The VIMOS Public Extragalactic Redshift Survey (VIPERS). A precise measurement of the galaxy stellar mass function and the abundance of massive galaxies at redshifts 0.5<z<1.3
I. Davidzon, M. Bolzonella, J. Coupon, O. Ilbert, S. Arnouts, S. de la Torre, A. Fritz, G. De Lucia, A. Iovino, B. R. Granett, G. Zamorani, L. Guzzo, U. Abbas, C. Adami, J. Bel, D. Bottini, E. Branchini, A. Cappi, O. Cucciati, P. Franzetti, M. Fumana, B. Garilli, J. Krywult, V. Le Brun, O. Le Fevre, D. Maccagni, K. Malek, F. Marulli, H. J. McCracken, L. Paioro, J. A. Peacock, M. Polletta, A. Pollo, H. Schlagenhaufer, M. Scodeggio, L. A. .M. Tasca, R. Tojeiro, D. Vergani, A. Zanichelli, A. Burden, C. Di Porto, A. Marchetti, C. Marinoni, Y. Mellier, L. Moscardini, T. Moutard, R. C. Nichol, W. J. Percival, S. Phleps, M. Wolk
aa r X i v : . [ a s t r o - ph . C O ] S e p Astronomy & Astrophysicsmanuscript no. gsmf_aa_appr c (cid:13)
ESO 2019April 5, 2019
The VIMOS Public Extragalactic Redshift Survey (VIPERS) ⋆ A precise measurement of the galaxy stellar mass function and the abundanceof massive galaxies at redshifts . < z < . I. Davidzon , , M. Bolzonella , J. Coupon , O. Ilbert , S. Arnouts , , S. de la Torre , A. Fritz , G. De Lucia ,A. Iovino , B. R. Granett , G. Zamorani , L. Guzzo , , U. Abbas , C. Adami , J. Bel , D. Bottini ,E. Branchini , , , A. Cappi , , O. Cucciati , P. Franzetti , M. Fumana , B. Garilli , , J. Krywult , V. Le Brun ,O. Le Fèvre , D. Maccagni , K. Małek , F. Marulli , , , H. J. McCracken , L. Paioro , J. A. Peacock , M. Polletta ,A. Pollo , , H. Schlagenhaufer , , M. Scodeggio , L. A. M. Tasca , R. Tojeiro , D. Vergani , A. Zanichelli ,A. Burden , C. Di Porto , A. Marchetti , , C. Marinoni , , Y. Mellier , L. Moscardini , , , T. Moutard ,R. C. Nichol , W. J. Percival , S. Phleps , and M. Wolk (A ffi liations can be found after the references) Received March 19, 2013 - Accepted July 12, 2013
ABSTRACT
We measure the evolution of the galaxy stellar mass function from z = . z = . z ≃ .
8, when the Universe was ≃ ff ectsassociated with the SED fitting procedure used to derive galaxy stellar masses. We estimate the galaxy stellar mass function at severalepochs between z = . .
3, discussing the amount of cosmic variance a ff ecting our estimate in detail. We find that Poisson noiseand cosmic variance of the galaxy mass function in the VIPERS survey are comparable to the statistical uncertainties of large surveysin the local universe. VIPERS data allow us to determine with unprecedented accuracy the high-mass tail of the galaxy stellar massfunction, which includes a significant number of galaxies that are too rare to detect with any of the past spectroscopic surveys. At theepochs sampled by VIPERS, massive galaxies had already assembled most of their stellar mass. We compare our results with bothprevious observations and theoretical models. We apply a photometric classification in the ( U − V ) rest-frame colour to compute themass function of blue and red galaxies, finding evidence for the evolution of their contribution to the total number density budget:the transition mass above which red galaxies dominate is found to be about 10 . M ⊙ at z ≃ . , and it evolves proportionally to(1 + z ) . We are able to separately trace the evolution of the number density of blue and red galaxies with masses above 10 . M ⊙ , ina mass range barely studied in previous work. We find that for such high masses, red galaxies show a milder evolution with redshift,when compared to objects at lower masses. At the same time, we detect a population of similarly massive blue galaxies, which areno longer detectable below z = .
7. These results show the improved statistical power of VIPERS data, and give initial promisingindications of mass-dependent quenching of galaxies at z ≃ Key words.
Galaxies: mass function, evolution, statistics – Cosmology: observations
1. Introduction
The past decade has seen significant advances in the study ofgalaxy evolution prompted by large astronomical surveys. Inparticular, such surveys sample large cosmic volumes and col-lect large amounts of data, thus facilitating a number of impor-
Send o ff print requests to : [email protected] ⋆ Based on observations collected at the European Southern Obser-vatory, Cerro Paranal, Chile, using the Very Large Telescope under pro-grammes 182.A-0886 and partly 070.A-9007. Also based on obser-vations obtained with MegaPrime / MegaCam, a joint project of CFHTand CEA / DAPNIA, at the Canada-France-Hawaii Telescope (CFHT),which is operated by the National Research Council (NRC) of Canada,the Institut National des Sciences de l’Univers of the Centre Nationalde la Recherche Scientifique (CNRS) of France, and the University ofHawaii. This work is based in part on data products produced at TER-APIX and the Canadian Astronomy Data Centre as part of the Canada-France-Hawaii Telescope Legacy Survey, a collaborative project ofNRC and CNRS. tant statistical studies. The galaxy stellar mass function (GSMF),defined as the co-moving number density of galaxies within astellar mass bin ( M , M + d M ), is one such fundamental statis-tic, allowing the history of baryonic mass assembly to be traced.Measurements of the GSMF help in constraining the cosmic starformation rate (SFR, e.g. Behroozi et al. 2013) and in investigat-ing how galaxy properties change as a function of stellar mass,redshift, and environments (e.g. in galaxy clusters, Vulcani et al.2011).In the nearby universe, the GSMF has been measured tohigh accuracy by exploiting the Two Micron All Sky Survey(2MASS), the 2dF Galaxy Redshift Survey (2dFGRS, Cole et al.2001), and the Sloan Digital Sky Survey (SDSS, e.g. York et al.2000). Its shape is parametrised well by a double Schechter(1976) function, with an upturn at M ≃ M ⊙ (Baldry et al.2008; Li & White 2009; Baldry et al. 2012). Such bimodal-ity, also visible in the SDSS luminosity function (Blanton et al.2005), reflects the existence of two distinct galaxy types: a pop- Article number, page 1 of 19 lation of star-forming galaxies, with blue colours and disc-dominated or irregular morphology, and a class of red early-typegalaxies that, in contrast, have their star formation substantiallyshut o ff (Kau ff mann et al. 2003a; Franx et al. 2008; Bell et al.2007).At higher redshift, such statistical studies are more challeng-ing because of the faintness of the objects. However, early sem-inal work took advantage of the Hubble Space Telescope to con-struct samples of a few hundred galaxies up to z ≃
3, findingevidence of an increase in the average stellar mass density withcosmic time (Rudnick et al. 2003; Dickinson et al. 2003; Fontanaet al. 2003). Later, deeper surveys were able to show the lack ofevolution at the high-mass end of the GSMF (GOODS-MUSICcatalogue, Fontana et al. 2006), which contrasted with an in-crease in galaxy density at lower masses (VVDS survey, Pozzettiet al. 2007). This is a result that is consolidated up to z ≃ / active from red / quiescent objects provided interest-ing results, despite the relatively limited statistics, and revealedthat within the GSMF the number of blue galaxies at interme-diate masses (about 10 M ⊙ ) decreases as a function of cosmictime, while the fraction of red galaxies increases (Bundy et al.2006; Borch et al. 2006). This early work was extended usinglarger galaxy samples (as in COSMOS and zCOSMOS, Droryet al. 2009; Ilbert et al. 2010; Pozzetti et al. 2010) or very deepobservations (GOODS-NICMOS survey, Mortlock et al. 2011),which produced robust results for the evolution in number den-sity of both these galaxy populations. They also showed that adouble Schechter function is a good fit to the GSMF data out to z ≃ N -body dark matter simulations (e.g. De Lucia& Blaizot 2007; Bower et al. 2006; Guo et al. 2011, 2013), re-quires a high level of complexity to parametrise all the physicalprocesses (star formation, supernova ejecta, etc.). On the obser-vational side, instead, it is hard to attain the precision requiredto constrain models, especially for the most massive galaxies,which are highly a ff ected by sample variance and small-numberstatistics. Moreover, uncertainties in redshift measurements andstellar mass estimates make the analysis even more complicated(Marchesini et al. 2009, 2010).The latest galaxy surveys are helping with improved mea-surements of the GSMF and could shed light on the discrepan-cies between data and models (BOSS, Maraston et al. 2012).State-of-the-art analyses provide new evidence suggesting thedependence on cosmic time and stellar mass of the physical pro-cesses that extinguish star formation: from z = z =
1, thedensity of quiescent galaxies increases continuously for M & . M ⊙ (Ilbert et al. 2013, using UltraVISTA data), while at z < z ∼ ff ective probing of the massive end of theGSMF at these redshifts: at the high-mass end, where a few in-terlopers can dramatically change the shape of the GSMF, accu-rate spectroscopic redshift measurements are crucial for avoid-ing contaminations.In this paper we present the first measurements of the GSMFfrom the up-to-date catalogue containing ∼
55 000 objects; inthis first analysis we concentrate on the evolution of the GSMFfrom z = . z = .
5, i.e. within the range covered bythe VIPERS data, for the whole galaxy sample and separatelyfor the blue and red populations. We also discuss in detail thesources of error and potential systematic e ff ects that could be-come dominant at the level of precision on the GSMF allowedby the VIPERS data.In Sect. 2 we present the VIPERS galaxy catalogue that hasbeen used in this work, and describe how stellar masses havebeen estimated through the SED fitting technique. The globalmass function is presented in Sect. 3, along with a discussion onthe sample completeness and the main sources of uncertainties.We compare those results with both previous surveys and modelsin Sect. 4. In Sect. 5, after applying a colour classification, westudy the mass function (and the related number density) of redand blue galaxies. Our results are summarised in Sect. 6. Unlessspecified otherwise, our cosmological framework assumes Ω m = . Ω Λ = .
75, and h = H / (70 km s − Mpc − ). All themagnitudes are in the AB system (Oke 1974).
2. Data
VIPERS is an ongoing redshift survey that aims at observ-ing approximately 100 000 galaxies and AGNs at intermediateredshifts ( h z i ∼ .
8) in the magnitude range of 17 . i .
5. At the completion of the survey, expected in 2014, ap-proximately 24 deg will have been covered within two fieldsof the Canada-France-Hawaii Telescope Legacy Survey Wide(CFHTLS-Wide) , namely W1 and W4. The sky region cov-ered at present is ∼ . in each of them, with an e ff ectivearea of 5 .
34 deg in W1 and 4 .
97 deg in W4, after accountingfor the photometric and spectroscopic masks. Once completed,VIPERS will be the largest spectroscopic survey at such redshiftsin terms of volume explored (1 . × Mpc h − ). All details onthe survey design and construction can be found in Guzzo et al.(2013).The main science drivers of VIPERS are the accurate mea-surement of galaxy clustering, bias parameter, and the growthrate of structures, along with the study of the statistical proper-ties of galaxies and their evolution when the Universe was abouthalf its current age. These topics are the subject of the paral-lel accompanying papers of this series (Guzzo et al. 2013; dela Torre et al. 2013; Marulli et al. 2013; Malek et al. 2013; Belet al. 2013). A previous smaller VIPERS sample has alreadybeen used to de-project angular clustering in the CFHTLS full http://vipers.inaf.it Article number, page 2 of 19. Davidzon et al.: VIPERS galaxy stellar mass functions
Fig. 1.
The coverage of ancillary data over the two VIPERS fields (W1 and W4 in the upper and lower panels, respectively). The W1 view islimited to the region sampled by VIPERS until now. Each survey is shown with a di ff erent colour (see bottom right legend), while grey quadrantsare the VIMOS pointings that led to the spectroscopic catalogue used in this work. catalogue (Granett et al. 2012) and to develop a galaxy classi-fication through principal component analysis (Marchetti et al.2013).The spectroscopic survey is complemented by photometricancillary data (Fig. 1), obtained from public surveys and dedi-cated observations, allowing us to estimate several galaxy prop-erties with high precision, in particular galaxy stellar masses andrest-frame magnitudes. The VIPERS spectroscopic sample has been selected from theW1 and W4 fields of the CFHTLS-Wide. Therefore, for eachgalaxy we have a photometric dataset consisting of u ∗ , g ′ , r ′ , i ′ , and z ′ magnitudes ( SExtractor ’s MAG_AUTO derived indouble image mode in order to maintain the same aperture in allbands, Bertin & Arnouts 1996), as measured by the Terapix teamfor the T0005 data release (Mellier et al. 2008). The Terapixphotometric masks, which discard areas around bright stars orwith problematic observations, have been revisited by our teamto recover regions within those masks where the photometricquality is deemed su ffi cient for our analysis (Guzzo et al. 2013).We took advantage of the full wavelength range of theVIPERS photometric dataset, since this significantly improvesthe results of our SED fitting; in particular, near-infrared (NIR)fluxes are critical to constraing physical parameters and breakdegeneracies between the mean age of the stellar population anddust attenuation, and they allow one to compute a robust estimateof stellar masses (e.g. Lee et al. 2009).To exploit the full potential of VIPERS in analysing thegalaxy properties as a function of time and environment, wehave undertaken a follow-up in the K -band in the two VIPERSfields with the WIRCAM instrument at CFHT and in the far-and near-UV ( FUV and
NUV ) channel with the GALEX satel-lite (Arnouts et al., in prep.). The K -band observations were col-lected between 2010 and 2012 with several discretionary time programmes. The K -band depth has been optimised to matchthe brightness of the spectroscopic sources: at the magnitudelimit ( K WIRCAM ≃ . σ ), 95% of the spectroscopic samplein W4 is observed in K WIRCAM , while in W1 this percentage isapproximately 80% (see Fig. 1).In addition to WIRCAM data, we matched our CFHTLS op-tical catalogue with the recent UKIDSS data releases using amatching radius of 0 . ′′ . The W1 field overlaps with UDS andDXS, whereas the W4 field is fully covered by the shallowerLAS and partially covered by DXS. Where available, we usePetrosian magnitudes in the Y , J , H , and K bands converted inthe AB system. When also considering K UKIDSS , the percentageof our spectroscopic sample with K -band magnitude increases to97% in W1 and 96% in W4.We compared the K -band photometry for optical sourcesmatched with both UKIDSS and WIRCAM surveys, and findgood agreement. In fact, we find a mean di ff erence h ∆ K i = h K WIRCAM − K UKIDSS i ≃ − .
05, with a small dispersion σ ∆ K ≃ .
10 and 0 .
15, for W1 and W4, respectively. These di ff erencescan be ascribed to the transmission functions of the filters andthe definition of the aperture used when measuring magnitudes,and are close to photometric errors. To not overweight the K -band magnitudes in the SED fitting, only the deeper K WIRCAM data have been used when both magnitudes were available forthe same object.The UV part of the spectrum can also be important for con-straining the galaxy dust content and the star formation rate. Wemake use of existing GALEX images observed with the deepimaging survey (integration time ∼ × s) in the NUV and
FUV channels, and we have completed the coverage in W1 re-gion with new observations in the
NUV channel alone and withintegration time T exp > . × s. Because of the GALEX largePSF ( ∼ DR9 for LAS and DXS, DR8 for UDS;
Article number, page 3 of 19 t al. 2011), which adopts the positions of U -band selected priorsand performs a modelled PSF adjustment over small tiles basedon the expectation maximisation algorithm (Guillaume et al.2006). For our spectroscopic sample, 63% (15%) of the sourceshave an NUV ( FUV ) flux measurement in W1. In contrast, theW4 field has modest GALEX coverage: 13% (5%) of spectro-scopic sources with an
NUV ( FUV ) flux. The WIRCAM andGALEX datasets in the VIPERS fields are described in Arnoutset al. (in prep.).Moreover, for ∼
30% of the spectroscopic targets in W1, wealso took advantage of the SWIRE observations in the XMM-LSS field. For our SED fitting we only considered magnitudesin the 3 . µ m and 4 . µ m bands, since beyond those wavelengthsthe survey is shallower, and source detection is very sparse.Moreover, at longer wavelengths the re-emission from dust be-gins to contribute to the flux of galaxies, and this feature is notreproduced by most of the models of stellar population synthesis(see Sect. 2.3). The spectroscopic catalogue used in this paper represents thefirst 60% of VIPERS. This sample includes 53 608 galaxy spec-tra and will be made available through the future VIPERS PublicData Release 1 (PDR-1). The VIPERS targets were selected viatwo criteria. The first was aimed at separating galaxies and stars,and relies on the combination of a point-like classification (basedon measuring the half-light radius) for the brightest sources andon comparing the five optical magnitudes with galaxy and stellarspectral energy distributions for the faintest ones (Coupon et al.2009). A fraction of the point-like sources are targeted as AGNcandidates, when located in the AGN loci of the two colour di-agrams ( g − r ) versus ( u − g ) and ( g − i ) versus ( u − g ). Thesecond selection criterion, based on ( g − r ) and ( r − i ) colours,was applied to exclude low-redshift ( z < .
5) objects, and hasbeen tested to ensure it does not introduce any significant bias.A complete description of the whole source selection procedureis included in Guzzo et al. (2013).The spectroscopic observations were carried out using theVIMOS instrument on VLT with the LR-Red grism ( R = λλ , λ σ z = . + z ) for our measured redshifts.To maximise the multiplex capability of VIMOS, we adoptedthe observational strategy described in Scodeggio et al. (2009) ofusing shorter slits than in the previous surveys carried out withthe same instrument. By virtue of this strategy, we reached asampling rate of approximately 40% with a single pass, essen-tial to estimating the large-scale environment (Cucciati et al., inprep.; Iovino et al., in prep.).The spectroscopic masks reproduce the footprint of the VI-MOS instrument, consisting of four quadrants and gaps betweenthem for each pointing, covering 224 arcmin . Vignetted parts ofthe quadrants have been removed to compute the e ff ective area(for a detailed description see Guzzo et al. 2013).Data reduction and redshift measurement were performedwithin the software environment Easylife (Garilli et al. 2012),which is based on the VIPGI pipeline (Scodeggio et al. 2005)and EZ (Garilli et al. 2010, Easy redshift). Once measured bythe EZ pipeline and assigned a confidence level, the spectro- scopic redshifts were then checked and validated independentlyby two team members. In case of any discrepancy, they werereconciled by direct comparison. In the vast majority of cases,this involves spectra with very low signal-to-noise ratios, whichend up in the lowest quality classes. In general, each redshift isin fact assigned a confidence level, based on a well-establishedscheme developed by previous surveys like VVDS (Le Fèvreet al. 2005) and zCOSMOS (Lilly et al. 2009). In detail, a spec-troscopic quality flag equal to 4 corresponds to a confidence levelof 99 . > i . ∼
41 100 galaxies in the redshift range0 . z .
3) were considered in the analysis. (We excludespectra classified as broad-line AGNs.) For a galaxy at redshift z with magnitude i , its statistical weight w ( i , z ) is the inverse of theproduct of TSR( i ), SSR( i , z ), and CSR( z ). Once each galaxy inthe spectroscopic sample is properly weighted, we can recoverthe properties of the photometric parent sample with good preci-sion (for a detailed discussion on TSR, SSR, and CSR see Guzzoet al. 2013). Considering the small fraction of objects without K band mag-nitude, we decided to rely on SED fitting to derive stellar massesand to not implement alternative methods, such as the Lin et al.(2007) relation between stellar mass, redshift, and rest-framemagnitudes.We thus derive galaxy stellar masses by means of an updatedversion of Hyperzmass (Bolzonella et al. 2000, 2010, softwareis available on request). Given a set of synthetic spectral en-ergy distributions, the software fits these models to the multi-band photometry for each galaxy and selects the model thatminimises the χ . The SED templates adopted in this proce-dure are derived from simple stellar populations (SSPs) mod- Article number, page 4 of 19. Davidzon et al.: VIPERS galaxy stellar mass functions
Fig. 2.
Distribution of the di ff erences between the values of stel-lar mass estimated using the two codes Hyperzmass and
MAGPHYS .Only results for the W1 field are shown (see text). To limit the e ff ectsof parameter degeneracy, we restrict the comparison to galaxies thatturn out to have solar metallicity, according to their best-fit templatesboth in Hyperzmass and
MAGPHYS . In this way the di ff erence between M MAGPHYS and M Hyperzmass cannot be due to a di ff erent metal contentassumed in the two SED fitting estimates. The dashed line gives thebest-fitting Gaussian of the distribution, corresponding to the mean andstandard deviation indicated. Also indicated are the size of the galaxysubsample ( N tot ) and the number of stellar mass estimates for which thediscrepancy is log( M MAGPHYS / M Hyperzmass ) > σ ( N exceed ). elled by Bruzual & Charlot (Bruzual & Charlot 2003, hereafterBC03), adopting the Chabrier (2003) universal initial mass func-tion (IMF) . The BC03 model is one of the most commonlyused ones (e.g. Ilbert et al. 2010; Zahid et al. 2011; Barro et al.2013). Another frequently used SSP library is the one by Maras-ton (2005, M05), which di ff ers from the former because of thetreatment of the thermally pulsing asymptotic giant branch (TP-AGB) stellar phase, a ff ecting NIR emission of stellar popula-tions aged ∼ . z . Z , which we chose to be solar( Z = Z ⊙ ) or subsolar ( Z = . Z ⊙ ). This choice allows us to takethe di ff erent metallicities of the galaxies in our redshift rangeinto account, which can be lower than in the nearby universe(Zahid et al. 2011), without significantly increasing the e ff ect ofthe age-metallicity degeneracy. Considering the low resolutionof our spectroscopic setup, it is di ffi cult to put reliable constraintson Z from the observed spectral features, and therefore it was The choice of a di ff erent IMF turns into a systematic mean o ff setin the stellar mass distribution: for instance, our estimates can be con-verted to Salpeter (1955) or Kroupa (2001) IMF by a scaling factor of ∼ . ∼ .
1, respectively. not possible to constrain this parameter a priori . Therefore, themetallicity assigned to each galaxy is what is obtained from thebest-fit model (smallest χ ).With respect to the galaxy dust content, we implemented theCalzetti et al. (2000) and Prévot-Bouchet (Prevot et al. 1984;Bouchet et al. 1985) extinction models, with values of A V rang-ing from 0 (no dust) to 3 magnitudes. As pointed out in previouswork (e.g. Inoue 2005; Caputi et al. 2008; Ilbert et al. 2009),Calzetti’s law is on average more suitable for the bluest SEDs,having been calibrated on starburst (SB) galaxies, whereas thePrévot-Bouchet law is better for mild star-forming galaxies,since it was derived from the dust attenuation of the Small Mag-ellanic Cloud (SMC) (see also Wuyts et al. 2011). Hereafter werefer to the Calzetti and Prévot-Bouchet models as SB and SMCextinction laws, respectively. We let the choice between the twoextinction laws be free, according to the best-fit model (smallest χ ), since we do not have su ffi cient data at UV wavelengths todi ff erentiate the di ff erent trends of the two laws.The SEDs constituting our template library are generatedfrom the SSPs following the evolution described by a givenstar formation history (SFH). In this work, we assume expo-nentially declining SFHs, for which SFR ∝ exp( − t /τ ), with thetime scale τ ranging from 0 . ∼ M ⊙ yr − ) is also considered. This evolution followsunequally spaced time steps, from t = t =
20 Gyr. No fixedredshift of formation is imposed in this model.Although such a parametrisation is widely used, recent stud-ies have shown how exponentially increasing SFHs can pro-vide a more realistic model for actively star-forming galaxies inwhich young stellar populations outshine the older ones (Maras-ton et al. 2010). This e ff ect becomes relevant at z ∼
2, whenthe cosmic star formation peaks, and can be reduced by setting alower limit on the age parameter, in order to avoid unrealistic so-lutions that are too young and too dusty (Pforr et al. 2012). In ourredshift range, galaxies whose SFH rises progressively have lowstellar masses (log( M / M ⊙ ) ∼ .
5, Pacifici et al. 2013) fallingbelow the limit of VIPERS. Moreover, Pacifici et al. (2013) iden-tify a class of massive blue galaxies that assembled their stellarmass over a relatively long period, experiencing a progressivereduction of their star formation at a later evolutionary stage.For such bell-shaped
SFH, neither increasing nor decreasing τ -models seem to be suitable. However, the resulting di ff erencesare smaller than the other uncertainties of the SED fitting method(cf. Conroy et al. 2009).Another issue concerning the SFH is the assumption ofsmoothness. In fact, a galaxy could have experienced severalphases of intense star formation during its past, which can betaken into account by superimposing random peaks on the ex-ponential (or constant) SFR (Kau ff mann et al. 2003a). Allow-ing the presence of recent secondary bursts, thereby making thecolours of an underlying old and red population bluer, can leadto a systematically higher stellar mass estimate. However, onlyfor a small fraction of objects is the di ff erence in M larger than0 . ff ect of using complex SFHs inVIPERS, by computing stellar masses using the MAGPHYS package (da Cunha et al. 2008). This code parametrises thestar formation activity of each galaxy template starting from thesame SSP models as
Hyperzmass (i.e., BC03), but using twocomponents in the SFH, namely an exponentially declining SFRand a second component of additional bursts randomly super-imposed on the former according to Kau ff mann et al. (2003a).The probability of a secondary burst occurring is such that halfof the galaxy templates in the library have experienced a burst Article number, page 5 of 19 n their last 2 Gyr. Each of those episodes can last 3 × –3 × yr, producing stars at a constant rate. The ratio betweenthe stellar mass produced in a single burst and the one formedover the entire galaxy’s life by the underlying exponentially de-clining model is distributed logarithmically between 0 .
03 and4 .
0. The dust absorption model adopted in
MAGPHYS is the oneproposed by Charlot & Fall (2000), which considers the opticaldepth of H II and H I regions embedding young stars along withthe extinction caused by di ff use interstellar medium. MAGPHYS treats attenuation in a consistent way, including dust re-emissionat infrared wavelengths; however, this feature does not representa significant advantage when dealing with VIPERS data sinceinfrared magnitudes are too sparse in our catalogue. Metallic-ity values are distributed uniformly between 0 .
02 and 2 Z ⊙ . Thewide range of tightly sampled metallicities, the di ff erent modelfor the dust extinction, and in particular the complex SFHs in the MAGPHYS library are the major di ff erences with respect to the Hyperzmass code.In Fig. 2 we compare the estimates obtained through
MAG-PHYS and
Hyperzmass , and verify that complex SFHs have aminimal impact on the results (see Sect. 3.4). Since
MAG-PHYS requires a much longer computational time than otherSED fitting codes, we only estimate the stellar mass for galax-ies in the W1 field between z = . z = .
3. More-over, for this comparison we selected objects with the same(solar) metallicity in both the SED fitting procedures, becausein this way we are able to investigate the bias mainly thanksto the di ff erent SFH parametrisations. The distribution of theratio between the two mass estimates is reproduced well bya Gaussian function plus a small tail towards positive val-ues of log( M MAGPHYS / M Hyperzmass ). We find a small o ff set( h ∆ log Mi = h log( M MAGPHYS / M Hyperzmass ) i ≃ .
05) and asmall dispersion ( σ ∆ M ≃ .
11) for most of the galaxy popula-tion, with significant di ff erences between MAGPHYS and
Hy-perzmass (i.e., ∆ log M > .
22) for only ∼
7% of the testingsample ( N exceed in Fig. 2). The consequences on the GSMF arediscussed in Sect. 3.4.Given the wide range of physical properties allowed in theSED fitting procedure, we decided to exclude some unphysicalparameter combinations from the fitting. In particular, we limitthe amount of dust in passive galaxies (i.e., we impose A V . /τ > τ timescales (i.e. we preventfits with models with τ . z form < . ∼ . FUV , NUV , 3 . µ m, and 4 . µ m bands available,we also estimate the stellar mass using just the optical-NIR pho-tometry. We find no systematic di ff erence in the two estimates ofstellar mass (with and without the UV and infrared photometry)and only a small dispersion of about 0 .
08 dex.In summary, the VIPERS galaxy stellar mass estimatesare obtained using the BC03 population synthesis models withChabrier IMF, smooth (exponentially declining or constant)SFHs, solar and subsolar metallicity, and the SB and SMC laws
Fig. 3.
The mass completeness threshold M lim as a function of red-shift, computed for the total sample (the one used in Sect. 3.2, filledcircles) and for the red (upward triangles) and blue (downward trian-gles) populations, defined as discussed in Sect. 5. In each redshift bin,the M lim estimate relies on the rescaled stellar mass M ( i = i lim ) of the20% faintest galaxies (see text). We show M ( i = i lim ) of the red andblue galaxies with small dots of analogous colours. for modelling dust extinction. Unless stated otherwise, this is thedefault parametrisation used throughout this paper.
3. From stellar masses to the galaxy stellar massfunction
In this section we exploit the VIPERS dataset described aboveby considering only our fiducial sample of 41 094 galaxies at z = [0 . , .
3] with spectroscopic redshift reliability >
95% (seeSect. 2.2). As mentioned above, broad-line AGNs ( ∼
850 in thepresent spectroscopic sample) are naturally excluded from thesample, being visually identified during the redshift measure-ment process. Instead, narrow-line AGNs are not removed fromour sample, but they do not constitute a problem for the SEDfitting derived properties, since in most of the cases their opti-cal and NIR emission are dominated by the host galaxy (Pozziet al. 2007). First of all, we try to identify the threshold abovewhich the sample is complete, and therefore the mass functioncan be considered reliable. After that, we derive the GSMF ofVIPERS in various redshift bins and discuss the main sources ofuncertainty a ff ecting it. In the literature, the completeness mass limit of a sample at agiven redshift is often defined as the highest stellar mass a galaxycould have, when its observed magnitude matches the flux limit(e.g. Pérez-González et al. 2008). This maximum is usuallyreached by the rescaled SED of an old passive galaxy. How-ever, this kind of estimate gives rise to a threshold that tends tobe too conservative. The sample incompleteness is due to galax-ies that can be potentially missed, because their flux is close tothe limit of the survey. Depending on the redshift, such a limitin apparent magnitude can correspond to faint luminosities; inthat case, only a small fraction of objects will have a high stellarmass-to-light ratio, since blue galaxies (with lower M / L ) willbe the dominant population (e.g. Zucca et al. 2006). Thus, ifbased on the SED of an old passive galaxy, the determinationof the stellar mass completeness is somehow biased in a redshift Article number, page 6 of 19. Davidzon et al.: VIPERS galaxy stellar mass functions range that depends on the survey depth (see also the discussionin Marchesini et al. 2009, Appendix C).To avoid this problem, we apply the technique devised byPozzetti et al. (2010). This procedure yields, for a given redshiftand flux limit, an estimate of the threshold M lim below whichsome galaxy type cannot be detected any longer. Following thisapproach, we estimate the stellar mass each object would haveif its magnitude, at the observed redshift, were equal to the i -band limiting magnitude i lim . This boundary mass M ( i = i lim ) isobtained by rescaling the original stellar mass of the source at itsredshift, i.e. log M ( i = i lim ) = log M + . i − i lim ). The threshold M lim is then defined as the value above which 90% of the M ( i = i lim ) distribution lies. According to this, at values higher than M lim , our GSMF can be considered complete. We include inthe computation only the 20% faintest objects to mitigate thecontribution of bright red galaxies with large M / L when theyare not the dominant population around the flux limit, as theymay cause the bias discussed at the beginning of this section.Since the 1 / V max method (Schmidt 1968, see Sect. 3.2) in-trinsically corrects the sample incompleteness above the lowerlimit of the considered redshift bin ( z inf ), we apply to each red-shift bin the M lim computed by considering the objects insidea narrow redshift interval ∆ z = .
05 centred on z inf . Figure 3shows M lim as a function of redshift for the global and for thered and blue samples used in Sect. 5, as well as the value of M ( i = i lim ) for each red and blue galaxy. As expected, the lim-iting mass increases as a function of z and the values for redgalaxies are significantly higher ( ∼ . M lim estimates by taking advantage ofthe VVDS-Deep field, which is located in the W1 field (see Fig. 4.
Distributions of stellar masses in six redshift bins for theVVDS-Deep sample in the CFHTLS-W1 field at its limiting magnitude( I
24, dark histograms), compared to the subset obtained by apply-ing a magnitude cut similar to VIPERS, at I . I .
5. The red solid line instead gives thelimiting mass for the VIPERS sample in the W1 field. Both limits, ingood agreement with each other, correctly identify the threshold belowwhich the shallower sample starts to miss a significant fraction ( > Guzzo et al. 2013, Fig. 2). The VVDS sample provides uswith spectroscopically observed galaxies down to a fainter limit,i.e. I AB =
24 (Le Fèvre et al. 2005). Since the CFHTLS-W1field contains both VVDS and part of VIPERS, we can comparethe stellar masses by relying on a similar photometric baseline( u , g, r , I , i , z , J ∗ , K ∗ ). When applying a VIPERS-like magnitudecut ( I < . I <
24 sample as a function of stellar mass.This test is shown in Fig. 4, where we compare the M lim valuesof VVDS (limited to I .
5) and VIPERS to the distributionof stellar masses belonging to the deeper (i.e., I
24) VVDSsample. The M lim values we computed are close to the thresh-olds at which the stellar mass distribution starts to be incompletewith respect to the deep VVDS sample (i.e. the limit where the I < . The number of galaxies and the volume sampled by VIPERS al-lows us to obtain an estimate of the GSMF with high statisticalprecision within six redshifts bins in the range 0 . z . ∆ z ≃ .
05 wide). However, in that case themeasurements start being strongly a ff ected by cosmic (sample)variance. A more detailed discussion is given in Sect. 3.3.We compute the GSMF within each redshift bin, using theclassical non-parametric 1 / V max estimator (Schmidt 1968). Withthis method, the density of galaxies in a given stellar mass bin isobtained as the sum of the inverse of the volumes in which eachgalaxy would be observable, multiplied by the statistical weightdescribed in Sect. 2.2. To optimise the binning in stellar mass,we use an adaptive algorithm that extends the width of a binuntil it contains a minimum of three objects. The errors associ-ated with the 1 / V max estimates are computed assuming Poissonstatistics and include statistical weights. The upper limits fornon-detections have been estimated following Gehrels (1986).The values of the 1 / V max GSMF and associated Poisson errorsare given in Table 1.It is well known that the 1 / V max estimator is unbiased incase of a homogeneous distribution of sources (Felten 1976),but it is a ff ected by the presence of clustering (Takeuchi et al.2000). At variance with the data sets on which the estimator wastested in the past, VIPERS has a specific advantage, thanks to itslarge volume over two independent fields. The competing e ff ectsof over- and under-dense regions on the estimate should cancelout in such a situation. The impact on our analysis will alsobe negligible because an inhomogeneous distribution of sourcesmainly a ff ects the faint end (i.e. the low mass end) of the lumi-nosity (stellar mass) function (Takeuchi et al. 2000), while weare mainly interested in the massive tail of the distribution.To verify this, we compare the 1 / V max estimates with thoseof a di ff erent estimator (i.e. the stepwise maximum-likelihoodmethod of Efstathiou et al. 1988) from another software package(ALF, Ilbert et al. 2005). We find no significant di ff erences inthe obtained mass functions, within the stellar mass range con-sidered in the present study.Finally, in addition to the non-parametric method, we fit aSchechter (1976) function, that is, Φ ( M )d M = Φ ⋆ MM ⋆ ! α exp − MM ⋆ ! d MM ⋆ , (1)to the 1 / V max estimates. The results are shown in Fig. 5 andin Table 2. Although the mass function does not show any ev- Article number, page 7 of 19 ig. 5.
The VIPERS galaxy stellar mass function at di ff erent redshifts. Circles give the values determined through 1 / V max in mass bins of ∆ M = . Φ where no detection is available. idence of a rapid decline below the completeness limit (as inDrory et al. 2009), points beyond this threshold should be con-sidered as conservative lower limits. These plots clearly showthe statistical power of the VIPERS sample, which includes asignificant number of the rare massive galaxies that populate theGSMF high-mass end, thanks to its large volume.At z < . M / M ⊙ ) ∼ .
2, with an upturn belowthat value as observed both locally (e.g. Baldry et al. 2012) andat intermediate redshifts (e.g Drory et al. 2009; Pozzetti et al.2010). However, this feature is located too close to M lim to beassessed e ff ectively. We avoid using a double Schechter functionin our fits also to ease comparison with the parameters derivedat higher redshifts. In fitting the points in the first bin (0 . < z < . α = − .
95. Above this redshift, however, the slope of thelow-mass end is only weakly constrained, given the relativelyhigh values of the completeness limit M lim . For this reason, inall the other bins we fix α to the value − .
95 (see Table 2).The results of Fig. 5 confirm, with impressive statistical pre-cision, the lack of evolution since z ≃ . M / M ⊙ ) >
11) of the galaxy mass function seen in previ-ous, smaller samples. The exponential tail of the Schechter fit isnearly constant across the five redshift bins, down to z ≃ . M / M ⊙ ) > . z = . < z < .
3. At lower masses (10 . < log( M / M ⊙ ) < . z ∼ . . . Fig. 6.
Evolution of the galaxy number density in di ff erent bins of stel-lar mass. The error bars of the density estimates include Poisson noiseand cosmic variance (see Sect. 3.3). At z ≃ .
2, for the lowest masssample, only a lower limit can be estimated, indicated by the arrow.Article number, page 8 of 19. Davidzon et al.: VIPERS galaxy stellar mass functions
Table 1.
Global GSMF: 1 / V max values in regular bins of stellar mass. log M [ h − M ⊙ ] log Φ [ h Mpc − ]0 . < z < . . < z < . . < z < . . < z < . . < z < . . < z < . . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . − . + . − . − . + . − inf − . + . − . − . + . − . − . + . − . − . + . − . Table 2.
Global GSMF: Schechter parameters ( α fixed at z > . z range α log M ⋆ Φ ⋆ [ h − M ⊙ ] [10 − h Mpc − ]0 . − . − . + . − . . + . − . . + . − . . − . − .
95 10 . + . − . . + . − . . − . − .
95 10 . + . − . . + . − . . − . − .
95 10 . + . − . . + . − . . − . − .
95 10 . + . − . . + . − . . − . − .
95 11 . + . − . . + . − . These trends are shown better in Fig. 6, where the numberdensity of galaxies ρ N within three mass ranges is plotted ver-sus redshift. This figure explicitly shows that the most massivegalaxies are virtually already in place at z ≃
1. In contrast,galaxies with lower mass keep assembling their stars in such away that their number density increases by a factor ∼ . z = . .
6, consistently with the so-called downsizing scenario (Cowie et al. 1996; Fontanot et al. 2009). These newmeasurements confirm previous evidence, but with higher statis-tical reliability (see Sect. 4).
When dealing with statistical studies using number counts, a se-vere complication is introduced by the field-to-field fluctuationsin the source density, due to the clustered nature of the galaxydistribution and the existence of fluctuations on scales compa-rable to the survey volume. This sampling or ‘cosmic’ variancerepresents a further term of uncertainty to be added to the Pois-son shot noise. It can be expressed by removing σ ≡ / h N i from the total relative error: σ = h N i − h N i h N i − h N i , (2) where h N i and h N i are the mean and the variance of galaxynumber counts (Somerville et al. 2004).Extragalactic pencil-beam surveys, even the deepest ones,are particularly limited by cosmic variance, given the small vol-ume covered per redshift interval. At z ∼ .
8, galaxy den-sity fluctuations are found to be still relevant up to a scale of ∼
140 Mpc h − (Scrimgeour et al. 2012), which roughly corre-sponds to 5 deg.This is the result of intrinsic clustering in the matter, aspredicted by the power spectrum shape and amplitude at thatepoch, amplified by the bias factor of the class of galaxies anal-ysed, which at high redshift can be very large for some classes.Also the last-generation, largest deep surveys are significantlya ff ected by this issue. For example, the COSMOS field, despiteits 2 deg area, turned out to be significantly overly dense be-tween z = . z = σ cv decreases mildly as a function of volume, with anapproximate dependence σ cv ∝ V − . (Somerville et al. 2004,Fig. 2), compared to σ Poiss ∝ V − . . Trenti & Stiavelli (2008)found similar results by characterizing Lyman break galaxiessurveys: at high values of h N i , the Poisson noise rapidly dropsand cosmic variance remains the dominant source of uncertainty.A more e ff ective way to abate cosmic variance is to observe sep-arated regions of sky. Since counts in these regions, if they aresu ffi ciently distant, are uncorrelated, their variances sum up inquadrature (i.e., σ cv decreases as the square root of the numberof fields, Moster et al. 2011). Multiple independent fields canthen result in a smaller uncertainty than for a single field, evenif the latter has a larger e ff ective area (Trenti & Stiavelli 2008).The current VIPERS PDR-1 sample is not only characterised bya significantly large area, compared to previous similar surveysat these redshifts, but it is also split into two independent andwell-separated fields of ∼ . each. We therefore expectthat the impact of cosmic variance should be limited.To quantify this e ff ect directly, we follow two approaches.The first one, based on the observations themselves, provides Article number, page 9 of 19 ig. 7.
Estimates of the contribution of sample (cosmic) variance tothe statistical uncertainty of the GSMF measurements. For each red-shift bin, the upper panels show the GSMF 1 / V max measurements ob-tained from five VIPERS subregions of 2 deg , located respectively inthe W1 field (three regions, blue diamonds, circles, and squares) and inthe W4 field (two regions, red triangles, and downward triangles). TheSchechter fit to the global GSMF of Fig. 5 is shown as reference (blacksolid line). The lower panels show the standard deviations estimated ineach redshift bin from these five measurements (purple squares, Eq. 3),together with the estimates of σ cv obtained from 57 SHMR mocks bymeans of Eq. 2 (green crosses). To highlight how the e ff ect of cosmicvariance decreases at higher z , we report σ cv , SHMR of the first redshiftbin in the other panels (green dashed lines). In addition, the samplevariance measured in 50 SAM mocks (grey solid line) and the estimatesprovided by Moster et al. (2011) method (black triangles) are shown asreference. an upper limit of the VIPERS σ cv . We select five rectangularsubregions of about 2 deg within the survey and estimate themass function Φ i in each of them, using the 1 / V max method de-scribed above. We choose non-contiguous regions (separated by ∼ M j ± ∆ M / σ tot , obs ( M j ) = n n X i = rh Φ i ( M j ) − Φ tot ( M j ) i , (3)where Φ tot is the global GSMF of VIPERS (at that redshift) and Φ i ( M j ) the number density of galaxies measured in the j -thmass bin for each of the n = & σ tot , obs . More in general, the small number of fields used toperform this test makes the computation of Eq. 3 statisticallyuncertain: for these reasons the estimates of the standard devia-tion obtained from the field-to-field fluctuations among the fivesubsamples ( σ tot , obs , squares in Fig. 7) show rather irregular be-haviour.The second approach is based on the use of simulated mocksurveys. First, we use a set of 57 mock samples (26 and 31 in W1and W4, respectively), built using specific recipes for the stellar-to-halo mass relation. They are based on the MultiDark darkmatter simulation (Prada et al. 2012) and have been constructedto reproduce the detailed geometry and selection function of theVIPERS survey up to z = .
2. (see de la Torre et al. 2013, fordetails). The dark matter haloes identified in the simulation, aswell as artificial sub-haloes drawn from the Giocoli et al. (2010)subhalo mass function, have been associated with galaxies usingthe stellar-to-halo mass relations of Moster et al. (2013). Thelatter are calibrated on previous stellar mass function measure-ments in the redshift range 0 < z <
4. We call these ‘SHMRmocks’. We apply Eq. 2 to estimate the amount of cosmic vari-ance independently among the 26 W1 and 31 W4 mocks. Theglobal estimate of cosmic variance ( σ cv , SHMR ) on the scales ofthe VIPERS survey is obtained by combining the results fromthe two fields (see Moster et al. 2011, Eq. 7). As expected, wefind that σ cv , SHMR decreases with redshift, since we are probinglarger and larger volumes, and increases with stellar mass owingto the higher bias factor (and thus higher clustering) of massivegalaxies (Somerville et al. 2004). Both trends are clearly vis-ible in Fig. 7, where measurements of σ cv , SHMR are presentedfor di ff erent bins of redshift and stellar mass. These values areincluded in the error bars of Fig. 5 to account for the cosmicvariance uncertainty. We notice that in the highest redshift bin σ cv , SHMR represents a conservative estimate, given the di ff erentredshift range in SHMR mocks (1 . < z < .
2) and observations(1 . < z < . getcv (Moster et al. 2011) for the same areaof the SHMR mocks. These results, limited at log( M / M ⊙ ) .
5, are in good agreement with σ cv , SHMR , with the exceptionof the highest redshift bin, mainly because of the z = . σ cv , SHMR to quantifythe cosmic variance uncertainty in that z -bin, although it shouldbe regarded as an upper limit, since the outcomes of Moster et al.(2011) code do not reach the high-mass tail of the GSMF, and arealso more uncertain because the galaxy bias function used in thismethod is less constrained at such redshifts.Besides these SHMR mocks, we also used another set of 50VIPERS-like light cones built from the Millennium simulation(Springel et al. 2005), in which dark-matter haloes are populated Article number, page 10 of 19. Davidzon et al.: VIPERS galaxy stellar mass functions with galaxies through the semi-analytical model (SAM) of DeLucia & Blaizot (2007). Galaxy properties were determined byconnecting the astrophysical processes with the mass accretionhistory of the simulated dark matter haloes. Each mock samplecovers 7 × , with a magnitude cut in the i band equal to thatof the observed sample. Although the geometry of these mocks(and therefore their volume) di ff ers slightly from the design ofthe real survey, they provide an independent test, with a com-pletely di ff erent prescription for galaxy formation. With respectto the SHMR mocks, SAM mocks in Fig. 7 show a trend similarto that of σ cv , SHMR , although with some fluctuations e.g. between z = . ff erences with respect to the other estimates may bedue to the di ff erent recipes in the simulations. In describing our procedure to derive stellar masses by means ofthe SED fitting technique (Sect. 2.3), we emphasised the num-ber of involved parameters and their possible influence on theestimates. The assumptions that have the strongest impact onthe results are the choices of the stellar population synthesismodel, IMF, SFH, metallicity, and dust extinction law. A thor-ough discussion about each one of the mentioned ingredients isbeyond the goals of this paper, but the reader is referred to Con-roy (2013), Mitchell et al. (2013), and Marchesini et al. (2009)for a comprehensive review of the systematic e ff ects induced bythe choice of the input parameters.Here we briefly test the impact on the GSMF of choosingdi ff erent values of Z (whether including subsolar metallicities ornot), the extinction laws (SB and SMC, or SB alone), and theaddition of secondary bursts to the smooth SFHs (i.e. complexSFHs instead of exponentially declining τ -models). We do notmodify the other two main ingredients in our procedure, i.e. theuniversal IMF that we assumed (Chabrier 2003) and the stellarpopulation synthesis model (BC03).To perform this test we use stellar mass estimates obtainedby assuming five di ff erent sets of SED fitting templates, four ofthem di ff ering in metallicity and extinction law: Z ⊙ only andSB; two metallicities ( Z ⊙ and 0 . Z ⊙ ) and SB; solar metallicityand two extinction laws (SB and SMC); two metallicities ( Z ⊙ and 0 . Z ⊙ ) and two extinction laws (SB and SMC). The fifthSED fitting estimate has been derived with the MAGPHYS code(see Sect. 2.3), assuming the following parameters: complexSFHs, extinction model derived from Charlot & Fall (2000), anda wider range of metallicity (including super-solar ones). Welimit these tests to the data in the VIPERS W1 field, i.e. abouthalf of the total sample, given the better overall photometric cov-erage in this area and the large computational time involved.The mass functions resulting from these five di ff erent SED-modelling assumptions are shown in Fig. 8. As expected (seediscussion in Sect. 2.3 and Fig. 2), the MAGPHYS mass func-tion corresponds to the highest estimated values of galaxy den-sity at high stellar masses (at least up to z ≃ . ff ect that is more evident in the high-mass tail. Fig. 8.
Dependence of the mass function on the details of the stellarmass estimates, considering five di ff erent cases. Specifically, the pointscorrespond to di ff erent choices of the stellar population synthesis code,metallicity ( Z ), extinction law (SB + SMC or SB alone), or the additionof secondary bursts to the smooth star-formation histories. Four casescorrespond to SED fitting using
Hyperzmass , for which the values ofthe adopted parameters are given in the bottom-left of the first panel.For details about the parameters adopted for
MAGPHYS (downward tri-angle), we refer to Sect. 2.3.
The other estimates, produced by
Hyperzmass , are in quitegood agreement with each other. The mass functions are slightlyhigher (on average by about 0 . . Z ⊙ and older ages, consequently resulting in higher stellarmass values. The e ff ect of the extinction law is instead marginal.
4. Comparison to previous work
In this section we compare the VIPERS GSMF with other massfunctions derived from di ff erent galaxy surveys (Sect. 4.1) andvarious semi-analytical models (Sect. 4.2). We compare here our estimate of the GSMF with results fromother galaxy surveys. We correct GSMFs (if necessary) to be inthe same cosmological model with Ω m = . Ω Λ = . h = z -bins, halfof them based on photometric redshifts (Fontana et al. 2006;Pérez-González et al. 2008; Ilbert et al. 2010; Bielby et al. 2012)and half on spectroscopic redshifts (Fontana et al. 2004; Pozzettiet al. 2007, 2010; Moustakas et al. 2013). The spectroscopicredshift sample used by Moustakas et al. (2013) is obtainedthrough a pioneering technique based on a low dispersion prismand slitmasks (Coil et al. 2011), which results in a precision of Article number, page 11 of 19 ig. 9.
The VIPERS galaxy stellar mass functions from z = . / V max determinations of previous surveys are also shown by di ff erent symbols, along with their respective Poisson error bars.In the left-hand panel, whereas the VIPERS range is 0 . < z < .
6, the other GSMFs are computed between z = . .
6, with the exception ofMoustakas et al. (2013) for which is 0 . < z < .
65, 0 . < z < .
8, 0 . < z < .
0; notice the very small error bars of the VIPERS data, despitethe narrower redshift range. In the other two panels, the bins of VIPERS are the same as the other surveys; also at these higher redshifts the errorbars of the VIPERS GSMF are small compared to them. σ z ≃ . + z ) (for their high quality sample Q >
3, see Coolet al. 2013), i.e. comparable to the precision of the best photo-metric redshifts (Ilbert et al. 2013, who obtain σ z ≃ . + z )and a very low percentage of outliers).The redshift ranges of the GSMFs shown in Fig. 9 are 0 . < z < .
6, 0 . < z < .
8, 0 . < z < .
0, with the exception ofPRIMUS (Moustakas et al. 2013), which is at 0 . < z < . . < z < .
8, 0 . < z < .
0, and the first bin of VIPERS (i.e.,0 . < z < . ), which is located in aregion of sky uncorrelated with the other surveys we selected.For the VIPERS GSMFs we plot error bars accounting only for σ Poiss , i.e. without adding the uncertainty due to sample vari-ance, in order to be consistent with most of the literature data,for which only Poisson errors are available. Our results lie on the lower boundary of the range covered byother GSMFs, and are in reasonably good agreement with mostof them. At 0 . < z < .
0, the di ff erence with Ilbert et al. (2010,COSMOS survey over 2 deg ) and Pozzetti et al. (2010, zCOS-MOS, 1 . ) is noteworthy: the likely reason is the presenceof a large structure detected in the COSMOS / zCOSMOS field Nonetheless, through the recipe of Moster et al. (2011) we can ob-tain, for each survey, an approximate estimate of the uncertainty dueto cosmic variance to a first approximation, and have a rough idea ofhow much the error bars would increase in Fig. 9 when accountingfor it. For Pozzetti et al. (2007), Pérez-González et al. (2008), andBielby et al. (2012), within the redshift ranges considered in Fig. 9,with only a small evolution with redshift, the GSMF uncertainty re-lated to cosmic variance is approximatively the same: ∼
15% betweenlog M / M ⊙ = . ∼
23% between log M / M ⊙ = . , but split in three fields.) For Ilbert et al. (2010)and Pozzetti et al. (2010), σ cv ≃
10% when 10 . < log M / M ⊙ < . σ cv ≃
17% when 11 . < log M / M ⊙ < .
5. In the same bins ofstellar mass, for Fontana et al. (2004) σ cv is 20% and 30%, respectively,while σ cv ≃
30% and 45% in Fontana et al. (2006). The estimatesprovided by Moustakas et al. (2013) in their paper are generally below10%, except at log M / M ⊙ > . − (Kovaˇc et al. 2010), demonstrating the importance of the cosmicvariance in this kind of comparison.Some discrepancy (nearly by a factor of two) is also evidentwith the estimates by Moustakas et al. (2013). The explanationcould be partly related to the statistical weighing, in particularfor the faintest objects, because the lower the sampling rate esti-mates, the greater the uncertainty in such a correction. At mag-nitudes i ≃ .
5, the SSR of PRIMUS is approximately 45%,dropping below 20% at the limit of the survey (Cool et al. 2013).Instead, in VIPERS the SSR is ∼
75% down to our magnitudelimit i = . z ≃
1, making the statistical weight correc-tions smaller and more robust. In addition to this, it should benoticed that although several overdensities have been observedin PRIMUS, cosmic variance seems unable to fully justify thedi ff erence between the GSMFs of the two surveys: the numberof independent fields (PRIMUS consists of five fields with a totalof 5 . ) should reduce this problem, at least to some degree.The disagreement could also be partially ascribed to the di ff er-ent ways stellar masses are estimated: Moustakas et al. derivedtheir reference SEDs according to the SSP model of Conroy &Gunn (2010), which results in stellar mass estimates systemati-cally higher than those obtained by assuming BC03 (see Mous-takas et al. 2013, Fig. 19).Regarding the choices of SEDs, it is worth noticing thatPérez-González et al. (2008) also used a template library dif-ferent from ours, which they derived from the PEGASE stellarpopulation synthesis model (Fioc & Rocca-Volmerange 1997),bounding the parameter space by means of a training set of ∼ z and wide photometricbaseline. The other surveys quoted in Fig. 9 (Fontana et al. 2004,2006; Pozzetti et al. 2007, 2010; Ilbert et al. 2010; Bielby et al.2012) adopt BC03.VIPERS data provide tight constraints on the high-mass endof the GSMF. Previous surveys, such as K20, MUSIC, andVVDS-Deep (i.e. Fontana et al. 2004, 2006; Pozzetti et al. 2007),were unable to probe this portion of the GSMF (log( M / M ⊙ ) & .
5) because of their relatively small area (about 52, 150, and1 750 arcmin respectively). Instead, GSMFs derived from pho-tometric redshift surveys are characterised by a Poisson noisethat is in general comparable to the level in VIPERS (Pérez- Article number, page 12 of 19. Davidzon et al.: VIPERS galaxy stellar mass functions
Fig. 10.
Comparison of the VIPERS mass function (red points, asin Fig. 5) with the semi-analytical models of Bower et al. (2006), DeLucia & Blaizot (2007), and Guo et al. (2011) (grey dotted, yellowsolid, green short-dashed lines), whose GSMFs have been derived di-rectly from the tables available in the Millennium database (Lemson &Virgo Consortium 2006). The Guo et al. (2011) stellar masses have alsobeen convolved with a Gaussian of dispersion 0 .
15 dex, to reproduceobservational uncertainty on stellar mass determinations; the resultingGSMFs are represented with green long-dashed lines.
González et al. 2008; Ilbert et al. 2010), but they can be af-fected by failures on photometric redshift estimates: even a smallfraction of catastrophic redshift measurements can be relevant athigh masses (Marchesini et al. 2009, 2010). Moreover, the skyarea generally covered by high- z photometric surveys is not largeenough for cosmic variance to be negligible.We postpone a detailed analysis of the evolution of theGSMF down to the local Universe to future work: di ff erences inthe details of the available estimates from 2dFGRS, SDSS, andGAMA (see Cole et al. 2001; Bell et al. 2003; Panter et al. 2004;Baldry et al. 2008; Li & White 2009; Baldry et al. 2012) pre-vent a robust comparison with our data. Only computing stellarmasses and mass functions in a self-consistent way can provideconstraints on the evolution of the GSMF down to z = Besides the comparison with other surveys, it is important tocheck the agreement of our results with simulations. In this pa- per we limit ourselves to a preliminary analysis. Nevertheless,this first test provides intriguing results.The four semi-analytical models (SAMs) we consider hererely on the halo-merger trees of the Millennium Simulation (MSSpringel et al. 2005) and the Millennium-II Simulation (MSIIBoylan-Kolchin et al. 2009); namely, three of them (Boweret al. 2006; De Lucia & Blaizot 2007; Mutch et al. 2013) usethe MS (comoving box size L =
714 Mpc h − , particle mass = . × M ⊙ h − ), while the last one (Guo et al. 2011) isbased on both MSI and MSII ( L =
143 Mpc h − , particle mass = . × M ⊙ h − ). The tight constraints posed by VIPERScan be very useful when studying whether these models ade-quately reproduce the real universe.In Fig. 10, we show the mass functions derived from themodels of Bower et al. (2006), De Lucia & Blaizot (2007),and Guo et al. (2011), together with the VIPERS results. Allthe model GSMFs are computed from snapshots at the sameredshifts. The narrow redshift binning we can set in VIPERS( ∆ z = .
1) allows us to compare simulated galaxies to observedones at cosmic times that are very close to the snapshot consid-ered. In the case of De Lucia & Blaizot model, we also derivedthe stellar mass functions from the VIPERS-like light cones in-troduced in Sect. 3.3, but we do not show them in Fig. 10 sincethey lead to results that are indistinguishable from those obtainedfrom snapshots. For all three SAMs, we find that the low-massend of the GSMF is over-estimated. Such a discrepancy, alreadyobserved in other work (Somerville et al. 2008; Cirasuolo et al.2010), is mainly due to an over-predicted fraction of passivegalaxies on those mass scales. This can be caused by an under-e ffi cient supernova feedback and / or some issue as to how the starformation e ffi ciency is parametrised at high redshifts (Fontanotet al. 2009; Guo et al. 2011). Rescaling the simulations to anup-to-date value of σ (in MS it is equal to 0 . M / M ⊙ ) & .
0, while the Guo et al. (2011) mass functionlies systematically below by ≃ . M / M ⊙ ) > ff ect of introducing observational uncertainties isshown in Fig. 10 only for the Guo et al. (2011) model, whichforesees a lower density of objects in the massive end with re-spect to the other two models. We recomputed the Guo et al.GSMFs after convolving stellar masses with a Gaussian of dis-persion 0 .
15 dex. The predictions of Guo et al. (2011) are thenin fair agreement with VIPERS. With respect to De Lucia &Blaizot (2007), the main distinguishing features of Guo et al.(2011) model are the high e ffi ciency of supernova feedback anda lower rate of gas recycling at low mass. The transition fromcentral to satellite status in the Guo et al. prescription also dif-fers, resulting in a larger number of satellite galaxies than in DeLucia & Blaizot model.It should be emphasised that only Guo et al. (2011) choosemost of the parameters in order to fit the observed local massfunction, whereas Bower et al. (2006) and De Lucia & Blaizot Article number, page 13 of 19 ig. 11.
Comparison of the VIPERS mass function (red points) withthe semi-analytical model of Mutch et al. (2013) (green shaded area at95% confidence limits). In several redshift bins Mutch et al. GSMFdoes not reach masses as high as VIPERS because the volume of thesimulation (with a comoving box size L = . h − ) is smaller. Inthe right-hand middle panel (0 . < z < . ff erent surveys (Pozzetti et al. 2007; Drory et al.2009; Ilbert et al. 2010, grey triangles,diamonds, and squares, respec-tively). In addition, the yellow shaded regions represent the dispersionof the mass functions derived from the 57 SHMR mocks (see Sect. 3.3),in the same redshift bins as the VIPERS ones. (2007) use the local luminosity function to adjust their recipes.In recent studies, the parameters of these models have been tuned[again] by means of a di ff erent approach, based on Bayesian in-ference (Henriques et al. 2009; Bower et al. 2010). From thisperspective, a particular kind of calibration has been proposedby Mutch et al. (2013), who modify the input parameters in theSAM of Croton et al. (2006) to match observations at z = z ≃ . M ≃ M ⊙ , not only at the redshift ofcalibration ( z ≃ .
83) but also in the other bins. The authors donot convolve their mass functions with a Gaussian uncertaintyon stellar masses, because at least part of the uncertainties thisprocedure accounts for should already be included in the obser-vational constraints they use. The Mutch et al. (2013) modelis calibrated at z = .
83 by using the results of Pozzetti et al.(2007), Drory et al. (2009), and Ilbert et al. (2010). Among thesethree GSMFs, only Pozzetti et al. (2007) is based on spectro- scopic data (VVDS-Deep), which are unfortunately quite limitedat high masses. The other two estimates (Drory et al. 2009; Ilbertet al. 2010) are derived from the COSMOS survey, which con-tains a significant over-density at z ≃ .
8. The strategy adoptedby Mutch et al. to combine such information may lead to over-confidence in the adopted constraints, especially in the highestmass range, where observations are most di ffi cult. To recon-cile SAM and observations at log( M / M ⊙ ) > .
8, Mutch et al.(2013) have assumed a star formation e ffi ciency much higherthan the one imposed by Croton et al. (2006), and consequentlythey were forced to parametrise supernova feedback e ffi ciencywith a range of values that is not completely supported by obser-vations (Rupke et al. 2002; Martin 2006). Intriguingly, we notethat the authors would significantly relieve these tensions if theywere to add VIPERS data to their analysis.From a di ff erent perspective, the SHMR mocks we intro-duced in Sect. 3.3 are also calibrated at multiple redshifts.We decided to test their reliability by deriving their GSMFs(Fig. 11). The agreement is remarkable: VIPERS data confirmthe validity of the stellar-to-halo mass relation of Moster et al.(2013) that was used to construct these mocks. This relationconnects galaxies with their hosting dark matter halo by meansof a redshift-dependent parametrisation that has been calibratedthrough the GSMFs of Pérez-González et al. (2008) and Santiniet al. (2012) up to z =
4. Because of the lack of tight constraintsused by Moster et al. for the most massive galaxies (the datafrom Pérez-González et al. 2008 have lower statistics than ours),the SHMR mass functions diverge at high mass from our esti-mates.
5. Evolution of the mass function of the red andblue galaxy populations
In order to distinguish the contribution of quiescent and activelystar forming galaxies to the global evolution, we now split thesample according to the galaxy rest-frame ( U − V ) colour (seeFritz et al. 2013 for extensive discussion). The absolute magnitudes for galaxies in the VIPERS cataloguewere computed from the same SED fitting procedure describedin Sect. 2.3, applying a k- and colour-correction, derived fromthe best-fit SED, to the apparent magnitudes in the bands thatmore closely match the rest-frame emission in the U and V fil-ters (see details in Fritz et al. 2013). In this way, ( U − V ) rest-frame colours can be reliably computed within the redshift rangeof the survey, showing the classical bimodality and allowing usto separate red-sequence from blue-cloud galaxies (cf. Stratevaet al. 2001; Hogg et al. 2002; Bell et al. 2004).The valley between the two populations is found to beslightly evolving toward bluer colours at earlier epochs. Despiteits simplicity, this photometric classification can be consideredas a good proxy for selecting quiescent and star-forming galax-ies. As discussed by Mignoli et al. (2009) using zCOSMOS data,86% (93%) of the galaxies selected as being photometrically red(blue) are also quiescent (star-forming) according to their spec-tra. To verify and validate our selection method, we also derivedgalaxy photometric types by fitting our photometry with the em-pirical set of 62 templates used in Ilbert et al. (2006), which wasoptimised to refine the match between photometric and spectro-scopic redshifts in the VVDS. The same set was also used to Article number, page 14 of 19. Davidzon et al.: VIPERS galaxy stellar mass functions
Fig. 12.
The galaxy stellar mass functions of the blue and red populations in VIPERS, derived using the 1 / V max . Symbols (circles and diamonds,respectively) are filled for data above the corresponding completeness limit M lim (vertical lines) and empty below. Error bars account for Poissonnoise alone. The Schechter fit of the two populations in the bin 0 . < z < . classify galaxies in several other papers (e.g. Zucca et al. 2006,2009; Pozzetti et al. 2010; Moresco et al. 2010). The classi-fication of VIPERS galaxies resulting from this second methodmatches reasonably well with the ( U − V ) colour selection. Morethan 70% of the red galaxies are defined as early-type objects bythe SED analysis, while more than 95% of blue galaxies are clas-sifed as late types. For red galaxies this worsens beyond z = . Using this classification, we are now in a position to quantifythe contribution of red and blue galaxies to the GSMF and, inparticular, to its high-mass end. The results are shown in Fig. 12.The mass functions for each class are estimated in bins of 0 . M ), using the same 1 / V max method as described in Sect. 3.2.Fits with the usual Schechter function are provided, as describedin the caption, to highlight evolution (or absence thereof) as afunction of redshift.The predominance of red objects among the massive galaxiesis clearly visible in all redshift bins, with blue galaxies mainlycontributing at lower masses ( M < M ⋆ ). Since the mass com-pleteness limit M lim for the blue population extends to su ffi -ciently low masses, we can perform the Schechter fit by leav-ing M ⋆ , Φ ⋆ , and α free. The slope of the low-mass end re-mains almost constant in redshift for the blue population, with1 . < α < .
3, up to z ≃ .
9, as seen in previous works (cf. Pozzetti et al. 2010). At redshift higher than this it can no longerbe constrained. With respect to the red population, the high val-ues of the mass completeness limit M lim (see Sect. 3.1) preventus from studying the red sample in the same mass range; for in-stance, it is not possible to determine the evolution of α (Ilbertet al. 2010) or an upturn of the GSMF (cf. Drory et al. 2009) ina reliable way.From these measurements we can determine the value of M cross , where the blue and red GSMFs intersect, i.e. the divid-ing line between the ranges in which blue and red galaxies re-spectively dominate the mass function (Kau ff mann et al. 2003b).The physical meaning of M cross has been questioned (Bell et al.2007), but it is in general considered as a proxy to the transi-tion mass of physical processes such the quenching of star for-mation, (responsible for the migration from the blue cloud tothe red sequence), or the AGN activity (e.g. Kau ff mann et al.2003a). Moreover, its clear dependence on environment (Bol-zonella et al. 2010) points to an interpretation of the galaxy trans-formation that is not only linked to secular processes.We quantify the value of the transition mass in each red-shift bin using the 1 / V max measurements. The transition massincreases from log( M cross / M ⊙ ) = . z ≃ .
55 tolog( M cross / M ⊙ ) = . z ≃ .
75, as shown in Fig. 13. Thistrend is very well fitted by a power law ∝ (1 + z ) . Beyond z = . M cross estimates should be formally considered asupper limits, since they fall below the mass completeness limitof red galaxies, but at least up to z = .
0, they can be consideredas a good approximation of the real values, given their proximityto the limit.
Article number, page 15 of 19 ig. 13.
The values of the transition mass M cross as computed fromFig. 12, plotted as a function of redshift. The VIPERS measurementsare given as black open circles, with a downward arrow when the tran-sition mass is below the completeness mass of at least one of the twoclasses. The solid line is a fit with a (1 + z ) power law to the VIPERSpoints between z = . z = .
8. These are compared to literatureestimates in grey. Points from Pozzetti et al. (2010) are obtained usingthree di ff erent classifications: a separation according to specific SFR(diamonds), a best-fit SED classification (triangles), and a morphologi-cal classification (squares). The points of Bundy et al. (2006) are basedon either the ( U − B ) bimodality or [OII] emission (upper and lowerhalf-circles respectively). The points by Vergani et al. (2008) (aster-isks) are based on a spectral classification (D4000 break). The valuefrom PRIMUS (Moustakas et al. 2013) at z = . ∝ (1 + z ) . , as suggested inthat paper; these authors classified active and quiescent galaxies withrespect to their position in the SFR vs M diagram. In Fig. 13 we also plot results from previous studies. Inthis respect, it is important to underline that the value of M cross provided by the various authors can di ff er significantly fromeach other, depending on the adopted classification. For in-stance, the results of the morphological classification used byBundy et al. (2006) on the DEEP2 survey fall above the massranges considered in the plot. This could be related to part ofthe “red and dead” galaxies at such redshifts becoming ellip-ticals (in a morphological sense) at a later stage (Bundy et al.2010). In fact, when we split the DEEP2 sample on the basisof the ( U − B ) bimodality, the results are in agreement with ourfindings. Our estimates of M cross are fairly consistent (within ± . M cross ∝ (1 + z ) . Pozzetti et al.(2010) derived M cross from the GSMFs of the zCOSMOS (10k-bright) sample split using di ff erent criteria: a cut in specific SFR(i.e. sSFR ≡ SFR / M ≷ − Gyr − ), morphology (spheroidalvs disc / irregular galaxies), and best-fit SEDs (same photomet-ric types discussed in Sect. 5.1). Moustakas et al. (2013) definestar-forming galaxies as lying in the so-called main sequenceof the SFR (estimated from the SED fitting) versus M dia-gram (Noeske et al. 2007). They find a flatter evolution, with M cross ∝ (1 + z ) . . To collect further evidence of star-formation quenching pro-cesses that cause the transition of galaxies from the so-calledblue cloud to the red sequence (Faber et al. 2007), we measuredthe evolution of the galaxy number density of blue and red pop-ulations, namely ρ blue N ( z ) and ρ red N ( z ). These estimates are derivedusing the 1 / V max method, taking both Poisson noise and cosmicvariance into account. We also verified, however, that the re-sults would essentially be the same if we had measured numberdensities by integrating the Schechter best-fitting functions. Weexplore four narrow bins of stellar mass to highlight the depen-dence of the quenching processes on this parameter. To improvestatistics at high stellar masses, we choose wider redshift binshere: 0 . .
7, 0 . .
9, 0 . .
1, 1 . . . < log( M / M ⊙ ) < . ρ red N increases by a factor of ∼ . z = z = .
6, whereas at higher masses thevariation is much smaller. Red galaxies with mass 11 . < log( M / M ⊙ ) < . ρ red N = (5 . ± . × − Mpc − h to (9 . ± . × − Mpc − h inthe same redshift interval (about 80% increase). The increase iseven smaller (45%) for galaxies with log( M / M ⊙ ) > .
4. Withthe VIPERS data we are able for the first time to provide sig-nificant evidence of this trend for such massive galaxies at theseredshifts. This result is in line with the mass-assembly downsiz-ing scenario highlighted in previous works (Cimatti et al. 2006;Pozzetti et al. 2010; Ilbert et al. 2010): barring systematic e ff ectsdue to the uncertainty on M , red galaxies with M > M ⊙ build their stellar mass well before the less massive ones anddo not experience any strong evolution between z ≃ . z ≃ .
6. At these redshifts, quenching mechanisms seem tobe more e ffi cient at low and intermediate masses, as also re-cently suggested by Moustakas et al. (2013). With respect toPRIMUS, the VIPERS survey extends this finding to highermasses (log( M / M ⊙ ) > .
4) and redshifts (up to ≃ . z ≃ z ≃ . . log( M / M ⊙ ) < .
8, with a 10% variation.For higher mass blue galaxies, for which the sample is completeat all redshifts, the density ρ blue N of objects with mass 10 . log( M / M ⊙ ) < . z ≃ . z = . M / M ⊙ ) > .
4) disap-pear at z . . ff at earlierepochs (i.e. z > .
6. Conclusions
We measured the GSMF between z = . z = . Article number, page 16 of 19. Davidzon et al.: VIPERS galaxy stellar mass functions
Fig. 14.
Evolution of the number density of the blue and red galaxy populations in VIPERS (filled circles and diamonds, respectively) withdi ff erent stellar masses. Upward arrows represent lower limits when ρ N is estimated in a bin of mass a ff ected by incompleteness, while a downwardarrow represents the upper limit in case of zero detection (rightmost panel). The error corridors reflect the overall uncertainties, which includeboth Poisson noise and cosmic variance added in quadrature. ticular, on a nearly full coverage of our fields with near-infrareddata. We performed several tests to verify that the systematics in-trinsic to the method of SED fitting (e.g. the parametrisation ofthe SFH) do not introduce any significant bias into our analysis.The large volume probed by VIPERS results in extremely highstatistics, dramatically reducing the uncertainties due to Poissonnoise ( σ Poiss ) and sample variance ( σ cv ). We estimated the lat-ter by using 57 galaxy mock catalogues based on the MultiDarksimulation (Prada et al. 2012) and the stellar-to-halo mass rela-tion of Moster et al. (2013). These mocks closely reproduce thecharacteristics of the VIPERS survey.We empirically determined a completeness threshold M lim above which the mass function can be considered complete.This limiting mass evolves as a function of z , ranging fromlog( M / M ⊙ ) = . . .
1. Wefocussed our analysis on the high-mass end of the GSMF, whereVIPERS detects a particularly high number of rare massivegalaxies. The main results we obtain follow. – VIPERS data tightly constrain the exponential tail of theSchechter function, which does not show significant evolu-tion at high masses below z = .
1. The same result is pro-vided by analysis of the co-moving number density ρ N , cal-culated in di ff erent bins of stellar mass. At z ≃ . M / M ⊙ ) > . M / M ⊙ ) = . , the galaxy num-ber density increases by a factor of ∼ . z ≃ . z ≃ . – We compared our observed GSMFs with those derived fromsemi-analytical models (De Lucia & Blaizot 2007; Boweret al. 2006; Guo et al. 2011). While the discrepancy at lowmasses between models and observations is well establishedand has been exhaustively discussed in literature, predictionsat the high-mass end of the GSMF have not yet been verifiedwith su ffi cient precision. We show that the high accuracyof the VIPERS mass functions makes them suitable for thiskind of test, although further improvement to reduce stellarmass uncertainties would be beneficial. From a first analysis,the VIPERS data appear to be consistent with the Guo et al.(2011) model at log( M / M ⊙ ) >
11, once the uncertainties in the stellar mass estimates are taken into account. A moredetailed analysis will be the subject of a future work. Wesuggest that VIPERS GSMFs can be e ff ectively used to con-strain models at multiple redshifts simultaneously, in smallsteps of ∆ z . This could shed light on the time scale of thephysical mechanisms that determine the evolution at highermasses (for instance, the AGN-feedback e ffi ciency). – We divided the VIPERS sample by means of a colour cri-terion based on the ( U − V ) bimodality (Fritz et al. 2013)and estimated the blue and red GSMF in the same range,0 . < z < .
3. We find that the transition mass abovewhich the GSMF is dominated by red galaxies is aboutlog( M cross / M ⊙ ) ≃ . z ≃ .
55 and evolves proportionalto (1 + z ) . – The number density of the red sample shows an evolutionthat depends on stellar mass, being steeper at lower masses.At high stellar masses, the quenching of active galaxies hasnot been thoroughly studied because of their rareness. Weobtained a first impressive result with VIPERS, by detectingat z ≃ M / M ⊙ ) > .
4, which have all migrated onto thered sequence by z = .
6, i.e. in about 2 Gyrs.The first data release of VIPERS has allowed us to study theevolution of the galaxy stellar mass function over an unprece-dented volume at redshifts z = . − .
3. We emphasise the con-straining power of this dataset, particularly for the abundance ofthe most massive galaxies, both quiescent and star-forming. Inforthcoming studies we will make full use of the growing sam-ple and of the measurement of spectral features, in order to in-vestigate the cosmic star formation history and compare galaxyformation models at high redshift.
Acknowledgements.
We are grateful to Lucia Pozzetti for useful suggestions andfor providing zCOSMOS results. We thanks Simon J. Mutch who provided theGSMF foreseen by the model described in Mutch et al. (2013) in our preferredredshift bins. ID warmly thanks Ivan Delvecchio for useful discussions. Weacknowledge the crucial contribution of the ESO sta ff for the management ofservice observations. In particular, we are deeply grateful to M. Hilker for hisconstant help and support of this programme. Italian participation in VIPERS hasbeen funded by INAF through PRIN 2008 and 2010 programmes. LG and BRGacknowledge support of the European Research Council through the DarklightERC Advanced Research Grant ( Article number, page 17 of 19 uropean Research Council through the EARLY ERC Advanced Research Grant( / / ERC grant agreement n. 202781.WJP and RT acknowledge financial support from the European Research Councilunder the European Community’s Seventh Framework Programme (FP7 / / ERC grant agreement n. 202686. WJP is also grateful for support from theUK Science and Technology Facilities Council through the grant ST / I001204 / / / / / INSU (Insti-tut National des Sciences de l’Univers) and the Programme National Galaxies etCosmologie (PNCG). CM is grateful for support from specific project fundingof the
Institut Universitaire de France and the LABEX OCEVU.
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