The Astrophysical Journal, 773:112 (21pp), 2013 August 20 doi:10.1088/0004-637X/773/2/112
C
2013. The American Astronomical Society. All rights reserved. Printed in the U.S.A.
NEWLY QUENCHED GALAXIES AS THE CAUSE FOR THE APPARENT
EVOLUTION IN AVERAGE SIZE OF THE POPULATION
C. M. Carollo
1
,T.J.Bschorr
1
, A. Renzini
2
,S.J.Lilly
1
, P. Capak
3
, A. Cibinel
1
, O. Ilbert
4
, M . Onodera
1
,
N. Scoville
5
, E. Cameron
1
, B. Mobasher
6
, D. Sanders
7
, and Y. Taniguchi
8
1
Institute for Astronomy, Swiss Federal Institute of Technology (ETH Zurich), CH-8093 Zurich, Switzerland; marcella@phys.ethz.ch
2
Istituto Nazionale di Astrofisica, Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35121 Padova, Italy
3
Spitzer Science Center, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, USA
4
Laboratoire d’Astrophysique de Marseille, 38 rue Frederic Joliot Curie, F-13388 Marseille, France
5
California Institute of Technology, MC 105-24, 1200 East California Boulevard, Pasadena, CA 91125, USA
6
Department of Physics and Astronomy, University of California, Riverside, CA 92508, USA
7
Institute for Astronomy, University of Hawaii, 2680 Woodlawn Dr, Honolulu, HI 96822, USA
8
Research Center for Space and Cosmic Evolution, Ehime University, Bunkyo-cho 2-5, Matsuyama 790-8577, Japan
Received 2013 February 18; accepted 2013 June 7; published 2013 August 1
ABSTRACT
We use the large COSMOS sample of galaxies to study in an internally self-consistent way the change in the number
densities of quenched early-type galaxies (Q-ETGs) of a given size over the redshift interval 0.2 <z<1 in order
to study the claimed size evolution of these galaxies. In a stellar mass bin at 10
10.5
<M
galaxy
< 10
11
M
, we see no
change in the number density of compact Q-ETGs over this redshift range, while in a higher mass bin at >10
11
M
,
where we would expect merging to be more significant, we find a small decrease, by ∼30%. In both mass bins, the
increase of the median sizes of Q-ETGs with time is primarily caused by the addition to the size function of larger
and more diffuse Q-ETGs. At all masses, compact Q-ETGs become systematically redder toward later epochs, with
a(U − V ) color difference which is consistent with a passive evolution of their stellar populations, indicating that
they are a stable population that does not appreciably evolve in size. We find furthermore, at all epochs, that the
larger Q-ETGs (at least in the lower mass bin) have average rest-frame colors that are systematically bluer than
those of the more compact Q-ETGs, suggesting that the former are indeed younger than the latter. The idea that new,
large, Q-ETGs are responsible for the observed growth in the median size of the population at a given mass is also
supported by analysis of the sizes and number of the star-forming galaxies that are expected to be the progenitors
of the new Q-ETGs over the same period. In the low mass bin, the new Q-ETGs appear to have ∼30% smaller
half-light radii than their star-forming progenitors. This is likely due to the fading of their disks after they cease
star formation. Comparison with higher redshifts shows that the median size of newly quenched galaxies roughly
scales, at constant mass, as (1 + z)
−1
. We conclude that the dominant cause of the size evolution seen in the Q-ETG
population is that the average sizes and thus stellar densities of individual Q-ETGs roughly scale with the average
density of the universe at the time when they were quenched, and that subsequent size changes in individual objects,
through merging or other processes, are of secondary importance, especially at masses below 10
11
M
.
Key words: galaxies: evolution – galaxies: formation – galaxies: fundamental parameters – galaxies: structure
1. INTRODUCTION
The evolution of the median size (i.e., the half-light
radius r
1/2
) of the population of massive (M
Galaxy
> 10
10
M
)
quenched early-type galaxies (Q-ETGs) at given stellar mass
has been widely highlighted in recent years ( e.g., Daddi et al.
2005; Trujillo et al. 2007; McGrath et al. 2008; van Dokkum
et al. 2008; Cassata et al. 2011; Szomoru et al. 2011;Barro
et al. 2013; Dullo & Graham 2013; Newman et al. 2012;
Poggianti et al. 2013; Shankar et al. 2013,justtociteafew).The
size of the effect is quite large, with a decrease in median r
1/2
with increasing redshift ∝ (1 + z)
−1
; in coarse terms, this im-
plies that, at a given stellar mass, the median half-light radius of
Q-ETGs i s about a factor of ∼2–3 smaller at z ∼ 2 than locally,
corresponding to an increase of over an order of magnitude in
the median mean stellar density within the half-light radius of
galaxies.
The wealth of studies quoted above have used a variety
of imaging data taken from space and from the ground, at
different wavelengths, and have focused on galaxy populations
at different redshifts. Quite naturally, there has been some debate
as to whether obvious observational biases might have affected
the results, such as the possible loss in the noise of outer, low
surface brightness parts of the galaxies, or the possible effects
of color gradients (e.g., Daddi et al. 2005; Mancini et al. 2010).
Younger stellar populations in the cores of galaxies could result
in smaller sizes in the rest-frame ultraviolet, where the sizes are
often measured, than at the longer wavelengths, which better
sample the stellar mass distribution.
Many of the studies cited above have attempted to deal with
these uncertainties (e.g., Mancini et al. 2010; Szomoru et al.
2011), and there is now a reasonable consensus that there is a real
effect to be explained. For example, there appear to be no strong
color gradients in high-z Q-ETG in those cases in which both
rest-frame UV and optical imaging are available (e.g., Toft et al.
2007; Guo et al. 2011). Thus, there is now general consensus
that indeed the median size of Q-ETGs is substantially smaller
at high redshifts, though apparently normally sized Q-ETGs
coexist with compact ones, especially among the most massive
galaxies (e.g., Saracco et al. 2010; Mancini et al. 2010; see also
Onodera et al. 2010 for a similar conclusion concerning the
velocity dispersion of Q-ETGs at z = 2).
With some exceptions (e.g., Valentinuzzi et al. 2010;
Cassata et al. 2011; Newman et al. 2012; Poggianti et al.
2013), this trend has been often entirely ascribed to the physical
growth of individual galaxies. Rather than a puff-up mechanism,
1
The Astrophysical Journal, 773:112 (21pp), 2013 August 20 Carollo et al.
decreasing the central stellar density of Q-ETGs, the favored
picture has been one in which Q-ETGs maintain a nearly con-
stant mass within their innermost few kiloparsecs, and gradually
grow inside-out, building up extended stellar envelopes/halos
around such compact, dense cores (e.g., Cimatti et al. 2008;
Hopkins et al. 2009, 2010; Taylor et al. 2010; Feldmann et al.
2010; Szomoru et al. 2011). Accretion of small satellites in mi-
nor gas-poor mergers has been widely entertained as the leading
mechanism to grow these stellar envelops (e.g., Naab et al. 2009;
Hopkins et al. 2009; Feldmann et al. 2010;Nipotietal.2009;
Oser et al. 2012) and thus increase the radius of individual high-z
compact Q-ETGs, until they reach their final z = 0 dimension.
Yet, this may be only part of the story, and possibly a minor
one. First, it is now solidly established that the population of
Q-ETGs has undergone a strong increase in comoving number
density between z ∼ 2 and the present epoch (e.g., Williams
et al. 2009;Ilbertetal.2010, 2013;Dom
´
ınguez S
´
anchez et al.
2011). The mass functions of different galaxy populations in
Ilbertetal.(2010, 2013), based on high-quality photometric
redshifts in the COSMOS field (Scoville et al. 2007), indicate
that the number density of quiescent galaxies has increased by
a factor of ∼2 since z ∼ 1, and by a factor of at least 10
since z ∼ 2. These observed number density growth factors for
Q-ETGs match those expected by applying a simple continuity
equation to the time evolution of the actively star-forming galaxy
population (Peng et al. 2010, 2012).
In addition, the analysis of Sloan Digital Sky Survey (SDSS;
York et al. 2007) mass functions shows that typical passive
galaxies with M<10
11
M
can only have increased their
masses by around 20% (and definitely less than 40%) after
quenching (Peng et al. 2010). Analysis of the mass functions of
SDSS central and satellite galaxies in Peng et al. (2012) refines
these estimates to an average post-quenching mass increase of
∼25% for typical central galaxies, and a negligible increase for
satellite galaxies. These constraints strongly limit the amount of
merging that may be available to increase the sizes of galaxies.
This, together with the evolution of the number density, can
explain why the minor dry merging scenario falls somewhat
short from quantitatively accounting the observed size growth
since z ∼ 2 (e.g., Oser et al. 2012).
It seems therefore quite likely that the advocated after-
quenching growth of individual Q-ETGs contributes only mod-
estly to the observed secular increase of the median size of the Q-
ETG population; given the large increase of the number density
of these systems since z ∼ 2, it is plausible that another effect
may dominate, namely, quenching of star formation in actively
star-forming galaxies that keeps producing, at later epochs, new
Q-ETGs with larger size than those of galaxies quenched at
earlier epochs, as partly advocated on heuristic evidence by,
e.g., Valentinuzzi et al. (2010), Cassata et al. (2011), Newman
et al. (2012), and Poggianti et al. (2013). The addition, at pro-
gressively lower redshifts, of progressively larger Q-ETGs will
progressively lower the relative fraction of the more compact
galaxies relative to the total Q-ETG population, and thus pro-
duce an upward evolution of the size–mass relation. There are
good reasons, in an expanding universe that grows structure hi-
erarchically, to entertain the notion that later-appearing Q-ETGs
will be larger and thus have lower stellar densities than galaxies
of similar stellar mass that are quenched at earlier epochs (e.g.,
Covington et al. 2011). The apparent disappearance of com-
pact Q-ETGs at later epochs may thus be a false reading of a
reality in which earlier populations of denser Q-ETGs remain
relatively stable in terms of numbers through cosmic time, but
become less and less important, in relative number, at later and
later epochs.
An important question to answer is thus how the number
density of compact Q-ETGs evolves from high redshifts all the
way down to the local universe. Searches for local analogs to
the compact, massive Q-ETGs observed at z ∼ 2 have been
undertaken to answer this question, and have given conflicting
results. Specifically, for compact Q-ETGs in massive galaxy
clusters, Valentinuzzi et al. (2010) have reported evidence for
little or no evolution between z ∼ 0.7 and z ∼ 0.04 in this
population. Comparing to SDSS DR7 (Abazajian et al. 2009),
other studies have also argued for not much evolution in the
number density of compact Q-ETGs between z ∼ 1.5 and the
present (e.g., Saracco et al. 2010). Other SDSS studies have
however reported a drop of at least a factor ∼20 between z ∼ 1.6
and z = 0.1 (Cassata et al. 2011
) or even more dramatic than
this (e.g., Taylor et al. 2010). Also, Szomoru et al. (2011) find
that the minimum growth in size required to reconcile the size
distribution of quenched galaxies at z ∼ 2 with that of their
counterparts at z = 0 is a factor ∼2 smaller than the total median
size growth observed in the same redshift interval.
Some of the difference between the apparently conflicting
results may in fact stem from compactness having been quanti-
tatively defined in different ways by different authors, e.g., either
in physical units, or relative to the average size–stellar mass re-
lation for local Q-ETGs. Quite often, the fraction of compact
Q-ETGs is considered, as opposed to their number density.
Other aspects of the analyses need, however, to come under
scrutiny to reconcile such widely diverse results. For example,
Taylor et al. (2010), Cassata et al. (2011), and Szomoru et al.
(2011) use published SDSS sizes as the comparison standard
at z = 0. This is risky, as the input photometric catalogs may
have missed compact galaxies through an imperfect statistical
star–galaxy separation (Scranton et al. 2002). Furthermore, as
shown by Cibinel et al. (2012) on the galaxy sample of the Zurich
Environmental Survey (ZENS; Carollo et al. 2012), galaxy sizes
smaller than the seeing point-spread function (PSF) are not reli-
ably recovered from ground-based imaging data. The generally
poor PSF (FWHM well above ∼1
) of the SDSS images casts
doubts therefore as to whether the published SDSS galaxy cat-
alogs are adequate for this purpose. Particularly suggestive is
the number density evolution of compact galaxies presented
by Cassata et al. (2011), which, based on the s elf-consistent
analysis of GOODS images (Giavalisco et al. 2004) is rather flat
from z ∼ 2.5downtoz ∼ 0.5, and dramatically drops since
z ∼ 0.5, due to the comparison of the GOODS-based data point
at z = 0.5 with the SDSS point at z = 0. Furthermore, the
analysis of the number densities in Cassata et al. sums up all
galaxies above 10
10
M
, and thus misses possible differential
evolution with stellar mass.
The present paper seeks to explore this issue in a carefully
controlled fashion by examining, in the redshift range 0.2 <
z<1, the evolution at constant size (i.e., half-light radius) of
the number densities of Q-ETGs, and of their plausible star-
forming progenitors. We perform our analysis in two bins of
stellar mass in which the I
814W
< 24 COSMOS sample is
complete up to z = 1, i.e., 10
10.5
–10
11
M
and >10
11
M
;
these two bins straddle across the nearly redshift-invariant
characteristic mass M
∗
∼ 10
11
M
in the Schechter (1976)
fit to the mass function of galaxies (e.g., Peng et al. 2012,
and references therein), enabling us to search for differential
effects above and below this mass scale. A strength of our
analysis is the self-consistent use of data from a single survey,
2
The Astrophysical Journal, 773:112 (21pp), 2013 August 20 Carollo et al.
i.e., COSMOS, thereby avoiding basing our conclusions on
comparisons between inhomogeneous samples, and in particular
relying on the SDSS data for the low-redshift reference sample.
The COSMOS field is ideal for this s tudy, being unique in having
both exquisite photometric redshift estimates for a very large
number of galaxies, based on deep multi-band photometry, and
high-resolution F814W (I-band) Hubble Space Telescope (HST)
Advanced Camera for Surveys (ACS) images (Koekemoer et al.
2007) over a large, ∼1.8 deg
2
area. While limiting the redshift
range between z = 1 and z = 0.2 restricts the evolutionary
lever-arm relative to comparing higher redshift samples with
SDSS catalogs, our approach has indeed the great advantage
that the sizes of the galaxies can be measured in a uniform way
from a single homogeneous data set of unparalleled statistical
significance.
In our analysis, we use aperture measurements for deter-
mining the sizes of the galaxies from the ACS F814W images
because of their higher stability relative to model fitting ap-
proaches when applied to the full morphological diversity of
faint high-redshift galaxies. We fully calibrate, however, our size
measurements against magnitude, size, ellipticity, and concen-
tration biases, and show that, once both aperture and model-fit
measurements are so calibrated, they agree well with each other,
giving us confidence in their robustness.
In detail, the paper is organized as follows. Section 2
summarizes the data set and the basic measurements and
describes the selection criteria for the final galaxy sample in
detail. Section 3 presents the approach utilized to correct sizes
and other structural parameters for systematic biases that affect
raw measurements as a function of galaxy magnitude, size,
concentration, and ellipticity. Section 4 presents the redshift
evolution of the number densities at constant size and surface
mass density (i.e., the size and surface mass density functions)
for Q-ETGs, and thus our core result, i.e., the constancy of
the compact Q-ETG population and the emergence of a newly
quenched population of large ETGs over the z =→0.2 period.
Section 5 presents the size and surface mass density functions
for star-forming galaxies, and compares the number densities
of the newly quenched galaxies with the number densities of
star-forming galaxies, of similar masses and sizes, that are
expected to quench in the z = 1 → 0.2 interval, based on a
continuity-equation argument (Peng et al. 2010). This section
also compares the rest-frame optical colors of compact and
large-size populations of Q-ETGs, and shows that compact
Q-ETGs become redder toward later epochs and, at least at
masses below 10
11
M
, they are also systematically redder at
any epoch, and thus likely older, than corresponding large-size
Q-ETGs. This reinforces the interpretation that the latter are the
newcomers in the Q-ETG population, which are responsible for
increasing the median size of ETGs toward later epochs, without
substantial increase in size of individual galaxies. In Section 6
we conclude.
Four appendices present some details of our analysis. Specif-
ically, Appendices A and B provide, respectively, extra infor-
mation on the robustness of the measured star formation rates
(SFR) and on the reliability of the corrections that we apply to the
structural/size parameters; Appendix C highlights the general
need to correct such latter parameters even for estimates based
on surface brightness fitting algorithms which take into account
the effects of the observational PSF; and Appendix D finally
summarizes the procedure that we follow to derive quenching
rates using the prescriptions of Peng et al. (2010).
A cosmological model with Ω
Λ
= 0.7, Ω
M
= 0.3, and
h = 0.7 is adopted, and magnitudes are quoted in the AB
system throughout.
2. THE DATA AND THE BASIC MEASUREMENTS
2.1. COSMOS
We base our study on the COSMOS survey data set (Scoville
et al. 2007), so as to capitalize on its high-quality compi-
lation of multiwavelength imaging, including HST/ACS data
(Koekemoer et al. 2007), over a wide-area field. For the
present analysis, we employ the ACS I-band source catalog of
Leauthaud et al. (2007) containing 156,748 sources (102,007
of these tested to be reliable galaxies) down to a flux limit of
I
814W
= 24 mag. The reliability of this catalog for galaxy pho-
tometry and morphological analysis was subsequently improved
via extensive visual inspection and cleaning to remove artifacts,
cosmic rays, and stars, and to identify deblending errors, leaving
a total of 102,007 sources flagged as reliable galaxy detections.
For the purpose of estimating photometric redshifts and
stellar masses, we match the ACS I-band source catalog
against the Canada–France–Hawaii Telescope (CFHT) i
∗
-band
(McCracken et al. 2010) and Subaru i
+
-selected COSMOS In-
termediate and Broad Band Photometry Catalog (Ilbert et al.
2009, 2010, hereafter the “I09 catalog”). This aperture-matched,
photometric database, constructed with an updated implementa-
tion of the source detection procedure described in Capak et al.
(2007), offers a large compilation of broad- and narrowband
flux measurements in 3 arcsec apertures across 31 bands from
UV–optical (u) through to infrared (8.0 μm). As described in
Capak et al. (2007) the use of PSF-matched, aperture magnitudes
allows for a single correction
9
to total flux across all bands for
each object; estimates of these corrections are pre-compiled in
the I09 catalog and we adopt these for the present analysis. Two
further filter-specific corrections to these total fluxes are then re-
quired prior to photometric redshift estimation: (1) a correction
against foreground Galactic dust reddening, for which we em-
ploy the Schlegel et al. (1998) extinction maps with wavelength-
dependent adjustment factor, k
λ
×E(B −V ), from Cardelli et al.
(1989) and (2) a correction against known zero point offsets in
the COSMOS photometry, for which we employ the estimates
derived from our photometric redshift package ZEBRA
10
run
in catalog-correction mode (Feldmann et al. 2006). These cor-
rections are consistent with those published for the COSMOS
photometry by Ilbert et al. (2009) and Capak et al. (2007); they
are based on χ
2
-minimization of fitting errors between the best-
fit spectral energy distribution (SED) template and observed
fluxes of galaxies with known redshifts from the zCOSMOS
20k sample (Lilly et al. 2007, 2009; s ee Feldmann et al. 2006).
For book-keeping purposes, we note that our procedure
for matching the HST/ACS I-band source catalog against the
I09 multiwavelength photometry catalog (2,017,800 sources)
using a 0.6 arcsec tolerance on the centroid offset yields a
total of 94,908 (93.0%) direct galaxy matches (i.e., unique
galaxy–galaxy associations). A further 5267 (5.2%) galaxies
9
The four Spitzer mid-IR IRAC bands (Sanders et al. 2007) are an exception
to this rule as it was unfeasible to degrade the optical data to the much broader
Spitzer PSF; rather, the compiled IRAC fluxes were measured in fixed
apertures of 1.9 arcsec and are corrected to total by dividing out factors of
0.76, 0.74, 0.62, and 0.58 at 3.6 μm, 4.5 μm, 5.6 μm, and 8.0 μm, respectively
(cf. Ilbert et al. 2009).
10
The Zurich Extragalactic Bayesian Redshift Analyzer (ZEBRA) code is
available online at our Web site,
http://www.astro.ethz.ch/research/Projects/ZEBRA.
3
The Astrophysical Journal, 773:112 (21pp), 2013 August 20 Carollo et al.
were identified as sharing their match in I09 with another object
in the HST/ACS catalog; based on our visual inspection of a
few hundred such systems drawn randomly from the sample,
these second matches are typically neighboring “junk sources”
or overdeblended fragments of the original matched galaxy.
We thus treat as successful matches the 3614 of these 5267
duplicates for which the primary match has a smaller centroid
offset against its I09 counterpart than the additional (junk)
candidate match. Conversely, due to the relatively broad PSF
of the ground-based imaging used in construction of the I09
catalog, only a small number (16, i.e., ∼0.02%) of galaxies
in the HST/ACS-based sample were matched against more
than one possible I09 counterpart within our 0.6 tolerance;
once again, after visual inspection of these few sources, we
adopted as the valid matches the sources displaying the smallest
offset between the HST and I09 centroids. A total of 98,538
galaxies were thus deemed successfully matched, leaving only
1816 (1.8%) galaxies in the parent HST/ACS catalog unmatched
to any object in I09.
One further issue to deal with in the so-obtained galaxy
sample is the large degree of flux contamination from interloper
objects within the 3 arcsec adopted aperture in the I09 catalog.
A total of 13,025 (13% of our successful matches) were flagged
by Capak et al. (2007) and Ilbert et al. (2009) as suffering
severe contamination from either brighter neighbors or from
the diffraction spikes of overexposed stars in at least one of
the Subaru B
J
, V
J
, i
+
,orz
+
filters. Using such flagged objects
may introduce errors in our scientific analysis, and hence we
exclude these systems from our study. The completeness of our
final galaxy sample is consequently ∼84% (85,513/102,007),
contributing a level of uncertainty to the absolute normalization
of the size and surface mass density Σ
MASS
functions at each
epoch computed herein comparable to that induced by cosmic
variance (Trenti & Stiavelli 2008) in the COSMOS field (Oesch
et al. 2010). We checked that the completeness of our galaxy
sample does not vary markedly with either size (i.e., half-light
radius) or concentration index, so we do not expect any size- or
morphology-dependent biases in the presented analysis.
2.2. Photometric Redshifts, Stellar Masses,
and Star Formation Rates
We estimate photometric redshifts for objects in our matched
source catalog using our ZEBRA code (Feldmann et al. 2006).
Calibration of the benchmark SED templates (Coleman et al.
1980;Kinneyetal.1996) employed in this analysis was achieved
by comparison against a sample of ∼20,000 galaxies with
secure spectroscopic redshifts from the zCOSMOS survey (Lilly
et al. 2007, 2009). Only 236 of the 85,513 input matched
galaxies were found to be outliers (i.e., a 0.3% failure rate). By
comparison against the zCOSMOS sample at I
814W
< 22.5 mag,
we estimate a photometric redshift uncertainty of Δ(z)/(1+z) ∼
0.007(1+z) at this brightness level. The uncertainty for galaxies
down to I
814W
= 24 mag was estimated to be 0.012(1 + z)by
artificially dimming the photometry of the zCOSMOS reference
sample. The statistical quality of the ZEBRA photo-z’s is very
similar to that of the COSMOS photo-z catalog of Ilbert et al.
(2009). The latter was used to further validate the robustness of
our results toward systematics uncertainties in the photo-z’s.
For each galaxy for which a photometric redshift estimate
could be obtained, we further employed a non-public extension
of ZEBRA (i.e., “ZEBRA+”; see Oesch et al. 2010) to estimate
the corresponding SFRs and stellar masses based on synthetic
SED fitting to 11 photometric broad bands, ranging from 3832 Å
(u
∗
,CFHT)to4.5 μm(Spitzer/IRAC channel 2).
11
The SED
library consists of a comprehensive set of star formation history
models, i.e., exponentially declining SFRs spanning a range of
metallicities from 0.05 to 2 Z
, decay timescales from τ ∼ 0.05
to 9 Gyr, and ages from 0.01 to 12 Gyr (with a Bayesian prior
to bound the latter at less than the age of the universe at any
given redshift). The construction of this library was achieved via
the Bruzual & Charlot (2003) stellar population synthesis code,
adopting a Chabrier initial mass function (Chabrier 2003). The
impact of dust extinction is handled during template matching
by allowing dust reddening (Calzetti et al. 2000) with the
E(B − V ) value treated as a free parameter of the fit. Synthetic
template matches were identified, and a stellar mass successfully
derived, for all but 1088 of the 85,277 COSMOS galaxies with
photometric redshifts (a 1.3% failure rate). Owing to the inherent
degeneracies in the choice of stellar population template and
dust-extinction model, which dominate the error budget in the
present analysis (given the thorough characterization of the
observational SEDs across our multiwavelength database), we
estimate an uncertainty of σ
log M
≈ 0.20 dex on our model stellar
masses.
For the purposes of separating star-forming from quenched
galaxies, we adopt a subdivision at an SED-fit specific star for-
mation rate (i.e., SFR per unit stellar mass, hereafter sSFR)
of 10
−11
yr
−1
; this corresponds closely to the inverse age of
the universe at z ∼ 0.3, the midpoint of the low redshift bin
used in our analysis. In Appendix A, we explain our choice
to use SFRs based on SED fits rather than (available)
IR/UV-derived estimates. In Figure 1 we show, on the rest-
frame near-UV (NUV) − J versus R−J diagram, the distribu-
tions of quenched and star-forming classified galaxies in the
0.2 <z<0.4 and 0.8 <z<1.0 redshift bins, respec-
tively; star-forming and quenched galaxies are known to ef-
fectively separate in different regions in this diagnostic plane
(e.g., Williams et al. 2009; Brammer 2009; Bundy et al. 2010).
Inspection of the figure offers confidence that our chosen cut
in sSFR well separates star-forming from quenched galaxies in
our sample.
2.3. Morphological Classification
The morphological classifications were derived with the
Zurich Estimator of Structural Types Plus (ZEST+), an up-
graded version of the ZEST approach described in detail in
Scarlata et al. (2007a). ZEST+ implements well-tested, robust
algorithms for measuring a variety of non-parametric indices,
including concentration, asymmetry, clumpiness, and Gini and
M
20
coefficients for a quantitative structural analysis and mor-
phological classification of faint distant galaxies (see also refer-
ences in Scarlata et al. 2007a). The new version of the algorithm,
ZEST+, features several substantial improvements relative to
ZEST in key computations, including a quality-controlled re-
moval of contaminating sources through substitution of optimal
sky-valued pixels, a more robust identification of the galaxy
centers, important especially for computations of asymmetry
and concentration parameters, and a more robust calculation of
the sources’ Petrosian radii, unaffected by noise and contami-
nations by nearby sources. ZEST+ also implements a support
vector machine (SVM) approach to estimate galaxy morpholo-
gies, in addition to the principal component analysis (PCA) of
11
Note that our stellar masses are defined as the integral of the SFR; they are
thus about 0.2 dex larger than stellar mass computations which subtract the
mass return from stellar evolution to the interstellar medium.
4
The Astrophysical Journal, 773:112 (21pp), 2013 August 20 Carollo et al.
0.2 < z < 0.4
Quenched
Star Forming
2.0
3.0
4.0
5.0
6.0
7.0
NUV
rest
− J
rest
(
AB mag
)
0.8 < z < 1.0
0.00 0.25 0.50 0.75 1.00 1.25 1.50
R
rest
− J
rest
(AB mag)
2.0
3.0
4.0
5.0
6.0
7.0
NUV
rest
− J
rest
(
AB mag
)
Figure 1. Rest-frame NUV−J vs. R−J color–color distributions of quenched
(in red) and star-forming (in blue) galaxies at 0.2 <z<0.4 (top panel)
and 0.8 <z<1.0 (bottom panel) in the I
814W
< 24 COSMOS sample.
Galaxies are classified as quenched or star-forming according to a threshold in
sSFR = 10
−11
yr
−1
. This threshold agrees well with the separation in quenched
and star-forming that would be derived using the presented color–color diagram.
To guide the eyes, we show as a gray dashed line the saddle line between
star-forming and quenched samples. Quenched galaxies are largely restricted to
[NUV−J −2.5×(R−J )] > 2.6 magandNUV−J > 4.5 mag. The color contours
shown are incremented by factors of 2.5, 10, and 25 in number density per bin
relative to the baseline, which is a factor of two lower in the high redshift bin.
the previous ZEST version; the morphological classification of
the COSMOS sample that we use in this work uses the SVM
approach.
Both SVM and PCA method require a training sample to
guide the morphological classification. The adopted training
set is classified in three main morphological types, i.e., “early-
type” (E/S0) galaxies, “disk” (Sa to Scd) galaxies, and “very late
type” (Sd/Irr/Pec) galaxies. The galaxies in the t raining set were
carefully selected as archetypal examples of their classes, well
separated from non-class members in (at least) concentration,
asymmetry, and Gini coefficient, and spanning a representative
range of ellipticities, sizes, and apparent magnitudes (corrected
for biases, as discussed in Section 3.2). The morphological
classification was performed on the reduced HST/ACS I
814W
frames. Visual inspection of the ZEST+ classified sample, and
a quantitative inspection based on simulated images, confirms a
relatively small (<15%) incidence of catastrophic failures in the
classification, down to and a much higher frequency of correctly
identified morphologies than in our earlier classification attempt
using the original version of ZEST (Cameron et al. 2010).
We emphasize that our main findings are not affected by
the choice to add a morphological selection to the samples
of quenched and star-forming galaxies. We indeed checked
that all results stand qualitatively unchanged by removing
all morphological constraints, with only minor quantitative
differences which do not affect our main conclusions (see also
Section 5.3 for a further remark on this point).
2.4. The Final Galaxy Sample
The final selection criteria applied to construct the master
sample of massive galaxies used in the present analysis were as
follows: (1) ZEBRA maximum likelihood photometric redshift
in the interval 0.2 <z<1.0 (see Section 2.2); (2) ZEBRA+
maximum likelihood stellar mass greater than 10
10.5
M
(see
again Section 2.2); (3) ZEST+ morphological type correspond-
ingtoE/S0 and Sa–Scd galaxies (see Section 2.3 above);
(4) no excessive flux contamination in the ground-based
CFHT/Subaru imaging from neighboring objects (as indicated
by Capak et al.’s “bad photometry” flag; see Section 2.1); and
(5) no contamination by artifacts, cosmic rays, neighboring
stars, or from deblending errors in the HST/ACS I
814W
imag-
ing (see again Section 2.1). Using these selection criteria, and
thanks to the excellent combination of relatively deep ACS im-
ages over a ∼1.8deg
2
field, COSMOS returns a final sample of
11,311 (5355 quenched) galaxies, split in redshifts as follows:
1743 (921) at 0.2 <z<0.4, 1751 (833) at 0.4 <z<0.6, 3093
(1566) at 0.6 <z<0.8, and 4724 (2035) at 0.8 <z<1.0. The
variations of numbers of galaxies in the redshift bins highlight
that even COSMOS is not unaffected by cosmic variance. This
is a well-known fact for this field, and needs attention in order
to perform studies that involve the evolution of the number den-
sities of sources of a given kind. Following the approach that
we also adopted in Oesch et al. (2010), we correct for cosmic
variance issues as discussed in Section 4.
Finally, we note that, in this paper, we define as “Q-ETGs”
galaxies that are quenched, according to our sSFR-based def-
inition of Section 2.2, and have an early-type morphology,
according to our classification of Section 2.3.
3. GALAXY SIZES: BIASES AND
CORRECTION FUNCTIONS
3.1. Raw Size Measurements
As indicated above, and as also done in the literature quoted
above, we adopt the half-light radius r
1/2
as a measure for
the size of galaxies in our sample. While size measurements
based on aperture fluxes are well known to prone to systematic
biases in the small-size and low surface brightness regimes (e.g.,
Graham et al. 2005; Cameron & Driver 2007), we nevertheless
favor this technique over a profile-fitting approach (cf. Sargent
et al. 2007; Mancini et al. 2010; Cassata et al. 2011; Whitaker
et al. 2011) for the present analysis due to its high stability—both
the stability of its performance across the full morphological
diversity of the high-redshift galaxy population, which becomes
increasingly irregular/clumpy and problematic for model fitting
codes (Elmegreen et al. 2009; Oesch et al. 2010), and the
stability (i.e., predictability) of its systematic biases, which can
thus be robustly corrected, as we demonstrate in Section 3.2
below. Conversely, profile-fit-based sizes are themselves prone
to increasingly unstable behavior (i.e., large random errors) in
the low surface brightness regime (H
¨
aussler et al. 2007) and
at faint magnitudes; the results of profile fits are unreliable for
typical galaxies fainter than I
814W
∼ 23 mag in the COSMOS
imaging, whereas we want to push our limit 1 mag fainter.
To measure the (aperture) sizes of the galaxies in our
sample, we used our custom-built software package ZEST+ (see
5
