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Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed1February2008 (MNLATEXstylefilev1.4) Abundance ratios in hierarchical galaxy formation D. Thomas Universitäts-SternwarteMu¨nchen, Scheinerstr. 1, D-81679 Mu¨nchen, Germany 1February2008 9 ABSTRACT 9 Thechemicalenrichmentandstellarabundanceratiosofgalaxieswhichforminahier- 9 archicalclustering scheme are calculated. For this purpose I adopt the star formation 1 histories(SFH)astheyaredeliveredbysemi-analyticmodelsinKauffmann(1996).It n turnsoutthattheaverageSFHofclusterellipticalsdoesnotyieldgloballyα-enhanced a stellar populations. The star burst that occurs when the elliptical forms in the major J merger plays therefore a crucial role in producing α-enhancement. Only under the 8 assumption that the IMF is significantly flattened with respect to the Salpeter value 1 duringtheburst,aMg/Feoverabundantpopulationcanbeobtained.Inparticularfor the interpretations of radial gradients in metallicity and α-enhancement, the mixing 1 of global and burst populations are of great importance. The model predicts bright v field galaxies to be less α-enhanced than their counterparts in clusters. 6 2 Keywords: stars:luminosityfunction,massfunction–galaxies:ellipticalandlentic- 2 ular,cD–galaxies:abundances–galaxies:formation–galaxies:evolution–cosmology: 1 theory 0 9 9 / h p 1 INTRODUCTION cal scheme, if metal enrichment and metallicity-dependent - population synthesis models are taken into account (Kauff- o Simulationsofhierarchicalgalaxy formation inaCDMuni- mann & Charlot 1998; Cole et al., in preparation). In such r t verse (Kauffmann, White & Guiderdoni 1993; Cole et al. models, theslope of theCMR is only driven by metallicity, s 1994)arebasedonsemi-analyticmodelsintheframeworkof asintheclassical modelsbyArimoto&Yoshii(1987).Note a : Press-Schechtertheory.They aim todescribetheformation however, that in the framework of the inverse wind models v of galaxies in a cosmological context, and therefore are de- (Matteucci 1994) the CMR slope could be in principle pro- i X signedtomatchanumberofconstraintslikeB andK lumi- ducedfromacombinationofbothageandmetallicity,since nosityfunctions,theTully-Fisherrelation,redshiftdistribu- in these models more massive galaxies are assumed to be r a tion,andslopeandscatterofthecolour-magnituderelation older. (CMR).Sinceinabottom-upscenariomoremassiveobjects InthispaperIaimtodiscusshowfarhierarchicalforma- formlater,andarethereforeyoungerandbluer–incontrast tionmodelsareabletoaccomplishafurtherimportantcon- totheobservedCMR–theoriginalworksweresubstantially straint,namelytheformation ofα-enhancedstellarpopula- sufferingfromtheproblemofcreatingluminousredelliptical tionshostedbyluminousellipticals(Peletier1989;Worthey, galaxies(Kauffmannetal.1993;Laceyetal.1993;Coleetal. Faber & González 1992; Davies, Sadler & Peletier 1993). 1994).Itisalsonotaprioriclearifthesemodelswhichyield Models of chemical evolution show that this constraint can strongevolutionatintermediateredshift(Kauffmann,Char- bematchedbythesinglecollapsemodelbeingcharacterised lot&White1996)wouldbeabletoreproducethesmallscat- by short star formation time-scales of the order 108 −109 ter of the CMR and the Mg-σ relation. On the other hand, yr (e.g. Matteucci 1994; Thomas, Greggio & Bender 1999; theseconstraintscanbeeasilyexplainedbytheclassicalsin- Jimenez et al. 1999), and it has been questioned by Ben- gle burst picture for elliptical galaxy formation, assuming der (1997) whether the observed [Mg/Fe] overabundance is passiveevolutionafterashortformation epochat highred- compatible with hierarchical models. However, abundance shift, provided that subsequent stellar merging is negligible ratios and the enrichment of α-elements have not been in- (Bower, Kodama & Terlevich 1998). However, the more re- vestigated so far in hierarchical models. For this purpose, I centmodelsbyKauffmann(1996,hereafterK96)andBaugh, consider typical star formation histories provided by semi- Cole & Frenk (1996) reproduce the above relations with a analyticmodelsforhierarchicalgalaxyformation(K96)and scatter which is in remarkably good agreement with obser- explore the resulting abundance ratios of magnesium and vationaldata(Bower,Lucey&Ellis 1992; Bender,Burstein iron. & Faber 1993; Jørgensen, Franx & Kjærgaard 1996). The correct slope of the CMR can be obtained in a hierarchi- Thepaperisorganisedasfollows.InSection2themodel (cid:13)c 0000RAS 2 D. Thomas of chemical enrichment is briefly described. Average and constraintslikesupernovarates,theage-metallicity relation bursty star formation histories are then analysed in Sec- and the trend of Mg/Fe as a function of Fe/H in the so- tions 3, 4 and 5. The results are discussed and summarised lar neighbourhood are reproduced. The SN II nucleosyn- in Sections 6 and 7. thesis prescription is adopted from Thielemann, Nomoto & Hashimoto (1996) and Nomoto et al. (1997), because the stellar yields from Woosley & Weaver (1995) are unable to account for the [Mg/Fe] overabundance in the solar neigh- 2 THE MODEL bourhood (Thomas et al. 1998). Theideaistofollowthechemicalevolutionofthegalaxyde- The IMF is truncated at 0.1 M⊙ and 40 M⊙. The scribingtheglobalchemicalpropertiesofthefinalobjectand slope above 1 M⊙ is treated as a parameter, below this itsprogenitorsasawholeduringthemerginghistory.Inthe threshold a flattening according to recent HST measure- hierarchical clustering scheme, structures are subsequently ments (Gould, Bahcall & Flynn 1997) is assumed. This build up starting from small disc-like objects. An elliptical flattening at the low-mass end does not significantly affect isformedwhentwodiscgalaxiesofcomparablemassmerge, α/Feratios.Itshouldbenotedthatstarsmoremassivethan which is called the ‘major merger’. Before this event many 40 M⊙ are expected to play a minor role in the enrichment ‘minor mergers’ between a central galaxy and its sattelite process, becauseof theirsmall numberand thefall-back ef- systemshappen.Itisimportanttoemphasise,thatthebulk fect(Woosley&Weaver1995).Moreover,themean[Mg/Fe] ofstars,namely70−90percent,formsatmodestratesinthe overabundanceinthemetal-poorhalostarsofourGalaxyis progenitordisc-galaxies beforethis‘major merger’ event.In well reproduced for an IMF with the above truncation and thestarburstignitedbythelatter,upto30percentofthe Salpeterslopex=1.35(Salpeter1955),ifThielemannetal. total stellar mass of the elliptical is created. In K96 many nucleosynthesis is adopted (Thomas et al. 1998). The V- Monte Carlo simulations are performed each corresponding luminosity averaged abundances in the stars are computed tooneindividual(final) galaxy.TheSFH which isspecified by using SSP models from Worthey (1994). For details I in K96 and adopted for the present analysis is an average refer thereader toThomas et al. (1998, 1999). about all these realizations. Finally,twosimplificationsofthepresentmodelshould bementioned: 2.1 Star formation rates (i) A one-phase interstellar medium (ISM) is assumed. TheSFHischaracterisedbytheagedistributionofthestel- Kauffmann & Charlot (1998), instead, distinguish between larpopulationsweightedintheV-bandlight.Inotherwords, cold and hot gas allowing mass transfer among these two thefractionalcontributionsLSVPbystellarpopulationstothe components. Since stars form out of cold gas, this process totalV-lightasafunctionoftheiragestarespecified.Equa- basically controls the feed-back mechanism of star formation 1 shows how this translates into a star formation rate tion. The resulting effects on the star formation rate, how- ψ: ever, are already covered, since I directly adopt the SFH from K96. Theinfluenceon theabundanceratio of Mg and LSVP(t0,t1)= RRttut0n1ivψψ(t()t)LLSVSSPSP(t()t)dtdt . (1) Fnoetismeixxpoenctseidgntiofibcaenntleygldigiffibelree,natstliomneg-sacsaltehse.seelementsdo 0 V (ii) The final galaxy is treated as the whole single-unit Here, theinterval [t0,t1] denotes theage bin of the popula- fromthebeginningofitsevolution,theeconomicsofthein- tion, tuniv is the assumed age of the universe, i.e. tuniv ≈ dividual progenitors are not followed separately as in K96. 13 Gyr for the cosmology adopted in K96 (Ωm = 1,- Hence,thesimulationsdonotdirectlyincludegalacticmass ΩΛ =0,h=0.5).TheV-light ofasimplestellar population loss takingplace duringdisc galaxy evolution (K96) as well LSVSP(t)asafunctionofitsageandmetallicityistakenfrom as mass transfer between the progenitor systems. The frac- Worthey(1994). In thispaper,thestar formation rateψ as tion ofgas convertedtostars isadjusted toglobal metallic- a function of time is chosen such that a set of stellar popu- ities typically observed in the respective galaxy type. The lationsofvariousagesandmetallicitiesisconstructedwhich impacton theglobal propertiesofthefinalgalaxy,however, exactly covers the age distribution of the K96 models. is expected to be small. In particular, abundance ratios of non-primordialelementslikeMgandFearenotsignificantly affected by mass loss and gas transfer, unless one allows 2.2 Chemical enrichment for selective mechanisms. However, in theframework of the Thechemicalevolutioniscalculatedbysolvingtheusualset present analysis, this option shall only be discussed in a ofdifferentialequations(e.g.Tinsley1980).Theenrichment qualitative fashion. process oftheelementshydrogen,magnesium, iron,and total metallicity is computed, no instantaneous recycling is assumed. In particular, the delayed enrichment by Type Ia 3 GLOBAL POPULATIONS supernovae is taken into account following the model by Greggio & Renzini (1983). The inclusion of Type Ia is cru- Figs. 1 and 2 show the global average SFHs as they are cial for interpreting Mg/Fe ratios, since SNe Ia substan- constrained for cluster elliptical and spiral galaxies in the tially contribute to the enrichment of iron. The evolution K96 model. The lower x-axis denote ages (look-back time), code is calibrated on the chemical evolution in the solar the evolutionary direction of time therefore goes from the neighbourhood (Thomas, Greggio & Bender 1998). The ra- righttotheleft.TheevolutionwithredshiftforanΩm =1, tio of SNe Ia to SNe II is chosen such that observational ΩΛ = 0 cosmology (adopted in K96) is given by the upper (cid:13)c 0000RAS,MNRAS000,000–000 Abundance ratios in hierarchical galaxy formation 3 Figure 1. The star formation history of an average cluster elliptical. The lower and upper x-axis specify age (look-back time) and redshift(Ωm=1,ΩΛ=0),respectively.Thelefty-axisdenotea‘fraction’.Thehistogramshowsthefractionalcontributiontothetotal lightinthe V-band fromeach stellarpopulation of aspecific age (see eqn. 1). The plus-signsdenote the respective contribution tothe totalmassoftheobject.ThescalesfortheunderlyingabundanceratiosMg/Fe(left-handpanel)andFe/H(right-handpanel)aregiven bythe right-hand y-axis:interstellar mediumabundance (solidline), V-average inthe composite stellar population (star symbols), the V-averageinthecompositestellarpopulationforaflatIMF(x=0.8,filledcircles).Thedottedhistogramindicatesthefractionalnumber distributionofthe majormergerepochs ofellipticalformationas theycome outintheindividual MonteCarlorealizations (K96). The arrows to the dotted line at the various merger epochs give the stellar abundance ratios of the newly created burst population formed in the major merger (see text). The horizontal dashed lines mark the observational constraints for α-enhancement and metallicity of ellipticalgalaxies,respectively. x-axis.ThehistogramshowsthequantityLSVP(t0,t1)asitis times, this discrepancy is more significant in such objects. explained in Section 2. In the elliptical case (Fig. 1), more The gas fraction which is ejected from the galaxy is chosen than70percentofthelightintheV-bandcomesfromstars suchthattheglobalstellarpopulationsoftheelliptical have which haveformed in thefirst 3 Gyr at redshift z >∼2. The solar metallicity at low redshift (Fig. 1). This leads to an SFH of the spiral (Fig. 2), instead, is much more extended ejection of roughly 30 per cent of the baryonic mass of the towards lower redshift. With a V-mean age of 6.2 Gyr, the galaxy duringits evolution. In thecase of the spiral (Milky latter thus leads to significantly younger populations than Way), instead, 55 per cent of the gas are assumed to be theSFHof theaverage elliptical (10.4 Gyr).Theplussigns ejected in orderto yieldsolar metallicity in theISMafter 9 inFigs.1and2denotethefractionalcontributionsfromthe Gyr,roughly when theSun was born (Fig. 2). various populations to the total mass of the object. Owing As a consequence, the metallicity of the ISM and the to their stellar remnants, old populations contribute more starsishigherintheellipticalthaninthespiral.TheMg/Fe tothetotalmassthantothelightoftheobject.Asaconse- ratios, instead, depend mainly on theshape of the star for- quence,intheopticalbandtheweightofyoung(old)popu- mationrateasafunctionoftime.Sincethereisnosignificant lations is larger (smaller) with respect totheiractual mass. starformation atlatetimesintheelliptical, NSNII/NSNIa is Thispatternisparticularlyprominentintheyoungandold 20 times lower than in the spiral galaxy, which leads to a spiral populations. lower Mg/Fe in the ISM by roughly 0.1 dex. The stars, in- The abundanceratios of Mg/Fe (left-hand panels) and stead, store the chemical abundances of the early epochs, Fe/H (right-hand panels) as they result from the chemical h[Mg/Fe]iV is 0.04 dex higher in the elliptical galaxy than evolution model are shown with the scale on the right y- in the spiral, which is in accordance with its older mean axis, respectively. The chemical evolution of the ISM is de- age. Still, the stellar populations in both galaxy types ex- noted by the solid line, the filled star symbols show the V- hibitroughlysolarMg/Feratiosatlowredshift,inparticular luminosityweightedaverageabundanceratiosoftherespec- h[Mg/Fe]iV ≈0.04dexfortheelliptical.Inspiteofthenegli- tivecompositestellarpopulationofthegalaxyasafunction giblecontributionofthelatestarformationtothemeanage of age (hence formation redshift). The filled circles in the ofthegalaxy,themean[Mg/Fe] ratio isdrivensignificantly left-hand panel of Fig. 1 represent the stellar mean Mg/Fe below0.2dex(Fig.1).Thisresultclearlystandsindisagree- ratio if a global flattening of the IMF with x = 0.8 is as- menttotheobservationalindicationsthat(bright)elliptical sumed.Otherwise, Salpeter slope above 1M⊙ (x=1.35) is galaxies host stellar populations which are α-enhanced by chosen. at least 0.2−0.3 dex (Peletier 1989; Worthey et al. 1992; Davies et al. 1993). In general, the mean abundances in the stellar populations differ from those in the ISM. Metallicity (Fe/H) is Fig. 1 demonstrates that with Salpeter IMF a super- always higher, and Mg/Fe always lower in the ISM than solar Mg/Fe ratio is only obtained at the very early stages in the V-average of the stars, because the stars archive the of the evolution, namely in the first Gyr. A star forma- abundancepatternsofearlyepochs.Since,inthecaseofthe tion mode which is more skewed towards these early for- elliptical,starformationismuchmoreskewedtowardsearly mation ages would lead to older ages and a higher de- (cid:13)c 0000RAS,MNRAS000,000–000 4 D. Thomas Figure 2.Thestarformationhistoryofanaveragespiral.AxisandsymbolsareexplainedinFig.1. gree of α-enhancement. One may argue that the average 4.1 Universal IMF SFH considered here does not apply to bright ellipticals in In Fig. 1 the dotted histogram denotes the distribution of whichtheobservedα-enhancementismostsignificant.How- thesemajor merger eventsamong theelliptical galaxy pop- ever,intheK96simulationsbrighterobjectsareonaverage ulation. Atthegiven epoch when thestar burstoccurs, the younger (Kauffmann & Charlot 1998), and do not experi- new stellar population forms out of the ISM whose abun- enceSFHsthataremoreskewedtowardshighredshiftthan dances are shown by the solid line in Fig. 1. Owing to the the present example. They are therefore unlikely to exhibit short duration of the star burst, the mean Mg/Fe ratios in higher Mg/Fe ratios than calculated here. the newly created stars are higher than the initial values The star formation time-scales that are required to in the ISM as indicated by the arrows and the dotted line obtain [α/Fe]≈ 0.2 for different IMF slopes are discussed (left-handpanelofFig.1).TheslopeoftheIMFisassumed in Thomas et al. (1999). The filled circles in the upper- Salpeteralso duringtheburst.Itturnsoutthat,duetothe left panel of Fig. 1 demonstrate that the shallower IMF extremelylowMg/Feratiosandthehighmetallicitiesinthe with x = 0.8 can reconcile the extended SFH with α- ISMatthemergerepoch,suchstarburstsareinappropriate enhancement. However, particularly in the hierarchical pic- to raise Mg/Fe up to a level consistent with observational ture in which the formation of different galaxy types can values. The resulting Mg/Fe does not differ from the mean be traced back to the same (or similar) building blocks at average in theglobal stellar populations. early epochs, a flattening of the IMF restricted to elliptical The metallicity Fe/H,instead, increases to even higher galaxies does not seem to providea compelling solution. values between 0.3 and 0.5 dex, depending on the burst From Fig. 1 one can also understand that only galaxy epoch (upper-right panel of Fig. 1). Under the assumption formationscenariosinwhichstarformationterminatesafter that theentire central population forms in the major burst 1−2Gyrleadtoh[Mg/Fe]iV >∼0.2dex.Theclassicalmono- the model leads to radial metallicity gradients of 0.3−0.5 lithic collapse provides such a star formation mode. In the dex from the inner to the outer parts of the galaxy, in con- hierarchical scheme, instead, (low) star formation at later tradiction to observational measurements of ∼ 0.2 dex per stages is unavoidable, which directly leads to lower Mg/Fe decade (Davies et al. 1993; Kuntschner 1998). A mixture ratiosinthestarsthatformoutofthehighlySNIaenriched of 3/4−1/3 between burst and global population in the ISMat lower redshift. galaxy nucleus is required to smooth the gradient down to theobserved value. TheresultsshowninFig.1unfoldtheprincipledilemma of the hierarchical picture: the initial conditions in the 4 BURST POPULATIONS ISMat theburstepoch, namely super-solar metallicity and The SFHs considered here apply to the global properties of sub-solar Mg/Fe, are highly unfavourable in producing α- thegalaxypopulations.However,inthepictureofhierarchi- enhanced populations. As shown in Thomas et al. (1999), calclusteringstarburststhatareinducedbymergersplayan this incapability of late merger events is independent of importantrolefortheinterpretationof(particularlycentral) the burst time-scale and SN Ia rates during the burst. The abundancefeatures.Thestarburstduringthemajormerger mostpromisingwayouttoreconcileanintermediateorlate forms 10−30 per cent of the final stellar mass, which is mergerwithα-enhancementistoassumeaflatteningofthe likelytodominatethegalaxycore,sincethegasisdrivento IMF duringthestar burst. the central regions of the merger remnant (Barnes & Hern- quist1996).InthissectionIshallinvestigatetheabundance 4.2 Variable IMF patterns of the population that results from a 0.1 Gyr star burst triggered by the major merger which forms the final The arrows and dotted lines in Fig. 3 show the abundance elliptical. patterns (left-hand panel: Mg/Fe, right-hand panel: Fe/H) (cid:13)c 0000RAS,MNRAS000,000–000 Abundance ratios in hierarchical galaxy formation 5 Figure3.Abundanceratiosfortheaverageclusterelliptical.AxisandsymbolsareexplainedinFig.1.AflatteningoftheIMF(x=0.8) duringthemajormergerburstisassumed.Fortheevolutionoftheglobalinterstellarmedium(solidline),instead,SalpeterIMF(x=1.35) isadopted. Table 1.Theaverageabundance ratiosfordifferentmixturesin Table2.Abundanceratiosinthethreezonesseparatedbyriand V-light of the global (IMF slope x = 1.35) and burst (x = 0.8) re. Thefirstcolumngives the fractionof total lightprovided by populations.[Fe/H]’denotesthemetallicityiftheefficiencyofthe therespectivezone,cols.2and3specifytheglobal-burstmixtures starburstisreducedfrom99to50percent.Theburstepochat withineachzone.[Fe/H]’isexplainedinthecaptionofTable1. 8Gyrischosen. zone light global burst [Mg/Fe] [Fe/H]’ global burst [Mg/Fe] [Fe/H] [Fe/H]’ 0<r<ri 0.05 0.1 0.9 0.21 0.45 ri<r<re 0.45 0.5 0.5 0.15 0.29 1.0 0.0 0.04 0.00 0.00 re<r<∞ 0.50 0.9 0.1 0.06 0.05 0.9 0.1 0.06 0.10 0.05 0.7 0.3 0.11 0.30 0.18 0.5 0.5 0.15 0.44 0.29 0.3 0.7 0.18 0.54 0.37 global population by providing 30 per cent of the total V- 0.1 0.9 0.21 0.63 0.45 light, the resulting [Mg/Fe] is reduced to 0.11 dex (row 3 0.0 1.0 0.23 0.66 0.50 in Table 1). Forsuch proportions, theextreme flatteningof x=0wouldberequiredtoobtainasignificantlyα-enhanced populationof[Mg/Fe]=0.2dex.Morelikely,however,isthat of the burst population if a shallow IMF (x = 0.8) during theburstpopulationsaremoreprominentintheinnerparts the burst is assumed. The chemical evolution of the global duetodissipationprocessesintheburstgas(Barnes&Hern- ISMisbasedonSalpeterIMF(x=1.35) asbefore.Itturns quist 1996). Table 1 can then beinterpreted in terms of in- outthat,withasignificantflatteningoftheIMF,themajor creasinggalaxyradiusfrombottomtotop.Abundancegra- mergerburstproducesametal-richα-enhancedstellarpop- dientsresultaccordingtotheglobal-burstmixturesassumed ulation. As demonstrated in the left-hand panel of Fig. 3, at different radii of theobject. thebulkofellipticalsexperiencetheirmajormergeratlook- I shall briefly discuss the following model, in which I backtimesof7−9Gyr(z≈0.7−1.5) andthereforeexhibit roughly devide the galaxy in three zones separated by the significant α-enhancement in theburst population. innerradiusriandtheeffectiveradiusre.Theresultingstel- larabundanceratiosineachzonefortherespectivedifferent global-burstmixturesareshowninTable2.Column 2gives theV-lightfractionofeachzone,namely5percentfromthe 5 GLOBAL–BURST MIXTURES mostinnerpart,andhalfofthelightwithintheeffecticera- Thequestionishowdotheglobalandtheburstpopulations dius re. Altogether, the fractional contributions are chosen mix? The value x= 0.8 represents the minimum flattening such that the burst population contributes 30 per cent of required for the case that the pure burst population is ob- thetotalV-lightofthegalaxy.Thestarformationefficiency served, i.e. in the centre of the galaxy. Apart from the fact of the burst population is assumed to be 50 per cent, in thatnomixingofthetwopopulationtypesseemsunlikely,it ordertoavoid metallicities thatexceedobservational deter- wouldproducemetallicitygradientsmuchtoosteep.Table1 minations. In Table 2, the quota of the burst population is gives theaverage abundanceratios for differentmixtures of steadily decreasing towards the outer zones of the galaxy, the global (IMF slope x = 1.35) and the 8 Gyr-burst pop- which leads to gradients such that both Mg/Fe and Fe/H ulations (x = 0.8). [Fe/H]’ denotes the metallicity if the are decreasing with increasing radius. efficiencyofthestarburstisreducedfrom99to50percent. Thegalaxynucleusismostmetal-rich andsignificantly Mg/Fe is not significantly affected (Thomas et al. 1999). α-enhanced, the gradients of both Mg/Fe and Fe/H within If the burst population mixes homogeneously with the re, however, are rather shallow. Thus this model predicts (cid:13)c 0000RAS,MNRAS000,000–000 6 D. Thomas theMg/Fe overabundancenottodecline remarkablyout to overall chemical initial conditions in the early universe do re, in accordance with Worthey et al. (1992) and Davies not alter theconclusions. et al. (1993). It is interesting to mention that thetendancy of aslight decrease in α-enhancementisfound in theComa 6.2 Selective mass loss cluster sample analysed by Mehlert et al. (in preparation). ThegradientinmetallicityasgiveninTable2isalsoconsis- Type Ia supernovae explode later than Type II, thus their tent with estimates byDavies et al. (1993) and Kuntschner ejection occurs at different dynamical stages of the merg- (1998). ing history. In a scenario in which Type Ia products (basi- Finallyitshouldbeemphasized,thatreasonablemetal- cally iron) are lost easier, the accomplishment of enhanced licities are only achieved if star formation during the burst Mg/Feratios issimplified.Theexamination ofthisalterna- isassumedtobeefficientbyonly50percent.Table1shows tive,however,requiresamoredetailedanalysisofthepossi- that otherwise metallicities above 3 Z⊙ would be obtained bleoutflowandstarformationprocessesduringthemerging in the centre, which exceeds observational determinations history, which by far exceeds the scope of this paper. On (Kuntschner& Davies 1998). the other hand it is important to notice, that α-enhanced giantellipticalgalaxiesenrich–forSalpeterIMF–theintra- clustermedium(ICM)withMg/Feunderabundant material (Thomas 1998b). A selective loss mechanism as mentioned 6 DISCUSSION above further increases this ICM-galaxy asymmetry (Ren- ItshouldagainbeemphasizedthattheSFHsdiscussedhere zini et al. 1993) and therefore causes a more striking dis- are averages over many Monte Carlo realizations, individ- agreement with observational measurementswhich indicate ual galaxies are therefore not considered. This approach is solar α/Fe ratios in the ICM (Mushotzky et al. 1996; Ishi- sensible because also the observational constraint is taken maru & Arimoto 1997). to be a mean α-enhancement about which the values mea- suredforthesinglegalaxiesscatter.Still,inamoredetailed 6.3 Cluster vs. Field analysis it would beof great interest toresolve theSFHsof individualgalaxiesandtocomparethetheoreticalscatterin The SFH discussed in this paper applies to cluster ellip- α-enhancement with theobserved one. ticals. In such a high density environment, the collapse of In thefollowing I will discuss uncertainties in chemical density peaks on galaxy scale is boosted to high redshifts evolutionthatmayhaveanimportantimpactontheresults. (K96). In the low-density surroundings of the field (haloes Furthermore possible implications on properties of cluster of1013 M⊙),instead,thesituation isentirelydifferent.The and field galaxies are mentioned. K96modelpredictsthatobjectsinthefieldarenotdestined tobeellipticalsorspirals,butactuallyundergotransforma- tions between both types due to gas accretion (formation 6.1 SN Ia rate and stellar yields of a disc galaxy) or merging of similar sized spirals (forma- tionof anelliptical). Asaconsequence,theobjects wehap- The model of chemical evolution applied for this analysis pen to observe as bright ellipticals in the field should have is calibrated such that the basic local abundance features mostlyhadarecentmergerinthepast1.5Gyr.Thisleadsto arecovered (Thomas et al. 1998). Besides stellar yields and youngermeanages,butalsotoamoreextendedSFH.Figs.1 IMF, this also includes the prescription of the Type Ia su- and3showthatlaterburstsyieldlowerMg/Feratios.From pernova, which is adopted from Greggio & Renzini (1983). the models, one should therefore expect a trend such that According to this model, the maximum of the SN Ia rate (bright)ellipticalsinthefieldareonaveragelessα-enhanced occurs roughly 1 Gyr after the birth of the stellar popula- thantheircounterpartsinclusters(seealsoThomas1998a). tion.Itisobviousthatthistime-scalehasagreatimpacton Thus,theintrinsicdifferencebetweenclusterandfieldellip- the results presented here. From the solar neighbourhood ticals (K96), which manifests itself most prominent in the data,onecannotentirelyexcludeaSNIaratewhichsetsin propertiesofbrightellipticalgalaxies,shouldbemeasurable laterandstronger.Suchamodelwouldbasically delay(not in their α-element abundancepatterns. prevent)thedecreaseoftheMg/Feratio,henceinthehierar- chical clustering scheme the global populations of ellipticals wouldstillnotappear α-enhanced.However,theMg/Fera- 7 CONCLUSION tios in the ISM would be higher at the major burst epochs, leading to more α-enhancementin theburst populations. In this paper, I analyse average star formation histories Uncertaintiesinstellaryields(Thomasetal.1998)allow (SFH) as they emerge from hierarchical clustering theory to raise the calculated Mg/Fe ratios. Note, however, that with respect to their capability of producing α-enhanced the degree of α-enhancement used as the main constraint abundanceratiosobservedinellipticalgalaxies.Forthispur- in this paper ([α/Fe]= 0.2 dex) represents the lowest limit pose, the V-luminosity weighted age distributions for the determined from observational data. stellar populations of the model spiral and cluster elliptical Averyearlychemicalpre-enrichmentbyPopIII-likeob- galaxy are adopted from Kauffmann (1996, K96). jects may induce initial conditions in favour of high Mg/Fe Owing to the constant level of star formation in spiral ratios. The results in this paper, however, are not seriously galaxies, their SFH leads to roughly solar Mg/Fe ratios in affected by such uncertainties, since it is argued differen- the stars and in the ISM, in agreement with observations tially to the solar neighbourhood chemistry on which the intheMilkyway.Forellipticalgalaxies,hierarchicalmodels chemical evolution model is calibrated. Thus details of the predict more star formation at high redshift and therefore (cid:13)c 0000RAS,MNRAS000,000–000 Abundance ratios in hierarchical galaxy formation 7 significantly older mean ages. However, the calculations in IshimaruY.,ArimotoN.,1997,PASJ,49,1 thispapershow,thattheirSFHisstilltooextendedinorder Jimenez R., Friaça A. C. S., Dunlop J. S., Terlevich R. J., Pea- toaccomplishasignifcantdegreeofglobalα-enhancementin cock J. A., Nolan L. 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