Formation and assembly history of stellar components in galaxies as a function of stellar and halo mass

1.1 MB·

by  Jaehyun Lee

Draftversion January27,2017
PreprinttypesetusingLATEXstyleemulateapjv.08/22/09
FORMATION AND ASSEMBLY HISTORY OF STELLAR COMPONENTS IN GALAXIES AS A FUNCTION OF
STELLAR AND HALO MASS
Jaehyun Lee1 and Sukyoung K. Yi2
Draft version January 27, 2017
ABSTRACT
7 Galaxy mass assembly is an end product of structure formation in the ΛCDM cosmology. As an
1 extension of Lee & Yi (2013), we investigate the assembly history of stellar components in galaxies
0 as a function of halo environments and stellar mass using semi-analytic approaches. In our fiducial
2 model,halomassintrinsicallydeterminestheformationandassemblyofthestellarmass. Overall,the
n ex situ fraction slowly increases in central galaxies with increasing halo mass but sharply increases
a for logM∗/M⊙ & 11. A similar trend is also found in satellite galaxies, which implies that mergers
J are essential to build stellar masses above logM∗/M⊙ ∼ 11. We also examine the time evolution of
6 the contribution of mass growth channels. Mergers become the primary channel in the mass growth
2 of central galaxies when their host halo mass begins to exceed logM200/M⊙ ∼13. However, satellite
galaxies seldom reach the merger-dominant phase despite their reduced star formation activities due

] to environmental effects.
A
Subject headings: galaxies: evolution – galaxies: elliptical and lenticular, cD – galaxies: formation –
G galaxies: stellar content
.
h
p 1. INTRODUCTION based on the ΛCDM cosmology in which galaxies are
- born earlier on shorter timescales in denser environ-
o Modern theories for galaxy formation and evo-
ments and larger ones are built up through gradual
r lution suggest that galaxies are formed in highly
t over-dense regions, namely haloes, while cosmological mergers. (e.g. De Lucia et al. 2006; De Lucia & Blaizot
s
2007; Guo & White 2008; Jim´enez et al. 2011; Lee & Yi
a structures are built up via smooth matter accretion
[ or the coalescence of haloes. Thus, some galaxies 2013). De Lucia & Blaizot (2007) demonstrated that
brightest cluster galaxies (BCGs) can have very high
are eventually involved in hierarchical mergers in
1 fractionsofexsitucomponents(>80%)intermsoftotal
the process of structure formation. Galaxy mergers
v stellar mass. Jim´enez et al. (2011) examined the assem-
play a pivotal role in the evolution of galaxies by
7 bly history of model galaxies in two clusters, and found
disturbing the kinematics of the stellar and gaseous
2
that BCGs acquire 35% of their final mass via mergers,
5 components, which induces morphology transformation,
andthefractionsmonotonicallydecreasewithincreasing
7 size growth, star formation, and active galactic nuclei
absolute magnitudes of galaxies. Lee & Yi (2013, here-
0 (AGNs) activities (e.g. Kauffmann & Haehnelt 2000;
after LY13) provide a quantitative prediction of the ex
. Springel et al. 2005; Daddi et al. 2005; Trujillo et al.
1 situ fractions of a complete set of galaxies in a cosmo-
2006; Croton et al. 2006; Schawinski et al. 2006;
0 logical volume as a function of the final stellar mass:
Cox et al. 2008; Naab et al. 2009; Hopkins et al. 2010;
7 van Dokkum et al. 2010; Oser et al. 2012; Ji et al. 20%, 40%, and 70% for logM∗/M⊙ ∼10.75, 11.25, and
1 11.75 galaxies at z = 0, respectively. According to
2014; Kaviraj 2014a,b; Kavirajet al. 2014). Therefore,
: them, in the main progenitors of local massive galax-
v galaxies, especially massive ones, are the end products
i of structure formation in the ΛCDM cosmology. ies (logM∗/M⊙ >11.5atz =0)galaxymergersbecome
X the leading channel in mass growth at z ∼ 2. For com-
Many puzzles in the evolution of galaxies are still
r waiting to be addressed, and there is no clear con- parison, there is no such transition in smaller galaxies
a sensus even on seemingly simple issues of the assem- (logM∗/M⊙ <11.0 at z =0).
Rapid advances in computing power have enabled
bly history of stellar masses in galaxies in a quanti-
us to carry out hydrodynamic simulations with reli-
tative aspect. Much effort has been made to system-
able resolution for numerous haloes in cosmological vol-
atically investigate these issues in a cosmological con-
umes.Oser et al.(2010)investigatedthestellarassembly
text. Semi-analytic models (SAMs) for galaxy forma-
historyof massive galaxiesby using zoom-insimulations
tion and evolution have been used to explore the for-
of 39 haloes. They showed that only ∼20% of the stars
mation and assembly history of stellar components of
galaxies in cosmological volumes by taking advantage in massive galaxies (logM∗/M⊙ & 11.5 at z = 0) are
formedinsitu,andtherestfallintothegalaxiesviamerg-
of their computing efficiency. Empirical downsizing
ers. The galaxies in the zoomed simulations performed
effects (e.g. Cowie et al. 1996; Glazebrook et al. 2004;
by Lackner et al. (2012) have ex situ fractions ∼ 1/3 of
Cimatti et al. 2004) are reasonablyreproducedin SAMs
those in Oser et al. (2010) in similarly massive galax-
1Korea Astronomy and Space Science Institute, 776, ies. The simulationsinthe twostudies wererunwithout
Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Ko- AGN feedback. The effect of AGN feedback on stellar
rea;[email protected] mass growth was investigated using zoomed simulations
2DepartmentofAstronomyandYonseiUniversityObservatory, by Dubois et al. (2013). AGN feedback effectively sup-
YonseiUniversity,Seoul03722, RepublicofKorea
2 Jaehyun Lee and Sukyoung K. Yi
pressesthe insitustarformationinmassivegalaxies,re- WeuseySAM(LY13)inthisinvestigationandprovide
sultingina30%higherexsitufractionthaninnon-AGN a summary of it in this section.
cases. In their zoomed simulations, Hirschmann et al.
2.1. Halo catalogue
(2015) showed that galactic winds play a role similar to
the AGN feedback in mass growth. To obtain a sufficient number of haloes in
Hydrodynamicsimulations forentire cosmologicalvol- logM200/M⊙ ∼ 10−15, we performed a cosmological
umes with moderate resolution have become avail- volume simulation with 10243 collisionless particles in
able recently (e.g.Vogelsberger et al.2014;Schaye et al. a 284Mpc (200h−1Mpc) periodic cube using the cosmo-
2015).Rodriguez-Gomez et al.(2016)examinedthecon- logical simulation code Gadget-2 (Springel 2005). The
tribution of mergers to the galaxy mass assembly initial condition of the simulation was generated using
history by using a complete set of galaxies identi- MPgrafic (Prunet & Pichon 2013), a parallel version
fied in a cosmological volume of the Illustris simula- of Grafic-1 (Bertschinger 1995). We adopted a set
tion (Vogelsberger et al. 2014; Genel et al. 2014). The of cosmological parameters derived from the seven-year
exsitufractionsofthegalaxiesinthevolumeareingood Wilkinson Microwave Anisotropy Probe observations
agreement with LY13, i.e., ∼ 20% for logM∗/M⊙ ∼ 11 by Komatsu et al. (2011), Ωm = 0.272, ΩΛ = 0.728,
and & 70% for logM∗/M⊙ ∼ 12 at z = 0. They and h = 0.704. A total of 125 snapshots were printed
also found that the ex situ components are less concen- out from the volume run, and Subfind (Springel et al.
trated than in situ components and half of them flow 2001) was used to search for sub-structures in the
intogalaxiesviamajormergersintheoverallmassrange friends-of-friends groups of the snapshots. The final
(logM∗/M⊙ >9 at z =0). halo catalogue consists of 118 time steps from z = 15.8
The aforementioned studies looked into the histo- to z =0.
ries of galaxy assembly primarily as functions of stel-
2.2. Halo merger trees
lar mass. However, the properties of galaxies are gov-
erned by halo evolution in the ΛCDM cosmology, as HalomergertreesaretheessentialbackbonesofSAMs,
implied by the strong correlation between the stellar and are composed of single or multiple branches. In
and halo masses (e.g Moster et al. 2010; Behroozi et al. this study, the branch linking the most massive progen-
2010, 2013). Furthermore, recent deep imaging obser- itor among all the progenitors of a halo at each time
vations revealed that a considerable fraction (∼ 40%) step is defined as the main branch of a halo merger
of bright (Mr < 20) early-type galaxies have post- tree(see De Lucia & Blaizot2007). Thesetrees arecon-
merger signatures in both isolated and dense environ- structed from the halo catalogue using the tree building
ments (van Dokkum 2005; Sheen et al. 2012). Post- codeySAMtm(Jung et al.2014),whichtracesthemost
merger signatures in satellite galaxies were expected to likely descendant or progenitor of a halo by comparing
be rare due to the high peculiar velocities in dense envi- theidentificationsofparticlesboundtothehaloesintwo
ronments. Yi et al. (2013) argued that the post merger snapshots. ySAMtm has been updated to provide the
features of non-central galaxies in dense environments number fraction of bound particles exchanged between
may have been pre-processedbefore becoming satellites. haloes. We assumethatthesamefractionofhotgasand
Thesestudiespointoutthatthegalaxyassemblyhistory diffuse stellarcomponentsaretransferredalongwith the
should be traced along with the evolution of environ- collisionless particle exchanges between haloes.
ments.
2.3. Semi-analytic model
The number of neighboring galaxies is widely used to
quantify the environments around galaxies in empirical ySAM allows a halo to form a galaxy in its cen-
studies, and this is closely connected to the host halo tral region (White & Rees 1978). In principle, a halo
mass (see Muldrew et al. 2012, and references therein). has one galaxy regardless of whether it is a host
Thus, host halo mass can be used as a reasonable proxy or sub. Satellite galaxies are treated as the cen-
of the environments of galaxies. Large cosmologicalvol- trals of subhaloes. ySAM performs tree cleaning
ume simulations are needed to cover a variety of envi- and repairing processes before planting galaxies onto
ronments. LY13investigatedthe originofstellarcompo- raw halo merger trees that possibly have problem-
nents only as a function of stellar mass without separat- atic branches (Muldrew et al. 2011; Elahi et al. 2013;
ingthemintocentralsandsatellites. Thesizeofthecos- Onions et al. 2013; Srisawat et al. 2013). Halo finding
mologicalvolumeLY13usedwas99.4Mpconasidewith codes sometimes fail to identify haloes embedded in
5123 collisionlessparticles, andless than 30 cluster-scale denseenvironmentsorclosetothemassresolutionlimit,
haloes (logM200/M⊙ > 14) being found in the volume. which eventually results in fragmented trees. ySAM
Up-to-datehydrodynamiccosmologicalsimulationscover removes any host halo branches that disappear with-
a scale of volumes similar to LY13 , which are not large out descendants before z = 0 and subhalo branches
enough to harvest many cluster-scale haloes. Therefore, that are identified to be newly formed with no pro-
semi-analyticapproachesarestilleffectiveforinvestigat- genitor. ySAM analytically calculates the orbits and
ing galaxy evolution in larger cosmological volumes. As mass of the subhaloes that merge into host haloes in
a follow-up of LY13, this study aims to separately scru- the raw merger trees before reaching the central re-
tinize the mass assembly history of central and satellite gions of their hosts (see Lee & Yi 2013; Lee et al.2014).
galaxies as a function of halo and stellar mass using our We adopt the prescriptions for gas cooling proposed
own SAM. by White & Frenk (1991). The prescription for quies-
cent star formation was updated from the original pre-
scription in ySAM. Star formation in a disk is per-
2. MODEL
mitted when the surface density of a cold gas disk is
Formation and assembly history of galaxies 3
TABLE 1
List offree parameterstunedforthe modelcalibration
Parameter Description Fiducialvalue Tuningrange
fscatter1 Fractionofstellarmassinsatellitesscatteredbymergers 0.4 0.2-0.5
αSF2 Starformationefficiencyofcoldgasdisks 0.075 0.02-0.10
ǫSN3 EfficiencyofSNfeedback 1.5 0.5-2
0
αSN3 SNfeedbackpower-lawslope 2.9 2-3
VSN3 CharacteristicvelocityofSNfeedback(kms−1) 250 150-250
fBH4 ColdgasaccretionefficiencyontoSMBHsinducedbymergers 0.035 0.01-0.04
κAGN5 EfficiencyofradiomodeAGNfeedback 3.5×10−5 10−5−10−4
αAGN5 RadiomodeAGNfeedbackpower-lawslope 2.3 2-3
VAGN5 CharacteristicvelocityofradiomodeAGNfeedback(kms−1) 150 150-250
Note: 1 Murante et al. (2004). 2 Eq. 16 in Croton et al. (2006). Sincethisprescription allows cold
gas disks to form stars when their surface densities exceed critical values, this efficiency is higher
than that (0.02) of the original prescription of ySAM (Eq. 5 in LY13) in which star formation
rates are in proportion to the total amount of cold gas. 3 Eq. 12 in Somerville et al. (2008). The
characteristic velocity fixed at 200 km s−1 in the equation was adjusted in this study. 4 Eq. 2
inKauffmann & Haehnelt(2000). 5 Eq. 10inCroton et al.(2006). Thecharacteristicvelocityand
the power fixedat 200 km s−1 and 3 in theequation were adjusted in this study.
larger than a critical density (Croton et al. 2006). We relation was used as the secondary calibration point in
usetheprescriptionsforsupernovafeedbackandmerger- our model. Three different observations with error bars
induced starbursts proposed by Somerville et al. (2008). and P(M |M ) of the fiducial model are shown
BH bulge
Quasar and radio mode feedback is implemented into in panel (d) of Figure 1. The red, blue, and green
ySAM as proposed by Kauffmann & Haehnelt (2000) crosses indicate the empirical M − M relation
BH bulge
andCroton et al.(2006). Wealsotracethemasslossand derived by Ha¨ring & Rix (2004), Kormendy & Bender
chemicalenrichmenthistoryofindividualstellarpopula- (2013), and McConnell & Ma (2013), respectively. The
tions in galaxies. Further details can be found in LY13. P(M |M ) distribution of our model is within the
BH bulge
observationalscatter. Anotablefeatureisthatthedistri-
2.4. Model calibrations butionofthe model atlogMbulge/M⊙ >11is muchnar-
rower than that in the low mass range. This is because
ySAMwas calibratedfor the cosmologicalvolume de-
the main channel that builds up bulges at the massive
scribed in §2.1 by tuning the set of free parameters
endisgalaxymergers,whichalsofeedtheSMBHsbyin-
listed in Table 1. More parameters are used in the pre-
jectinggasintoverycentralregionsorbyinducingSMBH
scriptions of ySAM (see LY13, and references therein).
mergers in our model. Dry mergers strengthen the rela-
Most of them are, however, fixed and we have mainly
tionship in the later stages of the evolution of massive
adjusted the listed free parameters that regulate feed-
galaxies. On the other hand, disk instability becomes
back and star formation efficiency. Figure 1 shows the
significantin the growthof(pseudo) bulges for less mas-
fitting of our fiducial model. The galaxy stellar mass
sive galaxies along with mergers. This results in a less
function (GSMF) is adopted as the primary calibration
point for ySAM. The panel (a) in Figure 1 displays tight MBH −Mbulge relation at logMbulge/M⊙ < 11, as
suggestedby the empirical studies (see Kormendy & Ho
two empirical GSMFs along with our fiducial model at
2013). This model is used as a fiducial model in this
z = 0. The GSMF marked by blue symbols comes
study.
from Panter et al. (2007), and the red symbols are a
composite GSMF of Baldry et al. (2008), Li & White
(2009), and Baldry et al. (2012). The two empirical 3. RESULTS
GSMFs are in goodagreementoverall,eventhough that All of the galaxies in ySAM are born as the central
of Panter et al. (2007) has a slightly higher massive end galaxy of each halo. Thus, the final galaxy of a halo
(M∗ > 1011M⊙). Our fiducial model is located in be- mergertreecomposedofNbranchesevolveswithamax-
tween these two GSMFs. The panel (b) in Figure 1 imum of N-1 galaxy mergers. The galaxies that grow
shows the evolution of the global star formation den- along the main branches of the halo merger trees are
sity (GSFD) overthe cosmic time. The empiricalGSFD called the main or direct progenitors of the final galax-
that was compiled and modified by Panter et al. (2007) ies. The stars formed in the main progenitors are clas-
is marked by red crosses. In panel (c), one can see the sified as in situ components, and those that are formed
star formation rate functions (SFRFs) of the empirical outside and then come into the main branches are la-
data (Gruppioni et al. 2015) and our fiducial model at belled as ex situ components. In this definition, the
z ∼ 0.15 for M∗ > 1010M⊙. The GSFD and SFRF stellar mass M∗ of the galaxy is the sum of the mass
are not calibration points in our model, but are used to of the two components, i.e., M∗ = Minsitu + Mexsitu,
cross-check whether our model reproduces reliable star following a conventional nomenclature (e.g. Oser et al.
formation histories. 2010;Lee & Yi2013;Rodriguez-Gomez et al.2016). We
A tight correlation between the mass of supermassive simply assume that the formation of in situ components
blackholes(SMBHs)andbulgestellarmasshasbeendis- is a self-assembly process. A host halo that habors N
covered (Magorrianet al. 1998; Marconi & Hunt 2003; subhaloes has one central galaxy and a maximum of N
Ha¨ring & Rix 2004; Hu 2009; Sani et al. 2011). This satellite galaxies.
4 Jaehyun Lee and Sukyoung K. Yi
Fig.1.— Fitting of the fiducial model in this study. (a) Galaxy stellar mass function at z ∼ 0. The blue symbols mark the empirical
GSMFderivedbyPanter etal.(2007). TheredsymbolsarethecompositeGSMFofthreedifferentempiricalGSMFs(Baldryetal.2008;
Li&White2009;Baldryetal.2012). ThemodelMFisindicatedbytheblacksolidline. (b)Globalstarformationdensityevolution. The
redcrossesaretheempiricaldata(Panter etal.2007)andtheblacksolidlinedisplaysthemodelevolution. (c)Starformationratefunction
atz∼0.15forM∗>1010M⊙. Theredsymbolspresenttheempiricaldata(Gruppionietal.2015). (d)Thesupermassiveblackhole-bulge
stellarmassrelation. Thegreysolidline,darkshade,andlightshadingindicatethemean,16−84thpercentiledistribution,and2.5−97.5th
percentile distribution of P(MBH|Mbulge), respectively. The red, blue, and green data points with error bars are from H¨aring&Rix
(2004),Kormendy&Bender(2013),andMcConnell&Ma(2013),respectively.
3.1. Formation and assembly history of stellar mass halfmassformationtime ofearlytype galaxiesusingthe
Sloan Digital Sky Survey.
We quantify the star formation history of a galaxy
LY13 found an upsizing trend in the assembly time
by finding the redshifts z by which half of the stel-
form of stellar mass, which is directly opposite to the down-
lar populations found in the final galaxies have been
sizing nature of formation time. This result is consis-
formed. The assembly time of a galaxy is defined as
tentwith recentobservations.Bundy et al.(2009) found
the epochz atwhichthe stellarmassofthe main
assembly fromthe GOODSfield thatthe pairfractionofredmas-
progenitor reaches half of the final mass. The equiva-
lencez =z ismadeonlywhengalaxiesevolve sivespheroidals(logM∗/M⊙ >11)ishigherthanthatof
form assembly smaller galaxies at z ∼ 1. They expected that the pairs
along single-branch merger trees. Figure 2 shows the
would eventually merge with each other, and form mas-
distributions of z and z −z of the central
form form assembly siveearlytypes.Matsuoka & Kawara(2010)showedthat
galaxies in the stellar-to-halo mass plane at z = 0. The
solid,dashed,anddottedlinesmarkthemedian,16-84th the number density of massive galaxies (logM∗/M⊙ ∼
11.5−12)increasesfasterthanthatoflessmassivegalax-
percentile distribution, and 2.5-97.5th percentile distri-
bution of P(M∗|M200). The downsizing trend is clearly ioefst(hloegmMa∗s/sMive⊙g∼ala1x1i−es1a1p.5p)efaorrt0o<bze <qu1e.ncThheed.mCajoonrsitey-
shownasafunctionofthehalomass. Thisfigureimplies
quently,mergersaretheir mostlikelymassgrowthchan-
that the empirical downsizing trend in which more mas-
nel during the period of time. In our fiducial model, the
sive galaxies have older stellar ages originates from the
centrals of more massive haloes have younger assembly
dependence of z on the halo mass and stellar-to-halo
form times, which results in the increase of z −z
massrelation. Theformationtimeofverymassivegalax- form assembly
with increasing halo mass (the right panel of Figure 2).
ies (logM∗/M⊙ > 11.5 at z = 0) is found at zform > 2, In summary, more massive galaxiesare older in terms of
inagreementwith Thomas et al.(2010)who derivedthe
Formation and assembly history of galaxies 5
Fig.2.— Left: Distribution of formation redshifts by which half of the stellar mass in central galaxies at z = 0 has been formed in
the stellar-to-halo mass plane. Right: Redshift differences between the formation and assembly epochs when half of the stellar mass is
locatedinthefinalcentrals. Bluerwhenzform∼zassembly. Theblacksolid,dashed,anddottedlinesmarkthemedian,16-84thpercentile
distribution,and2.5-97.5thpercentiledistributionofP(M∗|M200),respectively.
formationages but relativelyyoungerin terms ofassem- 2011;Steinhauser et al.2012). Inaddition,thereislittle
blyages(De Lucia et al.2006;De Lucia & Blaizot2007; opportunity to increase their mass via mergers.
Guo & White 2008; Jim´enez et al. 2011; Lee & Yi 2013; We trace the mass growth histories of central galax-
Lee et al. 2014), and this trend originates from the halo ies in the stellar-to-halo mass plane. Figure 4 shows
mass assembly. the mean mass evolution tracks of the main progeni-
tors of galaxies binned by final mass. Since we de-
3.2. Origin of stellar components fined M∗ = Minsitu + Mexsitu, the mass growth rate
3.2.1. Ex situ fractions in the stellar-to-halo mass plane of a galaxy at an epoch is M˙∗ = M˙insitu + M˙exsitu.
The black solid lines represent M˙ ≥ M˙ phase
We quantifiedthe overallcontributionof galaxymerg- insitu exsitu
and the dotted lines represent the opposite. The color
erstostellarmassgrowthbymeasuringthefractionofex
code of the filled circles indicates redshifts. It can be
situ components in galaxies, i.e., fexsitu = Mexsitu/M∗. seen that halo mass regulates which channel is domi-
Figure 3 shows the f distribution of central and
exsitu nant in mass growth. The central galaxies of the most
satellite galaxies in the stellar-to-host halo mass plane
at z = 0. The f distribution of the centrals has massive haloes (logM200/M⊙(z = 0) ∼ 14.7) enter
exsitu the merger-dominant phase at z ∼ 2 while those at
a strong correlation with M , but its dependency on
M∗ is not clear. This resul2t00suggests once again that logM200/M⊙(z = 0) ∼ 13.2 only reach this phase un-
til z = 0. This plot shows that galaxies migrate to the
the increase in fexsitu with increasing M∗ demonstrated merger-dominantphasewhentheirhosthalomassbegins
by previous studies (e.g. Oser et al. 2010; Lackner et al.
2012;Lee & Yi2013;Rodriguez-Gomez et al.2016)may to exceed ∼ 1013M⊙. As mentioned above, more merg-
ersinthecentralsoflargerhaloescauseearlierquenching
be a derivative of the f −M and the stellar to
exsitu 200 and higher ex situ fractions. Galaxies residing in haloes
halo mass relations.
The stellar-to-halomassrelationof satellites is broken belowlogM200/M⊙ ∼13increasetheirstellarmassindi-
rectly proportion to the increase in their halo mass. For
up as haloes are stripped during orbitalmotion in dense
environments (e.g. Boylan-Kolchinet al. 2008). There- example, central galaxies at logM200/M⊙(z =0)∼12.7
experience1.4dexofhalomassgrowthbetweenz =4−0
fore,thef distributionofsatellitesintherightpanel
exsitu andtheir stellar mass increasesto almostthe same scale
of Figure 3 is plotted as a function of their host halo
during the same period of time. On the other hand,
mass. As the stellar-to-halo mass relation is shuffled, no
halo mass growth does not accompany the same rate of
correlationwas found between the f distribution of
exsitu stellar mass growth in the most massive group. This is
satellites and their host halo mass. However, the corre-
because star formation is suppressed by strong feedback
lation between f and the mass of satellites appears
exsitu and not all of the stellar mass is concentrated in the
tobe clearerthanthatofcentrals. Whenthey areinthe
central regions. Stars in massive haloes are located in
same halo, satellite galaxies are generally less massive
satellite galaxies or intra-cluster (Feldmeier et al. 2002;
than centrals mainly because of low mass growth rates
Gonzalez et al.2005)as wellasinthe centralgalaxiesof
afterbecomingsatellites. Tidalorrampressurestripping
massive haloes.
effectively removesgas reservoirsin satellites,eventually
The peak of the stellar-to-halo mass fraction is
quenching star formation activities (Gunn & Gott 1972;
Abadi et al. 1999; Quilis et al. 2000; Chung et al. 2007; found at logM200/M⊙ ∼ 12 as logM∗/M200 ∼
−1.5 (Moster et al. 2010; Behroozi et al. 2010, 2013).
Tonnesen & Bryan 2009; Yagi et al. 2010; Kimm et al.
6 Jaehyun Lee and Sukyoung K. Yi
Fig.3.— The fractions of ex situ components in the stellar-to-host halo mass plane. Left and right panels are for central and satellite
galaxies,respectively. TheM200 ofthesatellitesistheirhosthalomass.
atz =0. Welookintohowthegalaxiesgainthatpartic-
ularly large M∗/M200 ratio. As the averaged evolution
track of the galaxies in the box marked by A indicates,
theyundergoseverehalostrippingatz <1. Theybarely
increase their stellar mass during the period of time be-
cause of gas loss. Besides, the degree of halo stripping
is not harsh enough to significantly strip stellar compo-
nents in central regions (Smith et al. 2016). All of the
central galaxies are typically located in dense environ-
mentswheretidalforceexertedbyneighbouringmassive
haloes disturbs small systems.
3.2.2. Ex situ fractions at a given stellar and halo mass
The marginal distribution of f in terms of M
exsitu 200
or M∗ is plotted in Figure 5. The grey shading dis-
plays the percentile distribution of P(f |M). Panel
exsitu
(a) demonstrates the gradual increase of f of the
exsitu
centrals with increasing M . However, in panel (b)
200
the f of the central galaxies stays below 0.1 at
exsitu
logM∗/M⊙ < 10.5 and rises sharply in logM∗/M⊙ >
11. This is because galaxies with logM∗/M⊙ ∼ 11 at
z = 0 are hosted by haloes in the wide mass range of
logM200/M⊙ ∼12−14.5. Therelationbetweenthestel-
larand halo massescauses the largedispersionof f
exsitu
Fig.4.—Meanhaloandstellarmassevolutionhistoriesofgalax- around logM∗/M⊙ = 11. The satellites show a slightly
iesonthestellar-to-halomassplane. Thegreysolidline,darkshad- lower fexsitu −M∗ relation than centrals, but the over-
ing, and light shading show the median, 16−84th percentile dis- all trend is similar, as shown in panel (c). Specifically,
atrtibzu=tio0n.,Tahnedfi2l.l5ed−r9e7d.5ctihrclpeeirncdenictailteeddibstyriAbuitsiotnheofavPer(Mag∗ed|Mm20a0s)s the fexsitu of the most massive satellites is comparable
ofthegalaxies inthemassrangemarkedbythedashed box. The to that of the centrals. This suggests that mergers are
otherfilledredcirclesindicatetheaveragedgalaxiesbinnedbyev- essentialtoformmassivegalaxies. Suchmassivegalaxies
ery 0.5 dex of halo mass from logM200/M⊙ = 11 at z = 0. The were centrals until recently, and have only just became
blacksolidanddottedlinesshowmassevolutiontracksofthemain
satellites.
progenitors of the averaged galaxies and the colored circles point
out redshifts. The epochs when in situ star formation or mergers The black solid and dotted lines with colored symbols
leadmassgrowtharemarkedbysolidordottedlines,respectively. in the upper panels of Figure 5 show the averaged evo-
lution tracks of the main progenitors in the f −M
exsitu
However, the galaxies in the dashed box have notably planes. The color code and line styles are the same as
large fractions. Their number fraction is actually neg- thoseinFigure4. Thegalaxiesarebinnedby1dexfrom
ligible, far outside the 97.5th percentile distribution of logM200/M⊙ = 12 or 0.5 dex from logM∗/M⊙ = 10
P(M∗|M200). Only 87 galaxies are found in the box out at z = 0. The main progenitors of the galaxies in
ofthe100,000plusgalaxiesatlogM200/M⊙ =11.0−11.2 the different mass bins are marked by different symbols.
Formation and assembly history of galaxies 7
Fig.5.— Upper: Marginal fexsitu distribution in terms of halo or stellar mass. The grey solid lines, dark shading, and light shading
showthemedian,16−84thpercentiledistribution,and2.5−97.5thpercentiledistributionofP(fexsitu|M)atz=0. Eachblacklinewith
thesamesymboldisplaysthemeanfexsitu−M evolutionofthemainprogenitorsofgalaxiesbinnedbythefinalhaloorstellarmass. The
epochswheninsitustarformationandmergersleadmassgrowtharemarkedbysolidanddottedlines,respectively. Thecoloredsymbols
indicate the five different redshifts, according to the color code in panel (a). The most massive, second most massive, and third most
massive groups are indicated by red circles, stars, and squares, respectively, in panels (b) and (c) and correspond to the massive galaxy
groups inLY13. Bottom panels: Redshiftevolution ofthe fexsitu−M relation. Thesolidlineswiththeerrorbarsmarkthe medianand
16-84thpercentile distributionoffexsitu. ThecolorcodeshowninPanel (a)isalsousedtoindicatetheredshifts. Massbinsincludingat
leastfivegalaxiesareplottedinallthepanels.
Panel (a) illustrates that galaxies that become merger- z ∼4likelyhavegrowthhistoriesradicallydifferentfrom
dominant before z = 0 are finally hosted by haloes of local low mass haloes. On the other hand, high redshift
logM200/M⊙ >13. In panels (b) and (c), the transition galaxies have a low median fexsitu in panels (e) and (f).
takesplaceonly inthe mostmassivegroupsofbothcen- The most massive haloes are always rare and their cen-
trals and satellites. Stochastic effects cause the uneven tralshavestellarmasseswithlargerdispersionsathigher
tracks of the most massive satellites in panel (c). redshifts. In other words, the stellar-to-halo mass rela-
LY13 provided a quantitative prediction of the mean tion is less tight at higher redshifts. The ex situ fraction
fexsituasafunctionofthefinalstellarmasswithoutsepa- beginstorapidlyincreaseatlogM∗/M⊙ =11,whichim-
ratinggalaxiesintocentralandsatellites: 20%,40%,and pliesthatgalaxymergersareessentialtobuildupgalax-
70% for the galaxies in logM∗/M⊙ =10.5-11, 11-11.5, ies above logM∗/M⊙ = 11. On the contrary, galaxies
and 11.5-12 at z =0, respectively. The red filled circles, similar in mass to the Milky Way (logM∗/M⊙ ∼ 10.5)
stars,andsquares,inpanels(b)and(c)ofFigure5indi- would increase their stellar mass mostly from in situ
cate the mean f of the three groups binned by the star formation, regardless of whether they are centrals
exsitu
final stellar mass. Because the majority of the galax- or satellites.
ies in the three groups are centrals, the fexsitu − M∗
relation of the centrals is comparable to that of LY13. 3.3. Evolution history of the two mass growth channels
The fexsitu − M∗ relation and the large dispersion at 3.3.1. Specific mass growth histories of the main
logM∗/M⊙ ∼ 11 are in good agreement with LY13 progenitors
and Rodriguez-Gomez et al. (2016).
The previous sections show that the leading mass
The bottom panels ofFigure 5 demonstrate the evolu-
growthchannelschangeovertime,dependingonthehalo
tion of the f −M relation at z ∼ 0−4. The dif-
exsitu orstellarmass. Inordertoexaminethetimeevolutionof
ferent redshifts are indicated by the color codes used in
the contributionofmergersandinsitustarformationto
panel(a). Atagivenhalomass,thecentralgalaxieshave
stellarmassgrowth,wemeasurethe specific stellarmass
a higher f at higher redshifts. This is because the
haloesthatexsshitouwupathigherredshiftsarelocatedinrel- accretionrate(SSAR) M˙exsitu/M∗ in the sameway that
thespecificstarformationrate(SSFR)isdefined. Inthis
atively denser environments than those having the same
study,accretionindicatestheinfallofstellarcomponents
mass at lower redshifts. Therefore, low mass haloes at
into galaxies only via mergers.
8 Jaehyun Lee and Sukyoung K. Yi
Fig.7.— Transitionredshifts at which galaxy mergers becomes
thedominantchannelinmassgrowth. Thegreyshademarkgalax-
iesthatdonotexperiencethephasetransitionbyz=0.
mass via more mergers. These two phenomena give rise
toatransitionofdominantmassgrowthchannels. Merg-
ersbecometheprimaryprocessinmassgrowthuntilz=0
for the main progenitors of central galaxies with haloes
of logM200/M⊙ >13.
The main progenitors of the most massive centrals in
panel (b) enter the merger-dominant phase at z ∼ 1.
The SSAR of the second most massive group, however,
does not meet its SSFR at all. Galaxies in this group
are finally hosted by haloes in a wide mass range of
logM200/M⊙ ∼ 12−14.5. Some of the galaxies resid-
ing in haloes above the group scales (logM200/M⊙ >
13) finally settle into the merger-dominant phase, as
shown in panel (a). However, the majority of the sec-
ond massive group are the centrals of the smaller haloes
(12 < logM200/M⊙ < 13). Thus, the main progenitors
of the second most massive galaxies marginally stay in
the SSAR.SSFR phase by z = 0. This result is consis-
tent with Woo et al. (2013), who found a strong corre-
lationbetweenthe quenchedfractionsofcentralgalaxies
Fig.6.—Evolutionofthemeanspecificstellarmassgrowthrate and their host halo mass. AGN feedback and decreasing
for the main progenitor galaxies binned by final halo or galaxy cooling efficiency naturally result in the trend found in
mass. The color code indicates the given mass ranges, and the
ySAM.
solid and dashed lines indicate the specific star formation rates
and specific stellar mass accretion rates via galaxy mergers, re- The evolution trend of the specific mass growth rates
spectively. ofsatellitesinpanel(c)appearstobealmostthesameas
that of the centrals in panel (b) in early epochs. This is
Figure6showstheSSFRsandSSARsofthemainpro- primarilybecausetheyallusedtobecentralsathighred-
genitors of galaxies grouped by final mass and status. shifts. As they graduallybecome satellites with decreas-
In all the panels, the SSFRs are lower in more massive ing redshifts, their specific growth rates are suppressed.
galaxies, while the opposite is true for SSARs, which Becausethesatellitesbarelymergewitheachother,their
gently and consistently decrease. However, the SSFRs SSARs are lower than those of the centrals. Environ-
rapidly decline by z ∼ 4 after which the decay rates de- mental effects, such as tidal and ram pressure stripping,
celerate. In all the panels, the two channels decrease suppressstarformationactivitiesinsatellitesbyblowing
similarly in the third and fourth most massive groups away gas reservoirs. However, AGN feedback is inactive
at z < 3. However, bigger groups experience a sharp in satellites due to little gas accretion. Therefore, the
decay in the SSFRs. As discussed in §3.2.1, galaxies en- most and second most massive satellites eventually have
ter a merger-dominant phase when their host halo mass slightly lower SSFRs than those of the centrals. The
increases above logM200/M⊙ ∼ 13 in our model. Cen- main progenitors of the most massive satellites exhibit
tral galaxies in larger haloes are effectively quenched by behavior similar to those of the most massive centrals.
more frequent AGN activities and acquire more stellar This is mostly because they only recently became satel-
Formation and assembly history of galaxies 9
lites. However, the SSARs of the other groups do not
even come close to their SSFRs.
The transition epochs of the two mass growth chan-
nels as a function of the final stellar mass are in good
agreementwithpreviousstudiesthatwerebasedonsemi-
analytic approaches (e.g. Lee & Yi 2013) and hydro-
dynamics (e.g. Oser et al. 2010; Rodriguez-Gomez et al.
2016). In Figure 7, the redshift transitions between
the two channels are plotted in the stellar-to-halo mass
plane. Thegreyshadingindicatesthemassrangesofthe
galaxies that stay in the star-formation-dominant phase
through z = 0 on average in each mass bin. The transi-
tions are found in galaxies that end up in haloes with
logM200/M⊙ & 13, as panel (a) of Figure 6 demon-
strates. Thissuggeststhatthehalomassevolutionplays
akeyroleinthetwo-phasescenarioofmassivegalaxyfor-
mation in which in situ star formation rapidly increases
thegalaxystellarmassatearlyepochsandmergersgrad-
ually build it up by z =0 (Oser et al. 2010).
3.3.2. Specific mass growth rates at each epoch
Thespecificmassgrowthratesofthemainprogenitors
in the previous section indicate how the galaxies cho-
sen at z = 0 have evolved over time. Thus, Figure 6
is plotted based on a theoretical viewpoint. However,
observations take a snapshot of the galaxies located at
various redshifts . In that sense, Figure 8 displays the
specific mass growthrates of galaxies binned by mass at
eachepoch. Themoremassivegalaxiesorthecentralsof
more massive haloes have higher SSARs and lower SS-
FRs. At a fixed stellar mass, the SSFRs decay by two
ordersofmagnitudeduringcosmictime,asshowninpre-
vious studies (Rodighiero et al. 2010; Karim et al. 2011;
Sparre et al. 2015; Furlong et al. 2015).
Cluster-scale haloes (logM200/M⊙ > 14) and very
massive galaxies (logM∗/M⊙ > 11.5) begin to appear
at z ≈2 in the co-movingvolume of this study. The SS-
FRs ofthe mostmassivegroupsarecomparableto those
oflessmassivegroupsforawhileafteremerginginallthe
panels. The SSFRs are sufficiently high at the moment
to increase the stellar mass by a factor of two within a
billion years. In our model, galaxies in the most mas-
sive ranges at early epochs have been built up by very
active star formation, along with galaxymergers. Rapid
halomassgrowthleadstoviolentbaryonicaccretioninto Fig. 8.—Meanspecificstellarmassgrowthrateofgalaxiesbinned
the central regions, eventually inducing very high star bythehaloorstellarmassateachepoch. Thecolorcodeandline
stylesarethesameasthoseinFigure6.
formation activities. However, the most massive groups
quickly experience a rapid drop in the SSFRs in all the
are always lower than those of centrals. Environmental
panels.
effects cause overall low SSFRs. Since satellite galax-
ThecentralgalaxiesofthehaloesinlogM200/M⊙ >13
ies are hardly involved in mergers with other satellites,
of panel (a) are in the merger-dominant phase most of
their SSARs are at least an order of magnitude lower
the time after they appear in all the panels. The differ-
thanthoseofthecentrals. Therefore,mergersdonotbe-
ences betweenthe SSFRs andthe SSARs increasein the
comeprimarymassgrowthchannelsinallgroups. Inour
massivehalogroupsascoldgasisdepletedandcoolingis
model,galaxymergersbetweensatellitesmainlyoccurin
furthersuppressedbyfeedback. Inthe middlepanel,the
sub groups that belong to host haloes that are not yet
two mass growth channels are almost equally important
virialized. Once the sub groups are dynamically dissoci-
for the second massive group of centrals (logM∗/M⊙ ∼
ated in dense environments, their member galaxies only
11.0− 11.5) all the time. In this panel, 0.5 dex more
fall into the central regions of their host haloes in our
massive central galaxies have SSARs 0.5 dex higher at
model.
z < 0.5. Consequently, a ten times larger stellar mass
fallsinto0.5dexmoremassivegalaxiesviamergers. Star
4. SUMMARY AND CONCLUSION
formation contributes an order of magnitude more to
mass growth than mergers in logM∗/M⊙ <11. LY13 examined the assembly history of stellar com-
The specific mass growthrates of satellites (panel (c)) ponents in galaxies as a function of final stellar mass
10 Jaehyun Lee and Sukyoung K. Yi
using semi-analytic approaches. Here we expand LY13 projection of their intrinsic halo mass dependence upon
in a cosmological context by investigating it in terms of the stellar-to-halo mass relation. When we looked into
extended parameter spaces using a larger cosmological the SSAR and SSFR evolution of galaxies in an empiri-
volume simulation. The size and resolution of the vol- calsense,i.e. binningthembygivenmassrangesateach
ume were designed to cover a wide range of halo masses epochwithnouseofprogenitor-descendantrelations,we
logM200/M⊙ ∼10−15. Thefiducialmodelofthisstudy foundthat mergersarea majorchannelfor massgrowth
was calibratedto fit a set of empiricaldata. We labelled at all times in the centrals of logM∗/M⊙ > 11 or the
the starsformedalongthe mainbranchesofhalomerger centrals of haloes with logM200/M⊙ > 13. However, in
trees as in situ components and the rest of the stars satellites, mergers are secondary or even negligible.
falling into galaxies via mergers as ex situ components. This study displayed a strong correlation between
The ΛCDM cosmology predicts earlier formation of the formation and assembly of galaxies and halo
primordial structures in denser environments and their mass which only represents local environments. In
hierarchical assembly over time. In this framework, the large scales, however, weaker correlations have been
formation and assembly of galaxies are expected to cor- found. Croton & Farrar (2008) compared the empirical
relate with the evolution of halo environments. In our luminosity function of void galaxies with their SAM,
model, we found that centrals of more massive haloes concluding that large-scale environments do not signif-
have older formation times and higher ex situ fractions. icantly affect galaxy properties but halo mass assembly
The marginal distribution of the ex situ fractions at isadecisivefactoringalaxyevolution.Jung et al.(2014)
z = 0 gradually increases with increasing halo mass. also presented a similar result using ySAM that galaxy
Theexsitucomponentsbecomethe majorityinthestel- growthratesarelargelyinsensitivetolarge-scaleenviron-
lar mass of the central galaxies in logM200/M⊙ > 13. ments. So, in sum, the evolution of local halo environ-
However, the distribution of ex situ fractions sharply mentsplaysaleadingroleintheformationandassembly
rises in terms of stellar mass with large dispersion in ofgalaxystellarmass. Centralgalaxiesindenseenviron-
logM∗/M⊙ > 11. This is because the central galaxies ments growwithvigorousgasinflow atearlyepochs and
at logM∗/M⊙ ∼ 11 are hosted by a wide range of halo the steady mergers of small structures over time. Some
mass logM200/M⊙ ∼ 12−14.5. As a result, they have galaxiesachievelogM∗/M⊙ ∼11eveninlowdensityen-
similar masses despite their diverse evolution tracks. vironments with active in situ star formation, but they
Satellite galaxies have slightly lower ex situ fractions come up againsta steep barrierto growingfurther with-
than centrals but the overall trend is similar. Like mas- outmergers. Once galaxiesarerelegatedto satellite sta-
sive centrals, massive satellites acquired a considerable tus, in situ star formation becomes the dominant chan-
fraction of their stellar mass via mergers mainly when nel for increasing mass despite the gradual suppression
they were centrals and have only recently become satel- of star formation activities due to environmental effects.
lites. The marginal distribution of the ex situ fractions Galaxy formation models are, of course, incomplete
evolves with decreasing redshifts. The centrals of the as yet and are unable to precisely describe the forma-
mostmassivehaloesalreadyreachf ∼0.5atz =4. tionofstellarmass(e.g.Sparre et al.2015;Furlong et al.
exsitu
The ex situ fraction rapidly increases as the galaxy stel- 2015; Knebe et al. 2015; Song et al. 2016). Nonethe-
lar mass begins to exceed logM∗/M⊙ ∼11. This can be less, the success of the concordance ΛCDM cosmology
interpreted to suggest that galaxy mergers are essential givescredibilitytotheeffortstounderstandgalaxymass
forbuildingupgalaxiesabovelogM∗/M⊙ ∼11,whether assembly, which is regarded as a consequential process
they end up becoming centrals or satellites. of structure formation in the cosmological framework.
Weexaminedthetimeevolutionofthespecificstarfor- This study demonstrates that similarly massive galax-
mationrates (SSFRs) and specific stellar mass accretion ies have a variety of evolution histories, depending on
rates(SSARs). First,wetracedthespecificgrowthrates their halo environments. Meanwhile, empirical studies
of the main progenitors of the galaxies grouped by final have found a considerable number of luminous galaxies
haloorstellarmass. The SSFRs ofthe mainprogenitors in low density environments as well as dense environ-
arealwayslowerinmoremassivegroupswhiletheSSARs ments (e.g. Croton et al. 2005; Khim et al. 2015). Mo-
behaveintheoppositemanner. Inveryearlyepochs,the tivated by these results, we will carry out a comparison
SSFRsfarexceedtheSSARsinallgalaxies,butthisdom- studyformassivegalaxiesthatendupwithsimilarprop-
inancerapidlydecreasesovertime. Furthermore,theSS- erties but reside in different local halo environments.
FRs decay even faster for more massive galaxies, which
results in a crossing of the two mass growth channels
in some cases. The transition takes place in the main
ACKNOWLEDGMENTS
progenitors of the central galaxies that finally reside in
the haloes of logM200/M⊙ > 13. In our model, this is We thank Rory Smith for his constructive comments
the mass range where the two phase scenario for mas- and proofreading. We acknowledge the support from
sive early types (Oser et al. 2010) is valid. With the the National Research Foundation of Korea (NRF-
aforementioned results, this suggests that the correla- 2014R1A2A1A01003730). Numerical simulations were
tion between the stellar mass and the empirical galaxy performed using the KISTI supercomputer under the
formation time (e.g. Cowie et al. 1996), and the frac- programme of KSC-2014-G2-003. S.K.Y. acted as the
tionofex situcomponentsproposedby theoreticalstud- corresponding author. This work was performed under
ies (e.g. Oser et al. 2010; Lackner et al. 2012; Lee & Yi thecollaborationbetweenYonseiUniversityObservatory
2013; Rodriguez-Gomez et al. 2016) may be merely the and Korea Astronomy and Space Science Institute.