On ths assembly history of stellar components in massive galaxies
aa r X i v : . [ a s t r o - ph . C O ] F e b Draft version August 20, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
ON THE ASSEMBLY HISTORY OF STELLAR COMPONENTS IN MASSIVE GALAXIES
Jaehyun Lee and Sukyoung K. Yi
Department of Astronomy and Yonsei University Observatory, Yonsei University, Seoul 120-749, Republic of Korea; [email protected]
Draft version August 20, 2018
ABSTRACTMatsuoka & Kawara (2010) showed that the number density of the most massive galaxies(log
M/M ⊙ = 11 . − .
0) increases faster than that of the next massive group (log
M/M ⊙ =11 . − .
5) during 0 < z <
1. This appears to be in contradiction to the apparent “downsiz-ing effect”. We attempt to understand the two observational findings in the context of the hier-archical merger paradigm using semi-analytic techniques. Our models closely reproduce the resultof Matsuoka & Kawara (2010). Downsizing can also be understood as larger galaxies have, on average,smaller assembly ages but larger stellar ages. Our fiducial models further reveal details of the historyof the stellar mass growth of massive galaxies. The most massive galaxies (log
M/M ⊙ = 11 . − . M/M ⊙ = 11 . − . M/M ⊙ = 10 . − . z = 0. The specific accreted stellarmass rates via galaxy mergers decline very slowly during the whole redshift range, while specific starformation rates sharply decrease with time. In the case of the most massive galaxies, merger accretionbecomes the most important channel for the stellar mass growth at z ∼
2. On the other hand, in-situ star formation is always the dominant channel in L ∗ galaxies. Subject headings: galaxies: evolution – galaxies: elliptical and lenticular, cD – galaxies: formation –galaxies: stellar content INTRODUCTIONDynamical realizations based on the concordanceΛCDM cosmology (e.g. Spergel et al. 2007) have beenremarkably successful at reproducing large-scale struc-tures in the universe (e.g. Springel et al. 2006). In thecommon perception of this paradigm, large galaxies growhierarchically through numerous galaxy mergers that fol-low mergers between dark halos.Supporting this view, galaxies with disturbed fea-tures have frequently been witnessed (e.g. Arp 1966;Schweizer & Seitzer 1988). With the advent of deep andwide field surveys, the arguments could be investigated ingreater detail. Recent studies based on ultra-deep imag-ing data are particularly noteworthy. From the µ r = 28mag arcsec − deep images, van Dokkum (2005) foundthat about 50% of red bulge-dominant galaxies in fieldenvironments show tidal debris. Merger galaxy fractionhas been found to be almost as high in cluster envi-ronments (Sheen et al. 2012). Kaviraj et al. (2007)and Kaviraj (2010) claimed that residual star formationfound in a large fraction ( ∼ < z <
1. From the GOODSfields, Bundy et al. (2009) found that the pair fractionof massive (logM / M ⊙ > .
0) red spheroidal galaxies ishigher than that of less massive systems (logM / M ⊙ ∼ . z .
1. Almost simultane-ously, from the UKIDSS and the SDSS II SupernovaSurvey, Matsuoka & Kawara (2010, hereafter MK10)found that, during z <
M/M ⊙ = 11 . − .
0) in-creased more rapidly than that of the next massive group(log
M/M ⊙ = 11 . − . z .
1, massive galaxies are mainly brought up via merg-ers.Not all observations naively support the hierarchi-cal merger picture. The tight color-magnitude rela-tion found among early-type galaxies is more simply, al-beit not exclusively, explained by monolithic formationscenarios (e.g. Bower et al. 1992; Kodama & Arimoto1997). Furthermore, the “downsizing” effect, wherelarger galaxies appear to be older and thus suspectedto have formed earlier, seems to be inconsistent withthe new paradigm (Cowie et al. 1996; Glazebrook et al.2004; Cimatti et al. 2004). On the face of it, the in-consistency seems a counter-evidence of the hierarchi-cal picture; however, some studies have pointed outthat downsizing can be understood by the hierarchicalparadigm reasonably enough. Based on semi-analyticmodels, De Lucia et al. (2006) showed that the star for-mation rates of all the progenitors of more massive galax-ies peak earlier and decrease faster than those of lessmassive galaxies. In fact, downsizing could be a nat-ural result of the hierarchical clusterings of dark ha-los. Neistein et al. (2006) demonstrated that downsiz- Jaehyun Lee and Sukyoung K. Yiing appears in the total (combined) mass evolution ofall the progenitors of a dark matter halo. If the stel-lar mass of a galaxy correlates with the mass of its darkmatter halo (Moster et al. 2010), downsizing may verywell originate from the bottom-up assembly of dark mat-ter halos. Using semi-analytic approaches, many stud-ies have shown that the assembly and formation his-tory of stellar components, especially in massive, redand luminous, or elliptical galaxies, can be different inthe hierarchical Universe (Kauffmann 1996; Baugh et al.1996; De Lucia et al. 2006; De Lucia & Blaizot 2007;Almeida et al. 2008). More direct hydrodynamic simu-lations performed for smaller volumes have yielded con-sistent results (Oser et al. 2010; Lackner et al. 2012).In this study, we look further into the details of the as-sembly history of stellar components in massive galaxies.We use semi-analytic approaches because these are moreeffective for constructing models of a large volume of theuniverse. Motivated mainly by the empirical results ofMK10, we investigate the factors that drive the growthof galaxy stellar mass as a function of time and mass. MODELWe have developed our own semi-analytic model forgalaxy formation and evolution. In this section, webriefly introduce physical ingredients, with more focus onthe prescriptions that play important roles in this study.2.1.
Dark Matter Halo Merger Trees and GalaxyMergers
In the context of the two-step galaxy formation the-ory (White & Rees 1978), the first step involves the con-struction of dark halo merger trees. We ran dark mat-ter N-body volume simulations using the GADGET-2code (Springel 2005). The simulation was performed us-ing the standard ΛCDM cosmology parameters derivedfrom the WMAP 7-year observations, Ω m = 0 . Λ =0 . σ = 0 . b = 0 . = 71 km s − Mpc − (Jarosik et al. 2011). The periodic cube size ofthe simulation was 70 h − Mpc on the side with 512 colli-sionless particles, mass of a particle was 1.9 × h − M ⊙ ,and mass resolution of a halo was ∼ h − M ⊙ . Weidentify halo structures in the simulation box, usinga halo finding code developed by Tweed et al. (2009),which is based on the AdaptaHOP (Aubert et al. 2004).Halo merger trees were generated by backtracing the in-fall histories of subhalos with increasing redshift. Wecalculate galaxy merger timescales, using the positionalinformation of subhalos extracted from our N-body sim-ulation. In this study, we assume that the mass distribu-tion of dark matter halos basically follows the Navarro-Frank-White (NFW) profile (Navarro et al. 1996).Subhalos can disappear before arriving at central re-gions if they are heavily embedded in their host halo den-sity profiles or their mass decreases below the resolutionlimit of our numerical simulation. We take these numeri-cal artifacts into consideration. Thus, once a halo entersinto a more massive halo, we additionally calculate itsmerger timescale, t merge , using the following fitting for-mula suggested by Jiang et al. (2008): t merge (Gyr) = 0 . ǫ . + 0 . C M host M sat M host /M sat )] R vir V c , (1)where ǫ is the circularity of the orbit of a satellite halo, C is a constant, approximately equal to 0.43, M host isthe mass of a host halo, M sat is the mass of a satellitehalo, R vir is the virial radius of a host halo, and V c isthe circular velocity of a host halo at R vir . If a subhalodisappears within 0 . R vir of its host halo, a galaxy inthe subhalo is regarded as having merged with its cen-tral galaxy. On the other hand, if it disappears out-side 0 . R vir , we assume that the galaxy in the subhalomerges with its central galaxy at t merge given by Eq. 1after the subhalo becomes a satellite of its host halo.In that case, we consider dynamical friction to analyt-ically compute the positions and velocities of subhalos.We adopt the dynamical friction prescription introducedby Binney & Tremaine (2008):d ~v d t dynf = − GM sat ( t ) r lnΛ (cid:18) V c v (cid:19) ( erf (cid:18) vV c (cid:19) − √ π (cid:18) vV c (cid:19) exp " − (cid:18) vV c (cid:19) ~e v , (2)where M sat is the mass of a subhalo, which is initiallydefined as the mass at a previous time step after whichthe subhalo cannot be resolved in the N-body simulationanymore, r is the distance between the subhalo and thecenter of its host halo, ln Λ is a Coulomb logarithm withΛ = 1 + M host /M sat adopted by Springel et al. (2001), V c is the circular velocity of the host halo at the virialradius, and v is the orbital velocity of the subhalo.During the orbital motion of a satellite halo in its hosthalo, the dark matter of the satellite halo is stripped dueto dynamical friction. If the satellite is resolved in anN-body simulation, dark matter of the satellite would benaturally stripped. On the other hand, if the halo is notresolved in the simulation but considered to orbit aroundits host halo, stripping due to dynamical friction shouldbe computed analytically. We evaluate the amount ofdark matter stripped by dynamical friction by adoptingthe concept of the sphere of influence ( r soi ) within whichdark matter particles are bound to the satellite halos,using the following formula (Battin 1987): r soi ∼ r "(cid:18) M sat , tot M host ( < r ) (cid:19) − . (1 + 3 cos θ ) . + 0 . θ θ θ ! − , (3) where r is the distance between the centers of the satel-lite and its host halos, M sat , tot is the total (baryon+darkmatter) mass of the satellite halo, M host ( < r ) is the to-tal mass of the central halo within r , and θ is the anglebetween the line connecting the particle to the center ofthe satellite halo and the line connecting the centers ofthe satellite and the host halos. During a time step, δt ,we assume that a satellite halo loses δM sat = M sat ( r >r soi ) δt/t dyn , where t dyn is the dynamical timescale of thesatellite halo, and M sat ( r > r soi ) is the mass of darkmatter outside r soi of the satellite halo.We assume that stellar components in satellite galax-ies merging with their hosts constitute the bulge com- In this paper, galaxies that are not the central one in a halo areall “satellite”. Only one galaxy is qualified as the central galaxy ofa halo and all the rest, regardless of brightness, are satellites. ssembly history of massive galaxies 3ponent of the host. If the mass ratio of bary-onic mass ( m cold + m ∗ ) between merging galaxies, m secondary /m primary , is greater than 0.25, then it is as-sumed that all the stellar components of the host galaxyquickly become bulge components of the remnant, aswell.Empirical studies have shown that intra-cluster lightoriginates from the extended diffuse stellar componentsof the brightest galaxies in groups or clusters (e.g.Feldmeier et al. 2002; Gonzalez et al. 2005; Zibetti et al.2005). They suggested that diffuse stellar componentsare the stars scattered from satellite galaxies duringtidal stripping or mergers into central galaxies. It hasbeen suggested that 10-40% of stellar components insatellite galaxies turn into diffuse stellar components ineach galaxy merger (Murante et al. 2004; Monaco et al.2006). We adopt the value of 40% in this study because itresulted in the best reproduction of empirical data. Theamount of stellar mass that a central galaxy acquires viamerger is (1 − f scatter ) M ∗ , sat , where f scatter is the fractionof scattered stellar components and M ∗ , sat is the stellarmass of a satellite galaxy.2.2. Gas Cooling, Star Formation, and Recycling
We assume that the baryonic fraction in accreteddark matter follows the global baryonic fraction, Ω b / Ω m .Baryons are accreted onto dark halos and shock-heatedto become hot gas components.Gas accretion onto a galactic disk plane via atomiccooling of hot gas is calculated based on the model pro-posed by White & Frenk (1991). The cooling timescaleat distance r from the center of a halo is estimated bythe following formula: t cool ( r ) = 32 ρ g ( r ) kTµ ( Z, T ) m P n e n i Λ( Z, T ) , (4)where ρ g is the gas density within radius r of a darkmatter halo, T is the temperature of gas, assumed tobe the virial temperature in the model, Z is metallicity, µ ( Z, T ) is the mean molecular weight of gas with Z and T , m P is the mass of a proton, n e is the number density ofelectrons, n i is the number density of ions, and Λ( Z, T )is the cooling function with Z and T . The values of µ ( Z, T ), n e , n i , and Λ( Z, T ) are determined by referringto Sutherland & Dopita (1993). We do not include self-consistent chemical evolution in our calculation. Instead,we take the metallicity of hot gas components in halos asa constant, 0 . Z ⊙ , which is comparable to the metallicityof observed clusters with various masses (Arnaud et al.1992). Because the cooling function, Λ( Z, T ), is sensi-tive to metallicity, our results should not be taken tooliterally. However, relative analysis, a main tool of thisstudy, is affected little by the details in the treatment ofchemical evolution.It is assumed that the gas density follows a sin-gular isothermal profile truncated at R vir : ρ g ( r ) = m hot / (4 πR vir r ). Substituting the formula for ρ g ( r )in Eq. 4 and adopting the dynamical timescale of ahalo, t dyn , as t cool , one can derive the cooling radius, r cool , within which hot gas can cool within t cool . Forthe case of r cool > R vir , the cooling rate is rather re-strained by the free-fall rate than the cooling rate, sothat ˙ m cool = m hot / (2 t cool ). In contrast, if r cool < R vir , ˙ m cool = m hot r cool / (2 R vir t cool ).In our model, stars can be formed through a quiescentmode, in which cold gas turns into disk stellar compo-nents via gas contraction on a disk, or a burst mode,which is induced by galaxy mergers. Star formation ratein the quiescent mode are delineated by a simple lawproposed by Kauffmann et al. (1993) as follows:˙ m ∗ = α m cold t dyn , gal , (5)where α is the empirically-determined star formation ef-ficiency, m cold is the amount of cold gas, and t dyn , gal isthe dynamical timescale of cold gas disk assumed to be0 . t dyn .Observations (e.g. Borne et al. 2000; Woods & Geller2007) and hydrodynamic simulations of galaxy merg-ers (e.g. Cox et al. 2008, hereafter C08) have shown thatgalaxy mergers can give rise to rapid star formation. Wefollow the conventional treatment: stars formed in thequiescent mode belong to a galactic disk, while stars bornin the burst mode become bulge components. We adoptthe prescription for merger-induced starbursts describedin Somerville et al. (2008, hereafter S08), which formu-lates the prescription based on C08. S08 defines burstefficiency, e burst , to parameterize the fraction of the coldgas reservoir involved in a merger induced starburst asfollows: e burst = e burst , µ γ burst , (6)where µ is the mass ratio between a host galaxy andits merger counterpart, γ burst is the bulge-to-total massratio(B/T) of the host galaxy, and e burst , is the burstefficiency fitted by the following formula: e burst , = 0 . V vir / (km s − )] . (1 + q EOS ) − . (1 + f g ) . (1 + z ) . , (7)where V vir is virial velocity, q EOS is the effective equationof state of gas, f g ≡ m cold / ( m cold + m ∗ ) is the fractionof cold gas, and z is the redshift when the disks of pro-genitor galaxies are constructed. q EOS was suggested toparameterize the multiphase nature of ISM: q EOS = 0 in-dicates an isothermal state, and q EOS = 1 represents thefully pressurized multiphase ISM. In this study, we adopt q EOS = 1 at which gas is dynamically stable, so that star-bursts are more suppressed than the case of q EOS = 0.The redshift dependency of e burst , is very weak, and thuswe assume (1 + z ) . ∼
1. The burst timescale, τ burst , isalso formulated by S08 as follows: τ burst = 191Gyr[ V vir / (km s − )] − . (1 + q EOS ) . (1 + f g ) − . (1 + z ) − . . (8)The mass ratio, µ , is the ratio of the total mass of centralregions ( m DM , core + m ∗ + m cold ) of a host galaxy to that ofits merger counterpart. Following S08, we calculate thecore mass of a dark matter halo, m DM , core = m DM ( r < r s ), where r s ≡ R vir /c NFW . The concentration index ofthe Navarro-Frenk-White profile, c NFW , is derived basedon the fitting function suggested by Macci`o et al. (2007).The parameter γ burst is determined by the B/T of a Jaehyun Lee and Sukyoung K. Yihost galaxy as follows: γ burst = ( .
61 B/T ≤ .
74 0.085 < B/T ≤ .
02 0.25 < B/T (9)C08 showed that the burst efficiency of a host galaxywith a high B/T is lower than that of a galaxy witha lower B/T, because more massive bulges stabilize thegalaxies and reduce the burst efficiency more effectively.Because C08 demonstrated that mergers with mass ra-tios below 1:10 are not associated with starbursts, weassume e burst = 0 if µ < .
1. With the ingredients,the amount of stars born in burst modes is calculated as m burst = e burst m cold . We assume that m burst turns intostars for τ burst in a uniform rate, ˙ m burst = m burst /τ burst .While merger-induced starbursts occur in a galaxy, thequiescent mode also still goes on in our models.In our model, the recycling of stellar mass loss is con-sidered in great detail. We compute the mass loss ofevery single population at each epoch after a new stel-lar population is born. The mass loss of a single pop-ulation is calculated as follows. We adopt the Scaloinitial mass function (Scalo 1986). The lifetime of astar with mass M , τ M , is computed by a broken-powerlaw (Ferreras & Silk 2000), which is obtained from thedata of Tinsley (1980) and Schaller et al. (1992). τ M (Gyr) = (cid:26) . M/M ⊙ ) − . M < M ⊙ . M/M ⊙ ) − . M ≥ M ⊙ (10)At the end of its lifetime (after τ M elapses), a star returnsmost of its mass into space, leaving small remnants suchas a white dwarf, a neutron star or a black hole. Theremnant mass of a star with mass M , ω M , is suggestedby Ferreras & Silk (2000) as follows: ω M M ⊙ = ( . M/M ⊙ ) + 0 . M < M ⊙ . M ⊙ ≤ M < M ⊙ . M/M ⊙ ) − . M ≥ M ⊙ . (11)In this study, we simply assume that half of the mass lossreturns to cold gas components and the rest becomes hotgas. 2.3. Environmental Effect
The Chandra X-ray Observatory revealed that massivesatellite galaxies in nearby clusters have hot gas compo-nents (Sun et al. 2007; Jeltema et al. 2007), in contra-diction to expectations based on an instantaneous hotgas stripping scenario for satellite galaxies in cluster en-vironments (e.g. Kauffmann et al. 1999; Somerville et al.2008). The old assumption predicted a higher fraction ofpassive satellites in large halos than observed, known asthe satellite overquenching problem (Kimm et al. 2009).Kimm et al. (2011) showed that a gradual, rather thaninstant, and more realistic stripping of the hot gas reser-voir relieves the above-mentioned problem to some de-gree. Therefore, we implemented the gradual hot gasstripping of satellite galaxies in our model by consideringtidal stripping (see Kimm et al. 2011) and ram pressurestripping that uses the prescriptions of McCarthy et al.(2008), which had been modified for semi-analytic mod-els by Font et al. (2008). However, we are still missinga realistic prescription on cold gas stripping. Empiri-cal evidence for cold gas stripping is clear (Vollmer et al. 2008; Chung et al. 2008a,b), and a theoretical study us-ing a semi-analytic approach shows its effect in galaxyevolution (Tecce et al. 2010). Thus, it should be consid-ered in our model in due course.2.4.
Feedback Processes
Feedback mechanisms have been introduced intogalaxy formation theory to reconcile the discrepancy be-tween galaxy and dark matter halo mass functions. Hy-drogen atoms, neutralized at the recombination, may bereionized at later epochs ( z <
10) due to backgroundhigh-energy photons. This mechanism may suppress thegrowth of small galaxies (Gnedin 2000; Somerville 2002;Benson et al. 2002a,b). Supernova feedback is thoughtto be effective at disturbing the growth of small galaxiesby ejecting cold gas (White & Rees 1978; Dekel & Silk1986), and AGN feedback is considered more effectivein massive galaxies with a large black hole (Silk & Rees1998; Schawinski et al. 2006, 2007).We utilize the reionization prescription of Benson et al.(2002b). The prescription allows an inflow of baryonsinto a dark halo via accretion of dark matter when V vir > V reionization throughout the age of the Universe,where V reionization is the suppression velocity of reioniza-tion . If a halo has a lower value of V vir than the criterion,the inflow of baryons is allowed only at z > z reionization ,where z reionization is the suppression redshift of reioniza-tion. In this study, we adopt V reionization = 30 km s − and z reionization = 8 following Benson et al. (2002b).We follow the prescriptions of S08 for supernova feed-back. These prescriptions take into account not only theamount of reheated gas but also the fraction of reheatedgas blown away from halos. The reheating rate of coldgas due to supernova feedback is formulated as follows:˙ m rh = ǫ SN0 (cid:18) − V disk (cid:19) α rh ˙ m ∗ , (12)where ǫ SN0 and α rh are free parameters, V disk is the ro-tational velocity of a disk, and ˙ m ∗ is the star formationrate. S08 assumes that the rotational velocity of a disk isthe same as the maximum rotational velocity of the DMhalo. We calculate the fraction of the reheated gas thathas enough kinetic energy to escape from the halo as f eject = (cid:20) . (cid:18) V vir V eject (cid:19) α eject (cid:21) − (13)where α eject = 6 and V eject ∼ − − . In thecase of a satellite halo, a fraction of reheated gas by su-pernova feedback, f eject m rh , is ejected from the satelliteand added to the hot gas reservoir of its host halo. Onthe other hand, it is assumed that the ejected gas frommain halos is diffused through inter-cluster medium.We take the quasar-mode and radio-mode AGN feed-back into account in our model. It has been sug-gested that the quasar mode is induced by an in-flow of cold gas into the central super-massive blackhole (SMBH) of the central galaxy during major merg-ers (Kauffmann & Haehnelt 2000). The increasing massof the SMBH via the accretion of cold gas can be ex-ssembly history of massive galaxies 5 Fig. 1.—
The cosmic star formation history. The gray dotswith error bars indicate the empirical cosmic star formation his-tory (Panter et al. 2007). The solid line shows the cosmic starformation history derived from the fiducial model. The dotted linedisplays the contribution to the cosmic star formation history frommerger-induced starbursts. pressed as ∆ m BH , Q = f ′ BH m cold − /V vir ) , (14)where f ′ BH is the efficiency of gas accretion. Inthis study, we take the modified parameter proposedby Croton et al. (2006): f ′ BH = f BH ( M sat /M host ), where f BH is the original form of the parameter introducedby Kauffmann & Haehnelt (2000), M host is the massof a host galaxy, and M sat is the mass of the hostgalaxy’s merger counterpart. In this study, we assumethat the lifetime of the quasar mode, t QSO , is 0.2Gyr,as Martini & Weinberg (2001) and Martini & Schneider(2003) suggested t QSO < . m BH , Q = ∆ m BH , Q /t QSO . It is generally thought thatthe quasar mode is caused by a high accretion rate ofcold gas, resulting in a rapid growth of an SMBH.The radio-mode feedback releases low-Eddington-ratioenergy through the accretion of hot gas distributedthroughout the halo. Although the energy released fromthe radio-mode AGN is far less than that from the quasarmode, it is regarded that the radio mode supplies enoughenergy to the surrounding medium to interrupt gas cool-ing or to blow away (some of the) cold gas. We imple-ment radio-mode feedback into our model following theprescription of Croton et al. (2006):˙ m BH , R = κ AGN (cid:18) m BH M ⊙ (cid:19) (cid:18) f hot . (cid:19) (cid:18) V vir − (cid:19) (15)where κ AGN is a free parameter with units of M ⊙ yr − , m BH is the black hole mass, f hot is the fraction of hotgas with respect to the total halo mass, and V vir is thevirial velocity.We assume that the amount of energy generated bythe accretion of gas into the SMBH is given as follows: L BH = η ˙ m BH c = η ( ˙ m BH , Q + ˙ m BH , R ) c , (16)where η = 0 . c is the speed of light. The Fig. 2.—
The galaxy stellar mass functions in the local Universederived by Panter et al. (2007) from SDSS DR3 (gray shade) andthe fiducial model at z=0 (black solid line). The thickness of theempirical data indicates the error range. reduced cooling rate of gas is computed by˙ m ′ cool = ˙ m cool − L BH . V (17)where the minimum of ˙ m ′ cool is set to be zero.2.5. Model calibrations
Our models are based on the conventional techniquesand ingredients used in up-to-date semi-analytic mod-els; hence, the output is not particularly noteworthycompared to other successful models. Our modelsroughly match the global star formation history, galaxymass functions, black hole mass versus bulge mass re-lation, etc. Figure 1 and 2 display comparisons ofthe cosmic star formation history and the galaxy stel-lar mass functions in the local Universe from empiricaldata (Panter et al. 2007) and our fiducial model. Whilethere still is a large room for improvement, we decide tofocus on the mass growth histories of massive galaxies. EVOLUTION OF GALAXY NUMBER DENSITYMK10 presented a rapid growth of massive galaxiessince z = 1, using the United Kingdom Infrared Tele-scope(UKIRT) Infrared Deep Sky Survey (UKIDSS) andthe Sloan Digital Sky Survey (SDSS) II Supernova Sur-vey. Figure 3 shows the number density evolution of themost massive (log M/M ⊙ = 11 . − .
0) and the nextmassive (log
M/M ⊙ = 11 . − .
5) galaxies in the empir-ical data derived by MK10 and from our fiducial model ateach redshift. The empirical data clearly show that thenumber of the most massive galaxies rapidly increasesbetween z = 1 and 0, while the next massive group expe-riences a milder evolution. The reproduction of the databy our fiducial model looks reasonably good. We also Jaehyun Lee and Sukyoung K. Yi Fig. 3.—
Number density evolution of massive galaxies as afunction of the age of the Universe. The red represents the evo-lution of the most massive galaxies (log
M/M ⊙ = 11 . − . M/M ⊙ =11 . − . M/M ⊙ = 10 . − .
0) at each redshift. The diamonds with er-ror bars come from empirical data in MK10 and the squares witherror bars are measurements taken from Cole et al. (2001). Thesolid lines present the predictions of the semi-analytic model. present the number density evolution of the third mas-sive group (log
M/M ⊙ = 10 . − . L ∗ galaxies”. We define “relative num-ber density growth rate”, Γ, as the ratio of the speeds innumber density evolution of the two most massive groupsof galaxies as a function of observational limit in redshift,as follows: Γ = n most ( z = 0) /n most ( z ) n next ( z = 0) /n next ( z ) , (18)where n most ( z = 0) and n next ( z = 0) are the number den-sities of the most massive and next massive groups at z = 0, and n most ( z ) and n next ( z ) are the number den-sities of the two groups at a redshift, respectively. Forexample, MK10 compared the number density evolutionof the two mass groups between redshift 0 and 1, in whichcase the observational limit is 1 and the relative numberdensity growth rate becomes 3. We present their observa-tions and our models in Figure 4. The MK10 data pointshould be compared with our model for the most andthe next massive galaxy groups (solid line). The modelthat compares the next massive group of galaxies with L ∗ galaxies (dashed line) exhibits a similar but mildertrend. Observational constraints are still weak but areat least roughly reproduced by the models. The relativegrowth rate is always greater than 1 in the models, whichindicates that the number density of more massive galax-ies undergoes a faster evolution than that of less massivegroups in the super- L ∗ range. The number evolution ismost dramatic when a comparison is made against themost massive galaxies. This is caused by the fact thatthe mass bin for the “most massive” galaxies has onlyinflux from less massive galaxies, whereas the mass binof less massive galaxies can have outflux to more mas-sive galaxy bins as well as influx from even less massivegalaxy bins.Primarily motivated by MK10, we focus on the massgrowth histories of super- L ∗ galaxies. We divide the Fig. 4.—
Relative galaxy number density growth rate, Γ, be-tween z=0 and observational redshift limits. The solid line showsΓ of the most/next and the dashed line indicates that of thenext/third in our model. The cross is derived from the empiri-cal data in Figure 3. model galaxies into three groups according to z = 0 mass:Rank 1: log M/M ⊙ = 11 . − .
0, Rank 2: log
M/M ⊙ =11 . − .
5, and Rank 3: log
M/M ⊙ = 10 . − .
0, whereRank 3 roughly represents L ∗ galaxies. From our simula-tion volume, we found 49 galaxies in Rank 1, 472 galaxiesin Rank 2, and 2,188 galaxies in Rank 3. EVOLUTION OF MASSIVE GALAXIES INMODELS4.1.
Evolution of Stellar Mass in Galaxies
In the hierarchical paradigm, a galaxy can have morethan one progenitor. Progenitors of a galaxy can be di-vided into “direct” and “collateral” progenitors. A di-rect progenitor is the galaxy in the largest halo whena merger between halos takes place. While there canbe numerous progenitors, there is only one direct pro-genitor at each epoch. Collateral progenitors are all theother galaxies that contribute to the final galaxy. In thisconcept, to build the evolutionary history of a galaxy,one should consider not only direct progenitors, but alsomerger counterparts or collateral progenitors. Figure 5shows the average mass evolution of the direct progeni-tors (solid lines) and all (direct and collateral combined)the progenitors (dotted lines) of Rank 1, 2, and 3 galax-ies. The mean stellar masses of the three groups at z = 0are 4 . × M ⊙ , 1 . × M ⊙ , and 5 . × M ⊙ ,respectively. Most of the Rank 1 galaxies in our volumeare brightest cluster galaxies.As all the progenitors merge with each other, the dot-ted lines and the solid lines finally meet at z = 0. Stel-lar mass loss and the scattering of stellar components insatellite galaxies into diffuse stellar components, whichtakes place when mergers occur, lead to a gradual de-crease in the total mass during the evolution. For exam-ple, one can see a slight decline in the total stellar mass(red dotted line at the top) after z ∼ .
5. This effect isnot clearly visible in Rank 2 and 3 galaxies in which starformation is more extended and mergers are less frequentthan in Rank 1 galaxies.It is useful to have a definition of the formation red-ssembly history of massive galaxies 7
Fig. 5.—
Average mass evolution of galaxies. The red, blue, andgreen represent three groups of galaxies: log
M/M ⊙ = 11 . − . M/M ⊙ = 11 . − .
5, and log
M/M ⊙ = 10 . − . z = 0,respectively. The solid lines indicate the mean mass evolution ofdirect progenitors and the dotted lines show the mean mass evo-lution of all (direct+collateral) progenitors. The black horizontaldashed lines denote half the mean galaxy mass at z = 0 of thegroups. A , A , and A , and the arrows indicate the epochs whenthe total stellar masses of all progenitors reach half of the finalmass. D , D , and D with arrows show the epochs at which thedirect progenitors of the three groups acquire half of their finalmass. shift, z f . We define it as the redshift at which half ofthe stellar mass at z = 0 has been assembled. In thecase of Rank 1 galaxies, half of the final mass is achievedat z f , D ∼ . in Figure 5) in direct pro-genitors and at z f , A ∼ . ) when all progenitors arecombined. Our models suggest ( z f , D , z f , A ) = (0.9, 2.1)for Rank 2, and ( z f , D , z f , A ) = (1.1, 1.6) for Rank 3.Models exhibit a monotonic mass dependence of z f , D and z f , A in the sense that, with mass, z f , D decreaseswhile z f , A increases. In other words, the mass of thedirect progenitors of a more massive group grows moreslowly, while its total mass of all the progenitors is as-sembled earlier than that of a less massive group. Theevolutionary histories of direct progenitors are oppositeto the pattern of cosmic downsizing. As Neistein et al.(2006) and Oser et al. (2010) pointed out, however, if thegrowth histories of collateral progenitors of galaxies arealso considered, downsizing would be a natural outcomeof the hierarchical concept of galaxy formation.The difference in the growth history between the threegroups can be understood in depth through Figure 6,which presents the evolutionary histories of star forma-tion rates (SFRs). The mean SFRs contain the star for-mation histories of both direct and collateral progenitors.We show the best fitting log-normal function to the threeSFR curves. The star formation rates of more massivegalaxies peak earlier, as marked by S1, S2, and S3 inthe figure, and decreases faster than those of less mas-sive groups. The same features were noted in an earlierstudy by De Lucia et al. (2006).Figure 6 also show the redshift at which half of the to-tal cumulative star formation has occurred in the threegroups of galaxies: (C1, C2, C3) = (2.0, 1.5, 1.4) in z .The general trend shown by these three values agreeswith that of z f , A discussed above. In a sense, it is thesevalues, rather than z f , A , that are closer to the general Fig. 6.—
Mean star formation histories of all the progenitorgalaxies of Rank 1(red), 2(blue), and 3(green). The gray dashedlines denote log-normal fitting. S , S , and S with arrows indicatethe epochs when SFRs peak. C , C , and C with arrows showthe epochs at which the cumulative stellar mass reach half of thetotal stellar mass born by z = 0. definition of formation redshift. Again, the more massivegalaxies are, the earlier they form their stars, consistentwith downsizing. In conclusion, the observational findingof downsizing is a result of the hierarchical galaxy for-mation process, where more massive galaxies have largerstellar ages and smaller assembly ages (see also e.g.De Lucia & Blaizot 2007; Kaviraj et al. 2009). Both thelarger stellar ages and the smaller assembly ages can beunderstood as a result of large-scale effect; that is, ina deeper potential well, progenitor galaxies and theirstars form earlier, and many more galaxies participatein galaxy mergers for a long period of time.4.2. Origin of Stellar Components
In this section, we investigate how stellar componentsare assembled into massive galaxies. Stellar componentsin a galaxy originate either from in-situ star formation orfrom “merger accretion”. Two modes of star formationare considered: “quiescent” mode and merger-induced“starburst”. Stars in a galaxy can therefore have fourdifferent origins: (1) in-situ quiescent star formation, (2) in-situ starburst, (3) merger accretion of stars formed inquiescent mode, and (4) merger accretion of stars formedin burst mode.Figure 7 shows the decomposition of the four channelsas a function of time for the three different mass groups.The top and bottom rows show the absolute stellar massevolution and relative mass fraction evolution, respec-tively.Several remarkable features are visible, more easilyin the bottom rows. First, in-situ quiescent star for-mation is an important channel for the stellar com-ponents in massive galaxies. Its fractional contribu-tion is (30, 60, 80)% in Rank (1, 2, 3) galaxies, re-spectively.
In-situ quiescent star formation takes placeon a galactic disk, and thus, one may wonder why itscontribution is so large in these massive, and prob-ably bulge-dominant galaxies. This is because mas-sive bulge-dominant galaxies at z = 0 have many late-type progenitors, and that is more pronounced in lessmassive galaxies (Rank 3) than in Rank 1 galaxies. Jaehyun Lee and Sukyoung K. Yi Fig. 7.—
Average mass evolution of stellar components in direct progenitors (upper) and the fraction of each component divided bythe mean total stellar mass of direct progenitors at each redshift (bottom). The left, middle, and right panels show the mean evolutionaryhistories of the direct progenitors of Rank 1, 2 , and 3 galaxies, respectively. Each color code represents each stellar component as follows:(1) sky blue: merger accretion of stars formed in quiescent mode, (2) orange: in-situ quiescent star formation, (3) blue: in-situ starburst,and (4) red: merger accretion of stars formed in burst mode.
This is a reflection of the progenitor bias discussed ear-lier (c.f. Franx & van Dokkum 2001; Guo & White 2008;Parry et al. 2009; Kaviraj et al. 2009).Second, the stars formed in burst mode are an ex-treme minority ( ∼ Fig. 8.—
Frequency of mergers (per Gyr per galaxy) with a massratio m /m & . mass difference between Ranks 1 and 2 comes from thedifferences in merger accretion. The value is ∼
60% be-tween Ranks 2 and 3. Massive galaxies are so mainlybecause they have a substantial amount of in-situ qui-escent star formation, but the most massive galaxies areso because they have acquired a large amount of massthrough merger accretion.
The result is supported byprevious studies. Aragon-Salamanca et al. (1998) con-firmed that BCGs have experienced no or negative evo-lution in luminosity during 0 < z <
Fig. 9.—
The specific star formation rates (upper) and the spe-cific stellar accretion rates via mergers (bottom) of the direct pro-genitors in the three groups. See the text for their definitions. Thesolid, dashed, and dotted lines represent Rank 1, 2, and 3 galaxies.
Hubble diagram for a sample of BCGs while they haveincreased their mass by a factor of two to four, depend-ing on cosmological parameters. Thus, it has been un-derstood that merger and accretion may be the mostplausible explanation for the evolution. Using a semi-analytic model, De Lucia & Blaizot (2007) showed thatmost stellar components in model BCGs are formed inthe very early age of the Universe (80 % at z ∼ z ∼ .
5) via mergers. Oser et al. (2010)presented similar results, using numerical simulations.About 80% of stellar components in simulated massivegalaxies ( M ∗ > . × M ⊙ at z=0) are formed outsidein the early age ( z >
3) and brought into the massivegalaxies via mergers and accretion. The massive galax-ies double their mass after z ∼
1. They revealed that thefraction gets smaller in less massive galaxies. Parry et al.(2009) also found a similar trend in their investigation ontwo separate semi-analytic models. They demonstratedthat the contribution of mergers to the bulge growth ex-ceeds that of disk instability at M ∗ > . M ⊙ . Consid-ering the fact that such massive galaxies ( M ∗ > M ⊙ )are likely early type (e.g. Bell et al. 2003), it implies thatmergers play a more important role in the growth of mas-sive galaxies. It should however be noted that disk in-stability which is more effective to the smaller late-typegalaxy evolution may play a role in such progenitor galax-ies of present-day massive early types.Figure 8 shows the merger rate evolution for bary- Fig. 10.—
Comparison of the mean specific star formation rates(solid lines) and the mean specific stellar accretion rates via merg-ers (dotted lines) of the direct progenitors of Rank 1(upper), 2(middle), and 3 (bottom) galaxies. onic mass ratios greater than or equal to 1:10. Althoughmerger rates show stochastic effects, there is a clear de-creasing tendency with time, whereas the star formationrates of the three groups drop more sharply, as shown inFigure 6. In general, more massive galaxies are likely tobe involved in galaxy mergers more frequently, so thatmore massive galaxies have many more stellar compo-nents born outside and accreted via mergers, as discussedabove. During the whole calculation, Rank 1 galaxies un-dergo about 9.0 mergers with a mass ratio greater than orequal to 1:10 while those in Ranks 2 and 3 experience 4.0and 1.0 mergers, respectively. During 0 < z <
1, Rank1, 2, and 3 galaxies experience 3.5, 1.8, or 0.6 mergers forthe same mass ratio criterion. This explains the highercontribution of merger accretion in more massive galax-ies, as illustrated in Figure 7.4.3.
Specific Star Formation Rates and MergerAccretion Rates
We found in the previous section that in-situ star for-mation and merger accretion were the two most signif-0 Jaehyun Lee and Sukyoung K. Yiicant channels for the stellar mass growth of massivegalaxies. In this section, we scrutinize their time evo-lution in greater detail. Specific star formation rates(SSFRs) are normalized growth rates of star formationhistories. Likewise, we hereby define the “specific stellaraccretion rate” (SSAR) to evaluate a normalized growthrate via mergers as follows:SSAR = ∆ MM ( t )∆ t , (19)where M ( t ) is the mass of a galaxy at an epoch, and∆ M is an increment of mass by mergers during a timestep ∆ t . Because we allow diffuse stellar components dueto galaxy mergers, mass increment can be expressed as∆ M = (1 − f scatter ) M ∗ , sat , as described in Section 2.1.Figure 9 shows the evolution of the SSFRs (up-per) and of the SSARs (bottom) of direct progeni-tors. In general, more massive galaxies have lowerSSFRs, as observations have shown (e.g. Salim et al.2007; Schiminovich et al. 2007), while they have higherSSARs than less massive galaxies. Star formationrates are decreased by the depression of gas coolingrates due to an increase in the cooling timescale viathe growth of halos, supernova feedback (White & Rees1978; Dekel & Silk 1986; White & Frenk 1991) and/orAGN feedback (Silk & Rees 1998). Furthermore, thecold gas reservoir of a galaxy could be reduced by feed-back processes. Besides, if a galaxy orbits around a moremassive galaxy, it becomes redder as it loses its hot gas,which is a source of cold gas, and its cold gas reservoirby tidal and ram pressure stripping (Gunn & Gott 1972;Abadi et al. 1999; Quilis et al. 2000; Chung et al. 2007;Tonnesen & Bryan 2009; Yagi et al. 2010). On the otherhand, accretion of stellar components via mergers is de-termined by gravitational interactions between host andsubhalos alone; hence, the accretion rate could remainrelatively steady as halos continue to fall into other moremassive halos over time.Figure 10 displays a comparison of the SSFRs andthe SSARs of direct progenitors. As illustrated in Fig-ure 7, quiescent star formation dominates the stellarmass growth history in L ∗ (Rank 3) galaxies (bottompanel). In Rank 2 galaxies, they are comparable to eachother most of the time. However, in the most massive(Rank 1) galaxies, merger accretion takes over star for-mation as the most important channel of stellar massgrowth around z ∼ SUMMARY AND DISCUSSIONWe have investigated the assembly history of stellarcomponents of massive (super- L ∗ ) galaxies, using semi-analytic approaches. Our major results can be summa-rized as follows. • More massive galaxies grow in number faster thanless massive galaxies, as a result of the hierarchicalnature of galaxy clustering. This result is consis-tent with the recent observation of MK10. • The conflict between the predictions from hierar-chical models and downsizing is reconcilable. If weconsider only direct progenitors of massive galaxies, our models suggest “upsizing” rather than downsiz-ing; that is, the direct progenitors of more massivegalaxies grow more slowly. However, if we consider all the progenitors, direct and collateral, the com-bined mass suggests downsizing. Our models sug-gest that more massive galaxies have older stellarages but younger assembly ages. • Merger-induced “bursty” star formation is negligi-ble compared to quiescent disk-mode star forma-tion despite the fact that massive galaxies formthrough numerous mergers. This is because mostof the gas-rich major mergers occur at high red-shifts when galaxies are small, and recent majormergers tend to be rare and “dry”. • Merger accretion is a growingly more importantchannel of stellar mass growth in more massivegalaxies. It accounts for 70% of the final stellarmass in the most massive galaxies in our sample(log
M/M ⊙ = 11 . − . • In the most massive galaxies, which are likelybrightest cluster galaxies, merger accretion has re-mained the most important channel of stellar massgrowth ever since z ∼ massive galaxy formation on theother hand seems to be more hinged upon our knowledgeof large-scale clusterings, and thus dark matter physics.Massive galaxies achieve their grandeur through mergers;thus, only by a realistic consideration of large-scale clus-tering information is it possible to accurately reconstructtheir formation history.ACKNOWLEDGMENTSWe thank Taysun Kimm and Sadegh Khochfar for theirfeedback in the early stage of our code development andIntae Jung for helping us run cosmological volume sim-ulations. We thank the anonymous referee for a numberssembly history of massive galaxies 11of comments and suggestions that improved the clarityof the paper. We acknowledge the support from the Na-tional Research Foundation of Korea through the Cen-ter for Galaxy Evolution Research (No. 2010-0027910), Doyak grant (No. 20090078756), and DRC grant.galaxy formation on theother hand seems to be more hinged upon our knowledgeof large-scale clusterings, and thus dark matter physics.Massive galaxies achieve their grandeur through mergers;thus, only by a realistic consideration of large-scale clus-tering information is it possible to accurately reconstructtheir formation history.ACKNOWLEDGMENTSWe thank Taysun Kimm and Sadegh Khochfar for theirfeedback in the early stage of our code development andIntae Jung for helping us run cosmological volume sim-ulations. We thank the anonymous referee for a numberssembly history of massive galaxies 11of comments and suggestions that improved the clarityof the paper. We acknowledge the support from the Na-tional Research Foundation of Korea through the Cen-ter for Galaxy Evolution Research (No. 2010-0027910), Doyak grant (No. 20090078756), and DRC grant.