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arXiv:astro­ph/0302599
v2
8
Apr
2003
Astronomy & Astrophysics manuscript no. April 22, 2003
(DOI: will be inserted by hand later)
The K20 survey. V The evolution of the near-IR Luminosity
Function ?
L. Pozzetti 1 , A. Cimatti 2 , G. Zamorani 1 , E. Daddi 3 , N. Menci 4 , A. Fontana 4 , A. Renzini 3 , M. Mignoli 1 , F.
Poli 5 , P. Saracco 6 , T. Broadhurst 3;7 , S. Cristiani 8;9 , S. D'Odorico 3 , E. Giallongo 4 , and R. Gilmozzi 3
1 Istituto Nazionale di Astrosica, Osservatorio Astronomico di Bologna, Via Ranzani 1, I-40127 Bologna, Italy
2 Istituto Nazionale di Astrosica, Osservatorio Astrosico di Arcetri, Largo E. Fermi 5, I-50125 Firenze, Italy
3 European Southern Observatory, Karl-Schwarzschild-Str. 2, D-85748, Garching, Germany
4 Istituto Nazionale di Astrosica, Osservatorio Astronomico di Roma, via Dell'Osservatorio 2, Monteporzio, Italy
5 Dipartimento di Astronomia, Universita \La Sapienza", Roma, Italy
6 Istituto Nazionale di Astrosica, Osservatorio Astronomico di Brera, via E. Bianchi 46, Merate, Italy
7 Racah Institute for Physics, The Hebrew University, Jerusalem, 91904, Israel
8 ST, European Coordinating Facility, Karl-Schwarzschild-Str. 2, D-85748, Garching, Germany
9 Istituto Nazionale di Astrosica, Osservatorio Astronomico di Trieste, via Tiepolo 11, Trieste, Italy
Received ... ; Accepted ...
Abstract. We present the galaxy rest-frame near-IR Luminosity Function (LF) and its cosmic evolution to z  1:5
based on a spectroscopic survey of a magnitude limited sample of galaxies with Ks < 20 (the K20 survey, Cimatti
et al. 2002b). The LFs have been derived in the rest-frame J and Ks bands. Their evolution is traced using three
dierent redshift bins (zmean ' 0:5; 1; 1:5) and comparing them to the Local near-IR Luminosity Function. The
luminosity functions at dierent redshifts are fairly well tted by Schechter functions at z < 1:3. The faint-end
of the LFs (L < L  ) is consistent with the local estimates, with no evidence for a change either in the slope or
normalization up to z < 1:3. At higher redshift this part of the luminosity function is not well sampled by our
data. Viceversa, the density of luminous galaxies (MKs 5 logh70 < 25:5) is higher than locally at all redshifts
and relatively constant or mildly increasing with redshift within our sample. The data are consistent with a mild
luminosity evolution both in the J - and Ks-band up to z ' 1:5, with an amplitude of about
MJ ' 0:69  0:12
and
MK ' 0:54  0:12 at z  1. Pure density evolution is not consistent with the observed LF at z  1.
Moreover, we nd that red and early-type galaxies dominate the bright-end of the LF, and that their number
density shows at most a small decrease (< 30%) up to z ' 1, thus suggesting that massive elliptical galaxies were
already in place at z ' 1 and they should have formed their stars and assembled their mass at higher redshift. There
appears to be a correlation of the optical/near-IR colors with near-IR luminosities, the most luminous/massive
galaxies being red/old, the low-luminous galaxies being instead dominated by blue young stellar populations. We
also investigate the evolution of the near-IR comoving luminosity density to z ' 1:5, nding a slow evolution with
redshift ((z) =  (z = 0)(1+z) () with (J) ' 0:70 and (Ks) ' 0:37). Finally, we compare the observed LFs
with the predictions of a set of the most updated hierarchical merging models. Such a comparison shows that the
current versions of hierarchical models overpredict signicantly the density of low luminosity galaxies at z  1
and underpredict the density of luminous galaxies at z  1, whereas passive evolution models are more consistent
with the data up to z  1:5. The GIF model (Kaufmann et al. 1999) shows a clear deciency of red luminous
galaxies at z  1 compared to our observations and predicts a decrease of luminous galaxies with redshift not
observed in our sample.
Key words. Galaxies: elliptical and lenticular, evolution, formation, luminosity function { cosmology: observations
{ infrared: galaxies
Send oprint requests to: Lucia Pozzetti, e-mail:
lucia@bo.astro.it
? Based on observations made at the European Southern
Observatory, Chile (ESO LP 164.O-0560).
1. Introduction
Over the past few years, a wealth of observations from
deep surveys of optically-selected high-redshift galaxies
(e.g. Madau et al. 1996, Steidel et al. 1999), complemented
by observations in the far-IR/sub-mm(Hughes et al. 1998,
Barger et al. 1999), allowed signicant progress in our un-

2 Pozzetti and K20 collaboration: The evolution of the near-IR LF
derstanding of the evolution of galaxies from the present-
epoch back to z ' 4 and beyond (Steidel et al 1999;
Madau, Pozzetti, & Dickinson 1998). However, since these
samples of high-z galaxies were all selected at optical or
far-IR/sub-mm wavelengths, they are dominated by ob-
jects with on-going star formation. Therefore, such stud-
ies placed constraints more on the evolution of the star
birth rate activity than on the formation and assembly of
stellar systems through cosmic time.
The study of faint galaxy samples selected in the near-
infrared represents an important and complementary pos-
sibility to address the still open questions on how the
formation and evolution of massive systems evolved with
time compared to the predictions of the dierent theoreti-
cal scenarios (Broadhurst et al. 1992). Another advantage
of the near-IR selection (in particular in the K-band) is
that the k{corrections are relatively insensitive to galaxy
type and fairly small also at high redshift (Cowie et al.
1994), and the dust extinction eects are less severe than
in optical samples.
Since the rest-frame near-IR light is a relatively good
tracer of the galaxy stellar mass (Gavazzi et al. 1996;
Madau, Pozzetti & Dickinson 1998) the near-IR galaxy
Luminosity Function (LF) can provide a reasonable esti-
mate of the Galaxy Stellar Mass Function (GSMF). Only
recently the 2MASS (Jarrett et al. 2000) surveys allowed
accurate determinations of the local near-IR luminosity
and of the Galaxy Stellar-mass functions (Cole et al. 2001,
Kochanek et al. 2001), while only few attempts have been
made to reconstruct their evolution with redshift using
deep surveys of near-IR selected samples (i.e. Cowie et al.
1996; Cohen et al. 1999, Cohen 2002).
In order to address the above questions, we per-
formed a new spectroscopic survey of a complete sam-
ple of galaxies selected with K s < 20 (the K20 sur-
vey; http://www.arcetri.astro.it/ k20/). The sur-
vey and the sample are described in detail in Cimatti et al.
(2002b, hereafter Paper III), while the spectral and clus-
tering properties of the Extremely Red Objects (EROs)
are discussed in Cimatti et al. (2002a, Paper I) and Daddi
et al. (2002, Paper II), respectively. The redshift distri-
bution for the whole sample of K s -band selected galaxies
is given in Cimatti et al. (2002c, Paper IV). Here we re-
call that the K20 sample includes 546 objects to K s < 20
(Vega system), selected from a 32.2 arcmin 2 area of the
Chandra Deep Field South (CDFS; Giacconi et al. 2001)
and from a 19.8 arcmin 2 eld centered at 0055-269. The
total area of the two elds is 52 arcmin 2 . Optical multi-
object spectroscopy was mainly obtained with the ESO
VLT + FORS1 and FORS2, while a small fraction ( 4%)
of the objects was observed with near-IR spectroscopy us-
ing the VLT + ISAAC. We have imaged the 0055-269
eld over 10 bands (UBGV RRw IzJK s ), obtained with
the ESO NTT + SUSI2 (UBGV Rw I) and SOFI (JK s ),
and VLT + FORS1 (R and z), for a total of about 45
hours of integration. In the CDFS eld, we used a combi-
nation of public EIS NTT data (UK s ) and deep FORS1
images (BV RIz, courtesy of P. Rosati & M. Nonino).
The spectroscopic redshift completeness is 94% and 87%
for K s < 19 and K s < 20, respectively, and it increases
to 98% if we include the photometric redshifts obtained
with the deep multi-band imaging for the spectroscopi-
cally unidentied or unobserved objects (Cimatti et al.
2002b). The K20 sample is the largest and most complete
spectroscopic sample of galaxies with K s < 20 available
to date.
Fig. 1. The magnitude-redshift diagram for all the galaxies in
the spectroscopic sample to Ks < 20. Filled circles represent
galaxies identied spectroscopically, while empty squares are
unidentied or unobserved galaxies plotted at z = zphot .
In this paper, we investigate the evolution of the near-
IR luminosity function up to z ' 1:5 based on the K20 sur-
vey sample. Thanks to the higher statistical signicance
and completeness of our sample, it is possible to use the LF
evolution to place new and more stringent constraints on
the formation and evolution of massive galaxies than was
possible from previous surveys (Cowie et al. 1996, Cohen
et al. 1999, Cohen 2002). In particular our survey has the
advantage to include a complete sample of EROs, partially
with spectroscopic identications, which usually were not
included in previous spectroscopic surveys (e.g. Cohen
2002) because of their selection. Finally, we compare the
LF evolution with the predictions of two competitive sce-
narios of galaxy evolution: the Pure Luminosity Evolution
(PLE) and the Hierarchical Merging Models (HMM). We
adopt H 0 = 70 km s 1 Mpc 1
,
m =
0:3;
 = 0:7.
2. The K20 spectroscopic sample
From the total K20 sample of 546 objects with K s  20
we have extracted a sample of 489 galaxies, after exclud-
ing objects classied as stars and AGN on the basis of

Pozzetti and K20 collaboration: The evolution of the near-IR LF 3
Fig. 2. K-corrections colors (see text) as a function of red-
shift: Jrest Ks (top panel) and K s;rest Ks (bottom panel).
Dierent curves are derived from dierent spectral models
which at low redshift reproduce spectra and colors of local
E, S0, Sa, Sb, Sc, Im (solid lines from bottom to top at z > 1)
and dusty star-forming galaxies (dashed line; see text). Dotted
line shows the 2:5log(1 + z) term for comparison.
their spectra. In addition to spectroscopic redshifts, pho-
tometric redshifts have been derived (Cimatti et al. 2002b)
with very high accuracy (hz spe z phot i = h
zi = 0:012
and 
z = 0:089(1+z spe )). Such an accuracy, made possi-
ble by the numerous photometric bands and the precision
of the magnitude measurements, is consistent with previ-
ous results on the HDF-N data set (Fontana et al 2000)
and with simulations made by Bolzonella et al. (2000) at
high redshift (1 < z < 2), where our sample is the largest
to date. The magnitude{redshift distribution of selected
galaxies is shown in Fig. 1. Thanks to the depth and com-
pleteness of our sample, the coverage of the K s { redshift
plane is such that the near-IR LF can be derived with
good accuracy and over a relatively large range of magni-
tudes at least up to z  1, still sampling with relatively
good statistics the high luminosity part of the LF up to
z  2. Since the sample spans a wide range in luminosity,
redshift and look-back time, it is therefore well suited to
study the evolution of the near-IR Luminosity Function
within the sample itself and in comparison to the local
population.
3. The estimate of the rest-frame near-IR
luminosities
The small variance of k-corrections in the K s -band (Cowie
et al. 1994, Mannucci et al. 2001) greatly simplies
the analysis with respect to optically-selected samples of
Fig. 3. The color-redshift (R Ks vs. z) diagram for galaxies
in the spectroscopic sample to Ks < 20. Dierent symbols as
in Fig. 1. Arrows indicate 3 lower limits in R Ks colors for
objects not detected in the R band. The curves show dierent
spectral models as in Fig. 2.
galaxies. Moreover, we take advantage of the fact that at
z ' 0:8 the observed K s -band corresponds to rest-frame
J-band. In order to compute the near-IR luminosity func-
tion, we derive the rest-frame J- and K s -band absolute
magnitudes (M J and MKs ) according to the following re-
lations:
M J = K s 5log(d L (z)=10pc) + (J rest K s )(z) (1)
MKs = K s 5log(d L (z)=10pc) + (K s;rest K s )(z); (2)
where K s is the total apparent magnitude measured with
SExtractor (see Cimatti et al. 2002b, Paper III, for more
details), dL (z) is the luminosity distance at redshift z and
(J rest K s ) and (K s;rest K s ) are the \k-correction col-
ors", i.e. the dierence between rest frame and observed
magnitude which includes also the 2:5log(1 + z) term (see
also Lilly et al. 1995). It should be noted that in Eq. (1) the
last term can be written as a conventional k-correction for
the K s -band (as in Eq. 2) plus a rest-frame (J-K s ) color.
The k-correction colors as a function of redshift are plot-
ted in Fig. 2. This gure clearly shows the small variation
of the k-corrections for dierent spectral types over most
of the redshift range covered by our data (for a compari-
son with a similar plot in the optical bands see Lilly et al.
1995).
These k-corrections for dierent spectral types are
computed using the Bruzual & Charlot (1993) models
(GISSEL 2000 version), in order to reproduce spectra, and
k-corrections of local galaxies (E, S0, Sa, Sb, Sc, Im) at
low redshift (cf. Pozzetti et al. 1996, Mannucci et al. 2001)

4 Pozzetti and K20 collaboration: The evolution of the near-IR LF
Fig. 4. The absolute J and Ks magnitudes as a function of
redshift derived (see text) for all galaxies in the spectroscopic
sample to Ks < 20. Symbols as in Fig. 1. Local estimates of
M 
J and M 
Ks (dotted horizontal lines) from Cole et al. (2001).
and the color-redshift diagram (R K s vs. z) observed in
our sample (Fig. 3). In order to take into account the dusty
star-forming population, we introduce an additional spec-
tral type dominated by star formation and strong dust
extinction consistently describing the SED of red emis-
sion line objects and reproducing the sub-class of emis-
sion line EROs with R K s > 5 (cf. Paper I). We have
adopted an exponentially declining star formation history
(SFR / exp( t= )), with  = 0:3; 1; 2; 4; 1 Gyrs (E,
S0, Sa, Sb, Sc galaxies, respectively), the Salpeter (1955)
Initial Mass Function (IMF) and an age of 12.5 Gyrs at
z = 0 (i.e. a formation redshift z f = 5:7). A model with
an age of 1 Gyr at all redshifts is adopted for Im galax-
ies, while a constant SFR and E(B V ) = 0:5 has been
assumed for the dusty star-forming galaxies (cf. Paper I).
We have then assigned a spectral model to each galaxy
according to their R K s color and spectral type.
We tested that dierent assumptions on the k-
corrections, i.e. by varying model parameters or using
the tting of multi-band photometry when available, did
not aect signicantly our results. For example, the k-
correction estimates which make use of multi-band tting
of the SED are in excellent agreement with our estimates
from R K s colors alone, with no systematic shifts in mag-
nitude and a dispersion of about 0.08 in the J-band and
0.13 in the K-band up to z  1:5. Varying parameters
in the synthetic spectral models, i.e. the IMF (Salpeter
1955, Scalo 1986 and Kennicutt 1983) and the formation
redshift (z f = 2; 3; 6), the systematic shifts and disper-
sions at z < 2 are always less than 0.05 magnitudes. We
note that magnitudes derived using the k-corrections esti-
mated from observed spectra of local galaxies (Mannucci
et al. 2001, Cowie et al. 1994) would be brighter by about
0.1 magnitudes at z > 0:7, and could be considered up-
per limits due to the possible evolutionary eect on the
galaxy spectrum. We are therefore condent that the de-
rived luminosities are robust with respect to varying this
set of assumptions. The resulting eects on the Luminosity
Functions induced by changes in our assumptions are all
comparable with or smaller than the statistical errors (see
Sect. 5).
Fig. 4 shows the absolute magnitudes of all galaxies in
the spectroscopic sample to K s < 20 as derived accord-
ing to our adopted recipes. For the unidentied or unob-
served galaxies we have adopted the photometric redshift
z phot . The photometric threshold of the survey, K s < 20, is
clearly visible in the data and translates into dierent lu-
minosity limits as a function of redshift, varying from less
than  0:1L  at z < 0:5 to about  0:4L  at z ' 1, assum-
ing M 
J = 23:13 + 5logh 70 and M 
Ks = 24:21 + 5logh 70
(horizontal lines in Fig. 4) for the local LF (Cole et al.
2001). Adopting the mean stellar mass-to-light ratio and
representative stellar mass (M stars =LK = 1:32 in solar
unit and M 
stars = 1:44  10 11 h 2
70 M for the Salpeter
IMF) in the local universe (Cole et al. 2001), the lim-
its in luminosities correspond to  0:1{0:5M 
stars or even
smaller stellar masses since the M stars =LK increases as
the stellar population ages (Madau, Pozzetti, & Dickinson
1998).
4. The estimate of the near-IR Luminosity
Function
After the estimate of the rest-frame near-IR luminosities,
we compute the J- and K s -band Luminosity Functions in
the following redshift bins: (a) 0:2 < z < 0:65 (z mean '
0:5), (b) 0:75 < z < 1:3 (z mean ' 1:0) and (c) 1:3 <
z < 1:9 (z mean ' 1:5). The redshift bin 0.65 been excluded from this analysis because dominated by
two groups/clusters (see Fig. 1 and Paper III for details).
The rst two redshift bins include respectively 132 and 170
galaxies, of which only few objects (2 and 21 respectively)
do not have a spectroscopic redshift. The highest redshift
bin includes a smaller number of galaxies (42) with a high
fraction of photometric redshifts (60%).
The Luminosity Functions in each redshift bin are es-
timated using both the 1=Vmax formalism (Schmidt 1968,
Felten 1976) and the maximum likelihood method STY
(Sandage, Tammann & Yahil 1979), in order to represent
our data with a Schechter (1976) parameterization. In the
1=Vmax analysis, for any given redshift bin (z 1 ; z 2 ) a max-
imum volume is assigned to each object. This volume is
calculated between z 1 and z up , the latter being the mini-
mum between z 2 and z max , i.e. the maximum redshift at
which this galaxy would have satised the magnitude limit
(K s < 20) of the survey. We use the model tracks in order
to compute z max . Since the STY method determines the
shape of the LF but not its overall normalization, we have
normalized the STY LF by matching the galaxy number

Pozzetti and K20 collaboration: The evolution of the near-IR LF 5
Table 1. Schechter Luminosity Function parameters ((M ) = 0:4ln(10)  10 0:4(M M  )(+1) exp[ 10 0:4(M M  ) ])
Band z range M 5 log h70 range  M  5 log h70   h 3
70 (10 3 Mpc 3 )
J 0:20 0:65 [ 18:7; 25:2] 1:22 +0:22
0:20 23:89 +0:51
0:69 1:99 +1:4
1:1
J 0:75 1:30 [ 21:8; 26:3] 0:86 +0:46
0:44 23:75 +0:40
0:51 3:44 +1:1
1:5
J 1:30 1:90 [ 23:3; 26:3]
Ks 0:20 0:65 [ 19:5; 26:0] 1:25 +0:25
0:20 24:87 +0:54
0:73 1:78 +1:5
0:9
Ks 0:75 1:30 [ 22:7; 27:2] 0:98 +0:47
0:42 24:77 +0:42
0:55 2:91 +1:3
1:4
Ks 1:30 1:90 [ 24:1; 27:1]
counts observed in each redshift bin. We have checked and
tested the reliability of our results with the independent
softwares developed by Zucca et al. (1997) and by Poli et
al. (2001), always nding a good agreement between the
dierent methods.
Because of the relatively small number of objects in
each redshift bin and only a part of the luminosity func-
tion can be recovered, the Schechter parameters (, M 
and   ) derived from our STY analysis are not very well
constrained by our data. In particular, the uncertainty on
the faint end slope  increases with redshift because of the
increase with redshift of the minimum observable luminos-
ity. A sample reaching K s  21:0{21:5 would be needed
to better constrain this parameter at z > 1. The results
will be discussed in Section 5.
4.1. The treatment of the unidentied objects
The treatment of the unobserved or spectroscopically
unidentied sources is not a major problem because of
the high spectroscopic redshift completeness in our sur-
vey. Moreover, as discussed in Sect. 2, tested and reliable
photometric redshifts were derived for most of the faint
unidentied or unobserved objects, leading to an almost
negligible number of objects (9 in total) without any red-
shift information (see Paper III).
The small uncertainty introduced by the unobserved
or unidentied objects has been addressed in two dierent
ways.
We rst use only the spectroscopic sample and take
into account the remaining redshift incompleteness (72
galaxies) by applying weights to each galaxy with spectro-
scopic redshift both in the Vmax analysis (Avni & Bahcall
1980) and in the standard STY formulation (Heyl et al.
1997, cf. also Zucca, Pozzetti & Zamorani 1994). The
weighting corrections are computed on the basis of the
fraction of galaxies with spectroscopic redshift in dierent
regions of the (R K s ) K s plane. This weighting scheme
assumes that unidentied objects have the same redshift
distribution as the spectroscopically identied with simi-
lar K s magnitudes and R K s colors. While this scheme
can be reasonably applied over most of the (R K s ) K s
plane, the weights are highly uncertain for the optically
faintest and reddest galaxies, most of which do not have a
spectroscopic redshift. Since the photometric redshifts of
these objects are statistically higher than those sampled
by the measured spectra, this method would not allow to
correctly estimate the luminosity function in the highest
redshift bin.
As a second approach, we therefore base the \best" es-
timate of the luminosity function on the sample of galaxies
with spectroscopic plus photometric redshifts. In this case,
the 9 objects without any redshift information (because of
the absence of the extended multi-band photometry) have
an almost negligible eect. To account for them we correct
the STY normalization (from 1% to 8% in the 3 redshift
bins) according to the fraction of such objects in each bin.
The results from the two methods (Fig. 5 and 6) are com-
pletely consistent with each other in the rst two redshift
bins, while some discrepancies are present in the highest
redshift bin because, as mentioned above, the weighting
correction function is unable to properly take into account
the optically faintest and reddest galaxies. Furthermore we
tested that the uncertainties in the photometric redshifts
did not aect signicantly our results. We extracted ran-
dom samples from the original photometric redshift cat-
alog using the measured dispersion. The derived uctua-
tions in each magnitude bin of the LFs resulted smaller
than Poisson errors and in general the simulated LFs are
consistent with the \best" estimate also in the higher red-
shift bin with no signicant systematic eects. In the fol-
lowing sections we will discuss the \best" LFs derived us-
ing spectroscopic plus photometric redshifts.
5. The cosmic evolution of the near-IR
Luminosity Function
Thanks to the high statistical signicance and complete-
ness of our sample it is possible to investigate the evolution
of the near-IR LF over a wide range of cosmic time. Figs.
5 and 6 show the 1=Vmax and the maximum likelihood
(STY) results for the LFs in the selected redshift bins and
in the J- and K s -bands, respectively.
We nd that the luminosity functions are fairly well
tted by Schechter functions in the rst two redshift bins.
The magnitude ranges and the best-t Schechter param-
eters are summarized in Table 1, with the uncertainties
derived from the projection of the 68% condence ellipse.

6 Pozzetti and K20 collaboration: The evolution of the near-IR LF
Fig. 5. The rest-frame J-band Luminosity Function in the red-
shift bins: zmean ' 0:5 (top panel) zmean ' 1:0 (middle panel)
and zmean ' 1:5 (bottom panel). Points have been derived
from 1=Vmax analysis (open circles using only spectroscopic z
and weighted incompleteness corrections, while lled small dots
using both spectroscopic and photometric z, see Section 4.1),
while solid curves are the LF Schechter ts derived from the
STY maximum likelihood analysis (thin solid lines are the ts
obtained xing the  parameter at the local value, see text).
The dotted curves and vertical dotted lines show the local LF
in the J-band and M 
J at z = 0 from Cole et al. (2001).
In the highest redshift bin, due to the bright and limited
range in magnitude, our data are well tted with a sin-
gle power law ( ' 2:7 +0:5
0:7 ). This does not mean that a
Schechter function can not be a good representation of the
luminosity function also in this redshift bin. This is shown
by the thin solid lines in the lower panels of Figs. 5 and
6, which represent ts with a Schecther function obtained
by xing the faint end slope  at the local value. However,
because of the bright limit in absolute magnitude at these
redshifts, which reduces signicantly the range of sampled
luminosities, the Schechter parameters are very poorly de-
termined by these data. For this reason the Schechter pa-
rameters for this redshift bin are not reported in Table 1.
We point out that a direct comparison of the Schechter
parameters could be quite misleading because the param-
eters are correlated.
In order to trace the evolution down to z  0, we
compared the observed LFs as derived from our sample to
Fig. 6. The same as in Fig. 5, but for the rest-frame Ks-band.
The dotted curves and vertical dotted lines show the local LF
in the Ks-band and M 
K at z = 0 from Cole et al. (2001), while
dashed curves show the local LF from Kochanek et al. (2001).
Table 2. Galaxy luminosity evolution at dierent redshift
Band
M(z = 0:5)
M(z = 1:0)
M(z = 1:5)
J 0:23 +0:16
0:17 0:69 +0:12
0:12 1:17 +0:22
0:24
Ks 0:11 +0:17
0:18 0:54 +0:12
0:13 1:07 +0:23
0:27
the Local Luminosity Function (LLF) by Cole et al. (2001)
in the J and K s bands (Figs. 5, 6) and by Kochanek et
al. (2001) in the K s -band. We then explored two possible
evolutionary scenarios: luminosity or density evolution.
Our analysis (both Vmax and STY) shows that the data
(Figs. 5 and 6) are consistent with a mild evolution from
z = 0 to z ' 1:5 both in J- and K s -bands. In particular
the faint-end of the LFs (L < L  ) is consistent with the
local estimates, with no statistically signicant evidence
for a change either in the slope or normalization up to
z < 1:3 (consistently with Cohen 2002). At higher redshift
this part of the luminosity function is not well sampled by
our data, but also in this bin a Schechter function with
local faint-end slope is consistent with the data (Figs. 5
and 6). Viceversa, it is interesting to note that the density

Pozzetti and K20 collaboration: The evolution of the near-IR LF 7
Fig. 7. Rest-frame Ks-band Luminosity Function in two red-
shift bins: zmean ' 0:5 (top panel) zmean ' 1:0 (bottom panel).
Points and lines derive from 1=Vmax and STY analysis for early
(lled symbols and dotted lines) and late (open symbols and
dashed lines) galaxies respectively. The solid curves are the
STY LF for the total sample in the Ks-band as in Fig. 6.
of luminous galaxies (e.g. MKs 5 logh 70 < 25:5) is
signicantly higher than locally.
Because of the statistical correlation between the
Schechter parameters (, M  and   ), in order to estimate
the luminosity and/or density evolution within our sample
and in comparison with the local LFs, we have xed the 
parameters of our LFs to the same values observed locally
(Cole et al. 2001),  J = 0:93 and Ks = 0:96 (thin
solid lines in Figs. 5, 6). We are allowed to do this be-
cause all our best t  values are consistent with the local
ones (see Table 1). Assuming local M 
J = 23:13+5logh 70
and M 
Ks = 24:21 + 5logh 70 from Cole et al. (2001)
we nd a luminosity evolution at z ' 1 of the order of

M J ' 0:69  0:12 and
MK ' 0:54  0:12 with
the normalizations (  ) in the rst two redshift bins con-
sistent with the local values, within from 3 to 20%. At
z > 1:3 there is an indication of an even higher luminos-
ity evolution (
M J ' 1:17,
MK ' 1:07), while the
  values decrease by a factor 4{5 with respect to the lo-
cal value. This last result should be taken with caution
because of the lower statistics in the highest redshift bin
and the smaller range in luminosity covered.
The luminosity evolution estimated from STY analysis
are summarized in Table 2 with the formal statistical 1
condence limits. The uncertainties introduced by the k-
correction, discussed in Section 3, are always less than the
statistical errors, and less than 0.03 and 0.10 magnitudes
at z < 1:3 and z ' 1:5, respectively.
We recall here that Cimatti et al. (2002b) discussed
the photometric selection eects present in the K20 sam-
ple and showed that, on average, the total ux of spirals
and ellipticals with L  L  are underestimated by 0.1
and 0.25 magnitudes respectively, while at higher L the
ux lost for elliptical galaxies could be even higher. For
this reason we are condent that our estimate of a posi-
tive luminosity evolution is quite conservative. The above
estimates of the luminosity evolution could increase on av-
erage by about 0:2 magnitudes if we take into account
this underestimate of the total ux.
6. The Luminosity Function by spectral or color
type
In order to investigate the role of dierent galaxy pop-
ulations, we divide the K20 sample in two subsamples
on the basis of the spectroscopic classication, i.e. early
type galaxies without strong emission lines and late type
galaxies with emission lines, and study the near-IR LF
for the dierent populations in the two redshift bins at
z mean ' 0:5 and 1. The high fraction of photometric red-
shifts without any spectroscopic information does not al-
low us to extend such studies to the highest redshift bin.
We take into account the spectral incompleteness using
two weighting functions (see Sect. 4.1) derived for each
spectral type and correcting the overall normalization in
the STY method using the color information of unclassi-
ed objects.
The results are shown in Fig. 7. Our analysis indi-
cates that the faint-end slope of the LFs at these red-
shifts shows the same general dependence on galaxy spec-
tral type as that found in numerous studies of the local
LF. Specically, the faint-end slope is much steeper for
late/emission line galaxies than for early type galaxies.
A similar result has been found by Cohen (2002) in the
HDF{north. More important, we nd, for the rst time,
that at z mean ' 0:5, early type galaxies clearly dominate
the bright-end of the Luminosity Function, in agreement
with local observations (Kochanek et al. 2001). A similar
result is also visible at z mean ' 1:0. Some of the pre-
vious surveys, selected in the optical bands with follow-
up K-band observations (e.g. Cohen 2002), present a bias
against identifying red early type galaxies at high redshift
because of substantial incompleteness of EROs in the sam-
ples.
The overall density of early type galaxies at z ' 0:5 is
consistent with the local estimate (Kochanek et al. 2001),
while at z ' 1, their number density shows at most a small
decrease (< 30%), consistent with recent results from Im
et al. (2002). This decrement could be due both to the
existence of a population of galaxies morphologically clas-
sied as early-type but with blue colors due to some recent
episodes of star formation (Menanteau, Abraham & Ellis
2001, Im et al. 2001) and to our spectral incompleteness,
more severe for red/early type galaxies.
Similar results are obtained if we divide the galaxies
in two samples according to their R K s colors (we adopt

8 Pozzetti and K20 collaboration: The evolution of the near-IR LF
Fig. 8. R Ks colors vs. rest-frame absolute Ks magnitudes
for K20 galaxy sample in 3 dierent redshift bins. Circles rep-
resent galaxies identied spectroscopically, while squares are
unidentied or unobserved galaxies plotted at z = zphot . In
each redshift bin empty and lled symbols refer to galaxies
with z < zmean and z  zmean , respectively.
the color of Sa galaxies to divide the sample in red and
blue).
We conclude that red and early type galaxies dominate
the bright-end of the Luminosity Function already at early
epoch and that their number density shows at most a small
decrease (< 30%) up to z ' 1.
Fig. 8 shows the optical/near-IR colors versus near-IR
luminosities in the three redshift bins. While the magni-
tude limit of the survey, K s < 20, corresponds to dierent
low luminosity limits in the dierent redshift bins, there
appears to be a correlation of the optical/near-IR colors
with near-IR luminosities. In rst approximation this cor-
relation can be interpreted as a correlation of age and/or
specic star formation rate with stellar mass, with the
most \massive" galaxies being \old" and the \low-mass"
galaxies being instead dominated by young stellar pop-
ulations. This is now well established for local galaxies
(Gavazzi et al. 1996, Boselli et al. 2001, Kaumann et
al. 2002) and we extend it to z  1:5. Fig. 8 (see empty
and lled circles representing galaxies with z < z mean and
z  z mean ) shows that the observed correlation is not in-
Table 3. Luminosity density a at dierent redshift
redshift log J b log J c log Ks b log Ks c
0:5 20:20 20:20 +0:01
0:02 20:19 20:17 +0:01
0:02
1:0 20:25 20:28 +0:05
0:03 20:21 20:26 +0:05
0:03
1:5 > 19:90 > 19:88
a: in h70 W/Hz/Mpc 3 units
b: observed
c: LF-corrected (see text).
Fig. 9. Comoving luminosity density in J (top panel) and
Ks-bands (bottom panel). The lled circles are the value de-
rived directly from observations (see text), while open circles
are the \LF-corrected" estimates. The solid lines show the best-
t power laws. The open squares are from Cole et al. (2001).
duced by a redshift eect within the bins. In Sect. 8 we
compare the observed correlation with HMM predictions.
7. The near-IR luminosity density evolution
Tracing the cosmic emission history of the galaxies at dif-
ferent wavelengths oers the prospect of an empirical de-
termination of the global evolution of the galaxy popu-
lation. Indeed, it is independent of the details of galaxy
evolution and depends mainly on the star formation his-
tory of the universe (Lilly et al. 1996, Madau, Pozzetti
& Dickinson 1998). Various attempts to reconstruct the
cosmic evolution of the comoving luminosity density have
been made previously mainly in the UV and optical bands
(Lilly et al. 1996, Cowie et al. 1999). Our survey oers the
possibility to investigate it in the near-IR using a LF ex-
tended over a wide range in luminosity.

Pozzetti and K20 collaboration: The evolution of the near-IR LF 9
We estimate the comoving luminosity density directly
from observed sources using the Vmax formalism (see for
details Lilly et al. 1996). The major source of uncertainty
is the contribution from galaxies fainter than the magni-
tude limit K s < 20. We have therefore estimated also the
\LF-corrected" luminosity density using the best-t LF
from STY method and extending it to fainter luminos-
ity (we adopt 0:02L  (z) as our lower limit in luminosity
for this extrapolation). A formal uncertainty in this proce-
dure was estimated by considering the range of acceptable
Schechter parameters values (see Table 1).
Fig. 9 shows luminosity densities derived in J- and
K s -band as a function of redshift. Up to z < 1:3 the un-
certainties due to faint galaxies and LF parameters are
small. At higher redshift the uncertainties in the LF pa-
rameters do not allow to constrain the luminosity density
values. We could therefore only estimate a lower limit to
the luminosity density using the observed value.
We nd a slow evolution with redshift of the observed
near-IR luminosity density, consistent with the results by
Cohen (2002) in the HDF-north, even if she had to apply a
large correction to her data because of the disappearance
of absorption galaxies at high redshift in her sample as
they became EROs. Using the observed local luminosity
densities derived from Cole et al. (2001), the luminosity
density evolution up to z  1:3 is well represented by a
power law,  (z) =  (z = 0)(1 + z) () . We nd (J) '
0:70 and (K s ) ' 0:37 (Fig. 9).
The near-IR luminosity density evolution is much
slower than that found in the UV and optical bands
( = 3:9{2:7 from 0.28 to 0.44 m by Lilly et al. 1996
and  = 1:5 at 0.15, 0.28 m by Cowie et al. 1999,
for
m = 1). Indeed, while the optical luminosity den-
sity evolution is mainly related to the star formation his-
tory, the evolution of the near-IR luminosity density is
more closely related to the stellar-mass density. The lo-
cal stellar mass density, derived by Cole et al. (2001) is

stars = (3:7  0:6)  10 3 h 1
70 . If we adopt the stellar
mass-to-light ratio for the galaxy spectral models which
best match colors and spectral types for each galaxy, the
mean M stars =LK in our sample becomes 0:63 and 0:54
at z = 0:5 and 1, with small variations due to the model
parameters adopted (see Sect. 3). With these values of
M stars =LK we
derive
stars = (2:0  0:1)  10 3 h 1
70
and
stars = (2:1  0:3)  10 3 h 1
70 at z = 0:5 and 1
respectively. This analysis suggests that the evolution of
the stellar mass density is relatively slow with redshift,
with a decrease of about a factor 1:8  0:4 from z = 0 to
z ' 1, consistently with recent results from Dickinson et
al. (2002a).
At z > 1 we can only give a lower limit to the near-
IR luminosity density. As discussed by Madau, Pozzetti,
Dickinson (1998) (cf. also Pozzetti & Madau 2001), a ro-
bust determination of the near-IR luminosity density at
z > 1 could be fundamental to disentangle between dif-
ferent cosmic histories of star formation (SFH). In fact,
SFHs peaked at intermediate redshift (1 < z < 2) predict
a decrease in the near-IR luminosity density at z > 1{2,
while if 50% of the stars formed at z > 2 (similar to the
PLE adopted here), the corresponding near-IR luminosity
density attens at z > 1 without a strong decrease (cf.
Fig. 6 in Pozzetti & Madau 2001). A detailed comparison
of luminosity and stellar-mass density with model predic-
tions and empirical star formation histories will be further
investigated in a forthcoming paper.
8. The comparison with model predictions
We have compared our LF with the predictions from two
competitive scenarios of galaxy evolution: the Hierarchical
Merging Models (HMMs) and the Pure Luminosity
Evolution (PLE) (Fig. 10). For the HMMs, we used
the predictions by Cole et al. (2000, C00, kindly pro-
vided us by C. Baugh), Menci et al. (2002, M02), and
GIF (Kaumann et al. 1999). For the GIF simulations,
which combine the large high-resolution N-body simula-
tions with semi-analytical models, we derive the LF at a
magnitude above which it can be considered complete in
luminosity given the mass limit of the simulated galaxy
sample (2 10 10 h 1
70 M ). For the PLE parameterization,
we adopted the predictions of Pozzetti et al. (1996, 1998,
PPLE) (for details see also Paper IV).
For a more reliable comparison with models, we cor-
rected the observed magnitudes by 0:2 mag, in order to
take into account the average loss of total ux in the K20
sample (see Papers III-IV).
As discussed in Paper IV at low-z (z = 0:5) the HMMs
by Cole et al (2000) and by Menci et al. (2002) predict
many more galaxies than observed (cf. Fig. 3 in Paper
IV). From the present study (upper panel of Fig. 10) we
can therefore conclude that such excess is due to low lu-
minosity, \low-mass\ objects, which dominate the steep
faint-end in the HMM LF. At z = 1, the HMMs predict
even steeper LFs because low-mass galaxies become more
numerous in the hierarchical scenario at higher redshift.
This is in contrast with the LF derived from our data at
z = 1, which does not show a similar behaviour. These
discrepancies are consistent with previous results both in
the local universe (cf. Fig. 1 in Baugh et al. 2002) and at
high redshift (z < 1 and z  3) for the B and UV rest-
frame LF, respectively (Poli et al. 2001, Somerville et al.
2001).
Also at the bright end of the LF the HMMs appear to
be in disagreement with our data at z ' 1, where they un-
derpredict the density of bright (MKs < 25:5 + 5logh 70 )
galaxies with respect to our data. For example, our data
at MKs = 25:6 + 5logh 70 and z ' 1 are about a fac-
tor 2.6 higher than the HMM predictions and even higher
at brighter magnitudes if we consider the STY maximum
likelihood t. In the highest redshift bin the excess over the
predictions becomes signicant at MKs < 26 + 5 logh 70 .
In comparison, the GIF simulated catalogue at z = 1 un-
derpredicts the K20 LFs at all magnitudes. As discussed
by Kaumann et al. (1999), the GIF model produces a
factor 2{3 too few galaxies at magnitudes around L  al-
ready at z = 0, while it produces an excess of bright local

10 Pozzetti and K20 collaboration: The evolution of the near-IR LF
Fig. 10. The rest-frame Ks-band Luminosity Function in the redshift bins: zmean ' 0:5 (top panels) zmean ' 1:0 (middle
panels) and zmean ' 1:5 (bottom panels) compared to PLE (right panels) and HMM (left panels) models. We have used
the models closer to zmean or interpolated between dierent redshifts. Data points derive from 1=Vmax analysis, while dotted
curves are the LF Schechter t derived from STY analysis. We have corrected the data on average by 0:2 magnitude because
photometric selection eects (see text).
galaxies. This problem with respect to the local LF aects
also the Cole et al. (2000) model (see Fig. 4 in Baugh et al.
2002). Therefore, as discussed in Sect. 5, while the density
of luminous objects (MKs 5 logh 70 < 25:5) is quite con-
stant or mildly increasing with z within our sample, and
higher than the local density, it is rapidly decreasing in
the Cole et al. (2000) and GIF models at z > 0:5 (Fig. 11)
in clear con ict with our data. The problem of a negative
evolution with redshift of luminous objects does not aect
instead the Menci HMM model, even if also this model sig-
nicantly and systematically underpredicts their number
density at all redshifts.
In addition to the comparison of the data and predic-
tions for the LF, it is also important to verify whether the
bright L > L  galaxies in the K20 survey have colors con-
sistent with the HMM predictions. Fig. 12 shows the com-
parison between the z = 1:05 GIF simulated catalogue and
data at 0:75 < z < 1:3 (z mean ' 1). While the deciency
of simulated blue low-luminosity (R K s < 4:2, MKs 5
log h 70 > 23:5) galaxies is due mainly to the mass limit
of the GIF catalogue, a serious discrepancy emerges in the
two distributions in the magnitude range where the GIF
catalogue is expected to be complete. The GIF simulated
catalogue shows an excess of blue high-luminosity galaxies
(R K s < 4:4, MKs 5 log h 70 < 24:5) and a deciency
of red luminous galaxies (see also the color distributions of
high-luminosity galaxies, MKs 5 log h 70 < 24:5, in the
right panel of Fig. 12, normalized to the same comoving
volume). This result is in agreement with the nding of a
deciency of EROs in the HMMs (Daddi et al. 2000, Firth
et al. 2002, Smith et al. 2002), but, since it is based not
only on colors but also on the luminosity of the galaxies,
it points out in particular a clear deciency of red lumi-
nous galaxies in the HMM predictions. This plot clearly
shows that a comparison of LF and colors is much more
powerful than that of the colors or LF alone and that
the GIF K s -band LF at z = 1 is obtained with a radi-
cally dierent mix of galaxies compared to the observed
one. While the bright end of the HMM LF at z = 1 is
dominated by actively starforming galaxies, in the K20
sample it is dominated by the passively evolving galax-
ies. Given that blue galaxies suggest younger stellar pop-
ulation and lower M stars =LK ratios, we expect that the
failure of this model in reproducing our LF (see Fig. 10)
should be even stronger in term of density of \massive"
galaxies at z  1 (cf. also the luminosity and stellar-mass
functions in Baugh et al. 2002).
The right panels of Fig. 10 show the comparison of our
data with the PLE predictions, computed with two dif-
ferent IMF (Scalo and Salpeter). The overall agreement
is much better than with the HMM predictions even if
some discrepancies, but at much lower level of signicance,
are present. In particular, in the highest redshift bin the
parameterization with the Salpeter IMF overpredicts the
total number of galaxies (see also Paper IV), while the
Scalo IMF (dominated by low/intermediate mass stars,
which induce a lower luminosity evolution compared to
Salpeter at z > 1) ts well the density of galaxies at

Pozzetti and K20 collaboration: The evolution of the near-IR LF 11
Fig. 11. Comoving number density of luminous galaxies
(MKs < 25:5 + 5 logh70 ) in the Ks-bands. The open cir-
cles are the values derived directly from observations, while
the lled square is from Cole et al. (2001). The dierent lines
show models as in gure 10.
Fig. 12. Left panel: R Ks colors vs. rest-frame absolute Ks
magnitudes for z = 1:05 GIF simulated catalogue (small dots)
and data (circles) at 0:75 < z < 1:3 (zmean ' 1) (empty and
lled circles refer to z < 1 and z > 1 respectively). Vertical
dashed line represents approximately the completeness mag-
nitude limit of GIF catalogue corresponding to its mass limit
(see text). Right panel: Color distribution of high-luminosity
galaxies (MKs 5 log h70 < 24:5) observed (dotted line) and
simulated (continue line), normalized to the same comoving
volume.
MKs > 26:0 + 5 logh 70 , but falls below the data for the
brighter galaxies. In Paper IV we found that in the con-
text of PLE models also the observed redshift distribution
of K20 galaxies is better tted assuming an IMF dom-
inated by low/intermediate mass stars (e.g. Scalo IMF)
than a Salpeter IMF (see also Pozzetti et al. 1996 and
Broadhurst & Bouwens 2000). PLE models with a atter
IMF (i.e. Salpeter-like) can be made consistent with the
data (redshift distribution and LF) only if the rapid evo-
lution induced by massive stars is suфciently suppressed
by dust attenuation (Totani et al. 2001, see Paper IV).
Indeed, such a dusty phase is predicted by many models
for the formation of high redshift spheroids and could be
associated to high redshift SCUBA sources.
9. Summary and discussion
The cosmic evolution of the K s -band selected eld galaxy
population has been studied over the redshift interval
0:2 < z < 1:9 using about 500 galaxies from the K20
spectroscopic survey. The sample spans a wide range in
redshift and look-back time and allows to study the evo-
lution of the near-IR Luminosity Function both within the
sample and in comparison to the local population.
We take advantage of the near-IR selection (in partic-
ular in the K-band), in which the k-corrections are rela-
tively invariant to galaxy type and relatively small also at
high redshift (Cowie et al. 1994), and the dust extinction
eects are less severe than in optical samples.
We derived the near-IR luminosity function in the rest-
frame J and K s -band in three redshift bins (z mean '
0:5; 1:0; 1:5). The detailed analysis of the observed LF at
dierent redshifts and the comparison with the local LF
and with the predictions of galaxy formation models pro-
vided the following results:
1- A mild evolution is observed both in the J and K s
Luminosity Functions to z ' 1:5, in agreement with previ-
ous indications by Cowie et al. (1996), Cohen (2002) and
Feulner et al. (2003). There is no evidence of a steepen-
ing of the faint-end LFs up to z  1:3. In particular, the
faint-end (L < L  ) is consistent with the local estimates
up to z < 1:3, while at the bright end the data show a
luminosity evolution of about
M J ' 0:69  0:12 and

MK ' 0:54  0:12 at z ' 1. The density of luminous
galaxies (MKs 5 logh 70 < 25:5) is relatively constant
or mildly increasing with redshift within our sample and
higher than locally at all redshifts.
2- Pure density evolution cannot reproduce the ob-
served LF at z  1:3.
3- Red and early-type galaxies clearly dominate the
bright-end of the Luminosity Function at z ' 0:5 and a
similar trend is also visible at z ' 1, showing that such
systems were already in place and fully assembled at that
cosmic epoch. Their number density shows at most a small
(< 30%) decrease up to z ' 1.
4- The evolution of the rest-frame near-IR comoving
luminosity densities up to z ' 1 can be described by power
laws,  (z) =  (z = 0)(1 + z) () , with (J) ' 0:70 and

12 Pozzetti and K20 collaboration: The evolution of the near-IR LF
(K s ) ' 0:37. Such an evolution is much slower than those
observed in the UV and optical bands.
5- The hierarchical merging models overpredict the LF
at low luminosity at all redshifts, whereas they under-
predict the density of high-luminosity galaxies at z > 1.
HMMs by Kauman et al. (1999) and Cole et al. (2000)
overpredict high luminosity galaxies at z = 0, and predict
a negative density evolution of the bright end of the LF
at z > 0:5 which is not observed.
6- The PLE predictions are in rather good agreement
with the mild luminosity evolution observed up to z ' 1:5.
7- There appears to be a clear correlation of the
optical/near-IR colors, i.e. in rst approximation the spe-
cic star formation rate and ages, with near-IR luminosi-
ties, i.e. the stellar mass. This correlation suggests that the
most \massive" galaxies are \old", while the \low-mass"
galaxies are instead dominated by young stellar popula-
tions. The GIF model shows instead a clear deciency of
red luminous galaxies at z  1 compared to the observa-
tions.
From the analysis of the LF and of the comoving
near-IR luminosity density, we can derive some indica-
tions on the evolution of the Galaxy Stellar-Mass Function
(GSMF). A detailed analysis will be presented by Fontana
et al. (2003). The present analysis suggests that the evo-
lution of the GSMF and of the stellar mass density is slow
with redshift up to z ' 1:5, in contrast with the rapid evo-
lution of the Galaxy Stellar Mass Function expected in the
hierarchical models at z < 2 (cf. Baugh et al. 2002). In our
sample, using galaxy spectral models which match colors
and spectral types, we found
that
stars decreases by a
factor about 1:8  0:4 from z = 0 to z ' 1, mainly due to
the decrease in the mass-to-light ratio, which is however
slower than in HMMs models. In at least one of these mod-
els (GIF) the small adopted M/L ratio corresponds to a
color distribution of galaxies at z  1 clearly inconsistent
with data (see Fig. 12).
Moreover, the fact that the bright-end of the
Luminosity Function is dominated by red/early type
galaxies and that the mean spectra of early type EROs
at z ' 1 are consistent with an old stellar population (see
Paper I), suggest that old and massive elliptical galaxies
were already in place at z ' 1 (see also Paper I) and, there-
fore, they should have formed their stars and assembled
their mass at higher redshift. These results are in contrast
with the current renditions of hierarchical models in which
the bulk of massive elliptical galaxies forms through merg-
ing at low redshift (z < 1{2) and suggest that most of the
merging which form elliptical galaxies in the hierarchical
models should occur at higher redshift (say, z > 2{3), fol-
lowed by a pure \luminosity-like" evolution. On the other
hand, HMMs overpredict the density of low-luminosity,
low mass, galaxies at z < 1, as previously noted in the
local universe (cf. Fig. 1 in Baugh et al. 2002) and in the
B and UV rest frame bands at z  1 (Poli et al. 2001,
Somerville et al. 2001, Poli et al. 2003).
Our results show the importance of sampling the faint-
end of the LF in even deeper near-IR selected samples.
Fig. 13. Predicted SIRTF+IRAC number densities for galax-
ies with z < 2 derived from K20 sample (see text) as a
function of AB magnitudes at 3 dierent wavelengths ( =
3:6; 4:5; 5:8m). Histograms refer to Ks < 20 galaxies in our
sample in the indicated redshift ranges, while lines have been
derived from K20 LFs extended to fainter luminosities (using
the at slope in the highest z range). Vertical dashed lines refer
to GOODS ux limits at the dierent wavelengths.
In addition, to derive the LF at z  1 in a wider
but shallow sample (say K < 18:5) will be essential to
trace the evolution of the most massive galaxies with
higher statistical signicance. In the near future direct
measurements of rest-frame K-band magnitude for high
redshift galaxies will be possible with space-based in-
frared surveys, in particular the SIRTF (Space Infrared
Telescope Facility) Legacy Science project GOODS (Great
Observatories Origins Deep Survey, P.I. M. Dickinson).
Our data allow to directly estimate the number densities
of z < 2 galaxies at the dierent SIRTF-GOODS wave-
lengths,  = 3:6; 4:5; 5:8m, which sample the rest-frame
K s -band at z ' 0:7; 1:1; 1:7 respectively, similar to the
z mean adopted for the K20 LFs. We have converted the ab-
solute MKs magnitudes, derived here for the K20 sample,
to SIRTF+IRAC uxes using the galaxy spectral models
described in Sect. 3 for normal galaxies and the spectral
model for M82 (Silva et al. 1998) for the dusty star form-
ing galaxies. The expected number densities for objects
with z < 2 are shown in Fig. 13. At the expected depth of
GOODS (see Dickinson et al. 2002b), SIRTF will detect
about 5000 galaxies at z < 2 within 330 arcmin 2 . GOODS
SIRTF Legacy Program, sampling the rest frame near-
IR luminosities directly, will allow to derive the K-band
Luminosity Function along with the stellar mass distri-
bution well below the K20 limit (see Fig. 13) and with
higher statistical signicance. With these data the stellar

Pozzetti and K20 collaboration: The evolution of the near-IR LF 13
mass assembly history of galaxies will be measured over a
wide range of redshifts and cosmic time.
We make publicy available the 1=Vmax estimates at
http://www.arcetri.astro.itk20/releases/index.html.
Acknowledgements. Part of this work was supported by
the MURST (Con 2000-2001), ASI and by the European
Community Research and Training Network \The physics of
the intergalactic medium". We are in debt with Carlton Baugh
for providing the HMM predictions.
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