Evolution of the Blue Luminosity-to-Baryon Mass Ratio of Clusters of Galaxies

20 Pages·0.25 MB·English

by  Kazuhiro Shimasaku

Evolution of the Blue Luminosity-to-Baryon Mass Ratio of Clusters of
Galaxies
Kazuhiro Shimasaku
Department of Astronomy, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113
Research Center for the Early Universe, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113
E-mail: [email protected]
0 (Received 1999 September1; accepted 1999 September1)
0
Abstract
0
2 Wederivetheratiooftotalblueluminositytototalbaryonmass,LB/Mb,formassive(Mgas attheAbell
n radiusis≥1×1013h−2.5M⊙•)clustersofgalaxiesuptoz ≃1fromtheliterature. Twenty-twoclustersinour
a sample are at z >0.1. Assuming that the relative mix of hot gas and galaxies in clusters does not change
J
during cluster evolution, we use LB/Mb to probe the star formation history of the galaxy population as a
1
3 whole in clusters. We find that LB/Mb of clusters increases with redshift from LB/Mb = 0.024(LB/M)⊙
at z =0 to ≃0.06(LB/M)⊙ at z =1, indicating a factor of 2−3 brightening (we assume H0 =70 km s−1
1 Mpc−1). Thisamountofbrighteningis almostidenticalto the brighteningoftheM/LB ratioofearly-type
v galaxies in clusters at 0.02 ≤ z ≤ 0.83 reported by van Dokkum et al. (1998). We compare the observed
1 brightening of LB/Mb with luminosity evolution models for the galaxy population as a whole, changing
2
the e-folding time of star formation τ by 0.1 ≤ τ ≤ 5 Gyr and the formation redshift z by 2 ≤ z < ∞.
5 F F
We find that τ = 0.1 Gyr ‘single burst’ models with z ≥ 3 and τ = 5 Gyr ‘disk’ models with arbitrary
1 F
0 zF are consistent with the observed brightening, while models with τ = 1−2 Gyr tend to predict too
0 steep brightening. We also derive the ratio of blue luminosity density to baryon density for field galaxies,
0 adopting Ωbh2 =0.02, and find that blue luminosity per unit baryon is similar in clusters and in fields up
/
h to z ≃1 within the observational uncertainties.
p Key words: Galaxies: clusters of — Galaxies: photometry — Galaxies: X-rays
-
o
r
t
s 1. Introduction In this paper, we study the global (or average) star
a
formationhistory of the galaxypopulation as a whole in
:
v clusters of galaxies. To do so, we derive the ratio of to-
Clusters of galaxies are suitable objects for study-
Xi ing the evolution of galaxies in the dense environments. tal blue luminosity (LB) to total baryon mass (Mb) for
r Recent observations based on large telescopes including clusters of galaxies up to z ≃ 1. The quantity LB/Mb,
a including its evolution, should reflect when (and what
Hubble Space Telescope (HST) have been revealing the
fraction of) baryons (= primordial gas) in clusters are
morphology-dependent evolution of galaxies in clusters
converted into stars. Similar studies have been done for
up to z ∼ 1. The evolution of elliptical and S0 galaxies
has been found to be reproduced well by the so-called fieldgalaxies. Thegloballuminositydensityl[L⊙•Mpc−3]
invariouswavelengthshasbeenmeasuredbymanywork-
single burst model (e.g., Schade, Barrientos,Lo´pez-Cruz
ersonthebasisofobservationsoffieldgalaxies(e.g.,Lilly
1997;Ellisetal. 1997;Kodamaetal. 1998;vanDokkum
et al. 1996; Madau, Pozzetti, Dickinson 1998). If the
et al. 1998). Schade et al. (1996) found that spiral
galaxiesinclustersbrightenby∼1magwithredshiftup densityparameterofbaryons(Ωb)isgiven,onecancom-
putefroml themeanluminosityperunitbaryonmassin
to z ≃ 0.5, and that this brightening is similar to that
fields (l/ρ ). We will derive B-band l/ρ in fields up to
of field spiral galaxies in the same redshift range (see, b b
however, Vogt et al. 1997 and Lilly et al. 1998 for the z ≃1 and compare it with LB/Mb of clusters.
evolution of field spiral galaxies). Morphological studies The structure of this paper is as follows. In section 2,
based on HST imaging suggest that a transition from we present the data of nearby and distant clusters used
spiral galaxies to S0 galaxies may have occurred in clus- to derive LB/Mb. We compare LB/Mb with predictions
ters since z ∼ 0.5 (Dressler et al. 1997). An attempt of of simple luminosity evolution models in section 3. A
measuring the star formation rate of individual galaxies comparison with l/ρb in fields is also given in section 3.
hasalsostarted(e.g.,Baloghetal. 1998;Poggiantietal. We summarize our conclusions in section 4.
1999). We adopt h = 0.7, Ω = 0.2, and λ = 0 throughout
0 0
No. 0] Luminosity Evolution of Galaxies in Clusters 1
thispaperunlessotherwisestated,wherehistheHubble Figure 2 shows L /M as a function of the frac-
V gas
constantinunitsof100kms−1 Mpc−1,Ω isthedensity tion of luminosity emitted from elliptical and S0 galax-
0
parameter, and λ is the cosmological constant. Under ies to the total luminosity for 18 clusters with type
0
this assumption, the present age of the universe is 11.8 mix data. It is found that L /M is constant for
V gas
Gyr. The value h = 0.7 is taken from recent determi- Mgas ≥ 1 × 1013h−2.5M⊙• clusters irrespective of type
nations of H (e.g., Freedman 1999). To adopt different mix. This implies that L /M is not sensitive to the
0 V gas
values for Ω and λ in the observationally reasonable changeinthepopulationsofgalaxiesformassiveclusters.
0 0
ranges of 0.2 ≤ Ω0 ≤ 1 and 0 ≤ λ0 ≤ 0.8 does not Figures 1 and 2 demonstrate that the dependence of
significantly change our results. L /M on L (or on M ) is much weak for massive
V gas V gas
clusters. This is also supported by Renzini (1997) who
found that rich clusters have a fairly constant M to
2. Data gas
B-band luminosity ratio. The reason why poor clusters
have a relatively higher L /M value is not clear, but
Wedivideclustersofgalaxiesintonearbyclusters(z ≤ V gas
apossibleexplanationisthatasignificantfractionofhot
0.1) and distant clusters (z > 0.1). We assume that
gasinpoorclusters hasescapedfromthe clusters during
evolutionary effects are negligible for z ≤ 0.1 clusters
clusterevolutionowingto theirshallowgravitationalpo-
and regard their properties as those of the present-day
tentials, resulting in a higher L /M value (e.g., Ren-
clusters. V gas
zini 1997).
We adopt the B band to measure the luminosity of
galaxies,andthink thatit is the best compromise. Clus- In any case, in what follows we assume that LB/Mb
ter luminosities have been measured mainly in optical is constant for Mgas ≥1×1013h−2.5M⊙• clusters and use
bandpassessuchasB,V,orR. Amongtheopticalband- themtoderivetheaverageLB/Mbofnearbyclusters. We
willseeinthenextsubsectionthatallthedistantclusters
passes,B is mostsensitiveto the luminosityevolutionof
galaxies. Though ultraviolet wavelengths such as U are adoptedinthispaperhaveMgas ≥1×1013h−2.5M⊙•. This
much better for measuring star formation, data in such promisesafaircomparisonofLB/Mbbetweennearbyand
distant clusters.
wavelengthsare very few. As for field galaxies,there are
alotofmeasurementsofluminositydensityoffieldgalax- For Arnaud et al.’s (1992) clusters which have mor-
ies in the B band, which enables us to compare LB/Mb phologicaltypemix,wecomputetotalB-bandluminosity
with lB/ρb. (LB)fromLV usingB−V =0.96(E),0.85(S0),and0.68
(S) (see Fukugita, Shimasaku, Ichikawa 1995). For clus-
terswithouttype mixdata,weadoptB−V =0.85±0.2
2.1. Nearby Clusters
as the average color of galaxies. We compute baryon
We use the sample of nearby clusters given in Arnaud mass Mb from gas mass Mgas using:
etal. (1992)toderiveLB/Mbofthepresent-dayclusters.
Arnaud et al. (1992)compiled a sample of 27 clusters of Mb =Mgas+(M/LB)⋆LB, (1)
galaxies, where total V-band luminosity (L ), morpho-
V
logicaltype mix ofgalaxies(E,S0, andS), and gasmass where (M/LB)⋆ is the mean mass-to-luminosity ratio of
within a radius of 1.5h−1 Mpc (the Abell radius) are the stellar population in galaxies. We neglect atomic
given. Morphological type mix is available for 18 clus- and molecular gas in galaxies. We adopt (M/LB)⋆ =
ters. (6 ± 3)h(M/LB)⊙, which roughly covers the mass-to-
Arnaud et al. (1992) found in their clusters a strong luminosityratioofellipticalgalaxies(vanderMarel1991;
dependence of L /M on L : L /M ∝ L−0.9. If Pizzella et al. 1997) and of spiral disks (Bahcall 1984;
V gas V V gas V
such a strong dependence holds in the whole mass range Broeils,Couteau1997). The errorsinLB/Mb contain(i)
of clusters, it would very much complicate a compari- errorsinLV whicharegiveninArnaudetal. (1992),(ii)
son of LB/Mb among clusters having different masses. errorsin the mean B−V (only for clusterswithout type
Thus, we first examine for what clusters such a strong mix data), and (iii) errors in (M/LB)⋆ in equation (1).
dependence exists. Figure 1 plots L against M for Since most of the baryons in clusters are in form of hot
V gas
allthe clusters in Arnaudet al. (1992). The dependence gas, the error in Mb due to (iii) is only about 5 %.
found in Arnaud et al. (1992) is shown as the dashed Figure 3 presents LB/Mb as a function of Mgas. The
line. The solid line, on the other hand, is a regression filled and open circles indicate Arnaud et al.’s (1992)
line between LV and Mgas for Mgas ≥ 1×1013h−2.5M⊙• clusters with and without type mix data, respectively.
clusters, L ∝ M0.8. This is close to a linear regres- As seen in figure 1, a clear trend is seen in figure 3 that
V gas
sion, i.e., a constant LV/Mgas, indicated as the dotted clusterswithMgas∼<1×1013h−2.5M⊙• havesystematically
line. Thus,the strongdependence ofLV/Mgas onLV (or higher LB/Mb. To derive LB/Mb of nearby clusters, we
equivalently on Mgas) found by Arnaud et al. (1992) is not only remove clusters with Mgas < 1×1013h−2.5M⊙•
probably due to the inclusion of less massive clusters. but also remove clusters without type mix data because
2 K. Shimasaku [Vol. 00,
the uncertainties in L of these clusters are on the aver- M and L are given in Squires et al. (1997). L is
B gas V B
agelargerthanthoseforclustershavingtypemix(Toin- computed assuming rest-frame B−V =0.8±0.2.
clude the clusters without type mix data hardly changes
(iv) CL0500-24(z =0.32)
the result, though).
M is taken from Schindler and Wambsganss (1997).
Twelve out of the 21 clusters with M ≥ 1 × gas
gas L is givenin Infante et al. (1994), and L is computed
1013h−2.5M⊙• havetypemixdata,andtheirmeanLB/Mb usVingrest-frameB−V =0.85(ThemeanaBpparentcolor
for h=0.7 is
of this cluster, V −I = 1.8, reported by Infante et al.
1994 corresponds to B−V =0.85 in the rest frame).
LB/Mb =(0.024±0.004)(LB/M)⊙, (2)
(v) CL0939+47(z =0.41)
which we regard as the representative value for the
Schindler et al. (1998) found two substructures in this
present-day clusters. The contribution from elliptical
cluster,implyingthatthis clusterhasnotbeenvirialized
and S0 galaxies to total B luminosity is on the aver-
yet. M andL adoptedherearethesumofthevalues
gas B
age (69±13)% for the 12 clusters, implying that these
forthetwosubstructuresgiveninSchindleretal. (1998).
clusters are dominated by early-type galaxies (See figure
Dressler et al. (1997)reported the fraction in number of
2). ClusterswhichhaveMgas <1×1013h−2.5M⊙• tendto elliptical and S0 galaxies to be 55%.
be less dominated by early-type galaxies. For example,
theVirgocluster,whichhasMgas =0.44×1013h−2.5M⊙•, (vi) RXJ1347.5-1145(z =0.45)
has LB(E+S0)/LB(tot)=45%. Mgas is taken from Sahu et al. (1998) and LB is com-
putedfromM andM /L giveninFischerandTyson
Forthe12clusters,weestimatetheratioofstellarmass tot tot B
to baryon mass to be M⋆/Mb = 0.10±0.05 (h = 0.7), (1997), where Mtot is the total mass of a cluster.
using (M/LB)⋆ = (6±3)h(M/LB)⊙. This means that (vii) CL0016+16(z =0.55)
only ∼10 % of baryons have been used to form stars to
M is taken from Neumann and B¨ohringer (1997) and
gas
date in rich clusters.
L is computed from the r-band total luminosity given
B
in Carlberg et al. (1996) using rest-frame B−r = 0.97,
2.2. Distant Clusters which corresponds to the observed g −r color of 1.455
(Carlberg et al. 1996). Dressler et al. (1997) reported
Searchingfortotalluminosityandgasmassdataofdis-
the fractionin number of elliptical and S0 galaxies to be
tantclustersintheliterature,wetake22clusters,among
73%.
whichthirteenarefromthe CNOC clustersample(Carl-
bergetal. 1996;Lewisetal. 1999). Wedonotapplyany (viii) AXJ2019+1127(z =1.01)
selection criterion to compile our sample. Data of these M is taken fromHattoriet al. (1997),and L is com-
gas B
clusters are given in table 1. All the clusters have rest- putedfromL (Benitezetal. 1998)assumingrest-frame
V
frame luminosity (either B, V, or r band) and gas mass B−V =0.7±0.3,whichroughlycoverstheexpectedcol-
measurements. For a cluster whose rest-frame luminos- ors of elliptical and spiral galaxies at z =1.
ity is in the V orr band, we use anobservedorassumed
CNOC Clusters
colorto convertthe luminosity to the rest-frameB-band
Carlberg et al. (1996) give rest-frame r-band luminosity
luminosity.
at the virial radius for 16 clusters at 0.17 < z < 0.55.
When computing Mb from Mgas by Mb =Mgas+M⋆, Out of them, 14 clusters have gas mass measurements
weuseM⋆/Mb =0.10(h=0.7)whichisthevalueforthe
(figure 4 of Lewis et al. 1999). Since the maximum ra-
nearbyclusters. DistantclustersmayhavelowerM⋆/Mb dius atwhichgas massis plotted, r =600h−1 kpc for all
values than the nearby clusters, but the uncertainties in
the clusters,is smallerthanthe virialradii,wederivefor
LB/Mb due to this effect are at most ≃ 10%, which is each cluster the r-band luminosity at 600h−1 kpc from
negligible for our discussion. Below are the references to
the valueatthe virialradiusassumingthatluminosityis
the nine clusters and the CNOC clusters.
proportional to radius. The ratio of 600h−1 kpc to the
(i) Abell 1413 (z =0.14) and Abell 1689 (z =0.18) virialradiiof14clustersis onthe average0.48,implying
These two clusters are taken from Cirimele, Nesci, that a large factor of conversion is necessary. For each
Tr`evese’s(1997)sample. Thissampleconsistsof12clus- cluster, we then transform the rest-frame r-band lumi-
ters with z <0.2 for which M and L within a radius nosityintotherest-frameB-bandluminosityonthebasis
gas V
of 0.75h−1 Mpc are given. We calculate L assuming of the observed g−r color given in figure 5 of Carlberg
B
rest-frame B−V =0.85±0.2. et al. (1996). CL0016+16 is among the 14 clusters. As
seen in (vii), we have adopted for gas mass of this clus-
(ii) Abell 2218 (z =0.18)
ter the measurement given in Neumann and B¨ohringer
We adopt M and L from Squires et al. (1996).
gas B (1997)because their value is at r =1.67h−1 Mpc, which
(iii) Abell 2163 (z =0.20) is verycloseto the virialradiuswherer-band luminosity
No. 0] Luminosity Evolution of Galaxies in Clusters 3
is measured. The numberofthe CNOCclusters adopted CL0939+47 and CL0016+16) are the CNOC clusters.
here is thus 13. Linesindicatemodelpredictions,whichwillbe discussed
cluTstheersraadnidi umseodstfoofrtmheemasuarriengsmLaBl/leMrbthdainffetrheamAobneglltrhae- iwnitthhezn,exfrtomsubLseBc/tMionb.=It i0s.0fo2u4n(LdBt/hMat)L⊙B/aMt bzin=cre0asteos
dius (See table 1). Unfortunately, it is not clear whether ≃ 0.06(LB/M)⊙ at z = 1, though the error in each dis-
tant cluster is fairly large. CL0939+47 deviates largely
LB/Mb measured at these small radii represent global from this trend. We suspect, however,that the observed
values, i.e., values at the Abell radius, though there is
acosntsutdanytthbaettwteheenLaB/rMadbiuosfotfhe≃C0o.m4ha−c1luMsteprcisanndeatrhlye LvaBlu/Me,bboecfatuhsisectlhuestoebrsdeorveesdnoLtBr/eMprbesisentthethvearlueael,fogrlotbwaol
substructureswhoseradiiareonlyr =0.14h−1Mpc. The
Abell radius (Taguchi et al. 1999). In this paper, we
assume that the values of LB/Mb derived here represent TChNiOs Cmacylusrteeflrescsteeumncetortahianvteieas ldauregetroscaatltaerrgeinfaLcBto/Mr obf.
the globalvalues of individual clusters (For CL0939+47,
the conversion of optical luminosity from the value at
see, however, the next section).
the virial radius to that at r =600h−1 kpc.
Figure 4 plots L againstM for the 12nearby clus-
B gas Therearetwooppositeexplanationsfortheincreasein
ters and the 22 distant clusters. Both L and M are
values at r = 1.5h−1 Mpc, which are deBrived frogmasraw LB/Mb with redshift. One is the brightening of LB due
tothe luminosityevolutionofthegalaxypopulationasa
values on the assumption that L (r) and M (r) are
B gas whole. Notethatgalaxymergings,eveniftheyoccur,do
proportional to radius r. The thick solid line indicates
not change the total mass of the galaxy population and
the best fit of a linear law, L ∝ M , to the nearby
B gas thatstarformationwhichcouldbetriggeredbymergings
clusters. The thin solid line and the dotted line corre-
can be treated in the framework of the ‘pure’ luminosity
spond to a similar fit to distant clusters at 0.1<z ≤0.4
evolution of the galaxy population. The other explana-
and 0.4 < z ≤ 0.7, respectively. It is found that the
tion is that the mass of baryons (≃ hot gas) per galaxy
average B luminosity at a given gas mass increases with
decreaseswithredshift. However,thisexplanationseems
redshift. This should reflect some evolution of L /M .
B gas to be less plausible, because no significant evolution has
Note that the range of gas mass is similar between the
been observationally found for the global properties of
nearby and distant clusters: there is no distant cluster
in our sample whose gas mass at r =1.5h−1 Mpc is less clusters at z∼<1 (e.g., Schindler 1999) (This result is,
than 1×1013h−2.5M⊙•. Note also that no clear depen- however, mainly for X-ray properties, and the evolution
of the galaxy distribution in clusters is not well known).
dence of L /M on M is seen either in the nearby
B gas gas
Inwhatfollows,wetaketheformerexplanationasour
cluster sample or in the distant cluster sample.
We mention here the effects of changing Ω and λ on hypothesis, i.e., we assume that the increase in LB/Mb
0 0
found here is due to pure brightening of the galaxy pop-
estimates of LB/Mb for distant clusters. Let dL(z) and
ulation as a whole. Then the increase found here corre-
dA(z) be the luminosity distance and the angular diam-
sponds to brightening by ≃ 1 mag of the galaxy popu-
eter distance to a cluster at z, respectively. The ratio
L /M is proportional to d−0.5(z), because of L ∝ lation. In the next subsection, we compare the observed
B gas L B
d2L(z), Mgas ∝d2A.5(z), anddL(z)=(1+z)2dA(z). Thus, brightening with predictions of simple luminosity evolu-
L /M depends on Ω and λ through d−0.5(z). Since tion models of galaxies.
B gas 0 0 L
Mb is dominated by Mgas, the dependence of LB/Mb on
Ω0 and λ0 is very close to that of LB/Mgas. Figure 5 3.1. Comparison with Luminosity Evolution Models
shows the ratio of L /M (Ω ,λ ) to L /M (Ω =
B gas 0 0 B gas 0 We characterize the evolution of L , the B-band lu-
0.2,λ = 0) as a function of redshift for two sets of B
0 minosity summed over all galaxies in a cluster, by two
(Ω0,λ0). Since dL(z) is a decreasing function of Ω0 and parameters: the star formation timescale τ and the for-
an increasingfunction of λ up to at leastz =1, we find
0 mation redshift z . In other words, we assume that all
from this figure that the change in L /M due to the F
B gas galaxiesare formed at the same redshift z and that the
change in Ω and λ in the ranges of 0.2 ≤ Ω ≤ 1 and F
0 0 0 e-folding time of star formation summed over all galax-
0≤λ ≤0.8 is less than ±10% for z <1 clusters, which
0 ies is τ (Gyr). We compute B-bandluminosityusing the
is negligible for our discussion below.
populationsynthesiscodedevelopedbyKodamaandAri-
moto (1997). The values of τ and z examined here are
F
3. Results and Discussion τ =0.1,1,2,3,and 5 Gyr and z =2,3, and ∞. Models
F
with τ = 0.1 Gyr correspond to elliptical galaxies and
Figure 6 shows LB/Mb of clusters as a function of models with τ = 5 Gyr are for spiral disks like that of
redshift. The filled circles present the distant clusters ourGalaxy. We donotexamineτ >5 Gyr,since to take
and the filled square indicates the average LB/Mb of τ >5 Gyr leads to too blue colorsatz =0 which arein-
the nearby clusters. Clusters without errors (but for consistent with the observed colors of galaxies in nearby
4 K. Shimasaku [Vol. 00,
clusters (The meanB−R ofthe Virgo andComa clus- VanDokkumetal. (1998)presentobservationsofM/L
C
tergalaxiesis1.2and1.8,respectively[Andreon1996for ratio inthe B band of early-typegalaxiesin five clusters
Coma and Young and Currie 1998 for Virgo], while the at0.02≤z ≤0.83. TheyfindthattheM/Lratioevolves
models with τ = 0.1 and τ = 5 Gyr give B−R = 1.6 as ∆logM/L ∝ −0.40z (Ω = 0.3,λ = 0), which is
C B 0 0
andB−R =1.1,respectively,atanageof12Gyr). We consistentwithsingle-burstmodelswithz >1.7−2.8. If
C F
also set the lower limit of z to be 2 following the tra- theevolutionofM/LfoundbyvanDokkumetal. (1998)
F
ditional pure luminosity evolution models which assume isunderstoodaspureluminosityevolutionofL ,thefor-
B
that elliptical/S0 galaxies and spiral galaxies are formed mula ∆logM/L ∝ −0.40z implies that L brightens
B B
at high redshifts (z∼>2) and which broadly succeed in by a factor of 2.5 from z = 0 to 1, which is in excellent
reproducing observed properties of these galaxies (e.g., agreement with the brightening of LB/Mb found in this
Kodama et al. 1998; Shimasaku and Fukugita 1998). study. Measurements of M/L of individual galaxies are
Figure 6 compares the observed LB/Mb with predic- a direct measurement of the effects of luminosity evolu-
tions. Predicted values of LB/Mb are normalized to tion occurredin galaxies,while measurements of LB/Mb
matchtheobservedvalueatz =0. Inotherwords,mod- of clusters are less direct. Note, however, that informa-
els are used to predict relative brightening (or fading) of tioncontainedinLB/Mb isdifferentfromthatinM/Lof
LB as a function of z. Panels (a), (b), and (c) are for individual galaxies. The quantity LB/Mb describes the
z = ∞,3, and 2, respectively. From panel (a), we find evolutionofluminosity summedoverall galaxiesin clus-
F
that all the models reproduce the observation. If, how- ters. LB/Mb also gives us a hint to the star formation
ever, z = 3 is adopted (panel [b]), models with τ = 1 efficiency in clusters (see below). In any case, the agree-
F
and 2 Gyr give too steep brightening comparedwith the ment of brightening between M/LB and LB/Mb found
observation. This trend is strengthened for the z = 2 here can be regarded as indirect support of our conclu-
F
case (panel [c]): the τ =0.1 Gyr model also becomes in- sionthatsingle-burstlikemodelsseemtobeplausiblefor
consistent with the observation, though the discrepancy describing the evolution of LB/Mb.
is at less than 2σ levels. The allowed range for τ is de- The absolute value of LB/Mb tells us a hint to the
pendent on z , and we cannot rule out any value of τ star formation efficiency in clusters, i.e., the fraction of
F
on the basis of the current data if we permit z = ∞, baryonsin clusters used to formstars. If the star forma-
F
though‘single burst’models with τ =0.1 Gyr and‘disk’ tion efficiency differs among clusters, the absolute value
models with τ = 5 (and τ = 3 Gyr models) match the of LB/Mb would also vary from cluster to cluster. The
observationforawiderrangeofz towardlowerredshifts fact that there exist models, such as those with τ = 0.1
F
than the other (τ =1,2 Gyr) models. Gyr,whichreproducetheobservedLB/Mb ofmanyclus-
Itisinterestingthat‘singleburst’(τ =0.1Gyr)models ters at different redshifts within the observational errors
and ‘disk’ (τ = 5 Gyr) models are consistent with the suggest that the star formation efficiency is universal
observation. In this paragraph, we concentrate on these among clusters up to z ∼1.
models,andexaminewhicharemoreconsistentwiththe In order to see when baryons are converted into stars,
observed luminosity evolution of individual galaxies in we plot in figure 7 the predicted evolution of M⋆/Mb,
clusters. Various observationssuggest that elliptical and where the evolution of M⋆ is calculated from mass-to-
S0 galaxies in clusters brighten by ∼ 1 mag from z = 0 luminosity ratios of galaxies predicted by the z = 3
F
to z =1, which is consistent with the single burst model models. The values of M⋆/Mb at z = 0 have been nor-
(e.g., Schade, Barrientos, Lo´pez-Cruz 1997; Ellis et al. malized so that they are consistent with the observed
1997; Kodama et al. 1998; van Dokkum et al. 1998). LB/Mb of the nearby clusters 1. The predicted values of
Spiral galaxies have also been found to brighten by ∼ 1 M⋆/Mb atz =0are0.05−0.13,dependingonτ, andare
mag (e.g., Schade et al. 1996), though observations are consistentwiththeobservedvalue(thefilledsquarewith
not as many as those of elliptical and S0 galaxies. The an error bar). This simply implies that the predicted
amounts of brightening of E/S0 and spiral galaxies are (M/LB)⋆ values at z = 0 fall within (6±3)h(M/LB)⊙,
similar to each other, and they are in agreement with which is the adopted value of (M/LB)⋆ for galaxies in
the predictions of τ = 0.1 Gyr models (with zF ≥ 3) nearby clusters. As expected, the evolution of M⋆/Mb
and τ = 5 Gyr models. However, our distant clusters largely differs among the models. A constant M⋆/Mb is
are rich clusters and thus it is likely that elliptical and predictedby theτ =0.1Gyrmodelinthe redshiftrange
S0 galaxies dominate in these clusters. Hence, the τ = of this figure, while for the τ =5 Gyr model, half of the
0.1 Gyr models seem to be more plausible for describing stars present today are formed at z <1.
the evolution of LB/Mb. This is also supported by the Finally,wementionhowtoputstrongerconstraintson
fact that the mean colorof galaxiesin the Coma cluster, modelsusingtheevolutionofLB/Mb. Unfortunately,the
which is a very rich nearby cluster and is likely to be a steepness of brightening up to z = 1 is not a monotonic
counterpart of the distant clusters studied here, agrees
with the color predicted by the τ =0.1 Gyr models. 1 M⋆/Mb(z=0)=(M/LB)p⋆red(z=0)×(LB/Mb)obs(z=0)
No. 0] Luminosity Evolution of Galaxies in Clusters 5
functionofτ: thebrighteningisthesteepestforτ =1−2 this paper, we regard the values at z ≃ 0.1 as the local
Gyr models, and models with τ =0.1 Gyr and τ =3−5 (z =0) value.
Gyr give similar brightening. In order to place further
constraintsusingtheevolutionofLB/Mb,oneneedsdata 3.2.1. Local values for LB/Mb and lB/ρb
at z > 1: for example, for z = 3 and 2, τ = 0.1 Gyr
F The filled circles in figure 8 indicate the LB/Mb of the
models predict much steeper brightening at z > 1 than
distant clusters of galaxies. The filled square at z = 0
τ =5 Gyr models.
corresponds to the average of the nearby clusters. We
find that the local LB/Mb agrees with the local lB/ρb:
3.2. Comparison with Evolution of Field Galaxies LB/Mb is(0.024±0.004)(LB/M)⊙ andtheaverageofthe
The quantity LB/Mb is the B-band luminosity per three lB/ρb values at z ≃0.1 is (0.026±0.002)(LB/M)⊙
unit baryon in clusters. The corresponding quantity for 3.
field galaxies is the ratio of the blue luminosity density This agreement implies that the blue luminosity per
lB [LB⊙ Mpc−3] to the mean baryon density ρb [M⊙• unitbaryonmassisveryclosebetweenclustersandfields.
Mpc−3]. Inthissubsection,wederivelB/ρboffieldgalax- Then the next questionmay be whether the stellar mass
ies up to z ∼ 1 from the literature and compare it with per unit baryon mass (M⋆/Mb), i.e., the star formation
LB/Mb of clusters. efficiency, is the same between clusters and fields (Note
Data of l are taken (or computed) from recent mea- thatmorphologicaltypemixlargelydiffersbetweenclus-
B
surements of luminosity function based on redshift sur- ters and fields and that (M/LB)⋆ of galaxies varies with
veys: Lilly et al. (1996; CFRS; data points are at morphology). In order to examine this, we do a sim-
z = 0.35,0.625,0.875), Ellis et al. (1996; Autofib; z = ple (but more detailed than that given in §2.1) esti-
0.085,0.25,0.55),Colless (1998; 2dF; z =0.11), Loveday mation of M⋆/Mb of clusters and fields below. We as-
et al. (1992; APM; z ≃ 0.05), Zucca et al. (1997; ESP; sume the (M/LB)⋆ of elliptical and S0 galaxies to be
z ≃ 0.1), and Marzke et al. (1998; SSRS2; z ≃ 0.025). 8h(M/LB)⊙ and that of spiral and irregular galaxies to
Lilly et al. (1996) give lB itself while the other papers be4h(M/LB)⊙ 4. Usingthesevaluesandtakingaccount
give only luminosity functions in the B band. For those ofthemeanmorphologicaltypemixofthe12clusters,we
exceptforLillyetal. (1996),weintegratetheluminosity obtainM⋆/Mb =0.114±0.020. A similarcalculationfor
function given in each paper from M = −25 to −10 to the field galaxies gives M⋆/Mb = 0.097±0.009 (We use
B
obtain lB. thetypemixgiveninColless1998: lB(E+S0)/lB(tot)=
Inordertocomputeρb,weadoptΩb =0.02h−2follow- 34.5% and lB(S+Irr)/lB(tot) = 65.5%). Hence, the
ingTytlerandhis coworkers’results(e.g.,Burles,Tytler M⋆/Mb of clusters is in agreement with that in fields
within errors. Renzini (1997)has alsoobtained a similar
1998). Their estimates ofΩb arebasedonmeasurements
of deuterium abundance (D/H) of QSO absorption sys- result from a rough calculation for M⋆/Mb of the Coma
cluster and field galaxies.
temsathighredshifts. NotethatthemeasurementsofΩb
have not completely converged among authors, ranging
fromΩbh2 ≃0.01to0.02,thoughTytleretal.’smeasure- 3.2.2. Evolution of LB/Mb and lB/ρb
ments seem to be the most reliable (e.g., Turner 1999). Fromfigure 8,it is found that the evolution ofLB/Mb
ThelB/ρb offieldgalaxiescalculatedaboveareplotted as a function of redshift is the same as for lB/ρb within
in figure 8 as open circles with error bars. A gradual the observational errors. Both ‘brighten’ by a factor of
increaseinlB/ρb with redshiftis seen. This is due to the 2−3 from z =0 to z =1.
brightening of lB 2. The agreement between the evolution of LB/Mb and
AfactwhichneedsattentionisthatthevaluesoflB/ρb lB/ρb may be interpreted as the mean star formation
atz∼<0.05aresmallerthanthoseatz ≃0.1byaslargeas history of cluster galaxies being similar to that of field
a factorof ≃2. It is unlikely that the luminosity density galaxies. However,wethink thatthis agreementis prob-
evolves so rapidly for such a short time from z = 0.1 to ably superficial. The observedglobalstar formationrate
the present. A possible explanation for this problem is of field galaxies increases by a factor of ∼ 3−10 from
that the number density of galaxiesin the local(z∼<0.1)
3 Anoteshouldbeadded. Theagreement foundheredoesnot
universe happens to be lower than the globalvalue (e.g.,
holdifverydifferentvaluesforΩb andhareadopted, because
Marzke et al. 1998), though further investigations are (i)lB/ρb changeslinearlywithΩ−b1 and(ii)thedependenceof
neededinorderto proveordisprovethis explanation. In lB/ρb andLB/Mb onhisdifferent(lB/ρb∝hifΩbh2 isfixed,
while LB/Mb ∝ h0.5), though we think that the values of Ωb
2 Forfieldgalaxies,theglobalstarformationrate(ρ˙⋆ [M⊙• yr−1 andhadopted inthispaperarethemostprobableatpresent.
Mpc−3]) has also been measured from UV and emission-line 4 The value for elliptical and S0 galaxies is based on van der
luminosities of galaxies (e.g., Madau et al. 1998; for recent Marel’s(1991)study,whichfoundthattheM/LB ofelliptical
observations, see Cowie, Songaila, Barger 1999). These mea- galaxieswith1×1010h−2LB⊙ is8.4h(M/LB)⊙. Thevaluefor
surements suggest that ρ˙⋆ increases by a factor of ∼ 3−10 theGalacticdisk,M/LB≃3(M/LB)⊙,isadoptedasthevalue
fromz=0to1,butthescatter amongthedataisstilllarge. forspiralandirregulargalaxies(4h≃3forh=0.7).
6 K. Shimasaku [Vol. 00,
the present epoch to z = 1, and then has a peak at We have made a simple estimate of star formation ef-
z = 1−2 (e.g., Madau et al. 1998; Cowie et al. 1999). ficiency (M⋆/Mb) to find no difference between clusters
Thoughthisstarformationhistory,whichreproducesthe andfields. To place further constraintsonthe meanstar
observed evolution of lB/ρb as well, should be a solution formation history of cluster galaxies needs new data at
for the mean star formation history of cluster galaxies, higherredshiftsordirectmeasurementsofstarformation
quite different models can also be solutions, as has been rate.
seen in §3.1. Simple models having just two parame-
ters(τ andz )wereexaminedin§3.1,andmanymodels Acknowledgements
F
have been found to reproduce the observed evolution of We thank the anonymous referee for useful comments
LB/Mb, and the color of galaxies in nearby rich clusters which improved the paper. This research was supported
suggests that τ =0.1 Gyr models are favored (see §3.1). in part by the Grants-in-Aid by the Ministry of Educa-
In any case, we cannot give a clear conclusion about tion, Science, Sports and Culture of Japan (07CE2002)
the mean star formation history of cluster galaxies on to RESCEU (Research Center for the Early Universe).
the basis of the current data. As was mentioned in §3.1,
data at z > 1 are useful to place further constraints on References
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Table 1. Distant Clusters.
name z L /Ma) Lb) Mc) radiusd) errore)
B b B gas
A1413 0.14 0.028 7.6 2.42 0.77 21
A1689 0.18 0.042 14.0 2.80 0.78 21
A2218 0.18 0.043 8.4 1.81 0.42 33
A2163 0.20 0.037 3.0 0.74 0.26 48
CL0500-24 0.32 0.037 3.9 0.95 0.53 30
CL0939+47 0.41 0.089 1.8 0.18 0.14 —
RXJ1347.5-1145 0.45 0.053 65.7 11.3 1.09 37
CL0016+16 0.55 0.044 50.6 10.4 1.67 —
AXJ2019+1127 1.01 0.075 5.6 0.68 0.30 30
A2390 0.23 0.030 11.3 3.3 0.60 —
MS0302+16 0.42 0.055 5.1 0.84 0.60 —
MS0440+02 0.20 0.027 2.5 0.84 0.60 —
MS0451+02 0.20 0.021 6.3 2.7 0.60 —
MS0451-03 0.54 0.036 14.7 3.7 0.60 —
MS0839+29 0.19 0.054 4.5 0.74 0.60 —
MS0906+11 0.17 0.066 9.2 1.3 0.60 —
MS1006+12 0.26 0.028 6.4 2.0 0.60 —
MS1008-12 0.31 0.051 11.2 2.0 0.60 —
MS1224+20 0.33 0.066 7.1 0.98 0.60 —
MS1358+62 0.33 0.062 11.4 1.7 0.60 —
MS1455+22 0.26 0.021 4.9 2.1 0.60 —
MS1512+36 0.37 0.028 4.2 1.4 0.60 —
a) In units of h0.5(LB/M)⊙.
b) In units of h−2×1011L⊙•.
c) In units of h−2.5×1013M⊙•.
d) Radius in units of h−1 Mpc adopted to measure L
B
and M .
gas
e) Relative error (%).
No. 0] Luminosity Evolution of Galaxies in Clusters 9
Figure Captions catethe22distantclustersandthefilledsquareisforthe
average LB/Mb of the nearby clusters. The open circles
Fig.1. LV plottedagainstMgas forArnaudetal.’s(1992) with error bars correspond to lB/ρb of field galaxies.
nearbyclusters. Thefilledandopencirclesindicateclus-
ters with and without type mix data, respectively. The
dashedandsolidlinesindicatethebestfitofapowerlaw
to all and massive (Mgas ≥ 1×1013h−2.5M⊙•) clusters,
respectively. The dotted line corresponds to the best fit
of L ∝M to the massive clusters.
V gas
Fig.2. L /M plottedagainstthefractionofluminosity
V gas
emitted fromelliptical and S0 galaxies to the totallumi-
nosity L (E/S0)/L for Arnaud et al.’s (1992) clusters
V V
havingtypemixdata. Thefilledandopencirclesindicate
Mgas ≥ 1×1013h−2.5M⊙• and Mgas < 1×1013h−2.5M⊙•
clusters, respectively.
Fig.3. LB/Mb as a function of Mgas for Arnaud et al.’s
(1992)clusters. The filled and opencircles indicate clus-
ters with and without type mix data, respectively.
Fig.4. L versus M for the 12 nearby and the 22 dis-
B gas
tant clusters adopted in this paper. Filled circles indi-
cate the nearby clusters. Open circles and crosses are
for 0.1 < z ≤ 0.4 and 0.4 < z ≤ 0.7 clusters, respec-
tively. The star corresponds to the most distant cluster
AXJ2019+1127 at z = 1.01. The thick solid line indi-
cates the best fit of L ∝ M to the nearby clusters.
B gas
The thin solid line and the dotted line correspond to a
similar fit to the distant clusters at 0.1 < z ≤ 0.4 and
0.4<z ≤0.7, respectively.
Fig.5. DependenceofthemeasurementofL /M onΩ
B gas 0
andλ . TheratioofL /M (Ω ,λ )toL /M (0.2,0)
0 B gas 0 0 B gas
is plotted as a function of redshift for (Ω ,λ ) = (1,0)
0 0
and (0.2,0.8) cases.
Fig.6. Observed LB/Mb of clusters as a function of red-
shift. The filled circles present the 22 distant clusters
and the filled square indicates the averageLB/Mb of the
nearby clusters. Model predictions are overlaid. Pre-
dicted values of LB/Mb are normalized to match the ob-
served value at z = 0. Panels (a), (b), and (c) are for
z = ∞,3, and 2, respectively. Thick and thin solid
F
lines indicate models with τ = 0.1 and 1 Gyr, respec-
tively. Dotted, dashed,andlong-dashedlinescorrespond
to models with τ =2,3, and 5 Gyr, respectively.
Fig.7. Theratioofstellarmasstobaryonmass,plottedas
a function of redshift. The five lines indicate predictions
of models with different τ. All models are for z = 3.
F
The meanings of lines are the same as in figure 6. The
filled square corresponds to the observed value.
Fig.8. lB/ρb of field galaxies as a function of redshift,
comparedwithLB/Mb ofclusters. Thefilledcirclesindi-