Astronomy & Astrophysics manuscript no. VVDS˙mf˙Pozzetti˙accepted c© ESO 2018
November 12, 2018
The VIMOS VLT Deep Survey ⋆
The Assembly History of the Stellar Mass in Galaxies: from the Young to the
Old Universe
L. Pozzetti1 , M. Bolzonella1 , F. Lamareille1,9,6, G. Zamorani1, P. Franzetti2, O. Le Fèvre3, A. Iovino4, S.
Temporin4, O. Ilbert5, S. Arnouts3, S. Charlot6,7, J. Brinchmann8, E. Zucca1, L. Tresse3, M. Scodeggio2, L.
Guzzo4, D. Bottini2, B. Garilli2, V. Le Brun3, D. Maccagni2, J.P. Picat9, R. Scaramella10,11, G. Vettolani10,
A. Zanichelli10, C. Adami3, S. Bardelli1, A. Cappi1, P. Ciliegi1, T. Contini9, S. Foucaud12, I. Gavignaud13,
H.J. McCracken7,14, B. Marano15, C. Marinoni16, A. Mazure3, B. Meneux2,4, R. Merighi1, S. Paltani17,18, R.
Pellò9, A. Pollo3,19, M. Radovich20, M. Bondi10, A. Bongiorno15, O. Cucciati4,21, S. de la Torre3, L.
Gregorini22,10, Y. Mellier7,14, P. Merluzzi20, D. Vergani2, and C.J. Walcher3
(Affiliations can be found after the references)
Received 04 04 2007; accepted 18 08 2007
ABSTRACT
We present a detailed analysis of the Galaxy Stellar Mass Function (GSMF) of galaxies up to z = 2.5 as obtained from the
VIMOS VLT Deep Survey (VVDS). Our survey offers the possibility to investigate it using two different samples: (1) an optical
(I-selected 17.5 < IAB < 24) main spectroscopic sample of about 6500 galaxies over 1750 arcmin
2 and (2) a near-IR (K-selected
KAB < 22.34 & KAB < 22.84) sample of about 10200 galaxies, with photometric redshifts accurately calibrated on the VVDS
spectroscopic sample, over 610 arcmin2. We apply and compare two different methods to estimate the stellar mass Mstars from
broad-band photometry based on different assumptions on the galaxy star-formation history. We find that the accuracy of the
photometric stellar mass is overall satisfactory, and show that the addition of secondary bursts to a continuous star formation
history produces systematically higher (up to 40%) stellar masses. We derive the cosmic evolution of the GSMF, the galaxy number
density and the stellar mass density in different mass ranges. At low redshift (z ≃ 0.2) we find a substantial population of low-mass
galaxies (< 109M⊙) composed by faint blue galaxies (MI −MK ≃ 0.3). In general the stellar mass function evolves slowly up to
z ∼ 0.9 and more significantly above this redshift, in particular for low mass systems. Conversely, a massive population is present
up to z = 2.5 and have extremely red colours (MI−MK ≃ 0.7−0.8). We find a decline with redshift of the overall number density of
galaxies for all masses (59± 5% for Mstars > 10
8M⊙ at z = 1), and a mild mass-dependent average evolution (‘mass-downsizing’).
In particular our data are consistent with mild/negligible (< 30%) evolution up to z ∼ 0.7 for massive galaxies (> 6× 1010M⊙).
For less massive systems the no-evolution scenario is excluded. Specifically, a large fraction (≥ 50%) of massive galaxies have been
already assembled and converted most of their gas into stars at z ∼ 1, ruling out the ‘dry mergers’ as the major mechanism of
their assembly history below z ≃ 1. This fraction decreases to ∼ 33% at z ∼ 2. Low-mass systems have decreased continuously in
number density (by a factor up to 4.1 ± 0.9) from the present age to z = 2, consistently with a prolonged mass assembly also at
z < 1. The evolution of the stellar mass density is relatively slow with redshift, with a decrease of a factor 2.3 ± 0.1 at z = 1 and
about 4.5± 0.3 at z = 2.5.
Key words. galaxies: evolution – galaxies: luminosity function, mass function – galaxies: statistics – surveys
1. Introduction
One of the main and still open question of modern cos-
mology is how and when galaxies formed and in particular
when they assembled their stellar mass. There are growing
but still controversial evidences in near-IR (NIR) surveys
that luminous and rather massive old galaxies were quite
common already at z ∼ 1 (Pozzetti et al. 2003, Fontana
et al. 2004, Saracco et al. 2004, 2005, Caputi et al. 2006a)
and up to z ∼ 2 (Cimatti et al. 2004, Glazebrook et al
Send offprint requests to: Lucia Pozzetti e-mail:
lucia.pozzetti@oabo.inaf.it
⋆ based on data obtained with the European Southern
Observatory Very Large Telescope, Paranal, Chile, program
070.A-9007(A), and on data obtained at the Canada-France-
Hawaii Telescope, operated by the CNRS of France, CNRC in
Canada and the University of Hawaii
2004). These surveys indicate that a significant fraction of
early-type massive galaxies were already in place at least
up to z ∼ 1. Therefore they should have formed their stars
and assembled their stellar mass at higher redshifts. As in
the local universe, at z ≃ 1.5 these galaxies still dominate
the near-IR luminosity function and stellar mass density
of the universe (Pozzetti et al. 2003, Fontana et al. 2004,
Strazzullo et al. 2006). These results favour a high-z mass
assembly, in particular for massive galaxies, in apparent
contradiction with the hierarchical scenario of galaxy for-
mation, applied to both dark and baryonic matter, which
predicts that galaxies form through merging at later cosmic
time. In these models massive galaxies, in particular, assem-
bled most of their stellar mass via merging only at z < 1
(De Lucia et al. 2006). From several observations it seems
that baryonic matter has a mass-dependent assembly his-
http://arxiv.org/abs/0704.1600v2
2 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
tory, from massive to small objects, (i.e. the ‘downsizing’
scenario in star formation, firstly defined by Cowie et al.
1996, is valid also for mass assembly), opposite to the dark
matter (DM) halos assembly. The continuous merging of
DM halos in the hierarchical models, indeed, should result
in an ‘upsizing’ in mass assembly, with the most massive
galaxies being the last to be fully assembled. If we trust
the hierarchical ΛCDM universe, the source of this discrep-
ancy between observations and simple basic models could
be due to the difficult physical treatment of the baryonic
component, such as the star formation history/timescale,
feedback, dust content, AGN feedback or to a missing in-
gredient in the hierarchical models of galaxy formation (for
the inclusion of AGN feedback, see Bower et al. 2006, Kang
et al. 2006, De Lucia & Blaizot 2007, Menci et al. 2006,
Monaco et al. 2006; and see Neistein et al. 2006 for the de-
scription of a natural downsizing in star formation in the
hierarchical galaxy formation models and a recent review
by Renzini 2007).
Considering optically selected surveys, a strong number
density evolution of early type galaxies has been recently
reported from the COMBO17 and DEEP2 surveys (Bell et
al. 2004, Faber et al. 2005), with a corresponding increase
by a factor 2 of their stellar mass since z ∼ 1, possibly
due to so called ‘dry-mergers’ (even if the observational
results on major merging and dry-merging are still contra-
dictory, see Bell et al. 2006, van Dokkum 2005, Lin et al.
2004 and Renzini 2007 for a summary). This is at variance
with results from the VIMOS-VLT Deep Survey (VVDS,
Le Fèvre et al. 2003b), conducted at greater depth and us-
ing spectroscopic redshifts in a large contiguous area. From
the VVDS, Zucca et al. (2006) found that the B-band lu-
minosity function of early type galaxies is consistent with
passive evolution up to z ∼ 1.1, while the number of bright
(MBAB < −20) early type galaxies has decreased only by
∼ 40% from z ∼ 0.3 to z ∼ 1.1. Similarly, Brown et al.
(2007), in the NOAO Deep Wide Field survey over ∼ 10
deg2, found that the B-band luminosity density of L∗ galax-
ies increases by only 36 ± 13% from z = 0 to z = 1 and
conclude that mergers do not produce rapid growth of lu-
minous red galaxy stellar masses between z = 1 and the
present day.
The VVDS is very well suited for this kind of stud-
ies, thanks to its depth and wide area, covered by multi-
wavelength photometry and deep spectroscopy. The simple
17.5 < IAB < 24 VVDS magnitude limit selection is signif-
icantly fainter than other complete spectroscopic surveys
and allows the determination of the faint and low mass
population with unprecedented accuracy. Most of the pre-
vious existing surveys are instead very small and/or not
deep enough, or based only on photometric redshifts.
Given the still controversial results based on morphol-
ogy or colour-selected early-type galaxies (see Franzetti
et al. 2007 for a discussion on colour-selected contamina-
tion), we prefer to study the total galaxy population us-
ing the stellar mass content. Here we present results on
the cosmic evolution of the Galaxy Stellar Mass Function
(GSMF) and mass density to z = 2.5 in the deep VVDS
spectroscopic survey, limited to 17.5 < IAB < 24, over
∼ 1750 arcmin2 and based on about 6500 galaxies with
secure spectroscopic redshifts and multiband (from UV to
near-IR) photometry. In addition, we derive the GSMF
also for a K-selected sample based on about 6600 galax-
ies (KAB < 22.34) in an area of 442 arcmin
2 and about
3600 galaxies in a deeper (KAB < 22.84) smaller area of
168 arcmin2, making use of photometric redshifts, accu-
rately calibrated on the VVDS spectroscopic sample, and
spectroscopic redshifts when available.
Throughout the paper we adopt the cosmology Ωm =
0.3 and ΩΛ = 0.7, with h70 = H0/70 km s
−1 Mpc−1.
Magnitudes are given in the AB system and the suffix AB
will be dropped from now on.
2. The First Epoch VVDS Sample
The VVDS is an ongoing program aiming to map the evo-
lution of galaxies, large scale structures and AGN through
redshift measurements of ∼ 105 objects, obtained with the
VIsible Multi-Object Spectrograph (VIMOS, Le Fèvre et
al. 2003a), mounted on the ESO Very Large Telescope
(UT3), in combination with a multi-wavelength dataset
from radio to X-rays. The VVDS is described in detail in
Le Fèvre et al. (2005). Here we summarize only the main
characteristics of the survey.
The VVDS is made of a wide part, with spectroscopy
in the range 17.5 ≤ I ≤ 22.5 on 4 fields (∼ 2 × 2 deg2
each), and a deep part, with spectroscopy in the range
17.5 ≤ I ≤ 24 on the field 0226-04 (F02 hereafter).
Multicolour photometry is available for each field (Le Fèvre
et al. 2004). In particular, the B, V , R, I photometry for
the 0226-04 deep field, covering ∼ 1 deg2, has been ob-
tained at CFHT and is described in detail in McCracken
et al. (2003). The photometric depth reached in this field
is 26.5, 26.2, 25.9, 25.0 (50% completeness for point-like
sources), respectively in the B, V , R, I bands. Moreover,
U < 25.4 (50% completeness) photometry obtained with
the WFI at the ESO-2.2m telescope (Radovich et al. 2004)
and Ks band (hereafter K) photometry with NTT+SOFI
at the depth (50% completeness) of 23.34 (Temporin et al.
in preparation) are available for wide sub-areas of this field.
Moreover, an area of about 170 arcmin2 has been covered
by deeper J and K band observations with NTT+SOFI
at the depth (50% completeness) of 24.15 and 23.84, re-
spectively (Iovino et al. 2005). The deep F02 field has been
observed also by the CFHT Legacy Survey (CFHTLS1) in
several optical bands (u∗, g′, r′, i′, z′) at very faint depth
(u∗ = 26.4, g′ = 26.3, r′ = 26.1, i′ = 25.9, z′ = 24.9, 50%
completeness).
Spectroscopic observations of a randomly selected sub-
sample of objects in an area of ∼ 0.5 deg2, with an average
sampling rate of about 25%, were performed in the F02
field with VIMOS at the VLT.
Spectroscopic data were reduced with the VIMOS
Interactive Pipeline Graphical Interface (VIPGI, Scodeggio
et al. 2005, Zanichelli et al. 2005) and redshift mea-
surements were performed with an automatic package
1 Based on observations 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 Science 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 TERAPIX and the Canadian
Astronomy Data Centre as part of the Canada-France-Hawaii
Telescope Legacy Survey, a collaborative project of NRC and
CNRS.
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 3
Fig. 1. Upper panel: Comparison of photometric and spec-
troscopic redshifts in theK-selected sample for objects with
highly reliable (confidence level > 97% , i.e. about 1400
galaxies with flag=3, 4) spectroscopic redshifts. The accu-
racy obtained is σ∆z = 0.02(1 + z)
2 (shown as solid lines)
with only 3.7% of outliers, defined as the objects outside
the region limited by the 2 dotted lines (zphoto = zspec ±
0.15(1 + zspec)) in the figure. Lower panel: Spectroscopic
(solid line) and photometric (dotted line) redshift distribu-
tion for the same comparison sample.
(KBRED) and then visually checked. Each redshift mea-
surement was assigned a quality flag, ranging from 0 (failed
measurement) to 4 (100% confidence level); flag 9 indicates
spectra with a single emission line, for which multiple red-
shift solutions are possible. Further details on the quality
flags are given in Le Fèvre et al. (2005).
The analysis presented in this paper is based on the first
epoch VVDS deep sample, which has been obtained from
the first spectroscopic observations (fall 2002) on the field
VVDS-02h, which cover 1750 arcmin2.
2.1. The I-selected Spectroscopic Sample
In this study we use the F02-VVDS deep spectroscopic sam-
ple, purely magnitude limited (17.5 ≤ I ≤ 24), in combi-
nation with the multi-wavelength optical/near-IR dataset.
From the total sample of 8281 objects with measured red-
shift, we removed the spectroscopically confirmed stars and
broad line AGN, as well the galaxies with low quality red-
shift flag (i.e. flag 1), remaining with 6419 galaxy spec-
tra with secure spectroscopic measurement (flags 2, 3, 4,
9), corresponding to a confidence level higher than 80%.
Galaxies with redshift flags 0 and 1 are taken into account
statistically (see Section 4 and Ilbert et al. 2005 and Zucca
et al. 2006 for details). This spectroscopic sample has a
median redshift of ∼ 0.76. Compared to previous optically
selected samples, the VVDS has not only the advantage
of having an unprecedented high fraction of spectroscopic
redshifts (compared, for example, to the purely photomet-
ric redshifts as in COMBO17, Wolf et al. 2003 and Borch
et al. 2006 for the MF), but also of being purely magnitude
selected (17.5 < I < 24), differently, for example, from the
DEEP2 (Bundy et al. 2006 for the MF) survey, which has
a colour-colour selection. Moreover, the VVDS covers an
area from 10 to 40 times wider than the GOODS-MUSIC
field (Fontana et al. 2006) and the FORS Deep Field (FDF,
Drory et al. 2005), respectively.
2.2. The K-selected Photometric Sample
A wide part of the VVDS-02h field (about 623 arcmin2)
has been observed also in the near-IR (Iovino et al. 2005,
Temporin et al. in preparation). This allows us to build a
K-selected sample with a total area of 610 arcmin2 (after
excluding low-S/N borders): 442 arcmin2 are 90% complete
to K < 22.34, while 168 arcmin2 are 90% complete to K <
22.84 (equivalent to KVega = 21).
This sample consists of 11221 objects, of which 2882
have VVDS spectroscopy. In particular, the deep sample
(K < 22.84) consists of 3821 objects, of which 749 have
VVDS spectroscopy, and 596 of them are galaxies with a
secure spectroscopic identification (flags 2, 3, 4, 9). This
latter deep sample is more than one magnitude deeper than
the samples from the K20 spectroscopic survey (Cimatti
et al. 2002) and the MUNICS survey (Drory et al. 2001).
Additionally, the total K-selected sample covers an area
more than 10 times wider than the K20 and the GOODS-
CDFS sample used by Drory et al. (2005) and 4 times wider
than the GOODS-MUSIC field (Fontana et al. 2006).
Since the spectroscopic sampling of the K-selected sam-
ple is less than satisfactory, we take advantage of the
high quality photometric redshifts (zphoto). The method
and the calibration are presented and discussed in Ilbert
et al. (2006). The comparison sample contains 3241 ac-
curate spectroscopic redshifts (confidence level > 97% ,
i.e. flag=3, 4) up to I = 24 obtaining a global accu-
racy of σ∆z/(1+z) = 0.037 with only 3.7% of outliers. Also
in the K-selected photometric sample the agreement be-
tween photometric and highly reliable spectroscopic red-
shifts (about 1400) is excellent (Figure 1). We note, how-
ever, a non-negligible number of catastrophic solutions with
zphoto
∼ 1.2 and zspec
∼ 1 which could introduce a bias at
high-redshift (see also discussion in Section 2.3). Even if we
cannot rely on a wide spectroscopic comparison sample at
high-z, the number of galaxies with zphoto > 1.2 is simi-
lar or only slightly higher (about 20%) than the number
of galaxies with zspec > 1.2 (63 vs. 51, see Figure 1) and
have very similar fluxes and colors. For this reason we do
not expect that our results on the mass function and the
mass density will be strongly biased by the effect of catas-
trophic redshifts (see Section 4). Furthermore, at high-z the
dispersion between photometric and spectroscopic redshifts
increases, but not drammatically, to σ∆z/(1+z) ≃ 0.05, 0.06
4 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
at z > 1.2, 1.4. Over the whole redshift range it can be
represented with σ∆z ≃ 0.02(1 + z)
2 (shown in Figure 1).
For the whole K-selected sample, the median errors on
photometric redshifts, based on χ2 statistics, are σzphoto =
0.06 (0.04 at z < 1, increasing to 0.14 at z > 1.5). As ex-
pected, there is also an increase of σzphoto for the faintest
objects, but this increase is only about 0.02 in the faintest
magnitude bin. As previously noted by Ilbert et al. (2006)
the statistical errors are consistent with σ∆z and could be
used as an indication of their accuracy. We will discuss in
the following sections the effects of these uncertainties and
conclude that they do not affect significantly our conclu-
sions.
We note, moreover, that the K-selected sample se-
lects a different population, in particular of Extremely Red
Objects (EROs) at zphoto > 1 (see Section 2.3 and Fig. 3),
compared to the I-selected sample used to calibrate the de-
rived photometric redshift. Actually, photometric redshifts
greater than 0.8-1.0 for the EROs population have been
confirmed spectroscopically with very low contamination of
low-z objects (Cimatti et al. 2002). Moreover, the near-IR
bands are crucial to constrain photometric redshifts in the
redshift desert since the J-band is sensitive to the Balmer
break up to z = 2.5. Indeed Ilbert et al. (2006) obtain for
the deep sample at K < 23 the most reliable photometric
redshifts on this sub-sample with only 2.1% of outliers and
σ∆z/(1+z) = 0.035 (see their figure 13).
In this paper we therefore use photometric redshifts for
the whole K-selected photometric sample and the highly
reliable spectroscopic redshifts when available.
In order to select galaxies from the total K-selected
photometric sample, we have used a number of photomet-
ric methods to remove candidate stars, as described be-
low. Some of the possible criteria to select stars are: (i)
the CLASS STAR parameter given by SExtractor (Bertin
& Arnouts 1996), providing the “stellarity-index” for each
object, reliable up to I ≃ 21; (ii) the FLUX RADIUS K
parameter, computed by SExtractor from the K band im-
ages, which gives an estimate of the radius containing half
of the flux for each object; this can be considered a good
criterion to isolate point-like sources up to K ≃ 19 (see
Iovino et al. 2005); (iii) the BzK criterion, proposed by
Daddi et al. (2004a), with stars characterized by colours
z − K < 0.3(B − z) − 0.5; (iv) the χ2 of the SED fitting
carried out during the photometric redshift estimate (Ilbert
et al. 2006), with template SEDs of both stars and galaxies.
To efficiently remove stars in the whole magnitude range
of our sample, avoiding as much as possible to lose galaxies,
we decided to use the intersection of the first three crite-
ria. We therefore selected as stars the objects fulfilling all
the constraints (i) CLASS STAR ≥ 0.95 for I < 22.5 or
CLASS STAR ≥ 0.90 if I > 22.5, (ii) FLUX RADIUS K
< 3.4 and (iii) z − K < 0.3(B − z) − 0.5. When it was
not possible to apply criterion (iii), because of non detec-
tion either in the B or z filters, we used criterion (iv) in its
place. Furthermore, we added to the sample of candidate
stars also the objects with K < 16 and FLUX RADIUS K
< 4, to be sure to exclude from the galaxy sample these sat-
urated point-like objects. The final sample consists of 653
candidate stars, which we have removed from the sample
in the following analysis. Comparing to the spectroscopic
subsample (we remind that stars were not excluded from
the spectroscopic targets of VVDS), we found about 87%
of efficiency to photometrically select stars, i.e. only 28 out
Fig. 2. Redshift distributions for the K-selected photomet-
ric sample (filled histogram) and for the I-selected spectro-
scopic sample (empty histogram).
of the 214 spectroscopic stars have not been selected in this
way, and only 3 (1.4%) with highly reliable spectroscopic
flag (3, 4), whereas 21 spectroscopic extragalactic objects
(less than 1%) fall inside the candidate star sample. Three
of them are broad line AGN and the others are all compact
objects, most of them with redshift flags 1 or 2 and only one
with flag 3. This latter object has not been eliminated from
the galaxy sample. We have furthermore removed from the
galaxy sample the spectroscopically confirmed AGNs and
the three secure spectroscopic stars which were not removed
with the photometric criteria.
The final K-selected sample consists of 10160 galaxies
with either photometric redshifts or highly reliable spec-
troscopic redshifts, when available, in the range between 0
and 2.5: 6720 galaxies in the shallow K < 22.34 area of 442
arcmin2 and 3440 galaxies in the deeper area (K < 22.84)
of 168 arcmin2.
2.3. Comparison of the Two Samples
As shown in Fig. 2, the redshift distribution in the K-
selected sample peaks at higher redshift than in the I-
selected spectroscopic sample, with the two median red-
shifts being 0.91 and 0.76, respectively. Even if we cannot
rely on a wide spectroscopic comparison sample at high-z,
we have better investigated the reliability of the high-z tail
in the K-selected sample in term of fraction and colors. We
found indeed that at K < 22 the fraction of objects with
z > 1, 1.5 (35, 13% respectively) is similar to previous spec-
troscopic (K20 survey, see Cimatti et al. 2002) or photomet-
ric studies (Somerville et al. 2004). Moreover, we have used
the BzK color-color diagnostic proposed and calibrated on
a spectroscopic sample to cull galaxies at 1.4 < z < 2.5
(Daddi et al. 2004). We found that most (92%) of the galax-
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 5
Fig. 3. Colour-magnitude diagram and colour distribution
at different redshifts for the K-selected photometric sam-
ple (filled squares and histogram) and for the I-selected
spectroscopic sample (open circles and empty histogram)
ies at 1.5 < zphoto < 2.5 lie in the high-z region of the BzK
diagram.
We conclude that our K-selected sample shows no indi-
cation of significant bias in its high-redshift tail. The global
(I −K) colour distributions of the two samples are similar
to each other up to z ∼ 1.2 (see right panels in Fig. 3), but
they are significantly different at higher redshift. At z > 1.2
the I-selected sample misses many red galaxies fainter than
the I limit, most of them being Extremely Red Objects
(EROs: defined as objects with colours I−K > 2.6), which
are instead included in the K sample (∼ 81% of EROs in
the deep K < 22.84 sample have I > 24). For this rea-
son the K-selected sample is more adequate to study the
massive tail of the GSMF at high-z. Vice versa, the K-
selected sample misses at all redshifts a number of faint
blue galaxies, which are included in the I-selected spectro-
scopic sample (see left panels in Fig. 3). These faint blue
galaxies are important in the estimate of the low-mass tail
of the GSMF.
3. Estimate of the Stellar Masses
The rest-frame near-IR light has been widely used as a
tracer of the galaxy stellar mass, in particular for lo-
cal galaxies (e.g. Gavazzi et al. 1996; Madau, Pozzetti &
Dickinson 1998, Bell & de Jong 2001). However, an accurate
estimate of the galaxy stellar mass at high z, where galax-
ies are observed at widely different evolutionary stages, is
more uncertain because of the variation of the Mstars/LK
ratio as a function of age and other parameters of the stel-
lar population, such as the star formation history and the
metallicity. The use of multiband imaging from UV to near-
IR bands is a way to take into account the contribution to
the observed light of both the old and the young stellar
populations in order to obtain a more reliable estimate of
the stellar mass.
However, even stellar masses estimated using the fit
to the multicolour spectral energy distribution (SED) are
model dependent (e.g. changing with different assumptions
on the initial mass function, IMF) and subject to various
degeneracies (age – metallicity – extinction). In order to re-
duce such degeneracies we have used a large grid of stellar
population synthesis models, covering a wide range of pa-
rameters, in particular in star formation histories (SFH).
Indeed, in the case of real galaxies the possibly complex
star-formation histories and the presence of major and/or
minor bursts of star formation can affect the derived mass
estimate (see Fontana et al. 2004).
We have applied and compared two different methods to
estimate the stellar masses from the observed magnitudes
(using 12 photometric bands from u∗ to K), that are based
on different assumptions on the star-formation history. For
both of them we have adopted the Bruzual & Charlot (2003;
BC03 hereafter) code for spectral synthesis models, in its
more recent rendition, using its low resolution version with
the “Padova 1994” tracks. Different models have also been
considered, e.g. Maraston 2005, and Pégase models (Fioc
and Rocca-Volmerange 1997). The results obtained with
these models are compared with those obtained with the
BC03 models at the end of Section 3.1.
Since most of previous studies at high-z assumed models
with exponentially decreasing SFHs, we have used the same
simple smooth SFHs (see Section 3.1) in order to compare
our results with those of previous surveys. In addition, to
further test the uncertainties in mass determination, we
have used models with complex SFHs (see Section 3.2), in
which secondary bursts have been added to exponentially
decreasing SFHs. These models have been widely used in
studies of SDSS galaxies (see Kauffmann et al. 2003 and
Salim et al. 2005 for further details). Table 1 summarizes
the model parameters used in the 2 methods described in
the following sections.
In our analysis we have adopted the Chabrier IMF
(Chabrier et al. 2003), with lower and upper cutoffs of
0.1 and 100 M⊙. Indeed, all empirical determinations of
the IMF indicate that its slope flattens below ∼ 0.5 M⊙
(Kroupa 2001, Gould et al. 1996, Zoccali et al. 2000) and
a similar flattening is required to reproduce the observed
Mstars/LB ratio in local elliptical galaxies (see e.g. Renzini
2005). As discussed extensively by Bell et al. (2003), the
Salpeter IMF (Salpeter 1955) is too rich in low mass stars
to satisfy dynamical constraints (Kauffmann et al. 2003,
Kranz et al. 2003). Moreover, di Serego Alighieri et al.
(2005) show a rather good agreement between dynamical
masses and stellar masses estimated with the Chabrier IMF
at z ∼ 1. Specifically, this is true at least for high-mass el-
liptical galaxies, less affected than lower-mass galaxies by
uncertainties in the estimate of their dynamical mass due to
possibly substantial rotational contribution to the observed
velocity dispersion.
At fixed age the masses obtained with the Chabrier IMF
are smaller by a factor ∼ 1.7, roughly independent of the
age of the population, than those derived with the classical
Salpeter IMF, used in several previous works that we shall
compare with (e.g. Brinchmann & Ellis 2000; Cole et al.
2001; Dickinson et al. 2003; Fontana et al. 2004). We have
checked this statement in our sample, finding a systematic
median offset of a factor 1.7 and a very small dispersion
6 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
(σ = 0.082 dex) in the masses derived with the two different
IMFs. Since this ratio is approximately constant for a wide
range of star formation histories (SFH), the uncertainty
in the IMF does not introduce a fundamental limitation
with respect to the results we will discuss in the following
Sections. Even if the absolute value of the mass estimate is
uncertain, the use of Salpeter or Chabrier IMFs does not
introduce any significant difference in the relative evolution
with redshift of the mass function and mass density.
One possible limitation of our approach to derive stellar
masses in our sample is the contamination by narrow-line
AGN (broad line AGN have been already excluded, see
Section 2.1). From the available spectroscopic diagnostic,
in the I-selected spectroscopic sample at the mean red-
shift z ≃ 0.7, we found that the contamination due to
type II AGN is less than 10%. Recently, several studies
(Papovich et al. 2006, Kriek et al. 2007, Daddi et al. 2007)
suggest that the fraction of type II AGN increases with
redshift and stellar mass. According to Kriek et al. (2007)
at 2 < z < 2.7 and K < 21.5 the fraction is about 20%
for massive (2.9 × 1011M⊙ for a Salpeter IMF) galaxies.
To derive the contribution of type II AGN to the massive
tail of the MF is beyond the scope of this paper. However
we note, as shown also by the above studies, that for most
of these objects the optical light is dominated by the in-
tegrated stellar emission. Therefore, both our photometric
redshift and mass estimates are likely to be approximately
correct also for them.
3.1. Smooth SFHs
Consistently with previous studies, we have used synthetic
models with smooth SFH models (exponentially decreas-
ing SFH with time scale τ : SFR(t) ∝ exp(−t/τ)) and a
best-fit technique to derive stellar masses from multicolour
photometry.
To this purpose we have developed the code
HyperZmass, a modified version of the public photomet-
ric redshift code HyperZ (Bolzonella et al. 2000): like the
public version, HyperZmass uses the SED fitting technique,
computing the best fit SED by minimizing the χ2 between
observed and model fluxes. We used models built with the
Bruzual & Charlot (2003) synthetic library. When the red-
shift is known, either spectroscopic or photometric, the best
fit SED and its normalization provide an estimate of the
stellar mass contained in the observed galaxy. In particu-
lar, we estimate the stellar mass content of the galaxies,
derived by BC03 code, by integrating the star formation
history over the galaxy age and subtracting from it the
“Return fraction” (R) due to mass loss during the stellar
evolution. For a Chabrier IMF, this fraction is already as
high as ∼ 40% at an age of the order of 1 Gyr and ap-
proaches asymptotically about 50% at older ages.
The parameters used to define the library of synthetic
models are listed in Table 1. Similar parameters have been
used in Fontana et al. (2004). The Calzetti (2000) extinction
law has been used. Following that paper, we have excluded
from the grid some models which may be not physical (e.g.
those implying large dust extinctions, AV > 0.6, in absence
of a significant star-formation rate, Age/τ > 4, see Table
1). To better match the ages of early-type galaxies in the
local universe and following SDSS studies, we also removed
models with τ < 1 Gyr and with star formation starting at
z < 1.
Table 1. Parameters Used for the Library of Template
Method Smooth SFHs Complex SFHs
IMF Chabrier Chabrier
SFR τ (Gyr) [0.1,∞]a [1,∞]
log(Age)b (yr) [8, 10.2] [8, 10]
burst age (yr) − [0, 1010]
burst fraction − [0, 0.9]
Metallicities Z⊙ [0.1Z⊙, 2Z⊙]
Extinction Calzetti law Charlot&Fall model
(n = 0.7, µ ∈ [0.1, 1])
Dust content AcV ∈ [0, 2.4] τV ∈ [0, 6]
a τ < 1 if star formation starts at z < 1.
b At each redshift, galaxies are forced to have ages smaller
than the Hubble time at that redshift.
c AV < 0.6 if Age/τ > 4.
We find that the “formal” typical 1σ statistical errors
(defined as the 68% range as derived from the χ2 statis-
tics) on the estimated masses, not taking into account the
error on the estimate of the photometric redshift for the
K-selected sample, are of the order of 0.04 dex for the
K-selected sample and 0.05 for the I-selected sample. A
more reliable estimate of the errors has been obtained us-
ing HyperZ to simulate catalogs to the same depth of our
sample (see Bolzonella et al. 2000). Using all 12 photo-
metric bands (from u∗ to K), available for a subset of our
data, and realistic photometric errors, the recovered stellar
masses reproduce the input masses with no significant offset
and a dispersion of 0.12 dex up to z ∼ 3. For comparison,
using only the optical bands (from u∗ to z′) the disper-
sion increases to ∼ 0.49 dex at z > 1. The best fit masses
obtained from input simulations built using randomly all
available metallicities and analyzed only with solar metal-
licity models are not significantly shifted from the input
masses, but the dispersion increases from 0.12 dex to 0.21
dex. These dispersions, computed using a 4σ clipping, pro-
vide an estimate of the minimum, intrinsic uncertainties of
this method at our depth. For the K-selected photometric
sample further uncertainties in the fitting technique are due
to the photometric redshift accuracy (σ∆z ≃ 0.02(1 + z)
up to z = 2.5) which corresponds on average to about 0.12
dex of uncertainty in mass, being larger at low redshift (∼
0.2 dex at z < 0.4) than at high-z (∼ 0.10 dex at z = 2).
Although in principle the best-fitting technique pro-
vides estimates also for age, metallicity, dust content and
SFH timescale, our simulations show that on average all
these quantities are much more affected by degeneracies
and therefore less constrained than the stellar mass.
In addition, we have compared our derived masses with
those obtained by using different population synthesis mod-
els, such as Pégase and Maraston (2005) models. In partic-
ular, Maraston (2005) models include the thermally pulsing
asymptotic giant branch (TP-AGB) phase, calibrated with
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 7
local stellar populations. This stellar phase is the dominant
source of bolometric and near-IR energy for a simple stellar
population in the age range 0.2 to 2 Gyr. We have tested
the differences with BC03 models using the I-selected spec-
troscopic sample and we found only a small but systematic
shift (∼ −0.14 dex and a similar dispersion) up to z ∼ 1.2
both with and without the use of near-IR photometry. On
the contrary, masses derived using Pégase models and sim-
ilar SFHs have instead no significant offset.
At higher redshifts the differences between our esti-
mated masses and those obtained with Maraston models in
the K-selected spectroscopic subsample are slightly smaller
and even smaller in the K-selected photometric sample
(∼ −0.11,−0.08, respectively). This differences are smaller
than that found by Maraston et al. (2006), ∼ −0.2, in their
SED fitting (from B up to Spitzer IRAC and MIPS bands)
of a few high redshift passive galaxies with typical ages
in the range 0.5 – 2.0 Gyr, selected in the Hubble Ultra
Deep Field (HUDF). This difference between our results
and those of Maraston et al. could be due to a combina-
tion of effects, such as the absence in our photometric data
of mid-IR Spitzer photometry, which at these redshifts is
sampling the rest frame near-IR part of the SED, mostly in-
fluenced by the TP-AGB phase, and also to the wide range
of complex stellar populations in our sample, in which the
effect of the TP-AGB phase may be diluted by the SFH.
3.2. Complex SFHs
Real galaxies could have undergone a more complex SFH,
in particular with the possible presence of bursts of star
formation on the top of a smooth SFH. Thus, we have com-
puted masses also following a different approach, which has
been intensively used in previous studies of SDSS galaxies
(e.g. Kauffmann et al. 2003, Brinchmann et al. 2004, Salim
et al. 2005, Gallazzi et al. 2005). In this approach we pa-
rameterize each SF history in terms of two components:
an underlying continuous model, with an exponentially de-
clining SF law (SFR(t) ∝ exp(−t/τ)), and random bursts
superimposed on it. We assume that random bursts occur
with equal probability at all times up to galaxy age. They
are parameterized in terms of the ratio between the mass
of stars formed in the burst and the total mass of stars
formed by the continuous model over the age. This ratio is
taken to be distributed between 0.0 and 0.9. During a burst,
stars are assumed to form at a constant rate for a time dis-
tributed uniformly in the range 30 – 300 Myr. The burst
probability is set so that 50% of the galaxies in the library
have experienced a burst in the past 2 Gyr. Attenuation by
dust is described by a two-component model (see Charlot
& Fall 2000), defined by two parameters: the effective V -
band absorption optical depth τV affecting stars younger
than 10 Myr and arising from giant molecular clouds and
the diffuse ISM, and the fraction µ of it contributed by the
diffuse ISM, that also affects older stars. We take τV to be
distributed between 0 and 6 with a broad peak around 1
and µ to be distributed between 0.1 and 1 with a broad
peak around 0.3. Finally, our model galaxies have metallic-
ities uniformly distributed between 0.1 and 2 Z⊙.
The model spectra are computed at the galaxy redshift
and in each of them we measure the k-shifted model magni-
tudes for each VVDS photometric band. We also force the
age of all models in a specific redshift range to be smaller
than the Hubble time at that redshift. The model SEDs
Fig. 4. Effect of NIR photometry in the mass determina-
tion: ratio between masses estimated without and with NIR
photometry vs. mass determined without NIR photometry.
The data have been splitted into different redshift ranges.
Left: masses determined using smooth SFHs. Right: The
same, but using complex SFHs
are then scaled to each observed SED with a least squares
method and the same scaling factor is applied to the model
stellar mass. We compare the observed to the model fluxes
in each photometric band and the χ2 goodness of fit of
each model determines the weight (∝ exp[−χ2/2]) to be
assigned to the physical parameters of that model when
building the probability distributions for each parameter
of any given galaxy. The probability distribution function
(PDF) of a given physical parameter is thus obtained from
the distribution of the weights of all models in the library
at the specified redshift. We characterize the PDF using its
median and the 16 – 84 percentile range (equivalent to ±1σ
range for Gaussian distributions), and also record the χ2 of
the best-fitting model.
Similarly to what has been done for the models with
smooth SFH (see Section 3.1), also in this case the stel-
lar mass content of galaxies is derived by subtracting the
return fraction R from the total formed stellar mass. We
find that the average “formal” 1σ error (defined as half of
the 16 – 84 percentile range) on the estimated masses is of
the order of 0.09 dex for the K-selected sample. The av-
erage error increases with redshift from ∼ 0.06 dex at low
redshift to ∼ 0.11 dex at 1 < z < 2 and decreases with in-
creasing mass from ∼ 0.08 dex for logM < 10 to ∼ 0.05 for
logM > 10 at z ≃ 0.7. In the K-selected sample the photo-
metric redshift accuracy induced a further uncertainty on
the mass of the order of 30% up to z > 1.5. In the I-selected
sample, where near-IR photometry is not always available,
the typical error on the mass is larger and is of the order
of ∼ 0.13 dex.
8 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
3.3. Effect of NIR Photometry
For about half of the sources in the I-selected sample only
optical photometry is available. We have therefore used the
results obtained for theK-selected spectroscopic subsample
to better understand the reliability of the mass estimates in
the whole I-selected sample and quantify potential system-
atic effects. We found that the mass estimates derived using
only optical bands are on average in rather good agreement
with those obtained using also NIR bands up to z ∼ 1.2. In
absence of NIR bands the galaxy stellar masses tend to be
only slightly overestimated, with a median shift < 0.1 dex;
this is due to the fact that already at z = 0.4, for example,
the z′-band (the reddest band used in the fit in absence of
NIR) samples the R-band rest-frame and therefore the SED
fitting is less reliable for the estimate of the stellar masses.
There is however a significant fraction of the galaxies for
which the ratio between the two masses is higher than a
factor of three (see upper panels of Fig.4). This fraction of
galaxies with significantly discrepant mass estimates is ∼
5% for the models with smooth SFH and ∼ 9 % for the
models with complex SFH.
At higher redshifts, where our reddest optical band, i.e.
the z-band, is sampling the rest-frame spectrum bluewards
of the 4000 Å break, the comparison of the two sets of
mass estimates (i.e. with and without near-IR photometry)
is significantly worse. Not only the median shift increases
significantly, but also the ratio of the two sets of masses
is significantly correlated with the mass derived without
using NIR photometry (see lower panels of Fig. 4). For this
reason, we have decided to use the whole I-selected VVDS
spectroscopic sample only up to z ∼ 1.2, whereas at higher
redshifts we use as reference the K-selected photometric
sample.
As shown in the upper panels of Fig.4, the ratio between
the masses computed without and with NIR photometry
has a non-negligible dispersion also for z < 1.2, with the
masses computed without NIR photometry being higher on
average. In order to statistically correct for this effect, we
have performed the following Monte Carlo simulation. For
each galaxy without near-IR photometry in the I-selected
spectroscopic sample we have applied a correction factor
to its estimated mass. This correction factor has been de-
rived randomly from the observed distribution, at the mass
of each galaxy, of the ratios of the masses with and with-
out NIR photometry. The effect on the mass function of
using these “statistically corrected” masses is shown and
discussed in Sect. 4.
3.4. Comparison of the Masses Obtained with the Two
Methods
In this section we compare the mass estimates we obtained
using the two different methods described above for the
VVDS galaxies. Since the ratio of the two estimates is al-
most independent of the mass, in Fig. 5 we show the his-
tograms of this ratio, integrated over all masses, for two dif-
ferent redshift bins. In the upper panel (z < 1.2), both data
from the I-selected and the K-selected samples are shown;
in the lower panel only data from the K-selected sample
are shown, since the I-selected sample is not used to derive
the mass function in this redshift range. Gaussian curves,
representing the bulk of the population, are drawn on the
Fig. 5. Histograms of the ratio of the masses derived with
the smooth and the complex star formation histories. In
the upper panel (z < 1.2) both data from the I-selected
and the K-selected samples are shown; in the lower panel
(z > 1.2) only data from the K-selected sample are shown,
since the I-selected sample is not used to derive the mass
function in this redshift range.
top of each histogram. The parameters of each Gaussian
are reported in the figure.
The global comparison of the two sets of masses is rather
satisfactory, even if it shows a systematic shift, larger for
theK-selected sample, between the two sets of masses, with
the ‘smooth SFH’ masses being on average smaller than the
‘complex SFH’ masses. The values of σ of these Gaussians
are similar, of the order of 0.13 dex. However, in two of the
three cases (i.e. the I-selected sample at low redshift and
the K-selected sample at high redshift) the distributions of
the ratio of the masses appear to be asymmetric, with tails
which are not well represented by a Gaussian distribution.
The fractions of these “outliers” are given in Fig. 5. This
tail is particularly significant for the I-selected sample, for
which there are galaxies with the ratio between the two
masses higher than 3 and in a few cases reaching a value of
We have analyzed the effect of the different parameters
used in the two methods. The impact of different extinction
curves on the mass estimates has already been investigated
by Papovich et al. (2001), Dickinson et al. (2003), Fontana
et al. (2004), and found to be small. We have repeated the
same exercise for the two different dust attenuation models
adopted, finding that for a given SFH the mass estimated
with different extinction laws are similar, with an average
shift of 0.02 dex.
Analyzing in some detail the properties of the galaxies
which are in the extended tail of large mass ratios for the I-
selected sample at low redshift (see the upper panel in Fig.
5), we found that, even if many of them do not have near-
IR photometry and therefore their mass is more uncertain
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 9
(see previous section), on average they are characterized by
blue colours in the bluer bands (B − I) and red colours in
the redder bands (I − z or I − K). Because of this, they
have been fitted typically with low values of the popula-
tion age by HyperZmass with a smooth SFH, while the
estimate obtained with a complex SFH corresponds to an
older, and therefore more massive, population plus a more
recent burst with a mass fraction in the burst of the order
of fburst < 0.15. Vice versa the low ratio outliers in the K-
selected sample at high redshift have been fitted typically
with moderately higher dust content by HyperZmass than
with complex SFHs. Finally, we conclude that the main dif-
ferences between the two methods to determine the masses
are largely due to different assumed SFHs and, in particu-
lar, to the secondary burst component allowed in the model
with complex SFHs.
To summarize, we have explored in detail two differ-
ent methods and a wide parameter space (see Table 1)
to estimate the stellar mass content in galaxies in order
to better understand the uncertainties in the photomet-
ric stellar mass determinations. Indeed, a good estimate of
the intrinsic errors may be critical for the GSMF measure-
ment and interpretation. We found that, within a given
assumption on the SFH, the accuracy of the photomet-
ric stellar mass is overall satisfactory, with intrinsic un-
certainties in the fitting technique of the order of ∼ 30%,
in agreement with similar results in the K20 (Fontana
et al. 2004), HDFN (Dickinson et al. 2003) and HDFS
(Fontana et al. 2003) at the same redshifts. These errors
are smaller than the estimates at higher redshift (z ≃ 3)
(Papovich et al. 2001, Shapley et al. 2001), since at our av-
erage redshifts (z ≃ 0.7−1) we can rely on a better sampling
of the rest-frame near-IR part of the spectrum, while are
similar to the uncertainties estimated at high-z using IRAC
data by Shapley et al. (2005). For theK-selected photomet-
ric sample the uncertainties in the stellar mass due to the
photometric redshift errors are on average of the order of
30% up to z > 1.5, giving a total fitting uncertainty up
to 45% at z > 1.5. Finally, systematic shifts, mainly due
to different assumptions on the SFHs, can be as large as
∼ 40% over the entire redshift range 0.05 < z < 2.5 when
NIR photometry is available. The uncertainty in the de-
rived masses is obviously higher also at low redshift when
NIR photometry is not available and in this case it becomes
extremely large at z > 1.2 (see Fig.4).
For what concerns the absolute value of the mass, its
uncertainty is mainly due to the assumptions on the IMF
and it is within a factor of 2 for the typical IMFs usually
adopted in the literature.
In the following sections we discuss in some detail the
effects of the two methods on the derivation of the GSMF.
3.5. Massive Galaxies at z > 1
Figure 6 shows the stellar masses for the 2 samples (I and
K-selected) derived using the smooth SFHs. It is inter-
esting to note the presence of numerous massive objects
(logM > 11) at all redshifts and up to z = 2.5. High-
z massive galaxies have been already observed in previous
surveys (Fontana et al. 2004, Saracco et al. 2005, Cimatti et
al. 2004, Glazebrook et al 2004, Fontana et al. 2006, Trujillo
et al. 2006). Here the relatively wide area (the K-selected
sample is more than 10 times wider and from 0.5 to 1 mag-
nitude deeper than the K20 survey) allows to better sam-
Fig. 6. Stellar Mass as a function of redshift for the I-
selected spectroscopic (left) and for the K-selected photo-
metric (right) samples for smooth SFHs.
ple the massive tail of the population. We note that mas-
sive galaxies have typically redder optical-NIR rest-frame
colours (〈MI −MK〉 ≃ 0.7) compared to the whole popu-
lation (〈MI −MK〉 ≃ 0.5), consistently with the idea that
massive galaxies host the oldest stellar population. Further
analysis of the stellar population properties and spectral
features of massive galaxies, as well as of red objects will
be presented in forthcoming papers (Lamareille et al. in
preparation, Vergani et al. 2007, Temporin et al. in prepa-
ration).
4. Mass Function Estimate
Once the stellar mass has been estimated for each galaxy
in the sample, the derivation of the corresponding Galaxy
Stellar Mass Function (MF) follows the traditional tech-
niques used for the computation of the luminosity function.
Here we apply both the classical non-parametric 1/Vmax
formalism (Schmidt 1968, Felten 1976) and the parametric
STY (Sandage, Tammann & Yahil 1979) method to esti-
mate best-fit Schechter (1976) parameters (α,M∗stars, φ
In the case of the K-selected sample, in order to take into
account the two different magnitude limits, we perform a
“Coherent Analysis of independent samples” as described
by Avni & Bahcall (1980).
Ilbert et al. (2004) have shown that the estimate of the
faint end of the global luminosity function can be biased,
because, due to different k-corrections, different galaxy
types have different absolute magnitude limits for the same
apparent magnitude limit. The same bias is present also for
the low mass end of the mass function. This is due to the
fact that, because of the existing dispersion in the mass-to-
light ratio of different galaxy types, at small masses the ob-
jects with the largest mass-to-light ratio are not included in
a magnitude limited sample (see Appendix B in Fontana et
10 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
Fig. 7. Effect on the I-selected MF of the use of the statistically corrected masses, which take into account the effect of
near-IR photometry on the mass determination (see text for details). Complex SFHs have been used to derive masses.
Empty circles represent the MF obtained using the original uncorrected masses, filled squares show the MF obtained
using the statistically corrected masses. For comparison the STY Schechter MF is shown for the subsample where near-IR
photometry is available. The vertical dashed lines represent the completeness limit of the sample as defined in the text.
al. 2004 for an extensive discussion). For this reason, when
computing the global mass functions with the STY method,
in order to fully avoid this bias, we should use in each red-
shift range only galaxies above the stellar mass limit where
all the SEDs are potentially observable. In both the K- and
I-selected samples these limits derive from the conversion
between photometry and stellar mass for early-type galax-
ies and are very restrictive. However, recent results show
that the faint-end and the low-mass end of the luminosity
and mass function is dominated by late-type galaxies up to
z ∼ 2 (Fontana et al. 2004, Zucca et al. 2006, Bundy et al.
2006). Therefore for the STY estimate we will use as lower
limit of the mass range the minimum mass above which
late-type SEDs (defined by rest-frame optical/NIR colours
MI −MK < 0.4) are potentially observable (see Fig. 9).
We have estimated the MF for both the deep I-selected
(17.5 < I < 24) spectroscopic sample and the photomet-
ric K-selected (K < 22.34 & K < 22.84) sample. For
each sample the MF has been estimated using masses com-
puted with both methods described in Section 2.3. In the
case of the spectroscopic sample, in order to correct for
both the non-targeted sources in spectroscopy and those
for which the spectroscopic measurement failed, we use a
statistical weight wi, associated with each galaxy i with
a secure redshift measurement (see Ilbert et al. 2005 for
details). This weight is the inverse of the product of the
Target Sampling Rate times the Spectroscopic Success Rate.
Accurate weights have been derived by Ilbert et al. (2005)
for all objects with secure spectroscopic redshifts, tak-
ing into account all the parameters involved (magnitudes,
galaxy size and redshift).
For the K-selected sample, we have tested the effect of
catastrophic photometric redshifts (see discussion in Sec.
2.2) on the evolution of the mass function and mass den-
sity. We have used the I-selected spectroscopic sample, re-
placing spectroscopic redshifts with photometric redshifts.
The two MFs (with either spectroscopic or photometric red-
shifts) are very similar in the whole mass and redshift range
(0.05 < z < 2.5) analyzed and even at z > 1.2, where we
note a not negligible number of catastrophic photometric
redshifts (see discussion in Sec. 2.2). There is no evidence
of a strong bias in the normalization and in the shape of the
MF; also the massive tails of the MFs are similar, within
the statistical errors. We conclude that the catastrophic
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 11
Fig. 8.K-selected MF derived from the 2 subsamples, deep (filled circles) and shallow (empty circles), separately (smooth
SFHs have been used to derive masses). For comparison the STY Schechter MF for the globalK-selected sample is shown.
The vertical dashed lines represent the completeness limit of the 2 K-selected subsamples.
solutions at high photometric redshifts (i.e. masses) do not
strongly affect our results.
4.1. The VVDS Galaxy Stellar Mass Function
The resulting stellar mass functions of the VVDS sample
are derived in the following redshift ranges: (a) 0.05 < z <
1.2 for the I-selected sample, because at higher redshift the
mass estimate becomes very uncertain (see figure 4) and
(b) 0.05 < z < 2.5 for the K-selected sample. We have
furthermore divided the 2 samples into different redshift
bins in order to sample evolution with similar numbers of
sources in each bin.
For the galaxies in the I-selected sample not covered
by near-IR data, we have used the statistically corrected
masses derived through a Monte Carlo simulation, to take
into account the effect of the near-IR photometry in the
mass determination (see Sec. 3.3). Figure 7 shows the ef-
fect in the MF for complex SFHs. The high mass tail is
significantly reduced if we use statistically corrected masses
when near-IR is not available. Consistent MFs have been
12 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
Fig. 9. Galaxy Stellar Mass Functions in the I-selected (squares) and K-selected (triangles) using both methods to
estimate the stellar masses (empty symbols for smooth SFHs and filled for complex SFHs). The STY Schechter fits for
the 2 methods limit the hatched regions (horizontal hatched for the K-selected and vertical hatched for the I-selected
samples). Vertical hatched regions represents the completeness limit of the 2 samples. The local MFs by Cole et al.
(2001), both original and “rescaled” version (Fontana et al. 2004), and by Bell et al. (2003) are reported in each panel
as dotted lines.
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 13
Table 2. STY parameters in the different redshift ranges
sample method z range mean redshift α logM∗stars(h
70 M⊙) φ
∗(10−3h370Mpc
I smooth 0.05 - 0.4 0.27 -1.26+0.01
−0.02 11 1.90
+0.08
−0.16
I smooth 0.4 - 0.7 0.58 -1.23+0.04
−0.04 11
+0.08
−0.08 1.72
+0.33
−0.28
I smooth 0.7 - 0.9 0.8 -1.23+0.12
−0.11 10.88
+0.15
−0.13 1.6
+0.55
−0.45
I smooth 0.9 - 1.2 1.05 -1.09+0.19
−0.17 10.85
+0.14
−0.14 1.3
+0.43
−0.46
I complex 0.05 - 0.4 0.27 -1.28+0.02
−0.01 11.15 1.75
+0.16
−0.08
I complex 0.4 - 0.7 0.58 -1.22+0.04
−0.04 11.15
+0.08
−0.08 1.58
+0.30
−0.26
I complex 0.7 - 0.9 0.81 -1.04+0.08
−0.07 10.83
+0.07
−0.07 3.02
+0.57
−0.51
I complex 0.9 - 1.2 1.04 -1.16+0.1
−0.09 10.89
+0.08
−0.07 1.80
+0.44
−0.39
K smooth 0.05 - 0.4 0.26 -1.38+0.02
−0.01 10.93 1.29
+0.10
−0.05
K smooth 0.4 - 0.7 0.57 -1.14+0.04
−0.04 10.93
+0.06
−0.06 1.83
+0.27
−0.24
K smooth 0.7 - 0.9 0.81 -1.01+0.07
−0.08 10.67
+0.07
−0.05 2.6
+0.38
−0.44
K smooth 0.9 - 1.2 1.05 -1.1+0.07
−0.08 10.78
+0.06
−0.05 1.83
+0.28
−0.30
K smooth 1.2 - 1.6 1.4 -1.15+0.12
−0.12 10.72
+0.07
−0.06 1.48
+0.30
−0.30
K smooth 1.6 - 2.5 1.96 -1.15 10.96+0.01
−0.02 0.9
+0.30
−0.30
K complex 0.05 - 0.4 0.26 -1.39+0.01
−0.02 11.12 1.17
+0.05
−0.09
K complex 0.4 - 0.7 0.57 -1.16+0.04
−0.04 11.12
+0.06
−0.06 1.58
+0.24
−0.22
K complex 0.7 - 0.9 0.81 -1.16+0.07
−0.07 10.98
+0.07
−0.07 1.74
+0.36
−0.30
K complex 0.9 - 1.2 1.05 -1.2+0.07
−0.06 11.07
+0.06
−0.06 1.34
+0.26
−0.21
K complex 1.2 - 1.6 1.4 -1.17+0.12
−0.12 10.93
+0.07
−0.06 1.39
+0.29
−0.28
K complex 1.6 - 2.5 1.96 -1.17 10.97+0.01
−0.02 1.25
+0.09
−0.04
obtained in the sub-area of I-selected sample where near-IR
photometry is available (see Fig. 7).
For the K-selected sample, we have analyzed the ef-
fect of the cosmic variance on small areas, deriving the MF
for the two K-selected subsamples, deep and shallow, sepa-
rately (see Figure 8). We find a significantly lower MF (by
a factor 1.8 and 1.6) in the redshift range 0.4 < z < 0.7 and
0.7 < z < 0.9 in the deep K-selected sample (K < 22.84
over 168 arcmin2) compared to the shallow K-band sam-
ple (K < 22.34 over 442 arcmin2). The significance of such
differences in the MF, is of ∼ 2 − 3σ in each mass bin at
0.4 < z < 0.7 and ∼ 1 − 2σ at 0.7 < z < 0.9. Globally,
i.e. for the total number densities over the complete mass
range, the differences are significant at about 5-3 σ level
in the two redshift ranges, respectively. This problem leads
to a clear warning on the results based on small fields, as
covered by most of the previous existing surveys.
In Figure 9 we show the MFs derived using the I-
selected spectroscopic sample and the K-selected photo-
metric sample for both methods (smooth and complex
SFHs) to derive the masses. The resulting mass functions
are quite well fitted by Schechter functions. The best-fit
Schechter parameters are summarized in Table 2, with the
uncertainties derived from the projection of the 68% confi-
dence ellipse. Since in the lowest and highest redshift bins
(z ≃ 0.2 and 2) the values of M∗stars and the low-mass-end
slope (α), respectively, are poorly constrained, they have
been fixed to the values measured in the following and pre-
vious redshift bins respectively.
We note, first, that the overall agreement between the
MF derived with the different methods for masses determi-
nation is fairly satisfactory, albeit complex SFHs estimates
provide typically larger masses. The systematic shift be-
tween the 2 methods (Section 3.4) is reflected in most of
the redshift bins also in the characteristic mass (M∗stars)
of the MF while the best fit slopes (α) and φ∗ Schechter
parameters agree within the errors between the different
methods in most of the redshift bins.
We note, furthermore, an overall agreement between the
2 samples (I- and K-selected), and in most of the redshift
bins the Schechter parameters agree within the errors, even
if some differences exist. More in detail, the I-selected sam-
ple in the range 0.4 < z < 0.9 has a higher low-mass
(< 9.5 dex) end and a slightly steeper MF (α ∼ −1.23)
than the K-selected one (α > −1.15). These differences are
probably due to the population of blue K-faint galaxies,
that are missed in the K-sample, as discussed in Section
3. These galaxies have, indeed, median colours in the I-
selected sample that are bluer than in the K-selected sam-
ple (I−K ≃ 0.45 compared to ≃ 0.89). A similar behaviour
has been noted in the local MF derived using an optically
selected sample (g band) compared to the local MF from
the near-IR (2MASS) sample (Bell et al. 2003). On the
contrary, at even lower masses (< 8.5 dex) at z < 0.4 the
K-selected MF is slightly steeper than the I-selected one,
but no significant differences in the colour of the two pop-
ulations is found.
4.2. Comparison with Previous Surveys
In general, previous efforts to derive MF have relied on
smaller or more limited samples, or often based mainly
on photometric redshifts (Drory et al. 2004, 2005). We
have compared our MF determination with literature re-
sults based on different surveys (K20, COMBO17, MUSIC,
DEEP2, FDF+CDFS), rescaled to Chabrier IMF (see
Figure 10). Our MFs rely on a higher statistics at inter-
mediate to high-mass ranges, and therefore present lower
statistical errors. At z < 0.2 we sample unprecedented mass
ranges, more than one order of magnitude lower than previ-
ous surveys, while at z > 0.4 the FDF and MUSIC surveys
reach lower mass limits even if on significantly smaller area.
14 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
Fig. 10. Comparison between the I-selected and the K-selected MFs in the VVDS (hatched vertical and horizontal STY
regions, respectively, see caption Figure 9) and the literature data (K20, COMBO17, MUSIC, DEEP2, FDF+CDFS; for
each the band of selection is indicated in the parenthesis). The vertical hatched regions represent the completeness limits
of the VVDS samples.
Our MFs are in fairly good agreement with previous studies
over the whole mass range up to z ∼ 1.2. However, some
differences exist, in particular at the massive end, which is
more sensitive to the different selections, methods, statis-
tics and to cosmic variance due to large scale structures: for
example, in the MUSIC-GOODS survey there are two sig-
nificant overdensities at z ∼ 0.7. The MFs from COMBO17
(Borch et al. 2006) and also from DEEP2 (Bundy et al.
2006) are systematically higher than previous surveys at
the massive-end, in particular in the range 0.7 < z < 1.2.
The MFs in the FDF+CDFS are instead systematically
lower than ours at the massive-end and higher than our
extrapolation to masses lower than our completeness limit.
At z > 1.2 our MF is systematically higher than previ-
ous studies. Given the area sampled (more than a factor
4 wider compared to FDF+CDFS and to MUSIC) and
the consistency at these redshifts of our MF in the 2 K-
selected separated areas (see Figure 8), we are confident
in our results. However at high-z the uncertainties on the
stellar masses estimate increase (up to 0.16 dex including
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 15
also the photometric redshift errors) and could produce a
partially spurios excess in the number densities of galax-
ies, in particular in the massive tail of the MF. This ef-
fect is discussed in Kitzbichler & White (2007) which take
into account in the hierarchical formation Millenium simu-
lation the effect of the dispersion in the mass determination
(0.25 dex, i.e. 78%). We have performed a similar analysis,
taking into account the uncertainty on the mass, due to
the fitting technique (∼ 30%) and to the uncertainty of
the photometric redshifts (both its dependence on redshift
and magnitudes as described in previous sections, i.e. up to
σz ≃ 0.2 at z = 2 and K > 21.5). We found that the effect
on the MF is always small, and only the very massive tail
(M > 2 × 1011M⊙) is systematically overestimated (up to
0.2 dex). This effect can not completely explain the excess
found compared to previous surveys, which are affected in
a similar way by the same bias.
4.3. The Evolution of the Galaxy Stellar Mass Function
The VVDS allows us to follow the evolution of the
MF within a single sample over a wide redshift range.
Difficulties in the interpretation of the evolution are, in-
deed, due to the comparison with the local MFs, which
have been determined with different methods and sample
selection. For example, no local MF has been derived using
complex SFHs for mass determinations. In our analysis we
use, as reference, the local MF by Bell et al. (2003) and Cole
et al. (2001) rescaled to Chabrier IMF. In particular, the
Cole et al. (2001) local mass function, derived with smooth
SFHs but with formation redshift fixed at z = 20, has been
rescaled to smooth SFHs method with free formation red-
shift by Fontana et al. (2004).
The first important result is that, thanks to our very
deep samples, both I- and K-selected, the low-mass end of
the MF is even better determined than in the local sam-
ple up to z < 0.4, probing for the first time masses down
to about 3 × 107M⊙. The low mass-end is rather steep
(−1.38 < α < −1.26), and could even be described by a
double Schechter function, and is steeper than the local es-
timates (α = −1.18±0.03 Cole et al. 2001, α = −1.10±0.02
Bell et al. 2003), possibly due to the fact they are not prob-
ing masses smaller than 109 M⊙ (more than one order of
magnitude more massive than in our sample). As evident
from Figure 9, we find a substantial population of low-mass
(< 109M⊙) galaxies at low redshifts (z < 0.4). This popu-
lation is composed by faint blue galaxies with similar prop-
erties in the 2 samples (I- and K-selected): I,K ≃ 22− 23,
MI ,MK ≃ −16,−17 with median MI − MK ≃ 0.3, and
median z ≃ 0.1− 0.2. This is a very strong result from our
survey which can rely on a wider area and a deeper sam-
ple than previous surveys at low redshifts. At z > 0.4 the
low-mass slope is on the contrary always consistent with
the local values. Even if we are not probing masses smaller
than 108M⊙ at z > 0.4, we found that the MF remains
quite flat (−1.23 < α < −1.04) at all redshifts, similar to
that of Fontana et al. (2006) which probe lower masses (see
figure 10).
From a visual inspection of Figure 9, we see that up to
z ∼ 0.9 there is only a weak evolution of the MF, as sug-
gested by previous results (Fontana et al. 2004, 2006, Drory
et al. 2005), while at higher redshifts there appears to begin
a decrease in the normalization of the MF, even if a massive
tail remains present up to z = 2.5. At intermediate masses
Fig. 11. Cosmological evolution of the galaxy number den-
sity as a function of redshift, as observed from the VVDS
in various mass ranges (> 108M⊙, > 10
9.77M⊙ and >
1010.77M⊙ from top to bottom). Observed data from Vmax
(shown as lower limit in the top panel) have been corrected,
when necessary, for incompleteness integrating the mass
function using the best fit Schechter parameters. VVDS
data (big filled circles), averaged over the I- and the K-
selected samples and the 2 methods to derive the mass, are
plotted along with their statistical errors (solid error bars)
and the scatter between the 2 different samples and meth-
ods (dotted error bars). The solid lines show the best-fit
power laws ∝ (1 + z)β, while the dashed lines correspond
to the no-evolution solution normalized at z = 0. Results
from previous surveys (small points and dot-dashed lines)
are also shown.
(9.5 < logM < 10.5), our VVDS MF is very well defined
and shows a clear evolution, i.e. the number density de-
creases with increasing redshifts compared to both the first
VVDS redshift bin and the local MF. This evolution is quite
mild up to z ≃ 0.9, while it becomes faster at higher z. At
larger masses the high mass end of the MF (> 1011 M⊙)
shows a small evolution up to z ≃ 2.5. However, its evolu-
tion is extremely dependent on the assumed local MF and
on the uncertainties in the mass determination, which pro-
duce a larger dispersion between the different methods and
samples compared to the intermediate-mass range.
In order to quantify the MF evolution, and its mass
dependency independently from the local MF, in the next
section we derive number densities for different mass limits.
16 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
Table 3. Number Density and Stellar Mass Density
zinf zsup Log(ρN ) Scatter Error Log(ρstars)Scatter Error
log(Mstars)> 8
0.05 0.40 -1.40 0.04 0.01 8.45 0.09 0.01
0.40 0.70 -1.63 0.08 0.02 8.34 0.08 0.02
0.70 0.90 -1.70 0.08 0.04 8.22 0.11 0.01
0.90 1.20 -1.78 0.13 0.05 8.14 0.12 0.01
1.20 1.60 -1.81 0.05 0.11 8.04 0.14 0.02
1.60 2.50 -1.90 0.13 0.01 8.05 0.11 0.01
log(Mstars)> 9.77
0.05 0.40 -2.20 0.06 0.01
0.40 0.70 -2.29 0.03 0.01
0.70 0.90 -2.33 0.04 0.01
0.90 1.20 -2.45 0.05 0.01
1.20 1.60 -2.54 0.02 0.01
1.60 2.50 -2.65 0.01 0.01
log(Mstars)> 10.77
0.05 0.40 -3.07 0.18 0.05 8.00 0.22 0.04
0.40 0.70 -3.04 0.10 0.02 8.04 0.14 0.02
0.70 0.90 -3.22 0.16 0.02 7.80 0.19 0.02
0.90 1.20 -3.28 0.15 0.02 7.76 0.18 0.02
1.20 1.60 -3.42 0.23 0.02 7.59 0.28 0.02
1.60 2.50 -3.35 0.11 0.01 7.70 0.11 0.01
4.4. Galaxy Number Density
Here we derive the number density of galaxies as a function
of redshift, using different lower limits in mass (Mmin). We
have estimated the number density from the observed data
(from Vmax), as well as from the incompleteness-corrected
MFs, i.e. integrating the best-fit Schechter functions over
the considered mass range. The corrections due to faint
galaxies dominate for Mmin = 10
8M⊙, while they are neg-
ligible for the other mass limits considered. A formal uncer-
tainty in this procedure was estimated by considering the
Vmax statistical errors and the range of acceptable Schechter
parameters values. In Figure 11 we plot our VVDS determi-
nations, averaged over the I- and K-selected samples and
the 2 methods for mass determination (listed in Table 3),
along with their statistical errors (always less than 10%)
and the scatter between the 2 different samples and meth-
ods (ranging between 10 and 45% and due mainly to the dif-
ferent methods rather than to the different samples). With
the two methods we find similar trends with redshift of the
number densities of galaxies, but with a systematic shift
which is significant only for the highest mass limit (for com-
plex SFHs the galaxy number densities are ∼ 50% higher
than for smooth SFHs). The effect of photometric redshift
and mass uncertainty on the number densities is always
small (< 15%) for the mass range shown in Figure 11, ex-
cept for the very massive galaxies (> 2 × 1011 M⊙, not
shown in the figure because of the small number of galaxies
in this mass range) where the intrinsic values could be up
to a factor ∼ 2 lower (see discussion in section 4.2). The
decrease in number density with redshift for all the adopted
mass limits is evident.
We have compared VVDS results to previous surveys
and with different local determinations. For the total num-
ber density (108 < Mstars < 10
13M⊙) VVDS data are very
well consistent with the evolutionary STY fit determined by
Fontana et al. (2006) in the GOODS-MUSIC survey. At in-
Fig. 12. Cosmological evolution of the stellar mass density
as a function of redshift as observed from the VVDS for
2 mass ranges: integrated over the whole range 108M⊙ ≤
Mstars ≤ 10
13M⊙ (upper panels) and for massive galax-
ies (> 1010.77M⊙) (lower panels). Symbols and lines as in
Figure 11.
termediate masses (> 109.77M⊙, corresponding to 10
for Salpeter IMF) our VVDS data have a better determina-
tion and smaller uncertainties than previous ones and are
consistent with most of them at z < 1.2 and in the upper en-
velope at higher z. For the high mass range (> 1010.77M⊙,
corresponding to 1011M⊙ for Salpeter IMF) we are quite
consistent with previous results, and even if our VVDS have
lower errors than previous ones, the dispersion within the
various VVDS measurements reflect the uncertainties for
massive galaxies.
If we represent the average number density evolution
by a power law ρN ∝ (1 + z)
β , we find that β(Mstars >
108) = −1.28 ± 0.15, β(Mstars > 10
9.77) = −1.26 ± 0.10,
and β(Mstars > 10
10.77) = −1.01 ± 0.05 (the errors on β
represent the uncertainties due to the 2 different methods).
We find on average a similar evolution for the 2 methods
analyzed and a slightly milder evolution with increasing
mass limit (‘downsizing’ in mass assembly). The average
evolution from z = 0 to z = 1 is a factor 2.4 ± 0.3 and
2.0± 0.1 from low to high-mass galaxies, respectively, and
increases to a factor 4.0 ± 0.9 and 3.0 ± 0.2, respectively,
at z = 2. We note moreover that for the highest mass limit
(Mstars > 10
10.77) at low redshift (z < 0.7) the number
density observed is consistent with no-evolution (fixing the
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 17
value to z = 0 we found an evolution < 30%), excluded
instead for the intermediate and low-mass limit. At high-z
(z > 1.5) for intermediate and high-mass range we note a
flattening in the number density from the VVDS data, sim-
ilar to Drory et al. (2005), but higher than Fontana et al.
(2006). This flattening is due to the high mass tail observed
in the range 1.6 < z < 2.5. This population shows ex-
tremely red colours (MI −MK ≃ 0.8) and could be related
to the appearance of a population of massive star forming
dusty galaxies, observed in previous surveys (Fontana et
al. 2004, Daddi et al. 2004b). The small excess induced by
uncertainties on the mass and photometric redshifts (see
discussion in section 4.2) can not completely explain the
difference with Fontana et al. (2006) survey, which is af-
fected by the same bias in a similar way.
The mass dependent evolution (“mass downsizing”) is
very debated and the results from different surveys are still
controversial. Deep surveys, such as the FDF & CDFS (an-
alyzed by Drory et al. 2005) find an evolution consistent
with ours (a decrease of about a factor 2.5 – 4 at z = 1− 2
in the number density of galaxies> 1010.77 M⊙). Fontana et
al. (2006) suggest a similar mild evolution up to z = 1, for
massive galaxies (> 1010.77M⊙) and a stronger evolution
at z > 1.5, reaching a factor about 10 at z = 3. Similarly,
Cimatti et al. (2006) show that the number density of lu-
minous (massive, Mstars > 10
11M⊙) early-type galaxies is
nearly constant up to z ∼ 0.8, while Bundy et al. (2006)
find a slight decrease, consistent with no evolution, only for
even more massive system (> 3×1011M⊙) and a more sig-
nificant decline for Mstars < 3× 10
11M⊙. Vice versa, data
from the MUNICS survey (Drory et al. 2004) show a faster
evolution of massive galaxies, even faster than for the less
massive systems (see also Figure 4 in Drory et al. 2005).
To summarize, our accurate results show that the MF
evolves mildly up to z ≃ 1 (about a factor 2.5 in the total
number density) and that a high-mass tail is still present
up to z = 2.5. Moreover, we find that massive systems
show an evolution that is on average milder (< 50% at
z < 1) than intermediate and low-mass galaxies and con-
sistent with a mild/negligible evolution (< 30%) up to
z ∼ 0.8. Conversely, a no-evolution scenario in the same
redshift range is definitely excluded for intermediate- and
low-mass galaxies.
This behaviour suggests that the assembly of the stellar
mass in objects with mass smaller than the localM∗stars was
quite significant between z = 2 and z = 0. Qualitatively,
this behaviour is expected for galaxies with SFHs prolonged
over cosmic time, which therefore continue to grow in terms
of stellar mass after z ∼ 1. Conversely, our results fur-
ther strengthen the fact that the number density of mas-
sive galaxies is roughly constant up to z ≃ 0.8, consistently
with a SFH peaked at higher redshifts, with the conversion
of most of their gas into stars happening at z > 1.5−2, rul-
ing out the ‘dry mergers’ as the major mechanism of their
assembly history, below z < 1.
5. Mass Density
Various attempts to reconstruct the cosmic evolution of the
stellar mass density have been previously made, mainly us-
ing NIR-selected samples (Dickinson et al. 2003, Fontana et
al. 2004, Drory et al. 2005). Our survey offers the possibil-
ity to investigate it using the MF derived from two different
optical- and NIR-selected samples, taking advantage of our
depth, and relatively wide area covered. Furthermore, the
different methods analyzed here to derive the stellar mass
content give us a direct measure of the uncertainties in-
volved.
We have estimated the stellar mass density from the
observed data, as well as from the incompleteness-corrected
MFs. Up to z < 1 the corrections due to faint galaxies are
relatively small. A formal uncertainty in this procedure was
estimated by considering the Vmax statistical errors and the
range of acceptable Schechter parameters values.
Figure 12 shows our results (averaged over the I- andK-
selected samples and the 2 methods with a typical scatter
of about 30-50% and statistical errors always less than 5%
see Table 3), for the total mass density and for the density
in massive galaxies (> 1010.77), along with their represen-
tative power laws (ρstars ∝ (1+z)
β), and compared to liter-
ature data (see references in the figure). For the total mass
density, even if the results from our survey cover a range
of values with some significant differences between the two
different methods (up to ∼ 40%), the general behaviour
and evolutionary trend is well defined by β = −1.19± 0.05.
We find that the evolution of the stellar mass density is
relatively slow with redshift, with a decrease of a factor
2.3 ± 0.1 up to z ≃ 1, up to a factor 4.5 ± 0.3 at z = 2.5.
The agreement of average total mass density with previous
surveys is reasonably good, and the range covered by VVDS
data reflect the different selection techniques and methods
used in different surveys. The average total mass density
evolution is milder than in the MUSIC sample (Fontana et
al. 2006) already at z > 0.5. Our evolutionary trend is con-
sistent with the upper envelope of previous surveys, even if
our highest-redshift value is uncertain because the low-mass
slope is poorly constrained. For comparison the analysis of
VVDS data using a IRAC-selected sample (see Arnouts et
al. 2007) finds similar values for the mass density, except
that the highest redshift point is lower than ours. Given the
present uncertainties on the low-mass slope of the GSMF,
the total mass density at z ≃ 2 remains poorly constrained.
The mass density of high-mass objects (> 1011M⊙ with
Salpeter IMF) varies by a factor up to 1.8 within the 2
methods adopted, but the evolutionary trend is similar
(β = −1.13± 0.01) and consistent with a decrease of about
a factor 2.18 ± 0.02 to z = 1 and 3.44 ± 0.04 to z = 2.0.
Moreover at low redshift (z < 0.7) the VVDS observed data
are consistent with a mild/negligible evolution (< 30%), as
indicated by the number density of massive galaxies (see
previous Section). Our data are roughly consistent with
Fontana et al. (2006) up to z = 1.5 (even if the slope of the
evolutionary trend is shallower), while at z > 1.5 the VVDS
mass-density of massive galaxies is significantly higher than
that in Fontana et al. (2006), reflecting the excess in MF at
high-z noted in the VVDS MF compared to previous ones
(see Section 4.2). This results, therefore, in a flatter evolu-
tionary trend over the total redshift range. Given the wider
area and completeness for high-mass objects, our samples
guarantee a higher statistical accuracy and confidence level
than before. However some caveat remains due to the effect
of photometric redshift and mass uncertainty on the mass
densities, which is anyhow always small (< 15%) except for
the massive galaxies (> 6 × 1010 M⊙) where the intrinsic
values could be up to 20-30% lower than our estimates (see
discussion in Section 4.2).
18 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
6. Summary and Discussion
We have investigated the evolution of the Galaxy Stellar
Mass Function up to to z = 2.5 using the VVDS survey
covered by deep VIMOS spectroscopy (17.5 < I < 24)
and multiband photometry (from U to K-band). For our
analysis we have used two different samples: (1) the opti-
cal (I-selected, 17.5 < I < 24) main spectroscopic sam-
ple, based on about 6500 secure redshifts over about 1750
arcmin2, and (2) a near-IR sample (K-selected, K < 22.84
& K < 22.34), in a sub-area of about 610 arcmin2 and
based on about 10200 galaxies with accurate photomet-
ric and spectroscopic redshifts. For the first time we have
probed masses down to a very low limit, in particular at
low-z (down to ∼ 3 × 107M⊙ at z ∼ 0.2), while the rela-
tively wide area has allowed us to determine the MF with
much higher statistical accuracy than previous samples.
In order to better understand uncertainties we have ap-
plied and compared two methods to estimate the stellar
mass content in galaxies from multiband SED fitting. The
2 methods differ in the explored parameter space (metal-
licity, dust law and content) and are based on different as-
sumptions on previous star formation history. The main
results from the stellar mass estimate can be summarized
as follows:
– The agreement between the 2 methods is fairly good
even if masses estimated with ‘complex SFHs’ are
systematically higher than ‘smooth SFHs’ masses.
For the K-selected sample the mean difference is
〈d logMstars〉 ≃ 0.12 dex, and the dispersion is σ =
0.13. The differences are mainly due to the secondary
burst component (complex SFHs) compared to smooth
SFHs.
– We found that mass estimates using only optical bands
are in rather good agreement with those using also NIR
bands up to z ∼ 1.2. We have used this information to
statistically correct masses for objects without near-IR
photometry. At higher redshifts the shift and dispersion
dramatically increase and the mass estimates become
unreliable if near-IR photometry is not available.
We have, thus, derived the MF using the VVDS I-
selected sample and extended it up to z = 2.5 thanks to
the K-selected sample. From a detailed analysis of the MF,
galaxy number density and mass density, in different mass
ranges, through cosmic time, we found evidences for:
– a substantial population of low-mass galaxies (<
109M⊙) at z ≃ 0.2 composed by faint (I,K ≃ 22, 23)
blue galaxies with median MI−MK ≃ 0.3, and absolute
magnitudes MI ,MK ≃ −16,−17;
– a slow evolution of the stellar mass function with red-
shift up to z ∼ 0.9 and a faster evolution at higher-z,
in particular for less massive systems. A massive popu-
lation is present up to z = 2.5 and have extremely red
colours (MI −MK ≃ 0.7− 0.8).
– at z > 0.4 the low-mass slope of the GSMF does not
evolve significantly and remains quite flat (−1.23 < α <
−1.04).
– the number density shows, on average, a mild differen-
tial evolution with mass, which is slower with increas-
ing mass limit. Such evolution can be described by a
power law ∝ (1 + z)β(>M). Within the VVDS redshift
range we found that β(> 108M⊙) = −1.28 ± 0.15,
β(> 109.77M⊙) = −1.26± 0.10 and β(> 10
10.77M⊙) =
−1.01± 0.05. For massive galaxies at low redshift (z <
0.7) the evolution is consistent with mild/negligible-
evolution (< 30%), which is excluded for low-mass sys-
tems.
– the evolution of the stellar mass density is relatively slow
with redshift, with a decrease of about a factor 2.3±0.1
to z ≃ 1, while at z ≃ 2.5 the decrease amounts to a fac-
tor up to 4.5± 0.3, milder than in previous surveys. For
massive galaxies the evolution at low redshift (z < 0.7)
is consistent with a mild/negligible evolution(< 30%),
and shows a flattening compared to previous results at
z > 1.5 due to a population with extremely red colours.
Our results provide new clues on the controversial ques-
tion of when galaxy formed and assembled their stellar
mass. Most of the massive galaxies seem to be in place up to
z = 1 and have, therefore, formed their stellar mass at high
redshift (z > 1), rather than assembled it mainly through
continuous galaxy merging of small galaxies at z < 1. On
the contrary, less massive systems have assembled their
mass (through merging or prolonged star formation his-
tory) later in cosmic time. In agreement with our results, a
substantial population of high-z (z ∼ 2−3) dusty and mas-
sive objects have been discovered in near-IR surveys (Daddi
et al. 2004b) and detected by Spitzer in the far-IR (Daddi
et al. 2005, Caputi et al. 2006b). This population could
be related to the initial phase of massive galaxy formation
during their strong star forming and dusty phase.
Finally, our results are not completely accounted for by
most of theoretical models of galaxy formation (see Fontana
et al. 2004, 2006 and Caputi et al. 2006a for a detailed com-
parison with models). For instance, models by De Lucia et
al. (2006) predict that the most massive galaxies generally
form their stars earlier, but assemble them later, mainly
at z < 1 via merging, than the less massive galaxies (i.e.
’downsizing in star formation but ’upsizing’ in mass assem-
bly, see Renzini 2007 for a recent discussion). Furthermore,
the stronger decrease with redshift of the low-mass popu-
lation, with a low-mass end of the GSMF which remains
substantially flat up to high redshift, is not reproduced by
most of the theoretical galaxy assembly models, which tend,
indeed, to overpredict the low-mass end of the MF (see
Fontana et al. 2006).
Understanding the mass assembly of less massive ob-
jects and disentangling merging processes from prolonged
star formation history is more complicated. In this respect
for a better comprehension of galaxy formation the VVDS
will allow us to further investigate the evolution of the stel-
lar mass function up to high-z also for different galaxy types
(spectral and morphological) and in different environments.
For example Arnouts et al. (2007) study the mass density
evolution of different galaxy population. Further analysis
of galaxy mass dependent evolution, using stellar popula-
tion properties, as well as observed spectral features, will
be presented in forthcoming papers (Lamareille et al., in
preparation, Vergani et al. 2007). Furthermore, it will be
possible to push the study of the galaxy stellar mass func-
tion at higher redshifts using SPITZER mid-IR observa-
tions. While most of present studies (Dickinson et al. 2003,
Drory et al. 2005) do not use rest-frame near-IR photome-
try to estimate stellar masses, our VVDS-SWIRE collabo-
ration will allow to combine the deep VVDS spectroscopic
sample with SPITZER-IRAC photometry.
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 19
Acknowledgements. This research has been developed within the
framework of the VVDS consortium.
This work has been partially supported by the CNRS-INSU and
its Programme National de Cosmologie (France), and by Italian
Ministry (MIUR) grants COFIN2000 (MM02037133) and COFIN2003
(num.2003020150).
The VLT-VIMOS observations have been carried out on guaranteed
time (GTO) allocated by the European Southern Observatory (ESO)
to the VIRMOS consortium, under a contractual agreement between
the Centre National de la Recherche Scientifique of France, heading
a consortium of French and Italian institutes, and ESO, to design,
manufacture and test the VIMOS instrument. We are in debt with
E. Bell, S. Salimbeni, and E. Fontana for providing the data from
their survey in electronic format, and to C. Maraston for her galaxy
evolution models in BC format.
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1 INAF-Osservatorio Astronomico di Bologna - Via Ranzani,1,
I-40127, Bologna, Italy
2 INAF-IASF - via Bassini 15, I-20133, Milano, Italy
3 Laboratoire d’Astrophysique de Marseille, UMR 6110
CNRS-Université de Provence, BP8, 13376 Marseille Cedex
12, France
4 INAF-Osservatorio Astronomico di Brera - Via Brera 28,
Milan, Italy
http://arxiv.org/abs/astro-ph/0506044
http://arxiv.org/abs/astro-ph/0611724
http://arxiv.org/abs/astro-ph/0311475
http://arxiv.org/abs/astro-ph/0410295
http://arxiv.org/abs/astro-ph/0702148
20 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
5 Institute for Astronomy, 2680 Woodlawn Dr., University of
Hawaii, Honolulu, Hawaii, 96822
6 Max Planck Institut fur Astrophysik, 85741, Garching,
Germany
7 Institut d’Astrophysique de Paris, UMR 7095, 98 bis Bvd
Arago, 75014 Paris, France
8 Centro de Astrofsica da Universidade do Porto, Rua das
Estrelas, 4150-762 Porto, Portugal
9 Laboratoire d’Astrophysique de Toulouse/Tabres
(UMR5572), CNRS, Université Paul Sabatier - Toulouse
III, Observatoire Midi-Pyriénées, 14 av. E. Belin, F-31400
Toulouse, France
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11 INAF-Osservatorio Astronomico di Roma - Via di Frascati
33, I-00040, Monte Porzio Catone, Italy
12 School of Physics & Astronomy, University of Nottingham,
University Park, Nottingham, NG72RD, UK
13 Astrophysical Institute Potsdam, An der Sternwarte 16, D-
14482 Potsdam, Germany
14 Observatoire de Paris, LERMA, 61 Avenue de l’Observatoire,
75014 Paris, France
15 Università di Bologna, Dipartimento di Astronomia - Via
Ranzani,1, I-40127, Bologna, Italy
16 Centre de Physique Théorique, UMR 6207 CNRS-Université
de Provence, F-13288 Marseille France
17 Integral Science Data Centre, ch. d’Écogia 16, CH-1290
Versoix
18 Geneva Observatory, ch. des Maillettes 51, CH-1290
Sauverny, Switzerland
19 Astronomical Observatory of the Jagiellonian University, ul
Orla 171, 30-244 Kraków, Poland
20 INAF-Osservatorio Astronomico di Capodimonte - Via
Moiariello 16, I-80131, Napoli, Italy
21 Universitá di Milano-Bicocca, Dipartimento di Fisica -
Piazza delle Scienze, 3, I-20126 Milano, Italy
22 Università di Bologna, Dipartimento di Fisica - Via Irnerio
46, I-40126, Bologna, Italy
	Introduction
	The First Epoch VVDS Sample
	The I-selected Spectroscopic Sample
	The K-selected Photometric Sample
	Comparison of the Two Samples
	Estimate of the Stellar Masses
	Smooth SFHs
	Complex SFHs
	Effect of NIR Photometry
	Comparison of the Masses Obtained with the Two Methods
	Massive Galaxies at z>1
	Mass Function Estimate
	The VVDS Galaxy Stellar Mass Function
	Comparison with Previous Surveys
	The Evolution of the Galaxy Stellar Mass Function
	Galaxy Number Density
	Mass Density
	Summary and Discussion

  We present a detailed analysis of the Galaxy Stellar Mass Function of
galaxies up to z=2.5 as obtained from the VVDS. We estimate the stellar mass
from broad-band photometry using 2 different assumptions on the galaxy star
formation history and show that the addition of secondary bursts to a
continuous star formation history produces systematically higher (up to 40%)
stellar masses. At low redshift (z=0.2) we find a substantial population of
low-mass galaxies (<10^9 Msun) composed by faint blue galaxies (M_I-M_K=0.3).
In general the stellar mass function evolves slowly up to z=0.9 and more
significantly above this redshift. Conversely, a massive tail is present up to
z=2.5 and have extremely red colours (M_I-M_K=0.7-0.8). We find a decline with
redshift of the overall number density of galaxies for all masses (59+-5% for
M>10^8 Msun at z=1), and a mild mass-dependent average evolution
(`mass-downsizing'). In particular our data are consistent with mild/negligible
(<30%) evolution up to z=0.7 for massive galaxies (>6x10^10 Msun). For less
massive systems the no-evolution scenario is excluded. A large fraction (>=50%)
of massive galaxies have been already assembled and converted most of their gas
into stars at z=1, ruling out the `dry mergers' as the major mechanism of their
assembly history below z=1. This fraction decreases to 33% at z=2. Low-mass
systems have decreased continuously in number and mass density (by a factor up
to 4) from the present age to z=2, consistently with a prolonged mass assembly
also at z<1.

Introduction
One of the main and still open question of modern cos-
mology is how and when galaxies formed and in particular
when they assembled their stellar mass. There are growing
but still controversial evidences in near-IR (NIR) surveys
that luminous and rather massive old galaxies were quite
common already at z ∼ 1 (Pozzetti et al. 2003, Fontana
et al. 2004, Saracco et al. 2004, 2005, Caputi et al. 2006a)
and up to z ∼ 2 (Cimatti et al. 2004, Glazebrook et al
Send offprint requests to: Lucia Pozzetti e-mail:
lucia.pozzetti@oabo.inaf.it
⋆ based on data obtained with the European Southern
Observatory Very Large Telescope, Paranal, Chile, program
070.A-9007(A), and on data obtained at the Canada-France-
Hawaii Telescope, operated by the CNRS of France, CNRC in
Canada and the University of Hawaii
2004). These surveys indicate that a significant fraction of
early-type massive galaxies were already in place at least
up to z ∼ 1. Therefore they should have formed their stars
and assembled their stellar mass at higher redshifts. As in
the local universe, at z ≃ 1.5 these galaxies still dominate
the near-IR luminosity function and stellar mass density
of the universe (Pozzetti et al. 2003, Fontana et al. 2004,
Strazzullo et al. 2006). These results favour a high-z mass
assembly, in particular for massive galaxies, in apparent
contradiction with the hierarchical scenario of galaxy for-
mation, applied to both dark and baryonic matter, which
predicts that galaxies form through merging at later cosmic
time. In these models massive galaxies, in particular, assem-
bled most of their stellar mass via merging only at z < 1
(De Lucia et al. 2006). From several observations it seems
that baryonic matter has a mass-dependent assembly his-
http://arxiv.org/abs/0704.1600v2
2 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
tory, from massive to small objects, (i.e. the ‘downsizing’
scenario in star formation, firstly defined by Cowie et al.
1996, is valid also for mass assembly), opposite to the dark
matter (DM) halos assembly. The continuous merging of
DM halos in the hierarchical models, indeed, should result
in an ‘upsizing’ in mass assembly, with the most massive
galaxies being the last to be fully assembled. If we trust
the hierarchical ΛCDM universe, the source of this discrep-
ancy between observations and simple basic models could
be due to the difficult physical treatment of the baryonic
component, such as the star formation history/timescale,
feedback, dust content, AGN feedback or to a missing in-
gredient in the hierarchical models of galaxy formation (for
the inclusion of AGN feedback, see Bower et al. 2006, Kang
et al. 2006, De Lucia & Blaizot 2007, Menci et al. 2006,
Monaco et al. 2006; and see Neistein et al. 2006 for the de-
scription of a natural downsizing in star formation in the
hierarchical galaxy formation models and a recent review
by Renzini 2007).
Considering optically selected surveys, a strong number
density evolution of early type galaxies has been recently
reported from the COMBO17 and DEEP2 surveys (Bell et
al. 2004, Faber et al. 2005), with a corresponding increase
by a factor 2 of their stellar mass since z ∼ 1, possibly
due to so called ‘dry-mergers’ (even if the observational
results on major merging and dry-merging are still contra-
dictory, see Bell et al. 2006, van Dokkum 2005, Lin et al.
2004 and Renzini 2007 for a summary). This is at variance
with results from the VIMOS-VLT Deep Survey (VVDS,
Le Fèvre et al. 2003b), conducted at greater depth and us-
ing spectroscopic redshifts in a large contiguous area. From
the VVDS, Zucca et al. (2006) found that the B-band lu-
minosity function of early type galaxies is consistent with
passive evolution up to z ∼ 1.1, while the number of bright
(MBAB < −20) early type galaxies has decreased only by
∼ 40% from z ∼ 0.3 to z ∼ 1.1. Similarly, Brown et al.
(2007), in the NOAO Deep Wide Field survey over ∼ 10
deg2, found that the B-band luminosity density of L∗ galax-
ies increases by only 36 ± 13% from z = 0 to z = 1 and
conclude that mergers do not produce rapid growth of lu-
minous red galaxy stellar masses between z = 1 and the
present day.
The VVDS is very well suited for this kind of stud-
ies, thanks to its depth and wide area, covered by multi-
wavelength photometry and deep spectroscopy. The simple
17.5 < IAB < 24 VVDS magnitude limit selection is signif-
icantly fainter than other complete spectroscopic surveys
and allows the determination of the faint and low mass
population with unprecedented accuracy. Most of the pre-
vious existing surveys are instead very small and/or not
deep enough, or based only on photometric redshifts.
Given the still controversial results based on morphol-
ogy or colour-selected early-type galaxies (see Franzetti
et al. 2007 for a discussion on colour-selected contamina-
tion), we prefer to study the total galaxy population us-
ing the stellar mass content. Here we present results on
the cosmic evolution of the Galaxy Stellar Mass Function
(GSMF) and mass density to z = 2.5 in the deep VVDS
spectroscopic survey, limited to 17.5 < IAB < 24, over
∼ 1750 arcmin2 and based on about 6500 galaxies with
secure spectroscopic redshifts and multiband (from UV to
near-IR) photometry. In addition, we derive the GSMF
also for a K-selected sample based on about 6600 galax-
ies (KAB < 22.34) in an area of 442 arcmin
2 and about
3600 galaxies in a deeper (KAB < 22.84) smaller area of
168 arcmin2, making use of photometric redshifts, accu-
rately calibrated on the VVDS spectroscopic sample, and
spectroscopic redshifts when available.
Throughout the paper we adopt the cosmology Ωm =
0.3 and ΩΛ = 0.7, with h70 = H0/70 km s
−1 Mpc−1.
Magnitudes are given in the AB system and the suffix AB
will be dropped from now on.
2. The First Epoch VVDS Sample
The VVDS is an ongoing program aiming to map the evo-
lution of galaxies, large scale structures and AGN through
redshift measurements of ∼ 105 objects, obtained with the
VIsible Multi-Object Spectrograph (VIMOS, Le Fèvre et
al. 2003a), mounted on the ESO Very Large Telescope
(UT3), in combination with a multi-wavelength dataset
from radio to X-rays. The VVDS is described in detail in
Le Fèvre et al. (2005). Here we summarize only the main
characteristics of the survey.
The VVDS is made of a wide part, with spectroscopy
in the range 17.5 ≤ I ≤ 22.5 on 4 fields (∼ 2 × 2 deg2
each), and a deep part, with spectroscopy in the range
17.5 ≤ I ≤ 24 on the field 0226-04 (F02 hereafter).
Multicolour photometry is available for each field (Le Fèvre
et al. 2004). In particular, the B, V , R, I photometry for
the 0226-04 deep field, covering ∼ 1 deg2, has been ob-
tained at CFHT and is described in detail in McCracken
et al. (2003). The photometric depth reached in this field
is 26.5, 26.2, 25.9, 25.0 (50% completeness for point-like
sources), respectively in the B, V , R, I bands. Moreover,
U < 25.4 (50% completeness) photometry obtained with
the WFI at the ESO-2.2m telescope (Radovich et al. 2004)
and Ks band (hereafter K) photometry with NTT+SOFI
at the depth (50% completeness) of 23.34 (Temporin et al.
in preparation) are available for wide sub-areas of this field.
Moreover, an area of about 170 arcmin2 has been covered
by deeper J and K band observations with NTT+SOFI
at the depth (50% completeness) of 24.15 and 23.84, re-
spectively (Iovino et al. 2005). The deep F02 field has been
observed also by the CFHT Legacy Survey (CFHTLS1) in
several optical bands (u∗, g′, r′, i′, z′) at very faint depth
(u∗ = 26.4, g′ = 26.3, r′ = 26.1, i′ = 25.9, z′ = 24.9, 50%
completeness).
Spectroscopic observations of a randomly selected sub-
sample of objects in an area of ∼ 0.5 deg2, with an average
sampling rate of about 25%, were performed in the F02
field with VIMOS at the VLT.
Spectroscopic data were reduced with the VIMOS
Interactive Pipeline Graphical Interface (VIPGI, Scodeggio
et al. 2005, Zanichelli et al. 2005) and redshift mea-
surements were performed with an automatic package
1 Based on observations 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 Science 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 TERAPIX and the Canadian
Astronomy Data Centre as part of the Canada-France-Hawaii
Telescope Legacy Survey, a collaborative project of NRC and
CNRS.
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 3
Fig. 1. Upper panel: Comparison of photometric and spec-
troscopic redshifts in theK-selected sample for objects with
highly reliable (confidence level > 97% , i.e. about 1400
galaxies with flag=3, 4) spectroscopic redshifts. The accu-
racy obtained is σ∆z = 0.02(1 + z)
2 (shown as solid lines)
with only 3.7% of outliers, defined as the objects outside
the region limited by the 2 dotted lines (zphoto = zspec ±
0.15(1 + zspec)) in the figure. Lower panel: Spectroscopic
(solid line) and photometric (dotted line) redshift distribu-
tion for the same comparison sample.
(KBRED) and then visually checked. Each redshift mea-
surement was assigned a quality flag, ranging from 0 (failed
measurement) to 4 (100% confidence level); flag 9 indicates
spectra with a single emission line, for which multiple red-
shift solutions are possible. Further details on the quality
flags are given in Le Fèvre et al. (2005).
The analysis presented in this paper is based on the first
epoch VVDS deep sample, which has been obtained from
the first spectroscopic observations (fall 2002) on the field
VVDS-02h, which cover 1750 arcmin2.
2.1. The I-selected Spectroscopic Sample
In this study we use the F02-VVDS deep spectroscopic sam-
ple, purely magnitude limited (17.5 ≤ I ≤ 24), in combi-
nation with the multi-wavelength optical/near-IR dataset.
From the total sample of 8281 objects with measured red-
shift, we removed the spectroscopically confirmed stars and
broad line AGN, as well the galaxies with low quality red-
shift flag (i.e. flag 1), remaining with 6419 galaxy spec-
tra with secure spectroscopic measurement (flags 2, 3, 4,
9), corresponding to a confidence level higher than 80%.
Galaxies with redshift flags 0 and 1 are taken into account
statistically (see Section 4 and Ilbert et al. 2005 and Zucca
et al. 2006 for details). This spectroscopic sample has a
median redshift of ∼ 0.76. Compared to previous optically
selected samples, the VVDS has not only the advantage
of having an unprecedented high fraction of spectroscopic
redshifts (compared, for example, to the purely photomet-
ric redshifts as in COMBO17, Wolf et al. 2003 and Borch
et al. 2006 for the MF), but also of being purely magnitude
selected (17.5 < I < 24), differently, for example, from the
DEEP2 (Bundy et al. 2006 for the MF) survey, which has
a colour-colour selection. Moreover, the VVDS covers an
area from 10 to 40 times wider than the GOODS-MUSIC
field (Fontana et al. 2006) and the FORS Deep Field (FDF,
Drory et al. 2005), respectively.
2.2. The K-selected Photometric Sample
A wide part of the VVDS-02h field (about 623 arcmin2)
has been observed also in the near-IR (Iovino et al. 2005,
Temporin et al. in preparation). This allows us to build a
K-selected sample with a total area of 610 arcmin2 (after
excluding low-S/N borders): 442 arcmin2 are 90% complete
to K < 22.34, while 168 arcmin2 are 90% complete to K <
22.84 (equivalent to KVega = 21).
This sample consists of 11221 objects, of which 2882
have VVDS spectroscopy. In particular, the deep sample
(K < 22.84) consists of 3821 objects, of which 749 have
VVDS spectroscopy, and 596 of them are galaxies with a
secure spectroscopic identification (flags 2, 3, 4, 9). This
latter deep sample is more than one magnitude deeper than
the samples from the K20 spectroscopic survey (Cimatti
et al. 2002) and the MUNICS survey (Drory et al. 2001).
Additionally, the total K-selected sample covers an area
more than 10 times wider than the K20 and the GOODS-
CDFS sample used by Drory et al. (2005) and 4 times wider
than the GOODS-MUSIC field (Fontana et al. 2006).
Since the spectroscopic sampling of the K-selected sam-
ple is less than satisfactory, we take advantage of the
high quality photometric redshifts (zphoto). The method
and the calibration are presented and discussed in Ilbert
et al. (2006). The comparison sample contains 3241 ac-
curate spectroscopic redshifts (confidence level > 97% ,
i.e. flag=3, 4) up to I = 24 obtaining a global accu-
racy of σ∆z/(1+z) = 0.037 with only 3.7% of outliers. Also
in the K-selected photometric sample the agreement be-
tween photometric and highly reliable spectroscopic red-
shifts (about 1400) is excellent (Figure 1). We note, how-
ever, a non-negligible number of catastrophic solutions with
zphoto
∼ 1.2 and zspec
∼ 1 which could introduce a bias at
high-redshift (see also discussion in Section 2.3). Even if we
cannot rely on a wide spectroscopic comparison sample at
high-z, the number of galaxies with zphoto > 1.2 is simi-
lar or only slightly higher (about 20%) than the number
of galaxies with zspec > 1.2 (63 vs. 51, see Figure 1) and
have very similar fluxes and colors. For this reason we do
not expect that our results on the mass function and the
mass density will be strongly biased by the effect of catas-
trophic redshifts (see Section 4). Furthermore, at high-z the
dispersion between photometric and spectroscopic redshifts
increases, but not drammatically, to σ∆z/(1+z) ≃ 0.05, 0.06
4 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
at z > 1.2, 1.4. Over the whole redshift range it can be
represented with σ∆z ≃ 0.02(1 + z)
2 (shown in Figure 1).
For the whole K-selected sample, the median errors on
photometric redshifts, based on χ2 statistics, are σzphoto =
0.06 (0.04 at z < 1, increasing to 0.14 at z > 1.5). As ex-
pected, there is also an increase of σzphoto for the faintest
objects, but this increase is only about 0.02 in the faintest
magnitude bin. As previously noted by Ilbert et al. (2006)
the statistical errors are consistent with σ∆z and could be
used as an indication of their accuracy. We will discuss in
the following sections the effects of these uncertainties and
conclude that they do not affect significantly our conclu-
sions.
We note, moreover, that the K-selected sample se-
lects a different population, in particular of Extremely Red
Objects (EROs) at zphoto > 1 (see Section 2.3 and Fig. 3),
compared to the I-selected sample used to calibrate the de-
rived photometric redshift. Actually, photometric redshifts
greater than 0.8-1.0 for the EROs population have been
confirmed spectroscopically with very low contamination of
low-z objects (Cimatti et al. 2002). Moreover, the near-IR
bands are crucial to constrain photometric redshifts in the
redshift desert since the J-band is sensitive to the Balmer
break up to z = 2.5. Indeed Ilbert et al. (2006) obtain for
the deep sample at K < 23 the most reliable photometric
redshifts on this sub-sample with only 2.1% of outliers and
σ∆z/(1+z) = 0.035 (see their figure 13).
In this paper we therefore use photometric redshifts for
the whole K-selected photometric sample and the highly
reliable spectroscopic redshifts when available.
In order to select galaxies from the total K-selected
photometric sample, we have used a number of photomet-
ric methods to remove candidate stars, as described be-
low. Some of the possible criteria to select stars are: (i)
the CLASS STAR parameter given by SExtractor (Bertin
& Arnouts 1996), providing the “stellarity-index” for each
object, reliable up to I ≃ 21; (ii) the FLUX RADIUS K
parameter, computed by SExtractor from the K band im-
ages, which gives an estimate of the radius containing half
of the flux for each object; this can be considered a good
criterion to isolate point-like sources up to K ≃ 19 (see
Iovino et al. 2005); (iii) the BzK criterion, proposed by
Daddi et al. (2004a), with stars characterized by colours
z − K < 0.3(B − z) − 0.5; (iv) the χ2 of the SED fitting
carried out during the photometric redshift estimate (Ilbert
et al. 2006), with template SEDs of both stars and galaxies.
To efficiently remove stars in the whole magnitude range
of our sample, avoiding as much as possible to lose galaxies,
we decided to use the intersection of the first three crite-
ria. We therefore selected as stars the objects fulfilling all
the constraints (i) CLASS STAR ≥ 0.95 for I < 22.5 or
CLASS STAR ≥ 0.90 if I > 22.5, (ii) FLUX RADIUS K
< 3.4 and (iii) z − K < 0.3(B − z) − 0.5. When it was
not possible to apply criterion (iii), because of non detec-
tion either in the B or z filters, we used criterion (iv) in its
place. Furthermore, we added to the sample of candidate
stars also the objects with K < 16 and FLUX RADIUS K
< 4, to be sure to exclude from the galaxy sample these sat-
urated point-like objects. The final sample consists of 653
candidate stars, which we have removed from the sample
in the following analysis. Comparing to the spectroscopic
subsample (we remind that stars were not excluded from
the spectroscopic targets of VVDS), we found about 87%
of efficiency to photometrically select stars, i.e. only 28 out
Fig. 2. Redshift distributions for the K-selected photomet-
ric sample (filled histogram) and for the I-selected spectro-
scopic sample (empty histogram).
of the 214 spectroscopic stars have not been selected in this
way, and only 3 (1.4%) with highly reliable spectroscopic
flag (3, 4), whereas 21 spectroscopic extragalactic objects
(less than 1%) fall inside the candidate star sample. Three
of them are broad line AGN and the others are all compact
objects, most of them with redshift flags 1 or 2 and only one
with flag 3. This latter object has not been eliminated from
the galaxy sample. We have furthermore removed from the
galaxy sample the spectroscopically confirmed AGNs and
the three secure spectroscopic stars which were not removed
with the photometric criteria.
The final K-selected sample consists of 10160 galaxies
with either photometric redshifts or highly reliable spec-
troscopic redshifts, when available, in the range between 0
and 2.5: 6720 galaxies in the shallow K < 22.34 area of 442
arcmin2 and 3440 galaxies in the deeper area (K < 22.84)
of 168 arcmin2.
2.3. Comparison of the Two Samples
As shown in Fig. 2, the redshift distribution in the K-
selected sample peaks at higher redshift than in the I-
selected spectroscopic sample, with the two median red-
shifts being 0.91 and 0.76, respectively. Even if we cannot
rely on a wide spectroscopic comparison sample at high-z,
we have better investigated the reliability of the high-z tail
in the K-selected sample in term of fraction and colors. We
found indeed that at K < 22 the fraction of objects with
z > 1, 1.5 (35, 13% respectively) is similar to previous spec-
troscopic (K20 survey, see Cimatti et al. 2002) or photomet-
ric studies (Somerville et al. 2004). Moreover, we have used
the BzK color-color diagnostic proposed and calibrated on
a spectroscopic sample to cull galaxies at 1.4 < z < 2.5
(Daddi et al. 2004). We found that most (92%) of the galax-
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 5
Fig. 3. Colour-magnitude diagram and colour distribution
at different redshifts for the K-selected photometric sam-
ple (filled squares and histogram) and for the I-selected
spectroscopic sample (open circles and empty histogram)
ies at 1.5 < zphoto < 2.5 lie in the high-z region of the BzK
diagram.
We conclude that our K-selected sample shows no indi-
cation of significant bias in its high-redshift tail. The global
(I −K) colour distributions of the two samples are similar
to each other up to z ∼ 1.2 (see right panels in Fig. 3), but
they are significantly different at higher redshift. At z > 1.2
the I-selected sample misses many red galaxies fainter than
the I limit, most of them being Extremely Red Objects
(EROs: defined as objects with colours I−K > 2.6), which
are instead included in the K sample (∼ 81% of EROs in
the deep K < 22.84 sample have I > 24). For this rea-
son the K-selected sample is more adequate to study the
massive tail of the GSMF at high-z. Vice versa, the K-
selected sample misses at all redshifts a number of faint
blue galaxies, which are included in the I-selected spectro-
scopic sample (see left panels in Fig. 3). These faint blue
galaxies are important in the estimate of the low-mass tail
of the GSMF.
3. Estimate of the Stellar Masses
The rest-frame near-IR light has been widely used as a
tracer of the galaxy stellar mass, in particular for lo-
cal galaxies (e.g. Gavazzi et al. 1996; Madau, Pozzetti &
Dickinson 1998, Bell & de Jong 2001). However, an accurate
estimate of the galaxy stellar mass at high z, where galax-
ies are observed at widely different evolutionary stages, is
more uncertain because of the variation of the Mstars/LK
ratio as a function of age and other parameters of the stel-
lar population, such as the star formation history and the
metallicity. The use of multiband imaging from UV to near-
IR bands is a way to take into account the contribution to
the observed light of both the old and the young stellar
populations in order to obtain a more reliable estimate of
the stellar mass.
However, even stellar masses estimated using the fit
to the multicolour spectral energy distribution (SED) are
model dependent (e.g. changing with different assumptions
on the initial mass function, IMF) and subject to various
degeneracies (age – metallicity – extinction). In order to re-
duce such degeneracies we have used a large grid of stellar
population synthesis models, covering a wide range of pa-
rameters, in particular in star formation histories (SFH).
Indeed, in the case of real galaxies the possibly complex
star-formation histories and the presence of major and/or
minor bursts of star formation can affect the derived mass
estimate (see Fontana et al. 2004).
We have applied and compared two different methods to
estimate the stellar masses from the observed magnitudes
(using 12 photometric bands from u∗ to K), that are based
on different assumptions on the star-formation history. For
both of them we have adopted the Bruzual & Charlot (2003;
BC03 hereafter) code for spectral synthesis models, in its
more recent rendition, using its low resolution version with
the “Padova 1994” tracks. Different models have also been
considered, e.g. Maraston 2005, and Pégase models (Fioc
and Rocca-Volmerange 1997). The results obtained with
these models are compared with those obtained with the
BC03 models at the end of Section 3.1.
Since most of previous studies at high-z assumed models
with exponentially decreasing SFHs, we have used the same
simple smooth SFHs (see Section 3.1) in order to compare
our results with those of previous surveys. In addition, to
further test the uncertainties in mass determination, we
have used models with complex SFHs (see Section 3.2), in
which secondary bursts have been added to exponentially
decreasing SFHs. These models have been widely used in
studies of SDSS galaxies (see Kauffmann et al. 2003 and
Salim et al. 2005 for further details). Table 1 summarizes
the model parameters used in the 2 methods described in
the following sections.
In our analysis we have adopted the Chabrier IMF
(Chabrier et al. 2003), with lower and upper cutoffs of
0.1 and 100 M⊙. Indeed, all empirical determinations of
the IMF indicate that its slope flattens below ∼ 0.5 M⊙
(Kroupa 2001, Gould et al. 1996, Zoccali et al. 2000) and
a similar flattening is required to reproduce the observed
Mstars/LB ratio in local elliptical galaxies (see e.g. Renzini
2005). As discussed extensively by Bell et al. (2003), the
Salpeter IMF (Salpeter 1955) is too rich in low mass stars
to satisfy dynamical constraints (Kauffmann et al. 2003,
Kranz et al. 2003). Moreover, di Serego Alighieri et al.
(2005) show a rather good agreement between dynamical
masses and stellar masses estimated with the Chabrier IMF
at z ∼ 1. Specifically, this is true at least for high-mass el-
liptical galaxies, less affected than lower-mass galaxies by
uncertainties in the estimate of their dynamical mass due to
possibly substantial rotational contribution to the observed
velocity dispersion.
At fixed age the masses obtained with the Chabrier IMF
are smaller by a factor ∼ 1.7, roughly independent of the
age of the population, than those derived with the classical
Salpeter IMF, used in several previous works that we shall
compare with (e.g. Brinchmann & Ellis 2000; Cole et al.
2001; Dickinson et al. 2003; Fontana et al. 2004). We have
checked this statement in our sample, finding a systematic
median offset of a factor 1.7 and a very small dispersion
6 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
(σ = 0.082 dex) in the masses derived with the two different
IMFs. Since this ratio is approximately constant for a wide
range of star formation histories (SFH), the uncertainty
in the IMF does not introduce a fundamental limitation
with respect to the results we will discuss in the following
Sections. Even if the absolute value of the mass estimate is
uncertain, the use of Salpeter or Chabrier IMFs does not
introduce any significant difference in the relative evolution
with redshift of the mass function and mass density.
One possible limitation of our approach to derive stellar
masses in our sample is the contamination by narrow-line
AGN (broad line AGN have been already excluded, see
Section 2.1). From the available spectroscopic diagnostic,
in the I-selected spectroscopic sample at the mean red-
shift z ≃ 0.7, we found that the contamination due to
type II AGN is less than 10%. Recently, several studies
(Papovich et al. 2006, Kriek et al. 2007, Daddi et al. 2007)
suggest that the fraction of type II AGN increases with
redshift and stellar mass. According to Kriek et al. (2007)
at 2 < z < 2.7 and K < 21.5 the fraction is about 20%
for massive (2.9 × 1011M⊙ for a Salpeter IMF) galaxies.
To derive the contribution of type II AGN to the massive
tail of the MF is beyond the scope of this paper. However
we note, as shown also by the above studies, that for most
of these objects the optical light is dominated by the in-
tegrated stellar emission. Therefore, both our photometric
redshift and mass estimates are likely to be approximately
correct also for them.
3.1. Smooth SFHs
Consistently with previous studies, we have used synthetic
models with smooth SFH models (exponentially decreas-
ing SFH with time scale τ : SFR(t) ∝ exp(−t/τ)) and a
best-fit technique to derive stellar masses from multicolour
photometry.
To this purpose we have developed the code
HyperZmass, a modified version of the public photomet-
ric redshift code HyperZ (Bolzonella et al. 2000): like the
public version, HyperZmass uses the SED fitting technique,
computing the best fit SED by minimizing the χ2 between
observed and model fluxes. We used models built with the
Bruzual & Charlot (2003) synthetic library. When the red-
shift is known, either spectroscopic or photometric, the best
fit SED and its normalization provide an estimate of the
stellar mass contained in the observed galaxy. In particu-
lar, we estimate the stellar mass content of the galaxies,
derived by BC03 code, by integrating the star formation
history over the galaxy age and subtracting from it the
“Return fraction” (R) due to mass loss during the stellar
evolution. For a Chabrier IMF, this fraction is already as
high as ∼ 40% at an age of the order of 1 Gyr and ap-
proaches asymptotically about 50% at older ages.
The parameters used to define the library of synthetic
models are listed in Table 1. Similar parameters have been
used in Fontana et al. (2004). The Calzetti (2000) extinction
law has been used. Following that paper, we have excluded
from the grid some models which may be not physical (e.g.
those implying large dust extinctions, AV > 0.6, in absence
of a significant star-formation rate, Age/τ > 4, see Table
1). To better match the ages of early-type galaxies in the
local universe and following SDSS studies, we also removed
models with τ < 1 Gyr and with star formation starting at
z < 1.
Table 1. Parameters Used for the Library of Template
Method Smooth SFHs Complex SFHs
IMF Chabrier Chabrier
SFR τ (Gyr) [0.1,∞]a [1,∞]
log(Age)b (yr) [8, 10.2] [8, 10]
burst age (yr) − [0, 1010]
burst fraction − [0, 0.9]
Metallicities Z⊙ [0.1Z⊙, 2Z⊙]
Extinction Calzetti law Charlot&Fall model
(n = 0.7, µ ∈ [0.1, 1])
Dust content AcV ∈ [0, 2.4] τV ∈ [0, 6]
a τ < 1 if star formation starts at z < 1.
b At each redshift, galaxies are forced to have ages smaller
than the Hubble time at that redshift.
c AV < 0.6 if Age/τ > 4.
We find that the “formal” typical 1σ statistical errors
(defined as the 68% range as derived from the χ2 statis-
tics) on the estimated masses, not taking into account the
error on the estimate of the photometric redshift for the
K-selected sample, are of the order of 0.04 dex for the
K-selected sample and 0.05 for the I-selected sample. A
more reliable estimate of the errors has been obtained us-
ing HyperZ to simulate catalogs to the same depth of our
sample (see Bolzonella et al. 2000). Using all 12 photo-
metric bands (from u∗ to K), available for a subset of our
data, and realistic photometric errors, the recovered stellar
masses reproduce the input masses with no significant offset
and a dispersion of 0.12 dex up to z ∼ 3. For comparison,
using only the optical bands (from u∗ to z′) the disper-
sion increases to ∼ 0.49 dex at z > 1. The best fit masses
obtained from input simulations built using randomly all
available metallicities and analyzed only with solar metal-
licity models are not significantly shifted from the input
masses, but the dispersion increases from 0.12 dex to 0.21
dex. These dispersions, computed using a 4σ clipping, pro-
vide an estimate of the minimum, intrinsic uncertainties of
this method at our depth. For the K-selected photometric
sample further uncertainties in the fitting technique are due
to the photometric redshift accuracy (σ∆z ≃ 0.02(1 + z)
up to z = 2.5) which corresponds on average to about 0.12
dex of uncertainty in mass, being larger at low redshift (∼
0.2 dex at z < 0.4) than at high-z (∼ 0.10 dex at z = 2).
Although in principle the best-fitting technique pro-
vides estimates also for age, metallicity, dust content and
SFH timescale, our simulations show that on average all
these quantities are much more affected by degeneracies
and therefore less constrained than the stellar mass.
In addition, we have compared our derived masses with
those obtained by using different population synthesis mod-
els, such as Pégase and Maraston (2005) models. In partic-
ular, Maraston (2005) models include the thermally pulsing
asymptotic giant branch (TP-AGB) phase, calibrated with
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 7
local stellar populations. This stellar phase is the dominant
source of bolometric and near-IR energy for a simple stellar
population in the age range 0.2 to 2 Gyr. We have tested
the differences with BC03 models using the I-selected spec-
troscopic sample and we found only a small but systematic
shift (∼ −0.14 dex and a similar dispersion) up to z ∼ 1.2
both with and without the use of near-IR photometry. On
the contrary, masses derived using Pégase models and sim-
ilar SFHs have instead no significant offset.
At higher redshifts the differences between our esti-
mated masses and those obtained with Maraston models in
the K-selected spectroscopic subsample are slightly smaller
and even smaller in the K-selected photometric sample
(∼ −0.11,−0.08, respectively). This differences are smaller
than that found by Maraston et al. (2006), ∼ −0.2, in their
SED fitting (from B up to Spitzer IRAC and MIPS bands)
of a few high redshift passive galaxies with typical ages
in the range 0.5 – 2.0 Gyr, selected in the Hubble Ultra
Deep Field (HUDF). This difference between our results
and those of Maraston et al. could be due to a combina-
tion of effects, such as the absence in our photometric data
of mid-IR Spitzer photometry, which at these redshifts is
sampling the rest frame near-IR part of the SED, mostly in-
fluenced by the TP-AGB phase, and also to the wide range
of complex stellar populations in our sample, in which the
effect of the TP-AGB phase may be diluted by the SFH.
3.2. Complex SFHs
Real galaxies could have undergone a more complex SFH,
in particular with the possible presence of bursts of star
formation on the top of a smooth SFH. Thus, we have com-
puted masses also following a different approach, which has
been intensively used in previous studies of SDSS galaxies
(e.g. Kauffmann et al. 2003, Brinchmann et al. 2004, Salim
et al. 2005, Gallazzi et al. 2005). In this approach we pa-
rameterize each SF history in terms of two components:
an underlying continuous model, with an exponentially de-
clining SF law (SFR(t) ∝ exp(−t/τ)), and random bursts
superimposed on it. We assume that random bursts occur
with equal probability at all times up to galaxy age. They
are parameterized in terms of the ratio between the mass
of stars formed in the burst and the total mass of stars
formed by the continuous model over the age. This ratio is
taken to be distributed between 0.0 and 0.9. During a burst,
stars are assumed to form at a constant rate for a time dis-
tributed uniformly in the range 30 – 300 Myr. The burst
probability is set so that 50% of the galaxies in the library
have experienced a burst in the past 2 Gyr. Attenuation by
dust is described by a two-component model (see Charlot
& Fall 2000), defined by two parameters: the effective V -
band absorption optical depth τV affecting stars younger
than 10 Myr and arising from giant molecular clouds and
the diffuse ISM, and the fraction µ of it contributed by the
diffuse ISM, that also affects older stars. We take τV to be
distributed between 0 and 6 with a broad peak around 1
and µ to be distributed between 0.1 and 1 with a broad
peak around 0.3. Finally, our model galaxies have metallic-
ities uniformly distributed between 0.1 and 2 Z⊙.
The model spectra are computed at the galaxy redshift
and in each of them we measure the k-shifted model magni-
tudes for each VVDS photometric band. We also force the
age of all models in a specific redshift range to be smaller
than the Hubble time at that redshift. The model SEDs
Fig. 4. Effect of NIR photometry in the mass determina-
tion: ratio between masses estimated without and with NIR
photometry vs. mass determined without NIR photometry.
The data have been splitted into different redshift ranges.
Left: masses determined using smooth SFHs. Right: The
same, but using complex SFHs
are then scaled to each observed SED with a least squares
method and the same scaling factor is applied to the model
stellar mass. We compare the observed to the model fluxes
in each photometric band and the χ2 goodness of fit of
each model determines the weight (∝ exp[−χ2/2]) to be
assigned to the physical parameters of that model when
building the probability distributions for each parameter
of any given galaxy. The probability distribution function
(PDF) of a given physical parameter is thus obtained from
the distribution of the weights of all models in the library
at the specified redshift. We characterize the PDF using its
median and the 16 – 84 percentile range (equivalent to ±1σ
range for Gaussian distributions), and also record the χ2 of
the best-fitting model.
Similarly to what has been done for the models with
smooth SFH (see Section 3.1), also in this case the stel-
lar mass content of galaxies is derived by subtracting the
return fraction R from the total formed stellar mass. We
find that the average “formal” 1σ error (defined as half of
the 16 – 84 percentile range) on the estimated masses is of
the order of 0.09 dex for the K-selected sample. The av-
erage error increases with redshift from ∼ 0.06 dex at low
redshift to ∼ 0.11 dex at 1 < z < 2 and decreases with in-
creasing mass from ∼ 0.08 dex for logM < 10 to ∼ 0.05 for
logM > 10 at z ≃ 0.7. In the K-selected sample the photo-
metric redshift accuracy induced a further uncertainty on
the mass of the order of 30% up to z > 1.5. In the I-selected
sample, where near-IR photometry is not always available,
the typical error on the mass is larger and is of the order
of ∼ 0.13 dex.
8 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
3.3. Effect of NIR Photometry
For about half of the sources in the I-selected sample only
optical photometry is available. We have therefore used the
results obtained for theK-selected spectroscopic subsample
to better understand the reliability of the mass estimates in
the whole I-selected sample and quantify potential system-
atic effects. We found that the mass estimates derived using
only optical bands are on average in rather good agreement
with those obtained using also NIR bands up to z ∼ 1.2. In
absence of NIR bands the galaxy stellar masses tend to be
only slightly overestimated, with a median shift < 0.1 dex;
this is due to the fact that already at z = 0.4, for example,
the z′-band (the reddest band used in the fit in absence of
NIR) samples the R-band rest-frame and therefore the SED
fitting is less reliable for the estimate of the stellar masses.
There is however a significant fraction of the galaxies for
which the ratio between the two masses is higher than a
factor of three (see upper panels of Fig.4). This fraction of
galaxies with significantly discrepant mass estimates is ∼
5% for the models with smooth SFH and ∼ 9 % for the
models with complex SFH.
At higher redshifts, where our reddest optical band, i.e.
the z-band, is sampling the rest-frame spectrum bluewards
of the 4000 Å break, the comparison of the two sets of
mass estimates (i.e. with and without near-IR photometry)
is significantly worse. Not only the median shift increases
significantly, but also the ratio of the two sets of masses
is significantly correlated with the mass derived without
using NIR photometry (see lower panels of Fig. 4). For this
reason, we have decided to use the whole I-selected VVDS
spectroscopic sample only up to z ∼ 1.2, whereas at higher
redshifts we use as reference the K-selected photometric
sample.
As shown in the upper panels of Fig.4, the ratio between
the masses computed without and with NIR photometry
has a non-negligible dispersion also for z < 1.2, with the
masses computed without NIR photometry being higher on
average. In order to statistically correct for this effect, we
have performed the following Monte Carlo simulation. For
each galaxy without near-IR photometry in the I-selected
spectroscopic sample we have applied a correction factor
to its estimated mass. This correction factor has been de-
rived randomly from the observed distribution, at the mass
of each galaxy, of the ratios of the masses with and with-
out NIR photometry. The effect on the mass function of
using these “statistically corrected” masses is shown and
discussed in Sect. 4.
3.4. Comparison of the Masses Obtained with the Two
Methods
In this section we compare the mass estimates we obtained
using the two different methods described above for the
VVDS galaxies. Since the ratio of the two estimates is al-
most independent of the mass, in Fig. 5 we show the his-
tograms of this ratio, integrated over all masses, for two dif-
ferent redshift bins. In the upper panel (z < 1.2), both data
from the I-selected and the K-selected samples are shown;
in the lower panel only data from the K-selected sample
are shown, since the I-selected sample is not used to derive
the mass function in this redshift range. Gaussian curves,
representing the bulk of the population, are drawn on the
Fig. 5. Histograms of the ratio of the masses derived with
the smooth and the complex star formation histories. In
the upper panel (z < 1.2) both data from the I-selected
and the K-selected samples are shown; in the lower panel
(z > 1.2) only data from the K-selected sample are shown,
since the I-selected sample is not used to derive the mass
function in this redshift range.
top of each histogram. The parameters of each Gaussian
are reported in the figure.
The global comparison of the two sets of masses is rather
satisfactory, even if it shows a systematic shift, larger for
theK-selected sample, between the two sets of masses, with
the ‘smooth SFH’ masses being on average smaller than the
‘complex SFH’ masses. The values of σ of these Gaussians
are similar, of the order of 0.13 dex. However, in two of the
three cases (i.e. the I-selected sample at low redshift and
the K-selected sample at high redshift) the distributions of
the ratio of the masses appear to be asymmetric, with tails
which are not well represented by a Gaussian distribution.
The fractions of these “outliers” are given in Fig. 5. This
tail is particularly significant for the I-selected sample, for
which there are galaxies with the ratio between the two
masses higher than 3 and in a few cases reaching a value of
We have analyzed the effect of the different parameters
used in the two methods. The impact of different extinction
curves on the mass estimates has already been investigated
by Papovich et al. (2001), Dickinson et al. (2003), Fontana
et al. (2004), and found to be small. We have repeated the
same exercise for the two different dust attenuation models
adopted, finding that for a given SFH the mass estimated
with different extinction laws are similar, with an average
shift of 0.02 dex.
Analyzing in some detail the properties of the galaxies
which are in the extended tail of large mass ratios for the I-
selected sample at low redshift (see the upper panel in Fig.
5), we found that, even if many of them do not have near-
IR photometry and therefore their mass is more uncertain
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 9
(see previous section), on average they are characterized by
blue colours in the bluer bands (B − I) and red colours in
the redder bands (I − z or I − K). Because of this, they
have been fitted typically with low values of the popula-
tion age by HyperZmass with a smooth SFH, while the
estimate obtained with a complex SFH corresponds to an
older, and therefore more massive, population plus a more
recent burst with a mass fraction in the burst of the order
of fburst < 0.15. Vice versa the low ratio outliers in the K-
selected sample at high redshift have been fitted typically
with moderately higher dust content by HyperZmass than
with complex SFHs. Finally, we conclude that the main dif-
ferences between the two methods to determine the masses
are largely due to different assumed SFHs and, in particu-
lar, to the secondary burst component allowed in the model
with complex SFHs.
To summarize, we have explored in detail two differ-
ent methods and a wide parameter space (see Table 1)
to estimate the stellar mass content in galaxies in order
to better understand the uncertainties in the photomet-
ric stellar mass determinations. Indeed, a good estimate of
the intrinsic errors may be critical for the GSMF measure-
ment and interpretation. We found that, within a given
assumption on the SFH, the accuracy of the photomet-
ric stellar mass is overall satisfactory, with intrinsic un-
certainties in the fitting technique of the order of ∼ 30%,
in agreement with similar results in the K20 (Fontana
et al. 2004), HDFN (Dickinson et al. 2003) and HDFS
(Fontana et al. 2003) at the same redshifts. These errors
are smaller than the estimates at higher redshift (z ≃ 3)
(Papovich et al. 2001, Shapley et al. 2001), since at our av-
erage redshifts (z ≃ 0.7−1) we can rely on a better sampling
of the rest-frame near-IR part of the spectrum, while are
similar to the uncertainties estimated at high-z using IRAC
data by Shapley et al. (2005). For theK-selected photomet-
ric sample the uncertainties in the stellar mass due to the
photometric redshift errors are on average of the order of
30% up to z > 1.5, giving a total fitting uncertainty up
to 45% at z > 1.5. Finally, systematic shifts, mainly due
to different assumptions on the SFHs, can be as large as
∼ 40% over the entire redshift range 0.05 < z < 2.5 when
NIR photometry is available. The uncertainty in the de-
rived masses is obviously higher also at low redshift when
NIR photometry is not available and in this case it becomes
extremely large at z > 1.2 (see Fig.4).
For what concerns the absolute value of the mass, its
uncertainty is mainly due to the assumptions on the IMF
and it is within a factor of 2 for the typical IMFs usually
adopted in the literature.
In the following sections we discuss in some detail the
effects of the two methods on the derivation of the GSMF.
3.5. Massive Galaxies at z > 1
Figure 6 shows the stellar masses for the 2 samples (I and
K-selected) derived using the smooth SFHs. It is inter-
esting to note the presence of numerous massive objects
(logM > 11) at all redshifts and up to z = 2.5. High-
z massive galaxies have been already observed in previous
surveys (Fontana et al. 2004, Saracco et al. 2005, Cimatti et
al. 2004, Glazebrook et al 2004, Fontana et al. 2006, Trujillo
et al. 2006). Here the relatively wide area (the K-selected
sample is more than 10 times wider and from 0.5 to 1 mag-
nitude deeper than the K20 survey) allows to better sam-
Fig. 6. Stellar Mass as a function of redshift for the I-
selected spectroscopic (left) and for the K-selected photo-
metric (right) samples for smooth SFHs.
ple the massive tail of the population. We note that mas-
sive galaxies have typically redder optical-NIR rest-frame
colours (〈MI −MK〉 ≃ 0.7) compared to the whole popu-
lation (〈MI −MK〉 ≃ 0.5), consistently with the idea that
massive galaxies host the oldest stellar population. Further
analysis of the stellar population properties and spectral
features of massive galaxies, as well as of red objects will
be presented in forthcoming papers (Lamareille et al. in
preparation, Vergani et al. 2007, Temporin et al. in prepa-
ration).
4. Mass Function Estimate
Once the stellar mass has been estimated for each galaxy
in the sample, the derivation of the corresponding Galaxy
Stellar Mass Function (MF) follows the traditional tech-
niques used for the computation of the luminosity function.
Here we apply both the classical non-parametric 1/Vmax
formalism (Schmidt 1968, Felten 1976) and the parametric
STY (Sandage, Tammann & Yahil 1979) method to esti-
mate best-fit Schechter (1976) parameters (α,M∗stars, φ
In the case of the K-selected sample, in order to take into
account the two different magnitude limits, we perform a
“Coherent Analysis of independent samples” as described
by Avni & Bahcall (1980).
Ilbert et al. (2004) have shown that the estimate of the
faint end of the global luminosity function can be biased,
because, due to different k-corrections, different galaxy
types have different absolute magnitude limits for the same
apparent magnitude limit. The same bias is present also for
the low mass end of the mass function. This is due to the
fact that, because of the existing dispersion in the mass-to-
light ratio of different galaxy types, at small masses the ob-
jects with the largest mass-to-light ratio are not included in
a magnitude limited sample (see Appendix B in Fontana et
10 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
Fig. 7. Effect on the I-selected MF of the use of the statistically corrected masses, which take into account the effect of
near-IR photometry on the mass determination (see text for details). Complex SFHs have been used to derive masses.
Empty circles represent the MF obtained using the original uncorrected masses, filled squares show the MF obtained
using the statistically corrected masses. For comparison the STY Schechter MF is shown for the subsample where near-IR
photometry is available. The vertical dashed lines represent the completeness limit of the sample as defined in the text.
al. 2004 for an extensive discussion). For this reason, when
computing the global mass functions with the STY method,
in order to fully avoid this bias, we should use in each red-
shift range only galaxies above the stellar mass limit where
all the SEDs are potentially observable. In both the K- and
I-selected samples these limits derive from the conversion
between photometry and stellar mass for early-type galax-
ies and are very restrictive. However, recent results show
that the faint-end and the low-mass end of the luminosity
and mass function is dominated by late-type galaxies up to
z ∼ 2 (Fontana et al. 2004, Zucca et al. 2006, Bundy et al.
2006). Therefore for the STY estimate we will use as lower
limit of the mass range the minimum mass above which
late-type SEDs (defined by rest-frame optical/NIR colours
MI −MK < 0.4) are potentially observable (see Fig. 9).
We have estimated the MF for both the deep I-selected
(17.5 < I < 24) spectroscopic sample and the photomet-
ric K-selected (K < 22.34 & K < 22.84) sample. For
each sample the MF has been estimated using masses com-
puted with both methods described in Section 2.3. In the
case of the spectroscopic sample, in order to correct for
both the non-targeted sources in spectroscopy and those
for which the spectroscopic measurement failed, we use a
statistical weight wi, associated with each galaxy i with
a secure redshift measurement (see Ilbert et al. 2005 for
details). This weight is the inverse of the product of the
Target Sampling Rate times the Spectroscopic Success Rate.
Accurate weights have been derived by Ilbert et al. (2005)
for all objects with secure spectroscopic redshifts, tak-
ing into account all the parameters involved (magnitudes,
galaxy size and redshift).
For the K-selected sample, we have tested the effect of
catastrophic photometric redshifts (see discussion in Sec.
2.2) on the evolution of the mass function and mass den-
sity. We have used the I-selected spectroscopic sample, re-
placing spectroscopic redshifts with photometric redshifts.
The two MFs (with either spectroscopic or photometric red-
shifts) are very similar in the whole mass and redshift range
(0.05 < z < 2.5) analyzed and even at z > 1.2, where we
note a not negligible number of catastrophic photometric
redshifts (see discussion in Sec. 2.2). There is no evidence
of a strong bias in the normalization and in the shape of the
MF; also the massive tails of the MFs are similar, within
the statistical errors. We conclude that the catastrophic
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 11
Fig. 8.K-selected MF derived from the 2 subsamples, deep (filled circles) and shallow (empty circles), separately (smooth
SFHs have been used to derive masses). For comparison the STY Schechter MF for the globalK-selected sample is shown.
The vertical dashed lines represent the completeness limit of the 2 K-selected subsamples.
solutions at high photometric redshifts (i.e. masses) do not
strongly affect our results.
4.1. The VVDS Galaxy Stellar Mass Function
The resulting stellar mass functions of the VVDS sample
are derived in the following redshift ranges: (a) 0.05 < z <
1.2 for the I-selected sample, because at higher redshift the
mass estimate becomes very uncertain (see figure 4) and
(b) 0.05 < z < 2.5 for the K-selected sample. We have
furthermore divided the 2 samples into different redshift
bins in order to sample evolution with similar numbers of
sources in each bin.
For the galaxies in the I-selected sample not covered
by near-IR data, we have used the statistically corrected
masses derived through a Monte Carlo simulation, to take
into account the effect of the near-IR photometry in the
mass determination (see Sec. 3.3). Figure 7 shows the ef-
fect in the MF for complex SFHs. The high mass tail is
significantly reduced if we use statistically corrected masses
when near-IR is not available. Consistent MFs have been
12 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
Fig. 9. Galaxy Stellar Mass Functions in the I-selected (squares) and K-selected (triangles) using both methods to
estimate the stellar masses (empty symbols for smooth SFHs and filled for complex SFHs). The STY Schechter fits for
the 2 methods limit the hatched regions (horizontal hatched for the K-selected and vertical hatched for the I-selected
samples). Vertical hatched regions represents the completeness limit of the 2 samples. The local MFs by Cole et al.
(2001), both original and “rescaled” version (Fontana et al. 2004), and by Bell et al. (2003) are reported in each panel
as dotted lines.
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 13
Table 2. STY parameters in the different redshift ranges
sample method z range mean redshift α logM∗stars(h
70 M⊙) φ
∗(10−3h370Mpc
I smooth 0.05 - 0.4 0.27 -1.26+0.01
−0.02 11 1.90
+0.08
−0.16
I smooth 0.4 - 0.7 0.58 -1.23+0.04
−0.04 11
+0.08
−0.08 1.72
+0.33
−0.28
I smooth 0.7 - 0.9 0.8 -1.23+0.12
−0.11 10.88
+0.15
−0.13 1.6
+0.55
−0.45
I smooth 0.9 - 1.2 1.05 -1.09+0.19
−0.17 10.85
+0.14
−0.14 1.3
+0.43
−0.46
I complex 0.05 - 0.4 0.27 -1.28+0.02
−0.01 11.15 1.75
+0.16
−0.08
I complex 0.4 - 0.7 0.58 -1.22+0.04
−0.04 11.15
+0.08
−0.08 1.58
+0.30
−0.26
I complex 0.7 - 0.9 0.81 -1.04+0.08
−0.07 10.83
+0.07
−0.07 3.02
+0.57
−0.51
I complex 0.9 - 1.2 1.04 -1.16+0.1
−0.09 10.89
+0.08
−0.07 1.80
+0.44
−0.39
K smooth 0.05 - 0.4 0.26 -1.38+0.02
−0.01 10.93 1.29
+0.10
−0.05
K smooth 0.4 - 0.7 0.57 -1.14+0.04
−0.04 10.93
+0.06
−0.06 1.83
+0.27
−0.24
K smooth 0.7 - 0.9 0.81 -1.01+0.07
−0.08 10.67
+0.07
−0.05 2.6
+0.38
−0.44
K smooth 0.9 - 1.2 1.05 -1.1+0.07
−0.08 10.78
+0.06
−0.05 1.83
+0.28
−0.30
K smooth 1.2 - 1.6 1.4 -1.15+0.12
−0.12 10.72
+0.07
−0.06 1.48
+0.30
−0.30
K smooth 1.6 - 2.5 1.96 -1.15 10.96+0.01
−0.02 0.9
+0.30
−0.30
K complex 0.05 - 0.4 0.26 -1.39+0.01
−0.02 11.12 1.17
+0.05
−0.09
K complex 0.4 - 0.7 0.57 -1.16+0.04
−0.04 11.12
+0.06
−0.06 1.58
+0.24
−0.22
K complex 0.7 - 0.9 0.81 -1.16+0.07
−0.07 10.98
+0.07
−0.07 1.74
+0.36
−0.30
K complex 0.9 - 1.2 1.05 -1.2+0.07
−0.06 11.07
+0.06
−0.06 1.34
+0.26
−0.21
K complex 1.2 - 1.6 1.4 -1.17+0.12
−0.12 10.93
+0.07
−0.06 1.39
+0.29
−0.28
K complex 1.6 - 2.5 1.96 -1.17 10.97+0.01
−0.02 1.25
+0.09
−0.04
obtained in the sub-area of I-selected sample where near-IR
photometry is available (see Fig. 7).
For the K-selected sample, we have analyzed the ef-
fect of the cosmic variance on small areas, deriving the MF
for the two K-selected subsamples, deep and shallow, sepa-
rately (see Figure 8). We find a significantly lower MF (by
a factor 1.8 and 1.6) in the redshift range 0.4 < z < 0.7 and
0.7 < z < 0.9 in the deep K-selected sample (K < 22.84
over 168 arcmin2) compared to the shallow K-band sam-
ple (K < 22.34 over 442 arcmin2). The significance of such
differences in the MF, is of ∼ 2 − 3σ in each mass bin at
0.4 < z < 0.7 and ∼ 1 − 2σ at 0.7 < z < 0.9. Globally,
i.e. for the total number densities over the complete mass
range, the differences are significant at about 5-3 σ level
in the two redshift ranges, respectively. This problem leads
to a clear warning on the results based on small fields, as
covered by most of the previous existing surveys.
In Figure 9 we show the MFs derived using the I-
selected spectroscopic sample and the K-selected photo-
metric sample for both methods (smooth and complex
SFHs) to derive the masses. The resulting mass functions
are quite well fitted by Schechter functions. The best-fit
Schechter parameters are summarized in Table 2, with the
uncertainties derived from the projection of the 68% confi-
dence ellipse. Since in the lowest and highest redshift bins
(z ≃ 0.2 and 2) the values of M∗stars and the low-mass-end
slope (α), respectively, are poorly constrained, they have
been fixed to the values measured in the following and pre-
vious redshift bins respectively.
We note, first, that the overall agreement between the
MF derived with the different methods for masses determi-
nation is fairly satisfactory, albeit complex SFHs estimates
provide typically larger masses. The systematic shift be-
tween the 2 methods (Section 3.4) is reflected in most of
the redshift bins also in the characteristic mass (M∗stars)
of the MF while the best fit slopes (α) and φ∗ Schechter
parameters agree within the errors between the different
methods in most of the redshift bins.
We note, furthermore, an overall agreement between the
2 samples (I- and K-selected), and in most of the redshift
bins the Schechter parameters agree within the errors, even
if some differences exist. More in detail, the I-selected sam-
ple in the range 0.4 < z < 0.9 has a higher low-mass
(< 9.5 dex) end and a slightly steeper MF (α ∼ −1.23)
than the K-selected one (α > −1.15). These differences are
probably due to the population of blue K-faint galaxies,
that are missed in the K-sample, as discussed in Section
3. These galaxies have, indeed, median colours in the I-
selected sample that are bluer than in the K-selected sam-
ple (I−K ≃ 0.45 compared to ≃ 0.89). A similar behaviour
has been noted in the local MF derived using an optically
selected sample (g band) compared to the local MF from
the near-IR (2MASS) sample (Bell et al. 2003). On the
contrary, at even lower masses (< 8.5 dex) at z < 0.4 the
K-selected MF is slightly steeper than the I-selected one,
but no significant differences in the colour of the two pop-
ulations is found.
4.2. Comparison with Previous Surveys
In general, previous efforts to derive MF have relied on
smaller or more limited samples, or often based mainly
on photometric redshifts (Drory et al. 2004, 2005). We
have compared our MF determination with literature re-
sults based on different surveys (K20, COMBO17, MUSIC,
DEEP2, FDF+CDFS), rescaled to Chabrier IMF (see
Figure 10). Our MFs rely on a higher statistics at inter-
mediate to high-mass ranges, and therefore present lower
statistical errors. At z < 0.2 we sample unprecedented mass
ranges, more than one order of magnitude lower than previ-
ous surveys, while at z > 0.4 the FDF and MUSIC surveys
reach lower mass limits even if on significantly smaller area.
14 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
Fig. 10. Comparison between the I-selected and the K-selected MFs in the VVDS (hatched vertical and horizontal STY
regions, respectively, see caption Figure 9) and the literature data (K20, COMBO17, MUSIC, DEEP2, FDF+CDFS; for
each the band of selection is indicated in the parenthesis). The vertical hatched regions represent the completeness limits
of the VVDS samples.
Our MFs are in fairly good agreement with previous studies
over the whole mass range up to z ∼ 1.2. However, some
differences exist, in particular at the massive end, which is
more sensitive to the different selections, methods, statis-
tics and to cosmic variance due to large scale structures: for
example, in the MUSIC-GOODS survey there are two sig-
nificant overdensities at z ∼ 0.7. The MFs from COMBO17
(Borch et al. 2006) and also from DEEP2 (Bundy et al.
2006) are systematically higher than previous surveys at
the massive-end, in particular in the range 0.7 < z < 1.2.
The MFs in the FDF+CDFS are instead systematically
lower than ours at the massive-end and higher than our
extrapolation to masses lower than our completeness limit.
At z > 1.2 our MF is systematically higher than previ-
ous studies. Given the area sampled (more than a factor
4 wider compared to FDF+CDFS and to MUSIC) and
the consistency at these redshifts of our MF in the 2 K-
selected separated areas (see Figure 8), we are confident
in our results. However at high-z the uncertainties on the
stellar masses estimate increase (up to 0.16 dex including
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 15
also the photometric redshift errors) and could produce a
partially spurios excess in the number densities of galax-
ies, in particular in the massive tail of the MF. This ef-
fect is discussed in Kitzbichler & White (2007) which take
into account in the hierarchical formation Millenium simu-
lation the effect of the dispersion in the mass determination
(0.25 dex, i.e. 78%). We have performed a similar analysis,
taking into account the uncertainty on the mass, due to
the fitting technique (∼ 30%) and to the uncertainty of
the photometric redshifts (both its dependence on redshift
and magnitudes as described in previous sections, i.e. up to
σz ≃ 0.2 at z = 2 and K > 21.5). We found that the effect
on the MF is always small, and only the very massive tail
(M > 2 × 1011M⊙) is systematically overestimated (up to
0.2 dex). This effect can not completely explain the excess
found compared to previous surveys, which are affected in
a similar way by the same bias.
4.3. The Evolution of the Galaxy Stellar Mass Function
The VVDS allows us to follow the evolution of the
MF within a single sample over a wide redshift range.
Difficulties in the interpretation of the evolution are, in-
deed, due to the comparison with the local MFs, which
have been determined with different methods and sample
selection. For example, no local MF has been derived using
complex SFHs for mass determinations. In our analysis we
use, as reference, the local MF by Bell et al. (2003) and Cole
et al. (2001) rescaled to Chabrier IMF. In particular, the
Cole et al. (2001) local mass function, derived with smooth
SFHs but with formation redshift fixed at z = 20, has been
rescaled to smooth SFHs method with free formation red-
shift by Fontana et al. (2004).
The first important result is that, thanks to our very
deep samples, both I- and K-selected, the low-mass end of
the MF is even better determined than in the local sam-
ple up to z < 0.4, probing for the first time masses down
to about 3 × 107M⊙. The low mass-end is rather steep
(−1.38 < α < −1.26), and could even be described by a
double Schechter function, and is steeper than the local es-
timates (α = −1.18±0.03 Cole et al. 2001, α = −1.10±0.02
Bell et al. 2003), possibly due to the fact they are not prob-
ing masses smaller than 109 M⊙ (more than one order of
magnitude more massive than in our sample). As evident
from Figure 9, we find a substantial population of low-mass
(< 109M⊙) galaxies at low redshifts (z < 0.4). This popu-
lation is composed by faint blue galaxies with similar prop-
erties in the 2 samples (I- and K-selected): I,K ≃ 22− 23,
MI ,MK ≃ −16,−17 with median MI − MK ≃ 0.3, and
median z ≃ 0.1− 0.2. This is a very strong result from our
survey which can rely on a wider area and a deeper sam-
ple than previous surveys at low redshifts. At z > 0.4 the
low-mass slope is on the contrary always consistent with
the local values. Even if we are not probing masses smaller
than 108M⊙ at z > 0.4, we found that the MF remains
quite flat (−1.23 < α < −1.04) at all redshifts, similar to
that of Fontana et al. (2006) which probe lower masses (see
figure 10).
From a visual inspection of Figure 9, we see that up to
z ∼ 0.9 there is only a weak evolution of the MF, as sug-
gested by previous results (Fontana et al. 2004, 2006, Drory
et al. 2005), while at higher redshifts there appears to begin
a decrease in the normalization of the MF, even if a massive
tail remains present up to z = 2.5. At intermediate masses
Fig. 11. Cosmological evolution of the galaxy number den-
sity as a function of redshift, as observed from the VVDS
in various mass ranges (> 108M⊙, > 10
9.77M⊙ and >
1010.77M⊙ from top to bottom). Observed data from Vmax
(shown as lower limit in the top panel) have been corrected,
when necessary, for incompleteness integrating the mass
function using the best fit Schechter parameters. VVDS
data (big filled circles), averaged over the I- and the K-
selected samples and the 2 methods to derive the mass, are
plotted along with their statistical errors (solid error bars)
and the scatter between the 2 different samples and meth-
ods (dotted error bars). The solid lines show the best-fit
power laws ∝ (1 + z)β, while the dashed lines correspond
to the no-evolution solution normalized at z = 0. Results
from previous surveys (small points and dot-dashed lines)
are also shown.
(9.5 < logM < 10.5), our VVDS MF is very well defined
and shows a clear evolution, i.e. the number density de-
creases with increasing redshifts compared to both the first
VVDS redshift bin and the local MF. This evolution is quite
mild up to z ≃ 0.9, while it becomes faster at higher z. At
larger masses the high mass end of the MF (> 1011 M⊙)
shows a small evolution up to z ≃ 2.5. However, its evolu-
tion is extremely dependent on the assumed local MF and
on the uncertainties in the mass determination, which pro-
duce a larger dispersion between the different methods and
samples compared to the intermediate-mass range.
In order to quantify the MF evolution, and its mass
dependency independently from the local MF, in the next
section we derive number densities for different mass limits.
16 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
Table 3. Number Density and Stellar Mass Density
zinf zsup Log(ρN ) Scatter Error Log(ρstars)Scatter Error
log(Mstars)> 8
0.05 0.40 -1.40 0.04 0.01 8.45 0.09 0.01
0.40 0.70 -1.63 0.08 0.02 8.34 0.08 0.02
0.70 0.90 -1.70 0.08 0.04 8.22 0.11 0.01
0.90 1.20 -1.78 0.13 0.05 8.14 0.12 0.01
1.20 1.60 -1.81 0.05 0.11 8.04 0.14 0.02
1.60 2.50 -1.90 0.13 0.01 8.05 0.11 0.01
log(Mstars)> 9.77
0.05 0.40 -2.20 0.06 0.01
0.40 0.70 -2.29 0.03 0.01
0.70 0.90 -2.33 0.04 0.01
0.90 1.20 -2.45 0.05 0.01
1.20 1.60 -2.54 0.02 0.01
1.60 2.50 -2.65 0.01 0.01
log(Mstars)> 10.77
0.05 0.40 -3.07 0.18 0.05 8.00 0.22 0.04
0.40 0.70 -3.04 0.10 0.02 8.04 0.14 0.02
0.70 0.90 -3.22 0.16 0.02 7.80 0.19 0.02
0.90 1.20 -3.28 0.15 0.02 7.76 0.18 0.02
1.20 1.60 -3.42 0.23 0.02 7.59 0.28 0.02
1.60 2.50 -3.35 0.11 0.01 7.70 0.11 0.01
4.4. Galaxy Number Density
Here we derive the number density of galaxies as a function
of redshift, using different lower limits in mass (Mmin). We
have estimated the number density from the observed data
(from Vmax), as well as from the incompleteness-corrected
MFs, i.e. integrating the best-fit Schechter functions over
the considered mass range. The corrections due to faint
galaxies dominate for Mmin = 10
8M⊙, while they are neg-
ligible for the other mass limits considered. A formal uncer-
tainty in this procedure was estimated by considering the
Vmax statistical errors and the range of acceptable Schechter
parameters values. In Figure 11 we plot our VVDS determi-
nations, averaged over the I- and K-selected samples and
the 2 methods for mass determination (listed in Table 3),
along with their statistical errors (always less than 10%)
and the scatter between the 2 different samples and meth-
ods (ranging between 10 and 45% and due mainly to the dif-
ferent methods rather than to the different samples). With
the two methods we find similar trends with redshift of the
number densities of galaxies, but with a systematic shift
which is significant only for the highest mass limit (for com-
plex SFHs the galaxy number densities are ∼ 50% higher
than for smooth SFHs). The effect of photometric redshift
and mass uncertainty on the number densities is always
small (< 15%) for the mass range shown in Figure 11, ex-
cept for the very massive galaxies (> 2 × 1011 M⊙, not
shown in the figure because of the small number of galaxies
in this mass range) where the intrinsic values could be up
to a factor ∼ 2 lower (see discussion in section 4.2). The
decrease in number density with redshift for all the adopted
mass limits is evident.
We have compared VVDS results to previous surveys
and with different local determinations. For the total num-
ber density (108 < Mstars < 10
13M⊙) VVDS data are very
well consistent with the evolutionary STY fit determined by
Fontana et al. (2006) in the GOODS-MUSIC survey. At in-
Fig. 12. Cosmological evolution of the stellar mass density
as a function of redshift as observed from the VVDS for
2 mass ranges: integrated over the whole range 108M⊙ ≤
Mstars ≤ 10
13M⊙ (upper panels) and for massive galax-
ies (> 1010.77M⊙) (lower panels). Symbols and lines as in
Figure 11.
termediate masses (> 109.77M⊙, corresponding to 10
for Salpeter IMF) our VVDS data have a better determina-
tion and smaller uncertainties than previous ones and are
consistent with most of them at z < 1.2 and in the upper en-
velope at higher z. For the high mass range (> 1010.77M⊙,
corresponding to 1011M⊙ for Salpeter IMF) we are quite
consistent with previous results, and even if our VVDS have
lower errors than previous ones, the dispersion within the
various VVDS measurements reflect the uncertainties for
massive galaxies.
If we represent the average number density evolution
by a power law ρN ∝ (1 + z)
β , we find that β(Mstars >
108) = −1.28 ± 0.15, β(Mstars > 10
9.77) = −1.26 ± 0.10,
and β(Mstars > 10
10.77) = −1.01 ± 0.05 (the errors on β
represent the uncertainties due to the 2 different methods).
We find on average a similar evolution for the 2 methods
analyzed and a slightly milder evolution with increasing
mass limit (‘downsizing’ in mass assembly). The average
evolution from z = 0 to z = 1 is a factor 2.4 ± 0.3 and
2.0± 0.1 from low to high-mass galaxies, respectively, and
increases to a factor 4.0 ± 0.9 and 3.0 ± 0.2, respectively,
at z = 2. We note moreover that for the highest mass limit
(Mstars > 10
10.77) at low redshift (z < 0.7) the number
density observed is consistent with no-evolution (fixing the
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 17
value to z = 0 we found an evolution < 30%), excluded
instead for the intermediate and low-mass limit. At high-z
(z > 1.5) for intermediate and high-mass range we note a
flattening in the number density from the VVDS data, sim-
ilar to Drory et al. (2005), but higher than Fontana et al.
(2006). This flattening is due to the high mass tail observed
in the range 1.6 < z < 2.5. This population shows ex-
tremely red colours (MI −MK ≃ 0.8) and could be related
to the appearance of a population of massive star forming
dusty galaxies, observed in previous surveys (Fontana et
al. 2004, Daddi et al. 2004b). The small excess induced by
uncertainties on the mass and photometric redshifts (see
discussion in section 4.2) can not completely explain the
difference with Fontana et al. (2006) survey, which is af-
fected by the same bias in a similar way.
The mass dependent evolution (“mass downsizing”) is
very debated and the results from different surveys are still
controversial. Deep surveys, such as the FDF & CDFS (an-
alyzed by Drory et al. 2005) find an evolution consistent
with ours (a decrease of about a factor 2.5 – 4 at z = 1− 2
in the number density of galaxies> 1010.77 M⊙). Fontana et
al. (2006) suggest a similar mild evolution up to z = 1, for
massive galaxies (> 1010.77M⊙) and a stronger evolution
at z > 1.5, reaching a factor about 10 at z = 3. Similarly,
Cimatti et al. (2006) show that the number density of lu-
minous (massive, Mstars > 10
11M⊙) early-type galaxies is
nearly constant up to z ∼ 0.8, while Bundy et al. (2006)
find a slight decrease, consistent with no evolution, only for
even more massive system (> 3×1011M⊙) and a more sig-
nificant decline for Mstars < 3× 10
11M⊙. Vice versa, data
from the MUNICS survey (Drory et al. 2004) show a faster
evolution of massive galaxies, even faster than for the less
massive systems (see also Figure 4 in Drory et al. 2005).
To summarize, our accurate results show that the MF
evolves mildly up to z ≃ 1 (about a factor 2.5 in the total
number density) and that a high-mass tail is still present
up to z = 2.5. Moreover, we find that massive systems
show an evolution that is on average milder (< 50% at
z < 1) than intermediate and low-mass galaxies and con-
sistent with a mild/negligible evolution (< 30%) up to
z ∼ 0.8. Conversely, a no-evolution scenario in the same
redshift range is definitely excluded for intermediate- and
low-mass galaxies.
This behaviour suggests that the assembly of the stellar
mass in objects with mass smaller than the localM∗stars was
quite significant between z = 2 and z = 0. Qualitatively,
this behaviour is expected for galaxies with SFHs prolonged
over cosmic time, which therefore continue to grow in terms
of stellar mass after z ∼ 1. Conversely, our results fur-
ther strengthen the fact that the number density of mas-
sive galaxies is roughly constant up to z ≃ 0.8, consistently
with a SFH peaked at higher redshifts, with the conversion
of most of their gas into stars happening at z > 1.5−2, rul-
ing out the ‘dry mergers’ as the major mechanism of their
assembly history, below z < 1.
5. Mass Density
Various attempts to reconstruct the cosmic evolution of the
stellar mass density have been previously made, mainly us-
ing NIR-selected samples (Dickinson et al. 2003, Fontana et
al. 2004, Drory et al. 2005). Our survey offers the possibil-
ity to investigate it using the MF derived from two different
optical- and NIR-selected samples, taking advantage of our
depth, and relatively wide area covered. Furthermore, the
different methods analyzed here to derive the stellar mass
content give us a direct measure of the uncertainties in-
volved.
We have estimated the stellar mass density from the
observed data, as well as from the incompleteness-corrected
MFs. Up to z < 1 the corrections due to faint galaxies are
relatively small. A formal uncertainty in this procedure was
estimated by considering the Vmax statistical errors and the
range of acceptable Schechter parameters values.
Figure 12 shows our results (averaged over the I- andK-
selected samples and the 2 methods with a typical scatter
of about 30-50% and statistical errors always less than 5%
see Table 3), for the total mass density and for the density
in massive galaxies (> 1010.77), along with their represen-
tative power laws (ρstars ∝ (1+z)
β), and compared to liter-
ature data (see references in the figure). For the total mass
density, even if the results from our survey cover a range
of values with some significant differences between the two
different methods (up to ∼ 40%), the general behaviour
and evolutionary trend is well defined by β = −1.19± 0.05.
We find that the evolution of the stellar mass density is
relatively slow with redshift, with a decrease of a factor
2.3 ± 0.1 up to z ≃ 1, up to a factor 4.5 ± 0.3 at z = 2.5.
The agreement of average total mass density with previous
surveys is reasonably good, and the range covered by VVDS
data reflect the different selection techniques and methods
used in different surveys. The average total mass density
evolution is milder than in the MUSIC sample (Fontana et
al. 2006) already at z > 0.5. Our evolutionary trend is con-
sistent with the upper envelope of previous surveys, even if
our highest-redshift value is uncertain because the low-mass
slope is poorly constrained. For comparison the analysis of
VVDS data using a IRAC-selected sample (see Arnouts et
al. 2007) finds similar values for the mass density, except
that the highest redshift point is lower than ours. Given the
present uncertainties on the low-mass slope of the GSMF,
the total mass density at z ≃ 2 remains poorly constrained.
The mass density of high-mass objects (> 1011M⊙ with
Salpeter IMF) varies by a factor up to 1.8 within the 2
methods adopted, but the evolutionary trend is similar
(β = −1.13± 0.01) and consistent with a decrease of about
a factor 2.18 ± 0.02 to z = 1 and 3.44 ± 0.04 to z = 2.0.
Moreover at low redshift (z < 0.7) the VVDS observed data
are consistent with a mild/negligible evolution (< 30%), as
indicated by the number density of massive galaxies (see
previous Section). Our data are roughly consistent with
Fontana et al. (2006) up to z = 1.5 (even if the slope of the
evolutionary trend is shallower), while at z > 1.5 the VVDS
mass-density of massive galaxies is significantly higher than
that in Fontana et al. (2006), reflecting the excess in MF at
high-z noted in the VVDS MF compared to previous ones
(see Section 4.2). This results, therefore, in a flatter evolu-
tionary trend over the total redshift range. Given the wider
area and completeness for high-mass objects, our samples
guarantee a higher statistical accuracy and confidence level
than before. However some caveat remains due to the effect
of photometric redshift and mass uncertainty on the mass
densities, which is anyhow always small (< 15%) except for
the massive galaxies (> 6 × 1010 M⊙) where the intrinsic
values could be up to 20-30% lower than our estimates (see
discussion in Section 4.2).
18 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
6. Summary and Discussion
We have investigated the evolution of the Galaxy Stellar
Mass Function up to to z = 2.5 using the VVDS survey
covered by deep VIMOS spectroscopy (17.5 < I < 24)
and multiband photometry (from U to K-band). For our
analysis we have used two different samples: (1) the opti-
cal (I-selected, 17.5 < I < 24) main spectroscopic sam-
ple, based on about 6500 secure redshifts over about 1750
arcmin2, and (2) a near-IR sample (K-selected, K < 22.84
& K < 22.34), in a sub-area of about 610 arcmin2 and
based on about 10200 galaxies with accurate photomet-
ric and spectroscopic redshifts. For the first time we have
probed masses down to a very low limit, in particular at
low-z (down to ∼ 3 × 107M⊙ at z ∼ 0.2), while the rela-
tively wide area has allowed us to determine the MF with
much higher statistical accuracy than previous samples.
In order to better understand uncertainties we have ap-
plied and compared two methods to estimate the stellar
mass content in galaxies from multiband SED fitting. The
2 methods differ in the explored parameter space (metal-
licity, dust law and content) and are based on different as-
sumptions on previous star formation history. The main
results from the stellar mass estimate can be summarized
as follows:
– The agreement between the 2 methods is fairly good
even if masses estimated with ‘complex SFHs’ are
systematically higher than ‘smooth SFHs’ masses.
For the K-selected sample the mean difference is
〈d logMstars〉 ≃ 0.12 dex, and the dispersion is σ =
0.13. The differences are mainly due to the secondary
burst component (complex SFHs) compared to smooth
SFHs.
– We found that mass estimates using only optical bands
are in rather good agreement with those using also NIR
bands up to z ∼ 1.2. We have used this information to
statistically correct masses for objects without near-IR
photometry. At higher redshifts the shift and dispersion
dramatically increase and the mass estimates become
unreliable if near-IR photometry is not available.
We have, thus, derived the MF using the VVDS I-
selected sample and extended it up to z = 2.5 thanks to
the K-selected sample. From a detailed analysis of the MF,
galaxy number density and mass density, in different mass
ranges, through cosmic time, we found evidences for:
– a substantial population of low-mass galaxies (<
109M⊙) at z ≃ 0.2 composed by faint (I,K ≃ 22, 23)
blue galaxies with median MI−MK ≃ 0.3, and absolute
magnitudes MI ,MK ≃ −16,−17;
– a slow evolution of the stellar mass function with red-
shift up to z ∼ 0.9 and a faster evolution at higher-z,
in particular for less massive systems. A massive popu-
lation is present up to z = 2.5 and have extremely red
colours (MI −MK ≃ 0.7− 0.8).
– at z > 0.4 the low-mass slope of the GSMF does not
evolve significantly and remains quite flat (−1.23 < α <
−1.04).
– the number density shows, on average, a mild differen-
tial evolution with mass, which is slower with increas-
ing mass limit. Such evolution can be described by a
power law ∝ (1 + z)β(>M). Within the VVDS redshift
range we found that β(> 108M⊙) = −1.28 ± 0.15,
β(> 109.77M⊙) = −1.26± 0.10 and β(> 10
10.77M⊙) =
−1.01± 0.05. For massive galaxies at low redshift (z <
0.7) the evolution is consistent with mild/negligible-
evolution (< 30%), which is excluded for low-mass sys-
tems.
– the evolution of the stellar mass density is relatively slow
with redshift, with a decrease of about a factor 2.3±0.1
to z ≃ 1, while at z ≃ 2.5 the decrease amounts to a fac-
tor up to 4.5± 0.3, milder than in previous surveys. For
massive galaxies the evolution at low redshift (z < 0.7)
is consistent with a mild/negligible evolution(< 30%),
and shows a flattening compared to previous results at
z > 1.5 due to a population with extremely red colours.
Our results provide new clues on the controversial ques-
tion of when galaxy formed and assembled their stellar
mass. Most of the massive galaxies seem to be in place up to
z = 1 and have, therefore, formed their stellar mass at high
redshift (z > 1), rather than assembled it mainly through
continuous galaxy merging of small galaxies at z < 1. On
the contrary, less massive systems have assembled their
mass (through merging or prolonged star formation his-
tory) later in cosmic time. In agreement with our results, a
substantial population of high-z (z ∼ 2−3) dusty and mas-
sive objects have been discovered in near-IR surveys (Daddi
et al. 2004b) and detected by Spitzer in the far-IR (Daddi
et al. 2005, Caputi et al. 2006b). This population could
be related to the initial phase of massive galaxy formation
during their strong star forming and dusty phase.
Finally, our results are not completely accounted for by
most of theoretical models of galaxy formation (see Fontana
et al. 2004, 2006 and Caputi et al. 2006a for a detailed com-
parison with models). For instance, models by De Lucia et
al. (2006) predict that the most massive galaxies generally
form their stars earlier, but assemble them later, mainly
at z < 1 via merging, than the less massive galaxies (i.e.
’downsizing in star formation but ’upsizing’ in mass assem-
bly, see Renzini 2007 for a recent discussion). Furthermore,
the stronger decrease with redshift of the low-mass popu-
lation, with a low-mass end of the GSMF which remains
substantially flat up to high redshift, is not reproduced by
most of the theoretical galaxy assembly models, which tend,
indeed, to overpredict the low-mass end of the MF (see
Fontana et al. 2006).
Understanding the mass assembly of less massive ob-
jects and disentangling merging processes from prolonged
star formation history is more complicated. In this respect
for a better comprehension of galaxy formation the VVDS
will allow us to further investigate the evolution of the stel-
lar mass function up to high-z also for different galaxy types
(spectral and morphological) and in different environments.
For example Arnouts et al. (2007) study the mass density
evolution of different galaxy population. Further analysis
of galaxy mass dependent evolution, using stellar popula-
tion properties, as well as observed spectral features, will
be presented in forthcoming papers (Lamareille et al., in
preparation, Vergani et al. 2007). Furthermore, it will be
possible to push the study of the galaxy stellar mass func-
tion at higher redshifts using SPITZER mid-IR observa-
tions. While most of present studies (Dickinson et al. 2003,
Drory et al. 2005) do not use rest-frame near-IR photome-
try to estimate stellar masses, our VVDS-SWIRE collabo-
ration will allow to combine the deep VVDS spectroscopic
sample with SPITZER-IRAC photometry.
L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History 19
Acknowledgements. This research has been developed within the
framework of the VVDS consortium.
This work has been partially supported by the CNRS-INSU and
its Programme National de Cosmologie (France), and by Italian
Ministry (MIUR) grants COFIN2000 (MM02037133) and COFIN2003
(num.2003020150).
The VLT-VIMOS observations have been carried out on guaranteed
time (GTO) allocated by the European Southern Observatory (ESO)
to the VIRMOS consortium, under a contractual agreement between
the Centre National de la Recherche Scientifique of France, heading
a consortium of French and Italian institutes, and ESO, to design,
manufacture and test the VIMOS instrument. We are in debt with
E. Bell, S. Salimbeni, and E. Fontana for providing the data from
their survey in electronic format, and to C. Maraston for her galaxy
evolution models in BC format.
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1 INAF-Osservatorio Astronomico di Bologna - Via Ranzani,1,
I-40127, Bologna, Italy
2 INAF-IASF - via Bassini 15, I-20133, Milano, Italy
3 Laboratoire d’Astrophysique de Marseille, UMR 6110
CNRS-Université de Provence, BP8, 13376 Marseille Cedex
12, France
4 INAF-Osservatorio Astronomico di Brera - Via Brera 28,
Milan, Italy
http://arxiv.org/abs/astro-ph/0506044
http://arxiv.org/abs/astro-ph/0611724
http://arxiv.org/abs/astro-ph/0311475
http://arxiv.org/abs/astro-ph/0410295
http://arxiv.org/abs/astro-ph/0702148
20 L.Pozzetti et al.: The VVDS: The Galaxy Stellar Mass Assembly History
5 Institute for Astronomy, 2680 Woodlawn Dr., University of
Hawaii, Honolulu, Hawaii, 96822
6 Max Planck Institut fur Astrophysik, 85741, Garching,
Germany
7 Institut d’Astrophysique de Paris, UMR 7095, 98 bis Bvd
Arago, 75014 Paris, France
8 Centro de Astrofsica da Universidade do Porto, Rua das
Estrelas, 4150-762 Porto, Portugal
9 Laboratoire d’Astrophysique de Toulouse/Tabres
(UMR5572), CNRS, Université Paul Sabatier - Toulouse
III, Observatoire Midi-Pyriénées, 14 av. E. Belin, F-31400
Toulouse, France
10 INAF-IRA - Via Gobetti,101, I-40129, Bologna, Italy
11 INAF-Osservatorio Astronomico di Roma - Via di Frascati
33, I-00040, Monte Porzio Catone, Italy
12 School of Physics & Astronomy, University of Nottingham,
University Park, Nottingham, NG72RD, UK
13 Astrophysical Institute Potsdam, An der Sternwarte 16, D-
14482 Potsdam, Germany
14 Observatoire de Paris, LERMA, 61 Avenue de l’Observatoire,
75014 Paris, France
15 Università di Bologna, Dipartimento di Astronomia - Via
Ranzani,1, I-40127, Bologna, Italy
16 Centre de Physique Théorique, UMR 6207 CNRS-Université
de Provence, F-13288 Marseille France
17 Integral Science Data Centre, ch. d’Écogia 16, CH-1290
Versoix
18 Geneva Observatory, ch. des Maillettes 51, CH-1290
Sauverny, Switzerland
19 Astronomical Observatory of the Jagiellonian University, ul
Orla 171, 30-244 Kraków, Poland
20 INAF-Osservatorio Astronomico di Capodimonte - Via
Moiariello 16, I-80131, Napoli, Italy
21 Universitá di Milano-Bicocca, Dipartimento di Fisica -
Piazza delle Scienze, 3, I-20126 Milano, Italy
22 Università di Bologna, Dipartimento di Fisica - Via Irnerio
46, I-40126, Bologna, Italy
	Introduction
	The First Epoch VVDS Sample
	The I-selected Spectroscopic Sample
	The K-selected Photometric Sample
	Comparison of the Two Samples
	Estimate of the Stellar Masses
	Smooth SFHs
	Complex SFHs
	Effect of NIR Photometry
	Comparison of the Masses Obtained with the Two Methods
	Massive Galaxies at z>1
	Mass Function Estimate
	The VVDS Galaxy Stellar Mass Function
	Comparison with Previous Surveys
	The Evolution of the Galaxy Stellar Mass Function
	Galaxy Number Density
	Mass Density
	Summary and Discussion
