Cosmic stellar relics in the Galactic halo

0.77 MB·English

by  S. Salvadori

Mon.Not.R.Astron.Soc.000,1–17() Printed5February2008 (MNLATEXstylefilev1.4)
Cosmic stellar relics in the Galactic halo
Stefania Salvadori1, Raffaella Schneider2 & Andrea Ferrara1
1SISSA/International School forAdvanced Studies, Via Beirut 4, 34100 Trieste,Italy
2INAF/Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, 50125 Firenze, Italy
7
ABSTRACT
0
We study the stellar population history and chemical evolution of the Milky Way in
0
a hierarchical ΛCDM model for structure formation. Using a Monte Carlo method
2
basedonthesemi-analyticalextendedPress&Schechterformalism,wedevelopanew
n
code GAMETE(GAlaxy MErgerTree & Evolution)to reconstructthe mergertreeof
a
the Galaxy and follow the evolution of gas and stars along the hierarchical tree. Our
J
approach allows us to compare the observational properties of the Milky Way with
2
model results, exploring different properties of primordial stars, such as their Initial
2
Mass Function (IMF) and the critical metallicity for low-mass star formation, Zcr.
In particular, by matching our predictions to the metallicity distribution function of
2
v metal-poor stars in the Galactic halo we find that: (i) a strong supernova feedback
0 is required to reproduce the observed properties of the Milky Way; (ii) stars with
3 [Fe/H]< −2.5 form in halos accreting Galactic Medium (GM) enriched by earlier
1 supernova explosions; (iii) the fiducial model (Zcr = 10−4Z⊙, mPopIII = 200M⊙)
1 provides an overall good fit to the MDF, but cannot account for the two HMP stars
1 with [Fe/H]< −5; the latter can be accommodated if Zcr ≤ 10−6Z⊙ but such model
6 overpopulatesthe“metallicitydesert”,i.e. therange−5.3<[Fe/H]<−4inwhichno
0
stars have been detected; (iv) the current non-detection of metal-free stars robustly
/
h constrains either Zcr > 0 or the masses of the first stars mPopIII > 0.9M⊙; (v)
p the statistical impact of truly second generation stars, i.e. stars forming out of gas
- polluted only by metal-free stars, is negligible in current samples; (vi) independently
o
of Z , 60% of metals in the Galactic Medium are ejected through winds by halos
r cr
st with masses M < 6×109M⊙, thus showing that low-mass halos are the dominant
a populationcontributingtocosmicmetalenrichment.Wediscussthelimitationsofour
: study and comparison with previous work.
v
i Keywords: stars:formation,populationIII,supernovae:general-cosmology:theory
X
- galaxies: evolution, stellar content -
r
a
1 INTRODUCTION dependson theproperties ofthefirst stars, which therefore
control the evolution of the ISM, IGM and of the cosmic
Thefirststarsrepresentthefirstsourceoflight,metalsand environment in which galaxies form.
dust after the Big Bang. Since they form out of gas of pri-
mordial composition, they are expected to be metal free. There are still many puzzling questions about the first
For this reason, they have been historically called popu- stars, related to the lack of observational evidences of such
lation III stars (Pop III) to make a distinction from the pristine objects. At present, the primordial Initial Mass
observed population II/I stars, which havetypicalmetallic- Function (IMF) represents one of the most discussed top-
ities Z > 10−5 10−4 and Z 0.02, respectively (Bromm ics in this field. Theoretical studies support the idea of
&Larso∼n2004)−.Theimpactof∼firststarsonthesubsequent a top-heavy IMF, biased towards massive and very mas-
structure formation history is very strong through different sive stars (Omukai & Nishi 1998; Abel, Bryan & Norman
feedback mechanisms: UV photons from the first stars are 2002;Bromm,Coppi&Larson2002;Ripamontietal.2002;
likely responsible for thereionization and heatingof thein- Nakamura&Umemura2002;Schneideretal.2002;Omukai
tergalactic medium (IGM); heavy elements are synthesized & Palla 2003; Bromm & Loeb 2004; O’Shea & Norman
insidesuchstarsandduringtheearlysupernova(SN)explo- 2006;Yoshidaetal.2006).Indeed,intheabsenceofmetals,
sions dust grains are formed. Dust and metals are released the collapsing star forming gas is predicted to fragment in
in the interstellar medium (ISM) and eventually enrich the 103M⊙ clumps, progenitors of the stars which will later
∼
IGMthroughSNwinds.Theefficiencyofalltheseprocesses form in their interiors accreting gas on the central proto-
(cid:13)c RAS
2 Stefania Salvadori, Raffaella Schneider & Andrea Ferrara
stellar core. Because of the poor understandingof thecom- large number of metal-poor stars contained in the most re-
plexphysicswhich controlsthelatephasesofaccretion and cent public data release of the Sloan Digital Sky Survey
protostellarfeedback,thefinalstellarmassesarestilllargely (Yorketal.2000),anditsplannedextensionwhichincludes
uncertainbutlikelytobeintherange30M⊙ 300M⊙ (Tan theprogram SEGUE, specifically targeted to collect metal-
−
& McKee 2004). poor stars with [Fe/H]< 2and to constrain thetransition
−
In contrast with the above speculations, present-day from thedisk population to thehalo.
star formation (Pop II/I stars) is known to be character- TheHEShasrecentlyrevealedtheexistenceoftwostars
iflzaetdtebnyinagSbaellpoewtemraIMsseFsionft0h.3e5mMa⊙ss(rLaanrgsoen0.119M98⊙).−S1in0c0eMth⊙e, wanitdh[F[Fee//HH]=]= −55.4.3(†H(EH1E32071-0273-2562,40F,reCbherlisettliaelb. 2e0t0a5l)..2B0o0t2h)
characteristic mass of local Pop II/I stars is 1M⊙, if our ofthesestars−showalargeoverabundanceofcarbonandni-
∼
current understanding of primordial star formation is cor- trogen with respect to iron and other heavy elements, sug-
rect, there must have been a transition in the properties gesting a similar origin for their abundancepattern. Essen-
of star-forming regions through cosmic times. Recent the- tially twoclasses ofmodelshavebeenproposedtointerpret
oretical studies suggest that the initial metallicity of the the observed abundances: (i) the stars were born in a pri-
star-forming gas represents thekey element controlling this mordial environment and had their surfaces polluted at a
transition (Bromm et al. 2001; Omukai et al. 2001, 2005; later time (Shigeyama, Tsujimoto & Yoshii 2003; Suda et
Schneider et al. 2002, 2003, 2006; Bromm & Loeb 2004). al. 2004); (ii) they had been pre-enriched by the yields of
Following the evolution of protostellar gas clouds with dif- one or more SNe (Christlieb et al. 2002, 2004; Umeda &
ferentvaluesoftheinitialmetallicityandincludingdustand Nomoto2003; Bonifacio, Limongi&Chieffi 2003; Schneider
moleculesascoolingagents,Schneideretal.(2002-2006)and etal.2003;Iwamotoetal.2005).Inthefirstcase,thesetwo
Omukai et al. (2005) find that when the metallicity is in stars would be low-mass Pop III stars, in conflict with the
the critical range 10−6 < Zcr/Z⊙ < 10−4 there occurs a proposedcriticalmetallicityscenario.Inthesecondcase,in-
transition in fragmentation scales from 103M⊙ to solar stead,thesestarswouldbesecondgenerationstarsenriched
∼
or subsolar fragments and argue that this is an indication by the ashes of the first SNe. At present, the available evi-
for a transition in characteristic stellar masses. The critical dence does not allow to exclude any of the above proposed
metallicity value depends on the fraction of metals locked scenarios but shows that the observational data on metal
in dust grains, which provide an additional cooling channel poor stars are starting to challenge theoretical models.
athighdensitiesenablingfragmentationtosolarandsubso- Thischallengeisevenmoreseriousasit resonateswith
larclumps(Schneideretal.2003, 2006; Omukaietal. 2005; additional constraints on the primordial IMF placed by
Tsuribe & Omukai 2006). Thus, according to this scenario completely independent observations. In particular, the re-
theonsetoflow-massstarformation intheUniverseistrig- centdownwardrevisionofThomsonscatteringopticaldepth
geredbythepresenceofmetalsanddustintheparentclouds foundintheanalysisoftheWilkinsonMicrowaveAnisotropy
to levels exceeding Zcr. Probe(WMAP)threeyearsdata(Pageetal.2006) predicts
In this scenario, stellar archeology of the most metal- a later reionization epoch, in agreement with a universal
poorstarsrepresentsapromisingwaytoexploreprimordial Salpeter IMF (Choudhury & Ferrara 2006; Gnedin & Fan
star formation. Due to their low metallicities, metal-poor 2006).Thesameconclusionisdrawnwhentheoreticalmod-
stars are expected to form out of gas enriched by members els(Salvaterraetal.2006)areconfrontedwiththeobserved
of the first stellar generation. Therefore, despite of the fact anisotropiesinthenear-infraredbackground(Kashlinskyet
that metal-poor stars are observed in the Galactic halo or al.2005).Theseresultstendtofavorarelativelyunevolving
innearbydwarfgalaxies,satellitesoftheMilkyWay(MW), Salpeter IMF upto the highest redshifts.
these objects might well be living fossils of the first star The motivation of the present study was to explore to
formation episodesintheUniverse.Oneofthemostimpor- whatextenttheshapeofthelow-metallicity tailofthehalo
tant observational constraints is provided by the distribu- MDF can provide insights on the nature of the first stars.
tion of stellar metallicities in the halo of the Galaxy, the In particular, we aim at addressing thefollowing questions:
so-called Metallicity Distribution Function (MDF). Intheir Whataretheimplications of theobservedlow-metallicity
earlystudies,Ryan&Norris(1991)andCarneyetal.(1996) •tail of thehalo MDF?
⋆
show that this function peaks at [Fe/H]= 1.6 with a tail DoesasharpMDFcutoffputconstraintsontheprimordial
extending down to [Fe/H] 4. Although−the compilation •IMF?
≈−
of Ryan & Norris (1991) is relatively old and consists only What is the relation between the MDF cutoff and the
of 300 stars, their MDFis consistent with that obtained by •critical metallicity ?
more recent and larger samples collected by the HK survey What is the origin of the “metallicity desert”, i.e. the
of Beers et al. (1992) and by the Hamburg/ESO objective a•bsence of stars in the range 5.3< [Fe/H] < 4?
prism survey (HES, Wisotzki et al. 2000; Christlieb 2003) What is the statistical impa−ct in the observed−samples of
whose analysis is still underway to quantify completeness •trulysecondgenerationstars,i.e.starsenrichedonlybythe
andselectioneffects(seeBeers&Christlieb2005forathor- ashes of the first stellar explosion, which then can be used
ough review). The joint HK and HES sample includes 2756 toconstrainthenucleosyntheticproductsandthemassesof
stars with [Fe/H]< 2. It will be further extended by the primordial stars?
−
⋆ Hereafter we use the notation [Fe/H]= log(NFe/NH) − † Arecentanalysisbasedonthedetection ofFeIIlinesleadsto
log(NFe/NH)⊙ normalized to the solar values of Anders & a downward revision of the iron abundance of HE0107-5240 to
Grevesse(1989). [Fe/H]=−5.7±0.2(Christlieb,Bessell&Eriksson2006).
(cid:13)c RAS,MNRAS000,1–17
Cosmic stellar relics in the Galactic halo 3
Several authors have attempted to interpret the im- merger tree of the Galaxy and we show that it successfully
plications of the observed halo MDF by applying different reproduces the predictions of the EPS theory. In Sec. 3, we
methods. Using a semi-analytical model, Hernandez & Fer- discuss the implementation of star formation and mechani-
rara (2001) deduced that a characteristic Pop III mass in- cal feedback; Sec. 4 discusses themodel calibration. In Sec.
creasing towards high redshift is requiredin ordertofit the 5 we present the results of the model, which are then com-
low-Z tail of the MDF. Prantzos (2003) also pointed out paredwiththemostrecentdatainSec.6.Abriefsummary
that the stellar metallicity distribution depends sensitively and discussion, given in Sec. 7, conclude thepaper.
on whether instantaneous recycling is adopted or relaxed.
The possible existence of a low-Z cutoff in the MDF has
beeninterpretedbyOey(2003)intheframeworkofstochas-
2 BUILDING THE MERGER TREE
tic chemical enrichment models, as a result of the various
metal diffusion/transport/mixing processes at work in the Themostpopularmodelforgalaxyformation(ΛCDM)pre-
Galactic environment. Along similar lines, Karlsson (2006) dictsthatgalaxiesformthroughaseriesofmergingprocesses
hasnoticedthatthemetallicitydesert,ifconfirmed,couldbe of lower mass fragments, in a hierarchical tree picture. We
usedtoextractinformationaboutthepastGalacticstarfor- haveusedasemi-analyticalapproachbasedontheExtended
mationhistory.Finally,Tumlinson(2006)presentedachem- Press&Schechter(EPS)theory(Bondetal.1991;Lacey&
ical evolution modelfortheMW whichfollows thestarfor- Cole 1993) to reconstruct the hierarchical merger history
mation history in a hierarchical galaxy formation scenario. of our Galaxy. Halo mass distributions drawn from Press
Such model accurately reproduces the halo MDF by Ryan & Schechter formalism (1974) show an excellent agreement
& Norris (1991). withthosederivedfromN-bodysimulations;itsmaindraw-
The method proposed in this paper is similar in spirit back consists in the lack of spatial information. There are
to that of Tumlinson; however, it introduces a number of several alternative methods to construct merger tree algo-
novelfeatures,particularlyforwhatconcernsthetreatment rithms from EPS (see Somerville & Kolatt 1999 for a criti-
ofmechanicalfeedbackandmodelcalibration.Moreover,we cal review); following Cole et al. (2000) and Volonteriet al.
compare our model results with a new MDF determination (2003) (herafter VHM), we have developed a binary Monte
obtainedfromjointHKandHESdata(including2756stars Carlo code with mass accretion.
with [Fe/H] 2) by Beers & Christlieb (2006). A detailed The main building block of the algorithm follows from
≤−
comparisonbetweenthetwostudiesisgiveninSec.6.Using equation (2.15) of Lacey & Cole (1993) re-written in terms
thenewlydevelopedcodeGAMETE (GAlaxyMErger Tree of theprogenitor mass M:
& Evolution) we follow the gradual build-up of the stellar
1 (δ δ )
population and metal enrichment of theMW along its past f(M,M0)dM = √2π(σ2 c−σ2c0)3/2 ×
hierarchical evolution. The code is based on a Monte Carlo M − M0
algorithm, along the lines of Cole et al. (2000) and Volon- (δ δ )2 dσ2
teri, Haardt & Madau (2003), standing on the Extended exp c− c0 M dM. (1)
× (cid:18)−2(σ2 σ2 )(cid:19)(cid:12)dM (cid:12)
Press Schecther (EPS) theory (Bond et al. 1991; Lacey & M − M0 (cid:12) (cid:12)
(cid:12) (cid:12)
Cole,1993).Wereconstructthehierarchicalevolutionofthe This equation gives the fractio(cid:12)n of m(cid:12)ass in a halo of mass
MW from redshift z = 20 and follow, jointly, the chemical M at redshift z which, at an earlier time z > z , belongs
0 0 0
enrichment and history of itsstellar population. The chem- to less massive progenitors having mass in the range M to
ical evolution of both proto-Galactic halos and of the gas M+dM (seealsoColeetal.2000).Thequantityδ =δ (z)
c c
reservoirintowhichtheyareembedded,whichwecallthere- (δ = δ (z )) is the critical linear overdensity threshold
c0 c 0
after the Galactic Medium (GM), is computed byincluding for collapse at redshift z (z ); σ2 (σ2 ) is thelinear r.m.s.
0 M M0
a physically based description of the mechanical feedback densityfluctuationsmoothedwithatop-hatfilterofmassM
produced by the energy deposition of massive stars. In ad- (M ).Byconstruction,theintegralofeq.(1)fromM =0to
0
dition, this allows us to evaluate the typical masses of ha- M =M must give unity,i.e. all halos were in less massive
0
los which mostly contribute to the GM enrichment and to fragments at earlier epochs. Multiplying f(M,M ) dM by
0
understand how the ejection and accretion of enriched gas M /M,themassfractioncanbetranslatedintothenumber
0
along the hierarchical tree is reflected in the resulting stel- of halos perunit mass,
larMDF.Tocalibratethetwofreeparametersofthemodel
dN M
(starformationandwindefficiency)wecomparetheinferred dM(M,M0)dM = M0 f(M,M0)dM. (2)
Galaxy average properties with their observed values. The
model can then be used to predict the shape of the halo Hereafterwedroptheargument(M,M0)tosimplifytheno-
MDF for different assumed properties of the first stars, i.e. tation.Takingthelimitz z0 ofeq.(2),onecanobtainan
→
theprimordial IMF and critical metallicity. expressionfortheaveragenumberofprogenitorsinthemass
Thepaperisorganizedasfollows:inSec.2,wedescribe rangeM,M+dM intowhich ahaloofmass M0 fragments
considering a step dz back in time (Cole et al. 2000):
the algorithm developed to construct the cosmological‡
dN 1 1 dδ dσ2
dM = c M dM dz, (3)
dM √2π(σ2 σ2 )3/2 dz (cid:12)dM (cid:12)
‡ We adopt a ΛCDM cosmological model with h=0.73, Ωm = M − M0 (cid:12)(cid:12) (cid:12)(cid:12)
0.24,ΩΛ=0.72,Ωbh2=0.02,n=0.95andσ8=0.74,consistent whereM <M0andz=z0+dz.This(cid:12)equati(cid:12)onrepresentsthe
with the 3-yr WMAP data (Spergel et al. 2006). We adopt the coreofouralgorithm.Weuseittobuildabinarymergertree
fittothepowerspectrumproposedbyBardeenetal.(1986)and that starts from the present day Galactic dark matter halo
modifiedbySugiyama(1995). anddecomposesitintoitsprogenitors,runningbackwardin
(cid:13)c RAS,MNRAS000,1–17
4 Stefania Salvadori, Raffaella Schneider & Andrea Ferrara
time up to redshift z = 20. Given the shape of the matter is thetop-hat window function.
power spectrum in ΛCDM models, the number of halos di- We now need to specify the free parameters of the
vergesas themass M goes tozero. Forthisreason, a cutoff model, M and dz. A high value of M would be re-
res res
(resolution)massM ,whichmarksthetransitionbetween quired to preserve the binarity of the code (eq. 4) and to
res
progenitors and mass accretion, is required. At any given control the computational cost implied by a very high time
time-step, halos can either (i) lose part of their mass, cor- resolution.However,weneedM tobesmallenoughtore-
res
respondingtothecumulativefragmentation intohaloswith solvethelow mass halos presumably hostingthefirst stars.
M < M , or (ii) fragment into two progenitor halos and In addition, M must be redshift dependent, decreasing
res res
lose mass. At each redshift, the mass below the resolution with increasing redshift, to reproduce the EPS predictions
limitaccountsfortheGMinwhichthehalosareembedded. (VHM).Indeed,hierarchicalmodelspredictlessmassiveha-
Notethat werefer tomass accretion as theprocess ofmass losathigherredshifts.Thehalomasswhich,atagivenred-
loss in the (backward stepping) merger algorithm. shift z corresponds toa virial equilibrium temperature T
vir
OnceM isfixed,onecan computethemeannumber can beapproximated as,
res
of progenitors in the mass range M <M <M /2 that a
res 0 10 3/2 T 3/2
haloofmassM0 atz0 isfragmentedintoduringatime-step M(Tvir,z)∼108M⊙ 1+z 10v4iKr (8)
dz (cid:16) (cid:17) (cid:16) (cid:17)
M0/2 dN (for an exact expression see Barkana & Loeb 2001). Given
Np =Z dM dM, (4) the above redshift dependence, taking Mres ∝ M(Tvir,z)
Mres appearsphysicallymotivated.Forreasonsthatwillbeexten-
and the accreted mass fraction sivelymotivatedinthenextSection,ouranalysisfocuseson
Mres dN M haloswithmassM ≥M(Tvir =104K,z)≡M4(z).Thus,we
Fa =ZM0 dM M0 dM. (5) ehnaavbelecshotsoenfolalorwestohluethioinstomryasosfMalrleMs(zW) =proMge4n(zit)o/r1s0hwavhiinchg
Boththesequantitiesdependondz(seeeq.3),suitablycho- M M4(z) up to z=20.
≥
sen to prevent multiple fragmentations (N <1). Since the Thetime-step dz isempirically selected in orderto ob-
p
numberofprogenitors decreases with dz,binaryalgorithms tain a good agreement between the EPS predictions and
generally requirea high temporal (redshift) resolution. numericalresults.Westartedbyconsidering 820time-steps
AteachtimestepandforeachprogenitormassM ,we logarithmically spaced in expansion factor between z = 0
0
generate a random number 0 < R < 1 and we compare it and z=20. However, since thenumberof halos in thehigh
with the value N derived by eq. (4). If N < R, the halo mass range was found to exceed the EPS predictions, we
p p
does not fragment at this step. However a new halo with havereducedthetime-stepbyafactor5withintheredshift
mass M (1 F ) is produced, to account for the accreted interval8<z<12.
0 a
matter. If i−nstead N R, fragmentation occurs: a new Finally,weneedtospecifytheassumedMWdarkmat-
p
randomvalueintherang≥eM <M <M /2isdrawnfrom terhalomass.FollowingBinney&Merrifield(1998),wehave
res 0
thedistribution eq.(3) toproducea progenitor of mass M; assumed MMW = 1012M⊙. This values likely represents a
massconservationsetsthemassofthesecond progenitorto lower limit to total halo mass, being estimated through ob-
M (1 F ) M.Thisprocedure,iteratedoneachprogenitor servations of the most distant galactic satellites currently
0 a
halo a−nd a−t each redshift, provides the whole hierarchical detected.
treeofanyinitiallyselectedgalaxy,fromthepresent-dayup Comparison between the code results and EPS predic-
to an initial redshift. tions is shown in Fig. 1, where the mean number of Milky
Togiveacompletepictureofthemergertreealgorithm Way halo progenitors is plotted at different redshifts as a
weneedtodescribethequantitiesinvolvedintheequations function of mass resulting from the average of 200 different
and specify the adopted free parameters. In particular, in MonteCarlorealizationsofthemergertree.Ateachredshift,
eq.(3)theexpressionsδ (z)andδ (z )representthevalues the agreement with EPS is satisfactory down to the lowest
c c 0
of the critical density extrapolated to z = 0. Specifically, halo masses M M4(z), i.e. for all the objects of interest
≥
δ (z) = 1.686/D(z) where D(z) is the linear growth factor toourstudy.Notethat,asexpectedforΛCDMmodels,the
c
(Carrol, Press & Turner 1992), typical population mass decreases with increasing redshift
and few collapsed halos exist at z = 15, most of the mass
D(z)= 5Ωm(z) 1 + 209Ω (z) Ω2m(z) +Ω4/7(z) −1(6) being below the resolution mass and therefore diffused in
2(1+z)(cid:18)70 140 m − 140 m (cid:19) theGM.
whereΩ (z)=Ω (1+z)3[1 Ω +(1+z)3Ω ]−1.Forthe
m m0 m0 0
−
adopted cosmological parameters theaboveequation repre-
sentsagood approximationofthelineartheorygrowth fac- 3 STAR FORMATION AND FEEDBACK
tor.Ontheotherhandthelinearrmsdensityfluctuationin
In hierarchical models for galaxy formation the first star-
eq. (3), smoothed with a top-hat filter, is given by
forming halos are predicted to collapse at redshift z 20,
σ2(M)= 1 ∞P(k)W2(kR)k2dk, (7) having masses M ∼106M⊙ and virial temperatures T∼vir <
2π Z 104 K. The neutral gas in these minihalos cannot cool via
0
atomichydrogenandreliesonthepresenceofmolecularhy-
wheretheintegralisperformedinthek Fourier-space,P(k)
drogen, H , to cool and collapse, ultimately forming stars.
is thecold dark matter power spectrum and 2
Theroleofminihalos in cosmic evolution hasbeen thesub-
W(kR)=4πR3[(sin(kR) kRcos(kR))/(kR)3], ject of a number of studies, suggesting that their star for-
−
(cid:13)c RAS,MNRAS000,1–17
Cosmic stellar relics in the Galactic halo 5
Figure1.NumberofprogenitorsofaMWparenthaloofmassMMW =1012M⊙asafunctionofmassatdifferentredshifts.Histograms
represent averages over 200 realizations of the merger tree, with errorbars indicating Poissonian error on the counts in each mass bin.
SolidlinesshowthepredictionsofEPStheory;dashedlinesindicatethevaluesofM4(z)atthecorrespondingredshift.
mation activity is easily suppressed by radiative and me- 3.2 Pop III and Pop II/I IMFs
chanicalfeedback(seeCiardi&Ferrara2005forathorough
We have assumed that the stellar IMF depends on the ini-
review). Empirical evidence for this suppression has been
tial metallicity of star forming clouds, in agreement with
recently provided by the 3-yr WMAP data. The downward
thecriticalmetallicityscenario.Astarforminghalowithan
revisionofthemeasuredopticaldepthtoelectronscattering
initial metallicity Z Z will be referred to as a Pop III
ofτ =0.09 0.03(Pageetal.2006) isconsistentwithmod- ≤ cr
elsinwhich±ionizingsourcespopulatehalosdowntoavirial halo§, and it will host Pop III stars with masses within the
temperatureofT =104K,requiringstrongsuppressionof rangeofpairinstabilitySNe(SNγγ,140M⊙ m 260M⊙).
vir ≤ ≤
Indeed,theseviolentexplosionsarepredictedtoprovidethe
starformation inearlierminihalos(Haiman&Bryan2006).
dominant contribution to metal enrichment at the lowest
Consistentwiththesefindings,wehavetrackedthestar
metallicities, releasing roughlyhalfof theirprogenitor mass
formation history and chemical enrichment of the Galaxy
inheavyelementsandleavingnoremnants.Thismeansthat
down to progenitor halos with masses M (z) and we have
4
all the initial progenitor mass is returned to the surround-
assumedthatattheinitialredshiftofz 20thegasinthese
∼ ing medium and that gas pollution by these objects is very
halos is still of primordial composition. This istheresult of
strong with respect to the contribution of all stars with
the effect that any given source photodissociates molecu-
lar hydrogen on scales much larger than those affected by m < 40M⊙ enriching the ambient medium through mass
loss or Type II SN (SNII) explosions. We have assumed a
itsmetalenrichment(Scannapiecoetal. 2006). Inanystar-
forming halo and at each time-step, stars are assumed to referencevalueofmPopIII =200M⊙ forthemassofPopIII
stars, but we have also explored the implications of adopt-
forminasingleburst;thetotalmassofstarsformedispro-
portionaltotheavailablegasmasswitharedshift-dependent ing the two extreme values of 140M⊙ and 260M⊙ in the
Appendix.
global efficiency f∗(z), M∗ = f∗Mgas. The initial gas con-
Conversely,if theinitial metallicity exceedsthecritical
tent of dark matter halos is equal to the universal ratio,
value, Z > Z , the host halo is referred to as a Pop II/I
M = (Ω /Ω )M which decreases after each star forma- cr
gas b m
haloandthestarsareassumedtoformaccordingtoaLarson
tion event (see eq.17).
IMF:
dN
Φ(m)= m−1+xexp( m /m), (10)
dm ∝ − cut
with x = 1.35, mcut = 0.35M⊙ and m in the range
−
3.1 Star formation efficiency [0.1 100]M⊙ (Larson 1998). This expression represents a
−
modification of the Salpeter law which reproduces the ob-
Starformation in gascloudsoccurs inafree-fall time t =
(3π/32Gρ)1/2 where G is the gravitational constant anffd ρ served present-day stellar population for m>1 M⊙; in the
low-masslimit,infact,theIMFbehaviorisstillveryuncer-
thetotal (dark+baryonic)mass density inside thehalo (as-
tain because of the unknown mass-luminosity relation for
sumed tobe200 times denserthan thebackground).Since,
the faintest stars. The Larson IMF matches the Salpeter
ateachredshift,theMonteCarlotimestep∆t(correspond-
law for m > 1 M⊙ while the cutoff at m 0.35M⊙ can
ingtodz)is∆t t (z),itispossibletoaccuratelysample ∼
≪ ff explain the absence of brown dwarfs in the observed stellar
time variations of the global star formation efficiency using
population.
thefollowing approximation:
∆t(z)
f∗(z)=ǫ∗ , (9)
t (z)
ff
§ We define Pop III as all the stars with Z ≤ Zcr. In addition,
where ǫ∗, physically corresponding to the “local” star for- Pop III stars are assumed to be massive if Zcr > 0, and dis-
mation efficiency, represents a free parameter of themodel. tributedaccordingtoaLarsonIMFifZcr =0(seeSec.6.1)
(cid:13)c RAS,MNRAS000,1–17
6 Stefania Salvadori, Raffaella Schneider & Andrea Ferrara
3.3 Instantaneous Recycling Approximation (1995) for SNII(8M⊙ <m<40M⊙), linearly interpolating
among grids of different initial metallicity when necessary.
VerymassivePopIIIstarsarecharacterizedbyafastevolu-
We have also followed the evolution of individual elements
tion,reachingtheendoftheirmainsequencephasein3 5
− relevant to thepresent study,Fe and O.
Myr. Conversely, thebroad mass range which characterizes
Pop II/I stars implies a wide range of stellar lifetimes, τ ,
sl
whichvaryfromafewMyrtoseveralGyr.Inourmodel,we 3.5 Mechanical Feedback
have assumed the Instantaneous Recycling Approximation
SNexplosions may power a wind which, if sufficiently ener-
(IRA,Tinsley1980),accordingtowhichstarsaredividedin
getic, may overcome the gravitational pull of the host halo
twoclasses:thosewhichliveforever,iftheirlifetimeislonger
leadingtoexpulsion ofgas and metalsintothesurrounding
thanthetimesincetheirformationτ >t(0) t(z );and
sl form
− GM. This mechanical feedback has important implications
those which die instantaneously, eventually leaving a rem-
forthechemical evolution along themerger tree,as thenu-
nant, if τ < t(0) t(z ). The transition mass between
sl form
− cleosynthetic products of the first stars can be efficiently
thetwopossibleevolutions,orturn-offmassm (z),hasbeen
1
ejected out of the shallower potential wells of the first star
computed at any considered redshift. All stars havingmass
forming halos and then be accreted by neighboring halos,
m < m (z) represent stellar fossils which can be observed
1
thusbeing incorporated into thenext stellar populations.
today. The turn-off mass is an increasing function of time
To modelmechanical feedback,we compare thekinetic
since [t(0) t(z )] 0 when z 0; in thislimit of
form form
− → → energy injected by SN-drivenwinds
course m1 100M⊙ i.e. all the stars are still alive. Using
→
the IRA approximation at each time-step, we can compute E =ǫ N E , (15)
SN w SN SN
h i
thenumberof stellar relics per unit stellar mass formed:
and thebinding energy of thehost halo with mass M,
m1(z)Φ(m)dm
N∗ = 1R000.M1M⊙⊙mΦ(m)dm, (11) Eb= 12GrMvir2 =5.45×1053erg(cid:16)hM−81(cid:17)5/3(cid:16)11+0z(cid:17)h−1
0.1M⊙
and thRe equivalentmass fraction in these stars whereM8 =M/108M⊙ (Barkana&Loeb1991).Inthefirst
equation,ǫ iswindmechanicalefficiency(i.e.thefractionof
w
m1(z)mΦ(m)dm explosion energy converted into kinetic form); it represents
fm∗ = R01.010MM⊙⊙mΦ(m)dm. (12) tmhoedseelc.oNnd friesethpearnaummebteerro(tfhSeNfierisnttihseǫ⋆b,usresetaenqd. 9)Eof thies
0.1M⊙ SN h SNi
R the average explosion energy, which we take to be equal to
By definition, there are no stellar fossils of Pop III stars in 2.7 1052 erg for SN and to 1.2 1051 erg for SNII. We
γγ
theSN progenitor mass range. × ×
γγ assume that ejection takes place when E > E , and the
SN b
gas is retained otherwise. We compute the ejected fraction
of gas and metals as
3.4 Nucleosynthetic products
α =(E E )/(E +E ). (16)
Massive stars can lose mass and heavy elements through ej SN − b SN b
stellar winds and supernova explosions. Using the IRA ap- Hence, the ejection fraction is directly proportional to the
proximation,wecancomputetheyield,i.e.themassfraction SNenergyprovideditislargerthanthebindingenergy.Note
of metals produced per unit stellar mass formed, that, according to this simple prescription, gas and metals
100M⊙m (m,Z)Φ(m)dm are ejected with same efficiency. This might not necessarily
Y = m1(z) Z , (13) bethecase,asshownbyseveralauthors(MacLow&Ferrara
R 100M⊙mΦ(m)dm 1999;Fujitaetal.2004);weneglectthiscomplicationinthis
R0.1M⊙ work.
as well as the returned fraction, or the stellar mass fraction Duetomechanicalfeedback,themassofgasandmetals
returned to thegas through winds and SN explosions: inahalocandecreasesubstantially.Followingastarforma-
100M⊙(m w (m))Φ(m)dm tion burst and mechanical feedback, the mass of gas left
R= m1(z) − m . (14) in the halo, Mgas, which represents the reservoir for sub-
R 100M⊙Φ(m)mdm sequent star formation events, is related to the initial gas
0.1M⊙ mass, Min , and thestellar mass, M , by
R gas ⋆
The quantity m (m,Z) represents the mass of metals pro-
duced by a staZr with initial mass m and metallicity Z, Mgas=[Mginas−M⋆+RM∗](1−αej)=
aPnodpwII(Im)stiasrsthienmtahses oSfNthe sdtoemllaarinremrentuarnnt.aNllont-hroeitratginags =Mginas(1−f∗+Rf∗)(1−αej), (17)
γγ
and metals to the surrounding medium, i.e. R = 1. We Similarly, thefinal mass of metals can bewritten as,
h(2a0v0e2)u.sIetdisfoinrtethreessteinsgtatrosntohteetrheasutlatlsthoofuHghegtehre&totWalomoselteayl MZ =[MZin(1−f∗)+YM∗](1−αej)=
yield is independent of the progenitor mass and equal to =Mginas(Zin(1−f∗)+Yf∗)(1−αej). (18)
Y = 0.45, the iron yield strongly depends on mass, being
YFe =(2.8×10−15,0.022,0.45) for m=(140,200,260)M⊙. 3.6 Metal mixing
As for Pop II/I stars we have used the grid of models
by van den Hoek & Groenewegen (1997) for intermediate Wehavereconstructed thestar formation and chemical en-
(0.9M⊙ < m < 8M⊙) mass stars and Woosley & Weaver richmenthistoryofourGalaxyapplyingiterativelyeqs.(17)-
(cid:13)c RAS,MNRAS000,1–17
Cosmic stellar relics in the Galactic halo 7
Figure 2. Global properties of the MW. Squared points are the model results (200 realizations) as a function of the star formation
efficiency,ǫ⋆.Errorbarsarenotshownbecausenegligibleintheselectedscale.Dashedlinesrepresentthe(typical)observedvalues.Left
panel:no-feedback model(ǫw =0);Right panel:feedbackmodelwithǫw=0.2.
(18), together with eqs. (11)-(16), along the hierarchical 4 MODEL CALIBRATION
merger tree. It is assumed that during a merger event the
Although we have kept our model as simple as possible, it
metal and gas content of two distinct progenitor halos are
includes a number of relatively poorly known (albeit im-
perfectly mixed in the ISMof the new recipient halo. Simi-
portant) physical processes that need tobe empirically cal-
larly,metalsandgasejectedintotheGMareassumedtobe
ibrated. To this aim we have used the observed properties
instantaneously and homogeneously mixed (we refer tothis
of the Milky Way as a benchmark to fix the best values
approximationas”perfectmixing”)withthegasresidingin
that component. The filling factor Q of the metal bubbles of the two model free parameters, ǫ∗ and ǫw. In particular,
we have compared the results of the simulations at redshift
insidethevolumecorrespondingtothesizeoftheMWhalo
z=0 with thefollowing observations:
today,givesanestimateofthevalidityofthelatterassump-
tion. The perfect mixing approximation is verified when Gas metallicity. The Galactic disk has a mean metal-
•
licity Zgas Z⊙. As this component contains the majority
Q(z)= Rb(z) 3 >1 (19) of the MW≃gas, we use this value as representative of the
λ(z) whole system.
(cid:0)h i(cid:1)
Stellar metallicity. The typical mean value quoted for
where R is the bubbleradius and •
b this quantity is Z∗ Z⊙. This value has been derived by
≃
weighting themean metallicity of each galactic stellar com-
V (z) V (0)(1+z)3
λ(z) = MW = MW (20) ponent with its corresponding mass.
h i N (z) N (z)
h h Stellar mass. Contributions to the stellar mass come
•
iivssotltuhhmeeeatvoVetMraalWgen(uzm)m,ebahnearvhionaflgohasaselspousamraaettdiorVneMdwsWhiti(hf0ti)nz∼,tha1evMperrapogpce;edrNMhov(Wzer) ((frM0o.2m∗bu−lgt1eh)e≈1d0i1s0(kM0.4(⊙M)−∗dcio1sm)kp1≈o0n10e(Mn4t⊙s−)(D6a)enh×den1tnh0e1en0M&ha⊙lBo)i,n(ntMheye∗h,ab1lo9u9lg8≈e;
Brown et al. 2005), summing up in a total mass of M
e2s0t0imreaatleidzaftrioomnsaofStehdeovm-Teargyelorrtbrelae.stTwhaevevasoluluetoiofnR:b can be 6×1010M⊙. ⋆ ≈
Gas-to-stellar mass ratio, Mgas/M∗ = 0.13. The mass
•
of gas has been derived using the observed mass of HI and
Rb(z)=(cid:2)hρEb((zz))i(cid:3)1/5t2H/5(z) (21) H10I9IMre⊙gion8sof1th09eMG⊙ala(Sxyta,hMlegras&=PMallHaI2+00M4)H.II ∼(6+2)×
∼ ×
where E(z) is the energy released by SN explosions within
Moreover, if mechanical feedback is considered, two addi-
each halo, ρ (z) is themean GM density and t (z) is the
h b i H tional quantities become meaningful:
Hubble time. If we assume that i) star forming halos have
Mh(z)=M4(z) and ii) E(z)=E0f∗(z)Ωb/ΩmM4(z) where Baryon to dark matter ratio, fb = (M⋆ +
•
E0=1.636 1049erg/M⊙isthePopIIexplosionenergyper Mgas)/MMW =0.07.
×
unit stellar mass formed, we find that Q> 1 when z <11. GMmetallicity.Althoughtheexactvalueforthisquan-
•
Such limit implies that regions with Z = 0 are no longer tityissomewhatuncertain,high-velocityclouds(supposedly
present beyond that epoch. Additional discussion on this constituted by leftover gas from the Galactic collapse, and
issue is given in Sec. 5.2 and Sec.7. currently accreting onto the disk) may be used as a rea-
(cid:13)c RAS,MNRAS000,1–17
8 Stefania Salvadori, Raffaella Schneider & Andrea Ferrara
model Zgas/Z⊙ <Z∗/Z⊙> ZGM/Z⊙ Mgas/M∗ M∗/M∗MW fb
nofeedback: ǫ∗=0.5,ǫw=0 1.261 1.13 −− 0.115 1.71 −−
feedback:ǫ∗=0.7,ǫw=0.2 0.93 1.01 0.41 0.11 0.85 0.085
observedvalues 1 1 0.25 0.1 1 0.066
Table 1.Averaged values oftheglobal propertiesof theMWderivedusingthetwobest-fitmodels:no-feedback ǫ∗ =0.5,ǫw =0, and
feedback ǫ∗=0.7,ǫw =0.2.Thevalueshave beenobtained averagingover200realizations ofthemergertree. Forcomparison,wealso
quotetheindicativeobservedvalues(seetext).
sonable template. For these objects, Ganguly et al. (2005) 4.2 Feedback Model
derive [O/H] 0.66 0.25Z⊙, a value that we take as an
∼− ∼ IntherightpanelofFig.2,weshowtheglobalpropertiesof
educated guess for Z .
GM theMW derivedusingafeedback model with ǫ =0.2. For
w
Obviously, in study cases in which mechanical feedback is lowvaluesofǫ⋆,theeffectofmechanicalfeedbackisnegligi-
turned off for comparison sakes, it follows that ZGM = 0 ble;similarly tothenofeedbackmodel fb ≈Ωb/Ωm =0.16,
and fb = Ωb/Ωm = 0.16. In principle, an acceptable fit to andZGM ≈0.Theseresultsarecoherentwithourfeedback
the above MW properties can be achieved both for models prescriptions(eqs.15and16)sincetheefficiencyofmechan-
including mechanical feedback and neglecting it (see next ical feedback depends on the number of SN explosions and
Sections). However, the best values of the free parameters thereforeonthelevelofstarformationactivity.Asexpected,
are different in the two cases. We will show later how it fb decreases with ǫ∗ while ZGM increases. Note that in the
is possible to assess the role of feedback by using the MDF range0.1<ǫ∗ <1thefeedbackmodelcloselyresemblesthe
properties.Notethatthecalibrationprocedureiscompletely no-feedback one, the major difference being the lower sat-
independentof Z and Pop III IMF. uration values for the stellar mass and metallicity. Instead,
cr
the metallicity of the gas is nearly unaffected because met-
alsandgasareejectedintotheGMwiththesameefficiency
(see eqs. 17 and 18). The best-fit model requires ǫ∗ = 0.7
4.1 No Feedback Model
(we stress again that this is not the global star formation
In Fig. 2 we compare the observed global properties of the efficiency,expressedbyf⋆(z),seeeq.9),andreproducesthe
Galaxy with the results of our model as a function of the MW global properties better that the no-feedback model
star formation efficiency, ǫ∗. We start by analyzing the no- (see Table 1).
feedback case, i.e. when ǫ = 0. A good overall agree-
w
ment with the four observed quantities is obtained for rel-
atively high values of ǫ∗ > 0.1. In fact, the derived values 5 MODEL RESULTS
of Zgas/Z⊙, Z∗/Z⊙, M∗/M∗MW rapidly increase when the
star formation efficiency increases from ǫ∗ = 0.01 to 0.1, 5.1 Metallicity Distribution Function
and remain nearly constant thereafter (note that the value
After having ensured that our models reproduce the global
ofMgas/M∗ actuallydecreases withǫ∗ inthisrange).These
properties of the MW, regardless of the value of Z and of
trends can be understood very simply. The gas mass de- cr
thePopIIIIMF,wearenowreadytoexplorethepredictions
creases due to star formation (eq. 17), forcing the gas frac-
of the calibrated models. The result shown below are the
tion to decrease with increasing ǫ∗. Thus, M∗ saturates be-
result of averages over 200 realizations of the MW merger
yond ǫ∗ > 0.1 because of the limited gas mass available.
tree;insomecasesweuseasinglerepresentativerealization
Given the proportionality between MZ and M∗ (eq. 18),
for illustration purposes.
Z∗ showsthesamebehavior.Conversely,themassofmet-
h i InFig.3wecomparetheMDF(i.e.thenumberofMW
als in the gas is determined by the balance between met-
relic stars as a function of their iron abundance, [Fe/H],
als synthesizedand ejected bystars, and metalslocked into
a quantity commonly used as a metallicity tracer) derived
newly formed stars (eq. 18); when the second effect domi-
usingthetwobest-fitmodels, with andwithout mechanical
nates,itproduceaslightdecreaseofZ .Thebest-fitmodel
requiresahighstarformation efficiengcays,ǫ∗ =0.5¶.Thede- afeneddbmacPkop(IsIeIe=Ta2b0l0eM1⊙),.for the specific value Zcr =10−4Z⊙
rived values for all the observed properties of the MW are
The first striking difference is that no stars with
listed in Table 1. The values shown represent an average
[Fe/H] < 1.5areproducedintheno-feedbackmodel.The
over200 realizations of themerger tree. reasoni∼st−hatthegasmetallicity isnotefficientlydilutedin
closed box models. A simple estimate elucidates this point.
FollowingaburstofPopIIIstars,thegasmetallicity ofthe
¶ Because of the assumed star formation law (eq. 9), ǫ∗ = 0.5 host halo is raised up to
iismopnlylyththaet hinasltfaonftathneeoguasssmtaarssfoirsmcaotnivoenrteeffidciinetnocystaanrdindaoessinngolet Z = MMgZas = MYMga∗s =Yf∗(z)∼> 0.146Z⊙, (22)
burst.Rather,forthismodelf∗(z)variesintherange(0.06−4)×
10−2 intheconsideredredshiftrange. where we have used Y = 0.45 and the smallest f∗(z)
∼
(cid:13)c RAS,MNRAS000,1–17
Cosmic stellar relics in the Galactic halo 9
Figure 3. Left panel: MDFs derived using the no-feedback model (shaded histogram), and the fiducial feedback model (unshaded)
bothsummarizedinTable1. Histogramshavebeenobtained as averageover 200realizations.Bothmodels assumeZcr =10−4Z⊙ and
mPopIII = 200M⊙. Right panel: Age-metallicity relation for the halos derived using the fiducial feedback model. The starred (solid)
pointsrepresentPopIII(PopII/I)star-forminghalos.Forclarityresultsareshownforasinglerealization.
6.5 10−3 value corresponding to ǫ∗ = 0.5 (appropriate metallicity. Contrary to self-enrichment by previous star-
×
for the no-feedback case). Note that the final metallicity burst within the same host halo and to hierarchical enrich-
depends only on the metal yield and on the star formation mentbycontaminatedprogenitors,thisaccretion-drivenen-
efficiency. From the previous equation it is easy to see that richment mode is present only when mechanical feedback
theresulting abundanceisk operates. Accretion of metal-enriched GM onto a halo of
primordialcompositionsetstheinitialconditionsfortheen-
[Fe/H] log(Z/Z⊙) 0.257 > 1.09 vironment in which most metal-poor stars will later form.
≃ − ∼ −
Indeed, the unshaded histogram in Fig. 3 shows that when
This value is larger than the low [Fe/H] cutoff in the dis-
mechanical feedback is active the MDF extends down to
tribution shown in Fig. 3. What is the reason for such
discrepancy? In the absence of mechanical feedback, met- [Fe/H] > log(Zcr/Z⊙)aslow-mass stellarrelicscanbepro-
duced o∼nly in gas clouds with Z >Z .
als can only be diluted through mass accretion of metal- cr
TherightpanelofFig.3showshowdifferentenrichment
free gas and through mergers with unpolluted progenitors
modesoperate along themerger tree in asingle representa-
(which at most can halve thegas metallicity Z if they have
tiverealization.Eachpointdenotesthemetallicityofahalo
a comparable mass). However, dilution purely provided by
atagivenredshift;inthisplanehalosmovefromlefttoright
accretion of unpolluted gas is not sufficient to account for
i.e.theyincreasetheirmetallicity.Theevolutionofeachha-
the low-Z tail of the MDF, which extends to values [Fe/H]
losisfollowed alongitstrackuntilitsuffersamergerevent.
4, with two outliers at [Fe/H] < 5. The same con-
≈ − − Two families of curves can be identified, corresponding to
clusion is achieved using different mass values for SN or
γγ
self-enrichmentandaccretionmode,respectively,asmarked
assumingaLarsonIMFformetalfreestarsthough,inboth
by the labels in the Figure. In general, at the onset of the
cases, the different value of the yields cause a shift in the
firstburstofstarformationahalocouldbeeithermetal-free
MDF cutoff. For example for the Larson IMF (Z = 0
cr
model) Y 0.01 and YFe 5 10−4 and the cutoff moves ([Fe/H] =−∞) or it could have a non-zero metallicity if it
∼ ∼ × has accreted gas from the GM previously polluted by met-
to [Fe/H] 2.44 4. A similar result is obtained for
⋆⋆
∼ − ≫ − alsejectedfromotherhalos .Inthefirstcase,thehalowill
mPopIII =140M⊙ shown in theAppendix.
hostPopIIIstars;ifmetalsproducedareretainedaftertheir
In conclusion mechanical feedback is required to effectively
explosionthehalobecomesself-enrichedandmovesdirectly
dilutemetalsinsidehalosindependentlyoftheZ valueand
cr
onthecorrespondingself-enrichedtrack.Inthesecondcase,
of the assumed PopIII IMF.
instead, depending on the relative ratio of the GM metal-
Heavy elements ejected by SN winds mix with the ex-
ternalGMandcanbeaccreted byotherhalos, raisingtheir licity Z and Zcr = 10−4Z⊙ the stars form could be either
Pop III or Pop II. In this particular realization at z 11
∼
theGMmetallicitycrossestheZ valueandsetsthetermi-
cr
k This relation follows from the definition of [Fe/H] that leads
to[Fe/H]=log(Z/Z⊙)+1.044+log(YFe/YZ),whereforPopIII
stars with m = 200M⊙ the iron yield is approximately YFe = ⋆⋆ The same conclusion applies to halos that are just about to
0.05Y. gravitationallycollapseandvirialize.
(cid:13)c RAS,MNRAS000,1–17
10 Stefania Salvadori, Raffaella Schneider & Andrea Ferrara
nation of thePop III formation epoch in accretion-enriched
halos. Such halos lie on the curve marked as “accretion”.
However the second star-formation episode will push again
thesehalosontothecorrespondingself-enrichedtracks.The
accretion-mode is crucial in order to form long-lived stars
with [Fe/H]< 2.5. The accretion-enriched branch ends at
−
z 1, when merger events dominate the evolution of MW
∼
progenitors. The last point of the branch corresponds to
[Fe/H] 1, reflecting the metallicity of the GM at the
∼ −
same redshift (see Fig. 4).
TheanalysisofthisFigurehelpsinterpretingtheMDF.
Ourmodelpredictsthatstarswith [Fe/H]< 2.5form only
−
in halos enriched through the accretion-mode. Conversely,
iron-richstars,with[Fe/H]> 1,forminself-enrichedhalos.
−
In the intermediate range, 2.5 [Fe/H] 1, stellar relics
− ≤ ≤−
originatefrombothself-enrichedandaccretion-enrichedha-
los,andtheircontributiontotheMDFcannotbeseparated.
However,atagiven[Fe/H],stellarrelicsalongtheaccretion-
enriched branch are systematically younger.
Notethatanotherpossibilitytoincreasemetaldilution
along the merger tree is to relax the hypothesis that all
PopIIIstarsendupasSN (f =1).Indeedifafraction Figure4.GMelementalabundanceasafunctionofredshiftfor
γγ γγ
of Pop III stars forms with m > 260M⊙ or m < 140M⊙ the fiducial feedback model (see Table 1) and Zcr = 10−4Z⊙,
(f < 1) and ends up as black holes (Heger & Woosley mPopIII =200M⊙.Solidlinesshowtheevolutionofoxygenand
γγ
ironabundance,averagedover200realizationsofthemergertree;
2002),metalenrichmentcanbesubstantiallyreduced.How-
the shaded area delimits the ±1σ dispersion region. The [O/H]
ever, Schneider et al. (2006) have recently studied the de-
contribution by Pop III (dotted line) and Pop II stars (dashed
pendenceofchemicalfeedbackfromtheparameterf (thus
γγ line)arealsoshownseparately.Thepointisthemeasured[O/H]
fromtheassumedPopIIIIMF),showingthatfγγ =1iscur- inhigh-velocityclouds(Gangulyetal.2005).
rently favored by observations of the cosmic star formation
history, high redshift number counts and cosmic reioniza-
tion. (t 0.1 Gyr for a 1011M⊙ galaxy) and becomes more uni-
≤
Inconclusionmechanicalfeedbackisnecessarytorepro- form at lower redshifts.
duceboththeglobalpropertiesoftheMWandtheobserved WecanseethatPopIIIstarsdominatetheGMenrich-
range of [Fe/H] in halo stars. Hereafter we will refer to the ment for 9 < z < 20 while Pop II stars are the dominant
best-fit feedback model of Table 1 as ourfiducial model. enrichment channel for 0 < z < 9. The GM enrichment
history is the result of 4 phases in which different physical
mechanism dominate; these phases are marked in Figure 4.
Thefirstone(phasea),intheredshiftrange17 < z < 20,is
5.2 Metallicity evolution of the Galactic Medium
characterizedbyaveryrapidincreaseoftheelem∼enta∼labun-
InFig.4weshowtheevolutionofGMironandoxygenabun- dances.Giventhesmallbindingenergyofthehigh-redshift,
dances together with the specific contribution to [O/H] by low-mass halos, both SN and the less energetic SNII ex-
γγ
Pop III and Pop II stars. For reference we also plot the ob- plosionscanovercomethegravitationalpullofparenthalos,
served [O/H] value measured in high-velocity clouds (Gan- contributingtotheGMenrichment.Asthetypicalhalomass
guly et al. 2005) which are taken as an indicator of left- scale grows, as a result of hierarchical formation process,
overGMintheMWhalo.Theseresultsrefertoourfiducial metals produced by SNII are retained inside galaxies and
modelwithZcr =10−4Z⊙ andmPopIII =200M⊙.Thepre- only SNγγ regulate theGM enrichment(phaseb).However
dicted[O/H]atz=0isinperfectagreementwiththedata. theabundancegrowislimitedbythefactthatanincreasing
The scatter of the [Fe/H] distribution increases with z and fractionoftheGMispollutedabovetheZ ,hencequench-
cr
becomes verylarge at z 11 asa result of thelarge fluctu- ing the formation of Pop III stars which eventually comes
∼
ationsinthemerginghistory(seeFig.1)andenrichmentof toanendatthebeginningofphase(c)whenthewholeGM
halos among different realizations at z > 10. This result is isenrichedtoZ >Z .Thankstothehigherstarformation
cr
consistent with thefact that Q=1 at z=11 (see Sec. 3.6) efficiencyoflargerhalos,PopIIstars,duringthisphase,can
andthereforenounpollutedregionsareexpectedbelowthat eject their heavy elements. Their ability to do so, though,
redshift. Thescattering inducedbythestochastic natureof decreases with time because of the counteracting effect of
the merger tree process is similar, although different in na- the gravitational potential of larger galaxies that are form-
ture, with respect to the abundance fluctuations produced ing below z = 5 (phase d). Note that the GM bears the
by inhomogeneous mixing, a process not describe by our nucleosyntheticsignatures of (predominantly) Pop III stars
perfectmixingapproximation.Thissimilaritycanbeappre- atz>10;theirabundancepatternbecomesmoreandmore
ciated by comparing our results with those found by Mori elusive at later times when Pop II stars start to dominate
& Umemura (2006) using a hybrid N-body/hydrodynamic the enrichment. This physical picture remains qualitatively
code. These authors conclude that the metallicity is highly unaffectedbychangingthevalueofZ althoughtherelative
cr
inhomogeneous duringtheearly phasesofgalaxy formation duration and amplitude of the different enrichment phases
(cid:13)c RAS,MNRAS000,1–17