On the nature of the Milky Way satellites

0.83 MB·English

by  Yang-Shyang Li

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:[email protected] 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. Mun˜ozetal.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’com-
ponent 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- wwiethfoMrbvidirc<oo5li×ng1i0n1h0aMlo⊙es.wInitahllTmviord<els1w04ithKt.heprefix‘satellite’,
rmesopdoenl,dwinegatsosuamhealaosoifmMplevirtw=o-s3ta.5te×va1lu0e8Mfor⊙F). In outor as⊙actceolulintet theceBnetlroawlM,wWe-blirkieeflgyaldaixsycuosnsothuerdcehpaenngdeesnfcoerozrfemioo,dtheelrceosoullitnsgfoinr
Zhot smallhaloesandmetalrecyclingthroughhotphase.Theresultsfor
fortheabovemassdependence:
thesatellitegalaxiesarepresentedinSection3.Table2summarises
FZhot = 00..095 iofthMervwiris>e.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),exceptforBo¨otesIforwhichweuseMun˜ozetal.(2006),Bo¨otesIIfromKochetal.(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(−16<M <−13,similartoSagittariusandFornax),
V
frompristinegas.Thesefourmetal-freesatellitesallhavepresent- intermediate(−12 < M < −10 likeLeo I and Sculptor),and
day MDM ∼< 109M and M of 104 −105M .Wedonot in- faint (−10 < M < −V8 i.e. Leo II, Sextans, Carina, UMi and
⊙ ∗ ⊙ V
clude these ‘metal-free’ satellites in the left panel of Fig. 5 and Draco).Satellitesbelongingtothesethreebinsareshownfromtop
(metallicity) related discussions. Fig. 5 shows the histograms of tobottominFig.6.Wedonotincludeherethetwomodelsatellites
themean[Fe/H]ofresolvedstarsineachMWsatellite.Thedis- (one inthe luminous and one inthe intermediate luminosity bin)
tributionofthe11classicalMWsatellitesisshownbythedotted- whichhavemorestellarmassthandarkmattermassatz =0,due
dashed histogram, while the corresponding distribution including tosignificanttidalinteractionswiththemainhalo.Werecallthatin
also11ultra-faintsatellitesisgivenbythedashedhistogram.The ourmodelling,wedonotaccountfortidalstrippingofstarsandfor
metallicitydistributionsofmodelandMWsatellitescoversimilar thelossofthecoldgasduetoe.g.ram-pressure.Therefore,wealso
ranges.However,thepeakofthemetallicitydistributionforthe22 refrainfromconsideringsystemswhichform>50percentoftheir
MWsatellitesisshiftedtolowervalueswithrespecttothecorre- starsafterbecomingsatellitesoftheMW-likehalo.Thischoiceis
spondingdistributionfromthesatellite-model.Theexcessofmodel motivatedbytheprevalenceofoldstars(i.e.>10Gyr)seeninthe
satellitesintherangeof−2<log(Z /Z )<−0.5corresponds MWdSphs(Dolphinetal.2005;Orbanetal.2008).Whenexclud-
tothebumpatMV ≃−10seeninthe∗lum⊙inosityfunction. ingthesegalaxies, thenumber of satellitesisreduced from16to
If we had set FZhot = 0 (as in satellite-model B), the pre- 13intheintermediatebin; 14to7inthelow luminositybin. We
dictedmetallicitydistributionwouldbeshiftedtowardsevenhigher willlaterseethatfaintsatellitesaremostlyaccretedbeforez = 1
metallicity. In this case, 36 satellites are more metal-rich than thustheirgasshouldhavebeenreducedduetotheinteractionswith
log(Z /Z ) = −1, and only 11 of them have log(Z /Z ) <
−1, in∗cons⊙istent with the observations. This is why ou∗r fid⊙ucial
modelispreferredtosatellite-modelB. 4 i.e.13satellitesare‘metal-free’inthiscase.
10 Y.-S. Li, G. DeLucia andA. Helmi
−16<M <−13
V
1.0
1010
0.8
= 0) 109
M(z * 0.6 (t)M
M(t) / * 0.4 MD 108
0.2 107
0.0 106
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
lookback time [Gyr] lookback time [Gyr]
−12<M <−10
V
1.0
1010
0.8
= 0) 109
M(z * 0.6 (t)M
M(t) / * 0.4 MD 108
0.2 107
0.0 106
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
lookback time [Gyr] lookback time [Gyr]
−10<M <−8
V
1.0
1010
0.8
= 0) 109
M(z * 0.6 (t)M
M(t) / * 0.4 MD 108
0.2 107
0.0 106
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
lookback time [Gyr] lookback time [Gyr]
Figure6.Evolutionofthestellarmass(left)anddarkmattermass(right)forsatellitesinthefiducialsatellite-model.SatellitesaresortedbyMV(z=0)into
threegroups:−16<MV <−13(toppanel);−12<MV <−10(middlepanel);−10<MV <−8(bottompanel).Stellarmassesarenormalisedby
thepresent-dayvalues,M (z=0).Differentcolourscorrespondtodifferentsatellites,andthearrowsindicatetheaccretiontime,definedaswhenasatellite
∗
wasidentifiedasacentralgalaxyforthelasttime.Thesamecolourisusedtoplotthestellarandthedarkmattermassforagivensatelliteinthepanelaside.
Theverticaldashedlinesmarktheendofthereionization,zr =11.5,inthesatellite-model.
thecentralgalaxyandthestarformationshouldhave(onaverage) litesbuilduptheirstellarcontentoveralongerperiodoftimecom-
ceasedshortlyafterbeingaccreted. paredtothefaintestonesasobservedintheLocalGroupsatellites
It isencouraging that the model satellitesshow in Fig. 6 all (Dolphinetal.2005).Thefivesystemsthathavebeenaccretedear-
contain stars older than 10 Gyr regardless of their luminosities, liest(>9Gyr),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.