A Comparison of Metal Enrichment Histories in Rich Clusters and Individual Luminous Ellipti

a r X i v :a s t r o -p h /9811258v 1 16 N o v 1998A COMPARISON OF METAL ENRICHMENT HISTORIES IN RICH CLUSTERS AND INDIVIDUAL LUMINOUS ELLIPTICAL GALAXIESFabrizio Brighenti 2,3and William G.Mathews 22University of California Observatories/Lick Observatory,Board of Studies in Astronomy andAstrophysics,University of California,Santa Cruz,CA 95064mathews@3Dipartimento di Astronomia,Universit`a di Bologna,via Zamboni 33,Bologna 40126,Italybrighenti@astbo3.bo.astro.itABSTRACTThe large spatial extent of hot,X-ray emitting gaseous halos around massive ellipticalgalaxies indicates that most of this gas has not been generated by stellar mass loss.Instead,much of this gas results from an intergalactic gaseous inflow toward the overdensity from which giant ellipticals and their associated galaxy groups formed.Since these hot gaseous halos are old,they contain important information about the star formation history of elliptical galaxies.In this paper we show that the enrichment history of this hot gas is closely linked to its gasdynamical history;supernovae provide both energy and metal enrichment.We find that Type II supernovae based on a Salpeter IMF,plus a small number of additional Type Ia supernovae,can explain the the density,temperature and abundance profiles currently observed in gaseous halos around massive ellipticals.Within the central,optically bright region of luminous ellipticals,approximately half of the interstellar iron is produced by Type Ia supernovae and half by mass lost from evolving stars which were originally enriched in iron by Type II supernovae.However,iron and silicon abundances in the intracluster gas within rich clusters suggest enrichment by a larger number of supernovae per unit optical light than we require for massive ellipticals.The additional supernovae implied by cluster data cannot be reconciled with our modelsfor individual massive ellipticals.Evidently,rich clusters cannot be constructed by simplycombining ellipticals and their associated groups since the enrichment history of clusters and massive ellipticals appears to be fundamentally different.Neither currently discussed resolution of this discrepancy –increased number of Type II supernovae (flat IMF)or strong Type Iaenrichment in clusters –is attractive.Although the global hot gas iron abundance is similarin all large galaxy clusters,silicon is enhanced in hotter,richer clusters.This Si/Fe variation implies that E and S0galaxies are not the only sources of cluster gas enrichment;perhaps spirals or low mass galaxies are also important.Subject headings:galaxies:elliptical and lenticular –galaxies:formation –galaxies:evolution –galaxies:cooling flows –x-rays:galaxies1.INTRODUCTIONLuminous elliptical galaxies are the astronomical analog of tree rings or geological core samples –within the hot gas in these massive galaxies resides important information about the earliest stages of galaxy formation and the enrichment of the cosmos with heavy elements from the first generations of stars.Thestellar density profile and low rotation of bright ellipticals indicate that they were assembled from smaller galactic objects containing stars.The most likely sites for the formation of giant elliptical galaxies are small groups of galaxies where mutual tidal interactions are strong and the likelihood of galactic merging is enhanced.In an idealized version of this formation hypothesis,the merging process within the group comes to completion after a few dynamical times when the massive central elliptical has consumed the dark and luminous matter of many original group galaxies of moderate mass.When this happens,the merging process shuts down and the elliptical evolves passively as a group-dominant elliptical in thefield or enters a large cluster.While there is clear evidence that some massive ellipticals contain younger stars and must have suffered significant mergers since the epoch of most intense galaxy formation,there is also evidence that other more venerable ellipticals have survived until the present time,relatively undisturbed by events that have occurred since their formation at early times.The hot interstellar gas in these old galaxies is most interesting since it still contains information about the earliest stages of star formation,including the heating and enrichment of the gas by supernovae.In this paper we investigate the production of iron and silicon by Type Ia and Type II supernovae (SNIa and SNII respectively)and follow the dynamical redistribution of these metals in the hot interstellar and intragroup gas until the present time.Gas enrichment and dynamical evolution are linked since the collective energy released by Type II supernovae can expel metal-enriched gas from elliptical galaxies in a wind.The energetics of Type II supernovae during early star formation can be constrained by comparing heavy metal abundances expected from evolutionary gas dynamical calculations with abundances provided by X-ray observations of individual massive ellipticals.In a similar fashion,metal abundances observed in rich clusters of galaxies provide global enrichment constraints on early type galaxies which are generally regarded as the principal source of metals in the intracluster gas.Rich clusters are thought to have retained all of the products of supernova enrichment either within galactic stars or in the hot intracluster medium. In this sense rich clusters are closed boxes.From an observational standpoint individual massive elliptical galaxies are certainly not closed boxes since most of the metals produced by supernovae have been carried out by supernova-driven winds.Much of these metals now resides in low density gas at large distances from the optical galaxy where detection is difficult or where the metal enriched gas has been tidally or dynamically removed.From the standpoint of our gas dynamical models,however,individual ellipticals are closed boxes since we can accurately follow the products of supernova enrichment into distant regions of very low density.Thermal X-ray emission from hot circumgalactic gas surrounding many bright ellipticals often extends far beyond the optical image of the galaxy(Mathews&Brighenti1998a).The large mass and extended spatial distribution of this gas cannot be understood only from normal evolutionary stellar mass loss.Our dynamical models indicate that the most distant gas in these galactic halos has accumulated by secondary infall into the perturbation that initially led to the formation of the group and its dominant elliptical (Brighenti&Mathews1998a,1998b;Mathews&Brighenti1998b).The objective of our recent gas dynamical calculations has been to follow the evolution of the hot gas within and around massive elliptical galaxies since the time of galaxy formation.A successful model can reproduce the radial density and temperature distributions as determined from X-ray observations.In our recent models we begin with an overdensity perturbation in a simpleflat cosmology.As dark matter accumulates in the core of the growing perturbation,we assume that a stationary NFW dark matter halo is formed(Navarro,Frenk and White1996).Exterior to this stationary halo the dark matter inflow is identical to the cosmic similarityflow of Bertschinger(1985).The baryonic gas evolves in this time-dependent potential:flowing inward,shocking at some radius and radiatively cooling near the center.At some earlytime,t∗,when enough baryons have accumulated in the perturbation,we form the de Vaucouleurs profile of the large elliptical observed today.By this means we circumvent the complex merging processes that occurred at very early times.Nevertheless,our calculation globally conserves dark and baryonic mass and treats the gas dynamics in full detail from t∗to the present time.In these simple models we release the Type II supernova energy at the same time t∗that the stellar system is formed but the Type Ia energy is released from t∗to the present according to some assumed variable rate.However,there is a degeneracy in our successful solutions.Wefind that the hot gas density and temperature profiles typical of massive ellipticals,n(r)and T(r),can be reproduced with different combinations of the fundamental model parameters:the time of star formation t∗,the total SNII energy released E II,and the universal baryon mass fractionΩb≈0.05±0.01as determined by big bang nucleosynthesis(Walker et al.1991).For example,solutions withΩb decreased by∼0.01are similar to those with E II increased by∼2or with t∗decreased by∼1Gyr.Much of the degeneracy involving these uncertain parameters can in principle be removed by considering the abundance and of iron and other elements produced in supernovae.The total mass of heavy elements in stars and gas today is directly related to the total number of supernovae of each type that have occurred. Unfortunately,many of the essential supernova-related parameters are poorly known:the average amount of iron or silicon created in each supernova event,the total mass of these elements locked into stars today, the initial mass function(IMF),etc.While we cannot attempt here a definitive theoretical resolution of the enrichment history of early type galaxies,we can make progress within the limitations of current theory and observational data.In view of the uncertainties involved,however,a highly detailed gas dynamical calculation including the effects of metal enrichment seems unwarranted.The approximate results we present here can be regarded as thefirst step in an iterative procedure that will become better defined in the future.Nevertheless,the metal enrichment history of elliptical galaxies that we describe here is sufficientto rule out several scenarios that have been widely discussed.One of our motivations for beginning this project is the apparent dissimilarity of iron abundance and gas fraction between galaxy groups and rich clusters which led David(1997)and Renzini(1997)to remark that present-day,rich clusters cannot be assembled from present-day groups.For example,most(50%-80%)of the mass of heavy metals in rich clusters resides in the intracluster gas where the iron mass per unit of stellar light M F e/L B consistently exceeds that in small groups or individual massive ellipticals.Moreover,the lower fraction of gas massin galaxy groups relative to clusters indicates that much of the metal-enriched gas produced in groups or individual ellipticals has been expelled into the environment by the release of supernova energy(Arnoud, et al.1992;David,Jones,&Forman1995).Perhaps,therefore,the gas and iron formerly within large ellipticals and galaxy groups has been expelled by supernova-driven winds into the low density environment where it escapes X-ray detection.However,this low density,metal-enriched gas can be followed in our gas-dynamical models.In successful models the metal rich gas remaining within the galaxy must agree with the gas abundance and abundance gradients observed in these bright galaxies.Our results reported here indicate,however,that the mass of metals that hasflowed out of luminous ellipticals into their low density environment is insufficient to account for the larger mass of metals observed in rich clusters.We are therefore faced with a fundamental inconsistency:parameters that allow the intracluster gas to be enriched by galactic winds from massive ellipticals are inconsistent with detailedX-ray observations of the metal content within individual ellipticals.The relative importance of SNII and SNIa in creating the metals observed in cluster gas has beenwidely debated.The total iron abundance in rich clusters is too large to be produced by SNII with a standard Salpeter IMF.Many authors have suggested that SNIa produce enough iron to account for the additional iron required(e.g.Ishimaru&Arimoto1997;Renzini1997;Wyse1997).This solution is appealing since approximately3stellar remnant(Woosley&Weaver1995;Gibson,Loewenstein&Mushotzky1997).In view of these difficulties,the relative influence of SNII and SNIa in enriching elliptical galaxies and rich clusters must be determined largely from observations of the metal abundance in stars and gas.The enrichment history of individual ellipticals and associated groups of galaxies is difficult to access since the total energy released in all SNII is sufficient to expel a significant fraction of metal-rich gas from these systems.However,rich clusters of galaxies are massive enough to have retained all of the material processed in supernovae over cosmic time.The“closed box”nature of rich clusters is supported by the relative constancy of the ratio of baryonic to total mass for cluster masses>∼5×1013M⊙(David1997).The data assembled by Renzini(1997)indicates that metal enrichment by supernovae in rich clusters remains confined within the cluster potential;M g/L B and the total iron mass per unit optical light M F e,g/L B are nearly constant for cluster masses>∼5×1013M⊙.Clusters and galaxy groups with masses less than this have lower gas to stellar mass ratios,suggesting gaseous outflow.In determining the past history of supernova enrichment,the silicon abundance is more useful than the iron abundance.The silicon abundance has been observed in the ICM of many rich clusters and is based on a well-understood K-line emission feature so that translation into abundances should be reliable.In addition,silicon yields from SNII and possibly SNIa may be better determined from theoretical supernova models than those of iron.While the iron yield from SNII y F e,II(m)increases monotonically with the pre-supernova stellar mass m,the silicon yield y Si,II(m)has a pronounced maximum at m∼22M⊙provided the energy released by the supernova is not too large(A and B models of Woosley&Weaver1995). Because of this maximum,the IMF-averaged yield y Si,II is very insensitive to the choice of parameters for power law IMFs provided the upper mass limit m u>∼22.Assuming that silicon is a reliable tracer of past supernova activity in rich clusters,we wish to construct an expression for the observed ratio of the total mass of silicon in the hot cluster gas(ICM)to the total optical luminosity of spheroidal system stars in the cluster,ΥSi,g=M Si,g/L B.The present mass of silicon in the ICM is determined by the total mass of silicon produced by SNII and SNIa less the amount of silicon currently within stars:ΥSi,g≡M Si,II+M Si,Ia−M Si,∗z F e g= M Si MF e,II+M F e,Ia−M F e,∗.(2)Note that R is the ratio of silicon to iron masses in absolute units and is not normalized with the solar ratio.We now seek expressions forΥSi,g and R in terms of the expected number of supernovae and the average silicon and iron yields for each supernova event.If we assume that all stars more massive than8M⊙produce SNII,the number of SNII per M⊙of stars formed,ηII,can be found for any assumed IMF.For a power law IMFφ(m)dm=φo m−(1+x)dm the number of SNII is equal to the total number of stars more massive than m8=8M⊙,thereforeηII=N IIxm−x8−m−x uFor example,ηII=6.81×10−3SNII per M⊙for a Salpeter IMF(slope x=1.35)having upper and lower masses of m u=100M⊙and mℓ=0.08M⊙respectively.In recent discussions of the metal enrichment of early type galaxies and galaxy clusters it has been fashionable to consider only single power law IMFs(e.g. Loewenstein&Mushotzky1996;Ishimaru&Arimoto1997;Gibson,Loewenstein&Mushotzky1997)with the Salpeter slope regarded as“normal.”However,many lines of evidence in our own Galaxy suggest that the normal IMF has some curvature,becomingflatter at subsolar masses(Leitherer1998).Scalo(1998) suggests the following triple power law approximation for a universal IMF:φ(m)dm=φi m−(1+x i)dm i=1,2,3withx1=0.2±0.3for0.1<m<1M⊙x2=1.7±0.5for1.0<m<10M⊙x3=1.3±0.5for10<m<100M⊙Evaluating the specific SNII frequency for this IMF wefindηII=7.81×10−3which differs by less than 15percent from the single-slope Salpeter value.In view of the many larger uncertainties involved in other parameters,we shall continue to use simple power law IMFs in this paper to determine the number of SNII, mean Type II supernova yields and the stellar mass loss rate.The total number of SNII explosions during the entire history of rich cluster stars is N II=ηII M∗o where M∗o is the total initial stellar mass in cluster E+S0galaxies.The current mass of all early type galaxies in a rich cluster can be estimated from the total B-band luminosity of all cluster galaxies, M∗=(M/L B)L B,where M/L B≈7is an average mass to light ratio for bright cluster ellipticals. Assuming that star formation in ellipticals can be approximated with a single burst at time t∗,the stellar mass at that time was M∗o=M∗/(1−β)whereβis the fraction of the initial mass that has been lost from the stars between t∗and the present time t n.For example,if stars form with a Salpeter IMF at time t∗=2Gyrs and t n=13Gyrs is the present time,thenβ=0.3.Since galactic stars in rich clusters are observed to be enriched by SNII ejecta,it is clear that the single burst approximation is only an approximation.However,if most of the stars are formed in several bursts concentrated near time t∗,the long term stellar evolution will be little altered although the single-burst value ofβwill be overestimated if some supernova-processed gas is formed into stars in nearly simultaneous multi-bursts.If a fraction f∗of SNII-produced metals formed into stars at time t∗,then a fractionF∗=f∗(1−β)is still locked in stars today.The total mass of SNII-produced silicon still remaining in the intracluster gas phase today is therefore(1−β)−1(M/L B)L BηII y Si,II (1−F∗)where the mean silicon yield y Si,II is the IMF-averaged mass of silicon(in solar masses)generated per SNII event.The total mass of iron in the ICM from SNII is given by the same expression with y Si,II replaced with y F e,II .By using the single burst assumption,modified by allowing some of the SNII ejecta to form stars,we are neglecting higher order details such as second generation SNII formed from stellar ejecta.The total amount of silicon produced in SNIa is the product of the total number of Type Ia supernovae and the silicon yield,N Ia y Si,Ia.Since the past rate of SNIa explosions in ellipticals is poorly known,we represent our ignorance with a power law:d N IaSNu(t)SNIa yr−11010100yrswhere L B is in units of L B,⊙andSNu(t)=SNu(t n)(t/t n)−pis the SNIa rate in SNu units(supernovae per1010L B per100years).The total number of SNIa since t∗is thereforeSNu(t n)N Ia=L B(3)M∗where z F e,∗is the abundance of iron by mass in stars relative to hydrogen and z F e,∗/1.4is the ratio of iron mass to total mass including helium.Following the notation introduced above,Equations(1)-(3)can be written asM Si,gΥSi,g=M F e g=(1−β)−1(M/L B)ηII y Si,II (1−F∗)+n Ia y Si,Ia(1−G∗)The stellar mass to light ratio in early type galaxies is a slowly increasing function of galactic luminosity,M/L B∝L B0.2(Faber et al.1984),and depends somewhat on the cluster luminosity function. For a representative value we choose M/L B=7(in solar units),characteristic of typical bright ellipticals.Values ofΥSi,g and R in Equations(4)and(5)must be supplied from X-ray observations.For three rich clusters(A2199,A496,and AWM7)observed with ASCA Mushotzky et al.(1996)find an average silicon mass to light ratioΥSi,g=0.0305±0.008in solar units.More extensive observational data indicates that there is a significant cosmic variation in the abundances of Si and Fe among rich clusters(Mushotzky &Loewenstein1997;Mushotzky1998).If real,this variation of galaxy-averaged values suggests that the IMF,star formation efficiency,supernova frequency or other supernova properties may vary dramatically among cluster galaxies.Nevertheless,for our purposes here we simply use average abundances from all of the clusters observed.ASCA observations indicate a silicon to iron ratio of Si/Fe=2.2±0.25(Mushotzky 1998)in solar units.But this abundance ratio,based on the so-called“photospheric”solar iron abundance, becomes Si/Fe=2.2(1.83/2.66)=1.51in units of the“meteoritic”solar ratio(Si/Fe)⊙=0.550adopted here.The corresponding absolute Si/Fe abundance ratio in equation(5)is therefore R=0.83 Solutions of Equations(4)-(6)forηII, y F e,II ,and f∗are shown in Figure1as functions of the total number of SNIa events N Ia and the current Type Ia supernova rate SNu(t n)evaluated with p=1,t n=13 Gyrs,and t∗=2Gyrs.Two representative solutions are illustrated:(i)with no enrichment of stars by SNIa ejecta g∗=0and(ii)with a significant SNIa enrichment g∗=0.5.The plotted solutions are based on a mass return parameter appropriate for a single burst Salpeter IMFβ=0.3.Type Ia supernova rates observed in elliptical galaxies favor low values of SNu(t n)whereηII,f∗and y F e,II in Figure1are almost independent of SNu(t n)and N Ia≪N II.In a recent study ofthe observed frequency of SNIa in ellipticals,Cappellaro et al.(1997)find a low current SNIa rate SNu(t n)=0.058(H/50)2in SNu units.The current SNIa rate is also restricted by our gas dynamical models for the evolution of hot gas in large elliptical galaxies.The computed radial variation of gas density and temperature agree with those observed only when SNu(t n)<∼0.25(with p=1),again suggesting low values for N Ia.However,when silicon and iron abundances are included in these hydrodynamical evolution, as discussed below,low values of SNu(t n)and N Ia are essential.In this low-SNu(t n)range of Figure1, solutions for the three parametersηII, y F e,II ,and f∗approach the limit of no SNIa enrichment,N Ia→0. In this limit solutions to Equations(4)-(6)forΥSi,g,R,and z∗F e simplify toy F e,II = y Si,II /R=0.16,(7)ΥSi,g+R(z F e,∗/1.4)(M/L B)ηII==0.16.(9)ηII y Si,IIThese numerical evaluations are based onΥSi,g=0.0305,R=0.83,z F e,∗=0.5z F e,⊙,M/L B=7,y Si,II =0.133,andβ=0.3.SinceΥSi,g dominates the numerator of Equation(8),the value ofηII is essentially unchanged if the mean stellar iron abundance is taken to be solar,z F e,∗=z F e,⊙.The value of y F e,II in Equation(7)is within the range of possible SNII iron yields calculated by Woosley&Weaver(1995);this provides some confidence in the veracity of other parameters determined from the equations above.However,the specific supernova rateηII=0.026is almost four times the value expected for a Salpeter IMF,ηstd=0.00681(x=1.35,m u=100M⊙and mℓ=0.08M⊙).Values ofηIIcomputed with single power law IMFs are sensitive to both the slope x of the IMF and the mass limits m u and mℓ.The variation ofηII andβwith x,m u and mℓfor several power law IMFs is illustrated in Figure2.It is difficult to assign errors to the quantities evaluated in Equations(7)-(9)because of the many uncertainties involved and the possibility of systematic errors.If all the quantities in Equation(8)are skewed to their limits of uncertainty in an effort to minimizeηII,it is possible to achieve a close agreement with a Salpeter IMF.For example,ifΥSi,g=0.0225,R=0.92,M/L B=9, y Si,II =0.32(model WW1ex from Loewenstein&Mushotzky1996),andβ=0.3thenηII=0.0068,close to the Salpeter value.Of course it is most unlikely that Nature would conspire in this manner.Also shown in Figure1are the fraction of all iron created by SNIa:F Ia=n Ia y F e,Ian Ia y F e,Ia(1−G∗)+(1−β)−1(M/L B)ηII y F e,II (1−F∗).Provided SNu(t n)is limited to values of interest,log[SNu(t n)]<∼−1,Type Ia supernovae can contribute to the stellar enrichment without substantially changingηII or y F e,II .Renzini et al.(1993),Ishimaru&Arimoto(1997),Renzini(1997)and Wyse(1997)have discussed the X-ray data for rich clusters in detail.These authors prefer models in which the overabundance of iron relative to that expected with a normal Salpeter IMF is due to a large additional iron contribution from Type Ia supernovae,corresponding to F Ia∼0.5in Figure1.Such a model would be very similar to the enrichment history of our own Galaxy.In particular,Renzini et al.(1993)suggest a model for richcluster enrichment in which∼34coming fromSNII.If only half of the iron in rich clusters has originated in SNIa,then the number of SNIa per L B is n Ia=N Ia/L B≈0.025.But such a large number of SNIa is incompatible with iron and silicon abundances in our calculated model of a single large elliptical,discussed below,where wefind n Ia=N Ia/L B<∼0.001. For the simple power law model for SNu(t)we adopt in Figure1(p=1,t∗=2Gyrs,t n=13Gyrs),the current SNIa rate would need to be very large,SNu(t n)>∼0.6,for Type Ia supernova to supply half of the iron.This is about ten times greater than the SNIa rate estimated from observations of bright ellipticals.An alternative explanation of the iron excess in rich clusters relative that produced by a Salpeter IMF(x,m u,mℓ=1.35,100,0.08)is to invoke aflatter IMF having a larger fraction of massive stars and associated SNII.This is the interpretation preferred by David(1997)and Gibson,Loewenstein& Mushotzky(1997).For consistency bothβandηII must be adjusted when the IMF slope is changed;the value of the mass return fractionβ=0.3used in Equation(8)is based on the Salpeter IMF.Logically compatible parameters can be found by simultaneously solving Equation(8)forηII(β)with the parametric variationsηII(x)andβ(x)plotted in Figure2.The result of this joint solution is that Equation(8)now givesηII=0.016withβ=0.55for(x,m u,mℓ=1.00,100,0.08)orηII=0.018withβ=0.51for(x,m u, mℓ=0.94,40,0.08).(Such large values of the mass returnβfrom evolving stars may be unrealistic since several generations of stars must have formed near time t∗,each consuming some of the metal-enriched gas ejected from previous generations of stars.)With theseflat IMFs almost all of the iron in rich clusters originates in SNII and the low SNIa rates are consistent with those observed in massive ellipticals.IMFs flatter than Salpeter are also supported by the large mass of oxygen in rich clusters;Gibson,Loewenstein &Mushotzky(1997)claim that the observed O/Si ratio can be produced by SNII alone with little or no contribution from SNIa.When silicon and iron abundances in the ICM are considered together with abundance constraints set by individual massive ellipticals,as we have done here,the metal enrichment of rich clusters by early type galaxies is shown to be almost exclusively due to Type II supernovae with a negligible contribution from Type Ia supernovae.Evidently,star formation conditions in rich clusters are quite unlike those that prevail in our own Galaxy.The controversy concerning the relative enrichment from Type II and Type Ia supernovae in rich clusters is further confounded by the gas dynamical solutions we discuss below.We describe a variety of supernova enrichment histories for massive elliptical galaxies in which the hot interstellar gas is constrained to evolve toward the radial distribution of gas density,temperature and metal abundance observed today. In particular we show that the production of SNII using a Salpeter IMF is sufficient to achieve simultaneous agreement with n(r),T(r)and z F e(r)indicated by X-ray observations of massive ellipticals.Gas dynamic solutions based on IMFsflatter than Salpeter are generally incompatible with the observed abundance variation z F e(r).The SNIa rate must also be low.If more supernovae of either type are involved,as indicated by the largeηII for rich clusters(Equation8),the iron and silicon abundances in the models greatly exceed those observed in massive elliptical galaxies.3.IRON AND SILICON IN NGC44723.1.Gas Dynamical Models for NGC4472In a recent paper(Brighenti&Mathews1998b)we discuss in detail the basic assumptions and equations used in our gas dynamical models that simulate the evolution of hot interstellar gas in elliptical galaxies.Since the models we discuss here are very similar to those in that paper,we provide only a brief summary.Our1D spherical calculations begin with an overdensity perturbation in aflat cosmology having an amplitude designed to produce a mass concentration similar to that of NGC4472after a few gigayears.The flow of dark and baryonic matter far from the center of the perturbation follows the self-similar solution described by Bertschinger(1985).An outward moving turn-around radius defines the instantaneous locus where the cosmicflow velocity vanishes.The“secondary infall”occurs within the turn-around radius, allowing baryonic and dark matter to collect near the origin.The central accumulation of dark matter grows from the inside out;although the collisionless darkfluid interpenetrates,after passing through the origin it continues to oscillate,spending most of its time at large radii.The net effect is that a quasi-stationary core of dark matter grows outward from the origin and is matched to the outer Bertschinger inflow in a manner that preserves the total mass of dark matter.However,we replace the inner power law core of the self-similar Bertschinger solution with a(less peaked)dark halo having an NFW profile as determined by Navarro et al.(1996)with full three-dimensional N-body calculations.The dark matter mass of NGC4472 inferred by X-ray data can befit reasonably well with an NFW dark halo of mass M h=4×1013M⊙within the current virial radius assuming D=17Mpc for the distance to NGC4472.The cold baryonic gas also participates in the Bertschingerflow,but deep within the turnaround radius it passes through an accretion shock,compresses and is heated to approximately the virial temperature of the galactic dark halo.At time t∗when enough baryonic matter has collected within the shock,some of which has radiatively cooled,we form the de Vaucouleurs stellar configuration having a total mass M∗=7.26×1011M⊙appropriate to NGC4472and corresponding to a stellar mass to light ratio M∗/L B=9.20(van der Marel1991).The stellar galaxy is constructed by removing a baryonic mass equal to M∗from gas within the accretion shock。