Mon.Not.R.Astron.Soc.000,1–18(2010) Printed18January2010 (MNLATEXstylefilev2.2) On the nature of the Milky Way satellites 1⋆ 2 1 Yang-Shyang Li , Gabriella De Lucia and Amina Helmi 0 1KapteynAstronomicalInstitute,UniversityofGroningen,P.O.Box800,9700AVGroningen,theNetherlands 1 2INAF-AstronomicalObservatoryofTrieste,viaG.B.Tiepolo11,I-34143Trieste,Italy 0 2 n 18January2010 a J 8 ABSTRACT 1 Wecombineaseriesofhigh-resolutionsimulationswithsemi-analyticgalaxyformationmod- elstofollowtheevolutionofasystemresemblingtheMilkyWayanditssatellites.Thesemi- ] analytic model is based on that developedfor the Millennium Simulation, and successfully A reproducesthe propertiesof galaxieson large scales, as well as those of the Milky Way. In G thismodel,weareabletoreproducetheluminosityfunctionofthesatellitesaroundtheMilky h. WaybypreventingcoolinginhaloeswithVvir <16.7kms−1(i.e.theatomichydrogencool- inglimit)andincludingtheimpactofthereionizationoftheUniverse.Thephysicalproperties p - ofourmodelsatellites(e.g.meanmetallicities,ages,half-lightradiiandmass-to-lightratios) o are in good agreementwith the latest observationalmeasurements.We do not find a strong r dependenceupontheparticularimplementationofsupernovafeedback,butaschemewhich t s ismoreefficientingalaxiesembeddedinsmallerhaloes,i.e.shallowerpotentialwells,gives a better agreementwith the propertiesof the ultra-faintsatellites. Our modelpredictsthatthe [ brightestsatellitesareassociatedwiththemostmassivesubhaloes,areaccretedlater(z ∼<1), 2 and have extended star formation histories, with only 1 per cent of their stars made by the v endofthereionization.Ontheotherhand,thefaintersatellitestendtobeaccretedearly,are 1 dominatedbystarswithage>10Gyr,andafewofthemformedmostoftheirstarsbeforethe 9 reionizationwascomplete.ObjectswithluminositiescomparabletothoseoftheclassicalMW 2 satellitesareassociatedwithdarkmattersubhaloeswithapeakcircularvelocity∼>10kms−1, 1 inagreementwiththelatestconstraints. . 9 0 Keywords: galaxies:dwarf–galaxies:formation–LocalGroup–cosmology:theory–dark 9 matter 0 : v i X 1 INTRODUCTION stellarpopulation (> 10Gyr), whichlikelykeeps theimprintsof r theyoungUniverse. a The satellites of the Milky Way (MW) are powerful touchstones In recent years, the number of known satellites around the for galaxy formation and evolution theories. Their proximity fa- MW has doubled, thanks to the discovery of very low surface cilitates detailed observations and characterisation of their prop- brightnessdwarfgalaxiesintheSloanDigitalSkySurvey(SDSS) erties and hence constrains ‘near-field’ cosmology. In addition, (Willmanetal.2005a,b;Belokurovetal.2006,2007;Zuckeretal. their shallow potential wells make them more sensitive to astro- 2006a,b; Irwinetal. 2007; Walshetal. 2007; Belokurovetal. physicalprocessessuchassupernova(SN)feedback(Larson1974; 2008, 2009). Since the sky coverage of SDSS DR5 is about 1/5 Dekel&Silk1986)or tothepresence of aphotoionization back- of the full sky and the surface brightness limit is about µ ∼ ground(Babul&Rees1992). Deep images have allowed the construction of colour- 30magarcsec−2 (Koposovetal.2008),manysatellitesarelikely yet to be discovered in the next generations of surveys. E.g. magnitudediagrams(CMD)oftheMWsatellites,fromwhichthe Tollerudetal. (2008) have used sub-samples of the Via Lactea I star formation histories have been deduced. These studies indi- (Diemandetal. 2007) subhaloes to conclude that the total num- cate that there is alarge variety in the star formation histories of berofMWsatelliteswithin400kpcshouldbebetween∼300and thesegalaxies(Mateo1998;Dolphinetal.2005).Thetwogas-rich ∼600anddominatedbysatellitesfainterthanM =−5. dwarf irregular (dIrr) Magellanic Clouds show on-going star for- V mationwhiletheotherdwarfspheroidalgalaxies(dSphs)aregas- ThenewSDSSsatelliteshavelowersurfacebrightness(µ > deficientandshow generallylittleevidenceforrecentstarforma- 27magarcsec−2)comparedtotheclassicalsatellites,butsimilar tion.Modernstudieshaverevealedthatallsatellitescontainanold physicalsizes.TheyhavecomparableluminositiestosomeGalac- ticglobular clusters, but aresignificantlybigger (Belokurovetal. 2007). The nature of these newly discovered satellites isstill un- clear.Theycouldbetheprolongationtowardsfainterluminosities ⋆ Email:ysleigh@astro.rug.nl oftheclassicalMWsatellites(Kirbyetal.2008),tidalfeatures(e.g. 2 Y.-S. Li, G. DeLucia andA. Helmi HerculesdSph,Colemanetal.2007;Sandetal.2009),orrepresent ingsatellitesarethosewhichformedwhiletheUniversewasstill acompletelynewclassofobjects. neutral. This study was carried out before the boost at the faint Kinematic modelling based on line-of-sight velocity disper- endofthesatelliteluminosityfunction.Althoughtheydidpredict sions,havedemonstratedthattheclassicalMWsatellitesaredom- alargenumberoffaintsatellitesbelowMV = −5,afterextrapo- inated by dark matter (Mateoetal. 1993; Mateo 1998). Recent latingtheirpredictionontheluminosity-sizespacetothefaintend, studies have shown that, under the assumption of virial equilib- Bensonetal.’sfaintsatellitestendtobetoosmallatagivenabso- rium, theultra-faint satelliteshavemass-to-light ratiosashigh as lutemagnitudecomparedtotheultra-faintsatellitesdiscoveredin ∼100−1000,implyingthattheseobjectsarethemostdarkmatter SDSS(Koposovetal.2008).Morerecentstudieshaveturnedtheir dominatedsystemsknown(e.g. Munõzetal.2006;Simon&Geha attentiontotheultra-faintsatellites:Maccio` etal.(2009)haveused 2007). The constraint on the total mass inferred by velocity dis- three different SA galaxy formation models to study the satellite persionsisstilluncertainbecauseofthemass-velocityanisotropy populationofMW-likegalaxies.Theyhaveusedbothanalyticand degeneracyandofthesmallnumber oftracersemployedinthese numericalmerginghistoriesofMW-likehaloesandshownthatall studies.RecentanalysessuggestthattheMWsatellites(including threemodelsreproduce theluminosityfunctionoftheMWdown thenewlydiscoveredSDSSsatellites)haveacommonmassscale toM =−2,withahintforabendingaroundM =−5. V V when considering their innermost regions within 600 or 300 pc In this paper we combine high-resolution simulations of a (Strigarietal.2007,2008). MW-likehalowithaSAgalaxyformationmodeltoinvestigatehow The cold dark matter (CDM) hierarchical paradigm suc- variousastrophysicalprocessesaffecttheformationandevolution cessfully explains the large scale structures of the Universe ofsatellitesaroundtheMilkyWay.Ourstudyextendstheanalysis (Spergeletal. 2007). Semi-analytic (hereafter SA) galaxy forma- presentedinDeLucia&Helmi(2008),whichfocusedonthefor- tion models coupled with merger trees extracted from N-body mationoftheMWgalaxyandofitsstellarhalo.Wefindthatbypre- simulations,representausefultechniquetodiagnosethecomplex ventingcoolinginhaloeswithTvir <104K(theatomichydrogen physicsinvolvedingalaxyformation,withmodest computational cooling limit) and including theimpact of the reionization of the costs. In recent years, SA models have been proved to success- Universe,ourmodelisabletoreproducethelatestmeasurementsof fullyreproduceanumberofobservationalmeasurements(e.g.spa- thesatelliteluminosityfunctionbyKoposovetal.(2008).Weshow tialandcolour-magnitudedistributions)forgalaxiesseeninthelo- thatthesamemodelreproducesthemetallicitydistributionfunction calUniverseandathigherredshift(forarecentreview,seeBaugh (MDF)oftheMWsatellites,byincludingaroutetorecyclemetals 2006).Inspiteoftheencouragingprogressonthelargescale,how- producedinnewlyformedstarsthroughthehotphase.Ourmodel ever, CDM still faces severe challenges on the galaxy-scale and satellitesexhibitseveralscalingrelationssimilartothosefollowed below.Anexampleisthe‘missingsatellitesproblem’:namelythe by the MW satellites, such as the metallicity-luminosity and the substructuresresolvedinagalaxy-sizeDMhalosignificantlyout- luminosity-sizerelations.Thepropertiesofthemodelsatellitesre- numberthesatellitesobservedaroundtheMW(Klypinetal.1999; semblingthenewlydiscoveredultra-faintSDSSsatellitesappearto Mooreetal.1999).Anumberofstudieshavesuggestedthatastro- besensitivetotheSNfeedbackrecipeadopted.Aswewilldiscuss physicalprocessessuchasthepresenceofaphotoionizationback- inthefollowing,ourmodelsuggeststhatthesurvivingsatellitesare ground might reconcile this discrepancy (e.g. Kauffmannetal. generally associated withhaloes whosepresent-day peak circular 1993; Bullocketal. 2000; Bensonetal. 2002; Somerville 2002), velocity,Vmax,∼> 10kms−1,totalmassexceededafew106M without invoking modifications on the nature of the DM parti- at z ∼ 10−20 and which acquired their maximum dark matte⊙r cles to reduce the power on small scales of the power spectrum masswellabovethecoolingthreshold,afterz∼6. (Kamionkowski&Liddle2000;Zentner&Bullock2003). This paper is organised as follows. Section 2.1 presents the Severalgroupshaverecentlyattemptedtomodel theproper- simulations used in this study, and in Section 2.2 we summarise tiesoftheMWanditssatellitesina(semi-)cosmological setting. oursemi-analyticalgalaxyformationmodel,emphasisingthenew Forexample,Kravtsov,Gnedin&Klypin(2004)haveanalysedthe featuresaddedtothemodelpresentedinDeLucia&Helmi(2008). dynamical evolution of substructures in high-resolution N-body InSection3wepresentourmainresultsandinSection4wediscuss simulations of MW-like haloes and suggested that all the lumi- theimplicationsofourstudy.WegiveourconclusionsinSection5. nousdwarfspheroidalsintheLocalGrouparedescendantsofthe relatively massive (∼ 109M ) high-redshift haloes, which were ⊙ notsignificantlyaffectedbytheextragalacticultravioletradiation. 2 THEHYBRIDMODELOFGALAXYFORMATION Fontetal.(2006)havesuccessfullyreproducedtheobservedchem- ANDEVOLUTION icalabundancepatternoftheMWstellarhalobycombiningmass accretionhistoriesofgalaxy-sizehaloeswithachemicalevolution 2.1 ΛCDMSimulationsofaMW-likehalo modelforindividualsatellites.Itshouldbenotedthatinthesestud- WehaveusedaseriesofhighresolutionsimulationsofaMW-like ies, thephenomenological recipesadopted for star formation and halo(Stoehretal.2002;Stoehr2006).Wenotethatthisistheex- feedback have been tunedtoreproduce someof the propertiesof actGAnewseriesusedinpreviousstudiesbyLi&Helmi(2008), thesatellitesintheLocalGroup. DeLucia&Helmi (2008) and Lietal. (2009). Wetherefore only Bensonetal. (2002) have used a SA model which success- summarise the basic properties of the simulations here, and re- fully reproduces the present-day field galaxy luminosity function fer the reader to those papers for more details. The simulations to study the properties of dwarf satellite galaxies known at the werecarriedoutwithGADGET-21(Springeletal.2001)adopting time. Their model calculates the influence of reionization self- aΛCDMcosmologicalmodel,withΩ0 =0.3,ΩΛ =0.7,h=0.7, consistently,basedontheproductionofionizingphotonsfromstars σ8(z =0)=0.9,andHubbleconstantH0=100hkms−1Mpc−1. and quasars, and the reheating of the intergalactic medium. This same model reproduces quite nicely the luminosity and size dis- tributions,gascontentandmetallicityoftheclassicalsatellitesof 1 TheGAnewsimulations wereinfactcarriedoutusinganintermediate theMW and M31. Theseauthors have suggested that the surviv- versionbetweenGADGETandGADGET-2. ThenatureoftheMW satellites 3 The target MW-like halo was simulated at four increasing reso- maryofthephysicalprocessesimplementedinourmodelswhich lution levels (the mass resolution was increased by a factor 9.33 arecrucialtothepropertiesofthesatellites. each time). In the highest resolution simulation (GA3new), there areapproximately107particleswithmassm =2.063×105M p h−1withinthevirialradius.Eachre-simulationproduced108ou⊙t- 2.2.1 Reionization puts,equallyspacedlogarithmicallyintimebetweenz=37.6and Following Crotonetal. (2006), we make use of the results by z=2.3,andnearlylinearlyspacedfromz=2.3topresent. Gnedin(2000)whosimulatedcosmologicalreionizationandquan- Mergertreesforallself-boundhaloeswereconstructedasde- tifiedtheeffectof photoionization onthebaryon fractionof low- scribedindetailinDeLucia&Helmi(2008).Virialisedstructures mass haloes. Gnedin found that reionization reduces the baryon were identified using the standard friends-of-friends (FOF) algo- contentinhaloeswhosemassaresmallerthanaparticular‘filter- rithmandlinkingallparticlesseparatedbylessthan0.2themean ingmass’scale,thatvarieswithredshift.Thefractionofbaryons, inter-particle separation. The algorithm SUBFIND (Springeletal. 2001) was then applied to each FOF group to find the gravita- fbhalo,inahaloofmassMviratredshiftz,isdecreasedcompared totheuniversalbaryonfraction2 accordingtotheratioofthehalo tionallyself-boundsubstructures.FollowingNavarroetal.(1997), massandthe‘filteringmass’,M : wedefineR200 astheradiusofasphereenclosingamass,M200, F whoseaveragedensityis200timesthecriticaldensityoftheUni- f verseatredshiftz,i.e.: fbhalo(z, Mvir)= [1+0.26MFb(z)/Mvir]3. (1) 4πR3 100H(z)2R3 For M (z), we use the analytical fitting function given in Ap- M200 = 3200 ·200δcrit(z)= G 200. pendixFBofKravtsovetal.(2004). In our fiducial satellite-model, we assume that reionization Thevelocity,V200,isdefinedasthecircularvelocityofthehaloat Rth2e0s0im(Vu2l0a0tio=nspanGdMus2e0d0/toRc2a0l0c)u.lMate20R02i0s0dairnedctVly20m0.eIansuoruedrmfroodm- tMsitoaWnrts-lamastotsrdefedolsrahadibfotopzute0td0=.z10125=Gayn8rd)a.enFndodrzsrsaimt=zprl7i=c(iitny1,1bw.o5te,hwrmehfoeilrdeetotlhstehreoeiroriengiiioznnaa--l els,weapproximatethevirialpropertiesofdarkmatterhaloes,e.g. virial radius (Rvir), virial mass (Mvir) and virial velocity (Vvir) giziavteisontheeproigchht,szhreaipoe,aasnzd0thheerneoarfmtear.liOsautriocnhofoicrethoefsfiaxteinllgitzerleuiom=ino1s5- by R200,M200 and V200 respectively, unless otherwise explicitly ityfunction.Wediscussthedependenceofthesatellitesluminosity stated. functionondifferentassumptionsforthereionizationepochinSec- Following DeLucia&Helmi (2008), we scaled down the tion3.1. original outputs by a factor of 1.423 for the mass and 1.42 for the positions and velocities, in order to have a MW-like halo withV200 ∼ 150kms−1 (Battagliaetal.2005;Smithetal.2007; 2.2.2 Cooling Xueetal.2008).Afterthescaling,thesmallestresolvedsubhaloes (containing 20 particles) have dark matter mass MDM ∼ 2 × In our model, the cooling of the shock-heated gas is treated as a 106M in the highest resolution run (GA3new). MDM denotes classicalcoolingflow(e.g. White&Frenk1991),withthecooling ⊙ thetotal bound massat z = 0determined bySUBFIND through- ratedepending on the temperature and metallicityof the hot gas. outthispaper.Thepresent-dayvirialmassandthevirialradiusfor As in DeLuciaetal. (2004), we model these dependences using the MW-like halo are M200 ∼ 1012M and R200 = 209 kpc, the collisional ionisation cooling curves of Sutherland&Dopita ⊙ respectively. (1993).Forprimordial(orlow-metallicity)composition,thecool- ing is dominated by bremsstrahlung (free-free) emission at high temperatures(T ∼> 106K)anditismostefficientatT ∼ 105K and ∼ 1.5×104K (the H and He+ peaks of the cooling func- 2.2 Semi-analyticmodelling tion).Linecoolingfromheavyelementsdominatesinthe106–107 Weuseasemi-analyticalgalaxyformationmodeltostudythebary- K regime for non primordial compositions. For T < 104K, i.e. onicpropertiesofaMW-likegalaxyanditssatellites.Thismodel belowtheatomichydrogencoolinglimit,thedominantcoolantis hasbeendeveloped mainlyattheMax–Planck–Institut fu¨rAstro- molecularhydrogen(H2).Thevirialtemperatureofahalocanbe physik and werefertoit asthe‘Munich model’ later inthetext. expressedasafunctionofitsvirialvelocityas: Theessentialideasofanysemi-analyticmodelcanbetracedback 2 taondthiencwluodrkespbhyysWicahlitpero&ceRseseesss(1u9ch78a)sathnedcWoohliitneg&ofFgreansk,s(t1ar99fo1r)-, Tvir(z)=35.9 Vkmvirs(z)1 . (2) − ! mationandfeedbackduetosupernovaexplosions.Overtheyears, theMunich model hasbeenenriched withnew ‘ingredients’, e.g. Therefore, a halo with Tvir = 104K corresponds to a virial ve- the growth of supermassive black holes (Kauffmann&Haehnelt locity of Vvir = 16.7kms−1, which is equivalent to Mvir ∼ 2000), the inclusion of dark matter substructures (Springeletal. 3×107M whenz=15,andMvir ∼2×109M whenz =0. 2001),chemicalenrichment(DeLuciaetal.2004)andAGNfeed- In the⊙MW-model, haloes with Tvir lower th⊙an 104K, are back (Crotonetal. 2006). The model we use in this study has able to cool as much gas as a 104K halo with the same metal- been presented in DeLucia&Helmi (2008) and builds upon licity. In the satellite-model, we forbid cooling in small haloes the model whose results have been made publicly available with Tvir < 104K, for any metallicities and at all times. This (DeLucia&Blaizot 2007). In order to reproduce the properties is a reasonable approximation since molecular hydrogen is very of the MW satellites, we have made a few modifications to the sensitivetophoto-dissociation causedbyUVphotonsfrom(first) original model. In the following, we refer to the model used by DeLucia&Helmi(2008)astheMW-modelandtothefiducialone usedinthisworkasthesatellite-model.Herewegiveabriefsum- 2 WeusetheWMAP3-yearvaluefb=0.17(Spergeletal.2007). 4 Y.-S. Li, G. DeLucia andA. Helmi stellar objects (Haimanetal. 2000, see also Kravtsovetal. 2004; Analternativesupernovafeedback Koposovetal.2009). Sincedwarfgalaxieshaveshallowpotentialwells,theirproperties areexpectedtobeparticularlysensitivetotheadoptedSNfeedback 2.2.3 Starformationandsupernovafeedback model.Toexplorethisdependency,wehavealsousedanalternative SNfeedbackrecipeinadditiontothe‘standard’recipementioned Thestarformation model used inthisworkisdescribed indetail above.Wenotethatthisalternativefeedbackrecipeisequivalentto inDeLucia&Helmi(2008),whilewerefertoCrotonetal.(2006) theejectionmodeldescribedinDeLuciaetal.(2004),andwerefer and DeLuciaetal. (2004) for details on the supernova feedback tothispaperformoredetailsonthisparticularfeedbackmodel.In models. Cold gas is assumed to be distributed in an exponential the ejection model, the gas reheated by SNe is computed on the diskandprovidestherawmaterialforstarformation,whichoccurs basisofenergyconservationargumentsanddependsonthegalaxy atarate: massas: ψ=αSFMsf/tdyn, (3) ∆M = 4ǫ VS2N ∆M . (9) reheat 3 V2 ∗ where αSF is a free parameter which controls the star formation vir efficiency,tdynisthediskdynamicaltimeandMsf isthegasmass Our choices of the feedback parameters (ǫ = 0.05 and VSN ∼ aboveacriticaldensitythreshold.AsinDeLucia&Blaizot(2007) 634kms−1) imply that galaxies with Vvir < 87kms−1 would and DeLucia&Helmi (2008), we fix αSF at 0.03, and adopt a haveinthismodelmoreheatedmassperunitofnewlyformedstel- ChabrierIMF.Thesurfacedensitythresholdtakesaconstantvalue lar mass, compared to the standard recipe (Eq. 6). In this model throughout the disk(see DeLucia&Helmi 2008, for details). At thematerialreheatedbysupernovaexplosionsincentralgalaxiesis eachtimestep,∆t,wecalculatetheamountofnewlyformedstars, assumedtoleavethehaloandtobedepositedinan‘ejected’component that canbe re-incorporated intothehot gasat later times. ∆M =ψ∆t. (4) ∗ ThematerialreheatedbySNeexplosionsinsatellitegalaxiesisas- Massive stars explode as SNe and inject energy in the sur- sumedtobeincorporateddirectlyinthehotcomponentassociated roundinginterstellarmedium.Inourmodel,wedonotconsiderthe withthecorrespondingcentralgalaxy. delaybetweenstarformationandSNenergy(andmetals)injection, Wewilldiscusslaterhowourresultsforthebaryonicproper- i.e.thelifetimeofsuchstarsisassumedtobezero.Theenergyin- tiesofthesatellitesdependontheadoptedfeedbackscheme. jectionbySNepersolarmasscanbeexpressedasVS2N =ηSN·ESN whereηSN =8.0×10−3M−1isthenumberofSNeperunitsolar massexpectedfromaChabr⊙ierIMF3 andESN = 1.0×1051 erg 2.2.4 Metalrecyclingthroughthehotphase istheaverageenergy per SN.Theenergy releasedbySNeinthe Ateach timestep, themassesexchanged among thefour phases: sametimeintervalis: Mhot,Mcold,M ,Meject,(i.e.hotgas,coldgas,starsandejecta) ∗ ∆ESN=ǫhalo·0.5VS2N∆M∗. (5) (a2re00u4p)d.aTtehdeamsedteaslclircibiteydiinneSaecchtipohna4s.e7iasnddeFniogt.e1diansDZexLauncdiaisetdael-. whereǫhalorepresentstheefficiencywithwhichtheenergyisable fined as the ratiobetween the mass in metals in each component toreheatdiskgas.Weassumethattheamountofcoldgasreheated (MZ)andthecorrespondingmass(M )wherethesuffixxishot, x x bySNeisproportionaltothenewlyformedstars: cold,staroreject.Inthesatellite-model,weincludearoutetore- cyclemetalsproducedbynewlyformedstarsthroughthehotphase ∆M =ǫ ∆M . (6) reheat disk ∗ ofagalaxy. Theequations giveninSection4.7ofDeLuciaetal. Ifthisgaswereaddedbacktothehotphasewithoutchanging its (2004)modifyasfollows: specificenergy,thetotalthermalenergywouldchangeby: M˙Z =+(1−R)·ψ·Z cold ∆E =0.5∆M V2 . (7) ∗ hot reheat vir If∆ESN >∆Ehot,SNfeedbackisenergeticenoughtoejectsome M˙hZot = −M˙cool·Zhot+M˙back·Zeject ofthehotgasoutsidethehaloandweassumethat: + (M˙reheat·Zcold)+FZhot·Y ·ψ sat ∆Meject = ∆ES0N.5−Vv∆2irEhot = ǫhaloVVSv22iNr −ǫdisk!∆M∗. (8) M˙Z = +XM˙ ·Z −(1−R)·ψ·Z cold cool hot cold The ejected material can be re-incorporated into the hot compo- +(1−F )·Y ·ψ−M˙ ·Z Zhot reheat cold nent associated with the central galaxy as the halo keeps grow- ing by accreting material from the surroundings (DeLuciaetal. 2004; Crotonetal. 2006). For thetwo parameters which regulate M˙eZject =+M˙eject·Zhot−M˙back·Zeject. thefeedback,ǫ andǫ ,weassumethevalues0.35and3.5re- halo disk Aconstant yieldY ofheavyelementsisassumedtobeproduced spectively, followingCrotonetal.(2006)and DeLucia&Blaizot persolarmassofgasconvertedintostars.Thegasfractionreturned (2007). This means that for galaxies with Vvir < 200kms−1, byevolvedstarsisR=0.43,appropriateforaChabrierIMF.Inthe ∆Meject >0for∆M∗ >0. aboveequations,M˙coolrepresentsthecoolingrate;M˙backprovides there-incorporationrate;M˙ isthereheatingratebySNe,and reheat 3 Thisisthefractionofstarswithmasslargerthan∼ 8M perunitof M˙ejectistherateofmassejectedoutsidethehalo. stellarmassformed.Notethat,sincewehaveadoptedaninst⊙antaneousre- ForthealternativeSNfeedbackrecipe,thereheatedgasisas- cyclingapproximation,itismoreappropriatetocomparethemetallicities sumedtobeejectedfromthecoldphasedirectlyforcentralgalax- ofourmodelgalaxieswithelementssynthesisedbyTypeIIsupernovae. ies.Inthiscase,themetallicityintheejectaisupdatedas ThenatureoftheMW satellites 5 M˙eZject =+M˙reheat·Zcold−M˙back·Zeject. correspondstothe‘satellite-model’(thefourthrowinTable1).In thismodel,reionizationstartsatz=15,and95percentofthenew IntheMW-model,allnewlyproducedmetalsreturnedtothe metals are deposited directly into the hot component in galaxies cold phase immediately, i.e. F = 0. Hydrodynamical simu- lbaltoiwonnsobuytfMroamcLsmowall&gaFlearxriaersawZ(h1iot9ht99g)assumgagsessbtetlhoawt m10e7taMls ca(ncobre- wwiethfoMrbvidirce.5×1010M⊙ tzhe=p0ro.perties of the MW-like galaxies indifferent SA models at (cid:26) TheresultscorrespondingtotheMW-modelaregiveninthe This means that for galaxies with a dark matter halo with virial firstrow(seealsoFig.2ofDeLucia&Helmi2008).Theonlydif- masslessthan5×1010M ,95percentofnewlyproducedmetals ference between the MW-model and the satellite-model A is the ⊙ aredepositeddirectlyintothehotphaseinthismodel. suppression of cooling in small haloes. Comparing the results of thesetwomodels,wefindnosignificantchangesintheproperties of the present-day MW-likegalaxy. Insatellite-model B, wealso 2.3 Treatmentofsatellitegalaxies changezreioto15andkeepFZhot =0.Theonlysignificanteffect Wefollowtheconventionestablishedalongthedevelopmentofthe of an early reionization is to bring down the black hole mass by Munich model to classify galaxies according to their association ∼ 15percentcomparedtothevalueobtainedintheMW-model. withadistinctdarkmattersubstructure.Thegalaxyassociatedwith Theearlyreionization alsoresultsinaslight increaseof thestel- the most massive subhalo in aFOFgroup isreferred toas ‘Type larmassbutthisisstillwellwithintheobservationaluncertainties 0’ or central galaxy. Other galaxies in a FOF group are usually (M ∼5−8×1010M ). referredtoassatellitesandarefurtherdifferentiatedinto‘Type1’ ∗Our fiducial satellit⊙e-model givesatotal stellarmass similar galaxies, iftheir darkmatter subhalo isstillidentified,and ‘Type tothat obtained from the MW-model and inagreement withcur- 2’,whentheirsubhalohasfallenbelowtheresolutionlimitofthe rentobservationalconstraints.Theresultsofthesetwomodelsare simulation. alsoverycloseintermsofthemassofthebulgeandthecoldgas Whenagalaxybecomesasatellite,thedarkmattermassofthe content. The black hole mass MBH = 6.9 × 106M from the parent subhalo is approximated using the number of bound dark satellite-model is in marginal agreement with the lates⊙t measure- matter particles given by SUBFIND. The disk size is fixed at the mentoftheMWblackholemassMBH = (4.5±0.4)×106M valueithadjustbeforeaccretion.Inourmodel,onlyType0central (Ghezetal.2008).Theejectionofmetalsintothehotcomponenti⊙n galaxiesareallowedtoaccretethematerialthatcoolsfromthehot smallgalaxies(cf.satellite-modelB)onlymakesthebulgeslightly gasassociatedwiththeparentFOFgroup.Satellitegalaxiesdonot moremetal-poor(∼ 0.06dex).ResultslistedinTable2showthat havehotandejectedcomponentsandthecoolingisforbidden,i.e. themodificationsdiscussedaboveinfluenceonlythepropertiesof Mhot =Meject =M˙cool =0.Whenagalaxybecomesasatellite, dwarf galaxies, while preserving the properties of the MW-like itshotandejectedcomponentsaretransferredtothecorresponding galaxiesdiscussedinDeLucia&Helmi(2008). components ofthecentralgalaxy.Asaconsequence, oncematter The5throwinTables1and2correspondstoamodelwhich leavesthecoldphase of asatellite,it doesnot rejointhe(Type1 incorporatesthe‘alternative’(orejection)SNfeedbackschemede- orType2) satelliteatalatertime,butitcanbeaccretedontothe scribedinSection2.2.3.Whencomparedtothe‘standard’scheme, correspondingcentralgalaxy. the dependency of the amount of reheated gas on 1/V2 in this vir schemeresultsinamoreefficientfeedbackforsmallgalaxiesand inalessefficientejectionformoremassivesystemsliketheMW 2.4 ModelimprovementsandthecentralMW-likegalaxy galaxy. These galaxies tend to have larger stellar masses, a more ThevaluesoftheparametersthatenterintheSAmodelwerecho- massivebulgeandtendtobemoremetal-richinthisscheme.Aswe sen so as to reproduce several observations of galaxies in the lo- willshowinSection3,however,thisalternativefeedbackscheme calUniverse,inparticularthelocalgalaxyluminosityfunctionand isabletobettermatchthepropertiesoftheMWsatellites. themassandluminosityofMW-likegalaxies(seeDeLuciaetal. We therefore propose a combination of these two feedback 2004;Crotonetal.2006;DeLucia&Blaizot2007).Itistherefore recipestoaccountforthepropertiesofgalaxiesonlargeandsmall notentirelysurprisingthatthissameparametersetprovidesresults massscales. Thismodel corresponds tothe‘satellite-model com- thatareinniceagreementwithobservationalpropertiesofourMW bined’,andinthisscheme,wecalculatetheamountofgasreheated galaxy(DeLucia&Helmi2008).Inordertoobtainagoodagree- bySNedependingonthelocalpotentialwell(massoftheassoci- mentwiththeobserved propertiesoftheMWsatellites,however, atedsubhalo): wefoundthatwehadtoimplementsomeslightmodifications. Inoursatellite-model,weadoptthesameparametersetusedin 4ǫ VS2N ∆M ifV2 < 4 ǫ V2 DeLucia&Helmi(2008)exceptforthereionizationepoch,zreio, Mreheat =( ǫ3diskV∆v2irM ∗ othevriwrise.3ǫdisk SN andfractionofmetalejectedintothehotcomponent,F .Table1 ∗ Zhot introducestheSAmodelsthatweemployinthisstudy.IntheMW- Thereheatedgasistreatedasintheejectionscenario,i.e.itisadded modelbyDeLucia&Helmi(2008),reionizationoccursatzreio = totheejectedcomponent ofacentralgalaxyandlostintothehot 8,haloeswithTvir < 104 Kareallowedtocoolatthesamerate componentforasatellite.The‘satellite-modelcombined’entryin ofa104 Khalowiththesamehotgasmetallicity,a‘standard’SN Table2liststhepropertiesoftheMW-likegalaxyinthisscheme. feedbackrecipeisadoptedandallnewmetalsarekeptinthecold Asexpected,thestellarmass,thetotalandbulgemetallicity,aswell gasphase(F =0).Ourfiducialmodelforthesatellitegalaxies asthetotalluminosityarenowverysimilartowhatwegetwiththe Zhot 6 Y.-S. Li, G. DeLucia andA. Helmi Table1.Nomenclatureandfeaturesofthesemi-analyticmodelsusedinthisstudy. ModelName z0,zr coolingforVvir<16.7kms−1 SNfeedback FZhot (1) (2) (3) (4) (5) MW-model (8,7) Yes Standard 0.0 satellite-modelA (8,7) No Standard 0.0 satellite-modelB (15,11.5) No Standard 0.0 satellite-model (15,11.5) No Standard (0.95,0.0) satellite-modelejection (15,11.5) No ejection (0.95,0.0) satellite-modelcombined (15,11.5) No combined (0.95,0.0) Differentcolumnslist:(1)themodelname;(2)thereionizationepoch;(3)theadoptedcoolingrecipeinhaloeswithTvir<104K;(4)theadoptedfeedback recipe;(5)thefractionofmetalsinjecteddirectlyintothehotcomponent. Table2.PropertiesoftheMilkyWay-likegalaxyinthesemi-analyticmodelsemployedinthisstudy,fortheGA3newsimulation. ModelName M∗ Mbulge Mcoldgas MBH LogZZ⊙∗ LogZZ⊙b MB [1010M ] [1010M ] [1010M ] [106M ] [dex] [dex] [mag] (1) (2) ⊙ (3) ⊙ (4) ⊙ (5) ⊙ (6) (7) (8) MW-model 5.73 0.64 1.06 8.2 −0.05 −0.28 −19.53 satellite-modelA 5.75 0.64 1.07 8.0 −0.05 −0.28 −19.50 satellite-modelB 5.85 0.62 1.11 7.1 −0.06 −0.30 −19.52 satellite-model 5.88 0.63 1.11 6.9 −0.06 −0.35 −19.52 satellite-modelejection 8.26 2.58 1.09 12.8 0.12 0.00 −19.08 satellite-modelcombined 5.02 0.84 0.95 12.0 −0.08 −0.25 −19.53 Differentcolumnslist:(1)themodelname;(2)stellarmass;(3)massofthebulge;(4)coldgascontent;(5)massoftheblackhole;(6)logarithmicvalueof thetotalstellarmetallicity;(7)logarithmicvalueofthebulgemetallicity;(8)B-bandabsolutemagnitudecorrectedforinternaldustattenuation. standardfeedbackscheme,albeitthebulge(andtheblackhole)are more than 97 per cent of their dark matter by present. Therefore nowmoremassive.ThelasttwomodelslistedinTable1populate it is quite unlikely that a bound stellar core would survive such thesamesetofsubhaloeswithstars,withalmostidenticalproper- aseveretidalstripping.WewilldiscussmoreaboutType2model ties.Forsimplicity,wewillnotdiscusstheresultsofthecombined galaxiesinSection4.2.Throughoutthispaper,wewillrefertosub- schemeforsatellitegalaxies. haloesthathoststarsas‘luminoussatellites’orsimply‘satellites’, andwillrefertothosethatdonothostanystarasdarksatellitesor subhaloes. 3 THEMILKYWAYSATELLITES 3.1 Thesatelliteluminosityfunction In thisSection, we define as SA model satellitesof the MW-like galaxy those that satisfy the following conditions at z = 0: (i) Our fiducial satellite-model gives 51 luminous satellites within a satellite has to belong to the same FOF group where the MW- 280kpcforGA3new.Thisisingoodagreementwiththeestimated like galaxy is; (ii) the distance to the MW-like galaxy must be ‘all sky’ number of satellites (∼ 45) brighter than M = −5.0 V < 280 kpc; (iii)the galaxy isassociated witha dark matter sub- byKoposovetal.(2008).Ifweremovethedistanceconstraint,the halo (i.e. it has to be Type 1 galaxies). The distance cut corre- number of satellitesis only increased by one, and the number of sponds to the current observational limits, but we include in our subhalosvariesfrom1865to1869. comparisontheverydistantandrecentlydiscoveredsatelliteLeoT Themassfunctionsforthefiducialsatellite-modelandofthe (at∼420kpcfromtheMilkyWay). survivingsubhaloeswithin280kpcinGA3newareshowninFig.1. Wedo not consider here satellitesthat had their dark matter Themassplottedhereisthedarkmattermassatz =0determined haloestidallystrippedbelowtheresolutionlimitofthesimulation bySUBFIND.Asindicatedbythedashedhistogram,allsubhaloes (Type2galaxies).Thisselectionismotivatedbythefactthatwhile withpresent-dayMDM >109M resolvedinGA3newhostlumi- ⊙ resolved,ourType1galaxiesaredarkmatterdominatedatallradii noussatellites.Themassfunctionofthesesubhaloesdeviatesfrom (seeSection 3.5, and inagreement withobservations of satellites thepower-lawshapemassfunctionofthefullsubhalopopulation aroundtheMWandM31,e.g. Simon&Geha2007;Strigarietal. andisfairlyflatbelow MDM = 109M ,down totheresolution 2007,2008;Walkeretal.2009).SinceType2galaxiesinourfidu- limit(MDM ∼ 106.5M ).Forcompari⊙son, thedottedhistogram ⊙ cial model, reach a maximum virial mass during their evolution inFig.1showsthemassfunctionofsurvivingsubhaloes,withinthe largerthan6.8×107M ,thismeansthatthesegalaxieshavelost samedistancerangefromthecentralgalaxy,fromthelowerreso- ⊙ ThenatureoftheMW satellites 7 10000 GA3new subhaloes (1865) surviving subhaloes (N = 1865) GA2new subhaloes (225) 1000 satelMlitWe-m-mooddele lA ( N(N = = 2 8886)) 1000 satellite-model (51) satellite-model B (N = 51) M M D D M M 100 g 100 g o o L L d d N/ N/ d d 10 10 1 1 6 7 8 9 10 11 6 7 8 9 10 11 Log M [M ] Log M [M ] DM O • DM O • Figure 1. The solid histogram shows the present-day mass function of Figure 2. Present-day mass functions (solid histograms) for dark matter model satellites using the satellite-model for the highest resolution sim- subhaloesassociatedwithsatellitespredictedbythesemi-analyticmodels ulation. Errorbarsdenote the1-σ Poissonuncertainties. Thedashedhis- listedinTable1.Thedashedhistogramagainindicates thesubhalomass togramshowsthesubhalomassfunctionforthehighestresolutionsimula- functionfortheGA3newsimulation. tion,whichsteeplyrisesuptotheresolutionlimit.Thedottedhistogramis thesubhalomassfunctionforalowerresolutionsimulation(i.e.GA2new). SDSS’power-lawluminosityfunctionofsatelliteswithin280kpc, estimatedbyKoposovetal.(2008).Forsatellite-modelB,weshow Table3.NumberofsatellitesaroundthemodelMWgalaxyforthedifferent the1-σPoissonnoise.Thefilledcirclesshowtheluminosityfunc- SAmodelsusedinthisstudyfortheGA3newsimulation. tionofthe22knownsatellitesoftheMW,includingthelatestultra- faintsatelliteLeoV(Belokurovetal.2008).Asareference,inthe ModelName Nsat z0,zr FZhot MW-model the number of surviving satellitesis286. The drastic (1) (2) (3) (4) differencebetweentheMW-andthesatellite-modelBismostlyat MW-model 286 (8,7) 0.0 thefaintendoftheluminosityfunction,anditisduetothecom- binedeffectofanearlyreionizationandnocoolinginsmallhaloes. satellite-modelA 88 (8,7) 0.0 In a model with no cooling in small haloes and a later reioniza- satellite-modelB 51 (15,11.5) 0.0 tion,thenumberofsatellitesis88(comparetheMW-modelandthe satellite-model 51 (15,11.5) (0.95,0.0) satellite-modelA).Thenumberofsatellitesisfurtherreducedto51 whenassuminganearlierreionizationepoch(zreio = 15),witha satellite-modelejection 51 (15,11.5) (0.95,0.0) reduction of galaxies in the luminosity range M ∈ [−7,−10] V satellite-modelcombined 51 (15,11.5) (0.95,0.0) comparedtoamodelwithalaterreionization.Wehavealsoexper- imentedvaluesforzreioatredshift10and12andfoundanumber Different columns list: (1) the model name; (2) the number ofluminous ofsurvivingsatellitesofNsat = 79and58,respectively.Tosum- satellites; (3) the adopted reionization epoch; (4) the fraction of metals marise,thesechoices ofzreio = [8,10,12,15] allgiveanumber ejecteddirectlyintothehotcomponent. of satellitesdown toM = −5which isconsistent withthees- V timationby Tollerudetal. (2008) (see their Fig. 6). However, af- lution simulation GA2new. The smallest subhalo which could be ter examining the shape of the luminosity functions with differ- resolvedinGA2newhasMDM ∼2×107M .Thesubhalomass ent zreio, wedecided touse zreio = 15 inour fiducial model, as functions from the two simulations agree we⊙ll down to 108M . thischoicegivesboththerightnormalisationandashapewhichis ⊙ At lower masses, numerical effectsstart tobecome important for inbetteragreementwiththeobservationalmeasurements(seenext GA2new.However,thenumberofsatelliteswithMDM <109M paragraphs).Werecallthatourresultsarebasedononlyonehalo, ⊙ is still lower than the number of subhaloes resolved in GA2new, withmasscomparabletothatestimatedforourMilkyWay.Acer- which suggests that numerical resolution should not be an issue tainscatterinmodelpredictions, duee.g.totheassemblyhistory and that the observed decline of luminous satellitesisa result of oftheparenthalo,isexpectedandthismightbesignificantlylarger howwemodelthebaryonicphysics,e.g.SNfeedback,aswewill thanthePoissonnoiseplottedinFig.3. seelater. TheleftpanelinFig.4showstheluminosityfunctionofthe Fig. 2 compares the mass function for the SA models ex- satellites in our fiducial satellite-model (solid histograms), com- plored in this study. In Table 3, we list the number of luminous paredtothe‘allskySDSS’luminosityfunctionbyKoposovetal. satellites for these models. Note that all the models which adopt (2008)andtheobservationaldataforthe22knownMWsatellites. zreio = 15andforbidcoolinginhaloeswithVvir <16.7kms−1, Themodel luminosity function covers a similarluminosity range i.e.satellite-modelB,satellite-model,satellite-modelejectionand as the 22 MW satellites though the model predicts a lower num- satellite-modelcombined, populategalaxiesinthesamesetof51 beroffaint(M >−5)satelliteswithrespecttotheexpected‘all V subhaloes. Themassfunctionsof thesefour modelsaretherefore sky’luminosityfunction.Infact,thesatellite-modeldoesnotpre- identical. dictanysatellitefainterthanM = −4mag.Ontheotherhand, V Fig. 3 shows the luminosity functions of the first three SA it shows an excess with respect to the data of 10 − 15 satellites modelslistedinthetables.The(red)dashedlineshowsthe‘allsky aroundM =−10.Thesesatellitesinexcessareallwithinadis- V 8 Y.-S. Li, G. DeLucia andA. Helmi ‘‘all sky SDSS’’ Koposov et al. (2008) ‘‘all sky SDSS’’ Koposov et al. (2008) satellite-model (N = 51) satellite-model ejection (N = 51) 10.0 10.0 V V M M d d N/ N/ d d 1.0 1.0 0.1 0.1 0 -5 -10 -15 -20 0 -5 -10 -15 -20 M M V V Figure4.LuminosityfunctionfortheobservedMWsatellites(filledcirclesandreddashedline)andforthemodelsatellites(blackhistograms).Theleftpanel isforourfiducialmodelandtherightpanelisforthemodelwithamoreefficientSNfeedbackforsmallgalaxies(seeSection2.2.3).Dataarethesameas thoseinFig.3. survivingsatellitesresultingfromthealternativefeedbackscheme (satellite model ejection). This model luminosity function agrees 100.0 MW-model (N = 286) very well with the observations. When compared with that from satellite-model A (N = 88) satellite-model B (N = 51) thestandardfeedbackscheme,thealternativeluminosityfunction extendstofainterluminosities,reachingM ∼ −3anddoesnot V show any excess atM ∼ −10. Notethat inthesatellite-model 10.0 V V ejection,thesame51subhaloesarepopulatedwithluminousgalax- M d ies.ThissuggeststhattheSNfeedbackaloneisunlikelytosolvethe N/ d ‘missingsatellitesproblem’ (Somerville2002),andthatthepres- ence/absenceofaluminousgalaxywithinadarkmattersubstruc- 1.0 tureisduetotheparticularassemblyanddynamicalhistoryofthe halo,andtothereionizationhistoryoftheUniverse. These different results are entirely due to the SN scheme 0.1 adopted. In the ejection scheme, the amount of gas reheated by 0 -5 -10 -15 -20 MV SNe scales as 1/Vv2ir, and for a galaxy with Vvir < 87kms−1, moregasisheatedbyperunitofnewlyformedstarswithrespect tothestandardscheme,wheretheamountofgasheatedbySNeis Figure3.LuminosityfunctionoftheobservedMWsatellites andforthe onlyproportionaltotheamountofnewlyformedstars.Inthislatter modelsatellitesaroundaMW-likegalaxy,forthefirstthreemodelslisted inTable3.TheintegratedV-bandluminositiesofMWsatellites(dots)are case,forgalaxieswithlowstarformationrates(asisthecasefor taken fromvarious sources. Theclassical dSphs arefrom Mateo (1998); galaxiesthatliveinsmallsubhaloes),onlyverylittlegasisheated. mostoftheultra-faintdwarfsarefromMartinetal.(2008),exceptLeoT As long as the density threshold for star formation is met, these (Ryan-Weberetal.2008)andLeoV(Belokurovetal.2008). galaxieskeepformingstars.Thisismostlikelythereasonwhyour fiducialmodelexhibitsanexcessofsatellitesaroundM ∼ −10 V andalackofultrafaintobjectsintheluminosityfunction. Inthe alternativefeedback model, when star formation occurs ina cen- tanceof200kpcfromthehostgalaxyandhavehalf-lightradiibe- tral galaxy, some cold gas is ejected outside the halo, and has to tween100and500pc.Theyshouldthereforehaveappearedinthe wait several dynamical time-scales to be reincorporated into the ‘all-sky’ SDSS luminosity function if they existed (provided the hothalo,delayinganysubsequentstarformation.Furthermore,the distribution for these bright satellites is isotropic, as assumed by impact on thestar formation of a satellitegalaxy associated with Koposovetal. 2008). It alsoseems that the model under-predicts the number of very bright satellites.Thisis, however, the regime a subhalo with Vvir < 87kms−1 is more drastic in this model, because the ejected gas cannot be re-incorporated onto the satel- whereboththedataandthesimulationssufferfromsmallnumber lite any longer. Small satellites therefore consume their cold gas statistics. reservoir more efficiently in this ejection scenario, which causes A comparison to Fig. 3 shows that the luminosity function thesurfacedensitiesofthecoldgastofallbelowthecriterionfor given by satellite-model B and by satellite-model are very simi- formingstars. lar,implyingthatsatelliteluminositiesdonotdependstronglyon thefractionofnewlyproducedmetalsputintothehotcomponent Given the reasonable match of the satellite-model and of of agalaxy. However, the metallicitydistribution functions differ satellite-modelejectiontotheobservedluminosityfunctions,inthe significantly(seeSection3.2). restofthepaperwewillconcentrateonthepropertiesofthesatel- The right panel of Fig. 4 shows the luminosity function of litepopulationsinthesetwoSAmodels. ThenatureoftheMW satellites 9 20 20 all MW sat. (22) all MW sat. (22) classic MW sat. (11) classic MW sat. (11) satellite-model (47) satellite-model ejection (38) 15 15 N 10 N 10 5 5 0 0 -4 -3 -2 -1 0 -4 -3 -2 -1 0 Log(Z/Z ) or <[Fe/H]> Log(Z/Z ) or <[Fe/H]> * O • * O • Figure 5. Histogram of the mean iron abundance [Fe/H] determined for red giant branch stars in the MW satellites. For the model satellites we plot log(Z /Z ).Theleftpanelcompares theMWsatellites withmodelsatellites fromourfiducial modelandtherightpanelfromthemodelwithamore efficien∗tSN⊙feedbackfordwarfgalaxies(seeSection2.2.3).DatafortheMWsatellites aretakenfromvarioussources:LMCandSMCfromWesterlund (1997);SgrfromCole(2001);UrsaMinorandDracofromHarbecketal.(2001);Sextans,Sculptors,CarinaandFornaxfromtheDARTsurvey(Helmietal. 2006);LeoIIfromKochetal.(2007);LeoIfromKochetal.(2007).ForthenewlydiscoveredSDSSultra-faint dwarfs,wetakethemeasurements from Kirbyetal.(2008),exceptforBoötesIforwhichweuseMunõzetal.(2006),BoötesIIfromKochetal.(2009)andLeoVfromWalkeretal.(2009). 3.2 Themetallicitydistribution In the right panel of Fig. 5 we plot the metallicity function ofthe38nonmetal-free4 satellitesinthesatellite-modelejection. The left panel of Fig. 5 compares the metallicity distribution of Thepeakofthisdistributionisalsoshiftedtoslightlyhighervalues model satellites in our fiducial satellite-model with the observed thanobserved,butithasamoreevendistributioncomparedtothe distribution.Themetallicityinourmodelismass-weightedandis standardrecipe.AsdiscussedinSection3.1,thisisduetothefact defined astheratiobetween themass of metalsinstarsand total stellarmass: thatsatelliteswithVvir < 87kms−1 loosemoreoftheircoldgas reservoir(andalargerfractionoftheirmetals,seeSection2.2.4)in Z =MZ/M . thismodelwithrespecttothestandardfeedbackscheme. ∗ ∗ ∗ Sinceourmodeldoesnotdistinguishthelong-livedmainironcon- tributors(SNIa)fromtheshort-livedα-elementsenrichers(SNII), 3.3 Starformationhistories adirectcomparisonofZ to[Fe/H]isquestionable.Nevertheless, InFig.6wepresenttheevolutionofthestellarmassandtheSUB- here we assume that the logarithmic value of the mass-weighted FIND dark matter mass predicted in our fiducial satellite-model. metallicitynormalisedtothesolarvalue(Z =0.02)canbecom- Weremindthatthismodeldoesnotgiveanysatellitefainterthan ⊙ pared qualitatively with the [Fe/H] derived from spectra of Red M =−4,andgivesonly2satellitesfainterthanM =−5.We V V GiantBranchstarsintheMWsatellites. therefore restrict our comparisons to the classical MW satellites, Amongthe51survivingsatellitesinthesatellite-model,four andwesortthemby theirpresent-day luminosityintothreebins: of them are free of metals since they have only made stars once luminous(−1650percentoftheir MWsatellitesisshiftedtolowervalueswithrespecttothecorre- starsafterbecomingsatellitesoftheMW-likehalo.Thischoiceis spondingdistributionfromthesatellite-model.Theexcessofmodel motivatedbytheprevalenceofoldstars(i.e.>10Gyr)seeninthe satellitesintherangeof−29Gyr),areassociatedwithfaintersatellites(M >−12), V in good agreement with observations5. The most luminous satel- and are dominated by old stars, which means that these galaxies 5 Inthefullsampleofmodelsatellites,43outof51madetheirfirstgen- populationsareexcludedintheanalysisherewiththecriterionthathalfof erationofstars∼>10Gyrago.Thosethatarenotdominatedbyoldstellar thestarswereinplacebeforetheaccretion.

On the nature of the Milky Way satellites

Similar On the nature of the Milky Way satellites