The effect of thermally pulsating asymptotic giant branch stars on the evolution of the rest-frame near-infrared galaxy luminosity function
Bruno Henriques, Claudia Maraston, Pierluigi Monaco, Fabio Fontanot, Nicola Menci, Gabriella De Lucia, Chiara Tonini
aa r X i v : . [ a s t r o - ph . C O ] D ec Mon. Not. R. Astron. Soc. , 1–11 (2009) Printed 6 December 2018 (MN L A TEX style file v2.2)
The effect of thermally pulsating asymptotic giant branchstars on the evolution of the rest-frame near-infraredgalaxy luminosity function
Bruno Henriques ⋆ , Claudia Maraston , Pierluigi Monaco , ,Fabio Fontanot , Nicola Menci , Gabriella De Lucia , Chiara Tonini Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, United Kingdom INAF - Astronomical Observatory of Trieste, via G.B. Tiepolo 11, I-34143 Trieste, Italy Dipartimento di Fisica - Sezione di Astronomia, Universita‘ di Trieste, via G.B. Tiepolo 11, I-34131 Trieste, Italy INAF - Osservatorio Astronomico di Roma, via di Frascati 33, I-00040 Monteporzio, Italy
Submitted to MNRAS
ABSTRACT
We address the fundamental question of matching the rest-frame K -band lumi-nosity function (LF) of galaxies over the Hubble time using semi-analytic models, aftermodification of the stellar population modelling. We include the Maraston evolution-ary synthesis models, that feature a higher contribution by the Thermally Pulsating -Asymptotic Giant Branch (TP-AGB) stellar phase, into three different semi-analyticmodels, namely the De Lucia and Blaizot version of the Munich model, morgana andthe Menci model. We leave all other input physics and parameters unchanged.We find that the modification of the stellar population emission can solve themismatch between models and the observed rest-frame K -band luminosity from thebrightest galaxies derived from UKIDSS data at high redshift. For all explored semi-analytic models this holds at the redshifts - between 2 and 3 - where the discrepancywas recently pointed out. The reason for the success is that at these cosmic epochsthe model galaxies have the right age ( ∼ K -band when including the TP-AGB contribution. At lower redshifts ( z <
2) some ofthe explored models deviate from the data. This is due to too short merging timescalesand inefficient ’radio-mode’ AGN feedback. Our results show that a strong evolution inmass predicted by hierarchical models is compatible with no evolution on the bright-end of the K -band LF from z=3 to the local universe. This means that, at high redshiftsand contrary to what is commonly accepted, K -band emission is not necessarily a goodtracer of galaxy mass. Key words: methods: numerical – methods: statistical – galaxies: formation – galax-ies: evolution – stars: AGB
Models for the formation and evolution of galaxies in aCold Dark Matter universe (e.g. the so-called semi-analyticmodels) predict the intrinsic properties of galaxies, suchas ages, metallicities, stellar masses, star formation rates, ⋆ E-mail: [email protected] etc.., after having tuned a number of free parametersthat make up for the poorly known aspects of baryonicphysics (see Baugh 2006, for an extensive review). Thecomparison between models and observations helps con-straining these parameters and robust statistical tools havebeen recently used to achieve this goal (Kampakoglou et al.2008; Henriques et al. 2009; Henriques & Thomas 2010;Bower et al. 2010; Lu et al. 2010). c (cid:13) Henriques et al.
The results of these comparisons are very sensitive tothe spectro-modelling of the stellar component. Either forextracting galaxy properties such as mass, age, star for-mation rate from data, and compare them to the intrin-sic quantities of the semi-analytic models, or for calculatingthe spectra of semi-analytic galaxies and compare it withthe observed light, the details on how the stellar modellingis performed influence the final result.In order to obtain the spectral energy distribu-tion (SED), or specific broad-band luminosities, of amodel galaxy of given mass and star formation his-tory, evolutionary populations synthesis (EPS) models(e.g. Tinsley 1972, Bruzual A. 1983, Buzzoni 1989,Bruzual A. & Charlot 1993, Worthey 1994, Vazdekis et al.1996, Fioc & Rocca-Volmerange 1997, Maraston1998, Leitherer et al. 1999, Bruzual & Charlot 2003,Thomas et al. 2003, Maraston 2005 (M05), Conroy et al.2009) are adopted. By relying on stellar evolution theoryand model atmosphere calculations or empirical libraries,EPS models provide the expected spectral energy dis-tribution of a galaxy of given mass and star formationhistory.In galaxy formation models the unit single burst EPSmodels or Simple Stellar Populations (SSPs) are used tomodel coeval stars with a homogeneous metallicity, afteradopting an Initial Mass Function (IMF). The total stellaremission from the synthetic galaxy composite population isthen obtained by combining SSPs. Hence, what matters onthe final result in terms of stellar evolution are the propertiesof the simple stellar population models.It is clear then that this modelling is a crucial aspectof galaxy formation and evolution theory. Uncertainties inthe conversion between masses/ages and light can createartificial discrepancies, which in turn could drive into dif-ficult attempts to modify the parametrization of the com-plicated physics of gas cooling, star formation or feedbackto account for this mismatch. The approach we take in thispaper, following our previous work (Tonini et al. 2009, 2010;Fontanot & Monaco 2010), is to check the impact of modi-fying the input stellar population model in galaxy formationmodels following recent progress in the literature.At present, the highest source of discrepancy betweendifferent SSP models is the treatment of the Thermally-Pulsating Asymptotic Giant Branch (TP-AGB) phase(Maraston 1998, M05, Marigo et al. 2008, Conroy et al.2009). The TP-AGB phase is the last luminous phase in theHertzsprung-Russel diagram before intermediate-mass starsevolve to their final destiny as planetary nebulae and whitedwarfs. TP-AGB stars are very luminous and cool. Theiremission affects the integrated model spectra at wavelengthslarger than ∼ A , peaking around the J, H, K bands(M05) and a recent study has highlighted their importancealso long-ward the rest-frame K (Kelson & Holden 2010).Due to difficulties in the stellar modelling of this phase,which in turn are due to mass-loss and the pulsating regime(see Iben & Renzini 1983, for a review), generally stellartracks did not include the full TP-AGB, so did not stel-lar population models based on these tracks (see M05 fordiscussion). Maraston (1998) and M05 include the TP-AGBsemi-empirically calibrating the theoretical energetics withMagellanic Cloud clusters, an approach now adopted for in- cluding the TP-AGB phase in isochrones (Marigo & Girardi2007; Charlot & Bruzual 2007).The galaxy formation models we use in this study,in their standard stellar populations, either neglector do not include a full contribution from the TP-AGB stellar phase. As pointed out by several papers(Maraston 1998, Maraston et al. 2001, Maraston et al.2004, M05, Maraston et al. 2006, van der Wel et al.2006, Marigo & Girardi 2007, Charlot & Bruzual 2007,Eminian et al. 2008, Conroy et al. 2009) the inclusionof TP-AGB stars provides an enhancement of the near-infrared emission of galaxies dominated by ∼ < z <
3) galaxies are considered, since we expect them to bedominated by young stellar populations.Semi-analytical techniques represent an obvious toolto perform such test. Predictions from these models havealready been compared with the evolution of the ob-served K -band Luminosity Function (LF) (Pozzetti et al.2003; Cimatti et al. 2004; Kitzbichler & White 2007;Cirasuolo et al. 2010). These works consistently found a lackof bright sources at high redshift. This apparent mismatchis being referred to as one of the strongest discrepanciesbetween models and data (in particular in connection withthe evolution of the stellar mass function, see Fontanot et al.2009b for a critical review of the latter issue). However, thesecomparisons involved spectro-photometric codes based onstellar tracks where the full effect of TP-AGB stars was nottaken into account.The first test of this kind is performed in Tonini et al.(2009, 2010). They run the GALICS semi-analytic model(Hatton et al. 2003) using M05 as input EPS and showthat the optical-to-near-IR colours of z ∼ morgana obtaining a good match on the numberdensity of extremely red objects (EROs) at high redshift.Here we investigate whether the inclusion of the TP-AGB phase has also an impact on the inability of semi-analytic models to match the galaxy rest-frame K -bandluminosity function at high-redshift, namely the UKIDSSdata from Cirasuolo et al. (2010). This homogeneous dataset covers an ideal redshift range (0 < z <
3) for this test.To perform this analysis, we use three differ-ent semi-analytic models of galaxy formation: theDe Lucia & Blaizot (2007) version of the Munich model, morgana (Monaco et al. 2007) and the Menci et al. (2006)semi-analytic model. We compare the predictions obtainedfor the properties of the galaxy population using both stel-lar populations with and without a full treatment of the TP-AGB phase. For the three models (De Lucia & Blaizot 2007;Monaco et al. 2007; Menci et al. 2006) outputs are producedusing, respectively Bruzual & Charlot (2003), Silva et al.(1998) and Bruzual A. & Charlot (1993), and M05. Notethat, despite including the contribution from TP-AGB starsin their model, Bruzual & Charlot (2003) only partially ac- c (cid:13) , 1–11 he rest-frame K-Band Luminosity Function count for the emission during this stellar phase, meaningthat 1 Gyr old populations are roughly only half as brightin the K -band when compared to more recent treatments(Charlot & Bruzual 2007)This paper is organized as follows. In Section 2, webriefly describe the semi-analytic models used in this study,and we explain how the M05 EPS is implemented in eachgalaxy formation model. In Section 3 we describe the dataused for comparison and clarify where the impact of the M05models is expected to be found. Section 4 presents the resultsfor the evolution of the rest-frame near-infrared luminosityfunction and in Section 5 we summarize our conclusions. A clear advantage of the work presented in this paper isthe use of three semi-analytic models developed by inde-pendent groups and implementing different techniques forthe description of the physics controlling galaxy formationand evolution. This allows us not only to assess the im-pact of the TP-AGB phase, but also to understand the in-terplay between the new ingredient and the other assump-tions regarding galaxy physics on the light of the samestellar evolution background. In particular we consider theDe Lucia & Blaizot (2007) version of the Munich model;
MORGANA (originally described in Monaco et al. 2007and updated by Lo Faro et al. 2009); and the Menci et al.(2006) model.The backbone for all models is a description of the red-shift evolution of the mass and number density of dark mat-ter halos in terms of their merger history (the so-calledmerger trees). The evolution of the baryonic componenthosted by these halos is then followed by means of an ap-proximated set of simplified formulae, aimed at describingthe physical processes acting on the gas (such as gas cooling,star formation and feedback) in terms of the physical prop-erties of each model galaxy and/or its components (i.e thestellar, hot and cold gas content and distribution). Theseanalytical recipes include a set of parameters which are usu-ally calibrated against a well defined subset of low-redshiftobservations.The three models adopt different techniques to describethe dark matter merger trees and slightly different cosmolo-gies. However, we do not expect these to have a significanteffect on our conclusions (see e.g. Wang et al. 2008).On the other hand, the different star formation histo-ries and the corresponding distribution of ages and the massbuild up in the models do matter. In the following, we willbriefly account for differences between the models, focusingin particular on the AGN feedback and the merging timescales, the processes most relevant for the evolution of thebright-end of the K -band LF. For more details on the treat-ment of these physical processes in the different models we The Munich model uses merger trees extracted from a di-rect N-Body simulation of a cosmological volume (the Millen-nium Simulation, (Springel et al. 2005)), morgana uses the La-grangian semi-analytic code pinocchio (Monaco et al. 2002) andMenci et al. (2006) uses Monte Carlo realizations of merger treesbased on the halo merging probability given by the ExtendedPress-Schechter formalism. refer the reader to the original papers, and to De Lucia et al.(2010); Fontanot et al. (2009b) for recent comparisons.
The recipe adopted to describe AGN feedback is of crucialimportance, since it largely determines the stellar populationproperties of the most massive galaxies, whose evolution isthe focus of our paper. Recent studies (e.g. Croton et al.2006) assume that the growth of Super-Massive Black-Holes(SMBHs) at the center of model galaxies follows two chan-nels, a “bright-mode” (or “quasar-mode”) and a “radio-mode”, related to the efficient production of radio jets. The“quasar-mode” is fueled by merger driven instabilities, it isthe dominant channel in terms of black hole growth andcan be effective in producing feedback at early times (wheremerging rates are high). The “radio-mode” is less impor-tant in terms of SMBH growth but is responsible for starformation quenching at low redshift.The details of the implementations of the two modesdiffer between the models considered in this study (see e.g.Fontanot et al. 2010b for a detailed discussion about mor-gana and De Lucia & Blaizot (2007)). While the net effectof the “quasar-mode” is quite similar between the variousmodels, even if the implementations are slightly different, itis the “radio-mode”, to be mostly responsible for differencesin the galaxy stellar populations towards low redshift.In the Munich model, the “radio-mode” feedback isthe result of quiescent gas accretion from a static hot halo(Croton et al. 2006), with no triggering mechanism required.In morgana , the “radio-mode” is due to the accretion (atvery low rates) of cold gas from a reservoir surroundingthe central SMBH (see Fontanot et al. (2006) for more de-tails). Note that some amount of star formation is requiredto destabilize the gas in the reservoir. Hence, star forma-tion is not completely quenched. This residual star forma-tion causes galaxies to have colours that are too blue at lowredshift with respect to both observations and other models(Kimm et al. 2009) and contributes to an excessive build upof massive objects at later times. Finally, the Menci et al.(2006) model does not include “radio-mode” feedback. Forthis reason, at low redshift, massive objects always have on-going star formation, which causes an excessive mass buildup in these objects. Relevant to our work is that this resultsin an over-prediction of the bright tail of the K-band LF, aswe will show in Section 4.
Dark matter substructures and their clustering have relevantconsequences on the evolution of galaxies. Gravitational pro-cesses such as dynamical friction and tidal stripping affectthe morphology, the stellar and the gaseous content of galax-ies. Two-body mergers are even more extreme processes,leading to the formation of a new object, whose final prop-erties depend on the properties of the progenitors.In the Munich model, dark matter substructures in theN-body simulation are explicitly tracked down until tidaltruncation and stripping reduce their mass below the resolu-tion limit of the simulation (De Lucia et al. 2004; Gao et al.2004). In Menci et al. (2006) dark matter is followed us- c (cid:13) , 1–11 Henriques et al. ing a Press-Schechter formalism and satellite halos are par-tially disrupted as the density in their outer parts becomeslower than the density of the host halo within the pericentreof its orbit (see Menci et al. (2002) for details). After thispoint the merging time of the satellite in both models iscomputed using the classical Chandrasekhar (1943) dynam-ical friction approximation. It is worth stressing that theDe Lucia & Blaizot (2007) model includes an additional pa-rameter in this formula, effectively doubling the expectedmerging times. This value was introduced to reduce theslight excess of bright galaxies that would be produced oth-erwise. morgana does not track explicitly dark matter sub-structures and assumes that satellite galaxies merge ontocentral galaxies after a dynamical friction time-scale which iscomputed using analytic formulae proposed by Taffoni et al.(2003).De Lucia et al. (2010) compare different approxima-tions for the dynamical friction merging time-scales used insemi-analytics. They find that while the De Lucia & Blaizot(2007) recipe is in good agreement with some recent re-sults based on N -body-simulations (Boylan-Kolchin et al.2008), the Taffoni et al. (2003) formulae predict significantlyshorter merging times. Note that the same is true forMenci et al. (2006) with merging times two times shorterthan in De Lucia & Blaizot (2007).Despite the overall agreement between different mod-els in terms of the mass build up found by Fontanot etal. (2009b), it can be seen that morgana shows an ex-cessive build up of massive galaxies at late times. We ex-pect Menci et al. (2006) to show a similar behaviour. This isdue to the combined effect from the enhanced merger activ-ity and the ongoing star formation due to inefficient AGNfeedback at low redshift. This will affect our results withboth models over-estimating the number density of bright K -band objects at later times (see Section 4). As recalled in the Introduction, the spectra of galaxies insemi-analytic models are obtained by means of spectro-photometric population synthesis models. The implemen-tation of the M05 models is straightforward in these semi-analytics. We use SSPs corresponding to four metallicities,1/20 Z ⊙ , 1/2 Z ⊙ , Z ⊙ and 2 Z ⊙ , which despite not beingexactly the same as for the stellar populations previouslyused (since the input stellar tracks of the M05 models aredifferent, see M05 for details), cover a similar range andare as coarse. Therefore, this difference has no impact onour predictions. The same IMF that was previously adoptedin the various semi-analytic models is retained, namely theChabrier (2003) for morgana and the Munich model, anda Salpeter (1955) for Menci et al. (2006).The predicted luminosities are then corrected for dustextinction. For all models we keep these prescriptions un-changed. The different treatment of dust extinction has non-negligible effects on the predicted magnitudes and colors, es-pecially at z > K -band emission is relatively insensitive to dust Note that the M05 stellar populations were implemented in morgana by Fontanot & Monaco (2010)
Figure 1.
A simple stellar population spectral energy distribu-tion from M05 is compared with the equivalent predictions frommodels used in semi-analytic models (here Bruzual & Charlot(2003) as an illustrative example). The plot refers to a 1 Gyr oldpopulation with solar metallicity. The full treatment of TP-AGBstellar phase in the M05 models gives significant emission for pop-ulations between 0.2 and 1 Gyr. For similar plots and discussionsee M05. attenuation, we do not expect these differences to substan-tially affect our results.Finally, It is worth stressing that we keep all other as-sumptions and parameters of the semi-analytic models as intheir original formulation. Therefore, we can highlight anymodification due just to the change in the stellar populationlibraries. K -BAND LUMINOSITYFUNCTION AT HIGH REDSHIFT In this paper we focus on a well documented discrep-ancy between semi-analytic models and observations, theinability of the models in matching the observed red-shift evolution of the rest-frame near-infrared galaxy lu-minosity function (Pozzetti et al. 2003; Cimatti et al. 2004;Kitzbichler & White 2007). This has recently been con-firmed over a wide redshift range (Cirasuolo et al. 2010).This paper uses a data set from the Ultra Deep Survey(UDS), the deepest survey from the UKIRT Infra-Red DeepSky Survey (UKIDSS), containing imaging in the J - and K -bands, with deep multi-wavelength coverage in BV Ri ′ z ′ filters in most of the field. The sample contains ≈ K
23. Cirasuolo et al. (2010) find thatthe space density of the most massive galaxies at high red-shifts (above 2) is under-predicted by semi-analytic models,in other words the theoretical luminosity function lacks thebrightest sources in the near-IR.Tonini et al. (2009, 2010); Fontanot & Monaco (2010)showed that the number of bright K -band objects at high c (cid:13) , 1–11 he rest-frame K-Band Luminosity Function redshift in semi-analytic models can be increased by includ-ing the M05 models with their treatment of the TP-AGBphase of stellar evolution. We briefly recall here the originof such an effect. The M05 models, predict that young pop-ulations have a significant contribution to the near-infrared.For the luminosity function analysis, the differences are ex-pected to be more significant at high redshift where a largerfraction of the galaxy population contains young stars. InFig. 1 we plot the spectral energy distribution (SED) for apopulation with 1 Gyr of age and solar metallicity, usingM05 and an illustrative example of the stellar populationspreviously implemented in semi-analytic models (see M05for similar plots and discussion). In the K -band the M05model predicts more than twice the emission, hence affectsthe prediction of semi-analytic galaxies at high redshift.In concluding this section, some words of caution mustbe given on the data/model comparison. In Cirasuolo et al.(2010) the galaxies have photometric redshifts, which wereobtained by fitting empirical as well as synthetic templatesfrom Bruzual & Charlot (2003). For consistency, photomet-ric redshifts and rest frame magnitudes should have beenderived for the data using the same stellar populations thatwe are implementing in the semi-analytic models, but thesedata are not available to us. However we emphasize that thedifferences that arise from using the M05 models to convertfrom mass to light (or light to mass) are considerably largerthan the ones originated from the determination of photo-metric redshifts (e.g. Maraston et al. 2006). The subsequentconversion from observed- to rest-frame magnitudes is moredifficult to track, as the different theoretical templates usu-ally give different fitted ages depending on the properties ofeach galaxy (e.g. Maraston et al. 2006; Cimatti et al. 2008).However, this will produce differences between derived k+ecorrections that are not systematic and therefore should notalter our conclusions.Finally, when comparing model results and data, oneshould consider that model magnitudes are “total”, whileobservational measurements are usually based on “aper-ture” magnitudes. At redshift zero, a significant fractionof light might be missed for large objects that exceedthe available aperture diameter (e.g. Lauer et al. 2007;von der Linden et al. 2007). At the higher redshifts stud-ied here, despite galaxies being smaller than the maximumavailable apertures, there can still be an issue of missinglight when small apertures are used to ensure high signal-to-noise. Moreover, the situation can be complicated by limitedinstrumental resolution that might blend together objectsin crowded regions. The first problem is minimized in thedata we use by applying point spread function (PSF) cor-rections to total magnitudes (Cirasuolo et al. 2010). Nev-ertheless, both aspects can influence the evolution of thebright end of the luminosity function. K -band Luminosity Function Fig. 2 compares the evolution of the K -band luminosityfunction from redshift 3 to redshift 0.5 for the semi-analyticmodels with the Cirasuolo et al. (2010) data (shown as openblack circles). De Lucia & Blaizot (2007) models are shown in red, morgana in green and Menci et al. (2006) in blue.Original model versions are shown as dashed lines and theM05 versions as solid lines.The three galaxy formation models in the M05 versionsshow an enhanced K -band emission (between 0.25 and 0.5mags) from the brightest objects ( M K −
24) which for z > K -band emission. For this reason,the bright end of the K -band luminosity function could onlybe built-up at lower redshifts, when old populations becomedominant in massive galaxies. The TP-AGB phase gives asimple and straightforward way to solve the problem withthe observed evolution of the K -band.The agreement between the semi-analytic-plus-M05models for bright K -band objects and observations athigh redshift is remarkable. In principle effects from theage/metallicity degeneracy could produce an artificial agree-ment between data and model. For example, a luminous K -band can originate from very metal-rich populations orfrom much older populations than those dominated by theTP-AGB emission. However, the wide redshift range thatis spanned by these observations and the trend of the ob-served K -band LF with redshift allows us to exclude sucheffects acting at all redshifts. This is particularly the caseat high redshift, where the time elapsed since the Big Bangis short enough such that this age degeneracy cannot enterthe game.These results suggest that, if masses and ages were es-timated from observational data using M05, these wouldbe in agreement with model predictions. The conver-sion to photometric properties was fully responsible forthe disagreement with observations that was pointedout by Cirasuolo et al. (2010) and previously found byother authors (Pozzetti et al. 2003; Cimatti et al. 2004;Kitzbichler & White 2007). This result has important impli-cations for the observational determinations of stellar massesand ages from photometric data, in particular for galaxies athigh redshift. Significant K -band emission can be producedby young populations at high redshift through the TP-AGBstellar phase. Without considering it, large K -band emissioncan only originate at older ages, which results in a system-atic over-estimation of stellar masses derived from emissionin this band (e.g. Maraston et al. 2006).Interesting differences among the models emerge at lowredshifts. The De Lucia & Blaizot (2007) model plus M05follows the bright tail in every redshift bin (z=0.5 to z=3.0).At redshift 1 the better match between data and the modelsimplies a certain fraction of 1 Gyr population in these galax-ies, a prediction that could be tested by acquiring rest-framenear-IR spectra.For morgana and Menci et al. (2006), the inclusion ofthe M05 models worsens an existing discrepancy at lowerredshift z < = 1 .
5, namely that the models over-predict thenumber density of massive galaxies. This discrepancy is em-phasized with M05 because existing ∼ c (cid:13) , 1–11 Henriques et al.
Figure 2.
The evolution of the K-band luminosity function from z=3.0 to z=0.5. The original predictions from three different semi-analytic models are shown as dashed lines and their version with the M05 as solid lines. Red lines refer to De Lucia & Blaizot (2007),green to Monaco et al. (2007) and blue to Menci et al. (2006). Data from Cirasuolo et al. (2010) are shown as black opened circles andthe solid line. (2006) and morgana are shorter than what is expected fromthe numerical analysis of Boylan-Kolchin et al. (2008), aspointed out by De Lucia et al. (2010). Moreover, both mod-els have AGN feedback implementations that are inefficientin shutting down star formation in massive objects at latertimes. In the Menci et al. (2006) model this is caused by theabsence of “radio-mode” AGN feedback. In morgana someamount of star formation is required to destabilize the reser-voir of gas and trigger this feedback mode. This results ingalaxy optical colours that are too blue (as pointed out byKimm et al. 2009, for morgana ) and in an excess of massivegalaxies as emphasised by both stellar population models inour study.In Fig. 3 we plot the K -band Luminosity function at redshift 3.0 for the Munich Model using the originalBruzual & Charlot (2003) stellar populations (red dashedline), the M05 (solid red line) and the Charlot & Bruzual(2007) (dotted red line) models. The similarity betweenthe M05 and Charlot & Bruzual (2007) results shows thatthe different treatment of the TP-AGB phase (respectivelyMaraston (1998) and Marigo et al. (2008)) has a minor im-pact in our conclusions. In order to clarify the different results obtained with thethree semi-analytic models, we show in Fig. 4 the mass- c (cid:13) , 1–11 he rest-frame K-Band Luminosity Function Figure 4.
The mass-weighted (left-hand panel) and K -band light weighted (right-hand panel) age distributions of model galaxies withM K < −
24. Red, green and blue colours refer to De Lucia & Blaizot (2007), morgana and Menci et al. (2006), respectively. Solid linesrepresent model versions with M05, whereas dotted lines refer to the original stellar populations. From top to bottom, panels refer toredshift z=0.5, z=1.0 and z=2.5. weighted and K -band light-weighted ages (left-hand andright-hand panels, respectively) for galaxies brighter thanM K =-24, as a function of redshift. The mass-weighted agesillustrate the relative contribution of galaxies with differentages to the total mass budget (with red, green and blue linesrepresenting the Munich, morgana and the Menci et al.(2006) models, respectively). At early times (z ≈ K -band luminosity function be-ing built up by a combination of young and old populations(with the latter, maintained by the “radio-mode” AGN feed- c (cid:13)000
24. Red, green and blue colours refer to De Lucia & Blaizot (2007), morgana and Menci et al. (2006), respectively. Solid linesrepresent model versions with M05, whereas dotted lines refer to the original stellar populations. From top to bottom, panels refer toredshift z=0.5, z=1.0 and z=2.5. weighted and K -band light-weighted ages (left-hand andright-hand panels, respectively) for galaxies brighter thanM K =-24, as a function of redshift. The mass-weighted agesillustrate the relative contribution of galaxies with differentages to the total mass budget (with red, green and blue linesrepresenting the Munich, morgana and the Menci et al.(2006) models, respectively). At early times (z ≈ K -band luminosity function be-ing built up by a combination of young and old populations(with the latter, maintained by the “radio-mode” AGN feed- c (cid:13)000 , 1–11 Henriques et al.
Figure 3.
The K -band luminosity function for the Munich modelat z=3.0. The solid, dotted and dashed red lines represent, re-spectively, runs using the M05, Charlot & Bruzual (2007) andBruzual & Charlot (2003) stellar populations. back, growing in importance as we move to lower redshifts).This bimodality is also present in Menci et al. (2006), butis weaker and the oldest population is ∼ morgana shows considerably younger ages, centered at ∼ ∼ morgana and Menci et al. (2006) (resulting in a simi-lar over-estimation of the number density of bright K -bandobjects). The Menci et al. (2006) model has a smaller frac-tion of younger ages. This is due to the assumed modelingof the “quasar-mode” feedback combined with the absenceof “radio-mode”. At very high redshift (z >
3) star forma-tion is high in the progenitors of massive galaxies due tomerger induced starbursts. At low redshifts only a fractionof these galaxies have their star formation quenched. On theother hand, morgana has continuous on-going star forma-tion but always at a moderate level, being self-regulated bythe “radio-mode” feedback.The mass-weighted age distribution of the modelshelped us understanding the results on the K -band lumi-nosity function and display the backbone of the models. Wenow consider a light-weighted age distribution, which em-phasises how the different input stellar population modelscan force such distributions to different age domains. Weconsider K -band light-weighted ages, because they empha-sise the distinction between the model ingredients. For tech-nical reasons, we cannot easily compute light-weighted agesin the morgana model. We therefore limit this test to thetwo other models. In the three right-hand panels of Fig. 4,red lines represent results from the Munich model while bluelines give ages for Menci et al. (2006). Solid lines representversions that include the TP-AGB phase with the M05 anddotted lines the original stellar populations.The strongest difference between the two model rendi- Figure 5.
The ages of the individual populations present in semi-analytic galaxies with M K < −
24. The solid red line representsDe Lucia & Blaizot (2007), the solid green line shows morgana predictions and the solid blue line gives Menci et al. (2006) agesat z=0.5. tions is displayed by the Munich model, because of the agebimodality mentioned above. Focussing on redshift 1 and0.5, the difference between light-weighted and mass weightedages is smaller for M05 than for BC03 (solid vs dotted lines),because the young populations coloured with the M05 getenough K -light such that the mass weighted histogram rel-ative weights are maintained. In case of the version withBC03, instead, the K -band light only comes from old pop-ulations, and as a result the weight of the bimodality ( k -light-weighted) is distorted, with a much higher fraction ofpopulations getting old ages. The behaviour is diluted for theMenci et al. (2006) models because galaxy ages do not showa clear bimodality between young and old ages. Therefore,mass-weighted and K -band light-weighted age distributionsare similar and the results for the different stellar populationmodels are similar as well.It should be noted that the mass-weighted age is an av-erage over the individual populations that compose the theo-retical galaxies. This implies that individual ages can extenddown to much lower values. This can be seen in Fig. 5, wherewe show the ages of the individual populations for galaxieswith M K < −
24 at z=0.5 in the three semi-analytic mod-els. The 1 Gyr old populations present in the three modelsexplain the impact of the TP-AGB phase even at this red-shift. It can also be seen that morgana exhibits the largerfraction of young stars, since the “radio-mode” feedback isregulated by star formation. Menci et al. (2006) ages areconsiderably older, due to the impact of the “quasar-mode”feedback at early times. However, as it starts being inef-fective at lower redshifts a considerable fraction of youngerpopulations emerge.Despite the significant improvement obtained in match-ing the evolution of the bright end of the K -band luminos-ity function, the faint end remains problematic. The lumi-nosity (as well as the stellar mass) function for faint ob-jects ( − M K −
24) is known to be much higherthan measured (Fontana et al. 2006; Weinmann et al. 2006;Henriques et al. 2008; Fontanot et al. 2009b) and the in- c (cid:13) , 1–11 he rest-frame K-Band Luminosity Function clusion of the M05 models worsens the case. This excesscan be removed in different ways at redshift zero, by us-ing a more up-to-date cosmology (Somerville et al. 2008) orcombining the disruption of stellar material from satellitesduring mergers (Monaco et al. 2006; Henriques et al. 2008;Somerville et al. 2008) with more efficient supernova feed-back (Henriques & Thomas 2010; Guo et al. 2010). Never-theless, the comparison presented in our work for high red-shift (as already shown by Fontanot et al. 2009b), showsthat for the early phases of galaxy evolution this might be aproblem, even considering problems of incompleteness withthe high redshift data. The main objective of this work is to re-address the fun-damental question of matching the observed rest-frame K -band luminosity function of galaxies over the Hubble time,using semi-analytic models. In the literature (Pozzetti et al.2003; Cimatti et al. 2004; Kitzbichler & White 2007;Cirasuolo et al. 2010), it has been pointed out that semi-analytic models underestimate the rest-frame K -bandgalaxy luminosity of the brightest objects at high redshift( ∼ − K -band emissionfrom the model galaxies. We use the M05 stellar popula-tion models, which include the full treatment of the emissionfrom the cool and luminous TP-AGB phase. The contribu-tion of this phase of stellar evolution in the M05 models isimportant at intermediate ages (between 0.2 and 2 Gyrs),which are expected to be predominant at 2 < z <
3. The rele-vance of this ingredient has been recently shown for the semi-analytic model GALICS in Tonini et al. (2009, 2010), wherethe observed near-IR colours of redshift 2 galaxies could onlybe matched by the model inclusive of the TP-AGB emis-sion. Similarly, Fontanot & Monaco (2010) showed that theinclusion of this stellar phase in MORGANA increases sig-nificantly the number density of EROs at high redshift.We consider several semi-analytic models - namelyDe Lucia & Blaizot (2007), morgana (Monaco et al. 2007)and Menci et al. (2006) and we implement the M05 stel-lar population models, keeping all other ingredients and as-sumptions unchanged.We find that the semi-analytic models with the M05models exhibit a brighter K -band LF by as much as 0.5 magsat the highest redshift bins. This is precisely the offset thatwas plaguing the comparison with the UKIDSS data for thebrightest objects in Cirasuolo et al. (2010). Models and dataat high redshift and for M K < −
24 now match very well.This result is confirmed when using the Charlot & Bruzual(2007) models as input for the Munich model. This confirmsthat different modelling of the TP-AGB phase has a minorimpact on our conclusions.This result is strongly suggestive that the models atredshift 2 − K -band LF from z=3 to the local universe.This means that, at high redshifts and contrary to what iscommonly accepted, K -band emission is not necessarily agood tracer of galaxy mass.At lower redshift, the details of the implementation ofAGN feedback and merging timescales produce differencesbetween the various semi-analytic models that are not al-tered by the inclusion of the M05 models. In particular, mor-gana and Menci et al. (2006) exhibit a K -band luminosityfunction bright tail that is higher than the data, which is dueto an excessive mass build-up connected to the lack of anefficient quenching of low-z cooling flows via ”radio-mode”feedback.Similarly, the faint end of the galaxy luminos-ity function remains substantially overestimated bythe models at all redshifts. This is a well docu-mented problem (Fontana et al. 2006; Weinmann et al.2006; Henriques et al. 2008; Henriques & Thomas 2010;Fontanot et al. 2009b; Guo et al. 2010) that we plan tostudy in future work.In recent years, our understanding of the various phasesof stellar evolution has improved. Moreover, we now havehigh-quality observational data covering a wide spectralrange (including the rest-frame near infra-red). Therefore,we should now be able to constrain galaxy formation mod-els with better accuracy and disentangle between differenttheoretical approaches. ACKNOWLEDGEMENTS
This project is supported by the Marie Curie ExcellenceTeam Grant MEXT-CT-2006-042754 ”UniMass” (PI: C.MAraston) of the Training and Mobility of Researchers pro-gramme financed by the European Community. PM and FFacknowledge support by the ASI/COFIS grant. FF acknowl-edges the support of an INAF-OATs fellowship granted on’Basic Research’ funds. GDL acknowledges financial supportfrom the European Research Council under the EuropeanCommunitys Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement n. 202781.The authors thank Emanuele Daddi and the refereeGustavo Bruzual for helpful comments. PM and FF thankLaura Silva for useful discussions. BH, CM and CT thanksEdd Edmondson for a computer network that always works.BH thanks Peter Thomas for his guidance and constant sup-port.
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