Mon.Not.R.Astron.Soc.000,1–??() Printed25January2010 (MNLATEXstylefilev1.4) Mining the Galactic Halo for Very Metal-Poor Stars S. Salvadori1, A. Ferrara2, R. Schneider3, E. Scannapieco4 & D. Kawata5 0 1SISSA/International School forAdvanced Studies, Via Beirut 4, 34100 Trieste,Italy 1 2Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy 0 3INAF/Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, 50125 Firenze, Italy 2 4School of Earth and Space Exploration, Arizona State University,P.O. Box 8714, Tempe, AZ, 85287-1404 n 5Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking, Surrey, RH56NT a J 5 2 ] O ABSTRACT We study the age and metallicity distribution function (MDF) of metal-poor stars C in the Milky Way halo as a function of galactocentric radius by combining N-body h. simulations and semi-analytical methods. We find that the oldest stars populate the p innermostregion,while extremely metal-poor stars aremore concentratedwithin r < - 60 kpc. The MDF of [Fe/H]≤ −2 stars varies only very weakly within the central o 50 kpc, while the relative contribution of [Fe/H]≤−2 stars strongly increases with r, tr varying from 16% within 7 kpc < r < 20 kpc up to ≥ 40% for r > 20 kpc. This is s due to the faster descent of the spatial distribution (as seen from Earth) of the more a [ enriched population. This implies that the outer halo < 40 kpc is the best region to search for very metal-poor stars. Beyond ∼ 60 kpc the density of [Fe/H]≤ −2 stars 2 is maximum within dwarf galaxies.All these features are imprinted by a combination v of (i) the virializationepoch of the star-forminghaloes,and (ii) the metal enrichment 9 history of the Milky Way environment. 7 2 Key words: stars:formation,populationII,supernovae:general-cosmology:theory 4 - galaxies: evolution, stellar content - . 8 0 9 0 1 INTRODUCTION ing function of [Fe/H]. Hence, understanding where these : v starsarepreferentiallylocatedisanurgenttheoreticalques- Xi Verymetal-poorstars([Fe/H]≤−2)representthelivingfos- tion. sils of the first stellar generations. Their observation is cru- r cial, as they may provide fundamental insights on both the a propertiesofthefirststarsandonthephysicalmechanisms Carollo et al. (2007) have recently done an accurate governingtheearlystagesofgalaxyformation,suchasfeed- kinematic study of ∼ 10.000 calibration stars of the SDSS backprocesses. Anintrinsicproblem thatobservershaveto Data Release 5, finding that the “outer” halo, r ≥ 15 kpc, faceisthatold,verymetal-poorstars,areextremelyrarein includes a larger fraction of [Fe/H]< −2 stars and peaks thesolarneighborhood,comprisingnomorethatthe∼0.1% at lower metallicity than the “inner” halo (r < 15 kpc). of thestars within afew kpcoftheSun(Beers et al. 2005). Thisevidenceposeschallengingquestionsaboutthephysical During the past years several surveys focused on such originofsuchsegregationandthevariationoftheMDFwith elusive stellar populations, both in the Milky Way (MW) galactocentric radius. halo and in nearby dwarf satellites, providing an increasing amountofdata.Atthemoment,themetallicitydistribution function (MDF) of Galactic halo stars (Beers et al. 2005) In this study we investigate the spatial distribution of represents one of the most important observational con- metal-poor halo stars by combining an high-resolution N- straints.Indeed,it consistsof 2756 halofieldstars observed bodysimulation fortheformation oftheMW (Scannapieco within ∼< 20kpcoftheSun(Beers&Christlieb 2005), cov- etal.2007),withasemi-analyticalmodel(Salvadori,Schnei- eringahugemetallicityrangewhichspansfrom[Fe/H]=−2 der & Ferrara 2007, hereafter SFS07) that follows the stel- downto[Fe/H]=−4.Despitesuchalargesample,thenum- lar population history and the chemical enrichment of the ber (≈ 300) of extremely metal-poor stars ([Fe/H]< −3) Galaxy along its hierarchical tree, successfully reproducing turns out to be still insufficient to put solid constraints on several properties of the MW and its dwarf satellites (Sal- theproperties of thefirst stars (Tumlinson 2006, Salvadori, vadori,Ferrara&Schneider2008,hereafterSFS08;Salvadori Schneider&Ferrara2007),astheMDFisarapidlyincreas- & Ferrara 2009). 2 Salvadori, Ferrara, Schneider, Scannapieco & Kawata 2 SUMMARY OF THE MODEL 2.1 The N-body simulation Webrieflysummarize themainfeaturesoftheN-bodysim- ulation referring to Scannapieco et al. (2007), and refer- ⋆ ences therein, for a detailed description. We simulate a MW-analoggalaxywiththeGCD+code(Kawata&Gibson 2003a)usingamulti-resolutiontechnique(Kawata&Gibson 2003b) to achieve high resolution in the regions of interest. The initial conditions at z = 56 are constructed using the publicsoftwareGRAFIC2(Bertschinger2001). Thehighest resolution region isaspherewitharadius4timesthevirial radiusofthesystem(i.e.theMW)atz =0,thedarkmatter (DM) particles mass and softening length are respectively 7.8×105M⊙ and540 pc.Thesystem consists onabout 106 particles within r ; its virial mass and radius are respec- vir tivelyMvir =7.7×1011M⊙andrvir =239kpc,roughlycon- sistent with the observational estimates (Mvir = 1012M⊙, r =258kpc)oftheMW(Battagliaetal.2005).Thesim- vir ulationdataisoutputevery22Myrbetweenz=8−17and every 110 Myr for z < 8. At each output a friend-of-friend group finder is used to identify the virialized DM haloes Figure 1. Left upper panel: comparison between the observed by assuming a linking parameter b = 0.15 and a threshold (rectangles) and simulated (shaded regions) age-metallicity dis- number of particles of 50. A low-resolution simulation in- tribution of MW stars. Rectangles show the observed relation cluding gas physics and star formation (SF) has been used for different Galactic components (Freeman & Bland-Hawthorn in order to confirm that theinitial conditions will lead to a 2002): the halo (blue solid rectangles); the thin and thick disk disk formation. While gas physics is essential to reproduce (black long-dashed rectangles); the bulge (violet short-dashed rectangles).Thecoloredshadedareascorrespondtoregionsthat thespatialdistributionofdiskstars,anN-bodyapproachis include, from the darkest to the lightest, the (30,62,90,100)% suitable to investigate the halo (and bulge) population we of the total number of relic stars produced in the simulation, are mostly interested in. Mt∗ot≈4×1010M⊙.Topupperandlowerpanels:comparisonbe- tweenthecumulativeMDFobservedintheGalactichalowithin ∼<20 kpc of the Sun (points with Poissonian error bars, Beers 2.2 The semi-analytical model et al. 2005) and those produced in the simulation at different radii (violet histograms) normalized to the number of observed We briefly describe the basic features of the model imple- stars.Thecyan histogram showsthe 7<(r/kpc)<20MDFfor mentedinthecodeGAMETE(GAlaxyMErgerTree&Evo- theinhomogeneousmixingcase.Foreachrangeofradiithenum- lution) referring the reader to SSF07 and SFS08 for more bersshowthepercentageof−2<[Fe/H]≤−1stars(shadedarea) details. We trace the evolution of gas and stars inside each withrespecttothetotalnumberof[Fe/H]≤−1stars. halo of the hierarchy (group of DM particles) by assuming the following hypotheses: (a) at the highest redshift of the merger tree, z = 17, the gas has a primordial composition; (b) stars can only form in haloes of mass Mh > M4(z) = 3 × 108M⊙(1 + z)−3/2 (Mh > M30(z) = 2.89 × M4(z)) such information propagated to the next integration step. prior to (after) reionization, here assumed to be complete The same procedure is applied to metals ejected into the at z = 6; (c) in each halo the SF rate is proportional to GM;asaresult,thechemicalcomposition ofnewlyvirializ- themassofcoldgas;(d)accordingtothecriticalmetallicity inghaloesdependsontheenrichmentleveloftheGMoutof scenario (Schneideret al.2002, 2006) low-mass starswith a whichtheyform.Finally,thepropertiesoflong-livingmetal- Larson InitialMass Functionform when thegas metallicity Z ≥ Zcr = 10−5±1Z⊙; for Z < Zcr massive Pop III stars poorstarshostedbyeachDMparticlearestoredtorecover theirspatial distribution at z=0. form with a reference mass mPopIII=200M⊙. As a rough estimate of the impact of the perfect Wedescribetheenrichmentofgaswithinproto-Galactic mixing assumption above we have also explored a simple haloes and diffused in the MW environment, or Galactic case of inhomogeneous metal mixing. The latter is mod- Medium (GM), by including a simple description of super- eled by computing the instantaneous filling factor Q = nova (SN) feedback. Metals and gas are assumed to be in- stantaneously and homogeneously mixed with the gas (im- (Pi4πRb3(i)/3VMW(z))ofthemetalbubblesinsidethecrit- ical MW volume V (z)=30(1+z)−3 Mpc3 and by ran- plications discussed in SSF07); we assume the Instanta- MW domlyenrichingafractionF =1−exp(−Q)ofGMparticles. neous Recycling Approximation (IRA, Tinsley 1980). At Notethatthis only providesan upperlimit on F,as aclus- eachtime-stepthemassofgas,metalsandstarswithineach teredsystem,suchasthestarsweareconsidering,willhave halo is equally distributed among all its DM particles, and asmallerfillingfactor.AsimpleSedov-Taylorblastwaveso- lution (Sec. 3.6 of SFS07) is used to estimate the bubble ⋆ WeadoptaΛCDMcosmologicalmodelwithh=0.71,Ω0h2= radii Rb(i). This case is compared with theperfectly mixed 0.135,ΩΛ=1−Ω0,Ωbh2=0.0224, n=1andσ8=0.9. one in Fig. 1 (lower panel on theleft). Mining the Galactic Halo for Very Metal-Poor Stars 3 The second region (Age < 13 Gyr, [Fe/H]< −0.3) is filledbystarswhichalmostspantheentirerangeofagesand metallicities along a relation on which the iron-abundance increases with decreasing age (halo, bulge, thick and thin disk). These stars formed in accreting haloes; theminimum [Fe/H] value of the stellar distribution at different epochs reflects the iron evolution of the MW environment. Stars locatedinthisareaonlyrepresent<10%ofthetotalstellar mass at z=0. The third region ([Fe/H]> −0.3) is populated by iron- rich stars formed in self-enriched haloes, which therefore span all the possible ages (bulge, thin and thick disk). The bulkofthestellarmassresidesinthisregionandcorresponds to the broad peak of the SF rate (2<z <5, see for a rep- resentative SF history Fig. 1 of Evoli, Salvadori & Ferrara 2008). Note that the most iron-rich stars in the simulation withages<12Gyr,arepoorerinironthanthoseobserved. This systematic effect may be a consequence of neglecting the contribution of SNIa to gas enrichment. However be- causethisstudyismostlyconcentratedonthespatialdistri- butionofoldandiron-poorGalactichalostarsthisdoesnot Figure 2. Average density profile of −2 <[Fe/H]< −1 (top or- affectthemainresults.Evenifweconsiderthepossibleexis- angehistogram)and[Fe/H]≤−2stars(bottomviolethistogram) tenceofa“prompt”SNIacomponent,withlifetime ofSNIa as a function of the distance from the Earth, R. Short- (long- of 0.1 Gyr (Mannucci, Della Valle & Panagia, 2006), this ) dashed curve is the β-model (1+(R/Rc)2)−3β/2 (power-law is typically longer than the evolutionary time-scale of SNII R−γ)best-fittothestellardistribution. (<0.03Gyr).Therefore,theironproducedbythefirstSNIa willonlymarginallycontributetopolluteanISMwhichhas been already largely pre-enriched by several generations of 3 RESULTS SNIIand Pop III stars. Themodeliscalibrated,i.e.theSFandSNwindefficiencies In the following we will focus on the properties of old are fixed,by simultaneously reproducing the global proper- metal-poor[Fe/H]<−1stars,whosefeaturesareunaffected ties of the MW (stellar/gas mass and metallicity) and the by the lack of disk formation and SNIa contribution of our Galactic halo MDF as in SSF07. study. By excluding from our sample all the stars residing at distances < 1 kpc from the Galactic plane, we remove possible contamination by thin/thick disk stars. 3.1 The age-metallicity relation A first test of our model results is a comparison with the 3.2 Metallicity distribution observedstellarage-metallicity;theresultsareshowninthe upper panel of Fig. 1. The simulated distribution can be In the left lower panel of Fig. 1 the Galactic halo MDF virtuallydividedintothreemainregionsdefinedbythepre- observed by Beers et al. (2005) is compared with the sim- vailing formation mode of thestars contained within them. ulated one at galactocentric distances 7 < (r/kpc) < 20. Thefirstregion(age>13Gyr,orz>7.5)ispopulated The agreement between the model results for a radial in- by old stars covering almost the entire metallicity range, terval representative of the observed region and the data is from [Fe/H]∼−0.3 to [Fe/H]=−4.2, and which correspond very good. In the same panel we show for comparison the to the observed bulge and halo components (see the rect- simulated 7 < (r/kpc) < 20 MDF for the inhomogeneous angles in the panel). These stars formed in proto-galactic mixingcase(cyanhistogram).Thetwomixingprescriptions haloes associated to high (> 2σ) density fluctuations, that onlyyieldamarginal difference,mostlyconcentratedin the virialized during the early stages of Galaxy formation at range −3.5 <[Fe/H]< −3 (see Sec. 4 for the discussion). z>7.5.Thesefirststellargenerationsenrichedtheinterstel- Theseresultsencourageustoformulateexplicit predictions larmedium(ISM)oftheirhostgalaxiesupto[Fe/H]>−2(a fortheradialdependenceofthesimulatedMDF.Toexplore processwedubasself-enrichment),quenchingtheformation this point, we compare the same observational data with ofadditional verymetal-poor stars. Atthesame time,met- theoretical MDFs obtained in different radial bins and nor- als are expelled by SN feedback in theGM, thusincreasing malized to the number of observed stars. We note that the its metallicity above Zcr by z =11 and allowing long-living all-radiiMDF(leftupperpanel)alreadyprovidesasatisfac- metal-poor stars to form in newly virialized haloes accret- torymatchofthedataimplyingthattheobservationalsam- ing their gas from the GM. From z = 11 to z = 7.5 coeval pleobtainedintheabover-rangeprovidesagood proxyfor formationofmetal-poorandmetal-richstarsoccursindiffer- theall-radii one. A marginal discrepancy at the low-Fe end entobjectsthroughaccretionandself-enrichmentprocesses. of the distribution is found when comparing the observed During this epoch −3<[Fe/H]<−2 stars are produced via data with theoretical MDFs derived for r > 20 kpc (lower mergingofself-enrichedandaccretedhaloes.UnlikeinScan- panels),whichbecomesmoresensibleasrincreases.Incon- napiecoetal.(2007),no[Fe/H]≤−4starsformbelowz=7 clusion,wefindthattheMDFvariesonly veryweakly with because of theGM mixing approximation assumed here. radius.Onthecontrary,and in agreement with recent find- 4 Salvadori, Ferrara, Schneider, Scannapieco & Kawata Figure 3. Mass distribution of metal-poor (MP) −2 <[Fe/H]≤ −1 (left panel), very metal-poor (VMP) −3 <[Fe/H]≤ −2 (middle panel),andextremelymetal-poor(EMP)−4<[Fe/H]≤−3(rightpanel)stars,inthecylindricalcoordinateplane(r,|ζ|),normalizedto thetotal MWstellarmassinthesimulationMt∗ot≈4×1010M⊙. ings by Carollo et al. (2007) and De Lucia & Helmi (2008), thevirialization epoch of thestar-forming haloes, which af- the relative contribution of −2 <[Fe/H]< −1 stars to the fects the final distribution of DM and hence of stars; (ii) totalMDFstronglydependsonr,varyingfrom84% within the metal enrichment history of the GM, setting the ini- 7 kpc<r<20 kpc,down to ≤60% for r>20 kpc. tialFe-abundanceof theISMin newly virializing haloes. In Tobetterunderstandthesefeaturesitishelpfultoana- Fig. 4 we show theaverage formation redshift of DMparti- lyzeFig.3,whichoffersaspatial visualization oftheMDFs cles hosting [Fe/H]< −1 stars, hzi, in the ρ−ζ plane. The in the ρ −ζ cylindrical coordinate plane, where z is the oldest stars populate the innermost region; moreover, hzi rotation axis and r2 = ρ2 +ζ2. We show the results for gradually decreases with r = pρ2+ζ2. Beyond ∼ 30 kpc the central 100×100 kpc2 region. Each panel of the fig- on average hzi <7. As for z <8 the GM has been already ure displays a subset of relic stars in a different metallicity enriched upto [Fe/H] ≈−3, extremely metal-poor stars GM range: metal-poor (MP), −2<[Fe/H]≤−1, very metal-poor become more rare in such outer regions; this explain their (VMP), −3 <[Fe/H]≤ −2, extremely metal-poor (EMP), spatialcondensation.Verymetal-poorstars,instead,extend −4 <[Fe/H]≤ −3. The colors show the total mass of stars up to 100 kpc as [Fe/H] ≈ −2 when z = 5. Finally, GM contained in an annulus of radial width within 1 kpc nor- asmetal-poor stars predominantlyform viaself-enrichment malized tothe total MW stellar mass. their spatial distribution is unaffected by the GM enrich- The stellar distribution closely follows the dark matter ment and it is solely determined by hierarchical history of one, i.e. it is denser towards the center and in the 10 dwarf collapsed structures. galaxies found in 50 kpc <r <100 kpc. The radial depen- Afinalremarkconcernsdwarfsatellitegalaxies.Beyond denceoftheMPsdistribution(leftpanel)isverysteep,vary- ∼ 30 kpc the dwarf systems can be identified as clumps of ingbymorethan2ordersofmagnitudeintheinner50kpc; high hzi against the more uniform background. All satel- intothesameregioninsteadVMP/EMPstars(middle/right lites found in the simulation are “classical” dwarf galaxies, panels) are much more uniformly distributed and exhibit a i.e. they have L > 105L⊙. Only two of them, correspond- centralcore.ThisisfurtherillustratedinFig.2,whichshows ing to rare > 2σ fluctuations, were hosting Pop III stars the average density profiles of MP and VMP/EMP stars astheyvirialized andbegan toform stars whenz >11 and as a function of the distance from the Earth, R. While for ZGM <Zcr.Thepowerfulexplosionsfollowingtheevolution R>10kpcthedensityofMPstarsclosely follows apower- ofPop IIIstars† caused thecomplete blow-away of gas and lawinradius,R−2.2,thatofVMP/EMPstarsiswellapprox- metals;long-livingstarsonlyformatlatertimeswhenmore imated by a β-function, [1+(R/Rc)2]−3β/2, with β = 1.4 pre-enrichedgasiscollectedbythedwarfsthroughaccretion and Rc = 20 kpc. It follows that the relative contribution andmergingprocesses.Noclearimprintoftheirpristinefor- to the MDF of more pristine stellar generations becomes mation can be found in these galaxies, which have similar gradually more important at large distances (Fig. 1). Be- stellarpopulations(h[Fe/H]i∼−2)of“normal”dwarfsatel- yond r ∼ 60 kpc very metal-poor stars are mostly concen- lites. Note however that these galaxies represent the most trated within dwarf satellites, which are clearly identified massive dwarfs we found with Mh = 1−2×109M⊙ and in Fig. 3. This is in agreement with well-known evidence M∗ =0.7−1.2×107M⊙.Theremaining80%ofdwarfscor- that the MDF in dwarf galaxies is shifted towards lower- respond to<2σ fluctuationswhich virialize at later epochs [Fe/H]withrespect totheGalactic one(Helmietal. 2006). z =(6−8) when [Fe/H] >−3. The lack of [Fe/H]<−3 GM Interestingly extremely metal-poor stars are found only in stars(Helmietal.2006)ishencenaturallyexplainedinthese twodwarfsand,evenintheseobjects,theyrepresentasub- objectswhichhaveadarkmatterMh =(1−7)×108M⊙and dominant stellar population (≤ 13%). Beyond 60 kpc the stellar mass content M∗ = (0.5−7.5)×106M⊙ consistent number of EMPs drops implying that this population is with that of the observed dwarf spheroidal galaxies. more condensed within such a region. What determines the spatial distribution of stars with different[Fe/H]?Inadditiontotheunderlyingstructurefor- † Massive Pop III stars evolve as pair-instability SN. For mation governed by DM, there are two key ingredients: (i) mPopIII=200M⊙ theexplosionenergyis2.7×1052 erg Mining the Galactic Halo for Very Metal-Poor Stars 5 Beyond 60 kpc the density of very metal-poor stars is maximum inside the “classical” (L > 105L⊙) dwarf galax- ies. We find that 8 out of 10 host [Fe/H]> −3 stars only, in agreement with observations by Helmi et al. (2006); in the remaining two extremely metal-poor stars represent a subdominant stellar population, making up only ≤ 13% of the total stellar mass. Typically these galaxies virialize at z ∼ 6−8, have a total mass Mh = (1−7)×108M⊙ (i.e. they are < 2σ fluctuations of the density field), and stellar massM∗ =(0.5−7.5)×106M⊙.Interestingly,noultrafaint dwarf galaxies (L < 105L⊙) are found in our simulation, confirmingthat thesenewly-discovered satellites areproba- blyleft-oversofH2 coolingmini-haloes(Salvadori&Ferrara 2009), whose physicsis not included in thepresent study. Wedevotethefinalremarktoour“perfectmixing”ap- proximation. As the porosity increases rapidly with time Figure 4. Average formation redshift of DM particles hosting (Q≈1forz≈7),theMDFsfromtheinhomogeneousmod- [Fe/H]<−1starsindifferentregionsofthe(ρ,|ζ|)plane. els are mostly consistent with those derived by using this approximation:theMDFsdifferencesbetween thetwomix- ing prescriptions (Fig. 1, left lower panel) are smaller than 4 DISCUSSION the ±1σ error expected from averaging over different hier- Old, [Fe/H]<−2 stars, are intrinsically rare in the Galaxy, archicalmergerhistories(seeFig.6ofSFS07).Ontheother representing only ≤ 1% (i.e. ≤ 5 × 108M⊙) of the to- hand,thetruescatterin[Fe/H]atlowmetallicitiesandlarge tal stellar mass. This makes the selection of VMP stars radiimaybesubstantiallylargerthanineitherofthesemod- one of the major challenges of stellar surveys dovoted to els,asstarsarestrongly clusteredtowardsthecenterofour theirinvestigation. Ourstudyshows that:(i) thedensity of simulation,whichwillreducethetruefillingfactor.Thefull −2<[Fe/H]<−1starsasafunctionofdistancefrom Earth physicalmodelingofmetalmixinganddiffusionremainsone is very steep, following a power-law, R−γ, with γ = 2.2; of the largest uncertainties in galaxy formation, and more on the contrary (ii) the density distribution of VMP/EMP work is required before onecan draw definiteconclusions. stars exhibits a central core, closely following a β-function, [(1+(R/R )2]−3β/2,with β=1.4 andR =20 kpc.Hence, c c thoughbothpopulationsaremoreconcentrated towardsthe ACKNOWLEDGEMENTS center, (iii) the relative contribution of [Fe/H]< −2 stars We are grateful to A. Verdini for providing his carefully increasesfrom16%intheinnerhalo(atGalactocentric dis- craftedIDLmacrosandtoT.Beers,D.Carollo&N.Prant- tances r < 20 kpc) to > 40% in the outer halo, in good zos for careful reading of thedraft and useful comments. agreement with the observational results by Carollo et al. ‡ (2007,2009) . Our findings suggest that the outer halo be- tween20kpc ∼< r∼< 40kpcisthemostpromising region to REFERENCES search for VMP stars, though it is obvioulsy harder to find more distant stars in magnitudelimited surveys. 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