Confronting theoretical models with the observed evolution of the galaxy population out to z=4
Bruno Henriques, Simon White, Gerard Lemson, Peter Thomas, Qi Guo, Gabriel-Dominique Marleau, Roderik Overzier
aa r X i v : . [ a s t r o - ph . C O ] D ec Mon. Not. R. Astron. Soc. , 1–14 (2011) Printed 29 October 2018 (MN L A TEX style file v2.2)
Confronting theoretical models with the observedevolution of the galaxy population out to z=4
Bruno Henriques ⋆ , Simon White , Gerard Lemson , Peter Thomas ,Qi Guo , , Gabriel-Dominique Marleau , , Roderik Overzier Max-Planck-Institut f¨ur Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching b. M¨unchen, Germany Astronomy Centre, University of Sussex, Falmer, Brighton BN1 9QH, United Kingdom Partner Group of the Max-Planck-Institut f¨ur Astrophysik, National Astronomical Observatories, Chinese Academy of Sciences,Beijing, 100012, China Department of Physics, Institute for Computational Cosmology, University of Durham, South Road, Durham DH1 3LE Department of Physics, McGill University, 3600 Rue University, Montr´eal, QC H3A 2T8, Canada
Submitted to MNRAS
ABSTRACT
We construct lightcones for the semi-analytic galaxy formation simulation of Guo et al.(2011) and make mock catalogues for comparison with deep high-redshift surveys. Pho-tometric properties are calculated with two different stellar population synthesis codes(Bruzual & Charlot 2003; Maraston 2005) in order to study sensitivity to this aspectof the modelling. The catalogues are publicly available and include photometry for alarge number of observed bands from 4000˚ A to 6 µ m, as well as rest-frame photometryand other intrinsic properties of the galaxies (e.g positions, peculiar velocities, stellarmasses, sizes, morphologies, gas fractions, star formation rates, metallicities, halo prop-erties). Guo et al. (2011) tuned their model to fit the low-redshift galaxy populationbut noted that at z > B , i , J , K and IRAC 3 . µ m, 4 . µ m and 5 . µ m bands, to the redshift distributions of K and 5 . µ m selected galaxies, the evolution of rest-frame luminosity functions in the B and K bands and the evolution of rest-frame optical versus near-infrared colours.The B , i and J counts are well reproduced, but at longer wavelengths the overabun-dant high-redshift galaxies produce excess faint counts. At bright magnitudes, countsin the IRAC bands are underpredicted, reflecting overly low stellar metallicities andthe neglect of PAH emission. The predicted redshift distributions for K and 5 . µ mselected samples highlight the effect of emission from thermally pulsing AGB stars.The full treatment of Maraston (2005) predicts three times as many z ∼ . µ m selected samples as the model of Bruzual & Charlot (2003), whereas thetwo models give similar predictions for K -band selected samples. Although luminosityfunctions are adequately reproduced out to z ∼ B , the same is true atrest-frame K only if TP-AGB emission is included, and then only at high luminosity.Fainter than L ⋆ the two synthesis models agree but overpredict the number of galax-ies, another reflection of the overabundance of ∼ M ⊙ model galaxies at z > z = 2 asrequired by observations. Key words: methods: numerical – methods: statistical – galaxies: formation – galax-ies: evolution – stars: AGB ⋆ E-mail:[email protected]
Semi-analytic models of galaxy formation aim to predictthe evolution of population properties such as the distri-butions of stellar mass, luminosity, star formation rate,size, rotation velocity, morphology, gas content and metal- c (cid:13) Henriques et al. licity, as well as the scaling relations linking these prop-erties. They follow astrophysical processes affecting thebaryonic components using a series of analytic, physicallybased models which are embedded either in an analytic rep-resentation (White & Frenk 1991; Kauffmann et al. 1993;Cole et al. 1994; Somerville & Primack 1999) or in a directnumerical simulation (Kauffmann et al. 1999; Springel et al.2001, 2005) of the evolution of the underlying dark mat-ter distribution. Uncertain efficiencies and scalings of theseastrophysical processes are represented by adjustable pa-rameters. These may be set a priori through a detailedcalculation or simulation of specific processes, or theymay be determined observationally by matching suitablychosen data (e.g. Croton et al. 2006; Bower et al. 2006;Menci et al. 2006; Cattaneo et al. 2006; De Lucia & Blaizot2007; Monaco et al. 2007; Somerville et al. 2008; Guo et al.2011). The extremely broad range of relevant data and theconsiderable freedom in specifying appropriate recipes com-plicate the systematic comparison of semi-analytic mod-els with data. New and robust statistical tools haverecently been developed to facilitate quantitative com-parisons (Kampakoglou et al. 2008; Henriques et al. 2009;Henriques & Thomas 2010; Bower et al. 2010; Lu et al.2010).Such comparisons are sensitive to stellar populationsynthesis models which are required both to derive in-trinsic galaxy properties such as mass, age and star for-mation rate from observational data, and to calculate lu-minosities, colours and spectra for model galaxies. Erro-neous conversions between physical and observable prop-erties lead to incorrect conclusions about galaxy forma-tion physics, so it is important to check the implica-tions of adopting differing stellar populations synthesismodels (e.g. Buzzoni 1989; Worthey 1994; Vazdekis et al.1996; Fioc & Rocca-Volmerange 1997; Leitherer et al. 1999;Bruzual & Charlot 2003; Thomas et al. 2003; Maraston2005; Conroy et al. 2009).For example, the impact of including models forthermally-pulsating asymptotic giant branch (TP-AGB)stars has been studied in some detail in recent years. Thecontribution from these stars can significantly enhance thenear-infrared emission of galaxies with Gyr-old populations(e.g. Maraston 1998; Maraston 2005; van der Wel et al.2006, Marigo & Girardi 2007; Charlot & Bruzual 2007;Conroy et al. 2009). The data of Conroy et al. (2009),Marchesini et al. (2009, 2010), Zibetti et al. (2009) andSantini et al. (2011) show that inclusion of this additionalemission can reduce the masses inferred from K-bandlight by as much as 0.6 dex. The semi-analytic models ofTonini et al. (2009, 2010), Fontanot & Monaco (2010) andHenriques et al. (2011) suggest that a substantial contri-bution from TP-AGB stars, as predicted by the model ofMaraston (2005) may explain the large number of extremelyred objects found at z ∼
2. Other examples of how uncer-tainties in stellar evolution modelling affect physical infer-ences from data are given by Conroy et al. (2010). Here wecompare predictions of the Guo et al. (2011) semi-analyticmodel for two different population synthesis models, the oneoriginally used by these authors (from Bruzual & Charlot2003) and that of Maraston (2005).Even neglecting uncertainties from stellar populationmodelling, mass-to-light ratios and other physical properties are often poorly constrained by available data. Estimatesrely on fitting theoretical models to observed photometryand spectral energy distributions (SEDs) and approximatelyequivalent fits can often be obtained for broad ranges ofassumed star formation history, chemical enrichment historyand obscuration by dust. Additional uncertainties arise frompossible variations in the initial mass function (IMF) withwhich stars form, and from possible spectral contributionsfrom an active galactic nucleus (AGN). It has been arguedin the past that a single optical colour (e..g. g − i ) is, inpractice, sufficient to derive light-to-mass ratios accurate to0.1 dex for most galaxies (Bell et al. 2003; Gallazzi & Bell2009). However, Zibetti et al. (2009) showed that this is onlytrue for relatively weak obscuration. For heavily obscuredyoung populations, resolved photometry is needed to achievean accuracy better than 0.2 dex and even that requires anadditional near-infrared colour (e.g. one may combine g − i and i − H ).Galaxy formation models directly predict star forma-tion and enrichment histories, so in the absence of obscura-tion a well defined SED can be predicted for each galaxy asa superposition of simple stellar populations (SSPs), eachmade up of coeval stars of a single metallicity. The “ob-served” photometry is then easily obtained by redshiftingthe SED and integrating over the appropriate photometricfilter functions. In practice, however, the conversion to ob-servables is heavily influenced by dust and is sensitive to thedetails of its distribution within a galaxy (e.g. Granato et al.2000; Cole et al. 2000). This significantly limits the preci-sion with which observables can be predicted from galaxyformation models. Current semi-analytic models often at-tempt to handle these uncertainties by using observationaldata to constrain the dust model (e.g. Granato et al. 2000;Cole et al. 2000; Kitzbichler & White 2007; Guo & White2009).Because of such difficulties it seems wise to comparetheory and observation for a broad range of properties, atdifferent redshifts, and at different “conversion levels”. Thelatter is particularly crucial at high-redshift, where very lim-ited data are available and the relations between mass, lightand star-formation rate are very uncertain. There is no pre-ferred “comparison frame” and conclusions are convincingonly if a consistent picture emerges which matches smoothlyonto the lower redshift galaxy populations. Guo et al. (2011)compare their model extensively to low-redshift galaxies butonly present limited predictions at high redshift. Specifically,they compare to published estimates of the evolution of thestellar mass function of galaxies out to z ∼
4, finding signif-icant discrepancies for stellar masses below 5 × M ⊙ .In this paper we extend this comparison considerably,analyzing the photometric properties of galaxies from highredshift to the present day, and comparing with observationsat a variety of levels from number counts as a function ofapparent magnitude, through redshift distributions of mag-nitude limited samples, to rest-frame luminosity functions asa function of redshift. In particular, we study predictions forthe near-infrared bands for which data have recently becomeavailable from the Spitzer satellite. To facilitate this work webuild lightcones using the MoMaF software (Blaizot et al.2005). We are then able to reproduce the observational selec-tion criteria of modern surveys such as the UKIRT InfraredDeep Sky Survey (UKIDSS) (Lawrence et al. 2007), the c (cid:13) , 1–14 volution of the Galaxy Population VIMOS-VLT Deep Survey (VVDS) (Le F`evre et al. 2005),the Deep Evolutionary Exploratory Probe 2 Galaxy RedshiftSurvey (DEEP2) (Davis et al. 2003) or the Cosmic Evolu-tion Survey (COSMOS) (Scoville et al. 2007).Similar studies were performed by Kitzbichler & White(2007), Guo & White (2009) and de la Torre et al. (2011)for earlier versions of the Munich semi-analytic model. Theresults here are based on the model of Guo et al. (2011)which is implemented simultaneously on the Millenniumand Millennium-II Simulations and was retuned to fit abroad range of “high precision” data on the low-redshiftgalaxy population, primarily from the Sloan Digital SkySurvey (SDSS). We also expand the photometric coveragefrom the ultraviolet to IRAC bands and test the depen-dence on stellar population synthesis modelling over thiswavelength range. In a recent paper, Somerville et al. (2011)compared a different semi-analytic model with photometryextending to even longer wavelengths (the far infrared). Thisrequired modelling the re-emission of starlight by heateddust, as also considered by Granato et al. (2000), Cole et al.(2000), Baugh et al. (2005), Lacey et al. (2010). Here weavoid this complication and compare only to directly ob-served starlight.This paper is organized as follows. In Section 2 we sum-marize the characteristics of the semi-analytic model we useand we describe how we construct lightcones for it. Section3 then presents results for number counts and redshift dis-tributions as a function of apparent magnitude, and for rest-frame B - and K -band luminosity functions as a function ofredshift. In Section 4 we present our conclusions. Modern semi-analytic models are built on merger treesfrom high-resolution dark matter simulations. These pro-vide a description of the evolution of the mass and num-ber density of dark matter halos and the subhalos withinthem, as well as of their spatial and kinematic distributions.The evolution of the baryonic components hosted by these(sub)halos is then followed using a set of simplified formu-lae describing each of the relevant astrophysical processes.The latest version of the Munich model (Guo et al. 2011)is implemented on two very large dark matter simulations,the Millennium Simulation (MS; Springel et al. 2005) andthe Millennium-II Simulation (MS-II; Boylan-Kolchin et al.2009). The MS follows the evolution of structure within acube of side 500 h − Mpc (comoving) and its merger treesare complete for subhalos above a mass resolution limitof 1 . × h − M ⊙ . The MS-II follows a cube of side100 h − Mpc but with 125 times better mass resolution (sub-halo masses greater than 1 . × h − M ⊙ ). Both adopt thesame WMAP1-based cosmology (Spergel et al. 2003) withparameters h = 0 . , Ω m = 0 . , Ω Λ = 0 . , n = 1 and σ = 0 .
9. These are outside the region preferred by morerecent analyses (in particular, σ appears too high) but thisis of no consequence for the issues we study in this paper.For consistency, we will use this cosmology whenever it isnecessary to derive the physical properties of galaxies fromobserved fluxes and redshifts. The distributions of physicalproperties converge in the two simulations for galaxies with10 . M ⊙ < M ⋆ < . M ⊙ . In this study we focus only on results from the MS, since its resolution limit is well belowthe stellar masses covered by the datasets with which wecompare. For a full description of the semi-analytic model used inthis work we refer the reader to Guo et al. (2011). Here webriefly describe changes from earlier versions of the Munichsemi-analytic model that significantly affect our results.Following Kitzbichler & White (2007) andGuo & White (2009), the model of Guo et al. (2011)includes a redshift-dependent model for internal extinctionwhich assumes that the dust-to-gas ratio increases withmetallicity but decreases with redshift. The effective opticaldepth is given by: τ λ = (cid:16) A λ A v (cid:17) Z ⊙ (1 + z ) − . (cid:16) Z gas Z ⊙ (cid:17) s (cid:16) h N H i . × atms cm − (cid:17) , (1)where h N H i represents the mean column density of hydro-gen, ( A λ /A v ) Z ⊙ is the extinction curve for the solar metal-licity taken from Mathis et al. (1983) and s = 1 .
35 for λ < s = 1 . λ > z >
1. This deficiency is reflected in our resultsbelow.Finally, Guo et al. (2011) introduced a more realistictreatment of satellite galaxy evolution and of mergers. Thehot gas content of satellite galaxies is gradually strippedinstead of being instantaneously removed at infall, as sug-gested by the simulations of McCarthy et al. (2008). Thisallows satellites to continue forming stars for a longer pe-riod and reduces the excessively rapid reddening of theseobjects. In addition, satellites of satellites remain connectedto their parent galaxies and can merge with them, ratherthan being automatically reassigned to the central galaxy ofthe group or cluster. The model also includes a treatmentof the tidal disruption of satellite galaxies. At high redshift, the observed fluxes at a limited number ofwavelengths are often the only data available for a galaxy,so that its redshift must be inferred through comparison ofthe observed colours to model templates. Even rest-framemagnitudes, colours and luminosities can then be subjectto substantial uncertainties, and the conversion to intrinsicproperties such as masses and star formation rates is prob-lematic. Results not only depend on the accuracy of the See Henriques & Thomas (2010) for an alternative extension ofthe Munich semi-analytic model modifying supernova feedbackand including tidal disruption of satellites.c (cid:13) , 1–14
Henriques et al. photometric redshift, but are also (almost) degenerate withrespect to the star formation history, metallicity and dustcontent of the galaxy. These quantities are direct predictionsof a semi-analytic model, so that the conversion from intrin-sic to observed properties is, in principle, well defined, givena stellar population synthesis model, an assumed IMF and aspecific model for intrinsic obscuration. It is thus often con-venient to consider conversion uncertainties as part of themodel and to compare theoretical predictions directly withobservables. To do this, we construct lightcones which allowthe models to be “observed” in a way that mimics real sur-veys as directly as possible. We use two different populationsynthesis models to predict observables in order to assess theimpact of the differing mass-to-light conversions they imply.We compute observed- and rest-frame fluxes from the ultra-violet to the near infrared so that our theoretical datasetsresemble those of modern observational surveys not only involume, but also in wavelength coverage.Our lightcones are built using the Mock Map Facil-ity (MoMaF) developed by Blaizot et al. (2005). We referthe reader to the original paper for a full description of themethod. Here we briefly summarize the complications thatarise when building lightcones from simulations of limitedsize and resolution.The Millennium Simulation has side of 500 h − Mpc(comoving). This is considerably smaller than, for example,the comoving distance to a galaxy observed at z ∼
2. Peri-odic replication of the simulation can lead to multiple ap-pearances of the same object within the lightcone, althoughtypically at different redshifts and so with different prop-erties and at offset positions (due to large-scale motions).Blaizot et al. (2005) suggested applying a series of transfor-mations (rotations, translations and inversions) when tilingspace with periodic replications. This does not, of course,prevent multiple appearances of a given object within thelightcone, but these duplicates are then viewed from differ-ent directions and no longer fall on a (nearly) regular lattice.Unfortunately, this technique also introduces disconti-nuities in large-scale structure at the boundaries betweenreplications, affecting clustering statistics in a way which isat least as difficult to model as that of the original periodic-ity. Kitzbichler & White (2007) showed that for lightconesof relatively small solid angle, the central line-of-sight canbe chosen to pass through the lattice of periodic replica-tions in such a direction that multiple images of the sameobject are minimised or eliminated altogether. The latter isnot possible if the comoving volume of the lightcone exceedsthat of the simulation, but this technique can still be used toensure that multiple appearances occur as far apart as pos-sible both on the sky and in redshift. We therefore use themethod of Kitzbichler & White (2007) in this paper. Spaceis filled with periodic replications of the simulation, a posi-tion is chosen for the observer, and the central line-of-sightof the survey field is given a previously chosen orientation.Galaxies whose positions intercept the lightcone are selectedand their comoving distance is converted into a redshift.As explained in Kitzbichler & White (2007), the timebetween stored snapshots for the Millennium Simulationvaries between 100 and 380 Myr. This means that the in-trinsic properties of galaxies are not generally available atthe time corresponding to their comoving distance. Ratherthey must be taken from the stored snapshot which is clos- est to their light-cone position. Hence, galaxies with redshift( z i + z i − ) / < z < ( z i + z i +1 ) / z i . The resulting discontinuity in galaxypopulation properties, at the boundaries between snapshots,could be reduced by interpolating, but this works poorly forpositions and velocities since the output separation is com-parable to orbital times within groups and clusters. More-over, it is not straightforward for other galaxy properties ei-ther since these change discontinuously on timescales shorterthan the output spacing, for example through mergers andstarbursts. We thus follow Kitzbichler & White (2007) anddo not attempt any interpolation. The semi-analytic calcu-lations are perfomed on these intermediate time-steps thatvary between 5 and 15 Myr. This means, for example, thata burst of star formation will have this duration and canhappen anywhere between (or at) output snapshots, withthe corresponding increase in flux being reflected in galaxyproperties at the snapshot.The apparent luminosities and colours of galaxies de-pend strongly on their redshifts through the conversionbetween rest- and observed-frame photometric bands andthrough the inverse square dependence of apparent lumi-nosity on distance. The final redshift of the galaxy in thelightcone is not available at the time observed-frame lumi-nosities are computed in the semi-analytic model. However,there will be two extreme redshifts that bracket it. We com-pute apparent observed-frame luminosities (for fixed intrin-sic properties) using these upper and lower limits, and oncethe galaxy is placed in the lightcone, we interpolate to obtainfinal observed-frame quantities.For this paper we construct lightcones for square areasof 1 . × . out to high redshift with no faint magnitudecut. They are however limited by the mass resolution of thedark matter simulation (1 . × h − M ⊙ in halo mass)corresponding to stellar masses of ∼ . M ⊙ at z=0. Whilethis does not matter for the questions we study in this paper,it should be borne in mind if the lightcones are used for otherpurposes. Semi-analytic models predict intrinsic properties of galaxies,such as stellar mass, star formation history, gas and dustcontent and metallicity. In order to convert these into ob-served spectral energy distributions (SED) or broad-bandphotometry, evolutionary population synthesis and dustmodels are required. The former predict the evolution of thelight associated with a single short burst of star formationof given metallicity and with an assumed Initial Mass Func-tion (IMF), a so-called Simple Stellar Population (SSP). Theintrinsic stellar emission from a model galaxy is then rep-resented as a superposition of SSPs weighted according toits star formation history. This emission must be processedthrough a dust model in order to predict the observable stel-lar emission. Uncertainties in the conversion between massand light can jeopardise any comparison between theory (cid:13) , 1–14 volution of the Galaxy Population Figure 1.
The response functions of the filters for which fluxes arecomputed for the lightcones produced in this paper. These extendfrom the far ultra-violet to the IRAC bands and include: in thetop panel, GALEX FUV and NUV, Johnson
UBV R c I c JHK s K and IRAC bands; in the second panel, SDSS ugriz ; in the thirdpanel, HST WFC3 UV and IR and ACS WFC; and in the bottompanel, HST WFPC2, VIMOS U and NICMOS. and observations. There are still significant differences be-tween published evolutionary population synthesis modelsand these should be considered as part of the systematic un-certainties when comparing semi-analytic model predictionsto data. Throughout this paper we present results from twodistinct stellar population synthesis codes: one that has beentraditionally used in the Munich model (Bruzual & Charlot2003) and the Maraston (2005) model implemented in thesemi-analytic code by Henriques et al. (2011). In both caseswe adopt the same Chabrier (2003) IMF and a similar metal-licity grid. We hope that the differences we find will givesome indication of the impact of mass-to-light conversionuncertainties on galaxy formation modelling. In order to increase the predictive power of the model andallow it to be tested against a wider range of observations,we also expand the number of photometric bands for whichfluxes are computed, covering all wavelengths dominated bydirect emission from stars, from the UV to the near-infraredIRAC bands. In Fig. 1 we plot the relevant filter transmis-sion curves. In the top panel we show the GALEX FUV andNUV, the Johnson
U, B, V, R c , I c , Z, Y, J, H, K s , K and theIRAC 3.6 µ m, 4.5 µ m, 5.8 µ m and 8.0 µ m bands; in the secondpanel, the SDSS u, g, r, i, z bands; in the third panel, bandsfrom HST instruments, three UV bands from the WFC3-UVIS (0.225 µ m, 0.275 µ m, 0.336 µ m), seven optical bandsfrom the ACS-WFC (0.435 µ m, 0.475 µ m, 0.606 µ m, 0.625 µ m, 0.775 µ m, 0.814 µ m, 0.850 µ m) and three near-infrared bandsfrom the WFC3-IR (1.05 µ m, 1.25 µ m, 1.60 µ m); and in thebottom panel, the VIMOS U band, the 2 NICMOS near-infrared bands (1.1 µ m and 1.6 µ m) and two WFPC2 bands(0.30 µ m and 0.45 µ m). While we will not give results for allthese bands in this paper, we will include the relevant ap-parent magnitudes in our light-cone catalogues in order toenhance their utility to others.All magnitudes are in the AB system. In order to be asclose as possible to observations, we use the K s -band whenpresenting results for number counts and redshift distribu-tions and the K -band when discussing the evolution of therest-frame luminosity function.The lightcones constructed and made public in thiswork provide a useful tool to test observational derivationsof intrinsic galaxy properties. The wide wavelength cover-age of observed- and rest-frame photometry, together withthe two stellar population synthesis models considered, canbe used to check derivations of rest-frame magnitudes fromobserved photometry, as well as the reliability of propertiesobtained from SED fitting, such as stellar masses, ages andstar-formation histories. In this section we compare predictions of our models to ob-servational data. We start with number counts as a functionof apparent magnitude in a wide range of photometric bands(from the optical blue to the IRAC bands) and move on toredshift distributions for K and IRAC 5 . µ m selected galax-ies. Finally, we investigate the evolution of the rest-frameoptical and near-infrared luminosity functions and colourswhich, although further from the directly observed quanti-ties, allow a better understanding of galaxy evolution.Kitzbichler & White (2007) and de la Torre et al.(2011) presented similar tests for an earlier version of theMunich semi-analytic model. Here, we take advantage ofrecent advances in the available observations and extendthese comparisons to higher redshift and to a wider range ofwavelengths. We also test the impact of population synthe-sis models by comparing results for the Bruzual & Charlot(2003) and the Maraston (2005) models. This follows upwork by Tonini et al. (2009, 2010); Fontanot & Monaco(2010) and Henriques et al. (2011), who showed that theinclusion of near-infrared emission from TP-AGB starsincreases the predicted number of massive and extremelyred objects at z ∼
2, as seems to be required by observation.Our comparison is based on a large number of lightconerealizations with areas and selection effects matching therelevant observational surveys.
Galaxy counts in a given observed band can be difficult to in-terpret. At each apparent magnitude they consist of galaxiesat a wide range of redshifts and thus with correspondinglywide ranges of absolute magnitude and of emitted wave-length. Nevertheless, such counts provide an important testof models because they are directly observed and so are in-dependent of uncertainties in redshift, k-correction, obscu-ration correction, etc. c (cid:13) , 1–14 Henriques et al.
Figure 2.
Galaxy number counts as a function of apparent magnitude. From top left to the bottom right, the panels show number countsin the B and i , J , K s , IRAC 3 . µ m, 4 . µ m and 5 . µ m bands. Theoretical predictions for the Maraston (2005) and Bruzual & Charlot(2003) population synthesis models are shown as solid red and dashed blue lines respectively. The filled regions represent the 1 σ field-to-field scatter for surveys of area 2 deg , except for the IRAC bands at faint magnitudes (M > fields are assumed.The B -band number counts are compared with data from SDSS (Yasuda et al. 2001), VVDS (McCracken et al. 2003) and HDF-N(Capak et al. 2004); i -band counts are also compared with data from SDSS and VVDS and with the COSMOS sample (Capak et al. 2007);for the J - and K s - bands we show observations from the CDF and HDF-S (Saracco et al. 2001), DEEP2 and Palomar (Conselice et al.2008) and MOIRCS (Keenan et al. 2010) with UKIDSS-UDF data (Cirasuolo et al. 2010) plotted for the K -band; Spitzer (Fazio et al.2004), FIREWORKS (Wuyts et al. 2008) and NEWFIRM (Whitaker et al. 2011) data are shown for the IRAC . µ m , IRAC . µ m andIRAC . µ m bands. Fig. 2 shows galaxy number counts for the B and i , J , K s , IRAC 3 . µ m, 4 . µ m and 5 . µ m bands (fromtop left to bottom right). Solid red and dashed bluelines are model predictions for the Maraston (2005) andBruzual & Charlot (2003) stellar population synthesis mod-els respectively. Filled regions show the 1 σ field-to-field scat-ter expected among surveys of area 2 deg , except that 100arcmin fields are assumed for the IRAC bands at faint mag-nitudes (M > B - and i -band number counts are com-pared with data from the Sloan Digital Sky Survey (SSDS;Yasuda et al. 2001) and the Vimos Very Deep Survey(VVDS; McCracken et al. 2003) at brighter magnitudes. Atfainter magnitudes we use the Hubble Deep Field - North(HDF-N; Capak et al. 2004) for the B -band and the COS-MOS sample (Capak et al. 2007) for the i -band. Both pop-ulation synthesis models match the data for bright galaxies(seen at low redshift in the rest-frame optical), while the Bruzual & Charlot (2003) model predicts more galaxies atfaint apparent magnitudes, in better agreement with obser-vations. Similar trends were found for previous versions ofthe Munich semi-analytic model (Kitzbichler & White 2007;de la Torre et al. 2011). It is difficult to draw firm conclu-sions from this result, however, since these faint counts cor-respond to rest-frame ultra-violet emission from galaxies athigh redshift where uncertainties affect not only the stel-lar population modelling, but also the simplistic treatmentsof starbursts and of dust obscuration in the semi-analyticmodel. Conroy et al. (2010) showed, for example, that in-creasing the number of blue stragglers or blue horizontalbranch stars increases the predicted ultra-violet emissionfrom passive galaxies.We compare the J - and K s -band counts to observationsfrom the Chandra Deep Field and the Hubble Deep Field- South (CDF and HDF-S; Saracco et al. 2001) from theDEEP2 and Palomar surveys (Conselice et al. 2008), and c (cid:13) , 1–14 volution of the Galaxy Population from the MOIRCS sample (Keenan et al. 2010) . In addi-tion, we show K-band counts based on the UKIDSS-UltraDeep Field data (UKIDSS-UDF; Cirasuolo et al. 2010). Thetwo stellar population synthesis models give similar predic-tions for the J -band number counts which agree with thedata. Both predict too many faint objects in the K s and Kbands. As shown by Guo et al. (2011), and as this paper willclarify, this is because the semi-analytic model overpredictsthe abundance of low-mass galaxies at high redshift. The twostellar population synthesis models predict similar counts atboth bright (low redshift, near infrared emission) and faint(high redshift, red optical emission) apparent magnitudes,but they disagree at intermediate apparent magnitudes. Aswe will see in more detail below, the difference is a con-sequence of TB-AGB emission from stars with ages of oneor two Gyr which is fully included in the Maraston (2005)but not in the Bruzual & Charlot (2003) stellar populationmodel.Predicted number counts for the IRAC 3 . µ m, 4 . µ mand 5 . µ m bands are plotted against Spitzer (Fazio et al.2004), FIREWORKS (Wuyts et al. 2008) and NEWFIRM(Whitaker et al. 2011) observations. Both the models andthe observations show a pronounced change in slope at anapparent magnitude near 20, but the break is stronger inthe observations than in the model and occurs at slightlybrighter apparent magnitudes. As a result, the modelsunder-predict the number of bright objects (low redshift,emission longwards of the rest-frame K-band) and over-predict the number of faint objects (high redshift, emissionin the rest-frame JHK region). The latter underpredictionis even more pronounced here than in the K-band and againis likely due to the overabundance of lower mass galaxies at z > z = 0 rest-frame K -band luminosity function(Fig. 5). Since Guo et al. (2011) tuned their semi-analyticmodel to match the observed low-redshift stellar mass func-tion, this deficit implies overly large mass-to-near-infrared-light ratios which might be explained by overly smallstellar metallicities. Indeed, Henriques & Thomas (2010)showed that the most massive low-redshift galaxies in theDe Lucia & Blaizot (2007) version of the model have stellarmetallicities which are too low by about a factor of two (thedashed red lines in their Figs 4 and 10). An increase in metal-licity could remove the discrepancy by reducing the mass-to-near-infrared-light ratios in model. Another importantfactor, particularly for the IRAC 5 . µ m band, is the possiblecontamination by emission from hot dust, specifically, emis-sion in the 3.3, 6.2 and 7.7 µ m PAH features (Draine et al.2007; Draine & Li 2007; da Cunha et al. 2008). Such emis-sion is not included in the models but may well be significantin the real low-redshift galaxies. The luminosity correction depends on the actual deficit inmetallicity, which in turn depends strongly on which stellar pop-ulation model is used to derive masses and metallicities for theobserved galaxies. K and IRAC . µ m selected samples In Fig. 3 we compare predictions from our models to theobserved photometric redshift distributions of galaxy sam-ples selected above K s and IRAC 5 . µ m apparent mag-nitude limits. As for the number counts, the solid redand dashed blue lines represent predictions based on theMaraston (2005) and Bruzual & Charlot (2003) stellar pop-ulation synthesis models. Filled regions show the expected1 σ scatter among fields with an area of 100 arcmin . In theleft panel the number of galaxies per unit area and redshiftis plotted for samples with K s < . K s < .
3, whilethe right panel gives similar results but for samples withIRAC 5 . µ m apparent magnitude brighter than 21.8 (and K s < . K s -band magnitude picksgalaxies on the basis of their rest-frame K -band emissionat low redshift, their rest-frame J band emission at z ∼ z > .
5. For bothmagnitude limits, the samples are dominated by intrinsi-cally faint objects at low-redshift but by intrinsically brightgalaxies beyond z ∼ K s < .
8) or z ∼ . K s < . < z < . M ⊙ and this discrepancy reflects the overabundance ofobjects of this mass and redshift unity that was flagged byGuo et al. (2011). The same problem was identified in ear-lier versions of the model by Kitzbichler & White (2007)and de la Torre et al. (2011). At higher and lower redshiftsthe abundances agree quite well in model and data, reflect-ing the fact that the semi-analytic model was tuned to fitgalaxy abundances at low redshift, and predicts an abun-dance of high-mass galaxies which fits observed estimatesquite well at high redshift.For the IRAC 5 . µ m selected samples shown in theright panel of Fig. 3, there is a significant difference be-tween the predictions of the two population synthesis mod-els. While the Bruzual & Charlot (2003) model predicts adistribution with similar shape to those in the left panel,the Maraston (2005) model makes a concordant prediction c (cid:13) , 1–14 Henriques et al.
Figure 3.
The redshift distribution of galaxies selected above observed-frame K s -band (left panel) and IRAC 5 . µ m-band (right panel)apparent magnitude limits. The solid red and dashed blue lines represent the mean predictions of our semi-analytic model for theMaraston (2005) and Bruzual & Charlot (2003) stellar population synthesis models. The filled regions show the 1 σ scatter among fieldswith area 100 arcmin . The left panel shows the total number of galaxies per unit area and redshift for samples with K s < . K s < .
3. Similar curves are shown in the right panel but for samples with IRAC . µ m < K s < only at z < .
2. Beyond this point there is a “bump” and athigher redshift it predicts roughly 3 times as many galaxiesas the Bruzual & Charlot (2003) model. A correspondingbump is not present in the observational data which arebetter described by the Bruzual & Charlot (2003) model,at least out to z ∼ .
5. The bump in the Maraston (2005)model is caused by strong rest-frame
JHK emission fromTP-AGB stars associated with intermediate age stellar pop-ulations. While this emission brings the predicted numbersof galaxies into rough agreement with the data at the high-est redshifts, it results in an overabundance at z ∼ JHK mass-to-light ratios. B -Band Luminosity Function Rest-frame luminosity functions and colour distributionsas a function of redshift provide direct estimates of theabundance evolution of various galaxy types (e.g. star-forming/passive, high/low mass). However, they require ac-curate redshifts and appropriate photometry if they are tobe determined reliably from observed-frame fluxes. The wide wavelength coverage of modern surveys produces robustphotometric redshifts, and, in addition, allows rest-frameoptical and near-infrared magnitudes to be determined byinterpolation over the full range 0 < z <
4, rather thanrequiring an uncertain extrapolation based on an SED fit.Guo et al. (2011) showed that their semi-analyticmodel reproduces observed z ∼ . g, r, i and z bands. At higher redshiftthey implemented the redshift-dependent dust model ofKitzbichler & White (2007). This reproduces the observedabundance of colour-selected galaxies at z ∼ z ∼ B -band luminosity function from z = 0 to z = 3for our current semi-analytic model. Solid red and dashedblue lines, represent versions with the Maraston (2005) andBruzual & Charlot (2003) stellar population models respec-tively. Filled regions give the expected 1 σ field-to-field scat-ter for surveys of area 1.4 deg , except that smaller fields(with area 150 arcmin ) were assumed for the 2 . < z < . . < z < . − . . < z < . − . z ∼ b j -band luminosity function is com-pared with the 6 Degree Field Galaxy Redshift Survey resultof Jones et al. (2006, 6DFGRS), repeated for reference as ablack dotted line in all panels. For the z ∼ We assume b j = B − . B − V ), (Norberg et al. 2002).c (cid:13) , 1–14 volution of the Galaxy Population Figure 4.
Evolution of the rest-frame B -band luminosity function from z = 3 to z = 0. Theoretical predictions for the Maraston(2005) and Bruzual & Charlot (2003) stellar population models are shown as solid red and dashed blue lines respectively. Filled regionsrepresent the 1 σ field-to-field scatter expected for surveys of area 1.4 deg , except in the highest redshift panel, where 150 arcmin fieldsare assumed. Fields of this size are also assumed for the intrinsically fainter galaxies in the 0.8 < z < < z < B > − . > − . z = 0 the model b j -band luminosity function ( b j = B − . B − V ); Norberg et al.2002) is compared with observations from the 6DFGRS (Jones et al. 2006), repeated at all redshifts as a dotted black line. At higherredshifts we show observational estimates from VVDS (Ilbert et al. 2005), DEEP 2 (Willmer et al. 2006), zCOSMOS (Zucca et al. 2009),HDF-S (Poli et al. 2003), HDF-N (Giallongo et al. 2005), GOODS-MUSYC plus FIRES (Marchesini et al. 2007) and GOODS-MUSYC(Salimbeni et al. 2008). finding excellent agreement with the 6DFRS result, just aswas the case for the corresponding SDSS luminosity func-tion (in the g band) in Guo et al. (2011). For the other z B -band luminosity function reasonably well out to z = 3.It overpredicts the abundance of faint objects at z ∼ z ∼
3, al-though it may still be compatible with the data given the rel-atively large error bars quoted by the observers and the sub-stantial scatter between the observational determinations.The two stellar population synthesis models give very sim-ilar results in this band. We note that the predicted fluxes are strongly affected by dust, and so are dependent on theadopted dust model. Further testing of the simplistic andrelatively poorly motivated model of Kitzbichler & White(2007) is clearly needed. K -Band Luminosity Function The K -band luminosity function has long been thought ofas a proxy for the stellar mass function. Recent resultshave shown, however, that this assumption, while moder-ately accurate at low redshift, can break down badly atearly times. Notably, the fact that the characteristic lumi-nosity L ⋆ increases with increasing redshift just as for theoptical bands (Cirasuolo et al. 2010) is inconsistent with atime-independent K -band mass-to-light ratio, which wouldimply the “evaporation” of material from the most massivegalaxies. This luminosity function behaviour is easily under-stood in the context of recent stellar population synthesismodels. In particular, a significant amount of K -band emis- c (cid:13) , 1–14 Henriques et al.
Figure 5.
Evolution of the rest-frame K -band luminosity function from z = 3 to z = 0. Predictions of our semi-analytic model for theMaraston (2005) and Bruzual & Charlot (2003) population synthesis models are shown by solid red and dashed blue lines respectively.Filled regions represent the expected 1 σ field-to-field scatter for surveys of area 0.7 deg . At z ∼ K s -band luminosity functionis compared with data from 2MASS (Bell et al. 2003) and 6DFGRS+2MASS (Jones et al. 2006). We repeat the latter at all redshiftsas a black dotted line. At higher redshifts we show observational estimates based on MUNICS (Drory et al. 2003), the UKIDSS-UDF(Cirasuolo et al. 2010), the K20 Survey (Pozzetti et al. 2003) and the HDF-S (Saracco et al. 2006). Note that in all surveys other thanthe UKIDSS-UDF, the rest-frame K-luminosities are not directly measured but are rather estimated by extrapolating from the observedframe K -band fluxes using an SED model. sion comes not from the old populations which dominatethe stellar mass, but rather from intermediate age stars ( ∼ K -band and they are only later replaced by predom-inantly old populations (Henriques et al. 2011).In Fig. 5 we plot the evolution of the K -band luminos-ity function out to z = 3. As in previous figures, the solidred and dashed blue lines represent predictions based onthe Maraston (2005) and Bruzual & Charlot (2003) stellarpopulation models, and filled regions outline the expected1 σ field-to-field scatter among surveys of area 0.7 deg . At z ∼ K s -band luminosity function is comparedwith observational data from 2MASS (Bell et al. 2003) and6DFGRS+2MASS (Jones et al. 2006). As a reference, werepeat the latter at all redshifts as a black dotted line.For the z ∼ K -band flux directly byinterpolating between observed-frame magnitudes at corre-sponding wavelengths (from Spitzer/IRAC). The other sur-veys extrapolate the observed-frame K flux to longer wave-length using an uncertain SED fit and thus may be subjectto substantial systematic errors.Our two population synthesis models give very similarpredictions for the rest-frame K -band luminosity functionout to z ∼ .
5. At higher redshifts their shapes and theirnormalisations remain similar but their characteristic lumi-nosities diverge with the Maraston (2005) prediction beingbrighter by about 0.4, 0.5, 0.6 and 0.75 magnitudes at red-shifts of 1.0, 1.5, 2.0 and 3.0 respectively. This reflects theincreasing contribution from TP-AGB stars as the mean ageof the galaxies gets younger. The predictions of both modelsare strongly at variance with observation at these redshifts.While the Maraston (2005) model agrees with the high-mass c (cid:13) , 1–14 volution of the Galaxy Population Figure 6.
The rest-frame U - V versus V - J colour diagram for 1 . < z < . . < z < . K < . tail of the observed luminosity functions at all redshifts, itseriously overpredicts the abundance of less massive galax-ies at z = 1 and earlier. For the lowest luminosity bin ofthe UKIDSS-UDF dataset the overprediction is by factorsof 2, 4, 6 and almost 8 at redshifts of 1.0, 1.5, 2.0 and 3.0respectively. The Bruzual & Charlot (2003) model fails toreproduce the rest-frame K luminosities of the most mas-sive systems (by about 0.7 mag by z ∼
3) but neverthelessoverpredicts the abundance of less luminous systems almostas badly as the Maraston (2005) model. This is the sub-stantial problem already pointed out by Guo et al. (2011);their galaxy formation assumptions produce moderate massgalaxies ( M ⋆ ∼ M ⊙ ) too early to be compatible withcurrent data on populations at z > K -band luminosities ofmassive low-redshift galaxies. This more subtle problemis due to these massive galaxies being too blue (see thecolour distributions in Fig. 12 of Guo et al. 2011). This is likely caused by an underabundance of heavy elements(Henriques & Thomas 2010).Similar results for the evolution of the rest-frame K -band luminosity function have been obtained foran earlier version of the Munich semi-analytic model(De Lucia & Blaizot 2007, as well as for the semi-analyticmodels of Menci et al. 2006, Monaco et al. 2007 andFontanot et al. 2009). In a recent paper Somerville et al.(2011) compared another independent semi-analytic modelto observational data on the evolution of the rest-frame1500˚ A , B and K band luminosity functions. The authorswere able to get a reasonable match to the bright tail with-out including TP-AGB emission, but they do obtain a muchweaker evolution of the characteristic L ⋆ than observed,in concordance with our Bruzual & Charlot (2003) results.They also overpredict the abundance of lower luminositygalaxies by very similar factors to those that we find here.It seems that whatever is causing the overly early formation c (cid:13) , 1–14 Henriques et al. of lower mass galaxies is common to all recent semi-analyticmodels.
Recent observations have shown that the local bimodalitybetween blue, star-forming and red, passive galaxies persistsat least up to z = 2 (e.g. Wuyts et al. 2007; Williams et al.2009; Ilbert et al. 2010; Whitaker et al. 2011). These au-thors have used a combination of a rest-frame near-infraredcolour and an optical color in order to separate dusty star-forming galaxies from passive objects. At fixed U - V , redpassive galaxies will have bluer V - J colors than dusty star-forming objects. In Fig. 6 we plot rest-frame U - V versus V - J diagrams in two redshift bins, 1 . < z < . . < z < . K -band = 23 .
0, roughly the90% completion limit quoted for observations. As describedin Whitaker et al. (2011), observational galaxies were care-fully deblended and only objects with S/N > K bandwere included. The contours represent the density of pointswith the total number of objects normalized by the area sur-veyed. The solid black line shows the empirical dividing linebetween active and passive objects.For both redshift bins, the models correctly predict theexistence of two distinct populations, although they fail tomatch the exact observational spread in colour. The twopopulations have less scatter and are closer to each otherin the models also covering a smaller range in V - J . Thismight in part result from incorrect physics in the modelbut it can also be explained by uncertainties in the con-version between aperture and total magnitudes, photomet-ric redshifts and the process of SED fitting when derivingtotal rest-frame magnitudes from observations. At z = 2,the colours of red galaxies seem to be better matched bythe Bruzual & Charlot (2003) prescription. The Maraston(2005) predictions are shifted to larger V - J colours. Never-theless, we note that the position of a galaxy population inthis diagram is strongly dependent on the dust model as-sumed. For both population models, passive galaxies do notform a distinct peak, but rather a cloud of objects depart-ing from the blue sequence towards redder U - V colours (at1 . < V − J < . . < V − J < . z = 2 in the model have masses between 10 M ⊙ and 10 . M ⊙ and black hole masses as big as 10 M ⊙ . We have constructed lightcones from the latest version ofthe Munich semi-analytic model (Guo et al. 2011) and usedthem to compare the model with the high-redshift galaxypopulation as revealed by recent deep surveys at opti-cal and near-infrared wavelengths. We have combined themodel with two different stellar population synthesis pack-ages (Bruzual & Charlot 2003; Maraston 2005) in order tounderstand how differences in the photometric modelling arereflected in inferences about galaxy evolution. We use mul-tiple independent lightcones to characterize cosmic varianceuncertainties in currently available datasets. Our mock cat-alogues are made publicly available and provide observer-frame photometry in 40 commonly used photometric bands,in addition to rest-frame photometry and a variety of phys-ical properties of the galaxies (positions, peculiar velocities,stellar masses, halo masses, sizes, morphologies, gas frac-tions, star formation rates, metallicities, halo properties).We now summarise the principal conclusions from ourcomparison of models and data. • For both stellar populations the model matches theobserved-frame
B, i and J number counts but overpredictsthe counts at faint magnitudes ( m AB >
20) in the K s ,IRAC 3 . µ m, 4 . µ m and 5 . µ m bands. This reflects theoverproduction of moderate mass galaxies (stellar masses M ⋆ ∼ M ⊙ ) at z > • At bright magnitudes ( m AB <
20) the model under-predicts the counts in the three IRAC bands. This is dueto an underestimation of the near-infrared luminosities oflow-redshift massive galaxies caused in part by the fact thatsuch galaxies are insufficiently metal-rich in the model, andin part by the model’s neglect of PAH emission from hotdust (which is particularly significant at 5 . µ m). • At magnitudes where the model K s -band counts agreewith observations the redshift distribution of K s -selectedsamples is also reproduced. At fainter magnitudes where thecounts are overpredicted, the excess galaxies occur primar-ily at 1 < z < .
5, again reflecting the overproduction of M ⋆ ∼ M ⊙ galaxies at these epochs. The two populationsynthesis models give similar results in both regimes. • The two population synthesis models predict differ-ent redshift distributions for galaxies selected to m AB ∼
22 in the IRAC 5 . µ m band. Emission from TP-AGBstars enhances the number of galaxies at z > . z ∼
2. Although theBruzual & Charlot (2003) model agrees with the observedredshift distribution for 0 < z <
3, this is a result of theoverabundance of moderate mass galaxies being cancelledby an overestimate of their near-infrared mass-to-light ra-tios. • The two population synthesis give similar results forthe evolution of the rest-frame B -band luminosity function,agreeing well with observation out to z = 1 .
2. At higher red-shift the agreement is less convincing. The overabundanceof lower mass model galaxies starts to become evident, and c (cid:13) , 1–14 volution of the Galaxy Population there is some indication that the models underpredict theabundance of the most luminous objects. Cosmic varianceand other uncertainties in the currently available data, to-gether with dust modelling uncertainties in the model, pre-clude any strong conclusions. • The Maraston (2005) population model reproduces thebright tail of the rest-frame K -band luminosity function allthe way out to z ∼
3, whereas the Bruzual & Charlot (2003)model underpredicts the near-infrared luminosities of thesemassive galaxies by an amount which increases from about0.3 mag at z ∼ z ∼
3. The overproduction of M ⋆ ∼ M ⊙ galaxies at these times causes both models tosubstantially overpredict galaxy abundances below the kneeof the luminosity function. • The model predicts that a population of red, passivegalaxies galaxies should be in place already at z = 2, as seenin observations. These are the most massive galaxies at thecentres of clusters and large groups which can rapidly growa central black hole capable of producing enough feedbackto stop star formation at early times.In the literature it has often been suggested thatsemi-analytic models fail to reproduce the rest-frame K -band galaxy luminosities of the brightest high-redshiftgalaxies (at z ∼ − M ⋆ ∼ M ⊙ are already present with a large fraction of their z = 0 abun-dance at redshifts of 2 or 3, whereas the observations indi-cate a drop in abundance by about an order of magnitude.Cosmic down-sizing thus appears much stronger in the realUniverse than in the models. Reconciling theory and obser-vation in the context of the ΛCDM cosmology will requirestar formation efficiencies to scale with mass and redshift ina very different way than current models (and simulations)assume. ACKNOWLEDGEMENTS
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