What determines the fraction of elliptical galaxies in clusters?
aa r X i v : . [ a s t r o - ph . C O ] S e p Mon. Not. R. Astron. Soc. , 1–8 (2011) Printed 17 November 2018 (MN L A TEX style file v2.2)
What determines the fraction of elliptical galaxies inclusters?
Gabriella De Lucia ⋆ , Fabio Fontanot and David Wilman INAF - Astronomical Observatory of Trieste, via G.B. Tiepolo 11, I-34143 Trieste, Italy Max-Planck-Institut f¨ur Extraterrestrische Physik, Giessenbachstraße, D-85748 Garching, Germany
17 November 2018
ABSTRACT
We study the correlation between the morphological mix of cluster galaxies and theassembly history of the parent cluster by taking advantage of two independently de-veloped semi-analytic models for galaxy formation and evolution. In our models, boththe number of cluster members and that of elliptical members increase as a func-tion of cluster mass, in such a way that the resulting elliptical fractions are approx-imately independent of cluster mass. The population of cluster ellipticals exhibit amarked bimodal distribution as a function of galaxy stellar mass, with a dip at masses ∼ M ⊙ . In the framework of our models, this bimodality originates from the com-bination of a strongly decreasing number of galaxies with increasing stellar mass, anda correspondingly increasing probability of experiencing major mergers. We show thatthe correlation between the measured elliptical fraction and the assembly history ofthe parent cluster is weak, and that it becomes stronger in models that adopt longergalaxy merger times. We argue that this results from the combined effect of a decreas-ing bulge production due to a reduced number of mergers, and an increasing survivalprobability of pre-existing ellipticals, with the latter process being more importantthan the former. Key words: galaxies: formation – galaxies: evolution – galaxies: bulges – galaxies:interactions – galaxies: clusters: general
It has long been known that early type galaxies (ellipticalsand lenticulars) reside preferentially in dense regions of theUniverse such as rich clusters, while late type galaxies rep-resent a larger fraction of the galaxy population inhabitingregions of ‘average’ density. Such a morphology-density rela-tion was noticed in early observational studies (indicationsof a correlation between the type of nebulae and the envi-ronment can be found in ‘The Realm of Nebulae’ by Hubble1936), and was firmly established by Dressler (1980).In the past decades, much observational information hasbeen collected on the morphological distributions of cosmicgalaxy populations, and on its dependence on the environ-ment. Butcher & Oemler (1978a, 1984) showed, for the firsttime, that the fraction of blue (star forming) galaxies inclusters increases with increasing redshift. Detailed morpho-logical studies have been carried out in the following years,demonstrating that the fraction of spiral galaxies increaseswith increasing redshift, and that this increase appears ap-proximately balanced by a decrease in the fraction of the ⋆ Email: [email protected] lenticular galaxies since z ∼ .
5. Over the same redshiftrange, the fraction of elliptical galaxies is approximately con-stant (Dressler et al. 1997; Fasano et al. 2000). In more re-cent years, detailed morphological studies have been pushedto lower mass ranges (Wilman et al. 2009), and to higherredshift, where the mean fraction of different morphologicaltypes does not appear to evolve significantly (Postman et al.2005; Desai et al. 2007).At a given redshift, clusters with similar mass (mea-sured from either X-ray luminosity, or velocity dispersion)exhibit a non negligible scatter in their morphological com-position (e.g. Poggianti et al. 2009). In the context of thecurrently accepted paradigm for structure formation (theΛCDM model), it is logical to relate this cluster-to-clustervariance to the dynamical history of the cluster. Althoughdifficult to test quantitatively, this expectation is confirmedby early observations that centrally concentrated clustershave typically large populations of ellipticals and lenticularsand relatively low numbers of spirals, while irregular, unre-laxed clusters are more spiral-rich and show weaker radialgradients in their morphological mix (e.g. Butcher & Oemler1978b). In this paper, we will address this issue by consider-ing two different semi-analytic models of galaxy formation, c (cid:13) G. De Lucia et al. and by relating the predicted fraction of elliptical galaxiesto the accretion history of the simulated cluster haloes.
In this paper, we take advantage of two independently de-veloped galaxy formation models: the ‘Munich’ model, withthe implementation discussed in De Lucia & Blaizot (2007)and applied to the Millennium Simulation, and the
MOR-GANA model, as adapted to the WMAP3 cosmology inLo Faro et al. (2009). Hereafter, we will refer to the formermodel as DLB07. We note that in previous work, we haveused the models presented in Wang et al. (2008) which cor-responds to the model by De Lucia & Blaizot (2007) usedhere, but has been adapted to a WMAP3 cosmology. In thispaper, we use the model applied to the Millennium Simula-tion as this provides a larger volume and therefore a largernumber of massive haloes.The simulations employed in this study assume a dif-ferent cosmology: the Millennium Simulation assumed a cos-mological model that is consistent with WMAP first-year re-sults . As shown in previous work, however, once the modelis re-tuned to account for the change in cosmology, the basicresults and trends do not change significantly (Wang et al.2008). In addition, we note that the two models adopt dif-ferent definitions for the halo mass: in DLB07, this is givenby M and is computed from the simulation outputs asthe mass contained in a sphere of radius R , for which themean overdensity is 200 times the critical density of the Uni-verse at the redshift of interest. For MORGANA , the massesare simply given by the sum of the particle mass associatedwith the halo, computed using
PINOCCHIO (Monaco et al.2002).In this section, we provide a brief summary of the modelelements that are relevant to the present study. We re-fer to the original papers for a more detailed discussion ofthe physical processes considered, and of the correspond-ing modelling adopted. Both models consider two differentchannels for the formation of bulges: galaxy-galaxy merg-ers and disk instabilities. The relative importance of thesechannels, in different environments and at different times,has been studied in detail in De Lucia et al. (2011), while inFontanot et al. (2011) we focused on the statistics and prop-erties of bulgeless galaxies. Both models used in this studyassume a Chabrier Initial Mass Function.Mergers are classified as minor or major according totheir baryonic (gas + stars) mass ratio. If this is smallerthan 0.3, the merger is classified as minor: the stellar massof the secondary is added to the bulge component of theprimary galaxy, and the merger is accompanied by a star-burst. The resulting stars are added to the bulge component(in MORGANA ) or to the disk component (in DLB07). Ifthe baryonic mass ratio of the merging galaxies is largerthan 0 .
3, we assume that we witness a major merger. Inthis case, both models assume that the disk components ofthe merging galaxies are completely destroyed. The remnant The most important difference between WMAP first and thirdyear data is a lower value for the amplitude of matter fluctua-tions on 8 h − Mpc scale ( σ ), which leads to a delay in structureformation (e.g. Wang et al. 2008). spheroidal galaxy can re-grow a new disk, if fed by an ap-preciable cooling flow. In previous work, we have found thatthe merger model adopted in MORGANA provides merg-ing times that are systematically shorter (by up to an orderof magnitude) than those adopted in the DLB07 model (seeSection 7 of De Lucia et al. 2010). The shorter merger timesadopted in
MORGANA lead to a more efficient formation ofbulges and to larger number densities of early type galaxies,particularly at high redshift. As we will show below, the dif-ferent modelling adopted for galaxy mergers also affects therelation between the morphological fraction and the accre-tion history of dark matter haloes. In order to quantify thesignificance of this effect, in the following we will also showor discuss the results obtained from
MORGANA using thesame dynamical friction timescale prescription adopted byDLB07.The treatment of disk instability differs significantly inthe two models considered: both adopt the same stabilitycriterion proposed in Efstathiou, Lake & Negroponte (1982)but use different definitions for the relevant physical quan-tities, and make different assumptions about the outcomeof instabilities: DLB07 only transfer to the bulge a fractionof the stellar disc that is enough to restore stability. In the
MORGANA model, half of the disk baryonic mass (bothgas and stars) is transferred to the bulge. As discussed andshown in De Lucia et al. (2011), this translates into a morerelevant contribution of disk instability to bulge formation.In the framework of our models, most of the ellipticalgalaxies acquire their morphology through major mergers.Disk instability can contribute significantly for low and in-termediate mass galaxies, depending on the adopted treat-ment for galaxy mergers and instabilities. As mentionedabove, bulge dominated galaxies can later grow a new disc, ifthey are fed by an appreciable cooling flow. We have shownthat the rates of disc regrowth are negligible for massivegalaxies and at low redshift. They represent, however, a non-negligible component of the evolution of low and intermedi-ate mass galaxies, particularly at high redshift (see Section 6of De Lucia et al. 2011). As we focus on galaxy clusters, themodel ellipticals considered in this paper are almost all satel-lite galaxies (with the exclusion of central cluster galaxies).For these galaxies, the bulge-to-total ratio is not affected af-ter accretion onto a more massive halo in the
MORGANA model. DLB07 accounts for mergers between satellites (thatare, however, rare) so that the bulges of satellite galaxies canstill grow through this physical mechanism. Finally, none ofthe models used in this study include ‘environmental’ pro-cesses such as tidal stripping or harassment, that can poten-tially affect the morphology of satellite galaxies orbiting ina massive cluster (e.g. Mastropietro et al. 2005).In our previous work, we have considered alternativeprescriptions to model bulge formation, including predic-tions obtained when the disk instability channel is switchedoff. We have verified that the results presented in the fol-lowing do not depend significantly on these assumptions.Therefore, we will discuss only results obtained by our de-fault models. As these data have not been used to ‘tune’the models in the first place, they can be considered as gen-uine model predictions, and compared with available obser-vational measurements. c (cid:13) , 1–8 he fraction of ellipticals in clusters Figure 1.
Total numbers of galaxies (left panel), numbers of ellipticals (middle panel), and elliptical fractions (right panel) inside thecluster virial radius, as a function of the cluster mass. Filled and open symbols (these are coloured black and red in the online edition ofthe Journal) are obtained considering all galaxies more massive than 10 and 10 M ⊙ , respectively. In this study we have considered galaxy clusters with massesin the range log M / M ⊙ = 14 − .
8, at redshift zero. In thesimulation used by
MORGANA , there are 100 clusters overthis mass range. To compare the predictions from this modelto those from DLB07, we have selected the same numberof haloes from the Millennium Simulation, uniformly dis-tributed in mass over the same mass range. In the follow-ing, we will define as ellipticals all galaxies that have a stel-lar bulge to total ratio larger than 0 .
9. When relevant, wewill comment on how results can be affected by a differentthreshold.Figure 1 shows the total number of galaxies (left panel),the number of ellipticals (middle panel), and the ellipticalfractions (right panels) as a function of the cluster virialmass. Only galaxies residing within R have been con-sidered in the DLB07 model. Since MORGANA does notprovide information on the position of galaxies within darkmatter haloes, we have simply considered in this case allgalaxies associated with the final cluster. Given the differ-ent definitions adopted, any difference between model pre-dictions (but we will see that these are very small) should be interpreted with caution. Filled and open symbols in Fig-ure 1 correspond to galaxies more massive than 10 and10 M ⊙ , respectively. The former limit corresponds to theapproximate resolution limit of the Millennium Simulation,while the latter corresponds to a typical limit for observa-tional studies.Figure 1 shows that both the total number of galaxiesand the number of ellipticals increase with increasing halomass. When a lower stellar mass threshold is chosen, thepredicted numbers are significantly higher. A cluster of mass2 . × M ⊙ contains on average ∼
50 ( ∼
60) galaxies moremassive than 10 M ⊙ in the DLB07 ( MORGANA ) model.When considering a mass limit of 10 M ⊙ , the average num-ber of cluster members within the virial radius increases to ∼
190 ( ∼
260 in
MORGANA ). The number of ellipticalsincreases too, but not as much as the total number of galax-ies. This is expected given that, as the stellar mass increases,a larger fraction of galaxies are classified as ellipticals (seeFig. 7 in De Lucia et al. 2011). Interestingly, the halo oc-cupation distribution of the two models used in this studyis different, with
MORGANA always predicting a slightlylarger number of cluster members with respect to DLB07.The difference is significant for the most massive clusters c (cid:13) , 1–8 G. De Lucia et al. included in our sample, and when considering all galaxiesmore massive than 10 M ⊙ . We stress, however, that a dif-ferent definition for cluster members has been adopted forthe two models. In addition, we are using the dynamicalinformation available from the simulations to define clustermembers, while an accurate comparison with observationalmeasurements should account for possible contamination byinterlopers along the line of sight. As mentioned above, themerger times adopted in MORGANA are about one order ofmagnitude shorter than those adopted in DLB07. By usinglonger merger times in
MORGANA , the number of clustermembers increases even further.The fraction of elliptical galaxies resulting from thenumbers shown in the left and middle panel of Figure 1does not vary significantly as a function of cluster mass,in agreement with observational measurements in the localUniverse (Wilman et al. 2009; Poggianti et al. 2009) . Thepredicted elliptical fractions are of the order of 10 per cent inboth models, when all galaxies more massive than 10 M ⊙ are considered. For a mass threshold of 10 M ⊙ , the ex-pected fractions increase, and the scatter becomes larger.Interestingly, the halo to halo scatter appears to increaseslightly with decreasing halo mass. This is more evidentin the MORGANA model, but we note that in this casehaloes are not distributed uniformly in mass and the num-ber of clusters at the largest masses considered is quite low.Therefore, the very narrow range of elliptical fractions pre-dicted by this model for the most massive haloes might befortuitous, and just due to poor number statistics.When considering all galaxies more massive than10 M ⊙ , the mean elliptical fraction is 0 .
22 for the DLB07model, and 0 .
24 for
MORGANA . This is lower than theaverage value of ∼ .
32 measured for the WIde-field NearbyGalaxy clusters Survey (WINGS), using a similar mass cut(Vulcani et al. 2011). We note, however, that only galaxieswithin 0 . have been considered in this observationalstudy, as this is the largest radius covered in all their clusterfields, and that the study is based on a definition of ellipti-cals that differs from that adopted in this paper (morpholo-gies have been assigned using V-band images). In previouswork (Simard et al. 2009), we have shown that the early-type fractions predicted by the DLB07 model compare wellto observational measurements from the Sloan Digital SkySurvey (SDSS) in the local Universe and from the ESO Dis-tant Cluster Survey (EDisCS) at redshift ∼ .
6. Also in thatstudy, however, a different (closer to that used in the obser-vations) definition of ‘early-type’ galaxies was adopted, sothat the predicted fractions shown in this study are not thesame as those shown in Simard et al. In a forthcoming pa-per (Wilman et al., in preparation), we will carry out a moredetailed comparison between the observed mix of differentmorphological classes and predictions from our galaxy for-mation models.The left panels of Figure 2 show the predicted distri-butions of stellar masses for all cluster galaxies (thin his-tograms) and for the cluster ellipticals (thick histograms).These distributions have been obtained by stacking the We note that both Wilman et al. (2009) and Poggianti et al.(2009) are based on magnitude limited samples, while we are usinga cut on total stellar mass. galaxies in all clusters, and have been normalized to the totalnumber of galaxies in each distribution. The two models pro-vide very similar predictions, but those from
MORGANA are more skewed towards less massive galaxies. Interestingly,both models predict a bimodal distribution for ellipticalgalaxies, with a pronounced ‘dip’ around ∼ M ⊙ . Unfor-tunately, this is below or approximately at the limit of theobservational measurements for the WINGS sample used inVulcani et al. (2011). We note that this bimodal behaviouris found in our models also when considering the globalelliptical population (i.e. not only ellipticals in clusters),which does not appear to be supported by available obser-vations (e.g. Trentham & Hodgkin 2002; Driver et al. 2003).We stress that our models (like most of the recently pub-lished models) overpredict the number densities of small tointermediate mass galaxies (Fontanot et al. 2009), so the im-portance of the peak at small masses is likely over-estimated.In both models, the bimodal distribution of the clusterelliptical masses is significantly reduced (but still apparentin the MORGANA model) when the adopted threshold fordefining a bulge dominated galaxy as an elliptical is loweredto ∼ .
7. In this case, only one peak is visible in the DLB07predictions at masses log( M star ) ∼ .
5. We have verifiedthat, in our model, this bimodality is not significantly af-fected when the disk instability channel for bulge formationis switched off, so a differential efficiency of bulge formationthrough disk instability is not responsible for the shape ofthe cluster elliptical mass distribution shown in Figure 2.In our previous work (De Lucia et al. 2011), we have shownthat disk regrowth is more efficient for intermediate massgalaxies. In order to test if this could be responsible for theobserved dip at intermediate masses, we have calculated themass distribution of all galaxies that have been ellipticalsin their past, either considering only those surviving at red-shift zero (i.e. excluding those that have merged with othergalaxies) or all galaxies in the merger trees of the cluster el-lipticals. In both cases, we find that the predicted mass dis-tribution exhibit a marked bimodality, with a pronounced‘deficit’ of elliptical galaxies at intermediate masses.We interpret this bimodality as a result of the increas-ing probability of suffering a major merger with increasingmass (see Figure 9 in De Lucia et al. 2006 and Figure 6 inWang & Kauffmann 2008), and of the strongly decreasingnumber of galaxies of larger masses (as shown by the thinlines in Figure 2). The convolution of these distribution func-tions results in a lower number of intermediate mass galaxiessuffering of major merger events in their past history, com-pared to galaxies residing in the low and high mass peaksof the distributions shown in the left panels of Figure 2.In particular, Figure 3 of Wang & Kauffmann (2008) showsthat the region where the dip in the mass distribution ofelliptical galaxies is visible, corresponds to a regime wherethe probability of suffering of a minor merger is significantlylarger than that of experiencing a major merger. This hap-pens because, during the time that elapses between a halomerger and the actual merger between the galaxies resid-ing at the centre of the merging haloes, the stellar mass ofthe satellite does not increase significantly, while the cen-tral galaxy grows in mass as it is fed by cooling from thesurrounding hot halo. As a consequence, the stellar massratio between the two galaxies decreases, so that a majormerger between two haloes can lead to a minor merger be- c (cid:13) , 1–8 he fraction of ellipticals in clusters Figure 2.
Distribution present day stellar masses (left panel) for model ellipticals in our cluster sample, and for their parent halo mass atthe time of accretion (right panels). The distributions shown have been obtained by stacking all clusters in the sample, and normalizingto the total number in each distribution. Solid and dashed lines refer to the cases when all galaxies more massive than 10 and 10 M ⊙ are considered, respectively. Thin and thick lines (black and red in the online edition of the Journal) are for all galaxies and for thosethat are classified as ellipticals, respectively. tween their galaxies. Figure 3 in Wang & Kauffmann (2008)shows that the probability of experiencing a minor merger islargest at intermediate masses, which explains why loweringthe adopted bulge-to-total threshold fills the intermediateregion, and tends to wash out the bimodality.For each cluster member in our sample, we have tracedback their main progenitor until the galaxy is for the lasttime a central galaxy of a dark matter halo, and we haverecorded the parent halo mass at this time. In the follow-ing, we refer to this as the ‘time of accretion’, although thiswill not always coincide with the time when the galaxy isaccreted onto the main progenitor of the final cluster (DeLucia et al., in preparation). The right panels of Figure 2show the distributions of halo masses at accretion for allcluster members (thin lines) and for the ellipticals (thicklines). Again, the distributions obtained for all clusters havebeen stacked and normalized to the total number of galaxiesin each of them. The figure shows that, in both models, elliptical galaxiestend to be accreted when they reside in more massive haloeswith respect to the total population of cluster members (thedistribution predicted by MORGANA has a higher lowermass limit than in the DLB07 model: i.e. in
MORGANA ,ellipticals tend to be accreted, on average, in more massivehaloes than in the DLB07 model). This is not surprisingconsidering that ellipticals represent a larger fraction of themost massive galaxies, and that there is a relatively tightcorrelation between the galaxy mass and that of the parenthalo mass for central galaxies (e.g. Wang et al. 2006).
In the previous section, we have shown that ellipticals tendto be accreted in larger haloes, with respect to the entire c (cid:13) , 1–8 G. De Lucia et al. cluster galaxy population. Given these results, one wouldexpect naively that haloes that have acquired a larger frac-tion of their mass through the accretion of ‘massive’ haloeswould host a larger fraction of ellipticals. One has to con-sider, however, that elliptical galaxies can also disappear from the sample of cluster members by merging with thecentral galaxies of the hosting halo (or with other satellitesin the DLB07 model).In order to address this issue, we have analysed theaccretion histories of all clusters included in our sample. Foreach halo, we have traced back in time its main branch, i.e.the branch of the tree that is obtained by connecting thehalo to its main progenitor . We have then considered allsubstructures residing in the main branch at each time, andhave traced each of them back in time until they were mainhaloes of a FOF-group. The top panels of Figure 3 show themass distributions of accreted haloes for the clusters thathost an elliptical fraction lower (thin dashed lines) than the10th percentile, and higher (thick solid lines) than the 90thpercentile of the distribution of elliptical fractions measuredfor all 100 haloes considered. Again, the distributions fromthe two cluster samples have been stacked. Different columnscorrespond to different models, as indicated by the legend,while the bottom panels show the corresponding cumulativedistributions. The differential distributions shown in the toppanels of Fig. 3 have been weighted by mass in order toremove the dominant mass dependency and emphasize thedifferences between the two samples.In the DLB07 model (left panels), there is a clear differ-ence between the two samples, which is more evident whenlooking at the cumulative distributions: clusters that hostthe highest elliptical fractions also accreted a larger num-ber of haloes more massive than ∼ M ⊙ , with respectto the clusters that host the lowest elliptical fractions. In-terestingly, the difference between the two samples persistover the entire mass range: this implies a lower contributionfrom diffuse accretion for clusters with large elliptical frac-tions. In the standard MORGANA model, no significantdifference is found between the two samples. If, however,longer merger times are adopted (right panels), then a dif-ference between the haloes with largest and lowest ellipticalfractions become visible, and it is of the same order of mag-nitude of that found in the DLB07 model. At first sight,this result appears counter-intuitive because one would ex-pect that shorter merger times would translate into a bettermatching between the morphological mix of the galaxy pop-ulation and the assembly history of the halo. One has toconsider, however, that changing the merger times wouldaffect the elliptical galaxy population in two distinct ways:on the one hand, longer merger times would tend to de-crease the number of mergers (and therefore the numberof bulge dominated galaxies). On the other hand, longermerger times would also tend to ‘preserve’ the pre-existing In MORGANA , this is simply the most massive progenitor ateach node of the tree. A different definition is adopted in DLB07:the main progenitor is selected by choosing the branch of themerger tree that accounts for most of the mass of the final system,for the longer period. As explained in De Lucia & Blaizot (2007),this avoids possible problems arising when the selection of themost massive progenitor would be ambiguous like, for example,when there are two progenitors of similar mass. ellipticals from being accreted onto the central galaxies (orfrom merging with other satellites if this physical processis included). When adopting longer merger times in
MOR-GANA , we find that the second process would be slightlymore important than the first. As a consequence, both thetotal number of cluster members and the number of ellipti-cal members would increase. This implies that longer mergertimes preserve a better memory of the accretion history ofthe parent dark matter haloes, thereby creating a strongercorrelation between the morphological mix of the clustergalaxy population and its dynamical status.
At fixed cluster mass, the observed properties of the clustergalaxy population exhibit a large variation. Such a scatteris in part due to observational uncertainties in the observedquantities. In the hierarchical framework, however, it is nat-ural to link the observed halo-to-halo scatter to a range ofdynamical histories of the parent cluster. In this paper, wehave investigated the link between the predicted fractionof elliptical galaxies and the accretion history of the parentdark matter halo, by taking advantage of two different semi-analytic models of galaxy formation. Our main results canbe summarized as follows: • For both models used in our study, the predicted el-liptical fractions do not vary significantly as a functionof the cluster mass, for the range of masses considered( M & M ⊙ ). This appears to be in qualitative agree-ment with observational measurements (Wilman et al. 2009;Poggianti et al. 2009; Simard et al. 2009). In our models, aconstant elliptical fraction results from an increasing num-ber of both cluster members and elliptical members, as afunction of cluster mass. • Cluster ellipticals exhibit a marked bimodal distribu-tion in stellar mass. In both models, the bimodality isreduced when a lower ( ∼ .
7) bulge-to-total threshold isadopted for selecting elliptical galaxies. The distribution ofstellar masses for elliptical galaxies preserves its bimodal be-haviour when considering all galaxies (i.e. is not limited tocluster ellipticals). • Since ellipticals are the dominant population amongmassive cluster members, one finds that these galaxies havebeen accreted, on average, onto the cluster when residingin relatively massive structures (more massive than those ofthe overall cluster galaxy population). This creates a corre-lation between the observed fraction of ellipticals and theaccretion history of the halo that is, however, not strong.In the framework of our models, the bimodal distribu-tion of elliptical stellar masses is not due to a more promi-nent role played by disk instability and/or disk regrowthfor intermediate mass galaxies (De Lucia et al. 2011). Weargue that this bimodality results simply from the convolu-tion between the strongly decreasing number of galaxies andthe increasing probability of experiencing a major mergerevent in the past, for increasing galaxy mass (De Lucia et al.2006; Wang & Kauffmann 2008). For galaxies with mass ∼ M ⊙ , the probability of having experienced a majormerger is not large, but there are many low-mass galaxies.On the other hand, almost all galaxies with mass & M ⊙ c (cid:13)000
7) bulge-to-total threshold isadopted for selecting elliptical galaxies. The distribution ofstellar masses for elliptical galaxies preserves its bimodal be-haviour when considering all galaxies (i.e. is not limited tocluster ellipticals). • Since ellipticals are the dominant population amongmassive cluster members, one finds that these galaxies havebeen accreted, on average, onto the cluster when residingin relatively massive structures (more massive than those ofthe overall cluster galaxy population). This creates a corre-lation between the observed fraction of ellipticals and theaccretion history of the halo that is, however, not strong.In the framework of our models, the bimodal distribu-tion of elliptical stellar masses is not due to a more promi-nent role played by disk instability and/or disk regrowthfor intermediate mass galaxies (De Lucia et al. 2011). Weargue that this bimodality results simply from the convolu-tion between the strongly decreasing number of galaxies andthe increasing probability of experiencing a major mergerevent in the past, for increasing galaxy mass (De Lucia et al.2006; Wang & Kauffmann 2008). For galaxies with mass ∼ M ⊙ , the probability of having experienced a majormerger is not large, but there are many low-mass galaxies.On the other hand, almost all galaxies with mass & M ⊙ c (cid:13)000 , 1–8 he fraction of ellipticals in clusters Figure 3.
Mass distribution of haloes accreted on the main branch of each cluster in our sample. Thin dashed lines (blue in the onlineedition of the Journal) are for haloes with an elliptical fraction that is lower than the 10th percentile of the distribution, while thicksolid lines (red in the online edition of the Journal) correspond to the haloes whose elliptical fraction is larger than the 90th percentileof the distribution. The differential distributions in the top panels have been weighted by mass, in order to remove the dominant massdependence and emphasize the differences between the two samples. have experienced at least one major merger during their life-time so, although the number of massive galaxies is low, thismass bin is dominated by elliptical galaxies.We argue that clusters that host larger fraction of ellip-ticals have a lower contribution from diffuse accretion thanclusters with lower elliptical fractions (i.e. they accrete morehaloes, over the entire mass range probed by our simula-tions). In addition, we find that the correlation between theobserved fraction of elliptical galaxies and the accretion his-tory of the halo can be weakened in the case of short mergertimes. This would reduce the number of elliptical clustermembers by having them accreted onto the central clus-ter galaxies or merged with other cluster members. In thisframework, elliptical satellites have been formed before theiraccretion onto the cluster. The measured fraction of ellipti-cals is determined by the balance between the disappearanceof ellipticals due to accretion and mergers, and the recentaccretion of relatively massive structures (that would likelyhost an elliptical central galaxy). A better ‘memory’ of theaccretion history is preserved when merger times are longer.In this case, a stronger correlation between the morpholog- ical mix of cluster populations and the dynamical status ofthe cluster is expected.
ACKNOWLEDGEMENTS
The Millennium Simulation databases used in this paperand the web application providing online access to themwere constructed as part of the activities of the GermanAstrophysical Virtual Observatory. GDL acknowledges fi-nancial support from the European Research Council un-der the European Community’s Seventh Framework Pro-gramme (FP7/2007-2013)/ERC grant agreement n. 202781.FF acknowledges the support of an INAF-OATs fellow-ship granted on ‘Basic Research’ funds and financial con-tribution from the ASI project ‘IR spectroscopy of theHighest Redshift BH candidates’ (agreement ASI-INAF1/009/10/00). DW acknowledges the support of the Max-Planck Gesellschaft. We thank Pierluigi Monaco and SimoneWeinmann for useful discussions.This paper is dedicated to my grandmother. c (cid:13) , 1–8 G. De Lucia et al.
This paper has been typeset from a TEX/ L A TEX file preparedby the author.
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