Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.arcetri.astro.it/science/k20/papers/0409041.ps Äàòà èçìåíåíèÿ: Tue Nov 30 19:23:30 2004 Äàòà èíäåêñèðîâàíèÿ: Fri Feb 28 06:57:47 2014 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: m 103

arXiv:astro­ph/0409041
v1
2
Sep
2004
DRAFT VERSION NOVEMBER 30, 2004
Preprint typeset using L A T E X style emulateapj v. 3/25/03
A NEW PHOTOMETRIC TECHNIQUE FOR THE JOINT SELECTION OF STAR­FORMING
AND PASSIVE GALAXIES AT 1:4 <
 z <
 2:5 1
E. DADDI 2 , A. CIMATTI 3 , A. RENZINI 2 , A. FONTANA 4 , M. MIGNOLI 5 , L. POZZETTI 5 , P. TOZZI 6 , G. ZAMORANI 5
2 European Southern Observatory, Karl­Schwarzschild­Str. 2, D­85748 Garching, Germany
3 INAF--Osservatorio Astrofisico di Arcetri, L.go E. Fermi 5, Firenze, Italy
4 INAF--Osservatorio Astronomico di Roma, via Dell'Osservatorio 2, Monteporzio, Italy
5 INAF--Osservatorio Astronomico di Bologna, via Ranzani 1, Bologna, Italy and
6 INAF--Osservatorio Astronomico di Trieste, via Tiepolo 11, Trieste, Italy
Draft version November 30, 2004
ABSTRACT
A simple two color selection based on B­, z­, and K­ band photometry is proposed for culling galaxies at
1:4 <
 z <
 2:5 in K­selected samples and classifying them as star­forming or passive systems. The method is
calibrated on the highly complete spectroscopic redshift database of the K20 survey, verified with simulations
and tested on other datasets. Requiring BzK = (z - K) AB - (B - z) AB > -0:2 allows to select actively star­
forming galaxies at z >
 1:4, independently on their dust reddening. Instead, objects with BzK < -0:2 and
(z - K) AB > 2:5 colors include passively evolving galaxies at z >
 1:4, often with spheroidal morphologies.
Simple recipes to estimate the reddening, SFRs and masses of BzK­selected galaxies are derived, and calibrated
on K < 20 galaxies. These K < 20 galaxies have typical stellar masses  10 11 M , and sky and volume density
of  1 arcmin -2 and  10 -4 Mpc -3 respectively. Based on their UV (reddening­corrected), X­ray and radio
luminosities, the BzK--selected star­forming galaxies with K < 20 turn out to have average SFR  200 M yr -1 ,
and median reddening E(B-V )  0:4. This SFR is a factor of 10 higher than that of z  1 dusty EROs, and
a factor of 3 higher than found for z  2 UV selected galaxies, both at similar K limits. Besides missing the
passively evolving galaxies, the UV selection appears to miss some relevant fraction of the z  2 star­forming
galaxies with K < 20, and hence of the (obscured) star­formation rate density at this redshift. The high SFRs
and masses add to other existing evidence that these z = 2 star­forming galaxies may be among the precursors
of z = 0 early­type galaxies. A V/V max test suggests that such a population may be increasing in number
density with increasing redshift. Theoretical models cannot reproduce simultaneously the space density of both
passively evolving and highly star­forming galaxies at z = 2. In view of Spitzer Space Telescope observations,
an analogous technique based on the RJL photometry is proposed to complement the BzK selection and to
identify massive galaxies at 2:5 <
 z <
 4:0. By selecting passively evolving galaxies as well as actively star­
forming galaxies (including strongly dust reddened ones), these color criteria should help in completing the
census of the stellar mass and of the star­formation rate density at high redshift.
Subject headings: galaxies: evolution --- galaxies: formation --- galaxies: high­redshift --- cosmology: obser­
vations --- galaxies: starburst
1. INTRODUCTION
Tracing and understanding the history of cosmic star forma­
tion and the growth of the cosmic stellar mass density are cur­
rently the objects of major observational efforts (e.g., Dickin­
son et al. 2003; Fontana et al. 2003; Rudnick et al. 2003), yet
much remains to be done before reaching fully satisfactorily
conclusions. Obtaining a complete census of the populations
of high­redshift galaxies, and their physical characterization
(stellar mass and star­formation rate, SFR) is necessary to ob­
servationally map the processes that lead to galaxy formation
and evolution. This requires direct spectroscopic identifica­
tion (e.g., Fontana et al. 2004; Glazebrook et al. 2004), but
building large samples of spectroscopically confirmed galax­
ies at high redshift is a time consuming process. This is espe­
cially true for magnitude­limited samples, as high­z galaxies
represent a small fraction of the galaxy counts at faint magni­
tudes in the optical and infrared bands. Therefore, techniques
for pre­selecting high redshift targets are required to focus the
1 Based on observations collected at the European Southern Observatory,
Chile (ESO programs 70.A­0140, 70.A­0548, 168.A­0485, 170.A­0788), and
with the NASA/ESA Hubble Space Telescope, which is operated by AURA
Inc, under NASA contract NAS 5­26555.
spectroscopic multiplex capability on the interesting objects.
Photometric redshifts from deep multicolor datasets offer an
alternative to massive spectroscopic efforts (e.g. Bolzonella
et al. 2002; Firth et al. 2002; Poli et al. 2003), but the results
may suffer from biases that are difficult to quantify, and their
accuracy depends critically on the quality of the photometry
and the colors and redshifts of the objects.
An efficient alternative to either photometric redshifts or
magnitude limited surveys is offered by simpler single or two­
color criteria, then followed by targeted spectroscopy. The
best known example is the dropout technique for selecting
Lyman­Break Galaxies (LBG, Steidel et al. 1996; 2003) from
their U n GR s rest­frame UV colors, which opened the research
field on normal star­forming galaxies at z  3. Recently, the
same technique has been extended to work at lower redshifts
1:4 < z < 2:5 (Erb et al. 2003; Adelberger et al. 2004) and
large samples of UV­selected objects have been spectroscopi­
cally confirmed at z  2 (Steidel et al. 2004).
Star forming galaxies can be selected as LBGs only if they
are UV bright (i.e. actively star forming) and not heavily
reddened by dust. Currently, the best possible alternatives
to find dust­enshrouded high redshift star­forming objects in­
clude detecting them from their far­IR or sub­mm emission

2 E. Daddi et al.
due to cold dust (Franceschini et al. 2001; Smail et al. 2002;
Champan et al. 2003), observing the emission at X­ray or ra­
dio wavelengths that are not extincted by dust (e.g., Norman
et al. 2004; Haarsma et al. 2000), and selecting very red ob­
jects in near­infrared samples that are less affected by dust
extinction (Cimatti et al. 2002a, 2003).
Besides targeting star­forming galaxies, color criteria have
also been used to search for passively evolving galaxies at
high redshifts. A simple criterion is the one used for Ex­
tremely Red Objects (ERO), selected according to their very
red optical to near­IR colors, e.g. R - K > 5 or I - K > 4
(Thompson et al 1999; Daddi et al. 2000a; 2000b; Firth et
al. 2002; Roche et al. 2002; 2003; Miyazaki et al. 2003; Mc­
Carthy 2004). Spectroscopy showed that EROs include both
old passive galaxies at 0:8 < z < 2 and dusty star­forming sys­
tems at similar redshifts (Cimatti et al. 2002a, 2003; Yan et
al. 2004). The bulk of EROs, however, is made of galaxies
at redshifts z  1 with only a small fraction being at z >
 2,
a crucial redshift range for the evolution of galaxies. In or­
der to identify old stellar systems at z  2 or beyond, color
criteria based on J and K imaging have been proposed (e.g.,
Pozzetti & Mannucci 2000; Totani et al. 2001; Franx et al.
2003; Saracco et al. 2004). As confirmed by van Dokkum
et al. (2003), objects with red spectral energy distributions at
z >
 2, can be selected requiring very red colors J - K > 2:3
(Vega scale).
Although the selection of objects with extremely red colors
has been quite successful, one could expect that moderately
old, or moderately reddened, objects exist at high redshift that
would be missed by both the ``red­color" techniques and by
the UV techniques. In addition, it appears unsatisfactory to
use so many different color criteria in order to build repre­
sentative samples of galaxies as a function of redshifts, as the
physical relations between these different classes remain un­
known, and the selection biases not fully understood.
The recently completed K20 survey (Cimatti et al.
2002a,b,c; Daddi et al. 2002; Pozzetti et al. 2003; Fontana et
al. 2004) has reached an unprecedented spectroscopic com­
pleteness (> 92%) for a sample of K < 20 galaxies. In par­
ticular, for one of the two K20 fields (included in the CDF­
S/GOODS­S field) the recent deep observations (Daddi et al.
2004, hereafter D04; Cimatti et al. 2003, 2004; Vanzella et
al. 2004 2 ) allowed to reach a spectroscopic completeness of
> 94%. This includes the presence of a significant fraction of
high redshift, z > 1:4, galaxies (redshift desert coverage).
In this paper we take advantage of the K20 spectroscopic
sample to define a simple two­color criterion based on the B­,
z­ and K­band photometry which, with a minimal contamina­
tion from lower redshift galaxies, is capable of identifying the
full range of high­redshift z > 1:4 galaxies in our K­selected
sample, including both actively star­forming (D04) and old
passive objects (Cimatti et al. 2004), and to distinguish be­
tween the two classes.
For galaxies identified with this criterion (at least to K = 20)
it is found that a K­band selection is close to a galaxy stellar­
mass selection, while a K­selected sample of star­forming
galaxies allows to reach completeness down to a given star­
formation rate limit almost independently of dust reddening.
Therefore, the technique offers a powerful tool to explore
with the minimum possible biases the histories of cosmic star­
formation and cosmic stellar­mass build­up at z  2. We dis­
2 Publicly available ESO observations obtained as part of the GOODS
project: http://www.eso.org/science/goods/
cuss in detail to which extent the cosmic stellar­mass and star­
formation rate density can be estimated with the properties of
galaxies in the proposed two­color diagram. The X­ray and
radio properties of K­selected star­forming galaxies are also
investigated in order to provide an independent estimate of
their star­formation rates.
The paper is organized as follow. The spectroscopic and
imaging datasets used in the paper are described in Sec­
tion 2. The BzK selection and classification technique for
1:4 < z < 2:5 galaxies is empirically calibrated in Section 3,
checked against stellar population models in Section 4 and
compared to HST morphological classification in Sect. 5. The
SFR and mass content of z  2 galaxies are described in Sec­
tion 6 and 7, together with methods to obtain ensemble aver­
ages from the BzK photometry alone. Section 8 compares the
samples selected with the BzK technique to those of other cri­
teria, including UV selected z  2 galaxies, EROs and J - K
red galaxies. We extend the technique for use at higher red­
shifts using Spitzer Space Telescope (SST) imaging in Sec­
tion 9. The results are discussed in Section 10 and summary
and conclusions are in Section 11.
We use the Salpeter IMF extending between 0.1 and 100
M and a WMAP cosmology
with

;
M = 0:73;0:27, and
h = H 0 [km s -1 Mpc -1 ]=100 = 0:71.
2. THE DATA
2.1. The K20/GOODS Field
The K20 survey has obtained spectra for 545 objects se­
lected in the K­band over two widely separated fields for a
total area of 52 arcmin 2 , including a 32 arcmin 2 region of
the GOODS­South field (Cimatti et al. 2002b). Of the 347
objects with K < 20 in this area, 328 have been spectro­
scopically identified at the moment by complementing the
K20 spectroscopy with a few additional redshifts from the
ESO/GOODS public spectroscopy (Vanzella et al. 2004). The
identified targets include 292 extragalactic objects and 36
stars, while the residual 19 objects have only photometric red­
shifts. Among these 311 galaxies, 19 have z spec > 1:4 (6% of
the sample) and 13 have z phot > 1:4, or  10% lie at an esti­
mated redshift beyond 1.4. As already pointed out in previous
K20 papers (Cimatti et al. 2002c; D04), no K20 galaxies were
expected to lie at these high redshifts (z  2) based on current
semi­analytical models of galaxy formation.
In addition to spectroscopy, deep and high quality imaging
and photometry is available for this field, including ground­
based BVRIzJHK imaging with very good seeing (gener­
ally 0.4--0.7 00 ) obtained with FORS1, FORS2 and ISAAC at
the VLT (the same imaging dataset used in D04), together
with the HST+ACS bviz data released by the GOODS Team
(Giavalisco et al. 2004). Shallower U­band imaging from
Arnouts et al. (2001) was also used, obtained at the ESO 2.2m
telescope. Photometric redshifts were computed for all galax­
ies with hyperz (Bolzonella et al. 2000) using the available
multiwavelength photometry. These are updated with respect
to D04 and Cimatti et al. 2002 because of the inclusion of the
final ACS photometry (bviz) from GOODS. Fig. 1 shows the
comparison of these photometric vs. the spectroscopic red­
shifts.
The B­, z­ and K­band photometry, on which most of the
paper is focused, is based on the Bessel B­band, F850LP z­
band and the K s ­band, (referred to as the K band in the rest
of this paper). The F850LP zeropoint was rescaled to match
the photometry of the z­band imaging based on VLT+FORS1

Joint selection of 1:4 <
 z <
 2:5 star­forming and passive galaxies 3
FIG. 1.--- Comparison of spectroscopic and photometric redshifts for the
311 extragalactic objects in the K20/GOODS area. Filled triangles show ob­
jects having BzK > -0:2 (Eq. 1), filled circles are old galaxies at z > 1:4,
circled symbols are X­ray detected sources and small symbols are z < 1:4
(or z > 2:5) galaxies. The photometric redshifts of old z > 1:4 galaxies are
slightly but systematically underestimated, probably because the Coleman et
al. (1980) templates are too red with respect to these  1--2 Gyr old passive
galaxies. Using the full library of BC03 SSP models with no dust reddening,
the photometric redshifts of old z > 1:4 galaxies become much more accurate
and without systematic effects.
Gunn­z filter, that is considerably less deep than the GOODS
z­band imaging. No color term was considered given the over­
all similarity of the two z­band filters whose effective wave­
lengths differ only by about 1%. Our ground based VLT
Bessel B­band imaging is instead significantly deeper than the
GOODS ACS imaging with F435W when measuring on aper­
tures >
 1'' comparable to the size of the K20 galaxies. The
K­band data was obtained with VLT+ISAAC. Fig. 2 shows
the total efficiency of the BzK photometric systems as a func­
tion of wavelength. In order to allow a fine tuning of the pho­
tometry of objects from surveys using slightly different BzK
filter sets we make publicly available 3 the B- z and z -K mag­
nitudes of the stars identified in the GOODS area of the K20
survey. By matching the colors of the stellar sequence to the
K20 one, it is possible to accurately apply the selection crite­
ria described in Section 3.
In addition to optical­IR data, the publicly available deep 1
Msec Chandra X­ray observations of the area (Giacconi et al.
2002), and deep VLA radio maps (Kellermann et al. 2004),
are used. Some details on the properties of the radio data
and data analysis methods were summarized in Cimatti et al.
(2003).
2.2. The K20/Q0055 Field
The K20 spectroscopic dataset from the 19 arcmin 2 area
centered on the QSO 0055­269 at z = 3:656 (Q0055 hereafter)
was also used as a valuable additional sample (Cimatti et al.
2002b). The spectroscopic completeness in the area is lower
3 http://www.arcetri.astro.it/k20/releases/
FIG. 2.--- The total transmission curves (including the detectors QE and
atmospheric transmission) of the BzK filters used to define the criteria for se­
lecting z > 1:4 galaxies. For the z­band filter, the HST+ACS curve is shown,
with the VLT filter being very similar and only slightly less extended to the
red. The best fit BC03 model to the SED of a galaxy at z = 1:729 is shown
for reference, on linear flux scale both for F  and F  .
(89%). Of the 198 objects, 176 have a spectroscopic redshift
identification at the moment, including 167 extragalactic ob­
jects and 9 stars. Of these, 13 lie at z > 1:4 (8% of the galax­
ies) and 12 have z phot > 1:4, for a total of 15% expected at
z > 1:4. The imaging (described in full detail in Cimatti et
al. 2002b) has worse seeing (generally  1 00 ) and is shallower
than in the K20/GOODS area, as the data were mainly ob­
tained at the ESO NTT 3.5m telescope (with SUSI2 and SOFI
instruments), except for the Gunn z­band obtained with the
VLT+FORS1 which has a similar depth and seeing to the one
of the K20/GOODS area (although shallower than the ACS
z­band imaging). For the above reasons, the photometry is
less accurate for this field. In particular for the BzK bands it
turns out that in general the galaxies still have very good pho­
tometry in the K­ and z­bands but the reddest galaxies have
quite poor B­band photometry in the Q0055 field, as the 5
limits in the photometric apertures are  26:0 and  27:6 AB
magnitudes for the K20/Q0055 and K20/GOODS regions re­
spectively. X­ray, radio and HST data are not available for
this field.
3. NEAR­IR COLOR SELECTION AND CLASSIFICATION OF
1:4 <
 z <
 2:5 GALAXIES
3.1. The BzK Criterion
Fig. 3 shows the B - z vs. z - K colors of the 311 galaxies
and the 36 stars in the K20/GOODS sample. The classifica­
tion of galaxies at z > 1:4 as star­forming objects relies on
[OII]3727 emission (1:4 < z <
 1:7), while those at z > 1:7
have UV spectra showing the typical features of star­forming
galaxies including e.g. the CIV absorption system at 1550 å
(D04, De Mello et al. 2004). It is found that z > 1:4 star­
forming galaxies occupy a narrow range and well defined re­
gion in this plane, well separated by lower redshift galaxies,

4 E. Daddi et al.
FIG. 3.--- Two color (z - K) vs (B - z) diagram for the galaxies in the GOODS area of the K20 survey. Galaxies at high redshifts are highlighted: solid
triangles represent galaxies at z > 1:4 with features typical of young star forming systems (D04); solid circles are for z > 1:4 galaxies with old stellar populations
(Cimatti et al. 2004); empty squares are objects with no measured spectroscopic redshift and z phot > 1:4. Sources detected in the X­ray catalog of Giacconi
et al. (2002) and/or Alexander et al. (2003) are circled. Stars show spectroscopically identified galactic objects. The diagonal solid line defines the region
BzK  (z - K) - (B - z)  -0:2 that is efficient to isolate z > 1:4 star forming galaxies. The horizontal dashed line further defines the region z - K > 2:5 that
contains old galaxies at z > 1:4. The error bar located in the top­left part of the diagram shows the median error in the (z -K) and (B - z) colors of objects at
z > 1:4 (either photometric or spectroscopic). The dotted diagonal defines the region occupied by stars. The four objects with z phot < 1:4 are not highlighted and
occupy the same region of z spec < 1:4 objects.
with the bluest B- z color at fixed z -K. By defining:
BzK  (z -K) AB - (B- z) AB ; (1)
it follows that z > 1:4 star­forming galaxies are all selected by
the criterion:
BzK  -0:2; (2)
i.e., to the left of the solid line in Fig. 3. In Fig. 3 are also
marked the spectroscopically confirmed passive systems at
z > 1:4. The classification of these old galaxies relies on
the detection of significant continuum breaks and absorption
features in the rest­frame 2500--3000 å region (Cimatti et al.
2004). Being the reddest objects in both B- z and z -K colors,
old stellar systems at z > 1:4 can also be readily isolated in a
BzK diagram using:
BzK < -0:2 \
(z -K) AB > 2:5: (3)
All objects with z phot > 1:4 are also selected by the above
criteria, as evident from Fig. 3. Thus, the overall BzK­selected
sample includes 25 star­forming galaxies at z > 1:4 having
BzK  -0:2 (15 z spec and 10 z phot ) and 7 old galaxies at z > 1:4
having BzK < -0:2 and z -K > 2:5 (4 z spec and 3 z phot ). The
above criteria are therefore quite efficient in singling out z >
1:4 galaxies, as the lower redshift interlopers are only 13%

Joint selection of 1:4 <
 z <
 2:5 star­forming and passive galaxies 5
FIG. 4.--- The BzK diagram for the Q0055 field of the K20 survey. Symbols
are as in Fig. 3, except that here circled symbols represent objects with a Type
1 AGN classification based on the optical spectra (X­ray data are not available
for the Q0055 region).
FIG. 5.--- The redshift histogram of the 57 K20 galaxies selected with the
criteria defined in Section 3. The shaded areas are for objects with photomet­
ric redshift only. The bottom panel shows the redshifts for all galaxies, center
panel for the old objects and top panel for the star­forming ones. The con­
tamination of galaxies at z < 1:4 is only 12% of the sample and often consists
of z  1 X­ray luminous galaxies, likely AGN.
of the resulting samples, i.e. 5 objects (including 3 Chandra
sources at 0:8 < z < 1:2 and 2 star­forming galaxies at 1:2 <
z < 1:4). It is not unexpected that X­ray luminous objects, i.e.
AGN, may contaminate these samples as a similar selection
technique to the one devised here was proposed to identify
FIG. 6.--- The BzK diagram for galaxies in the GDDS survey with K < 20:6
(Abraham et al. 2004). Large symbols are for galaxies with spectroscopic
redshift 1:4 < z < 2:2, small squares for z < 1:4 galaxies.
luminous QSOs (Sharp et al. 2002). A QSO at z = 2:8 (not
highlighted in Fig. 3) is instead not selected by the method.
Stars have colors that are clearly separated from the regions
occupied by galaxies (and in particular by those at z > 1:4),
and can be efficiently isolated with the criterion: (z - K) <
0:3(B - z) -0:5 (dotted diagonal line in Fig. 3).
The Q0055 dataset was used as an independent verification
for the validity of the BzK selection. Fig. 4 shows the result­
ing B- z versus z -K diagram analogue to Fig. 3. Also in this
field 18/23 of the galaxies with either spectroscopic or pho­
tometric redshift 1:4 < z <
 2:5 are selected by the method.
A few z > 1:4 objects remain marginally out of the BzK se­
lection regions. Most of these have either 1:4 < z < 1:5 or
very poor B­band photometry and all are consistent with ly­
ing in the selection regions within 1--1:5. Comparison of
Fig. 3 and 4 clearly shows that the objects in the BzK > -0:2
region are more scattered out in the K20/Q0055 field than in
the K20/GOODS area because of the worse quality of the pho­
tometry. Two objects, including a galaxy and an AGN at z > 3
(not highlighted in Fig. 4), are not selected by the criteria,
that appear to have its main efficiency at 1:4 < z <
 2:5, as jus­
tified from modeling in Section 4. The contamination from
low­redshift galaxies is also here quite reduced. There are 2
objects having BzK > -0:2 that lie at z < 1:4 and result to be
a z = 1:367 star­forming galaxy and an AGN at z = 1:119.
The criteria appear quite successful on the Q0055 dataset as
well, once accounting also for the overall lower quality of the
dataset, as discussed above.
These criteria thus allow a very efficient and highly com­
plete selection of the 55 galaxies with either spectroscopic or
photometric redshift 1:4 < z < 2:5 in the K20 survey. The
57 galaxies selected with the BzK criteria to K < 20 corre­
spond to a surface density of about 1:1  0:15 arcmin 2 and
have a redshift distribution mainly spread over 1:4 < z < 2:5
(see Fig. 5).

6 E. Daddi et al.
FIG. 7.--- Top: the BzK diagram for galaxies with 20 < K < 22 in the
GOODS­ISAAC region selected with 1:4 < z phot < 2:5. Bottom: the pho­
tometric redshift distribution of galaxies with 20 < K < 22 in the GOODS­
ISAAC region selected with the BzK criteria. It is not clear whether the nar­
row spike at z phot ' 1:5 is real or just an artifact of photometric redshifts.
3.2. BzK­selected Galaxies in the GDDS and GOODS
Fields
The BzK selection was applied to other available samples
in order to further verify its validity and test it at magnitudes
fainter than K  20.
The Gemini Deep Deep Survey (GDDS; Abraham et al.
2004) performed spectroscopy of galaxies selected to K <
20:6 (Vega). They spectroscopically observed a fraction of
their K­selected sample favoring the objects with the redder
colors. Two of the GDDS fields (SA12 and SA15) have BzK
photometry. After converting the GDDS B and K band pho­
tometry from Vega to AB scale, Fig. 6 shows that 7/9 GDDS
galaxies with z > 1:4 can be selected with the BzK technique,
with only two contaminants from z < 1:4. Two galaxies with
z > 1:4 are just outside the BzK selection regions. The photo­
metric errors in the BzK magnitudes in such a catalog are on
average significantly larger than for the K20/GOODS galax­
ies with z > 1:4. Within the errors, also the two outliers are
consistent with the BzK criterion.
As a further check, the galaxies within the deep ISAAC
imaging of GOODS were considered at depths K > 20 and
up to K = 22, i.e. two magnitudes fainter than reached by
the K20 survey, for the same 32 arcmin 2 region covered by
the K20 survey. Only the objects with well determined SEDs
were included, requiring errors smaller than 0.3, 0.15, 0.15
mags for the B­, z­, and K­bands, respectively. This en­
sures reasonably reliable photometric redshift determinations,
that were obtained using hyperz in a similar way as for the
brighter K20 galaxies and using the same UBV RIzJHK imag­
ing datasets. The BzK colors of the 125 galaxies selected
to have 1:4 < z phot < 2:5 are shown in Fig. 7, where they
indeed concentrate in the region with BzK > -0:2. About
10% of them are just marginally outside the BzK selection
region. No red, passively evolving galaxies and very few red
BzK > -0:2 galaxies are identified in the sample, most likely
because of the adopted, stringent criterion on the photomet­
ric errors. Fig. 7 also shows that the photometric redshift
distribution of the 159 galaxies selected with the BzK crite­
ria (for a lower limit to their sky density of >
 5 arcmin -2 at
K = 22) is indeed centered at z  2. Only about 10% of the
galaxies are at z phot < 1:4, while 15% of them has z phot > 2:5.
The galaxies in the deep samples of Fig. 7 have a median of
K(Vega) = 21:2.
These two checks are satisfactory and support the idea that
the method is valid also for samples selected at magnitudes
somewhat fainter than K = 20. Such a validity should be fur­
ther tested with future surveys.
4. STELLAR POPULATION MODELING
Bruzual & Charlot (2003) stellar population synthesis mod­
els were used to further elucidate the physical meaning and
the validity of these, phenomenologically established, BzK
criteria.
4.1. Galaxy Models in the BzK Diagram
All the four panels of Fig. 8 reproduce the B - z and z - K
range of Fig. 3 for different set of models.
The top­left panel shows the location of constant star­
formation (CSF) models, computed for ages from 10 -3 to 2
Gyr, 1:4 < z < 2:5, various levels of reddening (using the
Calzetti et al. 2000 extinction law), and solar metallicity.
The figure confirms that galaxies in such a redshift range
with ongoing star formation are indeed expected to lie in the
BzK > -0:2 region of the diagram. The duration of the star­
formation (age) has little influence on the B - z color, while
z - K increases with age, an effect due to the development
of strong Balmer/4000 å breaks falling beyond the z­band
for z  2. Very young bursts with age less than 10 Myr
(and no underlying older stellar populations) would be lo­
cated just below the threshold. Galaxies with similar prop­
erties are not present in the K20 database (K < 20) and are
at most only a minority in the GOODS photometric redshift
sample to K = 22 (Fig. 7). In order to include also such ob­
jects one should formally require BzK >
 - 0:8. In the K20
sample, this would increase significantly the contamination
by z < 1:4 galaxies.

Joint selection of 1:4 <
 z <
 2:5 star­forming and passive galaxies 7
FIG. 8.--- The evolutionary tracks in the BzK diagram from theoretical models.The top­left panel shows continuous star formation model tracks for ages from
1 Myr to 2 Gyr and for E(B­V)=0, 0.3, 0.6. Top right panel has simple stellar population models for ages from 0.1 to 2 Gyr and no reddening. The bottom­left
panel shows evolutionary models with various formation redshifts and SFR timescales and no reddening. At decreasing redshifts the tracks generally turn from
bottom­left to top­right. The bottom­right panel show colors for the local templates of various galaxy types from Coleman et al. (1980, CWW). All models are
plotted for the range 1:4 < z < 2:5, except in the bottom­right panel where plots are for 0 < z < 1:4. The limits and color ranges of all four panels reproduce
those of Fig. 3, for direct reference.
The reddening vector is virtually parallel to the BzK = -0:2
limiting line, implying that dust affects the B - z and z - K
colors by the same amount for 1:4 < z < 2:5 galaxies. This
appears to be the reason why the BzK > -0:2 criterion is
successful at identifying z > 1:4 star forming galaxies, vir­
tually regardless of their dust reddening. It can be noticed
that for E(B -V ) = 0 the tracks lie near the edge of the dia­
gram, where no galaxies are found in the K20 sample (see Fig.
3), suggesting that purely unreddened, star­forming galaxies
are rare at least in a K­selected sample at the relatively bright
K < 20 limit. Instead, in the K < 22 sample from GOODS
(Fig. 7), some fainter objects start to occupy also the region
with 0 < (z -K) AB < 1.
The top­right panel of Fig. 8 shows the location of simple
stellar population (SSP) models in the BzK diagram, for ages
of 0.1 to 2 Gyr, no reddening, and solar metallicity. For young
ages ( <
 0:2) Gyr the tracks are marginally redder but similar
to those of star­forming galaxies. As ages grow to >
 1 Gyr
the tracks occupy the region where passive z > 1:4 galaxies
are detected, as expected. There is an intermediate age regime
at  0:5 Gyr for SSP models in which such objects would be
missed by both criteria of Section 3 for z  2. SSP models
with young ages (i.e. comparable to the duration of major star
formation events in real galaxies) and no reddening might be
an unrealistic schematization, as real young galaxies are likely
to be to some extent still star­forming and dust­reddened.
As a more reasonable rendition and in order to explore the
redshift and aging effects, some evolutionary models were

8 E. Daddi et al.
FIG. 9.--- BzK versus redshift for galaxies in the K20/GOODS area. Sym­
bols are as in Fig. 3, except that here all objects with photometric redshift only
are shown as empty squares. Model tracks are also over­plotted showing the
expected BzK color as a function or redshift. Constant star­formation rate
models (solid lines) are shown for ages between 0.1 and 2 Gyr and reddening
E(B-V ) = 0:3 (but note that the BzK color is nearly reddening independentat
z > 1). Also shown is color evolution for evolving stellar populations formed
in an instantaneous burst at redshifts z = 2, 3 and 6 (dotted lines) and the
variation of color with redshift for the (non evolving) templates of E, Sbc,
Scd, and Im local galaxies from Coleman et al. (1980, CWW).
computed with star formation histories more extended in time,
as described in Daddi et al. (2000b). Left­bottom panel of
Fig. 8 shows the BzK colors in 1:4 < z < 2:5 for galaxies with
various formation redshifts and exponentially declining SFRs
( = 0:3 and 1 Gyr), with no reddening and solar metallic­
ity. For high formation redshifts (z f > 5) the implied color
evolution at z > 1:4 is such that objects move directly from
the star­forming galaxy region (BzK > -0:2) to the passive
galaxy region (BzK < -0:2 and z -K > 2:5) without crossing
the bluer regions populated by z < 1:4 objects.
The last panel of Fig. 8 finally shows that the color of nor­
mal galaxies at 0 < z < 1:4, computed using the Coleman et
al (1980) templates of E­Sbc­Scd­Irregular galaxies, are in­
deed expected to fall outside the range defined for z > 1:4 and
bracket quite well the range of colors observed for K20 galax­
ies at z < 1:4 (see Fig. 3). This additional test strengthens the
validity of the BzK selection to isolate galaxies at z > 1:4.
4.2. Modeling BzK versus Redshift
The key quantity in the selection and classification of z >
1:4 galaxies is the BzK term defined in Eq. 1. Fig. 9 shows the
BzK evolution as a function of redshift for the CSF models
described above. Objects with BzK >
 0 start to appear in sig­
nificant numbers only beyond z > 1:4. The CSF models enter
the region BzK > -0:2 at z >
 1:2, although models with ages
of 1--2 Gyr can marginally fulfill the BzK > -0:2 condition
even at much lower redshifts. CSF models evolve out of the
BzK > -0:2 region at z > 2:6--3.2, depending on age, because
the Ly forest starts entering the B­band at those redshifts,
thus producing a reddening of the B - z colors. Also shown
in the figure are BzK colors expected for passively evolving
(SSP) galaxies formed at z = 2, 3 and 6, and templates of
local galaxies (Coleman et al. 1980). Again, one notices
that in general passively evolving galaxies are contaminating
BzK > -0:2 samples only for very young ages close to the for­
mation redshift. The Coleman et al. (1980) templates bracket
the BzK color range observed for 0 < z < 1 galaxies, as well
as that of higher redshift z  2 galaxies (although they have
too old stellar populations to be truly representative of z  2
galaxies).
4.3. The Effects of Metallicity and Extinction Laws
We also explored the effects of using alternative choices for
the metallicity and the extinction law. Models with metallic­
ity significantly below solar seem inappropriate even for z  2
star­forming systems with K < 20, as these objects show deep
photospheric absorption spectra indicative of solar or higher
metallicity (De Mello et al. 2004). Old systems are consis­
tent with being fully assembled spheroids, that are known to
have nearly solar or higher metallicity today. We checked that
using above­solar metallicities the CSF galaxy tracks are ba­
sically unchanged, while the tracks of passive galaxies change
according to the well known age/metallicity degeneracy. We
also investigated the effect of using extinction laws other than
that of Calzetti et al. (2000). Using the extinction law pro­
posed by Silva et al. (1998) yields results fully consistent
with those obtained above with the Calzetti et al. law. The
SMC extinction curve produces a higher reddening to the B-z
color than to the z - K color, so that for very high reddening
(E(B-V ) >
 0:6) the model tracks would enter the BzK < -0:2
region of passive galaxies. However, with the SMC extinction
law the colors of the reddest galaxies with BzK > -0:2 are dif­
ficult to reproduce.
4.4. The Nature of the Reddest Galaxies with BzK > -0:2
Most of the K20 galaxies with no spectroscopic redshift
available and 1:4 < z phot < 2:5 have very red (z - K) AB >
2:5 colors and BzK > -0:2 (Fig. 3), qualifying thus as star­
forming galaxies based on the proposed classification crite­
ria. The top­left panel of figure 8 confirms that such objects
are fully consistent with being heavily reddened, star­forming
galaxies. Their full multicolor SEDs cannot generally be fit­
ted by models for old/passive galaxies with no star­formation
and reddening, implying that some amount of young­hot stars
is required for them to show the relatively high B­band fluxes
and blue B- z colors. This is quite reasonable, as they appear
to follow the trend of increasing reddening for the spectro­
scopically established star­forming galaxies at z > 1:4. Nev­
ertheless, some of the objects in that region may actually be
post­starburst galaxies, having passed their strongest episode
of star­formation, in which case part of their red colors could
be due to an aged burst of star­formation (see bottom­left
panel of Fig. 8). Additional evidence that, typically, these
are indeed actively star­forming galaxies will be derived from
their average X­ray and radio properties in Section 6.2.
5. HST/ACS MORPHOLOGY OF THE z > 1:4 GALAXIES
HST imaging provides a fundamental complement to in­
vestigate the nature of the BzK galaxies and to elucidate their
evolutionary status. In Fig. 10 ACS z­band imaging of the
z > 1:4 galaxies in the K20/GOODS sample are presented.
The z­band is centered at rest­frame wavelengths from 2500
å to 3700 å for the objects in 1:4 < z < 2:5. Objects with

Joint selection of 1:4 <
 z <
 2:5 star­forming and passive galaxies 9
FIG. 10.--- ACS z­band (F850LP) snapshot images (5 00 5 00 ) of the 32 K20/GOODS galaxies at z > 1:4 that can be selected with the BzK criteria. The galaxies
are divided between candidates star­forming ("S", defined as those with BzK  -0:2) and passive ("P", defined as those with BzK < -0:2 and z - K > 2:5),
according to the diagnostic discussed is Section 3. Galaxies in each category are sorted by increasing redshift ("zp" means that the redshift is photometric). A
subsample of these images had been shown in D04 and Cimatti et al (2004).
BzK  -0:2 appear generally irregular/merging­like and have
very large sizes, with an average half­light radius of about 6
kpc at z  2 (D04). Objects with BzK < -0:2 and z -K > 2:5
have instead generally a compact and regular morphology.
With only a few exceptions, there is a very good agreement of
the early­type/late­type morphological appearance with both
the BzK color classification and with the spectroscopic clas­
sification as passive or star­forming galaxies. This supports
the evidence that the BzK criteria allow to efficiently isolate
high redshift galaxies in a K­selected sample and to distin­
guish passive and star­forming objects.
6. STAR­FORMATION RATES
The critical question is then to investigate the level of star
formation activity present in the BzK (star­forming) galaxies.
This is done in this Section where we measure the SFRs of
galaxies at 1:4 < z < 2:5 in the K20/GOODS region (hence
with K < 20), selected and classified as star­forming with the
criterion BzK > -0:2, and we explore whether the BzK pho­
tometry alone can still provide an estimate of the SFRs of
these galaxies.
6.1. SFRs from the Rest­Frame UV­Continuum Luminosity
Estimating the SFR of a galaxy from its multicolor optical
photometry is generally based upon relations between the in­
trinsic UV continuum luminosity and SFR (e.g. Madau et al.
1998) and estimating the extinction by dust, necessary to de­
rive the intrinsic UV continuum luminosity from the observed
one. Both steps are in general quite uncertain and rely on as­
sumptions about star­formation history, dust reddening law,
metallicity (as well as on the IMF, fixed to Salpeter between
0.1 and 100 M in this work, but in a way that is generally
easy to factor­out so that the results can be easily scaled to
other choices of IMF).
Neglecting any reddening correction, the SFRs are of or­
der of  10--40 M yr -1 for the spectroscopically confirmed
galaxies (D04), and even smaller for the reddest ones with
only photometric redshifts. As well known, such estimates
are severely affected by dust extinction. In this section, we at­
tempt to infer the level of dust reddening from the photometric
properties, limiting this analysis to the case of CSF models
with solar metallicity and a Calzetti et al. (2000) extinction
law (as already done in D04). These assumptions appear rea­
sonably justified for our galaxies, as discussed in Section 4,
and allow a comparison with a broad variety of literature work
based on the same assumptions.
With the above assumptions and following the approach
of D04, best­fitting SFRs and E(B -V ) have been derived
for the 24 purely star­forming galaxies with z > 1:4 in the
K20/GOODS area, from their full observed SED from U
to K (an object with AGN signatures in the spectrum and
high X­ray to optical luminosity ratio has been excluded from
the SFR analysis). The derived SFRs are typically in 100--
600 M yr -1 and the reddening range is 0:2 <
 E(B-V ) <
 1.
Then, we have explored if, within the same assumptions,
the BzK photometry alone could allow an estimate of the SFR
content of the 24 galaxies equivalent to the one derived from
SED fitting. At z  2 the B­band samples quite well the rest­
frame ultraviolet at  1500 å (actually, the rest­frame 1250--
1800 å range for 1:4 < z < 2:5), and the UV luminosity at
1500 å of a star­forming galaxy is a calibrated measure of the
ongoing SFR (e.g. Madau et al. 1998). Fig. 11 suggests that
E(B-V ) estimated from SED fitting (and with the knowledge
of the galaxy redshift) correlates very well with the observed
B- z color (see also Fig. 8, top left panel), following the rela­
tion:
E(B-V ) = 0:25(B - z +0:1) AB (4)
that indeed for the models and assumptions described above
holds as an average over redshift and age. The rms disper­
sion of the residuals is only 0.06 in E(B -V ) for the objects
with measured spectroscopic redshift (mainly due to a single
outlier, with dispersion dropping to 0.026 with such object re­

10 E. Daddi et al.
FIG. 11.--- The B - z color is plotted vs. the reddening E(B -V ) for
the BzK­selected star­forming galaxies in the K20/GOODS region. The best
fitting E(B-V ) values from the full SED analysis are shown for individual
objects. Circles with error bars: objects with spectroscopic redshifts; trian­
gles: objects with only photometric redshifts. Also shown is the B- z color
vs. E(B-V ) for constant star­formation rate, 500Myr old models and various
redshifts within the range 1:4 < z < 2:5 (filled circles connected by vertical
lines). The 500 Myr age is the typical SED best­fitting age for K20 z  2
star­forming galaxies (D04). The diagonal line shows the relation defined in
Eq. 4.
moved), and the relation still holds quite well also for objects
with photometric redshift only. This tight relation between
E(B -V ) and B - z is related to the assumption of the "grey"
and self­similar Calzetti et al. (2000) extinction law and to the
fact that the UV shape of CSF models has little dependence
on age.
The observed flux at 1500 å rest­frame, de­reddened using
Eq. 4, can be used to estimate the 1500 å luminosity once the
redshift is known. For the BC03 models this can be converted
into a SFR using the relation:
SFR(M yr -1 ) = L 1500 [erg s -1 Hz -1 ]=(8:85 10 27 ): (5)
For objects lacking a spectroscopic (or even photometric)
redshift identification, this conversion can be done only as­
suming an average redshift for the sample galaxies. For in­
dividual objects, if they lie at lower (higher) redshift than the
average both the luminosity distance and 1500 å luminosity
(based on just the observed B­band flux) will be overestimated
(underestimated), typically by factors up to  2. However,
this procedure would still allow to derive a fairly correct en­
semble average of the SFR in the survey when a statistical
sample of galaxies is considered together.
With the above recipes we have derived a BzK color esti­
mate of the SFR of each galaxy in the following way: 1) the
observed B­band flux is used as a measure of the 1500 å UV
continuum flux; (2) E(B -V ) is derived from the observed
(B- z) AB color as in Eq. 4; and (3) the average redshift of the
sample < z >= 1:9 is used for all objects to derive the SFR
following Eq. 5.
For the 14 K20 star­forming galaxies with 1:4 < z spec < 2:3,
the SED fitting and the simple BzK color estimates described
above are all in agreement within a factor of 2, given our range
of redshifts, with a rms fluctuation of only 20%. The total
SFR from the 14 galaxies results to be 3600 M yr -1 from
SED fitting and 3400 M yr -1 with the BzK­based estimate,
in excellent agreement between them and indicating a quite
high average SFR 250 M yr -1 for these galaxies. The SFRs
derived for objects with only photometric redshifts are more
uncertain, but also in that case the agreement among the two
estimates is reasonable. The SFR estimated for the 10 galax­
ies with BzK  -0:2 and z phot > 1:4 (likely z  2 star­forming
galaxies with high reddening) is  1700 M yr -1 in total, cor­
responding to SFR 170 M yr -1 per object. Averaging over
the two samples yields SFR 210 M yr -1 for the typical ob­
jects among this population of K­selected starbursts.
These results show that, within the assumptions made, the
total SFR content of 1:4 < z < 2:5 galaxies can be estimated
from the BzK photometry alone with an accuracy similar to
that reachable by fitting to the whole SEDs with known spec­
troscopic redshifts. However, we notice that assuming expo­
nentially declining star­formation models the amount of red­
dening and SFR can be significantly reduced.
In order to derive more stringent clues, X­ray and radio data
were also used to derive independent estimates of the SFR
unaffected by dust extinction and to test the above results.
6.2. SFR from the X­ray Luminosity
Alternative measures of the SFR of galaxies can be obtained
from their X­ray and radio properties, as the X­ray and ra­
dio luminosities of star­forming galaxies (with no major AGN
contribution) are proportional to the SFR (e.g., Condon et al.
1992; Ranalli et al. 2003; Nandra et al. 2003). The X­ray and
radio properties also offer an additional opportunity (besides
optical spectra) to check for the presence of AGN contamina­
tion.
Two of the K20 objects at z > 1:4 with BzK > -0:2 are listed
as detections in the catalog based on the 1 Msec Chandra
Deep Field South observations (Giacconi et al. 2002). One
of these is the object with AGN line optical spectrum, and
we already mentioned that this was excluded from the star­
forming galaxy sample. Another galaxy at z = 2:223 with a
faint soft X­ray detection is present in the sample. This is also
detected as a faint radio source at 1.4 GHz and it is consis­
tent with being a vigorous starburst with SFR >
 500 M yr -1
(D04).
The X­ray emission in the observed soft (0.5--2 keV) and
hard (2--10 keV) bands have been measured at the position of
the remaining 23 star­forming objects to check for other pos­
sible detections. No other individual detection is found above
the 3 level. The stacked X­ray signal from the 23 individ­
ually undetected sources was then obtained to constrain the
average X­ray emission of the z  2 star­forming galaxies. In
the soft band  9623 net counts are recovered, after back­
ground subtraction. We performed Monte Carlo simulations
by placing at random positions in the X­ray image (exclud­
ing regions around known sources) and found that the chance
probability of recovering such a strong signal is 1:7  10 -5 .
The average 4.4 soft counts per objects are close to the de­
tection limits of the 2 Msec Chandra observations in the HDF
North (Alexander et al. 2003). Performing the analysis sepa­
rately on galaxies with or without spectroscopic redshift iden­
tification, it is found that the two samples have not statisti­

Joint selection of 1:4 <
 z <
 2:5 star­forming and passive galaxies 11
cally different X­ray properties and both samples are posi­
tively detected at the  3 level in the soft band. On the other
hand no significant detection is found from the stacked hard
band data, constraining the hardness ratio of the population to
be HR< -0:54 at the 2­sigma level. This is consistent with
the low hardness ratio expected for starbursts galaxies. AGN
are found generally to have -0:5 < HR < 0:5 (Szokoly et al.
2004). The low average HR for our sources thus disfavors
that the detected soft X­ray emission is due to low­level AGN
activity. A similar conclusion is supported by the low average
X­ray­to­optical flux ratio of log( f 0:5-2keV = f R )  -1:5 and by
the lack of AGN signatures in the spectra (see also D04). The
X­ray emission is therefore most likely due to star­formation.
Using = 2:1 appropriate for starbursts (e.g. Brusa et al.
2002), the counts correspond, for < z >= 1:9, to a rest frame
2--10 keV luminosity of L 2-10keV = 8:610 41 ergs s -1 , which
translates into an average SFR 170 M yr -1 (Ranalli et al.
2003; Nandra et al. 2002). When adding back to the sam­
ple the individually X­ray detected (non AGN) object one
obtains an average X­ray luminosity corresponding to an av­
erage SFR 190 M yr -1 , in quite good agreement with the
estimate from the reddening corrected UV luminosities and
constant star­formation rate models.
6.3. SFR from Radio Luminosity
Deep radio maps at 1.4 GHz and 5 GHz (Kellermann et al.
2004) were used to measure the radio properties of the z  2
star­forming galaxies in our sample. The radio data reach rms
flux densities of about 8 Jy at both 1.4 GHz and 5 GHz. Two
of the star­forming z  2 galaxies are individually detected at
1.4 GHz at better than the 3 level. One of the two is the vig­
orous starburst with SFR >
 500 M yr -1 also detected in the
X­ray and discussed in D04. The other object has a 1.4 GHz
flux density of  25Jy and is therefore a  3 detection. No
individual object is detected at 5 GHz.
The average flux density of non­detections has been evalu­
ated in a similar fashion as was done for the EROs by Cimatti
et al. (2003), and using the same dataset. The radio flux
densities were measured at the nominal optical position for
each of the galaxies averaging the flux density in the beam
(3.5 00 ) over a range of 1 00 radius in order to correct for possible
residual coordinate mismatch. An average signal is measured
of 7:4  1:8Jy at 1.4 GHz and 1:5  1:8Jy at 5 GHz, for
the 22 z > 1:4 K­selected star­forming galaxies that are indi­
vidually undetected both in radio and X­ray. The above flux
densities do not strongly constrain the radio continuum slope
, but are consistent with the value of -  0:6--0.8 typical
of starburst galaxies (Condon et al. 1992). For consistency
with the work at z = 2 of Reddy & Steidel (2004), a slope of
 = -0:8 is adopted to derive an average 1.4 GHz rest­frame
luminosity of 1610 22 W Hz -1 , corresponding to an average
SFR 160 M yr -1 per object, using the relation given by Yun
et al. (2004) and corrected for a binning error as in Reddy
& Steidel (2004) 4 . Including again into the sample the two
starburst galaxies detected at 1.4 GHz we obtain an average
SFR 270 M yr -1 per object, again with reasonable consis­
tency with both the optical and the X­ray estimates. Also in
this case, no statistically significant difference is found for the
average radio flux density of objects with or without known
spectroscopic redshift.
To summarize, all the available SFR indicators agree with
each other and confirm the presence of K­band luminous <
4 Reddy, private communication
FIG. 12.--- The stellar masses for the K20/GOODS objects at z > 1:4 are
shown as a function of K­band magnitudes. The two plots presented refer to
each of the two methods discussed by Fontana et al. (2004) to estimate the
galaxy stellar masses (see text). Symbols are as in Fig. 3.
z >' 2 star­forming galaxies with typical SFR 200 M yr -1
and a median reddening of E(B-V )  0:4 (cf. D04).
7. THE STELLAR MASS OF K­SELECTED GALAXIES
As part of the K20 project the stellar mass M  of each
galaxy was estimated from the known redshifts and full multi­
color photometry (Fontana et al. 2004; F04 hereafter). Using
the F04 results, in this section we explore the possibility of
estimating the stellar­mass content of K­selected galaxies at
z > 1:4 from the BzK photometry alone.
Fig. 12 shows the results of two different stellar mass es­
timates from F04: one based on synthetic stellar population
models fitting to the whole UBV RIzJHK SED, and one based
on fitting just the R - K color. The latter approach is de­
signed to provide an estimate of the maximal mass of each
galaxy (see F04). The masses estimated with the SED­fit tech­
nique are in reasonable agreement with those for the objects
at 1:7 < z < 2:3 analyzed in D04.
Fig. 12 shows a plot of M  from both methods as a func­
tion of the observed K magnitude for the sample of 31 out
of the 32 objects with z > 1:4 in the K20/GOODS sample.
One object was excluded because exhibiting a clearly AGN
dominated spectrum. Best­fitting linear relations between the
stellar­mass and the observed K­band flux were obtained, in
the form:
log(M  =10 11 M ) = -0:4(K tot -K 11 ) (6)
where K 11 is the K­band magnitude corresponding on aver­
age to a mass of 10 11 M . For the SED fit and single­color
method we find K 11 = 19:51 and K 11 = 20:14 (Vega scale),
respectively.
It can be noted that at z > 1:4 the single­color method yields
masses a factor of 1.7 higher, on average, than the SED­fit
technique (see also F04). The rms dispersions observed for
these relations are (
logM  ) = 0:25 and 0.15 for the best fit

12 E. Daddi et al.
and single color method, respectively. We searched for further
correlations between the residuals in the masses
logM  as
derived from Eq. 6 versus the F04 values, and the colors avail­
able from the BzK photometry. No significant trend was no­
ticeable for the masses derived with the single­color method.
Instead, the residuals in the SED fitting derived masses do
positively correlate with the z -K color, with:

logM  = 0:218[(z -K) AB -2:29]; (7)
a term that would reduce the rms dispersion to 0.20 if added
to the right­hand side of Eq. 6.
These relations allow to estimate masses with average un­
certainties on single objects of about 40% and 60% rela­
tive to the single­color and the SED­fit method, respectively.
This is an encouragingly good accuracy, given the large in­
trinsic differences in the luminosity distance and actual rest­
frame wavelength sampled by the observed K­band, for ob­
jects within the 1:4 < z < 2:5 range. Intrinsic differences in
the M=L ratio for given magnitudes and/or colors also con­
tribute to increase the scatter. However, when averaging over
large samples of galaxies these statistical fluctuations may be
largely mitigated.
Note also from Fig. 12 that the stellar masses of dusty star­
forming and old/passive galaxies are estimated to be on aver­
age quite similar at given observed K­band magnitude. This
seems to happen by chance: the star­forming galaxies have
lower mass to light ratio but their K­band light is attenuated
by an amount which produces similar observed magnitudes
to old objects with comparable stellar­masses. The mass of
substantially obscured stellar populations within the galaxies
would however obviously fail to be accounted for in such es­
timates.
It should be reminded that relations 6 and 7 were derived
for K < 20 galaxies, and it remains to be assessed whether
they are also valid at fainter K magnitudes.
8. THE BzK VS. OTHER HIGH­z GALAXY SELECTION CRITERIA
In this section, the properties of BzK­selected galaxies at
1:4 < z < 2:5 having K < 20 are compared to those of sam­
ples selected according to other color or multi­color selection
criteria. We will consider the U n GR s selection of z = 2 galax­
ies, the Extremely Red Objects (ERO) selection based on the
R-K > 5 threshold, and the infrared­selected galaxies found
with the criterion J -K > 2:3 proposed by Franx et al. (2003)
to isolate z > 2 evolved galaxies.
8.1. BzK­ vs. UV­selected Galaxies at z  2
Very recently, the UV technique for selecting LBGs has
been extended to z < 3 using a U n GR s two­color diagram
which isolates star­forming galaxies at 1:4 < z < 2:5 (Erb et
al. 2003; Steidel et al. 2004; Adelberger et al. 2004), a red­
shift range fully matching that of the BzK selection.
The UV­selection requires the UV continuum to be rela­
tively flat, thus limiting the overall dust extinction to E(B -
V ) <
 0:3 (Adelberger & Steidel 2000), while many of the K20
galaxies at z > 1:4 are more reddened (see Fig. 11). We esti­
mated how many of the galaxies at 1:4 < z < 2:5 could also
be selected by the UV criterion, in our sample. As no U n GR s
photometry is available to us for the K20 galaxies, synthetic
U n GR s magnitudes have been derived from the BC03 mod­
els providing the best fit to the observed UBVRIzJHK SEDs,
for the objects in the K20/GOODS region. Fig. 13 shows
the resulting synthetic (G - Rs) vs. (U n - G) colors. Of the
FIG. 13.--- The U n GR s two­color diagram for 1:4 < z < 2:5 galaxies in the
K20/GOODS region (top panel) that are selected by the criteria defined in
Section 3, and (bottom) fainter galaxies with 1:4 < z phot < 2:5 and 20 < K <
22 from the same K20/GOODS area (the sample also shown in Fig. 7). The
U n GR s colors were derived from the SED fitting. Symbols are as in Fig. 3
(in the bottom panels all redshifts are photometric). In both panels, the color
regions defined for the UV identification of z  2 are also shown (Steidel et
al. 2003 for z  3; Erb et al. 2003, solid line, and Adelberger et al. 2004,
dotted line, for z  2).
32 K < 20 objects at 1:4 < z < 2:5 in Fig. 3, only 2 (6%)
would be selected by the Erb et al. (2003) criteria, and 9
(28%) by the Adelberger et al. (2004) criteria, corresponding
to a surface density of about 0.3 arcmin -2 . We can compare
these numbers with those in the UV­selected surveys. The
Adelberger et al. (2004) BM and BX criteria result cumula­
tively in a sky density of 9 arcmin -2 candidate z  2 galax­
ies (Steidel et al. 2004). Roughly 90% of these is found
within 1:4 < z < 2:5 and about 8% of the z  2 objects has
K < 20. Based on the above numbers, we should have found
 20 galaxies UV­selectable with the Adelberger et al. (2004)
criterion in 1:4 < z < 2:5 in the K20/GOODS region, while

Joint selection of 1:4 <
 z <
 2:5 star­forming and passive galaxies 13
FIG. 14.--- The differential contribution to the SFR density at z ' 2 from
BzK galaxies as a function of their K­band magnitude (for K20 galaxies in
the K20/GOODS region). Note that this contribution is still increasing at
the K = 20 limit of the survey, suggesting a non­negligible contribution from
unaccounted K > 20 galaxies. Error bars are purely Poissonian.
only 9 are recovered. It is not clear what is the reason of this
possible discrepancy, that may be in part due to small number
statistics and/or to cosmic variance due to clustering (D04).
Some large fraction (perhaps as high as  70%) of the
K < 20 galaxies at z > 1:4 fail to be selected by the UV cri­
teria to identify galaxies at z  2. The lost fraction includes
not only the old passive systems but also a high proportion
of actively star­forming, highly reddened galaxies. As a con­
sequence, the UV­selection fails to recover most of the stel­
lar mass in K < 20 galaxies at z = 2, as expected given that
it was not devised with the aim of probing the galaxy mass
density, but rather the star­formation rate (Adelberger et al.
2004). However, a significant amount of the SFR density
is also missed. Using the SFRs estimated from reddening­
corrected UV luminosities (Section 6.1), it is found that the
9 K < 20 starbursts in our sample that satisfy the U n GR s cri­
teria produce only  15% of the SFR density at z = 2 from
K < 20 galaxies, with the residual  85% being missed be­
cause of dust reddening in excess of E(B -V )  0:3. The
missed objects include all the K20 galaxies with the most ex­
treme starbursts with SFR> 200M yr -1 .
Comparing the typical star­formation rate level per galaxy,
the bright K < 20 starbursts in the K20 survey appear to
be forming stars more vigorously than the UV­selected not
strongly reddened galaxies with K < 20 (Shapley et al. 2004),
with average SFRs larger by a factor of  3. Extending the
comparison including also fainter UV selected galaxies, the
radio and X­ray measurements (both in agreement with the
extinction­corrected estimates based on the UV continuum),
imply that the average radio and X­ray luminosities, hence the
SFRs, of our K < 20 z = 2 star­forming objects are higher than
those of the average of all UV selected galaxies (Reddy &
Steidel 2004) by a factor of  4. The U n GR s selected galaxies
studied by Reddy & Steidel (2004) have a significantly higher
space density than the K < 20 galaxies and sample regimes
with much lower SFRs.
8.2. Contributions to the z  2 Star­formation Rate Density
In this section we derive the contribution of the BzK­
selected galaxies to the integrated star formation rate density
(SFRD) at z  2, and compare it to an estimate of the SFRD
derived from the UV­selected galaxies.
For the volume in the redshift range 1:4 < z < 2:5, a SFRD
of 0:044 0:008 M yr -1 Mpc -3 is derived from the 24 K20
star­forming galaxies fulfilling the BzK > -0:2 criterion (and
of course K < 20), where the error is derived from bootstrap
resampling. This may well be an underestimate of the error,
given the small number of galaxies used in the estimate, and
to them belonging to a population likely to be strongly clus­
tered (D04). For example, assuming that these galaxies are
as clustered as z  1--3 red galaxies (r 0 <
 10 h -1 Mpc; e.g.,
Daddi et al. 2001; 2003), the error would become 35% larger
on the lower side and a factor of 3 larger on the upper­side.
This estimate of the SFRD contributed by the BzK > -0:2
objects with K < 20 is comparable to the global SFRD at z  2
as estimated from other surveys (in the same units:  0:08,
Connolly et al. 1997, corrected for extinction by Steidel et
al. 1999;  0:055, Heavens et al. 2004), or as predicted by
CDM semi­analytical models (0.05--0.10 M yr -1 Mpc -3 ,
Somerville et al. 2001) and by CDM hydrodynamical simu­
lations ( 0:055 M yr -1 Mpc -3 , Hernquist & Springel 2003).
However, our present estimate must be incomplete because it
does not include the contributions of all the K > 20 galaxies,
and in particular of those still fulfilling the BzK > -0:2 con­
dition. Fig.14 shows that the SFRD is not yet converging by
K  20, and a significant additional contribution from K > 20
galaxies is therefore expected.
The total SFRD produced by UV­selected galaxies at z  2
in the Steidel et al. (2004) sample has not been published
yet, but a crude estimate can be derived in comparison to the
BzK star­forming galaxies at K < 20 by considering that the
z  2U n GR s ­selected candidates down to R s = 25:5 have  10
times higher sky density (Steidel et al. 2004), that  90% of
them are in the redshift range covered by the BzK selection
(1:4 < z < 2:5), and that they have  4 times smaller av­
erage SFRs. This would yield an integrated contribution by
UV­selected galaxies (with R s < 25:5) a factor of 2--2.5 times
larger than that of bright K < 20 BzK galaxies. Hence, taking
into account that some galaxies are picked by both criteria,
the UV selection may miss of order of  20--30% of the total
SFRD provided by galaxies selected by at least one the two
criteria, while the BzK criterion limited to K < 20 allows to
select only a similar fraction.
On a broader perspective, discussing the potentials of the
two color criteria (BzK and U n GR s ) is perhaps more interest­
ing than comparing the existing samples drawn with them. As
mentioned above, much of the limitation of the present ap­
plication of the BzK criterion actually comes from the fairly
bright limiting K magnitude, rather than from the color cri­
terion itself. One may expect that applying it to fainter K
magnitudes a higher fraction of the total SFRD could be re­
covered. It is not presently known, however, if some frac­
tion of z = 2 galaxies would be missed by the BzK criterion,
especially at K > 20, where it may start loosing some very
young starburst, as suggested by the top­left panel in Fig. 8.
If they exist at faint K magnitudes, such young galaxies could
be more easily selectable in the UV. These points should be

14 E. Daddi et al.
tested by future surveys 5 .
The UV­selection appears to miss the most actively star­
forming galaxies not because of the limiting R magnitude,
but because they are much too reddened [E(B -V ) >
 0:3]
for satisfying the U n GR s color selection. The existence of
highly reddened star­forming galaxies also at K > 20 would
imply for the UV­selection additional losses of star­forming
galaxies (hence of part of the SFRD). A preliminary analy­
sis based on the GOODS/ISAAC sample at K < 22 (Fig. 7)
suggests that at K > 20 star­forming galaxies with z phot  2
and progressively bluer colors start to appear, and occupy the
bluest U n GR s region where most UV­selected galaxies also
lie (Fig. 13, see also Fig. 11 of Adelberger et al. 2004 for
comparison). This may be consistent with a general blueing
trend at fainter magnitudes, indicative of a trend to lower red­
dening. The fractional SFRD lost by the UV selection may
then therefore decrease with increasing K magnitude limit.
It should be mentioned, however, that the paucity of red star­
forming (as well as of passive) galaxies in the sample of Fig. 7
is at least in part due to the requirement of accurate photome­
try for the photometric redshifts determination and that, e.g.,
candidate star­forming galaxies with BzK > -0:2, z phot  2,
and 2 < (z - K) AB < 4 are found also down to K = 22. In
addition, a population of faint red galaxies at z >
 2 appear to
exist even down to K = 24. They tend to be more clustered
than LBGs, as expected for the precursors of early­type galax­
ies (Daddi et al. 2003). In summary, an application of the BzK
technique to much fainter K­selected surveys could shed light
on the amount of reddened star­formation at rates lower than
probed by the K20 survey, and better establish the fractions of
the SFRD recovered by each of the two criteria.
8.3. BzK­selected Galaxies and Extremely Red Objects
A simple method to select relatively high redshift galaxies
relies on requiring very red optical to near­IR colors, typically
R-K > 5 (e.g. Elston, Rieke & Rieke 1988; Hu & Ridgway
1994; Thompson et al. 1999; Daddi et al. 2000a; Roche et
al. 2002, 2003; for a comprehensive review see McCarthy
2004). K20 survey spectroscopy unveiled for the first time the
nature of EROs in a sizable sample, and showed that EROs in­
clude similar fractions of old and dusty star­forming systems
(Cimatti et al. 2002a, 2003; see also Yan et al. 2004).
The redshift range is one of the main differences among
the samples produced with the two BzK and ERO meth­
ods. Fig. 15 shows that EROs with K < 20 are found at
0:8 <
 z <
 2:5, coherently with the rationale for their selec­
tion (e.g. Daddi et al. 2000a). Many K20 galaxies exist
in the same redshift range that are not EROs. In contrast,
the strength of the BzK selection (Eq. 2 and 3) is that it pro­
vides a fairly complete sample of galaxies in the redshift range
1:4 < z < 2:5. The z-K > 2:5 condition of Eq. 3 that allows to
recover old passive galaxies is basically equivalent to the ERO
criterion R-K > 5, apart from the higher low­redshift cutoff
(z >
 1:4 instead of >
 0:8). A very similar z > 1:4 cutoff for
passive galaxies would be obtained requiring R-K >
 6, albeit
with a larger contamination by both lower redshift and red­
dened star­forming galaxies. Fig. 15 shows that only about
50% of BzK selected galaxies at z > 1:4 have EROs colors,
while only 35% of all the EROs are selected with the BzK
criteria, i.e. lie at z > 1:4.
5 We are grateful to the referee (C. Steidel) for having informed us prior of
publication that in his sample of z  2 galaxies (c.f. Sect. 8.1) the BzK > -0:2
selection appears to miss a fraction of star­forming galaxies with K > 21.
FIG. 15.--- The R - K (Vega) color versus redshift (top) and versus BzK
(bottom), for galaxies in the K20/GOODS region. Symbols are as in Fig. 9.
Particularly interesting is the comparison of the physical
properties of dusty star­forming EROs to those of z  2 star­
bursts. The two samples include a few common objects, but
it appears that on average the SFR of the z = 2 star­forming
galaxies is one order of magnitude higher than that of star­
forming EROs. Indeed, the average X­ray 2--10 keV luminos­
ity of dusty EROs in the K20 survey with < z spec >= 1:053
(Brusa et al. 2002) is a factor of  10 smaller than that mea­
sured for the z = 2 BzK­selected starbursts. Similarly, the av­
erage 1.4 GHz luminosity of the same EROs is a factor of
 6 smaller than found at z = 2 (Cimatti et al. 2003). As
these estimates are limited to EROs with known spectroscopic
redshift, they exclude the highest redshift z phot  2 EROs in
common with the BzK selected sample. Forming stars much
more vigorously, the reddened starburst galaxies seen at z  2
appear therefore to be of a different nature with respect to

Joint selection of 1:4 <
 z <
 2:5 star­forming and passive galaxies 15
FIG. 16.--- The J - K (Vega) color versus redshift (top) and versus BzK
(bottom), for galaxies in the K20/GOODS region. Symbols are as in Fig. 9.
dust­reddened galaxies at z  1.
Similarly to the method proposed by Pozzetti & Mannucci
(2000; PM2000 hereafter), requiring BzK  -0:2 would allow
to distinguish dusty EROs from the old ones, extending the
diagnostic in 1:4 < z < 2:5 (the PM2000 criterion is formally
valid only up to z  2). The two criteria are however sub­
stantially different and complementary to each other: while
the PM2000 criterion relies on detecting the signature of the
4000 å break of old galaxies, the BzK criterion aims at de­
tecting the UV tail in the SEDs due to the youngest stars,
even in the presence of substantial reddening. We verified that
8/9 of the EROs that are also star­forming galaxies at z > 1:4
with BzK > -0:2, mostly objects with photometric redshifts
only, are correctly classified as star­forming galaxies by the
PM2000 criterion.
It would be extremely interesting to apply the BzK diagnos­
tic to EROs samples in order to statistically distinguish z < 1:4
EROs from those at z >
 1:4, either old or star­forming ones.
This would allow to solve the long standing issue of whether
the EROs overdensities observed in the field of AGN/QSO
at z >
 1:5 are true spatial associations (i.e. clusters or proto­
clusters) or are just due to lensing effects (e.g., Cimatti et al.
2000; Best et al. 2003; Wold et al. 2003). In case of true spa­
tial associations one would also know if such enhancements
are due to dusty star­forming or passive galaxies with impor­
tant implications for galaxy formation in clusters.
Finally, we notice that the color properties of star­forming
galaxies at z  2, having blue B-z colors and the reddest z-K
color, are fully matching those of the mysterious population of
red outlier galaxies (Moustakas et al. 1997). These galaxies
were found to show blue V -I colors with respect to their large
I -K > 4 colors and their nature had remained so far unclear.
8.4. BzK­ vs. (J -K)­selected Galaxies
Recently, Franx et al. (2003) have proposed the criterion
J - K > 2:3 to select evolved galaxies at z > 2, and spec­
troscopic evidence that z > 2 galaxies are indeed selected
by this criterion has been provided for a sample of star­
forming galaxies and AGN (van Dokkum et al. 2003; 2004).
Based on a single color, the J - K > 2:3 criterion is simi­
lar to that for EROs (R - K > 5), and like this one it may
eventually result to select both reddened star­forming galax­
ies and evolved/passive ones. The properties of J - K > 2:3
galaxies in the K20 survey were then examined and compared
with those recovered by the BzK criteria. Fig. 16 shows the
BzK vs J - K diagram and the redshift vs J - K diagram for
galaxies in the K20/GOODS region. Only 4 galaxies with
J -K > 2:3 have a spectroscopic redshift, and lie in the range
0:6 < z < 1:3. Additional 3 galaxies have a photometric red­
shift z  1:5, and only 6 out of 13, of the J -K > 2:3 objects,
have z phot >
 2. Therefore, it seems that the contamination of
z < 2 galaxies among J -K red galaxies could be higher than
in the van Dokkum et al. (2003) sample. In part this could be
due to photometric errors, as the lowest z contaminants have
2:3 < J -K < 2:5, hence close to the edge of the J -K > 2:3
region. Note however that both the van Dokkum et al. spec­
troscopic sample and the K20/GOODS J -K > 2:3 sample are
quite small.
Only 9 out of 32 objects in the K20/GOODS sample at
1:4 < z < 2:5 fulfill the J - K > 2:3 condition, but the frac­
tion rises to 5/11 for the z > 2 galaxies. All the galaxies hav­
ing J - K > 2:3 and z phot > 1:9 have also BzK > -0:2, and
would be classified as reddened star­forming galaxies rather
than purely passive systems. This agrees with the recent re­
sults by van Dokkum et al. (2004) and FÆrster Schreiber et al.
(2004). The highest redshift passive systems at 1:6 < z < 2 in
the K20 survey (Cimatti et al. 2004) have J -K  1:7 - 2.
In summary, it appears that the BzK selection has the advan­
tage of allowing in principle to recover the bulk of the galaxy
population for the redshift range 1:4 < z < 2:5 for which it
is tuned, including the reddest and bluest ones, and to distin­
guish the passive from the star­forming ones. However, while
the BzK selection is efficient only up to z  2:5, the J -K > 2:3
criterion can allow to pick up the reddest galaxies up to much
higher redshifts z <
 4 (Franx et al. 2003).
We finally notice that most of BzK galaxies have J -K > 1:7
(Fig. 16). At this threshold the clustering of faint K­selected
galaxies at z >
 2 was observed to become quite strong, com­
pared to bluer galaxies (Daddi et al. 2003). This is consistent
with BzK­like galaxies contributing to such a clustering en­

16 E. Daddi et al.
FIG. 17.--- A possible reddening independent selection criterion for
2:5 <
 z <
 4:0 star­forming galaxies is obtained with RJL  J -L 3:6 -1:4(R -
J) > 0 (AB magnitudes). The above quantity is plotted for the galaxies in the
K20 survey (the L­band magnitudes were derived from the best­fitting SED)
and for constant star­formation rate models and 0.2, 0.5, 1 and 2 Gyr ages.
Circled points show X­ray detected sources.
hancement (as suggested by D04), together with the reddest
J -K > 2:3 galaxies.
9. EXTENDING THE TECHNIQUE TO SELECT z > 2:5 GALAXIES
WITH SPITZER PHOTOMETRY
The BzK criterion is based on the rest­frame colors of (red­
dened) star­forming and (unreddened) passive galaxies, and
then tuned to select those at z  2. Therefore, by choosing a
different set of bands that sample the same rest­frame wave­
lengths one can forge a new criterion tuned to select the same
kind of galaxies at a higher redshift.
By multiplying by 1.5 the central wavelengths of the BzK
bands one obtains values that roughly correspond to the cen­
tral wavelengths of the RJL bands, and correspondingly a cri­
terion based on the quantity:
RJL  (J -L 3:6 ) AB -1:4(R- J) AB (8)
can be used to select galaxies in the redshift range 2:5 <
 z <
 4,
i.e., complementary to the BzK criterion that can select galax­
ies up to z  2:5. The RJL quantity has its peak for star­
forming galaxies in the above redshift interval, again due to
the Balmer break being located between the J and L­band at
3.6 m. Given that the ratio of the central wavelengths of the
RJL bands to the BzK ones is not exactly constant, a factor
1:4 in Eq. 8 is necessary to make RJL reddening indepen­
dent in 2:5 < z < 4 (using the reddening law of Calzetti et al.
2000). Model tracks for the 1:4(R - J) AB versus (J - L 3:6 ) AB
colors in the range 2:5 < z < 4:0 are nearly identical to those
for the (B - z) AB versus (z - K) AB colors in 1:4 < z < 2:5,
already discussed in Section 4 and shown in the panels of
Fig. 8. By requiring RJL >
 0 one should thus in principle
cull z  2:5--4 star­forming galaxies in L­band limited sam­
ples, independently on their reddening, while objects having
RJL < 0 and J -L 3:6 >
 2--2.5 should turn out to be passive ob­
jects at z > 2:5 (if such a population of galaxies exists). As a
consistency check, synthetic L­band magnitudes were extrap­
olated for K20 galaxies from their best fitting SEDs to test for
contamination by z < 2 galaxies in RJL >
 0 selected samples,
that results to be small (Fig. 17), though the K20 sample does
not cover the redshift range z > 2:5 that should be sampled by
the RJL > 0 criterion. A few z > 2 galaxies in the K20 sample
start to show RJL > 0 following the models trend. A possible
problem of this RJL selection technique might be contamina­
tion by low redshift (e.g. z <
 0:5) galaxies that could arise if
significant contribution by dust (e.g. from AGN) is starting to
appear in the L­band. No contribution of this kind was con­
sidered in the derivation of K20 synthetic L­band magnitudes.
It is unclear how often this can happen for faint low­redshift
galaxies. Filtering of low­redshift interlopers may be desir­
able for the application of this technique if the above contam­
ination should result to be relevant.
If placed at z = 3:5 a typical z = 2 star­forming galaxy in
the K20 survey would have L 3:6  22--23 (AB). This is much
brighter than the limits that should have been reached by the
GOODS­SST observations at 3.6 m (Dickinson et al. 2002).
As an example, for E(B -V )  0:6 at z  3:5 one expects
colors (R-L 3:6 ) AB  5 and (J -L 3:6 ) AB  3, implying the need
to reach quite faint magnitudes in the optical/near­IR in order
to detect such galaxies, i.e., R  27--28 and J  25--26 (AB
scale magnitudes). A first check of this criterion should be
possible with the GOODS ACS+ISAAC+SST dataset, that is
expected to be deep enough in all the RJL bands. In particular,
it will be possible to test whether galaxies exist in the range
z  2:5-4:0 that are picked up by the RJL selection but missed
by the U n GR s UV­selection, in analogy to what found for the
BzK selection.
10. DISCUSSION
10.1. Early­Type Galaxies in Formation
The masses of the z  2 BzK galaxies in the K20 survey
are overall quite high, with a median of  10 11 M , and in
the local universe objects with such high masses are almost
uniquely found among early­type galaxies. In D04 we had
in fact suggested that the properties of K­selected galaxies at
z = 2 are consistent with those expected for the star­forming
precursors of massive spheroids. This was also supported by
the high SFRs, large sizes, merging­like morphologies and
strong redshift space spikes that hint for strong clustering.
Additional evidence in this direction comes from their strong
photospheric and interstellar lines, indicative of solar metal­
licity or above, typical of massive spheroids (de Mello et al.
2004).
The properties of the BzK­selected galaxies with K < 20
suggest that there is a whole population of vigorous starbursts
within the 1:4 < z < 2:5 range that can qualify as spheroids
in the making. Such properties are quite different from those
of star­forming galaxies at lower redshifts, e.g., the SFRs are
 10 times higher than those of z  1 dusty EROs, which in
turn may be much less strongly clustered than BzK­selected
galaxies (Daddi et al. 2002, 2004).
High redshift dusty star­forming galaxies selected at
submm/mm wavelengths (see Blain et al. 2002 for a re­
view) are often considered as the precursors of the present­
day massive spheroids. Although a detailed comparison be­
tween BzK­selected and submm/mm­selected galaxies is be­
yond the scope of this paper, we notice that the latter sys­

Joint selection of 1:4 <
 z <
 2:5 star­forming and passive galaxies 17
tems have a redshift distribution largely overlapping with that
of the former ones (median redshift of z  2:4; Chapman et
al. 2003), even higher SFRs (Blain et al. 2002), similarly
high masses (Genzel et al. 2003) and possibly similarly high
clustering (Blain et al. 2004). However, the space density
of submm/mm­selected galaxies is a factor of 10--100 lower
than that of the BzK­selected ones. Submm/mm sources may
be extreme subsets of BzK galaxies.
10.2. Entering the Spheroid­Formation Epoch? A V/V max
Test
Many lines of evidence suggest that ellipticals and bulges
formed the bulk of their stars at z >
 2:5 - 3, both in clusters
(e.g., Bower, Lucey, & Ellis 1992) and in the field (Bernardi
et al. 1998, 2003), with much evidence having been accumu­
lated from both low­ and high­redshift (z  1) observations
of passively evolving spheroids (see e.g., Renzini 1999 for an
extensive review; see also Thomas et al. 2002). This is fur­
ther reinforced by the recent discovery of passive early­type
galaxies at z  2, with UV­luminosity­weighted ages of 1--2
Gyr, implying formation redshifts beyond z >
 2:5--4 (Cimatti
et al. 2004). Therefore, a natural question is whether the
z  2 BzK­selected starbursts belong to the major epoch or to
the low redshift tail of spheroid formation.
In order to tentatively distinguish between these alterna­
tives, a V=V max test (Schmidt 1968) was performed on the
flux limited population of K­selected star­forming galaxies at
z > 1:4. For each object, V=V max is computed as the ratio
between the volume within the range 1:4 < z < z ob j and that
within 1:4 < z < z max , where z max is the maximum redshift for
which the object would still be detected with K < 20. To com­
pute z max we use the observed J - K color of each galaxy to
estimate the K­correction. In the case of a non evolving pop­
ulation the distribution of V=V max values should have an aver­
age of 0.5. For the 24 star­forming galaxies with z > 1:4 in the
K20/GOODS region we derive = 0:594 0:048.
Considering only the objects in 1:4 < z < 2:5, thus limit­
ing z max < 2:5, results in < V=V max > = 0:64  0:05. A
greater than 0.5 suggests that the comoving num­
ber density of these galaxies is increasing with redshift, but
given the small sample the effect is only at the 2--3 level.
Limits of these calculations are also that they are based in
part on the use of photometric redshifts and that the results
could be well affected by cosmic variance due to the cluster­
ing (D04).
The significance and rate of evolution could be however
higher than recovered here, because biases are likely to work
against the detection of objects at higher and higher redshifts.
For example, the above calculation assumes no intrinsic evo­
lution in the luminosity of the galaxies. On the other hand,
if objects at lower redshift (e.g., at z < 2) were forming stars
with similar rates also at higher redshift (e.g. z > 2), then
the former would be intrinsically more luminous than the lat­
ter ones, and the amount of evolution would be higher than
estimated above. Moreover, the strong bias due to surface
brightness dimming with increasing redshift was not consid­
ered. Given the typical large sizes and low surface brightness
of many of these star­forming galaxies (D04; Fig. 10) one ex­
pects this effect to be relevant and to bias to low values the
V=V max estimates.
Consideration of these effects would further enhance the
significance and amplitude of the evolution, suggesting that
by z  1:4 we may have just started entering the epoch
of widespread starburst activity, i.e., of major formation of
galactic spheroids. An application of the V=V max test with up­
coming larger redshift surveys should shed more light on this
important point.
10.3. The Space Density of Vigorous z  2 Starbursts:
Comparison with Models
We have shown that a substantial population of vigorous
starburst galaxies with average SFR  200 M yr -1 exists at
1:4 < z < 2:5. The number density of such BzK­selected star­
bursts can be further compared to predictions of theoretical
galaxy formation models.
For example, the GIF semi­analytical models (Kauffmann
et al. 1999; Kaviani, Haehnelt & Kauffmann 2003) pre­
dict that within 1:5 <
 z <
 2 the population of galaxies with
masses in the range 10:5 < log(M=M ) < 11:3 (similar to
the one derived for the K20 z > 1:4 objects) are either pas­
sive galaxies with no ongoing SF or very active starbursts
with SFR >
 50 M yr -1 . This is in very good agreement with
our observations, but in these models the number density of
objects with SFR> 100M yr -1 is  0:8  10 -5 Mpc -3 and
 1:3  10 -5 Mpc -3 respectively at z = 1:46 and z = 2:12,
which is a factor of 10--20 below the observed number densi­
ties. The space density of passive and massive galaxies is also
similarly underpredicted.
Somerville et al. (2004) provide a mock catalog of galax­
ies with K < 20 based on an updated semi­analytical model
with enhanced starburst activity. While predicting the highest
number density of z > 1:4 galaxies with SFR> 100M yr -1
compared to all other models of this class, still it falls short
by about an order of magnitude with respect to the present
findings. Also the space density of passively evolving galax­
ies with K < 20 at z > 1:4 appears to be underpredicted by a
similar factor by this model (Cimatti et al. 2004).
In general, CDM semi­analytical models fail to account
for the sheer number of z  2 galaxies with K < 20 (Cimatti
et al. 2002c; D04; Somerville et al. 2004). An exception is
the hierarchical model by Granato et al (2004) based on the
assumption of a coeval growth of QSOs and spheroids, which
succeeds in producing the high space density of near­IR bright
z = 2 galaxies (see also Silva et al. 2004). However, in its
current realization this model predicts that the z > 1:4 tail of
K­selected galaxies is predominantly populated by passively­
evolving spheroids (see Fig. 8 in Silva et al. 2004), at variance
with the observed prevalence of vigorous starbursts.
The recent CDM hydrodynamical simulations by
Nagamine et al. (2004) appear instead quite successful
in reproducing the space density of M > 10 11 M massive
galaxies at z = 2, as observed in the K20 survey, at least
in two out of three of its different realizations. In one of
their three simulation sets the authors also recover 2 galaxies
with old stellar populations and red G-Rs colors, consistent
with the colors of passive spheroids at z > 1:4 found in K20
(Fig. 13) and well matching to the K20 space density of pas­
sive sources when accounting for the different volumes. It is
not clear instead if these models can reproduce the observed
high density of vigorous starbursts with SFR> 100M yr -1 ,
as observed in our survey.
As recently pointed out by Cimatti et al. (2004) and Graze­
brook et al. (2004), in the traditional semianalytic models
the formation of massive spheroids appears to be delayed to
much too low redshifts. On the other hand, the Granato et
al. (2004) models appear to move in the right direction, by
pushing the formation to higher redshift with strong bursts of
star­formation, then quenched by strong AGN activity. How­

18 E. Daddi et al.
ever, in doing so they may exceed somewhat, as compared to
our findings they appear to underpredict the number of star­
bursting galaxies still present at z  2. The present results,
and an application of the BzK selection to substantially larger
samples, may help in further tuning theoretical models toward
a more realistic description of galaxy formation and evolution.
11. SUMMARY AND CONCLUSIONS
 We have introduced a new criterion for selecting galax­
ies within the redshift range 1:4 <
 z <
 2:5 which is based on
the BzK photometry and allows to identify both active star­
forming as well as passively­evolving galaxies, and to distin­
guish between the two classes. The criterion has been tested
empirically -- using the spectroscopic redshifts and spectral
types from the K20 survey (K < 20) including 32 z > 1:4
objects out of 504 with a spectroscopic redshift -- and justi­
fied by simulations showing that active and passive synthetic
stellar populations actually follow this selection criterion and
are correctly identified. Albeit smaller in size, other spec­
troscopic samples such as the GDDS and photometric red­
shift of faint galaxies from the GOODS samples (as currently
available) confirm that the criterion is effective in selecting
galaxies in the mentioned redshift range and also for limiting
K­band magnitudes somewhat fainter than K = 20. We have
shown that this BzK criterion provides a very efficient way of
selecting galaxies at z  2, that is not biased against passive
galaxies and star forming galaxies that are highly reddened.
 The classification of K < 20, z > 1:4 galaxies as actively
star forming or passive was then complemented by HST/ACS
morphologies from the GOODS database, showing that in­
deed the spectral and morphological classifications are gen­
erally consistent: star­forming galaxies show clumpy, asym­
metric morphologies typical of starbursts and mergers, while
passive galaxies show symmetric surface brightness distribu­
tion in general typical of early­type galaxies.
 It is shown that the BzK photometry can be used to esti­
mate the internal reddening for the K20 galaxies classified as
star­forming, and their intrinsic luminosity at 1500 å. This al­
lows an estimate of their dust­extinction corrected SFRs. The
X­Ray and radio luminosities of these galaxies provide SFR
estimates in very good agreement with the ones from the de­
reddened 1500 å luminosity.
 A significant population of z = 2 galaxies with K < 20, av­
erage SFR 200 M yr -1 , and median reddening E(B-V ) 
0:4 is uncovered as a result, with a high volume density of
 10 -4 Mpc -3 and sky density of  1 arcmin -2 . These vig­
orous starbursts produce a SFRD of  0:044 M yr -1 Mpc -3 ,
representing a sizeable fraction of the total SFRD at z = 2 as
currently estimated.
 For BzK­selected galaxies at 1:4 <
 z <
 2:5 the stellar
mass derived from their redshift and multicolor photometry
is tightly correlated to the observed K­band magnitude (with
a 1 dispersion of  50%), at least down to K = 20.
 The BzK selection and the above correlations (BzK vs.
E(B -V ) and BzK vs. stellar mass) provide a fairly accurate
and economic method that might be statistically applied to the
very large samples of galaxies coming from the current or im­
minent wide­area surveys and/or for galaxy samples beyond
the present spectroscopic capabilities.
 A comparison with the UV­selected galaxies at z  2
(Steidel et al. 2004), including those at the same K limit,
shows that BzK­selected star­forming galaxies have typically
higher reddening and SFRs. Among our K < 20 sample,
the galaxies satisfying the UGR selection criterion contribute
roughly  15% of the SFRD at z  2 produced by the whole
K20 sample. On the other hand the surface density of the Stei­
del et al. UV­selected galaxies down to R = 25:5 is  10 times
higher than that of K < 20 star­forming galaxies in the same
redshift range, and their contribution to the SFRD at z  2
is a factor >
 2 higher than that of the K < 20, BzK­selected
galaxies.
 The BzK galaxies at z  2 are characterized by a much
higher SFR (by a factor  8 on average) compared to dusty,
star­forming EROs (R-K > 5) at z  1, and K < 20. We con­
clude that these vigorous starbursts at z  2 are of a different
nature compared to highly reddened z  1 galaxies.
 A BzK analysis of the infrared­selected galaxies with J -
K > 2:3 (Franx et al. 2003) detected within the K20 survey
shows that those with z >
 2 are likely to be reddened star­
forming objects, rather than passively evolving galaxies. A
fraction  50% of J - K > 2:3 galaxies in the K20 survey is
estimated to lie at relatively low redshifts z  10:5.
 BzK­ and submm/mm­selected galaxies appear to share
properties such as the redshift distribution, high SFRs and
high masses, but the former ones have higher space density
while the latter ones have higher SFRs. An interesting hypoth­
esis is that submm/mm selected star­forming galaxies might
represent extreme subsets of BzK galaxies, at least when lying
at 1:4 <
 z <
 2:5.
 Being based on the rest­frame shape of the spectra of star­
burst and passive galaxies, the BzK criterion can be modified
to select the same kinds of galaxies within a higher redshift
range. In this mood, we propose a RJL criterion to select
galaxies within the range 2:5 < z < 4, which would com­
plement the BzK selection of 1:4 < z < 2:5 galaxies. With
uniquely deep L­band (3:6m) data that is becoming avail­
able from the Spitzer Space Telescope, this criterion should
allow a selection of massive galaxies at z  3 that may effi­
ciently complement the traditional LBG selection.
 The high masses, SFRs, and metallicities of the bright
BzK­selected galaxies at z  2, together with a hint for a
strong clustering of them, qualify these galaxies as possible
precursors of z  1 passively evolving EROs and z = 0 early­
type galaxies. A V=V max test indicates that the space den­
sity of these galaxies may increase with redshift in the range
1:4 <
 z <
 2:5. Current theoretical simulations of hierarchical
galaxy formation generally fail to account simultaneously for
the space density of both passively evolving and star­forming
galaxies at z = 2. Hydrodynamical simulations can reproduce
our observations better than semyanalitical models.
Some of the above conclusions may be affected by cosmic
variance, given the relatively small size of the explored field.
To cope with this limitation a project is underway to cull BzK­
selected galaxies over a  1000 arcmin 2 field,  20 times
larger than the full K20 survey area, by combining K­band
data from ESO telescopes with optical data from Suprime­
Cam at the SUBARU telescope (Kong et al. in preparation),
and to follow them up spectroscopically with VIMOS at the
VLT. The validity of the BzK selection at faint K > 20 mag­
nitudes will be further tested in great detail with a planned
VLT/FORS2 survey (GMASS project) targeting among oth­
ers BzK selected galaxies fainter than K = 20.
We are very grateful to Ken Kellermann and John Kelly for
having provided access to their VLA radio maps of CDFS,
and for having measured radio fluxes for our sources; to Piero

Joint selection of 1:4 <
 z <
 2:5 star­forming and passive galaxies 19
Rosati, Mario Nonino and the CDFS team for allowing us
to use their BV RI FORS images of the CDFS field; to Gian
Luigi Granato, Rachel Somerville and Kentaro Nagamine for
providing details of their models and for useful discussions;
to Micol Bolzonella for the assistence with the hyperz soft­
ware; to Alice Shapley for sending us the transmission curves
of the U n GR s system in a digital form, and for discussions. Fi­
nally, we would like to thank the referee, Charles Steidel, for
constructive comments and suggestions that resulted in a sig­
nificant improvement of this paper. This research was funded
in part with an ASI grant (IR­059­02). E.D. and A.R. grate­
fully acknowledge financial support from the ESO Office for
Science.
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