MOIRCS Deep Survey. X. Evolution of Quiescent Galaxies as a Function of Stellar Mass at 0.5

1.1 MB·English

by  Masaru Kajisawa

PASJ:Publ.Astron.Soc.Japan,1–??,
(cid:13)c 2011.AstronomicalSocietyofJapan.
MOIRCS Deep Survey. X. Evolution of Quiescent Galaxies as a
Function of Stellar Mass at 0.5 < z < 2.5
Masaru Kajisawa1, Takashi Ichikawa2, Tomohiro Yoshikawa3, Toru Yamada2, Masato Onodera4,
Masayuki Akiyama2, Ichi Tanaka5
[email protected]
1Research Center for Space and Cosmic Evolution, Ehime University, Bunkyo-cho 2-5, Matsuyama 790-8577, Japan
2Astronomical Institute, Tohoku University, Aramaki, Aoba, Sendai 980–8578, Japan
1
3Koyama Astronomical Observatory, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603–8555, Japan
1
0 4Institute for Astronomy, ETH Zurich, Wolfgang-Pauli-strasse 27, 8093 Zurich, Switzerland
2 5Subaru Telescope, National Astronomical Observatory of Japan, 650 North Aohoku Place, Hilo, HI 96720, USA

n
(Received ;accepted )
a
J
Abstract

0
2 Westudytheevolutionofquiescentgalaxiesat0.5<z<2.5asafunctionofstellarmass,usingverydeep
NIRimagingdatatakenwiththeMulti-ObjectInfraredCameraandSpectrographontheSubaruTelescope

] in the GOODS-North region. The deep NIR data allow us to construct a stellar mass-limited sample of
O
quiescent galaxiesdownto ∼1010 M evenat z∼2 for the firsttime. We selected quiescent galaxieswith
⊙
C age/τ >6 by performing SED fitting of the multi broad-band photometry from the U to Spitzer 5.8µm
. bandswiththe populationsynthesismodelofBruzual&Charlot(2003)whereexponentiallydecayingstar
h
p formation histories are assumed. The number density of quiescent galaxies increases by a factor of ∼3
- from1.0<z<1.5to 0.5<z<1.0,andby afactorof ∼10from1.5<z<2.5 to0.5<z<1.0,while thatof
o star-forming galaxies with age/τ <4 increases only by factors of ∼2 and ∼3 in the same redshift ranges.
r
t At 0.5<z<2.5, the low-massslope of the stellar mass function of quiescentgalaxiesis α∼ 0 – 0.6,which
s
is significantly flatter than those of star-forming galaxies (α∼ -1.3 – -1.5). As a result, the fraction of
a
[ quiescent galaxies in the overall galaxy population increases with stellar mass in the redshift range. The
v2 wfrahcilteiotnhaotfaqtu1ie0s1c0e–n1t0g10a.l5axMie⊙saintc1re0a11se–s10fr1o1m.5 M<∼⊙5%inctore∼as1e5s%froinmth∼e2s0a–m30e%readtshzif∼tr2atnoge∼.4T0h–6es0e%reastuzlt∼sc0o.u7l5d,
1 suggestthatthequenchingofstarformationhadbeenmoreeffectiveinmoremassivegalaxiesat1<∼z<∼2.
0 Suchamass-dependentquenchingcouldexplaintherapidincreaseofthe numberdensityof∼M∗ galaxies
0 relative to lower-mass galaxies at z>∼ 1–1.5.
0 Key words: galaxies:evolution— galaxies:formation— galaxies:high-redshift
.
1
0
1
1 1. Introduction quiescentpopulationbyquenchingofstarformation(Bell
: et al. 2004; Bell et al. 2007; Faber et al. 2007). Since re-
v
Determining how stars have been formed in galaxies cent studies suggest that the star formationrates in star-
i
X is crucial for understanding galaxy formation and evolu- forminggalaxiesseemtobesimplyalmostproportionalto
r tion. Inthepresentuniverse,itisknownthatgalaxiescan their stellarmass atleastat z<∼2 (e.g., Elbaz etal. 2007;
a be well separated into two populations, namely, passive- Daddi et al. 2007; Pannella et al. 2009; Kajisawa et al.
evolvinggalaxieswithredcolorsandstar-forminggalaxies 2010), how the quenching of star formation has occurred
with blue colors (e.g., Kauffmann et al. 2003; Baldry et in galaxiesbecomes a key issue to understandthe various
al. 2004; Brinchmann et al. 2004). Bimodal color distri- star formation histories of galaxies.
bution which consists of these two populations has also On the other hand, it is also knownfrom studies of the
beenobserveduptoz∼1–2(e.g.,Belletal.2004;Weiner ‘fossil record’ of present-day galaxies that the star for-
et al. 2005; Franzetti et al. 2007; Cirasuolo et al. 2007; mation histories of galaxies seem to depend strongly on
Cassata et al. 2008; Williams et al. 2009; Brammer et al. their stellar mass (e.g., Heavens et al. 2004; Jimenez et
2009). Atz<1,severalstudieshavefoundthatthestellar al. 2005). In the local universe, massive galaxies tend to
mass density of passively-evolvinggalaxies increases by a havereddercolorandolderstellarpopulation,whilemost
factorof∼2fromz∼1toz∼0,whilethatofstar-forming low-mass galaxies are young and actively star-forming
galaxies evolves only very mildly (e.g., Borch et al. 2006; (Kauffmann et al. 2003; Brinchmann et al. 2004). Since
Faber et al. 2007;Pozzetti et al. 2010; Ilbert et al. 2010). the pioneering work by Cowie et al. (1996), many ob-
Since passively-evolving galaxies hardly accumulate stel- servational studies at higher redshift have suggested that
larmassonlybystarformation,theseresultssuggestthat more massive galaxies have older stellar population even
some fraction of star-forming galaxies migrates into the at z∼1 and formed their stars earlier and more rapidly
2 Kajisawa et al. [Vol. ,
than low-mass galaxies (e.g., Brinchmann & Ellis 2000; to have high stellar mass-to-luminosity (M/L) ratios, the
Juneauetal.2005;Feulneretal.2005;Bundyetal.2006; observed fluxes of quiescent galaxies with a given stellar
Verganietal.2008). Forquiescentgalaxieswithlittlestar mass become relatively faint (e.g., Fontana et al. 2003).
formation, Ilbert et al. (2010) and Pozzetti et al. (2010) In order to sample low-mass quiescent galaxies with high
reported that the number density of low-mass quiescent completeness, very deep near-infrared (NIR) data are re-
galaxiesincreasesmorerapidlythanmassivegalaxiesfrom quired (e.g., Kajisawa & Yamada 2006).
z∼1 to z∼0. Recently, Peng etal. (2010)proposedthat Inthispaper,westudytheevolutionofquiescentgalax-
the mass-dependent quenching mechanism which ceases ies at 0.5 < z < 2.5 as a function of stellar mass using
star formation preferentially for more massive galaxies is verydeepNIRdata fromMOIRCSDeepSurvey(MODS,
needed to explain no evolution of the characteristic mass Kajisawa et al. 2006; Ichikawa et al. 2007). The MODS
M∗ for star-forming galaxies. On the other hand, the in- data reach ∼ 23–24 Vega magnitude (∼ 25–26 AB mag-
creaseoflow-massquiescentgalaxiesatz<∼1isexplained nitude) in the Ks band, and they allow us to construct a
by the environmental effects in their scenario. Since the stellar mass limited sample of quiescent galaxies down to
clustering of both bright and faint quiescent galaxies has ∼1010 M even at z∼2. Section 2 describes the obser-
⊙
been observed to be stronger than star-forming galaxies vational data and the procedures of source detection and
(e.g., Zehavi et al. 2005;McCracken et al. 2008), massive photometry. Details ofthe SEDfitting analysisofthe de-
dark matter halos may play some role in the quenching tected objectsaregiveninSection3. InSection4,we use
of star formation. It is important to investigate how the the results of the SED fitting to select quiescent galax-
evolution of quiescent galaxies and the quenching of star ies and constructa stellar mass-limited quiescent sample.
formation depend on stellar mass at higher redshift, as We show the evolution of the number density and frac-
previous studies of the evolutionof the globalstar forma- tion of quiescent galaxies as a function of stellar mass in
tion rate density and stellar mass density in the universe Section 5. In Section 6, we compare the results with pre-
suggest that the cosmic star formation rate has a peak vious studies and discuss their implications. A summary
around z∼2 and that a significant fraction of the stellar is presented in Section 7.
mass in the present universe had been formed at z∼ 1–3 We use a cosmologywith H =70km s−1 Mpc−1, Ω =
0 m
(e.g., Hopkins & Beacom 2006;Wilkins et al. 2008). 0.3 andΩ =0.7. The Vega-referredmagnitude systemis
Λ
At z∼ 1.5–2,severalstudies have found massive quies- used throughout this paper, unless stated otherwise.
cent galaxies by spectroscopic observations of red objects
(e.g., Cimatti et al. 2004; Saracco et al. 2005; Abraham 2. Observational Data and Photometry
et al. 2007; Kriek et al. 2006; Kriek et al. 2008; Kriek
et al. 2009; Onodera et al. 2010) and by color selection We use the K -selected sample of the MODS in the
s
techniques with imaging data (e.g., Daddi et al. 2004; GOODS-North region (Kajisawa et al. 2009, hereafter
Williams et al. 2009; Ilbert et al. 2010; Cameron et al. K09), which is based on our deep JHK -bands imag-
s
2010) or SED fitting techniques with multi-band pho- ing data taken with MOIRCS (Suzuki et al. 2008) on the
tometry (e.g., Grazian et al. 2007; Fontana et al. 2009; Subaru telescope. Four MOIRCS pointings cover ∼70%
Whitaker et al. 2010). Ilbert et al. (2010) reported that of the GOODS-North region (∼ 103.3 arcmin2, hereafter
the number density of massive quiescent galaxies with referred as “wide” field) and the data reach J = 24.2,
M ∼1011 M rapidly increases from z ∼1.75 and to H =23.1, K =23.1 (5σ, Vega magnitude). One of the
star ⊙
z∼1, while it evolves only mildly at z<∼1. Furthermore, four pointings is the ultra-deep field of the MODS (∼
Fontanaetal.(2009)alsofoundthatthequiescentfraction 28.2arcmin2,hereafter“deep”field),wherethedatareach
inmassivegalaxieswithM >7×1010 M significantly J=25.1,H=23.7,K=24.1. Afulldescriptionoftheob-
star ⊙
increases between z ∼2 and z ∼1. The low fraction of servations,reduction,andqualityofthe data ispresented
quiescent galaxies at z >∼2 reflects that there are many in a separate paper (Kajisawa et al. 2011).
active star-forming galaxies which dominates the massive ThesourcedetectionwasperformedintheK -bandim-
s
galaxy population (e.g., Papovich et al. 2007; Grazian et age using the SExtractor image analysis package (Bertin
al.2007). Thus1<z<2seemstobetheformationepoch & Arnouts 1996). At first, we limited the samples to
of these massive quiescent galaxies. K <23 and K <24 for the wide and deep fields, where
s s
On the other hand, Kajisawa et al. (2009) found that the detection completeness for point sourcesis more than
thenumberdensityof∼M∗ (∼1011 M )galaxiesevolves 90% (Kajisawa et al. 2011). Then we measured the
⊙
more strongly than low-mass galaxies at 1<∼z<∼3. Such optical-to-MIRSEDsofthesampleobjects,usingthepub-
mass-dependent evolution of the number density may in- liclyavailablemulti-wavelengthdataintheGOODSfield,
dicatesthatthestarformationhistoryand/orstellarmass namely KPNO/MOSAIC (U band, Capak et al. 2004),
assembly of galaxies already strongly depended on stellar Hubble Space Telescope/Advanced Camera for Surveys
mass at that epoch when most stars seen in the present (HST/ACS; B, V, i, z bands, version 2.0 data; M.
universe were formed. Thereforeit is interesting to inves- Giavalisco et al. 2010, in preparation; Giavalisco et al.
tigate the mass-dependence of the evolution of quiescent 2004) and Spitzer/IRAC (3.6µm, 4.5µm, 5.8µm, DR1
galaxiesuptoz∼2. However,low-massquiescentgalaxies and DR2; M. Dickinson et al. 2010, in preparation), as
atz>∼1–1.5hasnotyetbeeninvestigatedsofar. Sincequi- well as the MOIRCS J- and H-bands images. Details
escent galaxies with relatively old stellar population tend of the multi-band aperture photometry are presented in
No. ] MOIRCS Deep Survey. X. 3
Kajisawa et al. (2011). Following K09, we used objects (seethenextsection). WeassumeSalpeterIMF(Salpeter
whichare detected above2σ levelin more thantwo other 1955)withloweranduppermasslimitsof0.1and100M
⊙
bandsinadditionto the 5σ detectioninthe K -band,be- foreasycomparisonwiththeresultsinotherstudies. Ifwe
s
cause it is difficult to estimate the photometric redshift assume the Chabrier-like IMF (Chabrier 2003), the stel-
and stellar mass of those detected only in one or two lar mass is reduced by a factor of ∼ 1.8. The redshifts
bands. The number of those excluded by this criterion mentioned above and stellar M/L ratios from the best-fit
is negligible (21/6402and 42/3203 for the wide and deep templates were used to calculate the stellar mass. The
fields, respectively). estimated stellar mass is reasonably consistent with that
We also used public Spitzer/MIPS 24µm data in the inK09,andthe slightchangeinthe gridofthe modelpa-
GOODS-North (DR1+, M. Dickinson et al., in prepa- rameters does not affect the estimate of the stellar mass.
ration) to measure 24µm fluxes of the sample galaxies. The uncertainty of the stellar mass is estimated taking
The IRAF/DAOPHOT package (Stetson 1987) was used into account of the photometric redshift error for those
for the photometry to deal with many blended sources without spectroscopic redshift, and is discussed in detail
on the image properly. The DAOPHOT software fitted in K09. In the next section, we will discuss the effect of
blended sources in a crowded region simultaneously with the stellar mass error on the sample selection.
the PSF of the image. We used the source positions in
the MOIRCS K -band image as a prior for the centers 4. Sample selection
s
of the fitted PSFs in the photometry. For most objects,
4.1. Selection of quiescent galaxies
for which the residual of the fitting is negligible, the 5σ
limiting flux is ∼ 20 µJy. Details of the photometry on Taking advantages of the deep MOIRCS JHK -bands
s
the MIPS image and the error estimate are described in photometry and the wide wavelength coverage of the
Kajisawa et al. (2010) and Kajisawa et al. (2011). multi-wavelength ancillary data of the GOODS, we used
the results of the SED fitting described in the previous
3. SED fitting analysis section to select quiescent galaxies. Several studies have
used the SED fitting technique for the selection of qui-
K09 estimated the redshift and stellar mass of the K - escent galaxies (Zucca et al. 2006; Arnouts et al. 2007;
s
selectedgalaxiesmentionedaboveandconstructeda stel- Grazian et al. 2007; Salimbeni et al. 2008; Fontana et
larmass-limitedsampletostudytheevolutionofthestel- al. 2009). Following Fontana et al. (2009) and Grazian
lar mass function. We here use the same photometric et al. (2007), we use the criterion with age/τ, assum-
redshift as in K09 and carry out a similar SED fitting of ing SFR ∝ exp(−age/τ) in the SED fitting with the
the multi-band photometry where the grid of model pa- GALAXEV model. In this study, we adopt age/τ > 6
rameters is slightly changed from that in K09 in order to as in Fontana et al. (2009), which roughly corresponds
estimate age and star-formation time scale τ (see below) to SFR/Mstar <∼10−11 yr−1 for relatively small τ values
optimally for the selection of quiescent galaxies. (Fontana et al. 2009). It should be noted that our lower
In K09, we show the photometric redshifts agree well limit of τ ≥ 0.1 Gyr mentioned in the previous section
with spectroscopic redshifts (Figure 1 in K09). If avail- leads to a lower limit of age > 0.6 Gyr for galaxies with
able, we adopted spectroscopic redshifts from the litera- age/τ >6. The upper panels of Figure 1 show the distri-
ture (Cohen et al. 2000; Cohen 2001; Dawson et al. 2001; bution of age/τ as a function of stellar mass for galax-
Wirth et al. 2004; Cowie et al. 2004; Treu et al. 2005; ies at 0.5 < z < 1.0, 1.0 < z < 1.5, and 1.5 < z < 2.5.
Reddy et al. 2006; Barger et al. 2008; Yoshikawa et al. Thick dashed line shows the criterion of age/τ =6 and
2010), and performed the SED fitting fixing the redshift thin dashed lines represent age/τ =5 and 4. The MIPS
to each spectroscopic value for these galaxies. 24µmsources(>∼20µJy)arealsoshowninthefigure. The
We performed the SED fitting of the multi-band pho- mid-infrareddetectionindicatesdustenshroudedstarfor-
tometry(UBVizJHK,3.6µm,4.5µm,and5.8µm)witha mation(or AGN activity). It is seenthat at age/τ∼ 4–5,
population synthesis model. We adopted the GALAXEV many galaxiesaredetected onthe MIPS24µmimage,es-
population synthesis model (Bruzual & Charlot2003)for peciallyatMstar>∼1010.5 M⊙,whilethereareonlyasmall
direct comparison with previous studies (e.g., Grazian et number of 24µm sources at age/τ >6. The criterion of
al. 2007; Fontana et al. 2009). In the model, we assumed age/τ > 5 or 4 could lead to the contamination of the
exponentially decaying star formation histories with the quiescent sample with objects with some star-formingac-
decaying timescale τ ranging between 0.1 and 100 Gyr. tivities. Thereforeweusethecriterionofage/τ>6inthis
We used Calzetti extinction law (Calzetti et al. 2000) in paper,althoughwewillcheckthe resultswiththe criteria
the range of E(B−V)= 0.0-1.0. Metallicity is changed ofage/τ>5and4inSection6.1. Forthesamereason,we
from1/50to1solarmetallicity. Themodelageischanged excludedtheMIPS24µmsourceswithage/τ>6fromthe
from50Myrtotheageoftheuniverseattheobservedred- quiescentsampleasinFontanaetal.(2009). There are9,
shifts. We used 18 grid of τ and 60 grid of age (smaller 2,and3such24µmsourceswithage/τ>6at0.5<z<1.0,
number of grid at higher redshift depending on the age 1.0<z<1.5, and 1.5<z<2.5, respectively. The 24µm
of the universe), which are roughly equally spaced on a fluxes of these objects could be powered by AGN (e.g.,
logarithmic scale and are slightly finer than those used in Nardini et al. 2008). We show hard X-ray sources from
K09 to select quiescent galaxiesby a criterionwith age/τ the Chandra Deep Field North catalog (Alexander et al.
4 Kajisawa et al. [Vol. ,
10 9 10 10 10 11 10 12 10 9 10 10 10 11 10 12 10 9 10 10 10 11 10 12
10 2 10 2
0.5<z<1.0 1.0<z<1.5 1.5<z<2.5
10 1 10 1
u
e/ta 10 0 10 0
g
a
10 -1 10 -1
MIPS 24um source
Chandra hard-band source
10 -2 10 -2
2 2
K=24 K=24 K=24
K=23 K=23 K=23
1.5 1.5
a) 1 1
g
e
V
U-V ( 0.5 0.5
st
e
r
0 0
age/tau > 6
age/tau > 6 MIPS 24um source
-0.5 age/tau > 6 Chandra Hard-band sources -0.5
0.5<z<1.0 1.0<z<1.5 1.5<z<2.5
-1 -1
10 9 10 10 10 11 10 12 10 9 10 10 10 11 10 12 10 9 10 10 10 11 10 12
Stellar mass (Msun) Stellar mass (Msun) Stellar mass (Msun)
Fig. 1. top: age/τ vs. stellar mass for Ks-selected galaxies in the MODS field in each redshift bin. The uncertainty of age/τ
is shown as errorbars for galaxies with age/τ >6. Errors in age/τ also include the photometric redshift error for those with no
spectroscopic identification. Blue open squares represent objects detected in the MIPS 24µm image with S/N > 5 (f24µm >∼20
µJy). TheMIPS 24µm sources with age/τ>6 areshownas largebluesquares. Pentagons show Chandra hard-bandsources from
theCDF-Northcatalog (Alexander et al.2003). Thickdashed lineshows the criterionofage/τ =6forquiescent galaxies and thin
dashed linesrepresent age/τ =5and 4. bottom: rest-frameU−V color vs. stellarmass forthe sameKs-selected galaxies. Gray
opensquares show galaxies withage/τ >6inthe toppanels. Bluelargersquares andgreen pentagons shows the MIPS24µm and
Chandra hard-band sources with age/τ >6, respectively. Horizontal dashed line represents rest U−V =1.2. Short-dashed and
dashed-dottedlinesrepresenttheKs-bandmagnitudelimitforthewide(Ks=23)anddeep(Ks=24)fields,respectively(seetext
fordetails).
2003) in Figure 1, and only one of these 24µm sources quiescent galaxies. The bottom panels of Figure 1 show
with age/τ >6 is significantly detected in the hard X-ray the rest-frame U −V color vs. stellar mass for the K -
s
data. We alsofound that the other 13 24µmsourceshave selectedgalaxies. Quiescentgalaxiesselectedbyage/τ>6
the 1.6µm bump in their near- to mid-infrared SEDs and intheprevioussectionareshownasgraysquares. TheK -
s
do not show power-law SEDs. Therefore most of 24µm band magnitude limits for the wide (K =23) and deep
s
sources with age/τ >6 are considered to be star-forming (K =24) fields are shown as Short-dashed and dashed-
s
galaxies, and we excluded all these 24µm sources from dotted lines, respectively. All objects with stellar mass
the quiescentsampleas objectswith relativelyactivestar larger than the line at a fixed U−V color (on the right
formation. side of the line in the figure) are brighter than the mag-
nitude limit. We used the GALAXEV model with vari-
4.2. Limiting stellar mass for quiescent galaxies
ous star formationhistories to calculate the line (see K09
TheK -bandmagnitude-limitedsampledoesnothavea for details). The slope of the lines represents that galax-
s
sharplimitinstellarmassevenatafixedredshift,because ies with redder U −V colors tend to have higher stellar
thestellarM/Lratioatthe observedK bandvarieswith M/LratiosandthatatafixedK -bandflux(luminosity),
s s
different stellar populations (e.g., Kajisawa & Yamada the limiting stellar mass for red galaxiesis systematically
2006; K09). K09 investigated how the K -band mag- higher than that for blue galaxies.
s
nitude limit affects the stellar mass distribution of the In the figure, quiescent galaxies with age/τ > 6 tend
sample by using the distribution of the rest-frame U−V to have red U −V colors, typically U −V >∼ 0.8, espe-
color, which reflects the stellar M/L ratio well, as a func- cially at Mstar >∼1010 M⊙, and form the well-known red
tion of stellar mass (Figure 3 in K09). We here use the sequence. It is seen that the colordistribution of the qui-
similar method to determine the limiting stellar mass for
No. ] MOIRCS Deep Survey. X. 5
0.8 0.8
0.5<z<1.0 age/tau > 6 1.0<z<1.5 1.5<z<2.5
age/tau < 6
0.6 0.6
x)
e
d
Ms) ( 0.4 0.4
g(
o
_l
σ
0.2 0.2
0 0
109 1010 1011 1012109 1010 1011 1012109 1010 1011 1012
Stellar mass (Msun) Stellar mass (Msun) Stellar mass (Msun)
Fig. 2. Uncertainty of the estimated stellar mass as a function of stellar mass in each redshift bin. Red circles show quiescent
galaxies with age/τ >6 and blue dots represent those with age/τ <6. Solid lineshows the median values at each stellar mass for
quiescent galaxies. Vertical dashed-dotted line represents the limiting stellar mass for the quiescent sample. For objects without
spectroscopicredshift,thephotometricredshifterroristakenintoaccount intheestimateofthestellarmassuncertainty.
escent galaxies shifts to bluer with redshift. If we select galaxies, however, it could not be the case. Objects with
galaxieswithU−V >0.8,U−V >0.7,andU−V >0.6as largeextinctionareoftennotdetectedintheACSimages,
theredsequencepopulationat0.5<z<1.0,1.0<z<1.5, and the uncertainty in age/τ of these objects tend to be
and 1.5<z<2.5, respectively, following Whitaker et al. large. In fact, galaxies with large errorbars in the upper
(2010) and Brammer et al. (2009), the fraction of quies- panels of Figure 1 have relatively red SEDs in the NIR–
cent galaxies in the red sequence population is 46% (55% MIR region and are fitted with dusty model templates.
in the red sequence galaxies with M >1011 M ), 36% Sincethenumberofsuchobjectsinthequiescentsampleis
star ⊙
(40%), and 32% (32%) for the redshift bins. Since most small, however, the contamination from heavily obscured
quiescent galaxies show the rest U−V ∼1.2 or bluer, we star-forming galaxies does not seem to affect our results
adopt U−V =1.2 (horizontal dashed line in the figure) in the following.
as a reference to determine the limiting stellar mass for Figure 2 shows the uncertainty of the estimated stel-
the galaxies in the wide and deep fields. At 1.5<z<2.5, lar mass for the quiescent galaxies. At Mstar>∼1010 M⊙,
we can nearly completely sample the galaxies down to the stellar mass errors are relatively small and typically
∼1010.5 M for the wide field and to ∼1010 M for the <0.2 dex. Furthermore, as seen in the next section, the
⊙ ⊙
deep field. In the following, we use quiescent galaxies low-mass slope of the stellar mass function for quiescent
with M >1010.5 M in the wide field and those with galaxies are nearly flat or slightly positive (α ∼ 0–0.6).
star ⊙
M >1010 M in the deep field as a mass-limited qui- Sinceitsuggeststhatthenumberdensityoflow-massqui-
star ⊙
escent sample at 1.5<z<2.5. For the 0.5<z<1.0 and escentgalaxiesisrelativelysmall,thecontaminationfrom
1.0<z<1.5redshiftbins,wealsolimitthequiescentsam- lower-mass galaxies could not be significant even if these
ple to those with M >1010 M for a fair comparison low-mass galaxies have slightly larger stellar mass errors.
star ⊙
with the 1.5<z<2.5 bin, while the limiting stellar mass Therefore the incompleteness and contamination due to
is lowerthan 1010 M inthe both fields for these redshift the stellar mass error are expected to be negligible.
⊙
bins. The number of galaxies in the mass-limited quies-
centsampleis130at0.5<z<1.0,70at1.0<z<1.5and 5. Results
50 at 1.5<z<2.5.
Itshouldbe notedthatourmulti-banddataotherthan The left panel of Figure 3 shows the stellar mass func-
K -bandarealsodeepenoughtoselectquiescentgalaxies tion(hereafter,SMF) ofquiescentgalaxiesselectedinthe
s
down to the limiting stellar mass mentioned above. For previoussectioninthedifferentredshiftbins. Forcompar-
example,evenquiescentobjectsatz∼2–2.5withM > ison,thoseforstar-forminggalaxieswithage/τ<4andall
star
1010 M (>1010.5 M for the wide field) whose stellar stellar mass-selected galaxies are also shown. We use the
⊙ ⊙
age is as old as the age of the universe are expected to be V method to calculate the comoving number density.
max
detected at least in H, 3.6µm, and 4.5µm bands at S/N K09calculatedtheV fortheK -bandmagnitudelimit
max s
> 2 in addition to the K -band detection (also in J band (K =23 for the wide field or K =24 for the deep field)
s s s
forz<∼ 2.3). Furthermore,deepHST/ACSdataaredeep by using the best-fit model template for each object (see
enough to detect at least quiescent objects with M = Section 3.3 in K09 for details).
star
1010M andwithstellarageof∼0.6–1.0GyrinV,i,and It is seen that the number density of quiescent galaxies
⊙
z bands at z<2.5. Therefore we can judge whether the gradually increases from 1.5 < z < 2.5 to 0.5 < z < 1.0
criteriaforthequiescentpopulationaresatisfiedornotfor in all mass ranges. The increase of the number density
galaxieswithM ∼1010M evenatz∼2–2.5. Fordusty seems to be nearlyindependent ofstellar mass over1010–
star ⊙
6 Kajisawa et al. [Vol. ,
age/tau > 6 age/tau < 4 all
10 -2 10 -2
3)
^
c
p
M
y (/ 10 -3 10 -3
sit
n
e
d
ber 10 -4 10 -4
m
u
n
g
n
ovi 10 -5 0.5<z<1.0 10 -5
m 1.0<z<1.5
o
C 1.5<z<2.5
10 -6 z=0.1 red z=0.1 blue z=0.1 all 10 -6
1010 1011 1012 1010 1011 1012 1010 1011 1012
Stellar mass (Msun) Stellar mass (Msun) Stellar mass (Msun)
Fig. 3. Theevolution ofthestellarmassfunction ofquiescent galaxies withage/τ >6(left), star-forminggalaxies withage/τ <4
(middle), and allstellarmass-selected galaxies (right, fromK09). Circles,pentagons, and squares show the resultscalculated with
the 1/Vmax formalism for galaxies at 0.5<z<1.0, 1.0<z<1.5, and 1.5<z<2.5, respectively. Error bars are based on the
Poissonstatistics. Solid,long-dashed,andshort-dashedlinesrepresenttheresultswiththeSTYmethodforgalaxiesat0.5<z<1.0,
1.0<z<1.5, and 1.5<z<2.5, respectively. For reference, the local SMF for all, red, and blue galaxies at z∼0.1 by Bell et al.
(2003)isshownasthedouble-dotted dashedlineineachpanel.
1011.5 M . The number density increases by a factor of other hand, the characteristic mass M∗ for the quiescent
⊙
∼3 from 1.0<z <1.5 to 0.5<z <1.0 and by a factor sample is similar with that for the star-forming galaxies,
of ∼10 from 1.5<z <2.5 to 0.5<z <1.0 in this mass while it could be slightly smaller than the star-forming
range. On the other hand, the number density of star- galaxies at 1.5<z<2.5. The M∗ for the both quiescent
forminggalaxieswithage/τ<4increasesonlybyafactor and star-forming samples is lower than that for all mass-
of∼1.9from1.0<z<1.5to0.5<z<1.0andbyafactor selected galaxies by a factor of ∼ 2. This may be due
of ∼2.8 from 1.5<z<2.5 to 0.5<z<1.0. The number to the effects of the combination of the (quiescent and
density evolution of quiescent galaxies is clearly stronger star-forming)massfunctionswithdifferentshapes(differ-
than that of star-forming galaxies. ent α). K09 found a marginal upturn around ∼1010 M
⊙
In orderto evaluate the shape of the SMF, we usedthe in the stellar mass function for the stellar mass-selected
STYmethod(Sandageetal.1979)assumingtheSchechter sample, which cannot be fitted very well with the single
function form (Schechter 1976) as in K09. We estimated Schechter function form. On the other hand, the SMF
the best-fit values of the Schechter parameters, namely, for the star-forming galaxies seems to have a very weak
the characteristic mass M∗ and the low-mass slope α for or no upturn, and is fitted with the Schechter function
both the quiescent sample and the star-forming galaxies. better than that for all mass-selected galaxies in all red-
For the star-forming galaxies, we used the same limiting shift bins. The contribution of the flatter mass function
stellar mass as a function of redshift as in K09, which is of quiescent galaxies at Mstar>∼1010 M⊙ could cause the
estimated by using the 90 percentile of U −V color at upturn in the SMF for all mass-selected galaxies, which
eachstellarmass forallstellarmass-selectedgalaxies(see has been observed at z<1 (e.g., Drory et al. 2009; Peng
Section 3.2 of K09 for details). Such limiting stellar mass etal.2010). Fittingthemassfunctionwithsuchaupturn
is probablysuitable (or conservative)for the star-forming withthesingleSchechterfunctionmayleadtotheslightly
galaxies, because these galaxies tend to have relatively higher M∗.
low stellar M/L ratios except for extremely dusty galax- We found no significant evolution of the shape of the
ies. Further details of estimating the Schechter parame- SMF for the quiescent sample. Although M∗ and α for
ters with the STY method are explained in Section 3.3 of these galaxies might become slightly lower and more pos-
K09. itive values respectively at 1.5<z<2.5, the large uncer-
Figure 4 shows the best-fit Schechter parameters and tainty prevents us from confirming this. The evolution of
their uncertainty in the M∗-α plane for each redshift bin. the shapeoftheSMFforthestar-forminggalaxiesissim-
The best-fit values andtheir uncertainty arealsosumma- ilar with that for all mass-selected galaxies; the low-mass
rizedinTable1. Forcomparison,wealsoshowthebest-fit slopebecomesslightlysteeperwithredshiftatz>1,while
M∗ and α for all stellar mass-selected galaxies estimated the characteristic mass does not evolve significantly.
by K09. The low-mass slope α for the quiescent sample Figure5showsthefractionofquiescentgalaxiesateach
is significantly flatter than those for the star-forming and stellarmassforthedifferentredshiftbins. Thefractionof
all stellar mass-selected samples over 0.5 < z < 2.5, al- quiescent galaxies increases with stellar mass over 1010–
though the uncertainty of α for these quiescent galaxies 1011.5 M in all redshift bins, though the uncertainty of
⊙
is relatively large due to the small number of the sample the fraction at >1011.5 M is very large due to the very
⊙
and the relatively high limiting stellar mass. On the small number of such massive quiescent galaxies in our
No. ] MOIRCS Deep Survey. X. 7
2 2
age/tau > 6 0.5<z<1.0 1.0<z<1.5 1.5<z<2.5
age/tau < 4
1.5 1.5
all mass-selected
1 1
0.5 0.5
0 0
-0.5 -0.5
-1 -1
-1.5 -1.5
-2 -2
1010 1011 1012 1010 1011 1012 1010 1011 1012
MM** ((MMssuunn)) M* (Msun) MM* * ((MMssuunn))
Fig. 4. TheSchechter parameters inM∗–α planeforthe quiescent (red), star-forming(blue), and allstellar mass-selected(green)
samples ineach redshiftbin. Crossesshow the best-fit values determined with the STY method. 1σ (solid) and 2σ (dashed) error
contoursarealsoshown.
Table 1. Best-fitM∗ andαobtainedwiththeSTYmethodforquiescentandstar-forminggalaxies
quiescent (age/τ >6) star-forming (age/τ <4) all mass-selected (from K09)
redshift log M∗(M ) α log M∗(M ) α log M∗(M ) α
10 ⊙ 10 ⊙ 10 ⊙
0.5<z<1.0 10.92+0.08 -0.01+0.23 10.93+0.07 -1.30+0.02 11.33+0.10 -1.26+0.03
−0.08 −0.19 −0.05 −0.03 −0.07 −0.03
1.0<z<1.5 10.91+0.12 -0.03+0.29 11.04+0.09 -1.49+0.04 11.48+0.16 -1.48+0.04
−0.10 −0.29 −0.09 −0.04 −0.13 −0.04
1.5<z<2.5 10.69+0.12 +0.61+0.49 11.08+0.09 -1.47+0.05 11.38+0.14 -1.52+0.06
−0.10 −0.47 −0.07 −0.06 −0.12 −0.06
sample (1–2 such galaxiesin each bin). This mass depen-
1
denceofthefractionofquiescentgalaxiesover0.5<z<2.5 0.5<z<1.0
is consistent with the above result that the shape of the 1.0<z<1.5
1.5<z<2.5
SMF for these galaxies is flatter than those for the star-
0.8
forming galaxies. On the other hand, the fraction of qui-
escent galaxies at each mass decreases with redshift (in-
creases with time) over 1010–1011.5 M . The quiescent
⊙ n
fractionofgalaxieswithMstar=1011–1011.5 M⊙ increases ctio 0.6
a
wfrohmile∼th2a5t%ofatga1l.a5x<ieszw<it2h.5Mto ∼=501%01a0–t100.150.<5 zM<1i.n0-, ent fr z=0.1 red fraction
star ⊙ c
creases from <∼ 5% to ∼ 15% in the same redshift range. uies 0.4
This is also consistent with the stronger evolution in the Q
numberdensityofquiescentgalaxiesthanthatofthestar-
forming galaxies mentioned above.
0.2
6. Discussion
6.1. Comparison with other studies 0
1010 1011 1012
We have investigated the evolution of the number den- Stellar mass (Msun)
sity andthe fractionof quiescentgalaxiesas a function of Fig. 5. Fractionofquiescentgalaxiesasafunctionofstellar
stellarmassat0.5<z<2.5,usingtheverydeepNIRdata mass. Circles, pentagons, and squares represent galaxies at
of the MODS and the multi-wavelength ancillary data of 0.5<z<1.0, 1.0<z<1.5, and 1.5<z<2.5, respectively.
the GOODS. Here we compare our results with previous ErrorbarsarebasedonthePoissonstatistics. Forreference,
theredfractionforgalaxiesatz∼0.1fromBelletal.(2003)
studies in other general fields.
isshownasthedouble-dotted dashedline.
Verganietal.(2008)investigatedtheevolutionofearly-
type galaxies selected by spectral classification with the
numberdensityofearly-typegalaxiesincreasesbyafactor
Dn4000indexuptoz∼1.3,usingtheVVDSspectroscopic of ∼ 3 between 1.0<z<1.3 and 0.7<z<1.0,while that
sample (IAB <24). They found that the low-mass slope of late-type galaxies increases by a factor of ∼ 2 in the
oftheSMFforearly-typegalaxiesisflatter(∆α∼1)than
same redshift range. Our results seen in the 0.5<z<1.0
those of star-forming and overall galaxy population. The
and 1.0<z<1.5 bins are consistent with these results of
8 Kajisawa et al. [Vol. ,
1010 1011 1012 1010 1011 1012 1010 1011 1012
age/tau > 6 0.5<z<1.0 age/tau > 5 age/tau > 4
10 -2 1.0<z<1.5 10 -2
3) 1.5<z<2.5
^
c
p
M
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sit
n
e
d
ber 10 -4 10 -4
m
u
n
g
n
ovi 10 -5 10 -5
m
o
C
10 -6 10 -6
0.8 age/tau > 6 age/tau > 5 age/tau > 4 0.8
3) 0.7 0.7
^
c
p
M 0.6 0.5<z<1.0 0.6
sity (/ 0.5 11..05<<zz<<12..55 0.5
n
e
d
er 0.4 0.4
b
m
u
n 0.3 0.3
g
n
vi
o 0.2 0.2
m
o
C
0.1 0.1
0 0
1010 1011 1012 1010 1011 1012 1010 1011 1012
Stellar mass (Msun) Stellar mass (Msun) Stellar mass (Msun)
Fig. 6. Numberdensityandfractionofquiescent galaxiesasafunctionofstellarmassforthedifferentcriteriaofage/τ >6(left),
age/τ>5(middle),andage/τ>4(right). SymbolsarethesameasFigure5.
Vergani et al. (2008). the SED fitting, and the sample selection in this study
Ilbertetal.(2010)alsostudiedtheevolutionoftheSMF are similar with those in Fontana et al. (2009), a direct
ofquiescentgalaxiesselectedbyacolorselectionwiththe comparison is possible. They found that the fraction of
rest-frame NUV −r′ and r′−J up to z ∼2, using the the “redanddead”galaxiesgraduallydecreaseswithred-
Spitzer/IRAC3.6µm-selectedsample(m <23.9)inthe shift,andFigure5inFontanaetal.(2009)showsthatthe
AB
COSMOS 2 deg2 field. Although their sample reach only fractionis∼50%atz∼0.7,∼40%atz∼1.2,and∼20%
to ∼ 1011 M⊙ at z >∼ 1.5, they estimated the low-mass at z ∼2. If we limit our quiescent sample to those with
slope ofthe SMFfor quiescentgalaxiesupto z∼1.2,and M >7×1010 M as in Fontana et al. (2009), the frac-
star ⊙
foundthatthelow-massslopeforthesegalaxiesgradually tion of quiescent galaxies becomes 52% at 0.5<z <1.0,
flatten with redshift and becomes α∼0 at z ∼0.8. The 37% at 1.0<z <1.5, and 29% at 1.5<z <2.5. We es-
number density of these quiescent galaxies increases by a timated the cosmic variance for these galaxies with the
factorof∼3fromz∼1.2toz∼0.7andbyafactorof∼10 methodintroducedbyMosteretal.(2010),usingtheclus-
fromz∼2toz∼0.7. Suchevolutionofquiescentgalaxies tering strength of r ∼ 10 Mpc for quiescent galaxies at
0
is consistentwith ourresults seen in the previous section. 1<∼z<∼2 observed by Williams et al. (2009) and Hartley
We found that the flat low-mass slope for these galaxies et al. (2010). The correlation length of r ∼ 10 Mpc cor-
0
continuesuptoz∼2. Ilbertetal.(2010)alsopointedout responds to the galaxy bias of b ∼ 2 at z∼0.75, b ∼ 3
g g
that the evolution of the SMF for star-forming galaxies at z∼1.25, and b ∼ 4.5 at z∼2. The resulting relative
g
over 0.2<z <2 is relatively weak and that the number cosmic variance for our quiescent sample is σ ∼ 0.24 at
v
density of star-forming galaxies increases by a factor of 0.5<z<1.0, σ ∼ 0.30 at 1.0<z<1.5, and σ ∼ 0.26 at
v v
∼2.5 between z∼2 and z∼0.9. The star-forminggalax- 1.5<z<2.5. Ifwetakeaccountofthecosmicvarianceand
ies with age/τ < 4 in our sample also show the similar Poisson errors, the quiescent fractions in this study and
evolution (the middle panel of Figure 3). Fontana et al. (2009) agree well within the uncertainty.
Fontana et al. (2009) investigated the evolution of the On the other hand, Grazian et al. (2007)presented the
fractionof“redanddead”galaxieswithage/τ>6among SMFforgalaxieswithage/τ>4andthosewithage/τ<4
massive galaxies with M >7×1010 M up to z∼3.5, at 1.4 < z < 2.5. In order to compare our results di-
star ⊙
using the GOODS-MUSIC sample in the GOODS-South rectly with those in Grazian et al. (2007) and to check
field. Since the survey field layout, the filter set used in the effect of changing the selection criterion to our re-
No. ] MOIRCS Deep Survey. X. 9
sults, we estimated the SMF and the fraction of galaxies star-forming population including newly increased galax-
with age/τ >4 and 5 as a function of stellar mass, and ies at a given stellar mass range. For simplicity, other
compared them with those of galaxies with age/τ >6 in processes affecting this fraction such as the hierarchical
Figure 6. Although the overalltrenddoes notchangesig- merging is ignored. As a result, we expect that 7%, 18%
nificantlywhenthecriteriaofage/τ>5and4areused,the and 29% of the star-forming galaxies with M =1010–
star
low-massslopebecomesslightlysteeperandtheevolution 1010.5 M , 1010.5–1011 M and 1011–1011.5 M ceased
⊙ ⊙ ⊙
of the number density becomes weaker as the selection star formation between 1.5<z <2.5 and 1.0<z <1.5,
threshold is loosened. This may be due to the gradual respectively, and 10%, 23% and 41% of the star-forming
increase ofthe contaminationfrom galaxieswith star for- galaxies with the same stellar mass ranges became qui-
mation activities. For example, the fraction of massive escent between 1.0<z<1.5 and 0.5<z<1.0. It seems
quiescent galaxies with M = 1011–1011.5 M already thatmoremassivestar-forminggalaxiestendtoceasestar
star ⊙
reaches to ∼ 50% at z ∼2 in the case with age/τ >4. formation preferentially at 1<∼z <∼2. Recently, Peng et
This is consistent with the similar number densities of al. (2010) reported that such a mass-dependent quench-
galaxieswithage/τ>4andage/τ<4atM ∼1011 M ing processcould explainno evolutionof the shape ofthe
star ⊙
seen in Figure 8 of Grazian et al. (2007). SMF for star-forming galaxies and the flatter low-mass
In summary, the shape of the SMF of quiescent galax- slopeandthesimilarcharacteristicmassforpassivegalax-
ies at z ∼ 1 and the number density evolution of mas- ies at z<1. Such “mass quenching” might work even at
sive quiescent galaxies with Mstar>∼1011 M⊙ at 1<∼z<∼2 1 <∼z <∼2, when the rapid increase of the number den-
seenin the previoussectionare consistentwith the previ- sity of quiescent galaxies was observed. The character-
ous studies in other generalfields. Thus, the field-to-field istic mass M∗ of the SMF for the star-forming galaxies
variance does not seem to significantly affect our results. with age/τ <4 in our sample shows no significant evo-
Furthermore, in this paper, we found that the evolution lution at the redshift range (middle panel of Figure 3),
ofthenumberdensityofquiescentgalaxieswithrelatively which seems to be also consistent with the prediction by
low stellar mass (∼1010–1011 M ) is similar with that of Peng et al. (2010).
⊙
massiveones,andthattheflatlow-massslopeofquiescent K09 found the mass-dependent evolution of the num-
galaxies continues up to z∼2. ber density for all stellar mass-selected galaxies at z >∼
1–1.5. The number density of galaxies with M ∼1011
6.2. Quenching of star formation and mass-dependent star
M more strongly evolves than that for galaxies with
evolution of galaxies ⊙
M ∼ 1010 M (right panel of Figure 3). On the
star ⊙
In Section 5, we found that the number density of qui- other hand, the increase of the number density of qui-
escentgalaxieswithage/τ>6increasesbyafactorof∼3 escent galaxies is nearly independent of stellar mass as
from 1.0 < z < 1.5 to 0.5 < z < 1.0 and by a factor of discussed above. The mass dependence of the evolution
∼10from1.5<z<2.5to0.5<z<1.0overM =1010– forstar-forminggalaxiesisalsoratherweak(middlepanel
star
1011.5 M . We note that the number density of galaxies of Figure 3). The mass-dependent evolution for all popu-
⊙
at 0.5<z <1.0 in our sample could be slightly overes- lation could be explained by the differences between the
timated due to the known large-scale structures around quiescent and star-forming populations in the strength of
the HDF-North (K09; Wirth et al. 2004). Nevertheless, theevolutionofthenumberdensityandintheshapeofthe
the rapid increase of the number of quiescent galaxies in SMF. The quiescent population has the flatter low-mass
the universe seems to occur at 1<∼z <∼2. Furthermore, slope of the SMF and shows the stronger evolutionof the
the evolution of the number density is nearly indepen- numberdensity thanstar-forminggalaxies. Thereforethe
dent of stellar mass. The low-mass slope of the SMF for rapidincreaseofquiescentgalaxiescontributesstronglyto
these quiescent galaxies is significantly flatter than those thenumberdensityevolutionforgalaxieswith∼1011M ,
⊙
forstar-formingandallstellarmass-selectedgalaxiesover whiletheircontributionisnegligibleforthosewith∼1010
0.5<z<2.5. The fraction of quiescent galaxies for mas- M becauseoftheratherlowfractionofthesegalaxies. In
⊙
sive galaxies is higher than that for low-mass galaxies in this context, the more rapid increase of the number den-
the redshift range. Here we consider that the increase sity of ∼ M∗ galaxies than lower-mass galaxies at z>∼ 1–
of quiescent galaxies is caused by the cessation of star 1.5foundinK09mightbeexplainedbyamass-dependent
formation in some fraction of star-forming galaxies as in quenchingmechanismwhichpreferentiallyceasesstarfor-
previous studies at z <1 (e.g., Bell et al. 2007; Peng et mation in these massive galaxies.
al. 2010). Since the number density of quiescent galax- In Yamada et al. (2009), we found that X-ray selected
ies rapidly increases by a factor of ∼ 3 between z ∼ 2 AGNs at 2 < z < 4 are preferentially associated with
and z∼1.25 (∼1.6 Gyr) and by a factor of ∼3 between more massive galaxies, and that ∼ 30% of galaxies with
z∼1.25 and z∼0.75 (∼2.3 Gyr), the quenching of star M >1011 M show the AGN activity with the X-ray
star ⊙
formationisexpectedtooccurpreferentiallyinmoremas- luminosity largerthan∼1042 ergs−1. Brusaetal.(2009)
sivegalaxiesover1<∼z<∼2inordertomaintainthe mass- also found a similar mass-dependence of the AGN frac-
dependenceofthefractionofquiescentgalaxiesmentioned tionat1<∼z<∼4. The AGNfeedbackmaybe relatedwith
above. We estimated the quenching rate as a function of the mass-dependent star formation quenching. Bundy et
stellarmassbycalculatingthe fractionofnewly emerging al. (2008) investigated the fractions of red galaxies and
quiescentgalaxiesbetweentheredshiftbinsrelativetothe X-ray selected AGNs in stellar mass-selected galaxies at
10 Kajisawa et al. [Vol. ,
1 1
0.5<z<1.0 1.0<z<1.5 1.5<z<2.5
0.9 0.9
median quiescent
median age/rau < 4’
0.8 0.8
c)
e
cs 0.7 0.7
ar
s ( 0.6 0.6
u
di
a
ht r 0.5 0.5
g
alf-li 0.4 0.4
H
0.3 0.3
0.2 age/tau > 6 0.2
specscopic stars age/tau > 6 MIPS 24um source
0.1 0.1
16 17 18 19 20 21 22 23 16 17 18 19 20 21 22 23 16 17 18 19 20 21 22 23 24
Ks (Vega) Ks (Vega) Ks (Vega)
Fig. 7. Half light radius in the observed Ks band vs. Ks-band magnitude for Ks-selected galaxies in each redshift bin. Gray
squares represent the mass-selected (Mstar>1010 M⊙) quiescent galaxies with age/τ >6. Larger blue squares show MIPS 24µm
sourceswithage/τ>6. Solidanddashedlinesrepresentthemedianvaluesforthequiescentsampleandstar-forminggalaxieswith
age/τ<4ateach magnitude, respectively. It shouldbenoted that theKs-bandhalflightradiiaremeasuredonthemosaicimage
wherethe PSFvaries amongthe different pointings of MOIRCS(FWHM = 0.45–0.60 arcsec, seeKajisawaet al.2011 for details).
Forreference,spectroscopicallyconfirmedstarsareshownasgreentrianglesineachpanel.
0.4<z<1.4 as a function of stellar mass to compare the (approximately stellar mass), while it is observed at the
star formation quenching rate with the AGN triggering same redshift range that the clustering strength of the
rate. They found that the mass-dependence and normal- overall galaxy population is correlated with stellar mass
ization of the both rates agree well, although the esti- (e.g.,Ichikawaetal.2007;Foucaudetal.2010;Wakeetal.
mated normalization of the AGN triggering rate depends 2010). Theremaybeacriticalhalomassabovewhichgas
strongly on the assumed AGN lifetime. In order to com- cooling and star formation are shut down, for example,
pareourresultswiththestarformationquenchingratein due to the shock heating (e.g., Dekel & Birnboim 2006;
Bundy et al. (2008), we divided the quenching rates cal- Cattaneoetal.2006). Inthis scenario,the (stellar)mass-
culated above by the time intervals between the redshift dependentquenchingofstarformationcouldbeexplained
bins. The results are 4% Gyr−1, 10% Gyr−1, and 18% ifmassivestar-forminggalaxiestendtoinhabitmoremas-
Gyr−1 between z ∼ 1.25 and z ∼ 0.75 for galaxies with sive dark matter halos than low-mass star-forming ones,
1010–1010.5 M , 1010.5–1011 M ,and1011–1011.5 M ,re- which is naturally predicted by theoretical models where
⊙ ⊙ ⊙
spectively, and 4% Gyr−1, 11% Gyr−1, and 18% Gyr−1 the star formation activity is simply regulated by the gas
between z ∼ 2 and z ∼ 1.25 for the same mass ranges. (anddarkmatter)accretionrateinthe halo(e.g.,Bouch´e
Both the mass-dependence and normalization are consis- et al. 2010). In this context, it is interesting to investi-
tent with the results of Bundy et al. (2008),although the gate the mass-dependence of the clustering strength for
selection of quiescent galaxies is different between Bundy quiescent and star-forming samples at 1<∼z<∼2 more in-
et al. (2008) (rest-frame U −B color) and this study tensively.
(age/τ from the SED fitting). Our results may also sug- The quenching of star formation may be also related
gest that the star formationquenching rate per unit time with the surface stellar mass density of galaxies. Several
at a given stellar mass seems to be roughly constant over studies at low and high redshifts reported that the rest-
1<∼z<∼2. Ina future work,wewillstudy the evolutionof frame color or specific star formation rate of galaxies are
the AGN hosts in the MODS field at 1<∼z<∼2 and com- stronglycorrelatedwith their surface stellar mass density
pare it with the star formation quenching rate estimated (e.g., Kauffmann et al. 2006; Franx et al. 2008; Williams
here. et al. 2010). Most galaxies with the surface mass density
On the other hand, several studies reported that the higher than a threshold value have red color and low star
clustering of quiescent galaxies is stronger than that of formation activities at each redshift. The threshold sur-
star-forming galaxies even at z ∼2 (Hartley et al. 2008; face density seems to increase with redshift gradually. At
Hartley et al. 2010; Williams et al. 2009), which implies z∼2, many studies have found massive quiescent galax-
thatquiescentgalaxiestendtoinhabitmoremassivedark ies with much smaller sizes (e.g., Re ∼ 1 kpc) than the
matterhaloswhentheirnumberdensityrapidlyincreases. present massive ellipticals (Daddi et al. 2005; Zirm et
Therefore the dark matter halo mass may play some role al. 2007; Longhetti et al. 2007; Cimatti et al. 2008; van
inthe quenching ofstarformation. Williams etal.(2009) Dokkum et al. 2008; Damjanov et al. 2009; Ryan et al.
and Hartley et al. (2010) pointed out the possibility that 2010). Quiescentgalaxiesin oursample also tend to have
theclusteringstrengthofquiescentgalaxiesat1<∼z<∼2is small half light radii in the observed Ks band relative
nearlyindependentoftheirrest-frameK-bandluminosity tostar-forminggalaxieswithsimilarKs-bandmagnitudes