A & A 602, A 15 (2017)
D O I: 10.1051/0004-6361/201630113
© E S O 2017
Astronomy
&
Astrophysics
The VIMOS Public Extragalactic Redshift Survey (VIPERS)
The decline of cosmic star formation: quenching, mass, and environment connections*
O. Cucciati
1 , 2 ’ * *, I. Davidzon3,1, M. Bolzonella1, B. R. Granett4,5, G. De Lucia6, E. Branchini7,8’9, G. Zamorani1, A. Iovino4, B. Garilli10, L. Guzzo4,5, M. Scodeggio10, S. de la Torre3, U. Abbas11, C. Adami3, S. Arnouts3, D. Bottini10, A. Cappi1,12, P. Franzetti10, A. Fritz10, J. Krywult13, V. Le Brun3, O. Le Fevre3, D. M accagni10,
K. M ałek14, F. Marulli2,15,1, T. M outard16,3, M. Polletta10,17,18, A. Pollo14,19, L. A. M. Tasca3, R. Tojeiro20, D. Vergani21, A. Zanichelli22, J. Bel23, J. Blaizot24, J. Coupon25, A. Hawken4,5, O. Ilbert3, L. Moscardini2,15,1,
J. A. Peacock26, and A. Gargiulo10
(Affiliations can be found after the references)
Received 22 November 2016 / Accepted 25 January 2017
ABSTRACT
We use the final data of the VIMOS Public Extragalactic Redshift Survey (VIPERS) to investigate the effect of the environment on the evolution of galaxies between z = 0.5 and z = 0.9. We characterise local environment in terms of the density contrast smoothed over a cylindrical kernel, the scale of which is defined by the distance to the fifth nearest neighbour. This is performed by using a volume-limited sub-sample of galaxies complete up to z = 0.9, but allows us to attach a value of local density to all galaxies in the full VIPERS magnitude-limited sample to i < 22.5.
We use this information to estimate how the distribution of galaxy stellar masses depends on environment. More massive galaxies tend to reside in higher-density environments over the full redshift range explored. Defining star-forming and passive galaxies through their (N U V -r) vs. (r - K) colours, we then quantify the fraction of star-forming over passive galaxies, fa p, as a function of environment at fixed stellar mass. fa p is higher in low-density regions for galaxies with masses ranging from lo g (M /M ©) = 10.38 (the lowest value explored) to at least lo g (M /M Q) ~ 11.3, although with decreasing significance going from lower to higher masses. This is the first time that environmental effects on high-mass galaxies are clearly detected at redshifts as high as z ~ 0.9. We compared these results to VIPERS-like galaxy mock catalogues based on a widely used galaxy formation model. The model correctly reproduces fa p in low-density environments, but underpredicts it at high densities. The discrepancy is particularly strong for the lowest-mass bins. We find that this discrepancy is driven by an excess of low-mass passive satellite galaxies in the model. In high-density regions, we obtain a better (although not perfect) agreement of the model fa p with observations by studying the accretion history of these model galaxies (that is, the times when they become satellites), by assuming either that a non-negligible fraction of satellites is destroyed, or that their quenching timescale is longer than ~2 Gyr.
Key words. galaxies: evolution - galaxies: high-redshift - galaxies: statistics - cosmology: observations - large-scale structure of Universe
1. Introduction
S ince pioneering w ork ab o u t four decades ago (e.g. O em ler 1974; D avis & G eller 1976; D ressler 1980) , environm ental stud
ies have increased in im portance in the context o f galaxy evolution. T he first observations found tw o d istinct galaxy populations (red and elliptical vs. blu e and spiral) residing
* Based on observations collected at the European Southern Obser
vatory, Cerro Paranal, Chile, using the Very Large Telescope under programs 182.A-0886 and partly 070.A-9007. Also based on obser
vations obtained with MegaPrime/MegaCam, a joint project of CFHT and 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 National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. 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 of NRC and CNRS. The VIPERS web site is h ttp ://w w w .v ip e r s . i n a f . i t /
** Corresponding author: O. Cucciati, e-mail: o l g a .c u c c i a t i @ o a b o .i n a f .i t
in different environm ents in the local U niverse. M o re recent surveys extended this fundam ental resu lt to higher redshifts (e.g.
C ucciati et al. 2 0 0 6 ; C ooper et al. 2007), and/or rep laced the v i
sual o r colour classification w ith estim ates o f the star form ation rate (SFR ) o r o ther indicators o f the d o m inant stellar p o p u la
tion such as the m easurem ent o f the D 4000 A b rea k (see e.g.
B a lo g h e ta l. 1998; H ashim oto et al. 1998; G ó m e z e ta l. 2 0 0 3 ; K auffm ann e t al. 2 0 0 4 ; G rutzbauch e t al. 2011b) .
T he environm ent reconstruction has also been im proved over the years. T he system atic identification o f galaxy clusters and groups allow ed th e com m unity to perform m o re detailed analysis o f galaxy populations in different environm ents (see e.g. C ucciati et al. 2 0 1 0 ; Iovino e t a l. 2 0 1 0 ; G e r k e e ta l. 2 0 1 2 ; K nobel e t al. 2 0 1 3 ; K ovac et al. 2 0 1 4 ; A n nunziatella e t al. 2 0 1 4 ; H aines e t al. 20 1 5 , and references therein). F urtherm ore, the d e
velopm ent o f new m ethods to com pute the local density around galaxies (such as Voronoi tessellation) have enabled both the identification o f galaxy clusters an d the p aram eterisation o f the density field as a w hole to b ecom e m o re reliable (M arinoni e t al.
2 0 0 2 ; C ooper et al. 2 0 0 5 ; K ovac et al. 2 0 1 0 ; L em aux et al. 2 0 1 6 ; F o s s a tie ta l. 2017) . M oreover, the com plex topology o f the
large-scale structure (LSS) can now be dissected, spanning from the large-scale filam entary cosm ic w eb (e.g. T em pel et al. 2 0 1 3 ; E in a s to e ta l. 2 0 1 4 ; A lpaslan e t al. 2 0 1 4 ; M alavasi et al. 2017) to d etailed analysis focused on sm aller regions (e.g. single clusters or w alls, as in G avazzi e t al. 2 0 1 0 ; B oselli et al. 2 0 1 4 ; Iovino et al. 2016) .
In this context, spectroscopic galaxy surveys p lay a pivotal role in identifying LSS both on sm all and large scales. Several analyses have used som e o f the m ost p recise p hotom etric red- shifts available to date (S coville et al. 2 0 1 3 ; D arvish et al. 2 0 1 5 ; M alavasi e t al. 2016) . D espite this, spectroscopic m easurem ents o f galaxy redshifts (zspec) are generally req u ired in order to m in im ise the uncertainties in the radial p osition o f galaxies. In som e cases, the zspec m easurem ent error is so sm all that th e strongest lim itation is due to pecu liar velocities (K aiser 1987) . L arge and deep spectroscopic surveys com prise the b est data-sets to study how environm ent affects galaxy evolution, thanks to their large volum e a n d the long tim e-span covered. T hey are, how ever, very tim e consum ing to assem ble.
A t present, only the V IM O S P ublic E xtragalactic R edshift Survey (V IPER S, G uzzo et al. 2014) offers th e desired co m b i
nation o f large volum e (5 x 107 h -3 M p c3) and p recise galaxy redshifts a t z > 0.5. V IPER S was conceived as a high-redshift (0.5 < z < 1.2) analogue o f large local surveys like 2dFG R S (C olless et al. 2001) . W ith resp ect to other surveys a t in term e
diate redshifts - fo r exam ple, zC O SM O S (L illy et al. 2009), w hich has the sam e depth as V IPER S - th e larger volum e covered b y V IPER S significantly reduces the effect o f cosm ic variance (w hich has im portant effects in zC O SM O S: see e.g.
de la Torre et al. 2010) . This allow s us to study rare galaxy p o p ulations, such as the m ost m assive galaxies, w ith m o re solidity (see D avidzon et al. 2013) .
O f course w e also n ee d an interpretative architecture in w hich to fram e ou r observations. Fortunately, today w e have so
phisticated sim ulations and theoretical m odels o f g alaxy fo rm a
tion and evolution a t ou r disposal th at can help us in this task, to gether w ith sim ulations o f dark m atter (D M ) halo m erger trees.
W ith resp ect to the observations, these theoretical tools offer us the advantage to study the relatio n sh ip betw een b aryonic and dark m atter, to link g alaxy p opulations at different redshifts (e.g.
the p roblem o f finding th e progenitors o f a given galaxy p o p u lation), and study the environm ental history o f galaxies in detail (e.g. G abor et al. 2 0 1 0 ; D e L u cia et al. 2 0 1 2 ; H irschm ann et al.
2014) .
M uch progress has been m ad e w ith sim ulations in recent years, w ith larger sim ulated boxes (see e.g. the B olshoi sim u
lation, K ly p in e ta l. 2 0 1 1 ; and the M ultiD ark run, P r a d a e ta l.
2012), b etter spatial resolution (e.g. the M illennium II sim ula
tion, B oylan-K olchin e t al. 2009) , and the im plem entation o f hy- drodynam ical codes on cosm ological volum es (e.g. th e EA G LE sim ulation, S chaye et al. 20 1 5 , and the ILL U S TR IS sim ulation, V ogelsberger e t al. 2014) . M uch effort has also been m ade to im prove sem i-analytical m odels o f galaxy form ation and evolution (see e.g. G uo e t al. 2 0 1 1 ; D e L u cia e t al. 2 0 1 4 ; H enriques et al.
2 0 1 5 ; H irschm ann et al. 2016) . A lthough several w orks have studied the ro le o f the environm ent in m odels o f galaxy evolu
tion (see e.g. C en 2 0 1 1 ; D e L u cia e t al. 2 0 1 2 ; H irschm ann et al.
2 0 1 4 ; H enriques e t al. 2016), som e lim itations still rem ain, such as the environm ent definition, w hich has to b e linked to o b servational quantities in order to m ake a m eaningful com pari
son betw een the m odels and real d ata (see M uldrew et al. 2 0 1 2 ; H aas et al. 2 0 1 2 ; H irschm ann e t al. 2 0 1 4 ; F ossati et al. 2015) .
As a final note, w e rem a rk that the w ay in w hich w e ask o u r
selves the questions to b e answ ered has also evolved in recent
years. A s an exam ple, the w ide-spread scenario o f “n ature vs.
n u rtu re” in galaxy evolution has been questioned, and it m ight w ell be an ill-posed problem . In fact, even if w e possessed an ideal set o f sim ulations and observations, it w ould b e m isleading to analyse them by contrasting environm ental effects w ith the evolution driven by intrinsic galaxy properties (such as the stel
lar o r halo m ass). T hese tw o aspects are physically connected, and it is im possible to fully separate them (see the discussion in D e L u cia e t al. 2012) .
W ith this p icture in m ind, w e aim at using V IPER S to shed new light on galaxy evolution and environm ent. In another p a p er o f this series (M alavasi et al. 2017) w e show a reco n stru c
tion o f th e cosm ic w eb, w hile in this pap er w e present the d en sity field o f the final V IPER S sam ple. O ur goal is to study how environm ent affects the evolution o f the galaxy specific star for
m ation rate (sSFR) and com pare it w ith sim ulations to obtain new insights into the m echanism s that halt star form ation (i.e.,
“quenching” ). T he p ap e r is organised as follow s. In Sect. 2 w e briefly describe the V IPER S sam ple an d the m o ck galaxy ca ta
logues w e use in ou r analysis. In Sect. 3 w e p rese n t the V IPER S density field, and w e show how environm ent affects galaxy stel
lar m ass an d sSFR in Sect. 4 . In Sect. 5 w e com pare our results to a sim ilar analysis perfo rm ed in the m o c k galaxy catalogues.
W e discuss our findings in Sect. 6 and sum m arise our w ork in Sect. 7 . In the A ppendices w e give additional details on the re li
ability o f th e density field reconstruction, and w e show how the final V IPER S density field com pares to that reco n stru cted from V IPER S first data release.
E x cep t w here explicitly stated, w e assum e a flat A C D M co s
m ology throughout the p ap e r w ith Q m = 0.30, O a = 0.70, H 0 = 70 k m s -1 M p c-1 and h = H 0/1 0 0 . M agnitudes are ex pressed in the AB system (O ke 1974; F uk u g ita et al. 1996) .
2. Data and mock samples
2.1. Data
V IP E R S 1 (G uzzo e t a l. 2 0 1 4 ; Scodeggio et al. 2017) has m e a
sured redshifts for ~ 1 0 5 galaxies at red sh ift 0.5 < z < 1.2.
T he p ro ject h ad tw o b ro ad scientific goals: i) to reliably m easure galaxy clustering and the grow th o f structure through redshift- space distortions; ii) to study galaxy p roperties at an epoch w hen the U niverse w as about h a lf its current age, over a volum e co m p arable to that o f large existing local (z ~ 0.1) surveys, like 2dF- G RS and SDSS.
T he V IPER S global footprint covers a total o f 23.5 deg2, split over th e W 1 and W 4 fields o f the C anada-F rance-H aw aii Tele
scope L egacy S urvey (C FH T L S) W ide. Targets w ere selected to /ab < 22.5 from th e fifth d ata release (T0005, M ellier e t al.
2008) . A colour p re-selection in (r - i) vs. (u - g) was also ap plied to rem ove galaxies at z < 0.5. Together w ith an optim ised slit configuration (S codeggio e t al. 2009a) , this allow ed us to o b tain a target sam pling rate o f ~ 47% over th e red sh ift ran g e o f in terest, about doubling w hat w e w ould have achieved b y selecting a purely m ag n itude-lim ited sam ple to the sam e surface density.
T he V IPER S spectroscopic observations w ere carried out using the V Isible M u lti-O bject S pectrograph (VIM O S, L e F evre et al. 20 0 2 , 2003), using th e low -resolution R ed grism (R - 220 over the w avelength ran g e 5 5 0 0 -9 5 0 0 A ). T he n u m ber o f slits in each V IM O S pointing was m axim ised using the SSPO C algorithm (B ottini et al. 2005) . T he typical radial v e
locity error on the spectroscopic red sh ift (zs) m easurem ent o f 1 h t t p : / / v i p e r s . i n a f . i t
O. Cucciati et al.: Quenching, mass, and environment in VIPERS
a galaxy is = 0.00054(1 + z) (see S codeggio et al. 20 1 7 , for m o re details). A discussion o f th e survey d ata reduction and database system is p resented in G arilli e t al. (2 012) .
T he d ata u sed here correspond to the publicly released PD R - 2 catalogue (S codeggio et al. 2017), w ith the exception o f a sm all sub-set o f redshifts (340 galaxies m issing in the range 0.6 < z < 1.1), for w hich th e red sh ift an d quality flags w ere revised closer to the release date. C oncerning the analysis p re sented here, this has n o effect. W e retain only galaxies w ith reliable red sh ift m easurem ents, defined as having quality flag equal to 2, 3, 4, and 9. T he quality flag is assigned to each tar
geted o bject during th e process o f validating red sh ift m e asu re
m ents, according to a schem e th at has been adopted by previous V IM O S surveys (V V D S, L e F evre e t al. 2 0 0 5 ; and zC O SM O S, L illy et al. 2009) . T he average confidence level o f single redshift m easurem ents for the sam ple o f reliable redshifts is estim ated to be 96.1% (S codeggio et al. 2017) . In o ur case, this selection p ro duces a sam ple o f 74 835 galaxies.
W e com puted the survey selection function an d assigned a set o f three w eights to each galaxy w ith a reliab le redshift: the colour sam pling rate (CSR), the target sam pling rate (TSR ), and the spectroscopic success rate (SSR ). T he C S R takes into a c count the m odification o f the red sh ift distribution, n(z), o f a purely flux lim ited catalogue (iAB < 22.5) b y the colour p re selection applied to rem ove galaxies at z < 0.5 from the sam ple. As a consequence, the C S R depends on redshift, and so it sm oothly varies from 0 to 1 from z ~ 0.4 to z ~ 0.6, and it r e m ains equal to 1 for z > 0.6. T he T S R is the fraction o f galaxies in th e paren t p hotom etric catalogue (iAB < 22.5 and colour cut) that have a slit p laced over them . Finally, th e S SR is the fraction o f targeted galaxies for w hich a reliable red sh ift has been m e a
sured. C onsidering the T S R and SSR together, V IPER S has an average effective sam pling rate o f ~ 40% . In o ur com putation, the T SR depends on th e local p rojected density around each target, w hile th e SSR depends on i-band m agnitude, redshift, rest-fram e colour, B -band lum inosity, and the quality o f the V IM O S q u ad rants.
U nless otherw ise specified, w e use the W 1 and W 4 sam ples together as the “V IPER S sam ple” throughout this paper. W e r e fer to the sam ple o f galaxies w ith a reliable spectroscopic red- shift as defined above as “spectroscopic galaxies” , and to all the other galaxies w ith o nly a p hotom etric red sh ift and w ith i < 22.5 as “p hotom etric g alaxies” . W e refer to the entire flux lim ited c a t
alogue lim ited at iAB < 22.5, befo re the colour pre-selection, as the “p aren t p hotom etric catalogue” .
2.2. P h o to m etric red sh ifts, lum inosities, a n d ste lla r m a s s e s
As p art o f the V IPER S M ulti-L am bda S urvey (V IP E R S -M L S 2, see M o u ta rd e ta l. 2 016a, for further details), p hotom etry from the final C F H T L S3 release (T0007 4) in the ug riz filters w as o p tim ised to provide both accurate colours and reliable p se u d o total m agnitudes. F rom this photom etry, photom etric redshifts (zp) w ere com puted for all galaxies in the V IPER S photom etric catalogue. F ar-U V (FU V ) an d near-U V (N U V ) from G A L E X (M artin & G A L E X Team 2005) , Z Y J H K filters from VISTA (E m erson e t al. 2004) , and K s from W IR C am (P uget et al. 2004) w ere also used, w hen available. Z Y J H K observations are part o f V ID E O (Jarvis e t a l. 20 1 3 ) . D ow n to iAB < 22.5, the
2 h t t p : / / c e s a m . l a m . f r / v i p e r s - m l s /
3 h ttp ://w w w .c fh t.h a w a ii.e d u /S c ie n c e /C F H T L S /
4 h t t p : / / t e r a p i x . i a p . f r / c p l t / T 8 8 8 7 / d o c / T 8 8 8 7 - d o c . h t m l
p hotom etric red sh ift error is mzp = 0.035(1 + z), w ith a <2%
o f outliers rate (see F ig. 12 in M outard e t al. 2016a) .
A bsolute m agnitudes, stellar m asses, and SFR w ere obtained through a spectral energy distribution (SED ) fitting technique, using the code L e P h a re5 as in M o u ta rd e ta l. (20 1 6 b , M 16b from now on). T he SED fitting used all the photom etric bands described above.
W e used th e stellar population synthesis m odels o f B ruzual & C harlot (2003) , w ith tw o m etallicities (Z = 0.008 and Z = 0.02) an d exponentially declining star form ation histories, defined b y S F R <x e -t/T, w ith SFR being th e instantaneous star form ation rate and nin e different values for t , ranging betw een 0.1 G yr and 30 G yr as in Ilbert e t al. (2013) . W e adopted three extinction laws (P revot et al. 1984; C alzetti et al. 2 0 0 0 ; and an interm ediate-extinction curve as in A rnouts e t al. 2013) . W e im p o sed a m axim um d u st reddening o f E ( B - V ) < 0.5 for all g alax ies and a low extinction for low -S F R galaxies (E (B - V ) < 0.15 if a g e /r > 4). W e took into account the em ission-line contribu
tion as d escribed in Ilbert e t al. (2009) . To com pute the absolute m agnitudes, w e m inim ised their dependency on th e tem plate li
b rary b y using the observed m agnitude in the b an d closest to the redshifted absolute m agnitude filter, unless the closest apparent m agnitude had an error >0.3 m ag. W e refer to A ppendix A.1 o f Ilbert e t al. (2005) for m ore details. T he SFR assigned to each galaxy is the instantaneous SFR (see above) o f the best-fit tem p late at the red sh ift o f th e galaxy, an d it is n o t constrained by any prior. F ro m the stellar m ass M and the SFR w e also d e
rived the specific SFR (sSFR ), defined as s S F R = S F R / M . W e com puted absolute m agnitudes and stellar m asses w ith the sam e m eth o d for b oth the spectroscopic an d p hotom etric galaxies, u s
ing their zs and zp, respectively.
2.3. M o ck s a m p le s
W e m ak e use o f m o c k galaxy catalogues to test the reliability o f the density field reconstruction, and to investigate the physical p rocesses taking place in different environm ents b y com paring how environm ent affects galaxy evolution in the m o d el and in the data.
O ur m o c k galaxy catalogues w ere obtained b y em bedding the sem i-analytical m o d el (SA M ) o f g alaxy evolution described in D e L u cia & B laizot (2 007) w ithin D M halo m erging trees ex tracted from the M illennium S im ulation (S pringel e t al. 2005) . T he m ass o f the D M particles is 8.6 x 108 h -1 M 0 . T he D M run adopted a A C D M cosm ology w ith Q m = 0.25, Q b = 0.045, h = 0.73, Q a = 0.75, n = 1, an d ^ 8 = 0.9. T hese SA M m o ck catalogues contain, am ong o ther galaxy properties, the rig h t ascension, declination, red sh ift (including pecu liar veloc
ity), i-band observed m agnitude, B -band absolute m agnitude, galaxy stellar m ass, and SFR. W e rem ark th at this cosm ology is outdated, w ith fo r instance ^ 8 b ased on the first-year re sults o f the W ilkinson M icrow ave A nisotropy P robe (W M A P1, S pergel e t al. 2003) being larger than m o re recen t m easu re
m ents such as W M A P 7 (K om atsu et al. 2011) an d W M A P 9 (H inshaw et al. 2013) , w here they find ^ 8 to b e o f the order o f 0.8. D avidzon et al. (2016) show ed th at the density distribution is slightly different in tw o sim ulations b ased on th e cosm ologies from W M A P1 and W M A P 3, but W M A P 3 had a very low ^ 8 ( ^ 8 = 0.7). G iven th at ^ 8 (and also other cosm ological p ara m eters) from W M A P 7 and W M A P 9 is closer to th at o f W M A P1, w e do n o t expect a large difference betw een sim ulations b ased on 5 h ttp ://w w w .c fh t.h a w a ii.e d u /~ a rn o u ts /L E P H A R E /le p h a re . htm l
W M A P1 o r W M A P 7 and W M A P 9, as also show n in G uo et al.
(2013) .
W e u sed 50 pseudo-independent light cones, each covering an area corresponding to th e V IPER S W 4 field, from w hich w e built m o ck galaxy catalogues, as follow s.
- F irst, from each light cone w e extracted a purely flux-lim ited catalogue w ith the sam e m agnitude cu t as V IPER S (i <
22.5). W e refer to these catalogues as “reference m o ck ca ta
logues” (RM O C K S from now on). In the RM O C K S w e retained the apparent red sh ift (cosm ological red sh ift plus pecu liar v e
locity) w ithout adding any red sh ift m easurem ent error. The density contrast com puted w ith these catalogues (6R) is the standard on w hich w e assess how w ell w e can m easure 6 in a V IP E R S -like survey.
- Second, from each Rm o c k w e built tw o catalogues: a V IP E R S -like p h otom etric catalogue, and a V IP E R S -like spectroscopic catalogue. T he photom etric catalogue was o b tained b y m im icking th e V IPER S p hotom etric red sh ift m e a
surem ent error by adding a ran d o m value extracted from a G aussian distribution w ith <rzp = 0.035(1 + z) to the ap paren t red sh ift o f the Rm o c k. T he spectroscopic catalogue w as obtained from th e Rm o c k first by m odelling the n(z) at z < 0.6 to m im ic the V IPER S C SR , then b y applying the sam e slit-positioning softw are (SSPO C , see B ottini et al.
2005) as was used to select V IPER S targets. In this way, w e w ere able to obtain the sam e V IM O S footprint as in V IPERS (see F ig. A .1) and a T S R th at varied betw een quadrants as in V IPE R S. W e d id not m o d el the SSR in the m ock catalogue because it depends on a large variety o f factors, such as red- shift and m agnitude. N evertheless, to account for its n et e f
fect o f reducing the final n um ber o f m easured spectroscopic redshifts, w e random ly rem oved som e o f the galaxies left a f
ter applying SSPO C , in o rder to reach the sam e average SSR as th e V IPER S data. Finally, w e m im icked the V IPER S spec
troscopic red sh ift error b y adding a ran d o m value extracted from a G aussian distribution w ith <rz = 0.00054(1 + z) to the apparent redshift. W e refer to these p hotom etric an d spectro
scopic m o c k catalogues as “V IP E R S -like m ocks” (VMOCKS from now on).
3. VIPERS density field
We p aram eterised the local environm ent around each galaxy u s
ing the density contrast 6, w hich is defined as
6(r) = p (r) - (p(r(z))) (p(r(z))) ’
(1)
w here p ( r ) is th e local density at th e com oving position r o f each galaxy and (p (r(z))) is the m ean density at th at redshift.
We estim ate p ( r ) using counts-in-cells, as follow s:
P (r) = X
F (r, R)
(pi (m, z, R A , D ec...) (2)
In E q. (2) the sum runs over all the galaxies o f the sam ple u sed to trace the density field. W e call these galaxies “tracers” . F (r , R ) is the sm oothing filter (w ith scale R) over w hich the density is co m puted, and $ is th e selection function o f th e sam ple. W e alw ays w ork in red sh ift space. In this w ork w e use the fractional density perturbation 6, b u t w e often refer to it sim ply as “density” for the sake o f sim plicity.
T he com putation o f p depends on a variety o f options reg ard ing the filter shape, th e sam ple o f galaxies to b e used as tracers,
how to take into account th e spectroscopic sam pling rate, etc.
T hese choices are norm ally the resu lt o f a com prom ise betw een the characteristics o f the survey and the scientific goal. W e refer to K ovac e ta l. (2010) , for exam ple, for an extensive discussion o f these alternatives. See A ppendix A for a d etailed discussion o f o u r specific calculation for V IPER S and o f the tests w e have m ade to quantify th e reliability o f ou r calculation.
W e use th e density field com puted w ith cylindrical top-hat filters w ith a half-length o f 1000 k m s-1 an d radius correspond
ing to the distance to the fifth n earest neig h b o u r (“n.n.” from now on), using a volum e-lim ited sam ple o f tracers w ith a lum inosity cu t given by M B < - 2 0 .4 - z. This lum inosity lim it m akes the tracer sam ple com plete up to z = 0.9, and (m ore im portantly) this selection em pirically yields a com oving nu m b er density that does n o t evolve, so that th e m eaning o f our densities is n o t af
fected by discreteness effects that change w ith redshift. C ylin
ders are centred around all o f the galaxies in our sam ple. W ith this cylindrical filter, both p ( r ) an d (p (r(z))) have the dim ensions o f surface densities in red sh ift slices o f ± 1000 km s-1 centred on the red sh ift o f the galaxy around w hich w e com pute p (r).
F igure 1 shows a 2D view o f the V IPER S density field (in R A and redshift) com puted using the cylindrical counts-in-cells m ethod. A lthough w e apply boundary corrections to th e density field com putation (see A ppendix A ), in th e presen t w ork w e only use galaxies fo r w hich at least 60% o f the cylinder is w ithin the survey footprint (gaps an d b oundaries) p resented in Fig. A .1 .
W ith cylindrical filters w e can m itigate the pecu liar veloci
ties o f galaxies in high-density regions (for exam ple, non-linear red sh ift space distortions in galaxy clusters), and b y using a volum e-lim ited sam ple w e m easure the environm ent w ith the sam e tracer p opulation at all explored redshifts. Finally, w e chose cylinders w ith an adaptive radius to reach the sm allest possible scales at least in high-density regions, b ecause it is expected that th e physical processes affecting galaxy evolution m ainly o ccur on relatively sm all-scale overdensities.
W e m easured the p rojected distance to the fifth n.n. (D p 5), w hich w e used to com pute th e density field. F o r ou r volum e- lim ited tracers, D p,5 is ro ughly constant w ith redshift. F o r the volum e-lim ited tracers lim ited a t M B < - 2 0 .4 - z, w e find D p5 ~ 5.5, 3.5, 3.2, 2.0 h -1 M p c for 1 + 6 = 0.50, 1.74, 2.10, and 5.30, respectively. T hese density values correspond to the follow ing key values: 1 + 6 = 0.50 and 2.10 are the m edian values for galaxies in voids and for all V IPER S galaxies (see F ig. 2 ), w hile 1 + 6 = 1.74 and 5.30 are th e thresholds used here to define low -density and high-density environm ents (see Sect. 4) .
W e verified that, as expected, D p 5 increases for brighter trac
ers, at fixed 6. This is our prim ary m otivation fo r restricting our analysis to redshifts below z = 0.9 instead o f extending it out to z = 1 using even brig h ter tracers at the p rice o f com puting the density field on m uch larger scales. W e also verified that although V IPER S and zC O SM O S have the sam e flux lim it, in V IPER S the distance to the fifth n.n. is larger than in zC O SM O S because o f its low er sam pling ra te and larger p hotom etric red- shift error.
As a sanity check, w e verified the typical local density as m easured fo r galaxies in groups and in voids. G roups are identified in the flux-lim ited sam ple using a V oronoi-D elaunay- b ased algorithm as described in Iovino e t al. (in prep.). H ere w e distinguish betw een groups w ith few er than o r at least six m em bers. G alaxies in voids are identified as galaxies lo cated in the central region o f spherical voids w ith radius
> 10 .2 h - 1 M p c and w hose distance from the clo sest galaxy is > 9.8 h -1 M pc. T he void-finding algorithm is the sam e as presented in M icheletti e t al. (2014), b u t applied to the final
O. Cucciati et al.: Quenching, mass, and environment in VIPERS
Fig. 1. RA - z distribution of secure-redshift galaxies in W1 (top) and W4 (below), in comoving coordinates. For the sake of clarity, only the central degree in Dec is plotted. The colour used for each galaxy refers to the value of the local density computed around the galaxy (from light grey for the lowest density to black for the highest density, as in the colour bar). The density is computed in cylindrical filters with radius corresponding to the fifth n.n., using the volume-limited sample of tracers that is complete up to z = 0.9.
V IPER S sam ple. W e also refer to H a w k e n e ta l. (2017) for a study o f voids in V IPER S.
T he density distributions for all V IPER S galaxies and for galaxies in groups and voids are show n in F ig. 2 fo r three redshift bins. A t all redshifts, the high-density tail is m ostly p opulated by galaxies in groups, and th e rich est groups tend to reside in the hig h est densities (90% o f th e rich est groups m em bers fall in the tail o f the ~ 40% highest densities). In contrast, as expected, galaxies in voids are m o st often found in the low est densities, w ith 90% o f void galaxies residing in th e ~ 15% o f the low est densities. This b etter agreem ent w ith void galaxies than w ith group galaxies is expected. In fact, D p5 in low densities is co m parable w ith the typical dim ension o f voids, w hile in the highest densities it is still too large to b e com parable w ith the sm all d i
m ensions o f galaxy groups and clusters (see above).
In Fig. 2 w e also observe that there is n o significant evolution o f the density distribution. K ovac e t al. (2010) show ed that in the zC O SM O S b right sam ple there is also only a m ild evolution o f the density distribution, an d it is m ostly seen m oving to z < 0.4.
4. Dependence of stellar mass and sSFR on the local density
We w ish to study w hether and how the stellar m ass and SFR depend on environm ent, and w hether any dependence evolves
w ith red sh ift in the ran g e p robed by V IPE R S. In particular, w e focus on (a proxy of) the sSFR.
W e consider the three red sh ift bins 0.51 < z < 0.65, 0.65 < z < 0.8, and 0.8 < z < 0.9, w hich w ere chosen b e cause their m edian redshifts are nearly equally spaced in tim e (w ith tim e steps o f 0 .6 -0 .7 G yr). In each o f these bins, w e co n sider the V IPER S sam ple to b e com plete in stellar m ass above a given m ass lim it M ii m, nam ely the m ass lim it for passive g alax ies as defined in P ozzetti e t al. (2 010) . This lim it corresponds to lo g (Ml i m /M 0 ) = 10.38, 10.66, an d 10.89 in the three redshift bins, respectively.
W e selected a sub-sam ple o f galaxies w ith stellar m ass above the hig h est m ass lim it (lo g (Ml i m /M 0 ) = 10.89) in the entire red sh ift ran g e 0.51 < z < 0.9. W e u sed the first and fourth quar- tiles o f the density distribution o f these galaxies as thresholds to define th e low -density (“L D ” ) and high-density (“H D ”) en vironm ents: L D galaxies are defined b y 1 + 6 < 1.74, and HD galaxies by 1 + 6 > 5.30. T hese values are very sim ilar to those used in D avidzon e t al. (20 1 6 , D 16 from now on), w here they have been derived from an earlier sm aller V IPER S d ata set (the first V IPER S p u b lic release, PD R -1) and w ith a different SED fitting technique. This confirm s the consistency betw een the d en sity field com puted for the PDR -1 and the density field com puted for the final V IPER S sam ple (see A ppendix B for a quantitative com parison).
Fig. 2. Density distribution of the VIPERS galaxies in three redshift bins (three columns) for the entire sample (black histogram), for galax
ies in voids (blue triangles), in groups with at most five members (green squares), and in groups with at least six members (red circles). See the text for the definition of groups and voids. The density field is com
puted with cylindrical filters, with a radius given by the fifth n.n. using the volume-limited tracers, which are complete up to z = 0.9. To facil
itate comparison, in the second and third redshift bins the orange line is the density distribution of the entire sample in the first redshift bin, normalised to the total number of galaxies in each bin.
T he average pro jected distance D p,5 to th e fifth n.n. for 1+5 = 1.74 and 1 + 5 = 5.30 is ~ 3 .5 and ~ 2 .0 h -1 M pc, respectively (see Sect. 3) .
4.1. P a ssiv e a n d active g a la x ie s
We use th e colour-colour diagram ( N U V - r) vs. (r - K), N U V rK , to define passive an d star-form ing (“active” , from now on) galaxy populations. In this diagram , first d escribed in A rnouts et al. (2013) , the ( N U V - r) colour is th e m ain tracer o f recent star form ation (SF); in contrast, the ( r - K ) colour is less sensitive to SF than ( N U V - r) . (r - K ) traces the inter-stellar m edium absorption, allow ing us to separate quiescent and dusty galaxies, w hich show the sam e re d colours in a classical single
colour distribution (see e.g. M oresco et al. 2013) . W e consider a galaxy to b e passive w hen
(N U V - r) > 3.73, and
(N U V - r) > 1.37 x ( r - K ) + 3.18, and (3) (r - K ) < 1.35.
T hese boundaries follow the definition p rovided b y D 16 (their Eq. (2)), although the values o f our thresholds have been slightly m odified (by - 0 .0 2 and +0.05 m ag for the ( N U V - r) an d ( r - K ) colours, respectively) to take into account sm all differences in the absolute m ag n itu d e estim ates6.
To m ax im ise the difference betw een the galaxy p o p u la
tions, w e d ecided to exclude the galaxies that have in term e
diate colours in the N U V rK plane, com m only referred to as
“green valley” galaxies, from o ur analysis. F or this reason, our population o f active galaxies is n o t com plem entary to the p a s
sive galaxy population. W e set the u pper boundary o f the active g a la x ie s' locus to b e 0.6 m ag b lu e r in N U V - r than th e low er
6 D16 used the code Hyperz with a different photometric baseline.
Their galaxy templates and the algorithm with which they computed rest-frame magnitudes are also different from M16b.
boundary o f passive galaxies. O ur active p opulation is defined as (N U V - r) < 3.13, or
(N U V - r) < 1.37 x (r - K ) + 2.58, o r (4) (r - K ) > 1.35.
T he condition ( r - K ) > 1.35 (not u sed in A rnouts e t al. 2013) identifies edge-on disc galaxies w ith a flat attenuation curve.
T hese are the only galaxies that can have such extrem e re d ( r - K ) colours (C hevallard et al. 2 0 1 3 ; M outard e t al. 2016a) . B y using this cu t in Eqs. (3) and (4 ) , w e include these galaxies am ong the active galaxies. W e refer to F ritz e t al. (2014) and D 16 for a m ore detailed discussion.
W e keep the definitions in E qs. (3) an d (4 ) co nstant w ith red- shift. M 16b show ed th at these thresholds depend on redshift, but they can b e considered constant in th e relatively sm all redshift ran g e 0.51 < z < 0.9.
A rnouts e t al. (2 013) show ed that the position o f a galaxy in the N U V rK p lan e correlates w ith its sSFR . This is also show n in F ig. 2 o f D 16. W e exploit this correlation to facilitate the com parison betw een our data and the m o d el o f galaxy evolu
tion by D e L u cia & B laizot (2007) . T he light cones w e used (see Sect. 2.3) do n o t have NUV, r, an d K absolute m agnitudes, but they do have stellar m ass an d SFR, from w hich w e can com pute the sSFR . Practically, w e m u st define som e thresholds in sSFR to define the sam ples o f active and passive galaxies in the m odel.
T hese definitions need to correspond as closely as p ossible to o ur classification, w hich is b ased on the N U V rK diagram .
It is w orthw hile to rem ark the follow ing. S ince the m easu re
m e n t o f absolute m agnitudes using SED fitting techniques is m o re accurate than th e estim ate o f the SFR a t the level o f single galaxies, ou r prim ary definition o f the active and passive p o p u lations is the one b ased on the N U V rK plane. W e also use the definition b ased on sSFR to facilitate the com parison w ith the m o ck catalogues. It is b eyond the scope o f this p ap e r to inves
tigate the reliability o f the SFR derived from the SED fitting in detail (however, see e.g. C onroy et al. 2009) .
In Fig. 3 w e show the distribution o f the sS FR for our sam p le in the red sh ift ran g e 0.65 < z < 0.8 above the m ass lim it lo g (M iim/M o ) = 10.66. A b o u t 15-20% o f the galaxies in this red sh ift ran g e and above this m ass lim it have an sSFR low er than the m inim um value in the figure, and therefore their distri
bution is n o t p lo tted for the sake o f clarity. F or any given value o f sSFR , w e also show the fraction o f passive and active g alax ies as defined b y Eqs. (3) and (4 ) . T he correlation betw een this definition and th e sSFR values is evident. M oreover, w e rem ark th at this correlation is n o t an artefact o f the SED fitting p ro ce
dure: th e SFR com es directly from th e instantaneous SFR o f the best-fit tem plate, w hile the absolute m agnitudes are derived by m inim ising the tem plate dependence by using the observed m a g nitude w ith the clo sest w avelength (see Sect. 2.2) .
F igure 3 show s th at the classification o f passive and active galaxies b ased on the N U V rK p lan e ro ughly corresponds to lo g (sS F R ) < - 1 1 .2 and lo g (sS F R ) > - 1 0 .8 , respectively. The fractions o f active, interm ediate, and passive galaxies as a fu n c
tion o f the sS FR behave in a sim ilar w ay in th e tw o other redshift bins considered in this study, therefore w e ado p t th e sam e sSFR thresholds over the entire red sh ift ran g e 0.51 < z < 0.9.
In Fig. 3 w e also overplot th e sS FR distribution in the RM O C K S. T he m odel distribution is different from the d ata d is
tribution in several aspects. F irst, the tail o f high sS FR is m issing in the m odel. Second, the valley presen t in th e d ata distribution at log(sS F R ) — 10.8 appears as a p lateau in the m odel. It also seem s to b e shifted tow ards h igher values o f sSFR . Finally, w e
O. Cucciati et al.: Quenching, mass, and environment in VIPERS
lo g ( s S F R )
Fig. 3. Top: black histogram: distribution of the sSFR ( =S F R / M) for the VIPERS galaxies in the redshift range 0.65 < z < 0.8 and for log(M iim/ M 0) > 10.66, which is the completeness mass limit in that redshift range. Diamonds: sSFR distribution in the RM O C K S for galax
ies in the same redshift range and above the same mass threshold; the points with the vertical error bars correspond to the average and rms of the 50 mocks catalogues. The sSFR distribution of the RM O C K S is nor
malised to have the same total number of galaxies as in the VIPERS sSFR distribution. Both the real and simulated distributions have a tail of galaxies with sSFR values below the lowest sSFR limit in this plot, which we do not plot for the sake of clarity. Bottom: only for the VIPERS sample (same galaxies as in the top panel), fraction of passive (red circles) and active (blue triangles) galaxies as defined by Eqs. (3) and (4), as a function of their sSFR. We also overplot the frac
tion of “intermediate” galaxies, i.e. those that do not satisfy the passive or the active definition. The vertical lines at log(sSFR) = - 11.2 and log(sSFR) = - 10.8 are the thresholds adopted to define passive and active galaxies, respectively, using the sSFR as discussed in Sect. 4.1.
These results are very similar in the two other redshift bins (not shown).
no te th at in each red sh ift b in the tail o f the sSFR distribution b e low the low est value p lotted in the figure com prises abo u t 30%
o f the m odel galaxies, b u t only 15-20% o f the V lP E R S galaxies.
We refer to A ppendix C for th e analysis o f a p ossible cause o f these discrepancies, and to Sect. 5 for the classification o f p a s
sive and active galaxies in the m odel.
4.2. S te lla r m a s s se g re g a tio n in d iffere n t e n v iro n m e n ts
It is know n th at galaxy stellar m ass correlates w ith local environ
m en t (see e.g. K auffm ann et al. 2 0 0 4 ; S codeggio e t al. 2009b) . This correlation has been extensively studied in the V IPER S sur
vey in D 16 in term s o f the galaxy stellar m ass function (G SM F) in low - and high-density regions. This dependence can also be qualitatively studied using the cum ulative distribution function o f the stellar m ass. H ere w e perfo rm such an analysis, prim arily as a com parison w ith other w orks in the literature th at used the sam e tool. As a second step, w e w ish to define a set o f (narrow ) m ass bins so th at w e can study how th e environm ent affects star form ation at fixed stellar m ass.
Fig. 4. Stellar mass cumulative distributions in three redshift bins (0.51 < z < 0.65, 0.65 < z < 0.8, and 0.8 < z < 0.9 from top to bot
tom), for galaxies above the mass limits log(M lim/M o ) = 10.38, 10.66, and 10.89, respectively, in the three redshift bins. Orange lines show the galaxies in LD regions, and violet lines show galaxies in HD re
gions. The number of galaxies used in each distribution is reported in the corresponding panel. We use all the galaxies above the mass limit, regardless of their NUVrK classification. In each panel we also report the PKS values, i.e. the significance level in a Kolmogorov-Smirnov test for the null hypothesis that the LD and HD distributions are drawn from the same parent distribution.
F igure 4 show s the cum ulative distribution function o f galaxy stellar m ass in three red sh ift bins for galaxies above the respective M lim. In each red sh ift b in , w e com pare the distributions in the tw o environm ents (L D and H D ) using a K olm ogorov-S m irnov (KS) test. In all bins w e find that th e sig
nificance level P KS fo r th e null hypothesis, th at is, th at the tw o distributions are draw n from the sam e paren t distribution, is o f the order o f « 1 0 -5 (w ith the exception o f th e highest redshift bin, see below ). This excludes the null hypothesis. This is in agreem ent w ith th e different shapes o f the G SM F in LD and HD regions found in D 16 (see their F ig. 4).
In m o re detail, a t all explored redshifts the L D distribution rises m o re rapidly at the low est m asses, w hile the H D distri
bution has a m ore p ronounced tail tow ards the highest stellar m asses. This is in agreem ent w ith D 16, w ho found that th e LD G SM F is steeper at low m asses and th e high-m ass exponential tail o f th e G SM F is higher in H D regions than in LD regions.
M oreover, as in D 16, th e LD and H D distributions are m ore sim ilar in the highest red sh ift bin. W e verified th at the higher P KS at z > 0.8 is partly due to the low er n um ber o f galaxies. R educing
Table 1. Number of active and passive galaxies in each redshift and stellar mass bin for the LD and HD environments.
M b in [lo g (M /M o ) ] A ct/pass (LD ) A ct/pass (HD) 0.51 < z < 0.65
10 .38-10.66 666/243 243/111
10.66-10.89 285/204 137/132
10.89-11.09 102/82 67/96
11.09-11.29 35/41 24/53
11 .29-12.00 4/11 7/39
0.65 < z < 0.80
10.66-10.89 365/217 216/199
10.89-11.09 143 /149 86/122
11.09-11.29 39/54 51/107
11 .29-12.00 4/26 10/48
0.80 < z < 0.90
10.89-11.09 115/73 65/62
11.09-11.29 43/39 28/44
11 .29-12.00 11/7 8/20
Notes. Active and passive galaxies are defined according to their posi
tion in the NUVrK plane (Eqs. (3) and (4)).
the nu m b er o f galaxies in th e tw o first red sh ift bins to m ake them equal to th e third b in increases P KS to a few 10-4 a t z < 0.8. To verify w hether the h igher P KS a t z > 0.8 is also d ue to the sm aller m ass ran g e explored, w e com puted P KS at z < 0.8 im posing n o t only the sam e n um ber o f galaxies as at z > 0.8, b u t also the sam e stellar m ass lim it lo g (M iim/ M 0 ) = 10.89. R educing the m ass range, P KS rem ains o f the o rder o f a few 10-4 at z < 0.8.
This is still low er than P KS a t z > 0.8. This suggests th at the dependence on environm ent o f the high-m ass tail o f the stellar m ass distribution m ig h t strengthen w ith decreasing redshift.
4.3. s S F R a s a function o f e n v iro n m e n t
In this section w e investigate possible environm ental effects on the sS FR (either using the N U V rK definition as a proxy, o r the SFR an d stellar m ass through SED fitting). In particular, w e study the ratio o f the n um ber o f active to passive galaxies, f ap.
To separate the role o f stellar m ass and environm ent, w e need to study how environm ent affects galaxy evolution at a fixed stel
lar m ass. W e did this by dividing ou r sam ple into the follow ing narrow m ass bins in l o g ( M / M 0 ): 10.38-10.66, 10.66-10.89, 10.89-11.09, 11.09-11.29, and >11.29.
Table 1 show s the n um ber o f active and passive galaxies in LD and H D environm ents in each red sh ift and m ass bin. In the table, active and passive galaxies are defined according to the N U V rK diagram , b u t the num bers derived using the sSFR defi
nition are very similar.
B elow w e explain how w e built m ass-m atched sam ples in the tw o environm ents in each m ass and red sh ift bin. This w as to further m inim ise any p ossible rem aining difference in the stellar m ass distribution in L D an d H D , even in o ur narrow stellar m ass bins.
In each m ass and red sh ift bin, w e cu t the m ass distributions in the tw o environm ents so th at they have the sam e m inim um and m axim um m ass value, m eaning th at they cover exactly the sam e m ass range. Then, in each m ass and red sh ift bin, w e (a) take the m ass distribution in the environm ent w ith the sm aller num ber o f galaxies (usually the H D environm ent) as th e reference m ass
distribution, and (b) w e extract 100 sam ples o f galaxies from the m ass distribution in the o ther environm ent, w ith th e sam e m ass distribution as the reference, allow ing repetitions. E ach o f these 100 sam ples is constructed to have the sam e nu m b er o f galaxies as the reference.
T he left panel o f Fig. 5 show s / ap as a function o f stellar m ass in the red sh ift ranges defined above, separating L D from H D re gions. G alaxies are classified as passive and active according to the N U V rK diagram . In each m ass bin, w e p lo t f ap obtained by using all the galaxies in the bin (i.e., w ithout applying the m ass- m atching m ethod). F or the environm ent com prising the h ig h est n um ber o f galaxies (LD, w ith the exception o f the highest m ass bin) w e overplot the average f ap o f the 100 m ass-m atched sam ples.
W hen com puting f ap, in th e original or m ass-m atched sam ples, w e alw ays w eight th e galaxies b y a factor w th at cor
responds to th e inverse o f the total sam pling rate, i.e. w = 1/(C S R x T SR x S S R ) . However, w e verified th at ou r results do n o t change significantly if w e do n o t use these w eights.
W e observe the follow ing:
- T he m edian stellar m ass values in each m ass b in are slightly higher in H D than L D , suggesting that even in the narrow m ass bins the m ass distribution could be slightly different in the tw o environm ents. A fter the m ass-m atching, th e m edian stellar m ass values approach the m edian o f the opposite envi
ronm ent, as expected. f ap also varies very m ildly before and after th e m ass-m atching.
- f ap decreases for h igher m asses regardless o f environm ent, as expected given the relation betw een stellar m ass an d SFR (e.g. Speagle et al. 2014 and W hitaker e t al. 2014) . T he only exception is the hig h est m ass b in a t 0.8 < z < 0.9, w here f ap is sim ilar if n o t higher than in the adjacent m ass bin, although uncertainties are large.
- f ap is higher in L D than H D environm ents, at all m asses b e low lo g (M /M © ) = 11.29.
- A t fixed stellar m ass, f ap slightly decreases w ith redshift from z > 0.8 to 0.65 < z < 0.8 in both LD and HD , but it ceases to evolve a t z < 0.65.
T hese results are in qualitative agreem ent w ith those presented in D 16, w here w e separately studied th e G SM F as a function o f environm ent for active an d passive galaxies. In their Fig. 5, D 16 show th at the low -m ass en d is steeper (m ore negative a ) for active galaxies. This corresponds to our f ap increasing for low- m ass galaxies. M oreover, at 0.51 < z < 0.65 the low -m ass end o f the passive G SM F is m uch less steep in H D than in L D , w hich is m irrored b y f ap in L D increasing m o re steeply fo r low er m asses.
O n the other hand, w e observe th at in D 16 the ratio o f active to passive galaxies should d ecrease b y a factor ~ 2 from z ~ 0.85 to z ~ 0.55. B ased on th e uncertainty on the S chechter p ara m eters o f the G SM F s (see th eir Table 2), this tren d is significant to a < 2 ^ level. W e do n o t observe this red sh ift evolution in f ap, in agreem ent w ith th e m ild evolution o f the passive an d active G SM F s in M 16b. T he m ain reason w hy this trend is observed in D 16 b u t n o t M 16b is that they use different SED fitting p ro cedures, w hich resu lt in different classifications o f galaxy type for a fraction o f the total sam ple o f galaxies. A lthough the total G SM F s in the tw o studies are in excellent agreem ent w ith each other, after dividing their sam ple into active and passive galaxies, M 16b found an evolution in nu m b er density th at is m ilder than in D 16 (see Fig. 14 o f M 16b and Fig. 3 o f D 16). As stressed b y M 16b, w e are currently in an era in w hich large sam ples d e
crease random errors, and w e can now see th e sm all b u t do m i
n an t system atics pro d u ced by different SED fitting estim ates. In
O. Cucciati et al.: Quenching, mass, and environment in VIPERS
Fig. 5. Ratio of the number of active over passive galaxies (fa p) in LD (orange filled circles) and HD (violet filled circles) regions as a function of stellar mass in three different redshift bins. Active and passive galaxies are defined by means of the NUVrK diagram (left) or according to their sSFR (right). Horizontal error bars indicate the span of the mass bin, and the vertical error bars are derived from the propagation of the Poissonian noise in the counts of active and passive galaxies (if we use the error formula for small samples suggested in Gehrels (1986), the error bars do not change significantly). The x-axis value is the median stellar mass of the sample used to compute fa p. Dotted diamonds are for the mass-matched samples in the environment (LD or HD) with more galaxies in each mass and redshift bin. Diamonds are centred on the median fap value of the 100 mass-matched extractions, and the bottom and top vertices represent the 25% and 75% of the fap distribution, respectively. The x-axis values is the median of the median stellar mass in each extraction. See text for more details. The vertical dashed line in each redshift bin is the corresponding mass limit Mlim. The dotted horizontal line at fap = 1 is for reference.
this case, the differences rela ted to the SED fitting p rocedure in clude different C FH T LS p hotom etry (T005 release in D 16 and T007 in M 16b), m o re photom etric bands used in M 16b, and a different SED -fitting code.
F inally, it is w orthw hile briefly discussing our findings for the hig h est stellar m ass bin ( lo g ( M /M 0 ) > 11.29). T he n u m b er o f galaxies at such stellar m asses drops steeply, and the error on fa p is very large. F or these m asses, and a t z < 0.8, fa p does not appear to dep en d on environm ent, but its value is consistent w ith the general tren d o f fa p decreasing for higher m asses, r e gardless o f environm ent. A t 0.8 < z < 0.9, in contrast, w e do n ot see a clear dependence o f fa p on stellar m ass b ecause o f the sm aller span in stellar m ass and the relatively high values o f fa p at lo g ( M /M e ) > 11.29 w ith resp ect to th e previous m ass bins.
W e defer a m o re detailed analysis o f the properties o f very m a s
sive galaxies in V IPER S to future work.
As expected b y construction, w e obtain very sim ilar results (alw ays w ithin 1 ^ ) w hen w e define active and passive galaxies using the N U V rK diagram o r the sSFR thresholds, and this is crucial for the com parison w ith the m odel.
5. Comparison with the adopted model
W e m ake use o f the 50 SA M light cones to study th e d epen
dence o f fa p on stellar m ass, redshift, and environm ent in the D e L ucia & B laizot (2007) m odel, and w e com pare this to real data.
W e use the RMOCKS and Vm o c k s w ith tw o m ain aims:
i) com pare fa p in RMOCKS and VMOCKS to verify th at the V IPER S selection function does not introduce any spurious sig
n al into our m easurem ent o f fa p, an d ii) com pare fa p in the m odel and in the real data to investigate w hich p hysical process(es) could b e the cause o f the observed environm ental trends.
W e rem ark that these m ock catalogues cover a sm aller vol
um e than the entire V IPER S survey. E ach VM O CK has roughly the size o f th e V IPER S W 4 field, w hich is about one-third o f the w hole area w e probe. F o r the analysis in this section, w e grouped th e output (density m easurem ent, sSFR , stellar m ass, etc.) o f three Vm o c k s at a tim e for a total o f 16 larger output catalogues including 48 o f the original VM O C K S. This sim plifies the com parison w ith rea l data b ecause o f the sim ilar statistics
Fig. 6. Ratio of the number of active over passive galaxies (fap) in LD (light grey) and HD (dark grey) regions in the RMOCKS (filled sym
bols) and in the VMOCKS (empty symbols) in the same stellar mass bins and redshift ranges as in Fig. 5. In each mass bin, for the environ
ment with fewer galaxies (HD for lo g (M /M Q) < 11.29, LD otherwise) we plot f ap as computed directly from the mock catalogues, while for the environment with more galaxies we plot f ap derived from the mass- matched samples. For not mass-matched values, symbols are centred on the y-axis on the mean value of f ap of the 16 mock catalogues, and their height represents the rms around the mean. For mass-matched values, the y-axis position is computed as follows: first we compute the mean f ap of the 100 mass-matched samples in each mock catalogue, then we average the 16 mean values. The height is given by the rms around this mean. For all symbols, the extension on the x-axis indicates the span of the stellar mass bin. For lo g (M /M Q) > 11.29, we show f ap only for the RMOCKS because the statistics in the VMOCKS at these stellar masses is too low (see text). In each panel, the vertical and horizontal lines are the same as in Fig. 5 .
in each m ass an d red sh ift bin. F or consistency, w e grouped the RM O CK S o utput in the sam e way.
In the RM O CKS and VM O C K S, the local density is com puted as described in A ppendix A .3 , and LD and H D environm ents are defined as for th e V IPER S sam ple. In the m ock catalogues w e do n o t have the absolute m agnitudes in the filters n eed ed to divide active and passive galaxies according to th eir location in the N U V rK plane. In stead w e use their sSFR . In Fig. 3 w e have show n th at there is a clear difference betw een the distribution o f the sSFR in th e RM O CKS and in th e data. W e discussed these d if
ferences in Sect. 4.1 and A ppendix C . G iven these differences, w e decided n o t to use the thresholds lo g (s S F R ) < - 1 1 .2 and
lo g (sS F R ) > - 10.8 (see Sect. 4 .1 ) to define passive and active galaxies in th e m odel, but the extrem es o f the sSFR distribution defined as d escribed in A ppendix C . This choice im plies th at /a p
in the m odel is on average in agreem ent w ith /a p observed in V IPER S if w e consider the entire sam ple regardless o f environ
m ent.
W e com puted /a p in the m o d el in the sam e w ay as for the V IPER S sam ple, that is to say, w e b u ilt m ass-m atched sam ples in each m ass and red sh ift bin. To com pute /a p, the galaxies in the VM OCKS are w eighted by using statistical w eights analogous to those used in the real survey. T he C S R is defined here as a sm ooth function ranging from 0 to 1 from z = 0.4 to z = 0.6, and it only depends on redshift. T he T SR is obtained by applying SSPO C to the m o c k catalogues, an d the SSR is m im icked by further dow nsam pling th e population as described in Sect. 2 .3 . In the case o f the Vm o c k s, as fo r the real data, the results are n o t strongly d ependent on the use o f these w eights.
W e rem ark th at although w e use the Vm o c k s grouped 3 by 3, the statistics o f galaxies in th e h ighest stellar m ass bin is low er in these m erged m ock catalogues than in the total V IPER S sam ple. G iven the very sm all num bers, w e d id n o t study this stellar m ass regim e in the VM O C K S.
5.1. RMOCKS vs. VMOCKS
F igure 6 show s /a p in the RM OCKS and VM OCKS in the sam e red sh ift and m ass bins as in the data. W e verified th at the m ass- m atch ed sam ples in the m ock catalogues are alw ays in LD envi
ronm ents, w ith the exception o f the highest stellar m asses. The results are qualitatively sim ilar to the results obtained w ith the V IPER S data set (see Sect. 5.2), w ith no difference betw een the Rm o c k s and Vm o c k s. This confirm s that on average the V IPER S selection function does n o t introduce any strong bias in the m easurem ent o f /a p as a function o f environm ent.
T he scatter around the m ean values is larger in the VMOCKS than in the RM O C K S. This could b e b ecause o f the low er num ber o f galaxies (~40% , corresponding to th e average V IPER S sam pling rate), o r possibly also b ecause o f the typical uncertainties in the environm ent reconstruction (see Sect. A .3) . W e also note th at in the VM OCKS th e dependence o f /a p on stellar m ass in L D environm ents alm ost vanishes for log(M l i m/M0 ) > 10.66, w hile it is m ild b ut evident in th e RM O C K S. Finally, w e do n o t find any dependence o f /a p on red sh ift at fixed stellar m ass in either the Vm o c k s o r in the Rm o c k s.
G iven the differences betw een RM OCKS and VM O C K S, w e expect th at th e trends o f /a p w ith stellar m ass observed in the V IPER S sam ple in F ig. 5 are w eaker than th e true trends (es
pecially in L D ). W e also expect th at the difference o f /a p in LD and H D is less significant b ecause o f b oth the low (er) statistics and the errors in the environm ent reconstruction. M oreover, the lack o f dependence o f /a p on red sh ift at fixed stellar m ass that w e found in the V IPER S data set does n o t seem to b e due to the V IPER S selection function.
F ro m now on, since w e have verified th at th e /a p behaviour is com patible in th e RM O CKS an d VM O C K S, w e only use the Rm o c k s for sim plicity.
5.2. C o m p a riso n b e tw e e n d a ta a n d RMOCKS
F igure 7 shows the V IPER S /a p w ith /a p o f th e RM OCKS over
plotted. T he trends are qualitatively sim ilar, w ith /a p decreasing for h igher stellar m asses in b oth L D an d H D , and w ith /a p higher in LD than in H D at all m asses a t log(M /M0 ) < 11.29. The
