The VIMOS Public Extragalactic Redshift Survey (VIPERS) : environment-size relation of massive passive galaxies at 0.5 ≤ z ≤ 0.8

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A & A 631, A 15 (2019)

https://doi.org/10.1051/0004-6361/201833600

The VIMOS Public Extragalactic Redshift Survey (VIPERS)

Environment-size relation of massive passive galaxies at 0.5 < z < 0.8*

A. Gargiulo1, O. Cucciati2, B. Garilli 1, M. Scodeggio1, M. Bolzonella2, G. Zamorani2, G. De Lucia4, J. Krywult3, L. Guzzo5,6, B. R. Granett5,6, S. de la Torre7, U. Abbas8, C. Adami7, S. Arnouts7, D. Bottini1, A. Cappi2,9, P. Franzetti 1, A. Fritz1, C. Haines10, A. J. Hawken5,6, A. Iovino5, V. Le Brun7, O. Le Fevre7, D. Maccagni 1,

K. Małek12, F. Marulli11132, T. Moutard147, M. Polletta 1 1516, A. Pollo1217, L. A. M. Tasca7, R. Tojeiro18, D. Vergani2, A. Zanichelli 19, J. Bel20, E. Branchini21 22,23, J. Coupon24, O. Ilbert7,

L. Moscardini11,13,2, and J. A. Peacock25

(Affiliations can be found after the references) Received 8 June 2018 / Accepted 5 July 2019

Astronomy

&

Astrophysics

ABSTRACT

We use the unparalleled statistics of the VIPERS survey to investigate the relation between the surface mean stellar mass density £ = M /(2 nR2) of massive passive galaxies (MPGs, M > 1011 M0) and their local environment in the redshift range 0.5 < z < 0.8. Passive galaxies were selected on the basis of their NUVrK colors (~900 objects), and the environment was defined as the galaxy density contrast, S, using the fifth nearest-neighbor approach. The analysis of £ versus S was carried out in two stellar mass bins. In galaxies with M < 2 x 1011 M0, no correlation between £ and S is observed. This implies that the accretion of satellite galaxies, which is more frequent in denser environments (groups or cluster outskirts) and efficient in reducing the galaxy £, is not relevant in the formation and evolution of these systems. Conversely, in galaxies with M > 2 x 1011 M0, we find an excess of MPGs with low £ and a deficit of high-£ MPGs in the densest regions with respect to other environments. We interpret this result as due to the migration of some high-£ MPGs (<1% of the total population of MPGs) into low-£ MPGs, probably through mergers or cannibalism of small satellites. In summary, our results imply that the accretion of satellite galaxies has a marginal role in the mass-assembly history of most MPGs. We have previously found that the number density of VIPERS massive star-forming galaxies (MSFGs) declines rapidily from z = 0.8 to z = 0.5, which mirrors the rapid increase in the number density of MPGs. This indicates that the MSFGs at z > 0.8 migrate to the MPG population.

Here, we investigate the £-S relation of MSFGs at z > 0.8 and find that it is consistent within 1ix with that of low-£ MPGs at z < 0.8. Thus, the results of this and our previous paper show that MSFGs at z > 0.8 are consistent in terms of number and environment with being the progenitors of low-£ MPGs at z < 0.8.

Key words. galaxies: evolution - galaxies: formation

1. Introduction

It is now w ell established th at the physical param eters o f g alax ies (e.g., star form ation tim escale, form ation redshift, and m o r

phology) are closely correlated w ith the environm ent that these galaxies reside in and w ith their stellar m ass (e.g., D ressler 1980;

H ashim oto et al. 1998; G avazzi et al. 2 0 0 6 ; K auffm ann e t al.

2 0 0 4 ; S aracco et al. 2 0 1 7 ; Tam burri et al. 2 0 1 4 ; C ucciati et al.

20 1 7 , 2 0 0 6 ; B alogh et al. 2 0 0 4 ; E lbaz e t al. 2 0 0 7 ; B undy et al.

2 0 0 6 ; D avidzon et al. 2 0 1 6 ; Peng et al. 2 0 1 0 ; Thom as et al. 2 0 1 0 ; P ozzetti e t al. 2 0 1 0 ; H aines e t al. 2007) . T hese correlations in d i

cate that the stellar m ass-assem bly history in a galaxy depends both on stellar m ass an d environm ent (e.g., Peng et al. 2010) .

* 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 /

B ecause these tw o param eters are closely rela ted and depend on redshift, understanding the m ain processes that are resp o n si

ble for galaxy form ation and evolution requires a careful m u lti

param eter investigation.

H ow passive galaxies (PG s) form an d evolve is still unclear.

It has been show n th at at fixed stellar m ass, the m ean effective radius (Re> (w here R e is the radius th at encloses h a lf o f the total light) o f PGs increases b y a factor 4 betw een z = 2 and z = 0 (e.g., van der W el et al. 2014) . To explain the observed size evo

lution, a scenario involving galaxy m ergers has been proposed because the continuous accretion o f satellite galaxies increases both m ass and radius o f a galaxy. In this scenario, a highly d is

sipative process (e.g., a gas-rich m erger, H opkins e t al. 2008) at z > 2 form s th e com pact passive cores w e observe at high-z.

In the subsequent 10 Gyr, these com pact galaxies grow a low- density halo through the dry accretion o f sm all satellites (e.g., through dry m inor m ergers, cannibalism ) until they m atch the typical size o f local PG s (e.g., R obertson et al. 2 0 0 6 ; N aab e t al.

20 0 7 , 2 0 0 9 ; H ilz et al. 2 0 1 3 ; van D okkum e t al. 20 0 8 , 2010) . D ry m ergers are expected to b e m o re frequent in groups than in the field (e.g., Treu et al. 2003), an d cannibalism is m ore recur

rent for central galaxies, therefore this m odel predicts a positive correlation betw een environm ental density and galaxy size.

Several studies have found a positive correlation betw een galaxy size and environm ent at 0.7 < z < 2, w ith cluster galaxies

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3 0 -5 0 % larger than field counterparts o f sim ilar stellar m ass (e.g., C ooper et al. 2 0 1 2 ; P apovich e t al. 2 0 1 2 ; B assett et al. 2 0 1 3 ; S trazzullo e t al. 2 0 1 3 ; L ani et al. 2 0 1 3 ; D elaye e t al. 2014) . C o n versely, no correlation is found in the local U niverse betw een the m ean galaxy size and the environm ent (M altby et al. 2 0 1 0 ; N air e t al. 2 0 1 0 ; H uertas-C om pany e t al. 2 0 1 3 a; C appellari 20 1 3 , but see also P oggianti et al. 2 0 1 3 ; C ebridn & T rujillo 2014) . This app aren t discrepancy betw een the dependency o f size on environm ent a t high- and low -z can b e reconciled w ithin a sce

nario o f hierarchical assem bly. In this fram ew ork, cluster galaxies evolve faster (i.e., b ecom e larger earlier) than galaxies in the field because m ore m ergers p er unit tim e o ccur in h igh-density regions (e.g. D e L u cia et al. 2 0 0 4 ; A ndreon 2018) .

H owever, an increasing n um ber o f independent studies have cast doubts on the relevance o f dry accretion o f satellites in the assem bly history o f passive galaxies and suggested instead that they are m ostly star-form ing system s th at have p ro g res

sively halted th eir star form ation (e.g., L illy & C arollo 2 0 1 6 ; H aines et al. 2017) . G argiulo et al. (20 1 7 , h ereafter P aper I) found th at the increase in n um ber density o f m assive passive galaxies (M PG s, M > 1011 M0) from z ~ 0.8 to z ~ 0.5 is due to the continuous addition o f large galaxies w ith low surface stellar m ass density 2 (2 = M */(2nR^) < 1000 M0 p c-2). This increase is entirely accounted for b y the observed decrease in th e num ber density o f m assive star-form ing galaxies (M SFG s, i.e., all n o n passive M > 1011 M0 objects) in th e sam e red sh ift range. This evidence indicates th at these star-form ing system s cou ld re p re sent the progenitors o f the subsequent em erging class o f larger M P G s. In this scenario no correlation betw een galaxy size and environm ent is expected at any redshift. O ther studies a t high red sh ift find th at the galaxy size does n o t dep en d on the envi

ronm ent (e.g., H uertas-C om pany e t al. 2 0 1 3 b ; D am janov et al.

2 0 1 5 ; K elkar e t al. 2 0 1 5 ; S aracco et al. 20 1 4 , 2 0 1 7 ; R ettura e t al.

2 0 1 0 ; N ew m an et al. 2 0 1 4 ; A llen e t al. 2015). T he lack o f size- environm ent trends at low- and high-z, coupled w ith th e results on the n um ber densities, contradicts the expectations o f galaxy evolutionary m odels th at are b ased on hierarchial assem bly o f stellar m atter. T he study o f th e m ean size (or o f the m ean sur

face stellar m ass density) o f PG s as a function o f environm ent is a pow erful probe for m odels o f g alaxy form ation and evolution.

In particular, th e rec en t findings described above clearly show that the size-environm ent relatio n at high-z fo r passive galaxies needs to b e b etter defined.

In this context, M P G s deserve particular attention. T hese system s are expected to evolve m ainly through (dry) m ergers (e.g., H opkins e t al. 2 0 0 9 ; D e L u cia & B laizo t 2007) . If this is the case, w e should detect a stronger signal in this m ass ran g e for th e size - environm ent relation w ith resp ect to a low er m ass range. B ecause M P G s are extrem ely rare, very few studies so far have investigated the size-environm ent relatio n for this class o f objects at high-z

W e here take advantage o f the u n paralleled large statistics o f the V IM O S P ublic E xtragalactic R edshift S urvey (V IPER S, e.g., G uzzo et al. 2 0 1 4 ; S codeggio et al. 2018) to investigate the 2 -environm ent relation for M P G s a t 0.5 < z < 0.8. In Sect. 2 w e describe the M P G sam ple selection and define th e environm ent in term s o f the density contrast 6. In Sect. 3 w e determ ine the 2 - 6 relation and analyze it as a function o f stellar m ass. Finally, in Sect. 4 w e com pare the 2 - 6 relatio n found for M P G s w ith that o f their active counterparts at higher z. O ur results and co n clu sions are sum m arized in Sect. 5 . T h roughout th e p ap er w e adopt the C habrier (2 0 0 3 ) in itial m ass function (IM F) an d a flat A C D M cosm ology w ith O m = 0.3, O a = 0.7 and H 0 = 70 k m s-1 M p c-1.

Effective rad ii are circularized, m eaning th at R e = V ab, w here

a and b are the sem i-m ajor and sem i-m inor axes, respectively, o f the isophote th at contains h a lf o f the total light.

2. Data

T he data used in this paper are taken from a b eta version o f the final release o f the V IPER S survey (S codeggio e t al. 20 1 8 ) 1. The data set used here is alm ost identical to the publicly released P D R -2 catalog, w ith th e exception o f a subset o f a few redshifts (m ostly a t z > 1.2, thus b eyond ou r ran g e o f investigation).

In o rder to be consistent w ith P aper I, w e do n o t use the final release.

V IPER S is an E S O large program that has m easured redshifts for 89 128 galaxies to iA B = 22.5, distributed over an effective area o f 16.3 deg2. S pectroscopic targets w ere selected in th e W 1 and W 4 fields o f the C anada-F rance-H aw aii Tele

scope (C FH T) L egacy S urvey W ide. U sing the m ultib an d cat

alog o f the C FH T LS W ide p hotom etric survey (release T0005, com pleted b y th e subsequent T 0006), w e selected as targets all the objects th at satisfied the follow ing tw o conditions:

iAB < 22.5, (1)

(r - i) > 0.5 x (u - g) or (r - i) > 0.7, (2) w here iA B is co rrected for extinction. T he relatively b rig h t m a g nitude lim it ensures useful spectral quality in a lim ited expo

sure tim e, w hile the color-color p reselection in the ugri plane m inim izes th e nu m b er o f galaxies at z < 0.5 (for details, see G arilli e t al. 2014). N o additional criteria using photom etric red sh ift w ere im posed. T he observations w ere carried o u t w ith V IM O S a t th e Very L arge T elescope (VLT) using the low- resolution red grism (R ~ 220), w hich covers the w avelength ran g e 5 5 0 0 -9 5 0 0 A. W ithin each o f the four V IM O S q u ad rants, slits w ere on average assigned to ~ 47% o f the p o ssi

b le targets, thus defining the target sam pling rate (TSR). The rm s error o f the m easu red redshifts has been estim ated to be

^z(z) = 0.00054 x (1 + z) (S codeggio et al. 2018) . A com plete description o f the P D R -2 d ata release can b e fo u n d in Scodeggio et al. (2018) and references therein.

S tellar m asses and absolute m agnitudes w ere derived b y fit

ting the u g rizK p hotom etry w ith a g rid o f com posite stellar p o p  ulation m odels (B ruzual & C harlot 2003) for the w hole V IPER S sam ple. T he m odels assum e an exponentially declining star for

m ation history e- t/T (t = [0 .1 -3 0 ] G yr), and solar and subsolar ( 0 .2 Z0) m etallicities. D u st attenuation was m odeled assum ing the C alzetti et al. (2000) and P revot e t al. ( 1984) prescriptions (see m o re details in D avidzon et al. 20 1 3 , 2016 for the fit and in M outard e t al. 2016 for th e photom etry).

Structural param eters (e.g., R e, S ćrsic index n) for th e w hole V IPER S sam ple w ere derived from th e i-band C H F T LS -W ide im ages b y fitting the light profile o f the galaxies w ith a 2D p o in t spread function (PSF) convolved S ćrsic profile (K ryw ult et al. 2017) . T he fit w as p erform ed w ith th e G A L F IT code (Peng et al. 2002) . T he C FH TLS im ages have a pixel scale o f

~ 0 .1 8 7 " p x-1, and the full w idth at half-m axim um (FW H M ) o f point-like sources varies from ~ 0 .5 " to 0 .8 ". T he PSF is suc

cessfully m odeled w ith a 2D C hebychev approxim ation o f the elliptical M offat function over ~ 90% o f th e w hole V IPER S area. In regions th at lack suitable b rig h t and unsaturated stars for determ ining th e local PSF o r at the edge o f th e im ages, it was n o t possible to reco n stru ct a reliab le P SF m odel. B ecause these regions are w ell defined, w e rem oved them from our m o r

phological analysis. Errors o f the fitting param eters w ere derived 1 w w w .v ip e r s .in a f .it

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A. Gargiulo et al.: The VIMOS Public Extragalactic Redshift Survey (VIPERS)

through sim ulations. In particular, the error on R e is low er than 4.4% (12% ) for 68% (95% ) o f the sam ple.

2.1. G a la xy e n v iro n m e n t

T he environm ent in the V IPER S fields is ch aracterized b y the galaxy density contrast 6, w hich is described in C ucciati et al.

(2 0 1 4 ; 2 0 1 7 , see also D avidzon et al. 2016) and is defined as 6(RA , D ec, z) = [p(R A , D ec, z) - p(z)] /p(z), (3) w here p (R A , D ec, z) is the local nu m b er density o f the tracers (see below ) w ithin a certain volum e (or filter w indow ) centered at the galaxy position (RA , D ec, z), and p(z) is the m ean num ber density at th at redshift.

In this analysis w e refer to the local overdensity 6 th at is derived b y adopting as filter w indow a cylinder w ith center on the galaxy. Its depth is ± 1000 km s-1 , and the radius is equal to the distance o f the fifth n earest tracer.

B ecause V IPER S is a flux-lim ited survey, it includes galaxies w ith a low er lum inosity lim it th at becom es increasingly b righter w ith redshift. To com pute th e density contrast using a ho m o g e

neous galaxy p opulation in the entire red sh ift ran g e available for V IPE R S, w e used a “volum e-lim ited” sam ple (our “tracers”) that com prises galaxies w ith both spectroscopic and p hotom etric re d shift. This sam ple was selected to satisfy M B < ( - 2 0 .4 - z), and b ased on the V IPER S flux lim it, it is com plete for z < 0.9.

T he red sh ift dependence o f the lum inosity thresholds is designed to account fo r evolutionary effects b ecause it roughly follow s the sam e dependence on red sh ift as th e characteristic lum inosity o f the galaxy lum inosity function (see, e.g., K ovac et al. 2010) . C ucciati et al. (2 017) also estim ated the density contrast field w ith a sam ple o f tracers lim ited to MB < ( - 2 0 . 9 - z ) . This brig h ter sam ple is com plete up to z = 1, b u t it is sparser than the sam ple w ith M b < ( - 2 0 .4 - z), w hich m eans th at th e local density is com puted on average on larger scales, th at is, w ith a low er resolution.

F or this analysis, w e chose the density contrast field that was com puted using th e tracers w ith MB < ( - 2 0 .4 - z) b ecause it is a good com prom ise betw een the allow ed red sh ift extension (z < 0.9) and the scale dow n to w hich th e field is reconstructed (a factor ~ 2 sm aller than w ith the brig h ter sam ple). In order to study the effect o f the environm ent on the m ass assem bly o f M P G s, w e subdivided the sam ple o f M P G s into four subsam ples according to the quartiles o f the 1 + 6 distribution (see Sect. 3) . To take the p ossible variation o f the 1 + 6 distribution w ith z into consideration, w e estim ated the quartile values in four redshift bins o f equal w idth 0.1. In A ppendix A w e show th at th e 1+6 distribution o f M P G s at 0.8 < z < 0.9 is significantly different from the 1 + 6 distribution a t 0.5 < z < 0.8. F or this reason w e lim it ou r analysis a t z < 0.8.

2.2. Final s a m p le

F ollow ing P aper I, w e identified the V IPER S M P G s b y select

ing from the V IPER S spectroscopic catalog all o f the galaxies (i) w ith secure red sh ift m easurem ent (confidence level >95% , i.e., quality flag 2 < z flag < 9.5), (ii) in the red sh ift range 0.5 < z < 0.8, (iii) w ith M > 1011 M 0 , and (iv) defined as p a s

sive on the basis o f their rest-fram e near-ultraviolet (NU V ) -r and r-K colors. As in D avidzon e t al. (2016) and sim ilarly to P aper I, w e defined as quiescent those galaxies for w hich

N U V - r > 3.75, (4)

N U V - r > 1.37 X ( r - K) + 3.2, (5)

r - K < 1.3. (6)

Fig. 1. Distribution of the galaxy density contrast for MPGs at 0.5 < z < 0.8 with reliable S estimates (black solid line). The arrow at the top of the plot is the median value of the distribution with the cor

responding value of the projected distance of the fifth nearest neighbor in units of M pch-1. The solid blue dashed histogram shows the dis

tribution of 1 + S for the MPGs at 0.5 < z < 0.8 with reliable S and Re estimates.

As show n in D avidzon e t al. (2016) (see also D avidzon et al.

2013) , V IPER S is 100% com plete a t z = 0.8 both for passive and star-form ing galaxies w ith M > 1011 M 0 .

W hen the local density 6 is com puted, the p ro jected cylinder can fall outside the area o f the survey for galaxies n ea r the edges o f the survey or near the C C D gaps. This alters the local density estim ate. C ucciati e t al. (2017) show ed th at an accurate rec o n struction o f the local density is p rovided w hen m o re than 60%

o f the volum e o f th e cylinder is w ithin the survey area (for m o re details, see C ucciati e t al. 2 0 1 7 ; D avidzon et al. 2016) . F or this reason, w e included only th e galaxies in our sam ple that satisfied this condition. In Fig. 1 w e report the 1 + 6 distribution o f the selected sam ple (black line), its m ed ian value (black arrow ), and the corresponding p ro jected distance o f th e fifth n earest neighbor in M p c h -1 unit.

Sim ilarly to th e 6 estim ate, a reliable Re is n o t available for a sm all portion o f V IPER S galaxies even w hen th e P S F is w ell m odeled. This is either b ecause th e algorithm does n o t co n verge or b ecause the best-fit values o f n < 0.2 are u nphysical (see K ryw ult e t al. 2017) . T hese objects w ere rem oved from the sam ple. This choice reduced th e sam ple to 902 M P G s. This is the final sam ple w e used for the M P G 2 - 6 analysis.

In F ig. 1 the b lue histogram shows the local density distribu

tion o f th e final sam ple. W e verified th at the local density distri

butions o f galaxies w ith and w ith o u t a reliable Re m easurem ent are consistent w ith each other (the K o lm o gorov-S m irnov p ro b ability that the tw o distributions show n in Fig. 1 are extracted from the sam e paren t population is 0.99). A t the sam e tim e, w e verified th at th e lack o f a reliable 6 estim ate does n o t depend on 2.

F or each M P G o f the final sam ple w e derived the surface m ean stellar m ass density 2 . C onsistently w ith P aper I, w e defined a lo w -2 sam ple, an interm ediate-2 sam ple, and a high- 2 sam ple com posed o f M P G s w ith 2 < 1000 M 0 p c -2 , 1000 <

2 < 2000 M 0 p c -2 , and 2 > 2000 M 0 p c -2 , respectively.

W e rep eat th at to study the effect o f the environm ent on the size o f the M P G s, w e subdivided th e sam ple o f M P G s into four subsam ples according to the quartiles o f th e 1 + 6 distribution.

In F ig. 2 w e show th e local density 6 o f M P G s as a function o f z and th e 25th, 50th, and 75th percentiles o f the 1 + 6 distribu

tion at 0.5 < z < 0.8 (see Table 1 for the percentile values).

H ereafter, w e refer to the four density bins as D1 ((1 + 6) < 25th

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Fig. 2. Galaxy density contrast as a function o f z for the population of M PGs with reliable estimates o f S and R e (gray circles, m agenta squares, or cyan triangles). Solid lines indicate the m edian value of the (1 + S) distribution, while the 25th and the 75th percentiles are indicated with long-dashed and dot-dashed lines, respectively. M agenta filled squares are M PGs w ith £ < 1000 M0 pc-2 (i.e., the low -£ sample), cyan filled triangles are M PGs w ith £ > 2000 M 0 p c -2 (i.e., the high-£

sample) and gray circles are M PGs w ith 1000 < £ < 2 0 0 0 M0 pc-2.

p ercentile value), D 2 (25th < (1 + S) < 50th p ercentile value), D3 (50th < (1 + S) < 75th percentile value), and D 4 ((1 + S) > 75th p ercentile value). M o st galaxies in th e highest density bin (i.e., (1 + S) > 6.48) are in (sm all) groups, as show n b y C ucciati e t al.

(2 0 1 7 , see th eir Fig. 2). In the sam e paper, the authors show ed that m ore than 50% of the galaxies are expected to b e cen

tral galaxies at our M scales and red sh ift range, (see Fig. 8 in C ucciati e t al. 2017) . This im plies th at m oving from the D1 to D 4 density bin, th e p robability increases th at a galaxy assem bles stellar m ass through the accretion o f satellites (through a dry m erger o r cannibalism ).

O f the 902 M P G s in the final sam ple, 386 have £ < 1000 M 0 p c -2 and 255 have £ > 2000 M 0 p c -2 . T he low- (high-) £ subsam ple can b e split into four S bins w ith at least ~ 80(56) galaxies p er b in (see Table 1) .

3. G alaxy size versus environm ent at 0.5 < z < 0.8 In Fig. 3 w e p lo t the size-m ass relation (SM R ) o f M P G s in the tw o extrem e environm ents (i.e., M P G s w ith (1 + S) < 1.94 and (1 + S) > 6.48) (D1 and D 4 bins, respectively). T he figure q u a l

itatively show s that M P G s in the low est and hig h est S quartiles p opulate the sam e locus in the plane. This m eans th at at fixed stellar m ass, M P G s w ith a given £ can b e found in any environ

m ent. In A ppendix B w e verify th at this resu lt is n o t dependent on our choice o f the S values used to identify low- and high- density regions.

This does n o t tell us w hether a given environm ent can instead favor th e form ation o f a M P G w ith a given £ , however. To address this point, w e adopted th e follow ing approach. W e co m p ared the nu m b er o f low- and h ig h -£ M P G s in th e fo u r local d en sity bins. B y construction, each S b in contains the sam e num ber o f M P G s, therefore a co nstant n um ber o f the subpopulations o f low- and h ig h -£ M P G s as a function o f S im plies n o correlation betw een £ and S.

B efore w e carried this com parison out, w e h ad to apply a correction for the survey incom pleteness. V IPER S has three sources o f incom pleteness: the TSR , the success sam pling rate (SSR), and the color sam pling rate (CSR). As stated in Sect. 2 , the T SR is the fraction o f galaxies th at are effectively observed w ith resp ect to the p hotom etric paren t sam ple. T he S SR is the

fraction o f spectroscopically observed galaxies w ith a redshift m easurem ent. T he C S R accounts for the incom pleteness due to the color selection o f the survey. T hese statistical w eights depend on th e m agnitude o f the galaxy, on its redshift, color, and angular position. T hey have been derived for each galaxy in the full V IPER S sam ple (for a d etailed description o f their derivation see G arilli et al. 2 0 1 4 ; Scodeggio et al. 2018) . To correct the n um ber o f M P G s in each S b in fo r all o f these incom pletenesses, w e w eighted each galaxy i by the quantity Wi = 1/(TSR i x S S R i x C S R i). W e do n o t expect these sources o f incom pleteness to affect o ur results b ecause th e galaxy size was n o t considered in the slit assignm ent in V IPE R S. O n the other hand, the S SR could b e higher for dense M P G s w ith respect to less dense M P G s b ecause their lig h t profile is m ore strongly peaked. However, this higher S SR does n o t depend on the envi

ro n m en t b ecause it is only related to the intrinsic properties o f the galaxies. T he sam e holds for the C SR . This ensures th at the populations o f M P G s in dense and less dense environm ent are n o t b ia sed in £.

A nother factor th at can bias ou r results is the w ell-know n correlation betw een M and S, w hereby m ore m assive galaxies p opulate denser environm ents. W e exam ine th e stellar m ass d is

tribution o f our sam ple o f M P G s as a function o f S in the upper p anel Fig. 4 . T he figure show s th at th e m ost m assive galaxies are underrepresented in the low -density bin. W e quantify this differ

ence in the b ottom p an el o f F ig. 4 , w here the fraction o f M PG s in the low est and hig h est S quartiles is rep o rted as a function o f the stellar m ass. In agreem ent w ith previous results, w e find that the fraction o f M P G s in the d ensest regions increases (by a factor

~ 2 ) for stellar m asses increasing from 1011 M 0 to 5 x 1011 M 0 , and concurrently, the fraction o f M P G s in the less dense regions decreases w ith M .

F igure 3 show s th at at higher stellar m asses, lo w -£ M PG s prevail over the full M P G population, resulting in an increasing fraction o f lo w -£ M PG s w ith M . This trend, coupled w ith the M - S correlation show n in Fig. 4 , cou ld bias our results tow ard a false tren d o f larger galaxies in d enser environm ent.

To rem ove th e p ossible biases that are due to the d if

ferent stellar m ass distributions o f M P G s in low - and high- density regions, w e extracted four subsam ples o f M P G s w ith the sam e distribution in stellar mass from the four S bins (see A ppendix C ) . This red u ced the total n um ber o f M P G s to 165 galaxies in each local density quartile.

T he filled m agenta squares an d filled cyan triangles in F ig. 5 indicate the m ean n um ber o f low - and h ig h -£ M P G s in each S bin derived from the 100 m ass-m atched sam ples. E rro r bars take the Poisson fluctuations and th e error on the m ean into account. O pen sym bols indicate th e sam e values, b u t w ith no correction factor for incom pleteness. F or both low- and high-

£ M P G s, the trend w ith S th at is obtained considering the corrected estim ates is consistent w ith the trend obtained w ith uncorrected estim ates. This indicates th at the w eights w e applied do n o t alter the trends, an d it confirm s th at n one o f th e in co m pleteness factors depends on S o r £ . F or com pleteness, w e report in A ppendix D the sam e as in F ig. 5, b u t for the original sam ples, th at is, n o t m ass m atched. In the follow ing w e refer only to the results obtained w ith co rrected values (filled points in F ig. 5) .

F igure 5 show s sim ilarly to Fig. 3 th at low- and h ig h -£ M PG s are ubiquitous in all environm ents. In addition, it show s th at the n u m b er o f h ig h -£ M P G s is alm ost co nstant over the fo u r S bins (X2 = 3.3, the probability P th a tx 2 > 3.3 is 0.35). In particular, the nu m b er o f h ig h -£ M P G s in each S b in is co nsistent w ithin 1 ^ w ith th e m ean nu m b er derived w hen no tren d w ith S is assum ed.

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Table 1. N um ber o f M PGs and 1 + S percentiles in the full M PG sam ple and in subsamples subdived by z and M .

z Ntot

N

^D1

N

D2

N

D3

N

^{D 4} ^25th ^50th ^75th

Total M P G sam ple

All 0.5 < z < 0.8 902 226 225 226 225 1.94 3.37 6.48

M < 2 x 1011 Mq 0.5 < z < 0.8 742 186 186 185 185 1.90 3.26 6.18 M > 2 x 1011 M 0 0.5 < z < 0.8 160 40 40 40 40 2.22 3.94 6.81

L o w -£ M P G sam ple

A ll 0.5 < z < 0.8 386 80 102 95 109 1.94 3.37 6.48

M < 2 x 1011 Mq 0.5 < z < 0.8 313 67 84 82 80 1.90 3.26 6.18 M > 2 x 1011 Mq 0.5 < z < 0.8 73 14 17 17 25 2.22 3.94 6.81

H ig h -£ M P G sam ple

All 0.5 < z < 0.8 255 78 56 65 56 1.94 3.37 6.48

M < 2 x 1011 Mq 0.5 < z < 0.8 221 65 48 52 56 1.90 3.26 6.18 M > 2 x 1011 Mq 0.5 < z < 0.8 34 12 9 10 3 2.22 3.94 6.81

Total M S F G sam ple

A ll 0.8 < z < 1.0 533 134 133 133 133 1.28 2.54 4.27

M < 2 x 1011 Mq 0.8 < z < 1.0 477 120 119 119 119 1.22 2.46 4.28 M > 2 x 1011 Mq 0.8 < z < 1.0 56 14 14 14 14 2.00 3.11 4.27

L o w -£ M S F G sam ple

A ll 0.8 < z < 1.0 398 96 105 95 102 1.28 2.54 4.27

M < 2 x 1011 Mq 0.8 < z < 1.0 360 84 96 85 95 1.22 2.46 4.28 M > 2 x 1011 Mq 0.8 < z < 1.0 38 10 10 10 8 2.00 3.11 4.27

Notes. Colum n 1: sample. Column 2: redshift range. Colum n 3: total num ber o f galaxies. Colum ns 4, 5, 6, and 7: number o f galaxies in the considered sam ple in the four S bins defined according to the 25th, 50th, and 75th percentiles o f the (1 + S) distribution. The values o f these percentiles are listed in Cols. 8, 9, and 10 for each o f the considered samples.

J l [Me ]

Fig. 3. Size-mass relation of M PGs in the lowest (gray open circles) and highest (blue crosses) quartile of (1 + S) distribution (D1 and D4, respec

tively). The solid lines show the constant m ean stellar mass density £, as annotated.

T he nu m b er o f lo w -£ M P G s slightly an d steadily increases from the low est to th e highest S quartiles w ith a X = 8.6 and a probability P ( X > 8.6) = 0.035. In particular, the n um ber o f lo w -£ M P G s in th e D1 region is m ore than \ a low er than the nu m b er o f lo w -£ M P G s in the D 4 region. T he difference in the S distributions o f low- and h ig h -£ M P G s w as com pared through a K olm ogorov-S m irnov (KS) test. F ro m each m ass-m atched sam ple w e selected the low- and h ig h -£ M P G s and derived the KS probability p th at their (1 + S) distributions w ere extracted from the sam e p are n t sam ple. T he m edian value o f p over the 100 sim ulations is 0.11, suggesting th at w e cannot exclude th at the paren t p opulation o f the tw o distributions are the sam e single population. A lthough the trends w e found are m arginally signifi

cant, they m ig h t im ply th at g alaxy size and environm ent are also

Fig. 4. Upper panel, local density S as a function of galaxy stellar mass for our MPG sample. Filled gray circles, open violet squares, pink crosses, and filled blue triangles indicate MPGs in the D1, D2, D3, and D4 quartiles. The horizontal solid line indicates the S value above which MPGs cover the full range of stellar mass (1 + S = 1.5) (see Sect. 3).

Bottom panel: fraction of MPGs in the highest and lowest S quartiles as a function of galaxy stellar mass (blue triangles and gray full circles, respectively).

related at redshifts 0 .5 -0 .8 , and thus it is im portant to investigate it further.

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Fig. 5. Average number of low-£ (filled magenta squares) and high- E (filled cyan triangles) MPGs as a function of local density S derived from 100 mass-matched samples. The counts are corrected for the selec

tion function of the VIPERS survey. Error bars include the Poisson fluc

tuations and the error on the mean. The four S bins correspond to the four quartiles of the MPG (1 + S) distribution. Open symbols are the mean number of low- and high-E MPGs that are effectively observed (i.e., not corrected for the selection function) over 100 iterations. The ordinate scale on the right-hand side refers to the uncorrected counts.

3.1. D e p e n d e n c e o f th e S -£ relation o n ste lla r m a s s

Several relations involving th e stellar m ass (e.g., the SM R) show a sharp change in their trends at M ~ 2 x 1011 M 0 (e.g., C appellari et al. 2 0 1 3 ; B ernardi et al. 2 011a,b ; S aracco et al.

2017) . This feature is interpreted as an indication o f an in creas

ing role o f satellite accretion in the m ass-assem bly history o f galaxies w ith stellar m ass above such a threshold (B ernardi et al. 2 0 1 1 a,b ) . A ccording to this picture, w e m ig h t expect that M PG s w ith M > 2 x 1011 M 0 show a stronger positive co rrela

tion b etw een th eir size and the environm ent than the less m assive ones. To test this prediction, w e investigated w hether the higher n u m b er o f lo w -£ M P G s w e observe in denser environm ent is m ainly due to galaxies w ith M > 2 x 1011 M 0 .

In Fig. 6 w e report the sam e analysis as in F ig. 5, but now for M PG s w ith 1011 M 0< M < 2 x 1011 M 0 (low er panel), and w ith M > 2 x 1011 M 0 (upper panel). T he figure show s that, no significant difference in the n um ber o f high- and lo w -£ M PG s w ith S is detectable a t low er stellar m asses (bottom panel; all the values are co nsistent at < 1 ^ level). A t M > 2 x 1011 M 0 , the num bers o f b o th high- and lo w -£ M P G s are all consistent in the first three S bins, but in th e last bin, the n um ber o f lo w -£ M PG s suddenly increases by a factor ~ 2 , w hile th e n um ber o f h igh-£

M PG s drastically drops by a factor ~ 10. T he D 4 region appears to be lacking h ig h -£ M P G s w ith M > 2 x 1011 M 0 , and to have an overabundance o f lo w -£ M P G s w ith the sam e stellar m ass.

T he different £ - S trends in the tw o stellar m ass bins is also evident in Fig. 7 , w here w e report for the tw o stellar m ass bins the cum ulative distribution o f the K S-test probability p that the (1 + S) distributions o f low- and h ig h -£ M P G s from the 100 m ass- m atched sam ples are extracted from the sam e p arent population.

T he figure show s th at the m edian value o f p for th e high-m ass sam  ple is 5 x 10-3 , and for the low -m ass sam ple is ~ 0.3. F igures 6 and 7 indicate that the dependence on th e environm ent o f low - and h ig h -£ M P G s w ith M > 2 x 1011 M 0 is significantly different, w ith a higher p robability to find large (low -£) galaxies in denser environm ent. Conversely, w e do n o t detect any significant differ

ence in the p robability o f finding a low - o r a h ig h -£ M P G w ith 1011 M 0 < M < 2 x 1011 M 0 in a specific environm ent.

Very few w orks have investigated the relation betw een the size/£ an d the environm ent in the sam e red sh ift and m ass ranges as in this w ork. K elkar e t al. (2015) find no significant differences in the R e o f red galaxies w ith M > 1011 M 0 in clusters and fields

Fig. 6. Same as Fig. 5, but for M PGs with 1011 M 0 < M < 2 x 1011 M0 (lower panel) and M > 2 x 1011 M0 (upper panel). Light shaded m agenta and cyan areas indicate the ±1ix region around the mean value of low- and high-£ M PGs that are expected in each stellar mass bin when no trend w ith S is assumed.

Fig. 7. Cumulative distribution o f the K S-probability p that the (1 + S) distributions o f low- and high-£ M PGs are extracted from the same par

ent population that is obtained from all o f the 100 mass-m atched sam ples. The black line refers to M PGs with 1011 M 0 < M < 2 x 1011 M 0, and the blue line to MPGs w ith M > 2 x 1011 M0 .

at 0.4 < z < 0.8. This resu lt is partially at odds w ith our findings b ecause w e observe a correlation at the highest m ass-scales, but this discrepancy is entirely accounted fo r b y the different o b serv ables used in the tw o analyses. U sing their sam ples, w e selected red galaxies on the basis o f th eir £ instead o f their Re an d found th at th e n um ber o f lo w -£ galaxies w ith M > 2 x 101 1 M 0 in clu s

ters is m ore than tw ice the n um ber o f lo w -£ galaxies in the field (9 vs. 4, respectively). This qualitatively agrees w ith ou r find

ings (the n um ber o f lo w -£ M P G s in D 4 regions alm ost do u bles the nu m b er o f lo w -£ M P G s in D1 regions in this m ass range, as show n in th e top p an el o f Fig. 6) . Sim ilarly, L an i et al.

(2013) m easured th e local galaxy density in fixed physical aper

tures o f radius 400 kpc and found no dependence betw een size and environm ent o f quiescent (U V J selected) galaxies at 0.5 <

z < 1.0 w ith M ~ 10^{1 1}M 0 . A t M > 2 x 10^{1 1}M 0 they found no dependence betw een the Re an d the environm ent except for galaxies in the densest regions that are larger than those in other environm ents. T hese trends are consistent w ith the results show n

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in Fig. 6 . D ifferently from ou r findings, H uertas-C om pany e t al.

(2013b) found no dependence o f galaxy size on environm ent, regardless o f stellar m ass. In their w ork, they investigated the R e -6 relatio n for passive and elliptical galaxies, differently from our analysis, w hich is b ased on color-selected passive galaxies (as in L an i et al. 2 0 1 3 ; K elkar et al. 2015) . It is w ell know n that sam ples o f passive galaxies selected through colors co n tain 2 0 -3 0 % d isk galaxies (e.g., H uertas-C om pany e t al. 2 0 1 3 b ; Tam burri e t al. 2 0 1 4 ; M oresco et al. 2013) . T he different selec

tion m eth o d m ig h t explain th e difference betw een our M P G sam p le and their passive g alaxy sam ple, b u t w e are n o t in the position to quantify the effect o f this difference on the results.

3.2. R elation b e tw e e n 6 a n d 2 for M P G s: s u m m a r y a n d d isc u ssio n

T he results w e obtained for the m ass-m atched sam ples an d p re

sented in Fig. 6 indicate that

- at 1011 M 0 < M < 2 x 1011 M 0 w e do n o t observe a signifi

cant correlation betw een the 2 o f a M P G and th e environ

m en t in w hich it lives;

- at M > 2 x 1011 M 0 w e find a flat trend betw een the num ber o f low - and h ig h -2 M P G s and 6 in th e first three 6 bins. In the highest density bin, th e nu m b er o f lo w -2 M P G s instead suddenly increases b y ~ a factor 2 w ith resp ect to the bins at low er density, w hile the nu m b er o f h ig h -2 M P G s decreases b y a factor ~ 10.

T hese results indicate th at there is no environm ent th at favors (or disfavors) the form ation o f low- and h ig h -2 M P G s w ith 1011 M 0 < M < 2 x 1011 M 0 , th at is, the m echanism s favored in denser environm ents, such as satellite accretion o r cannibalism , do n o t appear to b e responsible for the low m ean surface stellar m ass density o f large M PG s.

T he picture is m o re com plex a t higher stellar m ass. W e observe a decline in the n um ber o f h ig h -2 M P G s in the d en s

est environm ent an d concurrently an increase in the num ber o f the lo w -2 M P G s. This suggests tw o m ain scenarios: (i) the densest environm ents favor th e form ation o f lo w -2 M PG s w ith M > 2 x 1011 M 0 and concurrently disfavor the form ation o f h ig h -2 M P G s w ith the sam e stellar m ass; (ii) low- and high- 2 M P G s are form ed in all environm ents w ith the sam e p ro b a

bility, that is, the form ation (at t = t0) o f d ense o r n o t dense passive galaxies does n o t dep en d on 6 as for less m assive c o u n terparts; but at a later tim e (t1 > t0), h ig h -2 M P G s disappear in the m o st d ense regions and lo w -2 M P G s appear. This m eans that their evolution does depend on the environm ent. T he hierarch i

cal accretion o f satellite galaxies around a com pact g alaxy could be th e driver o f a m igration o f M P G s from th e h ig h -2 sam ple tow ard th e lo w -2 sam ple, and consequently be the reaso n o f the abundance (deficit) o f low- (high-) 2 M P G s w ith resp e ct to the other 6 bins. P redictions o f standard hierarchical m odels (e.g., S hankar e t al. 2 0 1 2 ; H uertas-C om pany et al. 2013b) indicate that at these m ass scales, galaxies in groups should b e ~ 1 .5 tim es larger than galaxies in less dense fields. W e have estim ated the m ean R e o f M P G s w ith M > 2 x 1011 M 0 in the four density bins and found th at it is ~ 1 .4 tim es larger in the D 4 bin than in the other less dense environm ents « R e> = 6.24 ± 0.04, 6.18 ± 0.03, 6.21 ± 0.03, and 8.73 ± 0.08 k p c for the D 1, D 2, D 3, and D 4 bins, respectively). T he concordance b etw een hierarchical m odel p re

dictions and o ur observations indicates that accretion o f satellites could b e a viable m echanism s fo r the form ation and evolution o f those largest (e.g., less dense) M P G s w ith M > 2 x 1011 M 0 in excess in the densest regions. This supports the second scenario described above.

A nother w ay to distinguish betw een th e tw o scenarios w ould b e to investigate the 2 - 6 relatio n for M P G s w ith M > 2 x 1011 M0 a t higher z. In the first scenario, w e should observe n o evolution o f the 2 - 6 relation w ith tim e. Conversely, in th e second picture, w e should observe a flat 2 - 6 tren d at t = t0

b ecause the correlation betw een 2 and 6 observed in the top panel o f F ig. 6 should appear later, after satellite accretion has becom e relevant.

U nfortunately, M P G s w ith M > 2 x 1011 M0 a t z > 0.8 are very rare in V IPE R S. In spite o f the w ide coverage o f survey, w e find only 4 6 M P G s in the red sh ift ran g e 0.8 < z < 0.9. This p re vents an analysis at higher z (w e h ig hlight th at these 46 M PG s have to b e divided into four 6 bins and into low - and h ig h -2 sub

sam ples). N onetheless, the V IPER S sam ple offers a unique statis

tics at z > 0.8 fo rM S F G s. In Sect. 4 w e use th e sam ple o f M S FG s at 0.8 < z < 1.0 as a b enchm ark for testing our conclusions.

4. N um ber of M SFGs as a function of 6

T he analysis show n in Fig. 6 questions th e relevance o f satellite accretion in the m ass assem bly o f lo w -2 M P G s w ith 1011 M0 <

M < 2 x 1011 M0 . U sing a different p robe (e.g., the n um ber d en sity evolution o f M P G s and M S FG s), w e reached the sam e co n clusion in P aper I, w here w e suggested th at M S FG s a t z > 0.8 are th e d irect progenitors o f lo w -2 M P G s. I f th e interpretation w e draw b ased on these tw o w orks is correct, w e should find th at the lo w -2 M S FG s a t z > 0.8 follow th e sam e tren d w ith 6 as lo w -2 M P G s at z < 0.8 b ecause the form er are the p ro g en itors o f the latter. To te st this hypothesis, w e rep e ate d th e sam e analysis as in Sect. 3 for th e sam ple o f M S FG s a t 0.8 < z < 1.0. In this analysis w e refer to the density field 6 th at is estim ated using V IPER S galaxies w ith MB < ( - 2 0 .9 - z ) as tracers (see Sect. 2.1) . A lthough this density field is com puted on larger scales than the field used for M P G s, it allow s us to p ush the analysis up to z = 1.0. In A ppendix E w e show that this choice does n o t affect our results and conclusions.

In Table 1 w e rep o rt the total nu m b er o f M S FG s at 0.8 < z < 1.0 w ith the values o f the 25th, 50th, and 75th p er

centiles o f their (1 + 6) distribution. As for M P G s, w e also report the n um ber o f galaxies (and o f percentiles) for the tw o subsam ples w ith 1011 M0 < M < 2 x 1011 M0 a n d M > 2 x 1011 M0 .

In th e b ottom panel o f Fig. 8 w e rep o rt the n um ber o f low- 2 M S FG s at 0.8 < z < 1.0 w ith 1011 M0 < M < 2 x 1011 M0 as a function o f 6. F o r com parison, w e also rep o rt th e num ber o f lo w -2 M P G s a t 0.5 < z < 0.8, and in the sam e m ass range.

In this case, w e d id n o t use th e m ass-m atched values, b u t the values th at w ere ju s t co rrected for incom pleteness b ecause w e are interested in the relative change w ith 6 o f the tw o po p u lations. T he figure shows th at the tw o trends are consistent at the 1 ^ level. This result, com bined w ith the results in P aper I and Sect. 3 , strengthens the postulated evolutionary connection betw een M S FG s and M P G s. In P aper I w e dem onstrated that M S FG s at z ~ 0.8 are in the correct nu m b er to be the progenitors o f lo w -2 M P G s a t z < 0.8, and here w e show th at they are also in the correct environm ent. T he analyses o f the nu m b er density and o f th e environm ent concur in indicating th at lo w -2 M PG s w ith 1011 M0 < M < 2 x 1011 M0 at z < 0.8 are th e descendants o f M S FG s a t higher z and n o t th e resu lt o f satellite accretion.

In Sect. 3.2 w e have show n th at the accretion o f satel

lites could b e a viable m echanism s for th e form ation o f the exceedingly lo w -2 M P G s w ith M > 2 x 1011 M0 in the D 4 bin.

In this picture, the 2 - 6 trend o f lo w -2 M PG s a t z < 0.8 should n o t be consistent w ith th at o f M S FG s a t 0.8 < z < 1.0, as w e found for low er m ass-scales. T he tw o trends are expected to

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Fig. 8. Lower panel, number of low-E MSFGs at 0.8 < z < 1.0 (blue stars) with 1011 M0 < M < 2 x 1011 M0 as a function of local den

sity S. For comparison, we also report the number of low-E MPGs at 0.5 < z < 0.8 (magenta squares) with 1011 M0 < M < 2 x 1011 M0 . Their values are reported on the right y-axis. The four S bins correspond to the four quartiles of the MPG (1 + S) distribution. Upper panel: same as in the lower panel, but for MPGs with M > 2 x 1011 M0 .

deviate in the h ighest density bin b ecause the m ajority o f M SFG s becom e passive a t z < 0.8, b u t to these “shutdow n” M P G s w e should add in the highest density bin the large M P G s that are form ed b y the accretion o f satellites.

In the top p an el o f F ig. 8 w e rep o rt the E -S tren d for M SFG s w ith M > 2 x 1011 M 0 . It show s th at in the highest stellar m ass bin, the E -S trend for M S FG s at z > 0.8 is flat (all points are consistent w ithin 1 ^ ). W e observe instead a flat E -S tren d for M PG s a t z < 0.8 in the first three S bins and an increase in the nu m b er o f low -E M P G s in the highest density b in (see the m ag en ta points in the u pper p anel o f Fig. 8) . This evidence sup

ports th e second scenario w e p roposed in Sect. 3 .2 . T he flat trend o f M S FG s over th e fo u r S bins indicates th at at t = t0, the p ro b  ability th at a M S F G w ith M > 2 x 1011 M 0 (and consequently o f its d escendant M P G ) has a low -E is independent o f th e envi

ronm ent. A t t 1 > to, environm ent-related m echanism s, such as accretion o f satellites, are responsible for the surplus o f M PG s that is observed in the D 4 bin.

In sum m ary, our analysis shows that the larger size o f m o st o f the low -E M P G s is n o t a consequence o f a hierarchical assem bly o f th e stellar m atter. A lthough this is true for the m ajority o f the galaxies in ou r sam ple, w e cannot rule out satellite accretion as one o f the m ain m echanism s responsible for increasing the size, thus decreasing E, in a sm all fraction o f high-E M P G s w ith M > 2 x 1011 M 0 that resid e in th e densest environm ents (i.e.,

~ 10 high-E M P G s over ~ 902, w here 10 is the difference betw een the m ean value o f high-E M P G s in the D 1, D 2, an d D 3 bins and the value in the D 4 bin, see the upper panel o f Fig. 6 , and 902 is the total nu m b er o f M PG s).

5. Sum m ary

U sing the V IPER S spectroscopic survey, w e investigated the relation betw een the typical size o f M P G s an d th eir environ

m ent. In a hierarchical scenario, structures are expected to grow

in m ass and size through accretion o f sm aller units. T he ac cre

tion o f satellites is enhanced in groups (and for central galaxies), thus w e w ould exp ect to find larger galaxies in groups than in less dense environm ents. T he study o f galaxy sizes as a function o f the environm ent therefore is a p ow erful diagnostic fo r galaxy accretion m odels.

F ro m the V IPER S database w e extracted all th e galaxies at 0.5 < z < 0.8 w ith M > 1011 M 0 . F rom these system s w e selected the passive galaxies according to their N U V rK colors. T he sam p le is 100% com plete in stellar m ass at z = 0.8. F ro m the m assive and passive galaxies, w e selected those w ith reliable estim ates o f the effective radius R e an d o f the galaxy density contrast S. This led to a total final sam ple o f 902 M P G s in the red sh ift range 0.5 < z < 0.8.

F ro m this sam ple, w e selected a low -E subsam ple co m p o sed o f M P G s w ith a m ean surface stellar m ass density E <

1 0 0 0 M p c p c -2 , and a high-E subsam ple th at contains the M PG s w ith E > 2000 M pc p c -2 .

T he overall p icture w e obtained from our analysis o f size versus environm ent in V IPER S galaxies a t 0.5 < z < 0.8 is described below.

- T he E -S relation depends on stellar m ass. In particular, M P G s w ith 1011 M 0 < M < 2 x 1011 M 0 do n o t show any sig nificant trend betw een the E (or equivalently R e) and the environm ent (the KS probability p th at the density co n  trast distributions o f low - and high-E M PG s are extracted by the sam e p are n t sam ple is 0.3, see Fig. 7 ), w hile a signifi

can t correlation is detected for M P G s w ith M > 2 x 1011 M 0 (p = 5 x 10-3), w ith larger galaxies being m o re com m on in d enser environm ents.

- T he trend betw een E and S observed fo r M P G s w ith M > 2 x 1011 M 0 is due to an overabundance o f low -E M PG s and b y a dearth o f high-E M P G s in the densest regions (see Fig. 6 ) .

T he absence o f a correlation betw een E and S for M P G s w ith 1011 M 0 < M < 2 x 1011 M 0 indicates th at the accretion o f satel

lite galaxies is n o t the m ain driver o f the build-up o f low -E M PG s in this stellar m ass range. This resu lt is in line w ith ou r previous results. In P aper I (see F ig. 9), the analysis o f the nu m b er d en si

ties o f M P G s and M S FG s suggested th at the m o st p lausible p ro genitors o f the em erging low -E M P G s at z < 0.8 are the M S FG s at z > 0.8. W e further investigated this connection and in Fig. 8 com pared the E -S trends for M S FG s at z > 0.8 and low -E M PG s z < 0.8. T he tw o trends are co nsistent at the 1 ^ level, as it should b e if the tw o populations are evolutionary connected. In P aper I w e d em onstrated th at the M S FG s are in the correct n um ber to be the progenitors o f low -E M P G S , an d here w e show th at they are also in the correct environm ent.

F or the highest stellar m ass bin, ou r results on the E -S co rre

lation o f both M P G s and M S FG s are consistent w ith a scenario in w hich, overall, environm ent does n o t affect the form ation o f low- o r high-E M P G s. N onetheless, it seem s to play a relevant role in th e evolution o f a sm all fraction (< 1%) o f low -E M P G s in the densest environm ent. W e in terp ret the increased n um ber o f low -E M P G s in th e d ensest regions as a consequence o f a m ig ra

tion o f high-E M P G s in low -E M P G s th at is due to accretion o f satellite galaxies. T hese results are also confirm ed by com pari

son w ith predictions o f hierarchical m odels.

Acknowledgements. We acknowledge the crucial contribution of the ESO staff for the management of service observations. In particular, we are deeply grateful to M. Hilker for his constant help and support of this program. Italian participa

tion to VIPERS has been funded by INAF through pRiN 2008, 2010, and 2014 programs. LG, AJH, and BRG acknowledge support from the European Research Council through grant n. 291521. OLF acknowledges support from the European

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Research Council through grant n. 268107. TM and SA acknowledge financial support from the ANR Spin(e) through the French grant ANR-13-BS05-0005.

AP and JK have been supported by the National Science Centre (grants UMO- 2018/30/M/ST9/00757 and UM0-2018/30/E/ST9/00082). KM acknowledges support from the National Science Centre grant UM0-2018/30/E/ST9/00082.

WJP is also grateful for support from the UK Science and Technology Facil

ities Council through the grant ST/I001204/1. EB, FM and LM acknowledge the support from grants ASI-INAF I/023/12/0 and PRIN MIUR 2010-2011.

SDLT acknowledges the support of the OCEVU Labex (ANR-11-LABX-0060) and the A*MIDEX project (AnR -11-IDEX-0001-02) funded by the “Investisse- ments d ’Avenir” French government program managed by the ANR and the Pro

gramme National Galaxies et Cosmologie (PNCG). Research conducted within the scope of the HECOLS International Associated Laboratory is supported in part by the Polish NCN grant DEC-2013/08/M/ST9/00664.

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1 INAF - Istituto di Astrofisica Spaziale e Fisica Cosmica Milano, Via Corti 12, 20133 Milano, Italy

e-mail: a d r i a n a . g a r g i u l o @ i n a f . i t

2 INAF - Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy

3 Institute of Physics, Jan Kochanowski University, ul. Swietokrzyska 15, 25-406 Kielce, Poland

4 INAF - Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy

5 INAF - Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano - Via E. Bianchi 46, 23807 Merate, Italy

6 University degli Studi di Milano, Via G. Celoria 16, 20133 Milano, Italy

7 Aix Marseille Univ., CNRS, LAM, Laboratoire d ’Astrophysique de Marseille, Marseille, France

8 INAF - Osservatorio Astrofisico di Torino, 10025 Pino Torinese, Italy

9 Laboratoire Lagrange, UMR7293, Universitd de Nice Sophia Antipolis, CNRS, Observatoire de la Cote d’Azur, 06300 Nice, France

10 Instituto de Astronomia y Ciencias Planetarias, Universidad de Ata

cama, Avenida Copayapu 485, Copiapó, Chile

11 Dipartimento di Fisica e Astronomia - Alma Mater Studiorum Uni

versity di Bologna, Via Piero Gobetti 93/2, 40129 Bologna, Italy 12 National Centre for Nuclear Research, ul. Pasteura 7, 02-093

Warszawa, Poland

13 INFN, Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy

14 Department of Astronomy & Physics, Saint Mary’s University, 923 Robie Street, Halifax, Nova Scotia B3H 3C3, Canada

15 Aix-Marseille University Jardin du Pharo, 58 bd Charles Livon, 13284 Marseille Cedex 7, France

16 IRAP, 9 Av. du colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France

17 Astronomical Observatory of the Jagiellonian University, Orla 171, 30-001 Cracow, Poland

18 School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS, UK

19 INAF - Istituto di Radioastronomia, Via Gobetti 101, 40129 Bologna, Italy

20 Aix Marseille Univ., Univ. Toulon, CNRS, CPT, Marseille, France 21 Dipartimento di Matematica e Fisica, University degli Studi Roma

Tre, Via della Vasca Navale 84, 00146 Roma, Italy

22 INFN, Sezione di Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy

23 INAF - Osservatorio Astronomico di Roma, Via Frascati 33, 00040 Monte Porzio Catone, RM, Italy

24 Department of Astronomy, University of Geneva, Ch. d’Ecogia 16, 1290 Versoix, Switzerland

25 Institute for Astronomy, University of Edinburgh, Royal Observa

tory, Blackford Hill, Edinburgh EH9 3HJ, UK

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A ppendix A: 8distribution as a function of z

Fig. A.1. C umulative distribution o f (1 + S) for M PGs with reliable R^e and S at 0.5 < z < 0.8 (black solid line) and at 0.8 < z < 0.9 (dashed black line). The probability p that the two distributions are extracted from the same parent sample is rejected at ~3ix. Red solid and dashed lines indicate the cumulative distribution for M PGs at 0.5 < z < 0.6 and 0.7 < z < 0.8, respectively. The probability that they are extracted from the same parent sam ple is 0.64.

In this section w e investigate the dependence o f th e (1 + S) d istri

bution o f M P G s on z. In Fig. A.1 w e p lo t the cum ulative d istribu

tions o f the local density for M P G s w ith reliable R e and S in the tw o different red sh ift bins 0.5 < z < 0.8 and 0.8 < z < 0.9. The KS test indicates a p robability p = 0.07 th at the tw o distributions are extracted from the sam e paren t sam ple. Conversely, w e do n o t find a strong dependence betw een z and the S distributions at z < 0.8. As an exam ple, the re d lines in F ig. A.1 indicate the (1 + S) distribution for M P G s in the red sh ift bins 0.5 < z < 0.6 and 0.7 < z < 0.8. T he p robability that the tw o distributions are extracted from the sam e paren t sam ple is p = 0.64.

A ppendix B: Effect of the environm ent on the stellar mass distribution

Fig. B.1. Size-mass relation of MPGs in the final sample with (1 + S) <

1.5 (gray filled circles) and with (1 + S) > 7 (blue filled circles). Open blue and gray circles are the MPGs that were excluded from Fig. 3, i.e., MPGs with 1.5 < (1 + S) < 1.94 and 6.48 < (1 + S) < 7, respectively.

In this section w e investigate the size-m ass relation in tw o extrem e environm ents. In particular, w e rep o rt th e size-m ass relation fo r M P G s w ith (1 + S) < 1.5 and (1 + S) > 7 (see Fig. 4 and the text for th e choice o f these new cuts). W e find

th at M P G s in regions w ith (1 + S) > 7 populate sim ilar regions in the R e versus M p lan e o f M P G s w ith (1 + S) > 6.48 (see the filled and open blue points in Fig. B .1) . Conversely, the p o p u lation o f M P G s w ith (1 + S) < 1.5 does n o t include th e m ost m assive galaxies w ith resp ect to the population o f M P G s w ith (1 + S) < 1.94. D espite the lack o f m assive galaxies in th e low est density regions, F ig. B.1 show s th at in the stellar m ass range covered b oth b y M P G s w ith (1 + S) < 1.5 and by M P G s w ith (1 + S) > 7 (i.e., M < 3 x 1011 M 0 ) the range o f R e th at is covered is n o t significantly different. This indicates th at environ

m ent plays an im portant role in setting the stellar m ass (w e take this aspect into account in Sect. 3.2), as is know n, but it confirm s th at ou r results show n in F ig. 3 are robust against the choice o f the S cuts.

A ppendix C: C onstruction of the m ass-m atched sam ples

Fig. C.1. Stellar mass distribution of MPGs at 0.5 < z < 0.8 in the four S bins (cyan, blue, magenta, and red histograms for the D1, D2, D3, and D4 S bin, respectively). The dashed gray histogram indicates the stellar mass distribution of the mass-matched sample.

To co nstruct the m ass-m atched sam ples w e used in the analysis o f Sect. 3 , w e started from th e sam ples o f M P G s in th e four S bins. W e subdivided th e four sam ples into bins o f 0.05 dex in stellar m ass. F or any stellar m ass bin, w e identified the sam ple w ith the low est nu m b er o f objects, and then random ly extracted from th e others an equal n um ber o f galaxies. T he stellar m ass distributions o f M P G s in the four S bins and the stellar m ass distribution o f a m ass-m atched sam ple are show n in F ig. C .1 .

A ppendix D: N um ber of M PGs as a function of

£ and

6

for the not m ass-m atched sam ples

In F igs. 5 an d 6 in Sect. 3 w e rep o rt the n um ber o f M PG s as a function o f their 2 an d S for th e m ass-m atched sam ples.

In this appendix w e show th e results for the original sam ples.

In F ig. D.1 filled points show the num bers o f low- and h ig h -2 M P G s in the four S bins, co rrected for the T SR , S SR , an d C S R incom pleteness factors. O pen m a g en ta and cyan points show the sam e, b u t w ith o u t the com pleteness correction factors.

In F ig. D .2 w e show the nu m b er o f low- and h ig h -2 M PG s as a function o f S as in Fig. D .1 , b u t for the tw o subsam ples o f M P G s w ith 1011 M 0 < M < 2X 1011 M 0 (bottom panel) and w ith M > 2 X 1011 M 0 (upper panel). O verall, the trends w e found is sim ilar to the trends derived for the m ass-m atched sam ples.