The VIMOS Public Extragalactic Redshift Survey (VIPERS) : the distinct build-up of dense and normal massive passive galaxies

D O I: 10.1051/0004-6361/201630112

© E S O 2017

The VIMOS Public Extragalactic Redshift Survey (VIPERS)

The distinct build-up of dense and normal massive passive galaxies*

A. Gargiulo1, M. Bolzonella2, M. Scodeggio1, J. Krywult3, G. De Lucia4, L. Guzzo5,6, B. Garilli1, B. R. Granett5,6, S. de la Torre7, U. Abbas8, C. Adami7, S. Arnouts7, D. Bottini1, A. Cappi2,9, O. Cucciati2,10, I. Davidzon7,2, P. Franzetti1, A. Fritz1, C. Haines5, A. J. Hawken5,6, A. Iovino5, V. Le Brun7, O. Le Fevre7, D. Maccagni1, K. Małek11,

F. Marulli10, 12,2, T. Moutard13,7, M. Polletta1,14,15, A. Pollo11, 16, L. A. M. Tasca7, R. Tojeiro17, D. Vergani18, A. Zanichelli19, G. Zamorani2, J. Bel20, E. Branchini21,22,23, J. Coupon24, O. Ilbert7,

L. Moscardini10,12,2, and J. A. Peacock25

(Affiliations can be found after the references) Received 22 November 2016 / Accepted 19 May 2017

Astronomy

&

Astrophysics

ABSTRACT

We have used the final data from the VIPERS redshift survey to extract an unparalleled sample of more than 2000 massive M > 1011 M0 passive galaxies (MPGs) at redshift 0.5 < z < 1.0, based on their NUVrK colours. This has enabled us to investigate how the population of these objects was built up over cosmic time. We find that the evolution of the number density depends on the galaxy mean surface stellar mass density, £. In particular, dense (£ > 2000 M0 pc-2) MPGs show a constant comoving number density over this redshift range, whilst this increases by a factor of approximately four for the least dense objects, defined as having £ < 1000 M0 pc-2. We estimated stellar ages for the MPG population both fitting the spectral energy distribution (SED) and through the D4000n index, obtaining results in good agreement. Our findings are consistent with passive ageing of the stellar content of dense MPGs. We show that at any redshift the less dense MPGs are younger than dense ones and that their stellar populations evolve at a slower rate than predicted by passive evolution. This points to a scenario in which the overall population of MPGs was built up over the cosmic time by continuous addition of less dense galaxies: on top of an initial population of dense objects that passively evolves, new, larger, and younger MPGs continuously join the population at later epochs. Finally, we demonstrate that the observed increase in the number density of MPGs is totally accounted for by the observed decrease in the number density of correspondingly massive star forming galaxies (i.e. all the non-passive M > 1011 M0 objects). Such systems observed at z - 1 in VIPERS, therefore, represent the most plausible progenitors of the subsequent emerging class of larger MPGs.

Key words. galaxies: elliptical and lenticular, cD - galaxies: evolution - galaxies: formation - galaxies: high-redshift

1. Introduction

O ne o f the m o st d ebated issues in m odern astrophysics concerns the form ation and evolution o f passive galaxies (PG s). F ro m a theoretical p oin t o f view, it is still debated w hether these system s assem bled their stellar m ass m ostly by m ergers (e.g. N aab et al.

2 0 0 9 ; Q u e t al. 2017) , o r through o ther “in-situ” processes, such as the accretion o f clum ps through the disc (e.g. D ekel et al.

2009) .

F rom an observational p o in t o f view, deep im aging and dynam ical studies have show n that the PG s already in place a t z ~ 2 have average sizes sm aller than com parable

* 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 Na­

tional de la Recherche Scientifique (CNRS) of France, and the Uni­

versity of Hawaii. This work is based in part on data products pro­

duced at TERAPIX 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 t t p : / / w w w . v i p e r s . i n a f . i t /

galaxies at the cu rrent epoch (C im atti et al. 2 0 0 4 ; D a d d ie ta l. 2 0 0 5 ; T rujillo et al. 2 0 0 6 ; L onghetti et al. 2 0 0 7 ; van D okkum et al. 2 0 0 8 ; C im atti e t al. 2 0 0 8 ; van d er W el e t al.

2 0 0 8 ; B ezanson et al. 2 0 0 9 ; C a s s a ta e ta l. 2 0 1 1 ; B elli e ta l.

2014) . F or exam ple, high-z PG s w ith M ~ 1011 M 0 have an average effective radius o f R e ~ 1 -2 kpc w ith a m ean stellar m ass density £ = M /(2 n R e2) o f 2000 < £ < 6000 M 0 p c -2 w hile local PGs w ith sim ilar stellar m ass have R e ~ 5 kpc and

£ ~ 1000 M 0 p c -2 (e.g. Shen e t al. 2 0 0 3 ; K auffm ann et al. 2003) T hese d ata have been w idely interpreted w ithin a two- phases scenario (com m only called “inside-out” ). D uring the first phase, a highly dissipative process (e.g. a gas-rich m erger; H opkins e t al. 2008) o r in situ accretion o f cold stream s (K eres et al. 2 0 0 5 ; D ekel et al. 2009) form s the com pact passive cores w e observe a t high redshift. Subsequently, as tim e goes by, this com pact galaxy assem bles an external an d low -density halo through m any dry m in o r m ergers. T he overall effect o f these m ergers is to increase the galaxy radius till it m atches the typical dim ension o f a local P G (e.g. N aab e t al. 20 0 7 , 2 0 0 9 ; H ilz e t al.

2 0 1 3 ; van D okkum et al. 2008) .

This scenario is supported by the drastic decrease (m ore than tw o orders o f m agnitude) in th e n u m b e r density o f com pact P G s over tim e, observed in som e studies (e.g.

C a s s a ta e ta l. 2 0 1 3 ; van der W el e t al. 2014) . H owever, other

Article published by EDP Sciences A113, page 1 o f 14

idence highlights the necessity o f a hom ogeneous analysis over the cosm ic tim e to draw robust conclusions on this relevant issue.

E v idence shows th at in conjunction w ith an increase in the m ean radial size o f PGs b y a factor o f ~ 4 from z ~ 1 .5 - 2 to z = 0, th e n um ber o f PGs p er unit volum e increases by a factor o f approxim ately ten (e.g. P ozzetti et al. 2 0 1 0 ; Ilbert e t al. 2 0 1 0 ; B ram m er et al. 2011) . If the n u m b er density o f high-z d ense PGs drastically falls, as observed by som e authors, b ecause they in ­ crease their size, their contribution to the w hole population o f local PGs w ould have to b e less then 10%, since high-z PGs are ten tim es less num erous than local PGs. C onsequently, the m a ­ jo rity o f local PG s w ould n ee d to have fo rm ed through a m e ch a­

nism other than the inside-out m odel. O n th e other hand, if all lo ­ cal PG s w ere assem bled according to th e inside-out m odel, new com pact PG s w ould need to form continuously at z < 1 .5 -2 and then increase th eir sizes in o rder to sustain th e num erical grow th o f the w hole population. This p icture could help to ex ­ p lain the w orks that show a m ild o r n ull evolution in the num ber density o f com pact PG s. However, if this w ere th e case, further evidence w ould b e expected: the ag e o f dense PGs should not evolve significantly over tim e, since this sub-population w ould be constantly re fre sh ed b y new galaxies. In fact, if the num ber density o f com pact PG s is confirm ed to evolve slowly, a third h y ­ pothesis is also viable: com pact PG s m ig h t passively age and the increase b oth in m ean R e and in the n u m b er o f PG s over the tim e could then m ostly b e due to the fact th at galaxies th at quench at later epoch are larger (e.g. V alentinuzzi e t al. 2 0 1 0 ; C im atti et al.

2 0 0 8 ; C arollo e t al. 2013) . It is com m on habit to refer to this last scenario as p rogenitor bias (e.g. F ranx & van D okkum 1996) . In this p icture the age o f the stellar population o f com pact PGs over cosm ic tim e should b e consistent w ith passive evolution. Thus, valuable insights into the build up o f th e P G population can be gained by studying th e evolution o f the nu m b er density and the age o f the stellar p opulation together.

In this context, m assive ( M > 1011 M 0 ) PG s (M PG s) deserve p articular attention. T hese system s are expected to evolve m ainly through (dry) m ergers (e.g. H opkins et al. 2 0 0 9 ; D e L u cia & B laizot 2007) . I f this is th e case, in this m ass range w e should detect a stronger signal o f the size-grow th w ith r e ­ spect to a low er m ass range. So far, b ecause M P G s are ex ­ trem ely rare, there have been very few studies that have investi­

gated the com bined evolution o f the nu m b er density and o f the age o f M P G s as a function o f their com pactness (C arollo et al.

2 0 1 3 ; F a g io lie ta l. 2016) . C arollo e ta l. (2013) found th at the nu m b er density o f m assive quiescent and elliptical galaxies w ith R e < 2.5 kpc decreases b y ab o u t 30% from z ~ 1 to z ~ 0.2 an d th at th eir U - V colours are consistent w ith p a s­

sive evolution. T hey concluded th at the driving m echanism for the average size-grow th o f the w hole population is th e appear­

ance at la ter epochs o f larg er quiescent galaxies. M ore recently,

the authors suggest th at this class o f objects are the progenitors o f com pact quiescent galaxies. T hey conclude that a substantial fraction o f dense quiescent galaxies at z < 0.8 are new ly form ed.

D espite the efforts an d im provem ents o f re c e n t years, the overall p icture is far from clear. W h at is still m issing is a h o m o ­ geneous analysis o f the n um ber density and stellar population age at z ~ 0.8, th at is over th e red sh ift ran g e w here less co m ­ p act M P G s start to dom inate the U niverse (e.g. C assata e t al.

20 1 0 , 2013) . F or this goal to be achieved the follow ing three requirem ents m u st b e m et: significant sam ples o f M P G s at d if­

ferent redshifts, in o rder to have good statistics in each red sh ift and 2 bin; a large volum e to m inim ise the effect o f th e cosm ic variance (w hich is know n to affect the C O S M O S field); ro b u st estim ates o f the ages o f stellar populations.

T he V IM O S P ublic E x tragalactic R ed sh ift S urvey (V IPER S) represents an ideal b en ch m ark for this k in d o f study. D esp ite the fact galaxies w ith M > 1011 M 0 are rare, the w ide area (~ 1 6 ef­

fective deg2 over the W 1 and W 4 CFH TLS fields, m o re details in Sect. 2) and high sam pling rate o f the survey (~ 40% ) result in a sam ple o f ~ 2 0 0 0 M P G s w ith spectroscopic redshifts over the red sh ift ran g e 0.5 < z < 1.0 (see Sect. 2). T he unprecedented quality o f statistics over this re d sh ift ra n g e allow s us to study the evolution o f th e n um ber density o f M P G s as a function o f 2 (see Sect. 4). U sing D 4 000n as a spectroscopic d iagnostic and b y fitting the spectral energy distribution (SED ) w e constrained the age o f the stellar p opulation o f M P G s as a function both o f z and 2 (Sect. 5). This inform ation, together w ith th e evo­

lution o f the n um ber density, allow ed us to p u t constraints on the m ass accretion scenarios and on the origin o f new M PG s (Sect. 6). W e sum m arise all o f ou r results in Sect. 7. T h rough­

out the pap er w e ado p t the C habrier (2003) initial m ass fu n c­

tion (IM F) and a flat cosm ology w ith Q m = 0.3, Q a = 0.7 and H 0 = 70 k m s -1 M p c-1 . M agnitudes are in th e AB system . E f­

fective rad ii are circularised, m eaning that R e = Vob, w here a and b are th e sem i-m ajor and sem i-m inor axis o f the isophote containing h a lf o f th e total light, respectively.

2. Data

2.1. The VIPERS project

In this w ork w e analyse a b eta version o f th e final p ublic d ata re ­ lease o f V IPE R S. T he data set used here is alm ost identical to the publicly released P D R -2 catalogue (S codeggio e t al. 2017) , w ith the exception o f a sub-set o f a few redshifts (m ostly a t z > 1.2), w hich w ere rev ise d close to the re le ase date. This has no ef­

fect on the analysis p resented here. V IPER S has m easured red- shifts for 89 128 galaxies to iAB = 22.5, distributed over a total area o f 23.5 deg2. This reduces to an effective area o f 16.3 deg2 once detector gaps an d m asked areas such as those w ith bright

stars are accounted for. S pectroscopic targets w ere selected in the W 1 and W 4 fields o f the C anada-F rance-H aw aii Telescope L egacy Survey (C F H T L S ) W ide. T he star-galaxy classification criterion was defined after extensive tests on the V V D S sur­

vey (L e F evre e t al. 2 0 0 5 ; G a r illie ta l. 20 0 8 , 2014) . In detail, stars w ere classified as those system s w ith i) iAB < 21 and rh <

jurh + 3 ^ rh o r ii) ;'ab » 21, rh < jurh + 3 ^ rh and l o g ^ ^ a r ) <

lo g 10(xgal) + 1, w here rh is the h alf-light radius as derived from SE xtractor (B ertin & A rnouts 1996) , jurh and <rxh are the m ean and standard deviation o f the rh distribution, w hile Xtar and ^ g al are the x 2 o f the SED fitting applied to the ugriz C F H T LS p h o ­ tom etry. A robust colour-colour pre-selection in the u g ri plane was used to identify galaxies at z > 0.5. In particular, am ong all o f the objects classified as galaxies, w ere flagged as spectro­

scopic target those w ith:

(r - i) > 0.5(u - g) V (r - i) > 0.7. (1) S pectroscopic observations w ere carried o u t w ith V IM O S a t the VLT using the low -resolution red g rism (R - 220), w hich covers the w avelength range 5 5 0 0 -9 5 0 0 A. T he rm s error o f th e m e a­

sured redshifts has been estim ated to b e ^ z(z) = 0.00054 x (1 + z) (S codeggio e t al. 2017). In the sam e paper, a com plete descrip ­ tion o f the P D R -2 data rele ase can be found, w hile m o re infor­

m ation on the original survey design and data reduction p ro ce­

dures are found in G uzzo et al. (2014) and G arilli et al. (2014).

F or each galaxy o f th e V IPER S spectroscopic sam ple, p h y s­

ical properties such as the m ulti-band lum inosity and th e total stellar m ass w ere derived through the SED fit. T he p h o to m et­

ric m ulti-w avelength coverage com bines im proved ugriz-bands photom etry b ased on th e T 0007 release o f the C F H T L S 1 and K s-band observations from the V IPER S M u lti-L am bda Survey (V IP E R S -M L S 2, M o u tard e t al. 2 016a) or, w hen available, from the VISTA D eep E x tragalactic O bservations (V ID EO ; Jarvis et al. 2013) survey (m ore details in D avidzon e t al. 2 0 1 3 , 2 0 1 6 ; M outard et al. 2016b) .

T he fit w as p erform ed w ith the H yperzm ass softw are (B olzonella et al. 2000) . T he tem plate libraries adopted in the fit p rocedure are fully described in D avidzon e t al. (2013) and are b ased on B ruzual & C harlot (2003) m odels, w ith exponen­

tially declining star form ation history ( ^ e -t/T, w here t is the tim escale o f the star form ation), t in the ran g e [0.1-30] Gyr, sub­

solar (0.2 Zq) and solar m etallicity, and th e C habrier (2003) IMF.

T he im pact o f d u st extinction on the in put galaxy tem plates was m odelled according to tw o different prescriptions (C alzetti et al.

2 0 0 0 ; P revot e t al. 1984) w ith th e extinction param eters A V ra n g ­ ing from 0 (no dust) to 3 m ag.

T he structural param eters (effective radius Re, S ersic index n) for - 8 5 % o f the V IPER S sources w ere derived w ith G A LF IT (Peng et al. 2002) fitting th e i-band C H F T L S -W ide im ages w ith a 2 D -p sf convolved S ersic profile (K ryw ult et al. 2017) . The C FH TLS p u b lic im ages have a p ixel-scale o f - 0 .1 8 7 " /p x and the full w idth at h a lf m axim um (FW H M ) o f point-like sources varies from - 0 .5 " to 0 .8 " in the i band. To control the variability o f the P SF over th e w ide C C D area o f CFH TLS im ages (1° x 1°) K ryw ult e t a l. (2017) selected a set o f - 2 0 0 0 stars uniform ly distributed over each field and m odelled their profiles using a 2D C hebychev approxim ation o f the elliptical M offat function.

This approach allow ed the P S F to b e successfully described over - 9 5 % o f th e w hole V IPER S area. O nly regions w ithout b right and u nsaturated stars, or at the edge o f the im ages (hereafter b ad 1 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 /

2 h t t p : / / c e s a m . l a m . f r / v i p e r s - m l s /

P S F regions) w ere excluded. Since these regions are w ell d e­

fined, w e have rem oved them from ou r analysis. Taking this into consideration the effective final area w e used in this analysis is - 1 4 deg2.

K ryw ult et al. (2017) tested th e reliability o f R e and n derived from ground-based C FH TLS im ages. T hey found th at the typical effective galaxy radius is recovered w ithin 4.4% and 12% for 68% an d 95% o f the total sam ple respectively. W e re fe r to their pap er for further details.

2.2. The sample o f massive passive galaxies

F rom the V IPER S spectroscopic catalogue w e selected all g alax ­ ies w ith highly accurate red sh ift m easurem ents, i.e. w ith quality flag 2 < z f l a g < 9.5 (a confidence level >95% ; 7 5 4 7 9 g alax ­ ies in th e W 1 + W 4 field). W e defined galaxies as passive on the basis o f th eir location in the rest-fram e colour N U V -r vs.

r-K diagram , w hich is a pow erful alternative to the U V J d ia ­ gram (W illiam s e t al. 2009) to p roperly identify passive galaxies (for m o re details see A rnouts e t al. 2 0 1 3 ; D avidzon et al. 2 0 1 6 ; M outard e t a l. 2 0 1 6 a,b ) . Follow ing D avidzon et al. (2016), w e defined quiescent galaxies as those satisfying the follow ing conditions:

N U V - r > 3.75, (2)

N U V - r > 1.37 x (r - K ) + 3.2, (3)

r - K < 1.3. (4)

A m ong all galaxies satisfying these three conditions (7606 in W 1 and 3939 in W 4, respectively) - 9 5 % have sSFR <

10-11 y r-1 . F ro m th e quiescent population w e selected the sub­

sam ple w ith M > 1011 Mq (hereafter M P G s; 1905 galaxies in the W 1 field, and 902 in W 4) w hich is com plete up to z = 1.0 (see e.g. D avidzon e t al. 2 0 1 3 ; F ritz e t al. 2 0 1 4 ; D avidzon e t al.

2016) . B elow z = 0.5, V IPER S is highly incom plete due to the ugri colour cuts im posed in th e selection o f spectroscopic tar­

gets. Thus the follow ing analysis is lim ited to the red sh ift range 0.5 < z < 1.0. Finally, w e excluded from ou r analysis galaxies th at are in b ad P SF regions (see Sect. 2.1). T hese further cuts leaves us w ith a sam ple o f 2022 M PG s.

F or each o f these galaxies w e need to derive its m ean stel­

lar m ass density 2 . In the red sh ift ran g e 0.5 < z < 1.0, the i- b an d filter covers th e spectral region across the 4000 A break.

In particular, it sam ples the - V - b a n d (5000 A) rest-fram e at z = 0.5 and the - U - b a n d (3500 A) rest-fram e a t z = 1.0.

G iven the p resence o f radial colour variations in passive galaxies both at high and low red sh ift (see e.g. L a B arbera & de Carvalho 2 0 0 9 ; S aglia e t al. 2 0 1 0 ; G argiulo e t al. 2 0 1 2 ; G uo et al. 2011), the variation o f the rest-fram e b an d used to derive R e can induce a spurious tren d in the evolution o f the radius w ith redshift. To quantify this bias, the structural param eters for the w hole W 4 field (and for - 4 0 % o f th e W 1 field) have been derived in th e r- b an d (F W H M - 0 .8 ", - U - b a n d rest-fram e a t z < 0.8). F igure 1 shows the ratio betw een the Re o f M P G s in the r and i b and (Re,r/R e,i) as a function o f their R ej a t z < 0.8. F o r a rigorous an al­

ysis, w e derived the relations in three finer red sh ift bins (0.5 <

z < 0 .6 ,0 .6 < z < 0 .7 ,0 .7 < z < 0.8). T he general trend, as derived from the best-fit relations, is that for M P G s R ei < R e,r , m eaning th at the internal regions are redder than the outskirts, as expected for passive system s (e.g. L a B arbera & de C arvalho 2009) . F or the sm allest galaxies the difference betw een the tw o rad ii can be up to - 2 0 % . W e n o te th at a portion o f M P G s (especially at large

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Fig. 1. Ratio between the effective radius in r band (Rer) and the effective radius in i band (Re i) as a function of Rei for MPGs in three bins of redshift as indicated in the top left corner of each plot. In the three panels, the solid blue lines are the best fit relations derived with a sigma-clipping algorithm. Dashed blue lines set the 1ix deviation. The typical dimension of half of the PSF-FWHM of both i-band and r-band images is indicated in the top right corner of each plot with also the number of objects. Open red circles are galaxies at >3ix from this fit.

Fig. 2. Fraction of MPGs with available Re in the W1 field (magenta filled points), in the W4 field (blue filled points) as a function of z. At z < 0.8, MPGs with Re derived from i-band images are included. Red filled points indicate the completeness for the W1+W4 field.

R e) has R ei > R e,r , suggesting the presence o f a b lu e core. H ow ­ ever, a d etailed study on the internal colour variation in M P G s is beyond the scope o f this paper. G iven the evidence p resented in Fig. 1, in the derivation o f 2 w e referred to th e effective radius in the r b an d for M P G s at z < 0.8, an d to R e in the i b an d for those at z > 0.8. B y doing this, w e w ere able to approxim ately sam ­ p le the sam e U b an d rest-fram e over the w hole red sh ift range w e probe. F or those M P G s at z < 0.8 w ithout an R e,r estim ate (m ostly in th e W 1 field), w e estim ated R ej using the relations o f F ig. 1. W e checked th at the addition o f galaxies w ith R e,r d e­

rived from R e i does n o t change the 2 distribution o f the sam ple o f M P G s at z < 0.8.

In F ig. 2 w e show the fraction o f M P G s w ith available and reliable structural param eters for W 1 an d W 4 fields and for the total area as a function o f redshift.

O verall, ~ 85% o f M P G s in the tw o fields have a reliable R e.

F or ~ 15% o f M P G s structural param eters are n o t available since in som e cases w e are u nable to fit th e surface brightness profile.

T his is either b ecause the algorithm does n o t converge, m ostly because o f very close com panions, o r th e best-fit values o f n

< 0.2 are unphysical (see K ryw ult e ta l. 2017) . O nce these o b ­ jects have been excluded, the final sam ple o f M P G s w ith re li­

able R e (hence 2 ) in the red sh ift ran g e 0 .5 -1 .0 is com posed o f 1758 galaxies.

Table 1. Best-fit values (a, p ) of the size mass relation log Re = a lo g (M /1 0 11) + p o f VIPERS MPGs.

z a

p

0.5 < z < 0.7 0.59 ± 0.07 0.60 ± 0.01 4.0 0.7 < z < 0.9 0.70 ± 0.08 0.53 ± 0.02 3.4 0.9 < z < 1.0 0.52 ± 0.10 0.52 ± 0.02 3.3

Notes. Re11 indicates the value of Re at M = 1011 M0 as predicted by the best-fit relation.

3. The size mass relation of MPGs in VIPERS for 0.5 < z < 1 .0

In Fig. 3 w e show th e SM R for the V IPER S M P G s in the low ­ est and highest red sh ift bins o f ou r sam ple, th at is 0.5 < z <

0.7 and 0.9 < z < 1.0. W e fitted a SM R o f M PG s o f the form log Re = a log ( M /1 011) + p adopting an ordinary least squares fit w ith o u t taking into account errors on Re. T he best-fit re ­ sults are reported in Table 1. W e also added th e resu lt for the interm ediate bin (0.7 < z < 0.9). In agreem ent w ith previous studies (e.g. D am janov e t al. 2 0 1 1 ; van der W el et al. 2014) , w e find th at a t 1^ there is alm ost n o evolution o f the slope o f the SM R w ith tim e. H owever, there is an offset am ong the zero- points. O n average, at fixed stellar m ass, M P G s at (z) = 0.6 have Re ~ 1.25 larger than those a t z = 1.0. This increase shows th at th e grow th in th e m ean Re o f the passive p o p u la­

tion is gradual and continuous, extending o u t to z < 1. The increase in Re is in agreem ent w ith w hat has been found by other authors. D am janov et al. (2011) , for a sam ple o f early- type galaxies at 0.2 < z < 2.7, found (Re) ^ (1 + z)-L62±0'3 4, independently o f the stellar m ass o f the galaxy, that is an in ­ crease b y a factor ~ 1.4 ± 0.1 in the red sh ift ran g e 0 .6 -1 .0 . S im ­ ilarly, W illiam s e ta l. (2010) found (Re) ^ (1 + z)-1 3 for p a s­

sive galaxies (U V J selected) w ith M > 1011 M 0 w hich results in an increase o f a factor ~1.3 in our red sh ift range. F ro m the analysis o f passive galaxies (U V J colour selected) w ith M >

2 x 1010 M 0 , van der W el e t al. (2014) found (Re) ^ (1 + z)-1 4 8

over the red sh ift ran g e 0 < z < 3, still in fair agreem ent w ith our results.

In F ig. 4 w e directly show th e distribution o f Re o f M P G s in the sam e red sh ift bins as Fig. 3 . A lthough the tw o distributions are significantly different (KS te st probability <10-8), the figure

Fig. 3. Size-mass relation of passive VIPERS galaxies (grey open + red open points) in the two extrem e redshift bins o f our analysis (0.5 < z <

0.7 in the lower panel, and 0.9 < z < 1.0 in the upper panel). Blue open points are the MPGs analysed in this paper (vertical lines indicate the mass cut). Horizontal lines indicate half o f the FW H M at that redshift, while m agenta lines are the best fit o f the size-mass relation o f MPGs.

Black diagonal lines are lines o f constant £ (2000 and 1000 M0 pc-2).

Fig. 4. Distribution of the effective radius for MPGs in our lowest (blue histogram) and highest (red histogram) redshift bins. The solid lines indicate the median values of the two distributions. The probability p that the two distributions are extracted from the same parent sample are reported in the label.

shows that they cover th e sam e ran g e o f R e. This suggests that the p opulation o f com pact M P G s does n o t totally disappear w ith cosm ic tim e. In the next section w e w ill q uantify this qualitative trend b y estim ating the com oving n um ber density o f M P G s w ith different 2.

4. The number density of MPGs in VIPERS as a function of redshift and mean stellar mass density

In o rder to derive the n um ber density o f the M P G s as a function o f £ w e subdivided ou r sam ple into a “h igh-£

Table 2. Total number of massive quiescent galaxies and of the high-£

sample, interm ediate-£ sample, and low -£ sam ple in the four redshift bins 0.5 < z < 0.7, 0.7 < z < 0 .8 ,0 .8 < z < 0.9, 0.9 < z < 1.0.

z Ntot

Nhigh-£ Nint-£ Nlow-£

0 .5 -0 .7 782 165 185 352

0 .7 -0 .8 482 144 128 163

0 .8 -0 .9 386 103 92 116

0 .9 -1 .0 372 112 97 101

Notes. A t each redshift the sum of the high+interm ediate+low £ galax­

ies is sm aller than the total number of objects since not all the MPGs have a reliable Re.

sam ple” , consisting o f galaxies w ith £ > 2000 M 0 p c -2 , an

“in te rm e d ia te d sam ple” , consisting o f galaxies w ith 1000 < £ <

2000 M 0 p c -2 , an d a “lo w -£ sam ple” consisting o f galaxies w ith

£ < 1000 M 0 p c -2 . T he choice o f a cu t a t 2000 M 0 p c -2 was d e­

term ined b y the characteristics o f the C F H T LS im ages. In F ig. 3, the horizontal solid lines indicate h alf o f th e F W H M o f the PSF.

W e n o te th at all the M P G s w ith R e below h a lf the F W H M o f the im ages, at any redshift, have £ > 2000 M 0 p c -2 . A dopting this cu t ensures th at all galaxies w ith rad ii low er than th e resolution o f the im age (i.e. galaxies for w hich R e could b e overestim ated), are in th e sam e £ bin an d do n o t spuriously contam inate other bins. W e stress that this is a conservative choice. Effective radii are derived b y deconvolving the data for the real P SF o f th e im ­ ages. A t the typical S/N o f our galaxies, m easurem ents o f R e low er than the im age resolution are ro b u st as show n in the A p ­ pendix o f K ryw ult et al. (2017) .

In Table 2 , w e list th e total n um ber o f galaxies in each bin o f stellar m ass density, and for each red sh ift bin. T heir sum is sm aller than the total n um ber o f galaxies (Col. 1, Table 2) since for a fraction o f galaxies w e do n o t have a reliable estim ate o f their structural param eters (see Sect. 2.2).

T he V IPER S final sam ple (and hence ou r final sam ple o f M P G s) suffers from three sources o f incom pleteness. T hese are the target sam pling rate (TSR ), the success sam pling rate (SSR), and the colour sam pling rate (CSR). T he T S R is given by the ratio o f galaxies effectively observed w ith resp ect to th e p h o to ­ m etric paren t sam ple. T he SSR is the fraction o f spectroscopi­

cally observed galaxies w ith a red sh ift m easurem ent. T he C S R takes into account the com pleteness due to the colour selection o f th e survey. T hese statistical w eights (hereafter TSR(i), SSR(i), CSR(i)) depend on th e m agnitude o f the galaxy, on its redshift, colour, 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 e t al. 2 0 1 4 ; S codeggio e t al. 2017) . In the derivation o f the n um ber density, w e w eighted each M P G i in o ur sam ple b y the quantity w(i) = 1/(TSR (i)*SSR (i)*C SR (i)).

B esid e these sources o f incom pleteness, a fraction o f M PG s is lacking reliable structural param eters. In F ig. 2 w e show this fraction as a function o f redshift. W e checked w hether the galaxies w ith o u t structural param eters belong m ainly to a sub­

population o f galaxies o f a given £ . To address this issue, w e com pared the fraction o f high-, interm ediate- an d lo w -£ M PG s in different red sh ift bins (w hich have different levels o f co m ­ pleteness). W e d id n o t find any significant variation betw een red- shift bins. G iven th at there is n o dependence o f the lack o f struc­

tural param eters on £ (or vice versa), w e corrected the num ber densities o f M P G s for this source o f incom pleteness, using the values in Fig. 2 .

In F ig. 5 w e show the n um ber density o f M PG s as a function o f red sh ift an d m ean stellar m ass density, both in th e W 1 and W 4

A113, page 5 o f 14

Fig. 5. Number densities for massive passive galaxies with £ > 2000 M0 pc^-2 (right panel, dark red symbols), 1000 < £ < 2000 M0 p c^-2 (central panel, orange symbols), and £ < 1000 M0 pc^-2 (left panel, green symbols), for the W1 field (filled circles) and W 4 one (open circles). Number densities for the W 4 field are shifted in redshift to better visualize them. The error bars correspond to 1ix.

fields. E rro r bars w ere derived taking into consideration Poisson fluctuations, and the uncertainties on the Re estim ates. To co n ­ sider this last source o f uncertainty, w e com puted the standard deviation <r(z, £ ) over 100 n um ber density estim ates obtained by replacing for each galaxy the effective radius R^e w ith a value random ly draw n from a G aussian distribution w ith m ean value Re and standard deviation the typical erro r on Re (i.e. 0.05 Re, see Sect. 2.1).

T he estim ates o f the n um ber density in the W 1 and W 4 fields are in very good agreem ent, indicating th at th e w ide area o f V IPER S reduces the effect o f cosm ic variance even fo r the m ost m assive galaxy sam ple. This resu lt is in agreem ent w ith the ex ­ pected cosm ic variance o f ~ 10% derived for V IPER S m assive galaxies in D avidzon et al. (2013) . In Fig. 6 w e rep o rt the n u m ­ ber d ensity o f M P G s as a function o f £ (plus th e n um ber density for the w hole population o f M P G s) in the total V IPER S area (W1 + W 4). E rro r bars are derived as described above. T he evo­

lution o f the n u m b er density o f th e w hole population o f M PG s is w ell fitted b y a function p k (1 + z)a, w ith a = - 3 .3 ± 0.9.

In the ~ 2 .5 G yr from z = 1.0 to z = 0.5, th e n um ber density o f M PG s increases b y a factor ~ 2 .5 . Sim ilarly, w e fitted th e num ber density evolution o f the three sub-populations w ith a p ow er law, and found a = - 5 .0 ± 0.4 for lo w -£ M P G s, a = - 1 .8 ± 0.7 for in te rm e d ia te d M P G s and a = - 0 .7 ± 0.9 for h ig h -£ M P G s. W e find th at th e evolution o f the n u m b er density strongly depends on th e m ean stellar m ass density o f the system . In particular, the low er the m ean stellar m ass density, the faster the evolution. The n u m b er density o f the densest M P G s is approxim ately constant over th e w hole red sh ift range, w hile th e n u m b er density o f less dense M P G s constantly increases w ith tim e b y a factor o f ap ­ proxim ately four.

F igure 6 show s th at w e are looking at a crucial m o m en t in the b u ild up o f the M P G population, that is w hen less com pact galaxies, w hich constitute the b ulk o f th e local M P G population, start to dom inate. In fact, at z > 0.8, the population o f M P G s is com posed in equal parts o f high, interm ediate and lo w -£ g alax ­ ies. A t low er redshift, the contribution o f lo w -£ M P G s steadily increases. A t z = 0.5 com pact quiescent galaxies account for ju s t

Fig. 6. Number density o f MPGs with different mean stellar mass den­

sity in VIPERS field as a function o f the redshift. D ark red triangles refer to high-£ M PGs, orange circles refer to interm ediate-£ MPGs, and green squares to low -£ M PGs. Black circles show the num ber den­

sity for the total sample o f MPGs. N umber densities for the three sub­

populations are shifted in redshift to better visualize them. The error bars correspond to 1ix. We fitted the data with a power law and solid lines are the best-fit relations.

~15% o f the w hole population. L ess com pact system s, on the o ther hand, account fo r m o re than h a lf o f the w hole population.

This resu lt is in agreem ent w ith the analysis by C assata e t al.

(2011) w ho found th at n orm al (i.e. less dense) passive (sSFR <

10-11 y r-1) and elliptical galaxies w ith 1010 < M < 10115 M 0 start to becom e the dom inant sub-population at z ~ 0.9.

O ur results are in good agreem ent also w ith C arollo et al.

(2013) w ho found that the nu m b er density o f passive (sSFR <

10-11 y r-1) and elliptical galaxies w ith M > 1011 M 0 and R e <

2.5 k p c decreases b y ~30% in the 5 G y r betw een z ~ 1 and z ~ 0.2. D am janov e t al. (2015) found an alm ost co nstant num ber density over the red sh ift ran g e 0.2 < z < 0.8 for colour selected passive com pact galaxies w ith M > 8 x 1010 M 0 . G argiulo et al.

(2016) found p(z) ^ (1 + z)0'3±0'8 for a sam ple o f m orp h o lo g i­

cally selected elliptical dense galaxies (2 > 2500 M 0 p c -2) w ith M > 1011 M 0 in the red sh ift ran g e 0 < z < 1.6, consistent w ith our results. C assata e t al. (2013) found a very m ild decrease o f com pact galaxies ( 1 ^ below the local SM R ), and a m ild increase in the nu m b er density o f n orm al galaxies (consistent a t 1 ^ w ith the local SM R ) from z ~ 1 to z ~ 0.5, in qualitative agreem ent w ith our results. H ow ever, they found th at the n um ber density o f u ltra-com pact galaxies (0.4 dex sm aller than local SDSS c o u n ­ terparts o f the sam e m ass) dram atically decreases. A detailed com parison w ith our results is n o t possible given the different selection o f th e sam ples. N onetheless, w e verified th at the co n ­ stant trend for h ig h -2 M P G s w e show in F ig. 6 is n o t rela ted to the adopted cu t 2 = 2000 M 0 p c -2 . W e estim ated the num ber density for the sub-sam ple o f M P G s w ith 2 > 3000 M 0 p c -2 and 2 > 4000 M 0 p c -2 and found a = - 0 .5 ± 1.4 and a = - 1 .3 ± 1.5.

T hese results are co nsistent a t 1 ^ w ith th e results w e found for the h ig h -2 sub-population.

I f th e global population o f dense passive galaxies w ere to evolve in size, then in o rder to m aintain a constant n um ber d en ­ sity o f th e com pact sub-population over cosm ic tim e, new dense galaxies w ould have to appear at low er redshift. In particular, the tim escale o f th e size-grow th m echanism s and th at o f the ap ­ pearance o f new dense m assive quiescent galaxies w ould need to b e very sim ilar (e.g. C arollo et al. 2013). T he other possibility is th at the d ense M P G s passively evolve w ithout changing their structure. O ne w ay to discrim inate betw een these tw o p o ssib ili­

ties is to study o f the age o f the stellar population as a function o f th e m ean stellar m ass density.

5. The stellar population age of MPGs as a function of the redshift and mean stellar mass density F or any individual galaxy, w e constrained its stellar population age fitting th e p hotom etric SED (ageSED). Since w e are aw are o f the age-m etallicity degeneracy w hich can affect the SED fitting estim ates, w e adopted th e independent m easurem ents o f D 4 000n to validate our conclusions.

T he D 4 000n index (B alogh et al. 1999) is an age sensitive spectral feature (K auffm ann et al. 2003) defined as the ratio b e ­ tw een the continuum flux densities in the blu e region [3850­

3950] A and re d region [4000-4100] A across the 4000 A break:

D 4000„ =

. \ rred

(T2lue - F y dT

/ \ Tblue

( 4 ed - T f U b L Fv dT

(5)

A com plete description o f the D 4 000n m easurem ents for V IPER S galaxies is presen ted in G a r illie ta l. (2014) . S iu d e k e ta l. (2017) , using stacked spectra, have already investigated the star form ation epoch o f all o f V IPER S passive galaxies through th e analysis o f both the D 4 000n and th e H L ick index. T he authors selected passive galaxies using an evolving cu t in the rest-fram e U - V colour and found that, over the full analysed red sh ift and stellar m ass ran g e (0.4 < z < 1.0

and 10 < lo g (M /M 0 ) < 12, respectively), the D 40 0 0 n index increases w ith redshift, w hile H gets lower. H ere, instead o f looking for trends o f D 4 000n w ith stellar m ass and z, w e focused our analysis on a given stellar m ass bin, and investigate w ithin this bin th e tren d o f D 4 000n w ith 2 and z. W e selected M PG s w ith the error on D 4 000n sm aller than 8% in order to restrict the analysis to galaxies w ith a highly accurate estim ate o f D 4 000n.

This criterion further reduces the sam ple b y ~ 10% , b u t does not alter th e distribution in 2 . F igure A.1 shows how th e conversion o f the D 4 000n into a stellar p opulation age depends both on m etallicity Z and on the tim escale t o f the star form ation o f the galaxy (w e re p o rt the trend in the case o f an exponentially declining star form ation history). G iven the spectral coverage and reso lu tio n o f our spectra, w e can accurately m easure D 4 000n for each individual galaxy but conversely w e cannot constrain either Z o r the tim escale. Instead o f m aking a blin d assum ption o f Z and t, w e exploited th e capabilities o f our spectroscopic+ photom etric dataset. W e firstly constrained the evolution o f stellar p opulation ages as derived from SED fitting.

Starting from the best-fit m odels o f the SED , w e derived the m ean value o f AgeSED(z, 2 ) for M P G s in each bin o f z and 2 and investigated its evolution over the cosm ic tim e. S ince the estim ate o f the A ge from the SED fitting cou ld b e biased by the age-m etallicity degeneracy, w e com pared the predictions w e obtained w ith the in dependent m easurem ents o f stellar population ages obtained b y the spectroscopic index D 4 000n.

In details, together w ith AgeSED(z, 2 ), w e derived ZSED(z, 2), and t sed(z, 2 ) from the best-fit m odels o f the SED. U sing low -resolution (lr) BC 03 m odels (i.e. the sam e as those used to p erform th e SED fitting), w e derived the D 4 000n corresponding to these m ean values, D 4 000n,SED(z, 2 ), and com pared these estim ates w ith the m ean value o f th e distribution o f D 4 000n o f all o f the M P G s in th at bin o f z and 2 . F or sim plicity w e focus this p art o f o ur analysis on the tw o extrem e 2 sub-populations, the lo w -2 an d h ig h -2 M P G s. R esults for in term ed iate-2 M PG s are in betw een.

In Fig. 7 filled points show th e m ean values o f AgeSED and th e m ean value o f D 4 000n (left an d rig h t panels, resp e c­

tively) o f lo w -2 (green filled squares) and h ig h -2 (dark red tri­

angles) M P G s. E rro r bars indicate th e error on the m ean. The le ft panel o f F ig. 7 shows th at for h ig h -2 M P G s the evolution o f the stellar population ages derived from the SED fitting is consistent w ith a passive evolution o f the population. In fact, their A geSED increases b y ~ 2 G yr during the 1.8 G yr o f evo­

lution betw een z = 0.95 and 0.6. A t any redshift, th e m ean value o f the tim escale o f star form ation t, as constrained b y the SED fitting, is ~ 0 .4 Gyr, and the best-fit m odels have a m ean Z ~ 0.5 ± 0.3 Z0 3. U sing these constraints on age/T/Z and BC03 m odels, w e derived D 40 0 0 n,SED. A ctually, BC 03 m odels provide the theoretical SED fo r discrete values o f Z (e.g. Z = 0.2 Z0 , 0.4 Z0 , Z0 ). Thus, to derive th e D 4 000n,SED w e interpolated the estim ates o f the tw o m odels w hich encom pass the m ean values o f Z. T he resolution o f BC 03 lr m odels is 20 A w hile V IPER S spectra have a resolution o f ~ 17 A around the 4000 A break. U s­

ing th e high reso lu tio n (3 A) BC 03 m odels w e verified th at this difference affects the D 4 000n by ~0.01 (see A ppendix A). This is w ell b elow the typical error on D 4 000n and for this reason w e did n o t correct for it. T he values o f D 40 0 0 n,SED are show n in the rig h t h and p an el o f F ig. 7 w ith open dark re d triangles. T hey are

3 We caution that this value refers to the whole galaxy, not just to the central region known to have Z > ZSun (e.g. Gallazzi et al. 2005). This value is in agreement with the mean metallicity within Re of local mas­

sive ETGs (0.7+015 Z0, see Appendix C).

A113, page 7 o f 14

Fig. 7. Le ft panel: m ean stellar population ages of MPGs as derived from the SED fitting as a function of redshift and mean stellar mass density for high- and low-E M PGs (filled points). The colour and symbols code is the same as in Fig. 6. Error bars indicate the error on the mean. Points refer to the redshift bins 0.5 < z < 0.7,0.7 < z < 0.9, 0.9 < z < 1.0. The arrows track the increase o f the ages in case o f passive evolution from z = 0.95 to z = 0.6. Right panel: filled points: the m ean values o f D4000n directly m easured on spectra for M PGs w ith different E (symbol and color code the same as in the left panel). Open dark red triangles indicate the values o f D4000n of high-E MPGs derived from a BC03 m odel with age/r/Z equal to the mean values derived from the SED fitting o f this sub-population (D4000n,SED). Open green squares are the equivalent for low-E MPGs, once the aperture bias is taken into account. Actually, for high-E M PGs the slit aperture samples approximately the w hole galaxy (see Fig. 8 ), thus D4000n m easured directly from the spectra and D4000n,SED can be fairly compared. For low-E M PGs Fig. 8 shows that the slit samples ju s t the region within 0.5 Re. In the com parison o f D4000n and D4000n,SED hence, we have to take into account the effect o f colour gradients (see more details in Sect. 5.2). Open green circles indicate the values of D4000n,SED o f low-E w ithout any correction for aperture bias.

Fig. 8. Ratio between half of the aperture o f the slit and effective radius of the galaxies as a function o f the mean stellar mass density and z . The colour code is the sam e as in Fig. 6 .

in good agreem ent w ith th e m ean value o f D 4 000n m easu red on real spectra. T he results seen in Figs. 7 and 6 , thus, show that b oth the evolution o f the n um ber d ensity and o f the age o f stellar p opulation o f dense M P G s, are coherent w ith passive evolution since z = 1.0.

F or w hat concerns th e low -E M P G s, the left-hand p an el o f Fig. 7 show s th at a t any red sh ift they are system atically younger than high-E M P G s. In p articular th eir ages increase b y ju s t 0.4 G yr in the 1.8 G yr o f tim e th at passes betw een z = 0.95 and 0.6. B efore com paring the observed value o f D 4000n w ith D 4 000b,s e d it is im portant to note th at the D 4 000n w e u sed refers to the portion o f the galaxy th at falls into the 1" slit. C o n sid ­ ering the different dim ensions o f high, interm ediate, and low-E M P G s, the slit sam ples a different fraction o f total light for the three sub-populations. In F ig. 8, th e points indicate the portion o f galaxy covered by the slit in Re unit for the high-E and lo w ­ E sub-populations, as a function o f redshift. A lm ost all o f the light from high-E M P G s is included in the slit, thus the D 4000n

provides constraints on the age o f the w hole galaxy, sim ilarly to the SED fitting. F or low -E M P G s, the slit sam ples th e inner 0.5 Re. G iven the know n presence o f m etallicity gradients in p a s­

sive galaxies both in local U niverse an d at interm ediate redshift, this im plies that at any red sh ift i) w e cannot directly com pare the D 4000n o f high- and low -E M P G s; and ii) for low -E M P G s, w e cannot directly com pare the results from SED fitting w ith those derived from th e spectral features as w e d id for high-E M PG s.

A lthough a d irect com parison at fixed red sh ift is n o t straightfor­

w ard, w e h ig hlight th at the reg io n w hich is sam pled by th e slit is approxim ately co nstant over o ur red sh ift ran g e (see Fig. 8) and this assures us th at the evolutionary trends o f D 4000n are not affected b y aperture effects.

Taking advantage o f the spatially reso lv ed inform ation on stellar population properties pro v id ed b y ATLA S3 D survey (C appellari et al. 2011) for a sam ple o f 260 local elliptical g alax ­ ies (ETG s), w e quantified th at for low -E local m assive E T G s the m etallicity in the central (r ^< 0^.5R^e, Z Re^{/ 2}) region is - 2 0 % greater than the m etallicity w ithin R^e (see A ppendix C). A t the sam e tim e, w e found th at there is no significant tren d w ith r a ­ dius o f the tim escale o f the star form ation or age⁴. Taking this into consideration, w e derived D 4 000n, S E D applying the co rrec­

tion w e derived from local U niverse to the m ean values o f Z (we note that G allazzi et al. (2014) do n o t find any evolution in the m etallicities o f m assive quiescent galaxies since z - 0.8). R esults are show n as open green squares in the rig h t panel o f Fig. 7 . As for high-E M P G s, they are in good agreem ent w ith th e D 4 000n values m easured on re a l spectra. To qualitatively show the ef­

fect o f slit aperture, w e rep o rt in the figure also the values o f D 4 000b,s ED n o t co rrected for the aperture bias. T here is clear d is­

agreem ent betw een these values and the m ean values m easured from rea l spectra.

4 The population o f passive galaxies and elliptical galaxies are not co­

incident (see e.g. Tamburri et al. 2014; M oresco et al. 2013). However, at first order, the two populations share the same properties.

S um m arizing, both th e evolution o f th e n u m b er density and o f the stellar population ages o f lo w -£ M P G s strongly support a p icture in w hich younger lo w -£ M P G s continuously appear at low er redshift. T hese results indicate th at the increase both in n u m b er and in m ean size o f the p opulation o f M P G s is due to the continuous addition o f larger and younger quiescent galaxies over cosm ic tim e.

W e stress th at the com parison betw een D 4000n and D 4 000Bised in F ig. 7 is m eaningful o nly betw een th e m ean val­

ues o f the distributions and n o t for any single galaxy. C onven­

tionally SED m odelling uses a coarse grid o f Z /t, that ca n ­ n o t accurately reproduce the m o re realistic sm ooth distributions o f m etallicity and tim escale o f star form ation o f real galaxies.

N onetheless, although the single values o f stellar p opulation p a ­ ram eters cou ld b e biased, the m ean values are m o re rep resen ta­

tive o f the truth as suggested b y the consistency betw een D 4 000n and D 4 000BisED in F ig. 7 . A lthough the consistency betw een spectroscopic and p hotom etric d ata confirm s the robustness o f ou r conclusions, w e are conscious o f th e issues related to the A ge and Z derived from SED fitting. F or this reason w e derived the stellar population ages also using only the D 4000n m e asu re­

m ents. To do this, w e follow ed the standard approach o f assu m ­ ing som e fiducial values for Z an d t from local studies (e.g.

F a g io lie ta l. 2 0 1 6 ; Z a h i d e ta l. 2016) . W e caution th at in this analysis w e are in terested ju s t in relative values o f stellar p o p ­ ulation ages, i.e. in the A A ge from z = 1.0 and z = 0.5, and n o t in the absolute values. This relaxed requirem ent alleviates the issue related to the unknow n value o f t . In fact, F ig. A.1 shows that at fixed m etallicity a n d in the ran g e o f ages w e are interested in, the curves w ith different t are alm o st p arallel (see th e figure for m odels in w hich Z = Z 0 and t = 0 .3 ,0 .4 , and 0.6 G yr resp e c­

tively). This fact im plies that the A A ge does n o t depend m uch on t b u t m ostly on Z. U sing our analysis on A TLA S3D survey, w e fixed Z = 0.85Z0 for lo w -£ M P G s (see A ppendix C, [Z /H ]Re/2).

In Fig. A .1 , the evolution o f D 4 000n as a function o f age for this Z value is plotted. W e obtained the curve interpolating the m o d ­ els w ith Z = Z 0 and Z = 0.4 Z0 . T he value o f D 40 0 0 n for low -£

M PG s a t z = 1.0 and z = 0.5 (i.e. 1.74 and 1.84, see Fig. 7) is also shown. W e observe th at the corresponding A A ge is <1 Gyr, i.e. th e evolution o f th e stellar population ages is slow er than that expected in case o f passive evolution (AA ge = 2 G yr), as w e found in Fig. 7 . W e n otice th at this conclusion is still valid also fo r solar an d super-solar m etallicity. F ollow ing the sam e schem e, w e rep eat the analysis for h ig h -£ M P G s. In this case w e fixed Z = 0.7 Z 0 (see A ppendix C, [Z /H ]Re). As before, in Fig. A.1 w e indicate the evolution o f D 4 000n for this Z value and also p lo t the value o f D 4 000n at z = 1.0 and z = 0.5 (i.e. 1.67 and 1.80, see F ig. 7 ) . T he figure show s that A Age is ~ 1 .7 Gyr, w hich is consistent w ithin the errors w ith the A Age expected in case o f a passive evolution, in agreem ent w ith o u r conclusions o f Fig. 7 . F o r com pleteness, w e also p lo t the evolution o f D 4 000n

as a function o f age for Z = 0.5 Z0 , that is for the Z value w e obtained from the b est fit o f the SED .

E v idence fo r o lder ages o f the densest galaxies has been found b y m any authors both in the local U niverse and at high-z (e.g. S hankar & B ernardi 2 0 0 9 ; S aracco e t al. 2 0 0 9 ; V alentinuzzi e t al. 2 0 1 0 ; W illiam s e t al. 2 0 1 0 ; S aracco e ta l.

2 0 1 1 ; P oggianti et al. 2 0 1 3 a; C a r o llo e ta l. 2 0 1 3 ; F a g io lie ta l.

2016) . H ow ever m o st o f these w orks investigated a larger stellar m ass range, n o t focusing th eir analysis on the m assive end.

In the sam e m ass range, using U V colour to date stel­

la r population ages o f passive com pact m assive ellipticals, C a r o llo e ta l. (2 013) found th at they are consistent w ith p a s­

sive evolution, in agreem ent w ith ou r results. U sing a set o f

L ick absorption indices, O nodera e t al. (2015) investigated stel­

la r population properties fo r a sam ple o f m assive quiescent galaxies (U V J colour selected) at (z) = 1.6. T hey found a m ean age o f 1.1+0 2 Gyr. As stated by the authors, this value is in excel­

len t agree-m e n t w ith th e ag e o f local counterparts, if h ig h-z m a s­

sive quiescent galaxies evolve passively. W e verified that m ore than 8 0% o f their sam ple is com posed o f m assive passive g alax ­ ies w ith £ > 2000 M 0 p c -2 , thus w e can reasonably com pare their results w ith ours. I f w e assum e passive evolution betw een z = 1.6 and z = 0.95, the m ean age o f th eir m assive quiescent galaxies rises to 3.1+0 3 Gyr. This is in fair agreem ent w ith the m ean age o f h ig h -£ M P G s w e find a t z = 0.95 (3.7 ± 0.2 G yr) (see also W hitaker et al. 2013) .

D ifferent conclusions w ere reach ed by F 16. U sing stacked spectra, the authors constrained th e stellar population ages for dense and less dense passive galaxies in the zC O SM O S sam ple from z = 0.8 to z = 0.2. T hey found that the age o f dense m a s­

sive quiescent galaxies increases less than w ould b e expected from passive evolution alone. M oreover, they found n o co rrela­

tion betw een the ag e o f stellar p opulation and the dim ension o f the source. T he presen t analysis differs from the F 16 analysis in a n um ber o f ways: the selection o f passive galaxies (no em ission lines plus n o M IPS in F 16 vs. N U V rK colour in ou r w ork); the selection o f th e d ense sub-population (cut a t fixed R e o r along the SM R vs. cu t a t fixed £ ); and th e procedure adopted to co n ­ strain the stellar population age. U nfortunately, w e cannot ex ­ actly rep roduce th eir analysis w ith ou r data set. In A ppendix B, w e checked how our results change if w e adopt the sam e criteria used b y F 16 to select dense and less dense galaxies. W e found th at the m ean age o f dense M P G s is consistent w ith passive evo­

lution and th at less dense M P G s are y o unger than dense M PG s, independently o f th e criteria used to divide the sub-populations.

H owever, as stated above, w e stress that the previous checks rely on a sam ple o f M P G s selected in a different w ay and ado p t differ­

en t techniques to constrain th e stellar population age. In fact, w e cannot rep eat the sam e analysis w ith o ur data set, so w e cannot fully account fo r the effect o f these tw o factors on the results.

6. Where do new large MPGs come from?

T he evidence th at the new M P G s are system atically younger than h ig h -£ M P G s contrasts w ith the hypothesis th at all m a s­

sive galaxies are assem bled m ostly through dry m ergers (e.g.

H opkins e ta l. 2 0 0 9 ; C appellari e t al. 2012) . In fact, dry m e rg ­ ers should dilute any tren d betw een stellar p opulation age and tim e o f appearance by m ixing up the stellar population o f p re ­ existing system s. In fact, m o re recently new pieces o f ev i­

dence have com e to lig h t supporting a scenario in w hich PG s are m ostly the final evolutionary stage o f star-form ing galaxies (SFG s) th at p rogressively halt th eir star form ation until they b e ­ com e quiescent (e.g. L illy & C arollo 2 0 1 6 ; D river e t a l. 2 0 1 3 ; H uertas-C om pany et al. 2 0 1 5 , 2016) . In fact, a t any z and a t fixed stellar m ass, star-form ing galaxies are larger than passive ones (e.g. van der W el et al. 2014) . Thus, if passive galaxies are ju s t the quenched counterpart o f star-form ing galaxies, w e should ex ­ p ect a correlation betw een the stellar population age o f PG s and th eir m ean stellar m ass density in the direction o f y o unger age for less dense system s. This is exactly w hat w e have show n in Fig. 7 . In this case, however, further evidence is expected: the n u m b er o f PG s th at ap p ear a t any tim e, has to b e sim ilar to the n u m b er o f SFG s th at disappear. To test this sim ple hypothesis, in Fig. 9 w e com pare the nu m b er density o f th e w hole population o f M P G s, w ith the n um ber density o f m assive star-form ing g alax ­ ies (M SFG s). W e considered all n o n passive m assive galaxies to A113, page 9 o f 14

Fig. 9. Evolution of the number density of MPGs (filled red circles) and of star forming massive galaxies (MSFGs, blue filled stars). Open circles show the expected growth in the abundance of MPGs below z <

0.8, assuming that this is fully due to the observed decline of MSFGs.

Solid and open circles have been shifted for visualisation purposes.

be M S FG s. T he figure shows th at the nu m b er densities o f the tw o populations start to deviate at z < 0.8, that is w hen the U n i­

verse becom es efficient at producing lo w -2 M P G s. In particular, the n um ber density o f M S FG s is alm ost flat at z > 0.8 and then drops b y a factor o f approxim ately 2 at low er z. T he declining trend does n o t depend on the selection criterion used to id e n ­ tify M S FG s. H aines e t al. (2017) found the sam e trend study­

ing the n um ber density o f M > 1011 M 0 V IPER S galaxies w ith D 4 000n < 1.55. Starting from the very sim ple assum ption th at all the M S FG s th at disappear at z < 0.8, m u st necessarily m igrate in the population o f M P G s, w e derived the n um ber density o f M PG s expected at z < 0.8 b y considering their density a t z = 0.8 and th e observed decrem ent o f M S FG s at z < 0.8. O pen red sym ­ bols rep o rt th e results. In fact, they are in excellent agreem ent w ith the observed n um ber density o f M P G s. In this basic test w e did n o t take into account the fact th at som e star-form ing g alax ­ ies w ith M < 1011 M 0 can enter into ou r sam ple a t a later tim e.

N evertheless, the com parison show n in F ig. 9 show s that, to first order, the m igration o f M S FG s to M P G s fully accounts for the increase in the n um ber density o f M P G s w ith cosm ic tim e. In particular the ( R e ) o f M S FG s a t z - 0.8 is - 5 .7 kpc, in ag ree­

m en t w ith the value (Re) = 6 .3 ± 3 kpc o f low- and in term ediate-2 M PG s a t ( z ) = 0.5. I f a portion o f lo w -2 M P G s assem bled its stellar m ass inside-out, th at is starting from a com pact passive core, w e should add the n um ber o f these size-evolved M P G s to the open circles in Fig. 9, since the “p rogenitor” com pact core is n o t included in the population o f M S FG s. In fact, including other channels for M P G production in the m odel w ould overestim ate the n um ber density o f the population. W e can therefore exclude the p o ssibility th at the in side-out accretion scenario is the m ain channel for the build up o f the M P G population. This evidence confirm s in an in dependent w ay th e results w e found in Figs. 6 and 7 and th at w e sum m arise in the cartoon o f F ig. 10. In the - 2 .5 G yr o f tim e from z = 1.0 to z = 0.5, the nu m b er density o f h ig h -2 M P G s does n o t evolve, an d the ages o f their stellar p o p u ­ lations are consistent w ith a passive evolution. In the sam e tim e

the m ean age o f the stellar population o f M P G s as a function o f redshift, and o f the m ean surface stellar m ass density. F ro m the V IPER S d ata set, w e selected a sam ple o f - 2 0 0 0 M P G s over the red sh ift ran g e 0.5 < z < 1.0. W e divided this sam ple into three sub-populations according to their value o f 2 : h ig h -2 M PG s, interm ediate-2 M P G s, and lo w -2 M P G s.

W e studied th e evolution o f the nu m b er density for the three sub-populations o f M P G s and found th at it depends on 2 : th e low er 2 the faster th e evolution (see Fig. 6) . In p artic­

ular, w e found th at the n um ber o f dense galaxies p er unit vol­

um e does n o t increase from z = 1.0 to z = 0.5. Instead, over the sam e tim e interval, the n um ber density o f less dense M PG s increases b y a factor 4. This different evolution changes the com position o f the population o f M P G s w ith tim e. A t z > 0.8, high-, interm ediate- and lo w -2 M P G s contribute approxim ately equally to the population. A t z < 0.8, the n um ber density o f low- 2 M P G s p rogressively increases and this sub-population starts to dom inate over the other tw o classes.

W e then investigated the evolution o f th e stellar population ages as a function o f 2 (see F ig. 7) . W e constrained the ages u s­

ing both photom etry, th at is fitting the spectral energy distribu­

tion, and spectroscopy, through the D 40 0 0 n index (B alogh et al.

1999) . T hese tw o independent estim ates are in agreem ent and show that:

- T he evolution o f th e age o f h ig h -2 M P G s is fully consistent w ith a passive ageing o f their stellar population.

- T he evolution o f the age o f lo w -2 M P G s is slow er than w ould b e expected in the case o f passive evolution, i.e. new lo w -2 M P G s are younger than existing ones.

- A t any redshift, d ense M P G s are o lder than less dense M PG s.

B oth the evolution o f the n um ber density an d o f the age o f the stellar population o f h ig h -2 M P G s are consistent w ith passive evolution for this sub-population. O n the other hand, the results w e found for lo w -2 M P G s show th at their nu m b er density co n ­ tinuously increases w ith decreasing redshift, th at is new low -2 galaxies jo in th e p opulation o f M P G s as tim e goes by. T he study o f stellar p opulation ag e show s that these new galaxies are sys­

tem atically younger than the lo w -2 M P G s already in place.

T hese results indicate th at th e increase both in nu m b er d en ­ sity and in typical radial size observed fo r th e population o f M P G s is m ostly due to the addition o f less dense and younger galaxies at later tim es. Taking th e results for low - and h ig h -2 M P G s to gether w e found th at the population o f M P G s was built by th e continuous addition o f less dense M P G s: on top o f p a s­

sively evolving dense M P G s already in p lace at z = 1.0, new, larger and younger q uiescent galaxies continuously jo in the p o p ­ ulation o f M P G s at later tim es.

W e find evidence that these new M P G s are the d irect d escen­

dants o f m assive star-form ing galaxies (M SFG s) th at quenched