present the results of nanolensing of bi-modal mass distributions with different source sizes, including event amplitudes and durations." + In Section we 4 discusses the results and Section 5. contains our conclusions., In Section we \ref{discussion} discusses the results and Section \ref{conclusions} contains our conclusions. +" Throughout this paper. a cosmology with LfTOkms*Alpe |. ,,=0.3 and Qy=0.7 is assumed."," Throughout this paper, a cosmology with $H_0 = 70\rmn{km}\rmn{s}^{-1}\rmn{Mpc}^{-1}$ , $\Omega_{m} = 0.3$ and $\Omega_{\Lambda} = 0.7$ is assumed." + The properties of an image in a multiplv-imaged quasar are determined. mostly by the mass distribution of the lensing ealaxy. and the relative locations and distances of the galaxy and quasar (Schneider.Ehlers.&Falco.1992).," The properties of an image in a multiply-imaged quasar are determined mostly by the mass distribution of the lensing galaxy, and the relative locations and distances of the galaxy and quasar \citep{schneider1992}." +. For image modelling. two parameters are used to specify the mass in the lensing ealaxy at the image positions: the convergence (5). and shear (5).," For image modelling, two parameters are used to specify the mass in the lensing galaxy at the image positions: the convergence $\kappa$ ), and shear $\gamma$ )." + The convergence specificsthe clleet of mass close to the light path. and the shear is the οσοι of the overall mass of the galaxy.," The convergence specifiesthe effect of mass close to the light path, and the shear is the effect of the overall mass of the galaxy." + Within the convergence. a nis spectrum can be chosen for models. we will be using bi-mocdal distributions as described. above. where a small amount of mass is in TAL. stars. ancl the rest in either small objects. or smooth matter.," Within the convergence, a mass spectrum can be chosen for models, we will be using bi-modal distributions as described above, where a small amount of mass is in $_\odot$ stars, and the rest in either small objects, or smooth matter." + Phe distances to the lens and source are subsumed into a distance unit used. within lensing mocels: the Einstein Racius (yo)., The distances to the lens and source are subsumed into a distance unit used within lensing models: the Einstein Radius $\eta_0$ ). + Loa point source is perfectly in line with a point lens object. usually chosen to be 1M... the source will appear as a ring around the lens.," If a point source is perfectly in line with a point lens object, usually chosen to be $_\odot$, the source will appear as a ring around the lens." +" Projected onto the source plane. the ring radius is given by where Af is the mass of the lens and D,, refers to the angular diameter distance between ο and jy: the subscripts s./. and o representing source. lens. ancl observer respectively."," Projected onto the source plane, the ring radius is given by where $M$ is the mass of the lens and $D_{xy}$ refers to the angular diameter distance between $x$ and $y$ ; the subscripts $s, l,$ and $o$ representing source, lens, and observer respectively." + AMicrolensing and nanolensing requires the source to change location behind the lens (Wyithe2001:Poindex- to produce variation in the source magnification. so a region of the source plane. where the source maw Die. is defined.," Microlensing and nanolensing requires the source to change location behind the lens \citep{wyithe2001a,pointdexter2009a} to produce variation in the source magnification, so a region of the source plane, where the source may lie, is defined." + Each point in the region has, Each point in the region has +is essential for the derivation of the closed system of equations governing the evolution of A‘; aud dy (ie. equation (5)) in the non-helical case).,is essential for the derivation of the closed system of equations governing the evolution of $M_L$ and $K$ (i.e. equation \ref{eq:M_L}) ) in the non-helical case). + I the advecting flow is finite-time correlated. as it will be iu reality. these equatious canuot be obtained in closed [oru," If the advecting flow is finite-time correlated, as it will be in reality, these equations cannot be obtained in closed form." + Physically. oue might expect that the results of the 9-correlated model would smoothly matel onto the short-time correlated. case if the velocity correlation tine is much smaller than the Characteristic time for dyuamo action.," Physically, one might expect that the results of the $\delta$ -correlated model would smoothly match onto the short-time correlated case if the velocity correlation time is much smaller than the characteristic time for dynamo action." + However. the question remains as to what happeus as the correlation time of the [low increases.," However, the question remains as to what happens as the correlation time of the flow increases." + Lucdeed. it has recently been demonstrated that for the quasi wo-dimenusional dyuamo problem. two flows with the same velocity spectrum but differiug plase ooperties cau have very dillerent. dynamo properties (Tobias&Cattaneo2008a).," Indeed, it has recently been demonstrated that for the quasi two-dimensional dynamo problem, two flows with the same velocity spectrum but differing phase properties can have very different dynamo properties \citep{tobiasc2008a}." +. The goal of he present work is therefore to compare the characteristics of magnetic field generation iu the instantaneously correlated Ixazantsev [low with the dyuamo properties of flows that liave a similar spatial structure but that are solutions of the forced. incompressible. Navier-Stokes equation aud rence have finite correlation times.," The goal of the present work is therefore to compare the characteristics of magnetic field generation in the instantaneously correlated Kazantsev flow with the dynamo properties of flows that have a similar spatial structure but that are solutions of the forced, incompressible, Navier-Stokes equation and hence have finite correlation times." +W. Before proceeding. we would like to note that in the remainder of the paper it will sometimes oove useful to cousider the correlators of the Fourier coellicieuts of the velocity. rather thau the spatial correlators (2)) aud (3)).," Before proceeding, we would like to note that in the remainder of the paper it will sometimes prove useful to consider the correlators of the Fourier coefficients of the velocity, rather than the spatial correlators \ref{eq:corr_v}) ) and \ref{eq:kappa_ij}) )." + A further advantage is that the pliysical meaning of the functions Bir) aud g(r) then becomes apparent., A further advantage is that the physical meaning of the functions $\kappa_L(r)$ and $g(r)$ then becomes apparent. + We therefore introduce tle Fourier trausform of the velocity In the Wazautsey model. the velocity correlator in k-space then takes the form (assuming incompressibility) where * deuotes the complex conjugate.," We therefore introduce the Fourier transform of the velocity In the Kazantsev model, the velocity correlator in $\mathbf{k}$ -space then takes the form (assuming incompressibility) where $^*$ denotes the complex conjugate." + The functions κε) aud g(r) cau be obtained frou Fk) and G(h) through three-dimeusional Fourier trausforius (see Mouin&Yaelom (1971)))., The functions $\kappa_L(r)$ and $g(r)$ can be obtained from $F(k)$ and $G(k)$ through three-dimensional Fourier transforms (see \cite{moniny1971}) ). +" Iu particular. we will use the relation We note that (u(x./)u(x./47);=Jo(7)5,(0)29(7)fF(k)dk20(7)IxA?Ed."," In particular, we will use the relation We note that $\langle \mathbf{u}(\mathbf{x},t) \cdot \mathbf{u}(\mathbf{x},t+\tau)\rangle=3 \delta(\tau) +\kappa_L(0)=2 \delta(\tau) \int F(k) d\mathbf{k}=2 \delta(\tau) \int 4\pi k^2 F(k)dk$." + Similarly éu(x./)(Vκκ.7)))=—28(7){IxeGμ," Similarly $\langle \mathbf{u}(\mathbf{x},t)\cdot (\nabla \times \mathbf{u}(\mathbf{x},t+\tau)) \rangle=-2 \delta(\tau) \int 4 +\pi k^4 G(k)dk$." + Thus the functious F(/) and C() in equation (7)) are related to the kinetic energy aud helicity in the Ixazautsev model., Thus the functions $F(k)$ and $G(k)$ in equation \ref{eq:corr_v_k}) ) are related to the kinetic energy and helicity in the Kazantsev model. + The equivalent magnetic correlator in Fourier space is where again AZ)(r./) aud A(r./) are related to Fy(hk./) and Giyy(h./) through three-cliimeusional Fourier transforius.," The equivalent magnetic correlator in Fourier space is where again $M_L(r,t)$ and $K(r,t)$ are related to $F_B(k,t)$ and $G_B(k,t)$ through three-dimensional Fourier transforms." + Iu. particular. Ep(he!)=tah?Eph.) aud Hyphot)=Sah!Gtk.) are the spectrum functions of magnetic energy aud electric current helicity. respectively.," In particular, $E_B(k,t)=4\pi k^2 F_B(k,t)$ and $H_B(k,t)=-8 \pi k^4 G_B(k,t)$ are the spectrum functions of magnetic energy and electric current helicity, respectively." + , +and the total dark mass is Evidenth. with this assumption. larger clusters have a more massive dark component. but because the gas mass scales as r. the dark to gas mass decreases with increasing core radius or temperature.,"and the total dark mass is Evidently, with this assumption, larger clusters have a more massive dark component, but because the gas mass scales as ${r_c}^3$, the dark to gas mass decreases with increasing core radius or temperature." +" The procedure followed is identical to that. of. the pure MOND 2 moclels described above: L assume a σας distribution described by with 3=0.62. n,=0.006."," The procedure followed is identical to that of the pure MOND $\beta$ models described above: I assume a gas distribution described by with $\beta = 0.62$, $n_o = 0.006$." + Then for a given centra eas temperature. E determine the core radius of the moce for which the temperature gradient is minimized.," Then for a given central gas temperature, I determine the core radius of the model for which the temperature gradient is minimized." + The new aspect is the second component which makes its presence fel by contributing to the total cumulative mass (M(r) in 22) and hence the total gravitational force., The new aspect is the second component which makes its presence felt by contributing to the total cumulative mass (M(r) in 2) and hence the total gravitational force. + This has the ellect of decreasing the core radius at a given temperature comparec to the single component. MOND «1 mocdels., This has the effect of decreasing the core radius at a given temperature compared to the single component MOND $\beta$ models. + The enmission-weighted: temperature of as a function of projected. radius is shown by the solid line in 44 again for a model with a central temperature of 6.5 keV. This is the most-nearly isothermal mocel. and we see that the temperature gradients are much smaller than in the the single component ;-mocel.," The emission-weighted temperature of as a function of projected radius is shown by the solid line in 4 again for a model with a central temperature of 6.5 keV. This is the most-nearly isothermal model, and we see that the temperature gradients are much smaller than in the the single component $\beta$ -model." + The total variation about the central temperature 1s less than40%., The total variation about the central temperature is less than. +. In other words.densify.," In other words,." + The gas-mass-temperature relation of such models is shown by the solid. line in. Ll which is evidently consistent with the observations., The gas-mass-temperature relation of such models is shown by the solid line in 1 which is evidently consistent with the observations. + Phe luminosity-emperature relation for these two component cluster models is shown by the solid line in 22., The luminosity-temperature relation for these two component cluster models is shown by the solid line in 2. + FPhese models oovide a reasonable description of the observed. relation., These models provide a reasonable description of the observed relation. + This is due to the fact that. in the low temperature svstenis. a relatively larger fraction of the mass is not in gaseous orm.," This is due to the fact that, in the low temperature systems, a relatively larger fraction of the mass is not in gaseous form." + [Ht djs also not in the form of luminous material in galaxies as the implied. mass-to-light. ratios would. be too arge., It is also not in the form of luminous material in galaxies as the implied mass-to-light ratios would be too large. + Agreement of MOND with the cluster scaling relations is achieved at the expense of adding unseen matter., Agreement of MOND with the cluster scaling relations is achieved at the expense of adding unseen matter. + Individual clusters may be described by such (wo component models., Individual clusters may be described by such two component models. + Given the parameters of a model fit to the emission from an specific cluster (ic. 3. ni. ancl rV). and a characteristic temperature for the entire cluster. 1 determine. via eqs.," Given the parameters of a $\beta$ model fit to the X-ray emission from an specific cluster (i.e., $\beta$, $n_o$, and $r_c$ ), and a characteristic temperature for the entire cluster, I determine, via eqs." +" 1 and 2. the central temperature. 7). and the density (or. surface. density. related. by 111) of the dark component which vields the observed. emission weighted. temperature ancl the observed. core radius. à, of the 3 model."," 1 and 2, the central temperature, $T_o$, and the density (or surface density, related by 11) of the dark component which yields the observed emission weighted temperature and the observed core radius, $r_c$ of the $\beta$ model." + In all cases the dark component is assumed to extend to 2r., In all cases the dark component is assumed to extend to $r_c$. + Uniqueness is ensured by requiring that the temperature gradients be minimized Le. these are again the most nearly isothermal models.," Uniqueness is ensured by requiring that the temperature gradients be minimized– i.e., these are again the most nearly isothermal models." + The fitting parameter is the density of the central dark component which vields the total dark mass via 112 above., The fitting parameter is the density of the central dark component which yields the total dark mass via 12 above. + Table 1 lists the clusters which have been modeled. in this way along with the the parameters of the ;-moclel fit and the mean temperature. all from the compilation of Reiprich (2001) with cluster properties scaled to h=0.7.," Table 1 lists the clusters which have been modeled in this way along with the the parameters of the $\beta$ -model fit and the mean temperature, all from the compilation of Reiprich (2001) with cluster properties scaled to h=0.7." + The the οιντος central surface density of the dark component. Ny. is given along with the total gas mass (out to the cutoll radius) and the total mass of the dark. component.," The the required central surface density of the dark component, $\Sigma_d$, is given along with the total gas mass (out to the cutoff radius) and the total mass of the dark component." + The enclosed Newtonian dynamical mass is also given., The enclosed Newtonian dynamical mass is also given. + This sample was chosen to include a number of objects with significant inferred cooling Lows (such as Abel 1689 and 2029)), This sample was chosen to include a number of objects with significant inferred cooling flows (such as Abel 1689 and 2029). +" These clusters are characterized by relatively small core ασ (7,«100 kpe) and large central electron densities (πρc0.01 79.", These clusters are characterized by relatively small core radii $r_c<100$ kpc) and large central electron densities $n_o>0.01$ $^{-3}$ ). +" Phe sample also includes clusters at the other extreme large core radii (r,250 kpc) and low central electron densities (2,«0.005 7) with no inferred cooling Llow (such as Abel 119 and 2256).", The sample also includes clusters at the other extreme– large core radii $r_c > 250$ kpc) and low central electron densities $n_o < 0.005$ $^{-3}$ ) with no inferred cooling flow (such as Abel 119 and 2256). + 1n general. MOND reduces the classical Newtonian discrepaney for clusters of galaxies.," In general, MOND reduces the classical Newtonian discrepancy for clusters of galaxies." + For this sample. with MOND the ratio of the total dark mass to the gas mass is 1.60 + 1.7," For this sample, with MOND the ratio of the total dark mass to the gas mass is 1.60 $\pm$ 1.7." + The Newtonian dark mass-to-gas mass ratio is 7.14 4+ 2.7., The Newtonian dark mass-to-gas mass ratio is 7.14 $\pm$ 2.7. + While this is a significant reduction. ib is also clear that MOND oes not fully resolve the mass discrepancy in clusters.," While this is a significant reduction, it is also clear that MOND does not fully resolve the mass discrepancy in clusters." + Moreover. it should. be noted that the ratio of masses of the cark-to-hot gas components in the central two core radii (where the additional component is required) can be as large as 10. às was also pointed out by Aguirre. Schave Quataert. (2001).," Moreover, it should be noted that the ratio of masses of the dark-to-hot gas components in the central two core radii (where the additional component is required) can be as large as 10, as was also pointed out by Aguirre, Schaye Quataert (2001)." + This rigid component cannot be stars ofà normal population because the mass-to-light ratio within two core radii would still be. on average. in excess of about 50.," This rigid component cannot be stars of a normal population because the mass-to-light ratio within two core radii would still be, on average, in excess of about 50." + Phe principle question is whether or not this dark component is a funcamental problem or can be accomumoclatecl in the context of MOND., The principle question is whether or not this dark component is a fundamental problem or can be accommodated in the context of MOND. + Lt could be that a high. M/L population of low mass stars or sub-stellar objects is deposited in the central regions of clusters as a result. of cooling Lows., It could be that a high M/L population of low mass stars or sub-stellar objects is deposited in the central regions of clusters as a result of cooling flows. + 66 is a plot of the total mass in the dark component vs. the cooling rate as estimated by White. Jones Forman (1997).," 6 is a plot of the total mass in the dark component vs. the cooling rate as estimated by White, Jones Forman (1997)." + The solid. points are those clusters with a large. cliscrepancy: AlifAly1.5., The solid points are those clusters with a large discrepancy: $M_d/M_g>1.5$. +" The crosses are clusters with a smaller discrepancy: Ali/AL,<1.5.", The crosses are clusters with a smaller discrepancy: $M_d/M_g<1.5$. + We see that there is no obvious correlation between the total mass of the dark component and the cooling rate especially for those clusters with the largest discrepancy., We see that there is no obvious correlation between the total mass of the dark component and the cooling rate– especially for those clusters with the largest discrepancy. + On the other hand. in 27 we see a plot of the surface density of the dark component vs. the mass deposition rate.," On the other hand, in 7 we see a plot of the surface density of the dark component vs. the mass deposition rate." + Here there does appear to be a correlation., Here there does appear to be a correlation. + This is because those clusters with the highest central dark matter densities are not the clusters with the largestὃν mass ciüscrepancies., This is because those clusters with the highest central dark matter densities are not the clusters with the largest mass discrepancies. + ]t is unclear if this apparent correlation between surface density ancl mass deposition rate is significant., It is unclear if this apparent correlation between surface density and mass deposition rate is significant. + The mass deposition is not actually observed but caleulated from the central gas density., The mass deposition is not actually observed but calculated from the central gas density. + Phose clusters with large inferred cooling lows are clusters with high central gas densities ancl small core radii., Those clusters with large inferred cooling flows are clusters with high central gas densities and small core radii. + But it precisely these elusters which require a large surface density of clark matter to produce the small core radius., But it precisely these clusters which require a large surface density of dark matter to produce the small core radius. + While it may be the case that cooling [lows contribute to the dark component of those clusters with, While it may be the case that cooling flows contribute to the dark component of those clusters with +located at projected distances of more than 1755.,located at projected distances of more than 5. + Within ((~0.5 Alpe) we find. 15 neighbours. suggesting that the NGC 1512/1510 system is part of a loose (spiral) galaxy group L108: Garcia 1993).," Within $\sim$ 0.5 Mpc) we find 15 neighbours, suggesting that the NGC 1512/1510 system is part of a loose (spiral) galaxy group 108; Garcia 1993)." + The barred galaxy NGC 1512 and the blue compact chvarl (BCD) galaxy NGC 1510 are an interacting galaxy pair. separated by only ορ’ ((13.8 kpe).," The barred galaxy NGC 1512 and the blue compact dwarf (BCD) galaxy NGC 1510 are an interacting galaxy pair, separated by only $\sim$ (13.8 kpc)." + At the adopted distance of 9.5 Mpc. ccorresponcds to 2.76 kpc.," At the adopted distance of 9.5 Mpc, corresponds to 2.76 kpc." + Table 1 gives some basic properties of both galaxies., Table 1 gives some basic properties of both galaxies. + The optical appearances of both galaxies are well described. by. Llawarden ct al. (, The optical appearances of both galaxies are well described by Hawarden et al. ( +1979).,1979). + GC 1512 (11.AS 040224329) is a Large. strongly barred. galaxy. with two prominent star-forming rings.," NGC 1512 (IRAS 04022–4329) is a large, strongly barred galaxy with two prominent star-forming rings." + Its morphological tvpe is generally. given as SB(r)a or SB(r)b., Its morphological type is generally given as SB(r)a or SB(r)b. + The companion. NGC 1510 (RAS 040194332). is a much smaller. peculiar SO or lenticular galaxy.," The companion, NGC 1510 (IRAS 04019–4332), is a much smaller, peculiar S0 or lenticular galaxy." + Πο respective optical cliameters are S95/6 and 153077. e. NGC 15128 stellar disk is about seven times larger than that of NGC 1510.," Their respective optical diameters are $8\farcm9 \times 5\farcm6$ and $1\farcm3 \times 0\farcm7$, i.e. NGC 1512's stellar disk is about seven times larger than that of NGC 1510." + Beautiful multi-color LUST images of NGC 1512 by AMaoz et al. (, Beautiful multi-color HST images of NGC 1512 by Maoz et al. ( +"2001) clearly show the structure of the nuclear region (<20"" Lkpe): a bright nucleus surrounded by a smooth. clusty disk which is enveloped by a highly ordered. and narrow starburst ring. of ⋅⋠diameter 16⋅∕∕12"" iswith a position.. angle (PAY of —90..","2001) clearly show the structure of the nuclear region $<$ $\sim$ 1 kpc): a bright nucleus surrounded by a smooth, dusty disk which is enveloped by a highly ordered and narrow starburst ring of diameter $16\arcsec \times +12\arcsec$ with a position angle $PA$ ) of $\sim$ ." + This nuclear ring is also evident in the Jit map by Laurikainen οἱ al. (, This nuclear ring is also evident in the $J-K$ map by Laurikainen et al. ( +2006) ancl in the Spitzer mid-infrared images obtained as part of the SINGS project (Ixennicutt et al.,2006) and in the Spitzer mid-infrared images obtained as part of the SINGS project (Kennicutt et al. + 2003)., 2003). + Phe dust lanes hint at a tight inner spiral structure within the nuclear disk., The dust lanes hint at a tight inner spiral structure within the nuclear disk. + Fabry-Perot oobservations of NGC 1512 by Buta (LOSS) show that the nuclear ring has a rotational velocity of ~ (assuming an inclination angle o£ 357))., Fabry-Perot observations of NGC 1512 by Buta (1988) show that the nuclear ring has a rotational velocity of $\sim$ (assuming an inclination angle of ). + Beyond the nuclear ring. which lies within the bulge (C1 — AS kpc) at the centre of the bar. aappears to be roughly constant.," Beyond the nuclear ring, which lies within the bulge $\la$ = 2.8 kpc) at the centre of the bar, appears to be roughly constant." + iimages of the inner region («4 z 1 kpe) of NGC 1512 (SING project: Meurer et al., images of the inner region $<$ $\approx$ 11 kpc) of NGC 1512 (SINGG project; Meurer et al. + 2006) reveal a second star-lorming ring of approximate diameter 3Boat/ PA~45°. des," 2006) reveal a second star-forming ring of approximate diameter $3\arcmin \times 2\arcmin$ at $PA \sim 45\degr$, ie." +" about ten times larger than the nuclear starburst ring:. its. width. is20 20py40""."," about ten times larger than the nuclear starburst ring; its width is $20\arcsec - +40\arcsec$." + This inner ring is composed of dozens of independent rregions with typical sizes of 27ο., This inner ring is composed of dozens of independent regions with typical sizes of $2\arcsec - 5\arcsec$. +" ""Phe bar. which has a length of —3 ((8.3 κρο lies roughly along its major axis."," The bar, which has a length of $\sim$ (8.3 kpc), lies roughly along its major axis." + Some enhancement of the star formation is seen at both ends of the bar where the spiral arms commence., Some enhancement of the star formation is seen at both ends of the bar where the spiral arms commence. + The optical cata presented. by Ixinman. (1978). and Hawarden et al. (, The optical data presented by Kinman (1978) and Hawarden et al. ( +1979). revealed. for the first. time. signs of tidal interaction between NGC 1510 and. NGC 1512.,"1979) revealed, for the first time, signs of tidal interaction between NGC 1510 and NGC 1512." + Sandage Bedke (1994) describe NGC 1512 aspattern., Sandage Bedke (1994) describe NGC 1512 as. + Ehe stellar spiral armis are most »ominent in deep optical images (see Fig., The stellar spiral arms are most prominent in deep optical images (see Fig. + 1) as well as he GALEN ultraviolet (CV) images by Cil de Paz et al. (, 1) as well as the GALEX ultraviolet $UV$ ) images by Gil de Paz et al. ( +20072). all of which give a stunning view of the star-forming regions in NGC 1512's outer disk.,"2007a), all of which give a stunning view of the star-forming regions in NGC 1512's outer disk." + A sketch. identifving important stellar and features of the interacting svstem NGC 1512/1510. is oovided on the right side of Fig., A sketch identifying important stellar and features of the interacting system NGC 1512/1510 is provided on the right side of Fig. + 1., 1. + NGC 1510 is a low metallicity (Z0.2 Z.)) BCD ealaxy (see also Section 4.6)., NGC 1510 is a low metallicity $Z \sim 0.2$ ) BCD galaxy (see also Section 4.6). + Llawarden ct al. (, Hawarden et al. ( +1979) sugeested that its emission line spectrum and blue colors are the consequence of star formation activity in the material basically eos recently (300. Myr) acereted from NGC 1512. mimicing the properties of a red amorphous dwarf elliptical galaxy.,"1979) suggested that its emission line spectrum and blue colors are the consequence of star formation activity in the material — basically gas — recently $\sim$ 300 Myr) accreted from NGC 1512, mimicing the properties of a red amorphous dwarf elliptical galaxy." + This hypothesis is also supported by Iichendorf Nieto (1984). who identified several low-nictallicity. star-[orming regions in NGC 1510.," This hypothesis is also supported by Eichendorf Nieto (1984), who identified several low-metallicity star-forming regions in NGC 1510." + One of them (the SW component) reveals a broad. A4686 lline which is attributed to the presence of an important population of Woll-Rayet (WI). stars. in. the burst., One of them (the SW component) reveals a broad $\lambda$ 4686 line which is attributed to the presence of an important population of Wolf-Rayet (WR) stars in the burst. + NGC 1510 is therefore classified as Woll-Ravet galaxy (Conti 1991: Schaerer. Contini DPindao 1999).," NGC 1510 is therefore classified as Wolf-Rayet galaxy (Conti 1991; Schaerer, Contini Pindao 1999)." + Llawareen et al. (, Hawarden et al. ( +1979) also present remarkable delata for the galaxy pair.,1979) also present remarkable data for the galaxy pair. + Their 24-pointing mmap obtained with the Gm Parkes telescope reveals alarge neutral hydrogen envelope. around NGC 1512. encompassing its neighbour. NGC 1510.," Their 24-pointing map obtained with the 64-m Parkes telescope reveals alarge neutral hydrogen envelope around NGC 1512, encompassing its neighbour, NGC 1510." + Ixoribalski et al., Koribalski et al. +((Ilolbere et al.,(Holberg et al. + 2002: Liebert et al., 2002; Liebert et al. + 2005: Nepler et al., 2005; Kepler et al. + 2007)., 2007). + Separate low mass («0.45 )) and high mass (20.8 )) components are also observed with each one contributing and to the total mass budget. respectively (Liebert et al.," Separate low mass $<$ 0.45 ) and high mass $>$ 0.8 ) components are also observed with each one contributing and to the total mass budget, respectively (Liebert et al." + 2005)., 2005). + The magnitude-Iimited sample of WDs from the Palomar Green (DG) survey includes WDs with masses as low as 0.32AM., The magnitude-limited sample of WDs from the Palomar Green (PG) survey includes WDs with masses as low as 0.32. +.. Recent discoveries of several extremely low mass (M~ 0.2 )) WDs in the field (Liebert οἱ al., Recent discoveries of several extremely low mass $M\sim$ 0.2 ) WDs in the field (Liebert et al. + 2004: Eisenstein et al., 2004; Eisenstein et al. + 2006: Kawka οἱ al., 2006; Kawka et al. + 2006: Ixilie et al., 2006; Kilic et al. + 20072) and around pulsars (Bassa et al., 2007a) and around pulsars (Bassa et al. + 2006: van Ixerkwijk et al., 2006; van Kerkwijk et al. + 1996) show that WDs with mass as low as 0.17 aae formed in the Galaxy., 1996) show that WDs with mass as low as 0.17 are formed in the Galaxy. + The formation of low mass WDs require significant mass loss Irom a post main sequence star., The formation of low mass WDs require significant mass loss from a post main sequence star. + The only viable scenario for such mass loss has traditionally been the formation of a WD in a close binary system., The only viable scenario for such mass loss has traditionally been the formation of a WD in a close binary system. + If à post main sequence star has a close binary companion. il can lose ils outer envelope without reaching the asymptotic giant branch and without ever ieniting helium. ending up as a helium core WD.," If a post main sequence star has a close binary companion, it can lose its outer envelope without reaching the asymptotic giant branch and without ever igniting helium, ending up as a helium core WD." + Confirmation of the binary nature of several low mass WDs by Marsh οἱ al. (, Confirmation of the binary nature of several low mass WDs by Marsh et al. ( +1995). Marsh. 2000. Maxted et al. (,"1995), Marsh 2000, Maxted et al. (" +2006: 2007). and ]xilie et al. (,"2006; 2007), and Kilic et al. (" +2007b) supports this binary formation scenario.,2007b) supports this binary formation scenario. + An alternative scenario for the formation of low mass WDs through extreme mass loss from single metal-rich stars was proposed by Hansen (2005) to explain the WD sequence of NGC 6791., An alternative scenario for the formation of low mass WDs through extreme mass loss from single metal-rich stars was proposed by Hansen (2005) to explain the WD sequence of NGC 6791. + IIubble Space Telescope observations of NGC 6791 showed that it has a population of WDs brighter than expected for a Y Gyr old open cluster., Hubble Space Telescope observations of NGC 6791 showed that it has a population of WDs brighter than expected for a 7 Gyr old open cluster. + This population of WDs implied an age of 2.7 Gyr assuming thev are carbon-oxveen core stus (Berlin οἱ al., This population of WDs implied an age of 2.7 Gyr assuming they are carbon-oxygen core stars (Bedin et al. + 2005)., 2005). + ILansen (2005) suggested that the age degeneracy is removed by assuming the stars are lle-core WDs and that most of the observed. WDs in this cluster are actually low mass WDs created as a result of significant mass loss on the red giant. branch in this metal-rich svstem (ο = +0.3 — +0.5: Origlia et al., Hansen (2005) suggested that the age degeneracy is removed by assuming the stars are He-core WDs and that most of the observed WDs in this cluster are actually low mass WDs created as a result of significant mass loss on the red giant branch in this metal-rich system ([Fe/H] = +0.3 $-$ +0.5; Origlia et al. + 2006: Gratton οἱ al., 2006; Gratton et al. + 2006)., 2006). + Follow up spectroscopic work bv Ixalirai et al. (, Follow up spectroscopic work by Kalirai et al. ( +2007a) showed that the majority of the brighter WDs in this cluster are actually O.4 WWDs.,2007a) showed that the majority of the brighter WDs in this cluster are actually 0.4 WDs. + Since the binary star fraction of NGC 6791. seems to be low (on the order oftdi: Janes INassas 1997). these low mass WDs are most likely produced from single star progenitors.," Since the binary star fraction of NGC 6791 seems to be low (on the order of; Janes Kassas 1997), these low mass WDs are most likely produced from single star progenitors." + There is therefore direct observational evidence that low mass WDs max be copiously produced in a sulliciently old and metal rich star without. requiring binary interactions., There is therefore direct observational evidence that low mass WDs may be copiously produced in a sufficiently old and metal rich star without requiring binary interactions. + In this paper. we provide evidence for the existence of a metal-rich. population ol field stars in (he past 10 billion vears of the Galactic history and we show Chat such stars are likely to produce single low mass WDs.," In this paper, we provide evidence for the existence of a metal-rich population of field stars in the past 10 billion years of the Galactic history and we show that such stars are likely to produce single low mass WDs." + The age-metallicity relation for the local Galactic disk is discussed in 82. while (he observed populations of single aud binary low mass WDs," The age-metallicity relation for the local Galactic disk is discussed in 2, while the observed populations of single and binary low mass WDs" +than 75% of its final value.,than $75\%$ of its final value. +" On the other hand. lor the ΛΙΓΑ window. v; attains 0.95ορ no sooner than for r~470Mpe/h (~14.5 mag in the A, band). far bevond the completeness of the 2ALASS ASC."," On the other hand, for the 2MASS window, $v_c$ attains $0.95\,v_\mathrm{CMB}$ no sooner than for $r\simeq470\Mpch$ $\sim14.5$ mag in the $K_s$ band), far beyond the completeness of the 2MASS XSC." +" As an extreme case. in Figure 6 we additionally plot the prediction for the once-popular ‘Standard CDM model. currently strongly disfavored by observations (f=0.5. G4,=1. OQ),=0.05. no=1, σς= 1). with the top-hat window."," As an extreme case, in Figure \ref{Fig:predicted} we additionally plot the prediction for the once-popular `Standard CDM' model, currently strongly disfavored by observations $h=0.5$, $\Omm=1$, $\Omb=0.05$, $n_s=1$, $\sigma_8=1$ ), with the top-hat window." + Note how fast convergence would be expected in this case., Note how fast convergence would be expected in this case. + The most important result of this Paper is presented in Figure 7.., The most important result of this Paper is presented in Figure \ref{Fig:g_m and v_c}. + It shows the observed erowth ol the 241AS5 dipole compared with the conditional velocity calenlated from ((13))., It shows the observed growth of the 2MASS dipole compared with the conditional velocity calculated from \ref{eq:v_cond}) ). + As was already. discussed at the end of refSubseczTheory.. we rescale observational data by a best-fit parameter 3=OTED1/b.," As was already discussed at the end of \\ref{Subsec:Theory}, we rescale observational data by a best-fit parameter $\beta\equiv\Omm^{0.55}\slash b$ ." + The errorbars of the measured dipole were obtained from. 1000-Iold. bootstrap resampling of the catalog., The errorbars of the measured dipole were obtained from 1000-fold bootstrap resampling of the catalog. + The J parameter was fitted by a minimum-A? procedure. including both observational errors (from bootsirapping) aud the theoretical (cosmic) variance.," The $\beta$ parameter was fitted by a $\chi^2$ procedure, including both observational errors (from bootstrapping) and the theoretical (cosmic) variance." + Note that formally we are ‘over-filling’. as (he datapoints are correlated with each other. due to an integral nature of the measured dipole.," Note that formally we are `over-fitting', as the datapoints are correlated with each other, due to an integral nature of the measured dipole." + The observed growth. once rescaled. is well within lo range of the theoretical prediction (apart from the datapoints for the smallest. distances. where (he munber of galaxies is very small. hence the measurement is noisv).," The observed growth, once rescaled, is well within $1\sigma$ range of the theoretical prediction (apart from the datapoints for the smallest distances, where the number of galaxies is very small, hence the measurement is noisy)." + Remarkably. the best agreement is obtained in the range 100Mpc/hSrar300 Mpc/h. bbetween the extent of the 2\IRS catalog and the 2\IASS NSC completeness limit.," Remarkably, the best agreement is obtained in the range $100\Mpch\lesssim r_\mathrm{eff}\lesssim300\Mpch$ , between the extent of the 2MRS catalog and the 2MASS XSC completeness limit." + The result of the fitting gives ο)=0.38 with lo confidence intervals of 40.02., The result of the fitting gives $\beta=0.38$ with $1\sigma$ confidence intervals of $\pm0.02$. + Owing to the considerations of relSec:Data concerning the scatter introduced by the offset. added when passing from isophotal fiducial elliptical aperture magnitudes to total fluxes. as well as due to findings of οἳ the bias introduced by the fact of possibly improper masking of the Local Void. we double this formal error.," Owing to the considerations of \\ref{Sec:Data} concerning the scatter introduced by the offset added when passing from isophotal fiducial elliptical aperture magnitudes to total fluxes, as well as due to findings of \cite{BC10} on the bias introduced by the fact of possibly improper masking of the Local Void, we double this formal error." + IIence our estimate is This value is in agreement with the analvsis of 2.. where also data from 2\LASS were used. although from much smaller scales.," Hence our estimate is This value is in agreement with the analysis of \cite{Erdogdu}, where also data from 2MASS were used, although from much smaller scales." +" The clustering dipole was calculated (here [rom a subsample of the 2\TASS NSC with measured redshifts. namely 2\TASS Redshilt Survey. thencomplete up to ~100Mpc/h. naxinummagnitude in the Av, baud equal {ο 11.25 mag)."," The clustering dipole was calculated there from a subsample of the 2MASS XSC with measured redshifts, namely 2MASS Redshift Survey, thencomplete up to $\sim100\Mpch$ (maximummagnitude in the $K_s$ band equal to $11.25$ mag)." + Their result. based on," Their result, based on" +It is worth stressing that the CSFR is inferred from observations of the light emitted by stars at various wavelengths.,It is worth stressing that the CSFR is inferred from observations of the light emitted by stars at various wavelengths. +" These observable samples are flux-limited, and thus the intrinsic luminosity of the faintest objects in the sample changes with redshift."," These observable samples are flux-limited, and thus the intrinsic luminosity of the faintest objects in the sample changes with redshift." + This incompleteness of the samples is corrected by using a functional (Schechter function) to the luminosity function obtained from the observations themselves., This incompleteness of the samples is corrected by using a functional (Schechter function) to the luminosity function obtained from the observations themselves. + An important parameter on the determination of the CSFR is the obscuration by dust that is well known to affect measurements of galaxy luminosty at ultraviolet (UV) and optical wavelengths., An important parameter on the determination of the CSFR is the obscuration by dust that is well known to affect measurements of galaxy luminosty at ultraviolet (UV) and optical wavelengths. + Correcting for this effect is not always straightforward., Correcting for this effect is not always straightforward. +" Thus, there are large uncertainties associated to the determination of the CSFR as can be seen from Figures 1—3 (see, in particular, Hopkins2004;deAraujo&Miranda2005 who discuss these uncertainties with more details)."," Thus, there are large uncertainties associated to the determination of the CSFR as can be seen from Figures $1-3$ (see, in particular, \citealp{h2,d2} who discuss these uncertainties with more details)." +" In this section we use the CSFR (9,) obtained from the hierarchical model to determine the stochastic background of gravitational waves (SBGWs) generated by stars which collapse to black holes.", In this section we use the CSFR $\dot\rho_{\star}$ ) obtained from the hierarchical model to determine the stochastic background of gravitational waves (SBGWs) generated by stars which collapse to black holes. +" Initially, we present a quick overview on the formalism used to characterize a SBGWs because this subject is discussed in previous works (see, for example, deMiranda2005;Miranda,deAraujo&Aguiar 2004))."," Initially, we present a quick overview on the formalism used to characterize a SBGWs because this subject is discussed in previous works (see, for example, \citealp{d3,d4,d5,d2,m1}) )." + After this quick overview we display and compare the results of the models considered., After this quick overview we display and compare the results of the models considered. +" Let us write the specific flux received in GWs at the present epoch as where is the comoving specific luminosity density (given, e.g, in ergs!Hz! Mpc?), which obviously refers to the source frame."," Let us write the specific flux received in GWs at the present epoch as where is the comoving specific luminosity density (given, e.g, in ${\rm erg\, s^{-1}\, Hz^{-1}\, Mpc^{-3}}$ ), which obviously refers to the source frame." +" See that dV is the comoving volume element, and dir, is the luminosity distance."," See that $dV$ is the comoving volume element, and $d_{\rm L}$ is the luminosity distance." + 'The above equations are valid to estimate a stochastic, The above equations are valid to estimate a stochastic +period was reportedby Wenetal.tw(2006) because the uuderlvius period may actuallybe ice as long. or 19.2 davs (Corbetetal. 20075: see also Wane 2009).,"period was reported by \citet{wen06} because the underlying period may actually be twice as long, or $\sim 19.2$ days \citealt{corbmt07}; ; see also \citealt{wang09}) )." + Iu this regard. Corbetetal.(20075). found a signal at a period of P=19.2540.08 davs in Swiff/BAT data and a signal near the same period in ASM data.," In this regard, \citet{corbmt07} found a signal at a period of $P = 19.25 \pm 0.08$ days in /BAT data and a signal near the same period in ASM data." + Wane(2009) found a peak uear a period P=19.11 days in he ASM data., \citet{wang09} found a peak near a period $P= 19.11$ days in the ASM data. + Our power spectrum of ASAI data also shows peaks at frequencies corresponding to both periods (sce Fieure 22))., Our power spectrum of ASM data also shows peaks at frequencies corresponding to both periods (see Figure \ref{fig:pds2206}) ). + The more significant peak corresponds o a period of P=9.5581+0.0012 days.," The more significant peak corresponds to a period of $P = 9.5584 \pm 0.0012\,[\pm 0.0091]$ days." + Asstuing that the subharmonic corresponds to a [40.0091]period wice this value. we obtain P=19.117+0.003[40.013] davs.," Assuming that the subharmonic corresponds to a period twice this value, we obtain $P = 19.117 \pm 0.003\,[\pm 0.018]$ days." + Radial velocity measurements from optical or near IR spectroscopy are needed to unaiibiguously determine he true orbital period., Radial velocity measurements from optical or near IR spectroscopy are needed to unambiguously determine the true orbital period. + The estimates of the amplitudes of the periodic sienals hat are reported in Table 4. fall. for uost of 1ο cases just below the detection thresholds of the xeseut blind search.," The estimates of the amplitudes of the periodic signals that are reported in Table \ref{tbl:ampl} fall, for most of the cases, just below the detection thresholds of the present blind search." + They thereby illustrate the typical seusitivitv of the present search., They thereby illustrate the typical sensitivity of the present search. + We have also estimated jio amplitudes that approximately correspond to our detection thresholds iu a set of additional sources chosen ‘ther to help cover a wide ranee of iuteusities or because rev are of mterest for other reasons., We have also estimated the amplitudes that approximately correspond to our detection thresholds in a set of additional sources chosen either to help cover a wide range of intensities or because they are of interest for other reasons. + To accomplish this we have computationally superimposed siue waves onto ASAI light curves and repeated the search analyses ou the lieht curves for those particular sources in order to determine thesignal amplitudes that would have resulted in peaks reaching renormalized whitened powers of 25 in the power deusity spectra., To accomplish this we have computationally superimposed sine waves onto the ASM light curves and repeated the search analyses on the light curves for those particular sources in order to determine the signal amplitudes that would have resulted in peaks reaching renormalized whitened powers of $\sim 25$ in the power density spectra. + These estimates; which may be taken as upper limuts since we would have recognized veaks near these frequencies tha reached powers as snial as 15. are listed in Table 5..," These estimates, which may be taken as upper limits since we would have recognized peaks near these frequencies that reached powers as small as 15, are listed in Table \ref{tbl:uplim}." + This table also lists oxeviouslv reported periods for some of the sources as well as mussion-average intensities., This table also lists previously reported periods for some of the sources as well as mission-average intensities. +" Column 7 of the table eives the effective upper iuits on the amplitudes as ractions of the average source inteusities,", Column 7 of the table gives the effective upper limits on the amplitudes as fractions of the average source intensities. + Levine&Corbet(2006) reported modest significance detections of periodicities in ASM power density spectra or GRO) 10. lL VIGIL Ser and 11957|115 at or very close to the periods previously reported in the literature.," \citet{lcatel06} reported modest significance detections of periodicities in ASM power density spectra for GRO $-$ 40, $-$ 4, V4641 Sgr, and 1957+115 at or very close to the periods previously reported in the literature." + In the analyses using the eutire ASAI light curves that we rave done recently we do not confirm these yossible detections, In the analyses using the entire ASM light curves that we have done recently we do not confirm these possible detections. + Results of sensitivity analyses for these sources are included in Table 5.., Results of sensitivity analyses for these sources are included in Table \ref{tbl:uplim}. + Table 5 also includes entries for two xieht sources. Sco N-L anc Lt. with well-established periodicitics that we do not detect as well as cutrics for three sources. 1.6.. the Crab Nebula. 3310|0. aud L. that do not have known orbital periodicities.," Table \ref{tbl:uplim} also includes entries for two bright sources, Sco X-1 and $-$ 444, with well-established periodicities that we do not detect as well as entries for three sources, i.e., the Crab Nebula, 340+0, and $-$ 1, that do not have known orbital periodicities." +" Table 5 eives upper limits. calculated as describec above, on any nodulation near the reported periods."," Table \ref{tbl:uplim} gives upper limits, calculated as described above, on any modulation near the reported periods." + We note hat for Sco N-1 the noise is douinated by the intriusic source variations., We note that for Sco X-1 the noise is dominated by the intrinsic source variations. + Iu rare cases. such as that described ro Vanderlindectal.(2003).. specialized techniques nav be available to partially mitigate the effects of he iutriusic variation and improve the seusitivitv of a pertodicity search.," In rare cases, such as that described by \citet{vlr03}, specialized techniques may be available to partially mitigate the effects of the intrinsic variation and improve the sensitivity of a periodicity search." + We have not tried to apply iux such techniques iu the preseut ecucral search., We have not tried to apply any such techniques in the present general search. + The upper inits on periodicities in the power spectra for the Crab 23231010. and l are included iu this table to illustrate the vpical sensitivity of the present search iu he cases of belt sources.," The upper limits on periodicities in the power spectra for the Crab, 340+0, and $-$ 1 are included in this table to illustrate the typical sensitivity of the present search in the cases of bright sources." + We also clic uot detect the alias of the 290-8 pulse veriod in 619 that was reported in Levine&Cor-ot (20060)., We also did not detect the alias of the 290-s pulse period in $-$ 619 that was reported in \citet{lcatel06}. + This is not so unexpected since pulse periods end to chanee more rapidly than orbital periods aud could. change o a deeree that makes them siguificautlv ioncohlerenut aud therefore hard to detect ina Lf-vr data , This is not so unexpected since pulse periods tend to change more rapidly than orbital periods and could change to a degree that makes them significantly noncoherent and therefore hard to detect in a 14-yr data set. +Iu short. Tables aud 5 show that the search sensitivity depends on a ΠΟΡΟΙ of factors iucludiug source strength. degree of intrinsic source variability. and quality of the ASM light curve Gvhich. in turi depeuds ou the source location relative to nearby bright sources. ete).," In short, Tables \ref{tbl:ampl} and \ref{tbl:uplim} show that the search sensitivity depends on a number of factors including source strength, degree of intrinsic source variability, and quality of the ASM light curve (which, in turn depends on the source location relative to nearby bright sources, etc.)." + The preseut search for periodicities in the ASM light curves has proved to be more sensitive than the eurlier search doue by Wenetohal.{ 2006).., The present search for periodicities in the ASM light curves has proved to be more sensitive than the earlier search done by \citet{wen06}. . + The weighting aud of our aleorithius lave proved to be filteriugmajor aspectsfactors in the scusitivity nmuprovenoenuts., The weighting and filtering aspects of our search algorithms have proved to be major factors in the sensitivity improvements. + Another major factor is the use of light curves that cover L more vears., Another major factor is the use of light curves that cover $\sim$ 5 more years. + The result is the detection of the orbital periods in 5 LAINBs aud in ~12 IIMXDs that were uot detected. by Wenetal.(2006)., The result is the detection of the orbital periods in 8 LMXBs and in $\sim$ 12 HMXBs that were not detected by \citet{wen06}. +. Our detection of the 18.55-d period of 0311 represents the co-discovery with Seucractal.(2007) of the orbital period of this system.," Our detection of the 18.55-d period of $-$ 0311 represents the co-discovery with \citet{sguera07} + of the orbital period of this system." + Ou detectious of the orbital periods of 536 aud LAIC N-1 are the first for these svstenis. to ourknowledge. that have been accomplished on the basis of N-rav observations.," Our detections of the orbital periods of $-$ 536 and LMC X-1 are the first for these systems, to ourknowledge, that have been accomplished on the basis of X-ray observations." + It is interestingto compare the present list of detections together with those of Wenctal.(2006) with, It is interestingto compare the present list of detections together with those of \citet{wen06} with +"e»2,3 (0 e5.8) mean that a signilicant degree of dilution of original ISM of the LMC by HVC' infall is indispensable for explaining the observed low [N/II] in HLL regions and voung stars in the LMC.",$\sim 2.3$ to $\sim 5.8$ ) mean that a significant degree of dilution of original ISM of the LMC by HVC infall is indispensable for explaining the observed low [N/H] in HII regions and young stars in the LMC. +" For example. the original gas of the LMC with M,=7.8x10M, is converted into newstars for e=1.0 and. [N/II]uve=72.0 alter being mixed with the IIVCs with Alive=L8xLOM..."," For example, the original gas of the LMC with $M_{\rm g}=7.8 \times 10^5 {\rm M}_{\odot}$ is converted into newstars for ${\epsilon}=1.0$ and ${\rm [N/H]}_{\rm HVC}=-2.0$ after being mixed with the HVCs with $M_{\rm HVC}=1.8 \times 10^6 {\rm M}_{\odot}$." + Fig., Fig. + 2 shows that the required Mie is quite large (~6.3x10*M. ) if voung stars with ages less than LO“vr uniformly have low [N/IH] of —0.8., 2 shows that the required $M_{\rm HVC}$ is quite large $\sim 6.3 \times 10^7 {\rm M}_{\odot}$ ) if young stars with ages less than $10^8$ yr uniformly have low [N/H] of $-0.8$. + Fig., Fig. + 2 also shows that the required Mice depends weakly on [N/1HI]gvé. for a given e; in models with different fag., 2 also shows that the required $M_{\rm HVC}$ depends weakly on ${\rm [N/H]}_{\rm HVC}$ for a given ${\epsilon}_{\rm sf}$ in models with different $t_{\rm sf}$. + Onlv a small fraction of the Galactic IIVCs can interact with the LAIC owing to the small disk size of the LMC., Only a small fraction of the Galactic HVCs can interact with the LMC owing to the small disk size of the LMC. + We here estimate (1) a tvpical timescale for the LAIC to collide with one IVC (/44) for a given number densitv of the IIVCs within the distance of the LAIC from the Galactic center and (41) an expected accretion rate of ΗΝος onto the LMC disk (Muyo)., We here estimate (i) a typical timescale for the LMC to collide with one HVC $t_{\rm col}$ ) for a given number density of the HVCs within the distance of the LMC from the Galactic center and (ii) an expected accretion rate of HVCs onto the LMC disk ${\dot{M}}_{\rm HVC}$ ). + Since we can estimate the accretion rate required for explaining the observed IN/M| using the results shown in Fies., Since we can estimate the accretion rate required for explaining the observed [N/H] using the results shown in Figs. + 1 and 2 (Le. Miuye 1). we can compare the expected ancl the required accretion rates and (hereby assess (he viability of the present scenario.," 1 and 2 (i.e., $M_{\rm HVC}/t_{\rm sf}$ ), we can compare the expected and the required accretion rates and thereby assess the viability of the present scenario." + The time scale of a LAIC-IIVC collision event. (/44) can be estimated as lollows (e.g. Makino πας 1997): where mive. σ. and e are the mean number density of the IIVCs within the Galaxy. the geometrical cross section of the LAIC. and a relative velocity between a IVC and the LAIC.," The time scale of a LMC-HVC collision event $t_{\rm col}$ ) can be estimated as follows (e.g., Makino Hut 1997); where $n_{\rm HVC}$, $\sigma$, and $v$ are the mean number density of the HVCs within the Galaxy, the geometrical cross section of the LMC, and a relative velocity between a HVC and the LMC." + We here estimate myyc lor the central τὸ kpe of the Galaxy. (corresponding roughly to the mean of (he pericenter aud apocenter distances of (he LMC orbit: e.g.. Dekki Chiba 2005) and assume that o=πιο”. where Ric is the LMC size and ve is velocity dispersion (=nv). where ος is the circular velocity thus 220 km |) of the Galaxy halo.," We here estimate $n_{\rm HVC}$ for the central 75 kpc of the Galaxy (corresponding roughly to the mean of the pericenter and apocenter distances of the LMC orbit; e.g., Bekki Chiba 2005) and assume that $\sigma= \pi {R_{\rm LMC}}^2$, where $R_{\rm LMC}$ is the LMC size and $v$ is velocity dispersion $=v_{\rm c}/\sqrt(2)$, where $v_{\rm c}$ is the circular velocity thus 220 km $^{-1}$ ) of the Galaxy halo." + For convenience. we discuss /44 in terms of the total number of IVCs within 75 kpe Irom the Galaxy (Nive) rather than nive below.," For convenience, we discuss $t_{\rm col}$ in terms of the total number of HVCs within 75 kpc from the Galaxy $N_{\rm HVC}$ ) rather than $n_{\rm HVC}$ below." + Previous observations found more than 600 IIVC's (Wakker van Woerden 1991) vet many initial IIVCs have been already destroved bv tides and ram pressure (e.g.. See Wakker 2004 for a review).," Previous observations found more than 600 HVCs (Wakker van Woerden 1991) yet many initial HVCs have been already destroyed by tides and ram pressure (e.g., See Wakker 2004 for a review)." + Thus we consider (hat it is reasonable io investigateS models with VyyeLIN rangingSHS from a few hundreds to a few thousands., Thus we consider that it is reasonable to investigate models with $N_{\rm HVC}$ ranging from a few hundreds to a few thousands. + Fig., Fig. +" 3 shows that /.,,) is shorter for larger Nyjpye for a given Apc ancl shorter for larger Hye lor a given Nyuyve.", 3 shows that $t_{\rm col}$ is shorter for larger $N_{\rm HVC}$ for a given $R_{\rm LMC}$ and shorter for larger $R_{\rm LMC}$ for a given $N_{\rm HVC}$ . + Fig., Fig. + 3 also shows that /44 can be as low as ~ LO*vr if the total number of the IVC within the LAIC’s orbit is as large as ~1000 for the size of the LMC, 3 also shows that $t_{\rm col}$ can be as low as $\sim 10^8$ yr if the total number of the HVC within the LMC's orbit is as large as $\sim 1000$ for the size of the LMC +Thus. i£ SNAP detects a core-collapse SN. it appears likely that it will also be sensitive to the shock breakout.,"Thus, if SNAP detects a core-collapse SN, it appears likely that it will also be sensitive to the shock breakout." + As SNAP will sample further into the restframe UV down to restlrame Ly-a in its bluest bands. detections should be somewhat stronger. depending on the amount of dust extinction.," As SNAP will sample further into the restframe UV — down to restframe $\alpha$ in its bluest bands, detections should be somewhat stronger, depending on the amount of dust extinction." + For example at restframe 1800A. GRB 060218/SN 2006aj exhibited an absolute AD magnitude of —18.4 (Campana2006).," For example at restframe 1800, GRB 060218/SN 2006aj exhibited an absolute AB magnitude of $-18.4$ \citep{campana06}." +. The shock breakout for SN 1993J. having a RSG progenitor (Alderingetal.199.4:VanDvk2002).. is one example that SNAP should be capable of detecting oul to z~3.," The shock breakout for SN 1993J, having a RSG progenitor \citep{aldering94,vandyke02}, is one example that SNAP should be capable of detecting out to $z\sim3$." + SNAP samples any given pateh of sky with 4 exposures of 300 sec in each of the bluest (optical) fillers aud with 8 exposures of 300 sec in each of the recdest (NUR) filters., SNAP samples any given patch of sky with 4 exposures of 300 sec in each of the bluest (optical) filters and with 8 exposures of 300 sec in each of the reddest (NIR) filters. + Consecutive observations in each of the 9 SNAP fillers means that a given pateh of sky is monitored continuously for 1.1 hrs everv 4 davs in the observer frame., Consecutive observations in each of the 9 SNAP filters means that a given patch of sky is monitored continuously for 1.1 hrs every 4 days in the observer frame. + Thus. with fortuitous timing — likely for some fraction of the thousands of core-collapse SNe SNAP will detect SNAP may obtain multi-epoch coverage in up to 9 filters. possibly covering the most luminous period of an event even for fast-declining BSG progenitors.," Thus, with fortuitous timing — likely for some fraction of the thousands of core-collapse SNe SNAP will detect — SNAP may obtain multi-epoch coverage in up to 9 filters, possibly covering the most luminous period of an event even for fast-declining BSG progenitors." + This will allow a determination of (he Iuminosity. and temperature (spectral) evolution of the shock breakout., This will allow a determination of the luminosity and temperature (spectral) evolution of the shock breakout. + In simple shock breakout models (Matzner&Melxee1999). (his evolution is set. primarily by (he stellar radius. followed in importance by (he explosion energy. and finally the total ejecta mass.," In simple shock breakout models \citep{matznermckee} this evolution is set primarily by the stellar radius, followed in importance by the explosion energy, and finally the total ejecta mass." + Determinations of the recdshilt aud dust exüncton will be needed (o set the correct. scale for these quantities for each SN., Determinations of the redshift and dust extinction will be needed to set the correct scale for these quantities for each SN. + Some common plivsical parameters (such as opacities expected to be dominated bv electron scattering and characteristic clensity profiles) will need to be determined for the population as a whole in order obtain the best constraints (Matzner&Melee1999:Calzavara/Matzner2004).," Some common physical parameters (such as opacities — expected to be dominated by electron scattering — and characteristic density profiles) will need to be determined for the population as a whole in order obtain the best constraints \citep{matznermckee,calzavara04}." +.. IIowever. distinguishing between BSG and RSCG progenitors for shock breakout events with good temporal coverage should be straightforweadl. and (his discrimination is already sullicient to. provide more detailed constraints on the star formation historv of the universe than can be obtained from the integrated light of galaxies or from SN rates alone.," However, distinguishing between BSG and RSG progenitors for shock breakout events with good temporal coverage should be straightforward, and this discrimination is already sufficient to provide more detailed constraints on the star formation history of the universe than can be obtained from the integrated light of galaxies or from SN rates alone." + As part of its normal operation SNAP will discover ancl obtain lighteurves for thousands of SNe with z>1.7., As part of its normal operation SNAP will discover and obtain lightcurves for thousands of SNe with $z>1.7$. + For SNe Ia. we find that SNAP will have good sensitivity out (o ze3. where the nominal 4-day observer-Drame cadence will equal an unprecedented daily cadence in the rest-frame.," For SNe Ia, we find that SNAP will have good sensitivity out to $z\sim3$, where the nominal 4-day observer-frame cadence will equal an unprecedented daily cadence in the rest-frame." + llowever. we find that attempting to use z>1.7 standardized candles for cosmology," However, we find that attempting to use $z>1.7$ standardized candles for cosmology" +2002).,. + Thus lar CAT | provides a most complete open cluster sample concerning the iron abundance. distance aud age parameters together.," Thus far CAT 1 provides a most complete open cluster sample concerning the iron abundance, distance and age parameters together." + This sample could provide statistically nore significant information concerning the Galactic AMIR. radial iron gradient. as well as its evolution. etc.," This sample could provide statistically more significant information concerning the Galactic AMR, radial iron gradient as well as its evolution, etc." + In the second catalogue (hereafter CAT 2). we have listed observed kinematical data from ilerature for 144 clusters.available.," In the second catalogue (hereafter CAT 2), we have listed observed kinematical data from literature for 144 clusters,." + The nean radial velocity data are mostly (122 of 144 objects) from a compilation in WEDDA database (http://obswww.unige.ch/webda/meanvr.hinl)). primarily based on the work of Ttastorguevοἱal.(1999).," The mean radial velocity data are mostly (122 of 144 objects) from a compilation in WEBDA database ), primarily based on the work of \citet{ras99}." +. The absolute proper motion of 125 clusters. based on the Hipparcos svslem. are from: Daunmegardtetal.(2000).," The absolute proper motion of 125 clusters, based on the Hipparcos system, are from \citet{bau00}." +. Mean. proper motions of additional 16 cluster were added from compilation of Diasetal.(2001).. with cluster membership probability derived bv Tvcho2 proper motions.," Mean proper motions of additional 16 cluster were added from compilation of \citet{dia01}, with cluster membership probability derived by Tycho2 proper motions." + Data of NGC2355 comes [rom Soubiranetal.(2000).. and data of Coma Ber ancl Pleiade clusters are from Robichonetal.(1999).," Data of NGC2355 comes from \citet{sou00}, and data of Coma Ber and Pleiade clusters are from \citet{rob99}." +. In fact. the above observed kinematic information constitutes a sub-catalogue of that of Diasetal.(2002).," In fact, the above observed kinematic information constitutes a sub-catalogue of that of \citet{dia02}." +. Bul. here in CAT 2 we have further caleulated the three dimensional velocity of open clusters by combing with radial velocity aid mean absolute proper motion data aud give. for each cluster. the velocity components(II.O. 1H) in cvlindrical coordinates with respect to the Galactic Standard. Reference (GSR).," But, here in CAT 2 we have further calculated the three dimensional velocity of open clusters by combing with radial velocity and mean absolute proper motion data and give, for each cluster, the velocity $\Pi,\Theta,W$ ) in cylindrical coordinates with respect to the Galactic Standard Reference (GSR)." + In addition. lor each cluster. age and iron abundance data are also listed whenever available. (," In addition, for each cluster, age and iron abundance data are also listed whenever available. (" +Notice that in the spatial velocity calculation. following parameters are adopted [for (he Sun: galactocentric distance 8.5 kpe. velocity. components relative to LSR (10.0. 15.0. 8.0. )) and the rotation velocity: 225.0|.,"Notice that in the spatial velocity calculation, following parameters are adopted for the Sun: galactocentric distance 8.5 kpc, velocity components relative to LSR (10.0, 15.0, 8.0 ) and the rotation velocity: 225.0." +.. Our catalogue files (Table 1. Table 2) are sell-explanatory.," Our catalogue files (Table 1, Table 2) are self-explanatory." + CAT 1 (Tab.1) consists of data lor 119 (118—Derk29) open clusters., CAT 1 (Tab.1) consists of data for 119 (118+Berk29) open clusters. + For each cluster. we list its heliocentric galactic coordinates in D1950.0 aud (he following parameters. when available: galactocentric distance: distauce [rom the Sun: color excess E(D—V). age in Gvr: mean metallicity. and two reference codes separated by a coma. where the first number is for age. distance and £(2—V) data while the second number for iron abundance value.," For each cluster, we list its heliocentric galactic coordinates in B1950.0 and the following parameters, when available: galactocentric distance; distance from the Sun; color excess $E(B-V)$, age in Gyr; mean metallicity, and two reference codes separated by a coma, where the first number is for age, distance and $E(B-V)$ data while the second number for iron abundance value." + In CAT 2 (tab.2). we provide information of spatial motion for 144 clusters.," In CAT 2 (tab.2), we provide information of spatial motion for 144 clusters." + For each object. the following data are listed: galactic coordinates in D1950.0: mean radial velocity: mean proper motions: velocity components in cvlindical coordinates will respect to the GSR: mean spatial velocity ancl error: age and iron abundance when available.," For each object, the following data are listed: galactic coordinates in B1950.0; mean radial velocity; mean proper motions; velocity components in cylindrical coordinates with respect to the GSR; mean spatial velocity and error; age and iron abundance when available." + In order to check if the data in our CAT | has anv significant svstematic difference with other published catalogues. we have made a comparison wilh Friel’s catalogue 1995).. with 41 clusters in common.," In order to check if the data in our CAT 1 has any significant systematic difference with other published catalogues, we have made a comparison with Friel's catalogue \citep{fri95}, with 41 clusters in common." + We found that the average dillerence in metallicity is less than 0.10dex. well within the (wpical observational uncertainty.," We found that the average difference in metallicity is less than 0.10dex, well within the typical observational uncertainty." + The average difference, The average difference +simulations with resolution of up to 2048«2561. but we do not discuss these results because turbulence decayed on an orbital time-scale (i.e. Cowling’s anti-dynamo theorem holds),"simulations with resolution of up to $2048\times256\times1$, but we do not discuss these results because turbulence decayed on an orbital time-scale (i.e. Cowling's anti-dynamo theorem holds)." + We began the simulation with an equilibrium torus (Chakrabarti1985:DeVilliers&Hawley2003) with inner edge at r=20M and pressure maximum at r=35M and adjusted the model parameters sothe torus had //r=0.1 at 33M.," We began the simulation with an equilibrium torus \citep{chak85,dev03} with inner edge at $r=20M$ and pressure maximum at $r=35M$ and adjusted the model parameters sothe torus had $h/r=0.1$ at $35M$." + We found that placing the torus at a smaller radius led to results too sensitive to the initial mass distribution., We found that placing the torus at a smaller radius led to results too sensitive to the initial mass distribution. +" We define Ai/r to be the density-weighted root mean square angular thickness of the disk at any given r. Le. or written as AO,=(N07)7 with A0=0(05."," We define $h/r$ to be the density-weighted root mean square angular thickness of the disk at any given $r$, i.e. or written as $\Delta\theta_{\rm rms} = \langle \Delta\theta^2 \rangle^{1/2}$ with $\Delta\theta\equiv\theta-\langle\theta\rangle$." +" We also consider the mean density-weighted thickness: /7/r=A, (AOI)."," We also consider the mean density-weighted thickness: $h/r = +{\Delta\theta}_{\rm abs}=\langle|\Delta\theta|\rangle$ ." + We embedded the torus with a weak magnetic field with )—p/pp~100., We embedded the torus with a weak magnetic field with $\beta\equiv p/p_b\sim 100$. + The initial field consisted of two poloidal loops centered at r=28M and 38M to model a disorganized field with no net flux. (, The initial field consisted of two poloidal loops centered at $r=28M$ and $38M$ to model a disorganized field with no net flux. ( +During the simulation. there Is no organized flux threading the disk but some organized flux threads the BH.),"During the simulation, there is no organized flux threading the disk but some organized flux threads the BH.)" + The field strength was randomly perturbed by to seed the MRI instability., The field strength was randomly perturbed by to seed the MRI instability. + Recent GRMHD simulations (McKinney&Narayan2007a.b:Beckwithet2008a) indicate that the results for the disk (but not the jet) should be roughly independent of the initial field geometry," Recent GRMHD simulations \citep{mn07a,mn07b,beckwith08a} indicate that the results for the disk (but not the jet) should be roughly independent of the initial field geometry." + The MRL is initially resolved with much of the torus having 10 cells per wavelength of the fastest growing MRI mode., The MRI is initially resolved with much of the torus having $10$ cells per wavelength of the fastest growing MRI mode. +" In order to keep the aceretion disk thin. an ad hoc cooling/heating function was added to the energy-momentum equations as a covariant source term (—udu, /d7) with where 7 is the fluid proper time."," In order to keep the accretion disk thin, an ad hoc cooling/heating function was added to the energy-momentum equations as a covariant source term $-u^\mu\,du_g/d\tau$ ) with where $\tau$ is the fluid proper time." +" The gas cooling time zi) was set to 27/O,. where Oy2(ΜΙΤ is the Keplerian frequency."," The gas cooling time $\tau_{\rm cool}$ ) was set to $2\pi/\Omega_K$, where $\Omega_K=(r/M)^{-3/2}M$ is the Keplerian frequency." + Thus the gas was driven towards uy.NIE which we defined as that value of ες for which the specific entropy of the gas would be equal to the constant specific entropy (e.g.. píp) of the initial solution.," Thus the gas was driven towards $u_{\rm eq}$, which we defined as that value of $u_g$ for which the specific entropy of the gas would be equal to the constant specific entropy (e.g., $p/\rho^\gamma$ ) of the initial solution." + The simulation ran for a time of 10000M. corresponding to 108 orbits at the ISCO (risco= 6M) and 18 orbits at the initial inner edge of the torus.," The simulation ran for a time of $10000M$, corresponding to $108$ orbits at the ISCO $r_{\rm ISCO}=6M$ ) and $18$ orbits at the initial inner edge of the torus." + The results reported here correspond to averages computed over the period 6000M—10000M. when the accretion flow had reached a quasi-steadystate inside a radius of about 10M.," The results reported here correspond to averages computed over the period $6000M-10000M$, when the accretion flow had reached a quasi-steadystate inside a radius of about $10M$." + Figure 1. shows that the simulated disk had a thickness (given by eq. 1)), Figure \ref{thicknessplot} shows that the simulated disk had a thickness (given by eq. \ref{thickness}) ) + of Ar~0.06—0.10 over the radius range of interest., of $h/r\sim0.06-0.10$ over the radius range of interest. + The mean absolute thickness Αμ was smaller:0.04—0.07., The mean absolute thickness ${\Delta\theta}_{\rm abs}$ was smaller:$\sim0.04-0.07$. + At the ISCO. the two definitions of thickness gave /i/r0.05.0.06. respectively.," At the ISCO, the two definitions of thickness gave $h/r\sim0.08, ~0.06$, respectively." +" The flux of mass and specific angular momentum are given by respectively. where 77 is the r-o component of the energy tensor. and The specific energy flux E/M is found by replacing T. with 7"" in the above equations."," The flux of mass and specific angular momentum are given by respectively, where $T^{r}_{\phi}$ is the $r$ $\phi$ component of the stress-energy tensor, and The specific energy flux $\dot{E}/\dot{M}$ is found by replacing $T^r_\phi$ with $T^r_t$ in the above equations." +" In equation (5)). the term fi, represents the specific angularmomentum advected inward with the accretion flow."," In equation \ref{Ldot}) ), the term $\bar{\ell}_{\rm in}$ represents the specific angularmomentum advected inward with the accretion flow." +" Similarly. (44, represents outflow of specific angular momentum as a result of the magnetic shear stress."," Similarly, $\bar{\ell}_{\rm out}$ represents outflow of specific angular momentum as a result of the magnetic shear stress." + In steady state. each of these terms is independent of f. and their sum is independent of both r and r.," In steady state, each of these terms is independent of $t$, and their sum is independent of both $r$ and $t$." +" Figure 2. compares the time-averaged profile of (i, from the simulation. averaged over an angular range 67=«0.2 around the disk mid-plane (2 to 3 density scale heights). with that predicted by NT73."," Figure \ref{angmmtm} compares the time-averaged profile of $\bar{\ell}_{\rm in}$ from the simulation, averaged over an angular range $\delta\theta=\pm0.2$ around the disk mid-plane (2 to 3 density scale heights), with that predicted by NT73." +" In the latter. (5; 1s equal to the Keplerian specific angular momentum for all radii down to the ISCO; inside the ISCO. (i, is taken to be constant since. by assumption. no angular momentum ts removed from the gas in the plunging region."," In the latter, $\bar{\ell}_{\rm in}$ is equal to the Keplerian specific angular momentum for all radii down to the ISCO; inside the ISCO, $\bar{\ell}_{\rm in}$ is taken to be constant since, by assumption, no angular momentum is removed from the gas in the plunging region." +" The £i, profile from the simulation shows modest deviations from this idealized profile: (1) fin is slightly sub-Keplerian outside the ISCO; (11) (5, continues to decrease for a range of r insidethe ISCO: (it) (;; becomes essentially independent of r close to the horizon.", The $\bar{\ell}_{\rm in}$ profile from the simulation shows modest deviations from this idealized profile: (i) $\bar{\ell}_{\rm in}$ is slightly sub-Keplerian outside the ISCO; (ii) $\bar{\ell}_{\rm in}$ continues to decrease for a range of $r$ insidethe ISCO; (iii) $\bar{\ell}_{\rm in}$ becomes essentially independent of $r$ close to the horizon. + The surprising feature of Fig., The surprising feature of Fig. + 2 is that the two curves are so close to each other inside the ISCO., 2 is that the two curves are so close to each other inside the ISCO. +" While it is true that the profile of (i, from the simulation drops inside the ISCO to a value of 3.39M. this value is only less than the NT73 value of 3.464M."," While it is true that the profile of $\bar{\ell}_{\rm in}$ from the simulation drops inside the ISCO to a value of $3.39M$, this value is only less than the NT73 value of $3.464M$ ." + Thus. the magnetic coupling that technically operates inside rjsco does not have much real effect on the accreting gas.," Thus, the magnetic coupling that technically operates inside $r_{\rm ISCO}$ does not have much real effect on the accreting gas." + At the ISCO (442 0.075M. which is ~2.2% of fj.," At the ISCO $\bar{\ell}_{\rm out}=0.075M$ , which is $\sim2.2\%$ of $\bar{\ell}_{\rm in}$ ." + Further. £/M at the horizon is 0.940. which is only slightly different from the NT73 value of 0.9428. showing that the accretion efficiency is not enhanced by magnetic fields.," Further, $\dot{E}/\dot{M}$ at the horizon is $0.940$ , which is only slightly different from the NT73 value of $0.9428$ , showing that the accretion efficiency is not enhanced by magnetic fields." + For two-dimensional simulations of thicker disks with, For two-dimensional simulations of thicker disks with +ol galaxies leaking ionizing radiation. but we do not know how strong such a signature is in our target galaxies.,"of galaxies leaking ionizing radiation, but we do not know how strong such a signature is in our target galaxies." + Giallongo.Cristiani.D'OdoricoandFontana(2002) point oul that (hie escape Iraction for ionizing5 photons reported by SPA would allow the 5galaxiesalone to produce a cosmic ultraviolet background flux. which exceeds (he predictions of the proximity effect. [rom the Lya forests of quasars.L," \citet{gia02} point out that the escape fraction for ionizing photons reported by SPA would allow the galaxies to produce a cosmic ultraviolet background flux which exceeds the predictions of the proximity effect from the $\alpha$ forests of quasars.," +f however. galaxies at redshilts of 2 or 3 behave similarly to the ealaxies we measured αἱ z~ 1.2. galaxies would contribute less than as much ultraviolet light as would quasars. aud the flix estimates [rom both sources would be consistent. with the predictions of the proximity. effect.," however, galaxies at redshifts of 2 or 3 behave similarly to the galaxies we measured at z $\sim$ 1.2, galaxies would contribute less than as much ultraviolet light as would quasars, and the flux estimates from both sources would be consistent with the predictions of the proximity effect." + Dased on observations of eleven bright blue galaxies with redshifts 1.1 « z « LA. Lvman continuum was detected.," Based on observations of eleven bright blue galaxies with redshifts 1.1 $<$ z $<$ 1.4, Lyman continuum was detected." + A stringent. model-independent. upper limit < 2x10 P? eres 7 tLto was obtained for the FUV flux escaping from eleven normal galaxies al redshifts of 1.1 0. the Ilanle effect can. in certain cases. produce an EVPA rotation exceeding 45 deg relative to the tangential clireetion Innocenti.&Bueno 2005).," For the magnetic case, $g\Omega > 0$, the Hanle effect can, in certain cases, produce an EVPA rotation exceeding 45 $\deg$ relative to the tangential direction \citep{ramos05}." +. In (he case of m-anisotropic pumping in general. we would also expect to measure a functional shape for q(6). aud associated break angle θε. that differs from the standard Zeeman form noted above (Western&Watson1934).. and a higher degree ol linear polarization magnitude (Watson2002).," In the case of $m$ -anisotropic pumping in general, we would also expect to measure a functional shape for $q(\theta)$, and associated break angle $\theta_F$, that differs from the standard Zeeman form noted above \citep{western84}, and a higher degree of linear polarization magnitude \citep{watson02}." +. In Figure 10. we examine the variation of mean fractional linear polarization magnitude mo) against pulsation phase., In Figure \ref{fig-ml} we examine the variation of mean fractional linear polarization magnitude ${\overline m_l}(\phi)$ against pulsation phase. + This value was computed at each epoch [rom the sum of Stokes J and P—\/Q?+U?. using a pixel mask delined as the set of all pixels with a total intensity exceeding three times the Stokes J image rms. and corrected. [or statistical bias in P.," This value was computed at each epoch from the sum of Stokes $I$ and $P=\sqrt{Q^2 + U^2}$, using a pixel mask defined as the set of all pixels with a total intensity exceeding three times the Stokes $I$ image rms, and corrected for statistical bias in $P$." + The value of m;(ó) has a minimum near ὦ1 and a maximum near oc1.5., The value of ${\overline m_l}(\phi)$ has a minimum near $\phi \sim 1$ and a maximum near $\phi \sim 1.5$. + It has higher values when the inner edge of the shell is well-defined. and dominates the overall total intensity morphology., It has higher values when the inner edge of the shell is well-defined and dominates the overall total intensity morphology. + Unfortunately. this resull can be interpreted. either as evidence for linear polarization driven primarily by magnetic field enhancement (through shock compression. or is supportüve of m-anisotropic pumping as the dominant origin of linear polarization: both are expected to be stronger in the inner shell boundary.," Unfortunately this result can be interpreted either as evidence for linear polarization driven primarily by magnetic field enhancement through shock compression, or is supportive of $m$ -anisotropic pumping as the dominant origin of linear polarization: both are expected to be stronger in the inner shell boundary." + We note that the mean fractional linear polarization is broadly inversely correlated. with the shell width., We note that the mean fractional linear polarization is broadly inversely correlated with the shell width. + We identify several kev uncertainties that need to be futher constrained by observations before the remaining theoretical polarization (ransport uncertainties can be resolved. and that are amenable (ο observational tests: i) the statistical incidence of tangential linear polarization morphology in Mira. variables as a class; ii) independent measurement of the exact. degree of saturation of stellar SiQ masers: ancl iii) detailed measurements of the [functional form of g(@) in maser regions where this is possible.," We identify several key uncertainties that need to be further constrained by observations before the remaining theoretical polarization transport uncertainties can be resolved, and that are amenable to observational tests: i) the statistical incidence of tangential linear polarization morphology in Mira variables as a class; ii) independent measurement of the exact degree of saturation of stellar SiO masers; and iii) detailed measurements of the functional form of $q(\theta)$ in maser regions where this is possible." + We plan to address these issues in future papers., We plan to address these issues in future papers. + As vet. there is insufficient. observational data to distinguish the relative influence of m-auisotropic pumpine on the magnitude or orientation of the SiO emission The linear polarization maps we present here have significant fine-scale. locally-orderecl. polarization structure. as noted in the first SiO polarization observations of TX Cam by Ixemball&Diamond(1997).," As yet, there is insufficient observational data to distinguish the relative influence of $m$ -anisotropic pumping on the magnitude or orientation of the linearly-polarized SiO emission The linear polarization maps we present here have significant fine-scale, locally-ordered, polarization structure, as noted in the first SiO polarization observations of TX Cam by \citet{kemball97}." +. Recently. in their sample of O-rich AGB stars. Cotton.Perrin.&Lopez(2008) have cited locallv-ordered polarization morphologies alone jet-like features pointing raclially toward the central star.," Recently, in their sample of O-rich AGB stars, \citet{cotton08} have cited locally-ordered polarization morphologies along jet-like features pointing radially toward the central star." + Due to the persistence of the SiO linear polarization properties over a sullident fraction of the component lifetime in the polarization movie presented here. we are able to explore (he time evolution of the polarization morphology for individual maser components.," Due to the persistence of the SiO linear polarization properties over a sufficient fraction of the component lifetime in the polarization movie presented here, we are able to explore the time evolution of the polarization morphology for individual maser components." + In (his paper we undertake a preliminary analvsis confined to (wo isolated components selected subject to the criteria (hat thev: i) follow continuous, In this paper we undertake a preliminary analysis confined to two isolated components selected subject to the criteria that they: i) follow continuous +> 5 in both colors are plotted in the figure.,$>$ 5 in both colors are plotted in the figure. +" There are 58,793 sources that match the criteria."," There are 58,793 sources that match the criteria." +" In the color-color diagram, there is a distinct sequence consisting of Wolf-Rayet stars and Be stars, starting at about (B—V)~—0.2 and (V—S9W)~0 and extending towards (B—V)~0.5 and (V-$S9W)~3, up to (V—S9W)~9."," In the color-color diagram, there is a distinct sequence consisting of Wolf-Rayet stars and Be stars, starting at about $(B-V) \sim -0.2$ and $(V-S9W) \sim 0$ and extending towards $(B-V) \sim 0.5$ and $(V-S9W) \sim 3$, up to $(V-S9W) \sim 9$." + Some of these types of stars clearly show strong infrared excess in S 9W-band than ordinary B- or O-type stars., Some of these types of stars clearly show strong infrared excess in $S9W$ -band than ordinary B- or O-type stars. + Thermal emission from dust grains contributes to this infrared excess (Waters et al. 1987;;, Thermal emission from dust grains contributes to this infrared excess (Waters et al. \cite{waters1987}; +" Zhang et al., 2004))"," Zhang et al., \cite{zhang2004}) )" +" in addition to free-free and bound-free radiation from the surrounding nebulosity (e.g., Wright Barlow 1975;; Chokshi Cohen 1987))."," in addition to free-free and bound-free radiation from the surrounding nebulosity (e.g., Wright Barlow \cite{wright1975}; Chokshi Cohen \cite{chokshi1987}) )." +" In our plot, objects with circumstellar envelope include the Herbig Ae/Be star HD100546 and the Be star, v AAra, which have"," In our plot, objects with circumstellar envelope include the Herbig Ae/Be star HD100546 and the Be star, $\iota$ Ara, which have" +bootstrap re-sampling method described in 22 and represents the uncertainty in the mean value.,bootstrap re-sampling method described in 2 and represents the uncertainty in the mean value. + We also determine a c.l., We also determine a c.l. + upper limit(fec)<0.075., upper limit$\langle\fesc\rangle \le 0.075$. +" Parameterizing the cumulative ddistribution by F[10??cm-? have an Eddington ratio A<0.1, as expected if radiation pressure on dusty gas is important."," We see from the plots that most absorbed AGN with column densities $N_{\rm H}>10^{22}\pcmsq$ have an Eddington ratio $\lambda <0.1$, as expected if radiation pressure on dusty gas is important." + The observed objects are sub-Eddington in terms of radiation pressure on dusty gas and so the absorbing gas may be long-lived., The observed objects are sub-Eddington in terms of radiation pressure on dusty gas and so the absorbing gas may be long-lived. + The line defining the effective Eddington limit in the plots is determined for the mass of the black hole only., The line defining the effective Eddington limit in the plots is determined for the mass of the black hole only. + It shifts to the right (higher values of ) if larger masses associated with the stellar bulge are also involved., It shifts to the right (higher values of $\lambda$ ) if larger masses associated with the stellar bulge are also involved. +" Since the lines drawn seem to apply to the samples, most of the absorbing gas must be at small radii (much less than 100 pc)."," Since the lines drawn seem to apply to the samples, most of the absorbing gas must be at small radii (much less than 100 pc)." + The agreement between the expected location of absorbed AGN and the observed locations provides support for the idea that radiation pressure acts to blow gas away from galaxy bulges., The agreement between the expected location of absorbed AGN and the observed locations provides support for the idea that radiation pressure acts to blow gas away from galaxy bulges. + If the radiation is isotropic then it can stem the growth of both inner bulge and black hole., If the radiation is isotropic then it can stem the growth of both inner bulge and black hole. +" The inner gas directly exposed to the radiation pressure may be unstable to clumping (?;; ?)), the details of which will not be pursued here."," The inner gas directly exposed to the radiation pressure may be unstable to clumping \citealt{1979ApJ...233..479B}; \citealt{2007MNRAS.380.1172H}) ), the details of which will not be pursued here." + Most of the long-lived gas at column densities above 10?”cm? is shielded by the inner gas and so need not be clumped., Most of the long-lived gas at column densities above $10^{22}\psqcm$ is shielded by the inner gas and so need not be clumped. +" After blowing away the gas, AGN may decline in luminosity so creating unabsorbed sources at low Eddington ratios."," After blowing away the gas, AGN may decline in luminosity so creating unabsorbed sources at low Eddington ratios." + There is also some uncertainty in the boundary between the various regions of the diagrams due to factors such as source variability and clumpiness in the absorption., There is also some uncertainty in the boundary between the various regions of the diagrams due to factors such as source variability and clumpiness in the absorption. + The fact that most sources avoid the region of our diagrams above Ny~5x10?!cm? and to the right of the radiation pressure line demonstrates that variabilitity is not very important., The fact that most sources avoid the region of our diagrams above $N_{\rm H}\sim 5\times 10^{21}\psqcm$ and to the right of the radiation pressure line demonstrates that variabilitity is not very important. +" Lower levels of absorption below 10??cm-2 can be lived at large radii in a galaxy, since the relevant gravitating? mass there is due to the black hole and the bulge."," Lower levels of absorption below $10^{22}\pcmsq$ can be long-lived at large radii in a galaxy, since the relevant gravitating mass there is due to the black hole and the bulge." + The radiation limit in our Figures shifts to the right by a factor of Mbuige/Mpx with all gas above the line bound to the bulge., The radiation limit in our Figures shifts to the right by a factor of $M_{\rm bulge}/M_{\rm BH}$ with all gas above the line bound to the bulge. + The maximum boost A that can be obtained from radiation pressure on dusty gas is σα/σι~500 which means that the black hole is above the effective Eddington limit for the whole bulge if Mpu/Mbuige> 1/500., The maximum boost $A$ that can be obtained from radiation pressure on dusty gas is $\sigma_{\rm d}/\sigma_{\rm T}\sim 500$ which means that the black hole is above the effective Eddington limit for the whole bulge if $M_{\rm BH}/M_{\rm bulge}>1/500$ . + Consequently we envisage a scenario where a black hole smothered in gas could grow in a bulge in stages., Consequently we envisage a scenario where a black hole smothered in gas could grow in a bulge in stages. + It pushes the gas out to a distance in the bulge where the mass within that radius is 500 times the black hole mass. (, It pushes the gas out to a distance in the bulge where the mass within that radius is 500 times the black hole mass. ( +"The boost factor increases as the column density decreases, so once gas starts to move outward it continues to do so, see Fig.","The boost factor increases as the column density decreases, so once gas starts to move outward it continues to do so, see Fig." +" 1 and citeal2006MNRAS.373L..16F)) After the accretion disk empties,"," 1 and \\citealt{2006MNRAS.373L..16F}) ) After the accretion disk empties," +it has alwavs been shown that the Caussian correlation function of the excursion sets ancl peaks (a subset of the excursion sets) is casily clistinguishable from a non-Gaussian one. even if the underlying bispectra are not statistically cilferent (i.e. Ixogut et al.,"it has always been shown that the Gaussian correlation function of the excursion sets and peaks (a subset of the excursion sets) is easily distinguishable from a non-Gaussian one, even if the underlying bispectra are not statistically different (i.e. Kogut et al." + 1995: Barreiro et al., 1995; Barreiro et al. + 1998: Lleavens Gupta 2001). we suggest here that it may not be the case if the model of non-CGaussianity is of the local type. and the resolution adopted is not optimal.," 1998; Heavens Gupta 2001), we suggest here that it may not be the case if the model of non-Gaussianity is of the local type, and the resolution adopted is not optimal." + Our work is also motivated by another reason., Our work is also motivated by another reason. + In a previous analvsis (Rossi et al., In a previous analysis (Rossi et al. + 2009). we compared the pixel clustering statistics — properly extended: to. hanelle inhomogeneous Noise against WALAD [five-year data. and we detected deviations from the Gaussian theoretical expectations.," 2009), we compared the pixel clustering statistics – properly extended to handle inhomogeneous noise – against WMAP five-year data, and we detected deviations from the Gaussian theoretical expectations." + In particular. we found a remarkable dilference in the clustering of hot ancl cold pixels at. relatively small angular scales.," In particular, we found a remarkable difference in the clustering of hot and cold pixels at relatively small angular scales." + A similar trend. has also been reported. in the literature by Fojeiro et al. (, A similar trend has also been reported in the literature by Tojeiro et al. ( +2006). and by Hou. Banclay Gorski (2010). although at much larger scales.,"2006), and by Hou, Banday Gorski (2010), although at much larger scales." + Whether or not this ciscrepaney may arise from primordial non-CGaussianity of the local type is another key question of this analvsis., Whether or not this discrepancy may arise from primordial non-Gaussianity of the local type is another key question of this analysis. + The lavout of the paper is as follows., The layout of the paper is as follows. + Section 2. contains the theoretical tools developed ancl used. in this studs., Section \ref{NG theory} contains the theoretical tools developed and used in this study. + La Section 2.1. we briellv. describe the local {δι mocel.," In Section \ref{fnl_model} + we briefly describe the local $f_{\rm NL}$ model." + In Section 2.2. we explain how the simulated: non-Gaussian maps are constructed., In Section \ref{map_simulations} we explain how the simulated non-Gaussian maps are constructed. + In Section 2.3. we provide the basic ormalism for the excursion sets statistics. in the context of {νι scenarios.," In Section \ref{excursion_set_formalism} we provide the basic formalism for the excursion sets statistics, in the context of $f_{\rm NL}$ scenarios." + Expressions for the one- and two-dimensional oobability. distribution functions (PDEs) are given. under he assumption of weak non-Ciaussianitv: this is done via a »erturbative approach by the multidimensional Exlgeworth expansion around a Gaussian distribution function.," Expressions for the one- and two-dimensional probability distribution functions (PDFs) are given, under the assumption of weak non-Gaussianity; this is done via a perturbative approach by the multidimensional Edgeworth expansion around a Gaussian distribution function." + Those DES are then used. to characterize the number density and the clustering statistics above/below threshold as a ‘unction of fxn (some details are. provided. in Xppencdix AY)., Those PDFs are then used to characterize the number density and the clustering statistics above/below threshold as a function of $f_{\rm NL}$ (some details are provided in Appendix \ref{edgeworth_proxy}) ). + In Section 2.4. we relate the excursion sets formalism o other commonly used topological estimators., In Section \ref{history} we relate the excursion sets formalism to other commonly used topological estimators. + In Section 3.. computations of the number density and the clustering statistics above/below threshold. from non-Ciaussian. maps are presented ancl interpreted. according to our theory predictions.," In Section \ref{NG maps analysis}, computations of the number density and the clustering statistics above/below threshold from non-Gaussian maps are presented and interpreted according to our theory predictions." + Specifically. Section 3.1. shows the abundance of the excursion set regions in à variety of wavs. while in Section 3.2. we highlight some statistical tests developed using the number density.," Specifically, Section \ref{nd_subsection} shows the abundance of the excursion set regions in a variety of ways, while in Section \ref{nd_stat_subsection} we highlight some statistical tests developed using the number density." + We also argue that there are optimal thresholds which can maximize the non-Gaussian contribution. as well as levels which clo not allow to distinguish a Gaussian signal from a non-Gaussian one.," We also argue that there are optimal thresholds which can maximize the non-Gaussian contribution, as well as levels which do not allow to distinguish a Gaussian signal from a non-Gaussian one." + In Section 3.3. we present the clustering of hot ancl cold pixels for one of the optimal temperature thresholds as a function of the smoothing scale. and in Section 3.4 we propose a new statistical test derived. from the clustering statistics.," In Section \ref{clustering_subsection} we present the clustering of hot and cold pixels for one of the optimal temperature thresholds as a function of the smoothing scale, and in Section \ref{clustering_stat_subsection} we propose a new statistical test derived from the clustering statistics." + This procedure aims at minimizing the cosmic variance effect. and involves the computation of the power spectrum for any given. CAIB map.," This procedure aims at minimizing the cosmic variance effect, and involves the computation of the power spectrum for any given CMB map." + A final part (Section 4)) summarizes our findings. and. highlights ongoing and futuwe work.," A final part (Section \ref{NG_conclusions}) ) summarizes our findings, and highlights ongoing and future work." + We leave in Appendix B.C and LE some technical details regarding experimental artifacts such as inhomogeneous noise. incomplete sky coverage. errorbar estimates ancl confusion cllects caused by spurious non-CGaussianities: all these experimental complications will be examined in more detail in the forthcoming publications.," We leave in Appendix \ref{noise_analytic}, \ref{errors_analytic} and \ref{spurious_ng} some technical details regarding experimental artifacts such as inhomogeneous noise, incomplete sky coverage, errorbar estimates and confusion effects caused by spurious non-Gaussianities; all these experimental complications will be examined in more detail in the forthcoming publications." + In this paper we study the statistics of the excursion sets in CMD temperature maps. to examine 168 sensitivity to. primordial non-Gaussianity.," In this paper we study the statistics of the excursion sets in CMB temperature maps, to examine its sensitivity to primordial non-Gaussianity." +. Even though the chosen statistics should be sensitive to a wide class of non-Gaussian fields. in the present work we consider the local [νι mocel in cetail.," Even though the chosen statistics should be sensitive to a wide class of non-Gaussian fields, in the present work we consider the local $f_{\rm NL}$ model in detail." + Considerable interest has been recently focused on local tvpe fixe. by which the non-CGaussianitv of Bardeen's curvature perturbations is characterized in real space. up to second order. by: and in Fourier space by where © is a Gaussian field (Salopek Bond 1990: CGangui et al.," Considerable interest has been recently focused on local type $f_{\rm NL}$, by which the non-Gaussianity of Bardeen's curvature perturbations is characterized in real space, up to second order, by: and in Fourier space by where $\phi$ is a Gaussian field (Salopek Bond 1990; Gangui et al." + 1994: Verde et al., 1994; Verde et al. + 2000: Komatsu Spergel 2001)., 2000; Komatsu Spergel 2001). + The local type non-CGaussianitv is sensitive to the bispeetrum Ba(ky.A.As) with squeezed. configuration triangles (Le. Ayxhe~ky: Babich ct al.," The local type non-Gaussianity is sensitive to the bispectrum $B_{\rm \Phi} (k_1,k_2,k_3)$ with squeezed configuration triangles (i.e. $k_1 \ll k_2 \sim k_3$; Babich et al." +" 2004). defined as where dp is the Dirac delta. Ki»=ki|ksKs ancl κι, is a dimensionless parameter (or more generally a non-linearity function). while the function E describes the dependence on the shape of triangular configurations defined by the three wave-numbers fy.he.hy."," 2004), defined as where $\delta_{\rm D}$ is the Dirac delta, ${\bf k}_{\rm 123} = {\bf + k}_{\rm 1} + {\bf k}_{\rm 2} + {\bf k}_{\rm 3}$ and $f_{\rm NL}$ is a dimensionless parameter (or more generally a non-linearity function), while the function F describes the dependence on the shape of triangular configurations defined by the three wave-numbers $k_1, k_2, k_3$." + This parametrization was originally motivated hy the sinele-field inflation scenarios. and it became quite popular shortly thereafter because it is possible to cast many inflationary models. including the curvaton scenario (Lyvth et al.," This parametrization was originally motivated by the single-field inflation scenarios, and it became quite popular shortly thereafter because it is possible to cast many inflationary models, including the curvaton scenario (Lyth et al." + 2003). in the form of equation. (3)): namely. one can express departures from non-Caussianity in terms of a generic function E. which may assume cillerent. moclel-dependent shapes and it is broadly classified: into three classes (local squeezed. non-local equilateral. orthogonal). and the parameter or function fixe.," 2003), in the form of equation \ref{bispectrum_eq}) ); namely, one can express departures from non-Gaussianity in terms of a generic function F, which may assume different model-dependent shapes and it is broadly classified into three classes (local squeezed, non-local equilateral, orthogonal), and the parameter or function $f_{\rm NL}$." + Alternatives to inflation like New LEkpyrotic and evelic models are also expected to produce a large level of non-Caussianity of this type (Ixovama ct al., Alternatives to inflation like New Ekpyrotic and cyclic models are also expected to produce a large level of non-Gaussianity of this type (Koyama et al. + 2007: 3uchbineder et al., 2007; Buchbinder et al. + 2008: Lehners Steinhardt 2008)., 2008; Lehners Steinhardt 2008). + Therefore. the power of this formalism is that it allows one to rule out a large class of models bv putting constraints on fwp. ancl to reconstruct the inflationary action starting from a measurement of a Lew observables like {κι itself.," Therefore, the power of this formalism is that it allows one to rule out a large class of models by putting constraints on $f_{\rm NL}$, and to reconstruct the inflationary action starting from a measurement of a few observables like $f_{\rm NL}$ itself." + Note that in this paper we always use {νι dn its local meaning. even if the usual superscript is not present. ancl also that there are two distinct. definitions of [xL in the literature. corresponding to a CMD and a LSS convention.," Note that in this paper we always use $f_{\rm NL}$ in its local meaning, even if the usual superscript is not present, and also that there are two distinct definitions of $f_{\rm +NL}$ in the literature, corresponding to a CMB and a LSS convention." + In the CMD convention adopted here. the local non-Gaussianity is defined. by equations (1-3)) with the curvature perturbations 9 evaluated at carly times during the matter domination era. when their value was constant.," In the CMB convention adopted here, the local non-Gaussianity is defined by equations \ref{fnl_expansion_eq}- \ref{bispectrum_eq}) ) with the curvature perturbations $\Phi$ evaluated at early times during the matter domination era, when their value was constant." + 1n the LSS convention. one usually assumes & to be the value linearly extrapolated at present. time. and therefore it," In the LSS convention, one usually assumes $\Phi$ to be the value linearly extrapolated at present time, and therefore it" +"Noticeably, despite the noise. the probability that the true and svuthetic distribution of data points come from the same progenitor distribution clearly decreases monotonically as we increase the contribution of RC systelus. particularly iu the baud (Figeure 6)).","Noticeably, despite the noise, the probability that the true and synthetic distribution of data points come from the same progenitor distribution clearly decreases monotonically as we increase the contribution of RG systems, particularly in the band (Figure \ref{fig:ks}) )." + This strongly sugeests a minimal contribution of RGs to progenitors., This strongly suggests a minimal contribution of RGs to progenitors. + Similarly. an almost monotonic ≺∐∖≼⊳↥⋅↸∖⋜↧↴∖↴↸∖↕∐⋯⋅∪↴⋝⋜∏⋝∐↕↑⋅↖↽⋖↕↕∐⊳↥⋅↸∖⋜," Similarly, an almost monotonic decrease in probability (increase in c.l.)" +↧↴∖↴↸∖↕∐↸⊳∙↕∙⋟↕↴∖↴↸∖↖↽↕≼∐∖∐↑↕∐ ↑∐↸∖∖⊽↴⋝⋜⋯≼↧∙↑∐∪∏∶↴∙⊾∐↕," is evident in the band, though less pronounced." +↸∖↴∖↴↴∖↴↻↥⋅∪∐≺∏∐⊔⊳↸∖≼↧∙⊺↕∏↴∖↴↕↴∖↴↸∖⊼↻↸∖↸⊳↑↸∖≺↧∙ ou account of à smaller signature of shocking in redder bauds (see Figure 2)).," This is expected, on account of a smaller signature of shocking in redder bands (see Figure \ref{fig:models}) )." + Iu this section we investigate the chromatic bias in the shocking footprint., In this section we investigate the chromatic bias in the shocking footprint. + In absence of shocking. the expected time behavior of the SN explosion is a parabola. similar in aud baud.," In absence of shocking, the expected time behavior of the SN explosion is a parabola, similar in and band." + Thus. iu the rise portion of the lightcurves we would expect points drawn from a set of SNe to conie. statistically speaking. frou the same distribution iu aud baud.," Thus, in the rise portion of the lightcurves we would expect points drawn from a set of SNe to come, statistically speaking, from the same distribution in and band." + However. in the IK10 simulations (see Section 7T7)) the aud time behavior differ dramatically ii the rie portion of the lighteurve in the presence of RC progenitors.," However, in the K10 simulations (see Section \ref{sec:models}) ) the and time behavior differ dramatically in the rise portion of the lightcurve in the presence of RG progenitors." + We again perform a 2-s0uuple νο test., We again perform a 2-sample K-S test. + This time we want to asses the similarity of the D aud V populations of carly-rise data. so for the SNLS data aud we compare the D aud V. channel with a Ίντο test. aud we do the same for each svuthetic population.," This time we want to asses the similarity of the B and V populations of early-rise data, so for the SNLS data and we compare the B and V channel with a K-S test, and we do the same for each synthetic population." + We find that the hvpothesis that rest-frame aud Vopopulatious of data points from the composite me SNLS liehteurves. dav 0-10 after explosion. come statistically from the same distribution can onlv be rejected to «5% cl.," We find that the hypothesis that rest-frame and populations of data points from the composite true SNLS lightcurves, day 0-10 after explosion, come statistically from the same distribution can only be rejected to $<5\%$ c.l.," + or equivalently that the hypothesis hat the two chaunels come frou the same distribution sapvalue~0.95., or equivalently that the hypothesis that the two channels come from the same distribution has a $\pv \sim~0.95$. + We compare the svuthetic B aud. V. lighteuves. aud find. as expected. that the Ίντο uunmber mereases with he increasing RC contribution: the probability that the D aud V svuthetic data come from the same distribution decreases as more RG progenitors are used in the," We compare the synthetic B and V lightcurves, and find, as expected, that the K-S number increases with the increasing RG contribution: the probability that the B and V synthetic data come from the same distribution decreases as more RG progenitors are used in the" +approxinatious eiven by equations (2)) - (1)) aud the exact results from muuerical integrations of the Doltzuiaun equations.,approximations given by equations \ref{kq}) ) - \ref{alpha}) ) and the exact results from numerical integrations of the Boltzmann equations. + Next we exiuniue the liuear erowth suppression factor of the density feld iu equation (13)., Next we examine the linear growth suppression factor of the density field in equation \ref{pl}) ). + This function is well studied for ACDAL models (IHoath 1977: Lahav et al., This function is well studied for $\LCDM$ models (Heath 1977; Lahav et al. + 1991)., 1991). +" Au cuypivical fit is given by gy=2.50,,00400,(00)P7 and is accurate to ~2% for OLeho/(ldrgo) to acconunodate the effect of tensors on the normalization., One can rescale $A_Q$ by $A_Q \to A_Q/(1+r_{10})$ to accommodate the effect of tensors on the normalization. + Tn this section we cexanune if the simple linear to nonlinear mapping technique initiated by Wamilton ct al. (, In this section we examine if the simple linear to nonlinear mapping technique initiated by Hamilton et al. ( +1991) can be extended to QCDAL models.,1991) can be extended to QCDM models. + The basic approach is to search for a simple expression for the function Αμ)=Αι) that relates the linear aud nonlinear density variance Ath)=lah?Ph)., The basic approach is to search for a simple expression for the function $\Dnl(k) = f[\Dl(k_0)]$ that relates the linear and nonlinear density variance $\Delta(k) \equiv 4\pi k^3 P(k)$. + Note that Ay) and A) ave evaluated at differcut waveuunbers. where hy=WML)An)E? corresponds to the precollapsed scale of k.," Note that $\Dnl$ and $\Dl$ are evaluated at different wavenumbers, where $k_0=k(1+\Dnl)^{-1/3}$ corresponds to the precollapsed scale of $k$." + The strategv is to combine analytical clustering properties in asviuptotie regimes with fits to uuuerncal siuulation results., The strategy is to combine analytical clustering properties in asymptotic regimes with fits to numerical simulation results. + This recipe has been successtullv developed. for scale-free imiodels with a power-law Ph) (ILuuilton ct al., This recipe has been successfully developed for scale-free models with a power-law $P(k)$ (Hamilton et al. + 1991: Jain et al., 1991; Jain et al. + 1995). flat CDM. aud ACDM inodels (Jain et al.," 1995), flat CDM and $\LCDM$ models (Jain et al." + 1995: Peacock Dodds 1996. PD96 hereafter: Ma 1998). and flat €|IIDM models with hassive neutrinos (Ma 1998. Ma98 hereafter).," 1995; Peacock Dodds 1996, PD96 hereafter; Ma 1998), and flat C+HDM models with massive neutrinos (Ma 1998, Ma98 hereafter)." + We investigate if the PD96 and Ma98/— foriiulas xoposed. for Αλ models can be easily exteuded o QCDM models., We investigate if the PD96 and Ma98 formulas proposed for $\LCDM$ models can be easily extended to QCDM models. +" These two formulas incorporate the nue dependence of the iuapping iu differcut wavs. mt they share the feature that the dependence on xuanueters Q,, and O4 euters only through the linear erowth factor g."," These two formulas incorporate the time dependence of the mapping in different ways, but they share the feature that the dependence on parameters $\om$ and $\ov$ enters only through the linear growth factor $g$." + Iu order to test the application of his method to QCDAL models. we have performed V- simulations for three values of we: 2/3. 1/2. and = 1/3. each with several differcut realizations.," In order to test the application of this method to QCDM models, we have performed $N$ -body simulations for three values of $w_Q$ : $-2/3, -1/2$ and $-1/3$ , each with several different realizations." + These hnree values should be sufficient since extensive tests of so=d (e. ACDM inodels) havealready. been carried out in PD96 aud Ma9s., These three values should be sufficient since extensive tests of $w_Q=-1$ (i.e. $\LCDM$ models) havealready been carried out in PD96 and Ma98. + We restrict our attention to wezo1/3 aud cosmological parameter ranges that are in concordance with observations (Wang Steinhardt 1995: Wane et al., We restrict our attention to $w_Q < -1/3$ and cosmological parameter ranges that are in concordance with observations (Wang Steinhardt 1998; Wang et al. + 1999)., 1999). +" Specifically, (4:00.04.05)= for the (v)=2/2 aud 1/2 models."," Specifically, $(\om,\oq,\ob,h)= (0.4, 0.6, 0.047, +0.65)$ for the $w_Q=-2/3$ and $-1/2$ models," +"degeneracy further into the high og, low Qm region.","degeneracy further into the high $\sigma_{\rm 8}$, low $\Omega_{\rm m}$ region." +" The joint constraints (black solid contour) using both shear-shear and shear-position information show a preference for low og and high Q, but are still consistent with our fiducial cosmology.", The joint constraints (black solid contour) using both shear-shear and shear-position information show a preference for low $\sigma_{\rm 8}$ and high $\Omega_{\rm m}$ but are still consistent with our fiducial cosmology. +" The preference for higher Qm values occurs because, as noted in [Hirataetal](2007).., the shear-position data favours slightly steeper correlation functions than predicted by a standard fiducial cosmology (see also the L6 panel of Fig. "," The preference for higher $\Omega_{\rm m}$ values occurs because, as noted in \citet{hirataea07}, the shear-position data favours slightly steeper correlation functions than predicted by a standard fiducial cosmology (see also the L6 panel of Fig. \ref{fig:corrfns_hirata}) )." +Increasing Qm produces a correlation function that falls Bp.off faster at larger scales because the linear theory matter power spectrum peak is moved to the right (smaller scales) on increasing Qm due to the earlier epoch of matter-radiation equality., Increasing $\Omega_{\rm m}$ produces a correlation function that falls off faster at larger scales because the linear theory matter power spectrum peak is moved to the right (smaller scales) on increasing $\Omega_{\rm m}$ due to the earlier epoch of matter-radiation equality. +" 'This new constraint on cosmology from cosmic shear self-consistently takes into account IA effects and we find Qm=0.15+0.09, σε=0.88+0.18 at 68 96 confidence, as opposed to the results in which IAs are ignored, that give Qm=0.20+0.10, og=0.86+0.21."," This new constraint on cosmology from cosmic shear self-consistently takes into account IA effects and we find $\Omega_{\rm m}= 0.18 \pm 0.09$, $\sigma_8= 0.88 \pm 0.18$ at 68 $\%$ confidence, as opposed to the results in which IAs are ignored, that give $\Omega_{\rm m}=0.20 \pm 0.10$, $\sigma_8=0.86 \pm 0.21$." +" When we constrain simultaneously with shear-shear and shear position data we find Qm=0.29+0.09, og=0.74X:0.13, after marginalising over IA parameters."," When we constrain simultaneously with shear-shear and shear position data we find $\Omega_{\rm m}= 0.29 \pm 0.09$, $\sigma_8= 0.74 \pm 0.13$, after marginalising over IA parameters." +" There is a strong degeneracy between og and Qm when using current cosmic shear data alone, so it is better to look at the full two-dimensional contours (Fig. [9))"," There is a strong degeneracy between $\sigma_8$ and $\Omega_{\rm m}$ when using current cosmic shear data alone, so it is better to look at the full two-dimensional contours (Fig. \ref{fig:Cls_s8_Odm_joint}) )" + or at cross-sections., or at cross-sections. + When we fix Qm=0.3 our best self-consistent shear-shear result including IAs (right hand panel of Fig. is , When we fix $\Omega_{\rm m}=0.3$ our best self-consistent shear-shear result including IAs (right hand panel of Fig. \ref{fig:s8_z_IA}) ) +os=0.752:0.04 as compared to that when IAs are ignored[E]) of og=0.75+0.03., is $\sigma_8=0.75 \pm 0.04$ as compared to that when IAs are ignored of $\sigma_8=0.75 \pm 0.03$. +" A joint constraint from shear-shear and shear-position data, marginalising over IA parameters, gives og=0.75+0.03."," A joint constraint from shear-shear and shear-position data, marginalising over IA parameters, gives $\sigma_8=0.75 \pm 0.03$." + IAs are expected to be an important source of systematic error in cosmic shear measurements if completely ignored., IAs are expected to be an important source of systematic error in cosmic shear measurements if completely ignored. +" Several previous constraints on cosmology from shear-shear correlation functions have considered the possible levels of contamination from IAs, but the recent constraints presented have not included the impactet of IAs (Benjaminal|2009)."," Several previous constraints on cosmology from shear-shear correlation functions have considered the possible levels of contamination from IAs, but the recent constraints presented have not included the impact of IAs \citep{benjaminea07,fuea08_mnras,schrabbackea09}." +.. These surveys are therefore referredSchrabback to as “cosmic shear” surveys.," These surveys are therefore referred to as “cosmic shear"" surveys." +" In this paper we use three physically motivated IA models, of increasing complexity, to demonstrate how constraints on the amplitude of fluctuations og and matter density Qm are changed depending on the assumptions about IAs."," In this paper we use three physically motivated IA models, of increasing complexity, to demonstrate how constraints on the amplitude of fluctuations $\sigma_8$ and matter density $\Omega_{\rm m}$ are changed depending on the assumptions about IAs." + The size of the change in og depends on the redshift distribution of galaxies in the shear-shear survey and on the range of scales probed., The size of the change in $\sigma_8$ depends on the redshift distribution of galaxies in the shear-shear survey and on the range of scales probed. + In particular this affects the interplay between the two different types of IA (II and GI) which have competing effects on cosmological constraints., In particular this affects the interplay between the two different types of IA (II and GI) which have competing effects on cosmological constraints. + A simple examination of [As which assumes all galaxies are like the SDSS Main Red L4 sample suggests that og has previously been underestimated by about one standard deviation., A simple examination of IAs which assumes all galaxies are like the SDSS Main Red L4 sample suggests that $\sigma_8$ has previously been underestimated by about one standard deviation. + The underestimate appears to be larger using the non-linear matter power spectrum in the linear alignment model for IAs than when using the linear matter power spectrum., The underestimate appears to be larger using the non-linear matter power spectrum in the linear alignment model for IAs than when using the linear matter power spectrum. + On using the halo model for IAs the bias depends significantly on the range of scales probed by the survey due to the larger effect of II at intermediate scales which biases the measured og downwards when taken into account., On using the halo model for IAs the bias depends significantly on the range of scales probed by the survey due to the larger effect of II at intermediate scales which biases the measured $\sigma_8$ downwards when taken into account. + We have performed the first constraints on multiple IA model parameters from observed shear-position correlation functions using a physically motivated model for IAs., We have performed the first constraints on multiple IA model parameters from observed shear-position correlation functions using a physically motivated model for IAs. + We also show the first simultaneous constraints on IA and cosmological parameters from either shear-position or shear-shear correlation functions., We also show the first simultaneous constraints on IA and cosmological parameters from either shear-position or shear-shear correlation functions. +" As expected, the majority of the constraint on cosmology comes from the shear-shear correlation functions, and the majority of the constraint on IAs comes from the shear-position correlation functions."," As expected, the majority of the constraint on cosmology comes from the shear-shear correlation functions, and the majority of the constraint on IAs comes from the shear-position correlation functions." + We have used a motivated model for luminosity and colour evolution of shear-shear galaxy samples as a function of redshift to improve our constraints on cosmology from shear-shear correlation data in the presence of the halo model for IAs., We have used a motivated model for luminosity and colour evolution of shear-shear galaxy samples as a function of redshift to improve our constraints on cosmology from shear-shear correlation data in the presence of the halo model for IAs. +" In general this reduces the overall effect of IAs on cosmology, which we attribute to the decreased contribution from IA at low redshifts."," In general this reduces the overall effect of IAs on cosmology, which we attribute to the decreased contribution from IA at low redshifts." +" We consider constraints on the amplitude of fluctutions og from shear-shear data alone with fixed IA amplitude and luminosity dependence parameters, and compare this with constraints after marginalising over these parameters."," We consider constraints on the amplitude of fluctutions $\sigma_8$ from shear-shear data alone with fixed IA amplitude and luminosity dependence parameters, and compare this with constraints after marginalising over these parameters." +" As expected the constraints are weaker after marginalisation, but are not biased significantly."," As expected the constraints are weaker after marginalisation, but are not biased significantly." +" This is due to the relatively flat degeneracy between og and the IA amplitude arising from the competing effects of GI and II terms, and the ability of shear-shear information alone to place some constraint on the IA amplitude if other cosmological parameters are held fixed."," This is due to the relatively flat degeneracy between $\sigma_8$ and the IA amplitude arising from the competing effects of GI and II terms, and the ability of shear-shear information alone to place some constraint on the IA amplitude if other cosmological parameters are held fixed." +" The model we used for the luminosity and colour evolution of the shear-shear galaxy sample could be improved in its complexity, for example by allowing a population of faint blue galaxies at high redshift."," The model we used for the luminosity and colour evolution of the shear-shear galaxy sample could be improved in its complexity, for example by allowing a population of faint blue galaxies at high redshift." +" Furthermore we assumed the shear-shear galaxy sample had a single luminosity and colour at each redshift, whereas a more sophisticated analysis would integrate over ranges in each."," Furthermore we assumed the shear-shear galaxy sample had a single luminosity and colour at each redshift, whereas a more sophisticated analysis would integrate over ranges in each." + A joint analysis of shear-shear and shear-position correlation functions has been discussed as a promising tool for removing IAs from future cosmic shear datasets, A joint analysis of shear-shear and shear-position correlation functions has been discussed as a promising tool for removing IAs from future cosmic shear datasets +Magnetic reconnection has long been proposed as a mechanism for heating coronal plasma.,Magnetic reconnection has long been proposed as a mechanism for heating coronal plasma. +" In one early model DmainBodyCitationEnd17|Kopp1976, reconnection occurs between open field lines separated by a vertical current sheet (red line) creating new closed field lines (post-flare loops, grey)."," In one early model , reconnection occurs between open field lines separated by a vertical current sheet (red line) creating new closed field lines (post-flare loops, grey)." + Closing these field lines stops the solar wind upflow in a gas-dynamic shock (GDS) that estimated would raise the temperature by 80%., Closing these field lines stops the solar wind upflow in a gas-dynamic shock (GDS) that estimated would raise the temperature by $80\%$ . + found the direct magnetic energy conversion by reconnection to be a far more effective source of heating in this same model., found the direct magnetic energy conversion by reconnection to be a far more effective source of heating in this same model. + It could raise the temperature of post-flare loops by up to a factor of three to 6 MK., It could raise the temperature of post-flare loops by up to a factor of three to 6 MK. +" Even this higher value is, however, insufficient to explain the"," Even this higher value is, however, insufficient to explain the" +destruction/removal of IT; from thecloud?.,destruction/removal of $\H2$ from the. +". The term ~ is the net ""accretion rate of Πο. which includes all processes that create and destroy Πω aud are not directly coupled toeither M. or Agy,."," The term $\gamma$ is the net “accretion” rate of $\H2$, which includes all processes that create and destroy $\H2$ and are not directly coupled toeither $M_*$ or $M_\H2$." + Both a aud 5 could iu principle be time dependent., Both $\alpha$ and $\gamma$ could in principle be time dependent. + For siuplicitv we asstuue that they are constaut., For simplicity we assume that they are constant. +" Our model is τασας (compared with. οι, Matzuer2002:Tauctal.2006:Tutt&Stabler2006:I1uuholzetal. 2006)). but it has he advantage that we can paraietrize our ignorance of he relevant plivsical processes that destroy aud disperse he cloud iuto the parameters o and 5."," Our model is minimalistic (compared with, e.g., \citealt{2002ApJ...566..302M, 2006ApJ...641L.121T, 2006ApJ...644..355H, 2006ApJ...653..361K}) ), but it has the advantage that we can parametrize our ignorance of the relevant physical processes that destroy and disperse the cloud into the parameters $\alpha$ and $\gamma$." +" Together with appropriate initial conditions equations (1)) aud (5)) tly deteriiue the evolution of the masses of molecular wdrogen aud the stellar componcut ina CAC,", Together with appropriate initial conditions equations \ref{eq:dotMstar}) ) and \ref{eq:dotMgas}) ) fully determine the evolution of the masses of molecular hydrogen and the stellar component in a GMC. + We will also make the simplitving assumption that the yee-fall time does not evolve strongly over the history of the GAIC. ie. both the star formation efficiency. per yee fall time aud the star formation time scale are now fixed.," We will also make the simplifying assumption that the free-fall time does not evolve strongly over the history of the GMC, i.e. both the star formation efficiency per free fall time and the star formation time scale are now fixed." + This asstuuption is not crucial for the model. but we will use it for the following reasons.," This assumption is not crucial for the model, but we will use it for the following reasons." + First. there is no clear systematic trend of free fall time with mass over the ranee of GAICs that we are comparing to. see c.g. Table 2 of Murray(2010)..," First, there is no clear systematic trend of free fall time with mass over the range of GMCs that we are comparing to, see e.g. Table 2 of \cite{2010arXiv1007.3270M}." + Second. asstuning a non-evolviug frec-all time allows for a couveuieut analytical solution of the woblem.," Second, assuming a non-evolving free-fall time allows for a convenient analytical solution of the problem." + Third. we find that even with this asstuiption our model describes the observed data reasonably well.," Third, we find that even with this assumption our model describes the observed data reasonably well." + We stress that our main ain is to show that a simple uodel can produce au observational signal that could © nusinterpreted as evidence for evolution of the star ormation efficiencies., We stress that our main aim is to show that a simple model can produce an observational signal that could be misinterpreted as evidence for evolution of the star formation efficiencies. + We do not try to model the precise xoperties of the ensemble of CMCS in the Galaxy., We do not try to model the precise properties of the ensemble of GMCs in the Galaxy. + With te fixed (aud. of course. we asstune that the star formation efficiency. per free fall time is a constant. oo) we can iusert (19) iuto (5)) aud obtain a linear 2ud order differential equation for Mj. Le. the equation of a damped harmonic oscillator.," With $t_{\rm ff}$ fixed (and, of course, we assume that the star formation efficiency per free fall time is a constant, too) we can insert \ref{eq:dotMstar}) ) into \ref{eq:dotMgas}) ) and obtain a linear 2nd order differential equation for $M_\H2$, i.e. the equation of a damped harmonic oscillator." +" Solving the differeutial equation we obtain where 6=egfg ds the inverse of the star formation timescale. and w=vobbf lois the ""oscillation"" period."," Solving the differential equation we obtain where $b=\epsilon_{\rm ff}/t_{\rm ff}$ is the inverse of the star formation timescale, and $\omega = \sqrt{\alpha{}b- b^2/4}$ is the “oscillation” period." + Phase o and amplitude A depend on the initial conditions., Phase $\phi$ and amplitude $A$ depend on the initial conditions. + Iu the following we restrict ourselves to two special cases of the general iiodel (6)). (7)).," In the following we restrict ourselves to two special cases of the general model \ref{eq:MH2}) ), \ref{eq:Mstar}) )." +" We adopt the parameters eg=0.02 and tye=6 Myr. which are consistent with observations of eg over a ranec of deusitv scales (Ikrinuholz&Tau2007).. aud with the free fall times 6.1!MO Avr nieasured in the sample of Murray.(2010).. respectively,"," We adopt the parameters $\epsilon_{\rm ff}=0.02$ and $t_{\rm ff}=6$ Myr, which are consistent with observations of $\epsilon_{\rm ff}$ over a range of density scales \citep{2007ApJ...654..304K}, and with the free fall times $6.1^{+6.8}_{-4.0}$ Myr measured in the sample of \cite{2010arXiv1007.3270M}, respectively." + We note that only the ratio eg/fg=0.0033 + enters our model., We note that only the ratio $\epsilon_{\rm ff}/t_{\rm ff}=0.0033$ $^{-1}$ enters our model. +" The a parameter is chosen such that the lite time of the cloud. i.e. the tie tea at which Mi,(tina)=0. is ~20 Myr (Williams&Mel&ee1997).."," The $\alpha$ parameter is chosen such that the life time of the cloud, i.e. the time $t_{\rm final}$ at which $M_\H2(t_{\rm final})=0$, is $\sim{}20$ Myr \citep{1997ApJ...476..166W}." +" Hence. we use a=2\Ivr1 in the no accretion scenario aud à=8SMyr.fin the pure accretion scenario. respectively,"," Hence, we use $\alpha = 2 {\rm\, Myr}^{-1}$ in the no accretion scenario and $\alpha = 8 {\rm\, Myr}^{-1}$ in the pure accretion scenario, respectively." + Assundug eg/fg\epsilon_{\rm GMC}$ . +"the counterjet are 13.8+0.9 mJy and 0.8+0.3 nJy, with a similar ratio of (1.7+0.6)x10*.","the counterjet are $13.8\pm 0.9$ mJy and $0.8 +\pm 0.3$ nJy, with a similar ratio of $(1.7 \pm 0.6) \times 10^4$." + Figure 5 shows the profiles of X-ray and radio emission in the jet and counterjet in the region where X- emission is detected and spatially separated from nuclear and galaxy emission., Figure \ref{fig:xrprofile} shows the profiles of X-ray and radio emission in the jet and counterjet in the region where X-ray emission is detected and spatially separated from nuclear and galaxy emission. + The subtracted background was sampled locally to each X-ray data point., The subtracted background was sampled locally to each X-ray data point. +" There is no significant variability in the X-ray emission on the angular scale of these data points between the two observations, which were roughly 8 yr apart, and which are combined to make this plot."," There is no significant variability in the X-ray emission on the angular scale of these data points between the two observations, which were roughly 8 yr apart, and which are combined to make this plot." +" However, due to the low numbers of counts we cannot rule out variability of a factor of 2 or less within regions of area 0.3 kpc?."," However, due to the low numbers of counts we cannot rule out variability of a factor of 2 or less within regions of area 0.3 $^2$." + The plot is dominated by the 2008 data., The plot is dominated by the 2008 data. + Spectral extraction regions for both the jet and counterjet begin where these features are clearly separated from the point spread function (PSF) of the bright core., Spectral extraction regions for both the jet and counterjet begin where these features are clearly separated from the point spread function (PSF) of the bright core. +" If we assume that the jet and counterjet extend into the nucleus with their average measured surface brightness, their estimated 0.3—5 keV total luminosities and 1c uncertainties are (2.9+0.2)x10°° and (1.4+0.1)x10?? ergs s5, respectively."," If we assume that the jet and counterjet extend into the nucleus with their average measured surface brightness, their estimated 0.3–5 keV total luminosities and $1\sigma$ uncertainties are $(2.9\pm0.2)\times 10^{39}$ and $(1.4\pm0.1)\times 10^{39}$ ergs $^{-1}$, respectively." + Perhaps of more importance is the counterjet intensity ratio in the radio and X-ray., Perhaps of more importance is the jet-to-counterjet intensity ratio in the radio and X-ray. +" For this we should choose identical regions on each side of the nucleus, and so we adopt that of the counterjet and its mirror-image superimposed on the jet."," For this we should choose identical regions on each side of the nucleus, and so we adopt that of the counterjet and its mirror-image superimposed on the jet." +" The jet-to-counterjet intensity ratios in the radio and X-ray are then 1.8+0.1 and 1.6+0.3 (1c errors), respectively."," The jet-to-counterjet intensity ratios in the radio and X-ray are then $1.8\pm0.1$ and $1.6\pm0.3$ $1\sigma$ errors), respectively." +" There is some indication from the radio data that the jet-to-counterjet ratio decreases with distance from the core, as might be expected from a slowing flow."," There is some indication from the radio data that the jet-to-counterjet ratio decreases with distance from the core, as might be expected from a slowing flow." +" For example, regions of X-ray counterjet length an X-ray-jet's length away give ratio of 1.4+0.1."," For example, regions of X-ray counterjet length an X-ray-jet's length away give a ratio of $1.4\pm0.1$." +" However, our current radio data are not of sufficienta quality to explore such issues in depth."," However, our current radio data are not of sufficient quality to explore such issues in depth." + An X-ray hardness-ratio plot (Fig. 6)), An X-ray hardness-ratio plot (Fig. \ref{fig:hardness}) +"? shows a trend for the X-ray spectrum to get steeper away from the nucleus, but given the statistics the result is not highly significant."," shows a trend for the X-ray spectrum to get steeper away from the nucleus, but given the statistics the result is not highly significant." + We extracted the spectrum of the nucleus from a circle of radius 1.23 arcsec., We extracted the spectrum of the nucleus from a circle of radius 1.23 arcsec. + We used background either from a source-centered annulus of radii 2.8 and 8.8 arcsec (asinZezasetal.2005) or the rectangular region situated in the group gas.," We used background either from a source-centered annulus of radii $2.8$ and $8.8$ arcsec \citep[as +in][]{zezas} + or the rectangular region situated in the group gas." +" However, none of the interesting parameters in the fits was affected by the choice of background region, and results presented here use only the former region."," However, none of the interesting parameters in the fits was affected by the choice of background region, and results presented here use only the former region." +where is chosen to be 1.75. The [actors 1.5.2.0 and 1.75 are extracted fromthe,distribution of the hadron $H$ in the cascade processes is given by the distribution function +with colours or photometric redshifts compatible with being in our Y -drop redshift range. but which do not appear in our new catalog.,"with colours or photometric redshifts compatible with being in our $Y$ -drop redshift range, but which do not appear in our new catalog." + We mark with a 7 the candidates that would be within our selection window if we adopt the photometry originally presented. in the discovery papers. rather than remeasuring this with our new reduction of the IUDE WEC3 imaging and the latest photometric zero-points.," We mark with a $\dagger$ the candidates that would be within our selection window if we adopt the photometry originally presented in the discovery papers, rather than remeasuring this with our new reduction of the HUDF WFC3 imaging and the latest photometric zero-points." +" Alost of the other LIUDE candidates. from. cülferent eroups do not meet our selection criteria both because they are too Taint in the ραπ (class A in the Table 5)) and because hey are too blue. (tos,Jose)€O.9 (class D in the Table 5))."," Most of the other HUDF candidates from different groups do not meet our selection criteria both because they are too faint in the $J$ -band (class A in the Table \ref{tab:spare}) ) and because they are too blue, $(Y_{105w} - J_{125w}) < 0.9$ (class B in the Table \ref{tab:spare}) )." + Only one candidate (z8-SB27 in Yan οἱ 22010) meets our selection criteria for brightness in the J-band and the (Yios4Jiose) colour. but is rejected on the basis ofits location in the the J if:J colour:colour plane as a likely lower redshift Balmer-break galaxy (see Figure 2)).," Only one candidate (z8-SB27 in Yan et 2010) meets our selection criteria for brightness in the $J$ -band and the $(Y_{105w} - J_{125w})$ colour, but is rejected on the basis of its location in the the $J-H$ $Y-J$ colour:colour plane as a likely lower redshift Balmer-break galaxy (see Figure \ref{fig:cc_1}) )." + This galaxy is classified with letter ‘Co in the table., This galaxy is classified with letter `C' in the table. + We note tha Jouwens. candidate UDEVv-37636015 (our YD7) has inconsistent. photometry presented. in. Bouwens et. ((2009) and. Bouwens et ((2010a) adopting the more recent photometric values from Bouwens ct ((2010a) YDY would enter our Y -drop selection (Table 5)).," We note that Bouwens' candidate UDFy-37636015 (our YD7) has inconsistent photometry presented in Bouwens et (2009) and Bouwens et (2010a) – adopting the more recent photometric values from Bouwens et (2010a), YD7 would enter our $Y$ -drop selection (Table \ref{tab:spare}) )." + In summary. using our latest reduction of the WEC3 images of the ΕΕDE we are able to reproduce 4 of the 7 Y-band dropout galaxies we first reported in Bunker ct (2010): of two additional Y-drops in the new analysis. one has been reported elsewhere and one is a new discovery in the HIUDE. field.," In summary, using our latest reduction of the WFC3 images of the HUDF we are able to reproduce 4 of the 7 $Y$ -band dropout galaxies we first reported in Bunker et (2010); of two additional $Y$ -drops in the new analysis, one has been reported elsewhere and one is a new discovery in the HUDF field." + Remeasuring the photometry of Y-drop candidates presented elsewhere by other groups. we find that most would not enter our selection as they are too faint in J-band and/or are too blue in (YoJJ). and hence are not as robust candidate zS—9 galaxies as our core sample.," Remeasuring the photometry of $Y$ -drop candidates presented elsewhere by other groups, we find that most would not enter our selection as they are too faint in $J$ -band and/or are too blue in $(Y-J)$, and hence are not as robust candidate $z\approx 8-9$ galaxies as our core sample." + From the observed surface density of Y -drops. as a function of magnitude. we can recover the luminosity function. of 25N9 ealaxies in the rest-Lrame ultraviolet. (observed bv the WECS near-infrared. filters).," From the observed surface density of $Y$ -drops, as a function of magnitude, we can recover the luminosity function of $z\approx 8-9$ galaxies in the rest-frame ultraviolet (observed by the WFC3 near-infrared filters)." + However. there is not uniform sensitivity over the redshift range probed by the Y- ," However, there is not uniform sensitivity over the redshift range probed by the $Y$ " +The far-IR thermal dust cussion has also been used to trace (Ilughesetal.1998) although so far without the benefit of redshift information.,The far-IR thermal dust emission has also been used to trace \citep{hughes98} although so far without the benefit of redshift information. + All these measures have in conmmon the use of some kind of luminosity per unit voluue whose cliauge is proportional to the Qwith corrections)., All these measures have in common the use of some kind of luminosity per unit volume whose change is proportional to the (with corrections). + The debate over the :>1 slope reflects the uncertainty in the dust correction to the UV continu measurements. which are tle easiest to measure at lieh redshift but most affected bv dust.," The debate over the $z>1$ slope reflects the uncertainty in the dust correction to the UV continuum measurements, which are the easiest to measure at high redshift but most affected by dust." + The other lndicators are harder to measure and are affected by small uuuber statistics., The other indicators are harder to measure and are affected by small number statistics. + Iu this paper. we present new constraints on the history of star formation based ou the cuscuible stellar populations of relatively nearby present dav galaxies (2 0.3).," In this paper, we present new constraints on the history of star formation based on the ensemble stellar populations of relatively nearby present day galaxies $z<0.3$ )." + The concept is to use the average spectrum of nearby. galaxies ο constrain the earlier history of star formation leading up to that stellar population., The concept is to use the average spectrum of nearby galaxies to constrain the earlier history of star formation leading up to that stellar population. + The average spoectruu contains absorption features for stars of all ages aud probes ook-back times of 0.210 Corr., The average spectrum contains absorption features for stars of all ages and probes look-back times of 0.2–10 Gyr. + With the advent of the argo ealaxy redshift surveys. such as the Two-deeree Field Galaxy Redshift Survey (2dFCRS)}) aud the SloaP Dieital Sky Survey main galaxy sample (SDSS-nes). it ha secome feasible to combine the spectra of 101 10° ealaxicy. o form very high signal-to-noise intermediate resolutio- spectra that represent the average enission of the universc at various redshifts (0.03<2x 0.25).," With the advent of the large galaxy redshift surveys, such as the Two-degree Field Galaxy Redshift Survey ) and the Sloan Digital Sky Survey main galaxy sample (SDSS-mgs), it has become feasible to combine the spectra of $10^4$ $10^5$ galaxies to form very high signal-to-noise intermediate resolution spectra that represent the average emission of the universe at various redshifts $0.03 \la z \la 0.25$ )." + Effectively. the surveys ean be regarded as having a series of apertures o- the cosmic backeround emission rather than apertures o- individual galaxies.," Effectively, the surveys can be regarded as having a series of apertures on the cosmic background emission rather than apertures on individual galaxies." + What is novel about this method is that it is not based on any huninosity output with time of the Universe. uulike all the other indicators discussed above.," What is novel about this method is that it is not based on any luminosity output with time of the Universe, unlike all the other indicators discussed above." + The method uses an inteeral over the rather than attempting to track the derivative (the SFR) and uses the whole visible spectru at intermediate resolution., The method uses an integral over the rather than attempting to track the derivative (the SFR) and uses the whole visible spectrum at intermediate resolution. + Perhaps the nearest approach to this in the past has been the work of Abrahametal.(1999) who used the color distribution of +0.5 galaxies to derive their star-formation histories which were then combined to form a cosmichistory., Perhaps the nearest approach to this in the past has been the work of \citet{abrah99mar} who used the color distribution of $z\sim0.5$ galaxies to derive their star-formation histories which were then combined to form a cosmic. +.. Recently. Hopkis.Irwin.&Connolly(2001) estimated the global SER density frou nunueasurenieuts of the Local Croup.," Recently, \citet*{HIC01} estimated the global SFR density from measurements of the Local Group." + The problem here is that the Local Croup SER av not represent tle cosmic ean and ds subject to large cosmic variations such as recent “nui-bursts” of star formation in the Milkv. Wav., The problem here is that the Local Group SFR may not represent the cosmic mean and is subject to large cosmic variations such as recent “mini-bursts” of star formation in the Milky Way. + Au advantage of this kind o fossil cosmology approach over the direct measurement is a reduced seusitivitv to extinction., An advantage of this kind of `fossil cosmology' approach over the direct measurement is a reduced sensitivity to extinction. + Young stars are xr iu dustv reeious. this plagues the direct 1ieasuremeif approach.," Young stars are born in dusty regions, this plagues the direct measurement approach." + When they age they migrate out of such regious and contribute to the older stellar populations we o)UIVO., When they age they migrate out of such regions and contribute to the older stellar populations we observe. + Iu this paper. we describe the application of this method to 0000 spectra in the redsift range 0.030.25 from the citepcollessOL..," In this paper, we describe the application of this method to 000 spectra in the redshift range 0.03–0.25 from the \\citep{colless01}." + The plan of his paper is as follows., The plan of this paper is as follows. + Iu Section 2 we clescribe the ddata and our immethods for combining the spectra., In Section \ref{sec:data} we describe the data and our methods for combining the spectra. + Iu Section 3. woe describe our analytic models for cosmic star-formation scenarios., In Section \ref{sec:scenarios} we describe our analytic models for cosmic star-formation scenarios. + In Section Lo we describe our fitting procedure aud the best-fit modoels., In Section \ref{sec:results} we describe our fitting procedure and the best-fit models. + Iu Section 5. we discuss the impact of possible biases on our results from aperture effects aud απο] selection.," In Section \ref{sec:biases} + we discuss the impact of possible biases on our results from aperture effects and luminosity selection." + Finally in Section 6 we eive our conclusions., Finally in Section \ref{sec:conc} we give our conclusions. + The 2dF Galaxy Redshitt Survey is a iiagnitude-Imuited spectroscopic survey (Maddoxetal.1998:Colless1999.2001) usiug the Anelo-Australian Observatorvs 2dF facility which is capable of observing up to LOO ealaxies siuultziuecouslv (Tavlor&Cray1990:Lewis.Glazebrook.&Tavlor1998:Lewisetal. 2002).," The 2dF Galaxy Redshift Survey is a magnitude-limited spectroscopic survey \citep{maddox98,colless99,colless01} using the Anglo-Australian Observatory's 2dF facility which is capable of observing up to 400 galaxies simultaneously \citep*{TG90,LGT98,lewis02}." +.. The maguitude uit of the survey is au extinction-corrected oof 19.15 selected from the Automated Plate Measuriug CAPMD galaxy catalogue (Maddox.Efstathiou.&Suther-land1990a.1996: Maddoxetal.L990D)).," The magnitude limit of the survey is an extinction-corrected of 19.45 selected from the Automated Plate Measuring (APM) galaxy catalogue \citealp*{MES90,MES96}; ; \citealp{MESL90}) )." + By the eud of the survey (2002 Jauuarv). up to 2500000 unique galaxy redshifts are expected to have been measured.," By the end of the survey (2002 January), up to 000 unique galaxy redshifts are expected to have been measured." + The survey covers approximately 2000 dee? of sky distributed between the NCP and SCP in high-ealactic latitude fields., The survey covers approximately 2000 $^2$ of sky distributed between the NGP and SGP in high-galactic latitude fields. + A full description of the survey geometry is given by Collessetal.(2001).., A full description of the survey geometry is given by \citet{colless01}. . + Tn 2001 June. about 1720000 unique galaxy redshifts had been measured.," In 2001 June, about 000 unique galaxy redshifts had been measured." + This is the sample used iu the analvsis prescuted in this paper., This is the sample used in the analysis presented in this paper. +" The spectra are observed through a fixed 2""71-fiber aperture and the waveleusth coverage varies ouly slightly from observing run to run. consistcuthy covering the range with a 2.1-pixel resolution FWOAL of9."," The spectra are observed through a fixed $2''\!.1$ -fiber aperture and the wavelength coverage varies only slightly from observing run to run, consistently covering the range with a 2.1-pixel resolution FWHM of." +0A.. All the spectra in the survey have been eveballed aud assigned a quality Q from 1 to 5 (Collessetal.2001): 1. no identifiable redshift: 2. à possible redshift: 3. à reliable redshift: Loa reliable redshift: 5. a reliable redshift with a liel-quality spectrmm.," All the spectra in the survey have been eyeballed and assigned a quality $Q$ from 1 to 5 \citep{colless01}: 1, no identifiable redshift; 2, a possible redshift; 3, a reliable redshift; 4, a reliable redshift; 5, a reliable redshift with a high-quality spectrum." + The survey ds considered to consist of those galaxw spectra with Q23 (approximately of galaxies observed)., The survey is considered to consist of those galaxy spectra with $Q\ge3$ (approximately of galaxies observed). + These galaxies have a median redshift of about 0.11 and the typical spectral signal-to-noise ratio at the survey limit is about 10 per pixcl., These galaxies have a median redshift of about 0.11 and the typical spectral signal-to-noise ratio at the survey limit is about 10 per pixel. + We construct our ‘cosiic spectra’ m redshift slices 2>|At by applving an instrament response correction. de-redshifting to the rest frame and sumunine up all the Q53 spectra in the interval Az.," We construct our `cosmic spectra' in redshift slices $z \rightarrow z ++ \Delta z$ by applying an instrument response correction, de-redshifting to the rest frame and summing up all the $Q\ge3$ spectra in the interval $\Delta z$." + The galaxies are scaled o iatch their measured huninosity bv comparison with an iuteeration of the filter curve over the measured spectimm (n the observed iane), The galaxies are scaled to match their measured luminosity by comparison with an integration of the filter curve over the measured spectrum (in the observed frame). + The scaling allows for the fact that the fibres salple only a fraction of a galaxys helt aud for extinction and exposure-time variations between observations., The scaling allows for the fact that the fibres sample only a fraction of a galaxy's light and for extinction and exposure-time variations between observations. + A Παππά scaling is allowed (as a function of apparcut uaenitude) to avoid adding excessive nolse froni poor-quality spectra., A maximum scaling is allowed (as a function of apparent magnitude) to avoid adding excessive noise from poor-quality spectra. + This scaling limit is onlv applied to of the data., This scaling limit is only applied to of the data. + Finally the cosmicspectrumis normalized to aduean of unity over a set wavelength rauge — to re-iterate. our method of analysis uses spectral features not absolute huninositics other than for the weighting of the ealaxv," Finally the cosmicspectrumis normalized to a mean of unity over a set wavelength range – to re-iterate, our method of analysis uses spectral features not absolute luminosities other than for the weighting of the galaxy" +with one of the previously ideutified extinction cores. Lo.. at most one ROSAT source is associated to the on-core regions.,"with one of the previously identified extinction cores, i.e., at most one ROSAT source is associated to the on-core regions." + Iu a amore detailed look. we analyze three archival poiutiues of prominent regions in the Pipe Nebula. encompassing 559. the PAIR. aud D665.," In a more detailed look, we analyze three archival pointings of prominent regions in the Pipe Nebula, encompassing 59, the PMR, and 68." + We analyze the infrared SEDs of all N-vay sources with nemr-iufrared counterparts (As12.1 mag) iu the ou-core regions (plus most in the off-core regions. luted w data availability) aud fud that all sources in the on-core regious and all but oue source inthe off-core regions ean be explained by extincted stellar ohotospheres.," We analyze the infrared SEDs of all X-ray sources with near-infrared counterparts $K_S<12.4$ mag) in the on-core regions (plus most in the off-core regions, limited by data availability) and find that all sources in the on-core regions and all but one source inthe off-core regions can be explained by extincted stellar photospheres." + Among these three observations. he known cluster of YSOs in 559 is the only region where the deusitv of X-rav sources in he on-core regions is indeed higher than the vackeround source deusity.," Among these three observations, the known cluster of YSOs in 59 is the only region where the density of X-ray sources in the on-core regions is indeed higher than the background source density." + Without the known YSOs. 559 also shows au uuderdeusitv of sources in the on-core region. indicating that there is no significant YSO population bevou the sources that are already known.," Without the known YSOs, 59 also shows an underdensity of sources in the on-core region, indicating that there is no significant YSO population beyond the sources that are already known." + Roughly half of the previously known Spitzer—ideutified YSOs have A-rav counterparts with typical spectra: some show clear sigus of variability., Roughly half of the previously known -identified YSOs have X-ray counterparts with typical spectra; some show clear signs of variability. + Tn the on-core regions of the observations. we have found au upper linüt of 6 evolved YSOs since this is the number ofN-ray sources with As-baud counterparts. not counting the known YSOs.," In the on-core regions of the observations, we have found an upper limit of 6 evolved YSOs since this is the number ofX-ray sources with $K_S$ -band counterparts, not counting the known YSOs." + IIowever. the fact that the two regions with any detections iu the on-core regions. D559 aud the PAIR. both show unuderdeusities witli respect to the surrounding backerouud source densities (not taking into account the known YSOs in 559) sueeests that a amore realistic wpper liuüt is closer to zero.," However, the fact that the two regions with any detections in the on-core regions, 59 and the PMR, both show underdensities with respect to the surrounding background source densities (not taking into account the known YSOs in 59) suggests that a more realistic upper limit is closer to zero." + A inore stringent upper limit results whenadditionally requiring detections at μια. Ouly two sources in the ou-core regions of 559 aud only four more sources iu the 559 field fulBll that criterion., A more stringent upper limit results whenadditionally requiring detections at $\mu$ m. Only two sources in the on-core regions of 59 and only four more sources in the 59 field fulfill that criterion. + We therefore conclude from the available N-rav data that there is no indication of an extended population of class ΤΗ objects in the Pipe Nebula. corroborating the previously stated lack of star formation activity. NNINL. Spitzer... R," We therefore conclude from the available X-ray data that there is no indication of an extended population of class III objects in the Pipe Nebula, corroborating the previously stated lack of star formation activity. , , ," + We therefore conclude from the available N-rav data that there is no indication of an extended population of class ΤΗ objects in the Pipe Nebula. corroborating the previously stated lack of star formation activity. NNINL. Spitzer... RO," We therefore conclude from the available X-ray data that there is no indication of an extended population of class III objects in the Pipe Nebula, corroborating the previously stated lack of star formation activity. , , ," + We therefore conclude from the available N-rav data that there is no indication of an extended population of class ΤΗ objects in the Pipe Nebula. corroborating the previously stated lack of star formation activity. NNINL. Spitzer... ROS," We therefore conclude from the available X-ray data that there is no indication of an extended population of class III objects in the Pipe Nebula, corroborating the previously stated lack of star formation activity. , , ," + We therefore conclude from the available N-rav data that there is no indication of an extended population of class ΤΗ objects in the Pipe Nebula. corroborating the previously stated lack of star formation activity. NNINL. Spitzer... ROSA," We therefore conclude from the available X-ray data that there is no indication of an extended population of class III objects in the Pipe Nebula, corroborating the previously stated lack of star formation activity. , , ," + We therefore conclude from the available N-rav data that there is no indication of an extended population of class ΤΗ objects in the Pipe Nebula. corroborating the previously stated lack of star formation activity. NNINL. Spitzer... ROSAT," We therefore conclude from the available X-ray data that there is no indication of an extended population of class III objects in the Pipe Nebula, corroborating the previously stated lack of star formation activity. , , ," + We therefore conclude from the available N-rav data that there is no indication of an extended population of class ΤΗ objects in the Pipe Nebula. corroborating the previously stated lack of star formation activity. NNINL. Spitzer... ROSAT.," We therefore conclude from the available X-ray data that there is no indication of an extended population of class III objects in the Pipe Nebula, corroborating the previously stated lack of star formation activity. , , ," + We therefore conclude from the available N-rav data that there is no indication of an extended population of class ΤΗ objects in the Pipe Nebula. corroborating the previously stated lack of star formation activity. NNINL. Spitzer... ROSAT..," We therefore conclude from the available X-ray data that there is no indication of an extended population of class III objects in the Pipe Nebula, corroborating the previously stated lack of star formation activity. , , ," +"protoplanet and 7, is the torque per unit mass due to the disc.",protoplanet and $T_p$ is the torque per unit mass due to the disc. +" “Phe cise model used. for the particular set. of simulations presented in figure 1. was such that the disc surface. density. ο).=MurB1/2. ἐν=0.05. ancl the dimensionless viscosity coellicient a=4510""."," The disc model used for the particular set of simulations presented in figure \ref{fig1} was such that the disc surface density $\Sigma(r) = \Sigma_0 r^{-1/2}$, $H/r=0.05$, and the dimensionless viscosity coefficient $\alpha = 4 \times 10^{-3}$." +" In code units the inner boundary was located at τν=1. the outer boundary at Rov,=S. and the protoplancet was located abr, =3."," In code units the inner boundary was located at $R_{in}=1$, the outer boundary at $R_{out}=8$ , and the protoplanet was located at $r_p=3$." +" owe use the convention that r, is equivalent to 5.2 AU. ancl the central stellar mass is a solar mass. then the disc mass was normalised so that it contained the equivalent of 7.5 Jupiter masses between 1.56 and 20.8 AU."," If we use the convention that $r_p$ is equivalent to 5.2 AU, and the central stellar mass is a solar mass, then the disc mass was normalised so that it contained the equivalent of 7.5 Jupiter masses between 1.56 and 20.8 AU." + This dise model is equivalent to that described in Bate et al. (, This disc model is equivalent to that described in Bate et al. ( +2003). and figure 1. is directly. comparable with their figure 10.,"2003), and figure \ref{fig1} is directly comparable with their figure 10." +" The gravitational softening parameter was set to be b—0.7H, where ff, is the disc thickness at the position of the protoplanet.", The gravitational softening parameter was set to be $b=0.7H_p$ where $H_p$ is the disc thickness at the position of the protoplanet. +" We use the convention that 1 Earth mass corresponds to Ad,/Ad,=310”.", We use the convention that 1 Earth mass corresponds to $M_p/M_*=3 \times 10^{-6}$. + The black clots in figure 1. show the migration time scales obtained in the simulation., The black dots in figure \ref{fig1} show the migration time scales obtained in the simulation. + The dashed. line is obtained from equation. 1 assuming an identical disc model., The dashed line is obtained from equation \ref{ward-tmig} assuming an identical disc model. +" It is clear that a gravitational softening parameter of b—07H, gives good agreement with the migration time appropriate to a Lully three dimensional locally isothermal disc. and that two dimensional simulations can be used to study the migration of low mass protoplanets provided an appropriate gravitational softening parameter is used."," It is clear that a gravitational softening parameter of $b=0.7H_p$ gives good agreement with the migration time appropriate to a fully three dimensional locally isothermal disc, and that two dimensional simulations can be used to study the migration of low mass protoplanets provided an appropriate gravitational softening parameter is used." +" Figure 2. shows the migration time calculated: for simulations in which X(r)xrft. Hír=007. and the softening parameter was 6=0.3//,."," Figure \ref{fig2} shows the migration time calculated for simulations in which $\Sigma(r) \propto r^{-1}$, $H/r=0.07$, and the softening parameter was $b=0.3 H_p$." + These are the values adopted for the global turbulent disc. runs presented. in sections 3.2... 3.3... and. 3.4... because the potential is better represented close to the planet.," These are the values adopted for the global turbulent disc runs presented in sections \ref{G1}, \ref{G2}, and \ref{G3}, because the potential is better represented close to the planet." + The cise model here was normalised so that it. contained the equivalent of 0.02 AL. between 0 and 40 AU. and 22.5 Jupiter masses interior to the protoplanet radius rj.," The disc model here was normalised so that it contained the equivalent of $0.02$ $_{\odot}$ between 0 and 40 AU, and $\simeq 2.5$ Jupiter masses interior to the protoplanet radius $r_p$." +" Figure 2. shows that this results in migration times that are a factor of c2/3 shorter than those predicted. by Tanaka. Facheuchi. Ward. (2002) for the smaller masses but are in slightly closer agreement in the higher ~30AZ, range."," Figure \ref{fig2} + shows that this results in migration times that are a factor of $\simeq 2/3$ shorter than those predicted by Tanaka, Tacheuchi, Ward (2002) for the smaller masses but are in slightly closer agreement in the higher $\sim 30 M_{\oplus}$ range." + These shorter migration times arise because of the smaller softening parameter emploved., These shorter migration times arise because of the smaller softening parameter employed. + The global model Gl described. in table 1/— contained a protoplanet whose mass is equivalent to x3 Earth masses., The global model G1 described in table \ref{table1} contained a protoplanet whose mass is equivalent to $\simeq 3$ Earth masses. + Such a protoplanet is expected to provide a small perturbation to the disc., Such a protoplanet is expected to provide a small perturbation to the disc. + A snapshot of the midplane density is shown in figure 3.. and shows that the presence of the protoplanet is indiscernible due to the higher amplitude ensitv [Iuctuations generated by the turbulence.," A snapshot of the midplane density is shown in figure \ref{fig4}, and shows that the presence of the protoplanet is indiscernible due to the higher amplitude density fluctuations generated by the turbulence." + Figure 4 shows a series of closeup images of the midplane density in the near vicinity of the protoplanet. which again show that the protoplanet cannot be detected.," Figure \ref{fig5} shows a series of close–up images of the midplane density in the near vicinity of the protoplanet, which again show that the protoplanet cannot be detected." + A similar plot for an equivalent laminar cise run is presented in figure 5. for purposes of comparison.," A similar plot for an equivalent laminar disc run is presented in figure \ref{fig6} + for purposes of comparison." + It is worth noting that once the ensitv structure shown in figure ο. is established. in the laminar disc runs. it remains essentially time independent.," It is worth noting that once the density structure shown in figure \ref{fig6} is established in the laminar disc runs, it remains essentially time independent." + The changing censitv structure observed in figure 4.. combined with the larger amplitude of the turbulentwakes when compared with those generated by the protoplanet. suggest that the gravitational interaction between a low miss protoplanet ancl turbulent dise may cilfer substantially when compared with a laminar cise.," The changing density structure observed in figure \ref{fig5}, combined with the larger amplitude of the turbulentwakes when compared with those generated by the protoplanet, suggest that the gravitational interaction between a low mass protoplanet and turbulent disc may differ substantially when compared with a laminar disc." +All of these objects have spherical svinmetrie shells which implies that no source of asvinmetry is needed in (he mass-loss rate process [rom the AGB. and confirms our predictions that large CSE should be present around AGB stars.,"All of these objects have spherical symmetric shells which implies that no source of asymmetry is needed in the mass-loss rate process from the AGB, and confirms our predictions that large CSE should be present around AGB stars." + Probably. the existence of these huge dust shells is related to the mass-loss suffered by the stars during the TP-ACB.," Probably, the existence of these huge dust shells is related to the mass-loss suffered by the stars during the TP-AGB." + The formation ol structures with sizes as large as ~ 3.3 pe. like those found around AFGL 618. W Pic. RY Dra or R CrD. is not predicted by any of our models. however the distance errors and a lower density for the ISM (those are objects at high Galactic latitude). should be taken into account.," The formation of structures with sizes as large as $\sim$ 3.3 pc, like those found around AFGL 618, W Pic, RY Dra or R CrB, is not predicted by any of our models, however the distance errors and a lower density for the ISM (those are objects at high Galactic latitude), should be taken into account." +" With regards to the emission enhancements in the PPNe AFGL GIS and ΑΕΙ, 2055. speck (2000) related their existence to the occurrence of thermal pulses."," With regards to the emission enhancements in the PPNe AFGL 618 and AFGL 2688, Speck (2000) related their existence to the occurrence of thermal pulses." + By comparing the dynamical ümescales of the shells with the thermal pulses timescale (hev derived the mass of (he star., By comparing the dynamical timescales of the shells with the thermal pulses timescale they derived the mass of the star. + This kind of analvsis is widely done in the literature., This kind of analysis is widely done in the literature. + However. the non-linear evolution of the shells generated by the thermal pulses. and the deceleration introduced by the ISAT cause that the models with different evolutionary AGB give rise to the formation ol structures with similar sizes.," However, the non-linear evolution of the shells generated by the thermal pulses, and the deceleration introduced by the ISM cause that the models with different evolutionary AGB give rise to the formation of structures with similar sizes." + According to our models. does not seem possible to relate the dvnamical timescales derived from CSE with the theoretical timescales associated with the thermal pulses.," According to our models, does not seem possible to relate the dynamical timescales derived from CSE with the theoretical timescales associated with the thermal pulses." + The only known CSE surrounding an AGB star which shows multiple shell structures is IRC+10216., The only known CSE surrounding an AGB star which shows multiple shell structures is IRC+10216. + IRC+10216. is the CSE of the long period Mira-tvpe variable carbon star CW Leo has been widely observed at infrared. and millimeter wavelengths.," IRC+10216, is the CSE of the long period Mira-type variable carbon star CW Leo has been widely observed at infrared and millimeter wavelengths." + Its distance is estimated to be in the range 120 (Loup 1993) to 170 pe (Winters 1994) and is considered to be at the end of its AGB evolution with a mass-loss rate of 1.5x10 '(ngeins 1995) and a terminal wind velocity of ~ 14-15 (Olofsson 1993)., Its distance is estimated to be in the range 120 (Loup 1993) to 170 pc (Winters 1994) and is considered to be at the end of its AGB evolution with a mass-loss rate of $1.5\times10^{-5}$ (Huggins 1995) and a terminal wind velocity of $\sim$ 14-15 (Olofsson 1993). + It is the nearest carbon star that has a high mass-loss rate ancl consequently is one ol the best observed AGB stars., It is the nearest carbon star that has a high mass-loss rate and consequently is one of the best observed AGB stars. + Recently. deep B and. V-band and archival IST WEPC2 images revealed the existence of an extended circular halo with niultiple shell structures in the extended CSE IRC-10216 (Mauron Iuggis 2000).," Recently, deep B and V-band and archival HST WFPC2 images revealed the existence of an extended circular halo with multiple shell structures in the extended CSE IRC+10216 (Mauron Huggins 2000)." +" The envelope is detected out to 200"".", The envelope is detected out to 200. +. The brightness of the shells is explained in terms of the illumination of dust-scattered ambient Galactic lisht., The brightness of the shells is explained in terms of the illumination of dust-scattered ambient Galactic light. + The observed intensity is proportional to the column density. along anv line of sight for an optically thin limit. when (he source of illumination is the interstellar radiation field.," The observed intensity is proportional to the column density along any line of sight for an optically thin limit, when the source of illumination is the interstellar radiation field." + We have computed the optical intensity Irom our models assuming (hat it is proportional to the column density along the line of sight., We have computed the optical intensity from our models assuming that it is proportional to the column density along the line of sight. + We show (wo examples that could match the observed structure found in IRC+10216 (see Fig., We show two examples that could match the observed structure found in IRC+10216 (see Fig. + 7 from Mauron IIugeins 2000)., 7 from Mauron Huggins 2000). + The left panel of Fig., The left panel of Fig. + 15 corresponds to the 1 stellar models at of its AGB evolution and the right panel to the 1.5 stellar model at its of its AGB evolution., 15 corresponds to the 1 stellar models at of its AGB evolution and the right panel to the 1.5 stellar model at its of its AGB evolution. + These are the only, These are the only +"edge ry of thedisk. angular momentum from the binary feeds into the disk at a rate proportional to the surfacedensity δα, ","edge $r_{\rm i}$ of the, angular momentum from the binary feeds into the disk at a rate proportional to the surfacedensity $\Sigma_{\rm i}$." +The viscous torque exerted by the CB disk on the binary can be shown to be(Taam&Spruit2001:Taam2001) = fa.tis the mass transfer time. and pis a parameter determined by the viscosity.," The viscous torque exerted by the CB disk on the binary can be shown to be\citep{taam01,spru01} + where $\gamma^{2}=r_{\rm i}/a$, $t$ is the mass transfer time, and $p$ is a parameter determined by the viscosity." + Suppose z is the function of r and X with the following form (Spruit & Taam2001) then p=(a|L1)/[2(2i|2.0j].," Suppose $\nu$ is the function of $r$ and $\Sigma$ with the following form \citep{spru01} + then $p=(m+1)/[2(2m+2-n)]$." + Iu the following calculations we set =n= 1.50 p-1/3.," In the following calculations we set $m=n=1$, so $p=1/3$." + By simple algebra. from the above equations we obtain the aneular momentum loss rate via the CB disk where is the specific orbital angular momenta of the disk: mmaterial at 5.," By simple algebra, from the above equations we obtain the angular momentum loss rate via the CB disk where is the specific orbital angular momentum of the disk material at $r_{\rm i}$." + The viscous timescale f44 at the inner οσο of disk is and i4 is given with the standard à prescription (Shakura&Suuvaev1973) where ass. 0v Jf are the viscosity parameter (in the following calculations we set agy= 0.01). the sound speed. and the scale height of disk at ry respectively.," The viscous timescale $t_{\rm vi}$ at the inner edge of disk is and $\nu_{\rm i}$ is given with the standard $\alpha$ prescription \citep{Shak73} + where $\alpha_{\rm SS}$, $c_{\rm s}$, $H_{\rm i}$ are the viscosity parameter (in the following calculations we set $\alpha_{\rm SS}=0.01$ ), the sound speed, and the scale height of disk at $r_{\rm i}$, respectively." +" Assiuine that the disk is lydrostatically supported and ecometrically thin with {1η~0.03 (Belleetal.200L).. we have If we consider angular momentum loss ouly via the CB disk. the chauging rate of the orbital period is then where 4j2δέο, "," Assuming that the disk is hydrostatically supported and geometrically thin with $H_{\rm +i}/r_{\rm i}\sim 0.03$ \citep{bell04}, we have If we consider angular momentum loss only via the CB disk, the changing rate of the orbital period is then where $\eta=\delta(t/t_{\rm vi})^{1/3}$." +"Since AT,«0. the orbital period will decrease when For conservative evolution. à=jj0. Eq. ("," Since $\dot{M}_{2}<0$, the orbital period will decrease when For conservative evolution, $\delta=\eta=0$ , Eq. (" +19) recovers to q>Las expected.,19) recovers to $q>1$ as expected. + Iu Fig., In Fig. + 1 we plot jj against g in the solid curve when the orbital period is constaut aud àκI., 1 we plot $\eta$ against $q$ in the solid curve when the orbital period is constant and $\delta\ll 1$. + Ilere we take ία=5?LT (Artemowicz 1991).," Here we take $r_{\rm +i}/a=\gamma^{2}=1.7$ \citep{arty94}." + Figure 1 shows that the CB disk presents a plausible πουαπΙσ removing the orbital angular moment to explain the decrease of the orbital periods for reasonable values of η (or à)., Figure 1 shows that the CB disk presents a plausible mechanism removing the orbital angular momentum to explain the decrease of the orbital periods for reasonable values of $\eta$ (or $\delta$ ). + Generally a larger y is required for a sanaller 4., Generally a larger $\eta$ is required for a smaller $q$. + The dotted aud dashed lines show two examples of Aleol binary evolution. revealing how the orbital period evolution depends on the initial parameters.," The dotted and dashed lines show two examples of Algol binary evolution, revealing how the orbital period evolution depends on the initial parameters." + As seen from Eq. (, As seen from Eq. ( +HE) the larecr orbit. the larger angular momentum loss rate via the CB disk.,"14), the larger orbit, the larger angular momentum loss rate via the CB disk." + This naturally results i a positive correlation between {σι aud Pu., This naturally results in a positive correlation between $\dot{P}_{\rm orb}$ and $P_{\rm orb}$. + Tu this section we present the results of umiuerical calculations of the Aleol binary evolutions in two typical cases., In this section we present the results of numerical calculations of the Algol binary evolutions in two typical cases. + We have adopted an updated version of the evolution code developed by Egeletou(1971.1972) (seealsoTanetal.1991:Pols1995).," We have adopted an updated version of the evolution code developed by \citet{eggl71,eggl72} \citep[see also][]{han94,pols95}." +. We consider both the angular momentum loss mechanisnis described iu section 2. adopting the modified maguetic braking law (Eqs. |," We consider both the angular momentum loss mechanisms described in section 2, adopting the modified magnetic braking law (Eqs. [" +6|-|7]) for evolved stars with mass ZL5AL..,6]-[7]) for evolved stars with mass $\la 1.5M_{\odot}$. + We take solar chemical compositious (CXV= 0.7. Y— 0.28. and Z= 0.02) for both stars. and the ratio of the musing leneth to the pressure scale height to be 2.0.," We take solar chemical compositions $X=0.7$ , $Y=0.28$ , and $Z=0.02$ ) for both stars, and the ratio of the mixing length to the pressure scale height to be 2.0." + Tn a proto-Àlgol svstem with initial orbital period Pong<~12 davs the more massive star will fill its Roche lobe when itis still on," In a proto-Algol system with initial orbital period $P_{\rm +orb,i}<\sim 1-2$ days, the more massive star will fill its Roche lobe when itis still on" +"explanation for this effect is that matter beyond rooo, while still correlated to some extent with the cluster major axis, is more randomly distributed (see also ?)) and therefore reduces the impact of the triaxiality-induced concentration scatter a bit.","explanation for this effect is that matter beyond $r_{200}$, while still correlated to some extent with the cluster major axis, is more randomly distributed (see also \citealt{Becker_Kravtsov_2011}) ) and therefore reduces the impact of the triaxiality-induced concentration scatter a bit." +" While we have just demonstrated a strong influence of halo triaxiality on reconstructed NFW parametersclusters,, there remains some scatter which is not correlated with this."," While we have just demonstrated a strong influence of halo triaxiality on reconstructed NFW parameters, there remains some scatter which is not correlated with this." + In the right-most panel of Fig., In the right-most panel of Fig. +" 6 we therefore investigate the influence of substructure, quantified as the fraction fgup of the halo mass which is found in bound subhaloes within rooo identified by the algorithm (?).."," \ref{fig:mcrelative} we therefore investigate the influence of substructure, quantified as the fraction $\fsub$ of the halo mass which is found in bound subhaloes within $r_{200}$ identified by the algorithm \citep{Springel_et_al_2001}." + This fraction is generally small with only of haloes having fsup>0.1., This fraction is generally small with only of haloes having $\fsub > 0.1$. +" The plot shows some influence on the reconstructions, most notably on concentration, which tends to be underpredicted in high-substructure clusters."," The plot shows some influence on the reconstructions, most notably on concentration, which tends to be underpredicted in high-substructure clusters." +" However, as with the axis ratio, the influence is much less strong than that of cluster orientation."," However, as with the axis ratio, the influence is much less strong than that of cluster orientation." + We have shown above that the scatter in concentration can be ascribed largely to the influence of halo orientation., We have shown above that the scatter in concentration can be ascribed largely to the influence of halo orientation. +" However, for a large sample of clusters, oriented randomly towards the observer, this leads to overestimation of concentration in some haloes, and underestimation in others (see Fig. 6))."," However, for a large sample of clusters, oriented randomly towards the observer, this leads to overestimation of concentration in some haloes, and underestimation in others (see Fig. \ref{fig:mcrelative}) )." +" While this does not necessarily eliminate influence of triaxiality on the concentration bias even for arbitrarily large cluster samples, it can be expected to reduced it to a level where the effect of substructure becomes non-negligible."," While this does not necessarily eliminate influence of triaxiality on the concentration bias even for arbitrarily large cluster samples, it can be expected to reduced it to a level where the effect of substructure becomes non-negligible." + We explore the role of both effects in this context in Fig. 7.., We explore the role of both effects in this context in Fig. \ref{fig:biasresolution}. +" For this, the sample is split into five equally large quintiles, once in order of increasing axis ratio, and once by substructure fraction."," For this, the sample is split into five equally large quintiles, once in order of increasing axis ratio, and once by substructure fraction." +" For each of the 25 resulting combinations, the median concentration, normalised to cap, is then formed."," For each of the 25 resulting combinations, the median concentration, normalised to $\cdd$, is then formed." +" In this way, the figure shows both the variation with axis ratio at (nearly) fixed substructure level and vice versa and can therefore eliminate potential correlations between these two effects."," In this way, the figure shows both the variation with axis ratio at (nearly) fixed substructure level and vice versa and can therefore eliminate potential correlations between these two effects." +" For added clarity, the black line shows the concentration bias when the sample is split only according to axis ratio."," For added clarity, the black line shows the concentration bias when the sample is split only according to axis ratio." +" There are two clear trends in this figure: A decrease in concentration from left to right, corresponding to an increase in axis ratio (of ©5% in the case of the lowest substructure quintile), and from blue to red, as the substructure fraction increases (of ~10% for the least elongated clusters)."," There are two clear trends in this figure: A decrease in concentration from left to right, corresponding to an increase in axis ratio (of $\approx 5\%$ in the case of the lowest substructure quintile), and from blue to red, as the substructure fraction increases (of $\sim 10\%$ for the least elongated clusters)." +" Both triaxiality and substructure therefore tend to lower the concentration, but the influence of substructure appears to be dominant."," Both triaxiality and substructure therefore tend to lower the concentration, but the influence of substructure appears to be dominant." +" While the addition of substructure to the outer parts of a smooth NFW halo can be expected to reduce the best- concentration of both 2D and 3D analyses, its influence appears to be larger in 2D. This might be due to the low surface mass density in the projected outer cluster regions (see Fig. A1)),"," While the addition of substructure to the outer parts of a smooth NFW halo can be expected to reduce the best-fit concentration of both 2D and 3D analyses, its influence appears to be larger in 2D. This might be due to the low surface mass density in the projected outer cluster regions (see Fig. \ref{cutofftest}) )," +" which is affected more severely by the presence of substructure than the mass profile obtained in 3D. 'To summarise the results and interpretations of this section: Within rooo, substructure and triaxiality cause a negative bias (~ —12%) and strong scatter in WL concentration, but leave the reconstructed mass largely unaffected."," which is affected more severely by the presence of substructure than the mass profile obtained in 3D. To summarise the results and interpretations of this section: Within $r_{200}$, substructure and triaxiality cause a negative bias $\sim -12\%$ ) and strong scatter in WL concentration, but leave the reconstructed mass largely unaffected." +" Structure outside raoo, the “correlated large-scale structure"", biases concentration positively and mass negatively due to deviations of the mass profile from the NFW model at these"," Structure outside $r_{200}$, the “correlated large-scale structure”, biases concentration positively and mass negatively, due to deviations of the mass profile from the NFW model at these" +conrpression ratio and acquire a softer energy spectra compared to the usual assumption w= ue ,compression ratio and acquire a softer energy spectrum compared to the usual assumption $w=u$ . +We set ow—d|VaA/V23 upstream of the shock to accouu for the Alfvenic ciift effect there., We set $w=u+V_{A}/\sqrt{3}$ upstream of the shock to account for the Alfvenic drift effect there. + The damping of Alfven waves created by the cosmic rav streamuue instability results m a very inuportant effect of eas heating upstream of the shock described by the last term in Eq. (, The damping of Alfven waves created by the cosmic ray streaming instability results in a very important effect of gas heating upstream of the shock described by the last term in Eq. ( +3).,3). + This effect limits the total shock compression ratio., This effect limits the total shock compression ratio. +" The spatial depeudeuce of auplified maguetic Held is taken in the form Dr)νImpoRp where py is the gas deusitv of the circumstellarAMps uediuni aud AZ, is some constaut.", The spatial dependence of amplified magnetic field is taken in the form $B(r)=\sqrt{4\pi \rho _0}\frac {\dot{R}\rho }{M_A\rho _0}$ where $\rho _0$ is the gas density of the circumstellar medium and $M_A$ is some constant. + We emplov EOSIts of Volsetal.(2005) in the analysis of δνταν radialon from voung SNRs and assume ha iuagnetie. energy deusitvH BoD/sa* downsrealof the shock is 23.5 of the rani pressure puP ha determines the constant A4=23., We employ results of \citet{Voelk05} in the analysis of X-ray radiation from young SNRs and assume that magnetic energy density $B^{2}/8\mathrm{{\pi}}$ downstreamof the shock is $3.5$ of the ram pressure $\mathit{{\rho}u}_{\mathrm{sh}}^{2}$ that determines the constant $M_A=23$. + It is worth ioting that this relation is in good agreement with he modelling of cosmic rav streaming instability in voung SNRs (Zirakashvili&Ptuskin2008).., It is worth noting that this relation is in good agreement with the modelling of cosmic ray streaming instability in young SNRs \citep{Zir08b}. + The last term in Eq. (, The last term in Eq. ( +1) corresponds to the injection of thermal protons with momenta p=Pinj acd lass i at the shock at r=Rit).,4) corresponds to the injection of thermal protons with momenta $p=p_{inj}$ and mass $m$ at the shock at $r=R(t)$. + The dimensionless parameter + determines the injection effücienewv., The dimensionless parameter $\eta$ determines the injection efficiency. +" The injection efficicucy of therm ions in the process of shock acceleration y=lag,fe is taken iu accordance with the paper Zirakashvili(2007):: here a4) is the time-varving shock velocity.", The injection efficiency of thermal ions in the process of shock acceleration $\eta =0.1u_{\mathrm{sh}}/c$ is taken in accordance with the paper \citet{Zir07}; here $u_{\mathrm{sh}}(t)$ is the time-varying shock velocity. +"The naxinnun particle 1no1ieutui pyax reached lia xocess of diffusive shock acceleration can e roughly estimated from the condition Dp(paras)~depRoa, with Dp calculated for the wpstream maenetic feld. which is about 5 times smaller than the downstream field.","The maximum particle momentum $p_{\mathrm{max}}$ reached in a process of diffusive shock acceleration can be roughly estimated from the condition $D_{B}(p_{\mathrm{max}})\sim +0.1u_{\mathrm{sh}}R_{\mathrm{sh}}$ with $D_{B}$ calculated for the upstream magnetic field, which is about $5$ times smaller than the downstream field." +" This gives au order of maenitiide estimate pruase/Z20004,7100?hans!FB.5— TeV. where the shock radius is Roy, pe. aud the interstellar eas umber «cusity 5 5"," This gives an order of magnitude estimate $p_{\mathrm{max}}c/Z\sim 20(u_{\mathrm{sh}}/10^3\ \mathrm{km} \ +\mathrm{s}^{-1})^{2}R_{\mathrm{sh}}\sqrt{n}$ TeV, where the shock radius is $R_{\mathrm{sh}}$ pc, and the interstellar gas number density $n$ ${}^{-3}$." + It cau be shown. sec e.g. Ptuskdu&Zirakashvili (2005).. that the transformation of supernova explosion euergy to cosmic rays becomes efficient frou the beginning of the Sedov stage of the shock evolution (ie. when the mass of supernova cjecta becomes equal to the mass of swept-1p eas) and COlLiuues later ou.," It can be shown, see e.g. \citet{Ptus05}, that the transformation of supernova explosion energy to cosmic rays becomes efficient from the beginning of the Sedov stage of the shock evolution (i.e. when the mass of supernova ejecta becomes equal to the mass of swept-up gas) and continues later on." + As a result. the characteristic kuee arises in the overall spectrum of particles accelerated by the evolving superuova renimnant.," As a result, the characteristic knee arises in the overall spectrum of particles accelerated by the evolving supernova remnant." +" The position of knee pi. cau be estimated fron the above equations for ps Where #4, aud A. are determined at the time when the Sedov stage beeius.", The position of knee $p_{\mathrm{knee}}$ can be estimated from the above equations for $p_{\mathrm{max}}$ where $u_{\mathrm{sh}}$ and $R_{\mathrm{sh}}$ are determined at the time when the Sedov stage begins. + It givesapproximately Tere £54 is the kinetic enerey of the supernova explosion iu uuits of 1073 ere aud Ma is the ass of supernova ejecta measured in solar masses., It givesapproximately Here $E_{51}$ is the kinetic energy of the supernova explosion in units of $10^{51}$ erg and $M_{\mathrm{ej}}$ is the mass of supernova ejecta measured in solar masses. + If the presupernova had a deuse star wind with velocity αμ aud the mass loss rate AL before the explosion. the shock may cuter the Sedov stage while propagating through the wind material with mass density pu=Ar(Liter).," If the presupernova had a dense star wind with velocity $u_{w}$ and the mass loss rate $\dot{M}$ before the explosion, the shock may enter the Sedov stage while propagating through the wind material with mass density $\rho _{w}=\dot{M}/(4\pi u_{w}r^{2})$." + Eq. (, Eq. ( +5) should be replaced in this case by the following equation: We have performed nunerical simulations of cosmic rav acceleration for [| types of superuova relmnauts (they constitute about 90 percents of all SIpCLHovae}.,5) should be replaced in this case by the following equation: We have performed numerical simulations of cosmic ray acceleration for $4$ types of supernova remnants (they constitute about $90$ percents of all supernovae). +" 1, Type Ia SNRs with the following parameters: kinetic enerev of explosion E=10?!ere. νήσου density of he surrounding iuterstellar eas η=0.1 cni3 and mass of ejecta AL, LAL..."," $1.$ Type Ia SNRs with the following parameters: kinetic energy of explosion $E={10}^{51}\mathrm{erg}$, number density of the surrounding interstellar gas $n=0.1$ ${}^{-3}$ , and mass of ejecta $M_{\mathrm{ej}}=1.4M_{\odot }$ ." + Also nuportaut for accurate calculations is the iudex k.cwlüch describes the power law density profile Pare* of the outer part of the star that frecly expands after supernova explosious: fo=7 for Type Ia supernova.," Also important for accurate calculations is the index $k$, which describes the power law density profile $\rho _{s}\propto r^{-k}$ of the outer part of the star that freely expands after supernova explosions; $k=7$ for Type Ia supernova." +" 2. Type HP SNRs with parameters £ = 10 ere; p201 em7. Alig8M. aud b=12. 3. Type Ib/e SNRs with E=LO""! ere exploding Vhito the low density bubble with density à»=0.01 em? formed by a progenitor star that starts off as an O stir. goes through a RSC (Red Super Ciüant) phase. aud cuds its life as a WoltRavet star. see c.g. Dwarkadas (2007)."," $2.$ Type IIP SNRs with parameters $E$ = ${10}^{51 }\mathrm{erg}$ , $n=0.1 $ ${\mathrm{cm}}^{-3}$, $M_{\mathrm{ej}}=8M_{\odot }$ , and $k=12.$ $3.$ Type Ib/c SNRs with $E={10}^{51}$ erg exploding into the low density bubble with density $n=0.01$ ${}^{-3}$ formed by a progenitor star that starts off as an O star, goes through a RSG (Red Super Giant) phase, and ends its life as a Wolf-Rayet star, see e.g. \citet{Dwar}. ." +". The ejecta mass is Ajλεν and fk= 7. I. Type Hb SNRs with E=3-10"" erg. 0= 7 aud Af= LAL..."," The ejecta mass is $M_{\mathrm{ej}}=2M_{\odot }$ and $k=7$ $4.$ Type IIb SNRs with $E=3\cdot {10}^{51}$ erg, $n=0.01$ ${}^{-3}$ and $M_{\mathrm{ej}}=1M_{\odot }$ ." + Defore euteriug the rarefied bubble. the blast wave goes through the dense wind emitted by the progenitor starduring its finalRSC stage of evolution.," Before entering the rarefied bubble, the blast wave goes through the dense wind emitted by the progenitor starduring its finalRSG stage of evolution." +" Weassume thatthe mass loss rate by the winel is AF10HM,Vr and the outer wind radius is 5 pc.", Weassume thatthe mass loss rate by the wind is $\dot{M}={10}^{-4}M_{\odot }/\mathrm{yr}$ and the outer wind radius is $5$ pc. +and attenuation of the lowest energy radiation. with 97; finally reaching about -220 to -340 mK at large distances.,"and attenuation of the lowest energy radiation, with $\delta T_b$ finally reaching about -220 to -340 mK at large distances." + The PWHM size of the fluctuations are about 20. 80. and 400 Mpe for black holes of mass 10°. 107. and 10? M... respectively.," The FWHM size of the fluctuations are about 20, 80, and 400 Mpc for black holes of mass $10^5$, $10^7$, and $10^9$ $M_\odot$, respectively." + How do the black hole densities and masses we assume here compare to those observed at z~6 and expected at higher redshifts?, How do the black hole densities and masses we assume here compare to those observed at $z\sim 6$ and expected at higher redshifts? + ?/— constructed the mass function of black holes in the range 10°M...Mpy<3«M. at Q2Min=6. finding it to be well-fitted by dn/dlnMpggy~OΜ.Οexpi-Mpu/M.). with o.=5.34Gpc andM.=2.2«10M...," \citet{willott/etal:2010} constructed the mass function of black holes in the range $10^8\ M_\odot < M_{\rm BH} < 3\times 10^9\ M_\odot$ at $z=6$ , finding it to be well-fitted by $dn/d{\rm ln}M_{\rm + BH}\simeq \phi_*(M_{\rm BH}/M_*)^{-1}\exp(-M_{\rm BH}/M_*)$ , with $\phi_*=5.34~{\rm Gpc}^{-3}$ and$M_*=2.2\times 10^9\ M_\odot$." + Integrating the black hole mass function. one finds Mii)~7«10° and 3«10!MGpe. for Mpy=Pen10°. and 10°M... respectively. somewhat larger than the black hole mass density we find which maximizes the 21-em power spectrum (333.2).," Integrating the black hole mass function, one finds $\rho_{\rm + BH}(>M_{\rm BH})\simeq 7\times 10^9$ and $3\times 10^{10}\ +M_\odot{\rm Gpc}^{-3}$, for $M_{\rm BH}=10^9$, and $10^8\ M_\odot$, respectively, somewhat larger than the black hole mass density we find which maximizes the 21-cm power spectrum 3.2)." +"Matching the abundance of black holes greater than a given mass to the dark matter halo mass function of ?.— at z26 (""abundancematching""=eg.My2). we obtain =2.3s107 and 4.7«107M. for =10° and 10°Mya,M... respectively. implying a value of Myu/My23.107 to 21071 over the same range."," Matching the abundance of black holes greater than a given mass to the dark matter halo mass function of \citet{warren/etal:2006} + at $z=6$ \citep[``abundance matching'' -- e.g.,][]{kravtsov/etal:2004}, we obtain $M_{\rm + halo}=2.3\times 10^{12}$ and $4.7\times 10^{12}\ M_\odot$ for $M_{\rm BH}=10^8$ and $10^9\ M_\odot$, respectively, implying a value of $M_{\rm BH}/M_{\rm halo}\simeq 4\times 10^{-5}$ to $2\times + 10^{-4}$ over the same range." + More detailed predictions would require. extrapolating the Mgy—Mpa relationship to lower masses and higher redshifts. or making highly uncertain assumptions about the formation mechanism of the high-redshift seeds and their aceretion history.," More detailed predictions would require extrapolating the $M_{\rm BH}-M_{\rm halo}$ relationship to lower masses and higher redshifts, or making highly uncertain assumptions about the formation mechanism of the high-redshift seeds and their accretion history." +" For example. the ratio Myy/Mpaty7107 we determine here by abundance matching at z26 and Mgy=105—10?M would be a significant underestimate in atomic cooling halos.. where black hole formation by direct collapse took place. in which it is possible that Mag/Mya, could approach the limiting value of O5/O,,—0.17."," For example, the ratio $M_{\rm BH}/M_{\rm halo}\simeq 10^{-4}$ we determine here by abundance matching at $z=6$ and $M_{\rm BH}=10^8-10^9\ +M_\odot$ would be a significant underestimate in atomic cooling halos where black hole formation by direct collapse took place, in which it is possible that $M_{\rm BH}/M_{\rm halo}$ could approach the limiting value of $\Omega_b/\Omega_m\simeq 0.17$." + Clearly much more work is required m understanding the high-redshift quasar population. and for this reason the constraints provided by either detection or non-detection of the signal we predict here would be very valuable.," Clearly much more work is required in understanding the high-redshift quasar population, and for this reason the constraints provided by either detection or non-detection of the signal we predict here would be very valuable." + In this section. we estimate the detectability of individual sources as well the statistical detection of their power spectrum.," In this section, we estimate the detectability of individual sources as well the statistical detection of their power spectrum." + In the case of individual objects. we focus on a novel approach. using single-dish filled aperture telescopes like andFAST?.. while for the power spectrum we will simply refer to existing sensitivity estimates for facilities such asFAR?..MWA?.. and SKA“.," In the case of individual objects, we focus on a novel approach, using single-dish filled aperture telescopes like and, while for the power spectrum we will simply refer to existing sensitivity estimates for facilities such as, and ." + In order to determine the necessary integration time. we convolve the profiles shown in Fig.," In order to determine the necessary integration time, we convolve the profiles shown in Fig." + | with a half-power beamwidth of 226. yt. where djis the effective dish diameter.," \ref{fig1} with a half-power beamwidth of 26' , where $d_{\rm dish}$is the effective dish diameter." + Converting angle on the sky to comoving distance. we obtain the comoving resolution. 70 t," Converting angle on the sky to comoving distance, we obtain the comoving resolution, 70 ." + Converting angle on the sky to comoving distance. we obtain the comoving resolution. 70 ta," Converting angle on the sky to comoving distance, we obtain the comoving resolution, 70 ." + Converting angle on the sky to comoving distance. we obtain the comoving resolution. 70 tan," Converting angle on the sky to comoving distance, we obtain the comoving resolution, 70 ." +"values of P have a more centrally-concdensecd structure and. hence. their elective steepness of the dillerential rotation is smaller for smaller value of E for a given set of C, and A.","values of $\Gamma$ have a more centrally-condensed structure and, hence, their effective steepness of the differential rotation is smaller for smaller value of $\Gamma$ for a given set of $C_a$ and $\hat A$." + In Figures S.9. we display the snapshots of the density contour curves in the equatorial plane at selected time steps for (D.€)=(2.0.3.0.7) and (5/3. 0.3. 0.8).," In Figures 8–9, we display the snapshots of the density contour curves in the equatorial plane at selected time steps for $(\Gamma, \hat A, C_a)=(2, 0.3, 0.7)$ and (5/3, 0.3, 0.8)." + The value of 3 is about 0.071 and 0.045. respectively.," The value of $\beta$ is about 0.071 and 0.045, respectively." + La both cases. the nonaxisvmmetrie perturbation initially provided. grows. changing the shape of the rotating stars to be ellipsoidal.," In both cases, the nonaxisymmetric perturbation initially provided grows, changing the shape of the rotating stars to be ellipsoidal." + Llowever. the perturbation does not grow to the highly nonlinear stage and. hence. neither a spiral arm nor a large bar is formed in contrast to the outcome in the simulations with a high value of 320.2.," However, the perturbation does not grow to the highly nonlinear stage and, hence, neither a spiral arm nor a large bar is formed in contrast to the outcome in the simulations with a high value of $\beta \agt 0.2$." + Instead. the slightly deformed ellipsoid is the final outcome.," Instead, the slightly deformed ellipsoid is the final outcome." + Since the deformed ellipsoid is almost stationary. 7 and η. oscillate quasi-periodicallv in the late phase of the simulations.," Since the deformed ellipsoid is almost stationary, $\eta_+$ and $\eta_{\times}$ oscillate quasi-periodically in the late phase of the simulations." + This result is qualitatively the same as for the starsofthe j-constant-like angular velocity. profile (Shibataetal.2002)., This result is qualitatively the same as for the starsofthe $j$ -constant-like angular velocity profile \cite{SKE}. +". In Figures 10. and 11.. we show the frequeney f, of the oscillation of the ellipsoidal star in units of CA16,yh as a function of initial values of 3 for various sets of D and 2A."," In Figures \ref{FIG10} and \ref{FIG11}, we show the frequency $f_r$ of the oscillation of the ellipsoidal star in units of $(M/R_{\rm eq}^3)^{1/2}$ as a function of initial values of $\beta$ for various sets of $\Gamma$ and $\hat A$." + The value of f; is determined by the Fourier transform of + in the time domain., The value of $f_r$ is determined by the Fourier transform of $\eta_{+}$ in the time domain. + We note that the rotational period. of the ellipsoid is 2/f... and that the frequeney of gravitational waves is f.," We note that the rotational period of the ellipsoid is $2 /f_r$, and that the frequency of gravitational waves is $f_r$ ." +" Ht is interesting to notethat for P=2 and 5/3. a noncdimensional. quantity. f,....—fi(ee,3eu/M) js Lip...in a narrow range between 0.2 and 0.35 irrespective of A. 3 and angular velocity. profile."," It is interesting to notethat for $\Gamma=2$ and 5/3, a nondimensional quantity $\bar f_r \equiv f_r (R_{\rm eq}^3/M)^{1/2}$ is in a narrow range between $0.2$ and $0.35$ irrespective of $\hat A$, $\beta$ and angular velocity profile." + For P—7/5. f; is between 0.4 and 0.55. which is larger than the values for b=2 and 5/3.," For $\Gamma=7/5$, $\bar f_r$ is between $0.4$ and $0.55$, which is larger than the values for $\Gamma=2$ and 5/3." + However. it is still in a narrow range.," However, it is still in a narrow range." +" The fact that the value of f, depends weakly on ο suggests that the excited. mode may be the f modo.", The fact that the value of $\bar f_r$ depends weakly on $\beta$ suggests that the excited mode may be the $f$ mode. + As discussed in our previous paper (Shibataetal.2002).. the dvnamically unstable rotating stars. which are deformed to nonaxisvmmetrie ellipsoidal objects. are likely to be sources of quasi-periodic gravitational waves.," As discussed in our previous paper \cite{SKE}, the dynamically unstable rotating stars, which are deformed to nonaxisymmetric ellipsoidal objects, are likely to be sources of quasi-periodic gravitational waves." + In Figures 12- LL. we show the gravitational waveforms of the | mode along the c-axis (f) and the luminosity GE) as a Function of time for (L.A)=(2.0.3). (5/3.0.1) and (7/5. 0.1).," In Figures \ref{FIG12}- \ref{FIG14}, we show the gravitational waveforms of the $+$ mode along the $z$ -axis $h_{+}$ ) and the luminosity $\dot E$ ) as a function of time for $(\Gamma, \hat A)=(2, 0.3)$, (5/3,0.1) and (7/5, 0.1)." +" For all the models picked up here. €,=0.705."," For all the models picked up here, $C_a=0.705$." + Lhe value of 3 is &0.071. 0.046. ancl 0.047. respectively.," The value of $\beta$ is $\approx 0.071$, 0.046, and 0.047, respectively." + We note that the wavelorms for the moce are essentially the same as those for the | mode except for the phase dillerence hy z/4., We note that the waveforms for the $\times$ mode are essentially the same as those for the $+$ mode except for the phase difference by$\pi/4$ . + Here. we calculate eravitational waves in the quadrupole formula and define the waveforms by and the luminosity by," Here, we calculate gravitational waves in the quadrupole formula \cite{MTW} and define the waveforms by h_+ , and the luminosity by E ," +Both GCs (Cotéetal.2001:Larsen2002:Evansοἱ2003:CotéBeasleyetal.2004:Peng.Ford&Freeman2004c.amongothers) and PNe 1993:IIuietal.1995:ArnaboldiPeng.Ford&Freeman2004b.amongothers) can be used to estimate the total dvnanmiceal mass of their host galaxies.,"Both GCs \citep[][among + others]{cote01,larsen02,evans03,cote03,beasley04,pff04II} and PNe \citep[][among others]{ciardullo93,hui95,arnaboldi98,peng04} + can be used to estimate the total dynamical mass of their host galaxies." + A variety. of tools are in use imeluding derived mass models. the virial mass estimator (Baheall&Tremaine 1981).. (he projected mass estimator (Ileisler.Tremaine.&Balicall1985).. and (he tracer mass estimator (Evansetal.2003).," A variety of tools are in use including derived mass models, the virial mass estimator \citep{bahcall81}, the projected mass estimator \citep{heisler85}, and the tracer mass estimator \citep{evans03}." +". NGC 5128 does not have a large N-rav halo (detectedbyKraltοἱal.2003:O'Sullivan.Forbes.&Ponman2001.thelatterreportingameasurementoflogL,=40.10ergs !). such as is evidentin other giant ellipticals such as M87 (Cotéetal.2001). or NGC! 4649 (Briceesetal.2006)."," NGC 5128 does not have a large X-ray halo \citep[detected by][the latter +reporting a measurement of log $L_x = 40.10$ erg s$^{-1}$ , such as is evidentin other giant ellipticals such as M87 \citep{cote01} or NGC 4649 \citep{bridges06}." +. Thus it is difficult to model the dark matter profile of NGC 5128 withpriori constraints., Thus it is difficult to model the dark matter profile of NGC 5128 with constraints. + Without such a mass model. we turn to the (racer mass estimator for the dvnamical mass determination.," Without such a mass model, we turn to the tracer mass estimator for the dynamical mass determination." + The tracer mass estimator has the distinct. advantage over the virial and projected mass estimators that the (racer population does not have to follow the dark matter densitv in the galaxy - an extremely useful feature for stellar subsvstems such as GC's and PNe that might. in principle. have significantly different radial distributions (see Evansοἱal.(2003). for extensive discussion).," The tracer mass estimator has the distinct advantage over the virial and projected mass estimators that the tracer population does not have to follow the dark matter density in the galaxy - an extremely useful feature for stellar subsystems such as GCs and PNe that might, in principle, have significantly different radial distributions (see \cite{evans03} for extensive discussion)." + Below. we determine the mass of NGC 5128 using the (tracer populations of GCs and PNe (our mass estimates do not include stellar kinematics in the inner regions).," Below, we determine the mass of NGC 5128 using the tracer populations of GCs and PNe (our mass estimates do not include stellar kinematics in the inner regions)." +" The mass contributed by the random internal motion of the galaxy. (pressure-supported mass) is determined from the (racer mass estimator as where .N is the number of objects in the sample and vy, is the radial velocity of the tracer object removed.", The mass contributed by the random internal motion of the galaxy (pressure-supported mass) is determined from the tracer mass estimator as where $N$ is the number of objects in the sample and $v_{f_i}$ is the radial velocity of the tracer object . +" For an isotropic population of tracer objects. asstuned in this study. the value of C is where rj, and r,,; are the three-dimensional radii corresponding to the(wo-climensional projected radii of the innermost. A,. and outermost. A, tracers in the sample."," For an isotropic population of tracer objects, assumed in this study, the value of $C$ is where $r_{in}$ and $r_{out}$ are the three-dimensional radii corresponding to thetwo-dimensional projected radii of the innermost, $R_{in}$ , and outermost, $R_{out}$ , tracers in the sample." + The, The +Carbon monoxide (CO) is a fundamental tracer of interstellar molecular gas.,Carbon monoxide (CO) is a fundamental tracer of interstellar molecular gas. + However. since only the lowest 3 rotational transitions are relatively easily accessible with. ground-based telescopes. the diagnosticUB use of higher rotationalMN levels is poorly developed.," However, since only the lowest 3 rotational transitions are relatively easily accessible with ground-based telescopes, the diagnostic use of higher rotational levels is poorly developed." + This hiatusLl in. our knowledge is becoming. acute now that hish-/ CO. observations. ofun high-z galaxies. are Ιeom.E ‘ble, This hiatus in our knowledge is becoming acute now that $J$ CO observations of $z$ galaxies are becoming possible. + With this in posesmind. we have embarked on the Comprehensive (U)LIRG Emission Survey (HerCULES). an open time Key Project on the ESAHerschel Space (Pilbratt et al..," With this in mind, we have embarked on the Comprehensive (U)LIRG Emission Survey (HerCULES), an open time Key Project on the ESA Space (Pilbratt et al.," + this issue)., this issue). +" The HerCULES project will establish a comprehensive inventory of the gas cooling lines in a flux-Iimited sample of 29 (Ultra)uminous Infrared Galaxies or (U)LIRGs. using high spectral resolution observations with. the Fourier.. Transform"" Spectrograph. (FTS). of: the SPIRE instrument (Griffin et al."," The HerCULES project will establish a comprehensive inventory of the gas cooling lines in a flux-limited sample of 29 (Ultra)luminous Infrared Galaxies or (U)LIRGs, using high spectral resolution observations with the Fourier Transform Spectrograph (FTS) of the SPIRE instrument (Griffin et al.," + this issue). combined with observations-- of: the . [Cu] 158=ojum line. and the [Or] 634 and 146jim lines with PACS (Poglitsch et al..," this issue), combined with observations of the $\CII$ ] $158\mum$ line and the $\OI$ ] 63 and $146\mum$ lines with PACS (Poglitsch et al.," + this issue)., this issue). + Key, Key +for the evolution of the electron distribution in a two-temperature plasma wilh a given proton temperature.,for the evolution of the electron distribution in a two-temperature plasma with a given proton temperature. + In each zone. the Fokker-Planck equation is implicitly aud independently solved.," In each zone, the Fokker-Planck equation is implicitly and independently solved." + The Fokker-Planck technique takes into account heating/cooling by Moller inleractions. Compton scattering. svnchrotron/evclotron processes.," The Fokker-Planck technique takes into account heating/cooling by ller interactions, Compton scattering, synchrotron/cyclotron processes." + Initiallv. (he emission emanating from the IDRs was represented by blackbody spectra inserted at the upper and lower boundaries.," Initially, the emission emanating from the HDRs was represented by blackbody spectra inserted at the upper and lower boundaries." + Photons were also produced by svuchrotron/cvelotron processes in (he LDRs., Photons were also produced by synchrotron/cyclotron processes in the LDRs. + Photons were subjected to Compton scattering ancl reflection off the IIDRs., Photons were subjected to Compton scattering and reflection off the HDRs. + Escaping photons at the outer boundaries were added to an event file for later spectral ex(raction: this involves placing each escaping photon in a particular energy. bin., Escaping photons at the outer boundaries were added to an event file for later spectral extraction; this involves placing each escaping photon in a particular energy bin. + The proton temperature in the LDR was calculated from equation 7.. aud (he electron temperature was calculated. numerically within the MC/EP simulation 2005).. which was run until the electron temperature reached. a stable equilibrium.," The proton temperature in the LDR was calculated from equation \ref{kTp}, and the electron temperature was calculated numerically within the MC/FP simulation \citep[see][]{nm98,bjl03,bl01,fb05}, which was run until the electron temperature reached a stable equilibrium." + The AICEP simulation was run to extract the photon Πιν and spectrum incident on the boundaries between (he IIDIs and the LDR., The MC/FP simulation was run to extract the photon flux and spectrum incident on the boundaries between the HDRs and the LDR. + To ealeulate the expected spectral features from [orescence line emission. radiative recombination. aud Compton reflection. (he impinging spectrum was used as an input into the latest version of NSTAR. (IxXallman&Bantista 2001).," To calculate the expected spectral features from fluorescence line emission, radiative recombination, and Compton reflection, the impinging spectrum was used as an input into the latest version of XSTAR \citep{kb01}." +". Solar abundances of the most profuse astrophysical elements (IL. He. C. Ca, δν ο. Ne. Mg. Si. S. Ar. Ca and Fe) were assumed in the ΓΗ. based on Grevesse.Noels&Sauval.(1996)."," Solar abundances of the most profuse astrophysical elements (H, He, C, Ca, N, O, Ne, Mg, Si, S, Ar, Ca and Fe) were assumed in the HDR, based on \citet{gns96}." +. XSTAHR was run in constant pressure mode: the pressure was caleulated [rom the specilied density ancl the ideal eas law., XSTAR was run in constant pressure mode; the pressure was calculated from the specified density and the ideal gas law. + The main parameter in determining (he reflection spectrum5 shape and intensity is (he ionization parameter: Note that NSTAR uses the fIux ealeulated between | and 1000 Ry (13.6 eV to 13.6 keV)., The main parameter in determining the reflection spectrum's shape and intensity is the ionization parameter: Note that XSTAR uses the flux calculated between 1 and 1000 Ry (13.6 eV to 13.6 keV). +" In order to circiumvent NSTARs limitation to densities n,<1-1l0""cm 7. the impinging flux was re-scaled to keep the ionization £ at (he value corresponding to the physical situation."," In order to circumvent XSTAR's limitation to densities $n_e \lesssim +1 \cdot 10^{17}$ $^{-3}$, the impinging flux was re-scaled to keep the ionization $\xi$ at the value corresponding to the physical situation." + The inverse flux scaling was applied to the NSTAR. output spectrum., The inverse flux scaling was applied to the XSTAR output spectrum. +" Keeping © constant insures (hat (he scaling of a flux dominated by recombination features. Fxn, is properly recovered."," Keeping $\xi$ constant insures that the scaling of a flux dominated by recombination features, $F \propto n_e$ is properly recovered." + Testing of NSTAR with various densities but the same £ seems shows that this is appropriate for the energy range of interest., Testing of XSTAR with various densities but the same $\xi$ seems shows that this is appropriate for the energy range of interest. + The resulting reflection spectrum was then added to the intrinsic blackbody from the HDR as boundary sources in a second run of the AICEP code for (he final evaluation of the emanating X-ray spectrum., The resulting reflection spectrum was then added to the intrinsic blackbody from the HDR as boundary sources in a second run of the MC/FP code for the final evaluation of the emanating X-ray spectrum. + For an example of a simulation. with spectra at different radii. see Fig. 2..," For an example of a simulation, with spectra at different radii, see Fig. \ref{specradii}. ." +In (his section. we study the interaction of solar-like wave packets with the magnetic cvlinder.,"In this section, we study the interaction of solar-like wave packets with the magnetic cylinder." + The aim is to compare seismic travel-time shifts computed in the Born approximation and from (he exact solution., The aim is to compare seismic travel-time shifts computed in the Born approximation and from the exact solution. + For the sake of simplicity. we fix Αα.=0.," For the sake of simplicity, we fix $k_z=0$." +" Using Cartesian coordinates r—(xr.y) lor the horizontal plane. we choose an incoming Gaussian wavepackel propagating in the +a: horizontal direction: where vw,/27=3 mlz is (he dominant frequency of solar oscillations and o/20=1 mlz is (he dispersion."," Using Cartesian coordinates $\br=(x,y)$ for the horizontal plane, we choose an incoming Gaussian wavepacket propagating in the $+\bx$ horizontal direction: where $\omega_*/2\pi = 3$ mHz is the dominant frequency of solar oscillations and $\sigma/2\pi = 1$ mHz is the dispersion." +" Since we chose &.=0, we have f(w)=w/e."," Since we chose $k_z=0$, we have $k(\omega) = \omega/c$." + The wavepacket is centered on (he magnetic tube al time /=0., The wavepacket is centered on the magnetic tube at time $t=0$. + The scattered wave packet can be caleulatecl. exactly or in ihe Born approximation. from (he previous sections.," The scattered wave packet can be calculated, exactly or in the Born approximation, from the previous sections." + The three panels in Figure 4. show snapshots of the incoming ancl scattered pressure fields at time /=8.9 min., The three panels in Figure \ref{fig.frames} show snapshots of the incoming and scattered pressure fields at time $t=8.9$ min. + The parameters of the steady. background at infinity are ces and e=LL kan/s. which are roughly the conditions at a depth of 250 km below the solar photosphere.," The parameters of the steady background at infinity are $\rho_0=5\times10^{-7}$ cgs and $c=11$ km/s, which are roughly the conditions at a depth of $250$ km below the solar photosphere." + The incident wavepacket is shown in Figure faa. Figure 4bb shows the scattered wave which results from a 1-kG magnetic fhix tube with radius 2=0.2 Mm., The incident wavepacket is shown in Figure \ref{fig.frames}a a. Figure \ref{fig.frames}b b shows the scattered wave which results from a $1$ -kG magnetic flux tube with radius $R=0.2$ Mm. + The smaller (ube produces relatively more back scattering than the large tube in comparison with the forward scattering., The smaller tube produces relatively more back scattering than the large tube in comparison with the forward scattering. + The amplitude of the scattered wave is roughly three orders ol magnitude smaller than the incoming wave., The amplitude of the scattered wave is roughly three orders of magnitude smaller than the incoming wave. + Figure tee shows the scattered. wave lor a larger (ube radius of 2 Mm: the scattering is dominantly in the forward direction and has an amplitude only an order of magnitude smaller than (he incident wave., Figure \ref{fig.frames}c c shows the scattered wave for a larger tube radius of $2$ Mm; the scattering is dominantly in the forward direction and has an amplitude only an order of magnitude smaller than the incident wave. + We now deline the travel-lime shifts (hat are caused by the magnetic cvlinder., We now define the travel-time shifts that are caused by the magnetic cylinder. + By definition. the travel-time shift at location 7 is the time d/(r) which minimizes the function where f is the [ull wavefield that includes both the incident wavepacket and the scattered wave packet caused by (he magnetic field.," By definition, the travel-time shift at location $\br$ is the time $\delta t(\br)$ which minimizes the function where $p'$ is the full wavefield that includes both the incident wavepacket and the scattered wave packet caused by the magnetic field." + The travel-time shilis can be computed in (his wav for either the exact solution or the Born-approximation., The travel-time shifts can be computed in this way for either the exact solution or the Born-approximation. + In addition. it is also interesting (to compare wilh the rav approximation as given bv equation (14) from Ixosovichev&Duvall(1997).," In addition, it is also interesting to compare with the ray approximation as given by equation (14) from \citet{Kosovichev1997}." +. In our case. where κ.B=0 and the magnetic field strength is constant inside (he tube. the rax approximation becomes where L(r) is the path length through the tube along the rav which goes from coordinates (—2x.y) lor= (ry).," In our case, where $\bk\cdot\overline{\bB}=0$ and the magnetic field strength is constant inside the tube, the ray approximation becomes $\delta t(\br) = -L(\br) a^2/ (2 c^3) $ where $L(\br)$ is the path length through the tube along the ray which goes from coordinates $(-\infty,y)$ to $\br=(x,y)$ ." +considers the ratio of two standard. deviations rather than ol variances it does not deseribe a normally clistributec variable and it is not properly centered. with the mean expected value being zero: hence it is not à good. statistic and de Deigo (2010) concludes that the nominal critical value for the presence of variability (1.6... 2.576) is usually loo conservative.,"considers the ratio of two standard deviations rather than of variances it does not describe a normally distributed variable and it is not properly centered with the mean expected value being zero; hence it is not a good statistic and de Deigo (2010) concludes that the nominal critical value for the presence of variability (i.e., 2.576) is usually too conservative." + Another statistical method that can be used to quantify the presence of microvariability is the £-test. which has been recently been shown to be a more powerful and reliable tool for detecting microvariability (cle Diego 2010).," Another statistical method that can be used to quantify the presence of microvariability is the $F$ -test, which has been recently been shown to be a more powerful and reliable tool for detecting microvariability (de Diego 2010)." + The £ value is computed. as where αςsl). Varig52) and Ver(sl) are the variances of the quasar-starl. quasar-star2 and. starl-star2 DLCs. respectively.," The $F$ value is computed as where $Var(q-s1)$, $Var(q-s2)$ and $Var(s1-s2)$ are the variances of the quasar-star1, quasar-star2 and star1-star2 DLCs, respectively." +" These £ values are then compared individually with the critical £ value. ""mbee. where à is the significance level set for the test. and vos and vss are the degrees of freedom. of the quasar-star and: star-star DLCs. respectively."," These $F$ values are then compared individually with the critical $F$ value, $F^{(\alpha)}_{\nu_{QS}\nu_{SS}}$, where $\alpha$ is the significance level set for the test, and $\nu_{QS}$ and $\nu_{SS}$ are the degrees of freedom of the quasar-star and star-star DLCs, respectively." + The smaller the a value. the more improbable that the result. is produced. by chance.," The smaller the $\alpha$ value, the more improbable that the result is produced by chance." + Thus values of a= 0.0001. 0.001 or 0.01 (the Last assumed in our analysis) roughly correspond to 5o. 30 or a 2.60 detections. respectively.," Thus values of $\alpha=$ 0.0001, 0.001 or 0.01 (the last assumed in our analysis) roughly correspond to $5\sigma$, $\sigma$ or a $\sigma$ detections, respectively." + Lf f° is larger than the critical value. the null hypothesis (ic. no variability) is discarded.," If $F$ is larger than the critical value, the null hypothesis (i.e., no variability) is discarded." +" Here we also note that having two b-values. £4, and £2. allows us two choices in deciding the presence of variability: (i) to take the average of απ £5. and compare it with critical £ value: (ii) to compare £j and £> separately with the critical f value."," Here we also note that having two F-values, $F_1$ and $F_2$, allows us two choices in deciding the presence of variability: (i) to take the average of $F_1$ and $F_2$, and compare it with critical $F$ value; (ii) to compare $F_1$ and $F_2$ separately with the critical $F$ value." + We prefer the latter option. as it serves as further validation for the F-test: for if one DLC indicates variability and one doesn't. these mixed signals bring into question the reality of the putative variability.," We prefer the latter option, as it serves as further validation for the F-test; for if one DLC indicates variability and one doesn't, these mixed signals bring into question the reality of the putative variability." + Although the £-test is certainly better than the C'-test. it should be noted that for the £-test to give a truly reliable result the error due to random noise in the quasarstar and star-star DLCs should be of a similar order. apart from any additional scatter in the quasar-star. DLC due το possible QSO variability.," Although the $F$ -test is certainly better than the $C$ -test, it should be noted that for the $F$ -test to give a truly reliable result the error due to random noise in the quasar–star and star-star DLCs should be of a similar order, apart from any additional scatter in the quasar-star DLC due to possible QSO variability." + For instance. if both comparison stars are either brighter (fainter) than the monitored. quasar. then a false alarm detection (non-detection) is possible due to the very small (Large) photon noise variance of the star-star DLC compared to the quasar-star. DLCs.," For instance, if both comparison stars are either brighter (fainter) than the monitored quasar, then a false alarm detection (non-detection) is possible due to the very small (large) photon noise variance of the star-star DLC compared to the quasar-star DLCs." + This in practice can happen. as sometimes it is dillicult to fulfill the desiderata of having non-variable comparison stars within the quasar CCD image frame that are very similar in magnitude to the In our sample we have tried to choose non-variable comparison stars in proximity to the magnitude of the uasar (see sect. 4.1)).," This in practice can happen, as sometimes it is difficult to fulfill the desiderata of having non-variable comparison stars within the quasar CCD image frame that are very similar in magnitude to the In our sample we have tried to choose non-variable comparison stars in proximity to the magnitude of the quasar (see Sect. \ref{subs:stars}) )," + but it was not. possible to fulfill lis requirement for al quasars., but it was not possible to fulfill this requirement for all quasars. + So sometimes in performing re {οί we may have to compare the variance of star- DLCs involving stars substantially brighter han the uasar. where scatter due to photon noise is very small. with de Holster quasar-star DLC.," So sometimes in performing the $F$ -test we may have to compare the variance of star-star DLCs involving stars substantially brighter than the quasar, where scatter due to photon noise is very small, with the noisier quasar-star DLC." + In such cases. the standard statistics of the F-test do seem to give too much weight ο even very nominal fluctuations in a quasar-star DLC.," In such cases, the standard statistics of the $F$ -test do seem to give too much weight to even very nominal fluctuations in a quasar-star DLC." + A sensible way to deal with this real problem is to scale the star-star variance by a factor. s. which is proportional to 16 ratio of the noise in the equasar-star and star-star DLCs.," A sensible way to deal with this real problem is to scale the star-star variance by a factor, $\kappa$, which is proportional to the ratio of the noise in the quasar-star and star-star DLCs." +" One ogical choice along these lines is to consider the ratio of the average squared error in the quasar-star and star-star DLCs Le. where στ,sqs) and σὲ,Για9) are. respectively. the errors on individual points of the quasar-star anc"," One logical choice along these lines is to consider the ratio of the average squared error in the quasar-star and star-star DLCs i.e., where $\sigma^2_{i,err}(q-s)$ and $\sigma^2_{i,err}(s1-s2)$ are, respectively, the errors on individual points of the quasar-star and" +" One ogical choice along these lines is to consider the ratio of the average squared error in the quasar-star and star-star DLCs Le. where στ,sqs) and σὲ,Για9) are. respectively. the errors on individual points of the quasar-star ancl"," One logical choice along these lines is to consider the ratio of the average squared error in the quasar-star and star-star DLCs i.e., where $\sigma^2_{i,err}(q-s)$ and $\sigma^2_{i,err}(s1-s2)$ are, respectively, the errors on individual points of the quasar-star and" +HN (produced through the CNO evele in tle oxevious U-buruing phase) is transformed almost totally in tthrough TN Ga ποια. Ίνα ,"$^{14}$ N (produced through the CNO cycle in the previous H-burning phase) is transformed almost totally in through $^{14}$ $\alpha,\gamma$ $^{18}$ $\beta^+$ $^{18}$ $\alpha,\gamma$ $^{22}$ Ne." +Παring products (like n2 and ?2N60)) are expelled by he stellar winds of iuassivo stars during their WC oliase., He-burning products (like $^{12}$ C and ) are expelled by the stellar winds of massive stars during their WC phase. + The observed. GCR natio is obtained No assunüns dilution of WC material with matter of standard composition., The observed GCR ratio is obtained by assuming dilution of WC material with matter of standard composition. +" Subsequent studies put the aforenieutionued idea ona quantitative basis. with the use of detailed models of the evolution and uncleosvutlesis of assive., dass losing stars (Alacder 1983. Prautzos 1981. AMever 1985. Prautzos et al."," Subsequent studies put the aforementionned idea on a quantitative basis, with the use of detailed models of the evolution and nucleosynthesis of massive, mass losing stars (Maeder 1983, Prantzos 1984, Meyer 1985, Prantzos et al." + 1987)., 1987). + Iu those studies. the acceleration site of CCT was considered as decoupled from the uncleosvuthesis site. and unrelated to he fraction of acdimixtured WC material.," In those studies, the acceleration site of GCR was considered as decoupled from the nucleosynthesis site, and unrelated to the fraction of admixtured WC material." + Iledon and Linecuteltcr (2003) evaluated quantitativelv he yratio within a superbubble. created by the collective action of stellar winds aud SN shockwaves.," Higdon and Lingenfelter (2003) evaluated quantitatively the ratio within a superbubble, created by the collective action of stellar winds and SN shockwaves." + They adopted stellar wind viclds for aaud ffromu tle models of Schaller ct al. (, They adopted stellar wind yields for and from the models of Schaller et al. ( +1992) aud SN vields from the models ft Woosley aud Weaver (1995).,1992) and SN yields from the models of Woosley and Weaver (1995). + They found that the rratio iu the superbubble decreases with time (since ffrom the winds dominates the evolutio- of aat carly times) aud tha its time average valueis compatible with the GOR source inuferved. from observations., They found that the ratio in the superbubble decreases with time (since from the winds dominates the evolution of at early times) and that its time average value is compatible with the GCR source inferred from observations. + Iu a subsequent paper. Lingeufelter and IHiüedou (2007) recognised tha he Schaller et al. (," In a subsequent paper, Lingenfelter and Higdon (2007) recognised that the Schaller et al. (" +1992) vields of were lughly and. consequently. i new detailed calculations of the expected GCR isotopic ratio are called for...7. but they did rot attempt such a re-evaluation.,"1992) yields of were highly and, consequently, ""... new detailed calculations of the expected GCR isotopic ratio are called for..."", but they did not attempt such a re-evaluation." + Du the meautime. Diuus et al. (," In the meantime, Binns et al. (" +2005). usine updated wind vields of massive stars with rotation (from the Ceneva group. see Sec.,"2005), using updated wind yields of massive stars with rotation (from the Geneva group, see Sec." + 2.2). found good agreeineut between the observed atio zd an adinixture of ~20% material frou WR stars with material of standard composition.," 2.2), found good agreement between the observed ratio and an admixture of $\sim$ material from WR stars with material of standard composition." + According to Binus et al. (, According to Binns et al. ( +2008). since WR stars are evolutionary products of OB stars. such an agreenienut osuegeests that OB associations within superbubbles are the likely source ofat least a substantial fraction of CCR”,"2008), since WR stars are evolutionary products of OB stars, such an agreement ""...suggests that OB associations within superbubbles are the likely source of at least a substantial fraction of GCR""." + Tlowewer. theoretical studies in the past 10 voars απο based unostly oon the paracligin oof GCR being accelerated in SN remmauts. not iu superbubbles. e.g. Ptuskin&Zirakashvili(2005).Schureetal.(2010).Ellison&Bykov(2011) and references therein.," Howewer, theoretical studies in the past 10 years are based mostly on the paradigm of GCR being accelerated in SN remnants, not in superbubbles, e.g. \cite{Ptuskin05, Berezhko06,Berezhko09,Ptuskin10,Caprioli10,Schure10,Ellison11} and references therein." + The kinetic energv of the bulk motion of the forward shock of the ον explosion is converted. to GCR cherey through diffusive shock acceleration., The kinetic energy of the bulk motion of the forward shock of the SN explosion is converted to GCR energy through diffusive shock acceleration. + The Xxocess 1s hiehllv ron-linear aud involves the dynamical reaction of both the accelerated particles and of the magnetic field on the svstem., The process is highly non-linear and involves the dynamical reaction of both the accelerated particles and of the magnetic field on the system. + Those studies usually take iuto account the fact that the SN explosion often occurs within the cavity excavated in the iuterstellar πιοπα (ISM) by the wind of the massive star prior to the explosion (Dier1uaunctal.(2001))): however. the structure of the ciremustellar cuviroument iu that case is quite complex aud simplified: models are used for its description," Those studies usually take into account the fact that the SN explosion often occurs within the cavity excavated in the interstellar medium (ISM) by the wind of the massive star prior to the explosion \cite{Biermann01}) ); however, the structure of the circumstellar environment in that case is quite complex and simplified models are used for its description." + Although Capriolietal.(2011) considered the couposition of GCR (ILIIe.. CNO. MeSiAL. Fe) resulting roni such an acceleration site. none of those studies considered the ratio.," Although \cite{Caprioli11b} considered the composition of GCR (H,He, CNO, MgSiAl, Fe) resulting from such an acceleration site, none of those studies considered the ratio." + Iu this work we study the rratio of GCR accecrated bv the forward shocks of SN explosious. as they run through the presuperuova winds of massive stars and through the iuterstellur medi.," In this work we study the ratio of GCR accelerated by the forward shocks of SN explosions, as they run through the presupernova winds of massive stars and through the interstellar medium." + We cousider the whole mass spectrum of massive stars (from —10 to 120 AL..)). includiug stars with either small or large παν» losses prior to their ," We consider the whole mass spectrum of massive stars (from $\sim$ 10 to 120 ), including stars with either small or large mass losses prior to their explosions." +We consider stellar properties (1nasses of winds.pedoad ejecta. vields etc.)," We consider stellar properties (masses of winds, ejecta, yields etc.)" + from recent mocels with quass loss Or vitrout rotation (from Ihrschi et al., from recent models with mass loss and or without rotation (from Hirschi et al. + 2005 and Limonei aud Chieft 2006 respectively). the former having ]lueger eeuhauceiieuts in. their: winds.," 2005 and Limongi and Chieffi 2006, respectively), the former having larger enhancements in their winds." + We adopt a simplified prescription (suggested oei Ptuskin aud. Zirakashvili 2005 and reforiuulated oei Caprio 2011) to describe the structure of the cireunstella: medi at the nue of the explosion aud we consider that CCR start being accelerated iu the Sedov-Tavlor (ST) phase of he SN romnaut (see e.g. Ptuskin et al., We adopt a simplified prescription (suggested in Ptuskin and Zirakashvili 2005 and reformulated in Caprioli 2011) to describe the structure of the circumstellar medium at the time of the explosion and we consider that GCR start being accelerated in the Sedov-Taylor (ST) phase of the SN remnant (see e.g. Ptuskin et al. + 2010)., 2010). + By requiring the resultiug IME averaged iratio to equal the observed one Romar Veen 340.3 . we are able to coustrain the forward shock velocity to values 21900 lin/s for rotating stars (and to 2100 kin/s for uou rotating ones). Le. we find that GCR are accelerated during the early ST phase. lasting for a few 10° vr.," By requiring the resulting IMF averaged ratio to equal the observed one $R_{Obs}$ $_{GCR}$ $_{\odot}$ $\pm$ 0.3 we are able to constrain the forward shock velocity to values $>$ 1900 km/s for rotating stars (and to $>$ 2400 km/s for non rotating ones), i.e. we find that GCR are accelerated during the early ST phase, lasting for a few $^ 3$ yr." + Asstuninge that of the SN kinetic eneorev Is converted to GCR. we find that dung the acceleration oerod a few particles out of a nülliou eucouutered bv he forward shock are accelerated.," Assuming that of the SN kinetic energy is converted to GCR, we find that during the acceleration period a few particles out of a million encountered by the forward shock are accelerated." + Finally. we reassess he superbubble paracdigin for the origin of GCR. by evaluating consistently the rratio with the aforementioned stellar viclds.," Finally, we reassess the superbubble paradigm for the origin of GCR, by evaluating consistently the ratio with the aforementioned stellar yields." + We fud that it can not ) as high as observed. uuless some extremely favorable assunrptious are nade (onlv the early period of the superbubble lifetime considered. uo eas left over from he formation of the OB association).," We find that it can not be as high as observed, unless some extremely favorable assumptions are made (only the early period of the superbubble lifetime considered, no gas left over from the formation of the OB association)." + We conclude that superbubbles cannot be at the origin of the bulk of CCR., We conclude that superbubbles cannot be at the origin of the bulk of GCR. + The plan of the paper is as follows., The plan of the paper is as follows. + In Sec., In Sec. + 2 we xeseut the general xf-up of our model: the adopted stellar models (Sec.," 2 we present the general ""set-up"" of our model: the adopted stellar models (Sec." + 2.2) aud their wind vields (Sec., 2.2) and their wind yields (Sec. +" 2.3), the description of the ciretuustellar euvirouumieut (Sec."," 2.3), the description of the circumstellar environment (Sec." + 2.1) and the evolution of the forward shock in the ST phase (Sec., 2.4) and the evolution of the forward shock in the ST phase (Sec. + 2.5)., 2.5). + In Sec., In Sec. + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏↸," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏↸⊳," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏↸⊳↕," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏↸⊳↕↸," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏↸⊳↕↸∖," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏↸⊳↕↸∖↕," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏↸⊳↕↸∖↕∐," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏↸⊳↕↸∖↕∐⊳," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏↸⊳↕↸∖↕∐⊳⋅," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏↸⊳↕↸∖↕∐⊳⋅↖," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏↸⊳↕↸∖↕∐⊳⋅↖↽," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏↸⊳↕↸∖↕∐⊳⋅↖↽∪," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏↸⊳��↸∖↕∐⊳⋅↖↽∪↕," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏↸⊳↕↸∖↕∐⊳⋅↖↽∪↕↕," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏↸⊳↕↸∖↕∐⊳⋅↖↽∪↕↕∐," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" + 3 we preseut our results for the (time-dependent) composition of the accelerated particles. the μπιτς nuposed on the shock velocity bv . ⋅⋅ ↑∐↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽↸∖≺↧−−⋀∖↸∖−∪⋀∖↸∖↥⋅↥⋅⋜↧⊓∪⋜⋯≼↧↑↕∐∖↸∖↕−∏↸⊳↕↸∖↕∐⊳⋅↖↽∪↕↕∐∖," 3 we present our results for the (time-dependent) composition of the accelerated particles, the limits imposed on the shock velocity by the observed ratio and the efficiency of the" +The skv distribution of our Ser detections (Figure 19 aud top panel of Figure 13)) shows that the clusters ancl background features span the observed aud modelled width of the stream.,The sky distribution of our Sgr detections (Figure \ref{f:2masscomp} and top panel of Figure \ref{f:sgrsim}) ) shows that the clusters and background features span the observed and modelled width of the stream. + While we will address (he distance measures in rels:dlaambda.. the simplepresence of Ser debris is a useful constraint on Sers disruption.," While we will address the distance measures in \\ref{s:dlambda}, the simple of Sgr debris is a useful constraint on Sgr's disruption." + The detection of Ser over such a large range in 2. is consistent. with the breadth of the stream depicted in MÓO3 as well as the relatively hieh Ser core mass used in the LM10a model., The detection of Sgr over such a large range in $B_{\odot}$ is consistent with the breadth of the stream depicted in M03 as well as the relatively high Sgr core mass used in the LM10a model. + A smaller Ser mass would result in narrower streams that would be inconsistent with the spatial distribution shown in the figures., A smaller Sgr mass would result in narrower streams that would be inconsistent with the spatial distribution shown in the figures. + For example. reducing the Ser mass by a factor of (wo would leave the NGC! 6652 and NGC 6637 Ser leatures well outside (he tidal stream (while also giving a stream velocity dispersion inconsistent with observations see Figure 4 ol LM10a).," For example, reducing the Sgr mass by a factor of two would leave the NGC 6652 and NGC 6637 Sgr features well outside the tidal stream (while also giving a stream velocity dispersion inconsistent with observations – see Figure 4 of LM10a)." + Expanding the range of Ser pencil beams. especially across the face of the leading arm. would provide tighter constraints on the (hree-climensional orientation of Ser ancl the disruption models.," Expanding the range of Sgr pencil beams, especially across the face of the leading arm, would provide tighter constraints on the three-dimensional orientation of Sgr and the disruption models." + A munber of globular clusters are within the field depicted in Figure 13 (open squares in upper and could potentially provide this additional constraint., A number of globular clusters are within the field depicted in Figure \ref{f:sgrsim} (open squares in upper and could potentially provide this additional constraint. + Of the eleven clusters (hat could provide additional information. three have not been observed with IST/WEPC2 or HST/ACS.," Of the eleven clusters that could provide additional information, three have not been observed with HST/WFPC2 or HST/ACS." + The remaining eight appear in Piotto et al. (, The remaining eight appear in Piotto et al. ( +2002). but the IIST/WEPCO? data are not deep or precise enough to detect the [aint Ser stream.,"2002), but the HST/WFPC2 data are not deep or precise enough to detect the faint Sgr stream." + NGC 6522. NGC 6528. NGC 6544. NGC 6553 and NGC 6558 have been observed with ACS but the data are nol as deep as that of the ACS Treasury Program aad lack the photometric precision to delineate the [aint Ser sequence.," NGC 6522, NGC 6528, NGC 6544, NGC 6553 and NGC 6558 have been observed with ACS but the data are not as deep as that of the ACS Treasury Program and lack the photometric precision to delineate the faint Sgr sequence." + Published CMDs of NGC 6553 (Feltizing Gilmore 2000: Zoccali οἱ al..," Published CMDs of NGC 6553 (Feltzing Gilmore 2000; Zoccali et al.," + 2001: Bealieu et al., 2001; Bealieu et al. + 2001) and NGC 6528 (Brown et al., 2001) and NGC 6528 (Brown et al. + 2005) do not clearly show the stream., 2005) do not clearly show the stream. + Our deep precise IST imaging is (he first to clearly discern these [unl sequences., Our deep precise HST imaging is the first to clearly discern these faint sequences. + Future deep observations of (he above-named clusters or any field within (he Ser stream are recommended., Future deep observations of the above-named clusters – or any field within the Sgr stream – are recommended. +Although the clusters marked on Figure 13. ave further away [rom the ser core and would therefore have lower Ser debris densities (han even NGC 6652 the mere presence or absence of the Ser stream in (hese fields would help constrain the models of the disrupting core by providing hard limits on the breadth of the stream in D... This is,Although the clusters marked on Figure \ref{f:sgrsim} are further away from the Sgr core – and would therefore have lower Sgr debris densities than even NGC 6652 – the mere presence or absence of the Sgr stream in these fields would help constrain the models of the disrupting core by providing hard limits on the breadth of the stream in $B_{\odot}$ This is +Ultra-high cnerey cosmic ravs (ULECRs) may become a complementary probe of some astrophysical objects in addition to observations in multiple wavelengths.,Ultra-high energy cosmic rays (UHECRs) may become a complementary probe of some astrophysical objects in addition to observations in multiple wavelengths. + In fact. the detection of these particles with enough statisties would represent the awake of the development of multi-messenger astrophysics.," In fact, the detection of these particles with enough statistics would represent the awake of the development of multi-messenger astrophysics." + “Phe Pierre Auger observatory in. \lalaretice. Argentina (sce( 7)) has devoted a large ellort in the construction of an unprecedented array of water Ceerenkov tanks covering an area of 73.000 kn. together with four IIuorescence telescopes which allow for increased accuracy in energy measurements.," The Pierre Auger observatory in Malargüee, Argentina (see \citealt{2004NIMPA.523...50A}) ) has devoted a large effort in the construction of an unprecedented array of water Čeerenkov tanks covering an area of $\sim$ 3,000 $^2$, together with four fluorescence telescopes which allow for increased accuracy in energy measurements." + This effort has proven to be fruitful as the first relevant results were obtained. even before the completion of the entire experiment array., This effort has proven to be fruitful as the first relevant results were obtained even before the completion of the entire experiment array. + In. particular. the unprecedented. statistics on the detection of ultra-high energy cosmic ravs above LOEeV=lOlMelo1 with arrival directions measured with an accuracy better than 1 has allowed to search for possible astrophysical sources of these particles with higher reliability than previous experiments (e.g. 7)).," In particular, the unprecedented statistics on the detection of ultra-high energy cosmic rays above $10^{19}eV\simeq 1J$ with arrival directions measured with an accuracy better than $1^{\circ}$ has allowed to search for possible astrophysical sources of these particles with higher reliability than previous experiments (e.g. \citealt{2004APh....21..359F}) )." + ὃν the end of 2007. the Pierre Auger Collaboration concluded that the arrival directions of VLECRs above 55IeV correlate with the positions of nearby active galactic nuclei: CXGN). or other objects which trace. in the same way as AGNs. he Large Scale Structure of the Universe (?.. 7)).," By the end of 2007, the Pierre Auger Collaboration concluded that the arrival directions of UHECRs above 55EeV correlate with the positions of nearby active galactic nuclei (AGN), or other objects which trace, in the same way as AGNs, the Large Scale Structure of the Universe \citealt{2007Sci...318..938T}, \citealt{2008APh....29..188T}) )." + Statistics of these cosmic rav events has doubled since then (from 27 to 58 events). ancl vet the correlation with these objects has not strengthened as compared to previous estimations (2)..," Statistics of these cosmic ray events has doubled since then (from 27 to 58 events), and yet the correlation with these objects has not strengthened as compared to previous estimations \citep{2009arXiv0906.2347T}." + This supports the fact that this scenario is not the only one which can reproduce the observed data. although increasing statistics of ULLECTU events may be able," This supports the fact that this scenario is not the only one which can reproduce the observed data, although increasing statistics of UHECR events may be able" +that the ionizing star is now initially located towards one edge of the cloud. and the self-gravity of the gas is neglected.,"that the ionizing star is now initially located towards one edge of the cloud, and the self-gravity of the gas is neglected." + As a consequence of the intrinsic asymmetry in the initial conditions. the bursts out of the cloud on one side. and the remainder of the cloud on the other side 1s accelerated away by the rocket mechanism (Oort Spitzer 1955). and then ionized. (," As a consequence of the intrinsic asymmetry in the initial conditions, the bursts out of the cloud on one side, and the remainder of the cloud on the other side is accelerated away by the rocket mechanism (Oort Spitzer 1955), and then ionized. (" +iv) In Section 4.4. we consider a much lower-mass. uniform-density. self-gravitating cloud which is overrun by anregion.,"iv) In Section \ref{sec.rdi} we consider a much lower-mass, uniform-density, self-gravitating cloud which is overrun by an." + The ionization front propagating into the cloud is preceded by a shock front. which compresses the cloud.but does not trigger collapse.," The ionization front propagating into the cloud is preceded by a shock front, which compresses the cloud,but does not trigger collapse." +" In all simulations. the SPH particles are initially positioned randomly. and then settled to produce a uniform-density ""glass""; the temperature of the ionized gas is set to 7;=107K (except in the boundary layer. where the temperature is smoothed to values between these two extremes. as described in Section 3.6); the recombination coefficient into. excited states only is taken to be à,=2.7x10em?s!: and the volume occupied by the tonizing star is neglected."," In all simulations, the SPH particles are initially positioned randomly, and then settled to produce a uniform-density “glass”; the temperature of the ionized gas is set to $T_{\rm i}=10^4\,{\rm K}$ (except in the boundary layer, where the temperature is smoothed to values between these two extremes, as described in Section \ref{tempsmoothing}) ); the recombination coefficient into excited states only is taken to be $\alpha_{_{\rm B}}=2.7\times 10^{-13}\,{\rm cm}^3\,{\rm s}^{-1}$; and the volume occupied by the ionizing star is neglected." + The parameters of all simulations are listed in Table ].., The parameters of all simulations are listed in Table \ref{table.param}. +" In this table M is the mass of the cloud. R is its radius. 7), is the temperature of the neutral medium. X and Y are the fractions of hydrogen and helium respectively. jjj and µι are the mean molecular weights of the neutral medium and the ionized medium respectively. A, is the photon rate emission of the source. D is the distance of the source from the centre of the cloud. Ας is the initial Strómgren radius and N,,, is the number of SPH particles used in each simulation."," In this table $M$ is the mass of the cloud, $R$ is its radius, $T_{\rm n}$ is the temperature of the neutral medium, $X$ and $Y$ are the fractions of hydrogen and helium respectively, $\mu_{\rm n}$ and $\mu_{\rm i}$ are the mean molecular weights of the neutral medium and the ionized medium respectively, $\dot{\cal N}_{_{\rm LyC}}$ is the photon rate emission of the source, $D$ is the distance of the source from the centre of the cloud, $R_{_{\rm St}}$ is the initial mgren radius and ${\cal N}_{_{\rm SPH}}$ is the number of SPH particles used in each simulation." +" In this application. we create a uniform-density spherical cloud having mass M=1000M... initial radius R=|pe. and hence initial density py=1.6xI0"" gem™."," In this application, we create a uniform-density spherical cloud having mass $M\,=\,1000\,{\rm M_{\odot}}$, initial radius $R\,=\,1\,{\rm pc}$, and hence initial density $\rho_{\rm n}=1.6\times 10^{-20}\,{\rm g}\,{\rm cm}^{-3}$ ." +" An ionizing source is placed at the centre of the cloud. and emits ionizing photons at a constant rate N,,=10757."," An ionizing source is placed at the centre of the cloud, and emits ionizing photons at a constant rate $\dot{\cal N}_{_{\rm LyC}}\,=\,10^{49}\,{\rm s}^{-1}$." + Using Eqn. (2)).," Using Eqn. \ref{eq.stradius}) )," +" the initial Strómgren radius is R,=0.189pe."," the initial mgren radius is $R_{_{\rm St}}\,=\,0.189\,{\rm pc}$." +" The neutral gas is assumed to be at 7,=IOK."," The neutral gas is assumed to be at $T_{\rm n}=10\,{\rm K}$." + There are no gravitational forces., There are no gravitational forces. + In order to establish that our code is converged. we evolve this configuration using different numbers of SPH particles: Noy=3x10.6x109.105.and2x109.," In order to establish that our code is converged, we evolve this configuration using different numbers of SPH particles: ${\cal N}_{_{\rm SPH}}=3\times10^5,\;6\times10^5,\;10^6,\;{\rm and}\;2\times10^6$." + We terminate the simulations when the ionization front reaches the edge of the cloud., We terminate the simulations when the ionization front reaches the edge of the cloud. + In Fig., In Fig. +" 10. we plot the average radius of the ionization front. R,.. against time for all four simulations."," \ref{fig.ifall} we plot the average radius of the ionization front, $R_{_{\rm IF}}$, against time for all four simulations." +" We see that the curves converge forN,,,Siz10°.", We see that the curves converge for ${\cal N}_{_{\rm SPH}}\ga 10^6$. + In Fig., In Fig. +" 11. we plot the radius of the ionization front. R,,. and the radius of the shock front. R,.. against time. for the simulatio performed with N,,,=2x10° SPH particles."," \ref{fig.ifsf} we plot the radius of the ionization front, $R_{_{\rm IF}}$, and the radius of the shock front, $R_{_{\rm SF}}$, against time, for the simulation performed with ${\cal N}_{_{\rm SPH}}=2\times10^6$ SPH particles." +" We determine the radius of the shock front by finding the most distant particle from the source which has radial outward velocity v,>0.kms""! and density p. l.l1py."," We determine the radius of the shock front by finding the most distant particle from the source which has radial outward velocity $v_{_{\rm r}}>0.1\,{\rm km}\,{\rm s^{-1}}$ and density $\rho>1.1\rho_{\rm n}$ ." + The second condition is necessary because particles near the edge of the cloud move outwards due to the thermal pressure gradient there. long before they are overrun by the shock front.," The second condition is necessary because particles near the edge of the cloud move outwards due to the thermal pressure gradient there, long before they are overrun by the shock front." + The factor Γ.Γ is to accommodate numerical noise in the SPH estimate of the density of a particle., The factor $1.1$ is to accommodate numerical noise in the SPH estimate of the density of a particle. + In general. we find that the Spitzer solution (Eqn. 4))," In general, we find that the Spitzer solution (Eqn. \ref{eq.spitzersolution}) )" + predicts the radius of the ionization front well. whereas the semi-analytic solution (Eqn. 10))," predicts the radius of the ionization front well, whereas the semi-analytic solution (Eqn. \ref{semi_ode}) )" + predicts the position of the shock front., predicts the position of the shock front. + The advantage of the semi-analytic solution ts that it can also be used to treat situations in which the self-gravity of the gas is Important. as we show in the next application.," The advantage of the semi-analytic solution is that it can also be used to treat situations in which the self-gravity of the gas is important, as we show in the next application." +" In this application. we simulate a much larger. uniform-density spherical cloud. having mass M=1.5«10°M... initial radius R= |4.6pc.and hence initial densityp,=7.63x107-7gem."," In this application, we simulate a much larger, uniform-density spherical cloud, having mass $M\,=\,1.5\times 10^5\,{\rm M_{\odot}}$, initial radius $R\,=\,14.6\,{\rm pc}$, and hence initial density $\rho_{\rm n}=7.63\times10^{-22}\,{\rm g}\,{\rm cm}^{-3}$." + An ionizing source is placed at the centre of the cloud. and emits ionizing photons at a constant rate Αι=10?sl.," An ionizing source is placed at the centre of the cloud, and emits ionizing photons at a constant rate $\dot{\cal N}_{_{\rm LyC}}\,=\,10^{49}\,{\rm s}^{-1}$." + Using Eqn. (2)).," Using Eqn. \ref{eq.stradius}) )," + the initial Strémgren radius is Ro=1.43pe.," the initial mgren radius is $R_{_{\rm St}}\,=\,1.43\,{\rm pc}$." + The neutral gas is assumed to be at 7)=10K.," The neutral gas is assumed to be at $T_{\rm n}=10\,{\rm K}$." + We use 10’ SPH particles. and evolve the system for 4.5Myr.," We use $10^7$ SPH particles, and evolve the system for $4.5\,{\rm Myr}$." + In this simulation self-gravity is taken into account. but with the following two modifications.," In this simulation self-gravity is taken into account, but with the following two modifications." + First. once the radius of the shock front has been determined (as described in refsec.hydro)). we neglect the gravitational acceleration of allthe SPH particles outside this radius.," First, once the radius of the shock front has been determined (as described in \\ref{sec.hydro}) ), we neglect the gravitational acceleration of allthe SPH particles outside this radius." + This ts to prevent infallof the undisturbed neutral gas., This is to prevent infallof the undisturbed neutral gas. + Otherwise the outer parts of the cloud are already falling quite rapidly towards the centre by, Otherwise the outer parts of the cloud are already falling quite rapidly towards the centre by +systems.,systems. + Determining the velocity structure of the ionized and molecular gas Components can set stringent limits on the importance of galaxv-galaxy or ICM/racio-jet. interactions in these dense cooling How core regions., Determining the velocity structure of the ionized and molecular gas components can set stringent limits on the importance of galaxy-galaxy or ICM/radio-jet interactions in these dense cooling flow core regions. +" The recent detection of CO in many of the tarects in this survey by Edge (2001) allows us to compare the amount of shot’ (1000 IX) to ""cool (30 Ix). molecular hivelrogen.", The recent detection of CO in many of the targets in this survey by Edge (2001) allows us to compare the amount of `hot' $>$ 1000 K) to `cool' $\sim$ 30 K) molecular hydrogen. + Figure 7 shows the luminosity of the 1-0 S(1) line (or its cquivalent) against molecular hydrogen mass using cata from this paper. Cvenus-A from Wilman et al. (," Figure 7 shows the luminosity of the 1-0 S(1) line (or its equivalent) against molecular hydrogen mass using data from this paper, Cygnus-A from Wilman et al. (" +2000) ancl A478 from Jalle et al. (,2000) and A478 from Jaffe et al. ( +2001).,2001). + The luminosity is determined for the slit Hux only so the overall normalisation of the correlation may vary for the more extended emission., The luminosity is determined for the slit flux only so the overall normalisation of the correlation may vary for the more extended emission. + There is an apparent correlation similar to that found in Edee (2001) for the luminosity of La., There is an apparent correlation similar to that found in Edge (2001) for the luminosity of $\alpha$. + To confirm the validity of these luminosity-luminosity correlations we calculated the Spearmans rho statistic (as recommenced bv Feigelson Berg 1983) using the ASURY package for both the 1-0 S(1) and La luminosities correlated: against the molecular hydrogen mass estimated. from CO., To confirm the validity of these luminosity-luminosity correlations we calculated the Spearmans rho statistic (as recommended by Feigelson Berg 1983) using the ASURV package for both the 1-0 S(1) and $\alpha$ luminosities correlated against the molecular hydrogen mass estimated from CO. + The correlation is significant for CO vs. 1-0 S(1) (p=0.59. implving a probability of correlation of z-99.5 per cent).," The correlation is significant for CO vs. 1-0 S(1) $\rho$ =0.59, implying a probability of correlation of $>99.5$ per cent)." + The result for CO vs. Ho is even more significant (p—0.63. so Pc99.7 per cent).," The result for CO vs. $\alpha$ is even more significant $\rho$ =0.63, so $>99.7$ per cent)." + This result. improves if Cyvenus-A is removed from the analvsis (90.72)., This result improves if Cygnus-A is removed from the analysis $\rho$ =0.72). + As pointed out. by Feieclson Bere (1983). flux-Hux correlations are not. as reliable at determining whether an underlying correlation is present particularly for samples where most detections are close to the detection limit (as is the case in this stuels).," As pointed out by Feigelson Berg (1983), flux-flux correlations are not as reliable at determining whether an underlying correlation is present particularly for samples where most detections are close to the detection limit (as is the case in this study)." + We did. perform Dux-lux. correlations and. ect significant correlations for both optical ancl infrared. line correlations but only i£ Perseus is included., We did perform flux-flux correlations and get significant correlations for both optical and infrared line correlations but only if Perseus is included. + The correlations presented in Figure 7 and Figure 9 of Edge (2001) are significant. and are not an artifact., The correlations presented in Figure 7 and Figure 9 of Edge (2001) are significant and are not an artifact. + ]t is interesting to note the relatively low Iuxes of 1-0 S(1) and/or 5(3) in the most radio luminous objects., It is interesting to note the relatively low fluxes of 1-0 S(1) and/or S(3) in the most radio luminous objects. + The comparison with IIa shows the objects with powerful racio sources which have firm CO upper limits (c.g. Cvenus-A aud RAJO747-19) lie much further from the correlation between, The comparison with $\alpha$ shows the objects with powerful radio sources which have firm CO upper limits (e.g. Cygnus-A and RXJ0747-19) lie much further from the correlation between + AAOSAS. O584 and ÀA6716. 6731 Ad).,"$\lambda\lambda$ 6548, 6584 and $\lambda\lambda$ 6716, 6731 )." + The spectral resolution instrumental profile) is ~2 FWHM (~90 km +) and the accuracy in the determination of the position of the line centroid is ~0.2 (~10 km © for the strong observed emission lines)., The spectral resolution instrumental profile) is $\sim2$ FWHM $\sim90$ km $^{-1}$ ) and the accuracy in the determination of the position of the line centroid is $\sim0.2$ $\sim10$ km $^{-1}$ for the strong observed emission lines). + Four overlapped pointings were observed to obtain a mosaic of ~ 1/5 to cover the entire emission from HH 110 (see refpointings))., Four overlapped pointings were observed to obtain a mosaic of $\sim$ $\times$ $\farcm$ 5 to cover the entire emission from HH 110 (see \\ref{pointings}) ). + Table | lists the centre positions of each pointing. the exposure time and the HH 110 knots included in each pointing. following the nomenclature of Reipurth.Raga&Heath-cote (1996).," Table 1 lists the centre positions of each pointing, the exposure time and the HH 110 knots included in each pointing, following the nomenclature of \citet{Rei96}." +. Data reduction was performed using a preliminary version of theR3D software (Sánchez2006).. in combination with and the packages (Sánchez2004).," Data reduction was performed using a preliminary version of the software \citep{Sa06}, in combination with and the packages \citep{Sa04}." +. The reduction consists of the standard steps for tibre-based integral field spectroscopy., The reduction consists of the standard steps for fibre-based integral field spectroscopy. + A master bias frame was created by averaging all the bias frames observed during the night and subtracted from the science frames., A master bias frame was created by averaging all the bias frames observed during the night and subtracted from the science frames. + The location of the spectra on the CCD was determined using a continuum-illuminated exposure taken before the science exposures., The location of the spectra on the CCD was determined using a continuum-illuminated exposure taken before the science exposures. + Each spectrum was extracted from the science frames by co-adding the flux within an aperture of 5 pixels along the cross- axis for each pixel in the dispersion axis. and stored in a row-stacked-spectrum (RSS) tile (Sanchez2004).," Each spectrum was extracted from the science frames by co-adding the flux within an aperture of 5 pixels along the cross-dispersion axis for each pixel in the dispersion axis, and stored in a row-stacked-spectrum (RSS) file \citep{Sa04}." +. The wavelength calibration was performed by using the sky emission lines found in the observed wavelength range., The wavelength calibration was performed by using the sky emission lines found in the observed wavelength range. + The accuracy achieved for the wavelength calibration was better than ~0.1 (75 kms +)., The accuracy achieved for the wavelength calibration was better than $\sim0.1$ $\sim5$ km $^{-1}$ ). + Furthermore. the large scale diffuse emission from this Orion region was subtracted from our data by using the signal acquired through the 36 additional sky fibres.," Furthermore, the large scale diffuse emission from this Orion region was subtracted from our data by using the signal acquired through the 36 additional sky fibres." + Observations of a standard star were used to perform a relative flux calibration., Observations of a standard star were used to perform a relative flux calibration. + The four IFU pointings were merged into a mosaic using our own routines. developed for this task (see citealpSanO7 and references therein).," The four IFU pointings were merged into a mosaic using our own routines, developed for this task (see \\citealp{San07} and references therein)." + The procedure is based on he comparison and sealing of the relative intensity in a certain wavelength range for spatially coincident spectra., The procedure is based on the comparison and scaling of the relative intensity in a certain wavelength range for spatially coincident spectra. + The pointing orecision is better than 0.2 aresec. according to the pointing accuracy of the telescope using the Guiding System of PMAS in relative offset mode (used for these observations).," The pointing precision is better than 0.2 arcsec, according to the pointing accuracy of the telescope using the Guiding System of PMAS in relative offset mode (used for these observations)." + The overlap between adjacent pointings is ~ the field of view (more han 30 individual spectra)., The overlap between adjacent pointings is $\sim$ the field of view (more than 30 individual spectra). + The merging process was checked to uve little effect on the accuracy of the wavelength calibration of he final datacube making use of the sky lines aa common reference system) present in the spectra., The merging process was checked to have little effect on the accuracy of the wavelength calibration of the final datacube making use of the sky lines a common reference system) present in the spectra. + À final datacube containing the 2D spatial plus the spectral information of HH 110 was then created from the 3D data by using tasks to interpolate the data spatially until reaching a tinal grid of 2 aresec of spatial sampling and with a spectral sampling of 0.3, A final datacube containing the 2D spatial plus the spectral information of HH 110 was then created from the 3D data by using tasks to interpolate the data spatially until reaching a final grid of 2 arcsec of spatial sampling and with a spectral sampling of 0.3. + Further manipulation of this datacube. devoted to obtain integrated emission line maps. channel maps and position—velocity maps. were made using several common-users tasks ofSTARLINK.IRAF and astronomical packages and (García-Lorenzo.Acosta-Pulido&Megias-Fernández 2002).. a specitic software to analyse 3D data.," Further manipulation of this datacube, devoted to obtain integrated emission line maps, channel maps and position–velocity maps, were made using several common-users tasks of, and astronomical packages and \citep{Ga02}, a specific software to analyse 3D data." + Some morphological differences have been found in previous narrow-band images of HH 110 between the Hat[N aand eemissions., Some morphological differences have been found in previous narrow-band images of HH 110 between the $\alpha$ and emissions. + In an attempt to explore these differences. we obtained IFS-derived narrow-band images for each of the emission lines included in the observed spectral range(Ha. À 6584 aand À 6716.6731 Ay).," In an attempt to explore these differences, we obtained IFS-derived narrow-band images for each of the emission lines included in the observed spectral range$\alpha$, $\lambda$ 6584 and $\lambda$ 6716,6731 )." + For each position. the flux of the line was obtained by integrating the signal over the wavelength range of the line (A 6558.3-6565.0 ffor Ha: A 6579.6-6585.8 ffor11]:: A 6712.8-6718.1 ffor 6716 and A 6727.2-6733.1 ffor A67313. and subtracting a continuum. obtained from the adjacent wavelength range free of line emission.," For each position, the flux of the line was obtained by integrating the signal over the wavelength range of the line $\lambda$ 6558.3–6565.9 for $\alpha$; $\lambda$ 6579.6–6585.8 for; $\lambda$ 6712.8–6718.1 for $\lambda$ 6716 and $\lambda$ 6727.2–6733.1 for $\lambda$ 6731), and subtracting a continuum, obtained from the adjacent wavelength range free of line emission." + The narrow-band maps of HH 110 obtained from the IFS data refflux)) are in good agreement with those obtained for this jet through ground-based. narrow-band images by different authors (see citealpRei96:: Lópezetal. 2005)).," The narrow-band maps of HH 110 obtained from the IFS data \\ref{flux}) ) are in good agreement with those obtained for this jet through ground-based, narrow-band images by different authors (see \\citealp{Rei96}; \citealp{Lop05}) )." + However. since the IFS data allow us to properly isolate the Ha line emission from the lines. we obtained the first known image of HH 110 in the eemission.," However, since the IFS data allow us to properly isolate the $\alpha$ line emission from the lines, we obtained the first known image of HH 110 in the emission." + In this sense. the TFS maps are better suited for comparing the jet morphology in the Ha and eemissions. since the Ha emission is not affected by the contamination from lines.," In this sense, the IFS maps are better suited for comparing the jet morphology in the $\alpha$ and emissions, since the $\alpha$ emission is not affected by the contamination from lines." + Most of the HH 110 knots were detected in all the emission lines. although the brightness varies among different lines. being a signature of the excitation conditions. as we will discuss later.," Most of the HH 110 knots were detected in all the emission lines, although the brightness varies among different lines, being a signature of the excitation conditions, as we will discuss later." + There are a few emission features whose brightness in the aand llines should be very weak relative to the Ha brightness and were barely detected or not detected at all in the aand llines. namely: 6) the knot K. appearing quite isolated towards the western outflow edge. but outside the lower-brightness emission surrounding the knots. and (ii) the extended features towards the east of knots A to C. labeled X and Y. These faint Ha features were first detected in the ground-based. narrow-band image of Reipurth&Olberg (1991)..," There are a few emission features whose brightness in the and lines should be very weak relative to the $\alpha$ brightness and were barely detected or not detected at all in the and lines, namely: (i) the knot K, appearing quite isolated towards the western outflow edge, but outside the lower-brightness emission surrounding the knots, and (ii) the extended features towards the east of knots A to C, labeled X and Y. These faint $\alpha$ features were first detected in the ground-based, narrow-band image of \cite{Rei91}. ." + Our new IFS data indicate the X and Y features to be a “true” emission in the Ha line. having neither significant contributions from the extended nearby continuum (that," Our new IFS data indicate the X and Y features to be a ”true” emission in the $\alpha$ line, having neither significant contributions from the extended nearby continuum (that" +mentioned in? is added in quadrature. our prediction is well matched with HARPS M dwarls observation in the best case scenario.,"mentioned in \citet{Bonfils2007} is added in quadrature, our prediction is well matched with HARPS M dwarfs observation in the best case scenario." + ?. reported 0.6Lia-s | RMS errors for a planet system of a KOV star (i.e.. HD 60830). which is consistent with our prediction of 0.65 ms1.," \citet{Lovis2006} reported 0.64 $\rm{m}\cdot\rm{s}^{-1}$ RMS errors for a planet system of a K0V star (i.e., HD 69830), which is consistent with our prediction of 0.65 $\rm{m}\cdot\rm{s}^{-1}$." + It is plottedin the bin with Tey between 5000 Is aud 0000 Ix. because reported Tey of S385 El. For CG type stars. ?. reported 0.91 ms.+ RMS error for HD 47186 b aud €. a planetary system around a (25V star.," It is plottedin the bin with $T_{\rm{eff}}$ between 5000 K and 6000 K because reported $T_{\rm{eff}}$ of 5385 K. For G type stars, \citet{Bouchy2009} reported 0.91 $\rm{m}\cdot\rm{s}^{-1}$ RMS error for HD 47186 b and c, a planetary system around a G5V star." + In. comparison. we predict a total RV uncertainty of 1.1: mis.|.," In comparison, we predict a total RV uncertainty of 1.1 $\rm{m}\cdot\rm{s}^{-1}$." + The overestimation of RV ueasurement uncertainty is possibly due to an overestitnation of stellar noise or an increasing S/N yecause Of multiple measurements ii real observation., The overestimation of RV measurement uncertainty is possibly due to an overestimation of stellar noise or an increasing S/N because of multiple measurements in real observation. + We predict a total RV measurement uncertainty of 0.62. 0.65 and 1.1 ms.+ for spectral type 15V. INSV aud CV considering stellar spectral quality. RV calibration and stellar noise.," We predict a total RV measurement uncertainty of 0.62, 0.65 and 1.1 $\rm{m}\cdot\rm{s}^{-1}$ for spectral type M5V, K5V and G5V considering stellar spectral quality, RV calibration and stellar noise." + According o the calculations in 82.L. RV uncertainty due to stellar noise is 0.52. 0.55 and 1.05 m-s+ for he above three types of stars. accounting for70.356... and of total RV measurement uncertainty.," According to the calculations in \ref{sec:StellarNoise}, RV uncertainty due to stellar noise is 0.52, 0.55 and 1.05 $\rm{m}\cdot\rm{s}^{-1}$ for the above three types of stars, accounting for, and of total RV measurement uncertainty." + Based on comparisous of our predietious aud observation. we therefore conclude tliat stellar noise is one major contributor in error budget of precision Doppler measurement.," Based on comparisons of our predictions and observation, we therefore conclude that stellar noise is one major contributor in error budget of precision Doppler measurement." + M dwarls should be the primary targets in search of Earth-like planets in the HZ., M dwarfs should be the primary targets in search of Earth-like planets in the HZ. + Uulike CC and Ix stars. the RV signal of Earth-like planets in the HZ is not overwhelmed by stellar noise for M dwarls in the inost optimistic case.," Unlike G and K stars, the RV signal of Earth-like planets in the HZ is not overwhelmed by stellar noise for M dwarfs in the most optimistic case." + We provide a methocl of practically estimating the photou-Iimited RV precision based ou the spectral quality factor. stellar rotation. RV calibration uncertainty. stellar noise aud telluric liue contaiuination.," We provide a method of practically estimating the photon-limited RV precision based on the spectral quality factor, stellar rotation, RV calibration uncertainty, stellar noise and telluric line contamination." + The methodology described and the results presented in this paper can be use for design and optimization of planned and ongoing precision Doppler plauet surveys., The methodology described and the results presented in this paper can be used for design and optimization of planned and ongoing precision Doppler planet surveys. + For pure consideration of stellar spectral quality without artificial rotationally broadening the absorptio line profile. the optimal baud for RV planet search is B band for a wide range of spectral types from Ix to A. while it is Ror fy baud for mid-late type M clwarls.," For pure consideration of stellar spectral quality without artificial rotationally broadening the absorption line profile, the optimal band for RV planet search is $B$ band for a wide range of spectral types from K to A, while it is $R$ or $K$ band for mid-late type M dwarfs." + Nevertheless. the above conclusio remains unchanged after considering typical stellar rotation of each spectral type.," Nevertheless, the above conclusion remains unchanged after considering typical stellar rotation of each spectral type." + However. F anc A stars become tusuitable for precision RV measurements because of typically fast stellar rotatio," However, F and A stars become unsuitable for precision RV measurements because of typically fast stellar rotation." + We coulirm the findiug in ? that the NIR Doppler measurements gain advantage for mid-late AM cdwarls., We confirm the finding in \citet{Reiners2010} that the NIR Doppler measurements gain advantage for mid-late M dwarfs. + However. insteacl of findiug Y baud as the optimal baud. cousideriug stellar spectrum quality aud telluric masking. we fiud that both Y aud A bauds give the highest RV precisiou among V. Y. J aud A bands.," However, instead of finding $Y$ band as the optimal band considering stellar spectrum quality and telluric masking, we find that both $Y$ and $H$ bands give the highest RV precision among $V$, $Y$, $J$ and $H$ bands." + Iu a comparison to ?.. we find fy band is the optimal baud for precisiou Doppler measturement in-— a telluric-free case and A baud is optimal in a telluriccmasking case. while they fouud Y baud gives the highest RV precision iu both cases.," In a comparison to \citet{Rodler2011}, we find $K$ band is the optimal band for precision Doppler measurement in a telluric-free case and $H$ band is optimal in a telluric-masking case, while they found $Y$ band gives the highest RV precision in both cases." + Fundameutal photou-limitecd RV precision for evolved stars has been discussed by 2.. which is valuable for ongoing RV planet search arouud retired stars discussed in ?..," Fundamental photon-limited RV precision for evolved stars has been discussed by \citet{Jiang2011}, which is valuable for ongoing RV planet search around retired stars discussed in \citet{Johnson2007}. ." + We also cousider the uncertainties brought by current available RV calibration sources at different spectral resolutions (Fig. 2))., We also consider the uncertainties brought by current available RV calibration sources at different spectral resolutions (Fig. \ref{fig:Un_Cal_Res}) ). + Sub m-s! calibration precision can be reached for each, Sub $\rm{m}\cdot\rm{s}^{-1}$ calibration precision can be reached for each + , +to Mikolajewska et al (1995)) aud a low metal abundance. may play a role in reducing shifts between the resonance aud intercombination lines.,"to ajewska et al \cite{Mik95}) ) and a low metal abundance, may play a role in reducing shifts between the resonance and intercombination lines." + We shall here just cuiphasize oue of the results forAlDus., We shall here just emphasize one of the results for. +. The coustaney of the radial velocity mean at different orbital phases reminds us of the resonance line niean constant velocity. found by Mikolajewska. Friedjuug and Quiroga (2006)) forCye.. which like is a hieh inclination eclipsing svstem.," The constancy of the radial velocity mean at different orbital phases reminds us of the resonance line mean constant velocity, found by ajewska, Friedjung and Quiroga \cite{Mik06}) ) for, which like is a high inclination eclipsing system." + Uulike in the case ofτοι we do uot have very high resolution UST spectra forMus. but we may be able to invoke a similar explanation to that eiven by Mikolajewska. Exiedjuug aud Quiroga. explaing the redshift of the resouance doublet enission lines by the presence of a cimreun-binary region.," Unlike in the case of, we do not have very high resolution HST spectra for, but we may be able to invoke a similar explanation to that given by ajewska, Friedjung and Quiroga, explaing the redshift of the resonance doublet emission lines by the presence of a circum-binary region." + Such a region could be near the plaue of the orbit., Such a region could be near the plane of the orbit. + As far as ds concerned. the observatious available. do not enable us to sav anything certain about the variation of redshift with orbita plase.," As far as is concerned, the observations available, do not enable us to say anything certain about the variation of redshift with orbital phase." + According to Duuua et al (2000 low resolution UV spectra indicate a flux decrease in the continua between 1250 aand 1290 aat phase 0.78 relative to phase 0.71. which was almost over at phase 0.81.," According to Dumm et al \cite{Du00} low resolution UV spectra indicate a flux decrease in the continuum between 1250 and 1290 at phase 0.78 relative to phase 0.71, which was almost over at phase 0.81." +" Thev interpreted this result as due to additional appareut extinction Ravleigh scattering of neutral hydrogen aud due to iron forest absorption in an accretiou wake produced bv wind accretion,", They interpreted this result as due to additional apparent extinction Rayleigh scattering of neutral hydrogen and due to iron forest absorption in an accretion wake produced by wind accretion. + Our exanuination indicates no large variation m the values of rv-iutercomibination line radial velocity between phases in the range 0.719 to (0.525 ou the high resolution UST/STIS spectra., Our examination indicates no large variation in the values of -intercombination line radial velocity between phases in the range 0.749 to 0.825 on the high resolution HST/STIS spectra. + Iu auv case. there is no accretion wake. if accretion is by Roche lobe overflow. as suggested by the observations of ellipsoidal light variability in the near infrared according to Rutkowski. \lkolajewska aud Whitelock (2007)) aud another explanation is required or the observatious of ultraviolet fluxes m such a case wan that of Diam et al (2000)).," In any case, there is no accretion wake, if accretion is by Roche lobe overflow, as suggested by the observations of ellipsoidal light variability in the near infrared according to Rutkowski, ajewska and Whitelock \cite{Ru07}) ) and another explanation is required for the observations of ultraviolet fluxes in such a case than that of Dumm et al \cite{Du00}) )." + Another possibility is absorption due to impact of the stream., Another possibility is absorption due to impact of the stream. + Inu addition Duuua ct al (1999)) sugeest that the density distribution arom 1 ΑΙ eiaut of is assvinetric with additiona extinction than that due to Ravleigh scattering. which lev suggest is produced by the iron forest.," In addition Dumm et al \cite{Du99}) ) suggest that the density distribution around the M giant of is assymetric with additional extinction than that due to Rayleigh scattering, which they suggest is produced by the iron forest." + Uulike most of the spectra studied here. those of did lave a significant coutimuun. with P Cveni absorption components superposed onit. which could have contributed to some measured velocities of the ane lines," Unlike most of the spectra studied here, those of did have a significant continuum, with P Cygni absorption components superposed on it, which could have contributed to some measured velocities of the and lines." + The edge velocities relative to the systemic velocity ave lower than 200 kin +., The edge velocities relative to the systemic velocity are lower than 200 km $^{-1}$. + Let us note also the preseuce of broad wines of nore than 20 wwide aroun the resonance lines., Let us note also the presence of broad wings of more than 20 wide around the resonance lines. + It remains to he seen whether that can be explained by electron scattering., It remains to be seen whether that can be explained by electron scattering. + The high resolution UST/STIS spectra of cau be used to look at the line profiles. im order to better understand the racial velocity shifts.," The high resolution HST/STIS spectra of can be used to look at the line profiles, in order to better understand the radial velocity shifts." + Fig., Fig. + 11 shows profiles of the 1551e 1056 aand Ov] L101 Hines.," 11 shows profiles of the 1551, 1586 and ] 1401 lines." + The weak coutimuuu fluxes of less than the line ceutre fixes have been subtracted. the profiles beiug lnscnsitive to the contin and unaffected by the ion forest absorption.," The weak continuum fluxes of less than the line centre fluxes have been subtracted, the profiles being insensitive to the continuum and unaffected by the iron forest absorption." +" The profile was divided by 3 aud the Or1v] profile by 1.7. so as to make their red wings coincide approximately,"," The profile was divided by 3 and the ] profile by 1.7, so as to make their red wings coincide approximately." + One sees that the blue wines of the and OV] lines are reduced with respect to Nav]., One sees that the blue wings of the and ] lines are reduced with respect to ]. + The line is optically thick. so the reduction appears to be due to P. Cyveui absorption of liue euissio- starting at radial velocities which are positive relative to the xvsteuic velocity of 12.1 or 12.9 au 1 (both values being eiven as alternatives by Dolezvuski et al (200033 and A\iilsolajesweka (2003))) aud a cool giaut radial velocity TON lana losnaller than those values at phase 0825.," The line is optically thick, so the reduction appears to be due to P Cygni absorption of line emission, starting at radial velocities which are positive relative to the systemic velocity of 12.4 or 12.9 km $^{-1}$ (both values being given as alternatives by Belczynski et al \cite{Be00}) ) and Mikolajeswska \cite{Mik03}) )) and a cool giant radial velocity 7.8 km $^{-1}$ smaller than those values at phase 0.825." + This could sugecst the presence of a line absorbing wind youn the cool compoucnt absorbing some of of the line chussion comune frou regions rotating not very rapidly around the white dwarf with perhaps a contribution to he absorption at certain orbital phases by a stream from he inner Lagraugian point., This could suggest the presence of a line absorbing wind from the cool component absorbing some of of the line emission coming from regions rotating not very rapidly around the white dwarf with perhaps a contribution to the absorption at certain orbital phases by a stream from the inner Lagrangian point. + The latter is possible for Heh inclination eclipsing svstenis ike if the cool component fills its Roche lobe (Rutkowski. Mikolajewska and Whitelock (2007)).," The latter is possible for high inclination eclipsing systems like if the cool component fills its Roche lobe (Rutkowski, Mikolajewska and Whitelock \cite{Ru07}) )." + Let us note that the wind from 16 cool component cau be deviated by the eravitational field of the compact component., Let us note that the wind from the cool component can be deviated by the gravitational field of the compact component. + The 1v] line is optically in. so no explanation. iuvovlviug absorption can work or this line.," The ] line is optically thin, so no explanation, invovlving absorption can work for this line." + The effect iiw be explainable by a larec part ft the imtercombination cussion line flux comime frou 1e already. mentioned wind from the cool component in rout of an accretion disk. with the latter being opticaly uck in the coutimmun. so occultiug cussion belied it. aus a possible contribution to line. cussion due to the xeseuce of the already mentioned stream frou the imuer Lagraugian point in front of the disk.," The effect may be explainable by a large part of the intercombination emission line flux coming from the already mentioned wind from the cool component in front of an accretion disk, with the latter being opticaly thick in the continuum, so occulting emission behind it, plus a possible contribution to line emission due to the presence of the already mentioned stream from the inner Lagrangian point in front of the disk." + Such effects might, Such effects might +"These coefficients will be stored in order to compute οτι)and 5""(7,) in the succesive process. once the values of S(7,). ο(τι) as well as the set have been determined.","These coefficients will be stored in order to compute $S(\tau_{0})$and $S^{\prime\prime}(\tau_{0})$ in the succesive back-substitution process, once the values of $S(\tau_{1})$, $S^{\prime\prime}(\tau_{1})$ as well as the set $\lbrace I^{+}(\tau_{1},\mu_{J}), J = 1,ND\rbrace$ have been determined." + The above relations link any pair of succesive lavers., The above relations link any pair of succesive layers. + As already said. the determination of these relations constitutes the aim of this section.," As already said, the determination of these relations constitutes the aim of this section." +" 3em In parallel we are going to show also how to recover the initial conditions for £.(74.46)T and S”(7,). the values of the coeíIicients of the relations equivalent to ec.s (25) and (26). iow [or τι."," 3em In parallel we are going to show also how to recover the initial conditions for $I^{-}(\tau_{1},\mu_{J})$ and $S^{\prime\prime}(\tau_{1})$, the values of the coefficients of the relations equivalent to eq.s (25) and (26), now for $\tau_{1}$." + Let us detail our foregoing purpose., Let us detail our foregoing purpose. + At the beginning of the study of each succesive laver - jere (he [ist one - we must consider the implicit computation ofthe corresponding source unctüon at the upper limiting optical depth. here 7).," At the beginning of the study of each succesive layer - here the first one - we must consider the implicit computation ofthe corresponding source function at the upper limiting optical depth, here $\tau_{0}$." + The form of the incident downgoing intensities at 7). given by eq. (," The form of the incident downgoing intensities at $\tau_{0}$ , given by eq. (" +25). together with the implicit values of the set allow us to compute from eq. (,"25), together with the implicit values of the set $\lbrace I^{+}(\tau_{0},\mu_{J}), J = 1,ND\rbrace$ allow us to compute from eq. (" +"4) the coefficients of a linear relation among (7) and S(t).S674).5""(70).5""(7,) and the set (4.(qm.poy).J=1..NDI.","4) the coefficients of a linear relation among $J(\tau_{0})$ and $S(\tau_{0}), S(\tau_{1}), S^{\prime\prime}(\tau_{0}), +S^{\prime\prime}(\tau_{1})$ and the set $\lbrace I^{+}(\tau_{0},\mu_{J}), J = 1,ND\rbrace$." + Then eq. (, Then eq. ( +"2). where z(70) and D(7,) ave given. will vield the coefficients of the linear relation Üem where we have notsolved for 5(7,) again lor the sake of algorithmical ease.","2), where $\varepsilon(\tau_{0})$ and $B(\tau_{0})$ are given, will yield the coefficients of the linear relation 0em where we have notsolved for $S(\tau_{0})$ again for the sake of algorithmical ease." +" 3em We compute now for each direction yey the quadrature weights ws1(). ws2(J). wdl(J) and wd2(4) according to eq.s (17) through (20) - or alternatively eq.s (21) through (24) - for Ar,=τι—7."," 3em We compute now for each direction $\mu_{J}$ the quadrature weights ${\bf{ws1}}(J)$, ${\bf{ws2}}(J)$, ${\bf{wd1}}(J)$ and ${\bf{wd2}}(J)$ according to eq.s (17) through (20) - or alternatively eq.s (21) through (24) - for $\Delta\tau_{1} = \tau_{1} - \tau_{0}$." + These weights allow us an implicit equadrature of the source [unction in the description of the propagation of the upgoing intensities from {(74.46) to Lf(79.fey). and later of the downgoing intensities from 7.(tj.fey} to £.(74.40).," These weights allow us an implicit quadrature of the source function in the description of the propagation of the upgoing intensities from $I^{+}(\tau_{1},\mu_{J})$ to $I^{+}(\tau_{0},\mu_{J})$, and later of the downgoing intensities from $I^{-}(\tau_{0},\mu_{J})$ to $I^{-}(\tau_{1},\mu_{J})$." +" At this point we can introduce the implicit form for £(7).fr) in terms of 5(74). οτι). ο πι). S""(7,) and the set (4τι.py).J=1. ND}. given by eq. ("," At this point we can introduce the implicit form for $I^{+}(\tau_{0},\mu_{J})$ in terms of $S(\tau_{0})$, $S(\tau_{1})$, $S^{\prime\prime}(\tau_{0})$ , $S^{\prime\prime}(\tau_{1})$ and the set $\lbrace I^{+}(\tau_{1},\mu_{J}), J = 1,ND\rbrace$ , given by eq. (" +15). in eq. (,"15), in eq. (" +25) for I(am. qu). which is the iniual condition for the study of the laver (75. 74).By re-arrangement of the coefficients we canwrite,"25) for $I^{-}(\tau_{0},\mu_{J})$ , which is the initial condition for the study of the layer $(\tau_{0},\tau_{1})$ .By re-arrangement of the coefficients we canwrite" + u-band light clistributions.,$u$ -band light distributions. +" Phe regression. analysis shows the extent to which the spatial distribution. of physical parameters ancl OMM, are related.", The regression analysis shows the extent to which the spatial distribution of physical parameters and QMM are related. + For the concentration and. asvmnmetry perameters no correlation was seen., For the concentration and asymmetry parameters no correlation was seen. + Thus OMM. cannot describe. the distribution. of physical properties. any better. than dt can describe the ραπ σαι distribution for these two parameters., Thus QMM cannot describe the distribution of physical properties any better than it can describe the $r$ -band light distribution for these two parameters. + The clumpiness of physical parameters ds. clearly connected. better to QAIAL than is the clumpiness of the r-band or u-band σα distributions., The clumpiness of physical parameters is clearly connected better to QMM than is the clumpiness of the r-band or u-band light distributions. + This shows that QAIAL (which was developed. to quantify morphology) can describe at least some aspects of the distribution of physical ooperties better than the single. filter morphology. of a galaxy., This shows that QMM (which was developed to quantify morphology) can describe at least some aspects of the distribution of physical properties better than the single filter morphology of a galaxy. + This demonstrates the fact that QMM incorporates physical properties as well as the morphology of galaxics hrough its inelusion of colour information., This demonstrates the fact that QMM incorporates physical properties as well as the morphology of galaxies through its inclusion of colour information. +Solar flares observed im hard N-ravs are believed to provide the most direct measure of dissipated cucrey.,Solar flares observed in hard X-rays are believed to provide the most direct measure of dissipated energy. + Aun example of a frequency distribution of nonthermal cuerev in electrons at chereies of >25 keV is shown in Fig., An example of a frequency distribution of nonthermal energy in electrons at energies of $>25$ keV is shown in Fig. + 2. which shows a powerlaw with a slope of ag=1.5340.02 exteuding over au energy ranee of four orders of maguitude. i.e. E=10107? ere (Crosby. Asclavauden. aud Deunis 1993).," 2, which shows a powerlaw with a slope of $\alpha_E=1.53\pm0.02$ extending over an energy range of four orders of magnitude, i.e., $E=10^{28}-10^{32}$ erg (Crosby, Aschwanden, and Dennis 1993)." + This powerlaw slope iplies a fractal dimension of Dz1.92.0. which is perfectly cousisteut with a fractal 2-D energy dissipatiou domain. such as current sheets or separatrix surfaces in magnetic reconnection reeious (Fie.," This powerlaw slope implies a fractal dimension of $D\approx 1.9-2.0$, which is perfectly consistent with a fractal 2-D energy dissipation domain, such as current sheets or separatrix surfaces in magnetic reconnection regions (Fig." + 3. top).," 3, top)." + Au carly cellular automaton model was able to reproduce this value consistently for different svstem sizes (bu et al., An early cellular automaton model was able to reproduce this value consistently for different system sizes (Lu et al. + 1993)., 1993). + Other imieasuremeuts of hard N-rax cuereics vield similar values in the range of aps1.4.1.7 (Lee et al.," Other measurements of hard X-ray energies yield similar values in the range of $\alpha_E +\approx 1.4-1.7$ (Lee et al." + 1993: Bronmmud et al., 1993; Bromund et al. + 1995: Perez-Euriquez aud. \Groshuichenko 1999: Georeoulis et al., 1995; Perez-Enriquez and Miroshnichenko 1999; Georgoulis et al. + 2001: Chris5 et al., 2001; Christe et al. + 2008). which are approximately consistent with a fractal dimension of Dz2.," 2008), which are approximately consistent with a fractal dimension of $D\approx 2$." + Solar flares observed in soft N-ravs provide a measure of the thermal energy. which are also found to be in the range of ag=LLL1.6 (Drake ct al.," Solar flares observed in soft X-rays provide a measure of the thermal energy, which are also found to be in the range of $\alpha_E=1.44-1.6$ (Drake et al." + 1971: Shimizu 1995). except for one measurement with a solmewhat higher value of ag=Las (Veronig ct al.," 1971; Shimizu 1995), except for one measurement with a somewhat higher value of $\alpha_E=1.88$ (Veronig et al." + 2002a.b). which max be affected by issues.," 2002a,b), which may be affected by background-subtraction issues." + The general coincidence between cucrey distributions iu soft aud hard N-ravs can be taken as evidence for the Neupert effect. which implies that the thermal flare plasma is evaporated from the chromosphere by heating through precipitating nonthermal particles.," The general coincidence between energy distributions in soft and hard X-rays can be taken as evidence for the Neupert effect, which implies that the thermal flare plasma is evaporated from the chromosphere by heating through precipitating nonthermal particles." + Thus. although the spatial ecometiy of soft N-rav radiating postflare loops is 1-D. their cucrey distribution reflects the 2-D geometry of current sheets where the primary energy dissipation took place.," Thus, although the spatial geometry of soft X-ray radiating postflare loops is 1-D, their energy distribution reflects the 2-D geometry of current sheets where the primary energy dissipation took place." + For solar nanofiares observed in EUV we see two treuds: (1) Powerlaw slopes of cucrey distributions interred from single EUV temperature filters have values in the ranee of agz1.52.6 (Ixxucker aud Beuz 1998: Parucll aud Jupp 2000: Asclavaucden et al., For solar nanoflares observed in EUV we see two trends: (1) Powerlaw slopes of energy distributions inferred from single EUV temperature filters have values in the range of $\alpha_E \approx 1.8-2.6$ (Krucker and Benz 1998; Parnell and Jupp 2000; Aschwanden et al. + 2000: Benz and Krucker 2002). which suffer from the bias of nuderestimating the thermal cucrey due to the lack of high-temperature filters: (2) Powerlaw slopes inferred. from combined EUW and soft ταν tempcratuve filters vield a value of ag=1.512:0.03 (Asclovancden and Parnell 2002). which is again consistent with a fractal dimension of D=3/1512:2 as derived fro flare energies observed im soft and hard N-ravs.," 2000; Benz and Krucker 2002), which suffer from the bias of underestimating the thermal energy due to the lack of high-temperature filters; (2) Powerlaw slopes inferred from combined EUV and soft X-ray temperature filters yield a value of $\alpha_E=1.54\pm0.03$ (Aschwanden and Parnell 2002), which is again consistent with a fractal dimension of $D=3/1.54 \approx 2$ as derived from flare energies observed in soft and hard X-rays." + Solar energetic particle (SEP) events were reported to have flatter powerlaw distributions. je. (Gabriel and Fevuman 1996). which are prefercutially associated with the largest flares. aud thus their statistics is subject to a selection effect that is not representative for all flares.," Solar energetic particle (SEP) events were reported to have flatter powerlaw distributions, i.e., $\alpha_E \approx 1.2-1.4$ (Gabriel and Feynman 1996), which are preferentially associated with the largest flares, and thus their statistics is subject to a selection effect that is not representative for all flares." + Stellar flares were found to have a large range of powerlaw slopes. in the range of agzL3.2.1 (Audard et al.," Stellar flares were found to have a large range of powerlaw slopes, in the range of $\alpha_E \approx 1.3-2.4$ (Audard et al." + 2000:Robinson ct al., 2000;Robinson et al. + 1999). but cach star provides only very few eveuts per observing run (typically xh 15). aud thus the large spread can be explained by saínall-uuuber statistics.," 1999), but each star provides only very few events per observing run (typically $\approx 5-15$ ), and thus the large spread can be explained by small-number statistics." + Soft-ganuna repeaters were reported to have burst fluence distiibutions with powerluw slopes of (Coeus et al., Soft-gamma repeaters were reported to have burst fluence distributions with powerlaw slopes of $\alpha_E \approx 1.4-1.7$ (Gogus et al. + 1999. 2000: Chane et al.," 1999, 2000; Chang et al." + 1996) aud προς fractal geometries of DzLa2.1. which may reflect area-like fractures in neutron star crusts strained by evolving magnetic stresses (Thompson aud Duncan 1995).," 1996) and implies fractal geometries of $D\approx 1.8-2.1$, which may reflect area-like fractures in neutron star crusts strained by evolving magnetic stresses (Thompson and Duncan 1995)." +" Iu maenctosphericOo plysics. the enerevOo, of Ooeeoiuaenetie substorms was estimated from the area sizes of auroras (Fie."," In magnetospheric physics, the energy of geomagnetic substorms was estimated from the area sizes of auroras (Fig." + 3. muddle} and the dissipated power. which were found to have frequency distributions with powerlaw slopes of agz1.01.2 (Lui et al.," 3, middle) and the dissipated power, which were found to have frequency distributions with powerlaw slopes of $\alpha_E \approx 1.0-1.2$ (Lui et al." + 2000) and iuply a fractal dimension of D=απz3., 2000) and imply a fractal dimension of $D =3 / \alpha_E \approx 3$. + This suggests an Euclidean or volume-filline spreading of energy dissipation. which may reflect the 3-D ecometiy of the plasimoid that forms during the expansion phase in the ecotail (Bauujoliaun aud Tremman 1996).," This suggests an Euclidean or volume-filling spreading of energy dissipation, which may reflect the 3-D geometry of the plasmoid that forms during the expansion phase in the geotail (Baumjohann and Treuman 1996)." + Iu ecophysics. earthquakes were found to have powerlaw distributions of agz2.0 (Turcotte 1999). which inplies a fractal dimension of Dz 1.5. possibly reflecting a musture of LD carthquake fault ruptures (Fig.," In geophysics, earthquakes were found to have powerlaw distributions of $\alpha_E \approx 2.0$ (Turcotte 1999), which implies a fractal dimension of $D \approx 1.5$ , possibly reflecting a mixture of 1-D earthquake fault ruptures (Fig." + 3.," 3," +al... 1999).,", 1999)." +" The oulv remaining question mark is enüssion from an anisotropic source, but this would require a disk of 1075ei to survive the iuteuse + ray (aud X. and UV) fash: though not excluded. it does not look likely."," The only remaining question mark is emission from an anisotropic source, but this would require a disk of $10^{18}\; cm$ to survive the intense $\gamma$ ray (and X, and UV) flash: though not excluded, it does not look likely." + Raclio observations of the first burst observed so far (CRB 970508. Frailαι. 1997) showed puzzling fluctuations by about a factor of 2 in the fux. over a timescale of days. disappearing after about 30 days from the burst (Fig.," Radio observations of the first burst observed so far (GRB 970508, Frail, 1997) showed puzzling fluctuations by about a factor of $2$ in the flux, over a time–scale of days, disappearing after about $30$ days from the burst (Fig." + 1)., 4). + This extreme. and unique behaviour. was explained by Goodman (1997). who showed that it is due to interference of ravs travelling along differcut paths through the ISAL aud randomly deflected by the spatially varvine refractive iudex of the turbuleut ISA.," This extreme, and unique behaviour, was explained by Goodman (1997), who showed that it is due to interference of rays travelling along different paths through the ISM, and randomly deflected by the spatially varying refractive index of the turbulent ISM." +" The wonderful upshot of this otherwise mareiual phenomenon. is that these effects cease whenever the source expands bevoud a radius where vy ds the radio observing frequency iu units of 1019.Π.. d,dope as the distance of the ISM frou us (assmmed to be a uniform scattering screen). aud SAL is the Galactic scattering measure. scaled to a typical Galactic value."," The wonderful upshot of this otherwise marginal phenomenon, is that these effects cease whenever the source expands beyond a radius where $\nu_{10}$ is the radio observing frequency in units of $10^{10} \; Hz$, $d_{sc,kpc}$ is the distance of the ISM from us (assumed to be a uniform scattering screen), and $SM$ is the Galactic scattering measure, scaled to a typical Galactic value." + The existence of iterfereuce effects is made more convincing by the amplitude of the average increase (a factor of 2. as observed). the correctuess iu the prediction of the tineinterval between different peaks. aud of the decorrelation bandwidth.," The existence of interference effects is made more convincing by the amplitude of the average increase (a factor of 2, as observed), the correctness in the prediction of the time–interval between different peaks, and of the decorrelation bandwidth." + Since flares disappear after about 30 davs. it means that the average speed of," Since flares disappear after about $30$ days, it means that the average speed of" +of dissipation (see the left plot in Fig.,of dissipation (see the left plot in Fig. + 2 of their paper; the three Reynolds numbers values mentioned correspond to the three largest Elsasser numbers of their graph)., 2 of their paper; the three Reynolds numbers values mentioned correspond to the three largest Elsasser numbers of their graph). +" Perhaps the most significant new result of this work, disclosed on Figs."," Perhaps the most significant new result of this work, disclosed on Figs." +" 5 and 6,, is the existence of a double regime separated by a critical magnetic Prandtl number Pm,~1."," \ref{transp-pm} and \ref{transpReRm}, is the existence of a double regime separated by a critical magnetic Prandtl number $Pm_c\sim 1$." +" For PmPm., the transport seems to depend mostlyon Pmand only weakly on either Re or Rm (once Re= 103), although a larger number of Pm values need to be probed on this issue."," For $Pm < Pm_c$, at a given field strength, the transport correlates mostly with $Rm$; for $Pm > Pm_c$, the transport seems to depend mostlyon $Pm$and only weakly on either $Re$ or $Rm$ (once $Re \gtrsim 10^3$ ), although a larger number of $Pm$ values need to be probed on this issue." +" It is tempting to assume Pm,-2, as this is the critical value for the zero mean field problem, but this identification requires further work to be substantiated."," It is tempting to assume $Pm_c\simeq 2$, as this is the critical value for the zero mean field problem, but this identification requires further work to be substantiated." +" The identification of this double dissipation regime was made possible by the increased accuracy, with respect to our previous work, in the determination of the transport averages."," The identification of this double dissipation regime was made possible by the increased accuracy, with respect to our previous work, in the determination of the transport averages." +" In the small Prandtl regime, in contrast to the large one, our most resolved simulations show no sign of convergence with respect to dissipation, although values of Rm up to 20000 have been reached."," In the small Prandtl regime, in contrast to the large one, our most resolved simulations show no sign of convergence with respect to dissipation, although values of $Rm$ up to 20000 have been reached." +" The role of linear physics and parasitic modes on transport properties has also been investigated, and the major results on these questions can be summarized as follows: Note that all these results were obtained while the fastest growing channel and parasitic modes were always captured, so that they do not depend on limitations on this front."," The role of linear physics and parasitic modes on transport properties has also been investigated, and the major results on these questions can be summarized as follows: Note that all these results were obtained while the fastest growing channel and parasitic modes were always captured, so that they do not depend on limitations on this front." + It is worth pointing out that our results do not totally disqualify a saturation of the unstable linear modes by the parasitic modes; only the relevance of this process to the relation between transport and physical dissipation has been disproved., It is worth pointing out that our results do not totally disqualify a saturation of the unstable linear modes by the parasitic modes; only the relevance of this process to the relation between transport and physical dissipation has been disproved. + The role of the Prandtl number disclosed in this investigation makes more physical sense than a direct dependence of the transport on Pm., The role of the Prandtl number disclosed in this investigation makes more physical sense than a direct dependence of the transport on $Pm$. +" Indeed, it is very likely that the critical value Pm, relates to the switching of the magnetic and kinetic dissipations scales k, and k, in Fourier space: for Pm«Pm, Pmὁ Pm), ky< k,> k,)."," Indeed, it is very likely that the critical value $Pm_c$ relates to the switching of the magnetic and kinetic dissipations scales $k_\eta$ and $k_\nu$ in Fourier space: for $Pm +< Pm_c$ $Pm > Pm_c$ ), $k_\eta < k_\nu$ $k_\eta > +k_\nu$ )." +" For Pm« 1, k,« k,, the flow at scales k> or >k, in Fourier space is therefore purely hydrodynamic."," For $Pm \ll 1$ , $k_\eta \ll k_\nu$ , the flow at scales $k +>$ or $\gg k_\eta$ in Fourier space is therefore purely hydrodynamic." + As information flows, As information flows +not use Eq.,not use Eq. + 3 as iT depends on extrapolation of the light profile which introduces uncertainties., \ref{formula_magnitudes} as $m_{\rm T}$ depends on extrapolation of the light profile which introduces uncertainties. + Furthermore. it does not take into account bars and rings which are clearly present in some of the galaxies in our sample.," Furthermore, it does not take into account bars and rings which are clearly present in some of the galaxies in our sample." +" To determine total absolute magnitudes we used aperture magnitudes #7,), instead.", To determine total absolute magnitudes we used aperture magnitudes $m_{\rm ap}$ instead. + We summed all the light to 20 above sky (~25.5 mag 7) and converted this to magnitudes., We summed all the light to $2\sigma$ above sky $\sim 25.5$ mag $^{-2}$ ) and converted this to magnitudes. + We used the distances listed in Table | to derive total absolute magnitudes., We used the distances listed in Table \ref{sample_galaxies} to derive total absolute magnitudes. + Figure 4. shows the distribution of absolute magnitudes MEL derived in this way., Figure \ref{maghisto} shows the distribution of absolute magnitudes $M_{\rm{B}}^{\rm{T}}$ derived in this way. + It is evident that low surface brightness does not imply low lummosity., It is evident that low surface brightness does not imply low luminosity. + LSB galaxies can be very luminous., LSB galaxies can be very luminous. +hole mass. which is based on the application of the virial theorem to. broad. emission. lines in AGN spectra. and suggested that the black hole mass can be severely uncerestimated if the effect of radiation pressure is ignored.,"hole mass, which is based on the application of the virial theorem to broad emission lines in AGN spectra, and suggested that the black hole mass can be severely underestimated if the effect of radiation pressure is ignored." + Netzer(2009) then used the Αρησ. relation for a test of this suggestion. where Mgg is the black hole mass and σι is the velocity dispersion of host galaxies. concluding radiation pressure effect is unimportant. while Marconictal.(2009) ound the importance of radiation pressure by taking into account the intrinsic dispersion associated with the related parameters. in particular. column densities of BLAIR clouds.," \citet{net} then used the $M_{BH}-\sigma_*$ relation for a test of this suggestion, where $M_{BH}$ is the black hole mass and $\sigma_*$ is the velocity dispersion of host galaxies, concluding radiation pressure effect is unimportant, while \citet{mar09} found the importance of radiation pressure by taking into account the intrinsic dispersion associated with the related parameters, in particular, column densities of BLR clouds." + However. there are no reliable column density estimates fron observations up to date.," However, there are no reliable column density estimates from observations up to date." + In this paper. we will estimate column densities of quasars selected from the SDSS using1L. for investigating the exeitation mechanism of cemission and the BLE. gas dynamics.," In this paper, we will estimate column densities of quasars selected from the SDSS using, for investigating the excitation mechanism of emission and the BLR gas dynamics." +i ln section 2. we perform numerical calculations of eemission lines to establish a method for estimating column densities.," In section 2, we perform numerical calculations of emission lines to establish a method for estimating column densities." + In section 3. eemission lines in the UV and optical as well as cenussion lines are measured in the SDSS quasars.," In section 3, emission lines in the UV and optical as well as emission lines are measured in the SDSS quasars." +" The results and discussion about eemission. mechanism. radiation pressure. and the variety of quasar spectra called: as ""Eigenvector 17 are given in section 4."," The results and discussion about emission mechanism, radiation pressure, and the variety of quasar spectra called as “Eigenvector 1” are given in section 4." +" Throughout thispaper. we assume a cosmology with Q,,20.3. Q420.7 and dy2τὸkms.+Alpei"," Throughout thispaper, we assume a cosmology with $\Omega_m=0.3$, $\Omega_{\Lambda}=0.7$ and $H_0=70\ \mathrm{km\ s^{-1}\ Mpc^{-1}}$." + 1n the following. we use tto denote the UV cemission lines in 2000 10^3$ in order to transform UV lines to optical lines through a large number of scatterings (cf. \citealt{cj}) ). + Phus [flux ratio must strongly depend. on τιν and 755. which are the optical depths for photons emitted. through Level Level lL and Level Level 2 transitions. respectively.," Thus flux ratio must strongly depend on $\tau_{13}$ and $\tau_{23}$, which are the optical depths for photons emitted through Level $-$ Level 1 and Level $-$ Level 2 transitions, respectively." + Lf so. the ccan be an indicator of the columnV) clensity.," If so, the can be an indicator of the column density." + Llere we use a quite simple model to. indicate. the dependence of oon the column density., Here we use a quite simple model to indicate the dependence of on the column density. + First. we ignore the Level 4 in Figure 1 and consider the aas three-level system.," First, we ignore the Level 4 in Figure \ref{fig:grot_diag} and consider the as three-level system." +1 Second. we assume thermal equilibrium population between Level 1 and Level 2.," Second, we assume thermal equilibrium population between Level 1 and Level 2." + Third. we assume an expression. of the local escape probability given by Netzer&Wills(1983). às ο=(1Tij)iTaj.," Third, we assume an expression of the local escape probability given by \citet{nw} as $\epsilon_{ij}=(1-\tau_{ij})/\tau_{ij}$." + Although the model adopting these assumptions is obviously too oversimplified. it is useful to qualitatively understand how the line ratio depends on the physical parameters.," Although the model adopting these assumptions is obviously too oversimplified, it is useful to qualitatively understand how the line ratio depends on the physical parameters." + The Hux ratio is then written as where ny is the population of level 3. ancl sli; is the spontaneous emission rate from the level ¢ to the level j.," The flux ratio is then written as where $n_3$ is the population of level 3, and $A_{ij}$ is the spontaneous emission rate from the level $i$ to the level $j$." +" Following the fact that τιςZ91. the ratio can be roughly. reduced to xlοση, "," Following the fact that $\tau_{13} \gg 1$, the ratio can be roughly reduced to $\propto 1-e^{-\tau_{23}}$." +Sinee του is proportional to the column density. the ratio is an increasing function of the column density.," Since $\tau_{23}$ is proportional to the column density, the ratio is an increasing function of the column density." + We will cliscuss further on this matter in the following., We will discuss further on this matter in the following. + Lere we will show more sophisticated model caleulations of(UV)., Here we will show more sophisticated model calculations of. +.. We performed. photoionization model calculations with version 06009 of the spectral simulation code Cloudy. last described. by Ferland (1998).. combined with a 371 level model (up to —11.6 eV. Verneretal. 1999)).," We performed photoionization model calculations with version C06.02 of the spectral simulation code Cloudy, last described by \citet{fer98}, combined with a 371 level $^+$ model (up to $\sim$ 11.6 eV, \citealt{ver99}) )." + Phe incident continuum is defined as The first term in the right-hand. side of the equation (3)) expresses an accretion disk component. which is usually called Dump.," The incident continuum is defined as The first term in the right-hand side of the equation \ref{eq:sed}) ) expresses an accretion disk component, which is usually called ." +" The Ate, and the A775 indicate the higher and the lower cut olf energies. respectively."," The $kT_{BB}$ and the $kT_{IR}$ indicate the higher and the lower cut off energies, respectively." + The second term expresses a power-law X-ray component. which is set to zero below 1.36 eV. while to fall olf as à above," The second term expresses a power-law X-ray component, which is set to zero below 1.36 eV, while to fall off as $\nu^{-3}$ above" +"of HOA. was limited by the spectral resolution of the SDSS (7,TÜkms to SMDIIS of Migz10M. (assuming he σι relation o£ Gebhbardt et al.",of H04 was limited by the spectral resolution of the SDSS $ \sigma_* > 70 \kmps $ ) to SMBHs of $\Mbh \goa 3 \times 10^6 \Msun$ (assuming the $\sigma_*$ relation of Gebhardt et al. + 2000)., 2000). + Furthermore. due to attenuation of optical emission. by cust. source selection and ACN classification at optical wavelengths will oe biasecl against gas-rich. clust-obseurecl objects.," Furthermore, due to attenuation of optical emission by dust, source selection and AGN classification at optical wavelengths will be biased against gas-rich, dust-obscured objects." + These surveys are unlikely to include galaxies hosting the smallest )ulees. ancl consequently the lowest mass. SALBLIs. and may therefore be missing a significant proportion of SALBIL erowth in the local Universe.," These surveys are unlikely to include galaxies hosting the smallest bulges, and consequently the lowest mass SMBHs, and may therefore be missing a significant proportion of SMBH growth in the local Universe." + Indeed. the nearby Scd galaxy. GC 4045. hosting a low-mass SMDII (Albu5194 Q'M.: Τὸ) only displays evidence for ACN activity. in X-ray (?) and miclinfrared (mid-Hài) observations (?)..," Indeed, the nearby Scd galaxy, NGC 4945, hosting a low-mass SMBH $\Mbh \approx 1.4 \times 10^6 \Msun$ ; \citealt{greenhill97}) ) only displays evidence for AGN activity in X-ray \citep{iwasawa93} and mid-infrared (mid-IR) observations \citep{GA09}." + Dv contrast. the AGN in NGC 4945 (accreting at z30 »ercent. of the precictecl Eclclington limit: 2)) is completeA ridden at optical wavelengths. and classified as a starburst galaxy.," By contrast, the AGN in NGC 4945 (accreting at $\goa 30$ percent of the predicted Eddington limit; \citealt{itoh08}) ) is completely hidden at optical wavelengths, and classified as a starburst galaxy." + Clearly. using optical data alone. the intrinsic ACN ooperties of sources similar to NGC 4945 cannot be derived.," Clearly, using optical data alone, the intrinsic AGN properties of sources similar to NGC 4945 cannot be derived." + While optical emission-line diagnostics alone cannot reliably characterise the properties. of a non-negligable raction of the AGN population. they are readily identified at obscuration independent wavelengths (e... X-ray: (ΗΛ).," While optical emission-line diagnostics alone cannot reliably characterise the properties of a non-negligable fraction of the AGN population, they are readily identified at obscuration independent wavelengths (e.g., X-ray; mid-IR)." + llence. the identification of AGNs made at X-ray ancl mid-L~ wavelengths complements traditional UV/optical methocWu. o vield a more complete census of AGN activity.," Hence, the identification of AGNs made at X-ray and mid-IR wavelengths complements traditional UV/optical methods to yield a more complete census of AGN activity." + Indeed. using the high resolution mid-LH spectrograph on-board the CASA SSpace Telescope (Spifzer--LRs). 7. (2009: CLAO0) Found using the first complete volumce-Imited sample of all (zz94 percent) local (2<15 Alpe) bolomoetrically uminous galaxies (Lip3. 10°L.). that z50 percent. of ocal AGNs are not identified in sensitive optical surveys.," Indeed, using the high resolution mid-IR spectrograph on-board the NASA Space Telescope -IRS), \citeauthor{GA09} (2009; GA09) found using the first complete volume-limited sample of all $\approx 94$ percent) local $D<15$ Mpc) bolometrically luminous galaxies $\Lir > 3 \times 10^9 \Lsun$ ), that $\approx 50$ percent of local AGNs are not identified in sensitive optical surveys." + At cast 30 percent of these ACGNs were previously identified as »ure optical starburst galaxies. similar to NGC 4945 (Le. not even otherwise known to be transition-tvpe objects as defined by 2)).," At least $30$ percent of these AGNs were previously identified as pure optical starburst galaxies, similar to NGC 4945 (i.e., not even otherwise known to be transition-type objects as defined by \citealt{kauff03b}) )." + Furthermore. z30 percent. of the optically unidentified AGNs were found to reside in late-type spiral galaxies (SeSd: e.g. similar to NCC 4945).," Furthermore, $\approx 30$ percent of the optically unidentified AGNs were found to reside in late-type spiral galaxies (Sc–Sd; e.g., similar to NGC 4945)." + Complimentary to this. from a heterogenous sample of Palomar galaxies. ? and ? have also concluded that optically unidentified XCGNs exist in some late-tvpe spiral galaxies.," Complimentary to this, from a heterogenous sample of Palomar galaxies, \citet{sat07} + and \citet{sat08} have also concluded that optically unidentified AGNs exist in some late-type spiral galaxies." + With the inclusion of these new optically unidentified AGNs. it is natural to ask. what are the masses of local active SAIBLIs. what are their Eddington ratios. and hence. how rapidly are active SMDBIIS erowing in the local Universe?," With the inclusion of these new optically unidentified AGNs, it is natural to ask, what are the masses of local active SMBHs, what are their Eddington ratios, and hence, how rapidly are active SMBHs growing in the local Universe?" + In this paper. we investigate the growth rates and space clensity of actively accreting SAIBIIs using the 17 AGNs identified in the volume-limitecl survey of GAOO.," In this paper, we investigate the growth rates and space density of actively accreting SMBHs using the 17 AGNs identified in the volume-limited survey of GA09." + Whilst he source statistics considered here are significantly smaller han those studies using the SDSS. this work compliments hat of 1104 by including a relatively large number (given he considered small volume) of optically unidentified ACXGNs (10) which would not be reliably identified or characterised in the SDSS Furthermore. by including a significant »opulation of bolometrically Luminous (but. clust-obscurecl) ate-tvpe spiral galaxies (SeSd) we are able to extend the SMDII density function to Mpg«€3Lo?M...," Whilst the source statistics considered here are significantly smaller than those studies using the SDSS, this work compliments that of H04 by including a relatively large number (given the considered small volume) of optically unidentified AGNs (10) which would not be reliably identified or characterised in the SDSS Furthermore, by including a significant population of bolometrically luminous (but dust-obscured) late-type spiral galaxies (Sc–Sd) we are able to extend the SMBH density function to $\Mbh < 3 \times 10^6 \Msun$." + As many of the late-twpe spiral galaxies host small galactic bulges. ancl hence lower mass SAIBLIs. particular attention is paid to obtaining accurate mass estimates for. these SMDBLIIS.," As many of the late-type spiral galaxies host small galactic bulges, and hence lower mass SMBHs, particular attention is paid to obtaining accurate mass estimates for these SMBHs." + Civen their proximity. many of the sources in CLA09 are well-studied and have multiple estimates of SALBLL mass (Mpg) from a varietv of methods (16. reverberation mapping techniques: mapping of water maser spols: gas kinematical estimates: the σι relation: correlation of Mow with the luminosity of the galactic bulge): below we discuss the relative accuracy of each SAIBIL mass estimate technique.," Given their proximity, many of the sources in GA09 are well-studied and have multiple estimates of SMBH mass $\Mbh$ ) from a variety of methods (i.e., reverberation mapping techniques; mapping of water maser spots; gas kinematical estimates; the $\sigma_*$ relation; correlation of $\Mbh$ with the luminosity of the galactic bulge); below we discuss the relative accuracy of each SMBH mass estimate technique." + Furthermore. to determine. the relative mass accretion rates and hence average growth times of the SALBLIs in our sample we require the best available estimates of the AGN bolometric luminosity CLioνοκ).," Furthermore, to determine the relative mass accretion rates and hence average growth times of the SMBHs in our sample we require the best available estimates of the AGN bolometric luminosity $L_{\rm Bol,AGN}$ )." + Here we use two approaches: 1) for the AGNs with currently published data. we use high-quality well-constrained sensitive hare X-rav (210 keV) luminosities to cirectly measure {ωνκ: and 2) we accurately infer Lpcy using a well-constrained hard. X-ray to high-ionisation mid-LHi emission line relation.," Here we use two approaches: 1) for the AGNs with currently published data, we use high-quality well-constrained sensitive hard X-ray (2–10 keV) luminosities to directly measure $L_{\rm Bol,AGN}$; and 2) we accurately infer $L_{\rm + Bol,AGN}$ using a well-constrained hard X-ray to high-ionisation mid-IR emission line relation." + 1n £22 we outline the construction and. basic reduction analvsis of the AGN sample derived. from CLXO09., In 2 we outline the construction and basic reduction analysis of the AGN sample derived from GA09. +. In. 833 we present the SMDII mass estimates., In 3 we present the SMBH mass estimates. + For a minority of objects (three. out of 17. AGNs) without. published Albu estimates we outline the use of a bulge/disc decomposition method with 2ALASS A-band images. and following Marconi Lunt (2003). we use the Alay Liu relation to estimate their SMDII masses.," For a minority of objects (three out of 17 AGNs) without published $\Mbh$ estimates we outline the use of a bulge/disc decomposition method with 2MASS -band images, and following Marconi Hunt (2003), we use the $\Mbh$ $\Lbul$ relation to estimate their SMBH masses." + In. £44. we use hard (210 keV) X-rav measurements and. high-ionisation mid-Ilt. emission to estimate the intrinsic luminosity of the ACGNs considered in our sample., In 4 we use hard (2–10 keV) X-ray measurements and high-ionisation mid-IR emission to estimate the intrinsic luminosity of the AGNs considered in our sample. + Using our well-defined estimates for SMDBLIL mass and AGN bolometric luminosity. we investigate the relative nis accretion rates of our sample of active SMDlIIs in 855.," Using our well-defined estimates for SMBH mass and AGN bolometric luminosity, we investigate the relative mass accretion rates of our sample of active SMBHs in 5." + We use these estimates to provide new constraints on the volume-average SMBLII growth rates in the local Universe., We use these estimates to provide new constraints on the volume-average SMBH growth rates in the local Universe. + We further compare these results to the previous works of Lot and 7. by. producing a local AGN population density function., We further compare these results to the previous works of H04 and \citet{gre_ho07} by producing a local AGN population density function. + Finally. in 866 we present our conclusions.," Finally, in 6 we present our conclusions." + The sample of local [ACGINs is derived. from the 5plzer--IRS spectral investigation ofa volume-Iimited sample of Li-bright galaxies to D«15 Alpe by CLA09., The sample of local AGNs is derived from the -IRS spectral investigation of a volume-limited sample of IR-bright galaxies to $D<15$ Mpc by GA09. + Lieh-resolution Spilzer--LAS spectroscopy (2?~ 600) was obtained for sixty- of the sixty-cight (294. percent) galaxies detected in the Revised Bright Galaxy Sample (RBOS: 7)) with Lin< within the considered. AO particular advantageς to a volume-limited sample is that. unlike maenituce-limitecl surveys. they do not suller from. racial selection elfects and thus can be used to construct volume- statistics.," High-resolution -IRS spectroscopy $R \sim +600$ ) was obtained for sixty-four of the sixty-eight $\approx 94$ percent) galaxies detected in the Revised Bright Galaxy Sample (RBGS; \citealt{RBGS}) ) with $\Lir \goa 3 \times 10^9 \Lsun$ within the considered A particular advantage to a volume-limited sample is that, unlike magnitude-limited surveys, they do not suffer from radial selection effects and thus can be used to construct volume-averaged statistics." + By contrast. volume-liniitecl samples," By contrast, volume-limited samples" +iid 160/42. TRAC data cover the Mid-Tufrared wavelengths of 3.6. 15.5.8. and 8.0724. in Figure 1 they are illustrated as dashed lines aud available oulv for the cluster core.,"and $\mu$ m. IRAC data cover the Mid-Infrared wavelengths of 3.6, 4.5, 5.8, and $\mu$ m, in Figure \ref{spitzer_cov} they are illustrated as dashed lines and available only for the cluster core." + Each photometric xud ds analyzed on its own to produce a catalog of galaxies., Each photometric band is analyzed on its own to produce a catalog of galaxies. +" Dust eushrouded bright stars re-cuut them cucreyv at lneger wavelengths. aud the tran flax approaches this peak of the spectral energv distribution (SED). allowing for au cstimate of star formation rates,"," Dust enshrouded bright stars re-emit their energy at longer wavelengths, and the $\mu$ m flux approaches this peak of the spectral energy distribution (SED), allowing for an estimate of star formation rates." +" Although MIPS 70/22 and 16047 observations eo even further tow the SED peak. these detectors are not as sensitive as those a [n ""Therefore. we choose to base our catalogs on the tau sources."," Although MIPS $\mu$ m and $\mu$ m observations go even further toward the SED peak, these detectors are not as sensitive as those at $\mu$ m. Therefore, we choose to base our catalogs on the $\mu$ m sources." + Sources from the [iu catalog are then matched to candidates from each ofthe other photometric bands (see Section ?? for details)., Sources from the $\mu$ m catalog are then matched to candidates from each of the other photometric bands (see Section \ref{24cat} for details). + The iain steps in data processing are outlined below., The main steps in data processing are outlined below. + More detailed descriptions can be found iu ? aud ?7.., More detailed descriptions can be found in \citet{edw10} and \citet{fad06}. + The Basic Calibrated Data (BCDs} aud calibration files are downloaded from: Leopard. pipeline version S17.0.1. which uses a factor of 0.015 to convert iustruinental wuts to MJv .," The Basic Calibrated Data (BCDs) and calibration files are downloaded from Leopard, pipeline version S17.0.4, which uses a factor of 0.045 to convert instrumental units to MJy $^{-1}$." + These DCDs have already been corrected for dark subtraction. nuxbleed. detector linearization. flat fielding. auc cosmüe rays.," These BCDs have already been corrected for dark subtraction, muxbleed, detector linearization, flat fielding, and cosmic rays." + We redid the pipoline jailbar correction after masking bright sources. applied a droop and superflat correction for all BC'Ds in cach AOR. and apply a flat for cach »ositiou of the crvogenic scan mirror.," We redid the pipeline jailbar correction after masking bright sources, applied a droop and superflat correction for all BCDs in each AOR, and apply a flat for each position of the cryogenic scan mirror." + We removed he zodiacal light aud corrected the astrometry to natch the SDSS source positions., We removed the zodiacal light and corrected the astrometry to match the SDSS source positions. + The BCDs were lnosaiced sine MIOPEN (27)) and extended sources were extracted sine SExtractor.," The BCDs were mosaiced using MOPEX \citet{mako05,mak05}) ) and extended sources were extracted using SExtractor." + We ran SExtractor a second time on the residual image. after multiplying bw 111.08 to couvert My. | to jd (as listed du the AMUPS Data Handbook?.. p. 31).," We ran SExtractor a second time on the residual image, after multiplying by 141.08 to convert MJy $^{-1}$ to $\mu$ Jy (as listed in the MIPS Data Handbook, p. 31)." +" We computed aperture fluxes within a radius of 10:5 ""as well as Petrosian magnitudes8 with L radii aud a 1iuinnauua radius of 5.5"",", We computed aperture fluxes within a radius of $^{\prime\prime}$ as well as Petrosian magnitudes with 4 radii and a minimum radius of $^{\prime\prime}$. + We applied a factor of 1.167 for the aperture correction and divided by 0.961 to account for the color correction as listed in the AIIPS Data IIaudbook., We applied a factor of 1.167 for the aperture correction and divided by 0.961 to account for the color correction as listed in the MIPS Data Handbook. + The data were combined roni two different programs. leaving the central region much deeper.," The data were combined from two different programs, leaving the central region much deeper." + Although we included this deep strip in the reduced images. we uote that the mulls of our analysis is based on a spectroscopic sunple which corresponds only to the depth of he full MIPS iuase.," Although we included this deep strip in the reduced images, we note that the bulk of our analysis is based on a spectroscopic sample which corresponds only to the depth of the full MIPS image." + By measuring the noise iu he mosaiced frames. we arrived at a Soa depth of SOa Jy in the {μι mosaic.," By measuring the noise in the mosaiced frames, we arrived at a $\sigma$ depth of $\,$$\mu$ Jy in the $\mu$ m mosaic." + The final catalog includes sources with a signal to noise ratio (SNR) 3 sources. colmputed using an optimal aperture radius.," The final catalog includes sources with a signal to noise ratio (SNR) $>$ 3 sources, computed using an optimal aperture radius." +" There i9 one source. NGC 1921. which ds extremely exteuded aud has uanv star forming chuups at {μια SExtractor failed for this source. therefore. we calculated the photometry by haud. fitting a Petrosiaun radius to the portion of the helt profile which cucompasses the same region as secu at 1,"," There is one source, NGC 4921, which is extremely extended and has many star forming clumps at $\mu$ m. SExtractor failed for this source, therefore, we calculated the photometry by hand, fitting a Petrosian radius to the portion of the light profile which encompasses the same region as seen at $^{\prime}$." + For the longer wavelength MIPS observations. we downloaded the raw frames (DC'Es) from the Spitzer archive aud use the GeRT pipeline which finds and calibrates the slope of consecutive data reads.," For the longer wavelength MIPS observations, we downloaded the raw frames (DCEs) from the archive and use the GeRT pipeline which finds and calibrates the slope of consecutive data reads." + The conversion factor for iustrumenutal wits iuto My. | is 702 for the Tüjna data. aud ἔτι. for the 16072. data.," The conversion factor for instrumental units into MJy $^{-1}$ is 702 for the $\mu$ m data, and 47.4, for the $\mu$ m data." + For the 70/22 data. we TisCC a second pass filtering technique to remove streaking in the final nuage.," For the $\mu$ m data, we used a second pass filtering technique to remove streaking in the final image." + We ideutiled the causal bright sources ina first pass. and repeat the filtering on the masked image.," We identified the causal bright sources in a first pass, and repeat the filtering on the masked image." + We applied an additional correction to the BCDs to remove lateut stim artifacts by modelling aud then removing the (ffect ofthe stiméash on the median of the BCDs iat follow., We applied an additional correction to the BCDs to remove latent stim artifacts by modelling and then removing the effect of the stimflash on the median of the BCDs that follow. + Virtually all of the extragalactic sources at jiese longer waveleneths are point sources., Virtually all of the extragalactic sources at these longer wavelengths are point sources. + We nosaiced the frames aud conducted the extraction of the sources usingAPEX with a bottom outlicr οοι of 2 aud a top threshold of 3., We mosaiced the frames and conducted the extraction of the sources using with a bottom outlier threshold of 2 and a top threshold of 3. +" For je Tana data. we used an aperture radius of 15"". a color correction of 0.918. and an aperture correction of 2.211."," For the $\mu$ m data, we used an aperture radius of $^{\prime\prime}$, a color correction of 0.918, and an aperture correction of 2.244." +" For 16051. we use an aperture radius of 20"". a color correction of 0.959. aud au aperture correction of 3.121."," For $\mu$ m, we use an aperture radius of $^{\prime\prime}$, a color correction of 0.959, and an aperture correction of 3.124." + By measuring the noise In the mosaiced frames. we arrived at aὉσ depth of 32.01uJ¥ in the 704521 mosaic aud 12Jx iu the 160522. mosaic.," By measuring the noise in the mosaiced frames, we arrived at a$\sigma$ depth of $\,$ mJy in the $\mu$ m mosaic and $\,$ mJy in the $\mu$ m mosaic." +values every. 100 time-steps as we determined that this gives phenomenally good agreement with cleaning every time-step for considerably less cost.,values every 100 time-steps as we determined that this gives phenomenally good agreement with cleaning every time-step for considerably less cost. + Figure 7. shows the new temporal evolution of à once the cleaning has been carried out for the 327. which is case 6.," Figure \ref{remove1} shows the new temporal evolution of $\alpha$ once the cleaning has been carried out for the $32^3$, which is case 6." + Lt is clear that the elfeet of cleaning the mean values on ais to continue with the saturated level that we witnessed in the first part of figure 2.., It is clear that the effect of cleaning the mean values on $\alpha$ is to continue with the saturated level that we witnessed in the first part of figure \ref{fiden2}. + Pherefore. it is now possible to evaluate the cumulative average until it saturates.," Therefore, it is now possible to evaluate the cumulative average until it saturates." + Figure 7 not only shows the cumulative average but also the mean value for this case., Figure \ref{remove1} not only shows the cumulative average but also the mean value for this case. + Figure S shows a more detailed series of snapshots for à in this case ancl clearly shows that the randomised. turbulent. behaviour persists for all time and we do not now move to a repeated channel solution case.," Figure \ref{Removesnaps} shows a more detailed series of snapshots for $\alpha$ in this case and clearly shows that the randomised, turbulent, behaviour persists for all time and we do not now move to a repeated channel solution case." + The primary aim of this paper was to examine the οσοι of decreasing the dissipation scale (bv increasing the resolution) and we are now in a position to do so., The primary aim of this paper was to examine the effect of decreasing the dissipation scale (by increasing the resolution) and we are now in a position to do so. + Figure 9 show the οσοι of doubling the resolution (decreasing the dissipation scale) on a., Figure \ref{remove2} show the effect of doubling the resolution (decreasing the dissipation scale) on $\alpha$. + We note that the average value is increased as resolution is increased., We note that the average value is increased as resolution is increased. + Εις fact is amplified by the data in table 2) (cases 6-8). which shows a clear upward trend. as resolution is increased.," This fact is amplified by the data in table \ref{table2} (cases 6-8), which shows a clear upward trend as resolution is increased." + As such. this shows that small scales are important in these caleulations and the level at which the dissipation scale is set is crucial is determining that rate of enhanced transport.," As such, this shows that small scales are important in these calculations and the level at which the dissipation scale is set is crucial is determining that rate of enhanced transport." + 1n the above section we chose to focus on a domain where the aspect ratio is 1:1., In the above section we chose to focus on a domain where the aspect ratio is $1:1:1$. + This was selected to facilitate the longer time caleulations at higher resolutions., This was selected to facilitate the longer time calculations at higher resolutions. + However. as the earlier calculations considered a 1:2::1 and so in this section we examine what happens at mocest resolutions to the saturated level of a.," However, as the earlier calculations considered a $1:2\pi:1$ and so in this section we examine what happens at modest resolutions to the saturated level of $\alpha$." + We have considered boxes with the aspect ratios 1:2:1. 1:3: Land 1:6:1.," We have considered boxes with the aspect ratios $1:2:1$, $1:3:1$ and $1:6:1$ ." + The effect of clongating the is summarised in 2. (cases 7. 9-11) and the evolution is shown in figure 10..," The effect of elongating the is summarised in \ref{table2} (cases 7, 9-11) and the evolution is shown in figure \ref{121}." + There is a clear decrease in the saturation level as the box is increased in the azimuthal direction., There is a clear decrease in the saturation level as the box is increased in the azimuthal direction. + What we are seeing is the clfect that in short box lengths the parasitic instability is limited. (see Goodman&Xu(1994). for more details on this instability)., What we are seeing is the effect that in short box lengths the parasitic instability is limited (see \cite{GX} for more details on this instability). + In this paper we have returned to the original concept to uncerstand turbulent transport of angular momentum in an accretion disc., In this paper we have returned to the original concept to understand turbulent transport of angular momentum in an accretion disc. + As such. we considered the standard. local shearing box model in which the ideal MIID equations were solved.," As such, we considered the standard local shearing box model in which the ideal MHD equations were solved." + We chose to start by. considering a cube with sides of equal length because we wished to have laree integration times (1000 orbits) and a numerical dissipation that the same in all directions., We chose to start by considering a cube with sides of equal length because we wished to have large integration times (1000 orbits) and a numerical dissipation that the same in all directions. + Our calculations shown that. without correction. there is à shift in the aceretion rate (a shift in the turbulent transport rate).," Our calculations shown that, without correction, there is a shift in the accretion rate (a shift in the turbulent transport rate)." + Such a shift is interesting due to the fact that there are shifts in spectra of accretion disces. which imply a corresponding shift in accretion rate.," Such a shift is interesting due to the fact that there are shifts in spectra of accretion discs, which imply a corresponding shift in accretion rate." + However. in this case. the shift is unintentional and a by-procuct of the interpolation in the shearing box boundary conditions that introcluce errors because of the interpolation that is a necessary part of the procedure.," However, in this case, the shift is unintentional and a by-product of the interpolation in the shearing box boundary conditions that introduce errors because of the interpolation that is a necessary part of the procedure." + This error is unavoidable in such calculations and does remain small for low numbers of orbits., This error is unavoidable in such calculations and does remain small for low numbers of orbits. +" However. for large numbers of orbits the error in shown to compound to such an extent that the mean D, field. which should be zero. grows and becomes larger in magnitude that the imposed. D. field."," However, for large numbers of orbits the error in shown to compound to such an extent that the mean $B_y$ field, which should be zero, grows and becomes larger in magnitude that the imposed $B_z$ field." + This error filers into the various components of boththe velocity anc magnetic fielcls., This error filers into the various components of boththe velocity and magnetic fields. +We now examine if there is evidence for an enhancement in the molecular gas in the arms and if this enhancement is independent of higher total gas surface densities in the arms.,We now examine if there is evidence for an enhancement in the molecular gas in the arms and if this enhancement is independent of higher total gas surface densities in the arms. +" Figure 8 shows how the fraction of molecular gas, varies with radius when considering all pixels H2/HI,(black), those attributed to the arms with the mask (red) and those attributed to the interarm regions (blue)."," Figure \ref{gasr} shows how the fraction of molecular gas, $_{2}$ /HI, varies with radius when considering all pixels (black), those attributed to the arms with the mask (red) and those attributed to the interarm regions (blue)." +" For each galaxy and radius, we find the median H2/HI ratio in the arm regions is enhanced compared to both the interarm regions and overall trend."," For each galaxy and radius, we find the median $_{2}$ /HI ratio in the arm regions is enhanced compared to both the interarm regions and overall trend." +" The magnitude of this enhancement is small, less than a factor of 2."," The magnitude of this enhancement is small, less than a factor of 2." + Is this mild enhancement in the H2/HI ratio the result of shock-triggered molecular cloud formation or simply the enhancement of the local gas content?, Is this mild enhancement in the $_{2}$ /HI ratio the result of shock-triggered molecular cloud formation or simply the enhancement of the local gas content? +" Figure 9 shows the fraction of molecular gas, but this time in terms of the total gas surface density."," Figure \ref{gas} shows the fraction of molecular gas, but this time in terms of the total gas surface density." + We see that the arm regions have molecular gas fractions that extend up to very high total gas fractions and that the interarm regions have molecular gas fractions only at the lower end of the total gas surface density., We see that the arm regions have molecular gas fractions that extend up to very high total gas fractions and that the interarm regions have molecular gas fractions only at the lower end of the total gas surface density. +" However, the two overlap and there is no obvious enhancement of the molecular gas fraction in the arms for a given total gas surface density."," However, the two overlap and there is no obvious enhancement of the molecular gas fraction in the arms for a given total gas surface density." +" 'Thus, arms appear to concentrate gas to higher surface, and presumably volume, densities."," Thus, arms appear to concentrate gas to higher surface, and presumably volume, densities." +" There is not strong evidence that arms trigger the formation of Πο, though."," There is not strong evidence that arms trigger the formation of $_{2}$, though." +" Moreover, at a given gas surface density, the molecular gas fraction in the arm and interarm regions is about the same."," Moreover, at a given gas surface density, the molecular gas fraction in the arm and interarm regions is about the same." +" Combined with our SFE results, this suggests triggering by arms is not critical to the main star formation processes."," Combined with our SFE results, this suggests triggering by arms is not critical to the main star formation processes." +" Arms may drive the formation of molecular gas by bringing the total cold gas to high surface densities, but we do not see clear evidence that spiral shocks are contributing to form either clouds or stars."," Arms may drive the formation of molecular gas by bringing the total cold gas to high surface densities, but we do not see clear evidence that spiral shocks are contributing to form either clouds or stars." +" However, we remind the reader that our study does not encompass the outer regions of these galaxies outside ~ 0.35 ros)."," However, we remind the reader that our study does not encompass the outer regions of these galaxies outside $\sim$ 0.35 $r_{25}$ )." +" It is possible that in the outer regions,(1.e. where the average gas density is too low to form stars, that the molecular gas fraction is enhanced due to the spiral arms."," It is possible that in the outer regions, where the average gas density is too low to form stars, that the molecular gas fraction is enhanced due to the spiral arms." + Evidence for an enhanced star formation efficiency in the outer regions has been seen in some cases Bush et al., Evidence for an enhanced star formation efficiency in the outer regions has been seen in some cases Bush et al. + 2010)., 2010). +" We have used three spiral galaxies (NGC 5194, NGC 628 and NGC 6946) to determine the fraction of star formation and cold gas found in the interarm regions of spiral galaxies."," We have used three spiral galaxies (NGC 5194, NGC 628 and NGC 6946) to determine the fraction of star formation and cold gas found in the interarm regions of spiral galaxies." + We based our definition of the spiral arm areas on stellar mass density enhancements traced by 3.6um images., We based our definition of the spiral arm areas on stellar mass density enhancements traced by $\mu$ m images. +" We find that at least of the emission of star formation tracers (far-UV and 24 um images) must be located in the interarm region, showing that interarm star formation is significant even in grand design spirals."," We find that at least of the emission of star formation tracers (far-UV and 24 $\mu$ m images) must be located in the interarm region, showing that interarm star formation is significant even in grand design spirals." + We examined the star formation efficiency based on H3 in the arm and interarm areas., We examined the star formation efficiency based on $_{2}$ in the arm and interarm areas. +" We confirmed the results of L08 that this quantity is constant on average and any enhancement in the arm areas is less than for the grand design spirals, NGC 628 and NGC 5194."," We confirmed the results of L08 that this quantity is constant on average and any enhancement in the arm areas is less than for the grand design spirals, NGC 628 and NGC 5194." +" The flocculent spiral, NGC 6946, does show an enhancement of the SFE in the arm region, but this may be caused by an underlying weak spiral density wave, which has caused our spiral definition to be associated with isolated regions of high SFR."," The flocculent spiral, NGC 6946, does show an enhancement of the SFE in the arm region, but this may be caused by an underlying weak spiral density wave, which has caused our spiral definition to be associated with isolated regions of high SFR." + We then explored whether the arms were triggering the formation of molecular gas by comparing the fraction of molecular gas in the arm and interarm regions., We then explored whether the arms were triggering the formation of molecular gas by comparing the fraction of molecular gas in the arm and interarm regions. +" The arms showed a higher molecular gas fraction, but this was found to be due to higher gas surface densities in the arms."," The arms showed a higher molecular gas fraction, but this was found to be due to higher gas surface densities in the arms." +" Taken together these results show that interarm star formation is significant and that the spiral arms gather the gas into regions of higher surface densities, which leads to an enhanced molecular fraction, but they do not “shock trigger"" star formation nor molecular gas formation."," Taken together these results show that interarm star formation is significant and that the spiral arms gather the gas into regions of higher surface densities, which leads to an enhanced molecular fraction, but they do not “shock trigger"" star formation nor molecular gas formation." +" Thus, spiral arms act only to reorganize the"," Thus, spiral arms act only to reorganize the" +correlates strongly with the photometric g=; color.,correlates strongly with the photometric $g-i$ color. +" Εςdefined the Ag7) ""color excess” as the difference between a quasars g7 and the median quasar g7 at sale "," They defined the $\Delta(g-i)$ “color excess"" as the difference between a quasar's $g-i$ and the median quasar $g-i$ at the same redshift." +"The color excess correlates with ultravioletthe spectral redshift,iudex.ανν, as (€. Richards. private communication): the «xrclation is not a function of redshift."," The color excess correlates with ultraviolet spectral index, as (G. Richards, private communication); the correlation is not a function of redshift." + The median scatter iu aabout the correlation is approximately 0.1., The median scatter in about the correlation is approximately 0.1. + The top panel iu Figure 39. compares the dclistzibutious of radio-quiet quasars and radio quasars brighter than /=19.1. reproducing the ? result with a much larger sample.," The top panel in Figure \ref{fig:alphahists} compares the distributions of radio-quiet quasars and radio quasars brighter than $i=19.1$, reproducing the \citet{i02} result with a much larger sample." + The long tails toward negative values indicate sources with extremely red spectra., The long tails toward negative values indicate sources with extremely red spectra. + The radio quasars are shifted toward redder colors: the, The radio quasars are shifted toward redder colors: the +"In (he upper part of the plot we show the likelihood 0) for a ""standard model composed of (wo uncoupled (Iuid as in Eq. (4))",In the upper part of the plot we show the likelihood ) for a ” flat-space model composed of two uncoupled fluid as in Eq. \ref{standard}) ) +" with =0: a fraction of matter with equation of state 1 and a fraction of dark energy with constant equation of stateie,.", with =0: a fraction of matter with equation of state =1 and a fraction of dark energy with constant equation of state. +. This plot reproduces Che similar one in Perlmutter et al. (, This plot reproduces the similar one in Perlmutter et al. ( +1999) (see also Dalal et al.,1999) (see also Dalal et al. + 2001 [or a further generalization) and has been obtained by mareinalizing over (he “nuisance parameters ÀJ (the supernovae absolute magnitude) and (the slope of the stretch. [actor relation. see Perlmutter οἱ al.," 2001 for a further generalization) and has been obtained by marginalizing over the ” parameters M (the supernovae absolute magnitude) and (the slope of the stretch factor relation, see Perlmutter et al." + 1999 lor the definitions of these parameters)., 1999 for the definitions of these parameters). + In the limit οἱ 0 the luninositv distance becomes as in the stationary case (2)) withwy., In the limit of 0 the luminosity distance becomes as in the stationary case \ref{dl}) ) with. +".. Therefore. in the lower panel we show the one-dimensional likelihood i,).. corresponding to the section at =0 of the upper panel."," Therefore, in the lower panel we show the one-dimensional likelihood ), corresponding to the section at =0 of the upper panel." + As we will show in the following. it is necessary to decouple the barvons from (he dark energy. so that the simple stationary case (2)) has to be modified with the addition of a fraction of uncoupled barvons.," As we will show in the following, it is necessary to decouple the baryons from the dark energy, so that the simple stationary case \ref{dl}) ) has to be modified with the addition of a fraction of uncoupled baryons." +" The likelihood w,,) ol this case is shown as a thin line.", The likelihood ) of this case is shown as a thin line. + Finally. (he intermediate likelihood drawn in dashed line includes also the supernova SNLOOTIE," Finally, the intermediate likelihood drawn in dashed line includes also the supernova SN1997ff." + The conclusion is (hat al cl, The conclusion is that at c.l. + 0.1 al one sigma). with minimal variations including barvons and including SN199T71E.," 0.1 at one sigma), with minimal variations including baryons and including SN1997ff." + Notice that this is a one-parameter fit to the SNIa. wilh a /dd.o.F. =1.001 for the best fit. just as good as the reference mocel.," Notice that this is a one-parameter fit to the SNIa, with a / =1.001 for the best fit, just as good as the reference model." + Naturally. the stationary solution is acceptable onlv if one can show that the component Clusters while the dark energy component does not.," Naturally, the stationary solution is acceptable only if one can show that the component clusters while the dark energy component does not." + This is the argument of the next section., This is the argument of the next section. + Let us now identily the dark energy component with a scalar field., Let us now identify the dark energy component with a scalar field. + It has been shown in Amendola Tocchini-Valentini (2001) that. assuming and constant. the onlv scalar field model that reduces to the equations above requires a coupling with where (he second equality holds for pressureless dark matter. =1.. which is the case we study below.," It has been shown in Amendola Tocchini-Valentini (2001) that, assuming and constant, the only scalar field model that reduces to the equations above requires a coupling with where the second equality holds for pressureless dark matter, =1, which is the case we study below." + Moreover. it is easy to show that = cconst.," Moreover, it is easy to show that = const." + implies an ⋅ −, implies an exponential potential +CL1I358+62 to that measured locally.,CL1358+62 to that measured locally. + We have shown that the growth-curve structural parameters are consistent with those derived from directly fitting 2D models to the images., We have shown that the growth-curve structural parameters are consistent with those derived from directly fitting 2D models to the images. + However. the direct image fitting implemented by van Dokkum Franx (1996) is currently restricted to rather simple galaxy models: a single component with constant ellipticity and position angle.," However, the direct image fitting implemented by van Dokkum Franx (1996) is currently restricted to rather simple galaxy models: a single component with constant ellipticity and position angle." + Other. more sophisticated algorithms. such as those described by Simard ((1997). could be used as well.," Other, more sophisticated algorithms, such as those described by Simard (1997), could be used as well." + Given the magnitudes of the uncertainties in. half-light radii (cf., Given the magnitudes of the uncertainties in half-light radii (cf. +" Figure 5)). the more sophisticated methods will not likely result in more accurate half-light radii, but simply in greater accuracy in the estimation of their errors."," Figure \ref{rrat}) ), the more sophisticated methods will not likely result in more accurate half-light radii, but simply in greater accuracy in the estimation of their errors." + More distant galaxies. with smaller angular sizes. will require more sophisticated modeling to avoid serious systematic errors im structural parameters due to the under-sampling.," More distant galaxies, with smaller angular sizes, will require more sophisticated modeling to avoid serious systematic errors in structural parameters due to the under-sampling." + Despite these issues. we have shown that the measurements of r.()/7 are quite robust.," Despite these issues, we have shown that the measurements of $r_e \langle +I\rangle_e^{0.76}$ are quite robust." + The current errors m the structural parameters. as deduced by the differences in the results of our two methods. give us confidence that more complicated procedures would not greatly improve on the analysis.," The current errors in the structural parameters, as deduced by the differences in the results of our two methods, give us confidence that more complicated procedures would not greatly improve on the analysis." + What we do find. however. is that one can use 7 to distinguish between bulge- and disk-dominated systems.," What we do find, however, is that one can use $n$ to distinguish between bulge- and disk-dominated systems." + These r!:”-laws. however. do not give much insight into any particular physical properties of the galaxies. such as ratios of bulge to disk radit. or bulge fraction.," These $r^{1/n}$ -laws, however, do not give much insight into any particular physical properties of the galaxies, such as ratios of bulge to disk radii, or bulge fraction." + Given the uncertainties in the actual profile shapes of the CL1358+62 galaxies. the fundamental plane parameter must be constructed with care.," Given the uncertainties in the actual profile shapes of the CL1358+62 galaxies, the fundamental plane parameter must be constructed with care." + Use of the surface brightness at the half-light radius appears to be a strong function of the profile chosen for the fitting (see Figure ))., Use of the surface brightness at the half-light radius appears to be a strong function of the profile chosen for the fitting (see Figure \ref{sfn}) ). + Adopting the mean surface brightness within the half-light radius produces a fundamental plane parameter which is robust against the adopted profile shape., Adopting the mean surface brightness within the half-light radius produces a fundamental plane parameter which is robust against the adopted profile shape. + Although we have outlined. potentially large uncertainties in half-light radit. the correlation between r and (7) ensures that the fundamental plane parameter. r( is conserved. with à scatter of 3%.," Although we have outlined potentially large uncertainties in half-light radii, the correlation between $r$ and $\langle I\rangle$ ensures that the fundamental plane parameter, $r\langle +I\rangle^{0.76}$ is conserved, with a scatter of ." +. In Figure 10... we show the correlation between (7; and r explicitly for the entire sample.," In Figure \ref{errcor}, we show the correlation between $\langle I\rangle$ and $r$ explicitly for the entire sample." +" For every trial fitting range and r'""-law. we plot the mean surface brightness within the fitted half-light radius. normalized by the adopted mean effective surface brightness from the de Vaucouleurs profile fit. versus galaxy radius. normalized by the effective radius from the de Vaucouleurs profile fit."," For every trial fitting range and $r^{1/n}$ -law, we plot the mean surface brightness within the fitted half-light radius, normalized by the adopted mean effective surface brightness from the de Vaucouleurs profile fit, versus galaxy radius, normalized by the effective radius from the de Vaucouleurs profile fit." + The data do not deviate significantly from the correlation expected from pure r'7-]aw growth curves. shown by the dashed line.," The data do not deviate significantly from the correlation expected from pure $r^{1/4}$ -law growth curves, shown by the dashed line." + The slope running parallel to the fundamental plane. r(/j*=constant. is shown by the solid line.," The slope running parallel to the fundamental plane, $r\langle I\rangle^{0.76} = {\rm constant}$, is shown by the solid line." + Given the large uncertainties in half-light radii. the strong error correlation may not only be coincidentally parallel to the fundamental plane. but also likely seriously biases the measured slope of the scaling relation (Kelson1998.Kelson 1999)).," Given the large uncertainties in half-light radii, the strong error correlation may not only be coincidentally parallel to the fundamental plane, but also likely seriously biases the measured slope of the scaling relation \cite{thesis,models}) )." + Because the analysis most closely parallels earlier. ground-based work. we will use the results from the growth curve fitting in the derivation of the fundamental plane (see Kelsonetal. 1999b)).," Because the analysis most closely parallels earlier, ground-based work, we will use the results from the growth curve fitting in the derivation of the fundamental plane (see \cite{kelson99b}) )." + Using deep HST imaging. we have extracted growth curves for a sample of 53 galaxies in the cluster CL1358+62 at ςΞ 0.33.," Using deep HST imaging, we have extracted growth curves for a sample of 53 galaxies in the cluster CL1358+62 at $z=0.33$ ." +" These growth curves have been fit using integrated 7!/- integrated Sersic 7""""-law profiles. and bulge-plus-disk superpositions."," These growth curves have been fit using integrated $r^{1/4}$ integrated Sersic $r^{1/n}$ -law profiles, and bulge-plus-disk superpositions." + Comparisons of the fits between the different parameterizations of the profiles show an sseatter of in half-light radit. although the formal uncertainties in the half-light radii from a given fit are typically smaller by factors of three.," Comparisons of the fits between the different parameterizations of the profiles show an scatter of in half-light radii, although the formal uncertainties in the half-light radii from a given fit are typically smaller by factors of three." + The half-light radii derived from the Sersic profiles agree in the median with those found using the r'7-]aws at the level of1%., The half-light radii derived from the Sersic profiles agree in the median with those found using the $r^{1/4}$ -laws at the level of. +. The half-light radii derived using the bulge-plus-disk superpositions are systematically larger by10%., The half-light radii derived using the bulge-plus-disk superpositions are systematically larger by. +. Despite the potentially large uncertainties in. the half- radu. the quantity that enters the fundamental plane. r4L5076 has been shown to be quite stable.," Despite the potentially large uncertainties in the half-light radii, the quantity that enters the fundamental plane, $r_n\langle I\rangle_n^{0.76}$ has been shown to be quite stable." + This combination is shown to be nearly parallel to the correlation between radius and mean surface brightness for an r'-law growth curve., This combination is shown to be nearly parallel to the correlation between radius and mean surface brightness for an $r^{1/4}$ -law growth curve. + The median half-light radius of this sample is 0461 (2.9 kpe. Hy=65kms Mpe--1. go=0.1). with a range of 1.26 dex in 7. (," The median half-light radius of this sample is 61 (2.9 kpc, $H_0=65$ -1, $q_0=0.1$ ), with a range of 1.26 dex in $r_e$. (" +"Using B/D decompositions. or r'""-laws. only changes the median by -E0""01.)","Using $B/D$ decompositions, or $r^{1/n}$ -laws, only changes the median by $\pm0\Sec 01$ .)" + The range is smaller than the 1.6 dex spanned by the Jérrgensen ((1993) Coma sample. probably due to differences in selection criteria.," The range is smaller than the 1.6 dex spanned by the rgensen (1993) Coma sample, probably due to differences in selection criteria." + The median bulge fraction is about84%., The median bulge fraction is about. +. Many of the galaxies with larger bulge fractions show evidence for central exponential components in their surface brightness. profiles., Many of the galaxies with larger bulge fractions show evidence for central exponential components in their surface brightness profiles. + The few E+A galaxies in this sample invariably have disks (see also Franxefaf.1998.., The few E+A galaxies in this sample invariably have disks (see also \cite{franx98}. + Their bulge fractions are (see also.e.g.. Wirth.Koo.&Kron 1993)).," Their bulge fractions are (see also, \cite{wirth}) )." + Half of the sample shows evidence for disky structures after subtracting two-dimensional r!-law models from the galaxy images., Half of the sample shows evidence for disky structures after subtracting two-dimensional $r^{1/4}$ -law models from the galaxy images. + This result is consistent with the visual classifications in. which nearly half of the sample are of type SO/a trough Sb., This result is consistent with the visual classifications in which nearly half of the sample are of type S0/a trough Sb. + Two of the three E+A galaxies have evidence of spiral arms in their residual maps., Two of the three E+A galaxies have evidence of spiral arms in their residual maps. + In the future. we plan to derive accurate structural parameters for the entire sample of confirmed cluster members and investigate the global correlations of these parameters with the signatures of stellar populations (color). and environment (clustercentric radius and local densities) (Tranetαἰ. 2000).," In the future, we plan to derive accurate structural parameters for the entire sample of confirmed cluster members and investigate the global correlations of these parameters with the signatures of stellar populations (color), and environment (clustercentric radius and local densities) \cite{tran}) )." + The importance of these issues for the fundamental plane is discussed by Kelson ((1999b)., The importance of these issues for the fundamental plane is discussed by Kelson (1999b). + Studies of galactic structural parameters and sealing relations in distant clusters. like this program. clearly require wide-field imaging of the distant cluster fields.," Studies of galactic structural parameters and scaling relations in distant clusters, like this program, clearly require wide-field imaging of the distant cluster fields." + Two more WFPC?2 mosaics have now been taken. of MS2053-04 (220.58) and MS1054—-03 (z= 0.83).," Two more WFPC2 mosaics have now been taken, of MS2053-04 $z=0.58$ ) and MS1054–03 $z=0.83$ )." + With these clusters. the evolution of the properties of cluster galaxies can be accurately mapped to redshifts approaching unity and the Advanced. Camera for Surveys 1s expected to extend such studies to redshifts beyond cal.," With these clusters, the evolution of the properties of cluster galaxies can be accurately mapped to redshifts approaching unity and the Advanced Camera for Surveys is expected to extend such studies to redshifts beyond $z=1$." + We gratefully acknowledge D. Koo and S. Faber. who provided valuable comments on an early version of the paper.," We gratefully acknowledge D. Koo and S. Faber, who provided valuable comments on an early version of the paper." + Furthermore. we appreciate the effort of all those in the HST program that made this unique Observatory work as well asit does.," Furthermore, we appreciate the effort of all those in the HST program that made this unique Observatory work as well asit does." + The assistance of those at STScI who helped with the acquisition of the HST data is also gratefully acknowledged., The assistance of those at STScI who helped with the acquisition of the HST data is also gratefully acknowledged. + Support from STSel grants GOO05989.01-94A. GOO0599].01- and AROS798.01-94A and NSF grant AST-9529098 is gratefully acknowledged.," Support from STScI grants GO05989.01-94A, GO05991.01-94A, and AR05798.01-94A and NSF grant AST-9529098 is gratefully acknowledged." +"E— f) e fuUe fotur. (aln) where 7)=(n—n.)/n,and |=(P—T,)/T,..",f = f_0(t) + + ^2 + where $\eta = (n-n_c)/n_c$and $t=(T-T_c)/T_c$. + The value of 0 is 5.815., The value of $\sigma$ is 5.815. + The coefficient functions are (94) LU) πμ, The coefficient functions are f_0(t) =. + oyfl (4) =497) = constant(, f_1(t) = n_c _0 f_2(t) =. +98)The exponents are à.=0.11 and 5=124., = The exponents are $\alpha = 0.11$ and $\gamma = 1.24$. + The fi(/) and fo(/) are smooth functions of /., The $\bar{f}_0(t)$ and $\bar{f}_2(t)$ are smooth functions of $t$. + The critical amplitudes are related by b = and Pa sa buit (GE) eh 00) , The critical amplitudes are related by b_+ = and 2 a_+ = a_- + ( b_- . +From thermocvnamic relations (he smooth function, From thermodynamic relations the smooth function +". where Dj; ls some minimum impactor diameter and we have substituted Dj,x(Tv;“he,","=, where $D_{imin}$ is some minimum impactor diameter and we have substituted $D_{imin} \propto (T\;v_i^{-2q})^{1/3q}$." + Siuce the cdillereutial size tudex p2.8 (Stuart2001:Bottkeefaf2002)... NxI ," Since the differential size index $p \sim 2.8$ \citep{stu01,bottke02}, $N +\propto v_{imp}^{1.2}$ ." +For each simulated impact at a specific latitude aud longitude. we assign that unpact craters. where C is au arbitrary proportionality coustant.," For each simulated impact at a specific latitude and longitude, we assign that impact $N = C\;v_{imp}^{1.2}$ craters, where $C$ is an arbitrary proportionality constant." + The clepencdaiuce ou p is stall as our results are essentially the same when using au older determined value of p=2., The dependance on $p$ is small as our results are essentially the same when using an older determined value of $p = 2$. + The weak depeudance arises [rou the low orbial speed of the Moon relative to the eucounter speeds of the incomingOm projectiles., The weak dependance arises from the low orbital speed of the Moon relative to the encounter speeds of the incoming projectiles. + Thus for moons such as the Calileau satellites. whose orbital speeds are much higher compared to that of the incoming flux. the value for p becomes more important.," Thus for moons such as the Galilean satellites, whose orbital speeds are much higher compared to that of the incoming flux, the value for $p$ becomes more important." + Note tliat Dyjy aud g are actually irrelevant to our analysis since we are Interested in ouly the crater uumbers relative to au average rather than tle crater sizes., Note that $D_{min}$ and $q$ are actually irrelevant to our analysis since we are interested in only the crater numbers relative to an average rather than the crater sizes. + One expects the departure from uuilorm deusity in the lunar Latitude distribution to be more, One expects the departure from uniform density in the lunar latitude distribution to be more +Reionization marks a crucial event in the history of the universe. when the first sources of ultra-violet (UV) radiation ionize the neutral Intergalactic Medium (GM) and affect the subsequent formation of the cosmic structures.,"Reionization marks a crucial event in the history of the universe, when the first sources of ultra-violet (UV) radiation ionize the neutral Intergalactic Medium (IGM) and affect the subsequent formation of the cosmic structures." + When reionization ends. the small amount of left neutral hydrogen is responsible for the absorption lines that we observe today in the spectra of far objects.," When reionization ends, the small amount of left neutral hydrogen is responsible for the absorption lines that we observe today in the spectra of far objects." + However. the way in which this complex phenomenon occurs is still not well understood and the most recent observations paint it as a spatially inhomogeneous and not istantaneous process.," However, the way in which this complex phenomenon occurs is still not well understood and the most recent observations paint it as a spatially inhomogeneous and not istantaneous process." + While the Gunn Peterson trough of the high-z QSO spectra suggests a late epoch of reionization at 2z6 (Fanetal.2001:BeckerWhiteetal.2003:Fan 2006).. the very recent analysis of the 5-year WMAP data on the cosmic microwave background (CMB) polarization shows an IGM optical depth 7~0.084 which is in better agreement with an earlier reionization redshift. 2~10.5 (Komatsuetal.2008).," While the Gunn Peterson trough of the $z$ QSO spectra suggests a late epoch of reionization at $z\approx 6$ \citep{fan2001,becker2001,white2003b,fan2006}, the very recent analysis of the 5-year WMAP data on the cosmic microwave background (CMB) polarization shows an IGM optical depth $\tau\sim 0.084$ which is in better agreement with an earlier reionization redshift, $z\sim +10.8$ \citep{komatsu2008}." +. On the other hand. a late reionization end üt 2~6 is also probed by the IGM temperature measured at ><4 (Hui&Haiman2003) and by the lack of evolution in the luminosity function of Lyman-a galaxies between >=5.7 and >=6.5 (Malhotra&Rhoads2004.see.however. for evidences of a decline at high 2).," On the other hand, a late reionization end at $z\sim 6$ is also probed by the IGM temperature measured at $z<4$ \citep{hui2003} and by the lack of evolution in the luminosity function of $\alpha$ galaxies between $z=5.7$ and $z=6.5$ \citep[][see, however, {\protect \cite{ota2008}} for evidences of a decline at high $z$." + Overall. the present situation regarding reionization at redshift 2~6 as probed by QSO spectra is still unclear (Beckeretal.2007).," Overall, the present situation regarding reionization at redshift $z\sim6$ as probed by QSO spectra is still unclear \citep{becker2006}." +. Many analytic. semi-analytic and numerical models (see.e.g.al.2008) have been proposed to describe this poorly understood reionization process.," Many analytic, semi-analytic and numerical models \citep[see, e.g.][]{ + gnedin2000,ciardi2003b,wyithe2003,barkana2004, + haiman2003,madau2004,Wyithe2006,choudhury2007,iliev2007,ricotti2008} + have been proposed to describe this poorly understood reionization process." + They basically relate the statistical properties and morphology of the ionized regions to the hierarchical growth of the ionizing sources. making more or less detailed assumptions to describe the ionization and recombination processes acting on the IGM.," They basically relate the statistical properties and morphology of the ionized regions to the hierarchical growth of the ionizing sources, making more or less detailed assumptions to describe the ionization and recombination processes acting on the IGM." + Since the first sources of UV background radiation appear in the firstly formed dark matter haloes. which correspond to the highest peaks of the primordial density field. the reionization process is expected to strongly depend on the main parameters describing the cosmological model and the power spectrum of," Since the first sources of UV background radiation appear in the firstly formed dark matter haloes, which correspond to the highest peaks of the primordial density field, the reionization process is expected to strongly depend on the main parameters describing the cosmological model and the power spectrum of" +Lastly. the campaign that took place ou 2001 September { mace simultaneous observatious with,"Lastly, the campaign that took place on 2004 September 4 made simultaneous observations with" +volume at z—14.,volume at $z=14$. +" At z—6 the percentages are instead 63, 62, and 18, respectively."," At $z=6$ the percentages are instead 63, 62, and 18, respectively." +" When all cells are included, the evolution of [yr rises to a peak at z~8 (following the rising emissivity at z>6 in Eq. 4))"," When all cells are included, the evolution of $\Gamma_{\rm HI}$ rises to a peak at $z \sim 8$ (following the rising emissivity at $z>6$ in Eq. \ref{emiss2}) )" + but declines toward higher redshift., but declines toward higher redshift. +" This is because a larger number of neutral cells are present toward higher redshifts, lowering the volume averaged photo-ionisation rate."," This is because a larger number of neutral cells are present toward higher redshifts, lowering the volume averaged photo-ionisation rate." + The average photo-ionisation rate is slightly lower if only underdense cells are included because the overdense (and hence first to reionise) regions are discarded., The average photo-ionisation rate is slightly lower if only underdense cells are included because the overdense (and hence first to reionise) regions are discarded. +" In other words, the photo-ionisation rates are higher in the overdense cells since the ionising radiation is correlated with the underlying density field (see also ??))."," In other words, the photo-ionisation rates are higher in the overdense cells since the ionising radiation is correlated with the underlying density field (see also \citealt{Iliev08,MesingerFurlanetto09}) )." +" At z—6, by which time all the underdense regions in the simulation have been reionised, all curves converge to a similar value."," At $z=6$, by which time all the underdense regions in the simulation have been reionised, all curves converge to a similar value." +" Note, however, that in the cases where cuts in the neutral fraction are also applied, at z>6 the photo-ionisation rate is always higher compared to the average for all the underdense cells (red dotted curve)."," Note, however, that in the cases where cuts in the neutral fraction are also applied, at $z>6$ the photo-ionisation rate is always higher compared to the average for all the underdense cells (red dotted curve)." +" This is in part because the averages are, by definition, only for highly ionised cells which are assumed to be in ionisation equilibrium."," This is in part because the averages are, by definition, only for highly ionised cells which are assumed to be in ionisation equilibrium." +" The difference is more pronounced at z>8, however, when the ionised regions probed are the increasingly rare ionised bubbles around sources."," The difference is more pronounced at $z>8$, however, when the ionised regions probed are the increasingly rare ionised bubbles around sources." + We thus also expect higher photo-ionisation rates because the selected cells are closer to the ionising sources., We thus also expect higher photo-ionisation rates because the selected cells are closer to the ionising sources. +" However, these regions are rare and so only provide a small contribution to the overall volume averaged ionisation rate."," However, these regions are rare and so only provide a small contribution to the overall volume averaged ionisation rate." + In the lower panel of Figure 3 the evolution of the volume averaged Γη is shown for all five simulations in underdense cells which are highly ionised only (xur< 1075)., In the lower panel of Figure \ref{fig:gamma} the evolution of the volume averaged $\Gamma_{\rm HI}$ is shown for all five simulations in underdense cells which are highly ionised only $x_{\rm HI}<10^{-4}$ ). + Note that this cut most closely represents the regions of the IGM from which the photo-ionisation rates are measured at z~6 (?))., Note that this cut most closely represents the regions of the IGM from which the photo-ionisation rates are measured at $z\simeq 6$ \citealt{BoltonHaehnelt07}) ). +" The redshift evolution of Γη is, as might be expected, similar for all models."," The redshift evolution of $\Gamma_{\rm + HI}$ is, as might be expected, similar for all models." + Model £1.2- a3 typically gives a smaller photo-ionisation rate due to the lower normalisation of the emissivity., Model ${\mathcal E}$ $\alpha$ 3 typically gives a smaller photo-ionisation rate due to the lower normalisation of the emissivity. +" On the other hand, model £1.2-a1.8-H always has a slightly lower value of Cur compared to the case including helium, €1.2-a1.8."," On the other hand, model ${\mathcal E}$ $\alpha$ 1.8-H always has a slightly lower value of $\Gamma_{\rm HI}$ compared to the case including helium, ${\mathcal E}$ $\alpha$ 1.8." +" Note, however, the photoionisation rates are inferred from Eq. (6))"," Note, however, the photoionisation rates are inferred from Eq. \ref{eq:PIrate}) )" +" rather than directly obtained, and so variations in the gas temperature and electron number density in this model will be partly responsible for this difference."," rather than directly obtained, and so variations in the gas temperature and electron number density in this model will be partly responsible for this difference." +" Finally, as required, we find that for all models at z=6 the photo-ionisation rates are consistent with the observational constraints from the forest (?)) and proximity effect (?)), represented by triangles and stars with error bars in Figure 3, respectively."," Finally, as required, we find that for all models at $z=6$ the photo-ionisation rates are consistent with the observational constraints from the forest \citealt{Wyithe.Bolton_2011}) ) and proximity effect \citealt{Calverley11}) ), represented by triangles and stars with error bars in Figure \ref{fig:gamma}, respectively." +" On the other hand, the photo-ionisation rates at z=5 underpredict the observed valuesby a factor of 2-3, despite the fact we have deliberately used an ionising emissivity which agrees with these data when assuming a mean free path consistent with recent observational measurements (e.g. ?))."," On the other hand, the photo-ionisation rates at $z=5$ underpredict the observed valuesby a factor of $2$ $3$, despite the fact we have deliberately used an ionising emissivity which agrees with these data when assuming a mean free path consistent with recent observational measurements (e.g. \citealt{SongailaCowie2010}) )." +" This discrepancy may be understood by recalling that εΗιληι, Where Agi is the mean free path at the Lyman limit."," This discrepancy may be understood by recalling that $\Gamma_{\rm HI} \propto \epsilon_{\rm + HI}\lambda_{\rm HI}$ , where $\lambda_{\rm HI}$ is the mean free path at the Lyman limit." +" Assuming a power-law slope for the column density distribution of 8=1.3, ? measure Ayr~84 (49) comoving Mpc at z—5 (6)."," Assuming a power-law slope for the column density distribution of $\beta=1.3$, \cite{SongailaCowie2010} measure $\lambda_{\rm HI}\simeq 84$ (49) comoving Mpc at $z=5$ (6)." +" In comparison, our simulation volume is 48.7 comoving Mpc on a side."," In comparison, our simulation volume is $48.7$ comoving Mpc on a side." + This sets an effective upper limit on the mean free path of ionising photons in our simulations which is around half the observed value at z—5., This sets an effective upper limit on the mean free path of ionising photons in our simulations which is around half the observed value at $z=5$. +" Our small simulation box therefore most likely accounts for this apparent discrepancy, and we caution that the ionising emissivity in our simulations is underestimated at z<6 as a result."," Our small simulation box therefore most likely accounts for this apparent discrepancy, and we caution that the ionising emissivity in our simulations is underestimated at $z<6$ as a result." +" We have found that our simulations are in reasonable agreement with both the observed Thomson scattering optical depth and background photo-ionisation rate at z= 6, giving us confidence that we may now explore the"," We have found that our simulations are in reasonable agreement with both the observed Thomson scattering optical depth and background photo-ionisation rate at $z=6$ , giving us confidence that we may now explore the" +Using the ? estimator. the cross-correlation as a function of projected separation. 7. and line-of-sight separation. 7. is while the autocorrelation is The parallel and perpendicular components of the pair separations are distinguished in the data by and wheres=vy—Vo. ξνι+νο) and vy and v» are the redshift positions of the two objects in à pair (?)..,"Using the \citet{landy_szalay93} estimator, the cross-correlation as a function of projected separation, $r_p$, and line-of-sight separation, $\pi$, is while the autocorrelation is The parallel and perpendicular components of the pair separations are distinguished in the data by and where ${\bf s} \equiv {\bf v_1} - {\bf v_2}$, ${\bf l} \equiv \frac{1}{2} ({\bf v_1} + {\bf v_2})$ and ${\bf v_1}$ and ${\bf v_2}$ are the redshift positions of the two objects in a pair \citep{fisher_etal94}." + From the correlation function. the correlation function is where z is integrated to 7=34057! Mpe. large enough to include all significant clustering signal.," From the correlation function, the correlation function is where $\pi$ is integrated to $\pi = 40 h^{-1}$ Mpc, large enough to include all significant clustering signal." + The projected correlation is measured in logarithmic bins for projected radii between 10 A7! kpe to 6.3 A7! Mpe. with 14 total data points.," The projected correlation is measured in logarithmic bins for projected radii between 10 $h^{-1}$ kpc to 6.3 $h^{-1}$ Mpc, with 14 total data points." + Statistical errors in the correlation are estimated via Jackknife sampling (see.e.g..?)..," Statistical errors in the correlation are estimated via jackknife sampling \citep[see, e.g.,][]{lupton93}." + In the SDSS data. the survey area is divided into 205 equal area samples using the hierarchical pixel schemeSDSSPix.. which represents well the rectangular geometry of the SDSS stripes.," In the SDSS data, the survey area is divided into 205 equal area samples using the hierarchical pixel scheme, which represents well the rectangular geometry of the SDSS stripes." + The covariance matrices are estimated by the covariance between Jackknife samples — samples where one of the 205 equal area subsamples is omitted., The covariance matrices are estimated by the covariance between jackknife samples – samples where one of the 205 equal area subsamples is omitted. + In order to appropriately estimate the covariance matrix. the number of jackknife samples must be significantly greater than the number of bins in which the correlation function is estimated (2)..," In order to appropriately estimate the covariance matrix, the number of jackknife samples must be significantly greater than the number of bins in which the correlation function is estimated \citep{hartlap_etal07}." + Typically. each jackknife sample ts constructed to be larger thai the largest separation neasured in the corresponding correlation function. and. the number of jackknife samples is at least equal to the square of the number of bins.," Typically, each jackknife sample is constructed to be larger than the largest separation measured in the corresponding correlation function, and the number of jackknife samples is at least equal to the square of the number of bins." + With 14 bins. 196 is the minimum number of jackknifes samples.," With 14 bins, 196 is the minimum number of jackknifes samples." + The data sample uses slightly more. 205.," The data sample uses slightly more, 205." + The typical jackknife region. then. has a comoving volume of «19/7Mpc.," The typical jackknife region, then, has a comoving volume of $\sim19^3 h^{3} \rm Mpc^{-3}$." + The projected cross-correlation and corresponding autocorrelation functions are shown in Fig. I., The projected cross-correlation and corresponding autocorrelation functions are shown in Fig. \ref{fig:data}. + In the SDSS spectroscopic survey. no single pointing of the telescope can measure the spectra of objects that are separated by less than 55”. the fiber collision distance.," In the SDSS spectroscopic survey, no single pointing of the telescope can measure the spectra of objects that are separated by less than $55\arcsec$, the fiber collision distance." + At the median redshift of the sample. 55” is 30 A! kpc. well above the minimum separation of 10 47! kpe in the data.," At the median redshift of the sample, $55\arcsec$ is 30 $h^{-1}$ kpc, well above the minimum separation of 10 $h^{-1}$ kpc in the data." + To achieve the minimum separation. I employ a catalog corrected for collisions.," To achieve the minimum separation, I employ a catalog corrected for collisions." + For pairs of objects separated by less than the fiber collision distance in the target selection catalog. the unobserved target Is assigned the redshift of the observed object in the pair.," For pairs of objects separated by less than the fiber collision distance in the target selection catalog, the unobserved target is assigned the redshift of the observed object in the pair." + This could bias the sample by overestimating pairs. but significant error is unlikely given that pairs at those separations are extremely correlated (as in Fig. 1)).," This could bias the sample by overestimating pairs, but significant error is unlikely given that pairs at those separations are extremely correlated (as in Fig. \ref{fig:data}) )." + Previous studies have described systematic. errors. with angular dependence (???)..," Previous studies have described systematic errors with angular dependence \citep{masjedi_etal06,mandelbaum_etal06b,adelman_mccarthy_etal08}." +" Issues with sky subtraction may lead to underestimation of pairs by ~566 with angular separations between 40—90"" and an overestimation of pairs at angular separations less than 20—30"".", Issues with sky subtraction may lead to underestimation of pairs by $\sim5\%$ with angular separations between $40-90\arcsec$ and an overestimation of pairs at angular separations less than $20-30\arcsec$. + This effect is most acute for pairs of objects that consist of an apparently bright object and an apparently faint object (Rachel Mandelbaum 2006. private communication.," This effect is most acute for pairs of objects that consist of an apparently bright object and an apparently faint object (Rachel Mandelbaum 2006, private communication)." + In the cross-correlated sample. the estimated systematic error of for pairs with angular separations between 40” and 90” is smaller than the statistical errors in the correlation function. ~10%. indicating that such errors do not affect the results.," In the cross-correlated sample, the estimated systematic error of for pairs with angular separations between $40\arcsec$ and $90\arcsec$ is smaller than the statistical errors in the correlation function, $\sim10\%$, indicating that such errors do not affect the results." +" For the unconstrained overestimate of pairs with angular separations less than 20"". only the first bin of the estimated cross-correlation (containing objects with projected physical separation of less than 16 f7! kpc) is affected."," For the unconstrained overestimate of pairs with angular separations less than $20\arcsec$, only the first bin of the estimated cross-correlation (containing objects with projected physical separation of less than 16 $h^{-1}$ kpc) is affected." + In this bin. of the pairs could be possibly affected. while the fractional statistical error in the correlation function ts15%.," In this bin, of the pairs could be possibly affected, while the fractional statistical error in the correlation function is." +. Given that only one of the data points is affected. it seems unlikely that the parameter estimates are biased by this systematic.," Given that only one of the data points is affected, it seems unlikely that the parameter estimates are biased by this systematic." + However. I test the possible effects of this error in Sections 5.5 and 6.3..," However, I test the possible effects of this error in Sections \ref{sec:systematictest} and \ref{sec:robustnessresults}." + The correlation function can be modeled using the halo model — assuming that all galaxies anddark matter particles live in dark matter halos., The correlation function can be modeled using the halo model – assuming that all galaxies anddark matter particles live in dark matter halos. + First. the correlation function is decomposed into two parts: a one-halo term and a two-halo term.," First, the correlation function is decomposed into two parts: a one-halo term and a two-halo term," +Tt has long been kuown that differeut mixing processes in stellar cores stronely iuflueuce the overall evolution of stars.,It has long been known that different mixing processes in stellar cores strongly influence the overall evolution of stars. + The treatment of couvectively uustable zones aud overshooting regions in evolutionary models affects the outcoming luninosity. temperature. and main-sequence lifetime of the stars. among other One of the mixing processes that has been extensively studied in massive stars evolution is that ΠΕ ο Dinin," The treatment of convectively unstable zones and overshooting regions in evolutionary models affects the outcoming luminosity, temperature, and main-sequence lifetime of the stars, among other One of the mixing processes that has been extensively studied in massive stars evolution is that of semiconvection." +g the lvdrogen-burning phase the raciation pressure makes the core expand., During the hydrogen-burning phase the radiation pressure makes the core expand. + Opacitics are increased outside the core by electron scattering. where a chemical discontinuity appears as a result of this core expausion.," Opacities are increased outside the core by electron scattering, where a chemical discontinuity appears as a result of this core expansion." + Since the pioneer work of Sclawarzschild&Πατ(1958).. several authors have investigated the occurrence of seniconvective nixing n massive stars and its effects on stellar evolution (c.g.Stothers1970:&Chin1975:Langer1985).," Since the pioneer work of \citet{sh58}, several authors have investigated the occurrence of semiconvective mixing in massive stars and its effects on stellar evolution \citep[e.g.][]{rs70,sc75,nl85}." +. Although semiconvection was initially thought to occur only m massive stars. if was also found in low-nass stars as a consequence of a discontinuity iu the nolecular weight produced either by couvective core expansion due to the increasing importance of the evcle over the chain (Mitalas1972:Saio1975).. or by he retreating convective core leaving behind a chemical iscoutinuity (Faulkuer&Caunou1973). both cases xoduciug higher opacitics outside the convective We address the issue of the determination of couvective )oundaries and the treatment of mixing zones which xeseut a eradient in the molecular weight by the iuclusion of the Ledoux criterion for couvective instability and a diffusive approach for semiconvective mixiug iu our stellar evolution codo.," Although semiconvection was initially thought to occur only in massive stars, it was also found in low-mass stars as a consequence of a discontinuity in the molecular weight produced either by convective core expansion due to the increasing importance of the cycle over the chain \citep{rm72,hs75}, or by the retreating convective core leaving behind a chemical discontinuity \citep{fc73}, both cases producing higher opacities outside the convective We address the issue of the determination of convective boundaries and the treatment of mixing zones which present a gradient in the molecular weight by the inclusion of the Ledoux criterion for convective instability, and a diffusive approach for semiconvective mixing in our stellar evolution code." + The convective zoue boundaries are defined either with the Schwarzschild criterion (Schwarzschild&Παν1958) or the Ledoux criterion (Ledoux1917)., The convective zone boundaries are defined either with the Schwarzschild criterion \citep{sh58} or the Ledoux criterion \citep{pl47}. +. For the latter case. the Ledoux temperature gradient is defined. as," For the latter case, the Ledoux temperature gradient is defined as" +observations of M87 that lacked sufficient angular resolution to allow detailed comparison to the radio structures shown in the Owen et al. (,observations of M87 that lacked sufficient angular resolution to allow detailed comparison to the radio structures shown in the Owen et al. ( +2000) study.,2000) study. + Young. Wilson Mundell (2002) used a 37 ksee Chandra observation to. confirm previous structures. as well as to describe several new features including two nearly spherical “edges” at ~45” and ~3 that they attribute to activity in the nucleus associated with jet production.," Young, Wilson Mundell (2002) used a 37 ksec Chandra observation to confirm previous structures, as well as to describe several new features including two nearly spherical “edges” at $\sim45''$ and $\sim3'$ that they attribute to activity in the nucleus associated with jet production." + The Chandra images also show cavities and filaments i the eastern and southwestern X-ray arms., The Chandra images also show cavities and filaments in the eastern and southwestern X-ray arms. + Young et al., Young et al. + argued that the arms were overpressurized and multi-temperature., argued that the arms were overpressurized and multi-temperature. + Molendi (2002) used XMM-Newton observations to show that the X-ray arms required. temperature models with gas temperatures in the range 0.8—] keV and &7—1.6—2.5 keV. In this paper. we combine deep Chandra. ROSAT HRI. and XMM-Newton observations to study the impact of AGN outbursts on the gaseous atmosphere around M87 and the interaction of the radio emitting plasma with the hot gas.," Molendi (2002) used XMM-Newton observations to show that the X-ray arms required two-temperature models with gas temperatures in the range $kT\sim0.8-1$ keV and $kT\sim1.6-2.5$ keV. In this paper, we combine deep Chandra, ROSAT HRI, and XMM-Newton observations to study the impact of AGN outbursts on the gaseous atmosphere around M87 and the interaction of the radio emitting plasma with the hot gas." + As others have noted. the Chandra. XMM-Newton. and ROSAT HRI observations show rich structure on many angular scales.," As others have noted, the Chandra, XMM-Newton, and ROSAT HRI observations show rich structure on many angular scales." + These include knots in the jet. surrounding cavities. a coincident X-ray and radio bubble just budding from the southeast of the radio core region. a weak shock. filaments and cavities in the east and southwest arms. and an are-like region of enhanced emission coincident with the outer edge of the southern radio halo.," These include knots in the jet, surrounding cavities, a coincident X-ray and radio bubble just budding from the southeast of the radio core region, a weak shock, filaments and cavities in the east and southwest arms, and an arc-like region of enhanced emission coincident with the outer edge of the southern radio halo." + In this paper. we describe the X-ray observations and discuss the origin of these features in M87.," In this paper, we describe the X-ray observations and discuss the origin of these features in M87." + M$7 has been well studied at all wavelengths as well as by each new X-ray mission., M87 has been well studied at all wavelengths as well as by each new X-ray mission. + Here. we describe our analysis for Chandra. XMM-Newton. and the ROSAT HRI.," Here, we describe our analysis for Chandra, XMM-Newton, and the ROSAT HRI." + X-ray observations were obtained from the Chandra. XMM-Newton. or HEASARC archives.," X-ray observations were obtained from the Chandra, XMM-Newton, or HEASARC archives." + While Chandra provides unprecedented angular resolution; XMM-Newton and the ROSAT HRI yield large FOV images to study the larger scale structures around M87.," While Chandra provides unprecedented angular resolution, XMM-Newton and the ROSAT HRI yield large FOV images to study the larger scale structures around M87." + We adopt a distance for M87 of 16 Mpe (Tonry et al., We adopt a distance for M87 of 16 Mpc (Tonry et al. + 2001) which yields a scale of 4.65 kpe per are minute., 2001) which yields a scale of 4.65 kpc per arc minute. + For all analyses of radial distributions. projections. and spectra. point sources were detected and then excluded (231 for Chandra) as was the bright M87 nucleus and jet.," For all analyses of radial distributions, projections, and spectra, point sources were detected and then excluded (231 for Chandra) as was the bright M87 nucleus and jet." + M87 was observed with Chandra on 29-30 July 2000 (OBSID 352) and 6-8 July 2002 (OBSID 2707) for 37 ksee and 105 ksee respectively with ACIS-S at the focus., M87 was observed with Chandra on 29-30 July 2000 (OBSID 352) and 6-8 July 2002 (OBSID 2707) for 37 ksec and 105 ksec respectively with ACIS-S at the focus. + Details for the July 2000 and July 2002 observations are given by Young et al. (, Details for the July 2000 and July 2002 observations are given by Young et al. ( +2002) ànd Jordan et al. (,2002) and Jordan et al. ( +2003) respectively.,2003) respectively. + The July 2002 observation was used by Jordan et al. (, The July 2002 observation was used by Jordan et al. ( +2003) to analyze the point source population of M87.,2003) to analyze the point source population of M87. + We applied standard screening to the event list. omitting ASCA grades 1. 5. and 7. known hot pixels. bad columns. and chip node boundaries.," We applied standard screening to the event list, omitting ASCA grades 1, 5, and 7, known hot pixels, bad columns, and chip node boundaries." + Because the Virgo cluster is both bright and extended. we used the ACIS S1 chip to monitor the instrument background rate in the energy band 2.5-6.0 keV (see Markevitch 2001).," Because the Virgo cluster is both bright and extended, we used the ACIS S1 chip to monitor the instrument background rate in the energy band 2.5-6.0 keV (see Markevitch 2001)." + We found significant background flaring in both observations and the corresponding time intervals. were removed., We found significant background flaring in both observations and the corresponding time intervals were removed. + The remaining exposure times for OBSID's 2707 and 352 were 87.9 ksee and 30.0 ksee for a total observation. time of 117.9 ksec., The remaining exposure times for OBSID's 2707 and 352 were 87.9 ksec and 30.0 ksec for a total observation time of 117.9 ksec. + For all imaging analyses. we generated images. exposure maps. and backgrounds separately and then combined the results in sky coordinates.," For all imaging analyses, we generated images, exposure maps, and backgrounds separately and then combined the results in sky coordinates." + We normalized the exposure maps between frontside and backside illuminated CCD's. assuming the emission was characterized by thermal emission from hot gas with AT=2 keV. For spectral analyses. we extracted spectra separately from each observation and fit the spectra jointly in XSPEC.," We normalized the exposure maps between frontside and backside illuminated CCD's, assuming the emission was characterized by thermal emission from hot gas with $kT=2$ keV. For spectral analyses, we extracted spectra separately from each observation and fit the spectra jointly in XSPEC." + Response matrices and effective areas were averaged by weighting by the observed. X-ray emission., Response matrices and effective areas were averaged by weighting by the observed X-ray emission. + XMM-Newton observed M87 for 57.4 ksee on 19 June 2000., XMM-Newton observed M87 for 57.4 ksec on 19 June 2000. + Details for this observation are given by Bohringer et al. (, Details for this observation are given by Bohringer et al. ( +2001) and Belsole et al. (,2001) and Belsole et al. ( +2001).,2001). + We report on results obtained with the MOS instrument., We report on results obtained with the MOS instrument. + Calibrated event lists were generated using SAS v5.3., Calibrated event lists were generated using SAS v5.3. + The MOS background was calculated using the blank field data accumulated over a large number of observations (Lumb et al., The MOS background was calculated using the blank field data accumulated over a large number of observations (Lumb et al. + 2002) For analysis. we used MOS data with patterns in the range 0-12 and the recommended value of the flag EEA).," 2002) For analysis, we used MOS data with patterns in the range 0-12 and the recommended value of the flag EA)." + For generating the temperature map. we use one of the MOS response matrices provided by the XMM SOC and assume that the same response (corrected for energy dependent vignetting) is applicable for all regions.," For generating the temperature map, we use one of the MOS response matrices provided by the XMM SOC and assume that the same response (corrected for energy dependent vignetting) is applicable for all regions." + The gas temperature map was calculated as described by Churazov et al. (, The gas temperature map was calculated as described by Churazov et al. ( +1996; see also Churazov et al.,1996; see also Churazov et al. + 2003 for this method applied to XMM-Newton data for the Perseus cluster)., 2003 for this method applied to XMM-Newton data for the Perseus cluster). + An adaptive smoothing also is applied to the map so that each value of the temperature ts calculated using regions containing ~3600 counts., An adaptive smoothing also is applied to the map so that each value of the temperature is calculated using regions containing $\sim3600$ counts. + Comparison of the overall structure with the results of direct spectral fitting of individual regions shows good agreement., Comparison of the overall structure with the results of direct spectral fitting of individual regions shows good agreement. + M87 was observed seven times with the ROSAT HRI between 1992 and 1997 (ROSAT sequence numbers rh700214.. rh702081. rh704000. ΠΟ. rh702774. rh701713. rh702775) for a total observation length of 171.6 ksec.," M87 was observed seven times with the ROSAT HRI between 1992 and 1997 (ROSAT sequence numbers rh700214, rh702081, rh704000, rh701712, rh702774, rh701713, rh702775) for a total observation length of 171.6 ksec." + A detailed description of the ROSAT HRI observations is given by Harris. Biretta Junor (1997) and Harris et al. (," A detailed description of the ROSAT HRI observations is given by Harris, Biretta Junor (1997) and Harris et al. (" +2000).,2000). + We generated images from each observation using PHA channels 3-9 to reduce the instrumental background and improve the signal-to-noise for the diffuse emission., We generated images from each observation using PHA channels 3-9 to reduce the instrumental background and improve the signal-to-noise for the diffuse emission. + The images Were then summed for further analysis., The images were then summed for further analysis. + X-ray images of the two merged M87 Chandra observations are shown in Fig., X-ray images of the two merged M87 Chandra observations are shown in Fig. + | and 2.., \ref{fig:bl1sum} and \ref{fig:adapt}. + Fig., Fig. +" laa shows the central region at full resolution (1 pixel 2 0.392"") in the energy band 0.5-2.5 keV. Fig.", \ref{fig:bl1sum}a a shows the central region at full resolution (1 pixel $= 0.492''$ ) in the energy band 0.5-2.5 keV. Fig. + [bb covers a slightly smaller region and includes 6 em radio contours., \ref{fig:bl1sum}b b covers a slightly smaller region and includes 6 cm radio contours. + Fig., Fig. + lec labels the features discussed in the text below., \ref{fig:bl1sum}c c labels the features discussed in the text below. + Fig., Fig. + 2. 1s an adaptively smoothed image., \ref{fig:adapt} is an adaptively smoothed image. + On the smallest scales. Fig.," On the smallest scales, Fig." + 1. and Fig., \ref{fig:bl1sum} and Fig. + 2 show:," \ref{fig:adapt} + show:" +"while 7, scales as Decreasing the inclination of the orbit not only reduces the measured. duration. {δω but also reduces the transit depth. d.","while $\eta_\star$ scales as Decreasing the inclination of the orbit not only reduces the measured duration, $D_{\rm obs}$, but also reduces the transit depth, $d$." + Both [actors act to reduce 5. while they counteract each other for ο.," Both factors act to reduce $\eta_{\rm p}$, while they counteract each other for $\eta_\star$." + The latter has a much stronger dependence on Do). than d for the shallow events that are of interest. so decreasing Z also decreases i4.," The latter has a much stronger dependence on $D_{\rm obs}$ than $d$ for the shallow events that are of interest, so decreasing $Z$ also decreases $\eta_\star$." + Following this line of reasoning. the diagnostics will therefore be a maximum for central transits (with Z=1) and less lor ore erazine (rausils.," Following this line of reasoning, the diagnostics will therefore be a maximum for central transits (with $Z=1$ ) and less for more grazing transits." + Thus. (rue exoplanetary events would have a diagnostic less (han or equal {ο one. while stellar events (blends or grazing binaries) would often. bul not always. have diagnosties greater than one.," Thus, true exoplanetary events would have a diagnostic less than or equal to one, while stellar events (blends or grazing binaries) would often, but not always, have diagnostics greater than one." + some erazing stellar binaries and blended eclipsing binaries will have similar diagnostics to exoplanets. which will lead to some stellar contamination in the reduced set of candidates even alter the diagnostic has been applied.," Some grazing stellar binaries and blended eclipsing binaries will have similar diagnostics to exoplanets, which will lead to some stellar contamination in the reduced set of candidates even after the diagnostic has been applied." + Some grazing binaries can be identified via a Clearly V-shaped transit (Udalskietal.2002a).. the presence of ellipsoidal variations 2003:Sirko&Paczviski 2003).. or by virtue of the existence of a detectable secondary transit that has a different depth than that of the primary transit.," Some grazing binaries can be identified via a clearly V-shaped transit \citep{udalski1}, the presence of ellipsoidal variations \citep{drake,sirko}, or by virtue of the existence of a detectable secondary transit that has a different depth than that of the primary transit." + Also. binary svstems in which both stars are nearly identical will have a photometric period that is one-half the actual period. as it will have (wo identical transits per orbit.," Also, binary systems in which both stars are nearly identical will have a photometric period that is one-half the actual period, as it will have two identical transits per orbit." + Because of this. their diagnostics are increased by a [factor of 25. helping to push them out of the regime populated by exoplanetary evenis.," Because of this, their diagnostics are increased by a factor of $2^{\frac{1}{3}}$, helping to push them out of the regime populated by exoplanetary events." + Additionally. à large percentage of svstems involving transits of giant stars could in theory be identilied as non-plauetary. as their large radii lead (o very long transit durations.," Additionally, a large percentage of systems involving transits of giant stars could in theory be identified as non-planetary, as their large radii lead to very long transit durations." + The exoplanet diagnostic should also be useful in separating most blends [rom exoplanetary iransits., The exoplanet diagnostic should also be useful in separating most blends from exoplanetary transits. +" Dlended eclipsing binaries would have a high ,4+8,» compared to exoplanets and (he dilution of their transits to a shallower depth by a third component means that their transits would generally be more central than a grazing binary [or a given transit depth."," Blended eclipsing binaries would have a high $R_{\star,1}+R_{\star,2}$ compared to exoplanets and the dilution of their transits to a shallower depth by a third component means that their transits would generally be more central than a grazing binary for a given transit depth." + They would thus have a longer duration (auc a higher exoplanet diagnostic) relative to other events with a similar transit depth. whether (μον be grazing binaries or exoplanets.," They would thus have a longer duration (and a higher exoplanet diagnostic) relative to other events with a similar transit depth, whether they be grazing binaries or exoplanets." + This is potentially. verv useful for müssions such as lepler. which will likely identify large nunmbers of objects that. exhibit periodie transits of a variletv of depths. many of which will be blends.," This is potentially very useful for missions such as Kepler, which will likely identify large numbers of objects that exhibit periodic transits of a variety of depths – many of which will be blends." + The shallowest events are both the most interesting and the most cdiffieult to confirm: via follow-up observations: any technique that can eliminate some of these without follow-up will save significant astronomical resources., The shallowest events are both the most interesting and the most difficult to confirm via follow-up observations; any technique that can eliminate some of these without follow-up will save significant astronomical resources. +current quark mass. the Lagrangian becomes chirally svmmetric and (o0)(T) the corresponding order parameter.,"current quark mass, the Lagrangian becomes chirally symmetric and $\langle {\bar \psi} \psi \rangle(T)$ the corresponding order parameter." +" In the confined phase. with effective constituent quark masses M,0.5 GeV. (his chiral «νοον is spontaneously broken. while in (he deconfined phase. at hieh enough temperature. we expect ils restoration."," In the confined phase, with effective constituent quark masses $M_q \simeq 0.3$ GeV, this chiral symmetry is spontaneously broken, while in the deconfined phase, at high enough temperature, we expect its restoration." + In the real κοντα. with finite pion ancl hence finite current. quark mass. (his «vimetry is also only approximate. since (ce)(TL) now never vandshes al [inite 7.," In the real world, with finite pion and hence finite current quark mass, this symmetry is also only approximate, since $\langle {\bar \psi} \psi \rangle (T)$ now never vanishes at finite $T$ ." +" The behaviour of (C0)(T) and the corresponding susceptibility X5,~Olee)/Om, are shown in ref2; b. [13].. caleulated for the same case as above in a. We note here (he expected sudden drop of the effective quark mass and the associated sharp peak in the susceptibility."," The behaviour of $\langle {\bar \psi} \psi \rangle(T)$ and the corresponding susceptibility $\chi_m \sim \partial \langle {\bar \psi} +\psi \rangle / \partial m_q$ are shown in \\ref{2_4}$ $~\!$ b \cite{K&L}, calculated for the same case as above in \\ref{2_4}$ $~\!$ a. We note here the expected sudden drop of the effective quark mass and the associated sharp peak in the susceptibility." + The temperature at which (his occurs coincides with that obtained. through the deconfinement measure., The temperature at which this occurs coincides with that obtained through the deconfinement measure. + We therefore conclude that ad vanishing barvon number density. quark ceconlinement and the shift from constituent to current quark mass coincide.," We therefore conclude that at vanishing baryon number density, quark deconfinement and the shift from constituent to current quark mass coincide." +" We thus obtain for jj;=0 a rather well defined phase structure. consisting of a confined phase lor 2«T,. with L(f)~0 and (tYP)x0.and a deconfined phase for T>T;. with LIT)z0 and (00)(T)~0."," We thus obtain for $\mu_B=0$ a rather well defined phase structure, consisting of a confined phase for $T < T_c$, with $L(T) \simeq 0$ and $\langle {\bar \psi} \psi \rangle(T) \not= 0$,and a deconfined phase for $T>T_c$ with $L(T)\not= 0$ and $\langle {\bar \psi} \psi \rangle(T) \simeq 0$." +" The underlying svmmetries associated to the critical behaviour al 7=T. the Z4 symmetry of deconfinement and the chiral svmmetry of the quark mass shift. become exact in the limits m,—2€ and m,—0. respectively."," The underlying symmetries associated to the critical behaviour at $T=T_c$, the $Z_3$ symmetry of deconfinement and the chiral symmetry of the quark mass shift, become exact in the limits $m_q \to \infty$ and $m_q \to +0$, respectively." + In the real world. both svimnmnetries are only approximate: nevertheless. we see [from tL halbolhassocialedimeasuresrelainanalmosterilicalbehaviour.," In the real world, both symmetries are only approximate; nevertheless, we see from \\ref{2_4} that both associated measures retain an almost critical behaviour." + Next we come to the behaviour of energy density € and pressure 2 at deconfinement [14].., Next we come to the behaviour of energy density $\e$ and pressure $P$ at deconfinement \cite{thermo}. +" In refedens.. il is seenthat €/T changes quite abruptly at the above critical temperature T,.. increasing [rom a low hadronic value to one slightly below that expected for an ideal eas of massless quarks and gluons [15].."," In \\ref{edens}, it is seenthat $\e/T^4$ changes quite abruptly at the above critical temperature $T_c$, increasing from a low hadronic value to one slightly below that expected for an ideal gas of massless quarks and gluons \cite{Biele}." + -0.5em Besides the sudden increase at deconfinement. (hereare (wo futher points to note.," -0.5cm Besides the sudden increase at deconfinement, thereare two further points to note." + In the region 7.«T«2 T.. there still remain strong interaction effects., In the region $T_c\!<\! T\! <\! 2~T_c$ there still remain strong interaction effects. + As seen in refinter.. the interaction measure’ A=(€-3P)/T! remains sizeable and does not vanish.," As seen in \\ref{inter}, , the `interaction measure' $\Delta=(\e - 3P)/T^4$ remains sizeable and does not vanish," +logN(H 1))/cm-?>20.3.,$\log N$ $^{-2} \ge 20.3$. +" They appear to sample a range of galaxy types, from the extended disks of galaxies, to smaller subgalactic size haloes, as well as smaller clouds within larger galaxies (Wolfeetal.2005)."," They appear to sample a range of galaxy types, from the extended disks of galaxies, to smaller subgalactic size haloes, as well as smaller clouds within larger galaxies \citep{wol05}." +". Large scale surveys, such as the Sloan Digital Sky Survey, have increased ten-fold the number of known DLAs, which now number in excess of ~1000 (Noterdaemeetal.2009;Prochaska&Wolfe 2009)."," Large scale surveys, such as the Sloan Digital Sky Survey, have increased ten-fold the number of known DLAs, which now number in excess of $\sim 1000$ \citep{not09,pro09}." +". Follow-up high resolution spectroscopy of the most metal-poor DLAs is of particular interest, since the gas they trace may have been enriched by very few generations of stars (Pettinietal.2008;Penprase 2010)."," Follow-up high resolution spectroscopy of the most metal-poor DLAs is of particular interest, since the gas they trace may have been enriched by very few generations of stars \citep{pet08,pen10}." +". Moreover, measuring elemental abundances in DLAs is straightforward; the only potential complications are line saturation and dust depletion and both effects are of much reduced importance for metallicities Z<1/1007ᾳ9."," Moreover, measuring elemental abundances in DLAs is straightforward; the only potential complications are line saturation and dust depletion and both effects are of much reduced importance for metallicities $Z \ltsim 1/100 Z_\odot$." +" In addition, the chemical evolution of such systems is rather simple, whereas in more chemically evolved systems, there are uncertainties in the star formation history, gas inflow and outflow, large contributions from AGB stars and Type Τα supernovae, with the result that the signatures of the first stars can be easily washed out."," In addition, the chemical evolution of such systems is rather simple, whereas in more chemically evolved systems, there are uncertainties in the star formation history, gas inflow and outflow, large contributions from AGB stars and Type Ia supernovae, with the result that the signatures of the first stars can be easily washed out." +" Thus, if the most metal-poor DLAs hold the key to unravelling the chemical enrichment from the first stars, it is of great interest to compare their observed abundance patterns with the nucleosynthesis yields of metal-free stars."," Thus, if the most metal-poor DLAs hold the key to unravelling the chemical enrichment from the first stars, it is of great interest to compare their observed abundance patterns with the nucleosynthesis yields of metal-free stars." +" Cookeetal.(2010b) recently reported such a DLA with [Fe/H] ~-—3, which exhibits astrong carbon enhancement relative to all other available elements, including [C/Fe] ~+1.53."," \citet{coo10b} recently reported such a DLA with [Fe/H] $\simeq -3$, which exhibits astrong carbon enhancement relative to all other available elements, including [C/Fe] $\simeq +1.53$." + This reminds us of the CEMP stars in the solar neighborhood., This reminds us of the CEMP stars in the solar neighborhood. +" In this letter, we compare the elemental abundance pattern of the C-rich DLA with the nucleosynthesis yields of both core-collapse and pair-instability supernovae (§22)."," In this letter, we compare the elemental abundance pattern of the C-rich DLA with the nucleosynthesis yields of both core-collapse and pair-instability supernovae 2)." + In §33 we give a more general discussion of the chemical enrichment of the Universe by the first generation of stars., In 3 we give a more general discussion of the chemical enrichment of the Universe by the first generation of stars. + We summarize our main conclusions in §44., We summarize our main conclusions in 4. +" In stars with initial masses of >10M, the iron core undergoes gravitational collapse at the end of the star’s life."," In stars with initial masses of $\gtsim 10 M_\odot$, the iron core undergoes gravitational collapse at the end of the star's life." +" If sufficient amount of the released gravitational energy is transported to the outgoing shock wave, a supernova explosion occurs."," If sufficient amount of the released gravitational energy is transported to the outgoing shock wave, a supernova explosion occurs." +" The mechanism of core-collapse explosion and formation of a black hole remnant is still uncertain, although a few groups have presented feasible calculations of exploding supernovae (Marek&Janka2009, e.g.,).."," The mechanism of core-collapse explosion and formation of a black hole remnant is still uncertain, although a few groups have presented feasible calculations of exploding supernovae \citep[e.g.,]{mar09}." +" Thus, Umeda&Nomoto(2002),, Iwamotoetal. (2005),, and Tominagaetal.(2007) have calculated nucleosynthesis yields by promptly exploding the progenitor model without calculating further collapse and bounce, and by applying mixing-fallback."," Thus, \citet{ume02}, \citet{iwa05}, and \citet{tom07} have calculated nucleosynthesis yields by promptly exploding the progenitor model without calculating further collapse and bounce, and by applying mixing-fallback." +" During the supernova explosion, the elements synthesized in different stellar layers mix and a large fraction of this mixed material falls back onto the remnant black hole."," During the supernova explosion, the elements synthesized in different stellar layers mix and a large fraction of this mixed material falls back onto the remnant black hole." +" Physically, such a mixing-fallback process can be caused not only by the Rayleigh-Taylor instability (Hachisuetal.1990;Joggerstet2009) but also by a jet-induced explosion (Tominaga2009)."," Physically, such a mixing-fallback process can be caused not only by the Rayleigh-Taylor instability \citep{hac90,jog09} but also by a jet-induced explosion \citep{tom09}." +". In the present study, we calculate nucleosynthesis yields with two new models of faint core-collapse supernovae applying different mixing-fallback parameters."," In the present study, we calculate nucleosynthesis yields with two new models of faint core-collapse supernovae applying different mixing-fallback parameters." + Figure 1 shows their elemental abundance ratios from C to Zn relative to Fe., Figure \ref{fig:dla} shows their elemental abundance ratios from C to Zn relative to Fe. + We adopt the progenitor star model from Iwamotoetal.(2005) for an initial mass of M=25Mo and metallicity Z=0., We adopt the progenitor star model from \citet{iwa05} for an initial mass of $M=25M_\odot$ and metallicity $Z=0$. +" We implement two cases with different explosion energies: 1x10°! erg (supernova (SN), solid line) and 20x10?! erg (hypernova (HN), short-dashed line)."," We implement two cases with different explosion energies: $1 \times 10^{51}$ erg (supernova (SN), solid line) and $20 \times 10^{51}$ erg (hypernova (HN), short-dashed line)." +" An efficient mixing-fallback is adopted in both models: the mixing region of ejecta is assumed to be Min—Mou,=1.766.14M and 2.20—6.30Mo with the ejection fraction of f=0.008 and 0.004, respectively."," An efficient mixing-fallback is adopted in both models: the mixing region of ejecta is assumed to be $M_{\rm in}-M_{\rm out}=1.76-6.14M_\odot$ and $2.20-6.30M_\odot$ with the ejection fraction of $f=0.008$ and $0.004$, respectively." +" The resultant black hole masses are 6.1Mo and 6.3Mo, respectively."," The resultant black hole masses are $6.1M_\odot$ and $6.3M_\odot$, respectively." +" The ejected Fe masses are as small as =0.0018M and 0.0014Mo, respectively,M(°°Ni) and M(Fe)thus correspond to faint supernovae such as SN1997D. For comparison, M(Fe)~ for normal supernovae and 70.07M for normal hypernovae in Kobayashietal.(hereafterK06, 2006).."," The ejected Fe masses are as small as $M(^{56}{\rm Ni})=M({\rm Fe})=0.0018 M_\odot$ and $0.0014 M_\odot$ , respectively, and thus correspond to faint supernovae such as SN1997D. For comparison, $M({\rm Fe})\simeq 0.07 M_\odot$ for normal supernovae and $\gtsim 0.07 M_\odot$ for normal hypernovae in \citet[hereafter K06,][]{kob06}. ." + The parameter dependencies of elemental abundance ratios can be summarized as follows., The parameter dependencies of elemental abundance ratios can be summarized as follows. +shown in Fig. 3..,shown in Fig. \ref{fig:current}. + The heat current for a typical crust model is shown in Fig. 6.., The heat current for a typical crust model is shown in Fig. \ref{fig:heatcurrent}. +" Most of the energy flux is into the star, in the direction of increasing thermal conductivity."," Most of the energy flux is into the star, in the direction of increasing thermal conductivity." + The energy is then lost to neutrinos from the core., The energy is then lost to neutrinos from the core. + We now examine the stability of the equilibrium state., We now examine the stability of the equilibrium state. +" We perform a stability analysis of the outer crust using eq (8)), substituting T(t)=To+dTe™, where oT is the perturbation mode and »y is the growth (decay) rate."," We perform a stability analysis of the outer crust using eq\ref{eq:energy}) ), substituting $T(t) += T_0 + \delta T e^{\gamma t}$, where $\delta T$ is the perturbation mode and $\gamma$ is the growth (decay) rate." +" For the range of heating models we consider, instability growth rates are fast compared to magnetic diffusion and we neglect evolution of the magnetic field in our calculations."," For the range of heating models we consider, instability growth rates are fast compared to magnetic diffusion and we neglect evolution of the magnetic field in our calculations." + Appendix A contains further justification of this approximation., Appendix A contains further justification of this approximation. +" Neglecting magnetic evolution and neutrino emission, the perturbed energy balance equation is given by where primes indicate differentiation with respect to T' at fixed x."," Neglecting magnetic evolution and neutrino emission, the perturbed energy balance equation is given by where primes indicate differentiation with respect to $T$ at fixed $x$." +" To determine the perturbation mode gradient at the outer boundary, (p=109gcm 3), we integrate through the atmosphere for several values of T; to determine the dependence of the temperature gradient on the temperature."," To determine the perturbation mode gradient at the outer boundary, $\rho=10^6 g \, cm^{-3}$ ), we integrate through the atmosphere for several values of $T_s$ to determine the dependence of the temperature gradient on the temperature." +" Because there is no ohmic heating in the atmosphere section, the temperature at the outer boundary Του and the temperature gradient dT,;,/dx are uniquely defined for a given surface temperature."," Because there is no ohmic heating in the atmosphere section, the temperature at the outer boundary $T_{ob}$ and the temperature gradient ${dT_{ob}}/{dx}$ are uniquely defined for a given surface temperature." +" Therefore, dT,/dx is a function of Του: Allowing perturbations to the temperature at the outer boundary for eq. ("," Therefore, ${d T_{ob}}/{dx}$ is a function of $T_{ob}$ : Allowing perturbations to the temperature at the outer boundary for eq. (" +20) gives,20) gives +aud the improved accuracy of he ddeteriinations. see Nissen ο al. (,"and the improved accuracy of the determinations, see Nissen et al. (" +2007).,2007). + As discussed therein. differential values are determined with a of ~30 Ix for inetal-poor turnoff stars.," As discussed therein, differential values are determined with a of $\sim 30$ K for metal-poor turnoff stars." + Below. we compare with effective temperature estimates from other methods.," Below, we compare with effective temperature estimates from other methods." + Akerman ct al. (, Akerman et al. ( +2001) derived their values from (6.gy) and (V.A) colour iudices.,2004) derived their values from $b\!-\!y)$ and $V\!-\!K)$ colour indices. + Fie., Fig. + 2 shows the difference between their aud our values for the stars with ji -lincommonbetwecuthetwostudics., \ref{fabf:delta_teffs} shows the difference between their and our values for the stars with $ < -1$ in common between the two studies. +Forthesicinctal richstarswith|Fe/T] <> Lin the Akerman et al., For the six metal-rich stars with $>-1$ in the Akerman et al. + sample. it is very hard to determine accurate temperatures from IL) because of nau blending metal lines across its profile.," sample, it is very hard to determine accurate temperatures from $\beta$ because of many blending metal lines across its profile." + Those stars are not included im the preseut investigation. since we are nuuulv interested iu the behaviour of C/O at very low|Fe/T]].," Those stars are not included in the present investigation, since we are mainly interested in the behaviour of C/O at very low." +. Tuspection of Fig., Inspection of Fig. + 2 shows that our eniperature estimates are typically 150 KI hieher thau hose by Akerman et al. (," \ref{fabf:delta_teffs} + shows that our temperature estimates are typically $150$ K higher than those by Akerman et al. (" +2001) down to ~2% with a few stars showiug a difference of up Q Ον. while a few others have VOYV simular determinations iu the two studies.,"2004) down to $\sim -2.6$, with a few stars showing a difference of up to $\sim 300$ K, while a few others have very similar determinations in the two studies." + Iun contrast. our estimated effective temperatures teud to be lower (for τος out of four stars) at very low metallicitics.," In contrast, our estimated effective temperatures tend to be lower (for three out of four stars) at very low metallicities." + The advantage of the IL? method is that errors in eravitv. muctallicity aud in interstellar reddening do nof affect the determination ofTig.," The advantage of the $\beta$ method is that errors in gravity, metallicity and in interstellar reddening do not affect the determination of." + A comparison with vvalues based ou VA calibrations (Alouso et al., A comparison with values based on $V-K$ calibrations (Alonso et al. + 1996: Ramirez Moléuudez 200510: Masana. Jordi Ribas 2006) shows that the difference with those estimates tends to switch sign (and become larger) with decreasing metallicity.," 1996; rez Melénndez 2005b; Masana, Jordi Ribas 2006) shows that the difference with those estimates tends to switch sign (and become larger) with decreasing metallicity." + The based temperatures are higher bx LOOKS when 72. IIs butlowerbyaboutfor|Fe/T| <<2.5.," The $\beta$ -based temperatures are higher by K when $> -2$, but lower by about K for $<-2.5$." + In the transition region. 2.5<|Fe/T]€—2. there is a large scatter (Nissen ct al.," In the transition region, $-2.5 \le\feh\le -2$, there is a large scatter (Nissen et al." + 2007)., 2007). + This is essentiallv the same behaviour as just discussed when conariug with the estimates by Akerman et al. (, This is essentially the same behaviour as just discussed when comparing with the estimates by Akerman et al. ( +2001). except that in that case the residuals are larger in the 40regine,"2004), except that in that case the residuals are larger in the $> -2$ regime." + Phisisductousystematico ffsetof~ 50 LOOTNTS in the values of daderived by Akerman et al. (, This is due to a systematic offset of $\sim 50$ K in the values of derived by Akerman et al. ( +2001) compared with those by Ramirez Meléuudez (2005b) and Masana et al. (,2004) compared with those by rez Melénndez (2005b) and Masana et al. ( +2006).,2006). + Alasana auc co-workers sueeested that temperature estimates from the infrared flax inethod (CIREM) may be too high by ~200KEK for |Fe/II]i-2.5.," Masana and co-workers suggested that temperature estimates from the infrared flux method (IRFM) may be too high by $\sim 200$ K for $\,< -2.5$." +0wceer they- WealibrationsbyALasanactal," However, the $V-K$ calibrations by Masana et al." +arcin fairlygoodagreementwiththe o, are in fairly good agreement with the rez Melénndez scale for our sample of stars. +nccali," On the other hand, in their calibrations, Masana et al." +dfort.35 i(N-I))«1.15 and the other for 115z(VRA)<3.0., give two equations: one valid for $0.35 < (V-K)_0 < 1.15$ and the other for $1.15 \apprle (V-K)_0 < 3.0$. + One would then expect a continuous transition between cestimates obtained with the two calibrations., One would then expect a continuous transition between estimates obtained with the two calibrations. + However. lis is not the case.," However, this is not the case." +" Since may metal-poor turnoff stars rave indeed (WoAg values close to 1.15. the final result will depend on whether a star. after reddening correction. lappens to fall below or above that value. with important differences in the erived iu the two cases, αποπας to ~200 TN at very low|Fe/TII]."," Since many metal-poor turnoff stars have indeed $(V-K)_0$ values close to 1.15, the final result will depend on whether a star, after reddening correction, happens to fall below or above that value, with important differences in the derived in the two cases, amounting to $\sim 200$ K at very low." +. Iu particular. most of the largest discrepancies (>1001I.I) occur for values around the mentioned discoutiuuitv. within 0.1 of (VIx)1.19.," In particular, most of the largest discrepancies $>100$ K) occur for values around the mentioned discontinuity, within $\pm 0.1$ of $(V-K)_0 = 1.15$." + It therefore appears that the Masa ct al., It therefore appears that the Masana et al. + calibrations lay systematically overestimate ποπ (WVA)z1.15., calibrations may systematically overestimate around $(V-K)\approx 1.15$. + Ii any case. this apparent dincousisteney can not strüehtforw:udlv explain the differences with the IL; eniperatures. since the resulting values from the equations by Masaua ct al," In any case, this apparent inconsistency can not straightforwardly explain the differences with the $\beta$ -derived temperatures, since the resulting values from the equations by Masana et al." + agree reasonably well with those from the Ramirez Moeundez calibrations. which appareutly have 10 such inconsistencies.," agree reasonably well with those from the rez Melénndez calibrations, which apparently have no such inconsistencies." + Our IL/-derived temperatures παν thus be too low bv ~ LOOKS at the lowest metallicities., Our $\beta$ -derived temperatures may thus be too low by $\sim 100$ K at the lowest metallicities. + Iu eecneral (VWIV) calibrations are bouud to be less effective at very low aucetallicities. because of the siiall wmubers of such stars.," In general, $(V-K)$ calibrations are bound to be less effective at very low metallicities, because of the small numbers of such stars." + Furthermore. these objects are affectcc by an nucertain deeree of reddening. because they tei to be faiuter aud more distant.," Furthermore, these objects are affected by an uncertain degree of reddening, because they tend to be fainter and more distant." + Finally. the (V.KA) colour tends to saturate in metal-poor turnoff stars and is. hence. less Xsitive to (seo Fie.," Finally, the $(V-K)$ colour tends to saturate in metal-poor turnoff stars and is, hence, less sensitive to (see Fig." + 9 of Ramirez Meléuudez 2005a)., 9 of rez Melénndez 2005a). + The discrepancy between ddeteziuiunations derived with the various methods does indicate that the effective temperature scale for imetal-poor stars 15 still uncertain. anc that a “hotter” temperature scale at low ls not warranted.," The discrepancy between determinations derived with the various methods does indicate that the effective temperature scale for metal-poor stars is still uncertain, and that a ""hotter"" temperature scale at low is not warranted." + It is clear that further improvements ii model atmospheres and line broadeniug theory. cousideration of possible nonLTE effects on Balmer lues. and other factors will need to be explored iu," It is clear that further improvements in model atmospheres and line broadening theory, consideration of possible non–LTE effects on Balmer lines, and other factors will need to be explored in" +(e.g. Riess et al. 1998::,(e.g. Riess et al. \cite{riess98}; + Leibundgut 2001:: Perlmutter et al. 1999))., Leibundgut \cite{leibundgut01}; Perlmutter et al. \cite{perlmutter99}) ). + Most recently Perets et al. (2010)), Most recently Perets et al. \cite{perets10}) ) + showed that helium accretion onto a white dwarf may be responsible for a subclass of faint and calcium-rich SN Ib events., showed that helium accretion onto a white dwarf may be responsible for a subclass of faint and calcium-rich SN Ib events. + Due to the tidal influence of the companion in close binary systems. the rotation of the becomes synchronised to its orbital motion.," Due to the tidal influence of the companion in close binary systems, the rotation of the becomes synchronised to its orbital motion." + In this case it is possible to constrain the mass of the companion. if mass. projected rotational velocity and surface gravity of the sdB are known.," In this case it is possible to constrain the mass of the companion, if mass, projected rotational velocity and surface gravity of the sdB are known." + Geier et al. (2008.. 2010a.. 2010b))," Geier et al. \cite{geier08}, \cite{geier10a}, \cite{geier10b}) )" + analysed high resolution spectra of 41 sdB stars in close binaries. half of all systems with known orbital parameters.," analysed high resolution spectra of 41 sdB stars in close binaries, half of all systems with known orbital parameters." + In 31 cases. the mass and nature of the unseen companions could be constrained.," In 31 cases, the mass and nature of the unseen companions could be constrained." + While most of the derived companion masses were consistent with either late main sequence stars or white dwarfs. the compact companions of some sdBs may be either massive white dwarfs. neutron stars (NS) or stellar mass black holes (BH).," While most of the derived companion masses were consistent with either late main sequence stars or white dwarfs, the compact companions of some sdBs may be either massive white dwarfs, neutron stars (NS) or stellar mass black holes (BH)." + However. Geier et al. (2010b))," However, Geier et al. \cite{geier10b}) )" + also showed that the assumption of orbital synchronisation in close sdB binaries is not always justified and that their sample suffers from huge selection effects., also showed that the assumption of orbital synchronisation in close sdB binaries is not always justified and that their sample suffers from huge selection effects. + The existence of sdB+NS/BH systems is predicted by binary evolution theory (Podsiadlowski et al. 20031:, The existence of sdB+NS/BH systems is predicted by binary evolution theory (Podsiadlowski et al. \cite{podsi02}; + Pfahl et al. 2003))., Pfahl et al. \cite{pfahl03}) ). + The formation channel includes two phases of unstable mass transfer and one supernova explosion., The formation channel includes two phases of unstable mass transfer and one supernova explosion. + The predicted fraction of sdB+NS/BH systems ranges from about 1% to 2% of the close sdB binaries (Geter et al. 2010b::, The predicted fraction of sdB+NS/BH systems ranges from about $1\%$ to $2\%$ of the close sdB binaries (Geier et al. \cite{geier10b}; + Yungelson Tutukov 20051: Nelemans 2010)., Yungelson Tutukov \cite{yungelson05}; Nelemans \cite{nelemans10}) ). + The work of Geier et al. (2010b)), The work of Geier et al. \cite{geier10b}) ) + indicates that a population of non-interacting binaries with massive compact companions may be present in our Galaxy., indicates that a population of non-interacting binaries with massive compact companions may be present in our Galaxy. + The candidate sdB+NS/BH binaries have low orbital inclinations (15—307. Geier et al. 2010b)).," The candidate sdB+NS/BH binaries have low orbital inclinations $15-30^{\rm \circ}$, Geier et al. \cite{geier10b}) )." + High melination systems must exist as well., High inclination systems must exist as well. + A determination of the orbital parameters allows one to put a lower limit to the companion mass by calculating the binary mass function., A determination of the orbital parameters allows one to put a lower limit to the companion mass by calculating the binary mass function. + The RV semi-amplitude A and the period P can be derived from the RV curve: the sdB mass Mp. the companion mass Mp and the inclination angle / remain free parameters.," The RV semi-amplitude $K$ and the period $P$ can be derived from the RV curve; the sdB mass $M_{\rm sdB}$, the companion mass $M_{\rm comp}$ and the inclination angle $i$ remain free parameters." + We adopt Mug=0.47M. and i«90° to derive a lower limit for the companion mass.," We adopt $M_{\rm sdB}=0.47\,{\rm M_{\odot}}$ and $i<90^{\rm \circ}$ to derive a lower limit for the companion mass." + Depending on this minimum mass à qualitative classification of the companions! nature is possible in certain cases., Depending on this minimum mass a qualitative classification of the companions' nature is possible in certain cases. +" For minimum companion masses lower thar 0.45M, a main sequence companion can not be excludec because its luminosity would be too low to be detectable in the spectra (Lisker et al. 2005))."," For minimum companion masses lower than $0.45\,{\rm M_{\odot}}$ a main sequence companion can not be excluded because its luminosity would be too low to be detectable in the spectra (Lisker et al. \cite{lisker05}) )." + If the minimum companion mass exceeds 0.45M.. and no spectral signatures of the companior are visible. it must be a compact object.," If the minimum companion mass exceeds $0.45\,{\rm M_{\odot}}$ and no spectral signatures of the companion are visible, it must be a compact object." + If it exceeds the Chandrasekhar mass and no sign of a companion ts visible i the spectra. the existence of a massive compact companion Is proven without the need for any additional assumptions.," If it exceeds the Chandrasekhar mass and no sign of a companion is visible in the spectra, the existence of a massive compact companion is proven without the need for any additional assumptions." + This ts possible. if such a binary is seen at high inclination.," This is possible, if such a binary is seen at high inclination." + The project Massive Unseen Companions to Hot Faint Underluminous Stars from (MUCHFUSS) aims at finding sdBs with compact companions like supermassive white dwarfs (M.>1.0 Ms). neutron stars or black holes.," The project Massive Unseen Companions to Hot Faint Underluminous Stars from (MUCHFUSS) aims at finding sdBs with compact companions like supermassive white dwarfs $M>1.0\,{\rm M_{\odot}}$ ), neutron stars or black holes." + First results of our follow-up campaign are published in Geter et al. (2011))., First results of our follow-up campaign are published in Geier et al. \cite{geier11}) ). + There Is an interesting spin-off from this project: The same selection criteria that we applied to find such binaries are also well suited to single out hot subdwarf stars with constant high radial velocities in the Galactic halo like extreme population II stars or even hypervelocity stars., There is an interesting spin-off from this project: The same selection criteria that we applied to find such binaries are also well suited to single out hot subdwarf stars with constant high radial velocities in the Galactic halo like extreme population II stars or even hypervelocity stars. + To refer to this aspect we coin the term Hyper-MUCHFUSS for the extended project., To refer to this aspect we coin the term Hyper-MUCHFUSS for the extended project. + First results are presented in Tillich et al. (2011))., First results are presented in Tillich et al. \cite{tillich11}) ). +explosion the rotation of the cloud changes essentially.,explosion the rotation of the cloud changes essentially. + The core of the cloud now rotates with the smal anear velocity ugm0.85., The core of the cloud now rotates with the small angular velocity $\omega_{core}\approx 0.85$. + The ejecting matter ixwv lexks like an expanding shell., The ejecting matter now looks like an expanding shell. + At £=28.0 (the moneit of he “switeing onm of the evoluion of the toroidal nagneic field. he “immer” (core aix part of the envelope) of the ass of the cloud contained. of the aug 1uonieitu. at f=33.57 tre “inner” of he nx of the cloud. contained of the augular momentt," At $t=28.0$ (the moment of the ""switching on"" of the evolution of the toroidal magnetic field, the ""inner"" (core and part of the envelope) of the mass of the cloud contained of the angular momentum, at $t=33.57$ the ""inner"" of the mass of the cloud contained of the angular momentum." +" At f28.0 the of he aueular luonienruli are contaiwed in the outer part of the envelope of tjo. clou of the mass of the coud},", At $t=28.0$ the of the angular momentum are contained in the outer part of the envelope of the cloud of the mass of the cloud). + At t=33.57 the of the aneular momentum is concentrated im f15 OUter par of the euvelope of the cloud of the πω of the cloud)., At $t=33.57$ the of the angular momentum is concentrated in the outer part of the envelope of the cloud of the mass of the cloud). + At the last plot of Fig., At the last plot of Fig. + 15. the stycture of the cloud at the advanced stage of the maguetortational exposion is given.," \ref{escape} + the structure of the cloud at the advanced stage of the magnetorotational explosion is given." + At this stage the cloud consists of ali outflowiues envelope. a transitional region aud a1 altos rigidly rotating core.," At this stage the cloud consists of an outflowing envelope, a transitional region and an almost rigidly rotating core." + Iu the paper bv. Axdeljauetab.1979 it was ‘Olxl iu 1D calculations of the magnetorotational sloxnova explosion that during the evolution of the oroidal component and aneular moment transfer ouwards. the central core of the cloud starts to rotate nn the opposite direction to the 1utial one.," In the paper by \cite{ardbkpop} it was found in 1D calculations of the magnetorotational supernova explosion that during the evolution of the toroidal component and angular momentum transfer outwards, the central core of the cloud starts to rotate in the opposite direction to the initial one." + σιich uaenetorotational oscillations have |COL duvesleaed analvtically bv Disuovatvi-Ikogauctal.1976., Such magnetorotational oscillations have been investigated analytically by \cite{bkpopsam}. +. Wwith respect to the star formation problems 1 s«lisbtly differeut onuulation. these oscillations lave Όσοι. 1VCSleaed in the papers by Aoushovias&Paleologou.1919.. Aloushovias&Paleologou. 1980..," With respect to the star formation problems in slightly different formulation, these oscillations have been investigated in the papers by \cite{mospal79}, \cite{mospal80}." +. Iu. o1r sunlaticDI we do not get the opposite rotation of the core of the cOK iu the opposite direction., In our simulations we do not get the opposite rotation of the core of the cloud in the opposite direction. + However the core loses sienific:uat part of its angular momentum due to iiagnuetie breakig., However the core loses significant part of its angular momentum due to magnetic breaking. +oO The first 2D calculations of the magnetorotational explosion were performed by Le Blank Wilson (197QO}. where matter was expelled in the form of jets.," The first 2D calculations of the magnetorotational explosion were performed by Le Blank Wilson (1970), where matter was expelled in the form of jets." + Siich econmoetrv of the out nustowas the result of a specific ratler uurealistic choice of the magnetic field configuration. Wwuch was produced by a cuneut rius. af an equator. t of a stelar Colre. where th| mnuatter densifv was au der of magnitude less than a central ouc.," Such geometry of the outburst was the result of a specific rather unrealistic choice of the magnetic field configuration, which was produced by a current ring, at an equator, out of a stellar centre, where the matter density was an order of magnitude less than a central one." + The magnetic field of this rie had a zero radial component iu the ecuatorial plane. axd a immaeueti€ pressure eradient was orled in the τομection due to the ciffereutial rotation. which almos repeaed the iaguctic pressure eradieut of he initial configuraion.," The magnetic field of this ring had a zero radial component in the equatorial plane, and a magnetic pressure gradient was formed in the $z$ -direction due to the differential rotation, which almost repeated the magnetic pressure gradient of the initial configuration." + Such maeuetic field structure had ed to he uatter stream pattern appearing preferentiallv along the svunetrv axis of the maeuctic field., Such magnetic field structure had led to the matter stream pattern appearing preferentially along the symmetry axis of the magnetic field. + Th «UY calculations the magnetic fieα πας created by he op)ositcvy directed current rings iu the central region of the star., In our calculations the magnetic field was created by the oppositely directed current rings in the central region of the star. +" The uaenetic fiek had a quadrupole-like confietration with a nixinmni 3""lue close to the centre of the star. and large radial comeut at the equator."," The magnetic field had a quadrupole-like configuration with a maximum value close to the centre of the star, and large radial component at the equator." + Iu he papers ¢evoted to the siuulatious of the star formation problems (es. Ciolek Mousc10Vlas. 1995: Touisalka. 1998) 1 is often sipposed that the initial poloidal magnetic field has onlv au fJ. component.," In the papers devoted to the simulations of the star formation problems (e.g. Ciolek Mouschovias, 1995; Tomisaka, 1998) it is often supposed that the initial poloidal magnetic field has only an $H_z$ component." + It is often suggested for the collapse problemi of protostellar clouds., It is often suggested for the collapse problem of protostellar clouds. +" We should poiut out tiat the initial maguetic field of the coufietration {ἱμ.+0.Ly,=0 or"," We should point out that the initial magnetic field of the configuration $H_{0z}\ne 0,\> H_{0r}=0$ or" +A feature matching set is provided as a supplemental movie showing the 2010 November 3 event from the and points of view.,A feature matching set is provided as a supplemental movie showing the 2010 November 3 event from the and points of view. + All images have been reverse-scaled., All images have been reverse-scaled. + The SECCHI panels are shown using the 195 A channel., The SECCHI panels are shown using the 195 $\mbox{\AA}$ channel. + The top AIA panels are from 131 A while the bottom AIA images were taken with the 193 A bandpass., The top AIA panels are from 131 $\mbox{\AA}$ while the bottom AIA images were taken with the 193 $\mbox{\AA}$ bandpass. + The plasmas observed with the SECCHI 195 A bandpass are more similar to those seen in AIA 193 A., The plasmas observed with the SECCHI 195 $\mbox{\AA}$ bandpass are more similar to those seen in AIA 193 $\mbox{\AA}$. + The movie spans 2.5 days as the region rotates around the eastern solar limb., The movie spans 2.5 days as the region rotates around the eastern solar limb. + The thick dashed longitudinal line in the SECCHI images indicates the position of the solar limb as observed from Earth., The thick dashed longitudinal line in the SECCHI images indicates the position of the solar limb as observed from Earth. +" As prominent features appear throughout the event, they are highlighted in the adjacent center SECCHI and AIA images with common color annotations. ("," As prominent features appear throughout the event, they are highlighted in the adjacent center SECCHI and AIA images with common color annotations. (" +The outer panels are the same as the inner ones but are not annotated.),The outer panels are the same as the inner ones but are not annotated.) +" For example, the relatively small core flaring regions indicated by the red and blue dashed polygons in the SECCHI images are marked as arcade tops in the AIA images."," For example, the relatively small core flaring regions indicated by the red and blue dashed polygons in the SECCHI images are marked as arcade tops in the AIA images." + Limb obscuration and line-of-sight overlap cause substantial confusion within the AIA field of view., Limb obscuration and line-of-sight overlap cause substantial confusion within the AIA field of view. +" The erupting flux rope, inflows, and outflows are tracked in the exclusively AIA supplemental movie. ("," The erupting flux rope, inflows, and outflows are tracked in the exclusively AIA 8-panel supplemental movie. (" +The leading edge of the flux rope is manually tracked for each wavelength.,The leading edge of the flux rope is manually tracked for each wavelength. + A description of the manual tracking procedure used for the inflows is given in Section [2.3]., A description of the manual tracking procedure used for the inflows is given in Section \ref{inflow101103:inflow_measurements}. +" Finally, the apparent apexes of the descending outflowing loops as well as traveling density enhancements along loop legs, see Section 2.41, are also manually tracked.)"," Finally, the apparent apexes of the descending outflowing loops as well as traveling density enhancements along loop legs, see Section \ref{inflows101103:outflows}, are also manually tracked.)" +" From left to right and in general descending temperature order, the images were taken with the AIA 131, 211, 193, and 171 A channels."," From left to right and in general descending temperature order, the images were taken with the AIA 131, 211, 193, and 171 $\mbox{\AA}$ channels." + The top panels are the original images that have been log- and byte-scaled to enhance faint features., The top panels are the original images that have been log- and byte-scaled to enhance faint features. +" The bottom panels are the corresponding run-differenced versions of the top panels (i.e., preceding images have been subtracted from the current to enhance movement)."," The bottom panels are the corresponding run-differenced versions of the top panels (i.e., preceding images have been subtracted from the current to enhance movement)." + The white longitudinal line indicates the eastern solar limb., The white longitudinal line indicates the eastern solar limb. + Both movies are reverse-scaled., Both movies are reverse-scaled. + Features were tracked separately for each wavelength., Features were tracked separately for each wavelength. +" For the top panels, the numbers indicate the feature positions tracked within that wavelength."," For the top panels, the numbers indicate the feature positions tracked within that wavelength." + The positions indicated by symbols were tracked using a different wavelength., The positions indicated by symbols were tracked using a different wavelength. + The corresponding symbol is located in the legend below each wavelength’s panel. (, The corresponding symbol is located in the legend below each wavelength's panel. ( +Each symbol consists of a dark and a light,Each symbol consists of a dark and a light +eroup of ealaxies they fall short of the estimates derived in L1 bw at least a factor of 140)”.,group of galaxies they fall short of the estimates derived in \ref{sec:estim-substr-dens} by at least a factor of $10^5$. + These observatious lave important consequences for the Win Dark Matter AVDAD model., These observations have important consequences for the Warm Dark Matter (WDM) model. + The standard WDAL 1ocl is eugmecred to reproduces the dwart eaaxy distribution under the assuniptiou that a galaxy onus i1 every stall halo., The standard WDM model is engineered to reproduces the dwarf galaxy distribution under the assumption that a galaxy forms in every small halo. + It was shown iu 1.2 tha the number density of dwarf galaxies is extremely malisely to have produced the observed beut radio jets., It was shown in \ref{sec:contr-from-known} that the number density of dwarf galaxies is extremely unlikely to have produced the observed bent radio jets. + The standard WDM mode is thus ruled out if the beu il Bu52|199 is real., The standard WDM model is thus ruled out if the bend in B1152+199 is real. + A more accurate lower linit o ithe DM particle mass wil PCCjure Lore Observations aiC nore sinuulations of πια scale structure forlation iuthese moctels., A more accurate lower limit on the DM particle mass will require more observations and more simulations of small scale structure formation in these models. + Tigher resoutio1 observatioi of D11521799 are possibe., Higher resolution observations of B1152+199 are possible. + Tjese would make certain tiat the jet iu nuaee D is nx��ς4( bent aud improve the coustraints on the substructure mass., These would make certain that the jet in image B is indeed bent and improve the constraints on the substructure mass. + Also iuteresine would be igh resolution i11.ages of other multiply πασος jets., Also interesting would be high resolution images of other multiply imaged jets. + In the present sanie of three all appear to show some evidence of beiCn1ο, In the present sample of three all appear to show some evidence of bending. +", A moderatev larger sampe would ercatV Increase he power of this 116hod to prob structure ou smal scales.", A moderately larger sample would greatly increase the power of this method to probe structure on small scales. + ]t has been ound here tha a significantN larger 1111111jor of suma] scale objects are needed if f1C observations of D1152|199 are to be simply interpreted., It has been found here that a significantly larger number of small scale objects are needed if the observations of B1152+199 are to be simply interpreted. + Structures as ¢liffuse as SIS are disfavored bohi by direct modeling of D1152|199 aud on statisical exounucds., Structures as diffuse as SIS are disfavored both by direct modeling of B1152+199 and on statistical grounds. + If the strucures are compact (on the scale of their own Etustein radius) aud simall iu iiass Z10° M) they need not contain a laree fraction of the mass in the universe.," If the structures are compact (on the scale of their own Einstein radius) and small in mass $\simlt +10^7\msun$ ) they need not contain a large fraction of the mass in the universe." + DIowever. such concentrated halos come about iu the CDM model only through the tidal stripping of halos that originally contained ~10 times more mass.," However, such concentrated halos come about in the CDM model only through the tidal stripping of halos that originally contained $\sim 10$ times more mass." + This meaus that iu iuterealactic space these clumps would contain a large fraction of the mass. perhaps most of it.," This means that in intergalactic space these clumps would contain a large fraction of the mass, perhaps most of it." +as discussed in Jeffries et al. (,as discussed in Jeffries et al. ( +2006). where a similar procedure was followed. these correlations are very likely to be the genuine optical counterparts of the X-ray sources.,"2006), where a similar procedure was followed, these correlations are very likely to be the genuine optical counterparts of the X-ray sources." + The mean offset between the X-ray and optical positions was 0.11. areseconds. in RÀ and 0.59 areseconds in Dec. As the optical catalogues have an absolute accuracy better than 0.2 areseconds and an internal precision of about aareseconds. the X-ray positions were corrected for these offsets.," The mean offset between the X-ray and optical positions was 0.11 arcseconds in RA and 0.59 arcseconds in Dec. As the optical catalogues have an absolute accuracy better than 0.2 arcseconds and an internal precision of about arcseconds, the X-ray positions were corrected for these offsets." + The remaining dispersion in the offsets indicates an additional | aresecond uncertainty (in addition to the quoted astrometric uncertainty from the source searching routines) in the X-ray positions. concurring with the current astrometric calibration assessment of the science operations centre (Guainazzi 2010).," The remaining dispersion in the offsets indicates an additional 1 arcsecond uncertainty (in addition to the quoted astrometric uncertainty from the source searching routines) in the X-ray positions, concurring with the current astrometric calibration assessment of the science operations centre (Guainazzi 2010)." + The purpose of this paper is to study the properties of fast-rotating M-dwarts. so an investigation of the full X-ray source population is deferred to a later paper.," The purpose of this paper is to study the properties of fast-rotating M-dwarfs, so an investigation of the full X-ray source population is deferred to a later paper." + Here. we discuss cross-correlations between the astrometrically corrected X-ray source list and the catalogue of cool stars with Known rotation periods in NGC 2547. given by Irwin et al. (," Here, we discuss cross-correlations between the astrometrically corrected X-ray source list and the catalogue of cool stars with known rotation periods in NGC 2547, given by Irwin et al. (" +2008).,2008). + The Irwin et al. (, The Irwin et al. ( +2008) catalogue contains precise positions tied to the 2MASS reference frame. rotation periods and photometry in the V. and / bands.,"2008) catalogue contains precise positions tied to the 2MASS reference frame, rotation periods and photometry in the $V$ and $I$ bands." + We found significant systematic differences (of up to 0.2 mag) between the photometry of Irwin et al. (, We found significant systematic differences (of up to 0.2 mag) between the photometry of Irwin et al. ( +2008) and that found in Naylor et al. (,2008) and that found in Naylor et al. ( +2002) for stars common to both.,2002) for stars common to both. + As the accuracy of the Naylor et al., As the accuracy of the Naylor et al. + photometry has support from an independent study by Lyra et al. (, photometry has support from an independent study by Lyra et al. ( +2006). we transformed the Irwin photometry using the following best-fit relationships between the Naylor et al.,"2006), we transformed the Irwin photometry using the following best-fit relationships between the Naylor et al." + and Irwin et al., and Irwin et al. + photometry: where the calibrations transform the photometry onto the Johnson-Cousins calibration used by Naylor et al., photometry: where the calibrations transform the photometry onto the Johnson-Cousins calibration used by Naylor et al. + and are valid for 1d«V21 and 1.2.<(VO£)«3.4., and are valid for $14500$ ) to justify fitting a complex spectral model. + The median source is detected in the EPIC-PN camera with about 150 counts and a signal-to-noise ratio of only 10., The median source is detected in the EPIC-PN camera with about 150 counts and a signal-to-noise ratio of only 10. + Instead we designed a spectral model that agrees with the mean hardness ratio (AR) in the EPIC-PN camera. defined as (f/fS)/(/f|S) where 5 is the 0.3-1.0kkeV count rate and // is the kkeV count rate.," Instead we designed a spectral model that agrees with the mean hardness ratio (HR) in the EPIC-PN camera, defined as $(H-S)/(H+S)$ where $S$ is the keV count rate and $H$ is the keV count rate." + Our starting point was the analysis of an earlier. much shorter observation of NGC 2547 (Jeffries et al.," Our starting point was the analysis of an earlier, much shorter observation of NGC 2547 (Jeffries et al." + 2006)., 2006). + This showed that single-temperature thermal plasma models were insufficiently complex to fit the spectra of active stars in NGC 2547., This showed that single-temperature thermal plasma models were insufficiently complex to fit the spectra of active stars in NGC 2547. + A two-temperature AL™ model (Mewe. Kaastra Leidahl 1995) provided a satisfactory description. with 11-- KkeV. 752L.5kkeV and an emission measure ratio (hot/cool) of about 0.7. which was chosen to approximately match the mean HR.," A two-temperature ” model (Mewe, Kaastra Leidahl 1995) provided a satisfactory description, with $T_1 \simeq 0.6$ keV, $T_2 \simeq 1.5$ keV and an emission measure ratio (hot/cool) of about 0.7, which was chosen to approximately match the mean HR." + This erude approximation to the differential emission measure (DEM) of the coronal plasma reasonably matches detailed work on the coronal DEM of several nearby. rapidly-rotating low-mass stars. which show a DEM maximum at around 10* KK Alvarez et al.," This crude approximation to the differential emission measure (DEM) of the coronal plasma reasonably matches detailed work on the coronal DEM of several nearby, rapidly-rotating low-mass stars, which show a DEM maximum at around $10^{7}$ K (Garc\'iaa-Alvarez et al." + 2008)., 2008). + It was also established in Jeffries et al. (, It was also established in Jeffries et al. ( +2006) that the coronal plasma was best fitted with a sub-solar metallicity (Zcm0.3). which seems to be a common feature for very active stars. including fast-rotating K- and M-dwarfs (e.g. Briggs Pye 2003: Garcfaa-Alvarez et al.,"2006) that the coronal plasma was best fitted with a sub-solar metallicity $Z \simeq 0.3$ ), which seems to be a common feature for very active stars, including fast-rotating K- and M-dwarfs (e.g. Briggs Pye 2003; Garcíaa-Alvarez et al." + 2008)., 2008). + Adopting the same model we have used the software package and instrument response files appropriate for the EPIC-PN camera at the time of the observations. to calculate a conversion factor from KkeV. count rates to anunabsorbed 3.0kkeV flux.," Adopting the same model we have used the software package and instrument response files appropriate for the EPIC-PN camera at the time of the observations, to calculate a conversion factor from keV count rates to an keV flux." +" We assumed an interstellar absorbing column density of neutral hydrogen Ny=3«107"" ? (see section 2.5).", We assumed an interstellar absorbing column density of neutral hydrogen $N_H = 3\times 10^{20}$ $^{-2}$ (see section 2.5). + The derived flux conversion factor is 1.68.10.17 = per count and the derived HR is -0.42. which closely matches the mean HR in our sample (see section 3)).," The derived flux conversion factor is $1.68\times 10^{-12}$ $^{-2}$ per count and the derived HR is -0.42, which closely matches the mean HR in our sample (see section \ref{results}) )." + Analogous conversion factors for the EPIC-MOS cameras were derived by dividing the EPIC-PN conversion factor by the weighted mean ratio of the observed MOS and PN count rates., Analogous conversion factors for the EPIC-MOS cameras were derived by dividing the EPIC-PN conversion factor by the weighted mean ratio of the observed MOS and PN count rates. + This gave conversion factors of 6.22.10. > per count for both of the EPIC-MOS cameras., This gave conversion factors of $6.22\times10^{-12}$ $^{-2}$ per count for both of the EPIC-MOS cameras. + The unabsorbed KkeV. X-ray flux for each detected Irwin et al. (, The unabsorbed keV X-ray flux for each detected Irwin et al. ( +2008) star is found from a weighted average of fluxes from each detector.,2008) star is found from a weighted average of fluxes from each detector. + Uncertainties in these fluxes arise Tom the count rate errors. but we added a further 160 per cent systematic error in quadrature to each detector count rate to account for uncertainties in the instrument response and in the he point spread function modelling in the task (e.g. Saxton 2003: Guainazzi 2010).," Uncertainties in these fluxes arise from the count rate errors, but we added a further 10 per cent systematic error in quadrature to each detector count rate to account for uncertainties in the instrument response and in the the point spread function modelling in the task (e.g. Saxton 2003; Guainazzi 2010)." + From the average fluxes he coronal activity indicator {ρω was calculated. using the corrected V magnitudes. an extinction ly=0.19. a reddening L(VI)=0.071 (see Clariá 1982: Naylor et al.," From the average fluxes the coronal activity indicator $L_x/L_{\rm bol}$ was calculated, using the corrected $V$ magnitudes, an extinction $A_V=0.19$, a reddening $E(V-I)=0.077$ (see Clariá 1982; Naylor et al." + 2002) and he relationship between intrinsic 1{ and bolometric correction deseribed by Naylor et al. (, 2002) and the relationship between intrinsic $V-I$ and bolometric correction described by Naylor et al. ( +2002).,2002). + For the red stars in our sample with V1/-1.5. these bolometrie corrections are based on the empirical measurements of Leggett et al. (," For the red stars in our sample with $V-I> 1.5$, these bolometric corrections are based on the empirical measurements of Leggett et al. (" +1996).,1996). +" The bolometric corrections and L./£1,,,) values are reported in Table I.", The bolometric corrections and $L_x/L_{\rm bol}$ values are reported in Table 1. + There are 29 objects in the Irwin et al. (, There are 29 objects in the Irwin et al. ( +2008) catalogue within the field of view (for only a subset of the detectors in some cases) but not found as sources by the task.,2008) catalogue within the field of view (for only a subset of the detectors in some cases) but not found as sources by the task. + We inspected the X-ray images at the positions of these sources and found one example (N2547-1-6-5108) which is a reasonably bright X-ray source. that appears only in the MOS? image. and which was missed by the automated source searching.," We inspected the X-ray images at the positions of these sources and found one example (N2547-1-6-5108) which is a reasonably bright X-ray source, that appears only in the MOS2 image, and which was missed by the automated source searching." + We evaluated the X-ray count rates for this object using a 20 aresecond radius aperture (see below) and a local estimate of the background., We evaluated the X-ray count rates for this object using a 20 arcsecond radius aperture (see below) and a local estimate of the background. + This, This +"and is significantly larger than the standard Al~aefc)2.10""AL.vear Figure 2. shows the case ὁ=3 (Le. quite slow compression: £ doubles in 3 sound-crossing times).","and is significantly larger than the standard $\dot{M} \sim a\bg^3/G \sim 2 \times 10^{-6} +M_\odot\,{\rm year}^{-1}$ Figure \ref{phi3} shows the case $\phi = 3$ (i.e. quite slow compression; $P\xt$ doubles in 3 sound-crossing times)." + The evolution is somewhat less quasistatic (than for ὁ=10. Fig. 11).," The evolution is somewhat less quasistatic (than for $\phi = 10$, Fig. \ref{phi10}) )," + but basically it is very similar., but basically it is very similar. + Phe outer boundary is pushed. inwards. ancl the core becomes steadily more centrally condensed: throughout the prestellar phase (the first three rows of Fig. 2):," The outer boundary is pushed inwards, and the core becomes steadily more centrally condensed throughout the prestellar phase (the first three rows of Fig. \ref{phi3}) );" + the outer lavers start to move inwards at speeds in the range (0.05.0.07)kms whilst matter near the centre is approximately. stationary.," the outer layers start to move inwards at speeds in the range $(0.05,0.07) \, {\rm km} \, {\rm s}^{-1}$, whilst matter near the centre is approximately stationary." + Eventually the core becomes unstable. and the sink starts to accrete matter. marking the formation of the protostar and the start of the Class 0 phase.," Eventually the core becomes unstable, and the sink starts to accrete matter, marking the formation of the protostar and the start of the Class 0 phase." + At this stage the core radius is 0.05 pc., At this stage the core radius is $\sim$ 0.05 pc. + A freefall velocity field then develops. as material accretes onto the protostar (fourth ancl filth rows of Fig. 2)).," A freefall velocity field then develops, as material accretes onto the protostar (fourth and fifth rows of Fig. \ref{phi3}) )." + The accretion rate reaches a maximum of ~1.0810AL.vr and then decines monotonically (second row of Fig. 7)).," The accretion rate reaches a maximum of $\sim 1.08 \times 10^{-5} \,M_\odot \, +{\rm yr}^{-1}\,$ , and then declines monotonically (second row of Fig. \ref{accret}) )." + In Figure 3. we show results for 6=1.," In Figure \ref{phi1} we show results for $\phi = 1\,$." + Here the pressure doubles in one sound-crossing time. and so the evolution is more dvnamic (than in the ó=10 and ὁ=3 cases described above).," Here the pressure doubles in one sound-crossing time, and so the evolution is more dynamic (than in the $\phi = 10$ and $\phi = 3$ cases described above)." + A small compression wave is driven into the core increasing the density and leaving in its wake a moclest inward velocity field in the range (0.100.15)kms.," A small compression wave is driven into the core increasing the density and leaving in its wake a modest inward velocity field in the range $(0.10,0.15) \, {\rm km} \, {\rm s}^{-1}\,$." + -The oestellar phase ends. — and the Class 0 phase begins when ls compression wave impinges on the centre., The prestellar phase ends – and the Class 0 phase begins – when this compression wave impinges on the centre. + Up until this gaage. the central density has hardly changed. since the inner arts have been unaware of the increased external pressure: 1e radius of the core has decreased to ~ 0.045 pe.," Up until this stage, the central density has hardly changed, since the inner parts have been unaware of the increased external pressure; the radius of the core has decreased to $\sim$ 0.045 pc." + During 10 Class O phase. a frecfall velocity field. develops around 1e central protostar. but the outer parts of the envelope are still moving inwardsat approximately uniform sonic speed (rO.12kms+).," During the Class 0 phase, a freefall velocity field develops around the central protostar, but the outer parts of the envelope are still moving inwardsat approximately uniform sonic speed $(v \sim +0.12 \, {\rm km} {\rm s}^{-1})$." +" The accretion rate is significantly higher iun for the more quasistatic cases (larger ó). reaching a maximum of —1.50«10""AZ.vr and then decreasing into the Class 1 phase (third row of Fig. 7))."," The accretion rate is significantly higher than for the more quasistatic cases (larger $\phi$ ), reaching a maximum of $\sim 1.50 \times 10^{-5} M_\odot +\, {\rm yr}^{-1}\,$, and then decreasing into the Class I phase (third row of Fig. \ref{accret}) )." + Figure 4. shows detailed results for the case oO= V3. Le. quite rapid compression.," Figure \ref{phi03} shows detailed results for the case $\phi = 0.3\,$ , i.e. quite rapid compression." + In this case a strong compression wave 1s driven into the core. leaving a mareinally subsonic velocity. fiel in its wake. Le. ce in he range (0.12.0.14)kms+).," In this case a strong compression wave is driven into the core, leaving a marginally sonic velocity field in its wake, i.e. $v$ in the range $(0.12,0.14) \, {\small\rm km} +{\small\rm s}^{-1})$." + This leads to quite rapid accretion during the Class O phase. reaching a maximum of 1.65.10ΑΗ.ve1and then decreasing into ⋠⋠the Class . ) phase (fouth and fifth rows of Fig. 7)).," This leads to quite rapid accretion during the Class 0 phase, reaching a maximum of $\sim 1.65 \times 10^{-5} +M_\odot \, {\rm yr}^{-1}\,$, and then decreasing into the Class 0 phase (fouth and fifth rows of Fig. \ref{accret}) )." + Figure 5. shows detailed results for the case ó=0.1. i.c. very rapid compression.," Figure \ref{phi01} shows detailed results for the case $\phi = 0.1\,$, i.e. very rapid compression." + ln this case a very strong compression wave is driven into the core. leaving a mildly supersonic velocity Ποια in its wake. be. e in the range (0.25.0.30)kms.1).," In this case a very strong compression wave is driven into the core, leaving a mildly sonic velocity field in its wake, i.e. $v$ in the range $(0.25,0.30) \, {\small\rm km} +{\small\rm s}^{-1})$." +" At?=024Myr. the outer lavers have »ven swept up into afswreamd, The density at the head. of he ἐν ~3 times higher than at the centre."," At $t = 0.24 \, {\rm Myr}\,$, the outer layers have been swept up into a. The density at the head of the is $\sim 3$ times higher than at the centre." + This eads to very rapid accretion. during the Class 0. phase. reaching a maximum of ~2.6010CAL.vr and then decreasing into the Class 1 phase (fifth row of Fig. 7)).," This leads to very rapid accretion during the Class 0 phase, reaching a maximum of $\sim 2.60 \times 10^{-5} +M_\odot \, {\rm yr}^{-1}\,$, and then decreasing into the Class I phase (fifth row of Fig. \ref{accret}) )." + In he Class 0 phase. a freefall velocity. Ποιά develops in the centre. whilst the outer lavers continue to cruise inwards at Doc0.30kins ," In the Class 0 phase, a freefall velocity field develops in the centre, whilst the outer layers continue to cruise inwards at $v \sim 0.30 \, {\small\rm km} {\small\rm s}^{-1}$ ." +It the external pressure only increases for a finite timo. and then stavs constant at a new higher value. the results are somewhat changed. particularly for the cases of rapid compression (small 6).," If the external pressure only increases for a finite time, and then stays constant at a new higher value, the results are somewhat changed, particularly for the cases of rapid compression (small $\phi$ )." + This is illustrated on Fig. 6..," This is illustrated on Fig. \ref{phi01lim}," + where we show detailed: results for the ó=0.1 case when the pressure increase is halted as soon as the pressure has doubled.," where we show detailed results for the $\,\phi=0.1\,$ case when the pressure increase is halted as soon as the pressure has doubled." +" We refer to this case as ""oO=QO.Ll(finite). to distinguish it from the standard case “Oo=0.1 (indefinite)."," We refer to this case as $\phi=0.1\,$ (finite)”, to distinguish it from the standard case $\phi=0.1\,$ (indefinite)”." + In the case 7ó=0.1 (finite). the compression wave is much weaker and slower than for the case πώ=0.1 (indefinite). and so the inwarel velocity [field it engenders is also weaker.," In the case $\phi=0.1\,$ (finite)”, the compression wave is much weaker and slower than for the case $\phi=0.1\,$ (indefinite)”, and so the inward velocity field it engenders is also weaker." + In fact. the evolution for case πώ=0.1 (linite)” is more ike that for the case πώ=0.8 (indefinite): in. particular. he compression wave takes a comparable time to converge onto the centre.," In fact, the evolution for case $\phi=0.1\,$ (finite)” is more like that for the case $\phi=0.3\,$ (indefinite)”; in particular, the compression wave takes a comparable time to converge onto the centre." +" For this reason. the mass and acerction rate or the case πώ= O.L(finite)"" are displaved: with dashed ines on the same plot as the results for the case Gndelinitey” (Le. the fourth row of Fie. 7))."," For this reason, the mass and accretion rate for the case $\phi=0.1\,$ (finite)” are displayed with dashed lines on the same plot as the results for the case $\phi=0.3\,$ (indefinite)” (i.e. the fourth row of Fig. \ref{accret}) )." + For slower compression rates. óz1. halting the pressure increase when he pressure has doubled has little effect. because instability is trigeered. before the pressure doubles. ancl the collapse dvnanmies of the core are therefore alreacly well established.," For slower compression rates, $\phi \ga 1\,$, halting the pressure increase when the pressure has doubled has little effect, because instability is triggered before the pressure doubles, and the collapse dynamics of the core are therefore already well established." +" To test for convergence. we have repeated the case ὦ= Gincefinite)” with only AS,=20.000 particles in the core."," To test for convergence, we have repeated the case $\phi=1\,$ (indefinite)” with only ${\cal N}_{\rm int}=20,000$ particles in the core." + The time-dependence of the protostellar mass and aecretion rate are shown on the third row of Fig., The time-dependence of the protostellar mass and accretion rate are shown on the third row of Fig. + 7 with dotted lines., \ref{accret} with dotted lines. + We see that there is almost no change. except that with fewer particles the compression wave takes a little longer to converge on the centre. about longer.," We see that there is almost no change, except that with fewer particles the compression wave takes a little longer to converge on the centre, about longer." + We do not. know the reason for this. but in any case it is a very small effect.," We do not know the reason for this, but in any case it is a very small effect." + Apart from this time delay. the detailed density and velocity profiles are essentially. unchanged.," Apart from this time delay, the detailed density and velocity profiles are essentially unchanged." + Figure 7. shows the accretion rate onto the sink. as a [function of time. for the various values of ©.," Figure \ref{accret} shows the accretion rate onto the sink, as a function of time, for the various values of $\phi$." + The star indicates where the Class 0 phase gives wav to he Class L phase., The star indicates where the Class 0 phase gives way to the Class I phase. + Table 1 shows the clurations of the oestellar and. Class 0 phases. for representative values of ©.," Table 1 shows the durations of the prestellar and Class 0 phases, for representative values of $\phi\,$ ." + Since the sink particle is present. from the outset. the moment of protostar formation is not precisely defined. and herefore these durations are not. precisely defined.," Since the sink particle is present from the outset, the moment of protostar formation is not precisely defined, and therefore these durations are not precisely defined." +They simply illustrate the factthat the prestellar and. Class 0ohases are accelerated by. rapid. compression.,They simply illustrate the factthat the prestellar and Class 0phases are accelerated by rapid compression. + La all cases. Mοπα£Musas©0.05L0 0.10.," In all cases, $\Delta t_{\rm Class 0} +/ \Delta t_{prestellar} \sim 0.05\,{\rm to}\,0.10$ ." +factor. the difference in the Inuinosity evolution exponent. between optical/radio results and infrared/submillimeter resulis may not be sienificant.,"factor, the difference in the luminosity evolution exponent between optical/radio results and infrared/submillimeter results may not be significant." + We can compare (he previously determined evolution parameters with those we determine from the most luminous sources., We can compare the previously determined evolution parameters with those we determine from the most luminous sources. + For our results. the envelope describing maximum starburst luminosity to z = 2.5 shown in Figures 3 and 4 has the maximum Iuminositv of starbursts evolving as (12-z)?.," For our results, the envelope describing maximum starburst luminosity to z = 2.5 shown in Figures 3 and 4 has the maximum luminosity of starbursts evolving as $^{2.5}$." + For lower redshifts. to z — I. another envelope is shown with the Le [actor for huminositv evolution of (12-z)*.," For lower redshifts, to z = 1, another envelope is shown with the \citet{lef05} factor for luminosity evolution of $^{3.5}$." + Although the uncertainties in (he exponents indicate that our evolution factor and the LeFlochetal.(2005)5) [actor are simular within uncertainties. (he sleeper evolution does not track well the lower reclshilt starbursts in Figures 3 and 4 and would certainly overestimate himinosities at higher redshifts.," Although the uncertainties in the exponents indicate that our evolution factor and the \citet{lef05} factor are similar within uncertainties, the steeper evolution does not track well the lower redshift starbursts in Figures 3 and 4 and would certainly overestimate luminosities at higher redshifts." + Our results for the summary of starbursts in Figure 3 indicate. therefore. (hat luminosity evolution for the most luminous slarbursts scales more closely to the lower value of (2004).," Our results for the summary of starbursts in Figure 3 indicate, therefore, that luminosity evolution for the most luminous starbursts scales more closely to the lower value of \citet{hop04}." +. Figure 3 is also a clear demonstration that this Iuminosity evolution continues al least to z= 2.5., Figure 3 is also a clear demonstration that this luminosity evolution continues at least to z = 2.5. +" A possible explanation for the differences found for evolution of pure starbursts compared to the evolution derived from modeling total infrared source counts and redshift distributions. such as in LeFlochetal.(2005).. is that infrared sources include a significant fraction of AGN, and the evolution of AGN may differ from that of starbursts."," A possible explanation for the differences found for evolution of pure starbursts compared to the evolution derived from modeling total infrared source counts and redshift distributions, such as in \citet{lef05}, is that infrared sources include a significant fraction of AGN, and the evolution of AGN may differ from that of starbursts." + A sample of 243 starburst galaxies with infrared spectra obtained by The Infrared Spectrograph on Spritzer has been assembled with measurements of PAIL luminosities to determine (he most luminous starbursts discovered., A sample of 243 starburst galaxies with infrared spectra obtained by The Infrared Spectrograph on $Spitzer$ has been assembled with measurements of PAH luminosities to determine the most luminous starbursts discovered. + The sample includes sources [rom a varletv of Spitzer observing programs and covers 0 « z < 2.5 (Figure 3)., The sample includes sources from a variety of $Spitzer$ observing programs and covers 0 $<$ z $<$ 2.5 (Figure 3). +" Starburst Iuminosities are derived [rom the luminosity vb, (7.75) as determined [rom the peak flux density of the 7.7; PAIL feature.", Starburst luminosities are derived from the luminosity $\nu$ $_{\nu}$ $\mu$ m) as determined from the peak flux density of the $\mu$ m PAH feature. +" These luminosities for the most luminous starbursts scale with redshift as log[vL, (τιμη) = 44.63(20.09) + 2.48(50.28) log(12-z).", These luminosities for the most luminous starbursts scale with redshift as $\nu$ $_{\nu}$ $\mu$ m)] = $\pm$ 0.09) + $\pm$ 0.28) log(1+z). + This result demonstrates (hat pure Iuminosity evolution for starbursts scales approximately with (14+z)??. al least to z = 2.5.," This result demonstrates that pure luminosity evolution for starbursts scales approximately with $^{2.5}$, at least to z = 2.5." + This is less evolution than determined [rom previous inlrared-derived source counts but agrees with the evolution determined from optical and racio samples of star-forming galaxies., This is less evolution than determined from previous infrared-derived source counts but agrees with the evolution determined from optical and radio samples of star-forming galaxies. +" Transformations of pL, μα) to bolometric luminosities £;, and to star formation rates are determined empirically from local starbursts and are shown to be the same as such transformations derived by others using a variely of star formation indicators and a variety of sources.", Transformations of $\nu$ $_{\nu}$ $\mu$ m) to bolometric luminosities $L_{ir}$ and to star formation rates are determined empirically from local starbursts and are shown to be the same as such transformations derived by others using a variety of star formation indicators and a variety of sources. +" Using the conversions that log Lj, = logivL, τιμη) + 0.78. and that log/SFR|"," Using the conversions that log $L_{ir}$ = $\nu$ $_{\nu}$ $\mu$ m)] + 0.78, and that log[SFR]" +to sienificaut values for some of the protoplancts is observed. in line with the results for the planetesinials.,"to significant values for some of the protoplanets is observed, in line with the results for the planetesimals." + Tt is interesting to observe however. that the peak ecceutricities obtained are somewhat less than those obtained in the planctesimal cases. sugecsting that the eravitational interaction with the disk is providing ecceutricity damus to counteract the effects of the turbulent excitation.," It is interesting to observe however, that the peak eccentricities obtained are somewhat less than those obtained in the planetesimal cases, suggesting that the gravitational interaction with the disk is providing eccentricity damping to counteract the effects of the turbulent excitation." + This ina trend that continues as the protoplauet mass increases. as described in the following sections.," This is a trend that continues as the protoplanet mass increases, as described in the following sections." +" The orbital evolution of the 3 M, protoplancts is illustrated in figure 6..", The orbital evolution of the 3 $_{\oplus}$ protoplanets is illustrated in figure \ref{fig6}. + The left pane shows a simular evolution for the somiunnajor axes as lias oen deseribed for the planetesimals aud 1 AL). protoplaucts., The left panel shows a similar evolution for the semimajor axes as has been described for the planetesimals and 1 $_{\oplus}$ protoplanets. + The seimiiajor axes are again observed to undergo modification in a stochastic manner. with variations at the 5 percent level beiug observed.," The semimajor axes are again observed to undergo modification in a stochastic manner, with variations at the 5 percent level being observed." + The dotted lines show the results of a simulation in which six 3 M. protoplanets were evolved ina laminar disk., The dotted lines show the results of a simulation in which six 3 $_{\oplus}$ protoplanets were evolved in a laminar disk. + The iiouotonic Πατ migration of cach of these planets is clearly cüscernuible. sueecstineg hat the planets do not ereatly influence cach others mteraction with the disk.," The monotonic inward migration of each of these planets is clearly discernible, suggesting that the planets do not greatly influence each others interaction with the disk." + Bisvard uueration iu this case occurs close to the expected type I rate., Inward migration in this case occurs close to the expected type I rate. + The simulated torques are sanaller than those preseuted in Papaloizou Larwood (2000) bv a factor of 0.71., The simulated torques are smaller than those presented in Papaloizou Larwood (2000) by a factor of 0.71. + The eccentrieitv evolution ids illustrated im the right panel of figure 6., The eccentricity evolution is illustrated in the right panel of figure \ref{fig6}. + Significant variations im the eccentricities are again observed. with peak walues of €zm0.05 beime excited.," Significant variations in the eccentricities are again observed, with peak values of $e \simeq 0.05$ being excited." + It is interesting to compare the evolution with the planetesimal aud LAL). cases. as there is a clear trend toward obtaining lower eccentricities with Increasing planet mass.," It is interesting to compare the evolution with the planetesimal and 1 $_{\oplus}$ cases, as there is a clear trend toward obtaining lower eccentricities with increasing planet mass." + I is likely that he eccentricity evolution is determined by a balance between stochastic forcing due to the turbulence. and eccentricity damping due o interaction with the disk at coorbital Lindblad FOSOMALLCOS (CGoldreich Tremaine 1980: Artvinowicz 1993).," It is likely that the eccentricity evolution is determined by a balance between stochastic forcing due to the turbulence, and eccentricity damping due to interaction with the disk at coorbital Lindblad resonances (Goldreich Tremaine 1980; Artymowicz 1993)." + This poiut is examined and discussed further iu section T.., This point is examined and discussed further in section \ref{stochastic_torques}. . + The orbital evolution of the six 5 AL). protoplauets is shown in üegure 7.., The orbital evolution of the six 5 $_{\oplus}$ protoplanets is shown in figure \ref{fig7}. + The semiunajor axes in the left panel show a general nsvard trend. which might a first be hought to be evidence that the usual type I uieration is becomming dominant over the stochastic forcing as the dlanet mass increases.," The semimajor axes in the left panel show a general inward trend, which might at first be thought to be evidence that the usual type I migration is becoming dominant over the stochastic forcing as the planet mass increases." + Closer inspection of the figures shows that the protoplancts are still subject to substantial radon forcing., Closer inspection of the figures shows that the protoplanets are still subject to substantial random forcing. +" Furthermore the 10 AD). case discussed low sugeests that the general παντα, motion of the jlancts in figure 7 ois probably a statistical effect rather than evidence for type I migration overwhelming stochastic forcing.", Furthermore the 10 $_{\oplus}$ case discussed below suggests that the general inward motion of the planets in figure \ref{fig7} is probably a statistical effect rather than evidence for type I migration overwhelming stochastic forcing. + It is worth noting. however. that for all cases considered in which the planets have masses iy;> LAD). the inner most plauct migrates inward at a rate snular to or greater that the expected type Irate.," It is worth noting, however, that for all cases considered in which the planets have masses $m_{pi}> 1$ $_{\oplus}$, the inner most planet migrates inward at a rate similar to or greater that the expected type I rate." + This arises because the plauet moves iuto a region of the disk where it isless turbulent due to the initial set up.," This arises because the planet moves into a region of the disk where it isless turbulent due to the initial set up," +Alore than three decades since the discovery of. quasars the question of whether our knowledge of the quasar population is allected significantly by dust extinction. within host galaxies or galaxies along the line of sight. remains controversial.,"More than three decades since the discovery of quasars the question of whether our knowledge of the quasar population is affected significantly by dust extinction, within host galaxies or galaxies along the line of sight, remains controversial." + Obscuration by tori or other nonspherica components forms a key clement of unified. schemes for active galactic nucle: (AGN)., Obscuration by tori or other non–spherical components forms a key element of unified schemes for active galactic nuclei (AGN). + Similarly. while estimates of the extinction. optical cepth through the clises of spira galaxies diller. a number of gravitationally lensecl cuasars and AGN provide unambiguous evidence that extinction within the dellector or host. galaxies allects our view of the sources.," Similarly, while estimates of the extinction optical depth through the discs of spiral galaxies differ, a number of gravitationally lensed quasars and AGN provide unambiguous evidence that extinction within the deflector or host galaxies affects our view of the sources." + However. it is not clear if obscuration by dus merely perturbs our view. increasing the overall quasar space density. or the frequency ofa particular quasar sub.tvpe. by a factor two or less. or. whether objects in existing quasar surveys represent only a small fraction of the (unobscured) population.," However, it is not clear if obscuration by dust merely perturbs our view, increasing the overall quasar space density, or the frequency of a particular quasar sub–type, by a factor two or less, or, whether objects in existing quasar surveys represent only a small fraction of the (unobscured) population." + Aluch discussion concerning obscured quasars has focussed on whether such objects. with their spectral energy distributions (SEDs) steepened by the elfects of reddening by dust. would be detectable. using a particular cuasar identification technique. such as slitless spectroscopy or multicolour selection in the optical.," Much discussion concerning obscured quasars has focussed on whether such objects, with their spectral energy distributions (SEDs) steepened by the effects of reddening by dust, would be detectable using a particular quasar identification technique, such as slitless spectroscopy or multicolour selection in the optical." + In fact. given that most surveys [for quasars rely on flux.limited samples of. very limited dynamic range. the key problem is that quasars will be dimmed to the extent that they simply do not appear in the sample.," In fact, given that most surveys for quasars rely on flux–limited samples of very limited dynamic range, the key problem is that quasars will be dimmed to the extent that they simply do not appear in the sample." + Fortunately. the rapid advance in the fabrication of large nearinfrared detectors means it will soon be viable to undertake surveys for quasars over large areas of sky that are much less susceptible to the elfects of extinction by dust.," Fortunately, the rapid advance in the fabrication of large near–infrared detectors means it will soon be viable to undertake surveys for quasars over large areas of sky that are much less susceptible to the effects of extinction by dust." + In this paper we introduce a method. [for selecting samples of quasars. Εανlimited in the Ix band. that would include quasars whose Hux has been dimmoed by dust. and which may have eluded. conventional optical surveys.," In this paper we introduce a method for selecting samples of quasars, flux–limited in the K band, that would include quasars whose flux has been dimmed by dust, and which may have eluded conventional optical surveys." + The method is termed. “WAT. by analogy with the UVX method. as it similarly. exploits the dillerence between the powerlaw nature of quasar spectra and the convex spectra of," The method is termed “KX”, by analogy with the UVX method, as it similarly exploits the difference between the power--law nature of quasar spectra and the convex spectra of" +lack of correlation between the inner and outer disc tilts could. provide one explanation of the finding by Kinney et al. (,lack of correlation between the inner and outer disc tilts could provide one explanation of the finding by Kinney et al. ( +2000) that the directions of jets from low luminosity AGN appear to be uncorrelated with the cise plane of the host spiral galaxies.,2000) that the directions of jets from low luminosity AGN appear to be uncorrelated with the disc plane of the host spiral galaxies. + JEP is grateful to S'TSel for hospitality and for continued support uncer its Visitor Program., JEP is grateful to STScI for hospitality and for continued support under its Visitor Program. + GLO acknowledges the support of the Roval Society through a University Research Fellowship. and of NASA through erant no.," GIO acknowledges the support of the Royal Society through a University Research Fellowship, and of NASA through grant no." + NACG5-LO732., NAG5-10732. +tracks using the PradaMoroni&Straniero(2002). models.,tracks using the \cite{Pm:02} models. + It is important to note that the evolution of the evaporation rate shown in Fig., It is important to note that the evolution of the evaporation rate shown in Fig. + 6 is Clearly an oversimplication of (he real case. which involves factors other than the evolution of (he stellar luminosity.," \ref{hydro_time} is clearly an oversimplication of the real case, which involves factors other than the evolution of the stellar luminosity." + For instance. feedback processes are important because the evaporation rate depends on (he planets structure which is itself determined by the planets reaction to evaporation and heating.," For instance, feedback processes are important because the evaporation rate depends on the planet's structure which is itself determined by the planet's reaction to evaporation and heating." + In order (o establish the importance of the feedback processes in determining the evaporation rates we need an estimate of the relevant timescales., In order to establish the importance of the feedback processes in determining the evaporation rates we need an estimate of the relevant timescales. + The timescale over which significant reaction takes place is given bv the thermal timescale 75., The timescale over which significant reaction takes place is given by the thermal timescale $\tau_{\rm th}$. + For the case under consideration the heating by radiation is taking place in a thin laver near the surface of the planet where the opacity is verv hieh., For the case under consideration the heating by radiation is taking place in a thin layer near the surface of the planet where the opacity is very high. +" Therefore. the relevant thermal timescale is (he one associated to the heating of the planets external laver by an external heating source. 7,=GALAAL/2RL,. where AAJ is the mass that is being heated and L, is the stellar Iuminositv. arriving al the planets surface (multiplied by a correction [actor that accounts for the heating elliciency)."," Therefore, the relevant thermal timescale is the one associated to the heating of the planet's external layer by an external heating source, $\tau_{\rm th}=GM_{\rm p} \Delta M/2RL_*$, where $\Delta M$ is the mass that is being heated and $L_*$ is the stellar luminosity arriving at the planet's surface (multiplied by a correction factor that accounts for the heating efficiency)." +" Since Jupiter-like planets are believed to be mostly convective. with a radiative external zone that contains 22 of the mass 1996).. il is reasonable to assume that the stellar energv is mostly deposited in this laver. which then gives my,z10"". vvr (for à 0.56 star)."," Since Jupiter-like planets are believed to be mostly convective, with a radiative external zone that contains $\approx$ of the mass \citep{Gui:96}, it is reasonable to assume that the stellar energy is mostly deposited in this layer, which then gives $\tau_{\rm th}\approx 10^6$ yr (for a 0.56 star)." +" We should now compare 7, with the niass-loss ümescale 7,4. τν=AL,/Mp. and if we assume that M, = dj as given by Eq."," We should now compare $\tau_{\rm th}$ with the mass-loss timescale $\tau_{\dot{M}}$ , $\tau_{\dot{M}}~=~M_{\rm p}/\dot{M_P}$, and if we assume that $\dot{M_p}$ = $\Phi_{\rm H}$ as given by Eq." + then τι&LO? yvr (for L and 0.56 ))., \ref{loss} then $\tau_{\dot{M}}\approx 10^5$ yr (for 1 and 0.56 ). +" Therefore. for range of orbital distances. Ty,τιν Which implies that the planets mass is decreasing faster than the time the planet has to readjust to a new thermal equilibrium."," Therefore, for range of orbital distances, $\tau_{\dot{M}} \le \tau_{\rm th}$ which implies that the planet's mass is decreasing faster than the time the planet has to readjust to a new thermal equilibrium." + The planet has (wo wavs to adjust to a new thermal equilibrium: to increase ils radius or Lo increase its effective temperature., The planet has two ways to adjust to a new thermal equilibrium: to increase its radius or to increase its effective temperature. + If the planet reacts to the external heating by increasing ils effective temperature. then the evolution of the mass-loss rates computed using Eq.," If the planet reacts to the external heating by increasing its effective temperature, then the evolution of the mass-loss rates computed using Eq." + and the time-dependent stellar [lux are a good. first order. approximation to the actual evaporation rates., \ref{loss} and the time-dependent stellar flux are a good first order approximation to the actual evaporation rates. + However. given (he high mass-loss rates involved. the planet may react by increasing its radius on a timescale given bv τιν. in which case the mass-loss rates will be larger than estimated.," However, given the high mass-loss rates involved, the planet may react by increasing its radius on a timescale given by $\tau_{\rm th}$, in which case the mass-loss rates will be larger than estimated." +" In fact. once the mass-loss timescale becomes much shorter than the readjustment (thermal) timescale (ry,S 0.15). a runaway mass-loss may ensue (e.g. Daraffeetal. 2003))."," In fact, once the mass-loss timescale becomes much shorter than the readjustment (thermal) timescale $\tau_{\dot{M}} \lesssim 0.1 \tau_{\rm th}$ ), a runaway mass-loss may ensue (e.g. \citealt{Betal:03}) )." + There are other non-thermal processes (hat might contribute to the planet evaporation. e.&. photodisociation and ram pressure stripping.," There are other non-thermal processes that might contribute to the planet evaporation, e.g. photodisociation and ram pressure stripping." + An increase in the planet’s radius will decrease the density of the outer laver allowing theionization front to propagate inwarels.," An increase in the planet's radius will decrease the density of the outer layer allowing theionization front to propagate inwards," +continuum at low energies. such [lattenings are not usually. seen in active galaxies. and the intrinsic continuum would need to be exceptionally. hard.,"continuum at low energies, such flattenings are not usually seen in active galaxies, and the intrinsic continuum would need to be exceptionally hard." + Furthermore. we note that ROSAT versus ASCA calibration discrepancies cannot easily explain a systematically Latter IROSAT continuum (IROSAAT slopes. if anything. appear to be systematically steeper than ASCA slopes: see Iwasawa. Fabian Nandra 1999).," Furthermore, we note that ROSAT versus ASCA calibration discrepancies cannot easily explain a systematically flatter ROSAT continuum (ROSAT slopes, if anything, appear to be systematically steeper than ASCA slopes; see Iwasawa, Fabian Nandra 1999)." + 1£ we require the photon index to lie within the ASCA range of 1.2940.05 and the column density to Lie within the range consistent with the Galactic value. the fit can be statistically rejected with a probability of 98.7 per cent (A7 —150 for 114 d.o.E:," If we require the photon index to lie within the ASCA range of $\pm$ 0.05 and the column density to lie within the range consistent with the Galactic value, the fit can be statistically rejected with a probability of 98.7 per cent $\chi^2$ =150 for 114 d.o.f.;" + lower panel of Figure 1)., lower panel of Figure 1). + We conclude that plausible power-law models absorbed by the Galactic column density cannot provide an adequate fit to the ROSAT data., We conclude that plausible power-law models absorbed by the Galactic column density cannot provide an adequate fit to the ROSAT data. + A simple. power-law. Gt where the absorption column density and. the photon index are allowed: to be. free xwanmeters provides a better statistical fitLr to the ROSAT SPC data (47 = 100 for 113 cLo.L:, A simple power-law fit where the absorption column density and the photon index are allowed to be free parameters provides a better statistical fit to the ROSAT PSPC data $\chi^2$ = 100 for 113 d.o.f.; + ef, cf. + Figure 2)., Figure 2). + Using he d-test for the addition of one free parameter one gets 7 (cl., Using the $F$ -test for the addition of one free parameter one gets $\Delta \chi^2/\chi_{\nu}^2$ = 22.7 (cf. + La., Eq. + 1.50 of Bevington Robinson 1992)., 11.50 of Bevington Robinson 1992). + According to Table €.5 of Bevington Robinson (1992) this corresponds to a highly significant improvement 99.9 per cent) in the fit qualitv., According to Table C.5 of Bevington Robinson (1992) this corresponds to a highly significant improvement $>$ 99.9 per cent) in the fit quality. +". Most. important. the soft. X-ray absorption of ΔΑμι=(3.14d:0.35)107""em is larger than the Galactic column towards GB 1428|4217 at the 5 sigma level."," Most important, the soft X-ray absorption of $N_{\rm H, fit}^{\rm z=0}\rm=(3.14\pm0.35)\times10^{20}\ cm^{-2}$ is larger than the Galactic column towards GB 1428+4217 at the 5 sigma level." + The photon index is F—1.40-0.20. in agreement with the ASCA value.," The photon index is $\Gamma$ $\pm$ 0.20, in agreement with the ASCA value." + These results are robust to changes in the number of data points included in the lit., These results are robust to changes in the number of data points included in the fit. + A contour plot of 47 as à function of the absorbing column in the observers frame and the photon index is shown in Figure 3., A contour plot of $\rm \chi^2$ as a function of the absorbing column in the observer's frame and the photon index is shown in Figure 3. + Ehe displaved contour levels of 68.3. 95.4. 90.7. 90.00 and 99.9999 per cent clearly demonstrate the detection of excess absorption above the Galactic column towards the high recshift quasar GB 142s|4217.," The displayed contour levels of 68.3, 95.4, 99.7, 99.99 and 99.9999 per cent clearly demonstrate the detection of excess absorption above the Galactic column towards the high redshift quasar GB 1428+4217." + This excess low-cnerey cutoll translates into an intrinsic X-ray absorption of Αιστ=(152+028)«107em7? for neutral eas and solar abuncances.," This excess low-energy cutoff translates into an intrinsic X-ray absorption of $N_{\rm H, fit}^{\rm z=4.72} \rm += (1.52 \pm 0.28) \times 10^{22}\ +cm^{-2}$ for neutral gas and solar abundances." + With the current data we are unable to precisely constrain the ionization level of the absorbing eas: our only constraint is that oxvecn must not be completely stripped., With the current data we are unable to precisely constrain the ionization level of the absorbing gas; our only constraint is that oxygen must not be completely stripped. + However. we note that increasing the eas ionization level will require even Larger column densities than the substantial one already. derived for neutral gas.," However, we note that increasing the gas' ionization level will require even larger column densities than the substantial one already derived for neutral gas." + In the Appendix we have modeled. the inlluence. of different eain. values on the soft. X-ray. absorption., In the Appendix we have modeled the influence of different gain values on the soft X-ray absorption. + With ligure Al in the Appendix we demonstrate that even in the case of unusual gain values the excess absorption above the Galactic column is still present., With Figure A1 in the Appendix we demonstrate that even in the case of unusual gain values the excess absorption above the Galactic column is still present. + Interestingly. there is another bright X-ray source (the blazar CSO 0454 = ILD 14330|423. 2:= 0.129) in the field of view. which can be used to demonstrate that there is not a relevant svstematic ellect in determining the excess absorption.," Interestingly, there is another bright X-ray source (the blazar CSO 0454 = 1H 1430+423, $z=0.129$ ) in the field of view, which can be used to demonstrate that there is not a relevant systematic effect in determining the excess absorption." + The source is outside the gain hole and no other elfects. prevented. the reliable. analysis of the data for this source., The source is outside the gain hole and no other effects prevented the reliable analysis of the data for this source. +" A power-law fit combined with absorption bv neutral matter (Figure 4) results in Nga)=(1.5040.17)«107""em in good agreement with the Galactic column density."," A power-law fit combined with absorption by neutral matter (Figure 4) results in $N_{\rm H, fit}^{\rm z=0} \rm = (1.50 \pm 0.17) \times 10^{20}\ cm^{-2}$ , in good agreement with the Galactic column density." + In addition. the X-ray variability found in," In addition, the X-ray variability found in" +regions of the Milky Way by MEIL(G 15c-4kmstkpe 4). which also coincides with the value derived for SSO]by 7,"regions of the Milky Way by MF11 $-15 \pm 4 +\kmskpc$ ), which also coincides with the value derived for 891by \citet{Oosterloo+07}." + A second fundamental property of the Galaxy's thalo is its thickness., A second fundamental property of the Galaxy's halo is its thickness. + To obtain it we fitted the vertical density. profiles in. our models at cilferent raclii with exponential functions., To obtain it we fitted the vertical density profiles in our models at different radii with exponential functions. + Fig., Fig. + S. shows the (exponential) veight of the thalo of our best model as a function of Z7., \ref{scaleheight} shows the (exponential) scale-height of the halo of our best model as a function of $R$. + The thickness increases with /? because the gravitational restoring force o the plane diminishes outwards 1001., The thickness increases with $R$ because the gravitational restoring force to the plane diminishes outwards (FB06). + Phe halo density decreases abruptly for £22714kpce. so its hickness cannot »e reliably determined at. larger radii.," The halo density decreases abruptly for $R\!>\!14\kpc$, so its thickness cannot be reliably determined at larger radii." + The shape of the scaleheight as a function. of Rois partially due to. the assumption of our model that the kick velocity P does not change with radius (for a cliscussion sce FBOG)., The shape of the scaleheight as a function of R is partially due to the assumption of our model that the kick velocity $h_{\rm v}$ does not change with radius (for a discussion see FB06). + In the inner Galaxy there has long been evidence for a population of cclouds extending up to Lkpe above the midplane (222) 7," In the inner Galaxy there has long been evidence for a population of clouds extending up to $\sim1\kpc$ above the midplane \citep{Lockman84, Lockman02, Ford+10}." + assumed a constant thickness for the halo and derived a value of L.6kpe using a sech? formula. which corresponds to ~SOOpc for an exponential function.," \citet{MarascoFraternali11} assumed a constant thickness for the halo and derived a value of $1.6\kpc$ using a $\rm{sech}^2$ formula, which corresponds to $\sim 800\pc$ for an exponential function." + This value agrees well with the average of the scaleheights plotted in Fig. S.., This value agrees well with the average of the scaleheights plotted in Fig. \ref{scaleheight}. + 7 studied the vertical structure of the Galaxy's aver on the assumption that the laver is in hvdrostatic quilibrium., \citet{Kalberla+07} studied the vertical structure of the Galaxy's layer on the assumption that the layer is in hydrostatic equilibrium. + Using this assumption. they inferred that while at y the aver extends only a few hundred parsecs from the plane. at pP=35kpe the vertical structure of the aver can be fitted by a Gaussian cistribution with scale wieght 2.5kpe.," Using this assumption, they inferred that while at $R_0$ the layer extends only a few hundred parsecs from the plane, at $R\simeq35\kpc$ the vertical structure of the layer can be fitted by a Gaussian distribution with scale height $2.5\kpc$." + Phus they deduced a very extended aver with strong Uaring., Thus they deduced a very extended layer with strong flaring. + Γον also inferred the existence of a massive ring of dark matter between //=18 and 18.5kpe., They also inferred the existence of a massive ring of dark matter between $R=13$ and $18.5\kpc$. + The assumption of hyelrostatic equilibrium leads. however. o mocdels that [ai o match the data correctly (see??)..," The assumption of hydrostatic equilibrium leads, however, to models that fail to match the data correctly \citep[see][]{Barnabe06,Marinacci+10b}." + lf? hac used the prediction of a fountain model for the distribution of nnear Ay rather than a model based. on. hyelrostatic equilibrium. they would have come to different conclusions regarding the radii responsible for each quantity of emission in the ddatacube.," If \citet{Kalberla+07} had used the prediction of a fountain model for the distribution of near $R_0$ rather than a model based on hydrostatic equilibrium, they would have come to different conclusions regarding the radii responsible for each quantity of emission in the datacube." + Consequently. the distribution of the matter and the structure of the flare in the Alilky Way should be re-derived.," Consequently, the distribution of the matter and the structure of the flare in the Milky Way should be re-derived." + While this topic merits further work. our comparisons of the fountain model with the cata viele no compelling evidence for substantial Daring of the Πάνος much beyond 215kpe.," While this topic merits further work, our comparisons of the fountain model with the data yield no compelling evidence for substantial flaring of the layer much beyond $R\sim 15 \kpc$." + Infall of metal-poor gas to the star-forming disc is an essentia ingredient of current models of the Galaxys hemical evolution (e.g.22)..," Infall of metal-poor gas to the star-forming disc is an essential ingredient of current models of the Galaxy's chemical evolution \citep[e.g.][]{Chiappini+01,SchoenrichBinney09}." + Phe predictions of such models lepend to a significant extent. on the radial profile of 1e infall. but. hitherto there iis been no credible way of etermining this profile.," The predictions of such models depend to a significant extent on the radial profile of the infall, but hitherto there has been no credible way of determining this profile." + Phe prediction of our model for this profile is shown in Fig., The prediction of our model for this profile is shown in Fig. + 9 (bottom panel)., \ref{accretion} (bottom panel). + The curve shows 10 pristine gas that. condensing from the corona onto the fountain cloud. wakes. follows the cloud. orbits back to the isc.," The curve shows the pristine gas that, condensing from the corona onto the fountain cloud wakes, follows the cloud orbits back to the disc." + The shape of the aceretion profile is due to the variation of the mass outflow and the orbital time with radius., The shape of the accretion profile is due to the variation of the mass outflow and the orbital time with radius. + At RS3kpe the specific accretion rate essentially vanishes because the orbits of the fountain clouds are confined within few Πάνος of parsees from the cise (sce Fig. 8))., At $R\la3\kpc$ the specific accretion rate essentially vanishes because the orbits of the fountain clouds are confined within few hundred of parsecs from the disc (see Fig. \ref{scaleheight}) ). + H then rises to a peak at /?2Okpe as in this region both the orbital time and the star formation are sullicicntly high., It then rises to a peak at $R\simeq9\kpc$ as in this region both the orbital time and the star formation are sufficiently high. + At IHOkpe the aceretion rate falls again due to the low level of star formation at these radii. ancl drops to about. zero bevond &= 13kpc.," At $R>9\kpc$ the accretion rate falls again due to the low level of star formation at these radii, and drops to about zero beyond $R=13 +\kpc$ ." + The integral of this curve over the disc, The integral of this curve over the disc +Gratton 1997).,Gratton 1997). + The Zinn West scale (herealter ZW scale) emplovs the most complete data set but is not based on high resolution spectra., The Zinn West scale (hereafter ZW scale) employs the most complete data set but is not based on high resolution spectra. + However. the Carretta Gratton scale (hereafter CGOT scale) is based on systematic hieh resolution spectra obtained by their own team. and there is a (transformation relation between the ZW. scale and the CG97 scale in equation (7) of Carretta Gratton (1997).," However, the Carretta Gratton scale (hereafter CG97 scale) is based on systematic high resolution spectra obtained by their own team, and there is a transformation relation between the ZW scale and the CG97 scale in equation (7) of Carretta Gratton (1997)." + The CGOT scale is more robust since it relies on recent high resolution spectroscopic measurements and up-to-date atmospheric moclels., The CG97 scale is more robust since it relies on recent high resolution spectroscopic measurements and up-to-date atmospheric models. + Moreover. in order to compare our results directly with those of Ferraro et al. (," Moreover, in order to compare our results directly with those of Ferraro et al. (" +2000) which emploved the CG97 scale. we adopted the CG97 metallicity scale.,"2000) which employed the CG97 scale, we adopted the CG97 metallicity scale." + The CG97 scale metallicity of each GGC* is given in Table 2., The CG97 scale metallicity of each GGC is given in Table 2. + Since only 24 GGCs have metallicity determinations from direct high resolution spectra in (he CG97T scale. the metallicities of NGC 1351 and ALOT are interpolated [rom equation (7) of Carretta Gratton (1997). and the metallicity of M2. is adopted from the value determined by the morphological parameters of RGB stars bv Lee Carney (1999).," Since only 24 GGCs have metallicity determinations from direct high resolution spectra in the CG97 scale, the metallicities of NGC 1851 and M107 are interpolated from equation (7) of Carretta Gratton (1997), and the metallicity of M2 is adopted from the value determined by the morphological parameters of RGB stars by Lee Carney (1999)." + Recently. Carretta Gratlon’s group published high resolution spectroscopic metallicities of NGC 6553 (Cohen el al.," Recently, Carretta Gratton's group published high resolution spectroscopic metallicities of NGC 6553 (Cohen et al." + 1999: Carrettà οἱ al 2001) and NGC 6528 (Carretla et. al., 1999; Carretta et al 2001) and NGC 6528 (Carretta et al. + 2001. herealter. CG). extending the CG97 metallicity scale into the high metallicity region ([Fe/IH]ec; 0.00). and established a new transformation equation between ZW scale metallicity ancl CG scale metallicity.," 2001, hereafter CG), extending the CG97 metallicity scale into the high metallicity region $_{\rm CG}$ $\approx$ 0.00), and established a new transformation equation between ZW scale metallicity and CG scale metallicity." + However. in the metallicity range of [Fe/IH]ec;sz =—2.12~—0.70 the interpolated metallicity values are coincident within 0.1 dex in the two different transformation equations and it seems (hat transformation equation (7) of Carretta Gratton (1997) is üghter (han transformation equation (3) of Carretta et al. (," However, in the metallicity range of $_{\rm CG97}$ $= -2.12 +\sim -0.70$ the interpolated metallicity values are coincident within 0.1 dex in the two different transformation equations and it seems that transformation equation (7) of Carretta Gratton (1997) is tighter than transformation equation (3) of Carretta et al. (" +2001).,2001). + We did not revise the metallicities of NGC 18351. MIOT. M2. M55. ancl M69. which have no metallicity measurements [rom direct hieh resolution spectra in (he CGO97 metallicity scale.," We did not revise the metallicities of NGC 1851, M107, M2, M55, and M69, which have no metallicity measurements from direct high resolution spectra in the CG97 metallicity scale." + But for metallicities of NGC 6553 and NGC 6528. which were exirapolated by Ferraro et al. (," But for metallicities of NGC 6553 and NGC 6528, which were extrapolated by Ferraro et al. (" +1999) since their ZW scale metallicities are outside (he validitv. range of the transformation to the CGO7 scale metallicities by equation (7) of Carrettà Gratton (1997). we adopted the new high resolution spectroscopic measurements of Carretta et al. (,"1999) since their ZW scale metallicities are outside the validity range of the transformation to the CG97 scale metallicities by equation (7) of Carretta Gratton (1997), we adopted the new high resolution spectroscopic measurements of Carretta et al. (" +2001).,2001). + Metallicities of the other GGCs are taken from the directly determined values of Carretta Gratton (1997)., Metallicities of the other GGCs are taken from the directly determined values of Carretta Gratton (1997). + We also consider the global metallicity [M/TII] which incorporates a-element enhancement into the CG97 metallicity scale [Fe/1HI]ecoz according to equation (1) of Ferraro οἱ al. (, We also consider the global metallicity [M/H] which incorporates $\alpha$ -element enhancement into the CG97 metallicity scale $_{\rm CG97}$ according to equation (1) of Ferraro et al. ( +1999).,1999). + In the case of |ML/L we directly adopted the values in Table 1 of Ferraro et al. (, In the case of [M/H] we directly adopted the values in Table 1 of Ferraro et al. ( +1999) except for M22. M2. NGC 6553. and NGC 6528.,"1999) except for M22, M2, NGC 6553, and NGC 6528." + In the cases of M22 and M2 we calculated ΑΗ) as described in 5 3.1 and in the cases of NGC 6553 and NGC 6528 we first calculated [a /Fe] using equation (2) of Carney (1996) with the a-element abundances listed in Carretta et al. (, In the cases of M22 and M2 we calculated [M/H] as described in $\S$ 3.1 and in the cases of NGC 6553 and NGC 6528 we first calculated $\alpha$ /Fe] using equation (2) of Carney (1996) with the $\alpha$ -element abundances listed in Carretta et al. ( +2001) and then caleulated [MIL using equation (3) in § 3.1.,2001) and then calculated [M/H] using equation (3) in $\S$ 3.1. + Values of [a /Fe]| of NGC 6553 and NGC 6528 ave 0.20 + 0.07 and 0.21 z 0.04. respectively.," Values of $\alpha$ /Fe] of NGC 6553 and NGC 6528 are 0.20 $\pm$ 0.07 and 0.21 $\pm$ 0.04, respectively." +Lang (2002) and will be further detailed by Wang et al. (,Lang (2002) and will be further detailed by Wang et al. ( +2002).,2002). + We searched [or X-ray sources in individual observations (Wang. Gotthelf. Lang 2002).," We searched for X-ray sources in individual observations (Wang, Gotthelf, Lang 2002)." + The source position centroids are uncertain. both statistically and. svstematically.," The source position centroids are uncertain, both statistically and systematically." + The statistical uncertainty depends on the count rate of a source and on the point spread function. which is a finetion of the off-axis angle of the source in an observation.," The statistical uncertainty depends on the count rate of a source and on the point spread function, which is a function of the off-axis angle of the source in an observation." + In order to correct For the svstematic pointing offset. we select sources wilh 2o statistical uncertainty radii less than 176.," In order to correct for the systematic pointing offset, we select sources with $\sigma$ statistical uncertainty radii less than $1\farcs6$." + We examined position coincidences between the X-rav sources detected in the deep observation (ID 229945) ancl various optical/near-IB. objects (e.g.. ESO/ST-ECE USNO-A2.0 and 2ALASS catalogs).," We examined position coincidences between the X-ray sources detected in the deep observation (ID 945) and various optical/near-IR objects (e.g., ESO/ST-ECF USNO-A2.0 and 2MASS catalogs)." +" While no coincidence was found within the 2o statistical uncertainty radii of the X-ray source centroids. we considered objects projected within the 3"" radii ol the N-rav. sources."," While no coincidence was found within the $\sigma$ statistical uncertainty radii of the X-ray source centroids, we considered objects projected within the $^{\prime\prime}$ radii of the X-ray sources." + The foreground FO star. 1I1D316314 (B=9.94. V—9.51) stands out. which is the brightest optical object within the radii," The foreground F0 star, HD316314 (B=9.94, V=9.51) stands out, which is the brightest optical object within the radii." + The corresponding point-like X-ray counterpart has an ACIS-I count rate of 0.026. countss1 and a very soft spectrum., The corresponding point-like X-ray counterpart has an ACIS-I count rate of 0.026 ${\rm~counts~s^{-1}}$ and a very soft spectrum. + A, A +"HD 218566 is a V = 8.628 magnitude star of spectral class K3V. In comparison to the Sun, HD 218566 is quite metal-rich ([Fe/H] = 0.38).","HD 218566 is a V = 8.628 magnitude star of spectral class K3V. In comparison to the Sun, HD 218566 is quite metal-rich ([Fe/H] = 0.38)." +" Table 1 reports some of the salient stellar properties, as reported by NStEd, etal.(2004) and Takeda"," Table \ref{tab:allstars} reports some of the salient stellar properties, as reported by NStEd, \citet{Wright04} and \citet{Takeda07}." +etal.(2007).. Table 4 shows the 56 relative radial velocity observations for HD 218566., Table \ref{tab:rvdata_HD218566} shows the 56 relative radial velocity observations for HD 218566. + The radial velocity coverage spans approximately 14 years of RV monitoring., The radial velocity coverage spans approximately 14 years of RV monitoring. +" The median internal uncertainty for our observations is 1.27s-1,, and the peak-to-peak velocity variation is 28.46s-!."," The median internal uncertainty for our observations is 1.27, and the peak-to-peak velocity variation is 28.46." +. The velocity scatter around the mean RV in our measurements is 7.18s7!., The velocity scatter around the mean RV in our measurements is 7.18. +. The top panel of Figure 3 shows the individual RV observations for HD 218566., The top panel of Figure \ref{fig:data_HD218566} shows the individual RV observations for HD 218566. +" The middle panel shows the error-weighted Lomb-Scargle (LS) periodogram of the full RV data set, while the bottom figure shows the spectral window."," The middle panel shows the error-weighted Lomb-Scargle (LS) periodogram of the full RV data set, while the bottom figure shows the spectral window." + The FAP calculation for the strong Keplerian signal at P= 225.06 days in the RV dataset indicates an estimated FAP =<4x1079., The FAP calculation for the strong Keplerian signal at $P = $ 225.06 days in the RV dataset indicates an estimated FAP $\approx < 4 \times 10^{-6}$. + The dominant peak in the periodogram can be explained by a Keplerian orbit of period 225.73 days and semi-amplitude K=8.34s-l., The dominant peak in the periodogram can be explained by a Keplerian orbit of period 225.73 days and semi-amplitude $K = 8.34 $. + This amplitude suggests a minimum mass of Msini=0.21M; a stellar mass of 0.88 Mo)., This amplitude suggests a minimum mass of $\mass \sin i = 0.21 \mjup$ (assuming a stellar mass of 0.88 $\msun$ ). + The best-fit orbit for the (assumingplanet is moderately eccentric (e~ 0.37)., The best-fit orbit for the planet is moderately eccentric $e \approx 0.37$ ). +" This fit achieves a reduced x?=8.41, with an RMS of 3.48s-!."," This fit achieves a reduced $\chi^2 = 8.41$, with an RMS of 3.48." +". The expected jitter of HD 218566 is, the amount of jitter required to bring the reduced (thatx? of the best-fit solution to 1.0) is 3.23i."," The expected jitter of HD 218566 (that is, the amount of jitter required to bring the reduced $\chi^2$ of the best-fit solution to 1.0) is 3.23." + The top panel of Figure 4 shows the phased stellar reflex velocity of HD 218566 compared to the RV dataset., The top panel of Figure \ref{fig:bestfit_HD218566} shows the phased stellar reflex velocity of HD 218566 compared to the RV dataset. + The middle panel shows the residuals to the 1-planet solution., The middle panel shows the residuals to the 1-planet solution. +" The periodogram of the residuals to the best-fit solution, shown in the bottom panel, displays no strong peaks that would support the evidence for additional planets in the system."," The periodogram of the residuals to the best-fit solution, shown in the bottom panel, displays no strong peaks that would support the evidence for additional planets in the system." +randomized initial conditions.,randomized initial conditions. + Again. we find qualitatively simular results from all sets of the DEMCMZC analysis. but with some indication that the results have not truly converged.," Again, we find qualitatively similar results from all sets of the DEMCMC analysis, but with some indication that the results have not truly converged." + As such. we interpret these results as demoustrative that stable svstenis exist which can fit the RV data. aud moreover. the extremely narrow range of period ratios favored by the analysis (1.32 to ~ 1.36) shows that the current observations strouglv favor orbital solutions iu or close to the 1:3 AIMR.," As such, we interpret these results as demonstrative that stable systems exist which can fit the RV data, and moreover, the extremely narrow range of period ratios favored by the analysis $\sim 1.32$ to $\sim 1.36 $ ) shows that the current observations strongly favor orbital solutions in or close to the 4:3 MMR." + Next. we test the long-terin orbital stability of the orbital solutions identifiod bv the DEMCWMC analysis.," Next, we test the long-term orbital stability of the orbital solutions identified by the DEMCMC analysis." + ForL. 290% of the systems are clearly unstable diving a 10 year duteeration (Le. they experience a collision or a change im seminajor axes of more than 50%..)," For, $> 90\%$ of the systems are clearly unstable during a $10^7$ year integration (i.e., they experience a collision or a change in semimajor axes of more than .)" + We fiud that 1.000 of the 16.000 siuulatiouns remain stable for 10! vears.," We find that $\sim~1,000$ of the 16,000 simulations remain stable for $10^7$ years." + We interpret these as plausible orbital solutions cousisteut with the RV observations of TD 200961., We interpret these as plausible orbital solutions consistent with the RV observations of HD 200964. + As illustrated in Fie. L.," As illustrated in Fig. \ref{FIG:NBODY:B:1}," + the stable svstems occupy a reeion of paralcter space corresponding to a region of xuwaniter space near the [23 period ratio., the stable systems occupy a region of parameter space corresponding to a region of paramter space near the 4:3 period ratio. +" Taking ouly hese long-term stable systems iuto account. we find that ⋅ ∢≽↓⋅≩∙≺∖↴⊥⋡⊥⋟ ⋅ scninajor+H axisB aj,= AU.7 eccentricityee e;= ⋜↧⋜⊔≼↧⋯⋜↧↴∖↴↴∖↴⋀∐∣⊢∖↴⋯∣∶↓∙≺∖⋅↱⊐↴- ≻↕⋜⋯↸∖↑∐⋜↧↴∖↴⋜∏⋉∖↥⋅↕∪≼↧∫≽↙∶≺∖∖⊇⋅↱↗∙∩ ddavs. semimnajor. axis. e,— AU. eccentricity aye.= aaud mass M,sini=Ma"," Taking only these long-term stable systems into account, we find that the inner planet has a period $P_b =$ days, semimajor axis $a_b +=$ AU, eccentricity $e_b =$ and mass $M_b \sin{i} =$ , while the outer planet has a period $P_c =$ days, semimajor axis $a_c =$ AU, eccentricity $e_c =$ and mass $M_c \sin{i} =$." +p We detail all the fitted paraiucters from this umanalysis in Table 3.., We detail all the fitted parameters from this analysis in Table \ref{tab:nbodyplanets}. + We find that ost of the stable planetary orbits overlap. producing strouslv iuteracting svstenuis. resulting in significant oscillations— iu the the seiminajor— axes and the eccentricities of both plancts.," We find that most of the stable planetary orbits overlap, producing strongly interacting systems, resulting in significant oscillations in the the semimajor axes and the eccentricities of both planets." + An exainple stablesolution/ exhibits observable eccentricity, An example stablesolution exhibits observable eccentricity +"intensity Z,). £,(0) is(he intensity of the radiation incident on the electron laver aud j..(2.2) is (he emissivily ofthe electron.","intensitymainBodyEnd5807 mainInlineStart5808I_ωmainInlineEnd5808mainBodyStart5809), $I_{\omega }$ ),mainBodyEnd5809 mainInlineStart5810I_ω(0)mainInlineEnd5810 mainBodyStart5811is $I_{\omega }(0)$ ismainBodyEnd5811 mainBodyStart5812the themainBodyEnd5812 mainBodyStart5813intensity intensitymainBodyEnd5813 mainBodyStart5814of ofmainBodyEnd5814 mainBodyStart5815the themainBodyEnd5815 mainBodyStart5816radiation radiationmainBodyEnd5816 +mainBodyStart5817incident incidentmainBodyEnd5817 mainBodyStart5818on onmainBodyEnd5818 mainBodyStart5819the themainBodyEnd5819 mainBodyStart5820electron electronmainBodyEnd5820 mainBodyStart5821layer layermainBodyEnd5821 mainBodyStart5822and and\tikzmark{mainBodyEnd5822} \tikzmark{mainInlineStart5823}$j_{\omega }\left( z,T\right) $\tikzmark{mainInlineEnd5823} \tikzmark{mainBodyStart5824}is $j_{\omega }\left( z,T\right) $ ismainBodyEnd5824 mainBodyStart5825the themainBodyEnd5825 +mainBodyStart5826emissivity emissivitymainBodyEnd5826 mainBodyStart5827of ofmainBodyEnd5827 mainBodyStart5828the themainBodyEnd5828 mainBodyStart5829electron." + Since in (he present paper we are interested (to study only the effect of theouter electrons on(he quark matter emission. we shall take 0. j.(2.2)2 that is we shall neglect theemissivity ofthe electron laver.," electron.mainBodyEnd5829 mainBodyStart5830Since SincemainBodyEnd5830 mainBodyStart5831in inmainBodyEnd5831 mainBodyStart5832the themainBodyEnd5832 mainBodyStart5833present presentmainBodyEnd5833 mainBodyStart5834paper papermainBodyEnd5834 mainBodyStart5835we wemainBodyEnd5835 mainBodyStart5836are aremainBodyEnd5836 mainBodyStart5837interested interestedmainBodyEnd5837 mainBodyStart5838to tomainBodyEnd5838 mainBodyStart5839study studymainBodyEnd5839 mainBodyStart5840only onlymainBodyEnd5840 mainBodyStart5841the the\tikzmark{mainBodyEnd5841} \tikzmark{mainBodyStart5842}effect effectmainBodyEnd5842 +mainBodyStart5843of ofmainBodyEnd5843 mainBodyStart5844the themainBodyEnd5844 mainBodyStart5845outer outermainBodyEnd5845 mainBodyStart5846electrons electronsmainBodyEnd5846 mainBodyStart5847on onmainBodyEnd5847 mainBodyStart5848the themainBodyEnd5848 mainBodyStart5849quark quarkmainBodyEnd5849 mainBodyStart5850matter mattermainBodyEnd5850 mainBodyStart5851emission, emission,mainBodyEnd5851 mainBodyStart5852we wemainBodyEnd5852 mainBodyStart5853shall shallmainBodyEnd5853 mainBodyStart5854take takemainBodyEnd5854 mainInlineStart5855j_ω( z,T) ≈mainInlineEnd5855mainBodyStart58560, $% +j_{\omega }\left( z,T\right) \approx 0,mainBodyEnd5856mainBodyStart5857that that\tikzmark{mainBodyEnd5857} \tikzmark{mainBodyStart5858}is ismainBodyEnd5858 mainBodyStart5859we wemainBodyEnd5859 mainBodyStart5860shall shallmainBodyEnd5860 mainBodyStart5861neglect neglectmainBodyEnd5861 mainBodyStart5862the themainBodyEnd5862 +mainBodyStart5863emissivity emissivitymainBodyEnd5863 mainBodyStart5864of ofmainBodyEnd5864 mainBodyStart5865the themainBodyEnd5865 mainBodyStart5866electron electronmainBodyEnd5866 mainBodyStart5867layer." +" IIence. the variation of the intensity. due to absorption inthe electron laver. of the photon beam emitted by the quarks al the strange star surface canbe described bythe following equation: In the case of the scattering ofphotons byfree non-relativistic electrons. the opacity is: given: bvA, =oeqn.(z)/p., where op=(8x/3)MEM(e/m,c7) cross-section. 343.isthe Thomson (Derestetskiietal.1982;Rxbicki&Lightman 1979)."," layer.mainBodyEnd5867 mainBodyStart5868Hence, Hence,mainBodyEnd5868 mainBodyStart5869the themainBodyEnd5869 mainBodyStart5870variation variationmainBodyEnd5870 mainBodyStart5871of ofmainBodyEnd5871 mainBodyStart5872the themainBodyEnd5872 mainBodyStart5873intensity, intensity,\tikzmark{mainBodyEnd5873} \tikzmark{mainBodyStart5874}due duemainBodyEnd5874 +mainBodyStart5875to tomainBodyEnd5875 mainBodyStart5876absorption absorptionmainBodyEnd5876 mainBodyStart5877in inmainBodyEnd5877 mainBodyStart5878the themainBodyEnd5878 mainBodyStart5879electron electronmainBodyEnd5879 mainBodyStart5880layer, layer,mainBodyEnd5880 mainBodyStart5881of ofmainBodyEnd5881 mainBodyStart5882the themainBodyEnd5882 mainBodyStart5883photon photonmainBodyEnd5883 mainBodyStart5884beam beammainBodyEnd5884 mainBodyStart5885emitted emittedmainBodyEnd5885 mainBodyStart5886by bymainBodyEnd5886 mainBodyStart5887the themainBodyEnd5887 +mainBodyStart5888quarks quarksmainBodyEnd5888 mainBodyStart5889at atmainBodyEnd5889 mainBodyStart5890the the\tikzmark{mainBodyEnd5890} \tikzmark{mainBodyStart5891}strange strangemainBodyEnd5891 mainBodyStart5892star starmainBodyEnd5892 mainBodyStart5893surface surfacemainBodyEnd5893 mainBodyStart5894can canmainBodyEnd5894 mainBodyStart5895be bemainBodyEnd5895 mainBodyStart5896described describedmainBodyEnd5896 mainBodyStart5897by bymainBodyEnd5897 mainBodyStart5898the themainBodyEnd5898 mainBodyStart5899following followingmainBodyEnd5899 +mainBodyStart5900equation: equation:\tikzmark{mainBodyEnd5900} +\begin{equation} +I_{\omega }=I_{\omega }\left( 0\right) e^{-\tau _{\omega }}. \label{inu1} +\end{equation} + + +\tikzmark{mainBodyStart5901}In InmainBodyEnd5901 mainBodyStart5902the themainBodyEnd5902 mainBodyStart5903case casemainBodyEnd5903 mainBodyStart5904of ofmainBodyEnd5904 mainBodyStart5905the themainBodyEnd5905 mainBodyStart5906scattering scatteringmainBodyEnd5906 mainBodyStart5907of ofmainBodyEnd5907 mainBodyStart5908photons photonsmainBodyEnd5908 mainBodyStart5909by bymainBodyEnd5909 mainBodyStart5910free freemainBodyEnd5910 mainBodyStart5911non-relativistic non-relativisticmainBodyEnd5911 mainBodyStart5912electrons, electrons,mainBodyEnd5912 +mainBodyStart5913the themainBodyEnd5913 mainBodyStart5914opacity opacity\tikzmark{mainBodyEnd5914} \tikzmark{mainBodyStart5915}is ismainBodyEnd5915 mainBodyStart5916given givenmainBodyEnd5916 mainBodyStart5917by bymainBodyEnd5917 mainInlineStart5918k_ω=σ _Tn_e(z)/ρmainInlineEnd5918mainBodyStart5919, $k_{\omega }=\sigma _{T}n_{e}(z)/\rho $ ,mainBodyEnd5919 mainBodyStart5920where wheremainBodyEnd5920 mainInlineStart5921σ _T=(8π /3)( e^2/m_ec^2) ^2mainInlineEnd5921mainBodyStart5922 }$\tikzmark{mainBodyEnd5922} \tikzmark{mainBodyStart5923}is ismainBodyEnd5923 mainBodyStart5924the themainBodyEnd5924 mainBodyStart5925Thomson ThomsonmainBodyEnd5925 +mainBodyStart5926cross-section cross-section\tikzmark{mainBodyEnd5926} \tikzmark{mainBodyCitationStart5927}\citep{La,Ry79}.\tikzmark{mainBodyCitationEnd5927}\tikzmark{mainBodyStart5928}." +.This formula is valid only in the case of a non-degenerale gas al," .mainBodyEnd5928 mainBodyStart5929This ThismainBodyEnd5929 mainBodyStart5930formula formulamainBodyEnd5930 mainBodyStart5931is ismainBodyEnd5931 mainBodyStart5932valid validmainBodyEnd5932 mainBodyStart5933only onlymainBodyEnd5933 mainBodyStart5934in inmainBodyEnd5934 mainBodyStart5935the the\tikzmark{mainBodyEnd5935} \tikzmark{mainBodyStart5936}case casemainBodyEnd5936 mainBodyStart5937of ofmainBodyEnd5937 mainBodyStart5938a amainBodyEnd5938 mainBodyStart5939non-degenerate non-degeneratemainBodyEnd5939 mainBodyStart5940gas gasmainBodyEnd5940 mainBodyStart5941at atmainBodyEnd5941 +mainBodyStart5942low-temperatures." +low-temiperatures. Forsvstems al high densities aucl/or temperatures. (the corrections to the Thomson scatteringcross-section become important.," low-temperatures.mainBodyEnd5942 mainBodyStart5943For FormainBodyEnd5943 mainBodyStart5944systems systemsmainBodyEnd5944 mainBodyStart5945at atmainBodyEnd5945 mainBodyStart5946high highmainBodyEnd5946 mainBodyStart5947densities densitiesmainBodyEnd5947 mainBodyStart5948and/or and/or\tikzmark{mainBodyEnd5948} \tikzmark{mainBodyStart5949}temperatures, temperatures,mainBodyEnd5949 mainBodyStart5950the themainBodyEnd5950 +mainBodyStart5951corrections correctionsmainBodyEnd5951 mainBodyStart5952to tomainBodyEnd5952 mainBodyStart5953the themainBodyEnd5953 mainBodyStart5954Thomson ThomsonmainBodyEnd5954 mainBodyStart5955scattering scatteringmainBodyEnd5955 mainBodyStart5956cross-section cross-sectionmainBodyEnd5956 mainBodyStart5957become becomemainBodyEnd5957 mainBodyStart5958important." + For high-temperature non-degenerate electrons theopacity has been calculated first in Sampson (1959)..," important.\tikzmark{mainBodyEnd5958} + +\tikzmark{mainBodyStart5959}For FormainBodyEnd5959 mainBodyStart5960high-temperature high-temperaturemainBodyEnd5960 mainBodyStart5961non-degenerate non-degeneratemainBodyEnd5961 mainBodyStart5962electrons electronsmainBodyEnd5962 mainBodyStart5963the themainBodyEnd5963 mainBodyStart5964opacity opacitymainBodyEnd5964 mainBodyStart5965has hasmainBodyEnd5965 mainBodyStart5966been beenmainBodyEnd5966 +mainBodyStart5967calculated calculatedmainBodyEnd5967 mainBodyStart5968first firstmainBodyEnd5968 mainBodyStart5969in in\tikzmark{mainBodyEnd5969} \tikzmark{mainBodyCitationStart5970}\citet{Sa59}.\tikzmark{mainBodyCitationEnd5970}\tikzmark{mainBodyStart5971}." + These caleulations have been extended tothe semi-degenerate (740) case byChin(1965).," .mainBodyEnd5971 mainBodyStart5972These ThesemainBodyEnd5972 mainBodyStart5973calculations calculationsmainBodyEnd5973 mainBodyStart5974have havemainBodyEnd5974 mainBodyStart5975been beenmainBodyEnd5975 mainBodyStart5976extended extendedmainBodyEnd5976 mainBodyStart5977to tomainBodyEnd5977 +mainBodyStart5978the themainBodyEnd5978 mainBodyStart5979semi-degenerate semi-degeneratemainBodyEnd5979 (mainInlineStart5980T≠ 0mainInlineEnd5980mainBodyStart5981) $T\neq 0$ )mainBodyEnd5981 mainBodyStart5982case case\tikzmark{mainBodyEnd5982} \tikzmark{mainBodyStart5983}by bymainBodyEnd5983 mainBodyCitationStart5984 mainBodyCitationEnd5984 mainBodyStart5985and andmainBodyEnd5985 mainBodyCitationStart5986 mainBodyCitationEnd5986 mainBodyStart5987(see (seemainBodyEnd5987 mainBodyStart5988also alsomainBodyEnd5988 mainBodyCitationStart5989 mainBodyCitationEnd5989 mainBodyStart5990and andmainBodyEnd5990 mainBodyCitationStart5991)mainBodyCitationEnd5991mainBodyStart5992). +)). For a degenerate electron gas al1σὲ 0. the Rosseland mean opacity isgiven by Gs(T.3) (he inverse of the Rosseland mean) is a function ofthe temperature andof the degeneracy parameter= (Ejπρο) /kT. whereEy is the Fermienergy.," ).\tikzmark{mainBodyEnd5992} \tikzmark{mainBodyStart5993}For FormainBodyEnd5993 mainBodyStart5994a amainBodyEnd5994 mainBodyStart5995degenerate degeneratemainBodyEnd5995 +mainBodyStart5996electron electronmainBodyEnd5996 mainBodyStart5997gas gasmainBodyEnd5997 mainBodyStart5998at atmainBodyEnd5998 mainInlineStart5999T≠ 0mainInlineEnd5999mainBodyStart6000, $T\neq 0$ ,mainBodyEnd6000 mainBodyStart6001the themainBodyEnd6001 mainBodyStart6002Rosseland RosselandmainBodyEnd6002 mainBodyStart6003mean meanmainBodyEnd6003 mainBodyStart6004opacity opacitymainBodyEnd6004 mainBodyStart6005is ismainBodyEnd6005 mainBodyStart6006given givenmainBodyEnd6006 mainBodyStart6007by by\tikzmark{mainBodyEnd6007} \tikzmark{mainBodyCitationStart6008}\citep +{BuYu76} \tikzmark{mainBodyCitationEnd6008} +\begin{equation} +k_{\omega }=\frac{n_{e}\sigma _{T}}{\rho }G^{\deg }\left( T,\eta \right) . +\end{equation} + + +\tikzmark{mainInlineStart6009}$G^{\deg }\left( T,\eta \right) $\tikzmark{mainInlineEnd6009} \tikzmark{mainBodyStart6010}(the $G^{\deg }\left( T,\eta \right) $ (themainBodyEnd6010 mainBodyStart6011inverse inversemainBodyEnd6011 mainBodyStart6012of ofmainBodyEnd6012 mainBodyStart6013the themainBodyEnd6013 mainBodyStart6014Rosseland RosselandmainBodyEnd6014 mainBodyStart6015mean) mean)mainBodyEnd6015 mainBodyStart6016is ismainBodyEnd6016 mainBodyStart6017a amainBodyEnd6017 +mainBodyStart6018function functionmainBodyEnd6018 mainBodyStart6019of ofmainBodyEnd6019 mainBodyStart6020the themainBodyEnd6020 mainBodyStart6021temperature temperaturemainBodyEnd6021 mainBodyStart6022and andmainBodyEnd6022 mainBodyStart6023of of\tikzmark{mainBodyEnd6023} \tikzmark{mainBodyStart6024}the themainBodyEnd6024 mainBodyStart6025degeneracy degeneracymainBodyEnd6025 mainBodyStart6026parameter parametermainBodyEnd6026 mainInlineStart6027η =( +E_F-m_ec^2) /kTmainInlineEnd6027mainBodyStart6028, $\eta =\left( +E_{F}-m_{e}c^{2}\right) /kT$ ,mainBodyEnd6028 mainBodyStart6029where wheremainBodyEnd6029 mainInlineStart6030E_FmainInlineEnd6030 mainBodyStart6031is $E_{F}$ ismainBodyEnd6031 mainBodyStart6032the themainBodyEnd6032 mainBodyStart6033Fermi FermimainBodyEnd6033 mainBodyStart6034energy." + GI?(T.ij) can be represented in the form(Duchler& where€=exp(0.81637— 0.," energy.\tikzmark{mainBodyEnd6034} \tikzmark{mainInlineStart6035}$G^{\deg +}\left( T,\eta \right) $\tikzmark{mainInlineEnd6035} \tikzmark{mainBodyStart6036}can $G^{\deg +}\left( T,\eta \right) $ canmainBodyEnd6036 mainBodyStart6037be bemainBodyEnd6037 mainBodyStart6038represented representedmainBodyEnd6038 mainBodyStart6039in inmainBodyEnd6039 mainBodyStart6040the themainBodyEnd6040 mainBodyStart6041form form\tikzmark{mainBodyEnd6041} \tikzmark{mainBodyCitationStart6042}\citep{BuYu76} \tikzmark{mainBodyCitationEnd6042} +\begin{eqnarray} +G^{\deg }\left( T,\eta \right) &=&1.129+0.2965\xi -0.005594\xi ^{2}+\left( +11.47+0.3570\xi +0.1078\xi ^{2}\right) T\nonumber \\ +&&+\left( -3.249+0.1678\xi -0.04706\xi +^{2}\right) T^{2}, \label{G} +\end{eqnarray} + +\tikzmark{mainBodyStart6043}where wheremainBodyEnd6043 mainInlineStart6044ξ =exp( 0.8168η -0.05522η ^2)mainInlineEnd6044mainBodyStart6045." +055227). The variation of the functionG9 as a faction of the parameters ; andT isrepresented in Fig.," $\xi =\exp \left( 0.8168\eta -0.05522\eta ^{2}\right) $ .\tikzmark{mainBodyEnd6045} + +\tikzmark{mainBodyStart6046}The ThemainBodyEnd6046 mainBodyStart6047variation variationmainBodyEnd6047 mainBodyStart6048of ofmainBodyEnd6048 mainBodyStart6049the themainBodyEnd6049 mainBodyStart6050function functionmainBodyEnd6050 mainInlineStart6051G^mainInlineEnd6051 mainBodyStart6052as $G^{\deg }$ asmainBodyEnd6052 mainBodyStart6053a amainBodyEnd6053 mainBodyStart6054function functionmainBodyEnd6054 mainBodyStart6055of ofmainBodyEnd6055 mainBodyStart6056the themainBodyEnd6056 mainBodyStart6057parameters parametersmainBodyEnd6057 mainInlineStart6058ηmainInlineEnd6058mainBodyStart6059 $% +\eta mainBodyEnd6059mainBodyStart6060and andmainBodyEnd6060 mainInlineStart6061TmainInlineEnd6061 mainBodyStart6062is $T$ ismainBodyEnd6062 mainBodyStart6063represented represented\tikzmark{mainBodyEnd6063} \tikzmark{mainBodyStart6064}in inmainBodyEnd6064 mainBodyStart6065Fig." + 8., Fig.mainBodyEnd6065 mainBodyStart60668. + For a non-degenerate electron gas. obeving the Maxwell-Doltzmann distribution.the Rosseland mean opacity is givenby," 8.\tikzmark{mainBodyEnd6066} + +\tikzmark{mainBodyStart6067}For FormainBodyEnd6067 mainBodyStart6068a amainBodyEnd6068 mainBodyStart6069non-degenerate non-degeneratemainBodyEnd6069 mainBodyStart6070electron electronmainBodyEnd6070 mainBodyStart6071gas, gas,mainBodyEnd6071 mainBodyStart6072obeying obeyingmainBodyEnd6072 mainBodyStart6073the themainBodyEnd6073 mainBodyStart6074Maxwell-Boltzmann Maxwell-BoltzmannmainBodyEnd6074 +mainBodyStart6075distribution, distribution,mainBodyEnd6075 mainBodyStart6076the the\tikzmark{mainBodyEnd6076} \tikzmark{mainBodyStart6077}Rosseland RosselandmainBodyEnd6077 mainBodyStart6078mean meanmainBodyEnd6078 mainBodyStart6079opacity opacitymainBodyEnd6079 mainBodyStart6080is ismainBodyEnd6080 mainBodyStart6081given givenmainBodyEnd6081 mainBodyStart6082by" +On the other hand. since the chromospheric emission in Q1 752 A is larger when the svslenm is fainter. we conclude (hat (he emission of (his star should be dominated by clark spots rather than bright active regions.,"On the other hand, since the chromospheric emission in Gl 752 A is larger when the system is fainter, we conclude that the emission of this star should be dominated by dark spots rather than bright active regions." + In contrast. in the ease of GI 229 A. the data evidence that the active regions dominate the emission.," In contrast, in the case of Gl 229 A, the data evidence that the active regions dominate the emission." + These results are consistent with the ehromospheric-photospheric relations observed in solar-tvpe stars in the literature (Raclicketal.1993:Lockwood2007:Hall2009)..," These results are consistent with the chromospheric-photospheric relations observed in solar-type stars in the literature \citep{1998ApJS..118..239R,2007ApJS..171..260L,2009AJ....138..312H}." + We also analvzed simultaneous measurements of Ca Ik and Hea fluxes obtained from our CASLEO spectra. and found no evident correlation between both indices. in agreement with previous results by Cincuneguietal.(200T1b)..," We also analyzed simultaneous measurements of Ca K and $\alpha$ fluxes obtained from our CASLEO spectra, and found no evident correlation between both indices, in agreement with previous results by \cite{2007astro.ph..3511C}." + Also. Walkowicz&Hawley(2009) [ound some correlation for the most active stars. but 1 breaks down lor weakly active stars like (he ones we study in the present paper.," Also, \cite{2009AJ....137.3297W} found some correlation for the most active stars, but it breaks down for weakly active stars like the ones we study in the present paper." + The CCD and data acquisition svstem al CASLEO has been partly [financed by R. M. Rich through U.S. NSF erant. AST-90-15327., The CCD and data acquisition system at CASLEO has been partly financed by R. M. Rich through U.S. NSF grant AST-90-15827. + This research has macle use of the SIMDAD database. operated at CDS. Strasbourg. France.," This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France." + We would like to thank the CASLEO stalf and Mr. Pablo Valenzuela. for his invaluable help in the data reduction.," We would like to thank the CASLEO staff and Mr. Pablo Valenzuela, for his invaluable help in the data reduction." +"distance of the system (Harrington&Dahn1980),, are consistent with the broad-band spectral fitting results of Leggettetal.(2010)..","distance of the system \citep{1980AJ.....85..454H}, are consistent with the broad-band spectral fitting results of \citet{2010ApJ...720..252L}." + We infer similar for the WISE targets when the distance constraint is ysremoved., We infer similar s for the WISE targets when the distance constraint is removed. +" Surprisingly, a range of cloud parameters are indicated, with both WISE J1617+1807 and WISE J2313—8037 exhibiting evidence for the presence of photospheric cloud opacity."," Surprisingly, a range of cloud parameters are indicated, with both WISE J1617+1807 and WISE $-$ 8037 exhibiting evidence for the presence of photospheric cloud opacity." + We discuss some of these secondary parameters in further detail below., We discuss some of these secondary parameters in further detail below. +" The latest-type source in this sample is WISE J1812+2721, tentatively classified T8.5: based on spectral comparison to 2MASS J0415-0935 in Figure 5 and spectral indices."," The latest-type source in this sample is WISE J1812+2721, tentatively classified T8.5: based on spectral comparison to 2MASS J0415-0935 in Figure \ref{fig_class} and spectral indices." + It also has the reddest W1—W2 color in our sample., It also has the reddest $W1-W2$ color in our sample. +" While this classification is somewhat uncertain due to the lower signal-to-noise of the spectral data, its binned spectrum is very similar to that of Wolf 940B, itself classified T8.5 (Figure 12))."," While this classification is somewhat uncertain due to the lower signal-to-noise of the spectral data, its binned spectrum is very similar to that of Wolf 940B, itself classified T8.5 (Figure \ref{fig_comp1812}) )." + Near- and mid-infrared spectral model fits to Wolf 940B indicate = 585-625 K and = 4.83-5.22 cgs for an age Τοof 3-10 Gyr (Leggettetal. similar to the results we infer here.," Near- and mid-infrared spectral model fits to Wolf 940B indicate = 585–625 K and = 4.83–5.22 cgs for an age of 3–10 Gyr \citep{2010ApJ...720..252L}, similar to the results we infer here." +" For WISE J1812+27212010), we find a comparable but much lower surface gravity, age and mass."," For WISE J1812+2721 we find a comparable but much lower surface gravity, age and mass." +" WhileΤομ surface gravity determinations should in general be treated with caution below), the agreement in spectral morphology and (seeinferred confirms the cool nature of this source."," While surface gravity determinations should in general be treated with caution (see below), the agreement in spectral morphology and inferred confirms the cool nature of this source." +" WISE J1617+1807 and WISE J2313—8037 exhibit relatively red J—K spectrophotometric colors and large K/J ratios for their spectral types, and our spectral"," WISE J1617+1807 and WISE $-$ 8037 exhibit relatively red $J-K$ spectrophotometric colors and large $K/J$ ratios for their spectral types, and our spectral" +agy[Ryhy.he]. aud we have TIenee. we have a 2D-1D undecimated wavelet represcutation of the πηρα data D: we distinguish∙∙∙ four. kiuds. of. coefficients: As the 2D-1D is fully linear. a Craussian nolse ΕΡΕ Cassia after transformation.,"$\JF{a_{J_1}[k_x,k_y,k_z]}$, and we have Hence, we have a 2D-1D undecimated wavelet representation of the input data $D$: we distinguish four kinds of coefficients: As the 2D-1D is fully linear, a Gaussian noise remains Gaussian after transformation." + Therefore. all thresholding strategies which have been developed for wavelet Gaussian denoising are still valid with the 2D-1D wavelet trausform.," Therefore, all thresholding strategies which have been developed for wavelet Gaussian denoising are still valid with the 2D-1D wavelet transform." + Denoting TII the thresholding operator. the denoised cube in the case of additive white Gaussian noise is obtained by: A typical choice of ΤΗ is the hard thresholding operator. i.e. ΤΠ)=0 if |e| isbelow a given threshold d HG)=r fftimes=r.," Denoting $\mathrm{TH}$ the thresholding operator, the denoised cube in the case of additive white Gaussian noise is obtained by: A typical choice of $\mathrm{TH}$ is the hard thresholding operator, i.e. $\JF{\mathrm{TH}}(x) = 0$ if $ | x | $ below a given threshold $\tau$, and $\mathrm{TH}(x) = x$ $ | x | \ge \tau $." +The threshold 7 is eeucrally between 3 aud 5 the noise standard deviation, The threshold $\tau$ is generally between 3 and 5 times the noise standard deviation. + Putting all pieces together. we are now ready to plug the iuto the 2D-1D wavelet transform.," Putting all pieces together, we are now ready to plug the into the 2D-1D wavelet transform." + Again. we distinguish four of coefficients that take the followingformis: Tleuce. all/.," Again, we distinguish four of coefficients that take the following: Hence, all." +. Denoising is however not [straightforward because there i$ uo explicit recoustiructiou because of the form of the stabilization equations above., Denoising is however not straightforward because there is no explicit reconstruction because of the form of the stabilization equations above. + Formally. the stabilizing operators ντ ," Formally, the stabilizing operators $\mathcal{A}_{j_1,j_2}$ " +the Lick Observatory.,the Lick Observatory. + Details of the observations are given in Tables 3 and 5., Details of the observations are given in Tables 3 and 5. + In most cases. a long spectroscopic slit was centred on the optical identification and. aligned. with the radio axis. olfsetting from a nearby. star (positions of offset. stars are available from ML).," In most cases, a long spectroscopic slit was centred on the optical identification and aligned with the radio axis, offsetting from a nearby star (positions of offset stars are available from ML)." + In a few cases there was no identification on optical or infrared images. in which case the spectrum was taken blind. with the slit aligned along the radio axis.," In a few cases there was no identification on optical or infrared images, in which case the spectrum was taken blind, with the slit aligned along the radio axis." + The ISLS observations were made using both armis and a dichroic at either 540nm (in 1903) or 570nm (in 1995)., The ISIS observations were made using both arms and a dichroic at either 540nm (in 1993) or 570nm (in 1995). + In. 1993 June and August the red and blue arm detectors were an IV5 CCD and a TERK CCD respectively. in 1995 July both detectors were PEK CCDs.," In 1993 June and August the red and blue arm detectors were an EEV5 CCD and a TEK CCD respectively, in 1995 July both detectors were TEK CCDs." + The TEk CCD sullers from fringing at the τοῦ enc of the red arm. but was preferred. to the ELWS in 1995 because of its higher quantum ellicieneyv.," The TEK CCD suffers from fringing at the red end of the red arm, but was preferred to the EEV5 in 1995 because of its higher quantum efficiency." + In. practice. it proved possible to remove the fringing ellectively by taking tungsten lamp Lats inumeciately following cach observation. before moving the tclescope.," In practice, it proved possible to remove the fringing effectively by taking tungsten lamp flats immediately following each observation, before moving the telescope." + The IGI observations were mace as described in Paper LL., The IGI observations were made as described in Paper II. + Phe Ixast observations were mace with both red and blue aims. the beam being split by a dichroic at 550 nm.," The Kast observations were made with both red and blue arms, the beam being split by a dichroic at 550 nm." + IHeticon CCDs were used as detectors in both arms and 452 and 300 >eralingse were employed. in the blue and. red armis respectively., Reticon CCDs were used as detectors in both arms and 452 and 300 $^{-1}$ gratings were employed in the blue and red arms respectively. + Data reduction. of the WILT. and Lick cata Followed the standard procedure of bias subtraction. division by a Blatfield. wavelength calibration using are lamp spectra (Cur and. CuNe for the WLP data. Ce for the 107. data and Ceillellg and NeAr for the Lick data) and [lux calibration using spectrophotometric standard stars.," Data reduction of the WHT, $^{''}$ and Lick data followed the standard procedure of bias subtraction, division by a flatfield, wavelength calibration using arc lamp spectra (CuAr and CuNe for the WHT data, Cd for the $^{''}$ data and CdHeHg and NeAr for the Lick data) and flux calibration using spectrophotometric standard stars." + Errors in the spectrophotomoetry are expected to be z per cent: errors in the wavelengths of the bright spectral features are not expected to be larger than 0.2 nm in the WAIT and Lick data and 0.3 nm in the MeDonald data., Errors in the spectrophotometry are expected to be $\approx 15$ per cent; errors in the wavelengths of the bright spectral features are not expected to be larger than 0.2 nm in the WHT and Lick data and 0.3 nm in the McDonald data. + In LL we present the spectra of the objects in the sample with the main spectral features labelled., In 1 we present the spectra of the objects in the sample with the main spectral features labelled. + Lhe WIUE spectra in the figure have been smoothed with a 1.5 nn box-car filter. and the MeDonald and Lick spectra by a 1.2 nm one.," The WHT spectra in the figure have been smoothed with a 1.5 nm box-car filter, and the McDonald and Lick spectra by a 1.2 nm one." + If features appear in only one arm of the WIIT spectrum. the other has not. been shown.," If features appear in only one arm of the WHT spectrum, the other has not been shown." + ALL spectra for objects in the spectroscopic sub-sample are shown except for those alreads published in Paper IH. or Lacy ct (19900: jereafter LRAWLE). those for which spectra have been published. by Ixolleaard. et ((1995: hereafter. Ix95) and those for which there are no spectral features. visible.," All spectra for objects in the spectroscopic sub-sample are shown except for those already published in Paper II, or Lacy et (1999c; hereafter LRWLR), those for which spectra have been published by Kollgaard et (1995; hereafter K95) and those for which there are no spectral features visible." + These are shown separately in 22., These are shown separately in 2. + Derived redshifts and emission line properties (flux. equivalent width ancl velocity width) are listed in Table 4.," Derived redshifts and emission line properties (flux, equivalent width and velocity width) are listed in Table 4." + Phe emission line properties are derived. from Gaussian fits to the data., The emission line properties are derived from Gaussian fits to the data. + We have also obtained data on some objects in the original SC-NEC sample of Paper Lo which were just. below the Sis.= 0.53 flux density cutoll of the sample., We have also obtained data on some objects in the original 8C-NEC sample of Paper I which were just below the $S_{151}=0.5$ Jy flux density cutoff of the sample. + The observations are listed in Table 5 and the redshifts and other emission line. properties in Table 6. with the whole sample listed for completeness.," The observations are listed in Table 5 and the redshifts and other emission line properties in Table 6, with the whole sample listed for completeness." + The spectra are shown in 66. smoothed as in 11 except for SC 1758|676 which appears to be a faint quasar. and to which a smoothing of 4 nm has been applied to bring out the broad lines.," The spectra are shown in 6, smoothed as in 1 except for 8C 1758+676 which appears to be a faint quasar, and to which a smoothing of 4 nm has been applied to bring out the broad lines." + The redshifts in Tables 4 and 6 come from spectra in which the signal:noise anc number of spectral features. used: to estimate the recshift varied widelv., The redshifts in Tables 4 and 6 come from spectra in which the signal:noise and number of spectral features used to estimate the redshift varied widely. + Those which we consider “firm” are based on more than one strong spectral feature (emission or absorption lines or 4000 break). and are eracded a.," Those which we consider “firm” are based on more than one strong spectral feature (emission or absorption lines or ${\rm \AA}$ break), and are graded $\alpha$." + Those with either one strong spectral feature aud one or more low signal:noise ones. or with two or more low signal:nolse features are graded. 3.," Those with either one strong spectral feature and one or more low signal:noise ones, or with two or more low signal:noise features are graded $\beta$." + Those based on a single spectral feature (for emission lines we usually assume to be Lye if it appears in the blue arm spectrum or O11]372.7 if it appears in the red). or two very weak features are graced," Those based on a single spectral feature (for emission lines we usually assume to be $\alpha$ if it appears in the blue arm spectrum or ]372.7 if it appears in the red), or two very weak features are graded" +"transitions involving the groundP"" levels ane upper levels listed in the compilation of Verner. Verner Ferland (1996).. which is based on Opacity Project calculations.","transitions involving the ground$^3\mathrm{P}^e$ levels and upper levels listed in the compilation of Verner, Verner Ferland \shortcite{Verner}, which is based on Opacity Project calculations." +" Lf we adopt the radiation field of the Galaxy. (Conchalekar.Philips&Wilson1980).. then the corresponding incirect excitation rates will be Du;=3.510I""&+ and μμ”..."," If we adopt the radiation field of the Galaxy \cite{Gondhalekar}, then the corresponding indirect excitation rates will be $\Gamma_{01}=3.5\ 10^{-10}\ \mathrm{s}^{-1}$ and $\Gamma_{02}=2.8\ 10^{-10}\ \mathrm{s}^{-1}$ ." + In fig., In fig. +" 2. we have plotted the population ratios of the C"" fine-structure levels taking into account collisions by hvdrogen atoms (the main collision partner in ionization regions where the atom C"" is found). the CMDI and Iluorescence induced by the radiation field of the Galaxy."," \ref{figure:popCI} we have plotted the population ratios of the $^0$ fine-structure levels taking into account collisions by hydrogen atoms (the main collision partner in ionization regions where the atom $^0$ is found), the CMBR and fluorescence induced by the radiation field of the Galaxy." + We compared our results with the previous calculations bv Keenan (1989).. Hle., We compared our results with the previous calculations by Keenan \shortcite{KeenanCI}. + considered. the οσοι of collisions bv electrons ancl hydrogend atoms. as well as Iuorescence induced. by the. radiation. field. of the Galaxy.," He considered the effect of collisions by electrons and hydrogend atoms, as well as fluorescence induced by the radiation field of the Galaxy." + Test calculations revealed good overall agreement with the values obtained by. Keenan. with dillerences tvpically less than 15 percent.," Test calculations revealed good overall agreement with the values obtained by Keenan, with differences typically less than 15 percent." + The ground state of the ion consists of the 2572p “PY doublet levels.," The ground state of the $^+$ ion consists of the $^2$ 2p $^2\mathrm{P}^o_{\frac{1}{2},\frac{3}{2}}$ doublet levels." +" The energy. of the fine-structure excited level relatively to the eround state is 63.42 land the transition probability is sis9110ὃς 3, "," The energy of the fine-structure excited level relatively to the ground state is 63.42 $^{-1}$, andthe transition probability is $A_{\frac{3}{2}\frac{1}{2}}=2.291\ 10^{-6}\ \mathrm{s}^{-1}$ ." +"Our model ion includes the five lowest LS terms: 2872p 2peη and the 3o2s 32 configurations⋅: 4D"".e 22]ye7D'. Zee78"" and 24»71"". making a total of ten levels when the finc-structuresplitting is accounted for."," Our model ion includes the five lowest LS terms: $^2$ 2p $^2\mathrm{P}^o$ and the 2s $^2$ configurations $^4\mathrm{P}^e$, $^2\mathrm{D}^e$, $^2\mathrm{S}^e$ and $^2\mathrm{P}^e$, making a total of ten levels when the fine-structuresplitting is accounted for." + Phe energies were taken from Moore (1970) and the transition. probabilities fron he Lron Project calculation of is. Mendoza Zeippen (1998)..," The energies were taken from Moore \shortcite{MooreCI} and the transition probabilities from the Iron Project calculation of s, Mendoza Zeippen \shortcite{AijCII}." + As the fine-structure levels of απο more separated than the C levels. the CAIBR will play a significant. role at higher redshifts only. as one can see from the excitation rales eiven in table 1 We take into account. collisional excitation of the structure levels with several particles.," As the fine-structure levels of $^+$ are more separated than the $^0$ levels, the CMBR will play a significant role at higher redshifts only, as one can see from the excitation rates given in table \ref{table:Kij} We take into account collisional excitation of the fine-structure levels with several particles." + For the \laxwellian-averaged: collision strengths for collisions by electrons. we jwe adopted the calculation of Blum Pradhan (1992)., For the Maxwellian-averaged collision strengths for collisions by electrons we have adopted the calculation of Blum Pradhan \shortcite{gammaCII}. + As their results diller by only 2 percent. from the earlier calculation of Ixeenan οἱ al. (1986)...," As their results differ by only 2 percent from the earlier calculation of Keenan et al. \shortcite{KeenanCII}," + we have also included he later's results at. temperature. values not. covered: by Blum Pradhan's calculation as à means of broadening he available temperature range., we have also included the later's results at temperature values not covered by Blum Pradhan's calculation as a means of broadening the available temperature range. + We took excitation rates » Collisions with hydrogen atoms from Launay Ποιο (197 Tb).. extrapolated to 71000 Ix bv Ixeenan ct al. (1986)..," We took excitation rates by collisions with hydrogen atoms from Launay Roueff \shortcite{qH0_CII}, , extrapolated to $T>1000$ K by Keenan et al. \shortcite{KeenanCII}. ." + Other collision particlestaken into account are xotons (Foster.Keenan&Reid1997)— and molecular ivdrogen (Flower&Launay 1, Other collision particlestaken into account are protons \cite{q_proton_CII} and molecular hydrogen \cite{q_H2_CII}. . +977)., Fig. +. Fig.3. compares the excitation rates with the various particles.,\ref{figure:qijCII} compares the excitation rates with the various particles. + We have complemented the work of, We have complemented the work of +Type I X-ray bursts are thermonuclear explosions that occur on accreting neutron stars in low-mass X-ray binaries.,Type I X-ray bursts are thermonuclear explosions that occur on accreting neutron stars in low-mass X-ray binaries. + They are triggered by thermally unstable H or He burning near the stellar surface (forreviews.seeCumming2004:Strohmayer&Bildsten 2006).," They are triggered by thermally unstable H or He burning near the stellar surface \citep[for reviews, see][]{C04,SB03}." + For systems with accretion rates M—0. Mau. where My denotes the mass accretion rate at which the accretion luminosity is equal to the Eddington limit. the basic physics of the burst onset is well understood to be that ofthe thin shell thermal instability (Schwarzschild&Hérm1965:Hansen&vanHorn 1975).. and theoretical models have been rather successful at reproducing the gross characteristics of burst observations in this regime (e.g..Fujimotoetal.1981;&Heyl 2003).," For systems with accretion rates $\dot{M} \lesssim 0.1 +\dot{M}_{\mathrm{Edd}}$ , where $\dot{M}_{\mathrm{Edd}}$ denotes the mass accretion rate at which the accretion luminosity is equal to the Eddington limit, the basic physics of the burst onset is well understood to be that ofthe thin shell thermal instability \citep{SH65,HvH75}, and theoretical models have been rather successful at reproducing the gross characteristics of burst observations in this regime \citep[e.g.,][]{FHM81,FL87,CB00,NH03}." +. ThisLetter addresses a longstanding problem that afflicts nearly all burst models when the accretion rate M20.1Ma.," This addresses a longstanding problem that afflicts nearly all burst models when the accretion rate $\dot{M} \gtrsim 0.1 +\dot{M}_{\mathrm{Edd}}$." + Both simple one-zone burst models (Fujimotoetal.1981:Paezynski1983:Bildsten1998:Hegeretal.2005) and sophisticated time-dependent multi-zone models (Ayash&2005) predict that bursts should occur for all M up to zcMya.," Both simple one-zone burst models \citep{FHM81,P83,B98,HCW05} and sophisticated time-dependent multi-zone models \citep{AJ82,TWL96,FHLT03,HCW05} predict that bursts should occur for all $\dot{M}$ up to $\approx \dot{M}_{\mathrm{Edd}}$." + Observations. however. indicate that bursts do not occur for M>0.3Mpgu (vanParadijsetal.1979.1988;Cor-nelisseetal.2003:Remillard 2006).," Observations, however, indicate that bursts do not occur for $\dot{M} +\gtrsim 0.3 \dot{M}_{\mathrm{Edd}}$ \citep{vPCLJ79,vPPL88,Cetal03,RLCN06}." +. Furthermore. vanetal. found that.for 0.1©ΜΜ&0.3. a significant fraction of the accreted plasma burns. stably between consecutive bursts. leading to large values >1000 of the parameter o. the accretion energy released between successive bursts divided by the nuclear energy released during a burst.," Furthermore, \citet{vPPL88} + found that,for $0.1 \lesssim \dot{M}/\dot{M}_{\mathrm{Edd}} \lesssim +0.3$, a significant fraction of the accreted plasma burns stably between consecutive bursts, leading to large values $\gtrsim 1000$ of the parameter $\alpha$, the accretion energy released between successive bursts divided by the nuclear energy released during a burst." + Most theoretical models. on the other hand. predict that nearly all of the acereted matter burns unstably during bursts. giving a nearly constant a«100 at all M. Narayan," Most theoretical models, on the other hand, predict that nearly all of the accreted matter burns unstably during bursts, giving a nearly constant $\alpha < 100$ at all $\dot{M}$." +&Heyl(2003.hereafterNHO3) developed a global linear stability analysis of the acereted plasma on the surface of a neutron star., \citet[][hereafter NH03]{NH03} developed a global linear stability analysis of the accreted plasma on the surface of a neutron star. + They discovered a new regime of unstable nuclear burning for 0.1=M/My0.3 that they referred to as “delayed mixed bursts.”," They discovered a new regime of unstable nuclear burning for $0.1 +\lesssim \dot{M}/\dot{M}_{\mathrm{Edd}} \lesssim 0.3$ that they referred to as “delayed mixed bursts.”" + Their model reproduced both the occurrence of considerable stable burning preceding a burst (leading to values of a=1000) and the absence of bursts for M20.2Μπιμ. in agreement with observations.," Their model reproduced both the occurrence of considerable stable burning preceding a burst (leading to values of $\alpha \gtrsim 1000$ ) and the absence of bursts for $\dot{M} \gtrsim 0.3 \dot{M}_{\mathrm{Edd}}$, in agreement with observations." + However. the complexity of their model made it difficult to understand the basic physics behind delayed mixed bursts and to identify the reasons why their results differed from those of other theoretical models at high accretion rates.," However, the complexity of their model made it difficult to understand the basic physics behind delayed mixed bursts and to identify the reasons why their results differed from those of other theoretical models at high accretion rates." + To remedy this. Cooper&Narayan(2006.hereafterCNO6) constructed a simple two-zone model that helped elucidate the physics of delayed mixed bursts.," To remedy this, \citet[][hereafter CN06]{CN06} constructed a simple two-zone model that helped elucidate the physics of delayed mixed bursts." + They showed that the competition between nuclear heating due to triple-a reactions and hot CNO cycle H burning on the one hand. and radiative cooling via photon diffusion and emission on the other hand. drives an overstability that eventually triggers a thin-shell thermal instability and hence a delayed mixed burst.," They showed that the competition between nuclear heating due to $\alpha$ reactions and hot CNO cycle H burning on the one hand, and radiative cooling via photon diffusion and emission on the other hand, drives an overstability that eventually triggers a thin-shell thermal instability and hence a delayed mixed burst." + They asserted that H burning via the temperature-independent hot CNO cycle. augmented= by the extra seed nuclei produced from stable He burning. significantly lowers the temperature sensitivity of the total nuclear energy generation rate to such an extent as to suppress the thin-shell thermal instability for M>0.3Mau.," They asserted that H burning via the temperature-independent hot CNO cycle, augmented by the extra seed nuclei produced from stable He burning, significantly lowers the temperature sensitivity of the total nuclear energy generation rate to such an extent as to suppress the thin-shell thermal instability for $\dot{M} \gtrsim 0.3 +\dot{M}_{\mathrm{Edd}}$." + Therefore. H burning via the hot CNO cycle is ultimately responsible for the lower critical M above which bursts do not occur in nature.," Therefore, H burning via the hot CNO cycle is ultimately responsible for the lower critical $\dot{M}$ above which bursts do not occur in nature." + The above argument perhaps explains why one-zone models fail. since the models generally focus only on He burning and make large approximations with respect to H burning.," The above argument perhaps explains why one-zone models fail, since the models generally focus only on He burning and make large approximations with respect to H burning." + But why do detailed. time-dependent multi-zone models with large reaction. networks also. perform poorly in relation to observations?, But why do detailed time-dependent multi-zone models with large reaction networks also perform poorly in relation to observations? + These models are much more sophisticated than the models of NHO3 and CNOG and consequently ought to perform better. whereas in fact the latter models agree much better with observations.," These models are much more sophisticated than the models of NH03 and CN06 and consequently ought to perform better, whereas in fact the latter models agree much better with observations." + CNO6 hypothesized that the time-dependent multi-zone burst models may have used too large a rate for the experimentally poorly-constrained hot CNO cycle breakout reaction Οία.) Νε (Wagoner1969:Wallace&Woosley 2006)..," CN06 hypothesized that the time-dependent multi-zone burst models may have used too large a rate for the experimentally poorly-constrained hot CNO cycle breakout reaction $^{15}$ $\alpha$ $\gamma$ $^{19}$ Ne \citep{W69,WW81,LWFG86,WGS99,FGWD06}. ." + We test this hypothesis., We test this hypothesis. + We begin in $2? with a deseription of the model. and we present the results of the model in $2?..," We begin in \ref{themodel} with a description of the model, and we present the results of the model in \ref{results}. ." + We discuss the results in 322.. and we conclude ins κα.," We discuss the results in \ref{discussion}, , and we conclude in \ref{conclusions}. ." +addition. these are not all the largest or brightest. nor uniformly distributed.,"addition, these are not all the largest or brightest, nor uniformly distributed." + It is wortchile. then. to look into possible elfects of this uneven sampling.," It is worthwhile, then, to look into possible effects of this uneven sampling." + The average motion of all the galaxies in each sample will show up in the solar reflex velocity., The average motion of all the galaxies in each sample will show up in the solar reflex velocity. +" Subsidiary ""bulk flows.” motions of one part of the Volume with respect to the whole. will appear as peculiar velocities svstematicallv different in (hat partbut. only if there are galaxies there to show it."," Subsidiary “bulk flows,” motions of one part of the Volume with respect to the whole, will appear as peculiar velocities systematically different in that part—but only if there are galaxies there to show it." + Similarly. flows on a smaller scale (or a larger) than is sanipled will go unnoticed.," Similarly, flows on a smaller scale (or a larger) than is sampled will go unnoticed." + More subtle would be effects on overall parameters due to badly-distributed cata., More subtle would be effects on overall parameters due to badly-distributed data. + Το examine (hose. suppose that we are attempting to fit a model of anisotropic flow (as above) to an actual flow.," To examine those, suppose that we are attempting to fit a model of anisotropic flow (as above) to an actual flow." +" The ""real flow is described by a flow with noise. in part due to distance errors (which obev a distribution function or) and in part due to real peculiar. velocities (which obev a vector distribution function e)."," The “real” flow is described by a flow with noise, in part due to distance errors (which obey a distribution function $\delta r$ ) and in part due to real peculiar velocities (which obey a vector distribution function ${\bf e}$ )." + The quantity we attempt to minimize during least-squares filling is then where the subscript @ stands for “actual” and i0 Lor “model.” and the vector r is written as a product of magnitude and direction. r£.," The quantity we attempt to minimize during least-squares fitting is then where the subscript $a$ stands for “actual” and $m$ for “model,” and the vector ${\bf r}$ is written as a product of magnitude and direction, $r {\bf \hat{r}}$." + The various terms may be regrouped as follows: The first line. the squared. term. is the dillerence between the model and the actual situation in (he absence of errors or noise: ils minim is zero. when (he actual and model parameters are identical.," The various terms may be regrouped as follows: The first line, the squared term, is the difference between the model and the actual situation in the absence of errors or noise; its minimum is zero, when the actual and model parameters are identical." + The last line is the collected “noise” and does not contain the model parameters αἱ all: its only effect on the process is lo set a positive minimun to the quantity σ”., The last line is the collected “noise” and does not contain the model parameters at all; its only effect on the process is to set a positive minimum to the quantity $\sigma^2$. + The cross terms require some attention., The cross terms require some attention. + If we assume that the real peculiar velocity distribution e does not depend on direction or distance. the two cross terms containing it will average to zero.," If we assume that the real peculiar velocity distribution ${\bf e}$ does not depend on direction or distance, the two cross terms containing it will average to zero." + Also. if the distance errors," Also, if the distance errors" +of Figure {..,of Figure \ref{fig:chis}. +" One of our best fit parameter sets (05.Mp.5,)=(0.78.107247M...1.67) is compared with observed velocity functions in Figure 2.."," One of our best fit parameter sets $(\delta_{\rm h},M_{\rm h},\gamma_v)=(0.78,10^{12}h^{-1}M_\odot,1.67)$ is compared with observed velocity functions in Figure \ref{fig:vf}." + It is clearly shown that the prediction of our model shows good coincidence with observed velocity functions., It is clearly shown that the prediction of our model shows good coincidence with observed velocity functions. + The distribution of image separations in strong gravitational lensing becomes another test of our model., The distribution of image separations in strong gravitational lensing becomes another test of our model. + The distribution 15 caleulated from equation (15))., The distribution is calculated from equation \ref{dist}) ). + For the observed lens sample. we consider the Cosmic Lens All-Sky Survey (CLASS:Hel-big 2000).," For the observed lens sample, we consider the Cosmic Lens All-Sky Survey \citep[CLASS;][]{helbig00}." +" This sample is complete at image separations 0.3""<0<15” (Helbig2000:Phillipsetal.2001).. and has 18 lenses among ~12.000 radio sources."," This sample is complete at image separations $0.3''<\theta<15''$ \citep{helbig00,phillips01}, and has 18 lenses among $\sim 12,000$ radio sources." + Sources have the flux distribution da/dSxS! (Rusin&Tegmark2001).., Sources have the flux distribution $dn/dS\propto S^{-2.1}$ \citep{rusin01b}. + The mean redshift is estimated to be (cs)=1.27. although the redshift distribution of sources ts still poorly understood (Marlowal. 2000).," The mean redshift is estimated to be $\langle z_{\rm S} +\rangle=1.27$, although the redshift distribution of sources is still poorly understood \citep{marlow00}." +. As in the case of the velocity function. actually we consider the normalized image separation distribution: instead of usual probability distribution.," As in the case of the velocity function, actually we consider the normalized image separation distribution: instead of usual probability distribution." + This is because the absolute probability may suffer from uncertainties of source redshifts. magnification bias. and cosmological parameters.," This is because the absolute probability may suffer from uncertainties of source redshifts, magnification bias, and cosmological parameters." + On the other hand the distribution p(70) mainly contains information on the shape of the mass function. and effects of baryonic compression (Kochanek2001:Kochanek&White2001:Keeton 2001)..," On the other hand the distribution $p(>\theta)$ mainly contains information on the shape of the mass function and effects of baryonic compression \citep{kochanek01a,kochanek01b,keeton01a}." + And the distribution p>0) ts quite insensitive to the source population and cosmological parameters. thus can be used for samples in which the source population is unknown such as CASTLES sample.," And the distribution $p(>\theta)$ is quite insensitive to the source population and cosmological parameters, thus can be used for samples in which the source population is unknown such as CASTLES sample." + The distribution of image separations is tested by using a Kolmogorov-Smirnov (KS) test., The distribution of image separations is tested by using a Kolmogorov-Smirnov (KS) test. + For the observed distribution. we use the distribution of CLASS survey.," For the observed distribution, we use the distribution of CLASS survey." + The result is shown in Figure 3.., The result is shown in Figure \ref{fig:ks}. +" We plot contours in Mjy-, plane by fixing 4,= which is constrained from the velocity function (see Figure 1))."," We plot contours in $M_{\rm h}$ $\gamma_v$ plane by fixing $\delta_{\rm +h}=0.78$ which is constrained from the velocity function (see Figure \ref{fig:chis}) )." + From this figure. we find that the constraint from the distribution of Image separations is consistent with the constraint from the velocity function.," From this figure, we find that the constraint from the distribution of image separations is consistent with the constraint from the velocity function." + The exception ts the case, The exception is the case +that of W Aql.,that of W Aql. + The Mira AB system has been observed oi different scales and at different wavelengths., The Mira AB system has been observed on different scales and at different wavelengths. + studied the close circumstellar environment at mid-infrared wavelengths and found that Mira B is a main-sequence star (the data 1s founc consistent with à MMe K5 dwarf) surrounded by a AAL accretion disk., studied the close circumstellar environment at mid-infrared wavelengths and found that Mira B is a main-sequence star (the data is found consistent with a $_{\sun}$ K5 dwarf) surrounded by a AU accretion disk. + The nature of Mira B is however still a matter of debate and there are strong indications that it 1s a white dwarftherein)., The nature of Mira B is however still a matter of debate and there are strong indications that it is a white dwarf. +.. Mira B is found to have a accretion radius of j4/M5 AAU2).., Mira B is found to have an accretion radius of $M_{B}/M_{\sun}$ AU. +" If we perform the same calculatio for W Agl?).. although noting that the parameters of this system are even less known than for Mira AB. the accretion radius of W Aq] B is less than 6M/Mc, AU. making accretion from W Aql A to W Aqgl B less likely."," If we perform the same calculation for W Aql, although noting that the parameters of this system are even less known than for Mira AB, the accretion radius of W Aql B is less than $M_{B}/M_{\sun}$ AU, making accretion from W Aql A to W Aql B less likely." + Mira A is known to have a bipolar outflow on approximately the same scale as the asymmetry in W Αα., Mira A is known to have a bipolar outflow on approximately the same scale as the asymmetry in W Aql. + Also in a well-studied case like Mira. understanding the origin of circumstellar structure is not straightforward.," Also in a well-studied case like Mira, understanding the origin of circumstellar structure is not straightforward." + suggest that asymmetric. mass-loss due to e.g. non-radial pulsations. giant convection cells. and/or magnetic spots on the surface provide the most likely explanation for the asymmetries seen in the CO emission from the star.," suggest that asymmetric mass-loss due to e.g. non-radial pulsations, giant convection cells, and/or magnetic spots on the surface provide the most likely explanation for the asymmetries seen in the CO emission from the star." + find that their observations support a scenario where the structures are caused by interaction between the molecular gas and a rotating disk., find that their observations support a scenario where the structures are caused by interaction between the molecular gas and a rotating disk. + Observations required to investigate the kinematical properties of the asymmetry seen in W Agl are not available at this point., Observations required to investigate the kinematical properties of the asymmetry seen in W Aql are not available at this point. + Interferometric spectroscopy should be performed in order to determine the velocity field and to investigate whether the structures seen can be an earlier version of the outflow seen from Mira A. The CO emission from W Aq] has been observed at the PdB interferometer as part of the COSAS program(?)., Interferometric spectroscopy should be performed in order to determine the velocity field and to investigate whether the structures seen can be an earlier version of the outflow seen from Mira A. The CO emission from W Aql has been observed at the PdB interferometer as part of the COSAS program. +. The results are planned for a future publication., The results are planned for a future publication. + In order to properly evaluate the origin of the asymmetrical dust distribution around W Αα. a hydrodynamical simulation using the known parameters of this system needs to be done?).," In order to properly evaluate the origin of the asymmetrical dust distribution around W Aql, a hydrodynamical simulation using the known parameters of this system needs to be done." +. The possible shaping due to a magnetic field cannot be evaluated at this point as it has not yet been measured around this star., The possible shaping due to a magnetic field cannot be evaluated at this point as it has not yet been measured around this star. + The determined radius and width of the detached shell around U Cam (Table 3)) are in excellent agreement with the results of?.. who derived a shell radius of 7777 and a width of 0766 based on HST images.," The determined radius and width of the detached shell around U Cam (Table \ref{dcse_res}) ) are in excellent agreement with the results of, who derived a shell radius of 7 and a width of 6 based on HST images." + At the distance of U Cam. the radius and width presented here correspond to 5.1»1016 em and 5.8x1015 em. respectively.," At the distance of U Cam, the radius and width presented here correspond to $5.1\times10^{16}\,$ cm and $5.8\times10^{15}\,$ cm, respectively." + Measurements of the size of the CO shell, Measurements of the size of the CO shell +iowever. are much more important in the comparison of he unweighted MESZ.,"however, are much more important in the comparison of the un-weighted $MASE$." + Furthermore in this case the dillerences. between the Plummer. and. the homogeneous sphere are very large. while when the comparison is between he weighted. functions the dillerence is very small.," Furthermore in this case the differences between the Plummer and the homogeneous sphere are very large, while when the comparison is between the weighted functions the difference is very small." + Again his is in agreement with the results of section. 4.., Again this is in agreement with the results of section \ref{sec:twoplum}. + I£ we simulate all three spheres in the same configuration. we rave to use lor all cases the same softening and C = I., If we simulate all three spheres in the same configuration we have to use for all cases the same softening and ${\cal C}$ = 1. + ow the forces of the Dehnen sphere will be very bacly represented and those of the homogeneous sphere very. well., Now the forces of the Dehnen sphere will be very badly represented and those of the homogeneous sphere very well. + The situation is totally dillerent. if. we are simulating one of those spheres only. because then we have to calibrate the engths appropriately. so that all svstems have the same hall-mass racius.," The situation is totally different if we are simulating one of those spheres only, because then we have to calibrate the lengths appropriately, so that all systems have the same half-mass radius." + Now the Dehnen sphere will do much better han in the un-weighted case. and the homogeneous sphere much worse.," Now the Dehnen sphere will do much better than in the un-weighted case, and the homogeneous sphere much worse." + Thus the weighted ΑιS; is respectively 001. 0.001 and 0.01 for the homogeneous. Plummer and Dehnen spheres.," Thus the weighted $MASE_{opt}$ is respectively 0.001, 0.001 and 0.01 for the homogeneous, Plummer and Dehnen spheres." + In. particular the dillerences between the hummer and the homogeneous sphere are very. small., In particular the differences between the Plummer and the homogeneous sphere are very small. + The Διστον for the Dehnen sphere is considerably. larger han for the other two. presumably because. in the Dehnen sphere. we are trving with a single value of the softening to accommodate both very dense ancl very sparse regions.," The $MASE_{opt}$ for the Dehnen sphere is considerably larger than for the other two, presumably because, in the Dehnen sphere, we are trying with a single value of the softening to accommodate both very dense and very sparse regions." + Figures S and 9. compare weighted MS£u and cu as à function of N for the three configurations andconfir the trend. seen in Figure 7.., Figures \ref{3MASEopt} and \ref{3eopt} compare weighted $MASE_{opt}$ and $\epsilon_{opt}$ as a function of $N$ for the three configurations andconfirm the trend seen in Figure \ref{mase_hpd_w}. +" The dependence of ALASE, and c4; on IN for all three density. distributions can be represented by power laws and The values of the cocllicients are given in Table 1..", The dependence of $MASE_{opt}$ and $\epsilon_{opt}$ on $N$ for all three density distributions can be represented by power laws and The values of the coefficients are given in Table \ref{tab:hpd}. + Since the exponent in the above dependences depends somewhat on the range of IN. used (cf, Since the exponent in the above dependences depends somewhat on the range of $N$ used (cf. + X|98 and section 3.2)) . we used for the three mass distributions the same values of N for the linear fits. namely the values for NV = 1 000. 3 000. 10 000. 30 000. 100 000 ane 300 000.," A+98 and section \ref{sec:plummer_opt}) ), we used for the three mass distributions the same values of $N$ for the linear fits, namely the values for $N$ = 1 000, 3 000, 10 000, 30 000, 100 000 and 300 000." + The table and figures show clearly that more centrally concentrated. configurations ποσα smaller values of the softening for an optimal representation of the force. and the precision achieved. is never as good as for less centrally concentrated. configurations.," The table and figures show clearly that more centrally concentrated configurations need smaller values of the softening for an optimal representation of the force, and the precision achieved is never as good as for less centrally concentrated configurations." + Phe minimum error. ALASEu. decreases somewhat faster with JN. for the case of the Plummer sphere. but the differences are small.," The minimum error, $MASE_{opt}$, decreases somewhat faster with $N$ for the case of the Plummer sphere, but the differences are small." + ligure LO compares the histograms of the inter-particlc distances for the three mocdels after they have been rescalec so that the half-mass raclii are in all three cases the same., Figure \ref{histo_hpd} compares the histograms of the inter-particle distances for the three models after they have been rescaled so that the half-mass radii are in all three cases the same. + This scaling is appropriate for understanding the resulga obtained with weights., This scaling is appropriate for understanding the results obtained with weights. + Each histogram has been obtained rom ten 10 000 particle realisations of each model., Each histogram has been obtained from ten 10 000 particle realisations of each model. + We note hat the peak of the histogram is nearest to the center for he Dehnen sphere. followed by the Plummer sphere. whi he peak of the histogram for the homogeneous sphere is vet urther out.," We note that the peak of the histogram is nearest to the center for the Dehnen sphere, followed by the Plummer sphere, while the peak of the histogram for the homogeneous sphere is yet further out." + Lt is thus expected that there are more particles very close to cach other in the Dehnen sphere than in the ummer one. and even more compared to the homogeneous one.," It is thus expected that there are more particles very close to each other in the Dehnen sphere than in the Plummer one, and even more compared to the homogeneous one." + However the Dehnen sphere has also more particles with very [large inter-particle distances. while these are fewer for he Plummer sphere and even more so for the homogeneous sphere.," However the Dehnen sphere has also more particles with very large inter-particle distances, while these are fewer for the Plummer sphere and even more so for the homogeneous sphere." + The results shown in Figure 9. give us the optimal value of the softening. which gives the best representation of the orees. as a function of the number of particles IN.," The results shown in Figure \ref{3eopt} give us the optimal value of the softening, which gives the best representation of the forces, as a function of the number of particles $N$." + Llowever hey also show that a value of softening which is optimal or one type of mass distribution is not necessarily optimal or another. and that the optimal value depends. strongly on the central concentration of the distribution.," However they also show that a value of softening which is optimal for one type of mass distribution is not necessarily optimal for another, and that the optimal value depends strongly on the central concentration of the distribution." +" Thus. in order to find c;,; for a mass distribution other than the hiree discussed here. one can either co the full caleulations of the AS A;E. as above. or use the above results to obtain rough estimates."," Thus, in order to find $\epsilon_{opt}$ for a mass distribution other than the three discussed here, one can either do the full calculations of the $MASE$ , as above, or use the above results to obtain rough estimates." + Since the former is rather demanding. we," Since the former is rather demanding, we" +improve these detection rates. but observations pointing toward the Galactic centre should improve the number of detections significantly.,"improve these detection rates, but observations pointing toward the Galactic centre should improve the number of detections significantly." + Survevs targeted at the Galactic Center (Baganoll et al., Surveys targeted at the Galactic Center (Baganoff et al. + 2001) may find. Noc= per or Ποια., 2001) may find $7 N_9\epsilon_{-5}^{1.2}$ per or field. + 2mm The second assumption1 is that cach of the sources are transient. driven by the hyvdrogen-ionisation5 instability at radii in the ⋯∙≼∙↓⋅∢⊾⇂⊲↓∪⊔∠⇂⊲↓⊳∖≼⇍∖∖⋰⊔↓↕⊻⊽∿⋅↱≻∪∪∪↓∖⋡⋜↧⊳∖⊀↓⊔↓∪∖∖⊽−⊔↓⋜↧⊳∖⊳∖⇀∖−↓⋅," 2mm The second assumption is that each of the sources are transient, driven by the hydrogen-ionisation instability at radii in the accretion disc with $T\sim 5000$ K as in low-mass X-ray binaries." +⋜↧∙∖⇁∣⋡↕↓↕⋜↧↓⋅↕⋖⊾≻⊳↓↓↥↿↓↥↕≻≼∼⋜↧≻∢⋅⊳∖∖⊽∢⊾⋜↧⊳∖⊳∖⊔⊔↓⋖⊾⇂↓↕⋜∐↿↓↥⋖⋅⊳∖⋯⊔⋅≼⇍∢⊾⊳∖⊔⊔∠⇂⋖⋅↓⋅⋏∙≟∪⋯∐∣⋡⊔↓⋅≱∖↿≱∖ ⇂⋅∪↓⋅⊳∖⋖⊾∖⇁∢⊾↓⋅⋜↧↓⊔↓∪⊔↿↓↕⊳∖∖∖⋰∐↓↕↓⊔⊔↓⊲↓⊔∪⊳∖⊲↓↿⊀⊓⊾⊳∖⊔∢⋅⋜⊔⋅∣," In this case, we assume that the sources undergo outbursts for several months with luminosities near Eddington, while remaining faint for several decades." +⊲⇀⊲∠⇂∠⇂⊀↓⊔⋏∙≟↿∪⊔⊳∖∖⋎↓↥∐⋖⊾↓⋅∢⋅⊔↓⋜↧⊲↓⊔⊀↓⊔⋏∙≟⇂⋅⋜↧↕↓↕↿⇂⋅∪↓⋅⊳∖⋖⋅∖⇁⋖⊾↓⋅⋜↧↓∠⇂∢⋅≼⇍⋯⇂⋖⊾⊳∖⊳≺⊲↓↥∢⊾⊔⊳∺↓⊔⋅⋯⇂⋖⋅↓⋅⊾∖↽∟⋠↓∖⋰↓∪↿∖↓≤⋗≤⋗⊤∃ ↓↥⋜↧∖⇁∢⋅⊳∖⇂↥∪∖∖⋎⊔↿↓⋯∣⊳∖∪⇂⋅↿⇀∖−↓⋅⋜↧∙∖⇁↿↓⋅⋜⋯⊳∖⊲⊓⊾⊔↿⊳∖↿⋖⋅⊔∠⇂↿∪≻∢⊾⋜↧↳⋜∐∠⊓⋯∿∪⋅⇉∠⊔⊔∖∖⋰↓↿↓↕⋜⋯⋜↧∖⇁⋖⊾↓⋅⋜↧⋃∢⊾∠⇂⊔↓⋅⋜∐⊲↓∪⊔↿∖∠⇂∢⊾≼⇍⋜↧∙∖⇁↿⊲↓⊔↓⋖⊾⊳∖≼⇍⋜↧↓∢⊾∃∪⇂⋅∣⊓∿⇉∪ 5 clays and recurrence times varving from 2 vears to 60 vears for black holes.," Chen, Shrader Livio (1997) have shown that soft X-ray transients tend to peak at $L_{\rm out}\sim 0.2 L_{\rm Edd}$ with an average duration (decay time scale) of $t_o \sim 20$ days and recurrence times varying from 2 years to 60 years for black holes." + Phese are only the observed transients: transients with longer recurrence time scales may not have had time to repeat., These are only the observed transients; transients with longer recurrence time scales may not have had time to repeat. +" Lowe assume that cach black hole accretes cuicseently for a time /,. storing up mass in the accretion disk with a small fraction of gas accreting on to the black hole. and then all of this mass is released in an outburst of duration /,. then where c, is the radiative cllicicney of acerction during outburst."," If we assume that each black hole accretes quiescently for a time $t_q$, storing up mass in the accretion disk with a small fraction of gas accreting on to the black hole, and then all of this mass is released in an outburst of duration $t_o$, then where $\epsilon_o$ is the radiative efficiency of accretion during outburst." + Phe outburst rate in the Milky Way is then Assuming a 10 per cent cllicicney during outburst. we find Nou~536Na + for o.=40 km +.," The outburst rate in the Milky Way is then Assuming a 10 per cent efficiency during outburst, we find $\dot N_{\rm out} \sim 536N_9$ $^{-1}$ for $\sigma_v=40$ km $^{-1}$." + This is clearly inconsistent with observations. demonstrating that not all isolated black holes undergo transient outbursts if the assumptions of our calculation are correct.," This is clearly inconsistent with observations, demonstrating that not all isolated black holes undergo transient outbursts if the assumptions of our calculation are correct." + I£ only black holes accreting above AP»10b es * undergo outbursts. consistent with the observed X-ray. novae (van Paradijs 1996). then these numbers reduce to 50 vr.|. still large given that about ~1 transient is detected cach vear. and generally they are found to have companions.," If only black holes accreting above $\dot M > 10^{15}$ g $^{-1}$ undergo outbursts, consistent with the observed X-ray novae (van Paradijs 1996), then these numbers reduce to 50 $^{-1}$, still large given that about $\sim 1$ transient is detected each year, and generally they are found to have companions." + We conclude that only a small fraction of isolated black holes might experience transience similar to X-ray novae., We conclude that only a small fraction of isolated black holes might experience transience similar to X-ray novae. + The uncertainty in distance of the NLACTIO black-hole microlensing candidates leads to an uncertainty in their mass. and thus," The uncertainty in distance of the MACHO black-hole microlensing candidates leads to an uncertainty in their mass, and thus" +The planet mass in. global run G5 was equivalent to 3 Jupiter masses.,The planet mass in global run G5 was equivalent to 3 Jupiter masses. +" Phe computational domain in this case was restricted so that the azimuthal interval ran between 0.7/2] (thus allowing a reasonable run time). with the protoplanet being placed on a fixed circular orbit at (65:0,)=(2.5.7/4)."," The computational domain in this case was restricted so that the azimuthal interval ran between $[0,\pi/2]$ (thus allowing a reasonable run time), with the protoplanet being placed on a fixed circular orbit at $(r_p,\phi_p)=(2.5,\pi/4)$." + The physical parameters were identical to run Cid. for which the azimuthal domain covered the full 27.," The physical parameters were identical to run G4, for which the azimuthal domain covered the full $2 \pi$." + However. run C+ was only run for 211 planetary orbits. which is too short a," However, run G4 was only run for $\simeq 11$ planetary orbits, which is too short a" +estimated by Williams Maddalena for C216-2.5.,estimated by Williams Maddalena for G216-2.5. + The flix ratio is therefore 109/50)? = (3.7&5.5«10? for a distance to MSI of 3.7 Alpe. so the FUV fiux iucideut ou the molecular cloud is y= 5.5 ereem2stA«10=Ls Ἡ," The flux ratio is therefore $^2$ = } for a distance to M81 of 3.7 Mpc, so the FUV flux incident on the molecular cloud is $\chi$ = } $\times$ } = } ." +", The value for \g at 150 nm can be read from Fig.l in Van Dishoeck Black (1988) as photonscin2<107 24 ΤΑ TY 1.32«10H eves/photon = Serecm7stA2.60510 tsothat the ratio y/o 15."," The value for $\chi_0$ at 150 nm can be read from Fig.1 in Van Dishoeck Black (1988) as } $\,$ $^{-2}\,$ $^{-1}\,$ $^{-1} \times$ } ergs/photon = } so that the ratio $\chi/\chi_0 +\approx 18$ ." + From equation d. the deusitv » of the uuderlviug eas can be estimated from the observed FUV flux aud the ccohuun deusitv of the PDR., From equation \ref{dissociate} the density $n$ of the underlying gas can be estimated from the observed FUV flux and the column density of the PDR. + The extended regious of ecnission iu close proximity to = Gin2...iregionlllhaveN(ITI))2., The extended regions of emission in close proximity to region 44 have ) = } . +5«1025 There are more localised areas reaching a brigltuess of two or three times this value. but in our picture these chhancements are the result of viewing a thick blaukoet of ΠΟΙΟ or less edgc-on (cf. Fig.7)).," There are more localised areas reaching a brightness of two or three times this value, but in our picture these enhancements are the result of viewing a thick blanket of more or less edge-on (cf. \ref{cartoon}) )." + Taking G216-2.5 again as a model. the line of sight may reach 300 pc tangential to a laver of intrinsic thickness of only 50 pc.," Taking G216-2.5 again as a model, the line of sight may reach 300 pc tangential to a layer of intrinsic thickness of only 50 pc." + Accounting for our 150 pe beam. the uct chhancement would be of order (300/50) ς (50/150) = 2. im rough agreement with our cmZandoobservations.," Accounting for our 150 pc beam, the net enhancement would be of order (300/50) $\times$ (50/150) = 2, in rough agreement with our observations." +UsingNOII1))=2.5«1025 V/A\o=18 in equation 1.. we compute the density of the uuderlyving eas to be»zI07...," Using ) = } and $\chi/\chi_0 += 18$ in equation \ref{dissociate}, we compute the density of the underlying gas to be $n \approx 10$." + Although the accuracy of this result is not very high. the value is about the same as tha used by Baud et ((1992) in their “best” phlotodissociation models for the in M51.," Although the accuracy of this result is not very high, the value is about the same as that used by Rand et (1992) in their “best” photodissociation models for the in M51." + For G216-2.5. we calculate frou the values in Williams Macddelena that ΕΠΙ) z NU)/L = 1.5 wwith L = 50 pc. siguificautly less than the value n— u(VD) | μυ1) = 10 dderivedhere?.," For G216-2.5, we calculate from the values in Williams Maddelena that $n$ ) $\approx$ )/L = 1.5 with L = 50 pc, significantly less than the value $n = n$ ) + $n$ ) = 10 derived." +. Towever. the detected wwill have been heated by the photodissociatiou process to ~SO Ts. and the factor of ~6 in density is easilv understood if the kinetic temperature of the precursor Hs less than a plausible ~15 Ik. The plotodissociation picture provides a reasonable explanation for the nunorphologics and coluun densities iu the spiral armis of AISL.," However, the detected will have been heated by the photodissociation process to $\sim 80$ K, and the factor of $\sim 6$ in density is easily understood if the kinetic temperature of the precursor is less than a plausible $\sim 15$ K. The photodissociation picture provides a reasonable explanation for the morphologies and column densities in the spiral arms of M81." + The uuderlviug gas is of niodest density. ~10 IT uncleii but aust be widespread. since every UV source has photodissociated inuitsmunuediate vicinity.," The underlying gas is of modest density, $\sim 10$ H nucleii, but must be widespread, since every UV source has photodissociated in its immediate vicinity." +" The amount of o»present m the spiral arias of MSIE is uncertiin. but it is likely to be at least as mach as theIT. aud may )o significantly ereater,"," The amount of present in the spiral arms of M81 is uncertain, but it is likely to be at least as much as the, and may be significantly greater." + This result contrasts with the CO(CL-0) zurvevs of M1., This result contrasts with the CO(1-0) surveys of M81. + For instance. using the usual actor of Blocimen et ((L986) to couvert to N(IIo)). Browillet et ((1991) conclude that the inass im the aunulu region IxRRH<7 kpc coutaimine he major spiral arms in MSI is onlv of the wuss in the same area.," For instance, using the usual factor of Bloemen et (1986) to convert to ), Brouillet et (1991) conclude that the mass in the annular region $4 \leq {\rm R} +\leq 7$ kpc containing the major spiral arms in M81 is only of the mass in the same area." + The ratio varies frou o in specific regions along the spiral armis as observed with the 1210 NRAO millimeter radio telescope (beam EWIIM z10) when the Ds xnoothed to the same resolution (Brouillet ct Table 3)., The ratio varies from to in specific regions along the spiral arms as observed with the 12m NRAO millimeter radio telescope (beam FWHM $\approx 1'$ ) when the is smoothed to the same resolution (Brouillet et Table 3). + The conventional conversion factor linking ⋅≽↽↽4-0) surface. brightuess. aud ccoluin density mustieidercstimnate the quantity of uolecular gas in the spiral arms of ASL A similar discrepancy was noted by Ixaufuiu et ((1989b) in their study o| the dust anes in AISI., The conventional conversion factor linking (1-0) surface brightness and column density must the quantity of molecular gas in the spiral arms of M81 A similar discrepancy was noted by Kaufman et (1989b) in their study of the dust lanes in M81. + Allen (1996) reviewed the case for using |?CO((1-)) brightuesses to infer ccolumn deusities iu galaxy disks aud concluded that his practice is uneeliable., Allen (1996) reviewed the case for using (1-0) brightnesses to infer column densities in galaxy disks and concluded that this practice is unreliable. + Our prescut resul in [51 contributed to that conclusion., Our present result in M81 contributed to that conclusion. +" Qur detailed morphological study of the FUV. Ho. and in AISL at a resolution of 150 pc indicates that most of the is UV-dissociated.Πο, at least 1- he mner spiral arms of this galaxy."," Our detailed morphological study of the FUV, $\alpha$, and in M81 at a resolution of 150 pc indicates that most of the is UV-dissociated, at least in the inner spiral arms of this galaxy." + In this picture. the jin the spiral aris is aproduct of the star formation process rather than a precursor.," In this picture, the in the spiral arms is a of the star formation process rather than a precursor." + A corollary of this picture is that he disk of M81 must harbor a large reservoir of molecular eas which has so far escaped detection. iin the (LL line.," A corollary of this picture is that the disk of M81 must harbor a large reservoir of molecular gas which has so far escaped detection, in the (1-0) line." + Since M81 has a generallv low level of heat production. as evidenced by the faintuess of the nonthermal," Since M81 has a generally low level of heat production, as evidenced by the faintness of the nonthermal" + (e.g..Whiteetal.1993;Allen2004).. (Conroyetal.2007).. (e.g..Bodeetal.2009).," \citep[e.g.,][]{swhite93a,allen04}. \citep{conroy07}. \citep[e.g.,][]{bode09}. \citep[e.g.,][]{lin03b,gonzalez07,andreon10,balogh11}," +. z20.1—1 2009.hereafterGO9).., $z=0.1-1$ \citep[][hereafter G09]{giodini09}. + MienMj; Leauthaud/etal.2011)). Mic Mya. 2<0.6 z70.1 Explorer (WISE: Wrightetal.2010)) survey to determine Mj. while for the local clusters. we rely on data from the Two-Micron All-Sky Survey (2MASS. Skrutskieetal.2006).," $M_{\rm ICM}/M_{\rm star}$ \citealt{leauthaud11}) $M_{\rm ICM}$ $M_{\rm star}$ $z\le 0.6$ $z>0.1$ Explorer (WISE; \citealt{wright10}) ) survey to determine $M_{\rm star}$ , while for the local clusters, we rely on data from the Two-Micron All-Sky Survey (2MASS, \citealt{skrutskie06}) )." +" To ensure uniformity of our measurements and to facilitate comparison across the cosmic epochs. all quantities are measured within rsog. the radius within which the mean overdensity is 500 times the critical density of the Universe p, at the cluster redshift."," To ensure uniformity of our measurements and to facilitate comparison across the cosmic epochs, all quantities are measured within $r_{500}$, the radius within which the mean overdensity is 500 times the critical density of the Universe $\rho_c$ at the cluster redshift." + In this paper we have neglected neutral and molecular gas in the baryon budget. as their amount is believed to be small (e.g..Chungetal.2009).," In this paper we have neglected neutral and molecular gas in the baryon budget, as their amount is believed to be small \citep[e.g.,][]{chung09}." +. Our analysis does not include the intracluster stars either (as they are well below the surface brightness limit of WISE). although they may contribute a non-negligible fraction to the total cluster stellar mass (e.g.Gonzalezetal. 2007)..," Our analysis does not include the intracluster stars either (as they are well below the surface brightness limit of WISE), although they may contribute a non-negligible fraction to the total cluster stellar mass \citep[e.g.,][]{gonzalez07}." + Throughout this paper we adopt a (Komatsuetal.2009) ACDM cosmological model where Qy=1—0420.26. Hy=71/5)kms Mpc!.," Throughout this paper we adopt a \citep{komatsu09} $\Lambda$ CDM cosmological model where $\Omega_M=1-\Omega_\Lambda=0.26$, $H_0=71 h_{71}\,{\rm km\,s}^{-1} {\rm Mpc}^{-1}$ ." + Our analysis relies on the X-ray measurements to provide the cluster center. size. and the mass of the ICM.," Our analysis relies on the X-ray measurements to provide the cluster center, size, and the mass of the ICM." + The cluster samples used are deseribed in refsec:samples.., The cluster samples used are described in \\ref{sec:samples}. + We discuss the way artifacts and stars are rejected from the WISE catalogs in refsec:wise.., We discuss the way artifacts and stars are rejected from the WISE catalogs in \\ref{sec:wise}. + Throughout this study we only make use of WISE 3.4 jim data., Throughout this study we only make use of WISE 3.4 $\mu$ m data. + For each cluster. we use the background-subtracted total flux to estimate the total cluster luminosity and stellar mass.," For each cluster, we use the background-subtracted total flux to estimate the total cluster luminosity and stellar mass." + The method is deseribed fully in Linetal.(2003. 2004).," The method is described fully in \citet{lin03b,lin04}." +. In refsec:stellarmass we outline our modified procedures for analyzing the WISE data., In \\ref{sec:stellarmass} we outline our modified procedures for analyzing the WISE data. + We assemble our intermediate redshift (z20.1 —0.6) cluster sample from Maughanetal.(2008.hereafterMOS) and Vikhlininetal.(2009.hereafter V09).. both of which are basedon oobservations.," We assemble our intermediate redshift $z=0.1-0.6$ ) cluster sample from \citet[][hereafter M08]{maughan08} and \citet[][hereafter V09]{vikhlinin09}, , both of which are basedon observations." + Although the 115 clusters from MOS8 are a heterogeneous sample (selectedto be targeted ACIS-I observations. at z>0.1. publicly available in aarchive as of 2006). the largesample. analyzed in a uniform," Although the 115 clusters from M08 are a heterogeneous sample (selectedto be targeted ACIS-I observations, at $z>0.1$, publicly available in archive as of 2006), the largesample, analyzed in a uniform" +directly related with the spin of them dark halos aud cannot be solved easily by cnerectic feedback processes.,directly related with the spin of their dark halos and cannot be solved easily by energetic feedback processes. + We performed three simulations within a ACDM cosmoloeical universe with 04=0.3. Qy=0.7. h-—IIy/70 lan | Mpe+ aud oy=0.9.," We performed three simulations within a $\Lambda$ CDM cosmological universe with $\Omega_0=0.3$ , $\Omega_{\Lambda}$ =0.7, $h$ $_0/70$ km $^{-1}$ $^{-1}$ and $\sigma_8=0.9$." + The simulated volue was 15 h+ Mpe box size iu all ruus., The simulated volume was 15 $h^{-1}$ Mpc box size in all runs. + Each simmlation was performed using the publicly available version of the s1100tlied. particle lvdrodvnamics (SPIT) code CADGET (Spriugel. Yoshida & White 2001).," Each simulation was performed using the publicly available version of the smoothed particle hydrodynamics (SPH) code GADGET (Springel, Yoshida $\&$ White 2001)." + All runs started at redshifts μποτ] hieh to eusure that the absolute uaxinuunu density coutrast |o]<1., All runs started at redshifts sufficiently high to ensure that the absolute maximum density contrast $|\delta|\leq 1$. + The simulations begau frou a spatially uniform eid of 128° equalauass particles with Plunuuerequivalent softening comoving length of 10h! pe., The simulations began from a spatially uniform grid of $128^3$ equal-mass particles with Plummer–equivalent softening comoving length of $10 h^{-1}$ kpc. + The particle masses was 1.31s10% 5.1 ML..., The particle masses was $1.34 \times 10^8$ $h^{-1}$ $_{\odot}$. + We identify halos with the classic fricucd-oftriend (FOF) ucthod using a linking leusth that corresponds to the ποσα interparticle separation at that density contour hat defines the virial radius of an isothermal sphere. b—npo)p)>£30 1/5—(0.15. where » is the article nuniber density and pí;.(:) is the corresponding virial deusitv.," We identify halos with the classic friend-of-friend (FOF) method using a linking length that corresponds to the mean interparticle separation at that density contour that defines the virial radius of an isothermal sphere, $b=[n\rho_{vir}(z)/<\rho(z)>/3.0]^{-1/3}$ =0.15, where $n$ is the particle number density and $\rho_{vir}(z)$ is the corresponding virial density." + All halos at 2550 with masses between \[=101107 h! M... coutaining at least 1000 particles are meblded iu the analyses.," All halos at z=0 with masses between $=10^{11}-10^{12}$ $h^{-1}$ $_{\odot}$, containing at least 1000 particles are included in the analyses." + This restriction linüts the iuflucnce of nuinerical effects on global halo properties., This restriction limits the influence of numerical effects on global halo properties. + Disks with uou-ucelieible bulee components of D/(D|D)> O14. with D aud D the bulee and disk mass. respectively. require a major niergeer which iuvolved at least of the fal mass (ic. at least 100. particles).," Disks with non-negligible bulge components of $B/(B+D) \geq 0.1$ , with B and D the bulge and disk mass, respectively, require a major merger which involved at least of their final mass (i.e. at least 100 particles)." + Our focus on halos with final particle ους of at least 1000 therefore euaranutees that we dontf miss any relevaut lnajor mncrecr events due to softening., Our focus on halos with final particle numbers of at least 1000 therefore guarantees that we don't miss any relevant major merger events due to softening. + We also did not fiud a dependence of our results on the adopted mass range of dark halos at 2=0., We also did not find a dependence of our results on the adopted mass range of dark halos at $z=0$. + Therefore. neglecting smaller halos will not affect our conclusions.," Therefore, neglecting smaller halos will not affect our conclusions." + The angular momentum of a galaxy. J. is commonly expressed in terms of the dimensionless spin parameter A=IY E|/OAP where E is the total enerey. and M is the total mass.," The angular momentum of a galaxy, $J$, is commonly expressed in terms of the dimensionless spin parameter $\lambda=J\sqrt{|E|}/$ $^{5/3}$ where $E$ is the total energy, and M is the total mass." + The halo spin parameter distribution in simulations is found to be well approximated by the log-normal Iu practise. it is more couvenicut to use the modified spin vavalneter (Bullock et al.," The halo spin parameter distribution in simulations is found to be well approximated by the log-normal In practise, it is more convenient to use the modified spin parameter (Bullock et al." + 2001): A=fp/(V2Rei) where j=J/AL is the specific augular momentum., 2001): $\lambda'=j/(\sqrt{2}V_{vir}R_{vir})$ where $j=J/M$ is the specific angular momentum. + For a ACDAL cosinelogy the loe-ormal paraincters are found o be «A!>=0.035+0.006 and oy =0.5-0.6 (Bullock et al., For a $\Lambda$ CDM cosmology the log-normal parameters are found to be $<\lambda'>=0.035\pm 0.006$ and $\sigma_{\lambda'}$ =0.5-0.6 (Bullock et al. + 2001)., 2001). + We trace cach identi&ed halo backward in time. ollowius the mass of the most massive progenitor as a unction of redshitt during 0<:3.," We trace each identified halo backward in time, following the mass of the most massive progenitor as a function of redshift during $00.035 in the log-norinal distribution (filled svimbols iu Fig.l)., Many halos with high B/(B+D) ratios also show higher $\lambda'$ values than the average $<\lambda'> \approx 0.035$ in the log-normal distribution (filled symbols in Fig.1). + Most of these halos experieuced a recent major merger in the redshift rauge 0<:ld., Most of these halos experienced a recent major merger in the redshift range $00.023. sienificautly ower than the value of 0.035 correspouding to the average referred to all halos.," Halos that have not experienced any major mergers from $ \approx 0.023$, significantly lower than the value of 0.035 corresponding to the average referred to all halos." + This &udiug confiniis previous results hat the last major merecr even is affecting the fal halo spin paraiueter distribution (€01: Vitvitska et al., This finding confirms previous results that the last major merger event is affecting the final halo spin parameter distribution (G01; Vitvitska et al. + 2002. Poema ct al.," 2002, Peirani et al." + 2002)., 2002). +" Iu order o test how reasonable is o set to zero iu Fie. the Inlee masses of halos that ive not experienced uv majo ranereecr from Οκi<3, we traced back the ""quiescieut?| halos. attributing bulge nasses different from zero to hose halos with the last uajor mnerecr occurs before z=3ο"," In order to test how reasonable is to set to zero in Fig.1 the bulge masses of halos that have not experienced any major merger from $ 1$ GeV) and cannot be resolved by GLAST from other possible sources of gamma-ray emission, both from the cluster and from AGNs in the field." + In addition. the GLAST spatial resolution (~9IS arciuin at 10 and 1 GeV. respectively) cannot provide any clear spatial separation between the DAL gamma-ray signals (expected to be concentrated at the DM clumps) aud other )ossible eannmua-rav signals originating within the atmosphere of," In addition, the GLAST spatial resolution $\sim +9-18$ arcmin at 10 and 1 GeV, respectively) cannot provide any clear spatial separation between the DM gamma-ray signals (expected to be concentrated at the DM clumps) and other possible gamma-ray signals originating within the atmosphere of." + Radio telescopes have. im principle. excellent resolution and seusitivitv to xobe the differeut spectra and brightucss castribution of the DMEuduced svuchrotrou chussion.," Radio telescopes have, in principle, excellent resolution and sensitivity to probe the different spectra and brightness distribution of the DM-induced synchrotron emission." +" For the sake of illustration. we evaluated that the DALinduced svuchrotron eLulsson from the East DM chump is ~310 Jv (for a smooth or sinooth plus 50% mass chuupiness NEW DAL profile. AL,=LO GeV. (ocio=LT10Mens| anodel used by Colafraucesco et al."," For the sake of illustration, we evaluated that the DM-induced synchrotron emission from the East DM clump is $\sim 3-10$ mJy (for a smooth or smooth plus $50 \%$ mass clumpiness NFW DM profile, $M_{\chi}=40$ GeV, $\langle \sigma v \rangle_0 = 4.7 \cdot 10^{-25} cm^3 +s^{-1}$ model used by Colafrancesco et al." + 2006 for Coma. with a 1 Co magnetic field) at v=100 MIIz. stil mareinally detectable by LOFAR.," 2006 for Coma, with a $1$ $\mu$ G magnetic field) at $\nu = 100$ MHz, still marginally detectable by LOFAR." + Theoretical uncertainties associated to the auplitude of the maguetic field in the DAL chumps of reucer. however. the prediction of the expected signals quite Tn such a context. the possible detection of the SZpaz effect will provide au important complementary. and maybe unique. probe of the nature of DM.," Theoretical uncertainties associated to the amplitude of the magnetic field in the DM clumps of render, however, the prediction of the expected signals quite In such a context, the possible detection of the $_{DM}$ effect will provide an important complementary, and maybe unique, probe of the nature of DM." +The next step of this analysis consists in comparing the numerical simulations with the observations.,The next step of this analysis consists in comparing the numerical simulations with the observations. + In this comparison process. ib is essential to keep in mind two essential discrepancies between the model and the real sun: the driving mechanism for the meridional Low in these simulations is artificial. so that the typical Low velocities may be erroneous. anc the typical Ekman numbers of the simulations are several orders of magnitude larecr than in the sun.," In this comparison process, it is essential to keep in mind two essential discrepancies between the model and the real sun: the driving mechanism for the meridional flow in these simulations is artificial, so that the typical flow velocities may be erroneous, and the typical Ekman numbers of the simulations are several orders of magnitude larger than in the sun." + In the region of the tachocline. assuming that the low is not turbulent. the magnetic ancl viscous dilfusion coellicients. are of order of 6= I0cngs | and 1 emer s+. whieh implies that The main consequence of these discrepancies is that although the principal features of the interaction between Iluic motions ancl large-scale fields in the sun can be stuclicel through this method. it cannot. provide reliable quantitative estimates.," In the region of the tachocline, assuming that the flow is not turbulent, the magnetic and viscous diffusion coefficients are of order of $\nu = 10$ $^2$ $^{-1}$ and $\eta = 2\times 10^{3}$ $^2$ $^{-1}$, which implies that The main consequence of these discrepancies is that although the principal features of the interaction between fluid motions and large-scale fields in the sun can be studied through this method, it cannot provide reliable quantitative estimates." + Despite this obvious shortfall. some aspects of. the observations can be reproduced in the simulations.," Despite this obvious shortfall, some aspects of the observations can be reproduced in the simulations." + Finally. as mentioned in Section 4.2.. a useful point of comparison between. different theoretical. models and between models. and. the observations is the value of the interior angular velocity μι," Finally, as mentioned in Section \ref{sec:intfield2}, a useful point of comparison between different theoretical models and between models and the observations is the value of the interior angular velocity $\Omega_{\rm +in}$." +" Gough (1985) showed that for an incompressible tachocline controlled by viscous effects. Ou,=0.960..."," Gough (1985) showed that for an incompressible tachocline controlled by viscous effects, $\Oin = 0.96 \Oeq$." + MacGregor Charbonneau (1999) presentec simulations in a confined [field configuration which show a virtually uniform rotation profile for the radiative zone with Ou=0.970..., MacGregor Charbonneau (1999) presented simulations in a confined field configuration which show a virtually uniform rotation profile for the radiative zone with $\Oin = 0.97\Oeq$. +" The ciserepaney with the observe value. (Q,0.980... ) is significant. ancl comparison with the Gough Melntyre model shows that either meridiona motions and the elfects of heat transport anc stratification are dominant in the dvnamics of the tachocline. or tha such a class of models cannot. reproduce the observations and that very dilferent. dvnamies are in plav fas in the turbulent stress model proposed by Spiegel Zahn. 1992. or the nonlinear development of MIID instabilities presented bv Cally. 2001)."," The discrepancy with the observed value $\Oc = 0.93 \Oeq$ ) is significant, and comparison with the Gough McIntyre model shows that either meridional motions and the effects of heat transport and stratification are dominant in the dynamics of the tachocline, or that such a class of models cannot reproduce the observations and that very different dynamics are in play (as in the turbulent stress model proposed by Spiegel Zahn, 1992, or the nonlinear development of MHD instabilities presented by Cally, 2001)." + The prediction for the angular velocity presented in Fig., The prediction for the angular velocity presented in Fig. + 12. are not conclusive when comparing them with observations. as any discrepancy could be attributed to the large cilfusivities used in the simulations.," \ref{fig:omekm} are not conclusive when comparing them with observations, as any discrepancy could be attributed to the large diffusivities used in the simulations." + The ultimate aim of this work is to develop a self-consistent dynamical model of the tachocline which can be used. to explain the large range of observations available., The ultimate aim of this work is to develop a self-consistent dynamical model of the tachocline which can be used to explain the large range of observations available. + In order to do so. the idea proposed by Gough Moelntyre is graciually implemented into a numerically solvable nonlinear. MILD model.," In order to do so, the idea proposed by Gough McIntyre is gradually implemented into a numerically solvable nonlinear MHD model." + Although previous work on those lines (Itüdcdiger Ixitchatinov. 1997. AlacCregor Charbonneau. 1999) has alreacly investigated some of the aspects of the interaction of a large-scale field ancl differential rotation. two essential ingredients to the model remained to be studied carefully: This first paper focuses on the first point onlv by artificially driving a meridional How with Ekman-LHartmann pumping on the boundaries.," Although previous work on those lines (Rüddiger Kitchatinov, 1997, MacGregor Charbonneau, 1999) has already investigated some of the aspects of the interaction of a large-scale field and differential rotation, two essential ingredients to the model remained to be studied carefully: This first paper focuses on the first point only by artificially driving a meridional flow with Ekman-Hartmann pumping on the boundaries." + I0 is found that this artificial, It is found that this artificial +]teconstructions of convergence maps using flexion measurements were first introduced bv Baconetal.(2006).,Reconstructions of convergence maps using flexion measurements were first introduced by \cite{flexion:bacon06}. +. In their paper. a (non-paranmetric) convergence map is reconstructed from simulated [flexion measurements.," In their paper, a (non-parametric) convergence map is reconstructed from simulated flexion measurements." +" The simulations have a galaxy density of n,=60 eal/arcnmin? and a reported flexion dispersion of o7 —0.04 +.", The simulations have a galaxy density of $n_g=60$ $^2$ and a reported flexion dispersion of $\sigma_e^{\mathcal{F}}$ =0.04 $^{-1}$. + However. an error in the reconstruction code meant that the (rue flexion dispersion was 27 —0.007 !. which would only be achievable for the highest signal-to-noise," However, an error in the reconstruction code meant that the true flexion dispersion was $\sigma_e^{\mathcal{F}}$ =0.007 $^{-1}$, which would only be achievable for the highest signal-to-noise." +ga, Fig. +laxies!.. Fig. 3. compares the i0]se power spectrum on (he convergence map obtained from realistic shear measurements (solid black line) and [rom realistic flexion measurements (solid red line)., \ref{crossing_bacon} compares the noise power spectrum on the convergence map obtained from realistic shear measurements (solid black line) and from realistic flexion measurements (solid red line). +" The dashed rec ine gives (he result [rom the optimistic flexion measurements used by Baconetal.(2006) (o7 —0.00T ! and n, = 60 gal/aremin?).", The dashed red line gives the result from the optimistic flexion measurements used by \cite{flexion:bacon06} $\sigma_e^{\mathcal{F}}$ =0.007 $^{-1}$ and $n_g$ = 60 $^2$ ). +" These values are optimistic since to achieve (his dispersion the flexion of the highest signal-to-noise galaxies should be measured. which ead to a galaxy density significantly smaller than 1, = 60 gal/arenin-."," These values are optimistic since to achieve this dispersion the flexion of the highest signal-to-noise galaxies should be measured, which lead to a galaxy density significantly smaller than $n_g$ = 60 $^2$." + Doing so increases the ratio TDA. but decreases the ratio n (see equation [17]]) ς because ofB the small number of high signal-to-noise galaxies.," Doing so increases the ratio $\frac{\sigma_\epsilon^\mathcal{F}}{\sigma_\epsilon^\gamma}$, but decreases the ratio $\frac{n_g^\gamma}{n_g^\mathcal{F}}$ (see equation \ref{eq:flex8}] ]) because of the small number of high signal-to-noise galaxies." + At the end. the scale A4 should remain almost the same.," At the end, the scale $k^T$ should remain almost the same." + In Baconοἱal.(2006).. the reconstruction fidelitv from flexion measurements is therefore too optimistic and the result of the reconstruction should be closer to the right panel of Fig. 1..," In \cite{flexion:bacon06}, the reconstruction fidelity from flexion measurements is therefore too optimistic and the result of the reconstruction should be closer to the right panel of Fig. \ref{convergence}." + In Okuraetal.(2007).. the authors also use a (non-parametric) convergence map reconstruetion [from simulated flexion measurements.," In \cite{flexion:okura07}, the authors also use a (non-parametric) convergence map reconstruction from simulated flexion measurements." +" Bul the data are simulated with a rather optimistic galaxy density n,=LOO gal/arcmin?. and a very optimistic value has been chosen for the flexion measurement error o7.=0.009 +."," But the data are simulated with a rather optimistic galaxy density $n_g = 100$ $^2$, and a very optimistic value has been chosen for the flexion measurement error $\sigma^\mathcal{F}_\epsilon=0.009$ $^{-1}$." + The dashed red line of Fie., The dashed red line of Fig. + 4 shows the noise power spectrum that should be obtained with this optimistic value of flexion dispersion., \ref{crossing_okura} shows the noise power spectrum that should be obtained with this optimistic value of flexion dispersion. +" The intersection with the solid black line gives the scale below which the flexion dominates (4 = 50 arcsec),", The intersection with the solid black line gives the scale below which the flexion dominates $k^T$ = 50 arcsec). + As shown in Okuraetal.(2007).. the reconstruction of a binned convergence map by combining shear and flexion measurements is interesting wilh (his optimistic [lexion dispersion because the flexion is dominating for scales smaller (han 50 arcsec.," As shown in \cite{flexion:okura07}, the reconstruction of a binned convergence map by combining shear and flexion measurements is interesting with this optimistic flexion dispersion because the flexion is dominating for scales smaller than 50 arcsec." + But. using real data will a realistic Hexion dispersion. the result of the reconstruction of a binned convergence map rom flexion measurements should be close to what is shown in the right panel of Fig. 1..," But, using real data with a realistic flexion dispersion, the result of the reconstruction of a binned convergence map from flexion measurements should be close to what is shown in the right panel of Fig. \ref{convergence}." + In Okuraetal.(2008).. this convergence map reconstruction method is applied to real data (ground-based Subaru data).," In \cite{flexion:okura08}, this convergence map reconstruction method is applied to real data (ground-based Subaru data)." +" The flexion dispersion is found to be o?=0.11245 Ll,", The flexion dispersion is found to be $\sigma_e^{\mathcal{F}}=0.11245$ $^{-1}$. + The galaxy density is very small al ny=7.75 gal/arcmin? (only the 791 brightest ealaxies have been selected) and (he field is 9 x 9 sampled with a grid of 256 x 256 pixels., The galaxy density is very small at $n_g = 7.75$ $^2$ (only the 791 brightest galaxies have been selected) and the field is 9' x 9' sampled with a grid of 256 x 256 pixels. +The remainder of the paper is organized as follows.,The remainder of the paper is organized as follows. + In reklesc we describe our formulation of the magnetocentirifugal wind problem and the setup of numerical simulation.," In \\ref{desc} + we describe our formulation of the magnetocentrifugal wind problem and the setup of numerical simulation." + Our reference simulation is presented in detail in relreference.., Our reference simulation is presented in detail in \\ref{reference}. + We compare models with different mass loads and distributions of mass loading in relloachinagn. aud refloacldlist: respectively., We compare models with different mass loads and distributions of mass loading in \\ref{loadmagn} and \\ref{loaddist} respectively. + A discussion of these results. along with our conclussions. are given 1n refconclusion..," A discussion of these results, along with our conclussions, are given in \\ref{conclusion}." + We consider a svstem consisting of a central gravitatiug mass surrounded by an accretion disk threaded with a magnetic field., We consider a system consisting of a central gravitating mass surrounded by an accretion disk threaded with a magnetic field. + The svstems axisvmmetry suggests a evlindrieal coordinate svslem (z. a. ©) with the central mass situated at the origin. the aceretion disk lving in the z—0 plane. and the axis of rotation along the w=0 axis.," The system's axisymmetry suggests a cylindrical coordinate system $z$, $\varpi$, $\phi$ ) with the central mass situated at the origin, the accretion disk lying in the $z=0$ plane, and the axis of rotation along the $\varpi=0$ axis." + Our interest is in finding steady-state wind solutions for this model through numerical simulations., Our interest is in finding steady-state wind solutions for this model through time-dependent numerical simulations. +" The standard. MIID wind equations are where D is the magnetic field. v is the velocity field. p is the mass density. p is the (thermal pressure. and e, is the gravitational potential."," The standard MHD wind equations are where $\mathbf{B}$ is the magnetic field, $\mathbf{v}$ is the velocity field, $\rho$ is the mass density, $p$ is the thermal pressure, and $\Phi_{g}$ is the gravitational potential." + It is well known that. in steady. state. there are four conserved quantities along each," It is well known that, in steady state, there are four conserved quantities along each" +the estimator resulting from both the observed data. and simulations are rebinned to 25bins?.,the estimator resulting from both the observed data and simulations are rebinned to 25. +. The results are shown in the top panel of Figure 9. with each curve depicting the likelihood (without normalisation) for each smoothing scale., The results are shown in the top panel of Figure \ref{fig_wmap_likeli} with each curve depicting the likelihood (without normalisation) for each smoothing scale. + Phe likelihood functions are fitted by. Gaussian functions so that the best-fitting aand the corresponding le error are obtained ancl then marked in the same plot., The likelihood functions are fitted by Gaussian functions so that the best-fitting and the corresponding $1\sigma$ error are obtained and then marked in the same plot. +" The likelihood at the highest resolution indicates that the Gaussian hypothesis (νι,= 0) is rejected. only at O.Se-level. while it increases to 2.70. for ΕΛΛΗΝΕΣ2713."," The likelihood at the highest resolution indicates that the Gaussian hypothesis $f_{\rm NL}=0$ ) is rejected only at $0.8\sigma$ -level, while it increases to $2.7\sigma$ for $\rm FWHM=2\fdg13$." + Lt is apparent that the best-fitting vvalues show a positive correlation with the smoothing scale. which is unexpected since iis scale-independent according to. the. local-twpe Gaussian model and our simulations.," It is apparent that the best-fitting values show a positive correlation with the smoothing scale, which is unexpected since is scale-independent according to the local-type non-Gaussian model and our simulations." + As discussed in Section 4.1.3.. although the estimation is inevitably biased. by the point sources or other tvpes of foreground.> large angleo smoothinge renders the estimation insensitive to thoseὃν elfects.," As discussed in Section \ref{subsubsec_medfilt}, although the estimation is inevitably biased by the point sources or other types of foreground, large angle smoothing renders the estimation insensitive to those effects." + We repeat the estimation using meclian-Lilterecl samples from the first four smoothing scales., We repeat the estimation using median-filtered samples from the first four smoothing scales. + As shown in the middle panel of Figure 9.. the results are consistent in general. and the positive correlation between (xo) and the smoothing scales is identical to the unliltered analvsis.," As shown in the middle panel of Figure \ref{fig_wmap_likeli}, the results are consistent in general, and the positive correlation between $f_{\rm NL}^{\rm +best}$ and the smoothing scales is identical to the unfiltered analysis." + Lt is therefore. suggested. that the point sources contribute little to such correlation., It is therefore suggested that the point sources contribute little to such correlation. + Phe Le errors are robust according to the mecian-filter reference. but the best-fit values of {from the ΙΟΤΙΣ processing seem to be over-cstimatec by levels of 0.046. 0.260. 0.390 and 0.220 for EWIIM=0753. 0764. 0785 and 1728. respectively.," The $1\sigma$ errors are robust according to the median-filter reference but the best-fit values of from the KQ75B processing seem to be over-estimated by levels of $0.04\sigma$, $0.26\sigma$, $0.39\sigma$ and $0.22\sigma$ for $\rm FWHM=0\fdg53$, $0\fdg64$, $0\fdg85$ and $1\fdg28$, respectively." + In principle. cillerent heights of the the likelihoods represent variations in the soodness-o[-[it/— if 1c corresponding x7. values have the same number of degrees-ol-lreedom.," In principle, different heights of the the likelihoods represent variations in the goodness-of-fit if the corresponding $\chi^2$ values have the same number of degrees-of-freedom." + A higher likelihood implies the eexpectation fits the data better and it does appear that the likelihoods from. larger-angle smoothing (ΛΗΛ=- 2708 and 3740) show better results than for smaller ENIMS.," A higher likelihood implies the expectation fits the data better and it does appear that the likelihoods from larger-angle smoothing $\rm FWHM=2\fdg55$, $2\fdg98$ and $3\fdg40$ ) show better results than for smaller FWHMs." + However. in our analysis. we pick up only the diagonal elements of the covariance matrix to compute the V.," However, in our analysis, we pick up only the diagonal elements of the covariance matrix to compute the $\chi^2$." + Lt is inappropriate to make a theoretical interpretation of the &oodness-ol-fit., It is inappropriate to make a theoretical interpretation of the goodness-of-fit. + Consequently. the correlation. found above would be a false appearance because there might be some bad fittings.," Consequently, the correlation found above would be a false appearance because there might be some bad fittings." + For cach FWHM. the 47 value at the maximum Likelihood (ML) of the is represented as Vusm ," For each FWHM, the $\chi^2$ value at the maximum likelihood (ML) of the is represented as $\chi^2_{\rm min}$." +Accordingly.. there are 2500 sampled A72CLfsuMfeb)PN and each has a minimum within our sampling range.," Accordingly, there are 2500 sampled $\chi^2(\{f_{\rm NL}\}|f_{\rm NL}^{\rm ML})$ and each has a minimum within our sampling range." +" We: count the probability"" of02 παμεκιτ.κι}ALXμα2 o quantify the goodness of fit. for results. from. both he WKOTS5B ancl meclian-lilter processing. with a lower wobability corresponding to a better fit."," We count the probability of $\chi^2_{\rm +min}(\{f_{\rm NL}\}|f_{\rm NL}^{\rm ML}) < \chi^2_{\rm min}$ to quantify the goodness of fit for results from both the KQ75B and median-filter processing, with a lower probability corresponding to a better fit." +" The x2, values and the probabilities are listed in Table 4..", The $\chi^2_{\rm min}$ values and the probabilities are listed in Table \ref{tab_gof}. + The moderate wobabilities are consistent with cach other though they may be under-estimated for the last three FWILAIs., The moderate probabilities are consistent with each other though they may be under-estimated for the last three FWHMs. + On one ας. it is demonstrated that our skeleton statistic fits the »ossible feature in the WALAPSS cata anc our estimations are therefore. validated.," On one hand, it is demonstrated that our skeleton statistic fits the possible feature in the 5 data and our estimations are therefore validated." + On theother hand. it remains uncontirmecd what the source of the positive correlation tween. fpλος] s and smoothing. scales is.. and. which. we will. return to in Section 4.2.3..," On theother hand, it remains unconfirmed what the source of the positive correlation between $f_{\rm NL}^{\rm best}$ s and smoothing scales is, and which we will return to in Section \ref{subsubsec_Gauss_cosmic_var}." +" As presented in Section 3.2.2.. the combinations on clillerent smoothing scales are applied separately to the rebinned AL,(7) of the data and LN(p.νι) of the ssanmiples."," As presented in Section \ref{subsubsec_estimator}, the combinations on different smoothing scales are applied separately to the rebinned $\Delta \mathcal{L}_{a}(\nu)$ of the data and $\mathcal{L}^{\rm +NG}_{a}(\nu,f_{\rm NL})$ of the samples." + Lis verified that such a combination still leacls to an unbiased estimation of (Appendix. C)., It is verified that such a combination still leads to an unbiased estimation of (Appendix \ref{sec_app_3}) ). + 1n our analysis. the first 4 and all 9 scales are combined. vielding estimates of friΞ47.32534.9 anc fre=16.843.1 respectively. by fitting the likelihood using a Ciaussian function.," In our analysis, the first 4 and all 9 scales are combined, yielding estimates of $f_{\rm NL, C}=47.3\pm34.9$ and $f_{\rm NL, +C}=76.8\pm43.1$ respectively, by fitting the likelihood using a Gaussian function." + Phe likelihoods are shown in the bottom panel of Figure 9 and the goodness-of-Iit is also listed in Table 4., The likelihoods are shown in the bottom panel of Figure \ref{fig_wmap_likeli} and the goodness-of-fit is also listed in Table \ref{tab_gof}. + The estimates are consistent with the results discussed in Section 4.2.1. and the moderate probabilities ane 28.0)) validate the best-fit results., The estimates are consistent with the results discussed in Section \ref{subsubsec_gen_res} and the moderate probabilities and ) validate the best-fit results. + Phe median-liltered results are also combined over the first 4 ΙΝΕΝΕ and the corresponding likelihood is depictec by the dashed curve. resulting5 in the estimate fin.=39.8 34.9.," The median-filtered results are also combined over the first 4 FWHMs and the corresponding likelihood is depicted by the dashed curve, resulting in the estimate $f_{\rm NL, C} = 39.8\pm34.9$ ." + Phe point sources lead to an over-estimate of [κήςbest a," The point sources lead to an over-estimate of $f_{\rm NL, C}^{\rm best}$ at" +"9aa 9bb (My~10) 9aa CM~3—5). My (21 AL, Γρ V5. ec. Vor) AM. Γρ. Vp. View e. \ariVie «u. (Habiug&Olofssou.2003).. (0.1 GeV energy range is delaved relative to that in the <1 MeV energy range. (,"a) Most of the LAT GRBs do not show significant suppression at the high-energy end of their spectra, though observed LAT limits on the GeV fluence for the GRBs detected by the Gamma-ray Burst Monitor (GBM) onboard the satellite may suggest a steeping or cutoff in the high-energy spectrum \citep{Beniamini2011}; (b) Some of the LAT GRBs have an anomalous extra component in the $>0.1$ GeV range \citep{Abd+09c,Ack+10,Ackermann2011}, while others show a high-energy spectrum consistent with the Band function \citep{Band1993}; (c) In many cases, the emission onset in the $>0.1$ GeV energy range is delayed relative to that in the $<1$ MeV energy range. (" +d) Phe LAT CARBs often show the long-lived high-energy emission lasting onger than the duration of the sub-MeV. component: (e) οἱ only long GRBs but also short GltDs seem to have he above features (Ackermannetal.2010).,d) The LAT GRBs often show the long-lived high-energy emission lasting longer than the duration of the sub-MeV component; (e) Not only long GRBs but also short GRBs seem to have the above features \citep{Ack+10}. +. Understanding hese features is likely to give us important clues to GRB mechanisms ancl related astrophysics., Understanding these features is likely to give us important clues to GRB mechanisms and related astrophysics. + The Cherenkov “Telescope Array (CPA). under jan as the next generation international ganuna-ray observatory (C°VAConsortium2010.2011)... will. provide a great step forward. in studying these issues.," The Cherenkov Telescope Array (CTA), under plan as the next generation international gamma-ray observatory \citep{CTA10,CTA11}, will provide a great step forward in studying these issues." + CPA) will ο constructed. at. two sites. one each in the northern and. southern hemispheres. ancl comprises three types of elescopes: the Large Size Telescopes. (LSTs) with 23 m diameter and 4.67 field of view (CEOV) the Medium Size Telescopes. CMSTs) of 12 m and S FOV: and the Small Size Telescopes (SSTs) of 7 m and 107 FOV.," CTA will be constructed at two sites, one each in the northern and southern hemispheres, and comprises three types of telescopes: the Large Size Telescopes (LSTs) with 23 m diameter and $^\circ$ field of view (FOV); the Medium Size Telescopes (MSTs) of 12 m and $^\circ$ FOV; and the Small Size Telescopes (SSTs) of 7 m and $^\circ$ FOV." + With CEA. the sensitivity will improve by a factor of 510 in the 0.1 TeV range compared to existing Cherenkov telescopes.," With CTA, the sensitivity will improve by a factor of 5–10 in the 0.1--10 TeV range compared to existing Cherenkov telescopes." + lt will cover about 5 decades in energy. including energies below a few tens ofCieV and above LOO TeV. and the angular and energy resolution will be appreciably increased.," It will cover about 5 decades in energy, including energies below a few tens of GeV and above $100$ TeV, and the angular and energy resolution will be appreciably increased." + In the Following. we summarize open issues that can be unraveled bv CPA.," In the following, we summarize open issues that can be unraveled by CTA." + We refer the reader to Inoueetal.(2012). for an extensive overview on the science prospects for. GIU observations with CPA., We refer the reader to \citet{Ino+12} for an extensive overview on the science prospects for GRB observations with CTA. +with a dust source | the cosmological coustant. aud hence cannot be used to model systems with evolving pressure.,"with a dust source + the cosmological constant, and hence cannot be used to model systems with evolving pressure." + However. evolving dark energy can be modelled using the lensing approximation. but only iu the case when dark οποιον is homogeneous.," However, evolving dark energy can be modelled using the lensing approximation, but only in the case when dark energy is homogeneous." + This is because Eq. (5)), This is because Eq. \ref{dlen}) ) + assumes that the expansion rate. which euters via D4. behaves as in the homogeneous 1odel.," assumes that the expansion rate, which enters via $\bar{D}_A$, behaves as in the homogeneous model." +" When dark energy is a dynamical Πα, then two cases need to be considered: a clustering dark energy aud ion-clusteriug dark euergv."," When dark energy is a dynamical fluid, then two cases need to be considered: a clustering dark energy and non-clustering dark energy." + If dark euergv behaves as a relativistic fluid (like radiatiou) then its perturbations are described ouly by decaviug modes (Muklianov. 2005)., If dark energy behaves as a relativistic fluid (like radiation) then its perturbations are described only by decaying modes (Mukhanov 2005). + Iu his case. dark eο should renain alinost LOIMOLCUCOIUS.," In this case, dark energy should remain almost homogeneous." + Ilowever. if dark energw custers (like matter) the- its preset-daw cistribution can be as inhoHOLCUCOUS as4. uatter distribution.," However, if dark energy clusters (like matter) then its preset-day distribution can be as inhomogeneous as matter distribution." + Then the eusiug approximation |i.c. Eq. (63)], Then the lensing approximation [i.e. Eq. \ref{dDBa}) )] + cano be applied., cannot be applied. + This is because when clark. enerev is Inhomogeneous then the average of the expausio- rate will not be the same as the expansion rate of the backeround model ic. (7)zfy.," This is because when dark energy is inhomogeneous then the average of the expansion rate will not be the same as the expansion rate of the background model, i.e. $\av{H} \ne H_0$." + This is a cousequeuce of eracieuts in the pressure., This is a consequence of gradients in the pressure. + If dark energy is mbomogeueous and pressure eradieuts are non-neeslieible then the goo conrponeut of the metric must be position dependent., If dark energy is inhomogeneous and pressure gradients are non-negligible then the $g_{00}$ component of the metric must be position dependent. + We denote this bv a. Le. gop=e(f.r) aud for simplicity consider the spherical case.," We denote this by $\alpha$, i.e. $g_{00} = \alpha^2(t,r)$ and for simplicity consider the spherical case." + Then (Bolejko Lasky 2008) where €PdedPasats Pde Is the energy. density of dark cnerey. and pu; is the cucrey density of matter.," Then (Bolejko Lasky 2008) where $\epsilon = \rho_{de} + \rho_{mat}$, $\rho_{de}$ is the energy density of dark energy, and $\rho_{mat}$ is the energy density of matter." +" To estimate à we assunie wy,2 πο implies that €|pzmPot vad popl.", To estimate $\alpha$ we assume $w_{de} \approx -1$ which implies that $\epsilon + p \approx \rho_{mat}$ and $-p'\approx \rho_{de}'$. +" We also asstuue that the distribution of dark energy closely follows the matter distribution. aud that pq,7ρω Which imply that where the subseript mat has heen suppressed aud the subscript ο denotes the ""observers position. Le. a,=a(r=O)=l.p,pur 0)."," We also assume that the distribution of dark energy closely follows the matter distribution, and that $\rho_{de} \approx 3 \rho_{mat}$ which imply that where the subscript $mat$ has been suppressed and the subscript `o' denotes the `observer's position', i.e. $\alpha_o = \alpha(r=0) \equiv 1, \rho_o = \rho_{mat}(r=0)$ ." + The above approximation shows that inhomogeneities iu dark energy will have a nou-neeligible effect ou the dvuamics of the Universe., The above approximation shows that inhomogeneities in dark energy will have a non-negligible effect on the dynamics of the Universe. + Also. since a41 the result of averaging 1s different than when a=1 (ie. when the pressure eradicuts are uceligihle).," Also, since $\alpha \ne 1 $ the result of averaging is different than when $\alpha =1$ (i.e. when the pressure gradients are negligible)." + For example. Eq. (AL3)}) ," For example, Eq. \ref{avhb}) )" +becomes Since ó is non-zero. à deviates from unity aud therefore This feature was also observed within the second-order perturbative scheme.," becomes Since $\delta$ is non-zero, $\alpha$ deviates from unity and therefore This feature was also observed within the second-order perturbative scheme." + Clarkson. Ananda Larena (2009) showed that the average quautities (such as the expansion rate) within the second-order perturbative framework are uot the same as in the unperturbed backerouud. iu other words (7)xfy.," Clarkson, Ananda Larena (2009) showed that the average quantities (such as the expansion rate) within the second-order perturbative framework are not the same as in the unperturbed background, in other words $\av{H} \ne H_0$." + Thus. if dark energy cau cluster aud is as Inhomogeneous as the present-day matter distribution. then uot ouly the distance fails to oscillate about the unperturbed value but also the expansion rate.," Thus, if dark energy can cluster and is as inhomogeneous as the present-day matter distribution, then not only the distance fails to oscillate about the unperturbed value but also the expansion rate." + Therefore. in the next section when studyiug evolving dark cucrey it is dplicitly assiuned that dark cucrev is homogeneous.," Therefore, in the next section when studying evolving dark energy it is implicitly assumed that dark energy is homogeneous." + To test the effects of iuliomiogeneities on the results of the analysis of cosmological observations. we consider he following example.," To test the effects of inhomogeneities on the results of the analysis of cosmological observations, we consider the following example." + We assume that we have data roni future. very precise iueasurements of Di and II καν feno measurements of the barvon acoustic oscillaions (BAO) at redshifts 0.2.0.1.0.6.0...1.8.2. each neasurement having errors.," We assume that we have data from future, very precise measurements of $D_A$ and $H$ – say ten measurements of the baryon acoustic oscillations (BAO) at redshifts $0.2, 0.4, 0.6, ...,1.8, 2$, each measurement having errors." + We then take the Szekeres nodel and the CLAILE approxinatiou. aud in each case ecnerate mock observations (ten BAO. daa poluts).," We then take the Szekeres model and the lensing approximation, and in each case generate mock observations (ten BAO data points)." + Au exinuple of these data is presented in Fig. 3..," An example of these data is presented in Fig. \ref{fig3}," + where eoneratcc observations are scattered aronud the Szekeres model., where generated observations are scattered around the Szekeres model. + We later analyse these mock observations using the standard methods. ic. to find the equation of state of dark energv (dy and ay) we analyse the observations bv fittine Eqs. (8))," We later analyse these mock observations using the standard methods, i.e. to find the equation of state of dark energy $w_0$ and $w_1$ ) we analyse the observations by fitting Eqs. \ref{dl}) )" + aud (9)) to the data., and \ref{hz}) ) to the data. + Two scenarios are considered: non-evolving dark energy (i.c. the cosmological coustaut) aud an evolving one., Two scenarios are considered: non-evolving dark energy (i.e. the cosmological constant) and an evolving one. + The results are preseuted iu Fie. L. , The results are presented in Fig. \ref{fig4a}. . +"The case of nou- dark energv is presented in the left and micelle panels,", The case of non-evolving dark energy is presented in the left and middle panels. + As seen if the data is analysed oulv using the distance ieasuremenuts. the iuferred equation of state of dark energv differs from €=1.," As seen if the data is analysed only using the distance measurements, the inferred equation of state of dark energy differs from $w=-1$." + This is because the inhomogencitics are uot taken iuto account in the distance-redshift Eq. (51)., This is because the inhomogeneities are not taken into account in the distance-redshift Eq. \ref{dl}) ). + On the other haud. he analysis of the /7(:) data agrees with he true equation of state of dark cnerey.," On the other hand, the analysis of the $H(z)$ data agrees with the true equation of state of dark energy." + This is because. within the Swiss-Clecse model and within the lensing approximation. the average expansion rate coincides with the unperturbed value.," This is because, within the Swiss-Cheese model and within the lensing approximation, the average expansion rate coincides with the unperturbed value." + Illowewer. as poiuted out iu Sec. ?7..," However, as pointed out in Sec. \ref{evde}," + when dark cucrey is not homogeneous. pressure eradieuts iniplv hat (I5 Πρ.," when dark energy is not homogeneous, pressure gradients imply that $\av{H} \ne H_0$ ." + Iu this case. if pressure eradients are huge aud iot taken mto accom then the inferred value from Z7(:) data lav also differ from the true onc.," In this case, if pressure gradients are large and not taken into account then the inferred value from $H(z)$ data may also differ from the true one." + The evolving dark euergw case is presented in the right panel of Fig. L., The evolving dark energy case is presented in the right panel of Fig. \ref{fig4a}. + Oulv the lensing approximation is considered here. as the Szekeres ος] cauuot be used to describe the evolution of dark cucrev.," Only the lensing approximation is considered here, as the Szekeres model cannot be used to describe the evolution of dark energy." + As seen. the results are very simular to the case of nou-evolviug dark cucrey.," As seen, the results are very similar to the case of non-evolving dark energy." +" The above examples show the Muportance of Inhomoecueities. as not taking them iuto account can lead to large systematics,particularlywhen measuring the dark energv equation of state."," The above examples show the importance of inhomogeneities, as not taking them into account can lead to large systematics,particularlywhen measuring the dark energy equation of state." + Evolution of dark cucrev ix a subtle effect. hence even simall deviations of D4(:) from," Evolution of dark energy is a subtle effect, hence even small deviations of $D_A(z)$ from" + Evolution of dark cucrev ix a subtle effect. hence even simall deviations of D4(:) from.," Evolution of dark energy is a subtle effect, hence even small deviations of $D_A(z)$ from" +From the mathematical poit of view. the ΠΟΟΜΑΝ condition for the isotropy is the stochastic iudepeudeucy of the sky distribution of the bursts ou their observed physical ,"From the mathematical point of view, the necessary condition for the isotropy is the stochastic independency of the sky distribution of the bursts on their observed physical properties." +"This lucas it FU.Tsetu) dPday.das is the properties.probability of that.finding au object in the dF=coshdb jufinitesimal solid angle aud iu the (ανα|titydns) tuterval, oue timst. have Tere 0zxPx360"".90°cb90"" eive the celestial positions in Calactical coordinates. 6, (0z1) measure the plysical properties (peak fluxes. flucuces. durations. ete...) of GRBs and y is their probability density."," This means that, if $f(b,l, x_1,...,x_n)$ $dF dx_1...dx_2$ is the probability of finding an object in the $dF=\cos b\; dl\;db$ infinitesimal solid angle and in the $(x_1, x_1+dx_1, ..., x_n,x_n+dx_n)$ interval, one must have Here $0\leq l \leq 360^o,\; -90^o \leq b \leq 90^o$ give the celestial positions in Galactical coordinates, $x_n$ $n \geq 1$ ) measure the physical properties (peak fluxes, fluences, durations, etc...) of GRBs and $g$ is their probability density." + One may assume the fulfihuent of this equation for CRBs., One may assume the fulfilment of this equation for GRBs. + Tn the case of spatial isotropy. assunüug that the detection probability docs uot depeud on the celestial direction. oue has: (5)=L/Cli).," In the case of spatial isotropy, assuming that the detection probability does not depend on the celestial direction, one has: $\omega(l,b)=1/(4\pi) $ ." + In general case one may decompose the function w(b./) into the spherical harmonics.," In general case one may decompose the function $\omega(b,l)$ into the spherical harmonics." + One obtains: first term on the rielit-hand side is the monopole term. the following three ones are the dipole terms. the following five ones are the quadiupole terms.," One obtains: The first term on the right-hand side is the monopole term, the following three ones are the dipole terms, the following five ones are the quadrupole terms." + Since w is constant for isotropic istribution. on the rieht-haud side any terms. except for wy. should be ideutically zeros.," Since $\omega$ is constant for isotropic distribution, on the right-hand side any terms, except for $\omega_0$, should be identically zeros." + To tect this livpotlesis oue lias to compute the values of the corresponding spherical harmouic at the celestial positions of the observed GRBs and apply. e. the Student test in order to see that the iuezu of the computed values sienificantly differs from zero.," To test this hypothesis one has to compute the values of the corresponding spherical harmonic at the celestial positions of the observed GRBs and apply, e.g., the Student test in order to see that the mean of the computed values significantly differs from zero." + A further trivial consequence of the isotropy is the expected equal παν of bursts iu celestial regions of cual areas., A further trivial consequence of the isotropy is the expected equal number of bursts in celestial regions of equal areas. + For example. oue may divide the celestial sphere into two equal areas. e.g.. taking those regions in which the sien of a given harmonic iseither positive," For example, one may divide the celestial sphere into two equal areas, e.g., taking those regions in which the sign of a given harmonic iseither positive" +The low mass X-ray binary EXO —248 was discovered with Hakuebo in August 1980 (Alakishima οἱ 11981).,The low mass X-ray binary EXO $-$ 248 was discovered with Hakucho in August 1980 (Makishima et 1981). + The source showed Type-I X-ray bursts. with intervals as short as 8 min (Inoue et 149834).," The source showed Type-I X-ray bursts, with intervals as short as 8 min (Inoue et 1984)." + It was again detected in 2000 during a RATE/PCA scan of the galactic bulge as a transient X-ray burster (Alarkwardt Swank 2000)., It was again detected in 2000 during a RXTE/PCA scan of the galactic bulge as a transient X-ray burster (Markwardt Swank 2000). + EXO 1745-248 was also observed by (he Chandra X-ray Observatory in 2000 ancl 2003., EXO $-$ 248 was also observed by the Chandra X-ray Observatory in 2000 and 2003. +" ILeimke et ((2003) used the Chandra and RATE observations to suggest that the source is an ultracompact binary and also identified a possible infrared counterpart in the IIubble Space Telescope (IIST) images of (he cluster,", Heinke et (2003) used the Chandra and RXTE observations to suggest that the source is an ultracompact binary and also identified a possible infrared counterpart in the Hubble Space Telescope (HST) images of the cluster. + No burst oscillations have been reported [rom this source (Galloway et 22003)., No burst oscillations have been reported from this source (Galloway et 2008). + Terzan 5 is one of the most metal rich globular cluster in the galaxy. with a metallicity close (ο solar (Origlia et 22004).," Terzan 5 is one of the most metal rich globular cluster in the galaxy, with a metallicity close to solar (Origlia et 2004)." + Recently. Ortolani et ((2007) revisited the distance measurements to Terzan 5 using HST/NICMOS data.," Recently, Ortolani et (2007) revisited the distance measurements to Terzan 5 using HST/NICMOS data." + Using NICAIOS instrumental magnitudes and two separate reddening laws (Schlegel et al., Using NICMOS instrumental magnitudes and two separate reddening laws (Schlegel et al. + 1998: Lee et 22001) to obtain the infrared extinction slope in (he instrumental bands. they measured a distance of 6.3 kpe to Chis cluster.," 1998; Lee et 2001) to obtain the infrared extinction slope in the instrumental bands, they measured a distance of 6.3 kpc to this cluster." + The (wo main sources of error in (his measurement are related to uncertainties in the color and magnitude measurements of the IID of the cluster. as well as to metallicity uncertainties. while the slope of the reddening law introduces a much smaller error.," The two main sources of error in this measurement are related to uncertainties in the color and magnitude measurements of the HB of the cluster, as well as to metallicity uncertainties, while the slope of the reddening law introduces a much smaller error." + The combined error of 0.2 mag corresponds to a distance uncertainty of aboutLOY... which we will adopt here.," The combined error of 0.2 mag corresponds to a distance uncertainty of about, which we will adopt here." + Note that Ortolani et ((2007) also used (wo calibrations for the conversion of the NICMOS to JI. magnitudes. which resulted in different values for the distance.," Note that Ortolani et (2007) also used two calibrations for the conversion of the NICMOS to JHK magnitudes, which resulted in different values for the distance." + Due to the significant width and the large displacement of the NICMOS F110W filter compared to the J filter. the transformations between these bands are color dependent aid hence. suller from svstematic uncertainties that ave difficult to quantify.," Due to the significant width and the large displacement of the NICMOS F110W filter compared to the ground-based J filter, the transformations between these bands are color dependent and hence, suffer from systematic uncertainties that are difficult to quantify." + For this reason. we will only. use the distance measurement obtained from NICMOS instrumental magnitudes.," For this reason, we will only use the distance measurement obtained from NICMOS instrumental magnitudes." + In (his paper. we combine the distance measurement to Terzan 5 with (he observations of radius expansion bursts obtained by RATE to determine (he mass aud the radius of ihe neutron star in EXO 1745—243.," In this paper, we combine the distance measurement to Terzan 5 with the observations of radius expansion bursts obtained by RXTE to determine the mass and the radius of the neutron star in EXO $-$ 248." + In Section 2. we analvze the Eddington limited bursts from (his source.," In Section 2, we analyze the Eddington limited bursts from this source." + In Section 3. we use (hese observations to determine the mass and radius ol the neutron star ancl describe the formal method for assessing the uncertainties in the nmeasurenienis using (his technique.," In Section 3, we use these observations to determine the mass and radius of the neutron star and describe the formal method for assessing the uncertainties in the measurements using this technique." + In Section 4. we discuss our results and compare them to several equations of state for neutron star matter.," In Section 4, we discuss our results and compare them to several equations of state for neutron star matter." + EXO 1745-248 has been observed with RATE for 148 ks. during which two Tyvpe-I bursts were discovered. with clear evidence for photospheric radius expansion (Galloway," EXO $-$ 248 has been observed with RXTE for 148 ks, during which two Type-I X-ray bursts were discovered, with clear evidence for photospheric radius expansion (Galloway" +"gravitational lens of 11830-211 (Wiklind&Combes, 1996).",gravitational lens of 1830-211 \citep{Wiklind96}. +". The technique presented here allows us to probe the temperature of the CMB at high redshift, providing constraints that are independent from and stronger than those arising from the analysis of C? and C+."," The technique presented here allows us to probe the temperature of the CMB at high redshift, providing constraints that are independent from and stronger than those arising from the analysis of $^0$ and $^+$." + This demonstrates that the rotational excitation of interstellar CO molecules can provide a direct and precise measurement of Tcmp in the early Universe., This demonstrates that the rotational excitation of interstellar CO molecules can provide a direct and precise measurement of $T_{\rm CMB}$ in the early Universe. +" Fitting the measurements from different techniques with the expression Tcmp(Z)=Teex(142)? (Lima 2000)., we get the constraints on 8 summarised in Table 2.."," Fitting the measurements from different techniques with the expression $T_{\rm CMB}(z)=T_{\rm CMB}^0\times(1+z)^{1-\beta}$ \citep{Lima00}, we get the constraints on $\beta$ summarised in Table \ref{beta}." +" We note that combining CO measurements of Tcyp(z) with those obtained from other techniques, improves the precision of the B-measurement by more than a factor of two."," We note that combining CO measurements of $T_{\rm CMB}(z)$ with those obtained from other techniques, improves the precision of the $\beta$ -measurement by more than a factor of two." +" The measurement presented here, 8=—0.007+0.027, directly supports the adiabatic evolution of the CMB radiation temperature (6= 0), expected from the standard hot Big-Bang model."," The measurement presented here, $\beta=-0.007\pm0.027$, directly supports the adiabatic evolution of the CMB radiation temperature $\beta=0$ ), expected from the standard hot Big-Bang model." +" Considering alternative A cosmological models, Jetzeretal.(2010) demonstrated that measuring Tcwg at different redshifts allows one to constrain the effective equation of state of decaying dark energy (p=Wer fp)."," Considering alternative $\Lambda$ cosmological models, \citet{Jetzer10} demonstrated that measuring $T_{\rm CMB}$ at different redshifts allows one to constrain the effective equation of state of decaying dark energy $p=w_{eff} \rho$ )." + Fitting the measurements of Tcmp with their temperature-redshift relation (Eq., Fitting the measurements of $T_{\rm CMB}$ with their temperature-redshift relation (Eq. +" 22 in 2010)), taking Q,,=0.275+0.015 (Komatsuetal., and fixing y to the canonical value (4/3), we get Werf=—0.996+0.025 which is a tighter constraint compared to those previously derived from other methods (e.g.Kowalskietal.,2008;Riessetal.,2009;KesslerJullo 2010).."," 22 in \citealt{Jetzer10}) ), taking $\Omega_m=0.275\pm0.015$ \citep{Komatsu10} and fixing $\gamma$ to the canonical value (4/3), we get $w_{eff}=-0.996\pm0.025$ which is a tighter constraint compared to those previously derived from other methods \citep[e.g.][]{Kowalski08,Riess09,Kessler09,Jullo10}." +" Finally, large and deep QSO surveys such as SDSS III should provide more lines of sight along which CO can be detected while high-resolution spectrographs on future extremely large telescopes will allow for full de-blending of the CO lines in different rotational levels, yielding more accurate measurements."," Finally, large and deep QSO surveys such as SDSS III should provide more lines of sight along which CO can be detected while high-resolution spectrographs on future extremely large telescopes will allow for full de-blending of the CO lines in different rotational levels, yielding more accurate measurements." +Due to the high spatial resolution of the WRI many sources could be detected both iu the outer regions aud iu the optical bar region of the LMC.,Due to the high spatial resolution of the HRI many sources could be detected both in the outer regions and in the optical bar region of the LMC. + In rofknown IIRI sources identified with known objects aud known candidates are plotted ou a erev scale PSPC image (0.1 2tL keV) of the LAIC (οι IIP99b)., In \\ref{known} HRI sources identified with known objects and known candidates are plotted on a grey scale PSPC image (0.1 – 2.4 keV) of the LMC (from HP99b). + The sources are located iu differeut regions of he LMC anc show no spatial preferences. it is uot only backgrouud AGN or foreground stars and candidates which are distributed over the whole LMC region.," The sources are located in different regions of the LMC and show no spatial preferences, it is not only background AGN or foreground stars and candidates which are distributed over the whole LMC region." + There are still more than 250 non-identified »oiut sources which are homogencously distributed in all LMC regious which were covered by ROSAT IIRI »oimtfiues as it is shown in refunidentified.., There are still more than 250 non-identified point sources which are homogeneously distributed in all LMC regions which were covered by ROSAT HRI pointings as it is shown in \\ref{unidentified}. + Ta contrast. ia PSPC observations not many additional sources could be detected in the regions with strong diffuse enussion. because the lower spatial resolution hindered in distinguishing between exteuded alc point like euunssion (IIP99)).," In contrast, in PSPC observations not many additional sources could be detected in the regions with strong diffuse emission, because the lower spatial resolution hindered in distinguishing between extended and point like emission (HP99b)." + The IIRI allows to study the extent of the sources to scales of arcseconds., The HRI allows to study the extent of the sources to scales of arcseconds. + Therefore SNR candidates could be found not only in regions without surrounding diffuse cnussion., Therefore SNR candidates could be found not only in regions without surrounding diffuse emission. + Four out of five newly suggested SNR candidates are located in regions with diffuse emission between 30 Dor aud LAIC X-1 (sce rofunideutified))., Four out of five newly suggested SNR candidates are located in regions with diffuse emission between 30 Dor and LMC X-1 (see \\ref{unidentified}) ). + Within aud around the optical bar region several new stellar sources and candidates for N-ray binary or ACN were found., Within and around the optical bar region several new stellar sources and candidates for X-ray binary or AGN were found. + The analvsis of all 513 ROSAT TRI pointed observations performed between 1990 and 1998 with exposure times hieher than 50 sec is presented., The analysis of all 543 ROSAT HRI pointed observations performed between 1990 and 1998 with exposure times higher than 50 sec is presented. + Using a maxiuuuu Helibood. algorithim the source detection resulted in a catalogue of 397 sources which was cross-correlated with the SIMBAD data base aud the TYCIIO catalogue., Using a maximum likelihood algorithm the source detection resulted in a catalogue of 397 sources which was cross-correlated with the SIMBAD data base and the TYCHO catalogue. + Further A-ray properties could be obtained for ORI sources contained in the PSPC catalogue of IIP99b., Further X-ray properties could be obtained for HRI sources contained in the PSPC catalogue of HP99b. + The high spatial resolution of the IIRI enabled the identification of 91 ITRI sources with well known objects sed on the positional coincidence aud considering their extent and larducss ratios., The high spatial resolution of the HRI enabled the identification of 94 HRI sources with well known objects based on the positional coincidence and considering their extent and hardness ratios. + The coordinates of most of he identified sources could be inuproved to more accurate oositious and allowed the positional correction of other IIRI sources., The coordinates of most of the identified sources could be improved to more accurate positions and allowed the positional correction of other HRI sources. + Thus for 251 sources the svstematic error or their coordinates could be reduced to values smaller han wwhich ds the standard svstematic error of ROSAT observations., Thus for 254 sources the systematic error for their coordinates could be reduced to values smaller than which is the standard systematic error of ROSAT observations. +" For different source classes like SSS. N-rayv inary. SNR. Galactic stars. and backeround ACN classification criteria could be derived from the extent and bharduess ratios of the identified ποιαος,"," For different source classes like SSS, X-ray binary, SNR, Galactic stars, and background AGN classification criteria could be derived from the extent and hardness ratios of the identified sources." + We looked for flux variability of the SOUECOS and for likely optical counterparts., We looked for flux variability of the sources and for likely optical counterparts. + Five uewly detected ΠΕ sources were classified as candidates for SNRs because of thei extent. two IIRI sources which were identified with an LMC ο aud a D star as IIMXND candidates.," Five newly detected HRI sources were classified as candidates for SNRs because of their extent, two HRI sources which were identified with an LMC O and a B star as HMXB candidates." + Eleven sources with probable bright optical counterpart and snalb X-ray to optical flux ratio are classified as stellar sources., Eleven sources with probable bright optical counterpart and small X-ray to optical flux ratio are classified as stellar sources. + Three sources with hard and/or absorbed N-ray spectrum indicated by the PSPC harcuess ratios are likely candidates for N-rav binaries or ACN., Three sources with hard and/or absorbed X-ray spectrum indicated by the PSPC hardness ratios are likely candidates for X-ray binaries or AGN. + Two of tle hard N-rav sources show flux variability aud for each of these an optical counterpart was found., Two of the hard X-ray sources show flux variability and for each of these an optical counterpart was found. + With the help of IIRI observations niuiv new X- ποιαος WOYOC ound., With the help of HRI observations many new X-ray sources were found. + Further follow-up observations ii N-rayv. optical. or radio wavelengths with spectral information are needed to characterize these sources in more detail.," Further follow-up observations in X-ray, optical, or radio wavelengths with spectral information are needed to characterize these sources in more detail." + The ROSAT project is supported by the German Bunedesministerium ftir Bildune und Forschung (BAIBF) and the Alax-Planek-Gesellschalt., The ROSAT project is supported by the German Bundesministerium fürr Bildung und Forschung (BMBF) and the Max-Planck-Gesellschaft. +" ""his research. has been carried out by making extensive use of the SIAIBAD cata base operated at CDS. Strasbourg. France."," This research has been carried out by making extensive use of the SIMBAD data base operated at CDS, Strasbourg, France." +predicted that the fast-moce wave ahead of the “EIT wave” was jiidssed by SOHO/EIT due to its low cadence of 15 miu. and would be observed by imaging telescopes with a higher cadeuce.,"predicted that the fast-mode wave ahead of the “EIT wave"" was missed by /EIT due to its low cadence of $\sim 15$ min, and would be observed by imaging telescopes with a higher cadence." + However. after the lauuch of theSTEREO mission. the EUVI instrument with a high cadence of 2.5 min still did not catch the [ast-inode wave2009).," However, after the launch of the mission, the EUVI instrument with a high cadence of 2.5 min still did not catch the fast-mode wave." +". To check the eligibility of STEREO/EUVI in detecting the possible fasi-mocde wave aliead of the “EIT wave"". we degrade the temporal resolution of the topVY panel of Figure 2 [rom 12 s to 2.5 uin. aud re-plot it in Figure L."," To check the eligibility of /EUVI in detecting the possible fast-mode wave ahead of the “EIT wave"", we degrade the temporal resolution of the top panel of Figure \ref{fig2} from 12 s to 2.5 min, and re-plot it in Figure \ref{fig4}." + Ht is seen that the wave pattern becomes messy. αμα we canuot distinguish: a faster wave from the “EIT wave’.," It is seen that the wave pattern becomes messy, and we cannot distinguish a faster wave from the “EIT wave""." +" This meaus that. for au “EIT wave” event like tliat ou 2010 July 27. the 2.5-min cadence of EUV imaging observations even with a spatial resolution of 1"".2 cannot detect the fast-mocde wave (or coronal Moreton wave) ahead of the “EIT wave”."," This means that, for an “EIT wave"" event like that on 2010 July 27, the 2.5-min cadence of EUV imaging observations even with a spatial resolution of $1\arcsec .2$ cannot detect the fast-mode wave (or coronal Moreton wave) ahead of the “EIT wave""." +" We change the cadence and find that only. if the observational cadence is shorter than 70 s can the fast-mocde wave be distinguished (rom the “EIT wave"" for the 2010 July 27 event."," We change the cadence and find that only if the observational cadence is shorter than 70 s can the fast-mode wave be distinguished from the “EIT wave"" for the 2010 July 27 event." + With STERFO/EULVLI observations. did show a weak fast-mode wave component besices the ordinary “EIT wave”.," With /EUVI observations, did show a weak fast-mode wave component besides the ordinary “EIT wave""." +" They found that tle fast-inocde wave was coupled with the “EIT wave” when the CME was expaucineg laterally. aud the two waves ultimately decoupled when the “EIT wave"" [οί became stationary."," They found that the fast-mode wave was coupled with the “EIT wave"" when the CME was expanding laterally, and the two waves ultimately decoupled when the “EIT wave"" front became stationary." + Such a result may result from the low cadence of the STEREO/EUVI data. as people can get the same impression from Figure {..," Such a result may result from the low cadence of the /EUVI data, as people can get the same impression from Figure \ref{fig4}." + With a high cadence ol 12 s. Figure 2 clearly reveals that the [ast-mode wave was already distinct from the “EIT wave? [ront before the “EIT wave” stopped.," With a high cadence of 12 s, Figure \ref{fig2} clearly reveals that the fast-mode wave was already distinct from the “EIT wave"" front before the “EIT wave"" stopped." + ‘To sumunarize. we analyzed the “EIT wave” event on 2010 July 27 with the SDO/ALA data.," To summarize, we analyzed the “EIT wave"" event on 2010 July 27 with the /AIA data." + It is seen that even for a tiny flare. the high-resolution observations of the SDO/ALA telescope still revealed inany wave patterns.," It is seen that even for a tiny flare, the high-resolution observations of the /AIA telescope still revealed many wave patterns." + Iu this Letter. we fouud that a fast-inode magietoacoustic wave was propagating ahead of the “EIT wave”.," In this Letter, we found that a fast-mode magnetoacoustic wave was propagating ahead of the “EIT wave""." + As predicted by the lieldline stretching model of2005).. the [ast-inode wave had a speed ~3 times higher than that of the “EIT wave’.," As predicted by the fieldline stretching model of, the fast-mode wave had a speed $\sim 3$ times higher than that of the “EIT wave""." + The fast-mmocde wave kept propagating alter the “EIT wave” stopped at the magnetic separatrix.," The fast-mode wave kept propagating after the “EIT wave"" stopped at the magnetic separatrix." + Our results are strongly suggestive ofthat “EIT waves” are not fast-inode magnetoacoustic waves. aud can be well explained by our fiekdline stretching moclel.," Our results are strongly suggestive of that “EIT waves"" are not fast-mode magnetoacoustic waves, and can be well explained by our fieldline stretching model." + The authors thank A. Title aud N. Nitta for discussions and the ALA team for providing the calibrated data., The authors thank A. Title and N. Nitta for discussions and the AIA team for providing the calibrated data. +SOHO is a project of international cooperation between ESA aud NASA., is a project of international cooperation between ESA and NASA. + This research is supported by the Chinese foundations 2011CB&811102 and NSFC (10103003. 10933003. aud 10673001).," This research is supported by the Chinese foundations 2011CB811402 and NSFC (10403003, 10933003, and 10673004)." +This paper is organized as follows.,This paper is organized as follows. + In ‘efsec:rey we review the derivation and findings ii previous works as the starting point of this investigation., In \\ref{sec:rev} we review the derivation and findings in previous works as the starting point of this investigation. + Iu ‘efsec:lin we present the nature of linear wake as revealed in the 'e[secanor)). the density enhancement 'efseciden)). aud the velocity distribution 'e[sec:vel)). provided that the weak gravitatioual influence is thoroughly. described iu the linear »erturbation analysis.," In \\ref{sec:lin} we present the nature of linear wake as revealed in the \\ref{sec:mor}) ), the density enhancement \\ref{sec:den}) ), and the velocity distribution \\ref{sec:vel}) ), provided that the weak gravitational influence is thoroughly described in the linear perturbation analysis." + Du ‘efsec:non.. based ou the linear wake properties. we suggest a new explanation for nonlinear effects uaulfestecd ou the wake when the perturbation iu cdiscoutinuity is saturated.," In \\ref{sec:non}, based on the linear wake properties, we suggest a new explanation for nonlinear effects manifested on the wake when the perturbation in discontinuity is saturated." + Iu we suumumnarize the newly [found properties of the gravitationally induced wake of a circularly orbiting object ini a static uniform gaseous medium. aud briefly cousider applications to a lew astronomical objects.," In \\ref{sec:sum} we summarize the newly found properties of the gravitationally induced wake of a circularly orbiting object in a static uniform gaseous medium, and briefly consider applications to a few astronomical objects." +" Starting [rom the basic equations of hydrodynamics with au external time-dependent gravitational potential ®, but excluding sel(-gravity of the gaseous medium. one can obtain a linearized three dimensional wave equation for the density enhancement a=op/p under the assumption of a simnall perturbation (a« 1). Here. e=(5p/p)!? is the sound speed of unperturbed gas with deusity p. thermal pressure p. aud adiabatic iudex + in general."," Starting from the basic equations of hydrodynamics with an external time-dependent gravitational potential $\Phi_p$ but excluding self-gravity of the gaseous medium, one can obtain a linearized three dimensional wave equation for the density enhancement $\alpha=\delta\rho/\rho$ under the assumption of a small perturbation $\alpha\ll1$ ), Here, $\cs=(\gamma p/\rho)^{1/2}$ is the sound speed of unperturbed gas with density $\rho$, thermal pressure $p$, and adiabatic index $\gamma$ in general." + Ostriker(1999) applied it to the situation that the perturbiug object is in rectilinear motion through au intinite homogeneous gaseous medium. utiliziug the retarced Green's functiou technique (Jacksou1975). based on the Fourier trausforim &Ivegel 1990).," \citet{ost99} applied it to the situation that the perturbing object is in rectilinear motion through an infinite homogeneous gaseous medium, utilizing the retarded Green's function technique \citep{jac75} based on the Fourier transform \citep[see also][]{jus90}." +. A purely analyticsolution for the deusity enbancement was derived. which can be expressed as in the axisymunetric coordinates (4|. d.) with the origin at the perturbing object. d| along the tail (i.e.. in the opposite direction of the orbital motion) and d. iu the orthogonal clirectiou.," A purely analyticsolution for the density enhancement was derived, which can be expressed as in the axisymmetric coordinates $d_\|$, $d_\bot$ ) with the origin at the perturbing object, $d_\|$ along the tail (i.e., in the opposite direction of the orbital motion) and $d_\bot$ in the orthogonal direction." + Here. we define the most important. parameters in this paper. rg and Mj. as the Bondi accretion radius aud the orbital Mach uumnber of the object. respectively.," Here, we define the most important parameters in this paper, $r_B$ and $\mach$ , as the Bondi accretion radius and the orbital Mach number of the object, respectively." + In the sumauiatioun of the Heaviside step, In the summation of the Heaviside step +"Thus, we observe that when D=2, viz.,","Thus, we observe that when $D=2$, viz.," +" the total dimensions, N=D-424 then only the result does agree with the observational data and D>2, i.e., N> 4is not compatible with solar system (see Table 3)."," the total dimensions, $N=D+2=4$ then only the result does agree with the observational data and $D>2$, i.e., $N>4$ is not compatible with solar system (see Table 3)." +" It can be noted, from the Figs."," It can be noted, from the Figs." +" 4 - 8, that all the trajectories of the light rays almost same for all D due to the factor cos¢/Ro which is the dominating one."," 4 - 8, that all the trajectories of the light rays almost same for all $D$ due to the factor $cos\phi/R_0$ which is the dominating one." + The trajectory of light will show different graph for large D., The trajectory of light will show different graph for large $D$. +" Historically, it is important to note that on the basis of his ‘corpuscular’ theory including laws of mechanics and gravitation, Newton(1704) raised the pertinent issue that “Do not Bodies act upon Light at a distance, and by their action bend its Rays, and is not this action strongest at the least distance?”"," Historically, it is important to note that on the basis of his `corpuscular' theory including laws of mechanics and gravitation, \citet{Newton1704} raised the pertinent issue that “Do not Bodies act upon Light at a distance, and by their action bend its Rays, and is not this action strongest at the least distance?”" + He calculated the amount of bending of light rays for Sun as 2m/ro., He calculated the amount of bending of light rays for Sun as $2m/r_0$. +" For m=1475 meters, in the gravitational units, and ro=6.95x105 meters this equals 0.875 arcsec."," For $m=1475$ meters, in the gravitational units, and $r_0=6.95 \times 10^8$ meters this equals $0.875$ arcsec." +" However, though prediction of bending by Einstein(1911) was at first identical to that of Newton but later on he (1915) got the angular deflection of light as the size he predicted earlier which caused due to the general relativistic effect of the curved space-time."," However, though prediction of bending by \citet{Einstein1911} was at first identical to that of Newton but later on he (1915) got the angular deflection of light as the size he predicted earlier which caused due to the general relativistic effect of the curved space-time." + In 1919 scientific expeditions performed at Sobral in South America and Principe in West Africa by the leadership of Eddington., In 1919 scientific expeditions performed at Sobral in South America and Principe in West Africa by the leadership of Eddington. +" The reported observational results of angular deflections due to the solar eclipse were 1.98+0.16 and 1.61+0.40 arcsec, respectively."," The reported observational results of angular deflections due to the solar eclipse were $1.98 \pm 0.16$ and $1.61 \pm 0.40$ arcsec, respectively." + The mean of these two data was taken as confirmation of Einstein's predictionof 1.75 arcsec (see Table 2)., The mean of these two data was taken as confirmation of Einstein's predictionof $1.75$ arcsec (see Table 2). +" However, the experiments of Eddington and his co-workers had only 30 percent accuracy where the results were scattered between one half and twice the Einstein value (Will2001)."," However, the experiments of Eddington and his co-workers had only $30$ percent accuracy where the results were scattered between one half and twice the Einstein value \citep{Will2001}." +". An analysis of large amount of Very Long Baseline Interferometry (VLBI) observations has shown that the ratio of the actual observed deflections to the deflections predicted by general relativity is very close to unity (e.g., 0.9996+0.0017 (Lebachetal.1995),, 0.99994+0.00031 (Eubanksetal.1999),, 0.99992+0.00023 (Shapiro,Davis,Lebach&Gregory 2004)))."," An analysis of large amount of Very Long Baseline Interferometry (VLBI) observations has shown that the ratio of the actual observed deflections to the deflections predicted by general relativity is very close to unity (e.g., $0.9996 \pm 0.0017$ \citep{Lebach1995}, $0.99994 \pm 0.00031$ \citep{Eubanks1999}, $0.99992 \pm 0.00023$ \citep{Shapiro2004}) )." + GR predicted that the frequency of the light would be affected due to gravitational field and is observable as a shift of spectral lines towards the red end of the spectrum., GR predicted that the frequency of the light would be affected due to gravitational field and is observable as a shift of spectral lines towards the red end of the spectrum. +" Pound-Rebka-Snider (Pound&Rebka1959,1960;PoundSnider1964) confirmed this effect through their precision test, sometimes known as Harvard Tower Experiment."," Pound-Rebka-Snider \citep{Pound1959,Pound1960,Pound1964} confirmed this effect through their precision test, sometimes known as Harvard Tower Experiment." + In their first test they measured the redshift experienced by a 14.4 Kev γ-ταγς from the decay of Fe®” for a height of 22.5 meter tower and found z=2.57+0.26x 10:35.," In their first test they measured the redshift experienced by a 14.4 Kev $\gamma$ -rays from the decay of $Fe^{57}$ for a height of 22.5 meter tower and found $z=2.57 \pm +0.26 \times 10^{-15}$ ." +" Now, as usual, gravitational redshift for the solar system can be defined as"," Now, as usual, gravitational redshift for the solar system can be defined as" +to examine high-z systems.,to examine $z$ systems. +" The VIMOS IFU (Arribasetal.2008) has been used for a survey of Ultraluminous Infrared galaxies, and the PINGS survey of nearby disk galaxies (Rosales-Ortegaetal.2010)."," The VIMOS IFU \citep{Arribas08} has been used for a survey of Ultraluminous Infrared galaxies, and the PINGS survey of nearby disk galaxies \citep{Rosales10}." +". Finally, the SPIRAL instrument (Sharp&Bland-Hawthorn2010) has been employed to look at galactic winds."," Finally, the SPIRAL instrument \citep{Sharp10} has been employed to look at galactic winds." +" In this paper, we will describe data obtained of the superwind galaxy NGC 839 using the Wide Field Spectrograph (WiFeS)."," In this paper, we will describe data obtained of the superwind galaxy NGC 839 using the Wide Field Spectrograph (WiFeS)." +" This instrument is described in detail in Dopitaetal.(2007,2010)."," This instrument is described in detail in \citet{Dopita07,Dopita10}." +". NGC 839 is a nearly edge-on disk galaxy (I=67°,, ΡΑ.- 350°)) in a Hickson Compact Group (HCG 16): a dense, interacting group of seven spirals, six of which are actively star forming (Rubinetal.1991;Ribeiro1996)."," NGC 839 is a nearly edge-on disk galaxy $I=67$, $=350$ ) in a Hickson Compact Group (HCG 16): a dense, interacting group of seven spirals, six of which are actively star forming \citep{Rubin91,Ribeiro96}." +". NGC 839 may well be a recent addition to the group, more kinematically disturbed and showing signs of an ongoing or recent interaction (Rubinetal.1991;MendesdeOliveira1998;deCarvalho&Coz"," NGC 839 may well be a recent addition to the group, more kinematically disturbed and showing signs of an ongoing or recent interaction \citep{Rubin91,Mendes98,deCarvalho99}." +"iol 1999).. Belsoleetal.(2003) have detected diffuse, hot X-ray emitting gas encompassing the whole group, evidence that it forms a bound group even though it has no bright early-type galaxies."," \citet{Belsole03} have detected diffuse, hot X-ray emitting gas encompassing the whole group, evidence that it forms a bound group even though it has no bright early-type galaxies." + observations of NGC 839 indicate both ongoing star Multiwavelengthformation and LINER-like line ratios., Multiwavelength observations of NGC 839 indicate both ongoing star formation and LINER-like line ratios. +" Ribeiroetal.(1996) used the ratio to classify NGC 839 as a starburst, though their measured values actually fall in the composite starburst/AGNs region when the (2006) scheme is applied."," \citet{Ribeiro96} used the ratio to classify NGC 839 as a starburst, though their measured values actually fall in the composite starburst/AGNs region when the \citet{Kewley06} scheme is applied." +" In addition, deCarvalho&Co-ziol(1999) have employed the observed and ratios to classify NGC 839 as a LINER Seyfert double nucleus."," In addition, \citet{deCarvalho99} have employed the observed and ratios to classify NGC 839 as a LINER + Seyfert double nucleus." +" X-ray spectra of the galaxy indicate+ the presence of an active starburst coupled with slightly higher than solar metallicities and may indicate the presence of a low luminosity, obscured AGN (Turneretal."," X-ray spectra of the galaxy indicate the presence of an active starburst coupled with slightly higher than solar metallicities and may indicate the presence of a low luminosity, obscured AGN \citep{Turner01}." +2001).. González-Martínetal.(2006) however find no evidence for an unresolved point source in hard X-ray images and classify NGC 839 as starburst galaxy using X-ray morphology., \citet{GonzalezMartin06} however find no evidence for an unresolved point source in hard X-ray images and classify NGC 839 as a starburst galaxy using X-ray morphology. +" At a NGC 839 is classified as a Luminous Infrared IR-wavelengths,Galaxy (LIRG) with clearlyLrg~101!L5 (Armusetal.2009)."," At IR-wavelengths, NGC 839 is clearly classified as a Luminous Infrared Galaxy (LIRG) with $L_{IR}\sim10^{11}L_{\odot}$ \citep{Armus09}." +". This luminosity derives from a nuclear starburst, which is probably driving an M 82-like galactic wind, evidenced by the very extended polar funnels of emission seen by the Survey for Ionization in Neutral Gas Galaxies (SINGG) images (Meureretal.(2006);; see Figure 1))."," This luminosity derives from a nuclear starburst, which is probably driving an M 82-like galactic wind, evidenced by the very extended polar funnels of emission seen by the Survey for Ionization in Neutral Gas Galaxies (SINGG) images \citet{Meurer06}; see Figure \ref{fig1}) )." + The observations presented in this paper are the first results from the WiFeS GOALS survey., The observations presented in this paper are the first results from the WiFeS GOALS survey. + The WiFeS GOALS survey is a sub-sample drawn from the larger Great Observatory LIRG Survey (GOALS) , The WiFeS GOALS survey is a sub-sample drawn from the larger Great Observatory All-Sky LIRG Survey (GOALS) sample. +We discuss the All-Skyobservations and data reduction in sample.Section 2., We discuss the observations and data reduction in Section \ref{observations}. +". In Section 3, we present the results of our observations and analysis and present spectra, rotation curves, and line ratio maps."," In Section \ref{results}, we present the results of our observations and analysis and present spectra, rotation curves, and line ratio maps." +" In Section 4,, we compare new photoionization models and low-velocity shock models to the observations, and compare the derived properties of NGC 839 to the prototypical superwind galaxy M82."," In Section \ref{analysis}, we compare new photoionization models and low-velocity shock models to the observations, and compare the derived properties of NGC 839 to the prototypical superwind galaxy M82." + We conclude that the balance of evidence is in favor of the superwind of NGC 839 being shock-excited., We conclude that the balance of evidence is in favor of the superwind of NGC 839 being shock-excited. +" Finally, in Section 5,, we discuss the relationship of NGC 839 to ""composite "" (or transition) galaxies and suggest extended "" or LINER emission may be fueled shock emission."," Finally, in Section \ref{conclusions}, we discuss the relationship of NGC 839 to “composite ” (or transition) galaxies and suggest extended “composite "" or LINER emission may be fueled by shock emission." +" ""compositeWe also suggest that NGC 839 is one bypossible ""missing link"" to E+A galaxies and suggest an evolutionary scenario to explain how this class of objects might have arisen.", We also suggest that NGC 839 is one possible “missing link” to E+A galaxies and suggest an evolutionary scenario to explain how this class of objects might have arisen. +" this we the cosmological parameters Throughout 9270.5 km paper, 1Mpc!, QV adopt20.73, and (420.27, based on the 5 year WMAP results (Hinshawetal.2009)."," Throughout this paper, we adopt the cosmological parameters $H_{0}$ =70.5 km $^{-1}$ $^{-1}$ , $\Omega_{\mathrm{V}}$ =0.73, and $\Omega_{\mathrm{M}}$ =0.27, based on the 5 year WMAP results \citep{Hinshaw09}." +". With these parameters, and taking into effect both the Virgo and Shapley infall, the adopted distance to the HCG 16 is 55+1 Mpc (NASA Extragalactic Database, NED)."," With these parameters, and taking into effect both the Virgo and Shapley infall, the adopted distance to the HCG 16 is $55\pm1$ Mpc (NASA Extragalactic Database, NED)." + This gives a spatial scale for NGC 839 of 260 pc arcsec”., This gives a spatial scale for NGC 839 of 260 pc $^{-1}$. + Our data of NGC 839 were taken using the WiFeS at the Mount Stromlo and Siding Spring Observatory 2.3 m telescope., Our data of NGC 839 were taken using the WiFeS at the Mount Stromlo and Siding Spring Observatory 2.3 m telescope. +" WiFeS is a new, dual beam, image-slicing IFU described in detail by Dopitaetal.(2007,2010)."," WiFeS is a new, dual beam, image-slicing IFU described in detail by \citet{Dopita07,Dopita10}." +. The instrument is mounted in a stationary position at a Nasmyth focus to provide excellent stability., The instrument is mounted in a stationary position at a Nasmyth focus to provide excellent stability. +" The IFU field consists of 25x1” wide slitlets, each of which is long."," The IFU field consists of $25 \times 1$ wide slitlets, each of which is long." +" The spatial pixel is 0"".5 along the slitlet axis and 1’’.0 in the spectral direction.", The spatial pixel is $0''.5$ along the slitlet axis and $1''.0$ in the spectral direction. +" In the blue, the spectra cover the range of 3700-5700 A,, at a spectral resolution of R~3000 (zz100 km s—!)."," In the blue, the spectra cover the range of 3700-5700 , at a spectral resolution of $R\sim3000$ $\approx100$ km $^{-1}$ )." +" In the red, we cover 5700-7000 aat a resolution of R~7000 (z45 km 51)."," In the red, we cover 5700-7000 at a resolution of $R\sim7000$ $\approx45$ km $^{-1}$ )." +" Thus, the data have sufficient spectral resolution in the red to allow detailed dynamical studies, while the total wavelength coverage is sufficient to support excitation and chemical abundance analyses."," Thus, the data have sufficient spectral resolution in the red to allow detailed dynamical studies, while the total wavelength coverage is sufficient to support excitation and chemical abundance analyses." +" We observed NGC 839 on 2009 August 18, about 4 months after the instrument had been commissioned."," We observed NGC 839 on 2009 August 18, about 4 months after the instrument had been commissioned." +" Two pointings were made at a position angle(P.A.) of (see Figure 1)), so that the slitlets were aligned with the minor axis of NGC 839."," Two pointings were made at a position angle(P.A.) of (see Figure \ref{fig1}) ), so that the slitlets were aligned with the minor axis of NGC 839." + This allows us to best probe the previously detected extended emission which occurs in two funnels both above and below the disk, This allows us to best probe the previously detected extended emission which occurs in two funnels both above and below the disk +controlled by several factors: the point at which the burning laver ignites. the emission profile of any burning point alter ignition (set by the nuclear heating and cooling time scales): and the speed at which the burning front propagates across re stellar. surface.,"controlled by several factors: the point at which the burning layer ignites, the emission profile of any burning point after ignition (set by the nuclear heating and cooling time scales); and the speed at which the burning front propagates across the stellar surface." + Ignition is likely to occur at a point uxl spread. rather than occurring across the whole star Lgimultanceously. because of the discrepancy between the very gajiort burning time scales and the much longer accretion ime scale (Shara|1982).," Ignition is likely to occur at a point and spread, rather than occurring across the whole star simultaneously, because of the discrepancy between the very short burning time scales and the much longer accretion time scale \citep{SH}." +. Asvmmetric initialization is also nought necessary to explain the detection during the rise X burst oscillations. variations in brightness on the surface M the neutron star that are modulated. by the rapid. stellar Esxn (Strohmaver&Bilelsten2006).," Asymmetric initialization is also thought necessary to explain the detection during the rise of burst oscillations, variations in brightness on the surface of the neutron star that are modulated by the rapid stellar spin \citep{SB}." +. On a realistic neutron star. ignition location is unlikely to be random due to the various factors that break spherical symmetry.," On a realistic neutron star, ignition location is unlikely to be random due to the various factors that break spherical symmetry." + AXccretion [ow may not be spherically symmetric - it mav occur through an equatorial boundary laver (Inogamov&Sunvaev1999) or by channeling onto the magnetic poles (in which case the star may manifest às an A-ray pulsar)., Accretion flow may not be spherically symmetric - it may occur through an equatorial boundary layer \citep{IS} or by channeling onto the magnetic poles (in which case the star may manifest as an X-ray pulsar). + Whether either ofthese issues can allect local ignition conditions or lead to preferred ignition locations is not clear. since estimates suggest that fuel should. spread rapidly across the stellar surface between bursts.," Whether either of these issues can affect local ignition conditions or lead to preferred ignition locations is not clear, since estimates suggest that fuel should spread rapidly across the stellar surface between bursts." + Another [actor that will certainly have an impact is stellar rotation., Another factor that will certainly have an impact is stellar rotation. + Alost of the neutron stars that show Type E X-ray bursts ave thought to be rapidly rotating. which reduces the ellective gravity at the equator.," Most of the neutron stars that show Type I X-ray bursts are thought to be rapidly rotating, which reduces the effective gravity at the equator." + Centrifugal effects. coupled with the deformation of the neutron star due to the rapid rotation. combine to reduce the ellective gravity at. the equator as compared to the poles.," Centrifugal effects, coupled with the deformation of the neutron star due to the rapid rotation, combine to reduce the effective gravity at the equator as compared to the poles." + This results in a local accretion rate that is higher at the equator (Spitkovsky.Levin&Ushomursky 2002)., This results in a local accretion rate that is higher at the equator \citep{SLU}. +. The column depth required for ignition is achieved more rapidly. and ignition should occur preferentially at. this latitude.," The column depth required for ignition is achieved more rapidly, and ignition should occur preferentially at this latitude." + In fact there are accretion rates where olf-equator ignition is still expected., In fact there are accretion rates where off-equator ignition is still expected. +" Cooper&Naravan(2007a) considered the situation at high accretion rates mrmome, where helium burning is on the verge of stability.", \citet{CNa} considered the situation at high accretion rates $\dot{m} \approx \dot{m}_\mathrm{c3}$ where helium burning is on the verge of stability. + Phere will be à range of accretion rates (the more rapid the rotation. the larger this range) where m2mn at the equator but not at other latitudes.," There will be a range of accretion rates (the more rapid the rotation, the larger this range) where $\dot{m} > \dot{m}_\mathrm{c3}$ at the equator but not at other latitudes." + Although not discussed by Cooper&Naravan(2007a).. a similar region of oll-equator ignition is to be expected at rizmq (the transition to stable hydrogen burning).," Although not discussed by \citet{CNa}, a similar region of off-equator ignition is to be expected at $\dot{m} \approx +\dot{m}_\mathrm{c1}$ (the transition to stable hydrogen burning)." + Once ignition has occurred. the nuclear burning processes determine the emission [from a given point.," Once ignition has occurred, the nuclear burning processes determine the emission from a given point." + The burning laver will expand during a convective phase. and there is a delay before radiative processes take over and the light curve starts to rise.," The burning layer will expand during a convective phase, and there is a delay before radiative processes take over and the light curve starts to rise." + Light. curves from a single point (ignoring spreading effects) have been generated. by a number of authors (Taam—1980:Avasli&Joss.1982:2004:Weinberg.Bildsten&Schatz— 2006).," Light curves from a single point (ignoring spreading effects) have been generated by a number of authors \citep{T, AJ, FTWL, TWWL, W, WBS}." +. The shape. time scales and strength of the single point light curve can vary substantially depending on factors such as the burning regime and the composition of the accreted material.," The shape, time scales and strength of the single point light curve can vary substantially depending on factors such as the burning regime and the composition of the accreted material." + There are as vet no simple analytic models for this process that take into account all of the relevant. parameters., There are as yet no simple analytic models for this process that take into account all of the relevant parameters. + At the accretion. rates of relevance. to most. burst sources. the burning front is expected. t0. propagate by deHagration (Ervxell&Woosley|1982b:LlanawaFuji-moto|1984:Bilelsten1995) rather than by detonation (Fryxell&Woosley1982a:Zingaleetal.," At the accretion rates of relevance to most burst sources, the burning front is expected to propagate by deflagration \citep{FW, HF, B95} + rather than by detonation \citep{FWa, Z}." +2001).. In the simplest picture. spreading speed is set by the rate at which heat is transported across the burning front. (hy convective processes).," In the simplest picture, spreading speed is set by the rate at which heat is transported across the burning front (by convective processes)." + Spitkovsky.Levin&Ushomirskv(2002). have since shown that rapid rotation will also play a significan role: interaction between the uplift (vertical expansion) of burning material and a strong Coriolis force can act to slow spreading., \citet{SLU} have since shown that rapid rotation will also play a significant role: interaction between the uplift (vertical expansion) of burning material and a strong Coriolis force can act to slow spreading. + The degree of asymmetry in the spread. of the burning front is also relevant to the detectability of burs oscillations in the rise. if they are caused by a growing ho spot.," The degree of asymmetry in the spread of the burning front is also relevant to the detectability of burst oscillations in the rise, if they are caused by a growing hot spot." +" In this paper we attempt the. first systematic examination of how these various factors interact to allec the shape anc time scale of the rising portion of the ligh ""urve.", In this paper we attempt the first systematic examination of how these various factors interact to affect the shape and time scale of the rising portion of the light curve. + Previous studies in this area have focused on smal samples of bursts such as the rare multi. peaked bursts (Bhattacharyya&Strohmayer.2006a.b).. or bursts from the vecreting millisecond pulsars (Bhattacharvya&StrohmaverGe)...," Previous studies in this area have focused on small samples of bursts such as the rare multi peaked bursts \citep{BSa, BSb}, or bursts from the accreting millisecond pulsars \citep{BSc}." + In this study we adopt a much broader. remit. motivated by the wide variety. of shapes exhibited. hy the bursts of the LAINB αι 1686-536.," In this study we adopt a much broader remit, motivated by the wide variety of shapes exhibited by the bursts of the LMXB 4U 1636-536." + Εις particular source is an excellent candidate. for this twpe of study: there ave over 120 bursts from this source in theErplorer (RXTE) archive. and it lies in a binary with relatively wellconstrainecl properties.," This particular source is an excellent candidate for this type of study: there are over 120 bursts from this source in the (RXTE) archive, and it lies in a binary with relatively well-constrained properties." + By comparing the burst. properties. with the results of parameterized simulations. we show that simple measures of the burst shape can be profound diagnostics of ignition latitude and burning regimo.," By comparing the burst properties with the results of parameterized simulations, we show that simple measures of the burst shape can be profound diagnostics of ignition latitude and burning regime." + The paper is structured. as follows., The paper is structured as follows. + In Section 2. we define simple measures of burst morphology and classify the bursts of 4U 1636-536 accordingly., In Section \ref{obs} we define simple measures of burst morphology and classify the bursts of 4U 1636-536 accordingly. + Section 3. gives details of the parameterized. simulations that we carried. out to ecncrate moclel light curves. and looks at the cllects on shape using the same simple measures.," Section \ref{sims} gives details of the parameterized simulations that we carried out to generate model light curves, and looks at the effects on shape using the same simple measures." + In Section 4. we compare the results of our simulations with the data. ancl consider the implications in terms of ignition point ancl burning regime.," In Section \ref{disc} we compare the results of our simulations with the data, and consider the implications in terms of ignition point and burning regime." + We present a model that can explain our results (subject to the assumptions inherent in our simulations). and extend our analysis to other sources to test its feasibility.," We present a model that can explain our results (subject to the assumptions inherent in our simulations), and extend our analysis to other sources to test its feasibility." + We conclude in Section 5.., We conclude in Section \ref{conc}. + The bursting LAINB 4U. 1636-536 is a persistent atoll source ata distance of zz6 kpe (Gallowayctal.2006). in à 3.8 hour binary orbit with a low mass blue star. VSOI Ara.," The bursting LMXB 4U 1636-536 is a persistent atoll source at a distance of $\approx 6$ kpc \citep{GPMC} in a 3.8 hour binary orbit with a low mass blue star, V801 Ara." + The binary inclination 7 is in the range 36°607 (Casaresetal. 2000)..., The binary inclination $i$ is in the range $36^\circ-60^\circ$ \citep{CA}. + The bursts have been studied: extensively with both EXNOSAT (Lewin.vanParadijs&Taam1993) and INTE (Gallowayctal.2007).., The bursts have been studied extensively with both EXOSAT \citep{LVT} and RXTE \citep{GMCPH}. +. Burst oscillations at 5N] Hz are seen in both normal bursts ancl superbursts. he latter being longer bursts triggered by unstable carbon xirning (Strohmaveretal.1998:Strohmaver&Markwardt 2002).," Burst oscillations at 581 Hz are seen in both normal bursts and superbursts, the latter being longer bursts triggered by unstable carbon burning \citep{SZSWL, SM}." +. We include in our study. all of the bursts covered N w RATE burst catalogue (Gallowayetal.2007)., We include in our study all of the bursts covered by the RXTE burst catalogue \citep{GMCPH}. +. Phe catalogue includes over LOOO bursts observed by the RAPE 'roportional. Counter Array (PCA) from December 30th 995 to October 29th 2005. 123 of which originate from 4U 636-536.," The catalogue includes over 1000 bursts observed by the RXTE Proportional Counter Array (PCA) from December 30th 1995 to October 29th 2005, 123 of which originate from 4U 1636-536." + In order to studs the shape ancl time scales of the bursts! rises we started by constructing light curves from the, In order to study the shape and time scales of the bursts' rises we started by constructing light curves from the +In archival 57/NEPC2. data from several epochs covering the period 19949000. Andersonetal.(2003) found hat the object initially identified bv Sahuctal.(2001) asa microlensing event was 0.5 mag brighter through a lla filter han main-sequence stars of the same magnitude.,"In archival /WFPC2 data from several epochs covering the period 1994–2000, \cite{ack03} found that the object initially identified by \cite{sahu01} as a microlensing event was 0.5 mag brighter through a $\alpha{}$ filter than main-sequence stars of the same magnitude." + It was also a cluster member and coincident with a source., It was also a cluster member and coincident with a source. + This combination of factors led them to identify the object as the inst known CV in the cluster (CV1)., This combination of factors led them to identify the object as the first known CV in the cluster (CV1). + Interestingly. however. he broadband (230R75) and (Voos—£41) colours place he star to the red side of the main sequence. in the region generally associated with detached main-sequence binaries.," Interestingly, however, the broadband $(B_{439}-R_{675})$ and $(V_{606}-I_{814})$ colours place the star to the red side of the main sequence, in the region generally associated with detached main-sequence binaries." + Dv contrast. CVs typically appear bluer than main sequence stars owing to the presence of a hot accretion disc.," By contrast, CVs typically appear bluer than main sequence stars owing to the presence of a hot accretion disc." + As discussed. in Section. ??.. in order to further investigate the broad-band colours of CVI. we analysed archival12ST images from 2006 taken in near-UV. andV filters.," As discussed in Section \ref{sec:hstdata}, in order to further investigate the broad-band colours of CV1, we analysed archival images from 2006 taken in near-UV, and filters." +" In the STNLAG. photometric svstem. we find V3;= for the CW. with colours (Cssil)=0.19€0.12 mag and (nlVos,δρυ=0.2000.25 mag. assuming a foreground reddening of οV)=0.34(with an error of ten per cent) in the direction of M22 (llarris 1996).. ("," In the STMAG photometric system, we find $V_{555}=19.25\pm0.05$ for the CV, with colours $(U_{336}-V_{555})_{0}=0.19\pm0.12$ mag and $(nUV_{255}-U_{336})_{0}=0.20\pm0.25$ mag, assuming a foreground reddening of $E(B-V)=0.34$(with an error of ten per cent) in the direction of M22 \citep{harris96}. (" +We have chosen the SPALAG svstem because it is better calibrated than the svnthetic WEDPC2 svstem at UV wavelengths.),We have chosen the STMAG system because it is better calibrated than the synthetic WFPC2 system at UV wavelengths.) + Converting to the Johnson system. (see Section ??)). our measurements show that at (ου=0.13£0.13 mag CVI does not appear as UV-bright as field CVs in quiescence. which typically have (£7Y) colours in the ranee Olto 0.7 mag (e.g.Bruch&Engel 1994)..," Converting to the Johnson system (see Section \ref{sec:hstdata}) ), our measurements show that at $(U-V)_{0} = +0.13\pm0.13$ mag CV1 does not appear as UV-bright as field CVs in quiescence, which typically have $(U-V)$ colours in the range $-0.1$ to $-0.7$ mag \cite[e.g.][]{bruch94}. ." + This, This +Now. inserting this perturbation in the TPAGPE. Eq. (4)),"Now, inserting this perturbation in the TAGPE, Eq. \ref{quinnperi}) )" + and Eq. (5)), and Eq. \ref{quinnanom}) ) + are recovered., are recovered. + This apparent improvement to the original model of Nobili&Roxbureh(1950) is not so at all as pointed out by Saha&“Tremaine(1994)., This apparent improvement to the original model of \cite{Nob86} is not so at all as pointed out by \cite{satre94}. +. Phe point is that given an initial osculating eu the mean e generated by the evolution under Eq. (1)), The point is that given an initial osculating $a_0$ the mean $\bar{a}$ generated by the evolution under Eq. \ref{quinn}) ) + is dilferent from the mean αμ generated by the evolution uncer Eq. (72)., is different from the mean $\bar{a}_R$ generated by the evolution under Eq. \ref{saha}) ). + Then. model (7)) will not reproduce the secular evolution of an object with the correct e but with a cillerent mean semimajor axis given by αμ.," Then, model \ref{saha}) ) will not reproduce the secular evolution of an object with the correct $\bar{a}$ but with a different mean semimajor axis given by $\bar{a}_R$." + In consequence. the model introduces a secular drift in AZ and no evident progress is done in comparison with Eq. (6)).," In consequence, the model introduces a secular drift in $M$ and no evident progress is done in comparison with Eq. \ref{nob}) )." + This problem can be solved taking appropriate initial conditions as we explain in sec., This problem can be solved taking appropriate initial conditions as we explain in sec. + 4.3., 4.3. + The corrections exposed above. though computationally better than σαι (1))," The corrections exposed above, though computationally better than Eq. \ref{quinn}) )" + because the v-dependance is eliminated: still have the problem that near perihelion the perturbation can be high enough to introduce numerical errors in constant time-step One wav of overcoming this dillicultv is to look for a constant ¢-independent relativistic correction., because the -dependance is eliminated; still have the problem that near perihelion the perturbation can be high enough to introduce numerical errors in constant time-step One way of overcoming this difficulty is to look for a constant $r$ -independent relativistic correction. + To accomplish this task. we went back to Iq. (1)).," To accomplish this task, we went back to Eq. \ref{quinn}) )," + and assuming that the short period. terms in the orbital elements do not alfect the secular evolution of them. we time averaged the relativistic perturbation produced by a central body. obtaining: where ue is the versor pointing to the pericenter.," and assuming that the short period terms in the orbital elements do not affect the secular evolution of them, we time averaged the relativistic perturbation produced by a central body, obtaining: where $\mathbf{u_e}$ is the versor pointing to the pericenter." + The fact that this averaged acceleration is a constant along ue. gave us the idea of trving with a constant perturbation in this direction.," The fact that this averaged acceleration is a constant along $\mathbf{u_e}$, gave us the idea of trying with a constant perturbation in this direction." + In order to obtain the same cirift in c as Eq. (4)), In order to obtain the same drift in $\omega$ as Eq. \ref{quinnperi}) ) + using the TPAGPE it is necessary to introduce a factor 2 and in terms of 2 and J can be written as Inserting these expressions into the ΕλΙΟ. the elements a.6:;7.O have zero variation and the mean variation in the o is recovered. but for AZ we obtain: which is cdillerent. from the real effect. given. by (5)).," using the TAGPE it is necessary to introduce a factor 2 and in terms of $R$ and $T$ can be written as Inserting these expressions into the TAGPE, the elements $a,e,i,\Omega$ have zero variation and the mean variation in the $\omega$ is recovered, but for $M$ we obtain: which is different from the real effect given by \ref{quinnanom}) )." + Even so. one can also use a simpler constant radial. perturbation CE— 0) that generates the expected. variation in the argument of perihelion: Again. [rom the TAGPL. the elements a.60.7.O have zero variation and the mean variation in the w is recovered but for mean anomaly we obtain a different expression:," Even so, one can also use a simpler constant radial perturbation $T=0$ ) that generates the expected variation in the argument of perihelion: Again, from the TAGPE, the elements $a,e,i,\Omega$ have zero variation and the mean variation in the $\omega$ is recovered but for mean anomaly we obtain a different expression:" +(which we also exclude from our sample). NGC 2419 might be the tically stripped. core of a former dwarf. spheroidal galaxy.,"(which we also exclude from our sample), NGC 2419 might be the tidally stripped core of a former dwarf spheroidal galaxy." + To builc the mass ancl number density. profiles. our source for the galactocentric distances J and the absolute visual magnitudes AL. is the MeMaster database compiled and maintained by Larris (1996. updated February 2003).," To build the mass and number density profiles, our source for the galactocentric distances $D$ and the absolute visual magnitudes $_v$ is the McMaster database compiled and maintained by Harris (1996, updated February 2003)." +" Cluster absolute visual magnitudes have been turned. into luminous mass cstimates by assuming a Constant mass-to-licht ratio M/L,—2.35 (i.c. the average of the mass-to-light ratios of the halo clusters for which Pryor Alevlan (1993) obtained cvnamical mass estimates)."," Cluster absolute visual magnitudes have been turned into luminous mass estimates by assuming a constant mass-to-light ratio $_v$ =2.35 (i.e., the average of the mass-to-light ratios of the halo clusters for which Pryor Meylan (1993) obtained dynamical mass estimates)." + The Old. Lalo mass and number profiles are derived. by binning the cata with two dillerent bin sizes: «λος=0.1ancl0.2 (D is in kpe). corresponding to 10 and S points. respectively.," The Old Halo mass and number profiles are derived by binning the data with two different bin sizes: $\Delta {\rm log} D = 0.1~ {\rm and}~ 0.2$ $D$ is in kpc), corresponding to 16 and 8 points, respectively." + As for the size of the error bars. a Poissonian error on the number of clusters in cach bin is combined with a fixed error on the mass-to-light ratio.," As for the size of the error bars, a Poissonian error on the number of clusters in each bin is combined with a fixed error on the mass-to-light ratio." + In [act. not all globular clusters show the same mass-to-light ratio. the standard. deviation in the Pryor Alevlan (1993) compilation being of order OCLosiMLo)0.1.," In fact, not all globular clusters show the same mass-to-light ratio, the standard deviation in the Pryor Meylan (1993) compilation being of order $\sigma _{{\rm Log}(M/L_v)} = 0.17$." +" As already mentioned. the observed. racial distribution of halo clusters obeys D""UU except in the innner kkpce where the distribution ects shallower."," As already mentioned, the observed radial distribution of halo clusters obeys $D^{-3.5}$ except in the innner kpc where the distribution gets shallower." + As a result. it is often parametrized. by a power law with a core (see equation 1)).," As a result, it is often parametrized by a power law with a core (see equation \ref{eq:log_pl_core}) )." + Previous fits having been obtained for either the whole Galactic globular cluster svstem (e.g... Djorgovski Mevlan 1994) or the whole halo system (e.g... AeLaughlin 1999). we now consider the Old. Halo subsystem only.," Previous fits having been obtained for either the whole Galactic globular cluster system (e.g., Djorgovski Meylan 1994) or the whole halo system (e.g., McLaughlin 1999), we now consider the Old Halo subsystem only." + Using a Levenbere-Alarquardt algorithm (Press et al., Using a Levenberg-Marquardt algorithm (Press et al. +" 1992). we fit the Old Lalo number density profile with: The values obtained for the slope 5 and the core D, are presented in the left. part of ‘Table 1.."," 1992), we fit the Old Halo number density profile with: The values obtained for the slope $-\gamma$ and the core $D_c$ are presented in the left part of Table \ref{tab:fit_pl_core}. ." + For each fit. we also give. the 472 and the incomplete. gamma functionB. Qif2.\7/2) Gv is the number of degrees of freedom) which provides a quantitative measure for the goocness-ol-fit of the model7.," For each fit, we also give the $\chi ^2$ and the incomplete gamma function $Q(\nu /2, \chi ^2/2)$ $\nu$ is the number of degrees of freedom) which provides a quantitative measure for the goodness-of-fit of the model." +. Imposing a slope + of 3.5 or4. as found by Djorgovski," Imposing a slope $-\gamma$ of –3.5 or–4, as found by Djorgovski" +"anisotropy reaches a minimum value at Voy~0.5V4, whereas our Figure BJ shows that the alpha temperature anisotropy reaches its maximum value when V,,~0.5V4.","anisotropy reaches a minimum value at $V_{\alpha p} \sim 0.5 V_\mathrm{A}$, whereas our Figure \ref{fig.3} shows that the alpha temperature anisotropy reaches its maximum value when $V_{\alpha p} \sim 0.5 V_\mathrm{A}$." +" Moreover, the results of (2005) show that the average alpha temperature anisotropy is monotonically decreasing with increasing alpha/proton relativeeral] (2008)speed."," Moreover, the results of \citet{gary2005} show that the average alpha temperature anisotropy is monotonically decreasing with increasing alpha/proton relative speed." +" Unlike what Kasper and eral]0005) found previously, our Figure [4] shows that[Gary the perpendicular heating is reduced when V,,/V,4 is near zero."," Unlike what \citet{kasper2008} and \citet{gary2005} found previously, our Figure \ref{fig.4} shows that the perpendicular heating is reduced when $V_{\alpha p}/V_A$ is near zero." + This reduced ion heating corresponds to an observed concurrent decrease in the wave power of the transverse waves., This reduced ion heating corresponds to an observed concurrent decrease in the wave power of the transverse waves. + This results would be expected when the heating ultimately rests with the energy in those waves., This results would be expected when the heating ultimately rests with the energy in those waves. +" If V,,/V4 is near zero, we expect that the alpha-particle temperature ratio increases resulting in a strong perpendicular ion heating for sufficient wave power."," If $V_{\alpha p}/V_A$ is near zero, we expect that the alpha-particle temperature ratio increases resulting in a strong perpendicular ion heating for sufficient wave power." +" However, although the wave power is empirically found to be weak when the normalized ion differential speed is low, the alpha particles are still heated perpendicularly much more than the protons."," However, although the wave power is empirically found to be weak when the normalized ion differential speed is low, the alpha particles are still heated perpendicularly much more than the protons." +" For both ion species the interaction with transverse waves is expected to work against the radial trend caused by the solar wind expansion in a magnetic mirror, which tends to build up a much larger parallel than perpendicular temperature, and accordingly a strong fire-hose-type anisotropy."," For both ion species the interaction with transverse waves is expected to work against the radial trend caused by the solar wind expansion in a magnetic mirror, which tends to build up a much larger parallel than perpendicular temperature, and accordingly a strong fire-hose-type anisotropy." +" If we assume that the transverse fluctuations provide the energy input for the observed preferential perpendicular heating of the alpha particles, then their temperature-ratio profile as given in Figure] could be a signature of cyclotron-wave heating of the alpha particles."," If we assume that the transverse fluctuations provide the energy input for the observed preferential perpendicular heating of the alpha particles, then their temperature-ratio profile as given in Figure \ref{fig.4} could be a signature of cyclotron-wave heating of the alpha particles." +" It has been claimed that the alpha particles can only be heated through ion-cyclotron wave dissipation if the differential speed between alpha-particles and protons is approximately less than 0.5V4 (seee.g.,[Garyetal.|2005].."," It has been claimed that the alpha particles can only be heated through ion-cyclotron wave dissipation if the differential speed between alpha-particles and protons is approximately less than $0.5V_A$ \citep[see +e.g.,][]{gary2005}." +" Therefore, alpha-particles can be heated in the perpendicular direction as long as they stay in resonance with the ion-cyclotron waves."," Therefore, alpha-particles can be heated in the perpendicular direction as long as they stay in resonance with the ion-cyclotron waves." +" Moreover, the wave energy is an important input parameter that controls the heating of alpha-particles."," Moreover, the wave energy is an important input parameter that controls the heating of alpha-particles." + We expect that high wave energy can cause strong perpendicular heating of those alpha particles that are in resonance with ion-cyclotron waves., We expect that high wave energy can cause strong perpendicular heating of those alpha particles that are in resonance with ion-cyclotron waves. + Figure | shows that the perpendicular heating is reduced when γαρ/γα is near zero., Figure \ref{fig.4} shows that the perpendicular heating is reduced when $V_{\alpha p}/V_\mathrm{A}$ is near zero. +" This reduced ion heating corresponds to a decrease in the observed wave power of the transverse fluctuations, a result that is expected because the potential for heating ultimately rests with the energy contained in those waves."," This reduced ion heating corresponds to a decrease in the observed wave power of the transverse fluctuations, a result that is expected because the potential for heating ultimately rests with the energy contained in those waves." +" If V,,/V4 is near zero, we expect that the alpha-particle temperature ratio increases, resulting in strong perpendicular ion heating for sufficient wave power."," If $V_{\alpha +p}/V_\mathrm{A}$ is near zero, we expect that the alpha-particle temperature ratio increases, resulting in strong perpendicular ion heating for sufficient wave power." +" However, although the wave power is found empirically to be weak when the normalized ion differential speed is small, the alpha particles can still be perpendicularly heated much more than the protons."," However, although the wave power is found empirically to be weak when the normalized ion differential speed is small, the alpha particles can still be perpendicularly heated much more than the protons." +" Yet, for both ion species the interaction with transverse fluctuations works against the trend caused by the solar wind expansion in a magnetic-field mirror configuration, which tends to build up a high parallel temperature anisotropy."," Yet, for both ion species the interaction with transverse fluctuations works against the trend caused by the solar wind expansion in a magnetic-field mirror configuration, which tends to build up a high parallel temperature anisotropy." +" Furthermore, Coulomb collisions tend to thermalize the solar wind plasma and to reduce the differential speed between alpha particles and protons."," Furthermore, Coulomb collisions tend to thermalize the solar wind plasma and to reduce the differential speed between alpha particles and protons." +" But collisions are effective in removing the non-thermal ion features merely in the comparatively cold and dense slow solar wind, in which the collision age is found to be high and the average wave power observed to be weak."," But collisions are effective in removing the non-thermal ion features merely in the comparatively cold and dense slow solar wind, in which the collision age is found to be high and the average wave power observed to be weak." +" Another possible scenario that may occur as well is that the long-wavelength and high-amplitude fluctuations of the inertial-range turbulence may stochastically heat [2010) the ions in the perpendicular direction with respect to the background magnetic field (or non-resonantly drive a slowly varying T,/T| on both ion species).", Another possible scenario that may occur as well is that the long-wavelength and high-amplitude fluctuations of the inertial-range turbulence may stochastically heat \citep{chandran2010} the ions in the perpendicular direction with respect to the background magnetic field (or non-resonantly drive a slowly varying $T_\perp/T_{\parallel}$ on both ion species). +" The presence of this anisotropy can give rise to Alfvénn-cyclotron instabilities, which lead to the growth of relatively high-frequency modes (with frequencies ω~Ώρ, where Q, is the proton cyclotron frequency)."," The presence of this anisotropy can give rise to Alfvénn-cyclotron instabilities, which lead to the growth of relatively high-frequency modes (with frequencies $\omega \sim \Omega_p$, where $\Omega_p$ is the proton cyclotron frequency)." +" In other words, the ion temperature anisotropies could first be caused by low-frequency fluctuations in the inertial range, and then this thermal energy may be exchanged between ions and waves at the proton kinetic scale."," In other words, the ion temperature anisotropies could first be caused by low-frequency fluctuations in the inertial range, and then this thermal energy may be exchanged between ions and waves at the proton kinetic scale." +0.08 dex. respectively.,"0.08 dex, respectively." + These numbers are consistent with the quoted typical measurement uncertainties in the individual studies., These numbers are consistent with the quoted typical measurement uncertainties in the individual studies. + Of course. the standard error of the mean (s.eam.)," Of course, the standard error of the mean (s.e.m.)" + values for the average values of these quantities for those stars included in multiple studies are smaller., values for the average values of these quantities for those stars included in multiple studies are smaller. + Objective comparisons between the Li abundances. of SWPs anc comparison stars have proven to be cillicult., Objective comparisons between the Li abundances of SWPs and comparison stars have proven to be difficult. + some studies have cone nothing more than simple. visua comparisons on a plot like Figure 2. while others have attempted. to correct. for. dillerences in. Loy. bef] anc chromospheric activity (e.g.. Gonzalez&Laws (2000))).," Some studies have done nothing more than simple visual comparisons on a plot like Figure 2, while others have attempted to correct for differences in $_{\rm eff}$, [Fe/H] and chromospheric activity (e.g., \citet{gl00}) )." + We propose a new approach to comparing these samples., We propose a new approach to comparing these samples. + Observations of stars in open clusters and in the fick indicate that Li abuncdances are most sensitive to Tor ane age (see Cutispotoctal.(2003):Takedaet(2007a) ane references therein).," Observations of stars in open clusters and in the field indicate that Li abundances are most sensitive to $_{\rm eff}$ and age (see \citet{cut03,tak07} and references therein)." + In addition. the rate of Li destruction in a star's envelope should be sensitive to. οΗ]. since a stars convection zone is deeper for larger ο) (Montalbán<ebolo 2002).," In addition, the rate of Li destruction in a star's envelope should be sensitive to [Fe/H], since a star's convection zone is deeper for larger [Fe/H] \citep{mr02}." +. For cach star in our samples we have Tir. log e. Fe/H] and M. all corrected. for small. systematic dillerences among the various studies.," For each star in our samples we have $_{\rm eff}$, $\log$ g, [Fe/H] and $_{\rm v}$, all corrected for small systematic differences among the various studies." + lsochrone-basecl stellar ages can be derived. [rom the Tar ΜοΗ] and My values. and this has been done in several studies of SWPs (e.g... Takeda.ctal. (2007b))).," Isochrone-based stellar ages can be derived from the $_{\rm eff}$, [Fe/H] and $_{\rm v}$ values, and this has been done in several studies of SWPs (e.g., \citet{tak207}) )." + Uniform ago estimates are not available for all the stars in our SWP and comparison star samples., Uniform age estimates are not available for all the stars in our SWP and comparison star samples. + However. our method of comparison does not require that we calculate ages.," However, our method of comparison does not require that we calculate ages." + Instead. we caleulate an index that is a measure of the proximity of two stars in Tar. log g.. Fe/H]. Mé-space.," Instead, we calculate an index that is a measure of the proximity of two stars in $_{\rm eff}$, $\log$ g, [Fe/H], $_{\rm v}$ -space." + Lt is based on the following equation: Two stars with identical values of Pur. log ο. Fe/1] and Al. will have a Ay value of zero.," It is based on the following equation: Two stars with identical values of $_{\rm eff}$, $\log$ g, [Fe/H] and $_{\rm v}$ will have a $\Delta_1$ value of zero." + Vherefore. two stars with identical ages. masses and compositions will also have à Ay value of zero.," Therefore, two stars with identical ages, masses and compositions will also have a $\Delta_1$ value of zero." +" Our motivation in choosing these particular coellicients is to give comparable contributions to A, from each term for two stars that diller bv about 2e in cach parameter.", Our motivation in choosing these particular coefficients is to give comparable contributions to $\Delta_1$ from each term for two stars that differ by about $\sigma$ in each parameter. + We increased. the contribution of the log Tar term. however. to account for its greater importance in determining the Li abundance.," We increased the contribution of the $\log$ $_{\rm eff}$ term, however, to account for its greater importance in determining the Li abundance." + And. we reduced. the contribution of log &. given the relativel-— esser importance of this quantity.," And, we reduced the contribution of $\log$ g, given the relatively lesser importance of this quantity." + We calculated Ay for each SWIP relative to each comparison star. resulting in 5439 values.," We calculated $\Delta_1$ for each SWP relative to each comparison star, resulting in 5439 values." +" For cach SW. we then selected the comparison star with the smallest value of A,."," For each SWP, we then selected the comparison star with the smallest value of $\Delta_1$." + We plot the dillerences in Li abundances between each SWP and the closest matching comparison star in Figure θα., We plot the differences in Li abundances between each SWP and the closest matching comparison star in Figure 3a. + One weakness of this approach is that only a small subset of the data is used to calculate the dillerences in the Li abundances., One weakness of this approach is that only a small subset of the data is used to calculate the differences in the Li abundances. + ποσο results are sensitive to outliers., These results are sensitive to outliers. + We can improve upon our analysis as follows., We can improve upon our analysis as follows. + In our second approach we calculated weighted average values. of Li. abundance differences for cach SWP using all the comparison star data., In our second approach we calculated weighted average values of Li abundance differences for each SWP using all the comparison star data. + The weights are given by G4).7., The weights are given by $(\Delta_1)^{-2}$. + We show the results of this analvsis in Figure 3b., We show the results of this analysis in Figure 3b. + The low Li abundances evident for the SWI's near 5800 Ix in Figure 3a are also evident in Figure 3b., The low Li abundances evident for the SWPs near 5800 K in Figure 3a are also evident in Figure 3b. + Phe average Li abundance dillerence for SWPs with 5800«Tr <5950 Ix is 0.88£0.10 (s.c.m.), The average Li abundance difference for SWPs with $5800 < $ $_{\rm eff} < 5950$ K is $-0.38 \pm 0.10$ (s.e.m.) + dex., dex. + Figure 3b also shows a general excess of Li among ολος with Tr>5950 Ix. which have a mean Li abundance exess Of 0.12d0.04. (s.em.)," Figure 3b also shows a general excess of Li among SWPs with $_{\rm eff} > 5950$ K, which have a mean Li abundance excess of $0.12 \pm 0.04$ (s.e.m.)" + dex., dex. + To test the sensitivity of our results to the form of the A index. we repeated the above analysis with the following modified version: We show the resulting. Li abundance dilflerences calculated: using the As index in Figure 4.," To test the sensitivity of our results to the form of the $\Delta$ index, we repeated the above analysis with the following modified version: We show the resulting Li abundance differences calculated using the $\Delta_2$ index in Figure 4." + There are only a [few differences from Figure 3. but the pattern of low Li abundances among the cooler SWPs and the high. Li abundances among the hotter SWDPs evident in Figure 3b remain unchanged.," There are only a few differences from Figure 3, but the pattern of low Li abundances among the cooler SWPs and the high Li abundances among the hotter SWPs evident in Figure 3b remain unchanged." + The averages ancl cispersions are nearly identical to those caleulated with the Ay index., The averages and dispersions are nearly identical to those calculated with the $\Delta_1$ index. + Rotation is another important parameter that correlates with Li abundance (Cutispotoetal.2003)., Rotation is another important parameter that correlates with Li abundance \citep{cut03}. + Uniform rotational velocity (vsini) measurements are available from a single. source. for most of the stars we plotted in. Figures 3 and 4., Uniform rotational velocity (vsini) measurements are available from a single source for most of the stars we plotted in Figures 3 and 4. + Valenti&Fischer(2005) measured vsini for the 1040 stars in their SPOCS survey: they quote a typical uncertainty of 0.5 kms 1 This level of precision is adequate to resolve the range of vsini values measured for SWPs (< τος15 kms D., \citet{vf05} measured vsini for the 1040 stars in their SPOCS survey; they quote a typical uncertainty of 0.5 km $^{\rm -1}$ This level of precision is adequate to resolve the range of vsini values measured for SWPs $< 1$ to $\simeq 15$ km $^{\rm -1}$ ). + Of the 37 SWPs plotted in Figures 8 and 4. 33 have vsinb values [isted. in," Of the 37 SWPs plotted in Figures 3 and 4, 33 have vsini values listed in" +to determine the Fe abundance to within 5 per cent. the abundances of Si and S to within 5 per cent. the abundances of Ne. Mg. and Ni to within 10 per cent. and the abundances of Ar anc Ca to within 20 per cent statistical precision.,"to determine the Fe abundance to within $\leq3$ per cent, the abundances of Si and S to within $\leq5$ per cent, the abundances of Ne, Mg, and Ni to within $\leq10$ per cent, and the abundances of Ar and Ca to within $\leq20$ per cent statistical precision." + “Phe errors on the abundance profiles were determined from a Markov Chain Monte Carlo (AICAIC) analysis., The errors on the abundance profiles were determined from a Markov Chain Monte Carlo (MCMC) analysis. + Measurement errors were. eetermined from the 68 per cent confidence posterior distribution of the MCMC analysis., Measurement errors were determined from the 68 per cent confidence posterior distribution of the MCMC analysis. + Chain lengths were at least. 107. samples after correcting for burn-in., Chain lengths were at least $10^4$ samples after correcting for burn-in. +" Abundances in the paper are given with respect to the ""proto-Solar. values of Lodders (2003).", Abundances in the paper are given with respect to the `proto-Solar' values of Lodders (2003). + Our modelling makes use of the recently updated AtomDB v2.0.1 atomic database used by the thermal plasma model. implemented in., Our modelling makes use of the recently updated AtomDB v2.0.1 atomic database used by the thermal plasma model implemented in. +NSPEC. Phis represents a major update from. the previous AtomDB v1.3.2 with nearly all atomic data The update of the atomic database allects most significantly the Fe abundance. which is on average lower by ~20 per cent in v2.0.1 compared to v1.3.2.," This represents a major update from the previous AtomDB v1.3.2 with nearly all atomic data The update of the atomic database affects most significantly the Fe abundance, which is on average lower by $\sim20$ per cent in v2.0.1 compared to v1.3.2." + This change has a slight dependence upon the temperature of the plasma., This change has a slight dependence upon the temperature of the plasma. + The abundances of Si. S. Ar. Ca. Ne. Ale. and Ni are smaller by less than ~10 per cent in the updated: version.," The abundances of Si, S, Ar, Ca, Ne, Mg, and Ni are smaller by less than $\sim$ 10 per cent in the updated version." + The abundance ratios with respect to Fe are significantly higher as a result., The abundance ratios with respect to Fe are significantly higher as a result. + We note that our main conclusions based on the centrally peaked abuncances and abundance ratios are not sensitive to our choice of plasma code., We note that our main conclusions based on the centrally peaked abundances and abundance ratios are not sensitive to our choice of plasma code. +" We determine the abundance profiles for Fe. Si. S. Ar. Ca. ο, Me. and Ni and find that all elements have a centrally »ealed. distribution."," We determine the abundance profiles for Fe, Si, S, Ar, Ca, Ne, Mg, and Ni and find that all elements have a centrally peaked distribution." + We also measure the abundance ratios of the individual elements with respect to Fe., We also measure the abundance ratios of the individual elements with respect to Fe. + In the 440 kpe radial range. we fit a linear model of the form Z=a|br o these measurements. where Z is the abundance ratio. rà is he radius in kpe. e is the normalization of the linear trend. and b is the slope.," In the 4–40 kpc radial range, we fit a linear model of the form $Z=a+b r$ to these measurements, where $Z$ is the abundance ratio, $r$ is the radius in kpc, $a$ is the normalization of the linear trend, and $b$ is the slope." + Table 1. summarizes the best-fit linear relations for cach of the abundance ratio profiles., Table \ref{table:trends} summarizes the best-fit linear relations for each of the abundance ratio profiles. + For the “οο and. Ni/Fe ratios. which have significant. systematic uncertainties. we present the best-fit parameters for profiles determined using both the and plasma codes.," For the Ne/Fe and Ni/Fe ratios, which have significant systematic uncertainties, we present the best-fit parameters for profiles determined using both the and plasma codes." + The absolute abundances determined. by the plasma code are larger by 1:2 per cent for Si. by ~3 per cent for S. bx 15 per cent for Ar ancl Ca. and ον ~20 per cent for Fe than the values obtained. usingAPEC.," The absolute abundances determined by the plasma code are larger by 1–2 per cent for Si, by $\sim$ 3 per cent for S, by $\sim$ 15 per cent for Ar and Ca, and by $\sim$ 20 per cent for Fe than the values obtained using." + The slopes of the abundance ratio profiles for these elements are. however. consistent with those determined by the code.," The slopes of the abundance ratio profiles for these elements are, however, consistent with those determined by the code." + The abundances of Ne. Ni. and. Mg are significantly dillerent when determined by the plasma code.," The abundances of Ne, Ni, and Mg are significantly different when determined by the plasma code." + A discussion of modeling biases for the abundances of these elements can be found in Sect. 3.3.1., A discussion of modeling biases for the abundances of these elements can be found in Sect. \ref{section:bias}. + For gas with AT=2.0 keV. the O abundance is extremely dillicult. to. determine withChandra.," For gas with $kT\approxgt2.0$ keV, the O abundance is extremely difficult to determine with." + At the line οποιον of 0.65 keV the cllective area of the ACIS detectors. is significantly allected by buildup of contamination., At the line energy of 0.65 keV the effective area of the ACIS detectors is significantly affected by buildup of contamination. + Adcitionally. in the lower surface brightness areas at larger radii the O abundance measurements are sensitive to the assumed Galactic foreground model.," Additionally, in the lower surface brightness areas at larger radii the O abundance measurements are sensitive to the assumed Galactic foreground model." + Because our O abundance measurements have large systematic uncertainties and may be strongly biased. we do not report their best fit values.," Because our O abundance measurements have large systematic uncertainties and may be strongly biased, we do not report their best fit values." + We have examined the abundance ratios separately to the north ancl south of SST., We have examined the abundance ratios separately to the north and south of 87. +. Although the overall abundances are larger to the south (see Paper D). the abundance ratios determined from the northern απ southern sectors agree well with each other and the azimuthally-averaged analysis presented here.," Although the overall abundances are larger to the south (see Paper I), the abundance ratios determined from the northern and southern sectors agree well with each other and the azimuthally-averaged analysis presented here." + The top row of Fig., The top row of Fig. + 2. shows the Fe. Si. and S abundance profiles. respectively.," \ref{fig:FeSiS} shows the Fe, Si, and S abundance profiles, respectively." + The bottom row shows the abundance ratio profiles of Sifke. S/Ee. and SiS. We emphasize that these three elements have the most. τοσο determined abundances. with statistical uncertainties of less than 5 per cent.," The bottom row shows the abundance ratio profiles of Si/Fe, S/Fe, and Si/S. We emphasize that these three elements have the most robustly determined abundances, with statistical uncertainties of less than 5 per cent." + The Fe abundance profile (Fig., The Fe abundance profile (Fig. + 2aa) peaks at Zi. Solar in the central regions., \ref{fig:FeSiS}a a) peaks at $Z_{\rm Fe}>1.2$ Solar in the central regions. + The Si and S abundance wolfiles (Fig., The Si and S abundance profiles (Fig. + 2bb-c) peak at a slightly larger central value of Zeisv1.5 Solar., \ref{fig:FeSiS}b b-c) peak at a slightly larger central value of $Z_{\rm Si;S}\sim1.5$ Solar. + These profiles then exhibit steady declines 0o 0.6 Solar by kr—25 kpe., These profiles then exhibit steady declines to $\sim0.6$ Solar by $r\sim25$ kpc. +" A significant enhancement. or ""bump. in the Fe and Si (and. possibly 8) abundances is seen at r 730 kpc."," A significant enhancement, or `bump', in the Fe and Si (and possibly S) abundances is seen at $r\sim$ 30 kpc." + This is approximately the radius at which the bright N-rav. armis erminate., This is approximately the radius at which the bright X-ray arms terminate. + As discussed in Paper L this bump may be due o the uplift of cool. metal-rich material in the wake of xiovantly rising radio bubbles.," As discussed in Paper I, this bump may be due to the uplift of cool, metal-rich material in the wake of buoyantly rising radio bubbles." + Alost importantly. we observe. for the [first time. a racially decreasing trend in the Sifke and S/Fe abundance," Most importantly, we observe, for the first time, a radially decreasing trend in the Si/Fe and S/Fe abundance" +being the best approximation.,being the best approximation. + Fig., Fig. +" ?? compares this to values found from fitting to the true gas distributions inFig. Hl,"," \ref{Radii} compares this to values found from fitting to the true gas distributions inFig. \ref{halogas}," + the result looking favourable., the result looking favourable. + This straightforward scaling with the virial radius (??)) will therefore be used in the matched realisation., This straightforward scaling with the virial radius \ref{r_core}) ) will therefore be used in the matched realisation. +" The cold gas scalelengths, also shown in Fig.??,, are not inputs toGALFORM, but are calculated within the model as described in refDiskFormation.."," The cold gas scalelengths, also shown in \ref{Radii}, are not inputs to, but are calculated within the model as described in \\ref{DiskFormation}." +" To understand the relevance of the hot gas distribution on the system’s evolution as a whole, it is worth reviewing the precise treatment of gas cooling in GALFORM."," To understand the relevance of the hot gas distribution on the system's evolution as a whole, it is worth reviewing the precise treatment of gas cooling in ." + The cooling model described by Coleetal.(2000) determines the mass of gas able to cool in any timestep by following the propagation of the cooling radius in a notional hot gas density, The cooling model described by \scite{Cole00} determines the mass of gas able to cool in any timestep by following the propagation of the cooling radius in a notional hot gas density. +" This profile is fixed when a halo is flagged as ""forming"" profilq?].and is only updated when the halo undergoes another formation event.", This profile is fixed when a halo is flagged as “forming” and is only updated when the halo undergoes another formation event. + The mass of gas able to cool in any given timestep is equal to the mass of gas in this notional profile between the cooling radius at the present step and that at the previous step., The mass of gas able to cool in any given timestep is equal to the mass of gas in this notional profile between the cooling radius at the present step and that at the previous step. + The cooling time is assumed to be the time since the formation event of the halo., The cooling time is assumed to be the time since the formation event of the halo. +" Any gas which is reheated into or accreted by the halo is ignored until the next formation event, at which point it is added to the hot gas profile of the newly formed halo."," Any gas which is reheated into or accreted by the halo is ignored until the next formation event, at which point it is added to the hot gas profile of the newly formed halo." +" The notional profile is constructed using the properties (e.g. scale radius, virial temperature etc.)"," The notional profile is constructed using the properties (e.g. scale radius, virial temperature etc.)" +" of the halo at the formation event and retains a fixed metallicity throughout, corresponding to the metallicity of the hot gas in the halo at the formation event."," of the halo at the formation event and retains a fixed metallicity throughout, corresponding to the metallicity of the hot gas in the halo at the formation event." +" This work makes use of a new cooling model, which will be described in full detail in Bensonetal.(inprep.)."," This work makes use of a new cooling model, which will be described in full detail in \scite{Benson09}." +". Rather than arbitrary ""formation"" events, this model uses a continuously updating estimate of coolingtime and halo properties."," Rather than arbitrary “formation” events, this model uses a continuously updating estimate of coolingtime and halo properties." +" The properties described in refHotGas (density normalization, core radius) are reset at each timestep."," The properties described in \\ref{HotGas} (density normalization, core radius) are reset at each timestep." + The previous infall (i.e. the radius within which gas was allowed to infallradiud] and accrete onto the galaxy) is computed by finding the radius which encloses the mass previously removed from the hot component in the current notional profile., The previous infall (i.e. the radius within which gas was allowed to infall and accrete onto the galaxy) is computed by finding the radius which encloses the mass previously removed from the hot component in the current notional profile. +" 'The new model must supply an alternative estimate of the time available for cooling in the halo, ἕνα, from which the cooling radius can be computed in the usual way (i.e. by finding the radius in the notional profile at which t.oo1=lavai])."," The new model must supply an alternative estimate of the time available for cooling in the halo, $t_{\rm avail}$, from which the cooling radius can be computed in the usual way (i.e. by finding the radius in the notional profile at which $t_{\rm cool}=t_{\rm avail}$ )." +" This is done by considering the energy radiation rateparticle, ἐν and the thermal energyparticle, etn, which are estimated by making standard assumptions: A((Tv,Z)n In terms of these quantities, the cooling time (8) is simply: (r,t) "," This is done by considering the energy radiation rate, $\dot{\epsilon}_{\rm r}$ and the thermal energy, $\epsilon_{\rm th}$, which are estimated by making standard assumptions: ,Z)n In terms of these quantities, the cooling time \ref{t_cool}) ) is simply: (r,t) = ." +"At any time, the model needs to identify some radius in the hot halo, reoo1, where the gas has had just enough time to radiate all its thermal energy."," At any time, the model needs to identify some radius in the hot halo, $r_{\rm cool}$, where the gas has had just enough time to radiate all its thermal energy." +" Thisundetermined radius is defined to satisfy the condition that the cooling time for gas particles at this point is equal to thetime available for themto cool, which is estimated in terms of the mean energy radiation rate per particld?], έν: (t) "," This radius is defined to satisfy the condition that the cooling time for gas particles at this point is equal to thetime available for themto cool, which is estimated in terms of the mean energy radiation rate per , $\overline{\dot{\epsilon}}_{\rm r}$ : (t) = ." +Equating (14)) and (16) then gives: = A, Equating \ref{tcool})) and \ref{fudge}) ) then gives: = = +Equating (14)) and (16) then gives: = A(, Equating \ref{tcool})) and \ref{fudge}) ) then gives: = = +Equating (14)) and (16) then gives: = A(t, Equating \ref{tcool})) and \ref{fudge}) ) then gives: = = +Equating (14)) and (16) then gives: = A(t), Equating \ref{tcool})) and \ref{fudge}) ) then gives: = = +Equating (14)) and (16) then gives: = A(t)n, Equating \ref{tcool})) and \ref{fudge}) ) then gives: = = +Equating (14)) and (16) then gives: = A(t)n(, Equating \ref{tcool})) and \ref{fudge}) ) then gives: = = +Equating (14)) and (16) then gives: = A(t)n(r, Equating \ref{tcool})) and \ref{fudge}) ) then gives: = = +Equating (14)) and (16) then gives: = A(t)n(rc, Equating \ref{tcool})) and \ref{fudge}) ) then gives: = = +Equating (14)) and (16) then gives: = A(t)n(rco, Equating \ref{tcool})) and \ref{fudge}) ) then gives: = = +Equating (14)) and (16) then gives: = A(t)n(rcoo, Equating \ref{tcool})) and \ref{fudge}) ) then gives: = = +Equating (14)) and (16) then gives: = A(t)n(rcoor, Equating \ref{tcool})) and \ref{fudge}) ) then gives: = = +"Equating (14)) and (16) then gives: = A(t)n(rcoor,", Equating \ref{tcool})) and \ref{fudge}) ) then gives: = = +"Equating (14)) and (16) then gives: = A(t)n(rcoor,t", Equating \ref{tcool})) and \ref{fudge}) ) then gives: = = +"Equating (14)) and (16) then gives: = A(t)n(rcoor,t)", Equating \ref{tcool})) and \ref{fudge}) ) then gives: = = +"Equating (14)) and (16) then gives: = A(t)n(rcoor,t)—", Equating \ref{tcool})) and \ref{fudge}) ) then gives: = = +December with the 10.4 m telescope of the Caltech Submillimeter Observatory with a svslem (temperature of 600 Ix. The line was observed in the upper sideband ancl several different observing frequencies were used (to avoid blending from lines in the lower sidebaac.,December with the 10.4 m telescope of the Caltech Submillimeter Observatory with a system temperature of 600 K. The line was observed in the upper sideband and several different observing frequencies were used to avoid blending from lines in the lower sideband. + The spectrometer and observing procedure are described bv MentenandYoung(1995)., The spectrometer and observing procedure are described by \citet{menten95}. +. The CSO beamsize at 356 GlIz is aand we assumed a beum elliciency of (taken from the CSO webpage)., The CSO beamsize at 356 GHz is and we assumed a beam efficiency of (taken from the CSO webpage). + CRL 618 was observed in the /=13 direct (-0tvpe (transition (οἱ., CRL 618 was observed in the $J=13$ direct $\ell$ -type transition (cf. +" Table 2)) with the Very Large Array (VLA!)) in its D configuration. leading to an angular resolution of ""."," Table \ref{analysis}) ) with the Very Large Array ) in its B configuration, leading to an angular resolution of $^{\prime\prime}$." + At the time of the observations. 15 antennas were equipped with ccm receivers.," At the time of the observations, 15 antennas were equipped with cm receivers." + A total bandwidth of 6.25 MIIz was observed with 128 channels aud the spectral resolution was 48.8 kllz., A total bandwidth of 6.25 MHz was observed with 128 channels and the spectral resolution was 48.8 kHz. + The total time on source was hh. Regular observations of 0555-+398. 3C48 and 3C84 were used lor amplitude. (hax aud. bandpass calibration. respectively.," The total time on source was h. Regular observations of 0555+398, 3C48 and 3C84 were used for amplitude, flux and bandpass calibration, respectively." + The phase was selfcalibrated on the strong continuum emission from 66183., The phase was selfcalibrated on the strong continuum emission from 618. + The remaining non Q-band antennas were used to observe (he J=4 direct. (-tvpe transition at MMIIz., The remaining non Q-band antennas were used to observe the $J=4$ direct $\ell$ -type transition at MHz. + No line was detected at an RAIS noise level of 4 mJv in 0.8 kin/s wide channels., No line was detected at an RMS noise level of 4 mJy in 0.8 km/s wide channels. + The total continuum flix at this frequency is 2643 mJy., The total continuum flux at this frequency is $26\pm 3$ mJy. + Figure 6 shows the direct (-tvpe lines observed toward 6618 ancl the line parameters from Gaussian lits to the spectra are eiven in Table 2.., Figure \ref{lines_final} shows the direct $\ell$ -type lines observed toward 618 and the line parameters from Gaussian fits to the spectra are given in Table \ref{analysis}. +" The /=8.10.11.12.13.14 direct (-ivpe transitions appear as absorption lines towards the continuum of the reeion with line velocities of approximately vj,=—27kkmss '."," The $J=8,10,11,12,13,14$ direct $\ell$ -type transitions appear as absorption lines towards the continuum of the region with line velocities of approximately $v_L=-27$ $^{-1}$." +" The svstemic velocity ry. of 6618 is —24.2 | (Wyrowskietal.2002).. hence all of the observed lines are blueshifed relative (o c4, Indicating that the lines originate [rom a hot. expanding circumstellar envelope."," The systemic velocity $v_{sys}$ of 618 is $-$ $^{-1}$ \citep{wyr2002}, hence all of the observed lines are blueshifed relative to $v_{sys}$ indicating that the lines originate from a hot, expanding circumstellar envelope." + To determine (he physical conditions of the absorbing gas. we used a spherical LTE model of an expanding envelope. developed to interpret our observations of vibrationally excited," To determine the physical conditions of the absorbing gas, we used a spherical LTE model of an expanding envelope, developed to interpret our observations of vibrationally excited" +ratio of n/By or mass-to-maguetic [Iux. suggests that the very early stage of shock development in GAICs may be particularly inuportant to star formation.,"ratio of $n/B_y$ or mass-to-magnetic flux, suggests that the very early stage of shock development in GMCs may be particularly important to star formation." + The following sections examine this idea further., The following sections examine this idea further. + The mass-to-Hlux ratio is a crucial parameter definiug whether the magnetic field cau support a cloud against its own sell-gravity., The mass-to-flux ratio is a crucial parameter defining whether the magnetic field can support a cloud against its own self-gravity. + The critical value of AZ/@y for an uniform. spherical cloud has been derived to be ALl/@y;critσφήναzm0.126//G (Mouschovias&Spitzer 1976).. ," The critical value of $M/\Phi_B$ for an uniform, spherical cloud has been derived to be $M/\Phi_B \big|_\mathrm{crit}= c_\Phi/\sqrt{G} \approx 0.126/\sqrt{G}$ \citep{1976ApJ...210..326M}. ." +The uumerical coefficient eq differs with the geometry of the cloud: au infinite sheet-like cloud has eo=1/23z0.16 (Nakano&Nakamura 1978).. while Tomisakaetal.(1988). found cq—0.170.18 for clouds with various A/dp distributions (see review by Melee&Ostriker (2007))).," The numerical coefficient $c_\Phi$ differs with the geometry of the cloud: an infinite sheet-like cloud has $c_\Phi = 1/2\pi \approx 0.16$ \citep{1978PASJ...30..671N}, , while \cite{1988ApJ...335..239T} found $c_\Phi = 0.17 - 0.18$ for clouds with various $M/\Phi_B$ distributions (see review by \cite{2007ARA&A..45..565M}) )." + Since the value of eq varies only ~105€ with geometry. we choose the commonly-used ce=1/25 (e.g.Ixudoh&Vázquez-Semadeuietal.2011) as a reference value. while keepiug in mind that core geometry is uot explicitly defined for our slab system.," Since the value of $c_\Phi$ varies only $\sim 10\%$ with geometry, we choose the commonly-used $c_\Phi = 1/2\pi$ \citep[e.g.][]{2011ApJ...728..123K, 2011MNRAS.414.2511V} as a reference value, while keeping in mind that core geometry is not explicitly defined for our slab system." +" Practically. for maguetic field in the y-direction the ratio can be written as where we assume that if a core formed in the post-shock region. its effective length in the y-direction. L,. would be comparable to that in the .r-direction. L,. so that Ly."," Practically, for magnetic field in the $y$ -direction the ratio can be written as where we assume that if a core formed in the post-shock region, its effective length in the $y$ -direction, $L_y$, would be comparable to that in the $x$ -direction, $L_x$, so that $\langle B_y\rangle = \int{B_ydx}/\int{dx} \sim \int{B_y dx} / L_y$ ." +" The mass-to-Hux ratio. in units of the critical value A£/dycrit—(ην)do To convert the column of neutrals in our simulation to NCH). we use n—np,+Πιο=0.6."," The mass-to-flux ratio, in units of the critical value $M/\Phi_B\big|_\mathrm{crit} = \left(2\pi\sqrt{G}\right)^{-1}$, is To convert the column of neutrals in our simulation to $N(\mathrm{H})$, we use $n = n_\mathrm{H_2} + n_\mathrm{He} = 0.6n_\mathrm{H}$." +" Note that the true value of the normalized imass-to-Iux ratio would differ [rom Equation (51)) by a [actor Ly/L,. which could be up to ~2."," Note that the true value of the normalized mass-to-flux ratio would differ from Equation \ref{GammaDef}) ) by a factor $L_y/L_x$, which could be up to $\sim 2$." + [f the iuass-to-IHux ratio of a prestellar core is larger than the critical value (> 1). ie. the eravitatioual force exceeds the magnetic support. the core is supercritical aud is eligible lor collapse (subject to support by thermal pressure).," If the mass-to-flux ratio of a prestellar core is larger than the critical value $\Gamma >1$ ), i.e., the gravitational force exceeds the magnetic support, the core is supercritical and is eligible for collapse (subject to support by thermal pressure)." + In contrast. a subcritical core has a imass-to-flux ratio stnaller than the critical value (D< 1). aud cannot collapse unless it loses maguetic euergy iu either the strong-gravity inode (the fiekl lines diffuse outware ΟΦΗ ambipolar diffusion while gravity holds the gas material together) in which D~1 is required. or themaguetic-domiuated mocle (neutralmass moves toward the center wader the gravitatioual pull while ambipolar diffusiou allows the maguetic field lines to remain stationary) so the nass-to-Iux ratio Increases.," In contrast, a subcritical core has a mass-to-flux ratio smaller than the critical value $\Gamma < 1$ ), and cannot collapse unless it loses magnetic energy in either the strong-gravity mode (the field lines diffuse outward through ambipolar diffusion while gravity holds the gas material together) in which $\Gamma\sim 1$ is required, or themagnetic-dominated mode (neutralmass moves toward the center under the gravitational pull while ambipolar diffusion allows the magnetic field lines to remain stationary) so the mass-to-flux ratio increases." +as one must be able to model what happens in the gap between observed snapshots of the Universe.,as one must be able to model what happens in the gap between observed snapshots of the Universe. + In choosing parameters for our simulations. our aim was to generate simulation outputs for a range of different values of ελλ and m. so that we could examine galaxy clustering as a function of these quantities.," In choosing parameters for our simulations, our aim was to generate simulation outputs for a range of different values of $\Omega_\mathrm{M}$ and $\sigma_8$ so that we could examine galaxy clustering as a function of these quantities." + Given our focus on constraining ex. we opted to generate outputs with c taking values between 0.65 and 1.05. regularly spaced in steps of 0.05.," Given our focus on constraining $\sigma_8$, we opted to generate outputs with $\sigma_8$ taking values between 0.65 and 1.05, regularly spaced in steps of 0.05." + Measurements of the abundance of clusters constrain the high-mass end of the halo mass function. and hence constrain a combination of Qa; and e (teg...2).," Measurements of the abundance of clusters constrain the high-mass end of the halo mass function, and hence constrain a combination of $\Omega_\mathrm{M}$ and $\sigma_8$ \citep*[e.g.,][]{EKE96}." + This combination is. very approximately. 0:S7.," This combination is, very approximately, $\sigma_8\Omega_\mathrm{M}^{0.5}$." + To test i “we could break this degeneracy. we have generated two grids of n10dels.," To test if we could break this degeneracy, we have generated two grids of models." + For Grid |. the parameters of+ each model satisfy∡⊲ σον!Os=L8(0.3)7. while for Grid 2 they satisfy m.OW=0.9003).," For Grid 1, the parameters of each model satisfy $\sigma_8\Omega_\mathrm{M}^{0.5}=0.8(0.3)^{0.5}$, while for Grid 2 they satisfy $\sigma_8\Omega_\mathrm{M}^{0.5}=0.9(0.3)^{0.5}$." + Within each grid. os takes on its full range of values between 0.65 and 1.05.," Within each grid, $\sigma_8$ takes on its full range of values between $0.65$ and $1.05$." + It would be very difficult to distinguish between two cosmologies lying on the same grid using cluster abundances., It would be very difficult to distinguish between two cosmologies lying on the same grid using cluster abundances. +" The two ‘cluster normalization"" curves. with ex.)νο= const. are shown as the long-dashed and short-dashed lines in Fig. |.."," The two `cluster normalization' curves, with $\sigma_8\Omega_\mathrm{M}^{0.5}=\mathrm{const.}$ , are shown as the long-dashed and short-dashed lines in Fig. \ref{fig:outplot}." + The pairs (Q3.04) labelling the cosmologies we analyse are plotted as crosses on these curves.," The pairs $(\Omega_\mathrm{M},\sigma_8)$ labelling the cosmologies we analyse are plotted as crosses on these curves." + We extract the mass distribution for these cosmologies from two simulations run using the N-body code (2?)..," We extract the mass distribution for these cosmologies from two simulations run using the $N$ -body code \citep*{SPR01b,SPR05a}." + Each simulation follows the evolution of 512° particles in a 3005b+Mpe box., Each simulation follows the evolution of $512^3$ particles in a $300\ h^{-1}\ \mathrm{Mpc}$ box. + We have stored the simulation output at several redshifts., We have stored the simulation output at several redshifts. + Each of these snapshots of the mass distribution is then interpreted as a 2.=0.1 snapshot of a simulation with a different cosmology. to avoid having to run a great number of simulations.," Each of these snapshots of the mass distribution is then interpreted as a $z=0.1$ snapshot of a simulation with a different cosmology, to avoid having to run a great number of simulations." + We choose .=0.1 since this is near the median redshift of the main SDSS and 2dFGRS galaxy samples., We choose $z=0.1$ since this is near the median redshift of the main SDSS and 2dFGRS galaxy samples. + The output redshifts are chosen so that once the simulations are relabelled as 2=0.1 snapshots. the value of σε at >=0 for each simulation falls onto a regular grid.," The output redshifts are chosen so that once the simulations are relabelled as $z=0.1$ snapshots, the value of $\sigma_8$ at $z=0$ for each simulation falls onto a regular grid." + Each simulation then gives us snapshots with ox taking values between 0.65 and 1.05. regularly spaced by 0.05.," Each simulation then gives us snapshots with $\sigma_8$ taking values between 0.65 and 1.05, regularly spaced by 0.05." + Table |. gives the value of O3; and ox in these relabelled snapshots., Table \ref{tab:outputs} gives the value of $\Omega_\mathrm{M}$ and $\sigma_8$ in these relabelled snapshots. +" We have chosen the simulation parameters such that the first simulation. ""Run |. has £244=0.3 at its σε=0.5 output. while the second simulation. ""Run 2. has 94;=O43 atits ox=0.9 output."," We have chosen the simulation parameters such that the first simulation, `Run 1', has $\Omega_\mathrm{M}=0.3$ at its $\sigma_8=0.8$ output, while the second simulation, `Run 2', has $\Omega_\mathrm{M}=0.3$ at its $\sigma_8=0.9$ output." +" When we perform a further rescaling of O3, (see below) it is these central snapshots which remain unchanged.", When we perform a further rescaling of $\Omega_\mathrm{M}$ (see below) it is these central snapshots which remain unchanged. +" The initial conditions are calculated using a?) power spectrum with shape parameter LF=0.14 and with primordial spectral index n,= 1.", The initial conditions are calculated using a \citet{BBKS} power spectrum with shape parameter $\Gamma=0.14$ and with primordial spectral index $n_\mathrm{s}=1$ . +" A smooth power spectrum was most convenient in the light of the rescalings we carry out on the final output. but in fact the ? power spectrum with LF=0.14 was found to be a good fit to the (2) spectrum with Q),=0.045 used for the Millennium Simulation (2).. the parameters of which were chosen to be in agreement with the one-year WMAP results (?).."," A smooth power spectrum was most convenient in the light of the rescalings we carry out on the final output, but in fact the \citet{BBKS} power spectrum with $\Gamma=0.14$ was found to be a good fit to the \citep{SEL96} spectrum with $\Omega_\mathrm{b}=0.045$ used for the Millennium Simulation \citep{SPR05b}, the parameters of which were chosen to be in agreement with the one-year WMAP results \citep{SPE03}." + Once we have relabelled the simulation snapshots as 2=0.1 snapshots. they lie on a curve in (Qs;.x) space which reflects the way the dark matter density is reduced and the amplitude of clustering is increased as the simulation evolves.," Once we have relabelled the simulation snapshots as $z=0.1$ snapshots, they lie on a curve in $(\Omega_\mathrm{M},\sigma_8)$ space which reflects the way the dark matter density is reduced and the amplitude of clustering is increased as the simulation evolves." + These curves are shown as the solid and dotted lines in Fig. 1.., These curves are shown as the solid and dotted lines in Fig. \ref{fig:outplot}. + We rescale Os; in euch snapshot. so that instead the snapshots lie on one of the cluster-normalized curves described above.," We rescale $\Omega_\mathrm{M}$ in each snapshot, so that instead the snapshots lie on one of the cluster-normalized curves described above." + The rescaling is achieved in practice by applying the results of ?.., The rescaling is achieved in practice by applying the results of \citet{ZHE02}. + If the particle mass is scaled in the obvious way to obtain the desired O3. the particle velocities must also be scaled to compensate. else the haloes no longer satisfy the virial relation between their kinetic and potential energy. and the galaxy. populations of haloes are easily distinguished in the different cosmologies via dynamical observables.," If the particle mass is scaled in the obvious way to obtain the desired $\Omega_\mathrm{M}$, the particle velocities must also be scaled to compensate, else the haloes no longer satisfy the virial relation between their kinetic and potential energy, and the galaxy populations of haloes are easily distinguished in the different cosmologies via dynamical observables." + The rescalings in Os; which move a snapshot onto the cluster-normalization curve are shown schematically as red arrows in Fig. |.., The rescalings in $\Omega_\mathrm{M}$ which move a snapshot onto the cluster-normalization curve are shown schematically as red arrows in Fig. \ref{fig:outplot}. + Each cluster-normalized grid contains rescaled snapshots from both simulations. and the simulation parameters were chosen so that the rescalings would never have to be too large.," Each cluster-normalized grid contains rescaled snapshots from both simulations, and the simulation parameters were chosen so that the rescalings would never have to be too large." + For some of the cosmologies on our grid. we could choose to rescale from either of our simulation runs without having to change Os; by a large factor.," For some of the cosmologies on our grid, we could choose to rescale from either of our simulation runs without having to change $\Omega_\mathrm{M}$ by a large factor." + We have used these cosmologies to test that the results using either simulation run are consistent. and hence that our rescaling works as expected.," We have used these cosmologies to test that the results using either simulation run are consistent, and hence that our rescaling works as expected." + The simulation code runs (2) on the fly. providing us with a list of friends-of-friends haloes (2?) of more than 20 particles. and theirsubstructures.," The simulation code runs \citep{SPR01a} on the fly, providing us with a list of friends-of-friends haloes \citep{DAV85} of more than 20 particles, and theirsubstructures." + We use a linking length of 0.2 times the mean inter-particle separation in the friends-of-friends algorithm to identify the haloes., We use a linking length of $0.2$ times the mean inter-particle separation in the friends-of-friends algorithm to identify the haloes. + also allows us to identify the particle in the halo with the least gravitational potentialenergy. which we use in our galaxy placement scheme.," also allows us to identify the particle in the halo with the least gravitational potentialenergy, which we use in our galaxy placement scheme." +We used the colour excess ratio method described. hy Johnson (1968) for the study. of interstellar extinction law in the irection of both clusters uncler study.,We used the colour excess ratio method described by Johnson (1968) for the study of interstellar extinction law in the direction of both clusters under study. + For. this we used the stars of spectral type. earlier than AQ., For this we used the stars of spectral type earlier than A0. + We determined. the colour excesses by comparing the observed colours of the stars with its intrinsic colours derived from the MINI spectral type-Iuminosity class colour relation given by FizGeralel (1970) for (€1) and (5Vx by Johnson (1966) for (VB) and (Vo£): and by Ixoornnect (1983) for (V—7). (Vff) and (V.A).," We determined the colour excesses by comparing the observed colours of the stars with its intrinsic colours derived from the MKK spectral type-luminosity class colour relation given by FitzGerald (1970) for $(U-V)$ and $(B-V)$; by Johnson (1966) for $(V-R)$ and $(V-I)$; and by Koornneef (1983) for $(V-J)$, $(V-H)$ and $(V-K)$." + For normalisation. we selected the E(CVJ) colour excess due to reasons described in Yadav Sagar (2002).," For normalisation, we selected the $E(V-J)$ colour excess due to reasons described in Yadav Sagar (2002)." + In Fig., In Fig. +" 7 we plot the colour excess E(UBY RIBον BINOR) END. E(VdH) and Ον) against L(V""J)."," 7 we plot the colour excess $E(U-B)$, $E(B-V)$, $E(V-R)$, $E(V-I)$, $E(V-H)$ and $E(V-K)$ against $E(V-J)$." + In this Fie. straight line represents the least square linear fits to the cata points.," In this Fig, straight line represents the least square linear fits to the data points." + The values of correlation coellicient (0) and fit indicate that the data points are well represented by linear relation., The values of correlation coefficient (r) and fit indicate that the data points are well represented by linear relation. + Ehe slopes of these straight lines as given in Table S represent reddening directions in the form of colour excess ratios., The slopes of these straight lines as given in Table 8 represent reddening directions in the form of colour excess ratios. + For comparison. the colour excess ratios given by. C'ardelli ct al. (," For comparison, the colour excess ratios given by Cardelli et al. (" +1989) for the normal interstellar matter are also listed in the Table S.,1989) for the normal interstellar matter are also listed in the Table 8. + The present τοςσας directions agree well with those., The present reddening directions agree well with those. + 1n addition to this we have also estimated. the value of Roto know about the nature of interstellar extinction law in the direction of clusters under study., In addition to this we have also estimated the value of R to know about the nature of interstellar extinction law in the direction of clusters under study. + We used the relation l5 — L1E(V—NO)/E(GCD 13) (Whittet. Dreda 1980)which is generally. used at longer wavelengths., We used the relation R = $E(V-K)$ $E(B-V)$ (Whittet Breda 1980)which is generally used at longer wavelengths. + The average values of It = 3.51 40.80 (sd) ancl 3.04+0.22 (scl) for Basel 4 and NGC 7067 respectively are not too clillerent from the value 3.1 for normal extinction In the lisht of above analysis. we conclude that interstellar extinction law is normal towards both Basel 4 and NGC 7067 in agreement with our earlier result.," The average values of R = 3.51 $\pm$ 0.30 (sd) and $\pm$ 0.22 (sd) for Basel 4 and NGC 7067 respectively are not too different from the value 3.1 for normal extinction In the light of above analysis, we conclude that interstellar extinction law is normal towards both Basel 4 and NGC 7067 in agreement with our earlier result." + An infrared excess is produced by the stars which are having their own envelope of gas ancl dust., An infrared excess is produced by the stars which are having their own envelope of gas and dust. + To investigate the IR flux in the stars of the clusters under study. we plottec AVff) and (OUA) against L(V7) in Fig 8.," To investigate the near-IR flux in the stars of the clusters under study, we plotted $\Delta(V-H)$ and $\Delta(V-K)$ against $E(V-J)$ in Fig 8." + The cillerences between the observed colour excess in (V44) and (V0A) based on spectral classification and the derivec colour excess from. L(VJ) assuming normal extinction aw are calculated., The differences between the observed colour excess in $(V-H)$ and $(V-K)$ based on spectral classification and the derived colour excess from $E(V-J)$ assuming normal extinction law are calculated. +" ""The cilferences can be considere statistically significant only if their absolute values are larger jui 70.5 mag.", The differences can be considered statistically significant only if their absolute values are larger than $\sim$ 0.5 mag. + The short cashed lines in Fig 8 represen 1 extent of expected errors., The short dashed lines in Fig 8 represent the extent of expected errors. + Observational uncertainties in JIIN magnitudes. inaccuracies in estimation of (Vs) wel errors in spectral classification may play major role in e determination of cillerences.," Observational uncertainties in $JHK$ magnitudes, inaccuracies in estimation of $E(V-J)$ and errors in spectral classification may play major role in the determination of differences." + An inspection of Fig S leads jiu the absolute values of ACVff) and ACVfv) are lose to zero of all the members., An inspection of Fig 8 leads that the absolute values of $\Delta(V-H)$ and $\Delta(V-K)$ are close to zero of all the members. + This indicate that there is no signature of near-H excess Iuxes., This indicate that there is no signature of near-IR excess fluxes. + The ZAMS fitting procedure. was emploved. to derive the distances of the clusters., The ZAMS fitting procedure was employed to derive the distances of the clusters. + Fig 9 shows the intrinsic CAL diagrams for Basel 4 and NGC 7067 whieh is plotted by considering the probable cluster members., Fig 9 shows the intrinsic CM diagrams for Basel 4 and NGC 7067 which is plotted by considering the probable cluster members. + For converting apparent V magnitude and (0D) VWRR) and (VO2) colours into intrinsic one. we used average values of £(BNV) and Following relations for £(UD) (οἱ.," For converting apparent $V$ magnitude and $(U-B)$, $(B-V)$ , $(V-R)$ and $(V-I)$ colours into intrinsic one, we used average values of $E(B-V)$ and following relations for $E(U-B)$ (cf." + Ixamp, Kamp +Exponential fits are indicated with dashed lines. while the dotted lines indicate the sky level for each galaxy.,"Exponential fits are indicated with dashed lines, while the dotted lines indicate the sky level for each galaxy." + Vertical lines correspond to the end of the bar., Vertical dashed-dotted lines correspond to the end of the bar. + Where there are two vertical lines. they indicate the lower and the upper limit to the end of the bar.," Where there are two vertical lines, they indicate the lower and the upper limit to the end of the bar." + The squares show the limits of the intervals that we have used to fit the exponential dises., The squares show the limits of the intervals that we have used to fit the exponential discs. +A new. string theory inspired paradigm |l] proposed by Arkani-[amed. Dimopoulos. and Dvali (ADD) in 1998 sugeested the solution to the hierarcliv woblem of the standard model (SM) by introducing several (17) spatial extra dimensions (ED) with the compactification radi as laree as ~1 nuu.,"A new, string theory inspired paradigm \cite{ADD} proposed by Arkani-Hamed, Dimopoulos, and Dvali (ADD) in 1998 suggested the solution to the hierarchy problem of the standard model (SM) by introducing several $n$ ) spatial extra dimensions (ED) with the compactification radii as large as $\sim 1$ mm." + These are introduced to solve the hierarchy problem of the SM x lowers the Planck scale to a TeV energy rauge. (, These are introduced to solve the hierarchy problem of the SM by lowering the Planck scale to a TeV energy range. ( +We further refer to thisfundamental Plauck scale iu the (L117 )-cdiaensional space-time as Mp.),We further refer to this Planck scale in the $n$ )-dimensional space-time as $M_D$ .) + In this victure. eravity permeates the cutive multidimensional space. while all the other ficlds are constrained to the 3D-space.," In this picture, gravity permeates the entire multidimensional space, while all the other fields are constrained to the 3D-space." + Consequently. the Plauck scale Alpi=MAGN oulv reflects the streneth of eravity from the point of view of a 3D-observer aud therefore can be much higher than the fundamental 4) Plauck Scale.," Consequently, the Planck scale $M_{\rm Pl} = 1/\sqrt{G_N}$ only reflects the strength of gravity from the point of view of a 3D-observer and therefore can be much higher than the fundamental $n$ )-dimensional Planck Scale." +" The size of laree extra dimensions (J?) is fixed bx their nuuber. ο, aud the fundamental Plauck scale Mp."," The size of large extra dimensions $R$ ) is fixed by their number, $n$, and the fundamental Planck scale $M_D$ ." +" By applying Causs’s law. one finds |1.2]:: Mg,=Sz:M7 R""."," By applying Gauss's law, one finds \cite{ADD,GRW}: $M^2_{\rm Pl} = 8\pi M_D^{n+2}\, R^n$ ." + Tf onc requires Mp~1 TeV aud a suele extra dimension. its size has to be of the order of the radius of the solar system however. already. for two ED their size is ouly ~1 mu: for three ED itis ~ Lum. hes similar to the size of an atom: for larger nmuuber of ED it further decreases to subatomic sizes aud reaches —1 fii for seven ED.," If one requires $M_D \sim 1$ TeV and a single extra dimension, its size has to be of the order of the radius of the solar system; however, already for two ED their size is only $\sim 1$ mm; for three ED it is $\sim 1$ nm, i.e., similar to the size of an atom; for larger number of ED it further decreases to subatomic sizes and reaches $\sim 1$ fm for seven ED." + Almost simultaneously with the ADD paradigm a very differcut low-cucrey utilization of the idea of compact extra dimensions has been introduced by Dienes. Dudas. and Gherghetta |3]..," Almost simultaneously with the ADD paradigm a very different low-energy utilization of the idea of compact extra dimensions has been introduced by Dienes, Dudas, and Gherghetta \cite{DDG}." + In their model. additional dimension(s) of the “natural” EWSB size of R~1 TeVt [1]. are added to the SM to allow for low-cnerey unification of gauge forces.," In their model, additional dimension(s) of the “natural” EWSB size of $R \sim 1 $ $^{-1}$ \cite{itev} are added to the SM to allow for low-energy unification of gauge forces." + In conventional SAI aud its popular extensions. such as supersvuuuetry. gauge couplines ruu loearithinically with energv. which is a direct consequence of the renormalization eroup evolution (RCE) equations.," In conventional SM and its popular extensions, such as supersymmetry, gauge couplings run logarithmically with energy, which is a direct consequence of the renormalization group evolution (RGE) equations." + Caiven the values of the strong. EM. aud weal couplings at low eueregies. all three couplings are expected to “unit” (ie. reach the same κοπο) at the energy ~1057 TeV. now as the Grand. Unification Theory (GUT) scale.," Given the values of the strong, EM, and weak couplings at low energies, all three couplings are expected to “unify” (i.e., reach the same strength) at the energy $\sim 10^{13}$ TeV, know as the Grand Unification Theory (GUT) scale." + However. if one allows gauge bosons respousible for strong. EM. and weak interactions to propagate in extra dimension(s). the RGE equatious would change.," However, if one allows gauge bosons responsible for strong, EM, and weak interactions to propagate in extra dimension(s), the RGE equations would change." + Namely. once the euergv is sufficient to excite Ialuzia-IKxleiu (IIs) modes of gauge bosous (Le. ~1/R~1 TeV). ruuuiug of the couplings is proportional to a certain power of energv. rather than its logaritlin.," Namely, once the energy is sufficient to excite Kaluza-Klein (KK) modes of gauge bosons (i.e., $\sim 1/R \sim 1$ TeV), running of the couplings is proportional to a certain power of energy, rather than its logarithm." + Thus. the unification of all three couplings can be achieved at mich lower energies Ll.," Thus, the unification of all three couplings can be achieved at much lower energies than the GUT scale, possibly as low as 10-100 TeV \cite{DDG}." +...," While this model does not incorporate gravity and thus does not explain its weakness relative to other forces, it nevertheless removes another hierarchy of a comparable size – the hierarchy between the EWSB and GUT scales." + 41.," In 1999, Randall and Sundrum offered a rigorous solution \cite{RS} to the hierarchy problem by adding a single extra dimension (with the size that can range anywhere from $\sim 1/M_{\rm Pl}$ virtually to infinity) with a non-Euclidean, warped metric." +.. KATTT ," They used the Anti-deSitter (AdS) metric (i.e. that of a space with a constant negative curvature) $ds^2 = \exp(-2kR|\varphi|)\eta_{\mu\nu}dx^\mu dx^\nu - R^2d\varphi^2$, where $0 \le \varphi < 2\pi$ is the coordinate along the extra spatial dimension of radius $R$ , $k$ is the curvature of the AdS space (warp factor), $x^\mu$ are the convential (3+1)-space-time coordinates, and $\eta^{\mu\nu}$ is the metric of the Minkowski space-time." +D, A 3D-brane with positive tension is put at $\varphi = 0$. +g tT Jee De ," If gravity originates on this (Planck) brane, the wave function of the graviton has a peculiar feature that it is exponentially suppressed away from the brane in the direction of the extra dimension." +-Di," If all the SM fields were confined to the Planck brane, one would not have seen any low-energy effects in this model." +y OTE Od αυ - .," However, if a second (SM) brane with negative tension is put at $\varphi = \pi$, than the $M_{\rm Pl}$ -size operators on the Planck brane would result in low-energy effects on the SM brane with the typical scale of $\Lambda_\pi = \overline{M}_{\rm Pl}\exp(-k\pi R)$, where $\overline{M}_{\rm Pl} \equiv M_{\rm Pl}/\sqrt{8\pi}$ is the reduced Planck mass." +.," If the SM fields are confined to the SM brane, the hierarchy problem is solved for $\Lambda_\pi \sim 1$ TeV, which can be achieved with a little amount of fine tuning by requiring $kR \sim 10$." +.," Since the only fundamental scale in this model is $M_{\rm Pl}$, the hierarchy problem is solved naturally for $R \sim 1/M_{\rm Pl}$." +.," In the simplest Randall-Sundrum (RS) model \cite{RS}, gravitons are the only particles propagating in the AdS space." +..1]., Numerous attempts to find large ED or constrain the ADD model have beencarried out since 1998. +.," They include measurements of gravity at short distances, studies of variousastrophysical and cosmological implications of large ED, and numerous collider searches for virtual and real graviton effects." +1, For detailed +in the frequency doublet.,in the frequency doublet. + The main clleet of the third frequeney is to introduce slow amplitude changes., The main effect of the third frequency is to introduce slow amplitude changes. + We conclude that the 23.40 evele d+ frequeney consists of two close frequencies beating with each other., We conclude that the 23.40 cycle $^{-1}$ frequency consists of two close frequencies beating with each other. + The fit is improved by the addition of a small-aniplitucle third [requencey. which might not be an independent modo.," The fit is improved by the addition of a small-amplitude third frequency, which might not be an independent mode." + In the previous papers on FG. Vir. the amplitude variations in V of the 19.87 evele dot frequeney were already. noticed (1985/6: 2.6 mmag. relatively poor data: 1992/3: 4.3 mamag: 1995: 3.5 mmag. 1996: μπας 2002-4 1.4 to 2.0 nunag).," In the previous papers on FG Vir, the amplitude variations in $V$ of the 19.87 cycle $^{-1}$ frequency were already noticed (1985/6: 2.6 mmag, relatively poor data; 1992/3: 4.3 mmag; 1995: 3.5 mmag, 1996: 2.8 mmag; 2002-4: 1.4 to 2.0 mmag)." + A cursory inspection of the cata also. indicates phase variations., A cursory inspection of the data also indicates phase variations. + These are the signatures of the Dlazhko I-Hfect., These are the signatures of the Blazhko Effect. + However. the statistical significance of some of these variations still needs. to be examined. in a more detailed analvsis which excludes potential errors caused by the other [requencies of the pulsating star.," However, the statistical significance of some of these variations still needs to be examined in a more detailed analysis which excludes potential errors caused by the other frequencies of the pulsating star." + We consequently apply the technique outlined in the previous section to this frequency as well., We consequently apply the technique outlined in the previous section to this frequency as well. + We notice immecdiately that rapid. variations within a single observing season. found above for the other two modes. are not present.," We notice immediately that rapid variations within a single observing season, found above for the other two modes, are not present." + This is demonstrated. in Fig., This is demonstrated in Fig. + 4. where we have adopted 10 best single frequency. to fit the 1995 and. 2002-4 data (19.867908 evele d 13.," 4, where we have adopted the best single frequency to fit the 1995 and 2002-4 data (19.867908 cycle $^{-1}$ )." + Both the amplitudes and phases show gaOW variations on a time scale of many vears., Both the amplitudes and phases show slow variations on a time scale of many years. + Note that a requency value near 19.867801 evele ‘can fit the 2002-4 ohases. but produces large phase shifts for the 1995 (and for 10 less extensive 1992. 1993 ancl 1996 data as well).," Note that a frequency value near 19.867801 cycle $^{-1}$ can fit the 2002-4 phases, but produces large phase shifts for the 1995 (and for the less extensive 1992, 1993 and 1996 data as well)." + The observed variations can be successfully. mocelled with two close frequencies separated. by 0.00013. evcle (Blazhko period ~ 21 vears)., The observed variations can be successfully modelled with two close frequencies separated by 0.00013 cycle $^{-1}$ (Blazhko period $\sim$ 21 years). + The good fit is shown in the igure., The good fit is shown in the figure. + However. the question examined in this paper is whether the cata suggest that two frequencies are really excited in the star.," However, the question examined in this paper is whether the data suggest that two frequencies are really excited in the star." + For such a long Blazhko period. the question cannot. be answered in a definite way clue to the incomplete Blazhko phase coverage and lack of observed repeated Blazhko eveles., For such a long Blazhko period the question cannot be answered in a definite way due to the incomplete Blazhko phase coverage and lack of observed repeated Blazhko cycles. + Consequently. the two-frequeney fit might just be no more (and. no less) than an excellent mathematical representation of the observed amplitude and phase variations by two frequencies.," Consequently, the two-frequency fit might just be no more (and no less) than an excellent mathematical representation of the observed amplitude and phase variations by two frequencies." + Note that at 12.15 and ET n . −≻⇀∫≻⊳≟∪≼⇍∙∖⇁≼∼∢⊾∠⇂⋖⋅⇀∖⊓⊾∐∢⊾⊔↿⊔↓⋜∐↓↕⋖⋅⊔↓⋜⊔⊔∼⋜↧⇂∖∖⋎∪−⇂↓⋅∢⋅⊏↥⋯⋅↓⊔↛∙∖⇁↕∐⊳∖⋅ ⋅ were also available. but that the detailed observed. phasing between the amplitude. anc phase. changes provided an acdelitional excellent verification of the beating hypothesis.," Note that at 12.15 and 23.40 cycle $^{-1}$ excellent mathematical two-frequency fits were also available, but that the detailed observed phasing between the amplitude and phase changes provided an additional excellent verification of the beating hypothesis." + ‘This additional verification is weaker for 19.87 evele , This additional verification is weaker for 19.87 cycle $^{-1}$. +The results for the three tested regions with closest frequencies are summarized in Table 1: together with those for other close frequencies of potential interest., The results for the three tested regions with closest frequencies are summarized in Table 1 together with those for other close frequencies of potential interest. + In the previous sections we have examined the observed amplitude variability., In the previous sections we have examined the observed amplitude variability. + We have shown that at least for two modes this is caused by beating between close frequencies., We have shown that at least for two modes this is caused by beating between close frequencies. + We shall now turn. to the observed. ubiquity of close frequencies in FC Vir. using the definition of close frequencies as those with a separation less than 0.1 evcle d5.," We shall now turn to the observed ubiquity of close frequencies in FG Vir, using the definition of close frequencies as those with a separation less than 0.1 cycle $^{-1}$." + ‘The majority of these pairs are so well separated in frequency. that these pairs do not show up in data as single frequencies with variable aniplitucles., The majority of these pairs are so well separated in frequency that these pairs do not show up in data as single frequencies with variable amplitudes. + Consequently. amplitude/phase tests are not necessary or possible in order to exclude the possibility. of spurious results. from amplitude variability.," Consequently, amplitude/phase tests are not necessary or possible in order to exclude the possibility of spurious results from amplitude variability." + Ehe frequency. distribution. of close frequency pairs may contain important information about their physical origin., The frequency distribution of close frequency pairs may contain important information about their physical origin. + 55 shows that the frequeney. pairs are not randomly cüstributed., 5 shows that the frequency pairs are not randomly distributed. + In this figure we have plotted the frequency values for all pairs with a separation less than 0.1 evele ., In this figure we have plotted the frequency values for all pairs with a separation less than 0.1 cycle $^{-1}$. + Phe y-axis represents the frequcney separation for cach pair. and each point corresponds to two very close frequencies.," The y-axis represents the frequency separation for each pair, and each point corresponds to two very close frequencies." + Also shown are the computed. frequencies of the radial modes for the FO) Vir model which fits both empirically estimated. global stellar parameters ancl racial fundamental mode frequency at the observed. frequeney. 12.154 cycle dLO, Also shown are the computed frequencies of the radial modes for the FG Vir model which fits both empirically estimated global stellar parameters and radial fundamental mode frequency at the observed frequency 12.154 cycle $^{-1}$. +'phe observed mode was certainly identified as radial by Viskum et. al. (, The observed mode was certainly identified as radial by Viskum et al. ( +1998). Dreger et al. (,"1998), Breger et al. (" +2005) and. Daszviisska-Daszkiowlez et al. (,2005) and Daszyńsska-Daszkiewicz et al. ( +2005).,2005). + One acdcditional observed. mode. 16.071 evele dὃν was also identified by Daszviisska-Daskiewiez οἱ al. (," One additional observed mode, 16.071 cycle $^{-1}$, was also identified by Daszyńsska-Daskiewicz et al. (" +2005) as a racial mode.,2005) as a radial mode. + An observed close frequency. pair occurs here too (16.071 and 16.091 evele d+)., An observed close frequency pair occurs here too (16.071 and 16.091 cycle $^{-1}$ ). + However. the requeney values predicted by our model are slightly cillerent (sce values below) and this mode identification needs to be confirmed independently with different methods.," However, the frequency values predicted by our model are slightly different (see values below) and this mode identification needs to be confirmed independently with different methods." + The effective. temperature of FC Vir. has. been determined. from atmospheric models. and. Stromeren photometry., The effective temperature of FG Vir has been determined from atmospheric models and Stromgren photometry. + The luminosity has been determined. from the Llipparcos parallax., The luminosity has been determined from the Hipparcos parallax. + Phe following values have been obtained: logως3.8692:0.012. logL/h.=1170-50.055. in agreement with the values of Daszvisska-Daszkiowlez et al. (," The following values have been obtained: $\log T_{\rm eff}=3.869\pm 0.012$, $\log L/L_{\odot}=1.170\pm 0.055$, in agreement with the values of Daszyńsska-Daszkiewicz et al. (" +2005).,2005). + “Phe equatorial rotational velocity of FG) Vir is found to be 66516 kms + (Zima 2005)., The equatorial rotational velocity of FG Vir is found to be $66\pm 16$ km $^{-1}$ (Zima 2005). + The evolutionary FC Vir model. whose racial frequencies are given in Fig.55. has the following basic parameters: AM= LSOM..logT;y=3.8658. 1.120. logg=3.980 and View=62.5 kms FLU(ZAMS)=το km/s).," The evolutionary FG Vir model, whose radial frequencies are given in 5, has the following basic parameters: $M=1.80 M_{\odot}$, $\log T_{\rm eff}= 3.8658$, $\log~L/L_{\odot}=1.120$ , $\log~g=3.980$ and $V_{\rm rot} = 62.5$ km $^{-1}$ $V_{\rm rot}{\rm (ZAMS)} = 70$ km/s)." + The computations were performed starting with chemically uniform models on the ZAAIS. assuming an initial hyelrogen abundance No=0.70 and heavy clement thundance Z=0.02.," The computations were performed starting with chemically uniform models on the ZAMS, assuming an initial hydrogen abundance $X=0.70$ and heavy element abundance $Z=0.02$." + The proportions in the abundances of 10 elements heavier than helium: were adopted. according to Crevesse Nocls (1993)., The proportions in the abundances of the elements heavier than helium were adopted according to Grevesse Noels (1993). + For the opacities. we used the OPAL data (Iglesias Rogers 1996) supplemented: with 16 lowtemperature data of Alexander Ferguson (1994).," For the opacities, we used the OPAL data (Iglesias Rogers 1996) supplemented with the low–temperature data of Alexander Ferguson (1994)." + The newest version of the OPAL equation of state was used (ltogers Navlonoy 2002)., The newest version of the OPAL equation of state was used (Rogers Nayfonov 2002). + No overshooting from the convective core was allowed., No overshooting from the convective core was allowed. + In the stellar envelope. the standard mixine-leneth theory of convection with à mixing- parameter a = 0.5 was used.," In the stellar envelope, the standard mixing-length theory of convection with a mixing-length parameter $\alpha$ = 0.5 was used." + This relatively low value of the mixine-leneth parameter was chosen. taking, This relatively low value of the mixing-length parameter was chosen taking +This procedure rejects about of the data.,This procedure rejects about of the data. +" We are now able to build pixel light curves, made of about 1000 measurements spread over 120 days."," We are now able to build pixel light curves, made of about 1000 measurements spread over 120 days." +" The stability can be expressed in term of the relative dispersion o/¢ measured for each light curve, where $ stands for the mean flux and o for the dispersion of the light curve."," The stability can be expressed in term of the relative dispersion ${\sigma}/{\phi}$ measured for each light curve, where $\phi$ stands for the mean flux and $\sigma$ for the dispersion of the light curve." +" This dispersion gives us a global estimate of the errors introduced by the alignments, combined with all other sources of noise (photon noise, read-out no"," This dispersion gives us a global estimate of the errors introduced by the alignments, combined with all other sources of noise (photon noise, read-out )." +"ise...)). In Fig. 4,,"," In Fig. \ref{fig:stab}," +" we present the histogram of this dispersion for one 50x patch of one CCD field, which shows a mean dispersion of9."," we present the histogram of this dispersion for one $50\times 50$ patch of one CCD field, which shows a mean dispersion of." +1%.. We estimate the contribution of the photon noise alone to be as high as7%., We estimate the contribution of the photon noise alone to be as high as. +". With such a noise level, dominated at this stage by photon counting and flux interpolation errors, one does not expect a good sensitivity to luminosity variations."," With such a noise level, dominated at this stage by photon counting and flux interpolation errors, one does not expect a good sensitivity to luminosity variations." +" Fortunately, various improvements described in the following (namely the averaging of the images of each night, the super-pixels and the seeing correction) will further reduce this dispersion by a factor of 5."," Fortunately, various improvements described in the following (namely the averaging of the images of each night, the super-pixels and the seeing correction) will further reduce this dispersion by a factor of 5." + The motivation of this pixel analysis is to increase the sensitivity to long duration events (>5 days) in the mass range where all the known candidates have been observed., The motivation of this pixel analysis is to increase the sensitivity to long duration events $\ge 5$ days) in the mass range where all the known candidates have been observed. + It is crucial to note that a sampling rate of 1 measurement per day is sufficient., It is crucial to note that a sampling rate of 1 measurement per day is sufficient. +" The numerous images available each night (up to 20 per night) allow us to reduce the noise discussed in Sect. 3.5,,"," The numerous images available each night (up to 20 per night) allow us to reduce the noise discussed in Sect. \ref{sec:err}," +" by co-adding them, and are very useful for the error estimation as emphasised in Sect. 7.."," by co-adding them, and are very useful for the error estimation as emphasised in Sect. \ref{section:opteb}." + We average the images of each night., We average the images of each night. +" During the night m, we have, for each pixel p, N? measurements of flux (oPp j=L1, NP)."," During the night $n$ , we have, for each pixel $p$, $N^p_n$ measurements of flux $ \phi^p_{n,j} $; $ +j = 1,N^p_n $ )." + The number of measurements N? available each night is shown in Fig., The number of measurements $N^p_n$ available each night is shown in Fig. + 5 and ranges between 1 and 20 with an average of 10., \ref{fig:nbima} and ranges between 1 and 20 with an average of 10. +" The mean flux $P of pixel p over the night is computed removing the fluxes which deviate bymore than 3c from the mean, in order to eliminate"," The mean flux $\phi^p_n$ of pixel $p$ over the night is computed removing the fluxes which deviate bymore than $3\sigma$ from the mean, in order to eliminate" +Cheimical evolution is a key to uncderstauci£& the hybrid role of massive star formation in the early universe wihi regard to the epoch of reionization. the heavy element abuucdauces of the oclest stars ancl tie hie iz intergalactic medium. aud te inass outflows associated with galaxy formation.,"Chemical evolution is a key to understanding the hybrid role of massive star formation in the early universe with regard to the epoch of reionization, the heavy element abundances of the oldest stars and the high $z$ intergalactic medium, and the mass outflows associated with galaxy formation." + In adclition. precicted supernova rates p'ovide us with au indepeudent. probe of the early epoch ol star formation.," In addition, predicted supernova rates provide us with an independent probe of the early epoch of star formation." + Combining abundance and supernova rate predictious allows us to develop au inproved incdersauding of both the cosuic star formation history aud of the eurichiment of the IGM. as well as to elucidate tlie nature of Popuatiou ILL (see e.g. the recent review of ?)).," Combining abundance and supernova rate predictions allows us to develop an improved understanding of both the cosmic star formation history and of the enrichment of the IGM, as well as to elucidate the nature of Population III (see e.g. the recent review of \citet{ciardi:05}) )." + The prevaleit view is that the first sars eucompassed the mass rauge 100 to 1000 NL.. Recent support for thiW. yossibility stems from tie ueed to reionize the Universe at ligh redshift. as ludicated » the WALAP Lirst-vear data (2)..," The prevalent view is that the first stars encompassed the mass range 100 to 1000 $_\odot.$ Recent support for this possibility stems from the need to reionize the Universe at high redshift \citep[]{cen:03a,haiman:03,wyithe:03,bromm:04a} + as indicated by the WMAP first-year data \citep{kogut:03}." + The possibility for ea‘ly reionizatiou by the [first galaxies was cousicdeed by ? aud further support for this Lypotlesi sis based on chemical abundance patterus at loxv 1uetallicity (2???)..," The possibility for early reionization by the first galaxies was considered by \citet{ciardi:03} and further support for this hypothesis is based on chemical abundance patterns at low metallicity \citep{wasserburg:00,oh:01,qian:01,qian:05}." + However. the robjess of the conclusio tha very lnassive stars (VAIS) were necessarily present among the firs ars has been questioned (??7)..," However, the robustness of the conclusion that very massive stars (VMS) were necessarily present among the first stars has been questioned \citep{venkatesan:03b,tumlinson:04,tumlinsona:05}." +" A ""normal"" initial mass functiou (ALE) --jay be capable of proc‘jue ionization consiste jowlh WMAP (??).. aud witl intjese constraluts. --- was argued (2) tha a broad set of chemical abtdauces inay be better fit usiuο the vields of Or stars with masses in he 1- 50 M.. range tlall With the vields from pair-iIstajlty supernovae (PISN) (2)."," A “normal"" initial mass function (IMF) may be capable of producing ionization consistent with WMAP \citep{venkatesan:03a,wyithe:03}, and within these constraints, it was argued \citep{venkatesan:04} that a broad set of chemical abundances may be better fit using the yields of \citet{umeda:03} for stars with masses in the 1- 50 $_\odot$ range than with the yields from pair-instabilty supernovae (PISN) \citep{heger:02}." +. ludeed. these results were confirijed i ?.hereafterDOSVA where it was argued that a top-heavy IMF without VMS supplied a better fit to low metallicity aUicance data while still accounting lor the early re-ionization of tle Uuiverse when using a detailed nodel of cosmic," Indeed, these results were confirmed in \citet[][hereafter DOSVA]{daigne:04} where it was argued that a top-heavy IMF without VMS supplied a better fit to low metallicity abundance data while still accounting for the early re-ionization of the Universe when using a detailed model of cosmic" +cutoff.,cutoff. +" (From the 24 Cepheids in the final sample. least-squares fits to a line vield slopes of -3.067 + 0.204 in Ix. and -3.073 — 0.233 in J. respectively,"," >From the 24 Cepheids in the final sample, least-squares fits to a line yield slopes of -3.067 $\pm$ 0.204 in K, and -3.073 $\pm$ 0.233 in J, respectively." + These slope values are shallower than. but within 1l σ consistent with the slopes for the Cepheid PL relations in the LAIC. which are -3.261 in Ix. ancl -3.153 in J (Persson et al.," These slope values are shallower than, but within 1 $\sigma$ consistent with the slopes for the Cepheid PL relations in the LMC, which are -3.261 in K, and -3.153 in J (Persson et al." + 2004)., 2004). + Following the procedure we have used in our previous papers. we adopt the LMC slopes of Persson et al. (," Following the procedure we have used in our previous papers, we adopt the LMC slopes of Persson et al. (" +2004) in our fits.,2004) in our fits. + This vields the following PL relations for WLM in the J and Ix bands: J — -3.153 log P + (22.795 £ 0.055) & = 0.256 Kk = 3261 log P + (22.436 £ 0.048) & = 0.223 The dispersions are larger than the dispersions of (he J and Ix band PL relations found in (he LMC by Persson et al. (, This yields the following PL relations for WLM in the J and K bands: J = -3.153 log P + (22.795 $\pm$ 0.055) $\sigma$ = 0.256 K = -3.261 log P + (22.436 $\pm$ 0.048) $\sigma$ = 0.223 The dispersions are larger than the dispersions of the J and K band PL relations found in the LMC by Persson et al. ( +2004). which are 0.12 mag in both bands.,"2004), which are 0.12 mag in both bands." + These values should Closely resemble the dispersions of these relations. eiven that thev are based on almost a hundred Cepheils whose mean magnitudes were derived [rom full infrared. lieht curves.," These values should closely resemble the dispersions of these relations, given that they are based on almost a hundred Cepheids whose mean magnitudes were derived from full infrared light curves." + The dispersions of the present PL relations observed in WLM are lareer mainly because Chev are based on a smaller umber of stars. and on mean magnitudes which are less precise than in the LMIC work of Persson et al.," The dispersions of the present PL relations observed in WLM are larger mainly because they are based on a smaller number of stars, and on mean magnitudes which are less precise than in the LMC work of Persson et al." + due to the existence of a few phase points only for each Cepheid., due to the existence of a few phase points only for each Cepheid. + In order to determine the relative distance moduli between WLM and the LMC. we need to convert the NICMOS (LCO) photometric svstem used by Persson οἱ al. (," In order to determine the relative distance moduli between WLM and the LMC, we need to convert the NICMOS (LCO) photometric system used by Persson et al. (" +2004) to the UNIRT system utilized in this paper.,2004) to the UKIRT system utilized in this paper. + According to Hawarden et al. (, According to Hawarden et al. ( +2001). there are just zero point offsets between the UAIRT and NICAIOS systems (e.g. no color dependences) in the J and Ix. filters. which amount to 0.034 and 0.015 mag. respectively.,"2001), there are just zero point offsets between the UKIRT and NICMOS systems (e.g. no color dependences) in the J and K filters, which amount to 0.034 and 0.015 mag, respectively." + Applving these offsets. and assuming an LMC true distance modulus of 13.50 as in our previous work in the Araucaria Project. we derive distance moduli for WLM of 24.993 c 0.055 mag in the J band. and 24.915 + 0.045 mag in the Ix band.," Applying these offsets, and assuming an LMC true distance modulus of 18.50 as in our previous work in the Araucaria Project, we derive distance moduli for WLM of 24.993 $\pm$ 0.055 mag in the J band, and 24.915 $\pm$ 0.045 mag in the K band." + As in our previous work. we will combine the distance moduli obtained from the photometry with the values we had previously derived in the optical VI bands in Paper I. to obtain a very robust determination of both the true distance modulus of WLM. and the total (mean) reddening of (he WLM Cepheids in our sample.," As in our previous work, we will combine the distance moduli obtained from the near-infrared photometry with the values we had previously derived in the optical VI bands in Paper I, to obtain a very robust determination of both the true distance modulus of WLM, and the total (mean) reddening of the WLM Cepheids in our sample." + When re-analvzing the results of Paper Lin the course of this work. we detected that by accident we had interchanged the distance modulus results reported for the V. and Wesenheit bands (p. GOL of Paper I).," When re-analyzing the results of Paper I in the course of this work, we detected that by accident we had interchanged the distance modulus results reported for the V and Wesenheit bands (p. 601 of Paper I)." + The correct values for (he reddened distance moduli in V and 1 derived [rom our photometry in Paper I are 25.156 + 0.04 mag and 25.121 + 0.03 mag. respectively.," The correct values for the reddened distance moduli in V and I derived from our photometry in Paper I are 25.156 $\pm$ 0.04 mag and 25.121 $\pm$ 0.03 mag, respectively." + As in our previous, As in our previous +X-ray heating of three regions is generally believed. to contribute to optical variability in low mass X-ray. binary (LMXDB) systems.,X-ray heating of three regions is generally believed to contribute to optical variability in low mass X-ray binary (LMXB) systems. + These are the accretion disc. a brigh spot on the outer edge of the accretion disc clue to inllowing material and the hemisphere of the companion facing the neutron star.," These are the accretion disc, a bright spot on the outer edge of the accretion disc due to inflowing material and the hemisphere of the companion facing the neutron star." + In most LAIN the reprocessed. X-ray opica Hux dominates the optical lightBs from the rest of the svsten (van(νι Paradijsaradijs 1983.1083. vanνι Pavaclijsaradi|js MeClintock 1995). particularly in the outburst phase.," In most LMXBs the reprocessed X-ray optical flux dominates the optical light from the rest of the system (van Paradijs 1983, van Paradijs McClintock 1995), particularly in the outburst phase." + “Phe companion iself mav only be evident at a very faint level when the svstem is in quiescence., The companion itself may only be evident at a very faint level when the system is in quiescence. + More recently it has become apparent tha svnchrotron emission from matter [owing out of the svstenir via bipolar jets makes a highly variable contribution to radio ane LR. emission. from many clillerent classes ο Ν-rav binaries (Fender 2003)., More recently it has become apparent that synchrotron emission from matter flowing out of the system via bipolar jets makes a highly variable contribution to radio and IR emission from many different classes of X-ray binaries (Fender 2003). + In some cases this emission mav extend ino the optical region (IIvnes ct al., In some cases this emission may extend into the optical region (Hynes et al. + 2000)., 2000). + At least one other persistent millisecond X-ray. pulsar. SAX J18SOS.A3658. is known have a transient LR excess and racio emission. probably due to svnchrotron processes (Wane et al.," At least one other persistent millisecond X-ray pulsar, SAX J1808.4--3658, is known to have a transient IR excess and radio emission probably due to synchrotron processes (Wang et al." + 2001), 2001). + On 2002 April 30 an X-ray transient. was ciscovered by temüllard. et al. (, On 2002 April 30 an X-ray transient was discovered by Remillard et al. ( +2002) using the All Sky Monitor. (ASAI) (Levine et al.,2002) using the All Sky Monitor (ASM) (Levine et al. + 1996) on The Rossi X-ray Timing ExplorerRATE satellite., 1996) on The Rossi X-ray Timing Explorer satellite. + NPE JO929314. the subject of this paper. was subsequently found to also be a millisecond X-ray. pulsar w Remillarc swank Strohmaver (2002).," XTE J0929–314, the subject of this paper, was subsequently found to also be a millisecond X-ray pulsar by Remillard, Swank Strohmayer (2002)." + Using ackelitionalRANTE Proportional Counter Array (PCA) observations Calloway et al. (, Using additional Proportional Counter Array (PCA) observations Galloway et al. ( +"2002a: 2002b) reported a neutron star spin pequency of 185 111. à binary period. of2615-8 and an implied companion mass of )SAI.. about 8.5 ""meJupiter DIASSON.","2002a; 2002b) reported a neutron star spin frequency of 185 Hz, a binary period of 2615-s and an implied companion mass of $\sim 0.008 M_{\odot}$, about 8.5 Jupiter masses." + A blue and variable optic‘al couterpart was d w CGreenhill. Giles Lill ," A blue and variable optical couterpart was suggested by Greenhill, Giles Hill (2002)." +This identification was supported. by spectra obtained bv Castro-Tirado: et al. (, This identification was supported by spectra obtained by Castro-Tirado et al. ( +2002) who ound a number of emission lines superimposed on a blue continuum which is tvjxcal of soft X-ray transients in outburst.,2002) who found a number of emission lines superimposed on a blue continuum which is typical of soft X-ray transients in outburst. + A coincident radio source was also reported by tupen. Dhawan Mioduszewski (2002).," A coincident radio source was also reported by Rupen, Dhawan Mioduszewski (2002)." + NTE JO929314 was the third transient. millisecond. X- pulsar to be discovered., XTE J0929–314 was the third transient millisecond X-ray pulsar to be discovered. + Phe first (SAX JISOS.43658) its been studied extensively at ene hs(Ciles. m Greenhill 1999: NE et al.," The first (SAX J1808.4–3658) has been studied extensively at all wavelengths (Giles, Hill Greenhill 1999; Wang et al." +" ""ul2001: Homer ct al.", 2001; Homer et al. + ela ot al., 2002; Wachter et al. + 2000: in Millert Zand et , 2000; in 't Zand et al. +"""nSN: Wijhands et """, 1998; Wijnands et al. +"nOl: MMMarkwauct. Wijnanc ""nSX> mWijnands van Ixlis 1998: Chakrabarty S: Chakrabarty"," 2001; Markwardt, Miller Wijnands 2002; Wijnands van der Klis 1998; Chakrabarty Morgan 1998; Chakrabarty" +and the free of charge versionLBLRTM?.,and the free of charge version. +. LBLRTM is available as FORTRAN source code and can be compiled on various platforms., LBLRTM is available as FORTRAN source code and can be compiled on various platforms. + Its most common application ts the spectral retrieval from. ground. and satellite based measurements in climatology., Its most common application is the spectral retrieval from ground and satellite based measurements in climatology. + The code accepts a custom model atmosphere and uses the HITRAN database (see Sect. ??)), The code accepts a custom model atmosphere and uses the HITRAN database (see Sect. \ref{sec:database}) ) + as input for the line data., as input for the line data. + We found LBLRTM easy-to-use. yet flexible. and computed all spectra presented in this paper with this code.," We found LBLRTM easy-to-use, yet flexible, and computed all spectra presented in this paper with this code." + The choice of a representative model atmosphere ts crucial for a realistic theoretical spectrum of the atmosphere., The choice of a representative model atmosphere is crucial for a realistic theoretical spectrum of the atmosphere. + One of the more basic deseriptions of a model atmosphere is given by the 1976 US StandardAtmosphere?.. and its geographical subdivisions (tropical. mid-latitude and sub-arctic summer and winter models).," One of the more basic descriptions of a model atmosphere is given by the 1976 US Standard, and its geographical subdivisions (tropical, mid-latitude and sub-arctic summer and winter models)." + Due to the geographical location of Cerro Paranal and the fractional changes in the abundance of trace gases since its definition. the 1976 US Standard Atmosphere gives arather poor representation of the atmospheric conditions above Cerro Paranal.," Due to the geographical location of Cerro Paranal and the fractional changes in the abundance of trace gases since its definition, the 1976 US Standard Atmosphere gives a rather poor representation of the atmospheric conditions above Cerro Paranal." + For example. the average surface temperature of the model at mm is only KK and thus too low by about KK on average.," For example, the average surface temperature of the model at m is only K and thus too low by about K on average." + In addition to the semi-static distribution of atmospheric trace gases. one has to account for the slowly variable temperature and pressure levels as well as the highly variable water vapour content.," In addition to the semi-static distribution of atmospheric trace gases, one has to account for the slowly variable temperature and pressure levels as well as the highly variable water vapour content." +" Thus. one has to base the calculations on a more flexible and realistic model atmosphere which takes meteorological inputs into account,"," Thus, one has to base the calculations on a more flexible and realistic model atmosphere which takes meteorological inputs into account." + We consider here the use of meteorological models from the Air Resources Laboratory (ARL) at the US National Oceanic and Atmospheric Administration (NOAA)., We consider here the use of meteorological models from the Air Resources Laboratory (ARL) at the US National Oceanic and Atmospheric Administration (NOAA). + Sounding files for temperature. pressure and dew point temperature in the troposphere and lower stratosphere (surface height € kkm) are available at the ARL based on either Global Forecast System (GFS) or archived Global Data Assimilation System (GDAS) models.," Sounding files for temperature, pressure and dew point temperature in the troposphere and lower stratosphere (surface height $\leq$ km) are available at the ARL based on either Global Forecast System (GFS) or archived Global Data Assimilation System (GDAS) models." + GFS analysis data are available in 3 hr intervals for the next hhours and 12 hr intervals for the next hhours., GFS analysis data are available in 3 hr intervals for the next hours and 12 hr intervals for the next hours. + GDAS models are available in 3 hr intervals for all dates since Dec 2004., GDAS models are available in 3 hr intervals for all dates since Dec 2004. + The horizontal resolution of the GFS and GDAS models is (approx., The horizontal resolution of the GFS and GDAS models is (approx. + kkm)., km). + Given that Cerro Paranal is very close to the Pacific ocean - kkm). the influence of the ocean climate on the chosen grid point could compromise its validity.," Given that Cerro Paranal is very close to the Pacific ocean $\sim$ km), the influence of the ocean climate on the chosen grid point could compromise its validity." + We have thus also computed model atmospheres for three nights during CRIRES SV periods on October 10. 2006. and March 3-4. 2007. based on the Fifth-Generation NCAR / Penn State Mesoscale Model (MMS) (Grelletal..1995).. which uses the operational analyses of the European Centre for Medium-Range Weather Forecasts (ECMWEF) as start and boundary conditions and was refined for the local topography of the Paranal area with a final resolution of kkm in the inner integration area.," We have thus also computed model atmospheres for three nights during CRIRES SV periods on October 10, 2006, and March 3–4, 2007, based on the Fifth-Generation NCAR / Penn State Mesoscale Model (MM5) \citep{MM5}, which uses the operational analyses of the European Centre for Medium-Range Weather Forecasts (ECMWF) as start and boundary conditions and was refined for the local topography of the Paranal area with a final resolution of km in the inner integration area." + Both meteorological models reproduced the ambient pressure and temperature at the VLT as recorded in the file headers of the analysed observations to within hhPa and KK. respectively.," Both meteorological models reproduced the ambient pressure and temperature at the VLT as recorded in the file headers of the analysed observations to within hPa and K, respectively." + All atmospheric. models have to be supplemented with information on the vertical distribution of all molecules other than H»O and used in the radiative transfer calculations., All atmospheric models have to be supplemented with information on the vertical distribution of all molecules other than $_2$ O and used in the radiative transfer calculations. + Moreover. since the meteorological models are limited to estimated surface heights of ~26kkm. we also have to add temperature. pressure and water vapour profiles for the remaming atmospheric. layers (26.0.0 as observed in he very metal-poor stars require so deep a mass cut which results in |Mg/Fo| x0.2. contrary. to the observations.," Figures 17e-17h show that in the spherical models, [Cr/Fe] $\lsim 0.0$, [Mn/Fe] $\lsim -0.5$, and [(Co, Zn)/Fe] $\gsim 0.0$ as observed in the very metal-poor stars require so deep a mass cut which results in [Mg/Fe] $\lsim 0.2$, contrary to the observations." + We point out that the bipolar models naturally accouut or these features., We point out that the bipolar models naturally account for these features. + Large |(€0. Zu)/Fe| small ον. Mu)/Fe|. aud large [(O. Mg)/Fo| are simultaneously realized as seen in Figures Ll aud 17..," Large [(Co, Zn)/Fe], small [(Cr, Mn)/Fe], and large [(O, Mg)/Fe] are simultaneously realized as seen in Figures \ref{f14} and \ref{f17}." + Compared with he spherical models. the bipolar models vield large [(Co. Zu)/Fo] aud small [(Cr. Mu)/Fo] for given [(Alg. O)/Fe].," Compared with the spherical models, the bipolar models yield large [(Co, Zn)/Fe] and small [(Cr, Mn)/Fe] for given [(Mg, O)/Fe]." + This is due to the characteristic iu lvdrodvuamics of the pola models. ie. the ejection of higher temperature (and higher eutropv) matter alone the z-axis aud the accretion of lower temperature matter along the +-axis.," This is due to the characteristic in hydrodynamics of the bipolar models, i.e., the ejection of higher temperature (and higher entropy) matter along the $z$ -axis and the accretion of lower temperature matter along the $r$ -axis." + If the formation of metal-poor stars was manly driven wea supernova shock wave. |Fe/TI] iu those stars is approximately determined by the ratio of the ejected mass of Fe to the amount of interstellar lyvdrogen swept up w the shock wave (Ryan ct al.1996).," If the formation of metal-poor stars was mainly driven by a supernova shock wave, [Fe/H] in those stars is approximately determined by the ratio of the ejected mass of Fe to the amount of interstellar hydrogen swept up by the shock wave (Ryan et al.1996)." +" Then |Fe/TI] of the rewly boru metal-poor star is expressed as Tere AL(Fejsx is the mass of ejected iron and A(IIDaw is the mass of interstellar hydrogen swept up by the shock wave,", Then [Fe/H] of the newly born metal-poor star is expressed as Here $M({\rm Fe})_{\rm SN}$ is the mass of ejected iron and $M({\rm H})_{\rm SW}$ is the mass of interstellar hydrogen swept up by the shock wave. + According to Shieeviuna Tsujimoto (1998). ALTsw can be estimated as," According to Shigeyama Tsujimoto (1998), $M({\rm H})_{\rm SW}$ can be estimated as" +"Finally, we show that cosmic ταν optical depths comparable to the value in maw be derived by inaking the extreme assumption that the imagnetic energv deusitv iu the ealaxy is roughly in equipartitiou with the gas random kinetic euergyv density. ic. B?/8x—j2 at the characteristic radius Ry.","Finally, we show that cosmic ray optical depths comparable to the value in may be derived by making the extreme assumption that the magnetic energy density in the galaxy is roughly in equipartition with the gas random kinetic energy density, i.e. $B^2/8\pi\sim3/2\,\rho_{g}\sigma_\star^2$ at the characteristic radius $R_g$." +" If the cosiuic rav pyarscattering ds provided by backeround magnetic turbulence with a Iolueeorov spectrum. the optical depth up to ££, is where AyRy is the staring scale aud 6By~ the fluctuation amplitude at the stirringscale for the iuterstellar magnetic turbulence. aud 5, is the Lanmnor radius in the galactic maeguetic field B for a ~10GeV proton."," If the cosmic ray scattering is provided by background magnetic turbulence with a Kolmogorov spectrum, the optical depth up to $R_g$ is where $\lambda_0\sim R_g$ is the stirring scale and $\delta B_0\sim B$ the fluctuation amplitude at the stirringscale for the interstellar magnetic turbulence, and $r_\ditto{L,\dg}$ is the Larmor radius in the galactic magnetic field $B$ for a $\sim10\unit{GeV}$ proton." +" Iustead. if the cosmic rav opacity results frou. Alfvéuu waves sel£eeuerated via the streaming instability. the cosinic ray optical depth will be where cy,=BVvltpy is the Alfvéóuu velocity im the ealaxv."," Instead, if the cosmic ray opacity results from Alfvénn waves self-generated via the streaming instability, the cosmic ray optical depth will be where $v_{_{A,\dg}}=B/\sqrt{4\pi\rho_g}$ is the Alfvénn velocity in the galaxy." + Note that both scattering mechanisunis vield au optical depth comparable to the result iuC2?)., Note that both scattering mechanisms yield an optical depth comparable to the result in. +". As discussedin refseciber.. during epochs of powerful jet activity the cosmic rav πιπο £,,, iujected into the duterstellar παται of the host ealaxy iav exceed the galaxws Eddington limut iu cosmic ravs LJide (compare eqs. (το)."," As discussedin \\ref{sec:Lcr}, during epochs of powerful jet activity the cosmic ray luminosity $L_\ditto{CR}$ injected into the interstellar medium of the host galaxy may exceed the galaxy's Eddington limit in cosmic rays $L_\ditto{Edd,CR}$ (compare eqs. \ref{eq:l_cr_str}) )" + and CI)., and \ref{e: LeddCR}) )). + Due to the outward cosnüc rav pressure force. Lydrostatic balance is lost aud a cosmic rav monieutun-diveu wind develops. removing the fuel for further star formation aud black bole acerction.," Due to the outward cosmic ray pressure force, hydrostatic balance is lost and a cosmic ray momentum-driven wind develops, removing the fuel for further star formation and black hole accretion." + However. the bulge aud black hole growth is completely choked off oulv if the radio-loud phase lasts long enough such that the total cucrey output in cosmic ravs. which would eventually couple to the interstellar iiediun. is comparable to the binding energy of the ealactic gaseous component.," However, the bulge and black hole growth is completely choked off only if the radio-loud phase lasts long enough such that the total energy output in cosmic rays, which would eventually couple to the interstellar medium, is comparable to the binding energy of the galactic gaseous component." + Iu other words. the requirement La2 Laqaaasd8 A necessary prerequisite. but efficient selfreenlation of the black hole ealaxy system ds achieved ouly when the requirement discussecl above is fulfilled as well.," In other words, the requirement $L_\ditto{CR}\gtrsim L_\ditto{Edd,CR}$ is a necessary prerequisite, but efficient self-regulation of the black hole – galaxy system is achieved only when the requirement discussed above is fulfilled as well." +" A generic feedback iechanisin is capable of selt-reeulating the combined black hole galaxy erowth oulv if the total enerev injected iuto the imterstellay medi AF), is comparable to the gravitational cucrey of the eas:OPS! SIEhnaas where we have adopted an isothermal sphere."," A generic feedback mechanism is capable of self-regulating the combined black hole – galaxy growth only if the total energy injected into the interstellar medium $\Delta E_{\ditto{inj}}$ is comparable to the gravitational energy of the gas: ^2, where we have adopted an isothermal sphere." + Ia what follows. we assiune that the gas fraction fy is iudepeudoeut of black hole mass aud stellar velocity dispersion.," In what follows, we assume that the gas fraction $f_g$ is independent of black hole mass and stellar velocity dispersion." + We now contrast our jet-powered cosmic ray feedback model with seltregulatiou mechanisius that act duiug the optically-luminous “quasar phase., We now contrast our jet-powered cosmic ray feedback model with self-regulation mechanisms that act during the optically-luminous “quasar phase.” + The argument. along with the work of?.. indicates that supermassive black holes at the ceuter of galaxies buill up their mass primarily by an act of radiativelv-efficieut. accretion. mu a relatively short-lived hieh-hunünositv “quasar phase”.," The argument, along with the work of, indicates that supermassive black holes at the center of galaxies build up their mass primarily by an act of radiatively-efficient accretion, in a relatively short-lived high-luminosity “quasar phase”." +" During this epoch. the accretionIuminosity approaches the black hole Thomsou Eddington limit L,,,,.* If cnerey release during the optically-bright quasar phase is responsible for black hole selt£regulatioun. the total energy. AE, absorbed by the galactic gas duriug the quasar lifetime At... should satisfyAF.~E, as prescribed by(??)."," During this epoch, the accretionluminosity approaches the black hole Thomson Eddington limit $L_{\ditto{Edd,\bullet}}$ If energy release during the optically-bright quasar phase is responsible for black hole self-regulation, the total energy $\Delta E_{\ditto{QP}}$ absorbed by the galactic gas during the quasar lifetime $\Delta t_\ditto{QP}$ should satisfy$\Delta E_{\ditto{QP}}\sim E_g$, as prescribed by." +". Π ouly a fraction ει of the accretion luninosity Eo can couple to the interstellar medi of the host ealaxy. we require E, ."," If only a fraction $\epsilon_\ditto{QP}$ of the accretion luminosity $L_\ditto{acc}$ can couple to the interstellar medium of the host galaxy, we require E_g ." +"(112) Assuniug L,.~ LyQQ4,,'. this can be rewritten as A"," Assuming $L_\ditto{acc}\sim L_\ditto{Edd,\bullet}$ , this can be rewritten as ." +LLL) The quasar lifetime At... set bv the argument. is roughly comparable to the Salpeter time —of the black hole:," The quasar lifetime $\Delta t_\ditto{QS}$ , set by the argument, is roughly comparable to the Salpeter time of the black hole:" +comparison fit is necessary as this fit describes the data very well.,comparison fit is necessary as this fit describes the data very well. +" The semimajor axis of this orbit is 4.07AU and at a distance of 21.55pe the apparent separation of the companion would be -0.19"".", The semimajor axis of this orbit is 4.07AU and at a distance of 21.55pc the apparent separation of the companion would be $\sim$ $''$. + However. even though the solutions are better constrained than the liner plots. they are still lower limits as only one inflection is securely found and it is likely that. at best. only 2/3*'s of the orbit has been mapped.," However, even though the solutions are better constrained than the liner plots, they are still lower limits as only one inflection is securely found and it is likely that, at best, only $^{\rm{rd}}$ 's of the orbit has been mapped." + The stars absolute H magnitude is 3.39 magnitudes and with the best estimates of the companion’s absolute H set at 14.2mag. the upper limit on the contrast ratio is estimated to be 10.8 magnitudes.," The star's absolute H magnitude is 3.39 magnitudes and with the best estimates of the companion's absolute H set at 14.2mag, the upper limit on the contrast ratio is estimated to be 10.8 magnitudes." + The observations of each of the stars chosen às primary candidates were carried out on 02 March 2006 using. the NACO-SDI instrument mounted on the 8m ESO VLT4-Yepun telescope in Paranal. Chile.," The observations of each of the stars chosen as primary candidates were carried out on 02 March 2006 using the NACO-SDI instrument mounted on the 8m ESO VLT4-Yepun telescope in Paranal, Chile." + The average seeing throughout the observing night was ~0.8., The average seeing throughout the observing night was $\sim$ $^{''}$. + The NACO AO system is described in detail in 2.., The NACO AO system is described in detail in \citet{rousset03}. + Since all targets in this project are very bright (V < 8) the star itself was chosen as the guide., Since all targets in this project are very bright $V$ $<$ 8) the star itself was chosen as the guide. + The SDI system employs a double caleite Wollaston prism to split the incoming beam into four separate beams and then feeds them through a quad CH4 filter that is set in the focal plane., The SDI system employs a double calcite Wollaston prism to split the incoming beam into four separate beams and then feeds them through a quad CH4 filter that is set in the focal plane. + The filters are set at central wavelengths of 1.5754 (Fl). 1.6004 (F2) and 1.6254m (F3a and F3b) and with bandpasses of 0.0254. which helps to limit residuals due to speckles and calcite chromaties.," The filters are set at central wavelengths of $\mu$ m (F1), $\mu$ m (F2) and $\mu$ m (F3a and F3b) and with bandpasses of $\mu$ m, which helps to limit residuals due to speckles and calcite chromatics." + The non-common path errors are less than 1Onm RMS per Zernicke mode between the beams (?))., The non-common path errors are less than 10nm RMS per Zernicke mode between the beams \citealp{lenzen04}) ). + In this configuration the telescope has a projected field of view of 5 arcseconds square. reduced to 2.7x3.7 areseconds after the tilt of 133° from the SDI focal plane mask during this run is considered. and has a camera plate scale of 0.017”pixel.," In this configuration the telescope has a projected field of view of 5 arcseconds square, reduced to 2.7x3.7 arcseconds after the tilt of $^{\circ}$ from the SDI focal plane mask during this run is considered, and has a camera plate scale of $''$ $^{-1}$." + The observations were performed using an 8-point jitter pattern., The observations were performed using an 8-point jitter pattern. + One of the jitter frames was a pure sky-frame to better aid in sky background removal., One of the jitter frames was a pure sky-frame to better aid in sky background removal. + Each jitter integration (Detector Integration Time aka DIT) ranged from 2-6 seconds depending on the brightness of the central PSF., Each jitter integration (Detector Integration Time aka DIT) ranged from 2-6 seconds depending on the brightness of the central PSF. + Each DIT was determined by increasing the time until the central few pixels of the star were saturated. allowing very high S/N in the halo of the PSF.," Each DIT was determined by increasing the time until the central few pixels of the star were saturated, allowing very high S/N in the halo of the PSF." + However. we believe that we could further increase this S/N by increasing the DIT’s and saturating more of the stellar PSF. since we will gain a higher dynamic range.," However, we believe that we could further increase this S/N by increasing the DIT's and saturating more of the stellar PSF, since we will gain a higher dynamic range." + Each observation took around 60 minutes to complete. consisting of 44 jitter cycles per star.," Each observation took around 60 minutes to complete, consisting of 44 jitter cycles per star." + The reduction of all the NACO-SDI raw data nade use of the custom pipeline of ??..," The reduction of all the NACO-SDI raw data made use of the custom pipeline of \citet{biller05,biller07}." + First. all the raw frames were cleaned for any background sky noise by subtracting out the sky image from the jitter cycle.," First, all the raw frames were cleaned for any background sky noise by subtracting out the sky image from the jitter cycle." + A standard flat-field is ther applied by combining the flat images into a master flat anc dividing out the pixel-to-pixel variations from each individual image frame., A standard flat-field is then applied by combining the flat images into a master flat and dividing out the pixel-to-pixel variations from each individual image frame. + To further clean the image a bad pixel map ts created from the jittered images to flag any dead pixels o1 the CCD chip and these are removed from all image frames., To further clean the image a bad pixel map is created from the jittered images to flag any dead pixels on the CCD chip and these are removed from all image frames. + Apertures are then extracted around each filtered image anc the Airy pattern and flux is scaled., Apertures are then extracted around each filtered image and the Airy pattern and flux is scaled. + The frames are then unsharp masked by dividing through by a heavily smoothed version of the original image., The frames are then unsharp masked by dividing through by a heavily smoothed version of the original image. + A shift and subtract algorithm is used to align the jittered images. with the first frame in the series used as the reference image and all other images aligned to this first image.," A shift and subtract algorithm is used to align the jittered images, with the first frame in the series used as the reference image and all other images aligned to this first image." + Once all data frames have been fully reduced the next step is to setup the analysis procedure., Once all data frames have been fully reduced the next step is to setup the analysis procedure. + This was done by adding and subtracting the various narrow-band filters across the methane feature to provide the best conditions for detecting the faint companions., This was done by adding and subtracting the various narrow-band filters across the methane feature to provide the best conditions for detecting the faint companions. + The two combinations that provide the best contrasts and S/N ratios to detect cool dwarfs target both M.L-type and T.Y-type objects.," The two combinations that provide the best contrasts and S/N ratios to detect cool dwarfs target both M,L-type and T,Y-type objects." + The SDI instrument. by its pure design. is built to search for companions of mid-T spectral type or later. since the subtraction across the methane band suppresses the starlight and speckle pattern to highlight objects with strong methane absorption in their atmospheres.," The SDI instrument, by its pure design, is built to search for companions of mid-T spectral type or later, since the subtraction across the methane band suppresses the starlight and speckle pattern to highlight objects with strong methane absorption in their atmospheres." + However it can also be used to search for L-dwarfs by combining all the filters to create a broadband image that would detect any L-dwarf signature., However it can also be used to search for L-dwarfs by combining all the filters to create a broadband image that would detect any L-dwarf signature. + This. however. is heavily limited by the bright star and the bright super-speckles in the image.," This, however, is heavily limited by the bright star and the bright super-speckles in the image." + We employed both these approaches to search for faint companions around the five stars in this project., We employed both these approaches to search for faint companions around the five stars in this project. + Before discussing each system individually. Fig.," Before discussing each system individually, Fig." + 8 shows the SDI reduced contrasts for all the systems on the same plot and scale., \ref{all_conts} shows the SDI reduced contrasts for all the systems on the same plot and scale. + The key in the upper right of the plot indicates which curve represents which system., The key in the upper right of the plot indicates which curve represents which system. + Since the SDI reduced curve represents the limiting 5c. contrast for each system this plot highlights how deep the observations reach over the, Since the SDI reduced curve represents the limiting $\sigma$ contrast for each system this plot highlights how deep the observations reach over the +because ils corresponding frequency may be much less than the optical band of interest.,because its corresponding frequency may be much less than the optical band of interest. + Both a forward shock and a reverse shock emerge when an ultrarelativistie cold GRB ejecla wilh initial Lorentz factor of sy sweeps up a stationary cold interstellar medium: the forward shock propagates into the interstellar medium and the reverse shock propagates back into the ejecta (Ixatz1994:Sari&Piran1995).," Both a forward shock and a reverse shock emerge when an ultrarelativistic cold GRB ejecta with initial Lorentz factor of $\gamma_0$ sweeps up a stationary cold interstellar medium: the forward shock propagates into the interstellar medium and the reverse shock propagates back into the ejecta \citep{k94, sp95}." +". The emission of the forward shock is characterized by (Sari.Piran.&Naravan1993) where. {ως is the critical Gimes when the break frequency. νε Crosses the observed frequency vp. ἐμ is the fraction of the shock energv goes into the magnetic field. e. is the fraction of the shock energv goes into the electrons. gy=(p—0.67)(p2)/(pLY. Go=(p—0.46)e.PEP) Gage=p4-0.14 (Granot&Sari2002).. Ey, is the isotropic-equivalent kinetic energy. » is the densitv of interstellar medium in units of 1 em7. 2 is the redshift of the burst. D, is the corresponding Iuminositw. distance. and /y is the observers time in units of 1 day."," The emission of the forward shock is characterized by \citep{spn98} + where, $t_{m,f}$ is the critical times when the break frequency, $\nu_{m,f}$ crosses the observed frequency $\nu_R$, $\epsilon_B$ is the fraction of the shock energy goes into the magnetic field, $\epsilon_e$ is the fraction of the shock energy goes into the electrons, $g_m=(p-0.67)(p-2)^2/(p-1)^2$, $g_c=(p-0.46)e^{-1.16p}$, $g_{max}=p+0.14$ \citep{gs02}, $E_{iso}$ is the isotropic-equivalent kinetic energy, $n$ is the density of interstellar medium in units of 1 ${\rm cm^{-3}}$, $z$ is the redshift of the burst, $D_L$ is the corresponding luminosity distance, and $t_d$ is the observer's time in units of 1 day." + The above equations are valid lor p>2., The above equations are valid for $p>2$. + Alterglows with the hard electron spectrum of 1300 yr experience other collision types than sticking., We only used the first 300 yr of the simulation because particles at $t>300$ yr experience other collision types than sticking. +" Since the relative velocity of small particles is dominated by Brownian motion, similar sized aggregates collide (CCA-like growth) as long as the particle mass is less than 10:75 g. However, when the turbulent relative velocity dominates over Brownian motion (at masses above 10~° g), the collision rate between equal sized aggregates is reduced."," Since the relative velocity of small particles is dominated by Brownian motion, similar sized aggregates collide (CCA-like growth) as long as the particle mass is less than $10^{-5}$ g. However, when the turbulent relative velocity dominates over Brownian motion (at masses above $10^{-5}$ g), the collision rate between equal sized aggregates is reduced." + The large aggregates (mass of 1074 g) preferentially collide with smaller ones (mass of 10-5 g)., The large aggregates (mass of $10^{-4}$ g) preferentially collide with smaller ones (mass of $10^{-8}$ g). + Therefore the results of Wadaetal.(2008) (which is based on equal sized collisions) might not capture the full complexity of the aggregate restructuring phase., Therefore the results of \cite{Wada2008} (which is based on equal sized collisions) might not capture the full complexity of the aggregate restructuring phase. +" Ideally, à restructuring collision model considering different sized aggregates is needed."," Ideally, a restructuring collision model considering different sized aggregates is needed." +" As such a model — and its experimental verification — is not available yet, we for simplicity decide to stick with the Braunschweig lab-based model, as we did in previous works."," As such a model – and its experimental verification – is not available yet, we for simplicity decide to stick with the Braunschweig lab-based model, as we did in previous works." +" We acknowledge the potential caveats of our adopted collision model, which we further discuss and quantify in Sect. 5.1.."," We acknowledge the potential caveats of our adopted collision model, which we further discuss and quantify in Sect. \ref{sec:collmod}." +" We perform altogether 21 simulations to investigate the effects of different porosity models and turbulence, in which we gradually use more realistic collision models."," We perform altogether 21 simulations to investigate the effects of different porosity models and turbulence, in which we gradually use more realistic collision models." + 'The IDs and parameters of these simulations are shown in Tab. 1.., The IDs and parameters of these simulations are shown in Tab. \ref{table:sedi}. + First we compare our model against the results of DD05 for compact particles (model DD in Tab. 1))., First we compare our model against the results of DD05 for compact particles (model DD in Tab. \ref{table:sedi}) ). + Then we use the hit&sstick porosity model of Okuzumietal.(2009) to investigate the effects of porosity (model DDa)., Then we use the stick porosity model of \cite{Okuzumi2009a} to investigate the effects of porosity (model DDa). + So far we assume that the aggregates stick at all relative velocities and that the turbulence parameter a is zero., So far we assume that the aggregates stick at all relative velocities and that the turbulence parameter $\alpha$ is zero. +" In the next step we construct a more realistic collision model with sticking, bouncing and fragmentation (model SB1)."," In the next step we construct a more realistic collision model with sticking, bouncing and fragmentation (model SB1)." + We call this collision model the “simplified Braunschweig, We call this collision model the “simplified Braunschweig +Quasi-stellar objects (QSOs) have proved to be very. useful COSDLOogical probes of the high-redshift Universe.,Quasi-stellar objects (QSOs) have proved to be very useful cosmological probes of the high-redshift Universe. + The availability. of large homogeneous surveys has made it possible to study the spaial distribution of quasars using statistical tools such as the two-point spatial correlation function., The availability of large homogeneous surveys has made it possible to study the spatial distribution of quasars using statistical tools such as the two-point spatial correlation function. +" ‘These studies lave revealed: that quasars are strongv clustered at. scales ο ""x20h1 (e.g. lovino et al.", These studies have revealed that quasars are strongly clustered at scales of $r<20h^{-1}$ (e.g. Iovino et al. + 199 :Xndreani Cristiani 1992: Mo Fang 1993: Ixomberg e ai., 1991; Andreani Cristiani 1992; Mo Fang 1993; Komberg et al. + 1994: Shanks Bovle 1994 and references therein), 1994; Shanks Boyle 1994 and references therein). + AIthough there is still an ongoing discussion. about whether 1jese correlations are evolving with redshilt. the fact tha 1e amplitude and shape of the quasar correlation function :ue roughv similar to those of Iow-redshift. objects VOSLo Aridreani Cristiani. 1992: Mo Fang 1903: Ixomberg et a.," Although there is still an ongoing discussion about whether these correlations are evolving with redshift, the fact that the amplitude and shape of the quasar correlation function are roughly similar to those of low-redshift objects (e.g. Andreani Cristiani 1992; Mo Fang 1993; Komberg et al." + 1994: 8jiiunks Dovle 1994) shows that quasars may. possibly be used. as tracers of the matter clistribution at meciunm redshif ποσα. 2)., 1994; Shanks Boyle 1994) shows that quasars may possibly be used as tracers of the matter distribution at medium redshifts $z\sim1-2$ ). + 1n addition to the statisical resuls. evidence has been founcl For structures in the quasar distribution at even larger (100—1505+ Alpe) seaes (Webster 1982: Crampton. Cowον Llartwick 1987. 1980: Clowes Campusano 1991a. 1991b: Graham. Clowes Campusano 1995: IxXomboerg et al.," In addition to the statistical results, evidence has been found for structures in the quasar distribution at even larger $\sim 100-150h^{-1}$ Mpc) scales (Webster 1982; Crampton, Cowley Hartwick 1987, 1989; Clowes Campusano 1991a, 1991b; Graham, Clowes Campusano 1995; Komberg et al." + 1996)., 1996). + These structures. which we call Large Quasar rou28 (LOCGsS). consist of ~1025 quasars ancl have sizes au density contrasts similar to those of nearby superclusters of galaxies (Ixomberg ct al.," These structures, which we call Large Quasar Groups (LQGs), consist of $\sim 10-25$ quasars and have sizes and density contrasts similar to those of nearby superclusters of galaxies (Komberg et al." + 1996)., 1996). + Reeenthy. similar higrecishift structures have been found in the distribution of absorbers (e.g. Jakobsen et al.," Recently, similar high-redshift structures have been found in the distribution of absorbers (e.g. Jakobsen et al." + 1986: Sargent steicde 1987: Jakobsen Perryman 1992: Dinshaw Impey. 1996: Williger et. al., 1986; Sargent Steidel 1987; Jakobsen Perryman 1992; Dinshaw Impey 1996; Williger et al. + 1996) ‘This indicates that supercluster tvpe structures are observed at redshifts ~0.52.5 the [ας which may be used as a useful constraint for existing models of structure formation and evolution., 1996) This indicates that supercluster type structures are observed at redshifts $\sim 0.5-2.5$ – the fact which may be used as a useful constraint for existing models of structure formation and evolution. + Ifthe quasar large-scale structures are real. we should be able to detect them using statistical methods.," If the quasar large-scale structures are real, we should be able to detect them using statistical methods." + Deng ct al. (, Deng et al. ( +1994) used the second derivative of the integral two-point spatial correlation function to search lor typical scales in the distribution of quasars.,1994) used the second derivative of the integral two-point spatial correlation function to search for typical scales in the distribution of quasars. + They argued that there exists a typical scale of about 95.1 Alpe and that this scale may be related to the specific shape of the initial perturbation spectrum., They argued that there exists a typical scale of about $95h^{-1}$ Mpc and that this scale may be related to the specific shape of the initial perturbation spectrum. + In this paper we present a study of the quasar distribution in three deep surveys., In this paper we present a study of the quasar distribution in three deep surveys. + We have used statistical methods similar to those of Deng ct al. (, We have used statistical methods similar to those of Deng et al. ( +1994).,1994). + Our goals and strategies. however. were somewhat dillerent.," Our goals and strategies, however, were somewhat different." + First. we have chosen to study only the deepest quasar surveys.," First, we have chosen to study only the deepest quasar surveys." + The number density of quasars in these surveys is much higher than in the larger surveys which makes them more sensitive, The number density of quasars in these surveys is much higher than in the larger surveys which makes them more sensitive +There is currently oulv one syvuibiotic binary with convincing evidence for a strongly imaenuctized WD.,There is currently only one symbiotic binary with convincing evidence for a strongly magnetized WD. + Sokoloski Bildsten (1999) discovered the first sviubiotic iiagnetic accretor iu the prototypical sviubiotie Z Andromedae., Sokoloski Bildsten (1999) discovered the first symbiotic magnetic accretor in the prototypical symbiotic Z Andromedae. + They repeatedly detected a statistically siguificaut oscillation at P=1682.6d0.6 s. which they interpreted as the spin period of the accreting white dwiwf.," They repeatedly detected a statistically significant oscillation at $P = 1682.6 \pm 0.6$ s, which they interpreted as the spin period of the accreting white dwarf." + Thus. coherent brightness oscillations are also a signature of magnetic accretion in sviibiotie stars.," Thus, coherent brightness oscillations are also a signature of magnetic accretion in symbiotic stars." + To explain the jets aud differeut brightuess states in CT Creni. \Gkolajewski&Mikolajewska(1988) proposed a magnetic propeller model. based on the oblique rotator theory of Lipuuov (1987).," To explain the jets and different brightness states in CH Cygni, \cite{mm88} proposed a magnetic propeller model, based on the oblique rotator theory of Lipunov \nocite{lip87}." +. They sugeested that the iuner disk is ejected aud a jet produced when the accretion rate onto the WD drops aud the system changes from the accretor to the propeller state., They suggested that the inner disk is ejected and a jet produced when the accretion rate onto the WD drops and the system changes from the accretor to the propeller state. + In their model. the optical flickering is due to the interaction of the accreted material with a strong maguetie feld.," In their model, the optical flickering is due to the interaction of the accreted material with a strong magnetic field." + Later. \Gkolajewskietal.(1990b) reported the detection of an oscillation with a period of 500 s. which they claimed was the rotation period of the white dwarf.," Later, \cite{mski90} reported the detection of an oscillation with a period of 500 s, which they claimed was the rotation period of the white dwarf." + If confined. this oscillation would provide some support for the magnetic propeller 11odol for CTI Cyeui (clichiisdiscussedfurtherbye...Mikolajewskietal.1990a.b:Pauferov&Mikolajewski 2000).," If confirmed, this oscillation would provide some support for the magnetic propeller model for CH Cygni \citep[which is discussed further by e.g.,][]{mmk90,mski90,panmski00}." +. A-rav. radio. aud optical observations by other authors. however. do not support the magnetic interpretation of CTI Creni.," X-ray, radio, and optical observations by other authors, however, do not support the magnetic interpretation of CH Cygni." + Ezukaetal.(1998). observed stochastic N-rax," \cite{ezu98} + observed stochastic X-ray" +Among the most lone-staucdine observationa coals for uuderstaudiug cometary origius has been the searci for cometary noble gases.,Among the most long-standing observational goals for understanding cometary origins has been the search for cometary noble gases. + OwiiD>oO to their combination of high volatility ancl clisallinity to chemical reactions. noble gases provide a key cdiaguostic to he thermal history of cometary ices.," Owing to their combination of high volatility and disaffinity to chemical reactions, noble gases provide a key diagnostic to the thermal history of cometary ices." +" lore specifically. the imeribers oft je He. Ne. Ar. Ir sequence clispay successively higher stbliuaiol temperatures: as such. they orovikde a series of therilometes that can be exploited to COstrain the thermal histo""v. and tlerefore the sites of comeary origins."," More specifically, the members of the He, Ne, Ar, Kr sequence display successively higher sublimation temperatures; as such, they provide a series of thermometers that can be exploited to constrain the thermal history, and therefore the sites of cometary origins." + Although the iuterpretation of noble gas abuudances iu couetary comae is complicated bv the details of their trapping ane release efficiencies 1i cometary ice (Owenetal.1991).. their detectiou has nouetheless yeen hielily desired.," Although the interpretation of noble gas abundances in cometary comae is complicated by the details of their trapping and release efficiencies in cometary ice \citep{Oea91}, their detection has nonetheless been highly desired." + Uuforturately. however. altough sigtilicaut upper limits revealing He cleglelol sof 101iu comet Austin (9ernetal.1992) ad Ne depetions of 25 in comet Hale- (Ixras1opolscyetal.1997). have been obtained. no cetectiol of any cometary noble gas enuinanatiug [roni witliu a comet has previously been obal1ος.," Unfortunately, however, although significant upper limits revealing He depletions of $\sim$ $^4$in comet Austin \citep{Sea92} and Ne depletions of $\sim$ 25 in comet Hale-Bopp \citep{Kea97} have been obtained, no detection of any cometary noble gas emmanating from within a comet has previously been obtained." + He. Ne. Ar. aid Ixr each have resonance t‘ausitious iu je [ar anc extreme ultraviolet.," He, Ne, Ar, and Kr each have resonance transitions in the far and extreme ultraviolet." + Amone the noble gases. a‘eon offers a particilarly exxxl combiuaion of coriparatively high cosmogouic abundance. moderate sublimation temperatufe. and gocxl UV resoauce [luoresceuce μις together these pro»erties suggested soue time ago (Sterretal.1992:Numinaet1993) that argon may be the easiest noble gas to detect i comets.," Among the noble gases, argon offers a particularly good combination of comparatively high cosmogonic abundance, moderate sublimation temperature, and good UV resonance fluorescence efficiency; together these properties suggested some time ago \citep{Sea92, +Mea93} that argon may be the easiest noble gas to detect in comets." + We took advantage of the apparition of the unusually active aid bright comet C/]L995 O]| (Hale-Bopp) in order to conduct a new and more sensitive search for argon 1i Comets., We took advantage of the apparition of the unusually active and bright comet C/1995 O1 (Hale-Bopp) in order to conduct a new and more sensitive search for argon in comets. + With the objectives of (1) obtaining a general survey spectrum of Hale-Bopp in the EUV uear its periheliou. alle (ii) makiuge a more seitive search for argon than lac previously been attempted [or auy comet. we launched the EUV5 sounding rocket telescope/spectrometer payload on a suborbital wissiou imed to coincide with tle comet's perivelion.," With the objectives of (i) obtaining a general survey spectrum of Hale-Bopp in the EUV near its perihelion, and (ii) making a more sensitive search for argon than had previously been attempted for any comet, we launched the EUVS sounding rocket telescope/spectrometer payload on a suborbital mission timed to coincide with the comet's perihelion." + This timing also corresponcded closely to the epoch of Hale-Bopp's peak iu activitv., This timing also corresponded closely to the epoch of Hale-Bopp's peak in activity. + The 181 kg ElVS j»avload (Slateretal.1995). consists ο ‘a [Ü-c—1 diameter grazing iucideuce elescope. a long slit Rowland circle spectrograp1. alkd its accM9)upauviiο Ranicon 2-D microchannel slate detector. power system. and telemetry electronics.," The 184 kg EUVS payload \citep{Sea95} consists of a 40-cm diameter grazing incidence telescope, a long slit Rowland circle spectrograph, and its accompanying Ranicon 2-D microchannel plate detector, power system, and telemetry electronics." + The telescope is a diamoud-turted [/15 Wolter type II grazing iuckleuce design. with a 30-cim apertire (Cas1etal.1939).," The telescope is a diamond-turned f/15 Wolter type II grazing incidence design, with a 30-cm aperture \citep{Cea89}." +. The ΓΗΙΑΝ 111‘ror is Ni coated: the secoudary is SiC coated., The primary mirror is Ni coated; the secondary is SiC coated. +" For the Hale-Bopp light. EUVS was codieurec [9] study the bandpass from 820-1100A:: the characteristic elective a‘ea of the instrument iu this deidpass is"" 0.5- >cui."," For the Hale-Bopp flight, EUVS was configured to study the bandpass from 820–1100; the characteristic effective area of the instrument in this bandpass is 0.5 $^2$." + EUVS was launched to observe Hale-Bopp on a NASA Black Brant LX soucling rocket [rom Wwlite Sands. New Mexico. at 03:25 UT on 30 Mar 1997.," EUVS was launched to observe Hale-Bopp on a NASA Black Brant IX sounding rocket from White Sands, New Mexico, at 03:25 UT on 30 Mar 1997." + At this time Hale-Bopp was less than {5 hous from perihelion. with a geocentric distance of AX=1.31 AU. a heliocentric clisance of R=0.915 AU. and a heliocentric radial velocity of R=-1.20 kins +.," At this time Hale-Bopp was less than 48 hours from perihelion, with a geocentric distance of $\Delta$ =1.34 AU, a heliocentric distance of $R$ =0.915 AU, and a heliocentric radial velocity of $\dot{R}$ =–1.20 km $^{-1}$ ." + The lauuch occurred in darkness. with," The launch occurred in darkness, with" +an AL«.N orthogonal matrix that contains theoutput sis vectors for D. or the vectors associated with the observable space.,"an $M \times N$ orthogonal matrix that contains the basis vectors for ${\bf D}$, or the vectors associated with the observable space." + Wis a diagonal matrix that contains he of D., ${\bf W}$ is a diagonal matrix that contains the of ${\bf D}$. +" The key clement to this work is the description of the uatrixD. which we call the desigu matrix and cach clement is a partial derivative of cach of the observable with respect to each of the parameters of the svsteni. aking iuto account the measurement errors for cach of he observables: Tere DB, are each of the &=1.2....M. observables of the system with expected errors ej, aad P; are cach of the j=1.2.....N free parameters of the svstei (see section 2.2. for discussion on the observables aud the piariuneters)."," The key element to this work is the description of the matrix, which we call the design matrix and each element is a partial derivative of each of the observable with respect to each of the parameters of the system, taking into account the measurement errors for each of the observables: Here $B_k$ are each of the $k = 1, 2, ...M$ observables of the system with expected errors $\epsilon_k$, and $P_j$ are each of the $j = 1,2,...,N$ free parameters of the system (see section \ref{sect:models} for discussion on the observables and the parameters)." + By writing the design matrix with the measurement errors taken iuto account. we provide a quantitative deseriptiou of the information couteut of cach of the observables for doteriunius the stellar parameters aud their uncertainties.," By writing the design matrix with the measurement errors taken into account, we provide a quantitative description of the information content of each of the observables for determining the stellar parameters and their uncertainties." +" Starting frou, an initial close guess of the solution Py. SVD can be used as au inversion techuique to obtain the true solution Pg of the system."," Starting from an initial close guess of the solution ${\bf P}_0$, SVD can be used as an inversion technique to obtain the true solution ${\bf P}_{\rm R}$ of the system." + This is done by calculating ai set of parameter corrections àP that iinimizes some eoodnuess-offit function: àP=VW!UT$3B. where óB are the differencesbetween the set of actual observations and the calculated observables By given the initial parameters Py.," This is done by calculating a set of parameter corrections ${\bf \delta P}$ that minimizes some goodness-of-fit function: ${\bf \delta P = V\bar{W}^{-1}U^T \delta B}$, where ${\bf \delta B}$ are the differencesbetween the set of actual observations and the calculated observables ${\bf B}_{\rm 0}$ given the initial parameters ${\bf P}_{\rm 0}$." +" W is a modification of the matrixW such that the iuverses of all values below a certain threshold are set to 0,", ${\bf \bar{W}}$ is a modification of the matrix such that the inverses of all values below a certain threshold are set to 0. +" The formal errors comprise the sun of all of the where cach describes the direction and V,fuy.magnitude to change a Vf,parameter so that the true solution Pp, aud formal uncertainties cau be given by Thematrice consequently assumes a neat and compact forni: and the square roots of the diagonal elemieuts of the covariance matrix are the theoretical parameter uncertainties."," The formal errors comprise the sum of all of the ${\bf V}_q/w_q$, where each ${\bf V}_q/w_q$ describes the direction and magnitude to change a parameter so that the true solution ${\bf P}_{\rm R}$ and formal uncertainties can be given by The consequently assumes a neat and compact form: and the square roots of the diagonal elements of the covariance matrix are the theoretical parameter uncertainties." + Note that e is reserved forerror and σ foruncertainty Another useful property of SVD is thesignificance 5S of an observable., Note that $\epsilon$ is reserved for and $\sigma$ for: Another useful property of SVD is the $S$ of an observable. + This cau be quantified as a measure of the extent that a 1-e change in 2). shifts the inferred parameters towards the l-0 error cllipsoid iu parameter space., This can be quantified as a measure of the extent that a $\epsilon$ change in $B_k$ shifts the inferred parameters towards the $\sigma$ error ellipsoid in parameter space. + Iu this wav. 59 quantifies the mupact that au observable las for the determination of the parameter solution: Because of the orthonormality of the decomposition matrices. the value of ο varies between 0 aud 1.," In this way, $S$ quantifies the impact that an observable has for the determination of the parameter solution: Because of the orthonormality of the decomposition matrices, the value of $S$ varies between 0 and 1." + A low ο implies that the observable D; has relatively less influence on the solution. aud that a change iu the meastvement will have little or uo impact.," A low $S_k$ implies that the observable $B_k$ has relatively less influence on the solution, and that a change in the measurement will have little or no impact." + A hieh value of 5j nuplies that this observable is inuportaut for the solution and any change in the measurement will force a corresponding change in the solution., A high value of $S_k$ implies that this observable is important for the solution and any change in the measurement will force a corresponding change in the solution. +" Finally, the matrices and provide information about the role cach of the observables plavs in determing the stellar parameters."," Finally, the matrices and provide information about the role each of the observables plays in determining the stellar parameters." + Each colin vector of (0U;) is related uuiquely to cach column vector of and its nuportauce iu the solution is given bv the (Vj)correspouding singular value «; (cf., Each column vector of $U_j$ ) is related uniquely to each column vector of $V_j$ ) and its importance in the solution is given by the corresponding singular value $w_j$ (cf. + Fig 1))., Fig \ref{fig:dscuti_svd_sgla}) ). + In section 3.1.0 we elaborate ou this discussion., In section \ref{ssec:dscuti_dermat} we elaborate on this discussion. + Tn this section we investigate the roles that cach observable plavs for determining each parameter., In this section we investigate the roles that each observable plays for determining each parameter. + We study how these roles change when we include/exclude certain observables and when we cousider different values of the observational crrors., We study how these roles change when we include/exclude certain observables and when we consider different values of the observational errors. + Figure 2. shows the significance (Eq. 5))," Figure \ref{fig:signif_sets_s} + shows the significance (Eq. \ref{eqn:signif}) )" + of each of he observables for a sinele star for OSs (top panel) and OSs |AS3 Gower panel). using the measurement errors frou the second columa in Table 2..," of each of the observables for a single star for $_S$ (top panel) and $_S$ +AS3 (lower panel), using the measurement errors from the second column in Table \ref{tab:obsers}. ." + Because here is no information about / Guclination). the feure illustrates that csin/ is uot anu effective constraiut (S= 0).," Because there is no information about $i$ (inclination), the figure illustrates that $v \sin i$ is not an effective constraint $S=0$ )." + lis also a weak coustraint. because both R aud Tig xovilde similar information. but of better quality.," is also a weak constraint, because both $R$ and $T_{\rm eff}$ provide similar information, but of better quality." + If either of these were not available. then logywould have ai higher significance.," If either of these were not available, then $\log g$would have a higher significance." + S=1 muplies, $S=1$ implies +Since both GRAPE-3 and GRAPE-4 calculate the force only with a Plummer softening. we performed. all caleulations in this section on workstations. using racial A45£. rather than MESE. and 64 bit precision.,"Since both GRAPE-3 and GRAPE-4 calculate the force only with a Plummer softening, we performed all calculations in this section on workstations, using radial $MISE$, rather than $MASE$, and 64 bit precision." + The integration in radial ALLESE was done as described in section 2.., The integration in radial $MISE$ was done as described in section \ref{sec:notation}. + As a first example of an alternative force. caleulation we will use the spline approximations given by LHernquist katz (1980). namely F-mrf(r). where and gn—rfc.," As a first example of an alternative force calculation we will use the spline approximations given by Hernquist Katz (1989), namely ${\bf F}=-m{\bf r}f(r)$, where and $u=r/\epsilon$." + Note that for rzc2« the value of the force in this approximation is exactlv the Newtonian force., Note that for $r \geq 2\epsilon$ the value of the force in this approximation is exactly the Newtonian force. + In. other words contrary to the Plummoer softening. and to the power-law softening introduced. below. the spline softening is approximate only for small distances.," In other words contrary to the Plummer softening, and to the power-law softening introduced below, the spline softening is approximate only for small distances." + As a second example we will consider an extension of the Plummer softening to values of the exponent other than two., As a second example we will consider an extension of the Plummer softening to values of the exponent other than two. + This can be given by which for p=2 gives back equation (1))., This can be given by which for $p$ =2 gives back equation \ref{eq:force_plum}) ). + A point to note is that for all values of p. including the commonly: used value p = 2. these forces tend to the Newtonian one only asvmptoticallv. i.e. even at large distances there is a finite. albeit small. difference between the results they give and those of the Newtonian force.," A point to note is that for all values of $p$, including the commonly used value $p$ = 2, these forces tend to the Newtonian one only asymptotically, i.e. even at large distances there is a finite, albeit small, difference between the results they give and those of the Newtonian force." + In other words they introduce a small but. non-zero smoothing even at large clistances. where it isn't necessary.," In other words they introduce a small but non-zero smoothing even at large distances, where it isn't necessary." + ligure 16. compares the amplitude of 1e non-softened Newtonian force with those of the Plummer. he p= 4 power-law and spline softened forces.," Figure \ref{compare_soft} compares the amplitude of the non-softened Newtonian force with those of the Plummer, the $p$ = 4 power-law and spline softened forces." + For this figure we have taken the softening as well as the masses equal to unity., For this figure we have taken the softening as well as the masses equal to unity. + We note that the force that approximates best the Newtonian one is the spline. followed. by the higher power softening. while the Plummer softening does the least well of the three.," We note that the force that approximates best the Newtonian one is the spline, followed by the higher power softening, while the Plummer softening does the least well of the three." + Thus the forces agree better than with the Newtonian one for distances larger than roughly 1.3. 2.2 ancl 5 softening lengths. corresponcingly for the spline. p-4 and Plummer softening.," Thus the forces agree better than with the Newtonian one for distances larger than roughly 1.3, 2.2 and 5 softening lengths, correspondingly for the spline, p=4 and Plummer softening." + In order to assess how well each softening can represent the forces in a given mass distribution we calculated racial, In order to assess how well each softening can represent the forces in a given mass distribution we calculated radial +apart from hydrostatic equilibrium and spherical symmetry.,apart from hydrostatic equilibrium and spherical symmetry. +" Foremost, it must be emphasized that invoking HSE for systems that are not dynamically results in significant bias and systematic scatter at the level of tens of per cent 2007)."," Foremost, it must be emphasized that invoking HSE for systems that are not dynamically results in significant bias and systematic scatter at the level of tens of per cent ." +". For relaxed clusters and measurements made at intermediate radii (r~2500), bias and scatter due to residual departures from equilibrium should be at the ~10 per cent level or less."," For relaxed clusters and measurements made at intermediate radii $r \sim r_{2500}$ ), bias and scatter due to residual departures from equilibrium should be at the $\sim 10$ per cent level or less." +" However, even in relaxed clusters, the assumption of HSE should be avoided in the outer regions (r2,rsoo) where gas clumping and increased non-thermal pressure support may occur."," However, even in relaxed clusters, the assumption of HSE should be avoided in the outer regions $r \gtsim r_{500}$ ) where gas clumping and increased non-thermal pressure support may occur." + The same is true of the central few tens of kpc in systems where the influence of the central active galactic nucleus is often evident2007)., The same is true of the central few tens of kpc in systems where the influence of the central active galactic nucleus is often evident. +". Ideally, à non-parametric method would be used to estimate masses, for example the model recently described by(2010)."," Ideally, a non-parametric method would be used to estimate masses, for example the model recently described by." +" In this particular approach, the cluster is modeled as a series of concentric, spherical shells, with constant temperature and total (dark matter + baryons) density in each shell."," In this particular approach, the cluster is modeled as a series of concentric, spherical shells, with constant temperature and total (dark matter + baryons) density in each shell." +" These non-parametric temperature and mass profiles, with the addition of an overall gas density normalization and under the assumption of HSE, determine the gas density at all radii."," These non-parametric temperature and mass profiles, with the addition of an overall gas density normalization and under the assumption of HSE, determine the gas density at all radii." +" Although this method is advantageous in principle, in practice it is only feasible with very high-quality data2010)."," Although this method is advantageous in principle, in practice it is only feasible with very high-quality data." +". More generally, some kind of regularization, in the form of an analytic model, is required to constrain hydrostatic masses."," More generally, some kind of regularization, in the form of an analytic model, is required to constrain hydrostatic masses." +" Based on the considerations discussed in this paper, it is preferable to apply this model to the total mass profile (e.g. the model) rather than the ICM."," Based on the considerations discussed in this paper, it is preferable to apply this model to the total mass profile (e.g. the model) rather than the ICM." +" Considered as a modification ofthe above algorithm, the resulting semi-parametric model is parametrized by a set of temperatures in concentric shells, a normalization for the gas density, and the parameters of the chosen total mass model."," Considered as a modification ofthe above algorithm, the resulting semi-parametric model is parametrized by a set of temperatures in concentric shells, a normalization for the gas density, and the parameters of the chosen total mass model." +" Precisely this approach was used recently by(2011),, who adopted an description of the mass profile to model data for the Perseus The similar method of(1981),, in which the ICM is parametrized by the surface brightness in concentric annuli and a pressure normalization at large radius, has also found use in the literature2010)."," Precisely this approach was used recently by, who adopted an description of the mass profile to model data for the Perseus The similar method of, in which the ICM is parametrized by the surface brightness in concentric annuli and a pressure normalization at large radius, has also found use in the literature." +". We note that the use of a parametrized mass profile along with the assumption of HSE typically allows the non-parametric temperature profile to be modeled at higher spatial resolution than in either a fully non-parametric mass solution or a simple, geometric de-projection (e.g. using thePROJCT model in XSPEC"")) where the mass is not modeled at all."," We note that the use of a parametrized mass profile along with the assumption of HSE typically allows the non-parametric temperature profile to be modeled at higher spatial resolution than in either a fully non-parametric mass solution or a simple, geometric de-projection (e.g. using the model in ) where the mass is not modeled at all." +" For fitting the scaling relations themselves, we note that a full treatment generically requires simultaneous modeling of the cluster mass function due to selection effects2011)."," For fitting the scaling relations themselves, we note that a full treatment generically requires simultaneous modeling of the cluster mass function due to selection effects." + Only when the intrinsic covariance between the observable of interest and the observable used to select the cluster sample is sufficiently small can approximate results be obtained without explicitly modeling the mass function and selection process., Only when the intrinsic covariance between the observable of interest and the observable used to select the cluster sample is sufficiently small can approximate results be obtained without explicitly modeling the mass function and selection process. +" In this case, the analysis should still include a full treatment of heteroscedastic and possibly correlated measurement errors, and intrinsic scatter2007)."," In this case, the analysis should still include a full treatment of heteroscedastic and possibly correlated measurement errors, and intrinsic scatter." +". used X-ray Observatory data to measure hydrostatic masses at r2500 for 42 hot (kT> 4.5keV), dynamically relaxed clusters at redshifts 0.054.5\keV$ ), dynamically relaxed clusters at redshifts $0.052s99 values is at the few per cent level, typically smaller than the statistical error bars These average temperatures arelisted in C1,, along"," The temperatures are typically measured within larger radii than $r_{2500}$ , but (being emission-weighted) the difference between these measurements and true $kT_{2500}$ values is at the few per cent level, typically smaller than the statistical error bars These average temperatures arelisted in , along" +and more vertical (in the £/AL|Tr diagram).,and more vertical (in the $L/M-T_{\rm eff}$ diagram). + As the iron abundance is further increased X=0.75.Z0.02.f 10). a regionὃν develops which contains several excited modes and whieh is bluer than the Fe-bump instability finger seen when the entire Z-component varies together.," As the iron abundance is further increased $X=0.75, Z=0.02, f=10$ ), a region develops which contains several excited modes and which is bluer than the Fe-bump instability finger seen when the entire $Z$ -component varies together." + This is) precisely the phenomenon identified. hy Charpinetetal.(1997)., This is precisely the phenomenon identified by \citet{Cha97}. +. Phe overall extent of our instability zone is larger than identified before: the earlier calculations benefit [rom obeving a total iron conservation law hy using an iron distribution obtained [rom a self-consistent calculation of radiative levitation., The overall extent of our instability zone is larger than identified before; the earlier calculations benefit from obeying a total iron conservation law by using an iron distribution obtained from a self-consistent calculation of radiative levitation. + The significance here is. that earlier. results are reproduced in character. if not. in detail. using a. simple model.," The significance here is that earlier results are reproduced in character, if not in detail, using a simple model." + It tells us that the principal characteristics of p-mode instability in EC14026 stars may be derived. from a homogeneous stellar envelope with a factor 10 enhancement in iron abundance (assuming Z 0.02)., It tells us that the principal characteristics of p-mode instability in EC14026 stars may be derived from a homogeneous stellar envelope with a factor 10 enhancement in iron abundance (assuming $Z\sim0.02$ ). + EFhis provides useful pointers for a subsequent investigation of e-mocde instability., This provides useful pointers for a subsequent investigation of g-mode instability. + lt ds interesting that reducing hvdrogen concentration extends the instability finger towards lower L/A andlower Tar., It is interesting that reducing hydrogen concentration extends the instability finger towards lower $L/M$ and $T_{\rm eff}$. + Whether this region of parameter space is populated by any real stars is a matter for conjecture., Whether this region of parameter space is populated by any real stars is a matter for conjecture. + LE they do. theyare," If they do, theyare" +produced during (he after-pulse phase.,produced during the after-pulse phase. + In particular. Z4 is not maintained after a ," In particular, $R_*$ is not maintained after a thermal-pulse." +Rather. the star eventually contracts as the temperature in the IIe-burning shell decreases and a new thermal pulse begins.," Rather, the star eventually contracts as the temperature in the He-burning shell decreases and a new thermal pulse begins." +" The maximum stellar radius. A7"". is only reached briefly at the end of the AGB evolution as the star gets to the AGB tip huninosity."," The maximum stellar radius, $R_*^{max}$, is only reached briefly at the end of the AGB evolution as the star gets to the AGB tip luminosity." + Consequently. it is safe to neglect the tidal term in Eq.," Consequently, it is safe to neglect the tidal term in Eq." +" 1 for orbital radii larger than 27"".", 1 for orbital radii larger than $R_*^{max}$. + The AGB and post-AGD evolution of the stellar mass-loss rate. effective temperature. and Dhumninositwv thal we use have been obtained [romthe stellar evolution models of Vassiliadis&Wood(1993.1994).," The AGB and post-AGB evolution of the stellar mass-loss rate, effective temperature, and luminosity that we use have been obtained fromthe stellar evolution models of \cite{Vw:93, Vw:94}." +. From these. we have calculated (he maximum radii. 277. reached by stars of different masses during ihe AGB phase.," From these, we have calculated the maximum radii, $R_*^{max}$, reached by stars of different masses during the AGB phase." +" These values of 77"" are listed in Table 1.", These values of $R_*^{max}$ are listed in Table 1. + Neglecting tidal interaction for rcRR and integrating Eq., Neglecting tidal interaction for $r \ge R_*^{max}$ and integrating Eq. +" 1. the orbital radius is then given by where r, is the initial orbital radius and M,(/) is time-dependent stellar mass caused by miass-Ioss."," 1, the orbital radius is then given by where $r_o$ is the initial orbital radius and $M_*(t)$ is time-dependent stellar mass caused by mass-loss." + In Fig., In Fig. + 1 we show the evolution of the orbital radius during the late AGB phase bv using lsRe [or each initial mass considered., 1 we show the evolution of the orbital radius during the late AGB phase by using $r_o~=~R_*^{max}$ for each initial mass considered. + In (he caleulation of AL.) we have considered the fact that the AGB mass-loss accounts for most of the mass lost by low-ancl stars and that mass-loss previous to the AGB is negligible., In the calculation of $M_*(t)$ we have considered the fact that the AGB mass-loss accounts for most of the mass lost by low-and intermediate-mass stars and that mass-loss previous to the AGB is negligible. +" This is a consequence of ⊔∐↲↓≯≀↧↴≺∢↥⊔⋯↴↥∐↓≀↧↴⊳∖⊽⊳∖⇁−↥∪⊳∖⋱∖⊽↕⋅≀↧↴∥↲⋟∖⊽∩∐⊔∐↲∐⊂↽⊐∐≀↧↴↕⋅≼↲↕↽≻↕⋅∪↕↽≻∪↕⋅∐∪∐≀↧↴↥↥∪∫↘⋝↝⊢∠ *j/M, (Reimers1975).. ↕⋅≼↲⋟∖⊽∏∐↕∐≸≟↕∐≀↧↪∖⇁↕↖≺↽↔↴↕∏⇂∎↓≺∢≀↧↴∐≀↧↴∐↓∪∏∐↥∪↓⋟≼↲∐∖↽≼↲↥∪↕↽≻≼↲∐↓≀↧⊔∖⊽⋟∖⊽↥∪⋟∖⊽↥∣↽≻≼↲↓⋟∪↕⋅≼↲⊔∐↲↼≚⊂↽⊐∐↕↽≻∐≀↕↪∖⊽≼↲∪↕∐∡∖↽↓⋟∪↕⋅⋟∖⊽↥≀↧↴↕⋅⋟∖⊽ ∖∖"," This is a consequence of the fact that mass-loss rates on the RGB are proportional to $R_*L_*/M_*$ \citep{Rei:75}, resulting in a significant amount of envelope mass lost before the AGB phase only for stars with initial masses $M_*~<$ 1." +⊽↕⊔↥↕∐∐↕≀↧↴⊔⊔≀↧↪∖⊽⊳∖⇁≼↲⋟∖⊽⇀⊔↝⊢↙∖∕∖⋊⊥⇀∖↕⋅⋅⋅ The higher the initial mass. the higher the amount of mass lost during the AGD phliase and hence the larger (he planets orbital expansion.," The higher the initial mass, the higher the amount of mass lost during the AGB phase and hence the larger the planet's orbital expansion." +" Planets reach a final orbital distance al ihe end of the AGB phase. determined by multiplving the initial orbit by M,/Myp where Miyp is the white dwarf mass. given that mass-loss is negligible once the star leaves the AGB."," Planets reach a final orbital distance at the end of the AGB phase, determined by multiplying the initial orbit by $M_*/M_{WD}$ where $M_{WD}$ is the white dwarf mass, given that mass-loss is negligible once the star leaves the AGB." + The orbital expansion factors for each stellar mass are given in column (4) of Table 1., The orbital expansion factors for each stellar mass are given in column (4) of Table 1. + Another effect to consider is whether the planet becomesunbound due to the change in mass of the central star., Another effect to consider is whether the planet becomesunbound due to the change in mass of the central star. + Unbinding can be expected if the stellar mass-loss timescale. Tinass [ose ΝΑΙΠΙΟΣ Tousfoss< Τη. Where Tassfoss IS given by," Unbinding can be expected if the stellar mass-loss timescale, $\tau_{mass-loss}$ , satisfies $\tau_{mass-loss} < \tau_{dyn}$ , where $\tau_{mass-loss}$ is given by" +22001: Simith 22011).,2001; Smith 2011). + These are consistent wilh temperatures inferred fom observations of the [forest at z«5 (Becker 22011)., These are consistent with temperatures inferred from observations of the forest at $z < 5$ (Becker 2011). + Owing to gravitational instabilitv. a realistic IGM is inhomogenous and filamentary.," Owing to gravitational instability, a realistic IGM is inhomogenous and filamentary." + senmi-analvtical models of the reionization of (he universe often adopt a “clumping factor’. Cy=OD). to account for inhomogeneity in estimates of the enhanced recombination rate in denser IGM filaments.," Semi-analytical models of the reionization of the universe often adopt a “clumping factor"", $C_H \equiv \langle n_e^2 \rangle / \langle n_e \rangle^2$, to account for inhomogeneity in estimates of the enhanced recombination rate in denser IGM filaments." + The clumping [actor therefore plavs an important role in computing the critical SER density needed to maintain the reionization of the universe., The clumping factor therefore plays an important role in computing the critical SFR density needed to maintain the reionization of the universe. +" The clumping factor is also used in numerical simulations to implement “sub-erid physics”. in which changes in the density field occur on scales below the resolution of the simulation and are also approximated by the factor Cy, (Gnedin Ostriker 1997: Macau 11999: \livalda-Eseudeé 22000: Miralda-Escude 2003: IxXohler 22007)."," The clumping factor is also used in numerical simulations to implement “sub-grid physics”, in which changes in the density field occur on scales below the resolution of the simulation and are also approximated by the factor $C_H$ (Gnedin Ostriker 1997; Madau 1999; Miralda-Escudé 2000; Miralda-Escudé 2003; Kohler 2007)." +" We correct the recombination time for density. variations scaled to a [iducial Cy,23. found in the simulations described below."," We correct the recombination time for density variations scaled to a fiducial $C_H \approx 3$, found in the simulations described below." +" At zT. the IGM filaments have electron density n,£(10bem""D+z)/8|C3. and the characteristic times for hydrogen recombination and IIubble expansion are. In our calculations. we express (he reionizalion criterion as Nj(Mpe.7)=PeseeQLeo Fs where fe is the critical SFR density (AZ.vr!Mpe. 7) and Que is the conversion factor from fig to the LyC production rate (see Section 2.2)."," At $z \approx 7$, the IGM filaments have electron density $n_e \approx (10^{-4}~{\rm cm}^{-3})[(1+z)/8]^3 C_H$, and the characteristic times for hydrogen recombination and Hubble expansion are, In our calculations, we express the reionization criterion as $N_H ({\rm Mpc}^{-3}) = \dot{\rho}_{\rm crit} t_{\rm rec} Q_{\rm LyC} f_{\rm esc}$ , where $\dot{\rho}_{\rm crit}$ is the critical SFR density $M_{\odot}~{\rm yr}^{-1}~{\rm Mpc}^{-3}$ ) and $Q_{\rm LyC}$ is the conversion factor from $\dot{\rho}_{\rm SFR}$ to the LyC production rate (see Section 2.2)." + We define f. as the fraction of LvC photons that escape from their galactic sources intothe IGM (Dove Shull 1994)., We define $f_{\rm esc}$ as the fraction of LyC photons that escape from their galactic sources intothe IGM (Dove Shull 1994). + Recent statistical estimates (Nestor 22011) suggest that foc20.1 lor an ensemble of 26 Lvman-break galaxies ancl 130 Lya emilters al 2zz3.09+0.03. ancl it could be higher for the lower-mass galaxies that likely dominate theescaping LyvC at z>6 (Fernandez Shull 2011).," Recent statistical estimates (Nestor 2011) suggest that $f_{\rm esc} \approx 0.1$ for an ensemble of 26 Lyman-break galaxies and 130 $\alpha$ emitters at $z \approx 3.09\pm0.03$, and it could be higher for the lower-mass galaxies that likely dominate theescaping LyC at $z > 6$ (Fernandez Shull 2011)." +" The LyC production efficiency. Que. is expressed in units LO"" photons per AL. of star formation. since typical massive stars emit (1—10)xLO LvC photons over their lifetime."," The LyC production efficiency, $Q_{\rm LyC}$, is expressed in units $10^{63}$ photons per $M_{\odot}$ of star formation, since typical massive stars emit $(1-10) \times 10^{63}$ LyC photons over their lifetime." + To evaluate Que. we convert the SER. (bx mass) into nunbers of OB-stars and. compute the total number of ionizing photons produced by a star of mass m. over its lifetime.," To evaluate $Q_{\rm LyC}$, we convert the SFR (by mass) into numbers of OB-stars and compute the total number of ionizing photons produced by a star of mass $m$ over its lifetime." +" We then integrale overan IME. Wom)=Wim . with a rangeao mq,IninmManx mg."," We then integrate overan IMF, $\Psi(m) = K m^{-\alpha}$ , with a range $m_{\rm min} < m < m_{\rm max}$ ." + The standard mass rangeao is 0.1 M. , The standard mass range is 0.1 $M_{\odot}$ +"we have implicille assumed that the nebula is [fully ionized. aud that 5»=n,=ny.","we have implicitly assumed that the nebula is fully ionized, and that $n=n_e=n_{\rm H}$." + The absorption of photons by dust is given by where & is the effective dust opacity (per atom)., The absorption of photons by dust is given by where $\kappa $ is the effective dust opacity (per atom). + It follows that dust absorption becomes relatively more important as the strength of the ionizing field increases and dominates the absorption of photons in the photoionized plasma when lere 4=διο) is the dimensionless ionization parameter and ¢ is (he speed of light., It follows that dust absorption becomes relatively more important as the strength of the ionizing field increases and dominates the absorption of photons in the photoionized plasma when Here ${\cal U} = S_{*}/cn$ is the dimensionless ionization parameter and $c$ is the speed of light. + substituting numerical values appropriate for solar abundance. we find that the critical ionization parameter above which dust dominates (he absorption is 20.01.," Substituting numerical values appropriate for solar abundance, we find that the critical ionization parameter above which dust dominates the absorption is $\sim $ 0.01." + This is in good agreement wilh what is indicated by detailed modelling., This is in good agreement with what is indicated by detailed modelling. + In fact. we can quite readilv compute the fraction of ionizing photons absorbed by a dusty rregion model relative to a cdust-Iree model.," In fact, we can quite readily compute the fraction of ionizing photons absorbed by a dusty region model relative to a dust-free model." + Dropping the explicit dependence of a on {νι the radiative transfer equation for a plane-parallel (geometrically (hin) nebula including both the eas (equation 5)) aud the dust (equation 6)) terms is solving this in terms of the ionization parameteral the inner edge of the nebula 04: where wy is the thickness of the ionized laver (with dust). aud 7; is the optical depth in dust through the ionized laver.," Dropping the explicit dependence of $\alpha$ on $T_e$, the radiative transfer equation for a plane-parallel (geometrically thin) nebula including both the gas (equation \ref{5}) ) and the dust (equation \ref{6}) ) terms is Solving this in terms of the ionization parameterat the inner edge of the nebula ${\cal U}_{0}$; where $x_{d}$ is the thickness of the ionized layer (with dust), and ${\tau}_{d}$ is the optical depth in dust through the ionized layer." +" In the absence of dust. we can integrate equation 5 to solve for (he Chickness of the ionised laver: 1,=cUy/on."," In the absence of dust, we can integrate equation \ref{5} to solve for the thickness of the ionised layer; $ x_{o}= c{\cal U}_{0}/{\alpha}n$." + Therefore. in a nebula of uniform density. the ratio of the recombination line [lux with aud without dust is simply f=ΕμΓη(0)= vf.," Therefore, in a nebula of uniform density, the ratio of the recombination line flux with and without dust is simply $f=F_{{\rm H}\beta}/F_{{\rm H}\beta}(0)=x_d/x_o$ ." + Thus it follows from equation 9 that, Thus it follows from equation \ref{9} that +spectra used.,spectra used. + Initially it was classified as an early type dwarf. O4 V (?).. but subsequently was revised to an earlier giant O3 Πιτ) (?)..," Initially it was classified as an early type dwarf, O4 V \citep{conti86}, but subsequently was revised to an earlier giant O3 III(f*) \citep{garmany87}." + More recently. -71751. was classified as O3.— ΝΤ by ?..," More recently, $-71^{\circ}51$ was classified as O3 V((f*)) by \citet{walborn02}." + The present higher S/N ratio spectra indicate an even earlier main sequence star of type O2 V((f*)) due to a large .44640) ratio., The present higher S/N ratio spectra indicate an even earlier main sequence star of type O2 V((f*)) due to a large 4640) ratio. + Note also the presence of, Note also the presence of +"Iu this paper. we simulate uebular euission line profiles using photoionization models,","In this paper, we simulate nebular emission line profiles using photoionization models." +" Our main objective is to investigate whether line profiles could be used to study nebular plivsical conditious and the problem of ORL/CEL abundaice-discrepaucies In Όλο,", Our main objective is to investigate whether line profiles could be used to study nebular physical conditions and the problem of ORL/CEL abundance-discrepancies in PNe. + This paper is organized as follows., This paper is organized as follows. + Section 2 presents our method., Section 2 presents our method. + In Sect., In Sect. + 3. we use line profiles to study temperature and density variation within nebulae aud compare with observations.," 3, we use line profiles to study temperature and density variation within nebulae and compare with observations." + Discussions aud. conclusions are preseuted m Sect., Discussions and conclusions are presented in Sect. + 1., 4. + The basic method is simular to that used by Cesicki et al. (20033) , The basic method is similar to that used by Gesicki et al. \cite{gesicki03}) ) +and. Morisset Stasitisska (2006a))., and Morisset Stasińsska \cite{morisset06a}) ). + We first construct piotolonization nodels using the CLOUDY COCe (Ferland e al. 1998))., We first construct photoionization models using the CLOUDY code (Ferland et al. \cite{ferland98}) ). + A dack-body spectral cuerey distinition is adopted for the ioniziug stars., A black-body spectral energy distribution is adopted for the ionizing stars. + The nebulae are assed to be a spherical shell with a eiven radial deusa. vodistribition., The nebulae are assumed to be a spherical shell with a given radial density distribution. + CLOUDY calculates the cuissivity distribution of the CELs and ORLs for different ionic species aud the hermal structure of nebulae., CLOUDY calculates the emissivity distribution of the CELs and ORLs for different ionic species and the thermal structure of nebulae. + Using known slit yperture auc positions and based on an assumed radia-velocity field. we deduce the inteerating line profiles by suuuuug alone the line of sight.," Using known slit aperture and positions and based on an assumed radial-velocity field, we deduce the integrating line profiles by summing along the line of sight." +" For our modecllines. we assume that the slit width is far narrower than the jicbular radius since high-resolution spectra are. iu all cases, essential for the study."," For our modellings, we assume that the slit width is far narrower than the nebular radius since high-resolution spectra are, in all cases, essential for the study." + The predicted line profiles are then derived by convolving the broadening caused by cluperature. seeiug conditions. and insruneut.," The predicted line profiles are then derived by convolving the broadening caused by temperature, seeing conditions, and instrument." + Turbulence is not tasen iuto account in our modelling., Turbulence is not taken into account in our modelling. + Cesicki Zijlstra (200:3) studied the expausion-volocitv fields of a nmuuber of PNe and found that turbulence uieht be significaut 1i WolfRavet PNe., Gesicki Zijlstra \cite{gesicki03b}) ) studied the expansion-velocity fields of a number of PNe and found that turbulence might be significant in Wolf-Rayet PNe. + Based. on a 3D modelling. Morisset Stasiisska (200G6a)). however. argued. that uo turbulence is required to explain the observed line profiles if one cowsiders a nehbular-model departure from the assiuipion of spherical svuuncetry.," Based on a 3D modelling, Morisset Stasińsska \cite{morisset06a}) ), however, argued that no turbulence is required to explain the observed line profiles if one considers a nebular-model departure from the assumption of spherical symmetry." + It is therefore safe to assunue hat he effects of turbulence. on a normal PN. can be neglected.," It is therefore safe to assume that the effects of turbulence, on a normal PN, can be neglected." + Figure 1 provides an illustration of our modolliug of a 1nediun-excitation PN., Figure \ref{model} provides an illustration of our modelling of a medium-excitation PN. + The velocity field is assunuced to have a positive eradieut across the nebula., The velocity field is assumed to have a positive gradient across the nebula. + Au inspection of Fie., An inspection of Fig. + 1l shows that the ligh-jonization lines are narrower than the low-ionization lines.," \ref{model} + shows that the high-ionization lines are narrower than the low-ionization lines." + This is because the high-ionized species are mainly located within the internal regious where the radial velocity is lower., This is because the high-ionized species are mainly located within the internal regions where the radial velocity is lower. + The profiles of e1üission lines arising from species with ciffercut ionization potentials have different depeuences on the velocity fieds. and provide constraints of the nebular dynamics.," The profiles of emission lines arising from species with different ionization potentials have different dependencies on the velocity fields, and provide constraints of the nebular dynamics." + Ctesicki et al. (1996.1998))," Gesicki et al. \cite{gesicki96,gesicki98}) )" + aud Cesicki Zijlstra (2000. 2003)) investigated velocity fields for a «uuple of PNe bv fitting the strong II [N uj. aud [O if line profiles.," and Gesicki Zijlstra \cite{gesicki00,gesicki03}) ) investigated velocity fields for a sample of PNe by fitting the strong H, [N ], and [O ] line profiles." + They foiud that the CXpausion velocities generally increase οιtwards. consistewt with the predictions of bydrodvuamical calculations.," They found that the expansion velocities generally increase outwards, consistent with the predictions of hydrodynamical calculations." + Decp spectroscopic observations cuale weaker lines Πιοπιοὃν CELs and ORLs which cover a wider range of ionizatiol potetials to be detected. aad tighter constrains on the deternunation of velocity fields to be made.," Deep spectroscopic observations enable weaker lines including CELs and ORLs which cover a wider range of ionization potentials to be detected, and tighter constrains on the determination of velocity fields to be made." + In the deep eclhielle sectra of the vouug PN IC £15. Sharpee et al. (2001)}," In the deep echelle spectra of the young PN IC 418, Sharpee et al. \cite{sharpee04}) )" + etected profiles of a munber of CELs and ORLs aud ound a negative correlaion between line widths aud ionization potentials., detected profiles of a number of CELs and ORLs and found a negative correlation between line widths and ionization potentials. + This is an implication tha nebular expansion-velocitics increase outwards., This is an implication that nebular expansion-velocities increase outwards. + Throughout this paper. a nonotonously-increasing velocity field is adopted.," Throughout this paper, a monotonously-increasing velocity field is adopted." + Fort1C LOCel shown in Fig. 1..," For the model shown in Fig. \ref{model}," + the [O 11] line profiles are muore sensiive to the velocity field than the [O 1 and |O mj li1e profiles because the O! species are the dominuaut jouization-state for the modeled 1neciuu-excitation nebula., the [O ] line profiles are more sensitive to the velocity field than the [O ] and [O ] line profiles because the $^+$ species are the dominant ionization-state for the modelled medium-excitation nebula. + Figure 1 also shows that the line widths decrease when the slit is placed towards the nebular edec., Figure \ref{model} also shows that the line widths decrease when the slit is placed towards the nebular edge. + This teudeucy is particularly evideut for low-ionization lues originating iu external nebular regions., This tendency is particularly evident for low-ionization lines originating in external nebular regions. + For a οἼναι expanding shell. this tendency is present because the velocity projected aloug the line of sight decreases. from nebular ceutre to edge. auc velocity broadening becomes less nmuportant with distance frou the nebular centre.," For a given expanding shell, this tendency is present because the velocity projected along the line of sight decreases from nebular centre to edge, and velocity broadening becomes less important with distance from the nebular centre." + At ti6 outer edge of nebulae. thermal broadening is doniiit.," At the outer edge of nebulae, thermal broadening is dominant." + Therefore. the emission lines originating in the outer edee of nebula have a Gaussian profile which is essentiallv independent of expansion velocity aud ouly," Therefore, the emission lines originating in the outer edge of nebula have a Gaussian profile which is essentially independent of expansion velocity and only" +As v—c. the apparent velocity ορ=diep/d! approaches ¢/2 for the receding particle and approaches infinity for the approaching particle.,"As $v\rightarrow c$, the apparent velocity $v_{\mathrm{p}}=dx_{\mathrm{p}}/dt$ approaches $c/2$ for the receding particle and approaches infinity for the approaching particle." + This latter result. accounts for some astronomical objects purportedly having “superluminal” speeds (see for example Deissler (200513) ," This latter result accounts for some astronomical objects purportedly having “superluminal” speeds (see for example \citet{Rees, Rybicki, Deissler}) )." +In general. the observer is al (d.e.f) and the particle at. Grp.yp.25) in the rest frame of the observer when the light signal is eimitted detected by the observer at time /. equation (2)) then becomes IE (n5.Uy.cp.r) are the coordinates for the emission of the light pulse in the rest frame of the emitter with this frame moving with a velocity v in the wr.’ direction which coordinates Grp.qp.2p.7) for this event. then. From equation (1)) so that so that equation (6)) becomes If we solve equation (9)) for wry). then If theparticle is moving[e] in the direction of increasing[e] wv (lLe.. e> 0) the negative[e] root is appropriate in equation (10)).," In general, the observer is at $\left(d,e,f\right)$ and the particle at $\left(x_{\mathrm{p}},y_{\mathrm{p}},z_{\mathrm{p}}\right)$ in the rest frame of the observer when the light signal is emitted detected by the observer at time $t$, equation \ref{eq:distance}) ) then becomes If $\left(x_{\mathrm{p}}^{\prime},y_{\mathrm{p}}^{\prime},z_{\mathrm{p}}^{\prime},\tau^{\prime}\right)$ are the coordinates for the emission of the light pulse in the rest frame of the emitter with this frame moving with a velocity $v$ in the $x,x^{\prime}$ direction which coordinates $\left(x_{\mathrm{p}},y_{\mathrm{p}},z_{\mathrm{p}},\tau\right)$ for this event, then, From equation \ref{eq:lorentz}) ) so that so that equation \ref{eq:dist_gen}) ) becomes If we solve equation \ref{eq:dist_gen_b}) ) for $x_{\mathrm{p}}$, then If theparticle is moving in the direction of increasing $x$ (i.e., $v>0$ ) the negative root is appropriate in equation \ref{eq:xp_sol}) )." + Iu the limit where ;ep/fpzd=ef= Q0. equation (10))," In the limit where $x_{\mathrm{p}}^{\prime}=y_{\mathrm{p}}^{\prime}=z_{\mathrm{p}}^{\prime}=d=e=f=0$ , equation \ref{eq:xp_sol}) )" +Many previous ayplications of the Edgeworth seres also faced with the problem that the resulting pdf is negative in sole region.,Many previous applications of the Edgeworth series also faced with the problem that the resulting pdf is negative in some region. + Thisis often attributed to fact that there are an insufficient number of terms in the Edgeworth series., This is often attributed to fact that there are an insufficient number of terms in the Edgeworth series. + The conditions needed for the truncated. Edgeworth expausions to be non-negative have been addressed ii simple cases by a few worss dn the statistical literature (2??)..," The conditions needed for the truncated Edgeworth expansions to be non-negative have been addressed in simple cases by a few works in the statistical literature \citep{draper,balitskaya,jondeau}." + In this paper. we shall investigate this problem uuucericallv and show that the vositivity of the pdf generally depends not oulv ou the wmmber of terms in the series. but also on the available informvation on higher-order momeuts.," In this paper, we shall investigate this problem numerically and show that the positivity of the pdf generally depends not only on the number of terms in the series, but also on the available information on higher-order moments." + We shall present some ecneral guidelines ou how the Edgewortl expansion could be used to model a non-negative non-Coaussiau pdt., We shall present some general guidelines on how the Edgeworth expansion could be used to model a non-negative non-Gaussian pdf. + Having developec the necessary backeround for proper use of the Edgeworth expansion. we shall apply it to study the effects of gxp 01i the number deusities of massive clusters aud large voids.," Having developed the necessary background for proper use of the Edgeworth expansion, we shall apply it to study the effects of $\gnl$ on the number densities of massive clusters and large voids." + First. let us iutroduce the necessary parameters which will allow us to describe the distribution of density fluctuations statistically.," First, let us introduce the necessary parameters which will allow us to describe the distribution of density fluctuations statistically." + Let p. poe py. pa be the time-dependent energy. densities of cold dark matter. barvous. radiation and dark cnerey.," Let $\rho_c$ , $\rho_b$, $\rho_r$, $\rho_\Lambda$ be the time-dependent energy densities of cold dark matter, baryons, radiation and dark energy." +" Let p,,=p.|py.", Let $\rho_m=\rho_c+\rho_b$. + We define the density parameter for species / as where poe is the critical density defined by puMISsrG., We define the density parameter for species $i$ as _i where $\rho\sub{crit}$ is the critical density defined by $\rho\sub{crit}\equiv 3H_0^2/8\pi G $. + The Dubble constant. fy. is piuiuuetrized by the usual formmla Hy=1005kustMpe +.," The Hubble constant, $H_0$, is parametrized by the usual formula $H_0\equiv100h \mbox{ km\ff s}^{-1}\mbox{Mpc}^{-1}$ ." +" Results from a range of astrophysical observations are consisteut with fx0.7. ο,=0,23. Οι=0016 and Ὁ,27SG&107; with O4=1OO,O, [sce 7]."," Results from a range of astrophysical observations are consistent with $h\simeq 0.7$, $\Omega_c\simeq0.23$, $\Omega_b\simeq0.046$ and $\Omega_r\simeq 8.6\times10^{-5}$, with $\Omega_\Lambda=1-\Omega_m-\Omega_r$ [see \cite{komatsu,lahav+}] ]." +" The density fluctuation field. 6. is defined as where (p,,j is the mean matter euerev density."," The density fluctuation field, $\delta$, is defined as where $\bkta{\rho_m}$ is the mean matter energy density." +" In Fourier space. the density fluctuation field cau be decomposed as ite, As we shall be dealing mainiy with observables iieasured at the present time. ty. we simply write ó(K) to mean ok.fy)."," In Fourier space, the density fluctuation field can be decomposed as ,t) As we shall be dealing mainly with observables measured at the present time, $t_0$, we simply write $\delta(\mb{k})$ to mean $\delta(\mb{k},t_0)$." + The gravitational Newtouian poteutial ® is related to the density fluctuation by the cosinological Poisson equation., The gravitational Newtonian potential $\Phi$ is related to the density fluctuation by the cosmological Poisson equation. + For a Fourier mode k. this reads d((k))= ?p(k). Statistical information on (x) cau be deduced from that of ó(K).," For a Fourier mode $\mb{k}$, this reads ) = ^2 Statistical information on $\delta(\mb{x})$ can be deduced from that of $\delta(\mb{k})$." + The finite resolution of any observation. however. niens that we can only empircallv obtain information on the momeuts of thedistribution.," The finite resolution of any observation, however, means that we can only empirically obtain information on the moments of thedistribution." +" More precisely, eiven a leneth scale R. the simoothed density field. 05. observed today is given by where &=|k| and D(O)zz0.76 is the linear growth factor evaluated at το=0."," More precisely, given a length scale $R$, the smoothed density field, $\delta_R$, observed today is given by where $k=|\mb{k}|$ and $D(0)\approx 0.76$ is the linear growth factor evaluated at $z=0$." + We choose TV. to be the spherical top-hat fuuctiou of radius Z2., We choose $W$ to be the spherical top-hat function of radius $R$ . + Iu Fourier space. we have Tt is also useful to define the mass of matter enclosed by the top-hat window as S Wefollow the approach outlined in? aud usethe transfer function T of Dicus Iu addition. we also incorporate the barvouic correction of ?.. whereby the trausterfunctiou is evaluated at," In Fourier space, we have It is also useful to define the mass of matter enclosed by the top-hat window as ^3 Wefollow the approach outlined in \cite{weinberg} and usethe transfer function $T$ of Dicus In addition, we also incorporate the baryonic correction of \cite{eisenstein}, , whereby the transferfunction is evaluated at" +of disks with i«15°.,of disks with $i<15\degr$. +" This is where spectro-astrometry steps in by constraining the line emission to much smaller spatial scales (S;1 AU), regardless of inclination, thus ruling out formation in a Keplerian flow at the —100c level."," This is where spectro-astrometry steps in by constraining the line emission to much smaller spatial scales $\lesssim1\,$ AU), regardless of inclination, thus ruling out formation in a Keplerian flow at the $\sim$$100\sigma$ level." +" AS 205N is the prototypical example of a source with single-peaked, broad winged line profile."," AS 205N is the prototypical example of a source with single-peaked, broad winged line profile." + T'he astrometric spectra of the three clean single-peaked sources are shown in Figure 7.., The astrometric spectra of the three clean single-peaked sources are shown in Figure \ref{peaky_sources}. +" For these sources, one out of three position angles, separated by 60? shows an astrometric line signature centered on the line velocity, but entirely offset in one direction."," For these sources, one out of three position angles, separated by $60\degr$ shows an astrometric line signature centered on the line velocity, but entirely offset in one direction." + The other two angles show the antisymmetric signature that might be expected from a Keplerian velocity field., The other two angles show the antisymmetric signature that might be expected from a Keplerian velocity field. +" The amplitudeof the astrometric spectra are 1 AU, and the astrometric line is significantly narrower Kj."," It can be seen that the contours are elongated in the field parallel direction, indicating that the eddies are anisotropic with $k_\perp>k_\para$." + The data is also binned according to scale / and the angle 05 between I and Bjgca., The data is also binned according to scale $l$ and the angle $\theta_B$ between $\mathbf{l}$ and $\mathbf{B}_{\text{local}}$. +" Nine linearly spaced scale bins are used over the range 2,000 km to 20,000 km and nine linearly spaced angular bins are used between aand90?."," Nine linearly spaced scale bins are used over the range 2,000 km to 20,000 km and nine linearly spaced angular bins are used between and." +". Straight lines, in log-log space, are then fitted to the structure functions over the full scale range for each 0p bin and the power anisotropy is obtained by evaluating these fits at a scale of 10,000 km."," Straight lines, in log-log space, are then fitted to the structure functions over the full scale range for each $\theta_B$ bin and the power anisotropy is obtained by evaluating these fits at a scale of 10,000 km." +" The spectral index in each Og bin is found using the relation &@=g+1, where —q is the spectral index and g is the structure function scaling exponent (Monin&Yaglom1975)."," The spectral index in each $\theta_B$ bin is found using the relation $\alpha =g+1$, where $-\alpha$ is the spectral index and $g$ is the structure function scaling exponent \citep{monin75}." +". This is similar to the work of Osman&Horbury(2009),, except we bin the data with respect to the field direction, since this appears to be the relevant mean field for the fluctuations, and we use many more intervals."," This is similar to the work of \citet{osman09a}, except we bin the data with respect to the field direction, since this appears to be the relevant mean field for the fluctuations, and we use many more intervals." +" The results, averaged over all 65 slow wind intervals, are shown in Fig. 3,,"," The results, averaged over all 65 slow wind intervals, are shown in Fig. \ref{fig:swanisotropy}," + where the error bars are the standard error of the mean from averaging the intervals., where the error bars are the standard error of the mean from averaging the intervals. +" They are similar to previous single spacecraft observations in the fast wind that show that power increases with 05 and that the spectral index varies from —2 at small angles to between —5/3 and —3/2 at large angles (Horburyetal.2008;Podesta2009;Luo&Wu2010;Wicks2010, 2011).."," They are similar to previous single spacecraft observations in the fast wind that show that power increases with $\theta_B$ and that the spectral index varies from $-2$ at small angles to between $-5/3$ and $-3/2$ at large angles \citep{horbury08,podesta09a,luo10,wicks10a,wicks11}." +" This scale-dependent anisotropy, therefore, has now been seen in both fast and slow wind using two different measurement techniques."," This scale-dependent anisotropy, therefore, has now been seen in both fast and slow wind using two different measurement techniques." +" The power anisotropy is consistent with eddies elongated along the local magnetic field direction and wavevector anisotropy of the form Κι> (Chenetal.2010b)..The —2 scaling at small 6g is consistentkj with both the theories of Goldreich&Sridhar(1995) and Boldyrev(2006), which describe critically balanced tturbulence."," The power anisotropy is consistent with eddies elongated along the local magnetic field direction and wavevector anisotropy of the form $k_{\perp}>k_{\para}$ \citep{chen10a}.The $-2$ scaling at small $\theta_B$ is consistent with both the theories of \citet{goldreich95} and \citet{boldyrev06}, which describe critically balanced turbulence." +" It has been suggested (e.g.Galtier2010),, however, that the parallel scaling of —2 may be due to discontinuities in the data."," It has been suggested \citep[e.g.][]{galtier10}, , however, that the parallel scaling of $-2$ may be due to discontinuities in the data." +" Using the same technique at smaller scales in the dissipation range, the —2 scaling is not seen (Chenetal.2010a) because the physics of the turbulence is different at these scales."," Using the same technique at smaller scales in the dissipation range, the $-2$ scaling is not seen \citep{chen10b} because the physics of the turbulence is different at these scales." + This suggests that the —2 scaling in the inertial range seen here is in fact due to the properties of the turbulence and not unrelated discontinuities., This suggests that the $-2$ scaling in the inertial range seen here is in fact due to the properties of the turbulence and not unrelated discontinuities. + The perpendicular spectral index that we obtain here (for 20° 10° . and a luminosity Πα) = 114 x 10° L. based on the broad line flix measured in 1999 (Table 2). leads to an upper limit on the mass of inflowing ionizedgas*.. ομως 10 M...," The mass of emitting gas may be deduced from the broad ${\alpha}$ emission line luminosity assuming standard (Case B) recombination theory; Using an effective recombination coefficient ${\alpha^{eff}_{H\alpha}}$ = 1.16 x $^{-13}$ ${^{3}}$ ${^{-1}}$, assuming a average density n ${\ge}$ $^6$ $^{-3}$, and a luminosity $L (H{{\alpha}}$ ) = 1.14 x ${^6}$ ${_{\sun}}$ based on the broad line flux measured in 1999 (Table 2), leads to an upper limit on the mass of inflowing ionized, $M_{emitting}$ ${\le}$ 10 ${_{\sun}}$." + H only a fraction of the gas is ionized then the upper limit on the/ofal Gonizecd + neutral) gas mass could. of course. be higher.," If only a fraction of the gas is ionized then the upper limit on the (ionized + neutral) gas mass could, of course, be higher." + ]t is straight forward to calculate the volume Lilline factor. e. for (he ionized eas producing the Ila emission once the dimensions of the emitting region have been established.," It is straight forward to calculate the volume filling factor, ${\epsilon}$, for the ionized gas producing the ${\alpha}$ emission once the dimensions of the emitting region have been established." +" For a uniform density medium occupying a spherical volume of radius +. one finds Again. using an elfective recombination coelficient απa —]16x10 P""em?s |. ο"," For a uniform density medium occupying a spherical volume of radius $r$, one finds Again, using an effective recombination coefficient ${\alpha^{eff}_{H\alpha}}$ = 1.16 x $^{-13}$ ${^{3}}$ ${^{-1}}$, assuming" +VLT and public HST data. and concluded that host galaxies do not reside in high density environments.,"VLT and public HST data, and concluded that host galaxies do not reside in high density environments." + The semi-analytic catalogues used in our study provide the positions of the LGRB host galaxies. as well as of all other galaxies in the simulation box.," The semi-analytic catalogues used in our study provide the positions of the LGRB host galaxies, as well as of all other galaxies in the simulation box." +" We have used this information to study the auto-correlation function of host galaxies. and the eross-correlation function between hosts and all galaxies in the simulation (which we will call ""normal"" galaxies)."," We have used this information to study the auto-correlation function of host galaxies, and the cross-correlation function between hosts and all galaxies in the simulation (which we will call “normal” galaxies)." + In order to compute the two-point correlation function. we adopt the ? estimator: where 2D(r) is the number of galaxy-galaxy pairs at distance r. RAC) is the number of random-random pairs. and {ΤΗ} is the number of random-galaxy pairs.," In order to compute the two-point correlation function, we adopt the \citet{lan93} estimator: where $DD(r)$ is the number of galaxy-galaxy pairs at distance $r$, $RR(r)$ is the number of random-random pairs, and $DR(r)$ is the number of random-galaxy pairs." + Fig., Fig. + IO. shows the auto-correlation function for LGRB host galaxies in the ΠΟΡΤΟ sample (dashed line) and for normal galaxies (solid line)., \ref{fig:cor3} shows the auto-correlation function for LGRB host galaxies in the HOST2 sample (dashed line) and for normal galaxies (solid line). + The number of galaxies in the HOST3 sample are too low to compute a reliable correlation function., The number of galaxies in the HOST3 sample are too low to compute a reliable correlation function. + Results are shown for the WMAP3B model. but they are similar for the WMAP! simulation.," Results are shown for the WMAP3B model, but they are similar for the WMAP1 simulation." + At low redshift. the auto-correlation function of host galaxies is lower than the corresponding function for normal galaxies.," At low redshift, the auto-correlation function of host galaxies is lower than the corresponding function for normal galaxies." + The difference between t1ο two functions decreases with increasing redshift and the two fulactions almost perfectly overlap üt 2>d., The difference between the two functions decreases with increasing redshift and the two functions almost perfectly overlap at $z > 4$. + As explained in Sec. 4..," As explained in Sec. \ref{sec:sfr}," + this is due to the decrease of metallicity at high redshift which implies that an increasing fraction of the global galaxy population can host a LGRB event according o our selection (see Sec. 3))., this is due to the decrease of metallicity at high redshift which implies that an increasing fraction of the global galaxy population can host a LGRB event according to our selection (see Sec. \ref{sec:method}) ). + The two point auto-correlation functions for the HOST? sample and for normal galaxies at +=ϐ is repeated in Fig. |," The two point auto-correlation functions for the HOST2 sample and for normal galaxies at $z=0$ is repeated in Fig. \ref{fig:cor2}," + ogether with the cross-correlation function between host and normal galaxies (solid line)., together with the cross-correlation function between host and normal galaxies (solid line). + The cross-correlation function lies in between the two auto-correlation functions. suggesting that the orobability of finding another host near a GRB host is lower than he corresponding probability of finding a normal galaxy.," The cross-correlation function lies in between the two auto-correlation functions, suggesting that the probability of finding another host near a GRB host is lower than the corresponding probability of finding a normal galaxy." + Our results are in qualitative agreement with those found by 9 and suggest that LGRB host galaxies tend to populate regions with density lower than average., Our results are in qualitative agreement with those found by \citet{bor04} and suggest that LGRB host galaxies tend to populate regions with density lower than average. + This is not entirely surprising if one considers that host galaxies are typically low-mass star forming galaxies which preferentially live in low density environments (?).., This is not entirely surprising if one considers that host galaxies are typically low-mass star forming galaxies which preferentially live in low density environments \citep{Kauffmann_etal_2004}. + From the theoretical point of view. it is interesting to ask which are the “descendants” of high-redshift LGRB host galaxies.," From the theoretical point of view, it is interesting to ask which are the `descendants' of high-redshift LGRB host galaxies." + Do they preferentially end up in massive haloes?, Do they preferentially end up in massive haloes? +" What are the typical morphology. colour, mass and metallicity of the descendants?"," What are the typical morphology, colour, mass and metallicity of the descendants?" + While this is a very difficult Gf not impossible) question to address observationally. it can be easily addressed with the available semi-analytic catalogues. which contain the full merger tree information for all galaxies in the simulation box.," While this is a very difficult (if not impossible) question to address observationally, it can be easily addressed with the available semi-analytic catalogues, which contain the full merger tree information for all galaxies in the simulation box." + In this section. we use this information to study the fate of LBRG host galaxies selected at +~4 (hereafter progenitors) in the observed mass-metallieity and colour-magnitude planes. and," In this section, we use this information to study the fate of LBRG host galaxies selected at $z\sim 4$ (hereafter ) in the observed mass-metallicity and colour-magnitude planes, and" +slightly depeudent ou the V—7 color. uucertainties in (V—Z)UERGB) have little influence on the derived distance.,"slightly dependent on the $V-I$ color, uncertainties in $(V-I)$ (TRGB) have little influence on the derived distance." + The above distauce determination is based ou the assumption that the reddest ROB stars in NGC 2306 have he age of elobular cluster stars. Le. are 10 Gyr okl.," The above distance determination is based on the assumption that the reddest RGB stars in NGC 2366 have the age of globular cluster stars, i.e. are $\sim$ 10 Gyr old." + For younger ages of the RGB stars. theoretical isochrones. e.g. those of the Padua group (Bertellietal.199I:Girardi or tle Geneva group (Lejeuue&Sclaerer.2001).. may be more appropriate.," For younger ages of the RGB stars, theoretical isochrones, e.g. those of the Padua group \citep{Be94,Gi96,Gi00} + or the Geneva group \citep{Le01}, may be more appropriate." + These are most often used fyr the analysis of resolved stella‘populations in Local Group aud relatively nearby galaxies., These are most often used for the analysis of resolved stellar populations in Local Group and relatively nearby galaxies. + However. ans ciscussed by several autleys (e.g.DaCosta&Armanclroll1990:Lyudsal.1998:Izotov&Thuan 2002).. these theoreical isochrones do Lave problems: they do not fi those observed for elobar ¢‘lusters.," However, as discussed by several authors \citep[e.g.,][]{Da90,Ly98,Iz02}, these theoretical isochrones do have problems: they do not fit those observed for globular clusters." + La particular. lzotov&Thuan(2002) have slowl that. excep for the isochrones witl Z = 0.001 from Bertellietal.(199[).. all 10 Gyr Padua isochrones do not reproduce the observed ones for globular clisters. being too blue aud not exeudiug to brigh enough absolute μπας]tudes.," In particular, \citet{Iz02} have shown that, except for the isochrones with $Z$ = 0.001 from \citet{Be94}, all 10 Gyr Padua isochrones do not reproduce the observed ones for globular clusters, being too blue and not extending to bright enough absolute magnitudes." + Furthermore. the isochrones tla do fit were obtained Grom stellar evolutionary iuodels calculated with okler opacities.," Furthermore, the isochrones that do fit were obtained from stellar evolutionary models calculated with older opacities." + Isochroues obtained from models with 1ew opacities for the same metalicity are again too blue (Girardieal.2000)., Isochrones obtained from models with new opacities for the same metallicity are again too blue \citep{Gi00}. +. As or the theoretical 10 Gyr isochrones based οι the Geneva stellar evolutionary 11jodels. they are oo red compared to those observed for elol»lar clusters.," As for the theoretical 10 Gyr isochrones based on the Geneva stellar evolutionary models, they are too red compared to those observed for globular clusters." + However. despite all hese uncelaluties. Padua moc (Bertellietal.1991) cau p'ovide a good etude to the clepen¢οιce of AZ; (TRGB ou the age of RGB stars. since in this case we are cousideriug relative rather han absoltte values.," However, despite all these uncertainties, Padua models \citep{Be94} can provide a good guide to the dependence of $M_I$ (TRGB) on the age of the RGB stars, since in this case we are considering relative rather than absolute values." + These moc predict that AZ; CERGB) is1early constant lor RGB stars witl ages o> 3 Gyr., These models predict that $M_I$ (TRGB) is nearly constant for RGB stars with ages $\ga$ 3 Gyr. + This implies that distance of 3.12 Mpc derived above for NGC 2366 is valid as long as its oldest RGB stars a'e ϱ) Gyr or older. which is likely the case for NGC 2366 (see section. L.1).," This implies that the distance of 3.42 Mpc derived above for NGC 2366 is valid as long as its oldest RGB stars are $\sim$ 3 Gyr or older, which is likely the case for NGC 2366 (see section 4.4)." + Several generations of stellar populatious a' eviclently present in the CMD of NGC 2366 (Fig. 3)).," Several generations of stellar populations are evidently present in the CMD of NGC 2366 (Fig. \ref{Fig3}) )," + SugeO0esting that star formation in this ealaxy has occurred during the past several Gyr., suggesting that star formation in this galaxy has occurred during the past several Gyr. + Ongoing star formation is evidenced by tle pleseice of the supergiant. H regious I aud II at the southwestern edee of the galaxy., Ongoing star formation is evidenced by the presence of the supergiant H regions I and II at the southwestern edge of the galaxy. +" Past star formatiou is inferred from the preseuce of MS stars witli ages of only a few Myr. of BL aud RSC ars wilh ages raueine rom 20 Myr to 100 Myr. of AGB stars with ages > 100 Ayr ancl of RGB sta ""owlth ages = ] Gyr."," Past star formation is inferred from the presence of MS stars with ages of only a few Myr, of BL and RSG stars with ages ranging from $\sim$ 20 Myr to $\sim$ 100 Myr, of AGB stars with ages $\ga$ 100 Myr and of RGB stars with ages $\ga$ 1 Gyr." + The spatial distribution of these diffe'ent stellar »opulations. as delimited in Fig. V.3..," The spatial distribution of these different stellar populations, as delimited in Fig. \ref{Fig3}," + is shown in Fig. 6.., is shown in Fig. \ref{Fig6}. + To miuimize incoripleteness elects CTable 1)) and plotometric errors (Fig. 2)), To minimize incompleteness effects (Table \ref{Tab1}) ) and photometric errors (Fig. \ref{Fig2}) ) + which become important [or 4 > 2> mae. we will consider i1 Fig.," which become important for $I$ $\geq$ 25 mag, we will consider in Fig." + 6 aud in all the following discussions ou star counts ouly sources tlat are brighter than / = 25 mag., \ref{Fig6} and in all the following discussions on star counts only sources that are brighter than $I$ = 25 mag. + I can be seen that a large number ol the MS stars (Fig., It can be seen that a large number of the MS stars (Fig. + Gaa) are located i the HU 'Pglons {. IL. aud Π as well as in those in the northeast part of the eloigatecd main body.," \ref{Fig6}a a) are located in the H regions I, II, and III as well as in those in the northeast part of the elongated main body." + They show a Ctunpy distributiou. reflectiug the compactuess of the HII regiors.," They show a clumpy distribution, reflecting the compactness of the H regions." + But there are also sotje MS stars that are more evenly cistributed over the whole body of the galaxy. out to the edges o ‘the WEDPC? frames.," But there are also some MS stars that are more evenly distributed over the whole body of the galaxy, out to the edges of the WFPC2 frames." + BL and RSC stars are, BL and RSG stars are +sunulates blend lieht curves resultiug from the fux of the eclipsing pair diluted bv the brighter target (aud any additional stars that may fall within the photometric aperture).,simulates blend light curves resulting from the flux of the eclipsing pair diluted by the brighter target (and any additional stars that may fall within the photometric aperture). + Each simulated light curve is compared with the oobservations in a P seuse to ideutify which of them result in acceptable fits (to be defined later)., Each simulated light curve is compared with the observations in a $\chi^2$ sense to identify which of them result in acceptable fits (to be defined later). + The paranueters varied during the simulations are the mass of the secondary star (A5). the mass of the tertiary (Af. or its radius Πο if a planet). the impact parameter (b). the relative linear distance (d) between the eclipsing pair aud the target. aud the relative duration (D/Do) of the transit compared to the curation for a circular orbit (see bolow).," The parameters varied during the simulations are the mass of the secondary star $M_2$ ), the mass of the tertiary $M_3$, or its radius $R_3$ if a planet), the impact parameter $b$ ), the relative linear distance $d$ ) between the eclipsing pair and the target, and the relative duration $D/D_{\rm circ}$ ) of the transit compared to the duration for a circular orbit (see below)." + For convenience the relative linear distance is parametrized iu terms of the difference iu distance modulus. Ad. where Ad=5log(dgpdgio.," For convenience the relative linear distance is parametrized in terms of the difference in distance modulus, $\Delta\delta$, where $\Delta\delta = 5\log(d_{\rm EB}/d_{\rm KOI})$." + Iu he case of hierarchical triple configurations the isochrone or the binary is assumed to be the same as for the μι (uictallicityof|Fe/II] = 0.15 aud a nominal age of (στι2011). whereas or background bleuds we have adopted for the binary a represcutative Cyr isochrone of solar metallicity. although these pariuueters have a uunimeal impact ou he results.," In the case of hierarchical triple configurations the isochrone for the binary is assumed to be the same as for the primary \citep[metallicity of ${\rm +[Fe/H]} = -0.15 and a nominal age of Gyr;, whereas for background blends we have adopted for the binary a representative Gyr isochrone of solar metallicity, although these parameters have a minimal impact on the results." + For full details of the technique we refer he reader to the references above., For full details of the technique we refer the reader to the references above. + Three recent changes and nauprovenieunts that are especially relevant to the application to aare described next: G)) The relatively long orbital period of (615.3. days) precludes us from assunüug that the eccentricity (6) is zero. as we were able to suppose iu xevious applications of to Iepler-9 aud bb. which have periods of 1.59 and OL dddays. respectively.," Three recent changes and improvements that are especially relevant to the application to are described next: ) The relatively long orbital period of (45.3 days) precludes us from assuming that the eccentricity $e$ ) is zero, as we were able to suppose in previous applications of to d and b, which have periods of 1.59 and 0.84 days, respectively." + The reason this matters is that the duration of the transit is set. amone other actors. bv the size of the secondary star.," The reason this matters is that the duration of the transit is set, among other factors, by the size of the secondary star." + Eccentricity can alter the speed of the tertiary around the secondary. uakime it slower or faster than iu the circularcase depending on the orientation of the orbit (longitude of yeLVIastrou. we).," Eccentricity can alter the speed of the tertiary around the secondary, making it slower or faster than in the circularcase depending on the orientation of the orbit (longitude of periastron, $\omega$ )." + Given a fixed GQucasured) duration. blends with sinaller or larger secondary stars than in the circular case may still provide satisfactory fits to the light curve. effectively increasing the pool of poteutial false positives.," Given a fixed (measured) duration, blends with smaller or larger secondary stars than in the circular case may still provide satisfactory fits to the light curve, effectively increasing the pool of potential false positives." +" inow takes this iuto account. although rather than using as parameters c and το, which are the natural variables eniployed in the binary lighit-curve generating routine at he core of citep|see|[Torres:1l.. a iore convenient variable that captures the effects of both is the duration relative ο a circular orbit."," now takes this into account, although rather than using as parameters $e$ and $\omega$, which are the natural variables employed in the binary light-curve generating routine at the core of \\citep[see][]{Torres:11}, a more convenient variable that captures the effects of both is the duration relative to a circular orbit." + Following Winn(2010).. this may ο expressed as DiDee=~VLο|esinew).," Following \cite{Winn:10}, this may be expressed as $D/D_{\rm circ} +\approx \sqrt{1-e^2}/(1+e\sin\omega)$." + Operationally. then. we vary D/Da; over wide ranecs as we explore different blend scenarios. aud for cach value we oeinfer the corresponding values ofe aud w.," Operationally, then, we vary $D/D_{\rm circ}$ over wide ranges as we explore different blend scenarios, and for each value we infer the corresponding values of $e$ and $\omega$." + Iu practice. in order to solve for [6.2] from D/Deye it is only necessary to consider the limiting cases with w=90° and2707.. corresponding to transits occuniug at periastrou aud apastron. respectively. since these are the oricutations resulting in the nünnmuunn and maxiuuni durations for a eiven ecceutricitv.," In practice, in order to solve for $e$, $\omega$ from $D/D_{\rm circ}$ it is only necessary to consider the limiting cases with $\omega = 90\arcdeg$ and, corresponding to transits occurring at periastron and apastron, respectively, since these are the orientations resulting in the minimum and maximum durations for a given eccentricity." + Other combinations ofe aud w will lead to intermediate relative durations that are already: sampled in our D/D. exid., Other combinations of $e$ and $\omega$ will lead to intermediate relative durations that are already sampled in our $D/D_{\rm circ}$ grid. + It is worth noting that use of oulv these two values of w leads to predicted secondary eclipses in the simulated light curves that are always ocated at phase 0.5. whereas secondary eclipses in the real data might be preseut at uv plase.," It is worth noting that use of only these two values of $\omega$ leads to predicted secondary eclipses in the simulated light curves that are always located at phase 0.5, whereas secondary eclipses in the real data might be present at any phase." + For our purposes his is of uo consequence. as ibas already: hac its light curve screened for secondary eclipses at auy phase that might betray a false positive. as wt of the vetting process.," For our purposes this is of no consequence, as has already had its light curve screened for secondary eclipses at any phase that might betray a false positive, as part of the vetting process." + No such features are prescut down to the 100 ppim level., No such features are present down to the 100 ppm level. + Thus. any simulated leht curves οι that display a significant secondary eclipse will vield 2001’ fifa no matter where the secondary eclipse happeus o be. and will lead to the rejection of that particular lend scenario. (111)," Thus, any simulated light curves from that display a significant secondary eclipse will yield poor fits no matter where the secondary eclipse happens to be, and will lead to the rejection of that particular blend scenario. )" + For each false positive configuration οσα predict the overall photometric color of the blend. Or conparison with the measured color iudex of the candidate as reported in the Ihuput Catalog (IKIC:Brownetal.2011).," For each false positive configuration can predict the overall photometric color of the blend, for comparison with the measured color index of the candidate as reported in the Input Catalog \citep[KIC;][]{Brown:11}." +.. A color iudex such as NpIvy. where Apis the nunaeguitude aud Jv. derives from the 2\LASS catalog. provides a reasonable compromise between waveleusth leverage aud the precision of the iudex.," A color index such as $K\!p-K_s$, where $K\!p$ is the magnitude and $K_s$ derives from the 2MASS catalog, provides a reasonable compromise between wavelength leverage and the precision of the index." + The latter varies typically between 0.015. aud 0.030 mag. depending ou the passband aud the brightuess of the star (sceBrownetal 2011j.," The latter varies typically between 0.015 and 0.030 mag, depending on the passband and the brightness of the star \citep[see][]{Brown:11}." +. We consider a particular blend to be rejected when its predicted color deviates frou the KIC value by more than three times the error of the latter., We consider a particular blend to be rejected when its predicted color deviates from the KIC value by more than three times the error of the latter. + As it turus out. color is a particularly effective wav of rejecting blends that include secondary stars of a different spectral type than the primary. such as those that become possible when allowing for ecceutric orbits. (Hi)," As it turns out, color is a particularly effective way of rejecting blends that include secondary stars of a different spectral type than the primary, such as those that become possible when allowing for eccentric orbits. )" +) Recent refinements in the resolution of the snulatious to better explore parameter space. in addition to the inclusion of ecceutiicitv (or D/Da) as an extra variable. have increased the complexity of the problem as well as the computing time (bv nearly two orders of magnitude) compared to the relatively simple case of circular orbits.," Recent refinements in the resolution of the simulations to better explore parameter space, in addition to the inclusion of eccentricity (or $D/D_{\rm circ}$ ) as an extra variable, have increased the complexity of the problem as well as the computing time (by nearly two orders of magnitude) compared to the relatively simple case of circular orbits." + The muuber of different parameter conibinatious examined with ({ancd corresponding lelt-cirve fits) can approach Ts105 in some cases, The number of different parameter combinations examined with (and corresponding light-curve fits) can approach $7 \times 10^8$ in some cases. + Cousequeutlv the simulations are now performed on the Pleiades cluster at the NASA Advanced Supercomputing Division. located at the Ames Research Ceuter (California). typically on 1021 processors runniuse iu parallel.," Consequently the simulations are now performed on the Pleiades cluster at the NASA Advanced Supercomputing Division, located at the Ames Research Center (California), typically on 1024 processors running in parallel." +" For couvenicuce hierarchical triple coufiguratious (1 parameters] aud backeround/foreeround bleuds (5. parameters) are studied separately, cach for the two separate cases of stellar and planetary tertiarics (for a total of four erids)."," For convenience hierarchical triple configurations (4 parameters) and background/foreground blends (5 parameters) are studied separately, each for the two separate cases of stellar and planetary tertiaries (for a total of four grids)." + Oue additional fit is carried out using a true transiting planet mocel to provide a reference for the quality of the false positive fits iu the other eds., One additional fit is carried out using a true transiting planet model to provide a reference for the quality of the false positive fits in the other grids. + The discriminating value of the shape information contained iu the liebt curves. mcutioned at the beeiuniug of this section. is lighhehted bx our rresults for bb. as described by (2011)..," The discriminating value of the shape information contained in the light curves, mentioned at the beginning of this section, is highlighted by our results for b, as described by \cite{Batalha:11}. ." + In that study it was fouud that backeround eclipsing binary coufleurations with stellar tertiaries vield very poor fits to the Πιο curve. aud are casily rejected.," In that study it was found that background eclipsing binary configurations with stellar tertiaries yield very poor fits to the light curve, and are easily rejected." + The uuderlviug, The underlying +"are still very large, 720h!kpc, implying that this BH will be wandering within the host galaxy for several Gyrs before returning to the centre.","are still very large, $\ge 20 \,h^{-1} \, {\rm kpc}$, implying that this BH will be wandering within the host galaxy for several Gyrs before returning to the centre." +" In Figure 11,, we show the time evolution of BH mass, bolometric luminosity and SFR of the merging system."," In Figure \ref{mbh_merger}, we show the time evolution of BH mass, bolometric luminosity and SFR of the merging system." +" The selected time sequence starts before the two BHs merge, which happens at ~1.69 Gyrs."," The selected time sequence starts before the two BHs merge, which happens at $\sim 1.69\,$ Gyrs." +" In each panel, the blue continuous lines denote the case where the remnant BH does not experience a gravitational recoil, while the green dashed lines and the red triple dot-dashed lines are for the simulations where the remnant BH is kicked with ~0.9vesc and ~vesc, respectively."," In each panel, the blue continuous lines denote the case where the remnant BH does not experience a gravitational recoil, while the green dashed lines and the red triple dot-dashed lines are for the simulations where the remnant BH is kicked with $\sim 0.9\,v_{\rm esc}$ and $\sim v_{\rm esc}$, respectively." +" A number of interesting features can be seen in this figure:i) Prior to coalescence, both BHs grow rapidly, reaching the Eddington limit; During this period, the merging system also enters into a starburst phase, with a SFR peaking at 4000Moνττς Once the remnant BH is gravitationally recoiled its accretion rate drops, especially in the case where the BH leaves the dense central regions (i.e. for Uxick vesc), implying that the AGN will have a much lower bolometric luminosity and will grow less in mass; Because the remnant BH is wandering away from the centre, it becomes much less efficient in regulating the central properties of the host galaxy."," A number of interesting features can be seen in this figure: Prior to coalescence, both BHs grow rapidly, reaching the Eddington limit; During this period, the merging system also enters into a starburst phase, with a SFR peaking at $4000\, {\rm M}_\odot\,{\rm yr}^{-1}$; Once the remnant BH is gravitationally recoiled its accretion rate drops, especially in the case where the BH leaves the dense central regions (i.e. for $v_{\rm kick} \sim v_{\rm esc}$ ), implying that the AGN will have a much lower bolometric luminosity and will grow less in mass; Because the remnant BH is wandering away from the centre, it becomes much less efficient in regulating the central properties of the host galaxy." +" Thus, in the case of recoiled BHs, the central starburst activity will be prolonged, with more young stars formed in situ;v) 'The extended star formation activity has a direct impact on the BH growth once it returns to the centre: more stars have already formed, leaving less gas to fuel further BH accretion."," Thus, in the case of recoiled BHs, the central starburst activity will be prolonged, with more young stars formed in situ; The extended star formation activity has a direct impact on the BH growth once it returns to the centre: more stars have already formed, leaving less gas to fuel further BH accretion." +" This explains why the BH mass in the case of the ~0.9vesc kick stays much lower and cannot catch-up with that of the stationary BH, even though it returns to the centre already after 10° yrs;vi) While the amount of stars formed has a large impact on the BH growth, it does not significantly affect the total stellar mass, which changes by a few percent at most."," This explains why the BH mass in the case of the $\sim 0.9\,v_{\rm esc}$ kick stays much lower and cannot catch-up with that of the stationary BH, even though it returns to the centre already after $10^8\,$ yrs; While the amount of stars formed has a large impact on the BH growth, it does not significantly affect the total stellar mass, which changes by a few percent at most." + We hence find that the gravitational recoil for a single merger could in principle introduce more scatter in the BH mass (by up to factor of —2) than in the bulge mass when considering BH mass - bulge mass scaling relation (see ? for a comprehensive study of the scatter in the BH mass - host galaxy scaling relations for different simulated merging systems and e.g. ? who reaches simular conclusions adopting semi-analytical techniques)., We hence find that the gravitational recoil for a single merger could in principle introduce more scatter in the BH mass (by up to factor of $\sim 2$ ) than in the bulge mass when considering BH mass - bulge mass scaling relation (see \citet{Blecha2011} for a comprehensive study of the scatter in the BH mass - host galaxy scaling relations for different simulated merging systems and e.g. \citet{Volonteri2007} who reaches simular conclusions adopting semi-analytical techniques). +" While the findings discussed above should reflect the general characteristics of gas-rich mergers of galaxies, we would however like to stress that the quantitative details will be very sensitive to the physics of BH binary hardening, as well as to star formation and feedback."," While the findings discussed above should reflect the general characteristics of gas-rich mergers of galaxies, we would however like to stress that the quantitative details will be very sensitive to the physics of BH binary hardening, as well as to star formation and feedback." +" In our simulations, we cannot follow the BH binary hardening due to insufficient spatial resolution."," In our simulations, we cannot follow the BH binary hardening due to insufficient spatial resolution." +" Instead, we simply assume that the BH coalescence happens rapidly in a gas-rich environment."," Instead, we simply assume that the BH coalescence happens rapidly in a gas-rich environment." +" This is a plausible assumption, but obviously not guaranteed to be the case."," This is a plausible assumption, but obviously not guaranteed to be the case." +" If the final BH binary hardening should take longer, this would have a significant impact on the results."," If the final BH binary hardening should take longer, this would have a significant impact on the results." +" From the left-hand panel of Figure 11, we can infer that during a very short time interval of the order of <5x10"" yrs, from the merger of the galactic cores to the moment where the BH growth becomes self-regulated, the BH grows rapidly."," From the left-hand panel of Figure \ref{mbh_merger}, we can infer that during a very short time interval of the order of $\le 5 \times 10^7\,$ yrs, from the merger of the galactic cores to the moment where the BH growth becomes self-regulated, the BH grows rapidly." +" Thus, a delay in the BH coalescence relative to what we have assumed here, and hence a delay in the moment the recoil occurs, can significantly reduce the mass difference between a stationary and a recoiled BH."," Thus, a delay in the BH coalescence relative to what we have assumed here, and hence a delay in the moment the recoil occurs, can significantly reduce the mass difference between a stationary and a recoiled BH." +" Similarly, the efficiency of star formation in the innermost regions will affect the amount of gas that is still available for accretion once the BH returns to the centre."," Similarly, the efficiency of star formation in the innermost regions will affect the amount of gas that is still available for accretion once the BH returns to the centre." +" In this study, we have used numerical simulations to discuss the complex interplay between the baryonic component of gas-rich galaxies and the dynamics of supermassive BHs recoiling due to a gravitational wave induced binary merger."," In this study, we have used numerical simulations to discuss the complex interplay between the baryonic component of gas-rich galaxies and the dynamics of supermassive BHs recoiling due to a gravitational wave induced binary merger." + Our analysis has focused on understanding how BH accretion and feedback processes can possibly modify the orbit and return timescale of recoiled BHs., Our analysis has focused on understanding how BH accretion and feedback processes can possibly modify the orbit and return timescale of recoiled BHs. + This question has important implications both for the assembly history of the population of supermassive BHs as well as possible detections of displaced AGN in galaxies., This question has important implications both for the assembly history of the population of supermassive BHs as well as possible detections of displaced AGN in galaxies. +" In our simulations, we have deliberately chosen massive and gas-rich systems, which could be representative of high redshift progenitors of present day ellipticals and brightest cluster galaxies."," In our simulations, we have deliberately chosen massive and gas-rich systems, which could be representative of high redshift progenitors of present day ellipticals and brightest cluster galaxies." +" Using isolated disc galaxies, we were able to study the orbital evolution of kicked BHs for a variety of different assumptions about BH accretion and feedback, and about the treatment of the interstellar gas."," Using isolated disc galaxies, we were able to study the orbital evolution of kicked BHs for a variety of different assumptions about BH accretion and feedback, and about the treatment of the interstellar gas." +" We have then extended the analysis with simulation models of major galaxy mergers, yielding a more realistic accounting of the perturbed state of the systems that are expected to host merger recoil events of BHs."," We have then extended the analysis with simulation models of major galaxy mergers, yielding a more realistic accounting of the perturbed state of the systems that are expected to host merger recoil events of BHs." + Our main conclusions from these simulations are as follows:, Our main conclusions from these simulations are as follows: +Despite the slight differences in mean and width of the distributions. they are all roughly svinmetric. and it is likely that these lines indicate the svstemic velocity of the galaxy.,"Despite the slight differences in mean and width of the distributions, they are all roughly symmetric, and it is likely that these lines indicate the systemic velocity of the galaxy." + All of these lines from sinely ionized species have low critical densities. and so (μον arise either in (he outer parts of the narrow line region (NLR) or even further out. in the interstellar medium of the host galaxy itself.," All of these lines from singly ionized species have low critical densities, and so they arise either in the outer parts of the narrow line region (NLR) or even further out, in the interstellar medium of the host galaxy itself." + The 3 arcsecond diameter of (he SDSS fibers corresponds to a physical diameter of about 10.5 kpe at the sample median redshift of 0.22., The 3 arcsecond diameter of the SDSS fibers corresponds to a physical diameter of about 10.5 kpc at the sample median redshift of 0.22. + The mean of all visible low ionization lines in each object was adopted as its svstemic redshift. ancl the spectra were adjusted to reflect rest wavelengths using these new. small offsets.," The mean of all visible low ionization lines in each object was adopted as its systemic redshift, and the spectra were adjusted to reflect rest wavelengths using these new, small offsets." + From these corrected spectra. the wavelength of the [O Η A5007 line was measured in each object in a manner similar to that in whieh the low ionization lines were measured.," From these corrected spectra, the wavelength of the [O III] $\lambda$ 5007 line was measured in each object in a manner similar to that in which the low ionization lines were measured." + These [O III] wavlengths were converted to a relative velocity using a vacuum rest wavelength of Που this line., These [O III] wavlengths were converted to a relative velocity using a vacuum rest wavelength of for this line. + Figure 3 shows the distribution of these [O HI] redshifts relative to the systemic redshift caleulated from (he low ionization lines., Figure 3 shows the distribution of these [O III] redshifts relative to the systemic redshift calculated from the low ionization lines. + The solid histogram represents all the objects for which a low ionization systemic redshift could be determined and the [O IH] A5007 wavelength could be measured (638 objects: the total [O III] sample)., The solid histogram represents all the objects for which a low ionization systemic redshift could be determined and the [O III] $\lambda$ 5007 wavelength could be measured (638 objects; the total [O III] sample). + The dotted histogram represents only the objects for which low ionization redshilts could be determined from (wo or more ions (399 objects: the high confidence [O III] sample)., The dotted histogram represents only the objects for which low ionization redshifts could be determined from two or more ions (399 objects; the high confidence [O III] sample). + The bottom panel ol this figure shows the sum of the redshift distributions for the three low ionization lines. in each case relative to the one or two other lines measured.," The bottom panel of this figure shows the sum of the redshift distributions for the three low ionization lines, in each case relative to the one or two other lines measured." + The low ionization line distribution is well fit bv. a gaussian with a mean of zero (bv construction) and a width (o0) of 35 kan |. a fraction of which is due to the slight shift between the distributions.," The low ionization line distribution is well fit by a gaussian with a mean of zero (by construction) and a width $\sigma$ ) of 35 km $^{-1}$, a fraction of which is due to the slight shift between the distributions." + The [O III] distribution. however. has a broad shoulder on the blueshifted side. with a sprinkling of objects out to -400 km !|..," The [O III] distribution, however, has a broad shoulder on the blueshifted side, with a sprinkling of objects out to -400 km $^{-1}$." + Approximately. half the objects might be considered to be in a distribution like Chaat for the low ionization lines with the other half on the blueshifted side., Approximately half the objects might be considered to be in a distribution like that for the low ionization lines with the other half on the blueshifted side. + For the total [O III] sample. 135 (214)) of the 638 values have positive (redshifted) relative velocities: (his number is 93 (23%)) of 399 values for the high confidence sample.," For the total [O III] sample, 135 ) of the 638 values have positive (redshifted) relative velocities; this number is 93 ) of 399 values for the high confidence sample." + Note that both the total [O LL] sample and the high confidence ΕΕ sample are biased within the original sample of DRI objects toward the low redshift and low luminosity end., Note that both the total [O III] sample and the high confidence [O III] sample are biased within the original sample of DR1 objects toward the low redshift and low luminosity end. + This bias is due to the fact that the low ionization narrow lines are more connnonly found in the lower luminosity objects., This bias is due to the fact that the low ionization narrow lines are more commonly found in the lower luminosity objects. + The dashed ancl dotted lines in the two panels of Figure | show the distributions for the total [O III] and high confidence |O II) saniples respectively., The dashed and dotted lines in the two panels of Figure 1 show the distributions for the total [O III] and high confidence [O III] samples respectively. + In order to compare the properties of AGN with different [O III] velocity shifts. four," In order to compare the properties of AGN with different [O III] velocity shifts, four" +Iron has many usefully strong lines seattered through the spectrum.,Iron has many usefully strong lines scattered through the spectrum. + We have fit lines in three windows. 4488 -- 4542. 4820 — 4830. and 5026 — 5037A.," We have fit lines in three windows, 4488 – 4542, 4820 – 4830, and 5026 – 5037." +. All the numerous Fe lines in these regions are reasonably well fit with an abundance about 1.5 dex above the solar abundance., All the numerous Fe lines in these regions are reasonably well fit with an abundance about 1.5 dex above the solar abundance. + The weaker lines seen in Figure 4+ suggest that the abundance of Fe might be even a little larger than this value: in any case. they show the tendency. also found for Ti. that computed weak lines to be weaker than the observed lines.," The weaker lines seen in Figure \ref{spec50} suggest that the abundance of Fe might be even a little larger than this value; in any case, they show the tendency, also found for Ti, that computed weak lines to be weaker than the observed lines." + This result is roughly with the variation of Fe abundance with ffound in Ap stars by ?.., This result is roughly with the variation of Fe abundance with found in Ap stars by \citet{Ryabetal04}. + Four useful lines of Pr are found in the region 6098 6196A., Four useful lines of Pr are found in the region 6098 -- 6196. +. All are fit reasonably well with a mean abundance almost 5 dex larger than the solar value., All are fit reasonably well with a mean abundance almost 5 dex larger than the solar value. + Nd has limes seattered through the visible window., Nd has lines scattered through the visible window. + We have modelled lines at 4796. 4822 (Figure 3)) and 5050 A(Figure 4)). and find a mean abundance about 4.3 dex larger than the solar abundance.," We have modelled lines at 4796, 4822 (Figure \ref{spec48}) ), and 5050 (Figure \ref{spec50}) ), and find a mean abundance about 4.3 dex larger than the solar abundance." + This paper is the first in what is expected to be a series of reports describing modelling of stars from the survey of magnetic Ap stars in open clusters of known age., This paper is the first in what is expected to be a series of reports describing modelling of stars from the survey of magnetic Ap stars in open clusters of known age. + The aim of this project is to establish a preliminary model of the magnetic field structure. to estimate the chemical abundances of a number of common elements. and to extract whatever information is available in our data about the surface homogeneity or inhomogeneity of those elements by means of simple. rather schematic models whose parameters are derived by fitting synthesised spectra to observations.," The aim of this project is to establish a preliminary model of the magnetic field structure, to estimate the chemical abundances of a number of common elements, and to extract whatever information is available in our data about the surface homogeneity or inhomogeneity of those elements by means of simple, rather schematic models whose parameters are derived by fitting synthesised spectra to observations." + HD 318107 ts a relatively hot magnetic Ap star. with Zi=800 K. It has logL/L.=1.92. and mass M/M...=2.95.," HD 318107 is a relatively hot magnetic Ap star, with $\te = 11\,800$ K. It has $\log L/L_\odot = 1.92$, and mass $M/M_\odot = 2.95$." + The rotation period of the star is 9.7088 d. and it has vsin=7s7!.," The rotation period of the star is 9.7088 d, and it has $\vsi = 7$." +. From its membership in NGC 6405 we know that its age is log£=7.80 and that it has completed about of its main sequence lifetime., From its membership in NGC 6405 we know that its age is $\log t = 7.80$ and that it has completed about of its main sequence lifetime. + The star has a strong magnetic field. of order 15 kG globally.," The star has a strong magnetic field, of order 15 kG globally." + We have used previously published (and modelled) magnetic field measurements of ?.. ?.. ?.. and ?.. together with measurements of our own. to improve the rotation period of the star to P=9.7088+0.0007 d. which makes it possible to phase recent magnetic data and spectroscopy accurately with previous measurements. and thus to use the full set of magnetic and spectral data available to us to model the star.," We have used previously published (and modelled) magnetic field measurements of \citet{Mathys97}, \citet{MM2000}, \citet{LM2000}, and \citet{paper1}, , together with measurements of our own, to improve the rotation period of the star to $P = 9.7088 \pm 0.0007$ d, which makes it possible to phase recent magnetic data and spectroscopy accurately with previous measurements, and thus to use the full set of magnetic and spectral data available to us to model the star." + Our model of the magnetic field is a simple. low-order axisymmetric multipole expansion which retains the global topology of a dipolar field structure.," Our model of the magnetic field is a simple, low-order axisymmetric multipole expansion which retains the global topology of a dipolar field structure." + This model is used 1n the framework of the oblique rigid rotator model to describe the observed variations of aand wwith rotational phase., This model is used in the framework of the oblique rigid rotator model to describe the observed variations of and with rotational phase. + Fitting the predicted aand vvariations approximately to the observed variations allows us to determine the parameters of the model magnetic field as well as the inclination i of the rotation axis and the obliquity P of the magnetic field to the rotation axis., Fitting the predicted and variations approximately to the observed variations allows us to determine the parameters of the model magnetic field as well as the inclination $i$ of the rotation axis and the obliquity $\beta$ of the magnetic field to the rotation axis. + Because the variations of the field moments are rather complex. and in fact poorly determined for(B-).. the adopted model is only a rather coarse first approximation to the actual magnetic field geometry of HD 318107.," Because the variations of the field moments are rather complex, and in fact poorly determined for, the adopted model is only a rather coarse first approximation to the actual magnetic field geometry of HD 318107." + However. this model is appropriately simple considering the limited information available about the star. in particular the small number of mmeasurements and high-dispersion polarimetric spectra available.," However, this model is appropriately simple considering the limited information available about the star, in particular the small number of measurements and high-dispersion polarimetric spectra available." + The qualitative form of the field structure is clear from the nature of the field data shown in Figure |.., The qualitative form of the field structure is clear from the nature of the field data shown in Figure \ref{magfield}. + The fact that ddoes not reverse sign indicates that the line of sight to the star is confined to one magnetic hemisphere. which in turn means that the sum i+Bx90°.," The fact that does not reverse sign indicates that the line of sight to the star is confined to one magnetic hemisphere, which in turn means that the sum $i + \beta \lesssim 90^\circ$." + The fact that the minimum value of KG is considerably smaller than the maximum value shows that the line of sight does approach the magnetic equator. while the large ratio of the maximum value of |(5-)| relative to the value of lindicates that the line of sight does approach the magnetic pole.," The fact that the minimum value of $|\bz|$ is considerably smaller than the maximum value shows that the line of sight does approach the magnetic equator, while the large ratio of the maximum value of $|\bz|$ relative to the value of indicates that the line of sight does approach the magnetic pole." + The actual parameter values adopted are discussed 1 Sec 4.1., The actual parameter values adopted are discussed in Sec 4.1. + The resulting magnetic model does not reproduc[7 particularly well the detailed shape of the variations of(B-).. but it works surprisingly well as a description of the Zeema broadening (the dominant source of broadening) of the spectral lines we analysed.," The resulting magnetic model does not reproduce particularly well the detailed shape of the variations of, but it works surprisingly well as a description of the Zeeman broadening (the dominant source of broadening) of the spectral lines we analysed." + With only a dozen / spectra scattered through the rotatio cycle (but including spectra obtained near times of maximum and minimum(B8-):: Le. when the line of sight is near the magnetic pole and near the magnetic equator). it 15 not possible to do detailed mapping.," With only a dozen $I$ spectra scattered through the rotation cycle (but including spectra obtained near times of maximum and minimum; i.e. when the line of sight is near the magnetic pole and near the magnetic equator), it is not possible to do detailed mapping." + However. a preliminary reconnaissance of the abundances of several elements. and a first estimation of their variation over the surface. is possible.," However, a preliminary reconnaissance of the abundances of several elements, and a first estimation of their variation over the surface, is possible." + We have considered a model that uses three co-axial rings. one around each magnetic pole and one around the equator. but there ts no strong evidence for strong abundance variations on the global scale.," We have considered a model that uses three co-axial rings, one around each magnetic pole and one around the equator, but there is no strong evidence for strong abundance variations on the global scale." + The model finally adopted assumes uniform abundance over the stellar surface., The model finally adopted assumes uniform abundance over the stellar surface. + This model provides the simplest possible quantitative description of abundance variations on the star., This model provides the simplest possible quantitative description of abundance variations on the star. + Assuming uniform abundancees over the stellar surface. we find. as expected. that most elements have distinctly non-solar abundances.," Assuming uniform abundances over the stellar surface, we find, as expected, that most elements have distinctly non-solar abundances." + The abundance of O is slightly below solar. while Mg appears to be significantly lower than the solar abundances.," The abundance of O is slightly below solar, while Mg appears to be significantly lower than the solar abundances." + Ca has nearly solar abundance., Ca has nearly solar abundance. + Upper limits to the abundances of He and Mn are possible. the. former unambiguously classifying HD 318107 has a He-weak star and the latter suggesting an abundance no more than 0.6 dex above the solar value.," Upper limits to the abundances of He and Mn are possible, the former unambiguously classifying HD 318107 has a He-weak star and the latter suggesting an abundance no more than 0.6 dex above the solar value." +The other studied elements (Si. Ti. Cr. Fe. Pr. and Nd) are all present with higher abundance than in the Sun.,"The other studied elements (Si, Ti, Cr, Fe, Pr, and Nd) are all present with higher abundance than in the Sun." +lav form first. and the associated neutrmo enuüssion cau be responsible for a standard neutrino-uduced supernova kick to explain the observed space velocity. (,"may form first, and the associated neutrino emission can be responsible for a standard neutrino-induced supernova kick to explain the observed space velocity. (" +2) Material near the mass cut is mixed iuto the euvelope aud cau escape with it. explaining the abundance anomalies in the secondary. (,"2) Material near the mass cut is mixed into the envelope and can escape with it, explaining the abundance anomalies in the secondary. (" +3) The supernova explosion could be weaker aud rai-pressure stripping would then be less of a problem: this could allow for more οποιο capture of supernova material by the secondary (even in the case of a lypernova explosion. the ejecta in the equatorial plane could be moving relatively slowly).,"3) The supernova explosion could be weaker and ram-pressure stripping would then be less of a problem; this could allow for more efficient capture of supernova material by the secondary (even in the case of a hypernova explosion, the ejecta in the equatorial plane could be moving relatively slowly)." +" Iu order to simulate a fallback model with mixing. we nocified the model described in 2.1 by assiuunius that the aver between Mti aud AL|AAD is completely mixed during the collapse phase. where weix defined AM,=mnmALgaihack (see Fig."," In order to simulate a fallback model with mixing, we modified the model described in 2.1 by assuming that the layer between $M_{\rm +BH}^0$ and $M_{\rm BH}^0+\Delta M_{\rm mix}$ is completely mixed during the collapse phase, where we defined $\Delta M_{\rm mix} \equiv +m\,M_{\rm fallback}$ (see Fig." + 3b)., 3b). + The definition of Miu iucludes th. the inifial mass of the compact rocinant and any allback material that was not mixed with the material hat is ejected (this could. for example. be material from he inner parts of the disk that forms around the initial compact core. as in the collapsar 1nodels of MacFadyeu Woosley (1999) aud MacFadyen et ((2001) or material alling back from the equatorial region of the star iu an aspherical explosion (Maeda et 22001).," The definition of $M_{\rm BH}^0$ includes both the initial mass of the compact remnant and any fallback material that was not mixed with the material that is ejected (this could, for example, be material from the inner parts of the disk that forms around the initial compact core, as in the collapsar models of MacFadyen Woosley (1999) and MacFadyen et (2001) or material falling back from the equatorial region of the star in an aspherical explosion (Maeda et 2001)." + Iu Table 2b we preseut the results of these sinulations Or m=l. 2. 3. aud. |.," In Table 2b we present the results of these simulations for $m = 1$, 2, 3, and 4." + Most of the results are similar to he earlier calculations: the amount of fallback is similar. while the svstem velocities teud to be a bit larger.," Most of the results are similar to the earlier calculations: the amount of fallback is similar, while the system velocities tend to be a bit larger." + One sienificaut difference is that. with the inclusion of mixine. wpernova models are preferred over standard superuova uodels. which teud not to produce enough S. The size of the mixing region outside the initial compact remnant varies quite significantly between differeut nodels: in some hvperuova models. the mixing region contains less than12M... while in normal superuova uodels at least several aare required.," One significant difference is that, with the inclusion of mixing, hypernova models are preferred over standard supernova models, which tend not to produce enough S. The size of the mixing region outside the initial compact remnant varies quite significantly between different models; in some hypernova models, the mixing region contains less than, while in normal supernova models at least several are required." + So far. we have asstuned that the ejection of matter occurs in a inore-or-less spherically sviuuetric wav.," So far, we have assumed that the ejection of matter occurs in a more-or-less spherically symmetric way." + Towever. this is not ecnerally expected for hvpernova or collapsar models. in particular those associated with eginuni-rav bursts {(AlacFadven Woosley 1999).," However, this is not generally expected for hypernova or collapsar models, in particular those associated with gamma-ray bursts (MacFadyen Woosley 1999)." + Iu these models it is generally believed that the core is initially rapidly rotating aud that the accretion of matter onto the compact object occurs through an accretion disk., In these models it is generally believed that the core is initially rapidly rotating and that the accretion of matter onto the compact object occurs through an accretion disk. + Maeda ct ((2001) have receutlv constructed aspherical hvperuova models for the hypernova SN 1998sw. simulating both the lvdodvuamics and the nucleosvuthliesis in two clinieusious for a heliuui-star model of aat the beeimmine of heliuuni burning.," Maeda et (2001) have recently constructed aspherical hypernova models for the hypernova SN 1998bw, simulating both the hydrodynamics and the nucleosynthesis in two dimensions for a helium-star model of at the beginning of helium burning." + They showed that the chemical composition of the ejecta is strongly depeudoeut ou direction., They showed that the chemical composition of the ejecta is strongly dependent on direction. + In particular. Fe is mainly ejected im the polar direction. while O and Me are prefercutially ejected near the equatorial plane.," In particular, Fe is mainly ejected in the polar direction, while O and Mg are preferentially ejected near the equatorial plane." + To simulate the pollution by au aspherical hivperuova. we asstune that the secondary is located in the equatorial plane of the helium star (aud the black-hole accretion disk) and that the secoudaryv captures material that is within an anele 0 of the equatorial plane. where 0 is the angular radius subtended by the secondary as seen from the helinua star.," To simulate the pollution by an aspherical hypernova, we assume that the secondary is located in the equatorial plane of the helium star (and the black-hole accretion disk) and that the secondary captures material that is within an angle $\theta$ of the equatorial plane, where $\theta$ is the angular radius subtended by the secondary as seen from the helium star." + The results of these simulations (for their best model C) are prescuted in Tables 3 and { (models indicated by a ), The results of these simulations (for their best model C) are presented in Tables 3 and 4 (models indicated by a $^{*}$ ). + Somewhat surprisingly. none of our simulations produced acceptable fits (the results shown were obtained by increasing the acceptance paramcter Q from 1 to 2).," Somewhat surprisingly, none of our simulations produced acceptable fits (the results shown were obtained by increasing the acceptance parameter $Q$ from 1 to 2)." + This is a direct consequence of the large overabundance of O and Me near the equatorial plauc., This is a direct consequence of the large overabundance of O and Mg near the equatorial plane. + All models produce either an unacceptable overabundance of O aud Mg or an unacceptable underabuudauce of S and Si. depending ou where the cut-off below which matter cau be mixed iuto the ejecta occurs.," All models produce either an unacceptable overabundance of O and Mg or an unacceptable underabundance of S and Si, depending on where the cut-off below which matter can be mixed into the ejecta occurs." +" However, when modeling the shapes of spectral lines in SN LO9SInv. Maeda ot ((2001) found that the fits could be improved if there was some lateral mixing iu he ejecta, Le. between material ejected in the equatoria aue and material ejected more along the jet axis (6.9. due to a shear stabilitv)."," However, when modeling the shapes of spectral lines in SN 1998bw, Maeda et (2001) found that the fits could be improved if there was some lateral mixing in the ejecta, i.e., between material ejected in the equatorial plane and material ejected more along the jet axis (e.g., due to a shear instability)." +" To test this possibility we also considered a model where we assmuued complete latera uixiug iu the ejecta for the same hivperuova model as use above. c. Where all the material within eiven velocity dus was assuned to be mixed completely,"," To test this possibility we also considered a model where we assumed complete lateral mixing in the ejecta for the same hypernova model as used above, i.e., where all the material within given velocity bins was assumed to be mixed completely." + The results of these simulations are also shown iu Tables 3 and and indicated with a prine ()., The results of these simulations are also shown in Tables 3 and 4 and indicated with a prime ('). + Iu this case. excelleu fits are obtained. as one would lave expected. since lis model should approximate the spherical hyperuova uodel used earlier.," In this case, excellent fits are obtained, as one would have expected, since this model should approximate the spherical hypernova model used earlier." + Interestingly. the Tài abundance is significautly enhanced (QTi/If]-0.5) aud is marginally consistent with the observed value (Ti/II|-0.9+0.1).," Interestingly, the Ti abundance is significantly enhanced $\sim 0.5$ ) and is marginally consistent with the observed value $\sim 0.9\pm 0.4$ )." + This increased Tài abundance comes at the price of an increased Fe abundance., This increased Ti abundance comes at the price of an increased Fe abundance. +" While both the Ti and Fe abuudances are consistent with the observed values. the ratio [Ti/Fe] is still significautly below the observed. one (~0.2 instead of 0,8)."," While both the Ti and Fe abundances are consistent with the observed values, the ratio [Ti/Fe] is still significantly below the observed one $\sim 0.2$ instead of 0.8)." + We empliasize that the assmuption of complete lateral nüxiug is extreme: af present we can uot identity any plivsical process that would lead to sich a result., We emphasize that the assumption of complete lateral mixing is extreme; at present we can not identify any physical process that would lead to such a result. + We note. however. that Woflich. Nhokhlov Wang (2001) have shown that the jet in an aspherical supernova imodel is decelerated at the I/We intertace and that material spreads laterally. although only to a lanited extent.," We note, however, that Höfflich, Khokhlov Wang (2001) have shown that the jet in an aspherical supernova model is decelerated at the H/He interface and that material spreads laterally, although only to a limited extent." + Whether this could provide a viable model. requires computations with much ligher wmucrical resolution.," Whether this could provide a viable model, requires computations with much higher numerical resolution." +" Irrespectively, our results sugeest that the chhanced abundance of Ti (which results fou a mixture of the uucleosvuthesis products of complete aud iuconmplete Si burning: see Uineda Nomoto [2001] for a discussion) could potentially provide a signature for au asviunietric lypernova."," Irrespectively, our results suggest that the enhanced abundance of Ti (which results from a mixture of the nucleosynthesis products of complete and incomplete Si burning; see Umeda Nomoto [2001] for a discussion) could potentially provide a signature for an asymmetric hypernova." + The main conclusiou of this investigation is that. using standard supernova models aud a relatively simple model for the pollution of the secondary. we can explain the observed a-clement cuhancemeuts in the secondary of Nova Sco. confirming standard uucleosvuthlesis predictions (apart from the abundance of Ti. which is always too low).," The main conclusion of this investigation is that, using standard supernova models and a relatively simple model for the pollution of the secondary, we can explain the observed $\alpha$ -element enhancements in the secondary of Nova Sco, confirming standard nucleosynthesis predictions (apart from the abundance of Ti, which is always too low)." + Nova Sco prescuts a clear case for a two-step black-hole formation process. where a substantial fraction of the black-hole mass is the result of fallback.," Nova Sco presents a clear case for a two-step black-hole formation process, where a substantial fraction of the black-hole mass is the result of fallback." + In order for the secoudary to be polluted with material near the mass cut. this fallback material must either have reached the," In order for the secondary to be polluted with material near the mass cut, this fallback material must either have reached the" +a dispersionless signal from a certain binary is very simular to the dispersed signal from a binary with slightly different. parameters (e.g. a slightly different skv location). then the errors in A® could be very much larger than estimated here.,"a dispersionless signal from a certain binary is very similar to the dispersed signal from a binary with slightly different parameters (e.g. a slightly different sky location), then the errors in $\Delta \Phi$ could be very much larger than estimated here." + Also. a will depend upon the ivpe of svstem being studied.," Also, $\alpha$ will depend upon the type of system being studied." + It will generally be smaller for svstems where information in addition to the gravitational wave signal is available. e.g. Galactic binary svstems where optical measurements give accurate skv locations.," It will generally be smaller for systems where information in addition to the gravitational wave signal is available, e.g. Galactic binary systems where optical measurements give accurate sky locations." +" Note. however. that a enters the bound on A, only rather weakly. as A,xL//a. and so we hope that our ignorance of this factor will not change our qualitative conclusions."," Note, however, that $\alpha$ enters the bound on $\lambda_{\rm g}$ only rather weakly, as $\lambda_{\rm g} \propto +1/\sqrt{\alpha}$, and so we hope that our ignorance of this factor will not change our qualitative conclusions." + It is expected that gravitational radiation reaction will result in most binary svstenis detectable by ground. based. interferometers being nearly perfectly. circular (Peters.1964) and so will be unusable for deriving à bound of the sort. described here., It is expected that gravitational radiation reaction will result in most binary systems detectable by ground based interferometers being nearly perfectly circular \citep{pete64} and so will be unusable for deriving a bound of the sort described here. + We will therefore concentrate exclusively on (lwo sorts of) binaries in the LISA band., We will therefore concentrate exclusively on (two sorts of) binaries in the LISA band. + In equation (6)) we will sel à=10. as discussed above.," In equation \ref{eq:lambdageneral}) ) we will set $\alpha = 10$, as discussed above." + When caleulating p we will assume an integration lime of one vear., When calculating $\rho$ we will assume an integration time of one year. + We computed the LISA noise using the Online Sensitivity Curve (Larson2003).. which included a fit to the Galactic white dwarf background. 1991).," We computed the LISA noise using the Online Sensitivity Curve \citep{lars03}, which included a fit to the Galactic white dwarf background \citep{bh97}." +. We consider here the inspiral of a solar-mass (wpe black hole into a massive one., We consider here the inspiral of a solar-mass type black hole into a massive one. + These are excellent svstems from our point of view. as they are expected to dominate the LISA inspiral event rate and. crucially. many will have very large eccentricities Gairetal. 2004).," These are excellent systems from our point of view, as they are expected to dominate the LISA inspiral event rate and, crucially, many will have very large eccentricities \citep{bc04, +getal04}." +. To see if such svstems can indeed be used to obtain a bound on Ay. in Figure 1. we plot the eccentricitv-orbital frequency phase space fora (105.101). binary at a distance ol 1 GGpc.," To see if such systems can indeed be used to obtain a bound on $\lambda_{\rm g}$, in Figure \ref{fig1} we plot the eccentricity-orbital frequency phase space fora $(10^6, 10^1) +M_\odot$ binary at a distance of $1$ Gpc." + The upper curve describes the innermost stable orbit (ISO) (Will1005] binary svslems in Nature only exist this curve., The upper curve describes the innermost stable orbit (ISO) \citep{will98}; binary systems in Nature only exist this curve. + The lower curve gives the minimum eccentricity required for the svstem to be detectable. with multiple harmonics contributing significantly to p. [," The lower curve gives the minimum eccentricity required for the system to be detectable, with multiple harmonics contributing significantly to $\rho$. [" +"Our exact criterion is to see if p exceeds some detection threshold p, when the single strongest harmonic is removed [rom the sum.",Our exact criterion is to see if $\rho$ exceeds some detection threshold $\rho_{\rm min}$ when the single strongest harmonic is removed from the sum. +" We have set py,= 15. as would be reasonable"," We have set $\rho_{\rm min} = 15$ , as would be reasonable" +"We would like to point out that another effect that was not taken into account in this work is the dilference in the completeness of the sample in dilferent regions of the ΕΟΝ,",We would like to point out that another effect that was not taken into account in this work is the difference in the completeness of the sample in different regions of the FOV. + For instance. the cluster core is allected by croweling. thus having a fainter completeness limit than the background stars.," For instance, the cluster core is affected by crowding, thus having a fainter completeness limit than the background stars." + Using the ALP without any completeness correction may lead to an incorrect. surface density of stars. allecting mainly low mass stars.," Using the MF without any completeness correction may lead to an incorrect surface density of stars, affecting mainly low mass stars." + One conservative wav of resolving this issue ds to use the completeness limit of the most crowded field for all stellar sample analyzed. with the ME., One conservative way of resolving this issue is to use the completeness limit of the most crowded field for all stellar sample analyzed with the MF. + Another way is to run fake stars experiments to. properly access the completeness as a function of colour. magnitude and CCD position.," Another way is to run fake stars experiments to properly access the completeness as a function of colour, magnitude and CCD position." + We developed an implementation of the ME technique that is relatively user-independent ancl with great potential for ong used in large scale., We developed an implementation of the MF technique that is relatively user-independent and with great potential for being used in large scale. +" These features make it. suitable o be applied to deep and wide angle. such as DIES. SDSS. ""nSPAIS and LSST. in a systematic wav to find GC tidal ails and other MW. halo sub-structures."," These features make it suitable to be applied to deep and wide angle, such as DES, SDSS, PanSTARSS and LSST, in a systematic way to find GC tidal tails and other MW halo sub-structures." + The ME was tested on simulated data. showing that it increases the contrast of the tail relative to the background » a factor of 2.5 for a cluster projected against à. dense xickeround. similar to that of a low Latitude GC. such as ας 2298.," The MF was tested on simulated data, showing that it increases the contrast of the tail relative to the background by a factor of 2.5 for a cluster projected against a dense background, similar to that of a low latitude GC, such as NGC 2298." + The ME was also tested on a real scenario were it successfully recovered the tidal tail of Palomar 5., The MF was also tested on a real scenario were it successfully recovered the tidal tail of Palomar 5. + The Pal 5 tail closely resembles previous detections in the literature. reproducing both shape and. density.," The Pal 5 tail closely resembles previous detections in the literature, reproducing both shape and density." + We then study the GC NGC :208. which is à good candidate to have a tidal tail due to its previously stucticc PDAE and location.," We then study the GC NGC 2298, which is a good candidate to have a tidal tail due to its previously studied PDMF and location." + We found that the cluster has a tidal radius of r;=1591+1.07 when a Wine profile is fitted and keeping the core radius fixed ο5 0.29)., We found that the cluster has a tidal radius of $r_t=15\arcmin.91\pm 1\arcmin.07$ when a King profile is fitted and keeping the core radius fixed $r_c = 0\arcmin.29$ ). + Our ri value is almost twice what was previously found in the literature., Our $r_t$ value is almost twice what was previously found in the literature. + Lt is based on deeper photometry than previous photographic work and on a much wider area than previous high-resolution and deep photometry., It is based on deeper photometry than previous photographic work and on a much wider area than previous high-resolution and deep photometry. + The new value for ry changes the concentration pareumeter of NGC 2298 to c=144. pushing it further away from the aο relation from DeMarchi.Paresce.&PortegiesZwart(2010).," The new value for $r_t$ changes the concentration parameter of NGC 2298 to $c = 1.44$, pushing it further away from the $\alpha - c$ relation from \citet{marchi}." +.. Ehis discrepancy makes us wonder if the tidal radius of other clusters like NGC 6838 and NGC 6218 are not similarly allected by observational biases associated to small [fields or shallow photometry., This discrepancy makes us wonder if the tidal radius of other clusters like NGC 6838 and NGC 6218 are not similarly affected by observational biases associated to small fields or shallow photometry. + For instance NGC 6218 has a tical radius of 17.2’ whereas observations only cover 3.4. (DeAlarchi.Pulone.&Paresce 2006)., For instance NGC 6218 has a tidal radius of $17.2\arcmin$ whereas observations only cover $3.4\arcmin$ \citep{marchi06}. +. Phere are no publications available for NGC 6838 to properly access if its tidal racius determination uses data that extends bevond its literature tidal radius., There are no publications available for NGC 6838 to properly access if its tidal radius determination uses data that extends beyond its literature tidal radius. + We point out that the determination of the tidal racius of Palomar 14 by Sollimaetal.(2011) also shows an increase bv a factor of 4 when compared with to previous determinations in the literature., We point out that the determination of the tidal radius of Palomar 14 by \citet{Sollima} also shows an increase by a factor of 4 when compared with to previous determinations in the literature. + The increase of the tidal radius appears to be a trend in the sense that whenever large FOV are used the tidal radius increases., The increase of the tidal radius appears to be a trend in the sense that whenever large FOV are used the tidal radius increases. + Applving the ME technique to NGC2298. we find that this GC has several extra-tidal structures detected: above le confidence level.," Applying the MF technique to NGC2298, we find that this GC has several extra-tidal structures detected above $1\sigma$ confidence level." + The strongest feature is the elongation of the cluster along the direction of the disk. suggesting strong tidal interaction.," The strongest feature is the elongation of the cluster along the direction of the disk, suggesting strong tidal interaction." + We also find what appears to be faint leacling and trailing tails. both extending to the edges of the observed field. (17.5).," We also find what appears to be faint leading and trailing tails, both extending to the edges of the observed field $\sim 1^\circ.5$ )." + At last a large structure is founcl. spreading from the eluster towards the disk direction.," At last a large structure is found, spreading from the cluster towards the disk direction." + This structure may be a halo of NGC 2298 that got ejected on the last disk crossing., This structure may be a halo of NGC 2298 that got ejected on the last disk crossing. + Follow up observations are necessary to properly access the nature of cach extra-tidal structure found around NGC 2208., Follow up observations are necessary to properly access the nature of each extra-tidal structure found around NGC 2298. + We expect. DIES to give this follow up., We expect DES to give this follow up. + The survey is going to reach 1 mag deeper than our observations with a much larger area. better photometric calibrations. and 3 more passbands.," The survey is going to reach 1 mag deeper than our observations with a much larger area, better photometric calibrations, and 3 more passbands." + DES will thus allow us to analyze the extra-tidal structure of NGC 2298 in more detail and over larger distances., DES will thus allow us to analyze the extra-tidal structure of NGC 2298 in more detail and over larger distances. + A Larger area will also enable us to test sophistications to the SSP and. background: models underlying the ME. such às à varving background.," A larger area will also enable us to test sophistications to the SSP and background models underlying the MF, such as a varying background." + Finally. we simulate a cluster with and. without mass segregation to evaluate how mass segregation allects the AIF results. via an that does not adequately describe 16 CMD in the outer regions of a mass-seereeated cluster.," Finally, we simulate a cluster with and without mass segregation to evaluate how mass segregation affects the MF results, via an that does not adequately describe the CMD in the outer regions of a mass-segregated cluster." + We nd that there is no strong svstematic οσο in 10 reconstructed density. of stars., We find that there is no strong systematic effect in the reconstructed density of stars. + There is. however. a gaignificant. dillerence in the density [Luctuations relative to 1e truth table. in the sense that the the mass-segregated ‘luster has a larger cispersion. around. the. simulated ensities.," There is, however, a significant difference in the density fluctuations relative to the truth table, in the sense that the the mass-segregated cluster has a larger dispersion around the simulated densities." + Εις is the result. of its not. being able to vecomimocdate the variation in the CMD caused by à position ependent PDAIF., This is the result of its not being able to accommodate the variation in the CMD caused by a position dependent PDMF. + We thus conclude that the impact. of unaccounted for mass segregation in the ME process is to make it more cdillicult to detect the full extension and. the structural details of a GC tidal tail. rather than preventing the tidal tail detection per se.," We thus conclude that the impact of unaccounted for mass segregation in the MF process is to make it more difficult to detect the full extension and the structural details of a GC tidal tail, rather than preventing the tidal tail detection per se." + From our knowledge. this is the first time the ME was tested for an intrinsically variable and unaccounted for.," From our knowledge, this is the first time the MF was tested for an intrinsically variable and unaccounted for." +. We are grateful. to the CTIO. local stall for. the help during observationreduction., We are grateful to the CTIO local staff for the help during observation/reduction. + We acknowledge support from Conselho Nacional de Desenvolvimento Chientíllico e 'Tecnológeico (CNPq) in Brazil., We acknowledge support from Conselho Nacional de Desenvolvimento Científfico e Tecnológgico (CNPq) in Brazil. + We also. thank the support of the Laboratórrio Interinstitucional de e-Xstronomia (LincA) operated jointly by the Centro Brasileiro de Pesquisas Fisicas (CDBDPE). the Laboratórrio Nacional de ConputactikzmarkmainBoclyEnd65717mainBodyStart6572a00 Cientillica (LNCC) and the Observatórrio Nacional (ON) and funded by the Ministry. of Science. and Technology (MCT)," We also thank the support of the Laboratórrio Interinstitucional de e-Astronomia (LIneA) operated jointly by the Centro Brasileiro de Pesquisas Fisicas (CBPF), the Laboratórrio Nacional de Computa\c{c}\\tikzmark{mainBodyEnd6571}\~\tikzmark{mainBodyStart6572}aoo Científfica (LNCC) and the Observatórrio Nacional (ON) and funded by the Ministry of Science and Technology (MCT)" +The colour catalogue simulated in this way shows very similar colour-colour diagrams as the observed catalogue (seealso?) and is supposed to represent a realistic mix of galaxy types and low- and high-redshift objects.,"The colour catalogue simulated in this way shows very similar colour-colour diagrams as the observed catalogue \citep[see also +][]{2007A&A...462..865H} and is supposed to represent a realistic mix of galaxy types and low- and high-redshift objects." + In order to study the effect of the choice of the template set we re-run the simulations with the templates from? as a In general. the results are very similar to the ones with the template set from ?..," In order to study the effect of the choice of the template set we re-run the simulations with the templates from \cite{2006ApJ...652...85M} as a In general, the results are very similar to the ones with the template set from \cite{1993ApJ...405..538B}." + The scientific results in this study are hardly affected by this choice., The scientific results in this study are hardly affected by this choice. + Nevertheless. we show results for both template sets in the remainder of the paper.," Nevertheless, we show results for both template sets in the remainder of the paper." + Furthermore. we simulate the colours of stars in our fields from the TRILEGAL galactic model (?) taking into account the galactic coordinates of our survey fields and the depths of the images (seealso.?)..," Furthermore, we simulate the colours of stars in our fields from the TRILEGAL galactic model \citep{2005A&A...436..895G} taking into account the galactic coordinates of our survey fields and the depths of the images \citep[see also ][]{2007A&A...462..865H}." + From these simulations we identify regions in. colour-space where the efficiency of finding high-redshift star-forming galaxies is high due to their distinctive colours produced by the Lyman-break and where the contamination from low-redshift interlopers and stars is low., From these simulations we identify regions in colour-space where the efficiency of finding high-redshift star-forming galaxies is high due to their distinctive colours produced by the Lyman-break and where the contamination from low-redshift interlopers and stars is low. +" We dothis in the ση, eri. and riz colour-spaces to select u-dropouts. g-dropouts. and r-dropouts. respectively."," We dothis in the $ugr$ , $gri$ , and $riz$ colour-spaces to select $u$ -dropouts, $g$ -dropouts, and $r$ -dropouts, respectively." + In Fig., In Fig. + 2. the fraction of objects in the desired redshift range (4-dropouts: 2 0$." + We will require that the PDE be normalised: Since [lux of a source must be conserved. sources amplified in some directions must be deamplified in others.," We will require that the PDF be normalised: Since flux of a source must be conserved, sources amplified in some directions must be deamplified in others." + Εις (ux conservation constraint takes the form (?) The rav (racing techniques usec essentially assume point sources. which allows for arbitrarily high magnifications.," This flux conservation constraint takes the form \citep{Hilbert07} + The ray tracing techniques used essentially assume point sources, which allows for arbitrarily high magnifications." +— Phe consideration. of extended objects— imposes a maximum magnification limit. estimated by ? to be in the range LO30 for 110 kpe sources at. redshifts 14.," The consideration of extended objects imposes a maximum magnification limit, estimated by \citet{Perrotta02} to be in the range 10–30 for 1–10 kpc sources at redshifts 1–4." + The applicability of this estimate to SAIGs. however. is uncertain. since the characteristic size of emission is unknown.," The applicability of this estimate to SMGs, however, is uncertain, since the characteristic size of emission is unknown." + SAIGSs appear to be extended: objects of a [ων kpe. but may well be clumpy (227)... so small knots. of bright star-lormation would. have a higher potential for amplification by lensing than the galaxy considered. as a whole.," SMGs appear to be extended objects of a few kpc, but may well be clumpy \citep{Pope05, Chapman03}, so small knots of bright star-formation would have a higher potential for amplification by lensing than the galaxy considered as a whole." + Perhaps the best empirical constraint comes from ?.. who recently constrained the sizes of the submm emitting regions to LOkpe using interferometry.," Perhaps the best empirical constraint comes from \citet{Younger07}, who recently constrained the sizes of the submm emitting regions to $\la 10\,$ kpc using interferometry." + Until we have much more concrete information about the size distribution of SMCGs there is little we can do about the cllects of finite source size., Until we have much more concrete information about the size distribution of SMGs there is little we can do about the effects of finite source size. + For now we continue without a maximunt magnification limit. but will consider in section 5.1. how imposing such a constraint. would alfect our results.," For now we continue without a maximum magnification limit, but will consider in section \ref{sec:UncLensing} how imposing such a constraint would affect our results." + 7 give numerical data for à source plane at z=2.1. as well as the peak position fn(2) and full width at half maximum ΓΑΛΗΝΗ} of the cüstributions for other redshifts.," \citet{Hilbert07} give numerical data for a source plane at $z=2.1$, as well as the peak position $\mu_\rmn{p}(z)$ and full width at half maximum $\FWHM(z)$ of the distributions for other redshifts." +" We found that we could transform the z=2.1 PDE to other redshifts using a transformation of the form where fn, is the peak amplification at the reference 2. dA, is the shift in the peak between redshifts. 6 is determined by requiring that we obtain the correct ENIM. and the normalisation constant zl is determined. by requiring that we satisfy equation. (1))."," We found that we could transform the $z=2.1$ PDF to other redshifts using a transformation of the form where $\mu_\rmn{p}$ is the peak amplification at the reference $z$, $\delta \mu_\rmn{p}$ is the shift in the peak between redshifts, $b$ is determined by requiring that we obtain the correct FWHM, and the normalisation constant $A$ is determined by requiring that we satisfy equation \ref{eqn:pdf-normalisation}) )." + The peak shifts to lower f£ as increases. to balance the high sr tail. allowing the PDI to satisfy equation (2)).," The peak shifts to lower $\mu$ as $z$ increases, to balance the high $\mu$ tail, allowing the PDF to satisfy equation \ref{eqn:flux conservation}) )." + This transformation preserves the asyniptotic behaviour of the PDE. as discussed.— in section 2.3.. which is most crucial to our analysis.," This transformation preserves the asymptotic behaviour of the PDF, as discussed in section \ref{sec:ProbLimits}, which is most crucial to our analysis." + We plot the resulting fanuly of curves in Fig. 1.., We plot the resulting family of curves in Fig. \ref{fig:pdf-curves}. + For reference the values of the coellicients. are 61.6) = (0.473. 1.504). (0.968. 0.051). (1.383. 0.655). (1.681. 1.077) and CL.SS9. 1.346) for z = 1. 2. 3. 4 and 5. respectively.," For reference the values of the coefficients are $(A,b)$ = $0.473, -1.504$ ), $0.968, -0.051$ ), $1.383, 0.655$ ), $1.681, 1.077$ ) and $1.889, 1.346$ ) for $z$ = 1, 2, 3, 4 and 5, respectively." + The PDP for 2=2.1 is seento have aye? tail as predicted by theory (2). above an amplification of about ημων& 20.," The PDF for $z=2.1$ is seento have a $\mu^{-3}$ tail, as predicted by theory \citep{Schneider92} above an amplification of about $\mu_\rmn{high} \simeq 20$ ." + ‘Thus. the data are fit to where cliusn is an adjustable parameter. and this functional form can be used to extend the PDE to arbitrarily high amplifications.," Thus, the data are fit to where $A_\rmn{high}$ is an adjustable parameter, and this functional form can be used to extend the PDF to arbitrarily high amplifications." +" The fmi, mit is adjusted. for α other redshifts according to the transformation described above.", The $\mu_\rmn{high}$ limit is adjusted for all other redshifts according to the transformation described above. + Inaccuracy in the f£? behaviour above this limit may cause, Inaccuracy in the $\mu^{-3}$ behaviour above this limit may cause +mode with sampling times just under |-min.,mode with sampling times just under 1-min. + The three rolls for which we have data for 110195926 are long cadence in QO (quarter zero). which was a commissioning roll of less than dd. long cadence in Ql. and short cadence in Q3.3 dd during the last third of Q3).," The three rolls for which we have data for 10195926 are long cadence in Q0 (quarter zero), which was a commissioning roll of less than d, long cadence in Q1, and short cadence in Q3.3 d during the last third of Q3)." + reftab:journal gives a journal of the data., \\ref{tab:journal} gives a journal of the data. + reftig:le. shows the long cadence light curve for QO and QI together in the top panel and the short cadence light curve for Q3.3 in the middle panel., \\ref{fig:lc} shows the long cadence light curve for Q0 and Q1 together in the top panel and the short cadence light curve for Q3.3 in the middle panel. + À few outlying points were edited from the raw data and a linear trend to correct for instrumental drift was removed from the QI data., A few outlying points were edited from the raw data and a linear trend to correct for instrumental drift was removed from the Q1 data. + The data are inKepler magnitude. Ap. which is in broad-band white light.," The data are in magnitude, $Kp$, which is in broad-band white light." + It is obvious from reffig:le that 110195926 is an a? CCVn starz ie.. it has surface spots that produce a variation in brightness with rotation.," It is obvious from \\ref{fig:lc} that 10195926 is an $\alpha^2$ CVn star; i.e., it has surface spots that produce a variation in brightness with rotation." + This is a common feature of the magnetic Ap stars and implies that the star has a strong. global magnetic field. even though that field is yet to be detected. and we were only able to place an upper limit on it of KKG in," This is a common feature of the magnetic Ap stars and implies that the star has a strong, global magnetic field, even though that field is yet to be detected, and we were only able to place an upper limit on it of kG in." +refsec:spectroscopy.. In. some roAp stars. eg. 33831. (2) and HD999563 (?). the rare earth element surface spots are concentrated near to the pulsation or magnetic poles.," In some roAp stars, e.g. 3831 \citep{kochukhovetal04} and 99563 \citep{freyhammeretal09}, the rare earth element surface spots are concentrated near to the pulsation or magnetic poles." + These rare earth element spots often correlate with rotational light variations. particularly in the blue.," These rare earth element spots often correlate with rotational light variations, particularly in the blue." + With the advent of high precision space-based observations we can now see rotational light variations from spots in Ap stars that would not have been detected with ground- observations. or at least would have given a poorly defined light curve.," With the advent of high precision space-based observations we can now see rotational light variations from spots in Ap stars that would not have been detected with ground-based observations, or at least would have given a poorly defined light curve." + Such is the case for 110195926 where the peak-to-peak range in Ap is only slightly greater than mmmag., Such is the case for 10195926 where the peak-to-peak range in $Kp$ is only slightly greater than mmag. + We point out. however. that the rotational light variations of Ap stars are strongly wavelength dependent. as the result of flux redistribution caused by abundance spots. so that 110195926 may well show higher amplitude rotational light. variations observed in filtered light such as Johnson € or D.," We point out, however, that the rotational light variations of Ap stars are strongly wavelength dependent, as the result of flux redistribution caused by abundance spots, so that 10195926 may well show higher amplitude rotational light variations observed in filtered light such as Johnson $U$ or $B$." + To determine the rotational period of 110195926 we co-added the [-min integrations of Q3 to 30-min integrations and analysed all of the data listed in reftab:journal.., To determine the rotational period of 10195926 we co-added the 1-min integrations of Q3 to 30-min integrations and analysed all of the data listed in \\ref{tab:journal}. + There is à 158-d gap between the end of the QI data and the beginning of the Q3.3 data. giving rise to possible alias ambiguities in an analysis of the full data set.," There is a 158-d gap between the end of the Q1 data and the beginning of the Q3.3 data, giving rise to possible alias ambiguities in an analysis of the full data set." + As can be seen from the rotational light curve is highly nonsinusoidal. so Fourier analvsis is not the best choice for period determination.," As can be seen from \\ref{fig:lc} the rotational light curve is highly nonsinusoidal, so Fourier analysis is not the best choice for period determination." + We chose to fit a harmonic series by linear least-squares to the data to search for the greatest reduction in the variance in the data., We chose to fit a harmonic series by linear least-squares to the data to search for the greatest reduction in the variance in the data. + reffig:lsps. shows the results of a tifth-order harmonic series fit to the data., \\ref{fig:lsps} shows the results of a fifth-order harmonic series fit to the data. +" There is a clear best frequeney at yo,=0.17591 with no alias ambiguity.", There is a clear best frequency at $\nu_{\rm rot} = 0.17591$ $^{-1}$ with no alias ambiguity. + While significant harmonies are present up to 15.20 in the individualquarters of data. no discernible improvement in reffig:lsps can be seen with a higher-order tit.," While significant harmonics are present up to $15 - 20$ in the individualquarters of data, no discernible improvement in \\ref{fig:lsps} can be seen with a higher-order fit." + We then titted 20 harmonics of Mei=—0.17591 1 to the full data set by least-squares and then nonlinear least-squares to optimise the frequency and make an error estimate., We then fitted 20 harmonics of $\nu_{\rm rot} = 0.17591$ $^{-1}$ to the full data set by least-squares and then nonlinear least-squares to optimise the frequency and make an error estimate. +" This gave our best determination of the rotation frequency of Yor=OL1T5914+O.000004dd bt. which corresponds to a rotation period of Py,=5.68459+ 0.00013dd. This error estimate is internal."," This gave our best determination of the rotation frequency of $\nu_{\rm rot} = 0.175914 \pm 0.000004$ $^{-1}$, which corresponds to a rotation period of $P_{\rm rot} = 5.68459 \pm 0.00013$ d. This error estimate is internal." + Some systematic effects are still present in the data. such as small instrumental drifts and slight changes in amplitude between quarters.," Some systematic effects are still present in the data, such as small instrumental drifts and slight changes in amplitude between quarters." + These will be improved in future data reductions using more detailed pixel information., These will be improved in future data reductions using more detailed pixel information. + Since more data for 110195926 are being obtained. the rotation period will be determined to higher accuracy in future studies.," Since more data for 10195926 are being obtained, the rotation period will be determined to higher accuracy in future studies." + The precision given here is excellent for comparison with the pulsation phases within the oblique pulsator model., The precision given here is excellent for comparison with the pulsation phases within the oblique pulsator model. + reffig:phase-gOl shows the long cadence light curve for QO and QI phased with the rotational period., \\ref{fig:phase-q01} shows the long cadence light curve for Q0 and Q1 phased with the rotational period. + The double-wave character of the rotational light curve indicates two prineipal spots., The double-wave character of the rotational light curve indicates two principal spots. + The zero point of the time scale has been selected to coincide with the time of pulsation maximum. as determined in refsec:pulsations below.," The zero point of the time scale has been selected to coincide with the time of pulsation maximum, as determined in \\ref{sec:pulsations} below." + It can be seen that minimum rotational brightness coincides with pulsation maximum. as is expected in the oblique pulsator model (2).. in the case when the spots are associated with the magnetic/pulsation axis of the star.," It can be seen that minimum rotational brightness coincides with pulsation maximum, as is expected in the oblique pulsator model \citep{kurtz82}, in the case when the spots are associated with the magnetic/pulsation axis of the star." + This coincidence ean also be seen by comparing the middle and bottom panels of reftig:le.., This coincidence can also be seen by comparing the middle and bottom panels of \\ref{fig:lc}. . + The asymmetry of the light curve requires differences in spots on opposite hemispheres., The asymmetry of the light curve requires differences in spots on opposite hemispheres. + It does not appear that the spots seen, It does not appear that the spots seen +Lah Melia. 1988).,Lamb Melia 1988). + We discuss in the following whi these conditions for coupling disappear in the late state of secular binary evolution., We discuss in the following why these conditions for coupling disappear in the late state of secular binary evolution. + Iu the transition from a low-inass main-sequence star to a brown dwarf the overadiabatic structure aud couvection disappear., In the transition from a low-mass main-sequence star to a brown dwarf the overadiabatic structure and convection disappear. + No couvectiou-based dynamo exists aud uo containment of captured flux iu a convective zone (Mover 1991) is xossible auanore., No convection-based dynamo exists and no containment of captured flux in a convective zone (Meyer 1994) is possible anymore. + Ii both cases the magnetic field of the secondary. disappears., In both cases the magnetic field of the secondary disappears. + A further hint that the feld vanishes when the secondary becomes a brown ενα comes from the outbiurs behaviour of the dxwuf novae in late secular evolution., A further hint that the field vanishes when the secondary becomes a brown dwarf comes from the outburst behaviour of the dwarf novae in late secular evolution. + The modelling οἳ the extremely bright outbursts and the recurrence time of decades of WZ See stars requires an extremely low viscosity in the quiesceut accretion disk (Meyer-Ilofiicister et al., The modelling of the extremely bright outbursts and the recurrence time of decades of WZ Sge stars requires an extremely low viscosity in the quiescent accretion disk (Meyer-Hofmeister et al. + 1998)., 1998). + Tf the accretion disk viscosity di quiescence is caused bv the secondarys inaegnuctic field (Mever Alever-Hofiueister 1999.) this low viscosity value can be interpreted as due to the disappearance of the secondary stars magnetic field.," If the accretion disk viscosity in quiescence is caused by the secondary's magnetic field (Meyer Meyer-Hofmeister 1999,) this low viscosity value can be interpreted as due to the disappearance of the secondary star's magnetic field." + Tf the magnetic field of the secondary disappears no dipole-dipole interaction aud no conductive tving of primary field to secondary field are possible., If the magnetic field of the secondary disappears no dipole-dipole interaction and no conductive tying of primary field to secondary field are possible. + The primary feld caunot couple to a non-magnetic secondary because buovaucy tends to expell magnetic fields from the star aud there is no convective mixing to counteract this effect., The primary field cannot couple to a non-magnetic secondary because buoyancy tends to expell magnetic fields from the star and there is no convective mixing to counteract this effect. + Oluuic diffusion on the hotter radiated side does not suffice for efficicut penctration., Ohmic diffusion on the hotter irradiated side does not suffice for efficient penetration. + On the cool surface of the backside conductivity is too low for maguctic coupling (Meyer AMoever-Hofiucister 1999)., On the cool surface of the backside conductivity is too low for magnetic coupling (Meyer Meyer-Hofmeister 1999). + When magnetic coupling is lost the white dwarf starts to spin up., When magnetic coupling is lost the white dwarf starts to spin up. + No aneular momentum is returned to the secondary and thereby to the orbit., No angular momentum is returned to the secondary and thereby to the orbit. + We investigate how the mass transfer develops., We investigate how the mass transfer develops. + For the structure of the secondary we take a polvtrope with pressure p and density p A depends ou the secondarys mass Mo and radius Πο (Emden 1907)., For the structure of the secondary we take a polytrope with pressure $p$ and density $\rho$ $K$ depends on the secondary's mass $M_2$ and radius $R_2$ (Emden 1907). + We asstune that the star fills its Roche lohe Rio.," We assume that the star fills its Roche lobe $R_{R,2}$." +" We use Paczvüsskis (1971) approximation for simall lass ratios gq=Ab/AL, (M4 mass of the primary) where 4 is the separation of the binary stars.", We use Paczyńsski's (1971) approximation for small mass ratios $q = M_2/M_1$ $M_1$ mass of the primary) where $a$ is the separation of the binary stars. + The separation is related to the orbital period eravitational constant., The separation is related to the orbital period gravitational constant. + The mean density Py is then related to the orbital period P. po=Lose.hj? (Frank ct al.," The mean density $\overline{\rho}_2$ is then related to the orbital period $P$ $\overline{\rho}_2 = +110 /(P/\rm h)^2$ (Frank et al." + 1985)., 1985). +" For a Roche lobe filling secondary the coustant A cau be expressed where Ao 1s the orbital period in units of 80 minutes (a completely degencrate star of cosmic abundance would have K=1012°),", For a Roche lobe filling secondary the constant $K$ can be expressed where $P_{80}$ is the orbital period in units of 80 minutes (a completely degenerate star of cosmic abundance would have $10^{12.85}$ ). + The rate of mass transfer through the Lagrangian point L4 is given by the product of density. souud specd and effective cross section (see I&olb Ritter 1990).," The rate of mass transfer through the Lagrangian point $L_1$ is given by the product of density, sound speed and effective cross section (see Kolb Ritter 1990)." + For a polvtrope with 5=5/3 we oobtaiu with &(4) from the Roche geometry (compare Meyer Aever-Hofineister 1983). À(q4)—5.97 for q—0.1.," For $a$ polytrope with $\gamma = 5/3$ we obtain with $k(q)$ from the Roche geometry (compare Meyer Meyer-Hofmeister 1983), $k(q)$ =5.97 for $q$ =0.1." +" For 4=0.1 aud A,=0.073.. follows: We determine the change of AT.", For $q = 0.1$ and $M_2 = 0.07 M_\odot$ follows: We determine the change of $\dot M$. + Wo call } the fraction of the trausterred matter accreted ou the primary. iM. in the spiu-up phase 9=1.," We call $\beta$ the fraction of the transferred matter accreted on the primary, $\dot{M_1} += \beta \dot{M}$ , in the spin-up phase $\beta=1$." + The change of the Roche radius Ry» depends on the change of the quantities e and q.," The change of the Roche radius $R_{R,2}$ depends on the change of the quantities $a$ and $q$." + The time derivative of à is related to the derivative of the augular momentum J We consider orbital augular imionentun loss due to eravitational radiation. spiu-up of the white dwarf aud. iu the propeller phase. expulsion of matter We take ον according to Alisner ct al. (," The time derivative of $a$ is related to the derivative of the angular momentum $J$ We consider orbital angular momentum loss due to gravitational radiation, spin-up of the white dwarf and, in the propeller phase, expulsion of matter We take $\dot{J}_{\rm {GW}}$ according to Misner et al. (" +1973).,1973). + Additional braking. as considered by Koll Bavatte (1999) can be taken into account by applying a correspoudius factor to Je and Men.," Additional braking, as considered by Kolb Baraffe (1999) can be taken into account by applying a corresponding factor to $\dot{J}_{\rm {GW}}$ and $\dot M_{\rm {GW}}$ ." + Apinap results," $\dot{J}_ +{\rm {spin-up}}$ results" +depth and depends on the distribution of lensing matter along the lows. (,depth and depends on the distribution of lensing matter along the l.o.s. ( +"e.g. Kiraga&Paezynski 1994.. Jetzeretal.2002)) where p, is the mass density of the lenses. D, is the source- distance. and D, is the lens-observer distance.","e.g. \citealt{KP94}, , \citealt{Je02}) ) where $\rho_l$ is the mass density of the lenses, $D_s$ is the source-observer distance, and $D_l$ is the lens-observer distance." + If both lenses and sources are distributed along the Lo.s..," If both lenses and sources are distributed along the l.o.s.," + Eq., Eq. +" | becomes where p, is the mass density of sources and Jo=ΟνDa(1ODD,is3 a. normalization factor."," \ref{eqn_tau1} becomes where $\rho_s$ is the mass density of sources and $I\,=\,\int_0^{D_{max}}\,\rho_s(D_s)D_s^2\textrm{d}D_s$ is a normalization factor." +" .Throughout this paper[ we assume D,,,, =12kpe to include the contribution of the whole bulge (see Sect. ??))."," Throughout this paper we assume $D_{max}\,=\,12$ kpc to include the contribution of the whole bulge (see Sect. \ref{bd_model}) )." + The optical depth can also be defined as (Griest1991] )) where [is the rate of lenses entering the tube and (£z) is the average time scale of the observed events., The optical depth can also be defined as \citealt{Gr91}) ) where $\Gamma$ is the rate of lenses entering the tube and $\left\langle t_E \right\rangle$ is the average time scale of the observed events. + The duration of a single event depends on the mass of the lens and the geometry of the system where v. is the relative velocity between source and lens in a plane perpendicular to the Lo.s., The duration of a single event depends on the mass of the lens and the geometry of the system where $v_\bot$ is the relative velocity between source and lens in a plane perpendicular to the l.o.s. +" and Ry is the Einstein radius (e.g. Griest 1991)) where M ts the mass of the lens. x=Dj/D, and m=M/M; is the mass of the lens in solar units."," and $R_E$ is the Einstein radius (e.g. \citealt{Gr91}) ) where M is the mass of the lens, $x\,=\,D_l/D_s$ and $m\,=\,M\,/\,M_\odot$ is the mass of the lens in solar units." +" The differential rate of events 1s (e.g. Jetzeretal.2002.. CalchiNovatietal. 2008)) where 7; and 7, are the number density of the lenses and the sources along the l.o.s.."," The differential rate of events is (e.g. \citealt{Je02}, \citealt{CN08}) ) where $n_l$ and $n_s$ are the number density of the lenses and the sources along the l.o.s.," + while f(v_) is the distribution of the source-lens relative velocities., while $f(\bf{v_\bot})$ is the distribution of the source-lens relative velocities. + We model the Galactic bulge as in CalchtNovatietal. (2008).. Le. as a triaxial bulge with an exponential density profile and a major axis that forms an angle @=23.8Á with the Sun-Galactic center axis (e.g Staneketal. 1997)).," We model the Galactic bulge as in \cite{CN08}, i.e. as a triaxial bulge with an exponential density profile and a major axis that forms an angle $\phi\,=\,23.8°$ with the Sun-Galactic center axis (e.g \citealt{St97}) )." + The total mass of the bulge is ~2x10!M...," The total mass of the bulge is $\sim\,2\,\times\,10^{10}\,M_\odot$." +" For the disk. we adopt a thin + thick disk model. both described by an exponential density profile where the masses of the thin and thick disks are Mp,~2.510M. and Mp,~0.5x10!Mthe scale-lengths are Ly~2.6 kpe and Ls~3.6 kpe and scale-heights are Hj.~0.3 and Hs~0.9 kpe (e.g. 2)."," For the disk, we adopt a thin + thick disk model, both described by an exponential density profile where the masses of the thin and thick disks are $M_{D_1}\,\sim\,2.5\,\times\,10^{10}\,M_\odot$ and $M_{D_2}\,\sim\,0.5\,\times\,10^{10}\,M_\odot$, the scale-lengths are $L_1\,\sim\,2.6$ kpc and $L_2\,\sim\,3.6$ kpc and scale-heights are $H_1\,\sim\,0.3$ and $H_2\,\sim\,0.9$ kpc (e.g. \citealt{Ro03}) )." +" The mass of the thin disk accounts also for the interstellar medium. άν~0.5x10!""M..."," The mass of the thin disk accounts also for the interstellar medium, $M_{ISM}\,\sim\,0.5\,\times\,10^{10}\,M_\odot$." + According to Freudenreich(1998).. the stellar disk ts holec at Its center. the hole being likely produced by orbital resonances in the potential of the barred bulge (e.g. Contopoulosetal.1989)).," According to \cite{Fr98}, , the stellar disk is holed at its center, the hole being likely produced by orbital resonances in the potential of the barred bulge (e.g. \citealt{Co89}) )." + For the scale-length of the hole of both the thin and thick disks we assume Lj~1.3 kpe (Picaud&Robin.2004)..," For the scale-length of the hole of both the thin and thick disks we assume $L_h\,\sim\,1.3$ kpc \citep{PR04}. ." + The motion of bulge and disk stars has both bulk and random components., The motion of bulge and disk stars has both bulk and random components. + The Galactic bulge does not rotate as a whole like a rigid body but out of a certain radius the bulk velocity flattens (Richetal.2007))., The Galactic bulge does not rotate as a whole like a rigid body but out of a certain radius the bulk velocity flattens \citealt{Ri07}) ). +" Thus we assume that the velocity""nu v,rotation "" of the bulge grows linearly to 50kms""! out of a radius of | kpe from the Galactic center."," Thus we assume that the rotation velocity $v_{rot}^{(b)}$ of the bulge grows linearly to $50\,\textrm{km\,s}^{-1}$ out of a radius of 1 kpc from the Galactic center." +" Out of this radius.. we assume a flat rotation. curve. with. v7,th)=50kms7!.z-"," Out of this radius, we assume a flat rotation curve, with $v_{rot}^{(b)}=50\,\rm km\,s^{-1}$." + For disk stars. we compute the bulk motion self-consistently from the potential generated by disk and bulge stars. see Sect. ??..," For disk stars, we compute the bulk motion self-consistently from the potential generated by disk and bulge stars, see Sect. \ref{sect_icors}." + We assume for simplicity that the random motions of bulge and disk stars are isotropic. with dispersions Tu-100 and o.2kms! which reasonably agrees with the values inferred from observations (e.g. CalehiNovatietal.2008 and references therein).," We assume for simplicity that the random motions of bulge and disk stars are isotropic, with dispersions $\sigma_v^{(b)}=100$ and $\sigma_v^{(d)}=25\,\rm km\,s^{-1}$ which reasonably agrees with the values inferred from observations (e.g. \citealt{CN08} and references therein)." + In Paper I we studied the dynamies of a population of disk NSs born at a constant rate during the Milky Way lifetime. assuming a total of 10° NSs. consistently with chemical abundances observed in the Galaxy (e.g. Arnettetal. 1989)).," In Paper I we studied the dynamics of a population of disk NSs born at a constant rate during the Milky Way lifetime, assuming a total of $10^9$ NSs, consistently with chemical abundances observed in the Galaxy (e.g. \citealt{Ar89}) )." + As Of09 has pointed out. the total number of disk-born NSs inferred from the present-day supernova rate and from the formation history of the disk is x410? (Keane&Kramer2008 and references therein).," As Of09 has pointed out, the total number of disk-born NSs inferred from the present-day supernova rate and from the star-formation history of the disk is $\lesssim\,4\,\times\,10^8$ \citealt{KK08} and references therein)." + To explain this discrepancy. Of09 suggested that the remaining NSs have been generated in the bulge.," To explain this discrepancy, Of09 suggested that the remaining NSs have been generated in the bulge." + Because we are dealing with the microlensing rate of compact remnants toward the Galactic bulge. it is straightforward to think that the major contribution comes from bulge-born objects.," Because we are dealing with the microlensing rate of compact remnants toward the Galactic bulge, it is straightforward to think that the major contribution comes from bulge-born objects." + Thus we re-run our simulations. taking into account the contribution of the bulge.," Thus we re-run our simulations, taking into account the contribution of the bulge." + First. we estimate the total number of ICoRs born in the MW. following the approach of Gould(2000).," First, we estimate the total number of ICoRs born in the MW, following the approach of \cite{Go00}." +.. We adopt the initial mass function (IMF) proposed by Kroupa (2001).. 1.8. a triple power law model From the IMF we estimate the number and mass fractions of each stellar population - brown dwarfs. main sequence stars. white dwarfs(BDs. MSs and WDs hereafter). NSs and BHs.," We adopt the initial mass function (IMF) proposed by \cite{Kr01}, , i.e. a triple power law model From the IMF we estimate the number and mass fractions of each stellar population - brown dwarfs, main sequence stars, white dwarfs(BDs, MSs and WDs hereafter), NSs and BHs." + We assume thatall stars with aw>| have evolvedthrough the remnant phase. te. stars with |\,1$ have evolvedthrough the remnant phase, i.e. stars with $1\,<\,m\,<\,8$ arenow white dwarfs $m_{WD}\,=\,0.6$ ), while stars with masses $8\,<\,m\,<\,40$ and $40\,<\,m\,<\,100$ are treated as neutron stars $m_{NS}\,=\,1.4$ )" +The notion that some massive stars undergo a collapse without producing a SN first appeared as a Γάμο to produce SN explosions in hydrodynamical simulations. but later eained ground as a possible mechanism behind GRBs.," The notion that some massive stars undergo a collapse without producing a SN first appeared as a failure to produce SN explosions in hydrodynamical simulations, but later gained ground as a possible mechanism behind GRBs." + These theoretical considerations were left without any empirical evidence., These theoretical considerations were left without any empirical evidence. + If in binary svstems (hese failed SNe collapse into 115 without disrupting the binaries. one mieht be able detect such svstems astrometricallv.," If in binary systems these failed SNe collapse into BHs without disrupting the binaries, one might be able detect such systems astrometrically." + To (his end we suggest usingZA Esince it will observe vast number ofstars wilh great precision., To this end we suggest using since it will observe vast number of stars with great precision. + To estimate (he rate of SNe that fail. it is first neccessary to estimate the number of binaries that were born consisting of a G dwarf (a (vpical starZZLAE will observe). ancl a massive. short-lived D star (NS/DII progenitor).," To estimate the rate of SNe that fail, it is first neccessary to estimate the number of binaries that were born consisting of a G dwarf (a typical star will observe), and a massive, short-lived B star (NS/BH progenitor)." +" We can derive (this number using,MLALE detections of either currently existing G+B pairs. or by extrapolating from the number of G+WD binaries."," We can derive this number using detections of either currently existing G+B pairs, or by extrapolating from the number of G+WD binaries." +FAALE will be able to probe ~4x10* stars for DII companions., will be able to probe $\sim 4\times 10^7$ stars for BH companions. + The result of (his experiment would either discover a new phenomenon (BIL collapsar). or place stringent limits on SN and GRD moclels.," The result of this experiment would either discover a new phenomenon (BH collapsar), or place stringent limits on SN and GRB models." + This work was supported in part by JPL contract 1226901., This work was supported in part by JPL contract 1226901. +to the presence of the event horizon rather than a surface.,to the presence of the event horizon rather than a surface. + In this case we might imagine the aceretion [ow would produce a jet at some radius which was not allectecl by the nature of the accretor. but the ow was raciatively inellicient and acdvected a large fraction of its energy across the black hole event horizon (see c.g. Naravan. Alahadevan Quataert 1998).," In this case we might imagine the accretion flow would produce a jet at some radius which was not affected by the nature of the accretor, but the flow was radiatively inefficient and advected a large fraction of its energy across the black hole event horizon (see e.g. Narayan, Mahadevan Quataert 1998)." + Ht is interesting to note that in section +2 we found that the distribution of Py was significantlv. cülferent for the NS and DIIC samples: this would appear to support an X-ray quiet rather than a radio loud! description of the BUC sample. presuming that the BIIC's are on average more massive than the NS systems.," It is interesting to note that in section 3.2 we found that the distribution of $_X$ was significantly different for the NS and BHC samples; this would appear to support an `X-ray quiet' rather than a `radio loud' description of the BHC sample, presuming that the BHCs are on average more massive than the NS systems." + Further comparisons of the clistribution of Py for NS and BLICs. foreff transient events. would. be very interesting (but would also require more careful consideration of e.g. absorption and other selection ellects).," Further comparisons of the distribution of $_X$ for NS and BHCs, for transient events, would be very interesting (but would also require more careful consideration of e.g. absorption and other selection effects)." + It is interesting in this context to note the recent debate about the relative Iuminosities of BLIC and NS systems in cquiescence. and their ratio of outburst to quiescent X-ray Hux (e.g. Asai et al.," It is interesting in this context to note the recent debate about the relative luminosities of BHC and NS systems in quiescence, and their ratio of outburst to quiescent X-ray flux (e.g. Asai et al." + 1998: Menou οἱ al., 1998; Menou et al. + 1999: Campana Stella 2000)., 1999; Campana Stella 2000). + While still controversial. it has been suggested that the combination of advective [low and event. horizon results in a lower X-rav luminosity [or quiescent BIIC's compared to quiescent NS systems.," While still controversial, it has been suggested that the combination of advective flow and event horizon results in a lower X-ray luminosity for quiescent BHCs compared to quiescent NS systems." + The results here. while requiring further careful. interpretation.gray be further evidence for broad. observational dillerences between BLIC and NS svstems resulting from the presence or not of a solid surface.," The results here, while requiring further careful interpretation, be further evidence for broad observational differences between BHC and NS systems resulting from the presence or not of a solid surface." +" In Fie 5 we plot ""radio loudness! as a function of Py for all the systems in Table. 1. including the range of peak Iluxes displaved. in the repeated outbursts of Cye X-3. GRS 1915|105 and Cir N-1 (based somewhat subjectively on inspection of extended: X-ray ancl radio data sets)"," In Fig 5 we plot `radio loudness' as a function of $_X$ for all the systems in Table 1, including the range of peak fluxes displayed in the repeated outbursts of Cyg X-3, GRS 1915+105 and Cir X-1 (based somewhat subjectively on inspection of extended X-ray and radio data sets)." + In addition we indicate the direction of a shift to higher peak radio flux densities at. smaller inclinations. if the racio emission is significantly Doppler boosted.," In addition we indicate the direction of a shift to higher peak radio flux densities at smaller inclinations, if the radio emission is significantly Doppler boosted." + Several things are noteworthy upon careful inspection of the figure: We brielly discuss these points below: The position of the ETFs in Figs 2 and 3 reveals that their radio and X-rav peak [uxes are entirely consistent. with bright outbursts of BITC systems., Several things are noteworthy upon careful inspection of the figure: We briefly discuss these points below: The position of the FTs in Figs 2 and 3 reveals that their radio and X-ray peak fluxes are entirely consistent with bright outbursts of BHC systems. + This is consistent. with the results of Orosz et al. (, This is consistent with the results of Orosz et al. ( +2000a.b) who claim that the ETE VAG41 Ser is Likely to contain a black hole (see also the suggestion in Belloni et al.,"2000a,b) who claim that the FT V4641 Sgr is likely to contain a black hole (see also the suggestion in Belloni et al." + 1999 that the FL CL Cam may contain a black hole)., 1999 that the FT CI Cam may contain a black hole). + However. given the small samples anc strange behaviour in the past of the e.g. NS Cir N-1. this cannot be considered. as more than circumstantial support [or this interpretation.," However, given the small samples and strange behaviour in the past of the e.g. NS Cir X-1, this cannot be considered as more than circumstantial support for this interpretation." + Cve X-3 has the largest radio:iX-rav ratio ofany X-rav binary: in fact with multiple radio outbursts brighter than 10 Jw fee. Waltman et al., Cyg X-3 has the largest radio:X-ray ratio of X-ray binary; in fact with multiple radio outbursts brighter than 10 Jy (e.g. Waltman et al. + 1995). it ds. the brightest racio source ever associated with an X-ray binary.," 1995), it is the brightest radio source ever associated with an X-ray binary." + Furthermore. it was one of the earliest. sources in. which a clear correlation between X-ray. ancl racio outbursts was established. (Watanabe et al.," Furthermore, it was one of the earliest sources in which a clear correlation between X-ray and radio outbursts was established (Watanabe et al." + 1994: sce also AleCollough et al., 1994; see also McCollough et al. + 1999)., 1999). + Why is it so bright?, Why is it so bright? + Recent VLBA observations reveal a milliaresecond-scale jet which is clearly one-siced (Mioduszewski ct al., Recent VLBA observations reveal a milliarcsecond-scale jet which is clearly one-sided (Mioduszewski et al. + 1998. 2001) and may be interpreted as à xO.Se jet inclined within a few degrees of the line of sight.," 1998, 2001) and may be interpreted as a $\ga 0.8c$ jet inclined within a few degrees of the line of sight." + LD so. (νο X-3 is the ealactic equivalent of a blazar ancl may represent more or less the extreme of the possible racio:N-rav ratios.," If so, Cyg X-3 is the galactic equivalent of a blazar and may represent more or less the extreme of the possible radio:X-ray ratios." +" As Fig 5 clearly demonstrates. the repeated. simultaneous X-ravuadio outbursts of the ""microquasar GRS 1915|105 lic right in the middle of the BLIC clistribution."," As Fig 5 clearly demonstrates, the repeated simultaneous X-ray:radio outbursts of the `microquasar' GRS 1915+105 lie right in the middle of the BHC distribution." + This clearly, This clearly +One of the key questions in stellar astrophysics ts to understand the formation and earliest evolution of high-mass stars.,One of the key questions in stellar astrophysics is to understand the formation and earliest evolution of high-mass stars. + These objects play a major role in shaping the interstellar medium due to their strong UV radiation fields and stellar winds. and they enrich their environment with heavy elements when exploding as supernovae.," These objects play a major role in shaping the interstellar medium due to their strong UV radiation fields and stellar winds, and they enrich their environment with heavy elements when exploding as supernovae." + Despite their importance. the mechanism by which such massive stars form and. especially. the initial conditions of their birthplaces are poorly understood (??)..," Despite their importance, the mechanism by which such massive stars form and, especially, the initial conditions of their birthplaces are poorly understood \citep{2007prpl.conf..165B,2007ARA&A..45..481Z}." + One pathway to tackle especially the latter problem is to analyse so-called Infrared Dark Clouds (IRDCs)., One pathway to tackle especially the latter problem is to analyse so-called Infrared Dark Clouds (IRDCs). + They were first identified with the USO: and (MSX:: as dark extended features against the bright Galactic PAH background at mid-IR (MIR) wavelengths., They were first identified with the \citep[\emph{ISO\/}; and \citep[\emph{MSX\/}; as dark extended features against the bright Galactic PAH background at mid-IR (MIR) wavelengths. + The first studies (22?) showed that IRDCs are dense (510? cm). cold (x25 K) and can attain high column densities (2 107 em7*).," The first studies \citep{1998ApJ...494L.199E,1998ApJ...508..721C,2000ApJ...543L.157C} showed that IRDCs are dense $>$ $^5$ $^{-3}$ ), cold $<$ 25 K) and can attain high column densities $\ga$ $^{23}$ $^{-2}$ )." + All these properties make IRDCs excellent candidates for hosting very early stages of massive star formation., All these properties make IRDCs excellent candidates for hosting very early stages of massive star formation. + During the last years. additional studies of Infrared Dark Clouds at millimeter and submillimeter wavelengths were performed.," During the last years, additional studies of Infrared Dark Clouds at millimeter and submillimeter wavelengths were performed." + ? presented a catalog of almost 110000 IRDCs in the first and fourth quadrants of the Galactic plane., \citet{2006ApJ...639..227S} presented a catalog of almost 000 IRDCs in the first and fourth quadrants of the Galactic plane. + Using CO J21—0 molecular line emission. the kinematic distances to 313 clouds from this catalog were established (2)..," Using $^{13}\rm CO$ J=1–0 molecular line emission, the kinematic distances to 313 clouds from this catalog were established \citep{2006ApJ...653.1325S}." + This allowed to estimate sizes. masses and the Galactic distribution for this large sample.," This allowed to estimate sizes, masses and the Galactic distribution for this large sample." + The study showed that IRDCs have sizes of ~ 5 pe and LTE masses of ~ 5 x I0? M. comparable to cluster-forming molecular clumps., The study showed that IRDCs have sizes of $\sim$ 5 pc and LTE masses of $\sim$ 5 $ \times $ $^3$ $\rm M_\odot$ comparable to cluster-forming molecular clumps. + The galactic distribution of IRDCs follows the general distribution of molecular gas., The galactic distribution of IRDCs follows the general distribution of molecular gas. + A concentration of the clouds is associated with the so-called 5 kpe molecular ring. the Galaxy's most massive and active complex.," A concentration of the clouds is associated with the so-called 5 kpc molecular ring, the Galaxy's most massive and active complex." + Ammonia observations of some well-known IRDCs with the Effelsbere 100 m telescope (?) allowed to estimate additional chemical and physical properties. such as average gas temperature (between 10 and 20 K). velocity fields (significant velocity gradient between the cores. linewidths of 0.911.5 km/s) and the chemical state.," Ammonia observations of some well-known IRDCs with the Effelsberg 100 m telescope \citep{2006A&A...450..569P} allowed to estimate additional chemical and physical properties, such as average gas temperature (between 10 and 20 K), velocity fields (significant velocity gradient between the cores, linewidths of 1.5 km/s) and the chemical state." + According to this study. NH; in IRDCs is overabundant by a factor of 110 relative to Taurus or Perseus local dark clouds. while HCO is underabundant by a factor of ~ 50.," According to this study, $\rm NH_3$ in IRDCs is overabundant by a factor of 10 relative to Taurus or Perseus local dark clouds, while $\rm H_2CO$ is underabundant by a factor of $\sim$ 50." + Hence. the chemistry governing IRDCs might be complex and could be different from other parts of the molecular ISM.," Hence, the chemistry governing IRDCs might be complex and could be different from other parts of the molecular ISM." + Although significant progress has been made observationally. the number of IRDCs with well characterised properties is still small to date. especially regarding the southern hemisphere.," Although significant progress has been made observationally, the number of IRDCs with well characterised properties is still small to date, especially regarding the southern hemisphere." + To enlarge the sample of well-investigated. IRDCs. we selected 12 clouds in the southern hemisphere and started à program to measure the gas and dust properties of these objects.," To enlarge the sample of well-investigated IRDCs, we selected 12 clouds in the southern hemisphere and started a program to measure the gas and dust properties of these objects." + In Sect., In Sect. + 2 we describe our source selection and 1.2 mm continuum observations. with. the SIMBA/SEST telescope., 2 we describe our source selection and 1.2 mm continuum observations with the SIMBA/SEST telescope. + In Sect., In Sect. + 3. we discuss the data reduction. and the details concerning the calculation of dust masses and column densities.," 3, we discuss the data reduction and the details concerning the calculation of dust masses and column densities." + Also we present here the comparison of the MIR and millimeter techniques., Also we present here the comparison of the MIR and millimeter techniques. + In Sect., In Sect. + 4. we compare our results with previous results for high- and low-mass star-forming region and with the theoretical models.," 4, we compare our results with previous results for high- and low-mass star-forming region and with the theoretical models." +" The IRDCs for our study were selected in the ""pre-Spitzer era. by visual examination of the MIR images delivered by the ΜΟΝ satellite."," The IRDCs for our study were selected in the ""pre–Spitzer"" era, by visual examination of the MIR images delivered by the MSX satellite." + The MSX A band (6.8 — 10.8 jam) was the nost sensitive one among the MSX bands and presented the highest level of diffuse background emission (due to PAH emission at 7.7 and 8.7 yam). which also leads to the highest contrast between bright background and dark IRDCs.," The MSX A band (6.8 – 10.8 $\mu$ m) was the most sensitive one among the MSX bands and presented the highest level of diffuse background emission (due to PAH emission at 7.7 and 8.7 $\mu$ m), which also leads to the highest contrast between bright background and dark IRDCs." + We selected a sample of southern IRDCs from the A band images looking for high contrast andsizes sufficient to fill the main beam of, We selected a sample of southern IRDCs from the A band images looking for high contrast andsizes sufficient to fill the main beam of +"form for the power spectrum where L, is the correlation length of the field.",form for the power spectrum where $L_c$ is the correlation length of the field. +" Ilere. Af, is chosen such that there is an equal spacing in logarithmic &—space. over the finite interval FgShSlg. where Άμαν=LOOXΑμ and NV=100."," Here, $\Delta k_n$ is chosen such that there is an equal spacing in logarithmic $k-$ space, over the finite interval $k_{\mathrm{min}} \leqq k \leqq k_{\rm{max}}$, where $k_{\rm{max}} = 100 \times k_{\rm{min}}$ and $N = 100$." + where μμ=22/L. and a=11/3., where $k_{\rm{min}} = 2\pi/L_{\mathrm{c}}$ and $\alpha = 11/3$. + We have no reliable constraint for value of a from GRB observation. so we adopt the Kolmogorov turbulence Br(h)xh° tentatively. where the power spectrum has a peak at Ayn.," We have no reliable constraint for value of $\alpha$ from GRB observation, so we adopt the Kolmogorov turbulence $B^2(k) \propto k^{-5/3}$ tentatively, where the power spectrum has a peak at $k_{\mathrm{min}}$." +" Then we celine the streng(h parameter using σ and Aq, as We inject isotropically 32 monoenergetic electrons wilh >=10in the prescribed magnetic fields. and solve the equation of motion using 2nd order Runge-Ixutta method."," Then we define the strength parameter using $\sigma$ and $k_{\rm{min}}$ as We inject isotropically 32 monoenergetic electrons with $\gamma=10$ in the prescribed magnetic fields, and solve the equation of motion using 2nd order Runge-Kutta method." +" We pursue the orbit of electrons up to the time 300xT,. where T, is the gvro time T7,=235mc/eo."," We pursue the orbit of electrons up to the time $300 \times T_{\mathrm{g}}$, where $T_{\mathrm{g}}$ is the gyro time $T_{\mathrm{g}} = 2\pi \gamma m c / e \sigma$." + We caleulate radiation spectrum using acceleration 6=c., We calculate radiation spectrum using acceleration $\dot{\bm{v}} = \dot{\bm{\beta}}c$. + The energy dW emitted per unit solid angle dQ (around (he direction n) anc per unit frequency du to the direction 7 is computed as where r(/) is the electron trajectory. // is retarded time (Jackson 1999).," The energy $dW$ emitted per unit solid angle $d\Omega$ (around the direction $\bm{n}$ ) and per unit frequency $d\omega$ to the direction $\bm{n}$ is computed as where $\bm{r}(t^{\prime})$ is the electron trajectory, $t^{\prime}$ is retarded time (Jackson 1999)." + First. we show the radiation spectrum for α=3 in Figure 1..," First, we show the radiation spectrum for $a = 3$ in Figure \ref{a3}." + The frequency is normalized by the fundamental frequency wy=€o/(mc). and the magnitude is arbitrarily scaled.," The frequency is normalized by the fundamental frequency $\omega_{\mathrm{g}} = e\sigma/(\gamma mc)$, and the magnitude is arbitrarily scaled." + The jagged line is (he calculated spectrum. while the straight line drawn in the low frequency region is a line fitted to a power law spectrum.," The jagged line is the calculated spectrum, while the straight line drawn in the low frequency region is a line fitted to a power law spectrum." +" The fitting is made in the range of 1—350w, and (the spectral index turns oul to be 0.44.", The fitting is made in the range of $1-350\omega_{\mathrm{g}}$ and the spectral index turns out to be $0.44$. + The straight line drawn in the high lrequency region shows a spectrum of xw expected Lor diffusive svnchrotron radiation for reference (Toptvein Fleishman 1937)., The straight line drawn in the high frequency region shows a spectrum of $ \propto \omega^{-5/3}$ expected for diffusive synchrotron radiation for reference (Toptygin Fleishman 1987). + The spectrum is well described by a broken power law. and the spectral index of the low energy side is harder than svuchrotron (theory. predicts.," The spectrum is well described by a broken power law, and the spectral index of the low energy side is harder than synchrotron theory predicts." + The, The +found on the basis of the Abell clusters is complicated and has to be taken as a suggestion only.,found on the basis of the Abell clusters is complicated and has to be taken as a suggestion only. + Table 1| and table 2. show that in our sample there are three superclusters without any group/cluster with at least 30 member galaxies. and seven superclusters that do not contain Abell clusters.," Table \ref{tab:scldata} and table \ref{tab:sclabell} show that in our sample there are three superclusters without any group/cluster with at least 30 member galaxies, and seven superclusters that do not contain Abell clusters." + Among the superclusters eight have one group/cluster with at least 30 member galaxies., Among the superclusters eight have one group/cluster with at least 30 member galaxies. + All these systems are poor. comparable with the Local Supercluster. which has only one rich. cluster.," All these systems are poor, comparable with the Local Supercluster, which has only one rich cluster." + Two of the superclusters contain at least 10 groups/clusters with at least 30 member galaxies: these are the richest and most luminous superclusters in the sample: SCI 061 and the Corona Borealis., Two of the superclusters contain at least 10 groups/clusters with at least 30 member galaxies; these are the richest and most luminous superclusters in the sample: SCI 061 and the Corona Borealis. + We show the large-scale distribution of rich. clusters in superclusters in Fig., We show the large-scale distribution of rich clusters in superclusters in Fig. + 3. in cartesian coordinates., \ref{fig:sclid} in cartesian coordinates. + These coordinates are defined as in??:: where d is the comoving distance. and οἱ and 7 are the SDSS survey coordinates.," These coordinates are defined as in: where $d$ is the comoving distance, and $\lambda$ and $\eta$ are the SDSS survey coordinates." + To complement this figure. we present in Appendix AppendixC: a 3D version of Fig. 3.," To complement this figure, we present in Appendix \ref{sec:3dfig} a 3D version of Fig. \ref{fig:sclid}," + and the 3D distributions of groups in superclusters with the right ascensions. declinations. and distances of groups.," and the 3D distributions of groups in superclusters with the right ascensions, declinations, and distances of groups." + In Fig., In Fig. + 3 the superclusters SC] 060 and SCI 350 (Table 1)) are seen close to us., \ref{fig:sclid} the superclusters SCl 060 and SCl 350 (Table \ref{tab:scldata}) ) are seen close to us. + They belong to the Hercules supercluster. which is split into several superclusters in our sample.," They belong to the Hercules supercluster, which is split into several superclusters in our sample." + These are the nearby rich systems seen in Fig. 2..., These are the nearby rich systems seen in Fig. \ref{fig:scldistngal}. + A chain of poor superclusters connects the Hercules supercluster with rich superclusters at a distance of about 200 the superclusters SCI 349 and SCI 351 (the Bootes supercluster) among them., A chain of poor superclusters connects the Hercules supercluster with rich superclusters at a distance of about 200 the superclusters SCl 349 and SCl 351 (the Bootes supercluster) among them. + We mentioned in Sect., We mentioned in Sect. + 2 that at small distances the size of the sample cross-section is only 220x140 and these superclusters may be broken up by the sample borders., 2 that at small distances the size of the sample cross-section is only 220x140 and these superclusters may be broken up by the sample borders. + Therefore the data on nearby superclusters are less reliable than the data on the more distant ones., Therefore the data on nearby superclusters are less reliable than the data on the more distant ones. + Rich superclusters at distances of about 210-260 fform three chains. separated by voids.," Rich superclusters at distances of about 210–260 form three chains, separated by voids." + A 3D figure on our web pages shows that actually only one of these supercluster systems τα a clear chain-like system., A 3D figure on our web pages shows that actually only one of these supercluster systems ia a clear chain-like system. + This is the Sloan Great Wall (SGW). the richest galaxy system in the nearby Universe(222222?).," This is the Sloan Great Wall (SGW), the richest galaxy system in the nearby Universe." +. The SGW consists of several superclusters of galaxies., The SGW consists of several superclusters of galaxies. + The richest of them are the superclusters SCI 061 and SCI 024., The richest of them are the superclusters SCl 061 and SCl 024. + The other two supercluster chains are much poorer and cannot really be called chains., The other two supercluster chains are much poorer and cannot really be called chains. + One of them is separated from the SGW by a void: the Bootes supercluster is the richest supercluster in this system., One of them is separated from the SGW by a void; the Bootes supercluster is the richest supercluster in this system. + The richest supercluster in. the third system of superclusters ts the Ursa Majoris supercluster (SCI 336)., The richest supercluster in the third system of superclusters is the Ursa Majoris supercluster (SCl 336). + The very rich Corona Borealis supercluster is located at the joint of these systems., The very rich Corona Borealis supercluster is located at the joint of these systems. + This supercluster is a member of a huge system of rich superclusters located at the right angle with respect to the Local Supercluster. described by as the dominant supercluster plane.," This supercluster is a member of a huge system of rich superclusters located at the right angle with respect to the Local Supercluster, described by as the dominant supercluster plane." + At high positive values of the x coordinate there are no rich clusters. and the superclusters in this region are also poor.," At high positive values of the $x$ coordinate there are no rich clusters, and the superclusters in this region are also poor." + There are some poor superclusters farther away. perhaps connecting superclusters in our sample volume with more distant superclusters.," There are some poor superclusters farther away, perhaps connecting superclusters in our sample volume with more distant superclusters." + Thus the large-scale distribution of the superclusters is very inhomogeneous. as noted also in L10.," Thus the large-scale distribution of the superclusters is very inhomogeneous, as noted also in L10." + To make projection effects less significant. we do not show the chains of nearby superclusters in the right panel of Fig. 3..," To make projection effects less significant, we do not show the chains of nearby superclusters in the right panel of Fig. \ref{fig:sclid}." + The superclusters SCI 548. SCI 549. SCI 550. SC] 350. and SCI 060 are superimposed on the superclusters SCI 351 and SCI 354. and the superclusters SCI 779 and SCI 796 on the superclusters SCI 038. SCI 336. and SCI 525.," The superclusters SCl 548, SCl 549, SCl 550, SCl 350, and SCl 060 are superimposed on the superclusters SCl 351 and SCl 354, and the superclusters SCl 779 and SCl 796 on the superclusters SCl 038, SCl 336, and SCl 525." + The results on the morphology of superclusters are summarised in Table | where we list the following morphological characteristics for each supercluster: the maximum value of the fourth Minkowski functional των (clumpiness). the values of the shapefinders Ay (planarity) and A> (filamentarity) for," The results on the morphology of superclusters are summarised in Table \ref{tab:scldata} where we list the following morphological characteristics for each supercluster: the maximum value of the fourth Minkowski functional $V_{3,\mathrm{max}}$ (clumpiness), the values of the shapefinders $K_1$ (planarity) and $K_2$ (filamentarity) for" +2008).,. +". Due to the relatively cool temperature of dark stars and the high redshifts at which they are theorized to exist, even an enormous contribution such as that in the maximal model of Maureretal.(2010) would be at wavelengths too long for constraints to be derived, though this scenario would likely be difficult to reconcile with TeV-scale observations of lower-redshift blazars."," Due to the relatively cool temperature of dark stars and the high redshifts at which they are theorized to exist, even an enormous contribution such as that in the maximal model of \citet{maurer10} would be at wavelengths too long for constraints to be derived, though this scenario would likely be difficult to reconcile with TeV-scale observations of lower-redshift blazars." + We also strongly disfavor a scenario in which a near-IR excess proposed by Matsumotoetal.(2005) and a high EBL interpretation of the DIRBE 1.25 measurement (e.g. Cambrésyetal. 2001)) are produced by early stars., We also strongly disfavor a scenario in which a near-IR excess proposed by \citet{matsumoto05} and a high EBL interpretation of the DIRBE 1.25 measurement (e.g. \citealp{cambresy01}) ) are produced by early stars. + Our results in Fig., Our results in Fig. + 1 show that even a subdominant contribution to the EBL from high redshift at observed-frame wavelengths <1m can be in disagreement with high energy data., \ref{fig:ebllims} show that even a subdominant contribution to the EBL from high redshift at observed-frame wavelengths $\lesssim 1$ can be in disagreement with high energy data. +" We find good agreement with the result of Thompsonetal. (2007),, which disputes the detection of a high near-IR background, and attributes a possible contribution from high-redshift objects of 1-2 nW m""? sr! at 1.4 to 1.8 using fluctuation analysis methods."," We find good agreement with the result of \citet{thompson07}, which disputes the detection of a high near-IR background, and attributes a possible contribution from high-redshift objects of 1-2 nW $^{-2}$ $^{-1}$ at 1.4 to 1.8 using fluctuation analysis methods." +" In an analysis of TeV blazars, Orr,Krennrich&Dwek(2011) recently found that the ratio of near- to mid-IR EBL flux needed to be significantly larger than proposed in most recent models, including those described in Gilmoreetal.(2011) and Domínguezet (2011)."," In an analysis of TeV blazars, \citet{orr11} recently found that the ratio of near- to mid-IR EBL flux needed to be significantly larger than proposed in most recent models, including those described in \citet{gspd11} and \citet{dominguez11}." +". This work proposed a flux at 1.6 of 17+3 nW m? sr!, which is above the level produced by resolved"," This work proposed a flux at 1.6 of $17 \pm 3$ nW $^{-2}$ $^{-1}$ , which is above the level produced by resolved" +"here a brief summary of the main alternative AGN photoionization scenarios,",here a brief summary of the main alternative AGN photoionization scenarios. + There are 3 objects. highlighted as blue triangles in Fig.," There are 3 objects, highlighted as blue triangles in Fig." + |. which show hybrid properties of both AGNs and HIT galaxies.," 1, which show hybrid properties of both AGNs and HII galaxies." + Their line ratios in diagrams e. b and e fi better a classification as HIT galaxies.," Their line ratios in diagrams $a$ , $b$ and $c$ fit better a classification as HII galaxies." + Their lines are also relativey narrow compared with most objects in the sample. for which the median value is 530 km + while the hybrid objects have FWHMI[OIIIT«470 km +.," Their lines are also relatively narrow compared with most objects in the sample, for which the median value is 530 km $^{-1}$ while the hybrid objects have $<$ 470 km $^{-1}$." + They show among the lowest [OII/TOIII] and [OIIII/H.? values in the sample., They show among the lowest [OII]/[OIII] and $\beta$ values in the sample. + On the other hand. they show some features characteristic of active galaxies: they emit [NeV] and Hell (Fig.," On the other hand, they show some features characteristic of active galaxies: they emit [NeV] and HeII (Fig." + 1) and have large line luminosities (LTOIITLZI077 erg 1)., 1) and have large line luminosities $\ga$ $^{42}$ erg $^{-1}$ ). + The two objects for which [NIT] was measured occupy an intermediate region in the [OITII/H.5 vs. [NITI/Ho diagram (Fig., The two objects for which [NII] was measured occupy an intermediate region in the $\beta$ vs. $\alpha$ diagram (Fig. + 3) between HII galaxies and AGNs., 3) between HII galaxies and AGNs. + We will call these hybrid objects., We will call these hybrid objects. + Based on the arguments exposed in the previous sections. AGN photoionization must play an important role in the ionization of the gas in type 2 quasars in this sample.," Based on the arguments exposed in the previous sections, AGN photoionization must play an important role in the ionization of the gas in type 2 quasars in this sample." + The discrepancies of the standard AGN sequence show that a range of ionization and probably physical properties must exist within the type 2 quasar sample., The discrepancies of the standard AGN sequence show that a range of ionization and probably physical properties must exist within the type 2 quasar sample. + An internal range of cloud properties (e.g. density range. matter and bounded clouds. ionization level ete) is also likely to exist in individual objects.," An internal range of cloud properties (e.g. density range, matter and bounded clouds, ionization level etc) is also likely to exist in individual objects." + This is only natural. one cannot expect identical gas and continuum properties in all quasars. or ensembles of identical elouds in individual objects.," This is only natural, one cannot expect identical gas and continuum properties in all quasars, or ensembles of identical clouds in individual objects." + As we discussed above. more sofisticated models that take this into account solve the problems of the standard AGN sequence.," As we discussed above, more sofisticated models that take this into account solve the problems of the standard AGN sequence." + However. the emission line spectra of the three hybrid objects suggests that stellar photoionization might also be present with different degrees of importance relative to AGN photoionization from object to object.," However, the emission line spectra of the three hybrid objects suggests that stellar photoionization might also be present with different degrees of importance relative to AGN photoionization from object to object." + Interestingly. although uncommonly high [ONT] luminosities for HIT galaxies. the hybrid objects are at the lowest end of L[OIII] values within the type 2 quasar sample C52. [07 erg +. while the median value is —6. 107 erg lj," Interestingly, although uncommonly high [OIII] luminosities for HII galaxies, the hybrid objects are at the lowest end of L[OIII] values within the type 2 quasar sample $\la$ $\times$ $^{42}$ erg $^{-1}$, while the median value is $\sim$ $\times$ $^{42}$ erg $^{-1}$ )." + This tentatively suggests that low line luminosities might be associated with relatively stronger stellar photoionization., This tentatively suggests that low line luminosities might be associated with relatively stronger stellar photoionization. + We investigate next whether a contribution of stellar shotoionized gas could solve the problems of the standard AGN models discussed above., We investigate next whether a contribution of stellar photoionized gas could solve the problems of the standard AGN models discussed above. + For simplicity. we have assumed that the otal flux of a given line is due to the added contribution of the flux emitted by an AGN photoionized component (represented by ye standard AGN sequence) plus the flux emitted by a stellar shotoionized component.," For simplicity, we have assumed that the total flux of a given line is due to the added contribution of the flux emitted by an AGN photoionized component (represented by the standard AGN sequence) plus the flux emitted by a stellar photoionized component." + To represent the spectrum emitted by this gas. we have used the real spectra of a variety of HIT galaxies in Terlevichetal.(1991). catalogue.," To represent the spectrum emitted by this gas, we have used the real spectra of a variety of HII galaxies in \cite{ter91} catalogue." + We tind from this study that ye stellar ionized component must have [ON]/[ONMT2! in order o shift the models in the right direction in the diagrams., We find from this study that the stellar ionized component must have $\ga$ 1 in order to shift the models in the right direction in the diagrams. + As an example we take UM448., As an example we take UM448. + The reason to choose us particular. HIT galaxy is that it fulfills the [COIT/TOTTITZ:| requirement and has reported measurements of [OIII]A4363., The reason to choose this particular HII galaxy is that it fulfills the $\ga$ 1 requirement and has reported measurements of $\lambda$ 4363. + Unfortunately. as for all other objects in the catalogue with = |. ΠΟΠ is not measured.," Unfortunately, as for all other objects in the catalogue with $\ga$ 1, HeII is not measured." + The flux of any line ieb relative to H5stad is given by: where ic and He are respectively the flux of the line and the flux of Ht emitted by the stellar ionized gas., The flux of any line $Flux^{tot}$ relative to $\beta^{tot}$ is given by: where $Flux^*$ and $\beta^*$ are respectively the flux of the line and the flux of $\beta$ emitted by the stellar ionized gas. +" fuac! and Ht!"" are the flux of the line and that of H.} emitted by sas ionized by the AGN.", $Flux^{AGN}$ and $\beta^{AGN}$ are the flux of the line and that of $\beta$ emitted by gas ionized by the AGN. +" Let us ἀεΠῆο. =——MÀ-HHs and rearrange: We assume [NeV]I'/H.Z7.—<< [ΝΟΥ7 /H.H7,", Let us define $x=\frac{H\beta^*}{H\beta^{AGN}}$ and rearrange: We assume $^*$ $\beta^{*}<<$ $^{AGN}$ $\beta^{AGN}$. + When detected. HeIT/H-5 in HII galaxies is often in the range ~0.02- (values as high as 0.4 are also possible. but are more typical of objects with very small [OIT/TOITI] values).," When detected, $^*$ $\beta^*$ in HII galaxies is often in the range $\sim$ 0.02-0.1 (values as high as 0.4 are also possible, but are more typical of objects with very small $\la$ 0.2 values)." + We will assume Hell’ /H.?*=0.04., We will assume $^*$ $\beta^*$ =0.04. + Using a different value 0.2.within the expected range does not change our conclusions., Using a different value within the expected range does not change our conclusions. + We now create hybrid models by adding the stellar emission line spectrum to the AGN standard sequence of models and changing the . value from sequence to sequence (see equation above)., We now create hybrid models by adding the stellar emission line spectrum to the AGN standard sequence of models and changing the $x$ value from sequence to sequence (see equation above). + The ionizationparameter ( of the AGN photoionized gas (as in the standard AGN sequence) changes along each sequence., The ionizationparameter $U$ of the AGN photoionized gas (as in the standard AGN sequence) changes along each sequence. + The results are shown in Figs., The results are shown in Figs. + 6. 7 and 8 as red dashed-lines.," 6, 7 and 8 as red dashed-lines." + We tind that by varying the relative contribution of the stellar to the AGN photoionized gas:, We find that by varying the relative contribution of the stellar to the AGN photoionized gas: +"these processes for different masses and metallicities, as well as changes in the efficiency parameters of semiconvective mixing and overshooting, and the inclusionlgj of diffusive mixing.","these processes for different masses and metallicities, as well as changes in the efficiency parameters of semiconvective mixing and overshooting, and the inclusion of diffusive mixing." + It is also important to keep in mind that semiconvection will play an important role in the evolution of a star depending on the transition between the chain and the cycle as the main source of energy production (for a given metallicity)., It is also important to keep in mind that semiconvection will play an important role in the evolution of a star depending on the transition between the chain and the cycle as the main source of energy production (for a given metallicity). +" 'This transition is critically dependent on the value of the (N+ p) cross section, which has been subject of substantial reductions in the past years (e.g.Martaetal.2008)."," This transition is critically dependent on the value of the $\rm{N}^{14} + p$ ) cross section, which has been subject of substantial reductions in the past years \citep[e.g.][]{mm08}." +". Although accurate stellar parameters are of course of vital importance, asteroseismology can also be used as a tool to disentangle the observational degeneracy by focusing on the structural differences among the models produced by the mixing processes applied."," Although accurate stellar parameters are of course of vital importance, asteroseismology can also be used as a tool to disentangle the observational degeneracy by focusing on the structural differences among the models produced by the mixing processes applied." +" It has been shown that both p-modes (Popielski&Dziem-bowski2005) and g-modes (e.g.Miglioetal.2008) are sensitive to changes of the molecular weight in the interior of stars, and could in principle be applied to distinguish the type of mixing that has occurred in the stellar interior."," It has been shown that both p-modes \citep{pd05} and g-modes \citep[e.g.][]{am08} are sensitive to changes of the molecular weight in the interior of stars, and could in principle be applied to distinguish the type of mixing that has occurred in the stellar interior." +It can be seen from Figure 5 that this contribution falls short by four orders of magnitude to explain the observed changes in the projected semi-major axis x.,It can be seen from Figure \ref{fig:period} that this contribution falls short by four orders of magnitude to explain the observed changes in the projected semi-major axis $x$. +" As all other contributions are much smaller than the observed variation of the projected semi-major axis, they must originate from the last term of Equation (17)): the classical spin-orbit coupling (SOC) term."," As all other contributions are much smaller than the observed variation of the projected semi-major axis, they must originate from the last term of Equation \ref{eq:dotA1}) ): the classical spin-orbit coupling (SOC) term." +" Through SOC, the quadrupole of a rapidly rotating companion leads to apsidal motion and precession of the binary orbit."," Through SOC, the quadrupole of a rapidly rotating companion leads to apsidal motion and precession of the binary orbit." +" This in turn causes variation of the longitude of periastron (which is impossible to ameasure in a system with such small eccentricity) and of the projected semi-major axis, according to: (??),, where ny=27/P, is the orbital frequency, is the angle between the spin and orbital angular momentum and © is the longitude of the ascending node with respect to the invariable plane (plane perpendicular tothe total angular momentum)."," This in turn causes a variation of the longitude of periastron (which is impossible to measure in a system with such small eccentricity) and of the projected semi-major axis, according to: \citep{sb76, wex98}, where $n_{\rm b} = 2\pi/P_{\rm b}$ is the orbital frequency, $\theta$ is the angle between the spin and orbital angular momentum and $\Phi$ is the longitude of the ascending node with respect to the invariable plane (plane perpendicular tothe total angular momentum)." + The dimensionless quadrupole ( is related to the quadrupole Q by with J» the dimensionless measure of the quadrupole moment., The dimensionless quadrupole $\tilde Q$ is related to the quadrupole $Q$ by with $J_2$ the dimensionless measure of the quadrupole moment. +" Since no uniform change in z is detected, we can consider the companion to consist of a long-term stable component with spin axis aligned to the orbital angular momentum axis (i.e. 05’ 0) and in addition to that, a part of the star (like e.g. an outer shell) that changes its quadrupole moment by AQ and has an effective and variable angle 0 independent of the rest of the star."," Since no uniform change in $x$ is detected, we can consider the companion to consist of a long-term stable component with spin axis aligned to the orbital angular momentum axis (i.e. $\theta \approx 0$ ) and in addition to that, a part of the star (like e.g. an outer shell) that changes its quadrupole moment by $\Delta \tilde{Q}$ and has an effective and variable angle $\theta$ independent of the rest of the star." + This part will then give rise to a variation z/z of the order nyAQ., This part will then give rise to a variation $\dot{x}/x$ of the order $n_{\rm b} \Delta \tilde {Q}$. +" In Section ?? we have described how changes in the gravitational quadrupole moment of the companion could cause the observed P, variations.", In Section \ref{subsubsec:applegate} we have described how changes in the gravitational quadrupole moment of the companion could cause the observed $P_{\rm b}$ variations. +" Even though these direct GQC effects are insufficient to explain the x variations (i.e. 4€=0 as explained above), through the SOC mechanism they might have a more substantial effect."," Even though these direct GQC effects are insufficient to explain the $x$ variations (i.e. $\dot{x}^{\rm Q} += 0$ as explained above), through the SOC mechanism they might have a more substantial effect." +" Extending Equation 9 to arbitrary 0 and using Equation 23,, we have: Combining this with the observed P, values (Table 2)) and assuming Ó=0 for now, we get the maximum AQ values presented in Table 3.."," Extending Equation \ref{eq:dqdp} to arbitrary $\theta$ and using Equation \ref{eq:Qnorm}, , we have: Combining this with the observed $\dot{P}_{\rm b}$ values (Table \ref{tab:par}) ) and assuming $\theta = 0$ for now, we get the maximum $\Delta \tilde{Q}$ values presented in Table \ref{tab:DQnot}." +" Comparison to the z/z: values from Figure 5,, also listed in Table 3,, shows that while the order of magnitude is rougly correct, the sign does neither correlate nor anti-correlate, which means that the orientation of the quadrupole-moment changes (i.e. 0) must vary strongly from epoch to epoch, which may be unphysical."," Comparison to the $\dot{x}/x$ values from Figure \ref{fig:period}, , also listed in Table \ref{tab:DQnot}, shows that while the order of magnitude is rougly correct, the sign does neither correlate nor anti-correlate, which means that the orientation of the quadrupole-moment changes (i.e. $\theta$ ) must vary strongly from epoch to epoch, which may be unphysical." +" In order to examine more closely if the orbital variations can be produced by GQC and SOC arising from the same AQ, we have plotted in Figure 6 how |AQ| depends on 0, assuming 6=45° and using i=40°."," In order to examine more closely if the orbital variations can be produced by GQC and SOC arising from the same $\Delta Q$, we have plotted in Figure \ref{fig:|DQ|} how $|\Delta \tilde{Q}|$ depends on $\theta$ , assuming $\Phi = 45^{\circ}$ and using $i = 40^{\circ}$." +" The curves are plotted for SOC, as derived from Equation 22,, and for GQC, as derived from Equation 24.."," The curves are plotted for SOC, as derived from Equation \ref{eq:soc}, and for GQC, as derived from Equation \ref{eq:PbQtilde}." +" The intersection of the two lines clearly shows that for several values of 0 a AQ could explain both the orbital period and projected semi- axis variations for J2051—0827., though these 0 values change significantly with epoch and we do not see how this easily fits with the physical mechanism behind the thinshell model of ? (see also our Section ??))."," The intersection of the two lines clearly shows that for several values of $\theta$ a $\Delta \tilde Q$ could explain both the orbital period and projected semi-major axis variations for , though these $\theta$ values change significantly with epoch and we do not see how this easily fits with the physical mechanism behind the thinshell model of \citet{app92} (see also our Section\ref{subsubsec:applegate}) )." + In Section ?? we assumed a mostly stablecompanion star with, In Section \ref{sssec:GQCSOC} we assumed a mostly stablecompanion star with +"galaxies in the Local Group, and then scaling the numbers to match the field GSMF at high masses (> 10°Mo).","galaxies in the Local Group, and then scaling the numbers to match the field GSMF at high masses $>10^{9}\Msun$ )." + This assumes that the Local Group represents an average environment in which these galaxies are located., This assumes that the Local Group represents an average environment in which these galaxies are located. +" Taking the catalogue of galaxies from Karachentsevetal.(2004),, galaxies are selected within MMpc and with Galactic extinction less than mmag."," Taking the catalogue of galaxies from \citet{karachentsev04}, galaxies are selected within Mpc and with Galactic extinction less than mag." + The latter excludes two galaxies viewed near the Galactic plane (a biased direction in terms of detecting the lowest luminosity galaxies)., The latter excludes two galaxies viewed near the Galactic plane (a biased direction in terms of detecting the lowest luminosity galaxies). +" The B-band luminosities are converted to stellar masses assuming: M/Lg = 3.0 for early-type galaxies (RC3 type < 0); = 1.0 for M31, M33 and the Milky Way, which have already been corrected for internal attenuation; and M/Lg = 0.5 for type galaxies (RC3 type > 6)."," The $B$ -band luminosities are converted to stellar masses assuming: $_B$ = 3.0 for early-type galaxies (RC3 type $< 0$ ); $_B$ = 1.0 for M31, M33 and the Milky Way, which have already been corrected for internal attenuation; and $_B$ = 0.5 for late-type galaxies (RC3 type $>6$ )." +" From this, there are 6 galaxies with stellar mass =10°Mo, which are M31, M32, M33, M110, the Milky Way and LMC."," From this, there are 6 galaxies with stellar mass $\ga10^{9}\Msun$, which are M31, M32, M33, M110, the Milky Way and LMC." +" For this population the Local Group, taken to cover a volume of MMpc?, is approximately 50 times higher density than the cosmic average."," For this population the Local Group, taken to cover a volume of $^3$ , is approximately 50 times higher density than the cosmic average." +" Figure 16 shows GSMFs for the field and the Local Group scaled to match, in particular comparing the blue field number densities with that inferred for the early types by scaling."," Figure \ref{fig:compare-lg} shows GSMFs for the field and the Local Group scaled to match, in particular comparing the blue field number densities with that inferred for the early types by scaling." +" It is likely that the LG sample is complete down to 107 with only some recently discovered satellites of M31, AAnd McXXI (Martinetal. 2009),, suggesting that the bin shown here from 10° to 10” is a lower limit."," It is likely that the LG sample is complete down to $10^7\Msun$ with only some recently discovered satellites of M31, And XXI \citep{martin09}, suggesting that the bin shown here from $10^6$ to $10^7$ is a lower limit." +" This analysis is consistent with the blue dwarf population being the most common galaxy down to 10’Mo; at lower masses, it is not yet clear."," This analysis is consistent with the blue dwarf population being the most common galaxy down to $10^7\Msun$ ; at lower masses, it is not yet clear." +" The GAMA GSMF is reliable down to 10*M. (corresponding to M,~—16 with M/L,= 0.5), which confirms the SDSS result (BGD08) with minor modification to the distances, assuming that the M/L values are approximately correct as a function of a galaxy's colour."," The GAMA GSMF is reliable down to $10^8\Msun$ (corresponding to $M_r \sim -16$ with $_r = 0.5$ ), which confirms the SDSS result (BGD08) with minor modification to the distances, assuming that the M/L values are approximately correct as a function of a galaxy's colour." +" In addition, there are ~350 galaxies in this GAMA sample between 10"" and 10°Mo, and ~30 between 10° and 10’Mo."," In addition, there are $\sim350$ galaxies in this GAMA sample between $10^7$ and $10^8\Msun$, and $\sim30$ between $10^6$ and $10^7\Msun$." + There are a number of improvements to be made for the GAMA GSMF measurement at M«10°Mo: The expected currently missed detection of low-SB galaxies is critical., There are a number of improvements to be made for the GAMA GSMF measurement at $\mass < 10^8\Msun$: The expected currently missed detection of low-SB galaxies is critical. +" In this sample, the observed number density for galaxies with 10°° to 10’Mo is only ~0.02Mpc~?dex~! estimated using the density-corrected Vj, method."," In this sample, the observed number density for galaxies with $10^{6.5}$ to $10^{7}\Msun$ is only $\sim 0.02\,{\rm Mpc}^{-3}\,{\rm dex}^{-1}$ estimated using the density-corrected $\vmod$ method." + The predicted number by Guoetal.(2011) and by extrapolation of the double Schechter function is 0.1Mpc?dex!.," The predicted number by \citet{guo11} and by extrapolation of the double Schechter function is $>0.1\,{\rm Mpc}^{-3}\,{\rm dex}^{-1}$." + Thus we could be missing significant numbers of larger low-mass galaxies., Thus we could be missing significant numbers of larger low-mass galaxies. + Figure 17 shows the observed size-mass relation of galaxies from GAMA for blue and red galaxy populations., Figure \ref{fig:size-mass} shows the observed size-mass relation of galaxies from GAMA for blue and red galaxy populations. +" For comparison, also shown are measurements of irregular galaxies (HunterElmegreen2006) using M/Ly from the B—V relation of Belletal.(2003),, and Milky Way (Gilmoreetal.2007) and M31 dwarf spheroidals citealtMIO6,martin09)) using M/Ly=2."," For comparison, also shown are measurements of irregular galaxies \citep{HE06} using $_V$ from the $B-V$ relation of \citet{bell03}, and Milky Way \citep{gilmore07} and M31 dwarf spheroidals \\citealt{MI06,martin09}) ) using $_V = 2$." + The GAMA relation for the blue population follows an approximately linear relation above c»107°Mo but appears to drop below the linear extrapolation at lower masses., The GAMA relation for the blue population follows an approximately linear relation above $\sim10^{7.5}\Msun$ but appears to drop below the linear extrapolation at lower masses. + The dotted line outlines the region where possible low-SB galaxies missed by SDSS selection would be located., The dotted line outlines the region where possible low-SB galaxies missed by SDSS selection would be located. + These would have μ.ο~24-25 mmagaarcsec? for the low MIL blue population., These would have $\effsb\sim24$ $^{-2}$ for the low M/L blue population. + This is where an extrapolation of the mass-SB relation to low masses would lie (Fig. 11))., This is where an extrapolation of the mass-SB relation to low masses would lie (Fig. \ref{fig:mass-sb}) ). + Thus it is essential to use a detection algorithm that is sensitive to these types of sources citealtkniazev04)) at distances ~10-50MMpc in order to test whether the lowest-mass bins are incomplete within the GAMA survey volume., Thus it is essential to use a detection algorithm that is sensitive to these types of sources \\citealt{kniazev04}) ) at distances $\sim$ Mpc in order to test whether the lowest-mass bins are incomplete within the GAMA survey volume. +" For the star-forming population, obtaining redshifts is feasible but IFUs would be required if only part of each galaxy has detectable line emission."," For the star-forming population, obtaining redshifts is feasible but IFUs would be required if only part of each galaxy has detectable line emission." + The low-redshift sample here only uses 5 per cent of the GAMA r-band limited main survey., The low-redshift sample here only uses 5 per cent of the GAMA $r$ -band limited main survey. +" The GAMA survey is also well placed to measure theevolution of the GSMF out to z~0.6 for the most massive galaxies, study variations with environment and halo mass, and to studyvariations in properties with stellar mass."," The GAMA survey is also well placed to measure theevolution of the GSMF out to $z\sim0.6$ for the most massive galaxies, study variations with environment and halo mass, and to studyvariations in properties with stellar mass." + We present an investigation of the GSMF using the GAMA survey., We present an investigation of the GSMF using the GAMA survey. +,7. + Tuteractious of dust with the ambicut gas present the primary mechanisin of dissipatiug streaming motions of erains., Interactions of dust with the ambient gas present the primary mechanism of dissipating streaming motions of grains. + The damping rate of translational motion arising from the iuteractiou with neutral eas is essentially the inverse time for collisions with the mass of the eas equal that of a erain (Purcell 1969). where my. n4. and Z5 aro the mass. volume ceusity. and temperature of ueutrals py is the mass density of dust eraius and e is their radius.," The damping rate of translational motion arising from the interaction with neutral gas is essentially the inverse time for collisions with the mass of the gas equal that of a grain (Purcell 1969), where$m_n$ , $n_n$ , and $T_n$ are the mass, volume density, and temperature of neutrals, $\rho_d$ is the mass density of dust grains and $a$ is their radius." + When the ionization is sufBcientlv high. the interaction of charged grains with a plasma becomes iuportaut (Draine Salpeter 1979).," When the ionization is sufficiently high, the interaction of charged grains with a plasma becomes important (Draine Salpeter 1979)." + The jon-erain cross section due to long-range Coulomb force is larger than the atom-erain Cross section., The ion-grain cross section due to long-range Coulomb force is larger than the atom-grain cross section. + As a result. the rate of translational motion damping gets modified (Draine Salpeter 1979).," As a result, the rate of translational motion damping gets modified (Draine Salpeter 1979)." +" For subsonic motions the effective damping rate is⋅ renormalized.⋅ zi5,,1=OT, looWith the following:⋅⋡ renorlalizing factor: Tere jis the abundance of ion / (relative to hydrogen) with mass 17; and temperature Ty.— aud f(Z)is the grain charge distribution function (see M56;Toane. Draine Lazarian 2010)."," For subsonic motions the effective damping rate is renormalized, $\tau_{\rm damp}^{-1}=\alpha\tau_{dn}^{-1}$, with the following renormalizing factor: Here $x_{i}$ is the abundance of ion $i$ (relative to hydrogen) with mass $m_{i}$ and temperature $T_i$, $x=\sum_i x_i$, and $f(Z)$ is the grain charge distribution function (see Hoang, Draine Lazarian 2010)." +" When the erain velocity 0; relative to the gas becomes supersomic the dust interactions with the plasma is diminished. aud the damping rate in this case is renormalized due to the eas-dvnamic correction (Purcell 1969). where C,=VINEmy is the sound speed."," When the grain velocity $v_d$ relative to the gas becomes supersonic the dust interactions with the plasma is diminished, and the damping rate in this case is renormalized due to the gas-dynamic correction (Purcell 1969), where $C_{\rm s}=\sqrt{k_{\rm B}T/m_n}$ is the sound speed." + The Larmor rate for a eran is τι12[Zu]Pfima. where Zo(«) is the mean erain charge aud D is the magnetic field strength.," The Larmor rate for a grain is $\tau_{\rm L}^{-1}=|Z_0|eB/m_{d}c$, where $Z_0(a)$ is the mean grain charge and $B$ is the magnetic field strength." + If ris larger than Tau the effect of maeuctic field ou dust dyuauics is negligible., If $\tau_{\rm L}$ is larger than $\tau_{\rm damp}$ the effect of magnetic field on dust dynamics is negligible. + ας can interact with cach other through Coulonib orces if the Debye screening leugth is larecr than the distance between erains., Grains can interact with each other through Coulomb forces if the Debye screening length is larger than the distance between grains. +" In Figure 1 owe show the ratio of the Debye radius Ap to the separation d, vetween the erain of size e and eraius of a larger size. calculated for three differcut idealized interstellar phases: he cold neutral medium (CNAD. war neutral iiedium (ΣΑΟ uni ionized mediuu (WIAD)."," In Figure \ref{f1} we show the ratio of the Debye radius $\lambda_{\rm D}$ to the separation $d_a$ between the grain of size $a$ and grains of a larger size, calculated for three different idealized interstellar phases: the cold neutral medium (CNM), warm neutral medium (WNM), warm ionized medium (WIM)." +" Table 1 preseuts ο parameters for such environments [ucludiug also reflection nebula (RN) and photocissociation region (PDR). where my is the hydrogen deusitv. T aud Ty, are the eas temperature and dust material temperature. respectively. MID!afAL!) and Is) are ion hydrogen density. ion metal censity and imo0lecular hwdrogenu density. respectively."," Table \ref{tab1} presents physical parameters for such environments [including also reflection nebula (RN) and photodissociation region (PDR)], where $n_{\rm H}$ is the hydrogen density, $T$ and $T_{d{\rm s}}$ are the gas temperature and dust material temperature, respectively, $n({\rm H}^{+}), n({\rm +M}^{+})$ and $n({\rm H}_{2})$ are ion hydrogen density, ion metal density and molecular hydrogen density, respectively." + To represeut grain charge we use the chargiug data frou Hoang et al. (, To represent grain charge we use the charging data from Hoang et al. ( +2010).,2010). + It is clear that for eraius siualler than ~3«10*[ cm the erains do interact electrostaticallv with their larger neighbors., It is clear that for grains smaller than $\sim 3\times 10^{-7}$ cm the grains do interact electrostatically with their larger neighbors. + As a result of charge fluctuations. tle dust particles experience forces which can accelerate them.," As a result of charge fluctuations, the dust particles experience forces which can accelerate them." + We choose to depict distances to the grains of the size larecr than the given erain size. because such interactions will be most important iu terms of momentum transfer.," We choose to depict distances to the grains of the size larger than the given grain size, because such interactions will be most important in terms of momentum transfer." + Naturally. larger erains will be still interacting with sanaller ones aud therefore there should be no sharp off for the erains to stop being accelerated by the charge-fluctuation mechanisin.," Naturally, larger grains will be still interacting with smaller ones and therefore there should be no sharp cut-off for the grains to stop being accelerated by the charge-fluctuation mechanism." + Astrophysical erains are known to be charged (see Draine Sutin 1987)., Astrophysical grains are known to be charged (see Draine Sutin 1987). + The grain charges are uot coustaut they fluctuate around an equilibrium value Qy= ¢Zy., The grain charges are not constant – they fluctuate around an equilibrium value $Q_0=eZ_0$ . + Iuaplasina without external radiation Qy is negative. because electrons are qauch faster thin ious (Gu the preseuce of sufficicutly iuteuse external UW radiation it beconies positive. see Goree 1991).," Inaplasma without external radiation $Q_0$ is negative, because electrons are much faster than ions (in the presence of sufficiently intense external UV radiation it becomes positive, see Goree 1994)." + In general. one needs," In general, one needs" +Fig.,Fig. +2bb. We also used the analvtical secular theory to calculate (he eigenvector components E in the secular solution of the 2-planet svstem. for each value of Saturn's seminmajor axis.,"\ref{f:g6vsasat}b b. We also used the analytical secular theory to calculate the eigenvector components $E_j^{(6)}$ in the secular solution of the 2-planet system, for each value of Saturn's semimajor axis." + We adopted the same values for the initial conditions of Jupiter aud Saturn as in the direct nunerical integrations discussed above., We adopted the same values for the initial conditions of Jupiter and Saturn as in the direct numerical integrations discussed above. +" Finally. we computed (he values of the parameter 7 ab each location e, of the secular resonance."," Finally, we computed the values of the parameter $\varepsilon$ at each location $a_{\nu_6}$ of the secular resonance." + The result is plotted in Fig. 3.., The result is plotted in Fig. \ref{f:epsvsanu6}. + Despite the complexity of the computation. (he result shown in Fie.," Despite the complexity of the computation, the result shown in Fig." +" 3. is approximated well bv a simple exponential curve. 2£23.5x10./exp(2a,,AU). in the semimajor axis range 2«a,,/AU4."," \ref{f:epsvsanu6} is approximated well by a simple exponential curve, $\varepsilon\approx3.5\times10^{-9}\exp(2a_{\nu_6}/\mathrm{AU})$, in the semimajor axis range $2 207) above zero., Each cluster first needed to have a sufficient number of counts to measure a temperature that was significantly $ > 2\sigma$ ) above zero. + All of the clusters in this sample have more than an average of 1.000 counts per detector (3.000 for observations. 1.000 for observations) within two core radit. and the minimum luminosity of all clusters from zero to two core radii is 1x[07 erg sv!," All of the clusters in this sample have more than an average of 1,000 counts per detector (3,000 for observations, 1,000 for observations) within two core radii, and the minimum luminosity of all clusters from zero to two core radii is $1 \times 10^{44}$ erg $\rm{s^{-1}}$." + The second condition was morphological in nature. as it was necessary to have a reasonable p-fit to the data.," The second condition was morphological in nature, as it was necessary to have a reasonable $\beta$ -fit to the data." + Any observations that showed obvious visual signs of recent large merger activity were immediately excluded., Any observations that showed obvious visual signs of recent large merger activity were immediately excluded. + Beyond that. several sets were excluded based on the values derived from the f-fit.," Beyond that, several sets were excluded based on the values derived from the $\beta$ -fit." + In these cases the best fit core radius was larger than the furthest extent of the radial profile., In these cases the best fit core radius was larger than the furthest extent of the radial profile. + These sets often had8 values that were unrealistically large as well. usually well above 8.=2.," These sets often had $\beta$ values that were unrealistically large as well, usually well above $\beta =2$." + Since the fit was unreliable in both parameters. these clusters were not considered in this sample.," Since the fit was unreliable in both parameters, these clusters were not considered in this sample." + Table 6. lists all the observations investigated. but not included. in this study and why they were not considered.," Table \ref{Table6} lists all the observations investigated, but not included, in this study and why they were not considered." + The very luminous cluster RX J1347.5-1145 was also investigated using two observations: observation #33592 (2?) and observation 3800112960101 (?).., The very luminous cluster RX J1347.5-1145 was also investigated using two observations: observation 3592 \citep{Allen} and observation 0112960101 \citep{Gitti}. + Although it was sufficiently luminous and symmetric to be included here: the temperatures measured between these two observations did not agree within 3c., Although it was sufficiently luminous and symmetric to be included here; the temperatures measured between these two observations did not agree within $3\sigma$. + After this work began. ? found a hot bubble in the southeast region of this cluster.," After this work began, \cite{Ota1347} found a hot bubble in the southeast region of this cluster." + Thus. it was judged that this cluster is not relaxed enough to be considered in this study and was also excluded.," Thus, it was judged that this cluster is not relaxed enough to be considered in this study and was also excluded." + Spectra for each data set were extracted with routines 1n CIAO for or SAS for., Spectra for each data set were extracted with routines in CIAO for or SAS for. +. If the data set was from then the spectra were extracted using the specextract routine., If the data set was from then the spectra were extracted using the $\it specextract\rm$ routine. + If the data set was from.. then the OGIP Spectral Products routine found in the Graphical Interface of SAS after runningσι was used.," If the data set was from, then the OGIP Spectral Products routine found in the Graphical Interface of SAS after running was used." + Spectra were taken of all four annular regions in both scale lengths., Spectra were taken of all four annular regions in both scale lengths. +" When determiningσι the average cluster temperature and iron abundance a circular region from 0—27, region was used.", When determining the average cluster temperature and iron abundance a circular region from $0-2r_{\rm{c}}$ region was used. + Background regions were always circles with radit. comparable or larger than two core radit outside of the detectable emission and always on the same chip as the cluster image., Background regions were always circles with radii comparable or larger than two core radii outside of the detectable emission and always on the same chip as the cluster image. + The background regions remained consistent within each data set., The background regions remained consistent within each data set. + These background regions are specifically chosen to contain as many counts as possible without including sources., These background regions are specifically chosen to contain as many counts as possible without including sources. + Since radial symmetry is not a major concern with the spectral background. while the total number of counts is. this region is not the same background region used to determine the radial profiles.," Since radial symmetry is not a major concern with the spectral background, while the total number of counts is, this region is not the same background region used to determine the radial profiles." + The software used to do the spectral fitting was XSPEC 12.4.0. and the MEKAL model in XSPEC was always used along with the TBABS galactic absorption model.," The software used to do the spectral fitting was XSPEC 12.4.0, and the MEKAL model in XSPEC was always used along with the TBABS galactic absorption model." + Since the spectra often had low numbers of counts. the nodified Cash statistic was always used to determine the best-fit temperature and iron abundance simultaneously.," Since the spectra often had low numbers of counts, the modified Cash statistic was always used to determine the best-fit temperature and iron abundance simultaneously." + The modified Cash statistic is ideal for fitting spectra with a low number of counts in each bin (?) and also allows for the use of a local background spectrum instead of fitting the background to a model., The modified Cash statistic is ideal for fitting spectra with a low number of counts in each bin \citep{Cashstat} and also allows for the use of a local background spectrum instead of fitting the background to a model. + The only remaining free parameter in the fit was the normalization., The only remaining free parameter in the fit was the normalization. + The other parameters of the model were fixed: the redshifts were frozen at the values given by the NASA/IPAC Extragalactic Database (NED) while the hydrogen column densities were frozen to the values given by the //j; calculator on the HEASARC website., The other parameters of the model were fixed: the redshifts were frozen at the values given by the NASA/IPAC Extragalactic Database (NED) while the hydrogen column densities were frozen to the values given by the $n_{H}$ calculator on the HEASARC website. + The solar abundance values used were those from ?.., The solar abundance values used were those from \cite{Anders}. + For the spectra. all three instruments were fitsimultaneously to the same spectral model to ensure the best use of the available statistics.," For the spectra, all three instruments were fitsimultaneously to the same spectral model to ensure the best use of the available statistics." + The measured temperature, The measured temperature +l0.5 are sparse. we expect the form of ος) to be relatively well understood by the time of the fas. experiment.,"$z\gsim0.5$ are sparse, we expect the form of $s(z)$ to be relatively well understood by the time of the $f_{\rm gas}$ experiment." + In order to keep the interpretation of our results simple. we present results for. three sets. of. systematic allowances:for the parameters. dV.bye.dn.Su... We employ allowances of either £2 per cent (optimistic). 3:5 per cent (standard). or ELO per cent (pessimistic).," In order to keep the interpretation of our results simple, we present results for three sets of systematic allowances:for the parameters, $K, b_{\rm 0}, \alpha_{\rm b}, \beta_{\rm b}, s_{\rm 0}, \alpha_{\rm + s}, \beta_{\rm s}$, we employ allowances of either $\pm 2$ per cent (optimistic), $\pm 5$ per cent (standard), or $\pm 10$ per cent (pessimistic)." + In all cases. we emplov uniform priors with the exception of A and sy. for which Gaussian priors are more appropriate ancl therefore used.," In all cases, we employ uniform priors with the exception of $K$ and $s_{\rm 0}$, for which Gaussian priors are more appropriate and therefore used." + As noted above. a uniform allowance of (ΕΕ per cent on ~ is included by default. although the ellects of doubling the uncertainty in this parameter are also examined.," As noted above, a uniform allowance of $\pm4$ per cent on $\gamma$, is included by default, although the effects of doubling the uncertainty in this parameter are also examined." +" We stress that whether >=1 precisely. or à.6, ete are precisely zero. is not of primary importance to a future analvsis: if known. the exact values can be incorporated into the default mocel."," We stress that whether $\gamma=1$ precisely, or $\alpha_{\rm + b}, \alpha_{\rm s}$ etc are precisely zero, is not of primary importance to a future analysis: if known, the exact values can be incorporated into the default model." + lt is the uncertainties in the values that alfect the accuracy and. precision of the dark energy constraints., It is the uncertainties in the values that affect the accuracy and precision of the dark energy constraints. + For the true. underlying cosmology. the measurement. of the Compton y parameter from both the A-ray and. SZ data should match2?7).," For the true, underlying cosmology, the measurement of the Compton $y-$ parameter from both the X-ray and SZ data should match." +. kor a given. cosmology the v-parametoer predicted. by N-ray. cata depends on the square root of the angular diameter distance to the cluster. dA. whereas the observed SZ Dux at radio or sub-mum wavelengths is independent of the cosmology assumed.," For a given cosmology the y-parameter predicted by X-ray data depends on the square root of the angular diameter distance to the cluster, $d_{\rm + A}^{0.5}$, whereas the observed SZ flux at radio or sub-mm wavelengths is independent of the cosmology assumed." + Combining the yo parameter results. we can measure the distances to the clusters as a function. of redshift) and. therefore.constrain dark energy.," Combining the $y-$ parameter results, we can measure the distances to the clusters as a function of redshift and, therefore,constrain dark energy." + CDN : ∐∢⊾↓⋅∢⊾∕∣↽∖↕↓↓⇂↕⋖⋅⇀∖−↓⋅⋜↧∙∖⇁⊔↓⋖⋅⋜↧⊳∖⊔↓⋅⋖⋅⊔↓∢⊾⊔∣∪⇂↿⇂↕∢⊾∙∖⇁−↓≻⋜⊔⋅⋜⋯↓⋖⋅↿⋖⋅↓⋅ ⋅ ⋅ ⇂∪↓⋅↥↓↥⋖⊾↓⋅⋖⋅⇂⋖⋅↓⋅⋖⊾⊔≼∙⋖⋅≼∙∪⋡∖⊔↓∪⇂∪⋏∙≟∙∖⇁⋜↧⊔∠⇂∕∣∖∠↠⊳∣⋔∖ is the raclio/sub-mni ⊳⊔↓⊲↸∪∐∪∖∖⋰↓⊔⋏∙≟⋜↧⊳∖⊀↓⊔↓∐⋜⊔⋅⋜↧↓≻↓≻↓⋅∪⋯⇍↓↕⋯↿↓⋯↿ adopted: with the ∖∠⇂⋜∐⋜↧⊳∖∖⋎⋖⊾⊲↓↓⊔⇍∪↓⋅↓≻∪↓⋅⋜⋯⋅≱∖∙∖⇁≱∖↿⋖⋅⊔↓⋜⊔⋠⊔∙ allowances into equation (21)): Ας)=Eo(1|642) accounts for the combined systematic uncertainties in the X-ray and SZ data yparameter measurements due to. calibration. geometric elfects. gas clumping. etc.," Here $y^{\rm \Lambda CDM}$ is the X-ray measurement of the y-parameter for the reference cosmology and $y^{\rm SZobs}$ is the radio/sub-mm Following a similar approach to that adopted with the $f_{\rm gas}$ data, we incorporate systematic allowances into equation \ref{eq:ycompton}) ): $k(z)=k_{\rm 0}(1+\alpha_{\rm k}z)$ accounts for the combined systematic uncertainties in the X-ray and SZ data $y-$ parameter measurements due to calibration, geometric effects, gas clumping, etc.," + ancl their evolution., and their evolution. + We cniploy Gaussian priors on fy of size 2 (optimistic) or 5 (standardpessimistic) per cent ancl uniform priors on ay of size 2 (optimistic). 5 (standard) or LO (pessimistic) per cent.," We employ Gaussian priors on $k_{\rm 0}$ of size 2 (optimistic) or $5$ (standard/pessimistic) per cent and uniform priors on $\alpha_{\rm k}$ of size 2 (optimistic), $5$ (standard) or 10 (pessimistic) per cent." + We note that the best clusters to observe for. the XSZ experiment are the same svstems used for the fii experiment: the largest. most dynamically relaxed clusters.," We note that the best clusters to observe for the XSZ experiment are the same systems used for the $f_{\rm gas}$ experiment: the largest, most dynamically relaxed clusters." + These are the clusters for which the SZ signals are strongest and for which svstematic uncertainties associated with ecometry and thermodynamic. structure are. minimized., These are the clusters for which the SZ signals are strongest and for which systematic uncertainties associated with geometry and thermodynamic structure are minimized. + Note also that no additional X-ray observations are required to carry out the NSZ experiment. once the fi; data are in hand.," Note also that no additional X-ray observations are required to carry out the XSZ experiment, once the $f_{\rm gas}$ data are in hand." + In addition to the dark energy model parameters ancl the fons parameters ciscussecl in Section 4.2.. we vary the following eight. CALB-relatecd parameters in. the AICALC analysis: the mean physical barvon density. 0/7: the mean physical cold dark matter density. Ou: the (approximate) ratio of the sound. horizon at last scattering to the angular cliameter distance (2)... 6.: the optical depth to reionization (assumed lo occur in a sharp transition). 7: themean curvature density of the Universe. Q4: the scalar aciabatic spectral index. ni: and the scalar acliabatic amplitude. εἰς. ab &=0.05 1.," In addition to the dark energy model parameters and the $f_{\rm gas}$ parameters discussed in Section \ref{sec:cldata}, we vary the following eight CMB-related parameters in the MCMC analysis: the mean physical baryon density, $\Omega_{\rm b}h^{\rm 2}$; the mean physical cold dark matter density, $\Omega_{\rm dm}h^{\rm 2}$; the (approximate) ratio of the sound horizon at last scattering to the angular diameter distance , $\theta_{\rm s}$ ; the optical depth to reionization (assumed to occur in a sharp transition), $\tau$; themean curvature density of the Universe, $\Omega_{\rm k}$; the scalar adiabatic spectral index, $n_{\rm s}$; and the scalar adiabatic amplitude, $A_{\rm s}$, at $k=0.05 +\hbox{$ $}$." + We employ a uniform prior on In(-1.).," We employ a uniform prior on $\ln(A_{\rm + s})$." +" The combination of 8, and In(;1,) as parameters. rather than Io and -ἰ.. leads to a more Gaussian. probability density distribution which. in turn. aids sampling (?7?)."," The combination of $\theta_{\rm s}$ and $\ln(A_{\rm s})$ as parameters, rather than $H_{\rm 0}$ and $A_{\rm s}$ , leads to a more Gaussian probability density distribution which, in turn, aids sampling ." +". The cegeneracies between dark energy mocel parameters and ©, are of particular importance— in the analysis For.their forecasts.the DETE include priors in their Fisher matrix. analysis."," The degeneracies between dark energy model parameters and $\Omega_{\rm +k}$ are of particular importance in the analysis Fortheir forecasts,the DETF include priors in their Fisher matrix analysis," +The exponent g (which also effects the asymmetry) is expressed as where 6 is the slope of the cumulative mass distribution for the impactors N(im)(,The exponent $g$ (which also effects the asymmetry) is expressed as where $b$ is the slope of the cumulative mass distribution for the impactors N(>m). +1L) Based ou current observatious (Bottkee£af 2002)... 6=0.58+0.03. making g=2.81x0.05.," Based on current observations \citep{bottke02}, , $b = 0.58 \pm 0.03$, making $g += 2.81 \pm 0.05$." + Although Eq., Although Eq. + 1. may be fit to an observed crater distribution. this does not necessarily provide a convenient measure of the asymmetry.," \ref{eq:ass} may be fit to an observed crater distribution, this does not necessarily provide a convenient measure of the asymmetry." + Figure 1. shows that for our itupactor population (see Sec. 3.1)), Figure \ref{fig:dirs} shows that for our impactor population (see Sec. \ref{sec-source}) ) + the isotropic assumption fails. so one should expect deviatious from the functioual form ol Eq. 1..," the isotropic assumption fails, so one should expect deviations from the functional form of Eq. \ref{eq:ass}." + Note that increasing either a or g raises the leading/trailing asymmetry. introducing a degeneracy iu the [fuuctioual form. makine it difficult to decouple the two when deteriniuiug information about aud the size distribution.," Note that increasing either $\alpha$ or $g$ raises the leading/trailing asymmetry, introducing a degeneracy in the functional form, making it difficult to decouple the two when determining information about and the size distribution." + Iu fact the observatious actually permit a very arge range of parameter values., In fact the observations actually permit a very large range of parameter values. + Performing a maximum likelihood parameter cletermination using he raved crater data of MorotaancFurumoto(2003) yields Fig. 2.., Performing a maximum likelihood parameter determination using the rayed crater data of \citet{morota03} yields Fig. \ref{fig:like}. + Also. determinine P with a ugh degree of precision from a measured crater field is clifficult.," Also, determining $\bar\Gamma$ with a high degree of precision from a measured crater field is difficult." + To iminimüze these issues when examiniug the entire lunar surface. we adopt the couventiou of Zahulee£a.(2001) by taking the atio ofthose craters which fall within of the apex to those which are within of the autapex.," To minimize these issues when examining the entire lunar surface, we adopt the convention of \citet{zetal01} by taking the ratio of those craters which fall within of the apex to those which are within of the antapex." + 'Ehis ratio forms a statisticknown as the global measure of the apex-antapex cratering asymmetry (GMAACA)., This ratio forms a statisticknown as the global measure of the apex-antapex cratering asymmetry (GMAACA). +Our NIR imaging of this barred galaxy. reveals a lot οἱ structure. including a double peak in the central part. of the NIB. broad-band images5 (Fig.,"Our NIR imaging of this barred galaxy reveals a lot of structure, including a double peak in the central part of the NIR broad-band images (Fig." +5 2e)., 2e). + Reeent adaptive optics images obtained with theCAAT (by E. Combes JL. Ixnapen. private communication) confirm this double peak. but spectroscopic follow-up observations are needed to confirm whether these peaks are in fact two nuclei.," Recent adaptive optics images obtained with the (by F. Combes J.H. Knapen, private communication) confirm this double peak, but spectroscopic follow-up observations are needed to confirm whether these peaks are in fact two nuclei." + NoUST NIK imaging is available., No NIR imaging is available. + The colour index images show a pair of long and straight dust lanes that come into the CN] through the main bar. and intricate dust lane structure in the central region.," The colour index images show a pair of long and straight dust lanes that come into the CNR through the main bar, and intricate dust lane structure in the central region." + The nuclear double peak is very obvious in the colour index maps., The nuclear double peak is very obvious in the colour index maps. + Elmeereen et al. (, Elmegreen et al. ( +1997) showed a ring in JAN with five discrete clumps of SE.,1997) showed a ring in $J-K$ with five discrete clumps of SF. + The signal to noise ratio in our images is too low to reveal these SE clumps., The signal to noise ratio in our images is too low to reveal these SF clumps. + The previously reported isophote twist (e.g.. Ponipea tieke 1990) is obvious from our imaging. as well as from the A and ellipticitv profiles.," The previously reported isophote twist (e.g., Pompea Rieke 1990) is obvious from our imaging, as well as from the PA and ellipticity profiles." + The double bar. outlined by the wo separate peaks in the ellipticity profile. is most probably not exclusively due to the nuclear double peak. because the accompanying isophote twist in fact starts somewhat outside he region of influence of the double peak.," The double bar, outlined by the two separate peaks in the ellipticity profile, is most probably not exclusively due to the nuclear double peak, because the accompanying isophote twist in fact starts somewhat outside the region of influence of the double peak." + Phe surface xightness ane colour profiles show the hump at the CNR radius that is seen in many similar galaxies presented in this paper., The surface brightness and colour profiles show the hump at the CNR radius that is seen in many similar galaxies presented in this paper. + The only obvious feature in our images is the very red nucleus., The only obvious feature in our images is the very red nucleus. + Neither the broad-band 4457 H-image. nor our erouncd-based NUR. colour maps reveal any other structure (ig.," Neither the broad-band $H$ -image, nor our ground-based NIR colour maps reveal any other structure (Fig." + 1. 20).," 1, 2f)." + Reean Mulchaev (1909). used. anLST WEDPC2NICALOS colour index map to show that a single spiral dust pattern dominates the cireumnuclear morphology of this galaxy., Regan Mulchaey (1999) used an WFPC2–NICMOS colour index map to show that a single spiral dust pattern dominates the circumnuclear morphology of this galaxy. + They described a strong red dust lane that emerges from a blue feature north of the nucleus at a radius of 3., They described a strong red dust lane that emerges from a blue feature north of the nucleus at a radius of $\arcsec$. +" ""Phe spatial resolution of our images is not high enough to reveal such fine details.", The spatial resolution of our images is not high enough to reveal such fine details. + The differences between our images and{11 images are probably due to the longer spectral baseline that Reean Mulchaey. used (0.55 (im to 1.6 jum) and the different spatial resolution., The differences between our images and images are probably due to the longer spectral baseline that Regan Mulchaey used (0.55 $\mu$ m to 1.6 $\mu$ m) and the different spatial resolution. + Quillen ct al. (, Quillen et al. ( +1999) noticed. that the inner Z-band isophotes are slightly elongated. in. a direction. roughly perpendicular to the outer bar. so the galaxy may be doubly barred.,"1999) noticed that the inner $J$ -band isophotes are slightly elongated in a direction roughly perpendicular to the outer bar, so the galaxy may be doubly barred." + Our ff-band profile indeed shows an isophote twist of about ((Fig., Our $H$ -band profile indeed shows an isophote twist of about (Fig. + 20)., 2f). + Quillen et al. (, Quillen et al. ( +1999) sawa curved cust feature at,1999) sawa curved dust feature at +"of five more radio galaxies (NGC 1275: Abdoetal.(2009a),, M 87: Abdoetal.(2009b),, 3C 120, 3C 207, and 3C 380: Abdoetal. (2010b))).","of five more radio galaxies (NGC 1275: \cite{abdo09a}, M 87: \cite{abdo09b}, 3C 120, 3C 207, and 3C 380: \cite{abdo10b}) )." +" In this paper, we focus on the radio galaxy Cen A (Abdoetal.2009c)."," In this paper, we focus on the radio galaxy Cen A \citep{abdo09c}." +. The FR I Cen A is the nearest radio-loud active galaxy to Earth., The FR I Cen A is the nearest radio-loud active galaxy to Earth. + It has a redshift of 7—0.00183 at the distance of D=3.7 Mpc., It has a redshift of z=0.00183 at the distance of $D = 3.7 $ Mpc. +" Recently, the Auger collaboration reported that the arrival directions of the highest energy cosmic rays (E=>6x1013 eV) observed by the Auger observatory are correlated with nearby AGN, including Cen A 2007, 2008)."," Recently, the Auger collaboration reported that the arrival directions of the highest energy cosmic rays $E \gtrsim 6 \times10^{19}$ eV) observed by the Auger observatory are correlated with nearby AGN, including Cen A \citep{abraham07,abraham08}." +. This suggests that Cen A may be the dominant source of observed UHECR nuclei above the GZK cut off., This suggests that Cen A may be the dominant source of observed UHECR nuclei above the GZK cut off. + Cen A has an interesting radio structure on several size scales., Cen A has an interesting radio structure on several size scales. +" The most prominent features are its giant radio lobes, which subtend ~10° on the sky, oriented primarily in the north-south direction."," The most prominent features are its giant radio lobes, which subtend $\sim 10^0$ on the sky, oriented primarily in the north-south direction." + They have been imaged at 4.8 GHz by the Parkes telescope and studied at up to ~60 GHz by Hardcastleetal.(2009)., They have been imaged at $4.8$ GHz by the Parkes telescope \citep{junkes93} and studied at up to $\sim 60$ GHz by \cite{hardcastle09}. +. The radio lobes are the only extragalactic source structure that has so far been spatially resolved in GeV 4-rays, The radio lobes are the only extragalactic source structure that has so far been spatially resolved in GeV $\gamma$ -rays +Properties of natural numbers are (he fundamental question of mathematics.,Properties of natural numbers are the fundamental question of mathematics. + Investigations ol these properties in the Ancient Times (e.g. the infinitude of prime numbers which was shown by Euclid. Sieve of Eratosthenes lor prime numbers. consideration of Diophantine equations) led to the birth of elementary theory of numbers.," Investigations of these properties in the Ancient Times (e.g. the infinitude of prime numbers which was shown by Euclid, Sieve of Eratosthenes for prime numbers, consideration of Diophantine equations) led to the birth of elementary theory of numbers." + Later investigations (e.g. Fermat's Last theorem. investigations of zeta-finction by Euler ancl Riemann) have led to the development the great branch of mathematics - the analvtical theory. of numbers.," Later investigations (e.g. Fermat's Last theorem, investigations of zeta-function by Euler and Riemann) have led to the development the great branch of mathematics - the analytical theory of numbers." + The important problems of modern number theory. are the problems of effective search ol prime numbers and complexity (aud factorization) or primalitv of arbitrary natural number., The important problems of modern number theory are the problems of effective search of prime numbers and complexity (and factorization) or primality of arbitrary natural number. + Today essential efforts are applied for consicleration of (hese questions: many fast methods for factorization (e.g. Pollard p-algovithm [1|.. elliptic curve method [2].. quadratic sieve algorithm |3]..general number field sieve |4]}) and tests of primality (e.g. Miller-Rabin test [5|.. Lucas-Lehmer test |6].. AINS test |Y[)) are developed. projects on search of large prime numbers are running (GIMP [a]... PrimeGride [|9].. Seventeen or Bust [LO] and others). databases of prime numbers are updated (e.g. The List of Largest Ixnown Primes |11].. OEIS [12]).," Today essential efforts are applied for consideration of these questions: many fast methods for factorization (e.g. Pollard $\rho$ -algorithm \cite{b1}, elliptic curve method \cite{b2}, quadratic sieve algorithm \cite{b3},general number field sieve \cite{b4}) ) and tests of primality (e.g. Miller-Rabin test \cite{b5}, , Lucas-Lehmer test \cite{b6}, AKS test \cite{b7}) ) are developed, projects on search of large prime numbers are running (GIMP \cite{b8}, PrimeGride \cite{b9}, Seventeen or Bust \cite{b10} and others), databases of prime numbers are updated (e.g. The List of Largest Known Primes \cite{b11}, OEIS \cite{b12}) )." + Such interest is due to not only desire to understand the nature of numbers aud {ο resolve some Duidamental problems of mathematics but also due to opportunity of practical application of properties of natural numbers. e.g. for the ervptographie systems with public kev (for example RSA |13D). hash-tables. and generation of pseudorandonm numbers (e.g. Mersenne twister [0])).," Such interest is due to not only desire to understand the nature of numbers and to resolve some fundamental problems of mathematics but also due to opportunity of practical application of properties of natural numbers, e.g. for the cryptographic systems with public key (for example RSA \cite{b13}) ), hash-tables, and generation of pseudorandom numbers (e.g. Mersenne twister \cite{b14}) )." + The aim of this paper is {ο suggest a theoretical instrument [or investigation ol «quantity of divisors of natural number. which may be useful for further investigations of properties of natural numbers.," The aim of this paper is to suggest a theoretical instrument for investigation of quantity of divisors of natural number, which may be useful for further investigations of properties of natural numbers." + Main idea is similar to the one of method of trigonometric sums [0|.., Main idea is similar to the one of method of trigonometric sums \cite{b15}. + Using the fact that exp(277.0) equals unity only [or integer value of real number re one may sav that function: has zeros onlyfor values of 7 which are divisors of natural number s (we will denote these numbers as 27. where superscript s highlights dependence on natural number s. subscript j denotes integer sequence number of corresponding zero).," Using the fact that $\exp\left(2\pi i x\right)$ equals unity only for integer value of real number $x$ one may say that function: has zeros onlyfor values of $x$ which are divisors of natural number $s$ (we will denote these numbers as $x^{s}_{j}$, where superscript $s$ highlights dependence on natural number $s$, subscript $j$ denotes integer sequence number of corresponding zero)." + Note that Unfortunately. direct. use of f.Cr) (e.g. search of global minima of contif;Cr) by using numerical iteration methods) for factorization of natural number s or Lor ing nuniber ol clivisors of s is almost impossible because of Ireequent oscillations of function f.(e) (see fig. 1)).," Note that Unfortunately, direct use of $f_{s}(x)$ (e.g. search of global minima of $f_{s}(x)$ by using numerical iteration methods) for factorization of natural number $s$ or for counting number of divisors of $s$ is almost impossible because of frequent oscillations of function $f_{s}(x)$ (see fig. \ref{fig1}) )." + Number of zeros of this function in the interval |1:5| gives us the number of divisors ol s., Number of zeros of this function in the interval $[1;s]$ gives us the number of divisors of $s$ . + To count the number of zeros of f; one can use logarithmic residue of f., To count the number of zeros of $f_{s}$ one can use logarithmic residue of $f_{s}$ . + In general casethe logarithmic residue is the following(e.g. | p», In general casethe logarithmic residue is the following (e.g. \cite{b16}) ): +To conclude we remark (hat il is intriguing (hat the unique feature discovered here for the GRD's duration distribution depends just on the simple relation (Eq. 2)).,To conclude we remark that it is intriguing that the unique feature discovered here for the GRB's duration distribution depends just on the simple relation (Eq. \ref{tgamma}) ). + This implies (hat a similar plateau is expected in any transient source whose duration is determined by (wo unrelated processes in a similar manner., This implies that a similar plateau is expected in any transient source whose duration is determined by two unrelated processes in a similar manner. + la particular. in any case in which one process emits radiation and another independent one blocks it for a while.," In particular, in any case in which one process emits radiation and another independent one blocks it for a while." + For example. (his would take place in a source engulled by dust which will be obscured until the dust is destroved by the radiation wave.," For example, this would take place in a source engulfed by dust which will be obscured until the dust is destroyed by the radiation wave." + ‘This could be of importance in interpreting numerous transient observations. particularly now at the dawn of astronomy in the time domain.," This could be of importance in interpreting numerous transient observations, particularly now at the dawn of astronomy in the time domain." + This research was supported by an ERC advanced research grant. bv the Israeli center for Excellent for High Energy. AstvoPhysies CEP). by an ERC and IRG grants. and a Packard. Gueeenhein aud Badcliffe fellowships (RS). bv the ISF erant No.," This research was supported by an ERC advanced research grant, by the Israeli center for Excellent for High Energy AstroPhysics (TP), by an ERC and IRG grants, and a Packard, Guggenheim and Radcliffe fellowships (RS), by the ISF grant No." + 174/08 (EN), 174/08 (EN) +Here we examine how the flares of the two subclasses differ. and relate their differences to specific physical processes in the sources.,"Here we examine how the flares of the two subclasses differ, and relate their differences to specific physical processes in the sources." + Flares in BL Lacs have already been studied in Pageretal.(2009a) and related to current acceleration of the emitting electrons: so in this paper we focus on flaring activity of FSRQs., Flares in BL Lacs have already been studied in \citet{paggi1} and related to current acceleration of the emitting electrons; so in this paper we focus on flaring activity of FSRQs. + The SEDs of blazars include à basic SSC process., The SEDs of blazars include a basic SSC process. + The synchrotron component is produced the jets contain a magnetic fieldBB.. highly relativistic electrons with random Lorentz factors uptolo- —108. in addition to non-relativistic protons with a common density within acomoving sizeRR: all flow toward the observer with bulk Lorentz factors (see Bottcher 2007:: also Celottt&Ghis- 2008)).," The synchrotron component is produced the jets contain a magnetic field, highly relativistic electrons with random Lorentz factors up to ^6 -, in addition to non-relativistic protons with a common density within a size; all flow toward the observer with bulk Lorentz factors (see \citealt{bott}; ; also \citealt{celotti}) )." +with seed photons emitted inside or outside the jet. the same electrons also radiate by inverse Compton in the SSC or EC process. respectively.," seed photons emitted inside or outside the jet, the same electrons also radiate by inverse Compton in the SSC or EC process, respectively." + We will mainly adopt for the electron energy distributions curved. log-parabolic shapes: adding to their value as fitting tools for Here is the electron injection Lorentz factor and is a constant contribution to the slope.," We will mainly adopt for the electron energy distributions curved, log-parabolic shapes; adding to their value as fitting tools for Here is the electron injection Lorentz factor and is a constant contribution to the slope." + with curvature (Massaroetal.2004):: may vary during flares., with curvature \citep{massaro04}; may vary during flares. + The energetic content of such an electron population expressed in terms of the rms adimensional energyα spectral curvature the two SED peaks closely yield the total in each component., The energetic content of such an electron population expressed in terms of the rms adimensional energy; spectral curvature; the two SED peaks closely yield the total in each component. +δρ. For the synchrotronBy;nR. and the spectral curvature7/5.," For the synchrotron, and the spectral curvature." + For the7/10. in the Thomson BynR.regime.," For the, in the Thomson regime." + From an empirical standpoint. such curved spectra have been recognized to provideresiduals. from the X-ray (e.g..Landauetal.1986;saroetal.2004:Tramacere2007:Massaro2008) to the sub-mm band (González-Nuevoetal.2010)..," From an empirical standpoint, such curved spectra have been recognized to provide, from the X-ray \citep[e.g.,][]{landau,massaro04,tramacere,massaro08} to the sub-mm band \citep{gonzalez}." + In the FSRQs in particular. the higher energy component usually features substantially larger fluxes with respect to the synchrotron component.one.," In the FSRQs in particular, the higher energy component usually features substantially larger fluxes with respect to the synchrotron component,." +. This is often interpreted in terms of an additional EC component originated from seed photons emitted outside the jet. specifically by the broad line region (BLR) or by the inner accretion disk2002).," This is often interpreted in terms of an additional EC component originated from seed photons emitted outside the jet, specifically by the broad line region (BLR) or by the inner accretion disk." + The disk emission is modeled as a sum of annular concentric surfaces radiating locally as a black body: their temperatures follow along the radius the profile(see Franketal.2002).. where 1/4.. Wstheacceretionrateand .GMe/c is the radius of the last stable orbit.," The disk emission is modeled as a sum of annular concentric surfaces radiating locally as a black body; their temperatures follow along the radius the profile \citep[see][]{frank}, where , is the accretion rate and G is the radius of the last stable orbit." + The integrated emission has a peak flux at a peak frequencyο, The integrated emission has a peak flux at a peak frequency. +"ι The BLR instead comprises a number of A""clouds""1997)."," The BLR instead comprises a number of “clouds""." + Theseof external photons the electrons in the jet to yield EC radiation. with a SED again following shapes as represented by Eq. 2..," These external photons the electrons in the jet to yield EC radiation, with a SED again following shapes as represented by Eq. \ref{logparsed}." + For the photons coming from the diskDD.. the EC radiation has a peak flux—1.. a peak frequencyμμ]. and the spectral curvature close to the electroncurvature.," For the photons coming from the disk, the EC radiation has a peak flux, a peak frequency, and the spectral curvature close to the electron." + For photons coming from the BLR we have a peak flux peak requeneynu whiletties pectralcurvaturei | sagainbby;approx.," For photons coming from the BLR we have a peak flux, a peak frequency, the spectral curvature is again." +..Gamma We recall that the observed frequencies are enhanced by the beaming factor whilethe fluxesareboostedbydeltat.. with )forsmallviewingangles YBegelmanetal.," We recall that the observed frequencies are enhanced by the beaming factor, while the fluxes are boosted by, with for small viewing angles \citep{bbr}." +1984)..A theEC f luxisfurthermultiplie depending on the scattering geometry for the disk and the BLR photons. respectively (Dermer&Schlick-eiser2002;Ghisellini&Tavecchio 2009).," EC flux is further by factors depending on the scattering geometry for the disk and the BLR photons, respectively \citep{dermer02,ghisellinitavecchio}." +. Examples of theseemissions and contributions to the SEDs arenumerically computed and illustrated in Fig. ]..," Examples of theseemissions and contributions to the SEDs are computed and illustrated in Fig. \ref{examples}, ," + for both the low and high statesof a typical FSRQ with, for both the low and high statesof a typical FSRQ with +our approach nor Peacock’s) supports our claim (hat our Formula is the correct one.,our approach nor Peacock's) supports our claim that our formula is the correct one. + Most ealeulations previously: presented in the literature adopt the assumption of SPAS. in order to reduce the transport equation (Eq. 2))," Most calculations previously presented in the literature adopt the assumption of SPAS, in order to reduce the transport equation (Eq. \ref{eq:transport}) )" + to a Fokker-Planck equation. as shown in section ??..," to a Fokker-Planck equation, as shown in section \ref{sec:fp}." + In the approach presented in Paper I and here. the scattering occurs wilh arbitrary characteristics. embedded. in the scattering function. μ.μ).," In the approach presented in Paper I and here, the scattering occurs with arbitrary characteristics, embedded in the scattering function $w(\mu,\mu')$." + The case of a ic independent of pitch angles is (hat of strong scattering. which is expected to be achieved for large amplitude turbulence.," The case of a $w$ independent of pitch angles is that of strong scattering, which is expected to be achieved for large amplitude turbulence." + The case of small pitch angle scattering in (he assumption of isotropic scattering can be modeled in our approach by taking a peaked shape for the scaltering function. as explained in section 4.. with o«1.," The case of small pitch angle scattering in the assumption of isotropic scattering can be modeled in our approach by taking a peaked shape for the scattering function, as explained in section \ref{sec:numer}, with $\sigma\ll 1$." + We expect that in the limit of SPAS the result should not depend upon the detailed orm of the scattering function. provided this is strongly peaked (see Section 3).," We expect that in the limit of SPAS the result should not depend upon the detailed form of the scattering function, provided this is strongly peaked (see Section 3)." +" For a given Lorentz [actor of the shock (5,5). the velocity of the upstream fluid u=2»; is calculated."," For a given Lorentz factor of the shock $\gamma_{sh}$ ), the velocity of the upstream fluid $u=\beta_{sh}$ is calculated." + For the purpose of comparing our results with those of Ixirk et al. (, For the purpose of comparing our results with those of Kirk et al. ( +2000). we adopt a Synge (1957) equation of state for the downstream fIuid and assume that the nagnetic field is not cdvnamically important.,"2000), we adopt a Synge (1957) equation of state for the downstream fluid and assume that the magnetic field is not dynamically important." + These are the same assumptions as in (irk et al., These are the same assumptions as in (Kirk et al. + 2000)., 2000). + We can therefore calculate the velocity of the downstream fIuid vy from the conservation ol mass. momentum and energy al the shock surface.," We can therefore calculate the velocity of the downstream fluid $u_d$ from the conservation of mass, momentum and energy at the shock surface." + The values of à and uy are given in Table 1., The values of $u$ and $u_d$ are given in Table 1. +" Given these velocities and a width σ lor the scattering Iunction. we can solve the integral equations for £, ancl £2; iteratively,"," Given these velocities and a width $\sigma$ for the scattering function, we can solve the integral equations for $P_u$ and $P_d$ iteratively." + Following the procedure outlined in section 4.. we determine the slope of the power law spectrum and the angular part ο) of the distribution function.," Following the procedure outlined in section \ref{sec:numer}, we determine the slope of the power law spectrum and the angular part $g(\mu)$ of the distribution function." +present the parabolic treuds in ο€ diagraiuis typical of stella evolution are found to be extremely common.,present the parabolic trends in O–C diagrams typical of stellar evolution are found to be extremely common. + A survey by Chishkovaetal.(2005) cites a typical frequency of ~δν in both cluster aud field. Cepheids. for example. although their “anomalous” objects iuclude Cepheids like SV Vul in which the evolutionary trend is quite distinct (Turner&Berdiuikov2001).," A survey by \citet{gl05} cites a typical frequency of $\sim 80\%$ in both cluster and field Cepheids, for example, although their “anomalous” objects include Cepheids like SV Vul in which the evolutionary trend is quite distinct \citep{tb04}." + À imore realistic frequency for Milky Way Cepheids displaving evolutionary trends is du excess of ~90%., A more realistic frequency for Milky Way Cepheids displaying evolutionary trends is in excess of $\sim 90\%$. + For many of the remaiming objects. the evolutionary trends iav be more obvious in longer time baselimes of light curve coverage.," For many of the remaining objects, the evolutionary trends may be more obvious in longer time baselines of light curve coverage." + As also pointed out bv Fernie(1990)— and bv Derduikov&Turner(2001).. the οC trends indicative of evolution iu Cepheids need not be strictly parabolic.," As also pointed out by \citet{fe90} and by \citet{bt04}, the O–C trends indicative of evolution in Cepheids need not be strictly parabolic." + If the rate at which a massive star is evolving through the instability strip is not constant with time. the OC data for the associated Cepheid variable may be better described by a third or fourth order polvuouial.," If the rate at which a massive star is evolving through the instability strip is not constant with time, the O–C data for the associated Cepheid variable may be better described by a third or fourth order polynomial." + The Cepheids Y Oph (Fernie1990). aud WZ Car Derduikov&Turner2001) are two objects (of several huudred) where that appears to be the case., The Cepheids Y Oph \citep{fe90} and WZ Car \citep{bt04} are two objects (of several hundred) where that appears to be the case. + Such complications may affect the derived rates of period chanec. but iu most cases only by μια] amounts.," Such complications may affect the derived rates of period change, but in most cases only by small amounts." + In the large majority of studies of Cepheid period changes. the derived rate of period change reflects the evolution of the star through the instability strip (seeSzabados1983).," In the large majority of studies of Cepheid period changes, the derived rate of period change reflects the evolution of the star through the instability strip \citep[see][]{sz83}." +. Most computational evolutionary models for evolved stars are used for constructing evolutionary tracks rather than testing for pulsation instability., Most computational evolutionary models for evolved stars are used for constructing evolutionary tracks rather than testing for pulsation instability. + But. as noted bycitetpahs. it is possible to use the basic information they provide ou eracdual changes in Inminosity and effective temperature to predict expected rates of period change for Cepheids of differeut period.," But, as noted by, it is possible to use the basic information they provide on gradual changes in luminosity and effective temperature to predict expected rates of period change for Cepheids of different period." + A starting point is thewell known period-deusity relation: where Pis the pulsation period. pis the density.Af ds the stellar mass. is the stellar radius. andQ. the pulsation constant. has a small period dependence (o.g..Ikraft.1961:Feruie1967) that we assume here caries. as Psn based upon au clupizical analysis by Turner&Burke(2002).," A starting point is thewell known period-density relation: where is the pulsation period, $\rho$ is the density, is the stellar mass, is the stellar radius, and, the pulsation constant, has a small period dependence \citep[e.g.,][]{kr61,fe67} that we assume here varies as $P^{\frac{\rm 1}{\rm 8}}$ based upon an empirical analysis by \citet{tb02}." +. Differentiation of the period-density relation. iu conjunction with the standard equation for stellar Iuiminositv. therefore leads to the following result: The desired. quantity. the rate of period chanec P. is obtained. from. tabulated differences in stellar huuinositv aud effective temperature as a function of age as a model star evolves through the instability strip.," Differentiation of the period-density relation, in conjunction with the standard equation for stellar luminosity, therefore leads to the following result: The desired quantity, the rate of period change $\dot{P}$, is obtained from tabulated differences in stellar luminosity and effective temperature as a function of age as a model star evolves through the instability strip." +" For the present study we calculated values of P? from the above relationship using computational stellar evolutionary imodels frou, a variety of available published sources. namely Maeder&Alevuet (1988). Alibertetal.(1999).. Ποσο (€2001).. and Claret(2001)."," For the present study we calculated values of $\dot{P}$ from the above relationship using computational stellar evolutionary models from a variety of available published sources, namely \citet{mm88}, \citet{al99}, \citet{ls01}, and \citet{cl04}." +.. The published data were used to compute different paraueters. depending upon the availability of the necessary information.," The published data were used to compute different parameters, depending upon the availability of the necessary information." + Alibertetal.(1999) cite paraicters for stars of differeut lass reaching the ho and cool edges of the instability strip. so their data vield information oulv about rates of period change near the ceuter of the strip.," \citet{al99} cite parameters for stars of different mass reaching the hot and cool edges of the instability strip, so their data yield information only about rates of period change near the center of the strip." + Iu other cases such as Claret(2001). rere ds sufficicut time resolution iu the output xumaneters to track changes n pulsation period (Cross individual instability strip crossings.," In other cases, such as \citet{cl04}, , there is sufficient time resolution in the output parameters to track changes in pulsation period across individual instability strip crossings." + For le renidniug sources (Maeder&Alevuct105δ:Lejeune&Schaerer 2001).. including Claret 2001). we caleulated rates of period change for ic dutersection of the evolutionary tracks with ιο ohservationally delineated boundaries of the instability strip defued ciupirically by πο: (2001).. which are close to those predicted b nodels of pulsation instability (Alibertetαἱ. 1999).. ax well as for points wing within the strip )oundaries.," For the remaining sources \citep{mm88,ls01}, including \citet{cl04}, we calculated rates of period change for the intersection of the evolutionary tracks with the observationally delineated boundaries of the instability strip defined empirically by \citet{tu01}, , which are close to those predicted by models of pulsation instability \citep{al99}, as well as for points lying within the strip boundaries." + Pulsation periods were established using the period+vadius relation (Turner&Burke 2002)., Pulsation periods were established using the period-radius relation \citep{tb02}. +. The present results differ from those obtained earlier (Turner&Deorduikov2001.2003) in Όσιο tied to a larger varicty of models with a ereater range of inetallicity. aud by. the inclusion of a weak period depeudeuce for Q in the period- relation.," The present results differ from those obtained earlier \citep{tb01,tb03} in being tied to a larger variety of models with a greater range of metallicity, and by the inclusion of a weak period dependence for in the period-density relation." + The computed results on rates of period chanec are plotted im Fig., The computed results on rates of period change are plotted in Fig. + 2Ne for all of the accessible models., 2 for all of the accessible models. + Differentsviubols. denote the cdiffereut sources., Differentsymbols denote the different sources. + Values calculated fromthe models of, Values calculated fromthe models of +3C120 is a nearby (220.033) radio galaxy which las variously been classified as a Sevtert 1. a woad line radio galaxy. and a late type spiral.,"3C120 is a nearby (z=0.033) radio galaxy which has variously been classified as a Seyfert 1, a broad line radio galaxy, and a late type spiral." + The optical appearance is complex. with iultiple dust lanes and wo sugeestiveOO spiral arms which vecolme radial features at a projected distance of 6.3 kpe from the core (fig. 1)).," The optical appearance is complex, with multiple dust lanes and two suggestive spiral arms which become radial features at a projected distance of 6.3 kpc from the core (fig. \ref{fig:k4hst}) )." + The racio norphology auc luninosity are more similar to he ERI class radio galaxy (Fanaroff Riley 1971) han to the usual Seyfert., The radio morphology and luminosity are more similar to the FRI class radio galaxy (Fanaroff Riley 1974) than to the usual Seyfert. + A one sided pe scale jet has been exteusively studied with long baseline interferometry aud superluminal components have been identified (apparent speeds between 3 aud 6c. Walker et al.," A one sided pc scale jet has been extensively studied with long baseline interferometry and superluminal components have been identified (apparent speeds between 3 and 6c, Walker et al." + 2001)., 2001). + The kpe scale jet is shown iu fle., The kpc scale jet is shown in fig. + 2 and there is additional complex cussion at larger scales (bevoud the borders of fig. 2..," \ref{fig:lband} and there is additional complex emission at larger scales (beyond the borders of fig. \ref{fig:lband}," + Walker. Benson. Uinin 1987).," Walker, Benson, Unwin 1987)." +" At N-vav waveleneths. the nucleus is a stroug and variable source (e.g. Halper 1985). but it was the detection with ROSAT of a rather inconspicuous radio kno 25"" from the core (16 kpc. projected). which preseuted jew. problems for the conventional models of N-xav cussion frou. radio jets (ILlarris ct al."," At X-ray wavelengths, the nucleus is a strong and variable source (e.g. Halpern 1985), but it was the detection with ROSAT of a rather inconspicuous radio knot $''$ from the core (16 kpc, projected), which presented new problems for the conventional models of X-ray emission from radio jets (Harris et al." + 1999: IIIISSV. hereafter)., 1999; HHSSV hereafter). + Therefore we obtained new radio data at ligher frequencies to see if this knot was peculiar or unique either iu shock structure (as manifest bv, Therefore we obtained new radio data at higher frequencies to see if this knot was peculiar or unique either in shock structure (as manifest by +This paper is arrangecl as follows.,This paper is arranged as follows. + In Section 2 we review (he flat skv approximation and then we cliseuss the issue of [oregrounds. instrument noise and window function in Section 3.," In Section 2 we review the flat sky approximation and then we discuss the issue of foregrounds, instrument noise and window function in Section 3." + We test the Gaussianitv of the patches taken from WAIAP data in Section 4., We test the Gaussianity of the patches taken from WMAP data in Section 4. + We then emplov the method in Section 5.. and the Discussion is in Section 6..," We then employ the method in Section \ref{realdata}, and the Discussion is in Section \ref{discussion}." +" SGuidard treatment for whole-skyv CMD spectral analysis is via writing the temperature anisotropies as a sum of spherical harmonics Y,,: T(6.5)=32,30),demYim(@.c). where 0. 2 are the polar and azimuthal angle. e,=ανexpGon) is the spherical harmonic coefficient and ó;,, is the phase."," Standard treatment for whole-sky CMB spectral analysis is via writing the temperature anisotropies as a sum of spherical harmonics $\ylm$ : $T(\theta,\varphi)=\sum_\l \sum_m \alm \ylm(\theta,\varphi)$, where $\theta$, $\varphi$ are the polar and azimuthal angle, $\alm\equiv |\alm| \exp(i\phi_\lm)$ is the spherical harmonic coefficient and $\phi_\lm$ is the phase." +" The strict definition of an isotropic GRE requires the real aud imaginary part of the «4, mutually independent and both Gaussian. but a more convenient definition is (hat the phases are uniformly random on the interval [0.22]."," The strict definition of an isotropic GRF requires the real and imaginary part of the $\alm$ mutually independent and both Gaussian, but a more convenient definition is that the phases are uniformly random on the interval $[0,2\pi]$." +" The power spectrum can be estimated C,=(26+1)D35tem|?.", The power spectrum can be estimated $\cl=(2\l+1)^{-1}\sum_m |\alm|^2$. + To estimate (he power spectrum from small square patches. however. one can use Fast Fourier Translorm (FFT): where r=(6.2) and k=(hy.hk.) if the patches are chosen on the equator with sides aligned with the spherical coordinates.," To estimate the power spectrum from small square patches, however, one can use Fast Fourier Transform (FFT): where ${\bi r}\equiv(\theta, \varphi)$ and ${\bi k}\equiv (\kt, \kp)$ if the patches are chosen on the equator with sides aligned with the spherical coordinates." +" The power spectrum from the pateh is C,=(lag,2 where the angle brackets denote average for integer & over all he° for k-1/2//^2$, a quantity directly available from the \citet{Trac:07} simulations (See their Figure 12)." +" However. their estimate of C"" is an average over ihe entire comoving volume."," However, their estimate of $C'$ is an average over the entire comoving volume." + In practise. the clumpiness of gas which is within the halos is already f[actored into the estimate of escape fraction.," In practise, the clumpiness of gas which is within the source-forming halos is already factored into the estimate of escape fraction." + So. (he clumping factor V.10uld be a measure of the clumpiness of the IGM excluding halos with star-lormation in them (Figure 2a).," So, the clumping factor should be a measure of the clumpiness of the IGM excluding halos with star-formation in them (Figure 2a)." + Therelore. we use the exact relation as shown in Equation 6.," Therefore, we use the exact relation as shown in Equation 6." +" We adopt the most current estimate lor the reionization history. redshift dependent ]umping factor (Figure 2a). nm,. njgj and rjj Grom the high resolution simulations of Trac&Cen(2007)."," We adopt the most current estimate for the reionization history, redshift dependent clumping factor (Figure 2a), $n_{e}$ , $n_{{\rm HII}}$ and $n_{{\rm HeII}}$ from the high resolution simulations of \citet{Trac:07}." +. A comparison between the number of photons per barvon from these equations compared with a similar relation derived [ον complete reionization by (1999) is shown in Figure 2b., A comparison between the number of photons per baryon from these equations compared with a similar relation derived for complete reionization by \citet{Madau:99} is shown in Figure 2b. + The number of ionizing photons required is sensitive to the reionization history since the recombination rate is proportional to the square of the densitv., The number of ionizing photons required is sensitive to the reionization history since the recombination rate is proportional to the square of the density. + Η reionization is completed earlier. (he recombination rate is proportionatelv. higher than for a partially ionized medium.," If reionization is completed earlier, the recombination rate is proportionately higher than for a partially ionized medium." + In that case. (he number of photons per barvon needs to be higher to maintain the ionized state of the IGM as shown by the triple dot dashed line in Figure 2b.," In that case, the number of photons per baryon needs to be higher to maintain the ionized state of the IGM as shown by the triple dot dashed line in Figure 2b." +" We note that the reionization history of Trac&Cen(2007) corresponds to the ""late? reionization history whieh would result in a WMAP optical depth to Thomson scattering close to the measured. value of 7~0.0940.03 (Spergeletal.2007).", We note that the reionization history of \citet{Trac:07} corresponds to the “late” reionization history which would result in a WMAP optical depth to Thomson scattering close to the measured value of $\tau\sim0.09\pm0.03$ \citep{Spergel:07}. +.. As characterized in Greif&Bronun(2006) and Wvithe&Loeb(2003).. shifting the process of reionization {ο zoe10 would result in optical depth: values which are at the hieh end of the observed range.," As characterized in \citet{Greif_Bromm} and \citet{Wyithe}, shifting the process of reionization to $z\sim10$ would result in optical depth values which are at the high end of the observed range." + For each stellar initial mass function that we adopt. we obtain a library of template SED which are a function of the age of the starburst.," For each stellar initial mass function that we adopt, we obtain a library of template SED which are a function of the age of the starburst." + We first determine the combination of age and mass which results in a best fit to (he optical and ultraviolet luminosity density., We first determine the combination of age and mass which results in a best fit to the optical and ultraviolet luminosity density. + This vields the stellar mass density al 2=6 for that IME., This yields the stellar mass density at $z=6$ for that IMF. + The range of age and mass values or a subset of ΙΔΙΕΣ considered here is shown in Table 1., The range of age and mass values for a subset of IMFs considered here is shown in Table 1. + As emphasized earlier this is a naximal age [or a single stellar population since we adopt a single instantaneous burst., As emphasized earlier this is a maximal age for a single stellar population since we adopt a single instantaneous burst. + The Starburst99 model vields the number of hydrogen ionizing photons produced as a uncton of age of the starburst., The Starburst99 model yields the number of hydrogen ionizing photons produced as a function of age of the starburst. + The escape fraction is a measure of the number of ionizing photons escaping from star-lormine regions in galaxies. into the IGAL," The escape fraction is a measure of the number of ionizing photons escaping from star-forming regions in galaxies, into the IGM." + The escape Iraction ws been constrained to be ~10—15% (Sianaetal.2007:Shapley2006) in the Lyiman-break galaxy. population.," The escape fraction has been constrained to be $\sim10-15$ \citep{Siana:07, Shapley:06} in the Lyman-break galaxy population." + Thus. we adopt escape fractions of 0.1 and 0.15.," Thus, we adopt escape fractions of 0.1 and 0.15." + By integrating the number of ionizing photons over the derived stellar age. we can estimate the total number of photons produced over the lifetime of the evolving galaxies. multiply that with the escape fraction and compare (he result with the number of ionizing photonsrequired to keep the IGM ionizecl as determined from Equation 6.," By integrating the number of ionizing photons over the derived stellar age, we can estimate the total number of photons produced over the lifetime of the evolving galaxies, multiply that with the escape fraction and compare the result with the number of ionizing photonsrequired to keep the IGM ionized as determined from Equation 6." +The magnetic field pl:ws a kev role in the formation and propagation of astrophnvsical jets.,The magnetic field plays a key role in the formation and propagation of astrophysical jets. + Polarization nuüeasurenmieuts provide iuportaut information about the oricutatio rand the strcsneth of the maenetic field. which seclus to be higilv organized on a laree scale iu maux jets (sec. e.g. Cawthorne et al.," Polarization measurements provide important information about the orientation and the strength of the magnetic field, which seems to be highly organized on a large scale in many jets (see, e.g., Cawthorne et al." + 1993. Lepxunen. Zensus Diamoud 1995. Cabuzda 1999. Ciabuzda et al.," 1993, Leppännen, Zensus Diamond 1995, Gabuzda 1999, Gabuzda et al." + 200 Ίνα et al.," 2004, Kharb et al." + 2008)., 2008). + Τι» explain the observational data. simplified models of tlic| fhrec-dinieusional magnetic field distribution have beeu proposed (see. for exaniple. Laing 1951. 1993. Pushkarev et al.," To explain the observational data, simplified models of the three-dimensional magnetic field distribution have been proposed (see, for example, Laing 1981, 1993, Pushkarev et al." + 2005. Laiis et al.," 2005, Laing et al." + 2006 j, 2006 ). + Iu particular the yxduization data sieoost that the uaenetic field las a siguifeant transverse coniponent iu he mau ration of the jet volume., In particular the polarization data suggest that the magnetic field has a significant transverse component in the main fration of the jet volume. +" Iu accordance with he ""tradilonal interxetation (see. e.g. Laing 1993). his magnetic sructure cal be associated with a seres of shocks aloie the jet. wich eulauces the local transverse field."," In accordance with the ""traditional"" interpretation (see, e.g., Laing 1993), this magnetic structure can be associated with a series of shocks along the jet, which enhances the local transverse field." + However. Χαν Lo1ο Daseline Interferometry (VLBI) observations of DL Lac |8UST8l Πταανασα et al.," However, Very Long Baseline Interferometry (VLBI) observations of BL Lac 1803+784 (Hirabayashi et al." + 1998) revealed tiat the transverse magnetic structure can be ornued by a large-scale oroidal maeuetic field. and indeed recent observatious of a radio jet in the galaxy COCO 019-533 also reveal a predmuinantly toroidal magnetic field (Bagchi et al.," 1998) revealed that the transverse magnetic structure can be formed by a large-scale toroidal magnetic field, and indeed recent observations of a radio jet in the galaxy CGCG 049-033 also reveal a predominantly toroidal magnetic field (Bagchi et al." + 2007. Laine et al.," 2007, Laing et al." + 2006)., 2006). + AMaeuetic structures with a significant toroidal ficld-conmoueut are predicted by several theoretical 1nodels or jet formaion (Blandford Pavue 1982. Romauova Lovelace 1992. Ixoxle. Shibaa που 19958).," Magnetic structures with a significant toroidal field-component are predicted by several theoretical models for jet formation (Blandford Payne 1982, Romanova Lovelace 1992, Koide, Shibata Kudoh 1998)." +" m utiular ποue inodeIs of the jet propagation (sec, e.g.àY Deeechlinan. Blandford Rees 1981) propose that he tewoidal feld decas""o unore slowly tha1 the polokal OlC as a fuwetion of the cüstauce from the ceutral object. thereOre the toroidal field. shotld eveutualv yecole doniiut."," In particular some models of the jet propagation (see, e.g., Begelman, Blandford Rees 1984) propose that the toroidal field decays more slowly than the poloidal one as a function of the distance from the central object, therefore the toroidal field should eventually become dominant." + Other generation mechanisms based either on the conibiued iuflueice of tirhulence axd arge-scale shear (see. e.g.àY Urpii 2006) or on dynanio action along with maegueto-ceutrifusal aux reconnection oocesses (de Ctouvela Dal Piuo. 2005) also predict the occurence of a siguifican toroidal component.," Other generation mechanisms based either on the combined influence of turbulence and large-scale shear (see, e.g. Urpin 2006) or on dynamo action along with magneto-centrifugal and reconnection processes (de Gouveia Dal Pino, 2005) also predict the occurence of a significant toroidal component." + A situation where loops of the toroidal magnetic field domunuate the field distribution woul produce maportant ανασα] consequences for the jet structure. for mstance. providing pressure confnemeut trough maguctic tension forces (Chan Ieurikseun 1980. Eichler 1993).," A situation where loops of the toroidal magnetic field dominate the field distribution would produce important dynamical consequences for the jet structure, for instance, providing pressure confinement through magnetic tension forces (Chan Henriksen 1980, Eichler 1993)." + However. it ds well known from plasa plysics (see. e.g Nadomtzev 1966) that the toroidal naenetic field may cause various maenetolivdrodvuaimic (CMIID) iustabilities even iu simple cvliudical coufigurations.," However, it is well known from plasma physics (see, e.g., Kadomtzev 1966) that the toroidal magnetic field may cause various magnetohydrodynamic (MHD) instabilities even in simple cylindrical configurations." + Tn general. different types of instabilities can occur in astrophysical jets.," In general, different types of instabilities can occur in astrophysical jets." +" They can be caused by boundary effects, shear. stratification aud magnetic fields and are also likely to be responsilde for the observed morphological complexity of jes."," They can be caused by boundary effects, shear, stratification and magnetic fields and are also likely to be responsible for the observed morphological complexity of jets." + For this reason several analytical (sec. e.g. Ferrari. Trussoni Zaunetti 1980. Bodo ct al.," For this reason several analytical (see, e.g., Ferrari, Trussoni Zaninetti 1980, Bodo et al." + 1989. 1996. IIa1197. Ὡςd Sauty |999: sce also Birkinshaw 1997 for a review) and imcvical (Ibudee et al.," 1989, 1996, Hanasz, Sol Sauty 1999; see also Birkinshaw 1997 for a review) and numerical (Hardee et al." + 1992. App 1996. Lucek Dell 199€». Miu 1997. Ixudoh. Matsumoto Shibata 1999) works have been devoted to the study of the stability properticss of jets.," 1992, Appl 1996, Lucek Bell 1996, Min 1997, Kudoh, Matsumoto Shibata 1999) works have been devoted to the study of the stability properties of jets." + A systematic study of the Ikelviu-ITeliuiholΖ΄ stability in non-relativistic jets with the lougitidinal magnetic field has been »erforniec bv Dodo et al. (, A systematic study of the Kelvin-Helmholtz instability in non-relativistic jets with the longitudinal magnetic field has been performed by Bodo et al. ( +1989. 1996) includiug also the effect of rotation.,"1989, 1996) including also the effect of rotation." + Iu particu arseveral unstable modes including a slow iode associated with the maenetic field aud an inertial mode caused by rotation have heen found., In particular several unstable modes including a slow mode associated with the magnetic field and an inertial mode caused by rotation have been found. + Shear-dziven iustabilities cau also be very nuportaut in jets (Urpin. 2002).," Shear-driven instabilities can also be very important in jets (Urpin, 2002)." + Numerical simmlations (Alov ct al., Numerical simulations (Aloy et al. + 1999a. 1999») indicate that tn| yadial structure of jets may be lüore coniex with a trausition shear laver siiroundius the jet core.," 1999a, 1999b) indicate that the radial structure of jets may be more complex with a transition shear layer surrounding the jet core." + The thickress of f1ο shear laver depoeuds ontie distance being around of the jet radius near the iozzle mt broadoeniug near the head where it is of the «der of the jet racius., The thickness of the shear layer depends on the distance being around of the jet radius near the nozzle but broadening near the head where it is of the order of the jet radius. + This shear laver may have andnportawt consequence for various propertics of jets including their stability (sec. Ce. Tanasz Sol 1996. 1995. Alov Minica 20jh).," This shear layer may have an important consequence for various properties of jets including their stability (see, e.g., Hanasz Sol 1996, 1998, Aloy Mimica 2008)." + Iu this )pper. we cousider the mstabilitv associated with the toxilogv. of the magnetic feld iu jets.," In this paper, we consider the instability associated with the topology of the magnetic field in jets." + Magnetic, Magnetic +the reduced x? is 1.6 with 34 degrees of freedom.,the reduced $\chi^2$ is 1.6 with 34 degrees of freedom. +" The model with no pitch angle parameter is slightly worse, particularlyat |«—0.6°, with a reduced x? of 2.2 and 35 degrees of freedom."," The model with no pitch angle parameter is slightly worse, particularlyat $l < -0.6^\circ$, with a reduced $\chi^2$ of 2.2 and 35 degrees of freedom." +" A p of 0 is ruled out formally at the 3 σ level, although as discussed in 85.1.0 considering emissivity of the model will change some details of the best-fit parameters."," A $p$ of 0 is ruled out formally at the 3 $\sigma$ level, although as discussed in \ref{depol} considering emissivity of the model will change some details of the best-fit parameters." + 'The quality of the fit shows that a realistic GC electron distribution and magnetic field geometry can explain the observed RM longitude pattern., The quality of the fit shows that a realistic GC electron distribution and magnetic field geometry can explain the observed RM longitude pattern. +" In particular, the rapid change of RM with Galactic longitude is best explained by the rapidly changing magnetic field orientation within the central few hundred parsecs."," In particular, the rapid change of RM with Galactic longitude is best explained by the rapidly changing magnetic field orientation within the central few hundred parsecs." + This is consistent with our assumption that most of the polarized emission originates in the center and that the Faraday rotation happens on the near side of the GC., This is consistent with our assumption that most of the polarized emission originates in the center and that the Faraday rotation happens on the near side of the GC. +" Not only can the model fit the observed RM pattern, but the best-fit values are consistent with other observations."," Not only can the model fit the observed RM pattern, but the best-fit values are consistent with other observations." +" The magnetic field strength and electron density are degenerate in the model, but we constrain the horizontal component of the magnetic field to be roughly 5(10 cm~?/n8°)uG at heights of about 0556."," The magnetic field strength and electron density are degenerate in the model, but we constrain the horizontal component of the magnetic field to be roughly $5 (10\ \rm{cm}^{-3}/n_e^{\rm{gc}}) \mu$ G at heights of about $0\ddeg5$ ." + Considering the predominantly vertical orientation of, Considering the predominantly vertical orientation of +Tn this appendix. we describe the couplingο of temperature evolution aud burningoO used im the reaction networks used in this work.,"In this appendix, we describe the coupling of temperature evolution and burning used in the reaction networks used in this work." + For a Uchuholtz free energy. based thermodynamic system. the temperature T. deusity p. aud molar composition vector Y are the primary variables.," For a Helmholtz free energy based thermodynamic system, the temperature $T$, density $\rho$, and molar composition vector $\bf Y$ are the primary variables." + (3; are related to the mass fractious V; used clsewhere in this paper throueh .X;2-4;3;. where A; is the atomic mass umber of the th7 clement.)," $Y_i$ are related to the mass fractions $X_i$ used elsewhere in this paper through $X_i = A_i Y_i$, where $A_i$ is the atomic mass number of the $i^{\mathrm{th}}$ element.)" +" We'll want to expand thermodynamic quantities in terms of these variables. for example. All reasonable stellar equatious of state will return the OP/OT aud OP/Op partial derivatives ο), "," We'll want to expand thermodynamic quantities in terms of these variables, for example, All reasonable stellar equations of state will return the $\partial +P/\partial T$ and $\partial P/\partial \rho$ partial derivatives \citep[for a survey, see][]{timmesarnett99}." +The last term iu equation (AL)) is a bit tricker., The last term in equation \ref{eq1}) ) is a bit tricker. + Nearly all stellar equations of state use the mean atomic weieht A aud the mean charec Z to characterize the composition.," Nearly all stellar equations of state use the mean atomic weight ${\bar {\rm A}}$ and the mean charge ${\bar {\rm +Z}}$ to characterize the composition." + Thus. the last term iu equation (AL)) canbe expandedas All complete stellar equations of state will return the OP/OA and ο ters. so we will not be concerned with those terms (e.g...2).," Thus, the last term in equation \ref{eq1}) ) can be expanded as All complete stellar equations of state will return the $\partial +P/\partial {\bar {\rm A}}$ and $\partial P/\partial {\bar {\rm Z}}$ terms, so we will not be concerned with those terms \citep[\eg{},." + Iu terms of the molar composition the mean atomic weight A aud the mean charge Z are The partial derivatives of A and Z are then surprisingly simple., In terms of the molar composition the mean atomic weight ${\bar {\rm A}}$ and the mean charge ${\bar {\rm Z}}$ are The partial derivatives of ${\bar {\rm A}}$ and ${\bar{\rm Z}}$ are then surprisingly simple. + Operating with d/df ou equation (AL)) vields a pressure evolution equation The last two terms of equation CÀ6)) are easy to compute since the dY;/df are the vielt-hand sides of the ordinary differcutial equations that comprise a unclear reaction network equation., Operating with $d/dt$ on equation \ref{eq1}) ) yields a pressure evolution equation The last two terms of equation \ref{eq6}) ) are easy to compute since the $dY_i/dt$ are the right-hand sides of the ordinary differential equations that comprise a nuclear reaction network equation. +the low significance of the N-ravs/optical correlation is due to the simall nuniber of points in the optical leh curves) we also expect to observe time delavs within the optical baud.,the low significance of the X-rays/optical correlation is due to the small number of points in the optical light curves) we also expect to observe time delays within the optical band. + Assumiug the temperature structure of a steady-state accretion dise these delavs should follow the relationship 7XAY?m (Collier et al.," Assuming the temperature structure of a steady-state accretion disc these delays should follow the relationship $\tau \propto +\lambda^{4/3}$ (Collier et al." + 1998)., 1998). + In this case. TpvíTBη=(ApiveAy1/3jAr‘y=0. aud Tpντo;=(Apo163Ay3j(pg..Àjy=i0.22.," In this case, $\tau_{B-V}/\tau_{B-R}=(\lambda_{B}^{4/3}-\lambda_{V}^{4/3})/ +(\lambda_{B}^{4/3}-\lambda_{R}^{4/3})=0.4$ and $\tau_{B-V}/\tau_{B-I}=(\lambda_{B}^{4/3}-\lambda_{V}^{4/3})/ +(\lambda_{B}^{4/3}-\lambda_{I}^{4/3})=0.22$." + luterestiuelv.[m the ratio ofthe respecive observed lags (see section. 3.2) is ~(0.5 and ~0.31.," Interestingly, the ratio of the respective observed lags (see section 3.2) is $\sim 0.5$ and $\sim +0.34$." + This good aereenien between the expected ar the observed delays between the optical bands supports the idea that the variable optical coluponent is reprocessed XN-rav cluission frou. optically thick material., This good agreement between the expected and the observed delays between the optical bands supports the idea that the variable optical component is reprocessed X-ray emission from optically thick material. + The 36 upper lait on the time lag between N-ravs aud optical light. curves is 3.5 dave., The $3\sigma$ upper limit on the time lag between X-rays and optical light curves is $3.5$ days. + Consequently. the optical eiiission region should be at a distance siualler than 7-—1016 cii from the black hole. 1.6. at ~3T; along this curve the transition is a rapid crossover. whereas lor 7 T_c$ along this curve the transition is a rapid crossover, whereas for $T < T_c$ along this curve the transition is first order." +Fig. 1..,Fig. \ref{fig:covfrac}. + This strong redshift evolution in the covering fraction of cold filaments between z~3.8 and z~2.5 reflects the aforementioned rapid transition from cold to hot dominated accretion., This strong redshift evolution in the covering fraction of cold filaments between $z\sim3.8$ and $z\sim2.5$ reflects the aforementioned rapid transition from cold to hot dominated accretion. + We note that these results are consistent with theOPT08 value of 10?Mg for aat z—4., We note that these results are consistent with theOPT08 value of $\sim 10^{13}\msun$ for at $z=4$. + An interesting feature present in Fig., An interesting feature present in Fig. + 1 is that the covering fraction is higher in more massive haloes at a given redshift., \ref{fig:covfrac} is that the covering fraction is higher in more massive haloes at a given redshift. + This seems to contradict previous findings (OPT08) that it is the small haloes which are mainly fed by cold mode accretion., This seems to contradict previous findings (OPT08) that it is the small haloes which are mainly fed by cold mode accretion. +" It should be noted, however, that the covering fraction shown in Fig."," It should be noted, however, that the covering fraction shown in Fig." +" 1 does not account for the accretion of cold,diffuse gas (cold gas with lower column densities) which is only present in halos with masses incapable of sustaining a virial shock at all."," \ref{fig:covfrac} does not account for the accretion of cold, gas (cold gas with lower column densities) which is only present in halos with masses incapable of sustaining a virial shock at all." +" Indeed, these small haloes are usually located within (or around) filaments whose density is low, whereas the filaments around more massive haloes tend to be denser."," Indeed, these small haloes are usually located within (or around) filaments whose density is low, whereas the filaments around more massive haloes tend to be denser." +" Furthermore, in massive haloes, satellite galaxies contribute more importantly to the covering fraction, as do extended, warped, galactic disks and dense gas bridges which result from tidal interactions between galaxies."," Furthermore, in massive haloes, satellite galaxies contribute more importantly to the covering fraction, as do extended, warped, galactic disks and dense gas bridges which result from tidal interactions between galaxies." +" These latter effects partly explain the trend, but the primary driver of the covering fraction increase with halo mass is the density of the accreted gas, which is higher in more massive haloes."," These latter effects partly explain the trend, but the primary driver of the covering fraction increase with halo mass is the density of the accreted gas, which is higher in more massive haloes." + Fig., Fig. + 1 (dotted lines) substantiates this claim by showing how the covering fractions drop when the very dense gas (Nu> 10?'cm which belongs to the ISM of satellite galaxies is excluded?) from the measurement.," \ref{fig:covfrac} (dotted lines) substantiates this claim by showing how the covering fractions drop when the very dense gas $\rm N_H > +10^{21} cm^{-2}$ ) which belongs to the ISM of satellite galaxies is excluded from the measurement." +" In order to more carefully investigate the possibility of detecting cold filaments using metal absorption lines, we compute the strength of the CII1334 absorption."," In order to more carefully investigate the possibility of detecting cold filaments using metal absorption lines, we compute the strength of the ${\rm CII} ~\lambda 1334$ absorption." +" Our choice of line is dictated not only by the temperature of the filamentary gas which is not high enough to significantly produce more highly ionized metallic elements such as CIV, but also because it is empirically known to yield the strongest absorption feature (Steideletal.2010) We do not attempt to model absorption by CII accurately which would require detailed radiative transfer, but instead derive an upper limit by making several extreme assumptions."," Our choice of line is dictated not only by the temperature of the filamentary gas which is not high enough to significantly produce more highly ionized metallic elements such as CIV, but also because it is empirically known to yield the strongest absorption feature \citep{steidel10} + We do not attempt to model absorption by CII accurately which would require detailed radiative transfer, but instead derive an upper limit by making several extreme assumptions." +" Firstly, we assume that all the carbon present in filaments is eligible for the CIIA1334 transition."," Firstly, we assume that all the carbon present in filaments is eligible for the ${\rm C II}~ \lambda 1334$ transition." +" Secondly, we use the solar abundance ratio ([C/Z]o~ 0.178, Asplundet 2009)) to obtain the carbon column density for a given"," Secondly, we use the solar abundance ratio $[C/Z]_{\odot}\simeq 0.178$ , \citealt{asplund09}) ) to obtain the carbon column density for a given" +regime an instability can arise. [from both dissipative (resonant) and reactive (nonresonant) ellects.,regime an instability can arise from both dissipative (resonant) and reactive (nonresonant) effects. + As we focus on the nonresonant instability in the short wavelength regime. quasilinear dillusion in the long wavelength. regime is not discussed further.," As we focus on the nonresonant instability in the short wavelength regime, quasilinear diffusion in the long wavelength regime is not discussed further." + The right-hand side of Eq (24)) and (25)) can be evaluated in a general case in which the particle distribution is isotropic in pitch angles., The right-hand side of Eq \ref{eq:dpp}) ) and \ref{eq:dpep}) ) can be evaluated in a general case in which the particle distribution is isotropic in pitch angles. + The angular integration in (24)) and (25)) leads to where one uses the following integral ‘The second expression in (32)) is obtained by retaining he Cauchy principal value., The angular integration in \ref{eq:dpp}) ) and \ref{eq:dpep}) ) leads to where one uses the following integral The second expression in \ref{eq:I}) ) is obtained by retaining the Cauchy principal value. + Surprisingly. I5 (30)) and (31)) ie an opposite sign compared to their in he long wavelength regime (Ίσα 28. ancl 29 veal pe," Surprisingly, Eq \ref{eq:dpp2}) ) and \ref{eq:dpep2}) ) have an opposite sign compared to their counterpart in the long wavelength regime (Eq \ref{eq:dpp1} and \ref{eq:dpep1}) )." +rAlthough οί the firehose instability ane the cliscussecl iere are driven by anisotropy in the particle distribution in momentum space. there is an important dilference between he two.," Although both the firehose instability and the instability discussed here are driven by anisotropy in the particle distribution in momentum space, there is an important difference between the two." + The firehose instability is driven. by anisotropy in kinetic energv with π2., The firehose instability is driven by anisotropy in kinetic energy with $\langle u^2_\parallel\rangle>\langle u^2_\perp\rangle/2$. +Byconstrast. the streaming instability is due to the CR streaming motion uq? 40). which is also called streaming anisotropy. and he instability can develop even when the CR pressure is isotropic.," By constrast, the streaming instability is due to the CR streaming motion $\langle u_\parallel\rangle\neq0$ ), which is also called streaming anisotropy, and the instability can develop even when the CR pressure is isotropic." + Withthe specific choice of the distribution (1)). one can show that μη=ui2.," Withthe specific choice of the distribution \ref{eq:fcr}) ), one can show that $\langle u^2_\parallel\rangle=\langle +u^2_\perp\rangle/2$." + Since the current in (1)) is xy?+. it does not contribute to the average (1 if Y is proportional to an even powerol pt.," Since the current in \ref{eq:fcr}) ) is $\propto \mu^{2\sigma-1}$, it does not contribute to the average $\langle Y\rangle$ if $Y$ is proportional to an even power of $\mu$ ." + The instability can σαςto. pressure. anisotropy with perpendicular increasing., The instability can lead to pressure anisotropy with perpendicular pressure increasing. + Ln approximatlon Thisl. one has pressuredμηdic2fr and díwj)/dl(hez2/8r.," In the approximation $x\ll1$, one has $d\langle u^2_\parallel\rangle/dt\approx2/\tau$ and $d\langle u^2_\perp\rangle/dt\approx-2/3\tau$." + gives One should emphasize here that development of such anisotropy in kinetic energv ds driven bv the streaming motion of CRs., This gives One should emphasize here that development of such anisotropy in kinetic energy is driven by the streaming motion of CRs. + From (19)). one max calculate the rate of change in the streaming speed due to nonresonant dilfusion.," From \ref{eq:dEq1}) ), one may calculate the rate of change in the streaming speed due to nonresonant diffusion." + One starts with a particle distribution with streaming motion similar to (1)) but without specifying the specific form of g(p)., One starts with a particle distribution with streaming motion similar to \ref{eq:fcr}) ) but without specifying the specific form of $g(p)$. + Consider the case σ= 1. ie. the streaming component. is Xye ," Consider the case $\sigma=1$ , i.e., the streaming component is $\propto \mu$." +As in Sec 44. in the averaging. one can carry out the angular integration first.," As in Sec 4.4, in the averaging, one can carry out the angular integration first." +" This gives where £5, is given by (32)).", This gives where $I_{2n}$ is given by \ref{eq:I}) ). +" Since dei/df=ασfd. in the limit cI. one has One obtains de,4,/dl>0. contrary to what one would expect."," Since $dv_{_{\rm CR}}/dt=d\langle v_\parallel\rangle/dt$, in the limit $x\ll1$, one has One obtains $d v_{_{\rm CR}}/dt>0$ , contrary to what one would expect." + In Sec 4. ef," In Sec 4, cf." +" Eq (40)). we show that that resonant diffusion has dominant cllects on the evolution of Ch streaming motion. which ensures de,αι«0."," Eq \ref{eq:ratio}) ), we show that that resonant diffusion has dominant effects on the evolution of CR streaming motion, which ensures $d v_{_{\rm CR}}/dt<0$." + Waves generated from the nonresonant Clt-streaming instability can interact with CRs in resonance at ye=or., Waves generated from the nonresonant CR-streaming instability can interact with CRs in resonance at $\mu=x$. + Although the fraction of Clits in the resonance is small. we show that diffusion through such resonant interactions has a dominant effect on the CR streaming motion.," Although the fraction of CRs in the resonance is small, we show that diffusion through such resonant interactions has a dominant effect on the CR streaming motion." + Provided that the phase speed of the wave is «cfr. resonant dülfusion is equivalent to pitch angle scattering. in which particles change their direction of motion without eaining or losing energv.," Provided that the phase speed of the wave is $\ll c\mu$, resonant diffusion is equivalent to pitch angle scattering, in which particles change their direction of motion without gaining or losing energy." + Since the nonresonant instability isin the regine ELl. resonant scattering involves mainly CRs with pitch angles àπ ," Since the nonresonant instability isin the regime $x\ll1$, resonant scattering involves mainly CRs with pitch angles $\alpha\sim\pi/2\pm x$." +Since one deals with purely growing waves that can be regarded as a quasi-mocde with a»0. the assumption of low phase speed. «efr is valid. even for particles with piteh angles near 7/2.," Since one deals with purely growing waves that can be regarded as a quasi-mode with $\omega\to 0$, the assumption of low phase speed $\ll c\mu$ is valid even for particles with pitch angles near $\pi/2$." + The standard formalism involves writing down the diffusion equation involving pitch angles only (Melrose.1986)., The standard formalism involves writing down the diffusion equation involving pitch angles only \citep{m86}. +". Using Brg)=Porn) with. the replacements |=up and uy=4j[D5 and retaining only the pitch angle scattering part Vin (A3)). one obtains where is the density of magnetic energv at. the resonant wavenumber A,= QOjfenu|p|."," Using $F(u,\mu)=F(u_\parallel,u_\perp)$ with the replacements $u_\parallel=u\mu$ and $u_\perp=u\sqrt{1-\mu^2}$ and retaining only the pitch angle scattering part in \ref{eq:dFdt5}) ), one obtains where is the density of magnetic energy at the resonant wavenumber $k_r=\Omega/cu|\mu|$ ." + Using (1)). it can beshown that the resonant dilfusiondoes not contribute tochange in and (1).," Using \ref{eq:fcr}) ), it can beshown that the resonant diffusiondoes not contribute tochange in $\langle u^2_\parallel\rangle$ and $\langle u^2_\perp\rangle$ ." + Thus. the rate of change in parallel ancl μηperpendicular pressures is determined by nonresonant diffusion.," Thus, the rate of change in parallel and perpendicular pressures is determined by nonresonant diffusion." + The rate of change in the streaming speed is where, The rate of change in the streaming speed is where +rregion included this Fe I line with a g[-value from the Ixurucz database (log οἷ-- -1.32: from Alav et al.,region included this Fe I line with a gf-value from the Kurucz database (log gf= -1.82; from May et al. + 1974 but renormalized to an average multiplet)., 1974 but renormalized to an average multiplet). + However. the solar spectrum could not be aclequately fit with the Ixuruez ef-value as the svnthetic Mn I line at wwas Clearly too broad when compared to the observed solar spectrum.," However, the solar spectrum could not be adequately fit with the Kurucz gf-value as the synthetic Mn I line at was clearly too broad when compared to the observed solar spectrum." + Test. calculations indicated (hat the Fe I line gl-value would have to be decreased significantly in order to properly match the width of the Mn I line in the solar spectrum., Test calculations indicated that the Fe I line gf-value would have to be decreased significantly in order to properly match the width of the Mn I line in the solar spectrum. + Given (he uncertainties in the ef-value of the blending; Fe I line. the Mn I line at was rejected [rom this study.," Given the uncertainties in the gf-value of the blending Fe I line, the Mn I line at was rejected from this study." + The inclusion of hvperfine splitting (hls) in the computation of synthetic spectra is a requirement in order (o properly analvze the Mn DI: üQransitions. which are affected. by significant hyperline splitting.," The inclusion of hyperfine splitting (hfs) in the computation of synthetic spectra is a requirement in order to properly analyze the Mn I transitions, which are affected by significant hyperfine splitting." + The hfs data for both Mn I lines in this study were taken from Table 1 in Prochaska MeWilliam (2000)., The hfs data for both Mn I lines in this study were taken from Table 1 in Prochaska McWilliam (2000). + We have recomputed the hyperline structure of the 60134 MAIn I line using the magnetic dipole and electric equadrupole interaction constants for the upper level (οὐ) of multiplet 16 from Brodzinski (1937) and for the lower level (z6P*) from Iandrich et al. (, We have recomputed the hyperfine structure of the $6013$ Mn I line using the magnetic dipole and electric quadrupole interaction constants for the upper level (e6S) of multiplet $16$ from Brodzinski (1987) and for the lower level (z6P*) from Handrich et al. ( +1969).,1969). + The line equivalent widths of the 6013A llines computed with our hfs and that of Prochaska MeWilliam (2000) agree to within 1%., The line equivalent widths of the $6013$ lines computed with our hfs and that of Prochaska McWilliam (2000) agree to within $1\%$. + The e[-values of Mn I A aand aare trom Blackwell-Whitehead Bergemann (2007) and these are the same adopted in Bergemann Gehren (2007)., The gf-values of Mn I $\lambda$ and are from Blackwell-Whitehead Bergemann (2007) and these are the same adopted in Bergemann Gehren (2007). + Table 2 provides the line list used in the abundance analysis ol manganese., Table 2 provides the line list used in the abundance analysis of manganese. + Additional atomic lines from the Ixurucz line list were added along with CN lines from Davis Phillips (1963: which were kindly provided to us in digital form by A. AleWillian)., Additional atomic lines from the Kurucz line list were added along with CN lines from Davis Phillips (1963; which were kindly provided to us in digital form by A. McWilliam). + 5xntheüe spectra were computed and manganese abundances were adjusted in order to best match the observed Mn I profiles., Synthetic spectra were computed and manganese abundances were adjusted in order to best match the observed Mn I profiles. + The Unsólld approximation (Unsólld 1968) was adopted. without enhancements. for the van der Walls damping.," The Unsölld approximation (Unsölld 1968) was adopted, without enhancements, for the van der Walls damping." + The Unsólld interaction potentials are known to underestimate widths of strong metal lines in the solar spectrum (Gehren et al., The Unsölld interaction potentials are known to underestimate widths of strong metal lines in the solar spectrum (Gehren et al. + 2001a.b). and another approach to compute the line broadening due to elastic collisions with ll I atoms was developed by Anstee O'Mara (1995).," 2001a,b), and another approach to compute the line broadening due to elastic collisions with H I atoms was developed by Anstee O'Mara (1995)." + However. for the parameters of stars in our analvsis the dillerences in the profiles of Mn I Hines of multiplet 16 computed with the Unsólld or Anstee O'Mara (1995) formalisms are very small.," However, for the parameters of stars in our analysis the differences in the profiles of Mn I lines of multiplet 16 computed with the Unsölld or Anstee O'Mara (1995) formalisms are very small." + The spectral region containing the Mn I features is illustrated in Figure 1 which shows synthetic and observed spectra for the target star ROAS883., The spectral region containing the Mn I features is illustrated in Figure 1 which shows synthetic and observed spectra for the target star ROA383. + As a comparison the Mn I lines were also svnthesized in (he well-studied giant Arcturus using the spectral atlas from Hinkle et, As a comparison the Mn I lines were also synthesized in the well-studied giant Arcturus using the spectral atlas from Hinkle et +strongly with increasing redshift.,strongly with increasing redshift. + This result appears to be at odds with the increasing Iuctuations in the opacity towards higher redshift. suggesting that emission by hot gas actually contributes little to the ionization rate and that the estimates of the bremsstrahlung volume emissivity by MO4 may have been too large.," This result appears to be at odds with the increasing fluctuations in the opacity towards higher redshift, suggesting that emission by hot gas actually contributes little to the ionization rate and that the estimates of the bremsstrahlung volume emissivity by M04 may have been too large." + This is perhaps also not too surprising as the assumed density profile of the emitting gas in dark matter haloes is very uncertain., This is perhaps also not too surprising as the assumed density profile of the emitting gas in dark matter haloes is very uncertain. + More quantitative statements will require detailed modelling of the UVB using radiative transfer which is bevond the scope of this paper., More quantitative statements will require detailed modelling of the UVB using radiative transfer which is beyond the scope of this paper. + As an additional check on our assumptions for the and elective. optical depth. we plot as a dashed line in fisure 4. the median 5 obtained. from the artificial spectra with a uniform UVB (second. panel).," As an additional check on our assumptions for the and effective optical depth, we plot as a dashed line in figure \ref{fig:eta} the median $\eta$ obtained from the artificial spectra with a uniform UVB (second panel)." + The same Dine is repeated in the panels for the artificial spectra constructed using a [luctuating UV and the observations., The same line is repeated in the panels for the artificial spectra constructed using a fluctuating UVB and the observations. + Although the scatter in the column Ddensity ratio is much smaller for the artificial spectra with the uniform UWB. the median. value for η is consistent with Chat observed.," Although the scatter in the column density ratio is much smaller for the artificial spectra with the uniform UVB, the median value for $\eta$ is consistent with that observed." + This is encouraging. as it suggests that our fit for the elfective optical depth at 2«2«3 provides a reasonable representation of the true forest opacity.," This is encouraging, as it suggests that our fit for the effective optical depth at $2$ 20 and EW of the and lines larger than 20 856 spectra). + All spectra used for the training and the application of the amethod are derived from the Tth Data Release (DR?) of SDSS., All spectra used for the training and the application of the method are derived from the 7th Data Release (DR7) of SDSS. + Pixels with anv oof the flags: FFULLREJECT.SP.NMASRK.DBDRIGIFTSKY. SP.NMASK.NNODATA. NNOSKY or pixels that correspond tozero noise were treated as masked.," Pixels with any of the flags: FULLREJECT,BRIGHTSKY, NODATA, NOSKY or pixels that correspond tozero noise were treated as masked." + All the spectra aud their noise were moved to the rest-frame (assuimiug, All the spectra and their noise were moved to the rest-frame (assuming +that of the source environment.,that of the source environment. +" The overall synchrotron signal would then be amplified by a factor A//, where A denotes the relevant energy loss length, 4~100 Mpc for pion production of 10?? eV protons, A~1 (ρε for pair production of 10? eV protons and /;~40 Mpc is the typical separation between two filaments."," The overall synchrotron signal would then be amplified by a factor $\lambda/l_{\rm f}$, where $\lambda$ denotes the relevant energy loss length, $\lambda\sim100\,$ Mpc for pion production of $10^{20}\,$ eV protons, $\lambda\sim1\,$ Gpc for pair production of $10^{19}\,$ eV protons and $l_{\rm f}\sim 40\,$ Mpc is the typical separation between two filaments." +" Overall, one might expect an amplification as large as an order of magnitude for the contribution to the flux due to pair production, for sources located at several hundreds of Mpc, and a factor of a few for sources located at 100 Mpc; and, correspondingly, an amplification factor ~2—3 for the contribution to the flux due to pion production."," Overall, one might expect an amplification as large as an order of magnitude for the contribution to the flux due to pair production, for sources located at several hundreds of Mpc, and a factor of a few for sources located at $100\,$ Mpc; and, correspondingly, an amplification factor $\sim +2-3$ for the contribution to the flux due to pion production." +" Since the pair production channel contributes ~10% of the total flux at E,~10—100 GeV for a pure proton composition, the amplification factor should remain limited to a factor of a few, unless the interaction length with magnetized regions is substantially smaller than the above (expected) /;=40 Mpc."," Since the pair production channel contributes $\sim10$ of the total flux at $E_\gamma\sim 10-100~$ GeV for a pure proton composition, the amplification factor should remain limited to a factor of a few, unless the interaction length with magnetized regions is substantially smaller than the above (expected) $l_{\rm f}=40\,$ Mpc." + Let us briefly discuss the gamma ray signal expected from Compton cascades of ultra-high energy photons and pairs injected in the intergalactic medium., Let us briefly discuss the gamma ray signal expected from Compton cascades of ultra-high energy photons and pairs injected in the intergalactic medium. +" The physics of these cascades has been discussed in detail in ?,, ?,, ?,, 2, ? and ?.."," The physics of these cascades has been discussed in detail in \cite{WTW72}, \cite{Protheroe86}, \cite{PS93}, \cite{ACV94}, \cite{Ferrigno04} and \cite{Gabici07}." + The angular extent and time distribution of GeV-TeV gamma- resulting from inverse Compton cascades seeded by ultra-high energy cosmic rays produced by gamma-ray bursts have also been discussed by ?.., The angular extent and time distribution of GeV-TeV gamma-rays resulting from inverse Compton cascades seeded by ultra-high energy cosmic rays produced by gamma-ray bursts have also been discussed by \cite{1996ApJ...464L..75W}. + Inverse Compton cascades in the steady state regime have been considered in the study of ? (for a source located in a cluster of galaxies) but dismissed in the study of ? because of the dilution of the emitted flux through the large deflection of the pairs in the low energy range of the cascade., Inverse Compton cascades in the steady state regime have been considered in the study of \cite{ASM06} (for a source located in a cluster of galaxies) but dismissed in the study of \cite{GA05} because of the dilution of the emitted flux through the large deflection of the pairs in the low energy range of the cascade. +" Indeed, the effective inverse Compton cooling length of electrons of energy E,x 100TeV can be written as xe,~3.5kpc(E,/100TeV)""! and on this distance scale, the deflection imparted by a magnetic field of coherence length Ap>>Xey reads"," Indeed, the effective inverse Compton cooling length of electrons of energy $E_e\lesssim\,100\,$ TeV can be written as $x_{e\gamma}\,\simeq\, 3.5\,{\rm kpc}\,(E_e/100\,{\rm TeV})^{-1}$ and on this distance scale, the deflection imparted by a magnetic field of coherence length $\lambda_B\,\gg\,x_{e\gamma}$ reads" +consistent with purely passive evolution.,consistent with purely passive evolution. + However. it should also be pointed out that these results do not require that all 3C radio galaxies are formed in a monolithic collapse at high redshift. simply that the proto-galactic components. which eventually form the host galaxies are formed reasonably co-evallvs. and that the vast majority. of merger activity be completed at. z1l.," However, it should also be pointed out that these results do not require that all 3C radio galaxies are formed in a monolithic collapse at high redshift, simply that the proto-galactic components which eventually form the host galaxies are formed reasonably co-evally, and that the vast majority of merger activity be completed at $z>1$." + Furthermore. neither are the results presented in this section inconsistent with what would. be expected under the Ας interpretation proposed by Best et al. (," Furthermore, neither are the results presented in this section inconsistent with what would be expected under the $K-z$ interpretation proposed by Best et al. (" +1998).,1998). + AO satisfactory discrimination between {πο two interpretations of the Avz relation will rely on a consistent evaluation of the relative richness of the respective cluster environments at [ow and high. redshift., A satisfactory discrimination between the two interpretations of the $K-z$ relation will rely on a consistent evaluation of the relative richness of the respective cluster environments at low and high redshift. + Unfortunately. much of the work which has previouslv been done on the cluster environments. of radio galaxies. particularly ab low redshift. has relied. on statistical determinations from sinele-filter imaging which are known to be subject to large uncertainties (eg.," Unfortunately, much of the work which has previously been done on the cluster environments of radio galaxies, particularly at low redshift, has relied on statistical determinations from single-filter imaging which are known to be subject to large uncertainties (eg." + Barr ct al., Barr et al. + 2003)., 2003). + However. upon completion of our INP Wide Field. Camera follow-up observations of the ZP5 sample. together with our existing observations of radio-galaxy samples at z20.2 and z2OLS. we will be able to consistently investigate the evolution in the cluster environments of powerful radio galaxies. by using threc-colour imaging to successfully separate true. eluster members from foreground. and. background. contaminants (Jarvis et al:," However, upon completion of our INT Wide Field Camera follow-up observations of the ZP5 sample, together with our existing observations of radio-galaxy samples at $z\simeq0.2$ and $z\simeq0.8$, we will be able to consistently investigate the evolution in the cluster environments of powerful radio galaxies, by using three-colour imaging to successfully separate true cluster members from foreground and background contaminants (Jarvis et al.;" + MeLbure et al.," McLure et al.," + in prep), in prep). + The results. regarding the scalelengths. ancl integrated luminosities of the ZP5 sample presented in. Section 5 sugeest that the host galaxies of the ZP5 sample are directly comparable with brightest cluster galaxies (BC'Gs)., The results regarding the scalelengths and integrated luminosities of the ZP5 sample presented in Section 5 suggest that the host galaxies of the ZP5 sample are directly comparable with brightest cluster galaxies (BCGs). + This is in good agreement with the results of Dunlop et al. (, This is in good agreement with the results of Dunlop et al. ( +2003) and AleLure Dunlop (2001b) who concluded. that the hosts of powerful radio-loud AGN at z20.2 were cirectly comparable to the central BCGs of Abell class 0 clusters.,2003) and McLure Dunlop (2001b) who concluded that the hosts of powerful radio-loud AGN at $z\simeq0.2$ were directly comparable to the central BCGs of Abell class 0 clusters. + La this section we explore this issue further via comparison with the findings of the LIST imaging study of z20.5 BOCs by Nelson et al. (, In this section we explore this issue further via comparison with the findings of the HST imaging study of $z\simeq0.5$ BCGs by Nelson et al. ( +2002). and the ground-based 2 band surface,"2002), and the ground-based $R-$ band surface" +insufficient.,fficient. +Fig.,Fig. + | shows mass histograms al 110 Myr for coagulation calculations without grain accretion using ry = 1 km and the strong fragmentation parameters (fy)., \ref{fig:sd1} shows mass histograms at 1–10 Myr for coagulation calculations without grain accretion using $r_0$ = 1 km and the strong fragmentation parameters $f_S$ ). + After the first oligarchs with Af~ 0.01 [form at ~ 0.1 Myr. Che collisional cascade starts to remove leftover planetesimals from the erid.," After the first oligarchs with $M \sim$ 0.01 form at $\sim$ 0.1 Myr, the collisional cascade starts to remove leftover planetesimals from the grid." +" Ixdependent of Q,. the cascade removes ~ of the initial mass of the erid in ~ 4 pcQET Myr."," Independent of $Q_b$, the cascade removes $\sim$ of the initial mass of the grid in $\sim$ 4 $x_m^{-1.25}$ Myr." +" As the cascade proceeds. growth of the largest oligarchs stalls at a maximum mass Alona,& 0.1 or,"," As the cascade proceeds, growth of the largest oligarchs stalls at a maximum mass $M_{o,max} \approx$ 0.1 $x_m$." + These resulis depend weakly on ry., These results depend weakly on $r_0$. + The time to produce the first oligarch with +~ 1000 km increases with iy. πμ0.1rb?(ry10km)!? Mvr.," The time to produce the first oligarch with $r \sim$ 1000 km increases with $r_0$, $t_{1000} \sim 0.1~x_m^{-1.25}~(r_0/{\rm 10~km})^{1/2}$ Myr." + Caleulations with larger ro tend to produce larger oligarchs at 10 Myr: Miu55 1 ((2 )) for 7j = 10 km (100 km).," Calculations with larger $r_0$ tend to produce larger oligarchs at 10 Myr: $M_{o,max} \approx$ 1 (2 ) for $r_0$ = 10 km (100 km)." +" In ~ 50 caleulations. none produce cores with M,2 1M oon timescales of < 10 Myr."," In $\sim$ 50 calculations, none produce cores with $M_{o,max} \gtrsim$ 1 on timescales of $\lesssim$ 10 Myr." + For ryZi 100 km. our results depend on /;.," For $r_0 \lesssim$ 100 km, our results depend on $f_i$." +" In models with ry = 1 km and 10 km. the fy fragmentation parameters vield oligarchs with smaller maxinun masses. M,£z 0.6 ML..."," In models with $r_0$ = 1 km and 10 km, the $f_W$ fragmentation parameters yield oligarchs with smaller maximum masses, $M_{o,max} \approx$ 0.3--0.6 ." + Because leftover planetesimals with r 110 km fragment more easily. the cascade begins (and growth stalls) at smaller collision velocities when oligarchs are less massive (IXenvonοἱal... 2003).," Because leftover planetesimals with $r \sim$ 1–10 km fragment more easily, the cascade begins (and growth stalls) at smaller collision velocities when oligarchs are less massive \citep{kbod08}. ." +. Calculations with grain accretion produce cores rapidly., Calculations with grain accretion produce cores rapidly. + Fig., Fig. + 2. shows results at Myr for ealeulations with ry = 1 km and the [ς fragmentation parameters., \ref{fig:sd2} shows results at 1--10 Myr for calculations with $r_0$ = 1 km and the $f_S$ fragmentation parameters. +" As the first oligarchs reach masses of ~ 0.01 aad 0.1 Myr. the cascade generates many small collision fragments with r~ 1 mm to 1 m. These fragments rapidly settle to the disk midplane and grow to sizes of 0.1.1 τα, When the cascade has shattered ~ of the leftover planetesimals. oligarchs begin a second phase of runaway growth byrapidly accreting small particles in the midplane."," As the first oligarchs reach masses of $\sim$ 0.01 at 0.1 Myr, the cascade generates many small collision fragments with $r \sim$ 1 mm to 1 m. These fragments rapidly settle to the disk midplane and grow to sizes of 0.1–1 m. When the cascade has shattered $\sim$ of the leftover planetesimals, oligarchs begin a second phase of runaway growth byrapidly accreting small particles in the midplane." +" For caleulations with cy, d5. it takes e 1:2 0,2175ui Myr to produce at least one core with MOn: Z15M"," For calculations with $x_m$ = 1–5, it takes $\sim$ 1–2 $x_m^{-1.25}$ Myr to produce at least one core with $M_o \gtrsim$ 1–5." + .Thus cores form before (he gas clissipates.," Thus, cores form before the gas dissipates." + These results depend on ry., These results depend on $r_0$. + For ry = 10 km. fragmentation produces small erains 23 limes more slowly than calculations with ro = 1 km.," For $r_0$ = 10 km, fragmentation produces small grains 2–3 times more slowly than calculations with $r_0$ = 1 km." +" These models form cores more slowly. . in510 7,7;» Myr insteadn ofB 1:2i 7H,U?"" Myr."," These models form cores more slowly, in 5–10 $x_m^{-1.25}$ Myr instead of 1–2 $x_m^{-1.25}$ Myr." + For models with ry = 100 km. fragmentation vields a negligible mass in small grains.," For models with $r_0$ = 100 km, fragmentation yields a negligible mass in small grains." + Thus. cores never form in < 1020 Myr.," Thus, cores never form in $\lesssim$ 10–20 Myr." + The timescalesto form cores also depend on fj., The timescalesto form cores also depend on $f_i$ . + Calculations with the fij parameters form cores to faster than models with the fy parameters., Calculations with the $f_W$ parameters form cores to faster than models with the $f_S$ parameters. +and soft/hard colors are stummarized in Table 1.. their locations on the harc-LID are indicated in Figure 1..,"and soft/hard colors are summarized in Table \ref{tab:list}, their locations on the hard-HID are indicated in Figure \ref{fig:ccd_1608-522}." + These spectra and (heir ratios to their average spectrum are shown in Figure 2.., These spectra and their ratios to their average spectrum are shown in Figure \ref{fig:spec_1608_upper1}. . + In Figure 2.. By comparing them. it is clear (hat ihe intensitv in the hard οποιον band changes significantly. while that in the soft band is kept constant.," In Figure \ref{fig:spec_1608_upper1}, By comparing them, it is clear that the intensity in the hard energy band changes significantly, while that in the soft band is kept constant." + Moreover. in energies above ~ 15 keV. their ratios saturates as a function ol energv.," Moreover, in energies above $\sim$ 15 keV, their ratios saturates as a function of energy." + As originally proposed by Mitsudaetal.(1984)... these results can be explained and the normalization (but not the shape) of the changes between (he two spectra.," As originally proposed by \citet{mitsuda_z}, these results can be explained and the normalization (but not the shape) of the changes between the two spectra." + Indeed. the difference spectrum between them. shown in Figure 3. as Spec 1. is represented successfully by aBB model of which the temperature is FT~ 2.5 keV. slight changes inthe assumed stable soft component and/or those in /Tpp.," Indeed, the difference spectrum between them, shown in Figure \ref{fig:spec_1608_upper2} as Spec 1, is represented successfully by aBB model of which the temperature is $kT_{\rm BB} \sim$ 2.5 keV. slight changes inthe assumed stable soft component and/or those in $kT_{\rm BB}$." + From the above results. we consider (hat the harder part of the spectrum is carried bv a chard component which is approximated bv a AZpp~ 2.5 keV DD.," From the above results, we consider that the harder part of the spectrum is carried by a “hard component” which is approximated by a $kT_{\rm BB} \sim$ 2.5 keV BB." + Us variation causes significant. changes in the hard. color. but. does not affect the intensity verv much. because the total source counts are dominated by softer photons.," Its variation causes significant changes in the hard color, but does not affect the intensity very much because the total source counts are dominated by softer photons." + This explains (he formation of the vertical stripes in the hard IUD of Figure 1.., This explains the formation of the vertical stripes in the hard HID of Figure \ref{fig:ccd_1608-522}. + This hard component is most naturally attributed to emission from the NS surface. because the measured temperature agrees with (he local Eddington temperature of a 1.4 AL. NS. or ~2.0 keV. Contrary (o (he above case. the other two spectra.other. differ mainly in the soft energy band. with the hard energy end kept almost constant.," This hard component is most naturally attributed to optically-thick emission from the NS surface, because the measured temperature agrees with the local Eddington temperature of a 1.4 $M_{\odot}$ NS, or $\sim 2.0$ keV. Contrary to the above case, the other two spectra, differ mainly in the soft energy band, with the hard energy end kept almost constant." + This suggests Chat the source variation in this case is carried by a soft spectral component which is presumably identified as the stable component suggested by Spec A and Spee D. To constrain ils spectral shape. (he dillerence spectrum Spec 2) between Spec C and spec D. and show the results in Figure 4..," This suggests that the source variation in this case is carried by a soft spectral component which is presumably identified as the stable component suggested by Spec A and Spec B. To constrain its spectral shape, the difference spectrum Spec 2) between Spec C and Spec D, and show the results in Figure \ref{fig:spec_1608_upper3}. ." +" can be reproduced by either an MCD model(Fi, 1.7 keV)or a BB", can be reproduced by either an MCD model$kT_{\rm in} \sim$ 1.7 keV)or a BB +The relativistic linear Schróddiuger equation has been discussed at the carly vears of quantum mechanics but was disiissed promptly by the Klein-Cordou and the Dirac equatious.,The relativistic linear Schröddinger equation has been discussed at the early years of quantum mechanics but was dismissed promptly by the Klein-Gordon and the Dirac equations. + Receuth. relativistic versions of the Scladdeinger equation have been cousidered iu the study of relativistic quark-autiquark bound states [1]. and gravitational collapse of a boson star |2]..," Recently, relativistic versions of the Schröddinger equation have been considered in the study of relativistic quark-antiquark bound states \cite{BS}, and gravitational collapse of a boson star \cite{FL}." + A nonlinear version of the model has appeared in the form of seni-relativistie Wartrec-Fock equation [3).., A nonlinear version of the model has appeared in the form of semi-relativistic Hartree-Fock equation \cite{CO}. + But none ofthose models is kuown to be integrable., But none of those models is known to be integrable. + In the preset paper we construct an integrable relativistic nonlinear Schróddiuger equation. preserviug iutegrabilitv at auv order of L/e approximation.," In the present paper we construct an integrable relativistic nonlinear Schröddinger equation, preserving integrability at any order of $1/c$ approximation." + We start from the Schroddinger equation iu d. | 1 dimensions for a free particle with classical dispersion of the generalanalytic form E(p)., We start from the Schröddinger equation in 1 + 1 dimensions for a free particle with classical dispersion of the generalanalytic form $E = E(p)$ . + Hoyo Pi=a.} aud Py=hz.) are operators of. tho timeH aud space translations respectively. commuting with the Schróddiuger operator $ (GP [PyS|=0. 9= 0.1.," Here $P_0 = i\hbar \frac{\partial}{\partial t}$ and $P_1 = -i\hbar \frac{\partial}{\partial x}$ are operators of the time and space translations respectively, commuting with the Schröddinger operator $S = i\hbar \frac{\partial }{\partial t} - {\cal H}(P_1)$ : $[P_\mu, S] = 0$, $\mu = 0,1$ ." + The general boost operator. defined as FH). is also commuting with S$. |A.5|= 0.," The general boost operator, defined as $K = x - t {\cal H}'(P_1)$ , is also commuting with $S$, $[K,S] = 0$ ." + Commuting it with spaceand tine translations we have the algebra of svaunietry. operators, Commuting it with spaceand time translations we have the algebra of symmetry operators +Rees 1994. Hui €nedin 1997. Steinmetz Haehnelt 1997).,"Rees 1994, Hui Gnedin 1997, Steinmetz Haehnelt 1997)." + The dominant heat input is due to ionization of hydrogen and helium while the main cooling processes are C'ompton cooling at z5 and adiabatic cooling at lower redsult., The dominant heat input is due to ionization of hydrogen and helium while the main cooling processes are Compton cooling at $z\ga 5$ and adiabatic cooling at lower redshift. +" At rejionization the gas acquires an initial temperature where vy and ex are ionization energies and ionization absorption cross sections and 4, is the specific intensity. of the lonizine backeround.", At reionization the gas acquires an initial temperature where $\nu_{\rm X}$ and $\sigma_{\rm X}$ are ionization energies and ionization absorption cross sections and $I_{\nu}$ is the specific intensity of the ionizing background. + Afterwards the eas cools acliabatically within a Llubble time to the (recshilt dependent) equilibrium. temperature where. photo-heating balances adiabatic cooling., Afterwards the gas cools adiabatically within a Hubble time to the (redshift dependent) equilibrium temperature where photo-heating balances adiabatic cooling. + “Phe temperature. of the gas therefore depends on the spectrum of the ionizing source and on the redshift when reionization occurs., The temperature of the gas therefore depends on the spectrum of the ionizing source and on the redshift when reionization occurs. + We have investigated four different models to cover the uncertainty concerning the respective role of quasars and stars in the reionization of the Universe: Figures la and 1b show the evolution of the UV background for the four scenarios at the and ionization edges respectively., We have investigated four different models to cover the uncertainty concerning the respective role of quasars and stars in the reionization of the Universe: Figures 1a and 1b show the evolution of the UV background for the four scenarios at the and ionization edges respectively. +" At redshift three the üonizing Πας is 1 to 3 107""ergem7sHz+. slightly ower than estimates from the proximity effect but consistent with the mean Dux decrement in QSO absorption spectra (Boehold. 1994: Ciallongo et al."," At redshift three the ionizing flux is 1 to 3 $\times 10^{-22}\erg\cm^{-2}\s^{-1}\Hz^{-1}$, slightly lower than estimates from the proximity effect but consistent with the mean flux decrement in QSO absorption spectra (Bechthold 1994; Giallongo et al." + 1996: Cooke. Espey Carswell 997: Rauch ct al.," 1996; Cooke, Espey Carswell 1997; Rauch et al." + 1997)., 1997). + Model A was chosen wlardt Aladau to represent the UV. background. due ο οserved quasars., Model A was chosen by Haardt Madau to represent the UV background due to observed quasars. +" Model D. mimics the existence of an as vet undetected population of quasar at redshifts bevond ive,", Model B mimics the existence of an as yet undetected population of quasar at redshifts beyond five. + Models € and D address the possibility that the Llaaret XAacdau model overestimates the UV background. due to quasars a redshifts. larger than three., Models C and D address the possibility that the Haardt Madau model overestimates the UV background due to quasars at redshifts larger than three. + In the latter case he UV background would have to be dominated. by a stellar contribution at these redshifts., In the latter case the UV background would have to be dominated by a stellar contribution at these redshifts. + Figure le shows the emperature evolution of the LGAL for the mean density ata eiven redshift., Figure 1c shows the temperature evolution of the IGM for the mean density at a given redshift. + Phere are striking differences in the thermal ustory between the models., There are striking differences in the thermal history between the models. + In models A and B hydrogen and helium are reionized. almost simultaneously with a rather hard AGN-like spectrum., In models A and B hydrogen and helium are reionized almost simultaneously with a rather hard AGN-like spectrum. + This leads to an initial emperature of about 2«1011., This leads to an initial temperature of about $2\times 10^4\K$. + Thereafter the temperature approaches the redshift dependent equilibrium temperature., Thereafter the temperature approaches the redshift dependent equilibrium temperature. + In scenario Co and D the stellar component. of the UV xickeround is too soft to reionize helium at the same time as ivdrogen., In scenario C and D the stellar component of the UV background is too soft to reionize helium at the same time as hydrogen. + This results in an initial temperature of 710EK immediately. aller reionization significantly smaller. than in model A and DB. In. Model € the late reionization of relium due to the QO component of the UV. background eads to a corresponding jump in the temperature while in model D. Helium reionization occurs gradually before he QSO component of the UV. background. dominates., This results in an initial temperature of $7\times 10^{3} \K$ immediately after reionization – significantly smaller than in model A and B. In Model C the late reionization of helium due to the QSO component of the UV background leads to a corresponding jump in the temperature while in model D Helium reionization occurs gradually before the QSO component of the UV background dominates. + In he observationally relevant redshift range between five and hree the dilference in temperature between the different models is as large as a [factor 3 to 4., In the observationally relevant redshift range between five and three the difference in temperature between the different models is as large as a factor 3 to 4. +of 107.AL..,of $10^{8}$. +". The average line properties for Sevfert 1 ealaxies suggest that around SO per cent of the line emission arises within 10072, of the nucleus.", The average line properties for Seyfert 1 galaxies suggest that around $80$ per cent of the line emission arises within $\sim 100\ R_{\rm g}$ of the nucleus. + The fact that the We line is consistent with a linear change with Hux suggests that it originates predominantIv from one region., The fact that the $\alpha$ line is consistent with a linear change with flux suggests that it originates predominantly from one region. + Indeed. the clear change in the core is stronely indicative that this Εαν comes from close to the central engine.," Indeed, the clear change in the core is strongly indicative that this flux comes from close to the central engine." + An alternative hypothesis. that the broad component arises from an aceretion disk but that the line core is produced in a molecular torus. located far from the nucleus (Chisellini. Haardt Matt 1994: Ixrolik. Macau Zvcki 1994) is stronely disfavored.," An alternative hypothesis, that the broad component arises from an accretion disk but that the line core is produced in a molecular torus, located far from the nucleus (Ghisellini, Haardt Matt 1994; Krolik, Madau Zycki 1994) is strongly disfavored." + We conclude that the bulk of the iron Ka emission in NGC 3516. and most likely in the majority of Sevlert 1: galaxies. arises in an accretion disk extremely close to the central black hole.," We conclude that the bulk of the iron $\alpha$ emission in NGC 3516, and most likely in the majority of Seyfert 1 galaxies, arises in an accretion disk extremely close to the central black hole." + lt is interesting to compare our results with those presented for ALCG-6-30-15 ον Bwasawa et al. (, It is interesting to compare our results with those presented for MCG-6-30-15 by Iwasawa et al. ( +1996).,1996). + In that source. while the narrow core of the line was found to be well correlated. with the continuum variations. the broad. wing was anti correlated. at least on medium time scales (1 clay).," In that source, while the narrow core of the line was found to be well correlated with the continuum variations, the broad wing was anti correlated, at least on medium time scales $\sim$ 1 day)." + This is somewhat contrary to the behaviour expected. in simple accretion disk models. ancl may require the invocation of relativistic ellects within the X-ray source itself and/or changes in the pattern of X-ray illumination. as well as the lisht bending ancl gravitational ellects characteristic of a Ixerr black hole.," This is somewhat contrary to the behaviour expected in simple accretion disk models, and may require the invocation of relativistic effects within the X-ray source itself and/or changes in the pattern of X-ray illumination, as well as the light bending and gravitational effects characteristic of a Kerr black hole." + On the other hand NGC 7314 (Yaqoob et al., On the other hand NGC 7314 (Yaqoob et al. + 1996) shows more variability in the wing than the core. as predicted.," 1996) shows more variability in the wing than the core, as predicted." + This may also be true for MCC-6-30-15 on the shortest time scales (lwasawa et al., This may also be true for MCG-6-30-15 on the shortest time scales (Iwasawa et al. + 1996)., 1996). + Our results show no apparent change in profile. which is to be expected over 1e longer observation baseline (1 vr). where the total Lux of 1e line should track the continuum.," Our results show no apparent change in profile, which is to be expected over the longer observation baseline (1 yr), where the total flux of the line should track the continuum." + The stability of the line profile over this time period suggests that there are no gross 'hanges in the ecometry of the svstem (accretion disk and X-rav source)., The stability of the line profile over this time period suggests that there are no gross changes in the geometry of the system (accretion disk and X-ray source). + Further progress requires better-sampled. data with high signal-to-noise-ratio. but the results so far suggest ja. even with current instrumentation. such observations would be most rewarding.," Further progress requires better-sampled data with high signal-to-noise-ratio, but the results so far suggest that, even with current instrumentation, such observations would be most rewarding." + We thank the (team for their operation of the satellite. and the ος at NASA/GSEC. for. helpful discussions.," We thank the team for their operation of the satellite, and the GOF at NASA/GSFC for helpful discussions." + We acknowledge the financial support of the National Research Council (INN) ancl Universities Space Research Association (AIG.PIT).," We acknowledge the financial support of the National Research Council (KN) and Universities Space Research Association (IMG,TJT)." + This research has mace use of data obtained through the LEASARC on-line service. provided hy NASA/GSEC.," This research has made use of data obtained through the HEASARC on-line service, provided by NASA/GSFC." +" Fabian. A.C... Nandra. Ix... BRevnolds. ���.S... Brandt. N.N. Otani. C... Tanaka. Y... 1995.MNILAS.. 277. L11 Fabian. ALC.. Rees. MJ... Stella. Le. White. NE. 1989.AINILAS.. 238. 729 George. LAL. Fabian. A.C... 1991.NINILAS.. 249. 352 George. LAL.al... 1996. in preparation CGhisellini. αν, Haardt. be. Matt. €... 1994.MNILAS.. 267. 145 Iywasawa. Ix...al... 1996. AINRAS.. in press Ixolman. M.. Halpern. ος Martin. €. Awaki. LH. IXovama. ls 1993. ApJ. 403. 592 Ixriss. GALal... 1996. XpJ.. in press Ixrolik. J.LL. Madau. P.. Zeki. PT... 1994.XpJ.. 420. L57 Matt. C. Perola. GC. Piro. L.. 1991. AA. 245. 63 Alushotzky. οι. Fabian. A.C... bwasawa. Ix... Matsuoka. M.. ανα. Ix.. Tanaka. Y... 1995.MNILAS.. 272. L9 Nanelra. We. Pounds. Ix... 1994.MNILAS.. 268. 405 Nandra. Ix... George. LAL. Mushotzky. ILE... Furner. T.J.. Yaqoob. T... 1996a.XpJ.. in press Nandra. Ix... George. LAL. Mushotzky. ILE... Furner. T.J.. Yaqoob. T... 1996b.ApJ.. in press (NOG) ‘Tanaka. Y..al... 1995. Nat.. 375. 659 ‘Tanaka. Y.. Inoue. LE. Holt. S.S... 1994. PASJ. 46. L37 Warwick. 1.8... Yaqoob. T.. Pounds. Ix.X... Matsuoka. M. Yamauchi. M... 1989. PASJ. 41. 721"," Fabian, A.C., Nandra, K., Reynolds, C.S., Brandt, W.N. Otani, C., Tanaka, Y., 1995, 277, L11 Fabian, A.C., Rees, M.J., Stella, L., White, N.E., 1989, 238, 729 George, I.M., Fabian, A.C., 1991, 249, 352 George, I.M., 1996, in preparation Ghisellini, G., Haardt, F., Matt, G., 1994, 267, 743 Iwasawa, K., 1996, in press Kolman, M., Halpern, J.P., Martin, C., Awaki, H., Koyama, K., 1993, ApJ, 403, 592 Kriss, G.A., 1996, in press Krolik, J.H., Madau, P., Zycki, P.T., 1994, 420, L57 Matt, G., Perola, G.C., Piro, L., 1991, A, 245, 63 Mushotzky, R.F., Fabian, A.C., Iwasawa, K., Matsuoka, M., Nandra, K., Tanaka, Y., 1995, 272, L9 Nandra, K., Pounds, K.A., 1994, 268, 405 Nandra, K., George, I.M., Mushotzky, R.F., Turner, T.J., Yaqoob, T., 1996a, in press Nandra, K., George, I.M., Mushotzky, R.F., Turner, T.J., Yaqoob, T., 1996b, in press (N96) Tanaka, Y., 1995, 375, 659 Tanaka, Y., Inoue, H., Holt, S.S., 1994, PASJ, 46, L37 Warwick, R.S., Yaqoob, T., Pounds, K.A., Matsuoka, M., Yamauchi, M., 1989, PASJ, 41, 721" +"Finally, we consider a more speculative point.","Finally, we consider a more speculative point." +" From the point of view of constraining fundamental cosmological parameters, such as the tilt and running of the inflationary power spectrum, the optical depth to last scattering is a nuisance parameter."," From the point of view of constraining fundamental cosmological parameters, such as the tilt and running of the inflationary power spectrum, the optical depth to last scattering is a nuisance parameter." +" If could be independently measured to high accuracy, so that it was in effect a known quantity, then it could be removed from the uncertainty in CMB parameter estimates."," If could be independently measured to high accuracy, so that it was in effect a known quantity, then it could be removed from the uncertainty in CMB parameter estimates." +" At least in principle, 21 cm experiments, by placing direct constraints on x; in many redshift bins, could constrain directly."," At least in principle, 21 cm experiments, by placing direct constraints on $x_i$ in many redshift bins, could constrain directly." + Whether this is possible in practice will be determined by how much of the ionization history where x;>0 is accessible to 21 cm observations., Whether this is possible in practice will be determined by how much of the ionization history where $x_i>0$ is accessible to 21 cm observations. + Given that CMB constraints will approach στον0.005 most of the ionization history must be mapped for 21 cm constraints to be competitive., Given that CMB constraints will approach $\sigma_{\tau_{\rm CMB}}\approx0.005$ most of the ionization history must be mapped for 21 cm constraints to be competitive. +" Figure 15 shows the errors on achieved within our modeling by adding two 21 cm measurements of x;(z=8)>0.8 and z;(z=9)0.5+0.05, similar to what might be achieved by first generation experiments, to the data."," Figure \ref{fig:taudist} shows the errors on achieved within our modeling by adding two 21 cm measurements of $x_i(z=8)>0.8$ and $x_i(z=9)=0.5\pm0.05$, similar to what might be achieved by first generation experiments, to the data." +" Clearly, the distributions are not competitive with the WMAP5 constraint unless the source evolution is quite constrained."," Clearly, the distributions are not competitive with the WMAP5 constraint unless the source evolution is quite constrained." + Nonetheless constraints on from the directly measured ionization history may provide a useful consistency check with the results from CMB experiments., Nonetheless constraints on from the directly measured ionization history may provide a useful consistency check with the results from CMB experiments. +" In this paper, we have developed a framework for combining existing constraints on reionization from CMB and observations, and used them to place bounds on the reionization history."," In this paper, we have developed a framework for combining existing constraints on reionization from CMB and observations, and used them to place bounds on the reionization history." +" Modeling of reionization is very uncertain, both in terms of the sources of radiation (their evolution, spectrum, clustering, etc.),"," Modeling of reionization is very uncertain, both in terms of the sources of radiation (their evolution, spectrum, clustering, etc.)," + and in terms of their interaction with the neutral IGM., and in terms of their interaction with the neutral IGM. +" Rather than employ a semi-analytic model, with all the necessary assumptions2005),, we have therefore chosen a more general approach which utilises arbitrary forms for the evolution of ionizing emissivity."," Rather than employ a semi-analytic model, with all the necessary assumptions, we have therefore chosen a more general approach which utilises arbitrary forms for the evolution of ionizing emissivity." + This approach avoids theoretical prejudice regarding the model for reionization at the greatest possible level., This approach avoids theoretical prejudice regarding the model for reionization at the greatest possible level. + The framework that we have used here can easily be extended to incorporate more general parametrizations of the sources as improved data makes that worthwhile., The framework that we have used here can easily be extended to incorporate more general parametrizations of the sources as improved data makes that worthwhile. + The resulting analytic model for reionization and the is described in Appendix A.., The resulting analytic model for reionization and the is described in Appendix \ref{sec:modeling}. + This approach remains model dependent., This approach remains model dependent. + However the level of dependance has been quantified by considering two different parametrizations for the sources., However the level of dependance has been quantified by considering two different parametrizations for the sources. +" These give consistent predictions on z;(z), albeit with differing levels of precision."," These give consistent predictions on $x_i(z)$, albeit with differing levels of precision." +" Nevertheless, we are able to draw some relatively robust conclusions from our analysis."," Nevertheless, we are able to draw some relatively robust conclusions from our analysis." + The main conclusion is that current observations suggest reionization was largely complete by z—8 with the Universe likely to have been half ionized between z—910., The main conclusion is that current observations suggest reionization was largely complete by $z=8$ with the Universe likely to have been half ionized between $z=9-10$. + This result has important implications for upcoming 21 cm experiments., This result has important implications for upcoming 21 cm experiments. + In particular we have shown that the signal-to-noise ratio for these experiments is most likely to be at its maximum in the range z=9—10., In particular we have shown that the signal-to-noise ratio for these experiments is most likely to be at its maximum in the range $z=9-10$. +" Thus current observables of reionization can be used to guide the first attempts at 21cm observations, which will be very expensive in terms of observing time, and cover only a fraction of the reionization era at a time."," Thus current observables of reionization can be used to guide the first attempts at 21cm observations, which will be very expensive in terms of observing time, and cover only a fraction of the reionization era at a time." +" We also demonstrate that following a 21cm derived measurement of the ionization fraction midway through the reionization era, the constraints on the entire history will be"," We also demonstrate that following a 21cm derived measurement of the ionization fraction midway through the reionization era, the constraints on the entire history will be" +The importance of the statistical properties of gravitational lenses for investigating the geometry of the Universe has been discussed by Gott. Park Lee (1989) and bukugita et al. (,"The importance of the statistical properties of gravitational lenses for investigating the geometry of the Universe has been discussed by Gott, Park Lee (1989) and Fukugita et al. (" +1992).,1992). + A particularly promising route to constraining the value of the cosmological constant Qy (Carroll. Press Turner 1992: Ixochanek. 1996) would be ollered by a determination of the relative abundance of lensed and unlensecl galaxies and quasars.," A particularly promising route to constraining the value of the cosmological constant $\Omega_\Lambda$ (Carroll, Press Turner 1992; Kochanek 1996) would be offered by a determination of the relative abundance of lensed and unlensed galaxies and quasars." + Lniportant developments are expected in this field: when the next generation of submillimetre-wave telescopes becomes available. because the abundance of lensed images. formed by both intervening galaxies ancl clusters. is expected to be significantly. larger in this waveband as compared with other wavebancls (Blain 1996a.b. 190τ/).," Important developments are expected in this field when the next generation of submillimetre-wave telescopes becomes available, because the abundance of lensed images, formed by both intervening galaxies and clusters, is expected to be significantly larger in this waveband as compared with other wavebands (Blain 1996a,b, 1997b)." + A large sample. of perhaps several hundred eravitational lenses (Blain 1997a.c). could be compiled by combining the results of large-area extragalactic surveys using theSurveyor (Bersanelli et al.," A large sample, of perhaps several hundred gravitational lenses (Blain 1997a,c), could be compiled by combining the results of large-area extragalactic surveys using the (Bersanelli et al." + 1996). andLIRST (Beckwith et al., 1996) and (Beckwith et al. + 1993). space-horne telescopes with sub-aresec-resolution imaging of the detected: sources using a large ground-based millimetre/submillimetre-wave interferometer array (MEN: Brown 1996: Downes 1996)., 1993) space-borne telescopes with sub-arcsec-resolution imaging of the detected sources using a large ground-based millimetre/submillimetre-wave interferometer array (MIA; Brown 1996; Downes 1996). + The probability of lensing. and hence the size of the sample. depends on the world model and the normalisation and form of evolution of the mass distribution of lensing ealaxies.," The probability of lensing, and hence the size of the sample, depends on the world model and the normalisation and form of evolution of the mass distribution of lensing galaxies." + About LOO fainter lenses could also be detected ina small-area survey using an MEX alone (Blain 1996a.b).," About 100 fainter lenses could also be detected in a small-area survey using an MIA alone (Blain 1996a,b)." + Here the prospects for using such larec samples of galaxy lenses to investigate the values of cosmological parameters and the evolution of large-scale structures are discussed., Here the prospects for using such large samples of galaxy–galaxy lenses to investigate the values of cosmological parameters and the evolution of large-scale structures are discussed. + We also consider whether the magnilication bias of distant ealaxies in the field of a cluster of galaxies. (Broachurst. ‘Tavlor Peacock 1995: Blain 1997b). which also depends on the world. model. could. be used. to. impose. similar Constraints.," We also consider whether the magnification bias of distant galaxies in the field of a cluster of galaxies (Broadhurst, Taylor Peacock 1995; Blain 1997b), which also depends on the world model, could be used to impose similar constraints." + Existing observations in the optical wavchanc have allowed constraints to. be. imposed on the values. of cosmological parameters., Existing observations in the optical waveband have allowed constraints to be imposed on the values of cosmological parameters. + “Phe observed. numbers of lensed quasars appear to rule out world mocels with large values of Oy: IXochanek (1996) derives O4<0.66 at a confidence level of in a Lat world model., The observed numbers of lensed quasars appear to rule out world models with large values of $\Omega_\Lambda$; Kochanek (1996) derives $\Omega_\Lambda < 0.66$ at a confidence level of in a flat world model. + Observations of lensed images in clusters appear to favour a Lat world model with, Observations of lensed images in clusters appear to favour a flat world model with +"IN, determined by the above equation and the total mass of cold gas.",$N_t$ determined by the above equation and the total mass of cold gas. + The WS test results for the four statistics of DWOT for these four models are shown in Table 1.., The KS test results for the four statistics of PW97 for these four models are shown in Table \ref{tbfe}. + Phe most important failing of the models is in theAe statistic., The most important failing of the models is in the$\delv$ statistic. + Fig., Fig. + 1. shows the distribution of Av for the data and models., \ref{fdvfe} shows the distribution of $\delv$ for the data and models. + The Ar values produced by these models are peaked around 50 kms.ο with very few systems having Ar>100kms Loin sharp contrast to the data.," The $\delv$ values produced by these models are peaked around 50 $\kms$ with very few systems having $\delv > 100 \kms$, in sharp contrast to the data." + This is the same result found in PW97 for a single-disc CDM model (e.g. the model of IX96)., This is the same result found in PW97 for a single-disc CDM model (e.g. the model of K96). + Lt is not surprising. as it turns out that in these models most. DLAS are in [act produced. by a single disc. as shown in Fig. 2..," It is not surprising, as it turns out that in these models most DLAS are in fact produced by a single disc, as shown in Fig. \ref{fnumfe}." + Only for the EEXP6 mocel are hall of the DLAS the result of intersections with more than a single gas disc. and only this model has a Ar distribution that is not rejected at greater han 99.9% confidence.," Only for the EXP6 model are half of the DLAS the result of intersections with more than a single gas disc, and only this model has a $\delv$ distribution that is not rejected at greater than $99.9\%$ confidence." + Lt is easy to understand why there are so few multiple intersections in these models by examining Fig. 3.., It is easy to understand why there are so few multiple intersections in these models by examining Fig. \ref{fdiscs}. + This igure shows a projection of the gas clises residing within a 1alo of circular velocity 156 kms7., This figure shows a projection of the gas discs residing within a halo of circular velocity 156 $\kms$. + The sizes of gas discs in hese models are much smaller than the separation between hem and thus multiple intersections are rare., The sizes of gas discs in these models are much smaller than the separation between them and thus multiple intersections are rare. + The sizes of he gas dises in EXPL and the. KIENN model are rather similar., The sizes of the gas discs in EXP1 and the KENN model are rather similar. + Phe gas discs in the AMIAIW model are. generally Xgeer because there is more cold gas in cach disc and he log-normally distibuted Aq varies this compared to the EXPL and IXENN models., The gas discs in the MMW model are generally bigger because there is more cold gas in each disc and the log-normally distibuted $\lambda_H$ varies this compared to the EXP1 and KENN models. + In these three models almost all 10 gas is above the column density limit to be considered a amped system., In these three models almost all the gas is above the column density limit to be considered a damped system. + In IEEXP6 with more extended lower density ises we find some disces where a laree fraction of their area —ies below the clamped level., In EXP6 with more extended lower density discs we find some discs where a large fraction of their area lies below the damped level. + More extended: exponential κος than those considered here do not increase the number X DLAS coming from multiple intersections because the wea dense enough to be above the damped. limit. rapidly gawinks., More extended exponential discs than those considered here do not increase the number of DLAS coming from multiple intersections because the area dense enough to be above the damped limit rapidly shrinks. + In Fig., In Fig. + 4 we show the column density distribution {CN) [or these models in. comparison with the cata of (2000)., \ref{ffnfe} we show the column density distribution $f(N)$ for these models in comparison with the data of \nocite{sw:00}{ (2000). + Once again. of the four mocels only IEEXP6 comes close to fitting the data.," Once again, of the four models only EXP6 comes close to fitting the data." + Vhus although the mass of cold gas is in agreement with that derived from the observations. the total Lor damped absorption is too small if the gas and stars have a similar radial extent and. distribution. as predicted. by. standard models of disc formation.," Thus although the mass of cold gas is in agreement with that derived from the observations, the total for damped absorption is too small if the gas and stars have a similar radial extent and distribution, as predicted by standard models of disc formation." + We therefore conclude that we may need to consider a radically cilferent picture of gaseous discs at high recshift., We therefore conclude that we may need to consider a radically different picture of gaseous discs at high redshift. + In the previous section we found that models. in. which he sizes of gas disces at high redshift were calculated rom angular momentum conservation fail to reproduce the kinematics and column censitv distribution. of observed DLAS., In the previous section we found that models in which the sizes of gas discs at high redshift were calculated from angular momentum conservation fail to reproduce the kinematics and column density distribution of observed DLAS. + X model based on the observations of (1989) for local gas discs and the results of the mocel of KOG also failed., A model based on the observations of \nocite{kenn:89}{ (1989) for local gas discs and the results of the model of K96 also failed. + We noted that a common feature ofthese models is that the majority of DLAS arise [rom a single ealactic disc cause of the small radial extent of these disces compared ο their separation., We noted that a common feature of these models is that the majority of DLAS arise from a single galactic disc because of the small radial extent of these discs compared to their separation. + Lf we wish to investigate a scenario like he one proposed bv (1998). in which the kinematics of DLAS arise from lines of sight. intersecting multiple objects. it is clear that the gaseous discs must be much larger in radial extent.," If we wish to investigate a scenario like the one proposed by \nocite{hsr:98}{ (1998), in which the kinematics of DLAS arise from lines of sight intersecting multiple objects, it is clear that the gaseous discs must be much larger in radial extent." + Unfortunatelv there does. not. exist an. alternative heoretical framework for the sizes of gas disces. especially at high redshift. so in this section we will simply. develop a ov model for the distribution of cold gas.," Unfortunately there does not exist an alternative theoretical framework for the sizes of gas discs, especially at high redshift, so in this section we will simply develop a toy model for the distribution of cold gas." + We hope that the insight. gained [rom such a tov model will lead to a more shvsically motivated model in the future., We hope that the insight gained from such a toy model will lead to a more physically motivated model in the future. + In our tov models we assume a Alestel profile and assume that he LIL clises are runeated at a fixed. column density. perhao by a cosmic ionizing background.," In our toy models we assume a Mestel profile and assume that the HI discs are truncated at a fixed column density, perhaps by a cosmic ionizing background." + We investigate a range of values for this critical column density Ny. which is the only aciditional [ree," We investigate a range of values for this critical column density $N_t$ , which is the only additional free" +atleastGC)(.(j)(C) pp >(e— 1)pj(2e 3)L mostofthecL. machines.Consider anyJ; ((j)denote€2.,Lemmas \ref{lem:2rem1} and \ref{lem:2rem2} imply Theorem \ref{th:family}. +" There17;'s holdsloadp, < immediatelyL. Supposebeforethatthe assignment/,,canno", It remains to evaluate the number of job removals in the job migration phase. +t be o[wens4;.. scheduled o, We first consider . +t be o[wens4;.. scheduled on, We first consider . +t be o[wens4;.. scheduled onS, We first consider . +t be o[wens4;.. scheduled onSy, We first consider . +shown in Figure I..,shown in Figure \ref{figspectra}. + Absorption features due to IL} were fit with Gaussian functions in order to determine equivalent widths. velocity fullewidth at halfinaxima (EWIIMD. and interstellar eas velocities," Absorption features due to $_3^+$ were fit with Gaussian functions in order to determine equivalent widths, velocity full-width at half-maxima (FWHM), and interstellar gas velocities." + Our fitting procedure uses the functional form of a Caussian where area (as opposed to amplitude) is a free parameter. aud iucludes a fit to the coutimmiun level. gy.," Our fitting procedure uses the functional form of a Gaussian where area (as opposed to amplitude) is a free parameter, and includes a fit to the continuum level, $y_0$." +" In the case of the R(1.1)"" and R(1.0) lines. both absorption features are ft simmiltancously aud a sinele best-fit continu level is found."," In the case of the $R(1,1)^u$ and $R(1,0)$ lines, both absorption features are fit simultaneously and a single best-fit continuum level is found." + Uncertaiuties ou the equivalent widths (034) aud continmmu level (δ)both at the 1o levelwere output bv the fitting process., Uncertainties on the equivalent widths $\delta W_{\lambda}$ ) and continuum level $\delta y$ )—both at the $\sigma$ level—were output by the fitting process. + To estimate the svstematic nucertaimtics due to continmim placement. we forced the continuum level to gg|ὃν and yy89g aud re-fit the absorption lines.," To estimate the systematic uncertainties due to continuum placement, we forced the continuum level to $y_0+\delta y$ and $y_0-\delta y$ and re-fit the absorption lines." + Variations iu the equivalent widths due to this shift are small compared to those reported bv the fitting procedure and so are not iucluded iu our analysis (1.0. 0(1 450A).," Variations in the equivalent widths due to this shift are small compared to those reported by the fitting procedure and so are not included in our analysis (i.e., $\sigma(W_{\lambda})$ $\delta W_{\lambda}$ )." +" Assuninug optically thin absorption Lues aud taking transition dipole momeuts and wavelcneths from Cotoetal.(2002) aud references therein. col deusities were derived frou, equivalent widths using the standard relation."," Assuming optically thin absorption lines and taking transition dipole moments and wavelengths from \citet{goto2002} and references therein, column densities were derived from equivalent widths using the standard relation." + All of these results are shown in Table 2.., All of these results are shown in Table \ref{tbllineparam}. + These observations increase the total number of sight lines with both aud IL detectious from 2 to 5., These observations increase the total number of sight lines with both $_3^+$ and $_2$ detections from 2 to 5. + Colum deusities. IL| pera-fractions. and excitation temperatures for both species along all 5 sight lines are collected in Table 3..," Column densities, $para$ -fractions, and excitation temperatures for both species along all 5 sight lines are collected in Table \ref{tblresults}. ." +" IT» data come frou, Savageetal. and Rachtordetal.(2002).", $_2$ data come from \citet{savage1977} and \citet{rachford2002}. +.. Uncertainties on all values are1o., Uncertainties on all values are$1\sigma$. +" The excitation tempcratures iuferrec from the 1.0). ROL1)"". aud REAL.1)! absorption lines of I. ranee from 20xTl )z«16 Ix. while those reported for Πο vary from 51zxΤΠ)<68 Ik. Iu seht lines Zp, is greater than Tl) bv about 30 Kk. while for N Per τω aud Tl) are consistent within uncertainties."," The excitation temperatures inferred from the $R(1,0)$, $R(1,1)^u$, and $R(1,1)^l$ absorption lines of $_3^+$ range from $20\leq T$ $\leq 46$ K, while those reported for $_2$ vary from $51\leq T({\rm H}_2)\leq 68$ K. In 4 sight lines $T_{01}$ is greater than $T({\rm H}_3^+)$ by about 30 K, while for X Per $T_{01}$ and $T({\rm H}_3^+)$ are consistent within uncertainties." +" Still. these observatious clearly show tla for the same interstellar material along; 1 different diffuse molecular cloud sight lines the excitation teupcratures derived from IL} aud Hy do not agree,"," Still, these observations clearly show that for the same interstellar material along 4 different diffuse molecular cloud sight lines the excitation temperatures derived from $_3^+$ and $_2$ do not agree." +" Given the large discrepancies between Ty, interred from II5 aud the excitation temperature of IH. it is dunportant to re-examine the asstiuption that the interred Ty, accurately reflects the kinetic temperature of the diffuse molecular clouds."," Given the large discrepancies between $T_{01}$ inferred from $_2$ and the excitation temperature of $_3^+$, it is important to re-examine the assumption that the inferred $T_{01}$ accurately reflects the kinetic temperature of the diffuse molecular clouds." + Tfthis assumption were incorrect. it would beconceivable that IL} provides the true (lower) temperature of diffuse molecular clouds.," Ifthis assumption were incorrect, it would beconceivable that $_3^+$ provides the true (lower) temperature of diffuse molecular clouds." + There are at least L reasons this assumption could be invalid: (1) observational errors in the determination of the J=0 and /=1 coluun deusities of Πο (2) an insufiicicut frequency of IT! | IT collisions to achieve steady state: (3) the steady state of this reaction being different from the thermocdvwnuamic equilibrinm: aud (1) errors caused by a varving J=0:1 ratio along the line of sight., There are at least 4 reasons this assumption could be invalid: (1) observational errors in the determination of the $J=0$ and $J=1$ column densities of $_2$; (2) an insufficient frequency of $^+$ + $_2$ collisions to achieve steady state; (3) the steady state of this reaction being different from the thermodynamic equilibrium; and (4) errors caused by a varying $J=0:1$ ratio along the line of sight. + Iu the following subsections. we investigate cach of these possibilities iu turn.," In the following subsections, we investigate each of these possibilities in turn." + The measurement of the column densities of =0 and J=1 of IL is performed by profile fitting to spectra of ie Lyman CA-X ) baud in the ultraviolet. recorded witli Copernicus or FUSE.," The measurement of the column densities of $J=0$ and $J=1$ of $_2$ is performed by profile fitting to spectra of the Lyman $A$ $X$ ) band in the ultraviolet, recorded with Copernicus or FUSE." +" The IT, trausitious are optically ick. aud are completely opaque iu the line cores."," The $_2$ transitions are optically thick, and are completely opaque in the line cores." + Cave ie difficulties in accurately retrieviug column deusities roni optically thick transitions. one might worry that ιο duferred Z4 is contaminated by uncertainties caused w oradiative trauster.," Given the difficulties in accurately retrieving column densities from optically thick transitions, one might worry that the inferred $T_{01}$ is contaminated by uncertainties caused by radiative transfer." + According to D. L. Rachtord (private communication. WwH0). the detailed shape of the combined profile of we J=0 line and the two J=1 lines is quite sensitive to the ratio of the column deusities of these wo rotational levels. aud thus provides a verv useful xobe of Tjj.," According to B. L. Rachford (private communication, 2010), the detailed shape of the combined profile of the $J=0$ line and the two $J=1$ lines is quite sensitive to the ratio of the column densities of these two rotational levels, and thus provides a very useful probe of $T_{01}$." + Because iultiple vibronic bauds of IT». which are kuown to be relatively free of contiuuination o ostellar lines. are used iu the determination of τμ. it is απο to cuvision any systematic errors that could affect the measurements.," Because multiple vibronic bands of $_2$, which are known to be relatively free of contamination by stellar lines, are used in the determination of $T_{01}$, it is difficult to envision any systematic errors that could affect the measurements." + The statistical errors in the column density measurcuicnuts are typically —0.1 dex. and we can therefore couchide that the ultraviolet lucasurements provide an accurate and fairly precise measure of the ratioof Αθ) to N(1) for IT».," The statistical errors in the column density measurements are typically $\sim$ 0.1 dex, and we can therefore conclude that the ultraviolet measurements provide an accurate and fairly precise measure of the ratioof $N(0)$ to $N(1)$ for $_2$ ." +" The Jf=0 and J=1 rotational levels of IL, belong to different spin modifications (para and ortho. respectively) aud are therefore not thermalized by non- collisions or radiative transitions."," The $J=0$ and $J=1$ rotational levels of $_2$ belong to different spin modifications and , respectively) and are therefore not thermalized by non-reactive collisions or radiative transitions." + Ouly chemical reactions. iu which the protons are exchanged. cau affect the nuclear spin modification of Is.” ," Only chemical reactions, in which the protons are exchanged, can affect the nuclear spin modification of $_2$ " +Using the oobservation of NGC 65!53. we have spectrally identified oue candidate qLAINB in the GC.,"Using the observation of NGC 6553, we have spectrally identified one candidate qLMXB in the GC." + The best-fit parameters found are Rss=6.32lau (for Mss= LEM.) and fig.ya=136PBLaeajCV. and the best-fit254 PLD photon index is T=2.1!(x," The best-fit parameters found are $\rns = 6.3\ud{2.3}{0.8}\km$ (for $\mns=1.4\msun$ ) and $\kteff = 136\ud{21}{34}\eV$, and the best-fit PL photon index is $\Gamma=2.1\ud{0.5}{0.8}$." + The low-8/N sspectitma fds consistent best-fit values within the statistic permitted by the detected counts., The low-S/N spectrum finds consistent best-fit values within the statistic permitted by the detected counts. +" The modest precision of the NS radius measurement obtained with these short exposures docs not permitto place constraiuts on the deuse matter Eos. Deeper eexposures will provide the S/N necessary to coufirii the classification and to produce useful uncertainty on the radius measurement for the deteruünation of the deuse matter Eos, The number of candidates ideutified in NCC 6553 fonly 1) is in agrecmicnt with that predicted trom the relations Naxs~0.401&Pee|02 07) απ No= (2). where the authors used different normalizatious for Te: the encounter rate of the CC is defined bv Poexpyre (?).. Iu. "," The modest precision of the NS radius measurement obtained with these short exposures does not permit to place constraints on the dense matter EoS. Deeper exposures will provide the S/N necessary to confirm the classification and to produce useful uncertainty on the radius measurement for the determination of the dense matter EoS. The number of candidates identified in NGC 6553 (only 1) is in agreement with that predicted from the relations $N_{\rm qNS}\sim0.04\times\Gamma_{\rm GC}+0.2$ \citep{gendre03b} and $N=0.993\times\Gamma_{\rm GC}-0.046$ \citep{heinke03c}, where the authors used different normalizations for $\Gamma_{\rm GC}$; the encounter rate of the GC is defined by $\Gamma_{\rm GC} \propto +\rho_{0}^{1.5} r_{\rm c}^{2}$ \citep{verbunt03a}. ." +this last equation. po is the ceutral huninosity density Gu LZ. pe?) aud ro ds the core radius (Gu pe. uot angular distance).," In this last equation, $\rho_{0}$ is the central luminosity density (in $\unit{\lsun\,pc^{-3}}$ ) and $r_{\rm c}$ is the core radius (in pc, not angular distance)." + Quautitatively. using the same respective norlalizations. the umber of expected in NGC 65523. eiven Pounce6333=SIELipe? (2). qLMXDsare 0.13 and 0.31 using the wo relations cited above. respectively.," Quantitatively, using the same respective normalizations, the number of expected qLMXBs in NGC 6553, given $\rho_{0, {\rm NGC~6553}} = 3.84\unit{\lsun\,pc^{-3}}$ \citep{harris96}, are 0.43 and 0.34 using the two relations cited above, respectively." + Assiunuiug Poisson statistics. the probability of Πποπο oue GLAINB when 0.13 (0.31) are expected is )).," Assuming Poisson statistics, the probability of finding one qLMXB when 0.43 (0.34) are expected is )." + Therefore. our findings are not in dizagreemeut with these two empirical predictions.," Therefore, our findings are not in disagreement with these two empirical predictions." +" The total unabsorbed . XMM - ο...=Hanesο,ofthe“ergcues 7. candidateincludes a PLE coiiponent with a contribution to the flux."," The total unabsorbed flux of the candidate qLMXB, $\Fx=1.5\ud{4.3}{0.7}\tee{-13}\cgsflux$ , includes a PL component with a contribution to the flux." + If tutrinsic to the source. 335this PL component has one of the strougest contribution to the total fux ever observed for a qLMXD in a CC (othersareiuNGC6110and£7Tuc.2? respectivelvj..," If intrinsic to the source, this PL component has one of the strongest contribution to the total flux ever observed for a qLMXB in a GC \citep[others are in + NGC~6440 and 47Tuc,][respectively]{heinke03c,heinke05}." + However. we have shown evideuces for the presence of ucarby contaminating sources.," However, we have shown evidences for the presence of nearby contaminating sources." + This is tentatively supported by a short archived oobservation. but the low-siguificauce detection of the nearby sources does not coufriu with certainty the existence of cotamination.," This is tentatively supported by a short archived observation, but the low-significance detection of the nearby sources does not confirm with certainty the existence of contamination." + Onlv a louger would confini the spectral Classification of oobservationthe bright core source aud confi the detection of the faint neighboring core sources., Only a longer observation would confirm the spectral classification of the bright core source and confirm the detection of the faint neighboring core sources. + The candidate qEMXND did not display vvarlabilitv ou the time scale of the observation., The candidate qLMXB did not display variability on the time scale of the observation. + Specifically. there was no evidence that the iincorated light curve is significantly different from a linear distribution of counts.," Specifically, there was no evidence that the integrated light curve is significantly different from a linear distribution of counts." + Regarding the long tine scale variability. there is no significant change of flux between the aand oobservations.," Regarding the long time scale variability, there is no significant change of flux between the and observations." + We also searched for archived oobservation. but uo source was detected at the position of oon the PSPC survey. aud no HRI observation at the center of the GC was performed.," We also searched for archived observation, but no source was detected at the position of on the PSPC survey, and no HRI observation at the center of the GC was performed." +" To conclude. the candidate in the core of NGC 6553. with £x,=L2«10ore«3 (4—Gkpe). adds to the sanall list of known GC qLMXND."," To conclude, the candidate in the core of NGC 6553, with $L_{\rm + X,th}=4.2\tee{32}\cgslum$ $d=6\kpc$ ), adds to the small list of known GC qLMXB." + However. ouly a high enough S/N observation with wwill allow to confirm with certitude the spectral classification of the source. aud will be able to provide constraints on the deuse matter Eos. The authors thauk the anouvimous referee for the cohunents that contributed to the improvement of this article.," However, only a high enough S/N observation with will allow to confirm with certitude the spectral classification of the source, and will be able to provide constraints on the dense matter EoS. The authors thank the anonymous referee for the comments that contributed to the improvement of this article." + S.C. acknowledges the support of NSERC via the Vanier CCS program., S.G. acknowledges the support of NSERC via the Vanier CGS program. + R.E.BR. is supported by au NSERC Discovery eraut., R.E.R. is supported by an NSERC Discovery grant. + The work by GCP was partially supported by NASA (erant NNNOQACSLO) aud by the Miuistrv of Educationaud Science of the Russian Federation (contract 11.631.51.0001)., The work by GGP was partially supported by NASA (grant NNX09AC84G) and by the Ministry of Educationand Science of the Russian Federation (contract 11.G34.31.0001). + The authors also acknowledge the use of, The authors also acknowledge the use of +Quoted confidence intervals are at 90% level. if not otherwise specified.,"Quoted confidence intervals are at $90\%$ level, if not otherwise specified." + The Coma cluster was observed for the first time in December 1997[or ~91 ksec and re-observed in December 2000 lor ~300 ksec., The Coma cluster was observed for the first time in December 1997for $\sim$ 91 ksec and re-observed in December 2000 for $\sim$ 300 ksec. +" The pointing coordinates of are ab J(2000): 0:1258""52:0: 427°58!54"".", The pointing coordinates of are at J(2000): $\alpha:~12^h~ 58^m~ 52^s$; $\delta:~ +27^{\circ}~ 58'~ 54''$. + The total effective exposure times of the PDS in the two observations were 44.5 ksec and 122.2 ksec. respectively (hereafter ODSI and ODS2).," The total effective exposure times of the PDS in the two observations were 44.5 ksec and 122.2 ksec, respectively (hereafter OBS1 and OBS2)." + The PDS spectra of both the observations were extracted using the NAS v2.1 package (ChiappetGi Dal Fiume 1997)., The PDS spectra of both the observations were extracted using the XAS v2.1 package (Chiappetti Dal Fiume 1997). + The choice of using this software is dictated by the non standard pipeline needed {ο extract (he net count spectra (see below)., The choice of using this software is dictated by the non standard pipeline needed to extract the net count spectra (see below). + Because our Institute (i.e.. LASF/Dologna) was in charge of the design. construction and maintenance of the PDS. and we developed. and tested the. NAS package. specifically created. to handle the PDS peculiarities (while the SANDAS package. used for the standard analysis. is more suitable for handling imaging instruments. like MECS and LECS). we feli more confident in using XAS for the PDS analvsis.," Because our Institute (i.e., IASF/Bologna) was in charge of the design, construction and maintenance of the PDS, and we developed and tested the XAS package, specifically created to handle the PDS peculiarities (while the SAXDAS package, used for the standard analysis, is more suitable for handling imaging instruments, like MECS and LECS), we felt more confident in using XAS for the PDS analysis." + since (he source is rather [nint in the PDS band (~5 mCrab in 15100 keV) a careful check of the background subtraction must be performed., Since the source is rather faint in the PDS band $\sim$ 5 mCrab in 15–100 keV) a careful check of the background subtraction must be performed. + The background. sampling was performed by making use of the default rocking law of the two PDS collimators that samples ON/+OFF. ON/OFF fields for each collimator with a dwell time of 96 sec (Frontera 1997Ta).," The background sampling was performed by making use of the default rocking law of the two PDS collimators that samples ON/+OFF, ON/–OFF fields for each collimator with a dwell time of 96 sec (Frontera 1997a)." + When one collimator is pointing ON source. the other collimator is pointing toward one of the wo OFF positions.," When one collimator is pointing ON source, the other collimator is pointing toward one of the two OFF positions." + Initially. we used the standard procedure to obtain PDS spectra (Dal Fiume 1997): (his procedure consists of extracting one accumulated spectrum for each unit for each collimator position.," Initially, we used the standard procedure to obtain PDS spectra (Dal Fiume 1997); this procedure consists of extracting one accumulated spectrum for each unit for each collimator position." +" We then checked the (wo independently accumulated: background spectra in the two different +/OFF sky directions. offset. by 210' with respect to the on-axis pointing direction (+OFF pointing; a:1258""57.8: 0:+242855""] OFF pointing: a:1258""47.0%. 0.431°28'54"". 1)."," We then checked the two independently accumulated background spectra in the two different +/–OFF sky directions, offset by $210'$ with respect to the on-axis pointing direction (+OFF pointing: $\alpha:~12^h~58^m~ 57.8^s$; $\delta:~ +24^\circ~ 28'~ 55''.1$ –OFF pointing: $\alpha:~12^h~58^m~ 47.0^s$; $\delta:~ +31^\circ~ 28'~ 54''.7$ )." + The comparison between the two accumulated. backgrounds (dillerence between. the +OFF and OFF count rate spectra) shows that for OBSI the difference is compatible with zero (0.044+0.047 cts/s For a background level of 21.6640.02 cts/s in 15100 keV). while for the longer. more sensitive ODS2. there is an excess of 0.06440.021 cts/s (background 16.7650.01 cts/s)t..," The comparison between the two accumulated backgrounds (difference between the +OFF and –OFF count rate spectra) shows that for OBS1 the difference is compatible with zero $0.044\pm 0.047$ cts/s for a background level of $21.66\pm 0.02$ cts/s in 15–100 keV), while for the longer, more sensitive OBS2, there is an excess of $0.064\pm 0.021$ cts/s (background $16.76\pm 0.01$ ." + A careful check of possible variable sources in the PDS offset fields lead, A careful check of possible variable sources in the PDS offset fields lead +left plot).,left plot). + In the case of 85/2006 83. we observed a few Large jumps in semimajor axis over the timespan covered by our simulations (see fig. 22..," In the case of S/2006 S3, we observed a few large jumps in semimajor axis over the timespan covered by our simulations (see fig. \ref{chaos-gap}," + right plot)., right plot). + The evolutions of both the cecentricity and the inclination of the satellites appear more regular. with long period mocdulations and We applied the frequeney. analysis in order to identify the source. of the perturbations leading to the chaotic evolution of the two satellites.," The evolutions of both the eccentricity and the inclination of the satellites appear more regular, with long period modulations and We applied the frequency analysis in order to identify the source of the perturbations leading to the chaotic evolution of the two satellites." + By analysing the 5 and & non singular variables defined. with respect to the planet. we found among the various frequencies two with period of 900. vears ancl 1500 vear respectively.," By analysing the $h$ and $k$ non singular variables defined with respect to the planet, we found among the various frequencies two with period of $900$ years and $1800$ year respectively." + Phese values are close to the Creat Inequality period (S883 vears) of the almost resonance betwen Jupiter anc Saturn., These values are close to the Great Inequality period $\sim883$ years) of the almost resonance betwen Jupiter and Saturn. + This is possibly one source of the chaotic behaviour of the satellites., This is possibly one source of the chaotic behaviour of the satellites. + En addition. the inspection of the upper plot in fig.," In addition, the inspection of the upper plot in fig." +" 20. shows that the 5, parameters of the test particles populating this radial region increase when Titan and LIapetus are included.", \ref{retro-eta} shows that the $\eta_a$ parameters of the test particles populating this radial region increase when Titan and Iapetus are included. + By comparing the frequencies of motion of the two irregular. satellites with those of Titan and lapetus we find an additional commensurabilitv., By comparing the frequencies of motion of the two irregular satellites with those of Titan and Iapetus we find an additional commensurability. +ays sThe frequencies:⋅. -7.1101yr and T40103gr+ that ave present in the power spectrum of 5/2006 52 and 5/2006 SG. respectively. are about twice the requeney 245:101yrJL in the power spectrum of Titan.," The frequencies $7.1 \times 10^{-4}~yr^{-1}$ and $7.4 \times 10^{-4}~yr^{-1}$ that are present in the power spectrum of S/2006 S2 and S/2006 S6, respectively, are about twice the frequency $3.4 \times 10^{-4}~yr^{-1}$ in the power spectrum of Titan." + The cumulative elfects of the Great Inequality anc of Titan and lapetus lead to the large values of the 7 parameters in ig., The cumulative effects of the Great Inequality and of Titan and Iapetus lead to the large values of the $\eta$ parameters in fig. + 4 and 20.., \ref{etas-sat} and \ref{retro-eta}. + Phe chaotic evolution of the two satellites does not Lead to destabilisation in the timespan of our integration (107 vears). however longer simulations are needed to test he long term stabilitv.," The chaotic evolution of the two satellites does not lead to destabilisation in the timespan of our integration $10^{8}$ years), however longer simulations are needed to test the long term stability." + Lt is possible that the irregular »haviour takes the two satellites into other chaotic regions ultimately leading to their expulsion from the system., It is possible that the irregular behaviour takes the two satellites into other chaotic regions ultimately leading to their expulsion from the system. + 14 is also possible that. during their chaotic wandering. they cross the paths of more massive satellites and be collisionally. removed.," It is also possible that, during their chaotic wandering, they cross the paths of more massive satellites and be collisionally removed." +" This couldhave been the fate of possible other satellites which originally populated the region encompassed between 20.9410 Km and 22.4410"" kin.", This couldhave been the fate of possible other satellites which originally populated the region encompassed between $20.94 \times 10^{6}$ km and $22.44 \times 10^{6}$ km. + ‘To understand the present orbital structure of Saturn's satellite svstem anc how it evolved. (rom. the. primordial one we have to investigate the collisional evolution within he system., To understand the present orbital structure of Saturn's satellite system and how it evolved from the primordial one we have to investigate the collisional evolution within the system. + dmpacts between satellites. in fact. may rave removed smaller bodies and fragmented: the larger ones.," Impacts between satellites, in fact, may have removed smaller bodies and fragmented the larger ones." + Minor bodies in heliocentric orbits like comets and Centaurs may have also contributed to the svstenm shaping »w colliding with the satellites as accdressed by Nesvornyetal. (2004)., Minor bodies in heliocentric orbits like comets and Centaurs may have also contributed to the system shaping by colliding with the satellites as addressed by \cite{nes04}. +. At present. however. such events are not requent because of the reduced. Fux of minor bodies and he small sizes of irregular satellites (Zahnlectal.2003:resvornyetal.2004).," At present, however, such events are not frequent because of the reduced flux of minor bodies and the small sizes of irregular satellites \citep{zah03,nes04}." +. The last cletailed evaluation of the collisional oobabilities between the irregular satellites around he giant planets was the one performed by Nesvorny—ctal. (2003).. which showed that the probabilities of collisions »etween: pairs of satellites were rather low ancl practically unimportant.," The last detailed evaluation of the collisional probabilities between the irregular satellites around the giant planets was the one performed by \cite{nes03}, which showed that the probabilities of collisions between pairs of satellites were rather low and practically unimportant." + The computed average collisional lifetimes were tens to hundreds of times longer than Solar Systems lifetime., The computed average collisional lifetimes were tens to hundreds of times longer than Solar System's lifetime. + The. only notable exceptions were those pairs involving one of the big irregular satellites (e.g. Limatia. Phoebe. ete.)," The only notable exceptions were those pairs involving one of the big irregular satellites (e.g. Himalia, Phoebe, etc.)" + in the svstenis., in the systems. + In the Saturn svstem. Phoebe is between one ancl two order of magnitudes more active than any other satellite.," In the Saturn system, Phoebe is between one and two order of magnitudes more active than any other satellite." + Ehe authors computed. a cumulative number of collisions between 6 and 7 in 4.510° vears (Nesvornyetal.2003)., The authors computed a cumulative number of collisions between $6$ and $7$ in $4.5 \times 10^{9}$ years \citep{nes03}. + However. at the time of the publication of the work hy Nesvornyetal.(2003). only 13 of the 35 currently known irregular satellites of Saturn hac been discovered.," However, at the time of the publication of the work by \cite{nes03} only $13$ of the $35$ currently known irregular satellites of Saturn had been discovered." + We extend here their analysis taking advantage of the larger number of known bodies and of the improved orbital data., We extend here their analysis taking advantage of the larger number of known bodies and of the improved orbital data. + Using the mean orbital elements computed. with Mocel 2 we have estimated. the collisional probabilities using the approach described by Ixessler(1981)., Using the mean orbital elements computed with Model $2$ we have estimated the collisional probabilities using the approach described by \cite{kes81}. +". Since in the scenario described by the Nice Model the Late Heavy. Bombarcdamoent (LILB) represents a lower limit for the capture epoch of the irregular satellites (Comesetal.2005:Tsiganis2005).. we considered a time interval for the collisional evolution of 3.510 vears. making the conservative. assumption that the LUB took place after about LO"" vears since the beginning of Solar System formation."," Since in the scenario described by the Nice Model the Late Heavy Bombardment (LHB) represents a lower limit for the capture epoch of the irregular satellites \citep{gom05,tsi05}, we considered a time interval for the collisional evolution of $3.5 \times 10^{9}$ years, making the conservative assumption that the LHB took place after about $10^{9}$ years since the beginning of Solar System formation." + Since the collisional probability. depends linearly on time. our results can be imnmeciately extended to longer The results of our computations (see fig. 23))," Since the collisional probability depends linearly on time, our results can be immediately extended to longer The results of our computations (see fig. \ref{collisions}) )" + confirm. hat the only pairs of satellites with high probability of collisions involve. Phoebe., confirm that the only pairs of satellites with high probability of collisions involve Phoebe. + Phe satellite pairs with the ugher number of collisions over the considered. timespan are PhoebeIxiviue (0.7126). PhoebeYirac (0.7099) anc ἸπουροΠεν (0.6436).," The satellite pairs with the higher number of collisions over the considered timespan are Phoebe–Kiviuq $0.7126$ ), Phoebe–Ijiraq $0.7099$ ) and Phoebe–Thrymr $0.6436$ )." + Phe remaining pairs involving >hocbe have a number of collisions between 0.1 anc 1.35 (see fig. 23..," The remaining pairs involving Phoebe have a number of collisions between $0.1$ and $0.35$ (see fig. \ref{collisions}," + line/column 3). with the highest. values associated. with the progracde satellites Paaliacg. Siarnaq. Tarvos. Albiorix. Evriapo and Bebhionn (8/2004 S11).," line/column $3$ ), with the highest values associated with the prograde satellites Paaliaq, Siarnaq, Tarvos, Albiorix, Erriapo and Bebhionn (S/2004 S11)." + Al he other satellite pairs. due also to their small radii. have negligible (<10. 7) collisional probabilities.," All the other satellite pairs, due also to their small radii, have negligible $< 10^{-2}$ ) collisional probabilities." + The predicte otal number of collisions in Saturn's uregular. satellite system. obtained by summing over all the possible pairs. is of about 12 collisions over the considered. timespan.," The predicted total number of collisions in Saturn's irregular satellite system, obtained by summing over all the possible pairs, is of about $12$ collisions over the considered timespan." + Half of these impacts involve Phoebe., Half of these impacts involve Phoebe. +" This is probably at the origin of the eap centred at Phoebe and raclially extending from about 11.2210"" km to about. 14.9610"" km from Saturn (Le. between Liraeq's and πο mean orbits) for both prograde and retrograde satellites.", This is probably at the origin of the gap centred at Phoebe and radially extending from about $11.22 \times 10^{6}$ km to about $14.96 \times 10^{6}$ km from Saturn (i.e. between Ijiraq's and Paaliaq's mean orbits) for both prograde and retrograde satellites. + To further confirm this hypothesis we evaluated the impact probability for a cloud of test. particles populating this We filled with test bodies a volume in the phase space defined in the following wav: The sampling stepsize were ὅσα=4488.10! km. δοΞ0.1 and 9;= 2. for a total of 2860 prograde orbits aud 2860 retrograde ones.," To further confirm this hypothesis we evaluated the impact probability for a cloud of test particles populating this We filled with test bodies a volume in the phase space defined in the following way: The sampling stepsize were ${\delta}a=4.488 \times 10^{4}$ km, ${\delta}e=0.1$ and ${\delta}i=2^{\circ}$ , for a total of $2860$ prograde orbits and $2860$ retrograde ones." + A radius of 3 km has been adopted for the test particles to compute the cross sections., A radius of $3$ km has been adopted for the test particles to compute the cross sections. + The results are presented in the colour maps of fig., The results are presented in the colour maps of fig. + 24. for the prograde, \ref{pro-cloud-3} for the prograde +lield. with likely varving extinction. makes it à harsher test to the ME method that we implemented.,"field, with likely varying extinction, makes it a harsher test to the MF method that we implemented." + NGC 2298 is one of the GCs located in the footprint of DIES., NGC 2298 is one of the GCs located in the footprint of DES. + Therefore. DES will provide a much larger area coverage around the eluster. making it possible to make follow-up studies using the same methods developed for this paper.," Therefore, DES will provide a much larger area coverage around the cluster, making it possible to make follow-up studies using the same methods developed for this paper." + NGC 2 owas observed using the MOSAIC2. camera located at the + meter Blanco. Velescope at Cerro 'l'ololo International Observatory. (οΤΟ)., NGC 2298 was observed using the MOSAIC2 camera located at the 4 meter Blanco Telescope at Cerro Tololo International Observatory (CTIO). + The MOSAIC2 instrument is à SIO2pr SIO2p.r segmented. CCD camera with a Field of View (FOV) of 36«36., The MOSAIC2 instrument is a $8192 px \times 8192 px$ segmented CCD camera with a Field of View (FOV) of $36'\times36'$. + Each of the S camera segments is a CCD with 4096p.r«2048p.r., Each of the 8 camera segments is a CCD with $4096px\times2048px$. +" Separating cach CCD there is à gap of 35pr=9.2"" in the East-West direction and. 50pr=13.2"" in the North-South direction.", Separating each CCD there is a gap of $35~px = 9.2 \arcsec$ in the East-West direction and $50~px = 13.2 \arcsec$ in the North-South direction. + The wide field. of MOSAAIC2 makes it the best instrument or large area observations in the southern hemisphere., The wide field of MOSAIC2 makes it the best instrument for large area observations in the southern hemisphere. + The observations took place in the night of February lOth 2010 under photometric conditions., The observations took place in the night of February 10th 2010 under photometric conditions. + Phe mean seeing or the night was 0.77. which is normal for the epoch," The mean seeing for the night was $0.7""$, which is normal for the epoch." + We observed. 12 overlapping fields around NGC 2298 in wo passbands. V and L Figure 5. show the fields and heir CCD seements overlaid on a Digital Sky Survey (DSS) image around the cluster.," We observed 12 overlapping fields around NGC 2298 in two passbands, V and I. Figure \ref{observations} show the fields and their CCD segments overlaid on a Digital Sky Survey (DSS) image around the cluster." + The fields in the Figure have been corrected for geometric distortions. as explained latter.," The fields in the Figure have been corrected for geometric distortions, as explained latter." + The otal exposure time was of 240s (2190 3) in the V band and 3608 (37120 s) in the E band., The total exposure time was of $240~s$ $2\times120~s$ ) in the V band and $360~s$ $3x120~s$ ) in the I band. + The standard stars used or photometric calibration are taken from Stetson(2000)., The standard stars used for photometric calibration are taken from \citet{stetstd}. +. They are located within 30 of the cluster centre and were observed several times during the night. each time using one single short exposure in the V and LE bands.," They are located within $30'$ of the cluster centre and were observed several times during the night, each time using one single short exposure in the V and I bands." + MOSAIC? was set to 1 binning on the S-channel mocle., MOSAIC2 was set to $1\times1$ binning on the 8-channel mode. + The reduction of the data was carried out. using the package running on the environment., The reduction of the data was carried out using the package running on the environment. + All frames were reduced. using standard: procedures. (crosstalk. overscan. bias. Hatfield).," All frames were reduced using standard procedures (crosstalk, overscan, bias, flatfield)." + Some complications arise when dealing with large field instruments., Some complications arise when dealing with large field instruments. + Phe FOV of MOSAIC2 introduces a spatial variation on the pixel size. going from 0.2pr dn the centre of the POV to 0.297Yfpe on the edges.," The FOV of MOSAIC2 introduces a spatial variation on the pixel size going from $0.27""/px$ in the centre of the FOV to $0.29""/px$ on the edges." + This means that cach exposure from a eiven Ποιά must be corrected for distortion before. being stacked. since the projection depends on the pointing of the telescope.," This means that each exposure from a given field must be corrected for distortion before being stacked, since the projection depends on the pointing of the telescope." + To correct. for. distortion each. frame must have a reasonably accurate astrometric solution., To correct for distortion each frame must have a reasonably accurate astrometric solution. + This was done bv constructing an initial guess for the World. Coordinate System (WC€S)., This was done by constructing an initial guess for the World Coordinate System (WCS). + This initial guess. was determined: using USNO-A cataloguesο., This initial guess was determined using USNO-A catalogues. + With the initial guess for the WCS. we refine the astrometric solution frame by frame using the taskMSCCMATCH.," With the initial guess for the WCS, we refine the astrometric solution frame by frame using the task." +. Frames that will be later combined are registered. using and finally. using the taskMSCIMAGE.. all frames were corrected for distortions and combined into a single image.," Frames that will be later combined are registered using and finally, using the task, all frames were corrected for distortions and combined into a single image." + Since the process of distortion correction involves a re-sampling of the pixels. the bad pixel areas suller distortions in the process due to the artificial step discontinuity in the image.," Since the process of distortion correction involves a re-sampling of the pixels, the bad pixel areas suffer distortions in the process due to the artificial step discontinuity in the image." + To overcome this problem. the bad. pixel masks were also corrected for clistortions and later applied to the final combined image.," To overcome this problem, the bad pixel masks were also corrected for distortions and later applied to the final combined image." + With thefinal combined images we performed point spread function. (PSE) fit photometry using the broadly used software Stetson(1994)., With thefinal combined images we performed point spread function (PSF) fit photometry using the broadly used software \citet{stetson}. +. ALL the photometry was performed by an automated python script., All the photometry was performed by an automated python script. + “Phe script deals with cach of the S MOSAIC? chips independently since there mav be PSE variations from one chip to another., The script deals with each of the 8 MOSAIC2 chips independently since there may be PSF variations from one chip to another. + The list below shows the steps taken to accomplish the photometry [or each chip., The list below shows the steps taken to accomplish the photometry for each chip. + In addition. the PSE was allowed to vary over cach chip to account for any residual distortions.," In addition, the PSF was allowed to vary over each chip to account for any residual distortions." + After this process. we combined the photometric tables from the two filters using a positional matching in world coordinates.," After this process, we combined the photometric tables from the two filters using a positional matching in world coordinates." + The combined VI photometric table for cach Licld was calibrated using the following calibration equations: Where V (£) is the calibrated magnitude. 7 (7) is the instrumental magnitude. (VoZ) is the calibrated colour. .X is the airmass. and. ey (9) is the zero-point.," The combined VI photometric table for each field was calibrated using the following calibration equations: Where $V$ $I$ ) is the calibrated magnitude, $v$ $i$ ) is the instrumental magnitude, $(V-I)$ is the calibrated colour, $X$ is the airmass, and $v_0$ $i_0$ ) is the zero-point." + The coellicients (a.b.cd). as well as the zero-points. were obtained from a fit to the magnitudes and colours of the standard stars observed during the night with air-masses ranging from 1.01 to 2.60.," The coefficients $(a,b,c,d)$, as well as the zero-points, were obtained from a fit to the magnitudes and colours of the standard stars observed during the night with air-masses ranging from $1.01$ to $2.60$ ." +rare.,rare. + The resulting dust cross-sections and masses are listed in Table 2.., The resulting dust cross-sections and masses are listed in Table \ref{photometry}. + The computed mass in micron-sized grains is strictly a lower limüt to the total mass. since large particles may hold significant mass while presenting negligible scattering cross-section.," The computed mass in micron-sized grains is strictly a lower limit to the total mass, since large particles may hold significant mass while presenting negligible scattering cross-section." +" Both C. and AL, decreased. between December 27 and January 4 by about3054... indicating that the escape ol particles [rom the projected 64"" radius photometry aperture substantially exceeded (he supply of Που particles from (he nucleus in (his period."," Both $C_c$ and $M_c$ decreased between December 27 and January 4 by about, indicating that the escape of particles from the projected $\arcsec$ radius photometry aperture substantially exceeded the supply of fresh particles from the nucleus in this period." +" In addition to the diffuse coma. an approximately linear tail (ihe ""spike) is evident (anarked C in Figure 2)). with a position angle on Dec 27 and on Jan 04."," In addition to the diffuse coma, an approximately linear tail (the “spike”) is evident (marked $C$ in Figure \ref{composite}) ), with a position angle on Dec 27 and on Jan 04." +" The position angles are slightly dillerent from both the antisolar direction (position angles 276"" and 269"" on Dec 27 and Jan 04. respectively) and the projected orbit (position angle 286"" on both dates)."," The position angles are slightly different from both the antisolar direction (position angles $\degr$ and $\degr$ on Dec 27 and Jan 04, respectively) and the projected orbit (position angle $\degr$ on both dates)." + Therefore. it is not possible to interpret the spike as a simple svnchrone. as was done for P/2010 A2.," Therefore, it is not possible to interpret the spike as a simple synchrone, as was done for P/2010 A2." + Instead. it must consist of particles whose motion is determined bv their initial velocity as well as radiation pressure.," Instead, it must consist of particles whose motion is determined by their initial velocity as well as radiation pressure." + We set upper limits to the allowable brightness of co-moving companions to Scheila by digitally adding scaled. versions of the (unsaturated) nucleus., We set upper limits to the allowable brightness of co-moving companions to Scheila by digitally adding scaled versions of the (unsaturated) nucleus. +" At projected. distances Z6"" (10.000 km). anv companion with Vx 28 could not escape detection."," At projected distances $\geq$ $\arcsec$ (10,000 km), any companion with $V \leq$ 28 could not escape detection." + Assuming (hat any companion has (he same albedo as Scheila. a limit to the diameter of any secondary is sel al Two mechanisms considerecL previously as possible explanations for activity in comets are Inoperable on Sceheila. as à result of its large size and slow rotation.," Assuming that any companion has the same albedo as Scheila, a limit to the diameter of any secondary is set at Two mechanisms considered previously as possible explanations for activity in main-belt comets are inoperable on Scheila, as a result of its large size and slow rotation." + First. mass loss through rotational instability is ruled out bv the measured rotational period. (Warner 2006).," First, mass loss through rotational instability is ruled out by the measured rotational period, (Warner 2006)." + The latter greatly exceeds the critical period at which the centripetal acceleration al (he surface of a sphere equals the gravitational acceleration. assuming a bulk density second. the ejection of grains through electrostatic charging of the surface can be ruled οτί since the speeds generated electrostatically (Rennilson and Criswell 1974) are [ar smaller than the escape speed [rom the nucleus.," The latter greatly exceeds the critical period at which the centripetal acceleration at the surface of a sphere equals the gravitational acceleration, assuming a bulk density Second, the ejection of grains through electrostatic charging of the surface can be ruled out since the speeds generated electrostatically (Rennilson and Criswell 1974) are far smaller than the escape speed from the nucleus." + Another mechanism must be responsible for the ejection of dust., Another mechanism must be responsible for the ejection of dust. + The simplest explanation is (hat Scheila ejected material alter being struck by another. much smaller. asteroid.," The simplest explanation is that Scheila ejected material after being struck by another, much smaller, asteroid." + This is the explanation proposed elsewhere lor the inner-belt AIBC P/2010 A2 (Jewitt et al., This is the explanation proposed elsewhere for the inner-belt MBC P/2010 A2 (Jewitt et al. + 2010)., 2010). + In this interpretation. the estimated dust mass (Table 2)) eives a crude estimate of (he impactor properties.," In this interpretation, the estimated dust mass (Table \ref{photometry}) ) gives a crude estimate of the impactor properties." + The velocity dispersion amongst main-belt, The velocity dispersion amongst main-belt +"blackhole was formed at the epoch when the galaxy. formation was nearly completed s) so that the velocity dispersion does not change significantly between /, and present.",blackhole was formed at the epoch when the galaxy formation was nearly completed $t_b=10^{16}-10^{17}$ s) so that the velocity dispersion does not change significantly between $t_b$ and present. + Therefore our result is valid only for supermassive blackholes formed nearly at the end of the galaxy formation. same as in the Super Eddington Accretion ancl Ballistic model.," Therefore our result is valid only for supermassive blackholes formed nearly at the end of the galaxy formation, same as in the Super Eddington Accretion and Ballistic model." + The assumed existence of a decaving sterile neutrino halo inside each galactic center provides enough mass to form (he supermassive blackhole., The assumed existence of a decaying sterile neutrino halo inside each galactic center provides enough mass to form the supermassive blackhole. +" It can also solve the cooling flow problem in clusters (ChanandChu2007) and explain the reionization of the universe Haiman 2004).. all with the same decay rate Ts,=(5€1)x10ts ! and im;>10 keV. which are consistent with the standard see-saw mechanism."," It can also solve the cooling flow problem in clusters \citep{Chan} and explain the reionization of the universe \citep{Hansen}, all with the same decay rate $\Gamma_{3 \nu}=(5 +\pm 1) \times 10^{-17}$ $^{-1}$ and $m_s \ge 10$ keV, which are consistent with the standard see-saw mechanism." + This work is partially supported by a grant. fom the Research Grant Council of the Tong Kong Special Administrative Region. China (Project No.," This work is partially supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region, China (Project No." + 400805)., 400805). +"and CH30H(745-645) A (v;22) seem to form a shell around the continuum source Hot Core speaks against any internal heating scenario, rather suggesting that the heating to come from outside.","and $_3$ $_{4,3}$ $_{4,3}$ ) $^-$ $\nu_t$ =2) seem to form a shell around the continuum source Hot Core speaks against any internal heating scenario, rather suggesting that the heating to come from outside." +" The torsionally/vibrationally highly excited lines are exclusively placed along the densest and most highly obscured parts of Orion KL, i.e. on the Extended Ridge."," The torsionally/vibrationally highly excited lines are exclusively placed along the densest and most highly obscured parts of Orion KL, i.e. on the Extended Ridge." + We do not find any such emission associated with the Compact Ridge or the Northwest Clump., We do not find any such emission associated with the Compact Ridge or the Northwest Clump. +" This is in very good agreement with the observations of vibrationally excited HC3N(???).. However, comparison of our submillimeter line maps with those of millimeter wavelengths further reveals that the hottest molecular gas is only located in the northwest part of the millimeter/submillimeter source SMM3."," This is in very good agreement with the observations of vibrationally excited $_3$ N. However, comparison of our submillimeter line maps with those of millimeter wavelengths further reveals that the hottest molecular gas is only located in the northwest part of the millimeter/submillimeter source SMM3." +" The high angular resolution maps (< 1"") presented in differ considerably from ours as well as from the vibrationally", The high angular resolution maps $\leq$ $''$ ) presented in differ considerably from ours as well as from the vibrationally + , +lines.,lines. + In the bottom center panel. al /=1550 s. the hairpin has largely disappeared and αἱ (he same (ime we see the first evidence of the jet in the temperature plot to the right aud above the displaved field lines.," In the bottom center panel, at $t=1550$ s, the hairpin has largely disappeared and at the same time we see the first evidence of the jet in the temperature plot to the right and above the displayed field lines." + The bottom right panel. at /=1900 s. shows the emerging lied lines expanding and interacting with the pre-existing field and (hat cool gas has been ejecled into the corona to the right of the svstem ol field lines shown.," The bottom right panel, at $t=1900$ s, shows the emerging field lines expanding and interacting with the pre-existing field and that cool gas has been ejected into the corona to the right of the system of field lines shown." + The evolution of the Ποια lines shows (hey presumably have suffered reconnection before appearing at the surface: while in the eranule interior. emereing field lines seem to have reconnected with the pre-existing field resulting in the hairpin configuration of the emerging field lines.," The evolution of the field lines shows they presumably have suffered reconnection before appearing at the surface: while in the granule interior, emerging field lines seem to have reconnected with the pre-existing field resulting in the hairpin configuration of the emerging field lines." +Z/ybrid field lines (drawn in green in Fig. 4)), field lines (drawn in green in Fig. \ref{fig:emerg3d}) ) + result. linking the emerging svstem in (he granule interior with the pre-existing ambient coronal field. and with the higli-curvature stretch near the location where the reconnection is likely to have occured.," result, linking the emerging system in the granule interior with the pre-existing ambient coronal field, and with the high-curvature stretch near the location where the reconnection is likely to have occurred." + The portion of these field lines has a sharp hairpin shape which is difficult to reconcile with having resulted from processes other (han reconnection. such as¢.g.. the deformation caused by the exanular (lows.," The high-curvature portion of these field lines has a sharp hairpin shape which is difficult to reconcile with having resulted from processes other than reconnection, such as, the deformation caused by the granular flows." + This early reconnection may take place at different. heights in the eramue interior but in any case in high plasma-2 (1 Mm below the photosphere) aud it therefore does not have the spectacular consequences often associated wilh low plasma-5 reconnection: no jets or flows., This early reconnection may take place at different heights in the granule interior but in any case in high $\beta$ $1$ Mm below the photosphere) and it therefore does not have the spectacular consequences often associated with low $\beta$ reconnection; no jets or flows. + This kind of process might occur not only in (he quiet sun. network or internetwork. but also in plage. where the field is mostly unipolar.," This kind of process might occur not only in the quiet sun, network or internetwork, but also in plage, where the field is mostly unipolar." + Since our primary interest is to understand the consequences of these severely deformed field lines as (μον emerge into the chromosphere. we will not study. (he sub-surface reconnection in detail. onlv mention that this (or similar processes) can produce complex magnetic field configurations in the high plasma-2 part of the atmosphere (hat can survive emergence into the chromosphere.," Since our primary interest is to understand the consequences of these severely deformed field lines as they emerge into the chromosphere, we will not study the sub-surface reconnection in detail, only mention that this (or similar processes) can produce complex magnetic field configurations in the high $\beta$ part of the atmosphere that can survive emergence into the chromosphere." + Photospherice footpoint motions aud high curvature lead to laree magnetic field gradients and eventually a reorientation of the field in the chromospheric aud coronal lavers which is the ultimate source of the jet described in detail in section ??.., Photospheric footpoint motions and high curvature lead to large magnetic field gradients and eventually a reorientation of the field in the chromospheric and coronal layers which is the ultimate source of the jet described in detail in section \ref{sec:source}. + As mentioned above. the emereecl field lines and the pre-existing field [orm an angle to each other ancl a geometry similar (ο a rotational cliscontinuity. but the change in the orientation is small.," As mentioned above, the emerged field lines and the pre-existing field form an angle to each other and a geometry similar to a rotational discontinuity, but the change in the orientation is small." + Though we UV.ee Joule heating. such a small inclination may not be large enough to produce dvnamically V.ienificant reconnection in the chromosphere.," Though we see Joule heating, such a small inclination may not be large enough to produce dynamically significant reconnection in the chromosphere." + In the simulation. only a few granules show field configurations of sullicient complexity to lead to discontinuities in (he overlving chromosphere.," In the simulation, only a few granules show field configurations of sufficient complexity to lead to discontinuities in the overlying chromosphere." + Hence. only a few jets of the tvpe discussed here are formed aud launched during the entire numerical experiment.," Hence, only a few jets of the type discussed here are formed and launched during the entire numerical experiment." +If zo is taken as the injection point. i.e.. z;=οκ10!°em. we obtain: Eq. (3)),"If $z_0$ is taken as the injection point, i.e., $z_0\,=\,6\times +10^{10}\,\rm{cm}$, we obtain: Eq. \ref{prj}) )" + can be written in terms of the jet temperature (710) and the jet density έριο) at the injection point: Both cylindrical and slab simulations show that. initially. the jets are embedded in their cocoons.," can be written in terms of the jet temperature $T_{\rm j,0}$ ) and the jet density $\rho_{\rm j,0}$ ) at the injection point: Both cylindrical and slab simulations show that, initially, the jets are embedded in their cocoons." + However. as shown by the slab jet simulations. quickly the stellar wind starts to dynamically affect the bow-shock and the jet itself. and once the jet head has left the binary system. shocked wind will substitute cocoon material.," However, as shown by the slab jet simulations, quickly the stellar wind starts to dynamically affect the bow-shock and the jet itself, and once the jet head has left the binary system, shocked wind will substitute cocoon material." + We note that the properties of the wind change via shocking with the jet., We note that the properties of the wind change via shocking with the jet. + In this case. the relative pressure of the jet with respect to the ambient would also change. at least on the side where the wind impacts.," In this case, the relative pressure of the jet with respect to the ambient would also change, at least on the side where the wind impacts." + This, This +softwareNIGIITFALL.,software. +!.. We fixed the orbital period of the pulsar to the radio value and the surface temperature of COM-M2SIL to 7=6000 Ix. (as inferred [rom the position in the CAID)., We fixed the orbital period of the pulsar to the radio value and the surface temperature of COM-M28H to $T=6000$ K (as inferred from the position in the CMD). + We then used an iterative procedure letting the orbital inclination. (he mass ratio GCUxa/Meoy) and the Roche Lobe filling [actor vary respectively in Che ranges 0°—907. 1—20. and 0.1—I.," We then used an iterative procedure letting the orbital inclination, the mass ratio $M_{\rm NS}/M_{\rm COM}$ ) and the Roche Lobe filling factor vary respectively in the ranges $0\arcdeg-90\arcdeg$ , $1-20$, and $0.1-1$." + By using as selection criterion a A? test. the best-fit model (Figs.," By using as selection criterion a $\chi^2$ test, the best-fit model (Figs." + 4. and 6)) was obtained for an inclination /65. a mass ratio Mxa/Meoc1 and a Roche Lobe filline factor equal to 1.," \ref{Fig:lc_filters} and \ref{Fig:lc_combined}) ) was obtained for an inclination $i\simeq 65\arcdeg$, a mass ratio $M_{\rm + NS}/M_{\rm COM}\simeq 7$ and a Roche Lobe filling factor equal to 1." + These results confirm that a configuration with a highly distorted companion of about 0.2... orbiting a lay. MSP. in a plane with an orbital inclination of ~60—TO* well reproduces both the mass funcüon of the svstem derived from the radio observations. and the optical light curve of COM-M?2SIL. IC is worth noticing that a good fit can be obtained only if COALAI2Z811 completely filled its Roche Lobe. which. following Paczvuski (1971). we estimate to be ~0.6522...," These results confirm that a configuration with a highly distorted companion of about $0.2 M_\odot$, orbiting a $1.4 M_\odot$ MSP, in a plane with an orbital inclination of $\sim 60-70\arcdeg$ well reproduces both the mass function of the system derived from the radio observations, and the optical light curve of COM-M28H. It is worth noticing that a good fit can be obtained only if COM-M28H completely filled its Roche Lobe, which, following Paczynski (1971), we estimate to be $\sim 0.65 R_\odot$." + While such a large value of the stellar raclius allows to account Lor the observed huminositv of it is [ar too small to cause the observed radio eclipse., While such a large value of the stellar radius allows to account for the observed luminosity of it is far too small to cause the observed radio eclipse. + In fact an eclipse lasting for ~20% of the orbital period corresponds lo an eclipsing region of ~3.34. size.," In fact an eclipse lasting for $\sim +20\%$ of the orbital period corresponds to an eclipsing region of $\sim 3.3 R_\odot$ size." + This suggests that the eclipsing material is extending well bevond the Roche Lobe and that it is probably constantly replenished (see also Béeein 2006)., This suggests that the eclipsing material is extending well beyond the Roche Lobe and that it is probably constantly replenished (see also Béggin 2006). + Indeed. under the influence of the MISP intense radiation field. a (otherwise normal) MS star mav expand to fill its Roche Lobe (D'antona Erema 1993) and even start to lose mass. while (he accretion on the pulsar is inhibitecl by its magnetic pressure (as in (he case of MSP-A in NGC 6397: Ferraro et al 200110: see also Archibald et al.," Indeed, under the influence of the MSP intense radiation field, a (otherwise normal) MS star may expand to fill its Roche Lobe (D'antona Ergma 1993) and even start to lose mass, while the accretion on the pulsar is inhibited by its magnetic pressure (as in the case of MSP-A in NGC 6397; Ferraro et al 2001b; see also Archibald et al." + 2009)., 2009). + Moreover Bégein (2006) found a large orbital period derivative for this svstem. suggesting that the binary is losing material ancl is spiraling oul (to longer orbital period.," Moreover Béggin (2006) found a large orbital period derivative for this system, suggesting that the binary is losing material and is spiraling out to longer orbital period." + All these considerations indicate that COM-M28IE is a highlv-pertiurbed star which is ciurentlv losing mass. and that the svstem is surrounded by large clouds of gas.," All these considerations indicate that COM-M28H is a highly-perturbed star which is currently losing mass, and that the system is surrounded by large clouds of gas." + Whether or not part of the lost mass was accreted by the NS ancl served (o reaccelerate it in the past (as in the case of J10234-0038: Archibald et al., Whether or not part of the lost mass was accreted by the NS and served to reaccelerate it in the past (as in the case of J1023+0038; Archibald et al. + 2009) cannot be inferred. from the available cata., 2009) cannot be inferred from the available data. + We note however that. while from the natural cluster dvnamical evolution massive Objects are expected to be concentrated close to the centre. M281I is the second most olf-centered (alter M28F: Déggin et al.," We note however that, while from the natural cluster dynamical evolution massive objects are expected to be concentrated close to the centre, M28H is the second most off-centered (after M28F; Béggin et al." + 2010) and it is located outside the cluster core., 2010) and it is located outside the cluster core. + llence. such an offsetposition mav suggest the following scenario: (he NS was recvcled by," Hence, such an offsetposition may suggest the following scenario: the NS was recycled by" +suggests that a second flux rope formed from instabilities anc atmospheric reconnection is what lifts up the mass and forms the observed active region filaments.,suggests that a second flux rope formed from instabilities and atmospheric reconnection is what lifts up the mass and forms the observed active region filaments. + The main difference between the sheared arcade and the emerging flux rope models is the existence of a flux concentration stuck at photospherie levels in the latter scenario., The main difference between the sheared arcade and the emerging flux rope models is the existence of a flux concentration stuck at photospheric levels in the latter scenario. + The reader ts referred to the paper of ? for a recent review oi the magnetie structure of filaments., The reader is referred to the paper of \citet{mackay10} for a recent review on the magnetic structure of filaments. + In the past. only a few measurements of the magnetic field strength in AR filaments have been done.," In the past, only a few measurements of the magnetic field strength in AR filaments have been done." + For instance. ?.. using the same data set that is described in this. paper. found a predominance of Zeeman-like signatures in the Stokes profiles.," For instance, \citet{kuckein09}, using the same data set that is described in this paper, found a predominance of Zeeman-like signatures in the Stokes profiles." + Using three different methods. they inferred very strong magnetic fields in the filament GGauss). with a dominant transverse component (with respect to the line-of-sight).," Using three different methods, they inferred very strong magnetic fields in the filament Gauss), with a dominant transverse component (with respect to the line-of-sight)." + The aim of this paper is to study the strength and topology of the magnetic field in an active region filament at photospheric and chromospheric heights simultaneously., The aim of this paper is to study the strength and topology of the magnetic field in an active region filament at photospheric and chromospheric heights simultaneously. + Recently. several studies have presented analyses of the vector magnetic field in filaments or prominences from observations either in the photosphere (e.g..22222) or the chromosphere (e.g..?222).. but non of them have inferred the field at both heights at the same time.," Recently, several studies have presented analyses of the vector magnetic field in filaments or prominences from observations either in the photosphere \citep[e.g.,][]{lites05,lopez06,okamoto08,guo10,lites10} or the chromosphere \citep[e.g.,][]{lin98,casini03,merenda06,kuckein09}, but non of them have inferred the field at both heights at the same time." + The sspectral region. which includes a chromospheric triplet and a photospherie line. offers a unique spectral window to understand the physical processes that take place inAR filaments as already shown by ?..," The spectral region, which includes a chromospheric triplet and a photospheric line, offers a unique spectral window to understand the physical processes that take place inAR filaments as already shown by \citet{sasso11}." + In this work. we focus on the overall magnetic configuration observed simultaneously in the photosphere and the chromosphere.," In this work, we focus on the overall magnetic configuration observed simultaneously in the photosphere and the chromosphere." + The studied active region filament. NOAA AR 10781. was observed on 2005 July 3rd and Sth using the Tenerife Infrared Polarimeter (TIP-II.?) at the German Vacuum Tower Telescope (VTT. Tenerife. Spain).," The studied active region filament, NOAA AR 10781, was observed on 2005 July 3rd and 5th using the Tenerife Infrared Polarimeter \citep[TIP-II,][]{tip2} + at the German Vacuum Tower Telescope (VTT, Tenerife, Spain)." + TIP-II acquires images at 4 different modulation states and combines them in order to measure the Stokes parameters (7. Q. U and V) along the spectrograph slit.," TIP-II acquires images at 4 different modulation states and combines them in order to measure the Stokes parameters $I$, $Q$, $U$ and $V$ ) along the spectrograph slit." + The latitude and longitude of the filament region was (around ys~ 0.95) for the first day. and NI6-WI18 (jt.~ 0.91). for the second.," The latitude and longitude of the filament region was N16-E8 (around $\mu \sim 0.95$ ) for the first day, and N16-W18 $\mu \sim 0.91$ ), for the second." + During the observations. real time Ha images and SOHO//MDI (?) magnetograms were used as a reference to position the slit (0755 wide and 35”long) at the center of the AR. on top of the polarity inversion line.," During the observations, real time $\alpha$ images and /MDI \citep{mdi95} magnetograms were used as a reference to position the slit 5 wide and long) at the center of the AR, on top of the polarity inversion line." + Figure shows two Big Bear Ha images from July Ist and 5th where the filament can easily be recognized., Figure \ref{Fig:BBfil} shows two Big Bear $\alpha$ images from July 1st and 5th where the filament can easily be recognized. + OnJuly Ist. the filament shows a more diffusive nature than on July 5th. when it displays a rather compact configuration with brighter Hc emission from the plage flanking it.," OnJuly 1st, the filament shows a more diffusive nature than on July 5th, when it displays a rather compact configuration with brighter $\alpha$ emission from the plage flanking it." +" Scans were taken with TIP-II from east to west with the slit parallel to the PIL and step sizes of 0744 for July 3rd and 0733 for July Sth. making up at least a field of view (FOV) of ~30""x35"". with a pixel size along the slit of Q*117."," Scans were taken with TIP-II from east to west with the slit parallel to the PIL and step sizes of 4 for July 3rd and 3 for July 5th, making up at least a field of view (FOV) of $\sim 30\arcsec \times 35\arcsec$, with a pixel size along the slit of 17." + The TIP-II spectral range spanned from 10825 to 10836 wwith an original spectral sampling ofpx!., The TIP-II spectral range spanned from $10825$ to $10836$ with an original spectral sampling of. +. This spectral window included the photospherie line at aand the chromospheric triplet atAA., This spectral window included the photospheric line at and the chromospheric triplet at. +. It also contained at least one telluric H?O line which is used for the absolute velocity calibration., It also contained at least one telluric $_2$ O line which is used for the absolute velocity calibration. + All images were corrected for flat field. dark current and calibrated polarimetrically following standard procedures (??)..," All images were corrected for flat field, dark current and calibrated polarimetrically following standard procedures \citep{collados99,collados03}." + The adaptive optics system of the VTT (KAOS.?) was locked on nearby pores and orphan penumbrae. i.e.. penumbral-like structures not connected to any umbra (atermcoinedby ?).. and highly improved the observations which had changeable seeing conditions.," The adaptive optics system of the VTT \citep[KAOS,][]{kaos} was locked on nearby pores and orphan penumbrae, i.e., penumbral-like structures not connected to any umbra \citep[a term coined by][]{zirin91}, and highly improved the observations which had changeable seeing conditions." + A binning of 3 pixels in the spectral domain. ppx along the slit and ppx along the scanning direction was carried out to improve the signal-to-noise ratio needed for the full Stokes spectral line inversions.," A binning of 3 pixels in the spectral domain, px along the slit and px along the scanning direction was carried out to improve the signal-to-noise ratio needed for the full Stokes spectral line inversions." + Thus. the final spectral sampling was ~33.1 ppx!.," Thus, the final spectral sampling was $\sim 33.1$ $^{-1}$ ." +" The spatial resolution. when the KAOS system was locked. reached ~ .1"".."," The spatial resolution, when the KAOS system was locked, reached $\sim 1$ ." + However. the binned data used for the inversions (except when stated otherwise) had a resolution of," However, the binned data used for the inversions (except when stated otherwise) had a resolution of ." +our photometric detection threshold in all filters. ancl were not detected in the D band because the exposures were too short.,"our photometric detection threshold in all filters, and were not detected in the $B$ band because the exposures were too short." + The possible variability of the two sources was examined bv analvsing each frame separately., The possible variability of the two sources was examined by analysing each frame separately. + No clear indication of variability was revealed from this analysis. but we cannot strongly exelude this possibility since the S/N is quite low.," No clear indication of variability was revealed from this analysis, but we cannot strongly exclude this possibility since the $S/N$ is quite low." + Γον (1996) reported the absolute position of the MIAN-G source at Aeyuy=l6 41 44.0. 925400236 27 59.0.," Fox \shortcite{f96} reported the absolute position of the M13X-G source at $\alpha_{2000}$ =16 41 44.0, $\delta_{2000}$ =36 27 59.0." + Ligure 2. shows a region of ~60%ο) centered on the nominal position of M13X-CG. The contours of the X-ray emission from image retrived. from the archives have been overplotted on a numerical map of the FIGOBW image., Figure \ref{map} shows a region of $\sim 60\arcsec \times 60\arcsec$ centered on the nominal position of M13X-G. The contours of the X-ray emission from image retrived from the archives have been overplotted on a numerical map of the F160BW image. + The locations of he two UV objects are indicated by arrows., The locations of the two UV objects are indicated by arrows. + The position of star ZE2308] is ~a7 NW of the main bump of the X-ray map., The position of star $\#23081$ is $\sim 7$ NW of the main bump of the X-ray map. + Star 421429 is about IN of à 3.5m bump that Fox (1996). interpreted as a xickground. Uuctuation.," Star $\#21429$ is about N of a $\sigma$ bump that Fox \shortcite{f96} + interpreted as a background fluctuation." + We suggest that the Ποιατο) is real and will refer to it as MI3N-G-SIZ., We suggest that the “fluctuation” is real and will refer to it as M13X-G-SE. + Its approximate position and flux were measured. from the archival image and are given in Table 2., Its approximate position and flux were measured from the archival image and are given in Table 2. +" Because of the small number of counts the position is much less well determined than that of MI3X-G. While ccoordinates are generally good to (« 5"")). errors of iin absolute position are not uncommon in LH images (Davidetal.1992)."," Because of the small number of counts the position is much less well determined than that of M13X-G. While coordinates are generally good to $<5$ ), errors of in absolute position are not uncommon in HRI images \cite{davidetal92}." +. In our view. the connection between the UV stars and the X-ray. emission detected in the core of MIS is strong.," In our view, the connection between the UV stars and the X-ray emission detected in the core of M13 is strong." + Among the more than 3.000 measured stars in the WE2 region (50 SO arcsec). we found only 2 UV objects lving outside the CALD main branches.," Among the more than 3,000 measured stars in the WF2 region (80 $\times$ 80 arcsec), we found only 2 UV objects lying outside the CMD main branches." + Phere are only 3 faint UV objects in the entire [held of view containing more than 12.000 normal stars.," There are only 3 faint UV objects in the entire field of view containing more than 12,000 normal stars." + Only about 130. stars are withinDas ool the X-ray source. so the probability. of a chance coincidence of one UV object with MISN-€G is only aboutAA.," Only about 130 stars are within of the X-ray source, so the probability of a chance coincidence of one UV object with M13X-G is only about." + The case would be ereathy strengthened. if deeper observations confirm the reality of MI3X-CG-8SE., The case would be greatly strengthened if deeper observations confirm the reality of M13X-G-SE. + In subsequent data analysis we have found a third. UV object 331930) in WE3. but none in WE and the PC.," In subsequent data analysis we have found a third UV object 31930) in WF3, but none in WF4 and the PC." + The archival X-ray image shows no excess of emission. at the location of the third UV. star., The archival X-ray image shows no excess of emission at the location of the third UV star. + However. this UV star might also be associated with a LLGCN since LLGCXs are known to be hiehly time-variable (Llasingeretal.1994:llertz.Grindlay.&ανα 1993).," However, this UV star might also be associated with a LLGCX since LLGCXs are known to be highly time-variable \cite{hasinger94,hgb93}." +. Indeed. we predict. that further oobservations of MIS may find à LLGCN at this position.," Indeed, we predict that further observations of M13 may find a LLGCX at this position." + In addition to being associated with LLGCXs. we think itis likely that the UV stars are also CVs.," In addition to being associated with LLGCXs, we think it is likely that the UV stars are also CVs." + Perhaps. the most solid indication for this comes from Shara Drissen (1995).," Perhaps, the most solid indication for this comes from Shara Drissen (1995)." + Thev have recently found a UV object in the globular cluster ALSO. which they associate with T Sco. a nova observed in 1860.," They have recently found a UV object in the globular cluster M80, which they associate with T Sco, a nova observed in 1860." + The near UV. properties of T Sco are very similar to those of our objects., The near UV properties of T Sco are very similar to those of our objects. + There is possibly a LEGCX associated with T Sco. but the position from the PPSPC is not accurate enough for a definitive identification (Llakalaetal.1997).," There is possibly a LLGCX associated with T Sco, but the position from the PSPC is not accurate enough for a definitive identification \cite{hcjv97}." +. The derived: X-ray to optical Lux is also compatible with the value (fyffx~OS 412) found x Cool (1995) for three candidate CVs in NGC 6397.," The derived X-ray to optical flux is also compatible with the value $f_V/f_X \sim +0.8-4.2$ ) found by Cool (1995) for three candidate CVs in NGC 6397." + The UV to blue ratio of our objects is also similar to that of star Lin Sosin Cool (1995). a possible CV/LLGCX in iC 6624.," The UV to blue ratio of our objects is also similar to that of star 1 in Sosin Cool (1995), a possible CV/LLGCX in NGC 6624." + The connection to Ποιά CVs is more equivocal., The connection to field CVs is more equivocal. + From he photometric data Listed in Table 3.. we find Aly= and Ady=6.7 [ου H3081 and #21429. respectively.," From the photometric data listed in Table \ref{cands}, we find $M_V=7.8$ and $M_V=6.7$ for $\#23081$ and $\#21429$, respectively." + These figures are in good agreement with the typical absolute magnitude for CVs in the field ( \sim +7$, for the dwarf novae CVs; see van Paradijs 1983)." + The X-DHuninositv. of MIS3N-G. is Ly~6.5107cresee in the 24kkeV) band. quite compatible to that of Ποια CVs (Ly<107ergsec +) in the dkkeV band (Patterson&Itawvmond1985).," The X-luminosity of M13X-G is $L_X \sim 6.5 \times 10^{32} \ers$, in the keV) band, quite compatible to that of field CVs $L_X<10^{33} \ers$ ) in the keV band \cite{patterson85}." +. Phe ratio of X-ray to visible is Ly(0.12.4keV)~Lo which is well within the range covered by the field CVs (see Fig.," The ratio of X-ray to visible is ${{L_X(0.1-2.4\,{\rm keV})} / {L_V}} +\sim 1$, which is well within the range covered by the field CVs (see Fig." + 3 in Patterson Ravmonel 1985)., 3 in Patterson Raymond 1985). + We can make a similar comparison using only the softer X-rays observed by bby using Fig., We can make a similar comparison using only the softer X-rays observed by by using Fig. + 1 of Llakala (1997)., 1 of Hakala (1997). + They plot the PAPC counting rate in channels 11-235 against V., They plot the PSPC counting rate in channels 11-235 against $V$. + The 58 1Η! counts of Fox ((1996) correspond to about 200 PSPC counts and a counting rate of about 10.7etnsce+.," The 58 HRI counts of Fox (1996) correspond to about 200 PSPC counts and a counting rate of about $10^{-2}\,{\rm +ctn\,sec^{-1}}$." + This places it well above band occupied by CVs. but very near T Sco.," This places it well above band occupied by CVs, but very near T Sco." + The observed. Hux distribution also bears on this question., The observed flux distribution also bears on this question. + One can characterize the UV. radiation in terms of a blackbods: equivalent even if the radiation is not blackbods., One can characterize the UV radiation in terms of a blackbody equivalent even if the radiation is not blackbody. + Doing so we find a lower limit on the, Doing so we find a lower limit on the +and we used the origin conditions. (dzddr)= 1. and z(0)=0.,"and we used the origin conditions $[(dz/dr)(d\hat{R}/dz)]_0 = +[d\hat{R}/dr)]_0 = 1$ , and $z(0) = 0$." + It follows that Note that this equation dillers from the analogous one in Stoeger ct al their equation. (32) bv a factor of (1|z). and perhaps aptly illustrates the cilference in the coordinate systems.," It follows that Note that this equation differs from the analogous one in Stoeger et al — their equation (32) — by a factor of $(1+z)$, and perhaps aptly illustrates the difference in the coordinate systems." + To get the full model we have to solve the null Ravchaucdhuri equation (37)) to get r(2) (and thus 2(r))., To get the full model we have to solve the null Raychaudhuri equation \ref{eq:nraych}) ) to get $r(z)$ (and thus $z(r)$ ). + Equation (40)) is a first integral of (37))., Equation \ref{eq:fstint}) ) is a first integral of \ref{eq:nraych}) ). + This has to be integrated one more time to obtain r(2)., This has to be integrated one more time to obtain $r(z)$ . + We must also specify boundary conditions at the origin r=0. which we have already. used in getting to (40)): and also so that. integrating απας gives Subject to the conditions of appendix B.. for any given isotropic observations ἐς) n(z) with any given. source evolution functions {42) m(z). a set of LLB functions can be found to make the LPB observational relations fit the observations.," We must also specify boundary conditions at the origin $r += 0$, which we have already used in getting to \ref{eq:fstint}) ): and also so that, integrating $dr/dz$ gives Subject to the conditions of appendix \ref{ap2}, for any given isotropic observations $\ell(z)$ $n(z)$ with any given source evolution functions $\hat{L}(z)$ $\hat{m}(z)$, a set of LTB functions can be found to make the LTB observational relations fit the observations." + ‘To obtain the mass. energv and bangtime functions (M. I and fg respectively) from observational data and source evolution we would proceed as follows.," To obtain the mass, energy and bangtime functions $M$, $E$ and $t_B$ respectively) from observational data and source evolution we would proceed as follows." + 1n practice. these equations would. be solved numerically. and in. parallel rather than sequentially. nevertheless the above would determine the numerical procedure within each integration step.," In practice, these equations would be solved numerically, and in parallel rather than sequentially, nevertheless the above would determine the numerical procedure within each integration step." + By determining the 3 arbitrary functions. we have specified the LPB model that fits the given. observations and evolution functions.," $\Box$ By determining the 3 arbitrary functions, we have specified the LTB model that fits the given observations and evolution functions." + This result. simply asserts we can construct a (generally inhomogeneous) spherically svnunetric exact solution of the field. equations that will fit any given source observations combined with any chosen source evolution functions., This result simply asserts we can construct a (generally inhomogeneous) spherically symmetric exact solution of the field equations that will fit any given source observations combined with any chosen source evolution functions. + We assert. without proof. that if the given observations ancl source evolution functions are reasonable. then the LLB arbitrary functions will generate a reasonable LTD. model.," We assert, without proof, that if the given observations and source evolution functions are reasonable, then the LTB arbitrary functions will generate a reasonable LTB model." +" Our definition of ""reasonable is intentionally rather vague.", Our definition of `reasonable' is intentionally rather vague. + ὃν reasonable observations we obviously include the actual data. suitably processed. to account for selection. ellects.," By reasonable observations we obviously include the actual data, suitably processed to account for selection effects." +" We also include ""realistic hypothetical alternatives. but not functions that are wildly dillerent. from reality."," We also include `realistic' hypothetical alternatives, but not functions that are wildly different from reality." + Reasonable evolution functions are hard to define since the actual ones are not well known. especially at. larger z values.," Reasonable evolution functions are hard to define since the actual ones are not well known, especially at larger $z$ values." + By a reasonable LPB model. we mostly mean that the density and expansion rate will be within realistic ranges.," By a reasonable LTB model, we mostly mean that the density and expansion rate will be within realistic ranges." + AO less crucial criterion is that there will be no shell crossings too close to the past null cone., A less crucial criterion is that there will be no shell crossings too close to the past null cone. + Evolving the model a long time away from the null cone. either forwards or backwards. nay introduce shell crossings because the data is imprecise.," Evolving the model a long time away from the null cone, either forwards or backwards, may introduce shell crossings because the data is imprecise." + In general we don't expect shell crossings on the large scale Le. two or more cdillerent large scale Hows of galaxies in the sümeregion — nevertheless it is conceivable and in that case the LPB description is A LTD mocelcan be found to fitthe observations with zero evolution m= constant. £ = constant.," In general we don't expect shell crossings on the large scale — i.e. two or more different large scale flows of galaxies in the same region — nevertheless it is conceivable and in that case the LTB description is A LTB modelcan be found to fitthe observations with zero evolution — $\hat{m}$ = constant, $\hat{L}$ = constant." + This is an obvious consequence of (A)., This is an obvious consequence of (A). + , $\Box$ +"conservation equations that describe the downstream. Low are: pn—PsyPon=Pury (ne=syPon moto). poco. While the energy equation reads: where £ is the distance downstreamfrom the shock front. and. €, is the cooling due to the optically thin. hot plasma in CLE.","conservation equations that describe the downstream flow are: $\rho v = \rho_{sh} v_{sh} = \rho_0 v_0$ $n v = n_{sh} v_{sh} = n_0 v_0$ ), $\rho v^2 + p = \rho_0 v_0^2$ , while the energy equation reads: where $\xi$ is the distance downstreamfrom the shock front, and $Q_c$ is the cooling due to the optically thin, hot plasma in CIE." + In the steady-state case when cooling is elficient. the temperature decreases and the density increases downstream from the shock front.," In the steady-state case when cooling is efficient, the temperature decreases and the density increases downstream from the shock front." + The cooling. laver eventually ‘collapses’: that is. the gas velocity asvmptotically reaches zero.," The cooling layer eventually `collapses'; that is, the gas velocity asymptotically reaches zero." + Lt follows (see the momentum equation) that the gas pressure does not experience large variariations in the postshock plasma (3/4ppurs< Ll)., It follows (see the momentum equation) that the gas pressure does not experience large variariations in the postshock plasma $3/4 \leq p/\rho_0v_0^2 \leq 1$ ). + Thus. we adopt a constant-pressure approximation (CD) to describe the physical parameters of the postshock plasma.," Thus, we adopt a constant-pressure approximation (CPA) to describe the physical parameters of the postshock plasma." + As we will see below. this allows us to easily make use of the radiative shock moclel in the analysis of the X-ray emission.," As we will see below, this allows us to easily make use of the radiative shock model in the analysis of the X-ray emission." + Under the CPA. the energy. equation reads: where the cooling term is given explicith. 7 is the plasma temperature. & is the Bolzmann constant.=1./7 is the relative electron number density. μμ=nyη is the relative number density of hydrogen. and ACL) is the cooling function at CLE (e.g. Ravmond.Cox&Smith 1976)).," Under the CPA, the energy equation reads: where the cooling term is given explicitly, $T$ is the plasma temperature, $k$ is the Bolzmann constant, $x_e = n_e/n$ is the relative electron number density, $x_H = n_H/n$ is the relative number density of hydrogen, and $\Lambda(T)$ is the cooling function at CIE (e.g. \citealt{ray_76}) )." + To facilitate the caleulations. we followed a standard approach and made use of à plece-wise power-Iaw approximation to the cooling curve: (E)=Δον ," To facilitate the calculations, we followed a standard approach and made use of a piece-wise power-law approximation to the cooling curve: $\Lambda(T) = \Lambda_0 T^{\alpha}$." +In the high-temperature intervals (107<£x45lO and. Zxz4. 10°) the adopted values of the constants are Ay=75101.3στ and a=0.6.0.5 (e.g... Myasnikov.Zhekov&B," In the high-temperature intervals $10^5 \leq T \leq 4\times10^7$, and $T \geq 4\times10^7$ ) the adopted values of the constants are $\Lambda_0 = 7\times10^{-19}, 3\times10^{-27} $ and $\alpha = -0.6, 0.5$ (e.g., \citealt{myas_98}) )." +elov 1998)). Figure 1. shows a comparison between the exact. and the CPA solutions for the radiative shock and. illustrates that our choice (CPA) is acceptable for the purpose of the present study., Figure \ref{fig:rshock} shows a comparison between the exact and the CPA solutions for the radiative shock and illustrates that our choice (CPA) is acceptable for the purpose of the present study. + Moreover. as we will sce below. the CPA allows an easy incorporation of the radiative shock model in which. unfortunately. is not the case for the exact solution of the problem.," Moreover, as we will see below, the CPA allows an easy incorporation of the radiative shock model in which, unfortunately, is not the case for the exact solution of the problem." +" To determine the N-rav spectrum from a steady-state. plane-parallel. raciative shock (with ""surface! 21). we must integrate the hot plasma emissivity over a range of plasma temperatures in the temperature-stratified: postshock zone (Fig. 1):"," To determine the X-ray spectrum from a steady-state, plane-parallel, radiative shock (with `surface' $A$ ), we must integrate the hot plasma emissivity over a range of plasma temperatures in the temperature-stratified postshock zone (Fig. \ref{fig:rshock}) ):" +" where c(£.1) is the specific emissivity at given photon energy { and. plasma temperature 7 (its integral over the entire energv/spectral range gives the value of the cooling curve at Z7). £ is the distance from the shock front. and Z5, is the postshock temperature in keV. Then. using eq. (3))."," where $\epsilon(E,T)$ is the specific emissivity at given photon energy $E$ and plasma temperature $T$ (its integral over the entire energy/spectral range gives the value of the cooling curve at $T$ ), $\xi$ is the distance from the shock front, and $T_{sh}$ is the postshock temperature in keV. Then, using eq. \ref{eq:energy}) )," +" we can wrlte: where for numerical convenience we integrate over In7 insteacl of 7. ancl Pay, is the normalization. parameter."," we can write: where for numerical convenience we integrate over $\ln T$ instead of $T$, and $\Gamma_{sh}$ is the normalization parameter." + In this form. the X-ray spectrum from a radiative shock is well suited for modelling with : namely. we simply have a known power-law clistribution of emission measure at various temperatures. and we adopt an opticallv-thin plasma model (model caper in )) for the plasma spectrum at temperature % (given by the quantity ο1.," In this form, the X-ray spectrum from a radiative shock is well suited for modelling with : namely, we simply have a known power-law distribution of emission measure at various temperatures, and we adopt an optically-thin plasma model (model in ) for the plasma spectrum at temperature $T$ (given by the quantity $\epsilon[E,T]$ )." + Thus. our shock model have the following parameters: the postshock temperature με. chemical abundances and the normalization factor E;í. which is related to the total emission measure in the shock (some technical details are founcl in Appendix A)).," Thus, our shock model have the following parameters: the postshock temperature $T_{sh}$, chemical abundances and the normalization factor $\Gamma_{sh}$, which is related to the total emission measure in the shock (some technical details are found in Appendix \ref{app}) )." + Our global model assumes that X-rays. are. produced in radiative shocks which are randomly (and uniformly) distributed in. the stellar wind. most likely in the acceleration zone.," Our global model assumes that X-rays are produced in radiative shocks which are randomly (and uniformly) distributed in the stellar wind, most likely in the acceleration zone." + Therefore. the spectral lines in the total (integrated) X-ray spectrum from shocks are broadened. by the bulk (wind) gas velocity. but are not. shifted without including absorption.," Therefore, the spectral lines in the total (integrated) X-ray spectrum from shocks are broadened by the bulk (wind) gas velocity, but are not shifted without including absorption." + Qualitative physical considerations. also demonstrated by numerical modelling (ο... Owocki&Cohen 20013). show that the A-ray absorption effects. in the stellar wind result. in. blueshiftecl spectral lines with asvmmetrie line profiles.," Qualitative physical considerations, also demonstrated by numerical modelling (e.g., \citealt{ow_01}) ), show that the X-ray absorption effects in the stellar wind result in blueshifted spectral lines with asymmetric line profiles." + ‘To describe this physical situation we have constructed a new NSPEC mocel. whose technical aspects are given in Appendix A..," To describe this physical situation we have constructed a new XSPEC model, whose technical aspects are given in Appendix \ref{app}." + The main features of the model are: (1) shocks are characterized. by their postshock temperature and. the distribution of the total emission measures in the shocks is determined from the Chebyshev polynomial algorithm. as is used in the standard model eGpemAd (Lemenctal. 1989)..," The main features of the model are: (1) shocks are characterized by their postshock temperature and the distribution of the total emission measures in the shocks is determined from the Chebyshev polynomial algorithm, as is used in the standard model $c6pvmkl$ \citep{le_89}. ." + We note that a similar approach was successfully adopted in fitting the N-ray emission. from. an ensemble of adiabatic shocks (Zhekovetal. 2O00G6).. (, We note that a similar approach was successfully adopted in fitting the X-ray emission from an ensemble of adiabatic shocks \citep{zh_06}. . ( +2) The basis vectors for X-ray emission from the shock ensemble are those from the radiative shock model incorporated in (see 2.1). ,2) The basis vectors for X-ray emission from the shock ensemble are those from the radiative shock model incorporated in (see \ref{subsec:shock})). ( +3). Allshocks have the same elemental abundances andshare the same spectral line shifts.,3) Allshocks have the same elemental abundances andshare the same spectral line shifts. + Thus. the basic," Thus, the basic" +eov (CesffWa = (CB)(;LANs Here Ey=Figg/{1+0) is the energy associated with bulk motion of matter., ( = ( Here $E_K=E_{\rm iso}/(1+\sigma)$ is the energy associated with bulk motion of matter. + Only in the case ol zero magnetization rj; equals ray. since iu that case Ej=EyMu ," Only in the case of zero magnetization $r_{E}$ equals $r_{M}$, since in that case $ E_{\rm iso}=E_K = M_0 \gamma_w$." +"For highly magnetized outflow ""Mog "," For highly magnetized outflow $ +{r_{M} \over r_{E}} = \sigma^{-1/3} \ll 1 +$." +The above description of the lorward shock dynamics is. in fact. applicable ouly iu the so calledthin shell case. £>1 (see Eq. (3.1)).," The above description of the forward shock dynamics is, in fact, applicable only in the so calledthin shell case, $\xi >1$ (see Eq. \ref{xi}) )." + In this case the reverse shock quickly crosses the ejecta. which becomes causally couuected so that all of the ejecta interacts with the external inecdium.," In this case the reverse shock quickly crosses the ejecta, which becomes causally connected so that all of the ejecta interacts with the external medium." + Alternatively.in the thick shell case. £<1 (see Eq. (3.1)).," Alternatively,in the thick shell case, $\xi<1$ (see Eq. \ref{xi}) )," + the reverse shock does not have time to cross the ejecta before the causally connected shocked part starts to decelerate at smaller radius ray. Eq. (3.2)).," the reverse shock does not have time to cross the ejecta before the causally connected shocked part starts to decelerate at smaller radius $r_N$, Eq. \ref{rN}) )." + The Le'eutz [actor starts decreasing. but since new material aud uew momenttu is beiug added to the shocked part of the ejecta. the ejecta αμα the forward shock behave effectively as a self-similar shock with energy supply Siuce iu the thick shell case the Lorentz [actor starts to decelerate earlier than iu the thin shell case. the rate of energy trausler to the external inedium is smaller. so that the ejecta gives most of its initial enerey to the ISM at largerdistances ra>rp (?)..," The Lorentz factor starts decreasing, but since new material and new momentum is being added to the shocked part of the ejecta, the ejecta and the forward shock behave effectively as a self-similar shock with energy supply = ( = Since in the thick shell case the Lorentz factor starts to decelerate earlier than in the thin shell case, the rate of energy transfer to the external medium is smaller, so that the ejecta gives most of its initial energy to the ISM at largerdistances $r_\Delta > r_E$ \citep{Sari95}." + The weak reverse shock may form at (see Eq. (2.2))), The weak reverse shock may form at (see Eq. \ref{RSweak}) )) + — —qg, r = = + — —qgi, r = = + — —qgie, r = = + — —qgien, r = = + — —qgieny, r = = +The discovery of the X-ray PWN generated by BBIS30-08. suggestive of a pulsar bow-shock and a possible diffuse emission trailing the pulsar proper motion. provides new elements to the identification of J11834—087.,"The discovery of the X-ray PWN generated by B1830–08, suggestive of a pulsar bow-shock and a possible diffuse emission trailing the pulsar proper motion, provides new elements to the identification of J1834–087." + Accounting for a systematic uncertainty. the distance of BBIS30-08 is compatible with the one of W4I. 4.0+0.2 kpe (Tianetal.2007). which is likely associated to 111834—087 given the low probability of a chance superposition.," Accounting for a systematic uncertainty, the distance of B1830–08 is compatible with the one of W41, $4.0\pm0.2$ kpc \citep{tian07}, which is likely associated to J1834–087 given the low probability of a chance superposition." + The pulsar spin-down age is also consistent with the dynamical age of remnant. roughly 100 kyr (Tianetal. 2007).," The pulsar spin-down age is also consistent with the dynamical age of remnant, roughly 100 kyr \citep{tian07}." + As pointed out by Mukherjeeetal.(2009). the pulsar moves fast enough to have reached its current position starting only 40 kyr from the geometric centre of the remnant (see also Fig. 6..," As pointed out by \citet{mukherjee09}, the pulsar moves fast enough to have reached its current position starting only 40 kyr from the geometric centre of the remnant (see also Fig. \ref{B1830mosa}," + left panel)., left panel). + However. the Gamma-ray to X-ray flux ratio. Resppyffetoners~50 for the compact emission and 5.160 for the total X-ray emission. is lower than the one expected from the inverse correlation between this quantity and E (Mattanaetal. 2009).. which should be around 600 for BB1830-08.," However, the Gamma-ray to X-ray flux ratio, $F_{\mathrm{(E\,>\,1\,TeV})}/F_{\mathrm{(2-10\,keV)}} \sim 50$ for the compact emission and $\sim$ 10 for the total X-ray emission, is lower than the one expected from the inverse correlation between this quantity and $\dot{E}$ \citep{mattana09short}, which should be around 600 for B1830–08." + If JJ1834-08 is the relic PWN generated by BB1830-08. it is not very efficient in radiating in TeV gamma rays.," If J1834–08 is the relic PWN generated by B1830–08, it is not very efficient in radiating in TeV gamma rays." + Otherwise. it may be unrelated to BBIS30-08.," Otherwise, it may be unrelated to B1830–08." + The non-detection of a more extended X-ray emission trailing the pulsar does not support the association with JJ1834-O087 either., The non-detection of a more extended X-ray emission trailing the pulsar does not support the association with J1834–087 either. + Higher resolution and longer X-ray observations are needed to establish the nature of the halo and the detailed morphology of the compact emission. as well as singling out a possible contribution from the pulsar magnetosphere to the compact emission.," Higher resolution and longer X-ray observations are needed to establish the nature of the halo and the detailed morphology of the compact emission, as well as singling out a possible contribution from the pulsar magnetosphere to the compact emission." + We thank the referee. Vicky Kaspi. for valuable and constructive comments.," We thank the referee, Vicky Kaspi, for valuable and constructive comments." + This research is based on observations obtained withXMM-Newton. an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA.," This research is based on observations obtained with, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA." + We thank Norbert Schartel and the staff of the SScience Operation Center for promptly scheduling and executing our observations., We thank Norbert Schartel and the staff of the Science Operation Center for promptly scheduling and executing our observations. + The aand ddata were obtained through the HEASARC Online Service. provided by the NASA/GSFC.," The and data were obtained through the HEASARC Online Service, provided by the NASA/GSFC." + We thank the PPI. Neil Gehrels. the dduty scientists and science planners for making our ttarget of opportunity observations possible.," We thank the PI, Neil Gehrels, the duty scientists and science planners for making our target of opportunity observations possible." + We thank Hans Krimm for re-analyzing the Swi///BAT transient monitor and survey data for the time period following the outburst., We thank Hans Krimm for re-analyzing the /BAT transient monitor and survey data for the time period following the outburst. + We thank Philip Edwards of CSIRO for prompt allocations of observing time at the Parkes Observatory and the ATCA., We thank Philip Edwards of CSIRO for prompt allocations of observing time at the Parkes Observatory and the ATCA. + The Parkes Observatory and the ATCA are part of the Australia Telescope. which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO.," The Parkes Observatory and the ATCA are part of the Australia Telescope, which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO." + The Italian authors acknowledge the partial support from ASI (ASI/INAF contracts I/009/10/0.. I/011/07/0. I/010/06/0.. I/088/06/0. and AAE TH-058).," The Italian authors acknowledge the partial support from ASI (ASI/INAF contracts I/009/10/0, I/011/07/0, I/010/06/0, I/088/06/0, and AAE TH-058)." +" PE acknowledges financial support from the Autonomous Region of Sardinia through a research grant under the program PO Sardegna FSE 2007—2013. L.R. 7/2007 ""Promoting scientific research and innovation technology in Sardinia""."," PE acknowledges financial support from the Autonomous Region of Sardinia through a research grant under the program PO Sardegna FSE 2007--2013, L.R. 7/2007 “Promoting scientific research and innovation technology in Sardinia”." + FM and DG acknowledge the CNES for financial funding., FM and DG acknowledge the CNES for financial funding. + NR is supported by a Ramónn y Cajal fellowship., NR is supported by a Ramónn y Cajal fellowship. +The Galactic plane is an extended source of 5-racdiation.,The Galactic plane is an extended source of $\gamma$ -radiation. + This has been shown at energies 2 50 MeV with SAS 2 (Wartinan et al., This has been shown at energies $>$ 50 MeV with SAS 2 (Hartman et al. + 1979). COS-B (Strong ot al.," 1979), COS-B (Strong et al." + 1985). aud inost recentlv with EGRET (unter et al.," 1988), and most recently with EGRET (Hunter et al." + 1997)., 1997). + Observations made with COMPTEL have demoustrated that this cinission extends down to energies near d MeV (Strong ct al., Observations made with COMPTEL have demonstrated that this emission extends down to energies near 1 MeV (Strong et al. + 1996)., 1996). +" The diffuse Galactic continu at energies below 1 MeV is less well determined which is prinarilv duc to the presence of a nuuber of point sources, niuiv of which are variable."," The diffuse Galactic continuum at energies below 1 MeV is less well determined which is primarily due to the presence of a number of point sources, many of which are variable." + In an analysis of Galactic plane observations made with OSSE (Purcell et al., In an analysis of Galactic plane observations made with OSSE (Purcell et al. + 1996). it was found that. when the coutribution froun the prominent point sources nionitored cluring simultaneous observations with SIGALA is subtracted frou the Calactic center spectrmm measured with OSSE. the diffuse cussion is esscutially identical to that measured at /=25°.," 1996), it was found that, when the contribution from the prominent point sources monitored during simultaneous observations with SIGMA is subtracted from the Galactic center spectrum measured with OSSE, the diffuse emission is essentially identical to that measured at $l=25^\circ$." +" The residual iutensity is roughly coustaut over the central radian of the Galaxy. but is lower bv a factor Lat /z95"" (Skibo et al."," The residual intensity is roughly constant over the central radian of the Galaxy, but is lower by a factor 4 at $l\approx 95^\circ$ (Skibo et al." + 1997)., 1997). + If the residual chussion is due to discrete sources. 10 sources of flux 5.10P fem? /see/MeV at 100 keV nnst be preseut in the field of view of OSSE to make up 10 spectruni.," If the residual emission is due to discrete sources, 10 sources of flux $5\cdot 10^{-3}$ $^2$ /sec/MeV at 100 keV must be present in the field of view of OSSE to make up the spectrum." + Because no such class of sources with a uniform space density in longitude is kuowu. the cussion at about LOO seVoais probably of diffuse origi.," Because no such class of sources with a uniform space density in longitude is known, the emission at about 100 keV is probably of diffuse origin." + Estimdes based. ou he huninosities and muuiber-fix distributions of galactic sources indicate that the point source contrjbution to the wad X-ray endsson from the Galactic plane is less than (Yamasaki et al., Estimates based on the luminosities and number-flux distributions of galactic sources indicate that the point source contribution to the hard X-ray emission from the Galactic plane is less than (Yamasaki et al. + 1997: Kaneda 1997)., 1997; Kaneda 1997). + Similar results iwe been found i zu analysis of CRIS data CCebels et al., Similar results have been found in an analysis of GRIS data (Gehrels et al. + 1991)., 1991). + The residual source-subtracted spectrui of lis enuüssion changes from a photon index à=L7 at energies above 200x keV (Strong ot al., The residual source-subtracted spectrum of this emission changes from a photon index $\alpha =1.7$ at energies above 200 keV (Strong et al. + 1991) to a photou index a=2.7 at lower cnereies (Purcell et al., 1994) to a photon index $\alpha =2.7$ at lower energies (Purcell et al. + 1996)., 1996). + Thus the soft contimmim from the Galactic plane is more intense than the extrapolation of the lugher energv cuuission., Thus the soft continuum from the Galactic plane is more intense than the extrapolation of the higher energy emission. + Observations of the Galactic ridge in the hard X-rav range with CINGA (Yamasaki et al., Observations of the Galactic ridge in the hard X-ray range with GINGA (Yamasaki et al. + 1997) aud RXTE (Valinia Marshall 1998) indicate that the soft spectrum below 200 keV extends down to about 10 keV cnerey. though the best spectral fit between 15 keV aud 150 keV eives a photon iudex of à=2.3.," 1997) and RXTE (Valinia Marshall 1998) indicate that the soft spectrum below 200 keV extends down to about 10 keV energy, though the best spectral fit between 15 keV and 150 keV gives a photon index of $\alpha =2.3$." + The spectrum may also be represented by an exponentially absorped power-Itw of index ~1.7 and cut-off cuerey ~130 keV (Ixiuzer ct al., The spectrum may also be represented by an exponentially absorped power-law of index $\sim 1.7$ and cut-off energy $\sim 130$ keV (Kinzer et al. + 1995)., 1998). + Iu previous papers electron bremsstralhine has been considered. the iuost likely source of tιο soft) contimmun., In previous papers electron bremsstrahlung has been considered the most likely source of the soft continuum. + The power in cosimic rav elecrons required to produce a given amount of bremsstrahhme is a fixed quantity that depends ouly on the energy spectrum of the radiatiug electrons aud weakly on he ionization state of the interstellar inediuu., The power in cosmic ray electrons required to produce a given amount of bremsstrahlung is a fixed quantity that depends only on the energy spectrum of the radiating electrons and weakly on the ionization state of the interstellar medium. + Attributing this power input to injection iu cosmic rav clectrou sources it has been estimated. that a power of eLo!qup1057CLESπου1 ," Attributing this power input to injection in cosmic ray electron sources it has been estimated that a power of $10^{42}-10^{43} +\,{\rm ergs\ sec^{-1}}$ " +"aud where rg. 09. aud oy are the initial coordinates of a given photon. aud Ay. Ay. aud ο, are the components of its initial ποιοπια,","and where $r_0$ , $\theta_0$ , and $\phi_0$ are the initial coordinates of a given photon, and $k_{\rm r_0}$, $k_{\rm \theta_0}$, and $k_{\rm + \phi_0}$ are the components of its initial 3-momentum." + The time component of the Loimeutun is calculated from the 2-2uo1entuim Agsothat its nori vanishes., The time component of the 4-momentum is calculated from the 3-momentum $\vec{k}_0$sothat its norm vanishes. +Comparison of 1378 (1103) spectrum pairs results in median errors of 5x10~° and 1.4x10~* in the reproducibility of Az/(1+z) for and respectively.,"Comparison of 1378 (1103) spectrum pairs results in median errors of $\times$ $^{-5}$ and $\times$ $^{-4}$ in the reproducibility of $\Delta +z$ $z$ ) for and respectively." + The smaller error for results from the typically higher SNR of the emission compared to the line., The smaller error for results from the typically higher SNR of the emission compared to the line. +" Systematic trends, derived from linear fits to the redshift differences between and redshifts, are Azi(1+z)=2.1x107° per magnitude and Az/(1+z)=5.9x107° per unit redshift."," Systematic trends, derived from linear fits to the redshift differences between and redshifts, are $\Delta z$ $z$ $\times$ $^{-5}$ per magnitude and $\Delta z$ $z$ $\times$ $^{-5}$ per unit redshift." + The sense is that redshifts derived from the emission lines become systematically smaller for objects with higher luminosities(redshifts)., The sense is that redshifts derived from the emission lines become systematically smaller for objects with higher luminosities(redshifts). + The luminosity-dependent systematic is stronger than for redshift given the dynamic ranges of the variables present in the sample., The luminosity-dependent systematic is stronger than for redshift given the dynamic ranges of the variables present in the sample. + The trend is consistent with an increasing degree of blue-asymmetry present in the emission lines at increasing quasar luminosity., The trend is consistent with an increasing degree of blue-asymmetry present in the emission lines at increasing quasar luminosity. +" The effect is, however, small, amounting to a maximum of +4.5x 1075, or, +14kms~!,, about the mean relation for the sample."," The effect is, however, small, amounting to a maximum of $\pm$ $\times$ $^{-5}$, or, $\pm$, about the mean relation for the sample." + The empirically determined quasar-to-quasar rms-scatter of the individual redshifts about the redshifts is Cintrinzl.0x107* 1))., The empirically determined quasar-to-quasar rms-scatter of the individual redshifts about the redshifts is $\sigma_{intrin}$ $\times$ $^{-4}$ ). +" emission line redshifts compared to redshifts, calculatedexcluding the emission lines from the quasar template, for 24125500 quasars with emission line reshifts shows an undetectable offset, median |Az/(1+z)|<10~°."," emission line redshifts compared to redshifts, calculated the emission lines from the quasar template, for $\simeq$ 500 quasars with emission line reshifts shows an undetectable offset, median $|\Delta z$ $z$ $|$$<$ $^{-5}$." +" Systematic trends, from linear fits to the redshift differences, in sense - redshifts, are Az/(1+z)=+1x 107? per magnitude and Az/(1+z)=-1.1x10~* per unit redshift."," Systematic trends, from linear fits to the redshift differences, in sense - redshifts, are $\Delta z$ $z$ $\times$ $^{-5}$ per magnitude and $\Delta +z$ $z$ $\times$ $^{-4}$ per unit redshift." +" Both luminosity and redshift parameterisations lead to systematics of at most +3 x 107? (10kms~*)), for the dynamic ranges present in the sample, more than an order of magnitude below the uncertainties in the individual redshifts (Section ??))."," Both luminosity and redshift parameterisations lead to systematics of at most $\pm$ $\times$ $^{-5}$ ), for the dynamic ranges present in the sample, more than an order of magnitude below the uncertainties in the individual redshifts (Section \ref{sec:caii_host}) )." + The sense and amplitude of the small systematic is consistent with the results from the to emission line comparison (Section ??)) and is again almost certainly due to the increasing degree of blue-asymmetry present in the emission lines at increasing quasar luminosity., The sense and amplitude of the small systematic is consistent with the results from the to emission line comparison (Section \ref{sec:oxcomp}) ) and is again almost certainly due to the increasing degree of blue-asymmetry present in the emission lines at increasing quasar luminosity. +" The comparison shows that the redshifts are tied to the reference emission line redshifts to very high accuracy and that any systematics present are at most 107 in Az/(1+z), or ‘in velocity."," The comparison shows that the redshifts are tied to the reference emission line redshifts to very high accuracy and that any systematics present are at most $^{-4}$ in $\Delta z$ $z$ ), or in velocity." +" The empirically determined quasar-to-quasar scatter of the individual redshifts about the redshifts is Ointrin=2.5X 1074 or75kms~‘,, which represents an improvement of a factor of ~3 compared to careful determinations of the emission line location2008)."," The empirically determined quasar-to-quasar scatter of the individual redshifts about the redshifts is $\sigma_{intrin}$ $\times$ $^{-4}$ or, which represents an improvement of a factor of $\sim$ 3 compared to careful determinations of the emission line location." +". The luminosity-dependent correction to bring the and redshifts into coincidence is highly successful, as evidenced by Fig."," The luminosity-dependent correction to bring the and redshifts into coincidence is highly successful, as evidenced by Fig." + 7 and Fig. 8.., \ref{hw_ciii_mabs} and Fig. \ref{hw_ciii_z}. + After allowing for the uncertainty in the determination of the and redshifts due to the limited SNR of the SDSS spectra there is no evidence for an additional quasar-to-quasar redshift scatter associated with the use of the emission line region alone., After allowing for the uncertainty in the determination of the and redshifts due to the limited SNR of the SDSS spectra there is no evidence for an additional quasar-to-quasar redshift scatter associated with the use of the emission line region alone. + The diversity of the form of the emission line has been known through many studies going back decades., The diversity of the form of the emission line has been known through many studies going back decades. +" The removal of the systematic quasar luminosity-dependent behaviour, amounting to ~650 (over four magnitudes in quasar absolute magnitude), improves redshifts considerably."," The removal of the systematic quasar luminosity-dependent behaviour, amounting to $\simeq$ (over four magnitudes in quasar absolute magnitude), improves redshifts considerably." +" However, even for quasars with small AEW values the empirically determined quasar- scatter of the individual redshifts about the redshifts is Cintrin=8.0X10~*."," However, even for quasars with small AEW values the empirically determined quasar-to-quasar scatter of the individual redshifts about the redshifts is $\sigma_{intrin}$ $\times$ $^{-4}$." + The situation is much worse for quasars with significant absorption blueward of the emission line centroid., The situation is much worse for quasars with significant absorption blueward of the emission line centroid. + The systematic correction applied reaches a full 5x10? for the most affected quasars and the dispersion at fixed AEW value adds an additional rms-scatter of Cintrin zlX 107?., The systematic correction applied reaches a full $\times$ $^{-3}$ for the most affected quasars and the dispersion at fixed AEW value adds an additional rms-scatter of $\sigma_{intrin}$ $\times$ $^{-3}$. +" The number of quasars with large AEW values where only redshifts are available is small, just 574 objects, but the associated redshift uncertainty is accordingly large."," The number of quasars with large AEW values where only redshifts are available is small, just 574 objects, but the associated redshift uncertainty is accordingly large." + Fig., Fig. + 10 shows the redshift differences between the corrected and corrected redshifts for 0008 quasars with only modest absorption (AEW<20) blueward of the emission line., \ref{ciii_civ_z} shows the redshift differences between the corrected and corrected redshifts for 008 quasars with only modest absorption $\le$ 20) blueward of the emission line. + The small amplitude of the systematic differences illustrates the success of the statistical correction to the initial redshifts., The small amplitude of the systematic differences illustrates the success of the statistical correction to the initial redshifts. +" However, the systematic negative trend centred on z~2.8, which reaches ~-1.8x 107+ 1)), illustrates the limitations of the correction."," However, the systematic negative trend centred on $z$$\simeq$ 2.8, which reaches $\simeq$ $\times$ $^{-4}$ ), illustrates the limitations of the correction." + The SDSS quasar selection experiences a dramatic drop in efficiency over the interval 2c-2.1-2.9 that is much greater for non-BAL quasars than for BAL quasars., The SDSS quasar selection experiences a dramatic drop in efficiency over the interval $z$$\simeq$ 2.7–2.9 that is much greater for non-BAL quasars than for BAL quasars. +" Thus, the overall number of quasars drops significantly, while the BAL-fraction increases significantly."," Thus, the overall number of quasars drops significantly, while the BAL-fraction increases significantly." +" There are only 13 quasars with 2.7$ 20 All redshift estimates, except those taken direct from the SDSS, have been increased by (Section \ref{sec:caii_host}) ) to bring the" +over (he entire computational volume was weaker in the past. because the volume and mass fractions of strong-field regions were smaller.,"over the entire computational volume was weaker in the past, because the volume and mass fractions of strong-field regions were smaller." + To reproduce the cosmic space. we stacked simulation boxes up to z=5. basically following the conventional manner of cosmological data stacking2000).," To reproduce the cosmic space, we stacked simulation boxes up to $z=5$, basically following the conventional manner of cosmological data stacking." +. We took outpuls al zou= 0. 0.2. 0.5. 1.0. 1.5. 2.0. 3.0. ancl 5.0. ancl pul the outputs of the closest recshilt for stacking boxes: 56 boxes were required (ο reach z=5.," We took outputs at $z_{\rm out}=$ 0, 0.2, 0.5, 1.0, 1.5, 2.0, 3.0, and 5.0, and put the outputs of the closest redshift for stacking boxes; 56 boxes were required to reach $z=5$." + The stacking boxes were randomly selected [rom sixteen simulations and randomly rotated to avoid any artificial coherent. structure along the LOS., The stacking boxes were randomly selected from sixteen simulations and randomly rotated to avoid any artificial coherent structure along the LOS. + Ifa LOS went out of the boundary of a box. we applied the periodic boundary condition in which we replicated the box across the LOS.," If a LOS went out of the boundary of a box, we applied the periodic boundary condition in which we replicated the box across the LOS." + We also carried out (he caleulation with the open boundary condition in which we did not replicate the box but put different one [rom sixteen simulation outputs. and confirmed that the statistical properties of RM we examined are not sensitive to the boundary conditions.," We also carried out the calculation with the open boundary condition in which we did not replicate the box but put different one from sixteen simulation outputs, and confirmed that the statistical properties of RM we examined are not sensitive to the boundary conditions." + Our Galaxy is located in the Local Group., Our Galaxy is located in the Local Group. + Since the Local Group is probably filled with ihe magnetized WIIIM. the observed RAL could contain a contribution from the IGME of the Local Group (see Section 3.1).," Since the Local Group is probably filled with the magnetized WHIM, the observed RM could contain a contribution from the IGMF of the Local Group (see Section 3.1)." + It would have been ideal to place the “observer” where the IGME and eas density. are similar to those in the Local Group., It would have been ideal to place the “observer” where the IGMF and gas density are similar to those in the Local Group. + Unlortunately. however. nol much is known about (he plivsical states of the Local Group.," Unfortunately, however, not much is known about the physical states of the Local Group." + Hence. following(2008).. instead. we selected groups of galaxies identified im (he simulation data that have similar halo gas temperatures to the Local Group.," Hence, following, instead, we selected groups of galaxies identified in the simulation data that have similar halo gas temperatures to the Local Group." + We considered two cases: groups al ος with 0.05 keV < APY < 0.15 keV and groups al z=0 with 0.05 keV « Εν < 0.5 keV2001).. Here. Ty is the X-ray. temperature (see Section 2.7).," We considered two cases: groups at $z=0$ with 0.05 keV $<$ $k T_X$ $<$ 0.15 keV and groups at $z=0$ with 0.05 keV $<$ $k T_X$ $<$ 0.5 keV. Here, $T_X$ is the X-ray temperature (see Section 2.7)." +" Assuming that these groups are located in a phvsieal environment similar to that of the Local Group. we placed “mock observers"" at the center of the eroups."," Assuming that these groups are located in a physical environment similar to that of the Local Group, we placed “mock observers” at the center of the groups." + We aim to simulate wide-field. high-sensitivity IM survevs that will be achieved with [uture radio interferometers.," We aim to simulate wide-field, high-sensitivity RM surveys that will be achieved with future radio interferometers." + For instance. the upcoming POSSUM (Polarization Sky Survey ol the Universes Magnetism) project. one of the major surveys planned lor the ASINAD. will," For instance, the upcoming POSSUM (Polarization Sky Survey of the Universe's Magnetism) project, one of the major surveys planned for the ASKAP, will" +Space missions targeting Earth-sized planets in Earth-like orbits will search a different range of parameter space. seeking shallower (ransils bv objects in longer-period orbits.,"Space missions targeting Earth-sized planets in Earth-like orbits will search a different range of parameter space, seeking shallower transits by objects in longer-period orbits." + For (he purposes of these missions. all of the signal categories so far considered represent possible false alarms.," For the purposes of these missions, all of the signal categories so far considered represent possible false alarms." + The rightmost column of Table 1 shows their expected rates of occurrence per 104 target stars. for a survev that is magnitude-Iimited at R=L4. and for transit parameters in the ranges 30dv_H$. + The second expression describes (he mutual excitation among the large KBOs for e«ey., The second expression describes the mutual excitation among the large KBOs for $vος1072 W | that have Ty>IC.," There are no galaxies in the sample with $L_{4.8}> 2 +\times 10^{21}$ W $^{-1}$ that have $\Pi_0 > 4 \%$ ." +" Most eaaxies with Lp.<5«107"" W ! do ive Ty>|"," Most galaxies with $L_{4.8}< 5 \times 10^{20}$ W $^{-1}$ do have $\Pi_0 > 4 +\%$." + As shown in Figure l.. a galaxy can rave low Ty because of strong Faraday depolarization. or because of its inclination.," As shown in Figure \ref{diskpol_model-fig}, a galaxy can have low $\Pi_0$ because of strong Faraday depolarization, or because of its inclination." + There is no correlation vetween juclination auc huninositv iu the sample., There is no correlation between inclination and luminosity in the sample. + The ower integrated. polarization of luminous salaxies iu Figure 3bb sugeests stronecr Faraday. depolarization iu hese galaxies. or a lower degree of uniformity of the naenetic field as will be discussed iu Section 1.1..," The lower integrated polarization of luminous galaxies in Figure \ref{PI_L-fig}b b suggests stronger Faraday depolarization in these galaxies, or a lower degree of uniformity of the magnetic field as will be discussed in Section \ref{discussion1}." +. The principal cause of uct polarization of unresolved spiral ealaxies is the regular azimuthal maguetic field iu the disk projected on the sky along the apparent major axis., The principal cause of net polarization of unresolved spiral galaxies is the regular azimuthal magnetic field in the disk projected on the sky along the apparent major axis. + Faraday rotation and depolarization are affected bv the path leugth through the disk. the line-of-ieht component of the regular maeuetic field. aud fluctuations in thermal electron density aud maguctic field streneth.," Faraday rotation and depolarization are affected by the path length through the disk, the line-of-sight component of the regular magnetic field, and fluctuations in thermal electron density and magnetic field strength." + A first analysis of the integrated polarization of spiral ealaxies is best served with the simplest possible model that includes these factors., A first analysis of the integrated polarization of spiral galaxies is best served with the simplest possible model that includes these factors. + We consider axially svinmnetric models with a regular azimuthal magnetic field iu the disk. and an isotropic random componcut ofthe magnetic field.," We consider axially symmetric models with a regular azimuthal magnetic field in the disk, and an isotropic random component of the magnetic field." + Using this simple geometry. the integrated polarization of a spiral galaxy is modeled by considerimg each solid angle clement of the disk as a slab with a specified hue-ofsight componcut of the regular maguetic field that depends on inclination and location iu the disk.," Using this simple geometry, the integrated polarization of a spiral galaxy is modeled by considering each solid angle element of the disk as a slab with a specified line-of-sight component of the regular magnetic field that depends on inclination and location in the disk." + Sokoloffetal.(1998) provided. solutions of polarized intensity from a slab of Faraday-rotating medium mixed with relativistic electrons that produce svuchrotrou cluission., \citet{sokoloff1998} provided solutions of polarized intensity from a slab of Faraday-rotating medium mixed with relativistic electrons that produce synchrotron emission. + The polarized intensity ijs expressed as a complex quantity P=0Q|jU (Spangler1982).. where Q and C are Stokes parameters that describe the luear polarization.," The polarized intensity is expressed as a complex quantity $\mathcal{P} = Q + j U$ \citep{spangler1982}, where $Q$ and $U$ are Stokes parameters that describe the linear polarization." + Following the couveutious adopted bv Sokoloffetal.(1998)... P. Q. and C ire normalized bv the total iuteusitv of the svuchrotron radiation. so that the modulus of P is the fractional polarization.," Following the conventions adopted by \citet{sokoloff1998}, $\mathcal{P}$ , $Q$, and $U$ are normalized by the total intensity of the synchrotron radiation, so that the modulus of $\mathcal{P}$ is the fractional polarization." + The polarization angle of the complex polarization is Y=iowetan(UQ)., The polarization angle of the complex polarization is $\Psi = \onehalf \arctan (U/Q)$. + At hieher frequencies. a contribution from thermal cluission to the total intensity reduces the observed fractional polarization bv a factor (1fin). where fe is the fraction of the total intensity generated by thermal cussion.," At higher frequencies, a contribution from thermal emission to the total intensity reduces the observed fractional polarization by a factor $1-f_{th}$ ), where $f_{th}$ is the fraction of the total intensity generated by thermal emission." + We include thermal cussion by setting fe=023 at L8 GIIZ (Condon&Yin1990:Con-don1992:Niklasetal. 1997)..," We include thermal emission by setting $f_{th} = 0.23$ at 4.8 GHz \citep{condon1990,condon1992,niklas1997}. ." +" Determination of fj, iu individual galaxies is απο because of the need to separate thermal aud non-therual euissiou iu the radio spectriuu.", Determination of $f_{th}$ in individual galaxies is difficult because of the need to separate thermal and non-thermal emission in the radio spectrum. +" The rius scatter in fj, frou galaxy to galaxy is believed. to be at most a factor of 2 (Condon1992).", The rms scatter in $f_{th}$ from galaxy to galaxy is believed to be at most a factor of 2 \citep{condon1992}. +. This translates ito a spread of ~25% m (1——fen) from the adopted value of 0.77.," This translates into a spread of $\sim +25\%$ in $1-f_{th}$ ) from the adopted value of 0.77." + Tn this paper we adopt a solution for the polarized intensity from a uniform slab of finite thickness along the line of sight from Sokoloffetal.(1998)., In this paper we adopt a solution for the polarized intensity from a uniform slab of finite thickness along the line of sight from \citet{sokoloff1998}. +. For a eiven inclination 7. the component of the regular magnetic field along the line of sight aud perpendicular to the Ine of sight By can be evaluated.," For a given inclination $i$, the component of the regular magnetic field along the line of sight $B_\|$ and perpendicular to the line of sight $B_\bot$ can be evaluated." +By) The uniformity of the naenetic field is expressed as the ratio of the isotropic random magnetic field streneth to the regular magnetic Ποια streneth. defined as fp=συν8. where ap is the rns strength of the random component of the magnetic field in one direction.," The uniformity of the magnetic field is expressed as the ratio of the isotropic random magnetic field strength to the regular magnetic field strength, defined as $f_B=\sigma_{\rm B}\sqrt{3}/B$, where $\sigma_{\rm B}$ is the rms strength of the random component of the magnetic field in one direction." + The complex polarization can be written as the xoduct of a waveleneth-independent part that descriCR he polarization if Faraday rotation effects can be welected. and ai waveleneth-dependent part that includes Faraday rotation effects.," The complex polarization can be written as the product of a wavelength-independent part that describes the polarization if Faraday rotation effects can be neglected, and a wavelength-dependent part that includes Faraday rotation effects." +" The waveleneth-independent part of the complex polarization is where p;20.75 is the intrinsic maxiuun polarization for svuchrotron emission ina regular magnetic field. aud D, aud D, are the components of the regular maguetic field along two orthogonal axes in the plane of the sky."," The wavelength-independent part of the complex polarization is where $p_i \approx 0.75$ is the intrinsic maximum polarization for synchrotron emission in a regular magnetic field, and $B_x$ and $B_y$ are the components of the regular magnetic field along two orthogonal axes in the plane of the sky." + Equation 1 assumes aconstaut spectral index of 1 for the svuchrotron emission of a galaxy., Equation \ref{P0-eq} assumes aconstant spectral index of $-1$ for the synchrotron emission of a galaxy. + We define the soaetsalong the apparent major axis of the disk., We define the $x-axis$along the apparent major axis of the disk. + The brackets indicate that the cussion is averaged over, The brackets $\langle \cdot \rangle$ indicate that the emission is averaged over +wave frequency of the fluid (Balbus2003): Aneular momentiun is likely to be transported inwards by loug-period. iucomrpressible perturbations: aud. outwards by μισο]οποιον. compressible disturbances.,"wave frequency of the fluid \citep{balbus03b}: Angular momentum is likely to be transported inwards by long-period, incompressible perturbations; and outwards by high-frequency, compressible disturbances." + Still. other authors have poiuted out that hvdrodsynanic waves orienmate by the gravitational field of a companion star could possibly transport augular momentum (Vishiuniac&Diamoud1989:RozvezkaSpruit 1993).," Still, other authors have pointed out that hydrodynamic waves originated by the gravitational field of a companion star could possibly transport angular momentum \citep{VD89, RS93}." +. This iiechanisuni however. makes use of an OexterualO source to excite. and maintain. such deusity waves: therefore it can not explain accretion in stars that do not belong to numultiple systems.," This mechanism, however, makes use of an ÔexternalÕ source to excite, and maintain, such density waves; therefore it can not explain accretion in stars that do not belong to multiple systems." + Finallv. although eravitational instabilities (c.g.Adams.Ruden&Shu1989:Duriseuοal.2007) iav play a role. these may ο effective mostly during carly stages of evolution of hese objects. and for particularly massive disces.," Finally, although gravitational instabilities \citep[e.g.][]{ARS89, D07a} may play a role, these may be effective mostly during early stages of evolution of these objects, and for particularly massive discs." + It is increasingly clear that the two most eenerallv applicable angular momentum transport processes are uecdiated by the action of maguetic fields aud their interaction with disc matter., It is increasingly clear that the two most generally applicable angular momentum transport processes are mediated by the action of magnetic fields and their interaction with disc matter. + They are the following., They are the following. + These processes are. in turn. likely to strongly affect he structure. dvuauies. evolutionary path aud plauct-ornüue capabilities of their host disces.," These processes are, in turn, likely to strongly affect the structure, dynamics, evolutionary path and planet-forming capabilities of their host discs." + Iu the next wo sections I describe in more detail the operation of these two forms of augular momentum transport iu xotostellar discs., In the next two sections I describe in more detail the operation of these two forms of angular momentum transport in protostellar discs. + I then briefly consider the possibility or their operation at the same racius. but at different icielits above the dise midplane.," I then briefly consider the possibility for their operation at the same radius, but at different heights above the disc midplane." + Fast. collinmated winds are commonly observed iu accreting astrophysical svstcis.," Fast, collimated winds are commonly observed in accreting astrophysical systems." + It is likely that these outflows transport aneular momentum away from the disc that surrounds the central object aud thus. play an Huportant role in regulating accretion2011).," It is likely that these outflows transport angular momentum away from the disc that surrounds the central object and thus, play an important role in regulating accretion." +. The apparent correlation between outflow aud accretion signatures in these svsteuis (6.8.etal.1995).. lends support to this interpretation.," The apparent correlation between outflow and accretion signatures in these systems \citep[e.g.][]{CES90, CA91, HEG95}, lends support to this interpretation." + The details of this inflow-outflow mechanism are far οι being well understood. but it is thought that this process iav be mediated by magnetic stresses [Blandford&Payne1982: Wardle&Ionigl1993 (hereafter DPS2 and WIS93. respectively}: Li.1996]].," The details of this inflow-outflow mechanism are far from being well understood, but it is thought that this process may be mediated by magnetic stresses \citealt{BP82}; \citealt{WK93} (hereafter BP82 and WK93, respectively); \citealt{L96}] ]." + Fie., Fig. + 2) shows a typical cdisc-wind solution. plotted as a function of τπι T," \ref{fig:illus} shows a typical disc-wind solution, plotted as a function of $z/h_{\rm T}$." +his solution has been computed using the procedure detailed in IKSWIO aud Saliicrouetal.(2011.hereafterSNW11):: in turn a generalisatiou of the formulation bv W893., This solution has been computed using the procedure detailed in KSW10 and \citet[][hereafter SKW11]{SKW11}; in turn a generalisation of the formulation by WK93. + The model parinoeters are: We will also use the expression Y=pis/Og. the ratio of the Keplerian rotation time to the neutral-1ο. inoluentuni exchange time (e.g. WI&K93: see also footnote 2)).," The model parameters are: We will also use the expression $\Upsilon \equiv \rho_{\rm i} \gamma_{\rm i}/\Omega_{\rm K}$, the ratio of the Keplerian rotation time to the neutral-ion momentum exchange time (e.g. WK93; see also footnote \ref{foot:note2}) )." +" It can be shown that in the ambipolar regime A=Y. whereas in the Tall limit A=Τη (e.g, IKSW10)."," It can be shown that in the ambipolar regime $\Lambda = \Upsilon$, whereas in the Hall limit $\Lambda = \Upsilon |\beta_{\rm i}|$ (e.g. KSW10)." + The left pancl of Fig., The left panel of Fig. + 2 displavs the eas density (normalised bv its value at the nüdpluie) as well as the radial aud. azimuthal components of the magnetic field (normalised by the vertical field. which uuder the," \ref{fig:illus} displays the gas density (normalised by its value at the midplane) as well as the radial and azimuthal components of the magnetic field (normalised by the vertical field, which under the" +constraints. and the data points of CDM. show a large scatter. preventing one to conclude a meaniusful AL/£ correlation.,"constraints, and the data points of CDM show a large scatter, preventing one to conclude a meaningful $M_*/L$ correlation." + The SPS predictions of AL./L ratios ave scusitive o the adopted IME., The SPS predictions of $M_*/L$ ratios are sensitive to the adopted IMF. + The AL/£ ratios inferred from Salpeter’s TIATF are notably higher than those obtained roni Ikxroupa s., The $M_*/L$ ratios inferred from Salpeter's IMF are notably higher than those obtained from Kroupa's. +MIONDS3 favors Iroupas IME., MOND3 favors Kroupa's IMF. + It produces ower M./L aud nmaplies lesser disk masses., It produces lower $M_*/L$ and implies lesser disk masses. +"iutrachluster imecdiun the Mach απο is AM~ 2.1-2.7 and the angle of the Mach cone (half of the openiug auele) is a=su(ij 22.28"".",intracluster medium the Mach number is $M \sim 2.1$ $2.7$ and the angle of the Mach cone (half of the opening angle) is $\alpha=\sin^{-1}(\frac{1}{M})=22$ $28^{\circ}$. + On the other haud. since the verv temous (n~10! 35) iutracluster medium is fully ionized aud inaguetized. the sound speed has to be replaced by the maguetosonic velocity ey.=VIS| e). where the Alfvénn speed is (4=B ," On the other hand, since the very tenuous $n \sim 10^{-4}$ $^{-3}$ ) intracluster medium is fully ionized and magnetized, the sound speed has to be replaced by the magnetosonic velocity $v_{\rm ms}=\sqrt{(c^2+v_{\rm A}^2)}$ , where the Alfvénn speed is $v_{\rm a}=\frac{B}{\sqrt{4\pi n m_{\rm p}}}$." +Typical iiagnetie field streugths iu galaxy clusters are of the order of a few µ (Ferrari et al., Typical magnetic field strengths in galaxy clusters are of the order of a few $\mu$ G (Ferrari et al. + 2008)., 2008). + We overlaid a Mach cone on the Nay e1uission distribution of NGC 1569 in Fie. r.., We overlaid a Mach cone on the X-ray emission distribution of NGC 4569 in Fig. \ref{fig:n4569m}. + The direction is based on the dynamical model whereas the openius augle is fitted by eve to the triangular form of tle Nav distribution., The direction is based on the dynamical model whereas the opening angle is fitted by eye to the triangular form of the X-ray distribution. +" In this wav we find an apparent opening anele of 755"" or an apparent Mach cone augle of a=37.5ο...", In this way we find an apparent opening angle of $75^{\circ}$ or an apparent Mach cone angle of $\alpha=37.5^{\circ}$. + The true Mach. cone angle depeuds on the projection uuder which the Mach coue is observed. i6. the angle 9 between the ealaxws normalized 3D velocity vector aud the plane of the sky," The true Mach cone angle depends on the projection under which the Mach cone is observed, i.e. the angle $\beta$ between the galaxy's normalized 3D velocity vector and the plane of the sky." +" Given the normalized 3D model velocity vector (-0.61.0.53.0.56) (Vollmer 2009). this anele iso=31"" aud the true Mach. cone augle is 307."," Given the normalized 3D model velocity vector (-0.64,0.53,0.56) (Vollmer 2009), this angle is $\beta=34^{\circ}$ and the true Mach cone angle is $30^{\circ}$." +" For y=207/107 the true Mach cone angles are 367 aud 287. respectively,"," For $\beta=20^{\circ}/40^{\circ}$ the true Mach cone angles are $36^{\circ}$ and $28^{\circ}$, respectively." +" NGC 1569's lieh radial velocity with respect o the Virgo cluster mean favors higher values of οὐ,", NGC 4569's high radial velocity with respect to the Virgo cluster mean favors higher values of $\beta$. + The rue Mach cone augle is thus consistent. but nüght be somewhat higher than our estimates based on the sound speed of the intracluster medimm.," The true Mach cone angle is thus consistent, but might be somewhat higher than our estimates based on the sound speed of the intracluster medium." + We thus sugecst that he magnetic field plavs a role and that the maguetosouic velocity is relevant for the determination of 1ο Mach uber., We thus suggest that the magnetic field plays a role and that the magnetosonic velocity is relevant for the determination of the Mach number. + Based onu true Mach cone angles between 307 , Based on true Mach cone angles between $30^{\circ}$ +the ratio more than the other statistics.,the ratio more than the other statistics. + Still. this ratio constraints à sliehtlv better than the other statistics.," Still, this ratio constraints $\alpha$ slightly better than the other statistics." + Overall. measurement crrors of the amplitude we consider here have not degraded the ability of the method at constraiine o.," Overall, measurement errors of the amplitude we consider here have not degraded the ability of the method at constraining $\alpha$." + Therefore. the method does not require unrealistically accurate data.," Therefore, the method does not require unrealistically accurate data." + The method assumes a constant eravitational potcutial., The method assumes a constant gravitational potential. + However. the Galactic disk may have erown substantially in the last SCar or so.," However, the Galactic disk may have grown substantially in the last 8Gyr or so." + Here we check whether this eradual erowth seriously hampers the application of the method., Here we check whether this gradual growth seriously hampers the application of the method. +" We solve for the orbits of tracers assuming that tle masVA distribution of the disk erows like "".", We solve for the orbits of tracers assuming that the mass distribution of the disk grows like $t^{0.3}$. + The method iρα then applied to the resultaut distribution of tracers im phase space assunuineg a constant disk., The method is then applied to the resultant distribution of tracers in phase space assuming a constant disk. + In Fie., In Fig. +" 12. we show the coufidence level Qi, as a function of a where in this case the mass in the disk is assumed to be known aud à describes the ratio of the assuned ος to the actual value.", \ref{fig:adia} we show the confidence level $\Qks$ as a function of $\alpha$ where in this case the mass in the disk is assumed to be known and $\alpha$ describes the ratio of the assumed $\vh$ to the actual value. + The ergodic method preseuted here requires a paramcetrumC functional form for the Cwavitational poteutial. but does uot impose anv special svuuuetry on the mass distribution.," The ergodic method presented here requires a parametric functional form for the Gravitational potential, but does not impose any special symmetry on the mass distribution." + The method assiunes that the observations of a class of tracers are spatially complete., The method assumes that the observations of a class of tracers are spatially complete. + Tracers with observed clistauces smaller than dy. could be present bevoud dy iu snapshots at later times.," Tracers with observed distances smaller than $d_0$, could be present beyond $d_0$ in snapshots at later times." + Therefore. Observational selection against tracers at distances ody will make the statistical comparison between observations alc snapshots at later times extremely dif&cult.," Therefore, Observational selection against tracers at distances $>d_0$ will make the statistical comparison between observations and snapshots at later times extremely difficult." + The completeness is not too demanding a condition for tracers like elobular clusters and Galactic satellites for which future observations should be accurate enough for quite large Galactic distances., The completeness is not too demanding a condition for tracers like globular clusters and Galactic satellites for which future observations should be accurate enough for quite large Galactic distances. + We have preseuted oulv partial testing of the method. with oulv a one paraiecter family for the form of the Galactic. potential.," We have presented only partial testing of the method, with only a one parameter family for the form of the Galactic potential." + Method is able to constrain the parameter to a good accuracy with measurements errors that are even larger than those expected to be achieved by future data., Method is able to constrain the parameter to a good accuracy with measurements errors that are even larger than those expected to be achieved by future data. + The tests show that the method could provide unbiased constraints on the Cravitational potential. but a more elaborate testing which inclides a more realistic treatment of the errors should be done.," The tests show that the method could provide unbiased constraints on the Gravitational potential, but a more elaborate testing which includes a more realistic treatment of the errors should be done." + Observations will likely assign distance and velocity lüeasurenaent errors to tracers on an iudividual basis., Observations will likely assign distance and velocity measurement errors to tracers on an individual basis. + Therefore. random errors aud svsteniatie biases tailored to the specific sample of tracers used by the method could be determined robustly.," Therefore, random errors and systematic biases tailored to the specific sample of tracers used by the method could be determined robustly." + The accuracy of the method is mainly Buüted by the iunuber of tracers., The accuracy of the method is mainly limited by the number of tracers. + The most obvious tracers are elobular clusters and Galactic satellites., The most obvious tracers are globular clusters and Galactic satellites. + Our Galaxy tachides 158 shown globular clusters. and 23 known satellites (c.g.7)..," Our Galaxy includes 158 known globular clusters, and 23 known satellites \cite[e.g.][]{SG07}." + Distance measurements of RR Lyrae stars from their xeriod-Iunuuositv relation will be ereatlv improved by CATA and SIM calibration of the zero poi using a jiearby saiple of these stars., Distance measurements of RR Lyrae stars from their period-luminosity relation will be greatly improved by GAIA and SIM calibration of the zero point using a nearby sample of these stars. + Therefore. bhUuniuous halo RR Lyrae stars could siguiicautlv enlarge the sample of racers.," Therefore, luminous halo RR Lyrae stars could significantly enlarge the sample of tracers." + The method requires a svsteui of tracers in cdviaimical equilibriuni in the current Galactic potential., The method requires a system of tracers in dynamical equilibrium in the current Galactic potential. + Α pre-requist for dynamical equilibrium is that au recent changes in the Galactic potential must have occurred on a time scale longer that the ανασα] time of the svstem of tracers., A pre-requist for dynamical equilibrium is that any recent changes in the Galactic potential must have occurred on a time scale longer that the dynamical time of the system of tracers. + Spectroscopic studies stars in the Galaxy do not present evidence for substantial merecrs in the ast SCor (77). maplviug a uearly static eravitational xo»teutial.," Spectroscopic studies stars in the Galaxy do not present evidence for substantial mergers in the last 8Gyr \cite[]{GWN,Helmi}, implying a nearly static gravitational potential." + We have demonstrated that adiabatic erowth of the Galactic disk is not expected to pose a problem or the implementation of the ioethod., We have demonstrated that adiabatic growth of the Galactic disk is not expected to pose a problem for the implementation of the method. + The effect of any deviation from that should be modeled., The effect of any deviation from that should be modeled. + One issue which is exclusive to using disk stars as racers ds the effect of transient porturbatious on the dvuaiics of those stars (e.g.2?)..," One issue which is exclusive to using disk stars as tracers is the effect of transient perturbations on the dynamics of those stars \cite[e.g.][]{FAM05,QUIL}." + However. the transicut effects cause velocity perturbations at the level of 10 aufs which is much smaller that the total velocitics of tracers.," However, the transient effects cause velocity perturbations at the level of 10 km/s which is much smaller that the total velocities of tracers." + Observational uncertainties are larger than hat and do not seen to cause significant biases in the results as indicated bv the tests described above., Observational uncertainties are larger than that and do not seem to cause significant biases in the results as indicated by the tests described above. + Anotler issue to be considered is iio substructure which. iu xuiciple. could act as a stochastic component in the eravitatioual potential.," Another issue to be considered is halo substructure which, in principle, could act as a stochastic component in the gravitational potential." + Such a component is extremely difficult to model in the method proposed here., Such a component is extremely difficult to model in the method proposed here. + We offer he following argument demoustrating that substructure should not have an nuportaut effect ou the long term dviuauies of tracers., We offer the following argument demonstrating that substructure should not have an important effect on the long term dynamics of tracers. + In the lnüt of fast encounters. a racer passing a substructure at distance & will chauge its velocity by Vàzg(b)b/V where Wis the relative velocity and g&GAL/D is the exavitational force field of he substructure assume that 5 is larger than its tidal radius.," In the limit of fast encounters, a tracer passing a substructure at distance $b$ will change its velocity by $V_1\approx g(b)b/V$ where $V$ is the relative velocity and $g\approx G M/b^2$ is the gravitational force field of the substructure assuming that $b$ is larger than its tidal radius." + Performing the usual sunuuing in quadratures over encounters occurius in one orbital time we ect hat the ταις change «VeshenALYR/V where 0 ds the nuuber density of substructures and 2 is the distance travelled by the tracer in one orbital time., Performing the usual summing in quadratures over encounters occurring in one orbital time we get that the r.m.s change $^{1/2}\approx M\sqrt{\bar n R}/V$ where $\bar n$ is the number density of substructures and $R$ is the distance travelled by the tracer in one orbital time. + Taking V?2CAL.(ΠΠ with AL(R) the mass of the halo within radius R. we get the condition ~Galacticνα)>Mas for having M_{_{\rm MW}}$ for having $^{1/2}\sim V$." + This means that neither single eucouuters nor collective stochastic effects can dominate the long terii evolution of tracers even if the fraction of mass in substructures is large which is contrary to recent sinulatious, This means that neither single encounters nor collective stochastic effects can dominate the long term evolution of tracers even if the fraction of mass in substructures is large which is contrary to recent simulations +galaxies have very few far-IR detections and the appropriate corrections are unclear.,galaxies have very few far-IR detections and the appropriate corrections are unclear. + The resulting fluxes are then converted to L(Ha) using the prescription given in van Zee (2001)., The resulting fluxes are then converted to $\alpha$ ) using the prescription given in van Zee (2001). + A histogram of L(Ho) values is shown in Figure 9., A histogram of $\alpha$ ) values is shown in Figure 9. +" For comparison, the bright dwarf sample of Hunter Elmegreen (2004) and van Zee (2001) are also shown."," For comparison, the bright dwarf sample of Hunter Elmegreen (2004) and van Zee (2001) are also shown." +" The mean Ha luminosity of our sample is about a factor of 3 fainter than Hunter Elmegreen, but similar to van Zee's."," The mean $\alpha$ luminosity of our sample is about a factor of 3 fainter than Hunter Elmegreen, but similar to van Zee's." + There is a strong correlation between absolute magnitude and L(Ho)., There is a strong correlation between absolute magnitude and $\alpha$ ). +" As can be seen in Figure 10, the correlation between stellar luminosity (which measures stellar mass under an assumed IMF) and Ha luminosity is evident in both the van Zee and Elmegreen samples (red symbols) and our LSB sample (black symbols)."," As can be seen in Figure 10, the correlation between stellar luminosity (which measures stellar mass under an assumed IMF) and $\alpha$ luminosity is evident in both the van Zee and Elmegreen samples (red symbols) and our LSB sample (black symbols)." +" Neither Ha flux or apparent magnitude are correlated with distance, so we believe that distance effects are not responsible for the correlation seen in Figure 10."," Neither $\alpha$ flux or apparent magnitude are correlated with distance, so we believe that distance effects are not responsible for the correlation seen in Figure 10." + We note that there is a 0.5 shift in log L(Ha) between our samples and the dwarf irregular samples (lower Ha luminosities per stellar mass for the LSB galaxies)., We note that there is a 0.5 shift in log $\alpha$ ) between our samples and the dwarf irregular samples (lower $\alpha$ luminosities per stellar mass for the LSB galaxies). +" We have marked the eight galaxies in common with Hunter Elmegreen, a bias flux calibration for our sample does not seem"," We have marked the eight galaxies in common with Hunter Elmegreen, a bias flux calibration for our sample does not seem" +Different and independent evolutionary codes must provide the same result. i1) there is no conventional way to account for the presently observed slope of the white dwarf luminosity function. 111) there is no contradiction with other well established astrophysical or cosmological phenomena. and iv) there are some phenomena that are better explained if the axion hypothesis is adopted.,"Different and independent evolutionary codes must provide the same result, ii) there is no conventional way to account for the presently observed slope of the white dwarf luminosity function, iii) there is no contradiction with other well established astrophysical or cosmological phenomena, and iv) there are some phenomena that are better explained if the axion hypothesis is adopted." + Concerning this last point. it is important to realize that the value of the mass of the axion found in Isern et al. (," Concerning this last point, it is important to realize that the value of the mass of the axion found in Isern et al. (" +2009) ts close to the upper limit obtained from astrophysical constraints.,2009) is close to the upper limit obtained from astrophysical constraints. + This means that axions with this mass will not dramatically change our current understanding of stellar evolution. but instead some subtle changes that accurate observations could detect and quantify would be apparent.," This means that axions with this mass will not dramatically change our current understanding of stellar evolution, but instead some subtle changes that accurate observations could detect and quantify would be apparent." + The case of the white dwarf luminosity function is just an example., The case of the white dwarf luminosity function is just an example. + The drift of the pulsation periods of variable white dwarfs. the topic of this paper. is another one that will be discussed in the following sections.," The drift of the pulsation periods of variable white dwarfs, the topic of this paper, is another one that will be discussed in the following sections." + We note however that this 1s not the case of core collapse supernovae. where axions with this mass can drain an important amount of gravitational energy and modify the process of collapse/explosion.," We note however that this is not the case of core collapse supernovae, where axions with this mass can drain an important amount of gravitational energy and modify the process of collapse/explosion." + Unfortunately. the nucleon-axion interaction. which is dominant in supernovae. is not well understood and deserves additional work that is out of the scope of this paper.," Unfortunately, the nucleon-axion interaction, which is dominant in supernovae, is not well understood and deserves additional work that is out of the scope of this paper." +" Finally note as well that if cos?B. was small. the mass of the axion would be higher than the values quoted here and. consequently, the interaction axion-photon would be strengthened."," Finally note as well that if $\cos^2 \beta$ was small, the mass of the axion would be higher than the values quoted here and, consequently, the interaction axion-photon would be strengthened." + This could be used to rule out our results or to constrain the values that cos?8 can adopt., This could be used to rule out our results or to constrain the values that $\cos^2 \beta$ can adopt. +" During the process of cooling. white dwarfs experience several phases of pulsational instability powered by the «-mechanism and the ""convective driving"" mechanism (Winget Kepler 2008)."," During the process of cooling, white dwarfs experience several phases of pulsational instability powered by the $\kappa$ -mechanism and the “convective driving” mechanism (Winget Kepler 2008)." + Depending on their location in the Hertzsprung-Russell diagram and their atmospheric composition they are called pulsating PGI1159 or GW Vir stars. which includes stars with a surrounding nebula (the PNNV stars) and stars without nebula (the DOV stars) at των~70.000—170.000 K and He-. C-. and O-dominated atmospheres. DBV or V777 Her stars. with 4p~25.000 K and He-dominated atmospheres. and DAV or ZZ Ceti stars. with Tay~12.000 K and H-dominated atmospheres.," Depending on their location in the Hertzsprung–Russell diagram and their atmospheric composition they are called pulsating PG1159 or GW Vir stars, which includes stars with a surrounding nebula (the PNNV stars) and stars without nebula (the DOV stars) at $T_{\rm eff} \sim 70,000 - +170,000$ K and He-, C-, and O-dominated atmospheres, DBV or V777 Her stars, with $T_{\rm eff} \sim 25,000$ K and He-dominated atmospheres, and DAV or ZZ Ceti stars, with $T_{\rm eff} \sim 12,000$ K and H-dominated atmospheres." + All of them display multiperiodie pulsations with periods in the range of 100 to 1000 s. although PNNV stars can pulsate with periods as long as 3000 s. The length of these periods clearly indicates that these objects are experiencing g-mode non-radial pulsations. where the main restoring force Is gravity — see Winget Kepler (2008) for a recent review.," All of them display multiperiodic pulsations with periods in the range of 100 to 1000 s, although PNNV stars can pulsate with periods as long as 3000 s. The length of these periods clearly indicates that these objects are experiencing $g$ -mode non-radial pulsations, where the main restoring force is gravity — see Winget Kepler (2008) for a recent review." + One of the main characteristics of g-mode pulsations ts that they experience a secular drift that can be used to test the white dwarf cooling theory., One of the main characteristics of $g$ -mode pulsations is that they experience a secular drift that can be used to test the white dwarf cooling theory. + This secular drift can be approximately described by where « and b are constants of the order of unity that depend on the details of the model. and R and T are the stellar radius and the temperature at the region of period formation. respectively (Baglin Heyvaerts 1969: Winget et al.," This secular drift can be approximately described by where $a$ and $b$ are constants of the order of unity that depend on the details of the model, and $R$ and $T$ are the stellar radius and the temperature at the region of period formation, respectively (Baglin Heyvaerts 1969; Winget et al." + 1983)., 1983). + This equation reflects the fact that as the star cools down. the degeneracy of the plasma increases. the buoyancy decreases. the Brunt-Vaisala frequency becomes lower and. as a consequence. the spectrum of pulsations gradually shifts to lower frequencies.," This equation reflects the fact that as the star cools down, the degeneracy of the plasma increases, the buoyancy decreases, the Brunt-V\""aiis\""all\""a frequency becomes lower and, as a consequence, the spectrum of pulsations gradually shifts to lower frequencies." + At the same time. since the star contracts. the radius decreases and the frequency tends to increase.," At the same time, since the star contracts, the radius decreases and the frequency tends to increase." + In general. DAV and DBV stars are already so cool that the radial term is negligible and the change of the period of pulsation can be directly related to the change in the core temperature of the star.," In general, DAV and DBV stars are already so cool that the radial term is negligible and the change of the period of pulsation can be directly related to the change in the core temperature of the star." +" The timescales involved are of the order of ~107! s/s for DOVs. ~107"" to ~J0- s/ for DBVs and ~107% to ~10779 s/s for DAVs."," The timescales involved are of the order of $\sim 10^{-11}$ s/s for DOVs, $\sim 10^{-13}$ to $\sim 10^{-14}$ s/ for DBVs and $\sim 10^{-15}$ to $\sim 10^{-16}$ s/s for DAVs." + The measurement of such drifts is a difficult task but. as was proved. it is feasible (Winget Kepler. 2008).," The measurement of such drifts is a difficult task but, as was proved, it is feasible (Winget Kepler, 2008)." + These properties allow us to build a simple relationship (Isern et al., These properties allow us to build a simple relationship (Isern et al. +" 1992; [sern a-Berro 2008) to estimate the influence of an extra sink of energy. like axions. on the period drift of variable white dwarfs: where the Throvelsuffix ""model"" refers to those models built using standard physics."," 1992; Isern a–Berro 2008) to estimate the influence of an extra sink of energy, like axions, on the period drift of variable white dwarfs: where the suffix “model” refers to those models built using standard physics." + GI1I7-BISA is a ZZ Ceti star (McGraw Robinson 1976) with a dominant period of pulsation of ~ 215 s. This star. in an exceptional observational effort. has been observed for more than 30 years to obtain the secular evolution of the pulsation period.," G117–B15A is a ZZ Ceti star (McGraw Robinson 1976) with a dominant period of pulsation of $\sim$ 215 s. This star, in an exceptional observational effort, has been observed for more than 30 years to obtain the secular evolution of the pulsation period." + Kepler et al. (, Kepler et al. ( +1991a: 1991). after ~15 years of observations. found a secular drift of Mon.=(12.043.5)*107? s/s that was more than a factor of two larger than the expected value in the case of a normal carbon-oxygen white dwarf.,"1991a; 1991b), after $\sim 15$ years of observations, found a secular drift of $\dot{\Pi}_{\rm obs} = (12.0 \pm 3.5) \times +10^{-15}$ s/s that was more than a factor of two larger than the expected value in the case of a normal carbon-oxygen white dwarf." + In order to account for this discrepancy. Isern et al. (," In order to account for this discrepancy, Isern et al. (" +1992) proposed the introduction of an extra cooling term due to,1992) proposed the introduction of an extra cooling term due to +Comet dust provides us with insight into (vo fundamental aspects of our solar svstem: (a) the composition of both the solar svstem's initial ingredients and formation products: and. (b) the spatial and temporal heterogeneity of the proto-planetary disk.,"Comet dust provides us with insight into two fundamental aspects of our solar system: (a) the composition of both the solar system's initial ingredients and formation products; and, (b) the spatial and temporal heterogeneity of the proto-planetary disk." + Comet dust comae are optically thin. providing a unique laboratory for the study of preserved dust erains that observations of Ixuiper Belt objects and primitive asteroids cannot provide.," Comet dust comae are optically thin, providing a unique laboratory for the study of preserved dust grains that observations of Kuiper Belt objects and primitive asteroids cannot provide." + The compositions of both comet dvnanmical Eunilies. ecliptic comets (ECs) and nearly-isotropic comels (NICS). have been preserved in (heir interiors during (heir residences in the Scattered Disk and Oort Cloud.," The compositions of both comet dynamical families, ecliptic comets (ECs) and nearly-isotropic comets (NICs), have been preserved in their interiors during their residences in the Scattered Disk and Oort Cloud." + Knowledge of cometary materials enables better understauding of planetary aud small body formation as well as evolutionary processes in the protoplanetary disk., Knowledge of cometary materials enables better understanding of planetary and small body formation as well as evolutionary processes in the protoplanetary disk. + The NASA space mission was designed to bring back samples of comet dust from 81P/Wild 2., The NASA space mission was designed to bring back samples of comet dust from 81P/Wild 2. + The terrestrial laboratory analvsis of grain samples captured in the aerogel have helped us to understand the properties of comet relractory materials. revealing. among others. hieh-temperature crystalline materials (Ενα2008).," The terrestrial laboratory analysis of grain samples captured in the aerogel have helped us to understand the properties of comet refractory materials, revealing, among others, high-temperature crystalline materials \citep{flynn08}." +". In the preliminary analysis ofsaniples. ~65% of the aerogel tracks were ""carrot-shaped. indicative of large solid grains that upon inspection included micron- to tens of nicron-sized forsterite (Ale-vich ervstalline silicate) and FeS crvstals (Burchelletal.2008:Zolensky 2008)..."," In the preliminary analysis ofsamples, $\simeq 65$ of the aerogel tracks were `carrot-shaped,' indicative of large solid grains that upon inspection included micron- to tens of micron-sized forsterite (Mg-rich crystalline silicate) and FeS crystals \citep{burchell08, zolensky08}. ." + A fraction. ~35%... of the aevogel tracks were bulbous and attributed to porous aggregates which sulfered significant heating upon impact with the aerogel (Roskosz.Leroux.&Watson2008:Lerouxetal. 2008).," A fraction, $\simeq 35$, of the aerogel tracks were bulbous and attributed to porous aggregates which suffered significant heating upon impact with the aerogel \citep{roskosz08, leroux08}." +. ILowever. analvsis of microcrater impacts in (he foil suggest that ~85% are clustered with irregular. non-circular outlines likely originating from composite. ie. aggregate erains (Dorgetal. 2007)..," However, analysis of microcrater impacts in the foil suggest that $\simeq 85$ are clustered with irregular, non-circular outlines likely originating from composite, i.e., aggregate grains \citep{borg07}. ." + Incontrast to the samples thal were, Incontrast to the samples that were + Recently. we have discovered an error in our Monte-Carlo spectral fitting routine. more specifically where the errors on the fluxes were rescaled to get a reduced y of 1.," Recently, we have discovered an error in our Monte-Carlo spectral fitting routine, more specifically where the errors on the fluxes were rescaled to get a reduced $\chi^2$ of $1$." +" The rescaled errors were too big. resulting in too wide a range of ""good' fits in our 100 step Monte-Carlo routine."," The rescaled errors were too big, resulting in too wide a range of 'good' fits in our 100 step Monte-Carlo routine." + This problem affects 77-9 and AA.1-A.2 in 2.. 33 in ?.. and 44 in ?..," This problem affects 7-9 and A.1-A.2 in \citet{gielen08}, , 3 in \citet{gielen09}, , and 4 in \citet{gielen09b}." + We corrected for this error and present the new values and errors in the tables below., We corrected for this error and present the new values and errors in the tables below. + The new values and errors nearly all fall within the old error range., The new values and errors nearly all fall within the old error range. + Our best y values and overall former scientific results are not affected., Our best $\chi^2$ values and overall former scientific results are not affected. + With these new errors some possible new trends in the dust parameters might be observed., With these new errors some possible new trends in the dust parameters might be observed. + These will be discussed in an upcoming paper where we extend the sample presented in ? with newly obtainedSPITZER-IRSdata., These will be discussed in an upcoming paper where we extend the sample presented in \citet{gielen08} with newly obtainedSPITZER-IRSdata. +isotropic equivalent energv of E~10°! erg may not be implausible for population III IINe (Frver.Wooslev.&Heeger2001:etal.2003).,"isotropic equivalent energy of $E\sim 10^{54}$ erg may not be implausible for population III HNe \citep{fryer01,heger03}." +. IXeeping in mind the hypothetical nature of (his assumption. we examine an extreme 11ο alfterglow case with isotropic equivalent energv E=10°! erg. ejecta opening hall-angle @=1/42 (nearly spherical) and initial Lorentz [actor 54=2 (mildly relativistic).," Keeping in mind the hypothetical nature of this assumption, we examine an extreme HNe afterglow case with isotropic equivalent energy $E=10^{54}$ erg, ejecta opening half-angle $\theta=1/\sqrt{2}$ (nearly spherical) and initial Lorentz factor $\gamma_{0}=2$ (mildly relativistic)." + Other parameters are (he same as in the standard GRB case., Other parameters are the same as in the standard GRB case. + We note that dilferent authors define ILNe differently., We note that different authors define HNe differently. + Here. our definition of ILNe is SNe with a large energy and a mildly relativistie ejecta.," Here, our definition of HNe is SNe with a large energy and a mildly relativistic ejecta." + Figure 11. shows the total flixes of the forward: ancl reverseshock emission at the observed frequency v=5 GIlz and observed times /—1 vi. 3 vrs and LO vrs. as a [function of redshift z. together with the 5e sensitivities of the VLA and SIXÀ.," Figure \ref{fig:HN:z} shows the total fluxes of the forward and reverseshock emission at the observed frequency $\nu=5$ GHz and observed times $t=1$ yr, $3$ yrs and $10$ yrs, as a function of redshift $z$, together with the $5 \sigma$ sensitivities of the VLA and SKA." + This shows that the current VLA may be able to detect such energetic LN afterglows up to z~20 with ~1 day integration limes. while SISA ean easily detect them bevond :~30.," This shows that the current VLA may be able to detect such energetic HN afterglows up to $z \sim 20$ with $\sim 1$ day integration times, while SKA can easily detect them beyond $z \sim 30$." + We have also calculated a more moderate enerev LN case with E1007 erg. as well as a high external density LIN case wilh n~10? 7.," We have also calculated a more moderate energy HN case with $E \sim 10^{53}$ erg, as well as a high external density HN case with $n \sim 10^{2}$ $^{-3}$."