The K-band Hubble diagram for the brightest cluster galaxies: a test of hierarchical galaxy formation models

9 Pages·0.27 MB·English

by  A. Aragon-Salamanca

Mon.Not.R.Astron.Soc.000,1–9(—) Printed5February2008 (MNLATEXstylefilev1.4)
The K-band Hubble diagram for the brightest cluster
galaxies: a test of hierarchical galaxy formation models.
Alfonso Arag´on-Salamanca,1 Carlton M. Baugh2 and Guinevere Kauffmann3
1Institute of Astronomy, Madingley Road, Cambridge CB3 0HA,England
2Department of Physics, Science Laboratories, South Road, Durham DH13LE, England
3Max-Plank-Institut fu¨r Astrophysik, D-85740 Garching bei Mu¨nchen, Germany
8
9 Accepted —.Received—;inoriginalform—
9
1

n ABSTRACT
a
J We analyse the K-band Hubble diagram for a sample of brightest cluster galax-

8 ies (BCGs) in the redshift range 0 < z < 1. In good agreement with earlier stud-
2 ies, we confirm that the scatter in the absolute magnitudes of the galaxies is small
(0.3magnitudes). The BCGs exhibit very little luminosity evolution in this redshift

1 range: if q0 =0.0 we detect no luminosity evolution; for q0 =0.5 we measure a small
v negative evolution (i.e., BCGs were about 0.5magnitudes fainter at z = 1 than to-
7
day). If the mass in stars of these galaxies had remained constant over this period
7
of time, substantial positive luminosity evolution would be expected: BCGs should
2
have been brighter in the past since their stars were younger. A likely explanation
1
for the observed zero or negative evolution is that the stellar mass of the BCGs has
0
8 been assembled over time through merging and accretion, as expected in hierarchi-
9 cal models of galaxy formation. The colour evolution of the BCGs is consistent with
/ that of an old stellar population (z > 2) that is evolving passively. We can thus
h form
use evolutionarypopulation synthesis models to estimate the rate of growthin stellar
p
mass for these systems. We find that the stellar mass in a typical BCG has grown by
-
o a factor ≃ 2 since z ≃ 1 if q0 = 0.0 or by factor ≃ 4 if q0 = 0.5. These results are
r in good agreement with the predictions of semi-analytic models of galaxy formation
t
s andevolutionsetinthecontextofahierarchicalscenarioforstructureformation.The
a
modelspredictascatterinthe luminositiesofthe BCGsthatissomewhatlargerthan
:
v the observedone, but that depends on the criterion used to select the model clusters.
i
X Key words: galaxies:clusters—galaxies:formation—galaxies:evolution—galax-
r ies: elliptical and lenticular, cD — infrared: galaxies
a
1 INTRODUCTION (Rakos & Schombert 1995); (Oke, Gunn & Hoessel 1996);
(Lubin1996);(Stanford,Eisenhardt&Dickinson1997))im-
plying that the Hubble diagram could be seriously affected
Brightest cluster galaxies (BCGs) have been extensively
byevolutionarychangesevenatrelativelymodestredshifts.
studied at optical wavelengths ((Peach 1970), 1972; (Gunn
& Oke 1975), (Sandage, Kristian & Westphal 1976); (Kris- Conclusionsconcerningq0 cannotbederivedfromsuchdia-
grams until these changes are well-understood. Indeed, the
tian, Sandage & Westphal 1978); (Kristian, Sandage &
Hubblediagram fortheBCGsmay wellhavemoretoteach
Westphal 1978); (Hoessel 1980); (Schneider, Gunn & Hoes-
usabout galaxy evolution than about cosmology.
sel 1983a),b; (Lauer & Postman 1992); (Postman & Lauer
1995)). The small scatter in their absolute magnitudes (< The study of the BCGs in the near-infrared K-band
0.3magnitudes up to z ∼0.5, see e.g. (Sandage 1988)) and (2.2µ) has two main advantages over optical studies: first,
their high luminosities make them useful standard candles the k-corrections are appreciably smaller (indeed, they are
for classical cosmological tests involving the Hubble dia- negative) and virtually independent of the spectral type
gram, such as the determination of q0 and the variation of of the galaxies (see, e.g., (Arag´on-Salamanca et al. 1993),
H0 with redshift. However, there is now firm evidence that 1994); and second, the light at long wavelengths is domi-
significantevolutionhastakenplaceinthecoloursandopti- nated by long-lived stars. Thus the K-band luminosity is a
calluminosities ofearly-typegalaxies(includingtheBCGs) good measure of thetotal stellar mass in thegalaxies.
from z ≃ 0 to z ≃ 1 (e.g. (Arag´on-Salamanca et al. 1993); The K-bandHubblediagram haslong been used as an
(cid:13)c —RAS
2 A. Arag´on-Salamanca, C.M. Baugh and G. Kauffmann
evolutionarydiagnosticforradiogalaxies((Grasdalen1980); & Olowin (1989) catalogues. At higher redshifts they have
(Lebofsky 1980); (Lebofsky & Eisenhardt 1986); (Lilly & beenfoundfromtheprojecteddensitycontrastindeepopti-
Longair1982),1984; (Lilly1989a),b),whichalsohavearel- calimagingsurveys((Gunn,Hoessel&Oke1986);(Couchet
ativelysmallintrinsicdispersionintheirluminosities(≃0.4 al. 1991)) and should represent the richest clusters present
magnitudesfor1<z <2.2;(Lilly1989a)). Substantialpos- at each redshift.
itive luminosity evolution was found: radio galaxies were The K-band data analysed here come from the photo-
about one magnitude brighter at z ≃ 1 than they are to- metricstudycarriedoutbyArag´on-Salamancaetal.(1993)
day. Arag´on-Salamanca et al. (1993) measured K-band lu- of galaxy clusters in the 0 < z < 1 redshift range (19
minosities for a sample of 19 BCGs in the redshift range BCGs) complemented with new K-band images of 3 clus-
0<z<1andfoundthattheK magnitude-redshiftrelation ters at z ≃ 3 ((Barger et al. 1996)) and 6 clusters with
istighter(scatter=0.3magnitudes)thanforradiogalaxies. 0.39≤z≤0.56 ((Bargeretal. 1997)).Theimages wereob-
Moreover, these authors did not detect significant K lumi- tainedatthe3.8-mUKInfraredTelescope,the3.9-mAnglo-
nosityevolutionfortheBCGs,andconcludedthattheirevo- Australian Telescope and the Palomar Observatory 1.52-m
lutionarypropertiesweredifferentfromthoseofradiogalax- Telescope. There is some overlap in the clusters observed
ies:powerfulradiogalaxiesareapparentlylesshomogeneous by Arag´on-Salamanca et al. and Barger et al., bringing the
in theirevolutionary behaviourand showstronger luminos- numberofBCGsstudiedheretoatotalof25(seeTable1).
ity evolution. Arag´on-Salamanca et al. also found that the For the clusters in common, both sets of photometry agree
colours of the early-type galaxies (including the BCGs) in very well (within the estimated errors) and we have chosen
these clusters have evolved since z ≃ 1 at a rate consistent thebetterquality image in each case.
with a scenario in which the bulk of their stars formed at Wereferthereadertotheoriginalpapersforadetailed
relativelyhighredshifts(z>2)andevolvedpassivelythere- description of the data. We will concentrate here on the
after. This conclusion has been confirmed by several more aspects relevant to this paper. The photometric zero-point
recent studies ((Rakos & Schombert 1995); (Oke, Gunn & uncertaintiesintheK-bandimageswerealwayssmall(0.02–
Hoessel 1996); (Lubin 1996); (Ellis et al. 1997); (Stanford, 0.04magnitudes)andarecompletelynegligibleforouranal-
Eisenhardt & Dickinson 1997)). ysis. As in Arag´on-Salamanca et al. (1993), K photometry
Therecentdevelopmentofsemi-analytictechniques has for the BCGs was obtained inside a fixed metric aperture
⋆
providedtheoristswiththetoolstomakepredictionsforthe of 50kpc diameter so that the minimum aperture at high
formation and evolution of galaxies, using physically moti- redshift is ∼ 5arcsec thus minimising the effect of seeing.
vatedmodelssetinthecontextofhierarchicalstructurefor- Because of the ambiguity of what constitutes a “galaxy”
mation in the universe (e.g., (White & Frenk 1991); (Cole (∼ 30% of local first-ranked cluster galaxies are multiple-
1991); (Lacey & Silk 1991); (Kauffmann, White & Guider- nucleussystems:i.e., morethanone“galaxy”occurswithin
doni 1993); (Kauffmann, Guiderdoni & White 1994); (Cole ourmetricaperture—see(Hoessel1980)) wefollow theap-
et al. 1994); (Heyl et. al. 1995)). The properties of galaxies proach of Schneider, Gunn & Hoessel (1983a) and adopt a
inthesemodelsareinbroadagreementwiththepresentday working definition of the brightest cluster galaxy as the re-
characteristics of galaxies, such as the distribution of lumi- gion of maximum cluster light enclosed in our metric aper-
nosities,coloursandmorphologiesandwiththepropertiesof ture.ThephotometrydatafromtheAATandPOwastrans-
galaxies at high redshift, including the faint galaxy counts, formed intotheK-bandsystem of theUKIRT(wheremost
colours and redshift distributions (e.g. (Kauffmann 1995); ofthedatacomesfrom)usingcolourtermsdeterminedfrom
(Kauffmann 1996); (Kauffmann & Charlot 1997); (Baugh, the known filter responses. The colour terms were always
Cole & Frenk 1996a); (Baugh et. al. 1997)). In this paper, ≤ 0.08magnitudes, and we estimate that the uncertainty
we will test whether the models also predict the right be- in the transformation is well below 2% and thus negligible.
haviourfor aspecial class ofgalaxies, namely theBCGs. In GalacticreddeningcorrectionswereestimatedfromBurstein
themodels,thesegalaxiesgrowinmassbothfrom thecool- &Heiles’ (1982) maps,butsincethegalactic latitudeswere
ing of gas from thesurrounding hot halo medium and from alwaysreasonablyhigh,theywereverysmallintheK-band.
the accretion of “satellite” galaxies that fall to the cluster Finally,smallseeingcorrections andk-correctionswerealso
centreas result of dynamical friction and then merge. applied as in Arag´on-Salamanca et al. Table 1 contains the
Insection2wepresenttheobservationalresultsandde- corrected K-magnitudes for the BCG sample. Values for
rivetheluminosityevolution oftheBCGs inthesample.In q0 = 0.0 and 0.5 are given to account for the difference in
section 3 we briefly describe two independentsemi-analytic projected aperture at a given metric aperture as a function
modelsofgalaxyformation,outlinetheirbasicassumptions, of the deceleration parameter. We estimate that the total
limitations and uncertainties, and discuss the predictions uncertainty of the corrected magnitudes is below 10%, and
they make for the evolution of the BCGs. Section 4 com- willcontributeverylittletotheobservedscatter(seeoriginal
pares themodel predictions with theobservational results. data papers for a detailed discussion of the uncertainties).
Figure 1 shows the K magnitude–redshift relation
(Hubble diagram) for the BCGs in our sample. The solid
linesshowno-evolutionpredictionswhichonlytakeintoac-
2 OBSERVATIONAL RESULTS count the distance modulus as a function of z, normalised
2.1 Photometric data
The clusters in our sample are all optically-selected, al- ⋆ H0 = 50kms−1Mpc−1 assumed throughout. Because of the
though most of them havealso been detected in X-rays.At uncertainty inthevalue ofq0 wewillcarryout parallelanalyses
z≤0.37theycomefromtheAbell(1957)andAbell,Corwin forq0=0.0and0.5
(cid:13)c —RAS,MNRAS000,1–9
The K-band Hubble diagram for the brightest cluster galaxies 3
Table1.Correctedrest-frameK-bandmagnitudesfortheBCGs
Cluster z K0 K0 reference
q0=0.0 q0=0.5
Abell1656a(NGC4889) 0.023 8.89 8.88 (1)
Abell2199(NGC6166) 0.030 9.50 9.49 (1)
Abell2197(NGC6173) 0.031 9.54 9.53 (1)
Abell2151(NGC6034) 0.037 10.49 10.38 (1)
Abell963 0.206 13.61 13.55 (1)
Abell1942 0.224 13.92 13.88 (1)
AC103 0.310 14.62 14.56 (2)
AC114 0.310 14.54 14.46 (2)
AC118 0.310 14.77 14.67 (2)
Cl2244−02 0.329 15.35 15.31 (1)
Abell370 0.374 15.05 14.95 (1)
Cl0024+16 0.391 15.29 15.14 (1),(3)
3C295 0.460 15.26 15.14 (3)
Cl0412−65b 0.510 15.60 15.55 (3)
Cl1601+42 0.540 16.23 16.13 (3)
Cl0016+16 0.546 16.21 16.02 (1),(3)
Cl0054−27c 0.563 16.50 16.37 (1),(3)
Cl0317+1521 0.583 17.08 17.01 (1)
Cl0844+18d 0.664 16.93 16.80 (1)
Cl1322+3029 0.697 16.90 16.72 (1)
Cl0020+0407 0.698 17.06 17.01 (1)
Cl1322+3027 0.751 16.97 16.79 (1)
Cl2155+0334 0.820 17.22 17.12 (1)
Cl1603+4313 0.895 17.78 17.64 (1)
Cl1603+4329 0.920 18.24 18.02 (1)
aComacluster.
bAlsoknownasF1557.19TC (Couchetal.1991).
cAlsoknownasJ1888.16CL(Couchetal.1991).
dAlsoknownasF1767.10TC (Couchetal.1991).
References.—(1)Arago´n-Salamancaetal.1993;(2)Bargeretal.
1996;(3)Bargeretal.1997
to the threelowest redshift points. Since we do not have K shift clusters from theground-basedimages. Many of inter-
magnitudes for many low redshift galaxies, the normalisa- mediate and high redshift clusters have been imaged with
tion of the no-evolution line could be somewhat uncertain. HST, thus morphological information exists for 16 of the
However,extensiveopticalphotometryexistsand,giventhe z > 0.3 clusters ((Smail et al. 1996), 1997; (Couch et al.
homogeneity in the colours of these galaxies ((Postman & 1997)).Ingeneral,theBCGsareeithercDgalaxiesorgiant
Lauer1995)),wefeeljustifiedtousetheR-bandphotometry ellipticals,althoughforthehighest-z clusterstherecouldbe
ofLauer&Postman(1992)toestimateK-bandmagnitudes. some ambiguity since the extended cD halos might not be
The shaded area at low-redshift in Figure 1 represents the clearly visible given the relatively high surface brightness
K-band magnitudes for z <0.06 BCGs estimated from the limits achievable with HST. Thus some of the BCGs clas-
R-band data of Postman & Lauer, corrected to our met- sified as ellipticals could be cD galaxies. The exception to
ric aperture (using dlogL/dlogr = 0.5; from the same au- this rule is the BCG in the 3C295 cluster, which is a radio
thors), and assuming a typical R−K = 2.6 (cf. (Bower, galaxyandshowsanun-resolvedAGN-likemorphologyina
Lucey & Ellis 1992a),b). The width of the shaded area re- disturbed disk or envelope.
flects the observed scatter. The agreement with our local The optical and optical-infrared colours (from ground-
normalisation is remarkably good. basedandHSTdata)oftheBCGsarecompatiblewiththose
of the colour-magnitude sequence of cluster ellipticals and
In agreement with the results of Arag´on-Salamanca
S0s. The exception is, again, 3C295, which is substantially
et al., the scatter of the observed magnitudes around the
bluer (by ≃ 0.8mag in R−K). The peculiar colours and
no-evolution prediction is 0.30mag. Assuming that the K-
morphology of this galaxy are probably related to its being
band light provides an estimate of the total stellar mass
a powerful radio source. However, its K-band luminosity
of the galaxies, this very low scatter implies that BCGs at
agrees very well with that of the rest of the BCGs in our
a given redshift have very similar masses in stars (within
sample, and we have kept it in our analysis. Taking it out
30% r.m.s.),whichhasyettobeexplainedbyanymodelof
would not alter ourconclusions.
galaxy formation (see section 3).
Morphological information is available for the low red-
(cid:13)c —RAS,MNRAS000,1–9
4 A. Arag´on-Salamanca, C.M. Baugh and G. Kauffmann
Figure1.(a)Magnitude-redshiftrelation(Hubblediagram)for Figure 2. (a) Top panel: The same data presented in figure 1
the Brightest Cluster Galaxies in the rest-frame K-band. The aftersubtractingtheno-evolutionprediction.Middleandbottom
K magnitudes have been measured inside a projected 50kpc- panels: the same data after subtracting models for luminosity
diameter aperture. Thesolidlineshows theno-evolution predic- evolution inwhich the BCG stars form at zfor =2 and zfor =5
tion,normalisedto thelow-redshiftdata. Thedashed linecorre- respectively and evolve passively thereafter (for q0 = 0.0). The
spondstotheluminosityevolutionexpected forastellarpopula- solid lines represent least-squares linear fits. (b) As (a) but for
tionformedatzfor=2evolvingpassively.Thedottedlineshows q0=0.5.
the evolution expected for zfor = 5. The shaded area at low-
redshift represents the K-band magnitudes of z < 0.06 BCGs
estimatedfromtheR-banddataofPostman&Lauer.Thewidth A convenient parametrisation of the luminosity evolu-
of the shaded area reflects the observed scatter (see text for de- tion is L (z)=L (0)×(1+z)γ. Least-squares fits to the
tails). H0 = 50kms−1Mpc−1 and q0 = 0.0 were assumed. (b) datayielKd γ =−0.K06±0.3 and−0.6±0.3, for q0 =0.0 and
As(a)butforq0=0.5. 0.5respectively.ThustheBCGsshowno ormarginallyneg-
ative luminosity evolution. However, as mentioned above,
thecoloursofthesegalaxiesshowthesameevolutionasthe
2.2 Interpretation using evolutionary synthesis
early-typeclustergalaxies:theygetprogressivelybluerwith
models
redshift at a rate which indicates that their stellar popula-
Figure 1 shows that the luminosity of the BCGs (inside a tionswereformedatz >2andevolvedpassivelythereafter.
fixed metric aperture of 50kpc diameter) does not evolve If the total stellar mass of the galaxies has remained con-
strongly with redshift. This is shown more clearly on the stant, we would expect them to get progressively brighter
toppanelofFigure2,wheretheno-evolutionpredictionhas with redshift, as the average ages of their stellar popula-
been subtracted from the data. It is clear that for q0 =0.0 tions get younger. Since that brightening is not observed,
theobservedmagnitudesdonotseemtoevolvewithredshift. the most likely explanation is that the total mass in stars
For q0 = 0.5 there is a hint of negative evolution: BCGs at intheBCGshasnotremainedconstantbuthasgrownwith
highredshifttendtobemarginallyfainterthanlowredshift time. Wewill now estimate therate of this growth.
ones. We used evolutionary population synthesis models
(cid:13)c —RAS,MNRAS000,1–9
The K-band Hubble diagram for the brightest cluster galaxies 5
((Bruzual & Charlot 1997); see also (Bruzual & Charlot 3 GALAXY FORMATION AND EVOLUTION
1993)) to predict the expected luminosity evolution of a MODELS
passively-evolving stellar population formed at a given red-
In this section, we discuss the predictions of the semi-
shift. That should represent the brightening of the stellar
analytic models of the Durham and Munich groups. Full
populations due to the decrease in average stellar age with
details of the Durham models can be found in (Cole et al.
redshift. A Scalo (1986) Initial Mass Function with stellar
1994) and(Baugh,Cole&Frenk1996b).Theversionofthe
masses in the range 0.1M⊙ ≤ m ≤ 125M⊙ was assumed.
Munich models used here is the same as that described in
Theexactvalueoftheuppermasslimitisnotcritical given
(Kauffmann&Charlot1997).FurtherdetailsabouttheMu-
theexpectedages of thestellar populationsin theobserved
nichmodels can befoundin (Kauffmann,White& Guider-
redshift range, provided that it is above the turn-off mass
doni 1993). Although the two models are very similar in
at the ages corresponding to z < 1. The model predictions
outlineandintheirbasicframework,manyfeatures,forex-
are plotted on Figure 1 (LE lines) for formation redshifts
ample the simple parameterisations used to describe star
zfor =2and zfor =5. Thesemodels produceacolour evolu-
formation and feedback, are different in detail.
tion compatible with the observations of early-type cluster
Briefly, the hierarchical collapse and merging of an en-
galaxies. Note that zfor < 2 is clearly ruled out by the ob-
semble of dark matter halos is followed using Monte Carlo
servedslow colourevolution(cf.section1).Makingzfor >5
techniques.Gasvirialisesinthedarkmatterhalos,coolsra-
makesverylittle differenceto theage of thestars. Wehave
diativelyandcondensesontoacentral galaxy at thecoreof
assumed solar metallicity, but changing the metal content
each halo. Star formation occurs at a rate proportional to
does not significantly alter the predictions. Other models
themassofcoldgaspresent.Thesupplyofcoldgasisregu-
(e.g. (Arimoto & Yoshii 1986; Kodama & Arimoto 1997))
lated by feedback processes associated with star formation,
predict very similar luminosity evolution, thus we believe
such as stellar winds and supernovae. As time proceeds, a
thatthemodelsconsideredherebracketreasonablywellthe
halowillmergewithanumberofothers,forminganewhalo
luminosity evolution expected from the colour constraints
of larger mass. All gas which has not already cooled is as-
and that thepredictions are not very model-dependent.
sumed to be shock heated to the virial temperature of this
In Figure 2 (lower two panels) we have plotted the ob-
newhalo.Thishotgasthencoolsontothecentralgalaxyof
served magnitudes after subtracting the luminosity evolu-
the new halo, which is identified with the central galaxy of
tionpredictions.Sincethemodelsassumeaconstantstellar
its largest progenitor. The central galaxies of the other pro-
mass,therateofchangewithredshiftintheK magnitudes,
genitors become satellite galaxies, which are able to merge
after correcting for theexpected brightening dueto passive
withthecentralgalaxyonadynamicalfrictiontimescale.If
evolution, should be a direct measurement of the rate of
amergertakesplacebetweentwogalaxiesofroughlycompa-
changeinstellarmass.Notethatstrictlyspeaking,whatwe
rablemass,themergerremnantislabelledasan“elliptical”
call “mass in stars” really means “mass in luminous stars”,
andallcoldgasistransformedinstantaneously intostarsin
i.e., thosewhich contributetothegalaxy K-bandlight.Pa-
rameterising the evolution as M (z) = M (0)×(1+z)γ, a“starburst”.Thesamestellarpopulationmodels((Bruzual
⋆ ⋆
& Charlot 1997)) used in Section 2.2 are employed to turn
least-squares fitsgive thefollowing results:
thestarformationhistoriesofthemodelgalaxiesintobroad
q0 =0.0 zfor =2 γ =−1.2±0.3 band luminosities.
zfor =5 γ =−0.7±0.3 Inthesemodels,therearethreedifferentwaysinwhich
q0 =0.5 zfor =2 γ =−2.2±0.3 the stellar masses of the brightest galaxies in clusters can
zfor =5 γ =−1.7±0.3 grow:
These rates imply that the mass in stars of a typical (i) merging of satellite galaxies that sink tothecenterof
BCGgrewbyafactor≃2ifq0 =0.0or≃4ifq0 =0.5from thehalo through dynamical friction
z≃1 to z≃0, i.e., in the last ≃8–10Gyrs.
(ii) quiescentstarformationasaresultofgascoolingfrom
At this point we would like to make a historical com-
thesurroundinghot halo medium
ment.Oneofus(AAS)carriedouttheanalysisdescribedin
(iii) “bursts”ofstarformation associated withtheaccre-
thissection independently of therest oftheauthorsand in-
tion of a massive satellite.
vited the Durham and Munich groups to make predictions,
using the semi-analytic models described in section 3, for
As noted by (Kauffmann, White & Guiderdoni 1993),
the growth of the stellar mass in BCGs as a function of
thecoloursandabsolutemagnitudesofcentralclustergalax-
redshift. In the first instance, this was done without any
ies are predicted to be bluer and brighter than observed if
prior knowledge of the observationally determined rates and
all the gas present in the cooling flows of massive clusters
without any interaction between the two groups to ensure
turns into visible stars. To fix this problem, these authors
that the predictions where truly independent. The surpris-
simplyswitchedoffstarformationincoolingflowswhenthe
ing level of agreement of the model predictions with each
circularvelocityofthehaloexceeded500kms−1.Thisvalue
other,andwiththeobservations,encouragedustocompare
was chosen so as to obtain a good fit to the bright end of
themodel outputwith thedata in more detail. This is pre-
the Virgo cluster luminosity function. Another solution is
sented in thenext section.
to assume that gas in the central regions of halos follows a
differentdensityprofiletothatofthedarkmatter.Inpartic-
ular, if the gas has a constant density core, cooling is very
much less efficient in the centres of massive clusters. The
precise form of the gas density profile is much less impor-
(cid:13)c —RAS,MNRAS000,1–9
6 A. Arag´on-Salamanca, C.M. Baugh and G. Kauffmann
12
11
10
9
12
11
10
9
1 2 3 4 1 2 3 4
Figure 4. The average stellar mass of BCGs as a function of
Figure3. Thebuildupinstellarmassofthelargestprogenitor redshift. We have selected galaxies at each epoch that reside in
infourexamples ofBCGstakenfromtheMunichmodels,which haloswithcircularvelocitiesgreaterthan700kms−1.Thepoints
reside in dark matter halos with circular velocity 1000kms−1 at have been normalisedby dividingby the average stellar mass of
thepresent day. Star formationisswitchedoffinanyprogenitor the BCGs ineach model at z =0. (a) shows the predictions for
halo whose circular velocity is in excess of 500kms−1. The solid aColdDarkMatteruniversewiththecriticaldensity,whilst(b)
linesshowtheaccumulationofstellarmassfrommergingevents, shows an open universe with a present day density parameter
thedashedlinesshowthemasscontributedbystarsformingfrom of Ω0 = 0.2. In each panel, the filled circles show the results
gascoolingfromthesurroundinghothalomedium,andthedot- fromtheMunichmodelsandtheopentrainglesshowtheresults
tedlinesshowthemasscontributedbystarformationburstsas- of the Durham models. The curves show the trends in stellar
sociatedwithmajormergers. mass deduced in Section 2.2; the dotted curve corresponds to
zfor =5 and the dashed curve to zfor =2. The open circles in
(a)and(b)showtheevolutionintheaveragestellarmassofthe
BCGs predicted by the Munich model when a cut in halo mass
tant for cooling in low mass halos, since these objects are of2×1014h−1M⊙ isappliedtoselectclustersateachredshift.
denser and havemuch shorter cooling times.
Infigure3,we considertheevolution of asubsetof the
z = 0 BCGs in a model with star formation switched off objects with increasing redshift. We also explore the effect
in haloswith circular velocity greater than500kms−1.The of selecting clusters by mass instead of circular velocity.
solid line shows the cumulative growth in stellar mass of We present the model predictions for two Cold Dark
theBCG duetomergingevents.Thedashedlineshows the Matter cosmologies; one with the critical density and an
cumulativecontributionfrom starsformedfrom quiescently open model with density parameter Ω0 = 0.2. The density
coolinggas,andthedottedlineisthecontributionfromstars fluctuations in each case are normalised to reproduce the
formedinburstsduringmajormergers.Ascanbeseen,star abundanceofrichclusters(e.g.(White,Efstathiou &Frenk
formationfromburstsandcoolinggasaccountforonlyafew 1993); (Eke, Cole & Frenk, 1996); (Viana & Liddle 1996)).
percent of the final mass of the BCG. The rest comes from Atseveralredshiftsintherange0≤z≤1,wehaveselected
accreted galaxies. The four panels in the figure represent ∼200haloswithcircularvelocitiesgreaterthan700kms−1.
independent Monte Carlo realizations of the formation of a Note that the clusters are weighted so that they are rep-
BCGinahaloofcircularvelocity1000kms−1.Itisstriking resentative of the mass distribution of halos at the given
thatalthougheachBCGhasasignificantlydifferentmerging redshift.
history, their final stellar masses differ very little from one Theevolution oftheaveragestellar massof thebright-
realization toanother. est galaxies in the halos with redshift is shown in Figure 4.
Wewillnowmakeacomparisonwiththedatapresented WehavedividedtheaveragemassoftheBCGsateachred-
in section 2. The observational selection picks out the rich- shiftbytheaveragemassofBCGsfoundintheredshiftzero
est clusters ateachredshift,butthesampleisnotcomplete clusters.TheopentrianglesshowtheresultsoftheDurham
inanywell-definedsense.Wemimictheobservationalselec- models, which adopt the halo density profile of (Navarro,
tion as best we can by calculating the masses of BCGs in Frenk & White 1996) for the dark matter. The gas is as-
halos with circular velocities greater than some fixed value sumed to follow a different density profile, with a constant
as a function of redshift. This means we are selecting rarer densityatthecoreofthehalo(fulldetailsoftheseextensions
(cid:13)c —RAS,MNRAS000,1–9
The K-band Hubble diagram for the brightest cluster galaxies 7
Figure 5. The rest frame V −I colour of the model BCGs as
a function of redshift. Again, (a) shows the results for a critical
Figure 6. (a) The average stellar mass of BCGs at z =0 as a
densityCDMuniverse,whilst(b)showsthemodeloutputforan
function of the circular velocity cut used to select clusters. The
openuniversewithΩ0=0.2.ThefilledsymbolsshowtheMunich mean BCG mass increases by a factor of two over a range in
models and the open symbols show the Durham models. The
circular velocity that corresponds to a increase by a factor of 5
openstarsin(a)showaDurhammodelinwhichthegasdensity
in dark matter halo mass. The filled symbols show the Munich
profileisthesameasthatofthedarkmatterinthehalo.Hence,
resultsand the opensymbols show the Durham results.(b) The
gas cools more efficiently and more recent star formation takes
scatterintheabsoluteK-magnitudesofBCGsasafunctionofthe
place, makingthe BCG’s bluer. The lineisa fit to the observed
circular velocity used to define the cluster sample. The Durham
colour evolution of the BCG’s taken from Arago´n-Salamanca et
modelspredictalargerscatter thantheMunichmodels.
al.(1993).
exhibit opposite trends in colour. The Munich models are
totheoriginal(Coleetal.1994)modelwillbegiveninCole redderthaninaflatcosmology,becausetheBCGsformear-
etal,inpreparation).Thefilledcirclesshowthepredictions lierandcontainolderstars.Ontheotherhand,theDurham
of the Munich models, in which isothermal density profiles modelsarebluer.Thisisbecausehalosinalow-densityUni-
areassumedforboththegasandthedarkmatter.Starfor- versearemoreconcentratedandgasstillcoolsatthecluster
mation is switched off in halos with a circular velocity in centres, even if a different density profile is assumed.
excess of 500kms−1. The curves show the growth in stellar An important question to consider is how our results
mass with redshift of theBCGs deducedin Section 2.2; the would beaffected byadoptingadifferentselection criterion
dottedlinesshowtheparameterisation withz =5whilst for the clusters in the model. To explore this, Figure 6a
for
thedashedlineshowsz =2.Bothmodelsfittheobserved shows how the average mass of a z = 0 BCG changes as
for
evolution verywell. a function of circular velocity cutoff for both the Munich
In Figure 5, we show the evolution in the average rest- and Durham models. This plot shows that more massive
frame V −I colours of the BCGs. Once again, the open BCGs are found in more massive halos. The stellar mass of
triangles showtheDurhammodels andthefilled circles the aBCGchangesbyafactorof2forafactor5increaseinhalo
Munich models. The curves are a fit to the observed colour mass.Figure 6bshows howthepredictedscatterin K-band
evolution given in (Arag´on-Salamanca et al. 1993). For the absolutemagnitudechangesasafunctionofcircularvelocity
Ω = 1 cosmology, both models fit the observed colour evo- cutoff.Ascanbeseen,thescatterdecreasesasricherclusters
lution reasonably well. The Durham models predict larger are selected. Both the Munich and Durham models predict
scatter in the colours because the BCGs are still undergo- largerscatterthanthatobserved,thoughthediscrepancyis
ingsomelow-levelstarformation, whereastheBCGs inthe worse for theDurham models.
Munich models have ceased forming stars altogether. For Itshouldbenotedthatclustersoffixedcircularvelocity
reference, we also show a model (shown by the open stars) arelessmassiveathighredshiftbyafactor≃(1+z)3/2(this
where cooling and star formation are efficient at the cen- scaling arises from thefact that halos collapse and virialize
tresofmassiveclusters.Thisisamodelwhereboththegas at a density ∼ 200ρ¯(z), where ρ¯(z) is the mean density of
andthedarkmatterfollow thestandard(Navarro,Frenk& theUniverseatredshiftz).Selectingclustersaccordingtoa
White1996) densityprofile.Inthiscase,thecoloursaretoo halo mass cutoff, rather than a circular velocity cutoff, will
blue by ∼0.1−0.2 magnitudes. In the low-density cosmol- thus select more massive BCGs at high redshift. The effect
ogy, it is interesting that the Durham and Munich models of mass selection on the predicted evolution is shown by
(cid:13)c —RAS,MNRAS000,1–9
8 A. Arag´on-Salamanca, C.M. Baugh and G. Kauffmann
theopencirclesinFigure4,wherewehaveselectedclusters ACKNOWLEDGMENTS
greaterthan2×1014M⊙ateachredshift.Themassevolution
AAS acknowledges generous financial support from the
isnowslightlyweaker,buttheeffectissmallandthemodel
Royal Society. We thank T. Shanks for encouraging us to
results are still in good agreement with theobservations.
have a closer look at the K-band Hubble diagram, and
G.BruzualandS.Charlotforallowingustousetheirmodel
results prior to publication. We thank the anonymous ref-
4 DISCUSSION eree for useful comments. The version of theDurham semi-
analyticmodelsusedtoproducethepredictionsinthispaper
We have shown that the K-band Hubble diagram for a
is the result of a collaboration between Shaun Cole, Carlos
sample of brightest cluster galaxies in the redshift range
Frenk,CedricLaceyandCMB,supportedinpartbyaPar-
0<z<1hasaverysmallscatter(0.3magnitudes),ingood
ticlePhysicsandAstronomyResearchCouncilrollinggrant.
agreementwithearlierstudies.TheBCGsexhibitverylittle
This work was carried out under the auspices of EARA, a
luminosityevolutioninthisredshiftrange:ifq0 =0.0wede- European Association for Research in Astronomy, and the
tectnoluminosityevolution;forq0 =0.5wemeasureasmall TMR Network on Galaxy Formation and Evolution funded
negative evolution (i.e., BCGs were about 0.5magnitudes
bythe European Commission.
fainter at z = 1 than today). But substantial positive lu-
minosity evolution would be expected if the mass in stars
of these galaxies had remained constant over this period of
time:BCGsshouldhavebeenbrighter inthepastsincetheir
REFERENCES
stars were younger. Themost likely explanation for theob-
served zero or negative evolution is that the stellar mass of Abell,G.O.1957, ApJS,3,221
the BCGs has been assembled over time through merging Abell,G.O.,Corwin,H.G.&Olowin,R.P.1989, ApJS,70,1
and accretion, as expected in hierarchical models of galaxy Arago´n-Salamanca, A., Ellis, R.S., Couch, W.J. & Carter, D.
1993,MNRAS,262,764
formation. Since the colour evolution of the BCGs is con-
Arago´n-Salamanca,A.,Ellis,R.S.,Schwartzenberg,J.-M.&Berg-
sistent with that of an old stellar population (z > 2)
form eron,J.1994,MNRAS,421,27
that is evolving passively, we have used evolutionary pop-
Arimoto,N.&Yoshii,Y.1986,A&A,164,260
ulation synthesis models to estimate the rate of growth in
Barger, A.J., Arago´n-Salamanca, A., Ellis, R.S., Couch, W.J.,
stellarmassforthesesystems.Wefindthatthestellarmass Smail,I.&Sharples,R.M.1996,MNRAS,279,1
in a typical BCG has grown by a factor ≃ 2 since z ≃ 1 if Barger,A.J,Arago´n-Salamanca,A.,Smail,I.,Ellis,R.S.,Couch,
q0 =0.0 or by factor ≃4 if q0 =0.5. W.J., Dressler, A., Oemler, A., Poggianti, B.M. & Sharples,
Twoindependentgroupsofgalaxyformation modellers R.M.1997,ApJ,inpress
predicted thedecrease in stellar mass of theBCGs with in- Baugh,C.M.,Cole,S.&Frenk,C.S.,1996,MNRAS,283,L15
creasingredshift,inadvanceofseeingthedataandwithout Baugh,C.M.,Cole,S.&Frenk,C.S.,1996b,MNRAS,283,1361
anyfinetuningoftheirsemi-analyticmodelparameters.We Baugh, C.M., Cole, S., Frenk, C.S. & Lacey, C.G., 1997, ApJ
submitted,astro-ph/9703111
haveextractedthepropertiesofBCGsinmassivehaloswith
circularvelocitiesgreaterthan700kms−1ormassesgreater Bower,R.G.,Lucey,J.R.&Ellis,R.S.,1992a,MNRAS,254,589
Bower,R.G.,Lucey,J.R.&Ellis,R.S.,1992b,MNRAS,254,601
than 2×1014M⊙, at various redshifts. The average stellar BruzualA.,G.&Charlot,S.1993,ApJ,405,538
massoftheBCGsincreasesbyafactorof∼4−5inthecrit-
BruzualA.,G.&Charlot,S.1997,inpreparation
ical density models. In the low density models, the growth Burstein,D.&Heiles,C.1982,AJ,87,1165
instellarmassismoremodest,betweenafactor2to3.This Cole,S.,1991,ApJ,367,45
isbecauseclustersassemble athigherredshift inalowden- Cole, S., Arago´n-Salamanca, A., Frenk, C.S., Navarro, J.F. &
sity Universe. Note, however, that both models agree well Zepf,S.E.1994,MNRAS,271,781
with the data when the appropriate value of q0 is used in Couch,W.J.,Ellis,R.S.,Malin,D.F.&MacLaren,I.1991, MN-
the analysis. It is not possible to make statements about a RAS,249,606
Couch,W.J.etal.1997,inpreparation
preferred cosmology from this exercise.
Eke,V.R.,Cole,S.,Frenk,C.S.,1996,MNRAS,282,263
We also find that in order to reproduce the observed
Ellis,R.S.,Smail,I.,Dressler,A.,OemlerJr.,A.,Butcher, H.&
colours of the galaxies, some mechanism must act to sup-
Sharples,R.M.1997, ApJ,483,582
press visible star formation in thecooling flows of themost
Fabian,A.C.,Nulsen,P.E.J.&Canizares,C.R.,1982,MNRAS,
massive halos. It has been postulated that much of this
201,933
gas may be forming low-mass stars ((Fabian, Nulsen & Grasdalen, G.L. 1980, in Objects of High Redshift, IAU Symp.
Canizares, 1982)) or cold gas clouds ((White et al. 1991)). No. 92, ed. G.O. Abell & P.J.E. Peebles, Reidel, Dordrecht:
Another possibility we have explored is that the gas may Reidel,269
belessconcentratedinthecentresofclustersthanthedark Gunn,J.E.&Oke,J.B.1975,ApJ,195,255
matter,andhencenotabletocoolefficiently.Inbothcases, Gunn,J.E.,Hoessel,J.G.&Oke,J.B.1986,ApJ,306,30
theevolutionintheK-bandluminositiesoftheBCGscomes Heyl, J.S., Cole, S., frenk, C.S., Navarro, J.F., 1995, MNRAS,
274,755
aboutalmost exclusivelyasaresultofthemerging ofsatel-
Hoessel,J.G.1980, ApJ,241,493
litegalaxies inthecluster.Animportantandunanticipated
Kauffmann,G.,1995,MNRAS,274,161
result of our analysis is that the predicted scatter in the
Kauffmann,G.,1996,MNRAS,281,487
stellar masses of the BCGs built through merging and ac-
Kauffmann,G.,White,S.D.M.&Guiderdoni,B.1993,MNRAS,
cretion is still quite small, although somewhat larger than 264,201
the observed one. The scatter depends on the criteria used Kauffmann,G.,Guiderdoni,B.&White,S.D.M.1994,MNRAS,
to select the model clusters. 267,981
(cid:13)c —RAS,MNRAS000,1–9
The K-band Hubble diagram for the brightest cluster galaxies 9
Kauffmann, G., & Charlot, S., 1997, MNRAS, in press, astro-
ph/9704148
Kristian,J.Sandage, A.&Westphal, J.A.1978,ApJ,221383
Kodama,T.&Arimoto,N.1997,A&A,320,41
Lacey, C.G.&Silk,J.1991,ApJ,381,14
Lauer,T.R.&Postman,M.1992, ApJ,400,L47
Lebofsky, M.J. 1980, in Objects of High Redshift, IAU Symp.
No. 92, ed. G.O. Abell & P.J.E. Peebles, Reidel, Dordrecht:
Reidel,257
Lebofsky,M.J.&Eisenhardt,P.R.M.1986,ApJ,300,151
Lilly,S.J.&Longair,M.S.1982,MNRAS,199,1053
Lilly,S.J.&Longair,M.S.1984,MNRAS,211,833
Lilly,S.J.,1989a, ApJ,340,77
Lilly, S.J., 1989b, in The Epoch of Galaxy Formation, ed. C.S.
Frenketal.,Dordrecht:Kluwer,63
Lubin,L.M.1996,AJ,112,23
Navarro,J.F.,Frenk,C.S.&White,S.D.M.,1996,ApJ,462,563
Oke,J.B.,Gunn,J.E.&Hoessel,J.G.1996,AJ,111,29
Peach,J.V.1970,ApJ159, 753
Peach,J.V.1972,inExternalGalaxiesandQuasi-StellarObjects,
IAUSymp.No.44,ed.D.S.Evans,Dordrecht:Reidel,314
Postman,M.&Lauer,T.R.1995, ApJ,440,28
Rakos,K.D.&Schombert, J.M.1995,ApJ,439,47
Sandage, A.1988,ARA&A,26,561
Sandage, A.,Kristian,J.&Westphal,J.A.1976,ApJ,205,688
Scalo,J.M.1986, Fund.CosmicPhys.,11,1
Schneider,D.P.,Gunn,J.E.&Hoessel,J.G.1983a,ApJ,264,337
Schneider, D.P., Gunn, J.E. & Hoessel, J.G., 1983b, ApJ, 268,
476
Smail, I, Dressler, A., Kneib, J.-P., Ellis, R.S., Couch, W.J.,
Sharples,R.M.&OemlerJr.,A.1996,ApJ,469,508
Smail, I, Dressler, A., Couch, W.J., Ellis, R.S., Oemler Jr., A.,
Butcher,H.&Sharples,R.M.1997, ApJS,110,213
Stanford, S.A., Eisenhardt, P.R.M. & Dickinson, M.E. 1997, in
preparation
Viana,P.T.P.&Liddle,A.R.,1996,MNRAS281,
White,D.A.,Fabian,A.C.,Johnstone,R.M.,Mushotsky,R.F.&
Arnaud,K.A.,1991,MNRAS,252,72
White,S.D.M.,&Frenk,C.S.,1991, ApJ,379,52
White, S.D.M., Efstathiou, G., & Frenk, C.S., 1993, MNRAS,
262,1023
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