The formation of the brightest cluster galaxies in cosmological simulations: the case for AGN ...

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Year: 2012
The formation of the brightest cluster galaxies in cosmological simulations:
the case for active galactic nucleus feedback
Martizzi, Davide ; Teyssier, Romain ; Moore, Ben
Abstract: We use 500 pc resolution cosmological simulations of a Virgo-like galaxy cluster to study the
properties of the brightest cluster galaxy (BCG) that forms at the centre of the halo. We compared
twosimulations; oneincorporatingonlysupernovafeedbackandasecondthatalsoincludesprescriptions
for black hole growth and the resulting active galactic nucleus (AGN) feedback from gas accretion. As
previous work has shown, with supernova feedback alone we are unable to reproduce any of the observed
properties of massive cluster ellipticals. The resulting BCG rotates quickly, has a high Sérsic index, a
strong mass excess in the centre and a total central density profile falling more steeply than isothermal.
Furthermore, itisfartooefficientatconvertingmostoftheavailablebaryonsintostarswhichisstrongly
constrained by abundance matching. With a treatment of black hole dynamics and AGN feedback the
BCGpropertiesareingoodagreementwithdata: theyrotateslowly,haveacoredsurfacedensityprofile,
a flat or rising velocity dispersion profile and a low stellar mass fraction. The AGN provides a new
mechanism to create cores in luminous elliptical galaxies; the core expands due to the combined effects
of heating from dynamical friction of sinking massive black holes and AGN feedback that ejects gaseous
material from the central regions.
DOI: https://doi.org/10.1111/j.1365-2966.2011.19950.x
Posted at the Zurich Open Repository and Archive, University of Zurich
ZORA URL: https://doi.org/10.5167/uzh-70061
Journal Article
Published Version
Originally published at:
Martizzi, Davide; Teyssier, Romain; Moore, Ben (2012). The formation of the brightest cluster galaxies
in cosmological simulations: the case for active galactic nucleus feedback. Monthly Notices of the Royal
Astronomical Society, 420(4):2859-2873.
DOI: https://doi.org/10.1111/j.1365-2966.2011.19950.x
Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed13April2012 (MNLATEXstylefilev2.2)
The formation of the brightest cluster galaxies in
cosmological simulations: the case for AGN feedback
2
1 Davide Martizzi1⋆, Romain Teyssier1,2 and Ben Moore1
0
2 1Institute for Theoretical Physics, Universityof Zurich, CH-8057 Zu¨rich, Switzerland
r 2CEA Saclay, DSM/IRFU/SAP, Bˆatiment 709, F-91191 Gif-sur-Yvette,Cedex, France
p
A
13April2012
2
1

ABSTRACT
]
O We use 500pc resolution cosmological simulations of a Virgo–like galaxy cluster to
study the propertiesofthe brightestclustergalaxy(BCG) thatformsatthe centerof
C
the halo. We compared two simulations; one incorporating only supernovae feedback
.
h and a second that also includes prescriptions for black hole growth and the resulting
p AGN feedback from gas accretion. As previous work has shown, with supernovae
- feedback alone we are unable to reproduce any of the observed properties of massive
o
cluster ellipticals. The resulting BCG is rotating quickly, has a high S´ersic index,
r
t a strong mass excess in the center and a total central density profile falling more
s
a steeply than isothermal. Furthermore, it is far too efficient at converting most of the
[ available baryons into stars which is strongly constrained by abundance matching.

With a treatment of black hole dynamics and AGN feedback the BCG properties are
4
in good agreementwith data: they rotate slowly, have a cored surface density profile,
v
a flat or rising velocity dispersion profile and a low stellar mass fraction. The AGN
1
7 provides a new mechanism to create cores in luminous elliptical galaxies; the core
3 expands due to the combined effects of heating from dynamical friction of sinking
5 massive black holes and AGN feedback that ejects gaseous material from the central
. regions.
6
0 Key words: blackholephysics–cosmology:theory,large-scalestructureofUniverse
1
– galaxies: formation, clusters: general – methods: numerical
1
:
v
i
X
r 1 INTRODUCTION fromthecoldgasthatisexpectedtocollect atthecentreof
a thepotential.Thesatellite galaxiesthemselvescanundergo
In the standard ΛCDM cosmological scenario, galaxy for-
further evolution inside the cluster due to the interaction
mation proceeds hierarchically and galaxy clusters are the
with the hot intracluster medium, or gravitational interac-
largest and most recently assembled bound systems in the
tions with the cluster potential and other massive galaxies.
universe.TheentireHubblesequencecanbefoundingalaxy
There’s growing evidencethat present daymassive galaxies
clusters;fromblueextendedspiralstoredmassiveelliptical
areformedintwophase(Oseret al.2010):atredshiftz&2
spheroids.Forthisreason galaxy clusterscan beconsidered
stars are formed within galaxies from infalling cold gas, at
asidealenvironmentsforthestudyofgalaxyformation and
redshift z . 3 galaxies mainly grow through accretion of
evolution. The brightest cluster galaxy (BCG), is usually
stellar material. Massive early type galaxies can assemble
the largest galaxy that lives at the bottom of the cluster
more than half of their present day mass through dry mi-
dark matter halo. Its stars can get there in a number of
nor mergers at z . 2 (Naab et al. 2009). These processes
ways. Some of the stars will form within the rarest peaks
affecttheirstar-formation historiesandtheirmorphological
collapsing at high redshift - those galaxies and their dark
appearance.
matterhalosquicklyvirialisethroughviolentrapidmerging
and end up at the centre of the cluster. Stars can also be
Explaining the formation of very massive BCGs at
aquiredaftertheclusterformedthroughthedynamicalfric-
the center of galaxy clusters is one of the most challeng-
tionandmergingwithotherBCGsorwiththemostmassive
ing open problems in galaxy formation research. Standard
satellites of the cluster. Finally, the stars may form in-situ
galaxy formation models in the context of ΛCDM cosmol-
ogy are affected by the so–called ”overcooling problem”:
massive galaxies are predicted to be too bright and too
⋆ E-mail:[email protected] blue when compared to massive galaxies in the nearby
2 D. Martizzi et al.
universe (Borgani & Kravtsov 2009). These models find a withothernumericalsimulationstudies.Thefinalsectionis
stellar content in massive cluster galaxies that is signif- left for discussion.
icantly above the observed values (Kravtsov et al. 2005),
even if extreme supernovae feedback recipes are included
(Borgani et al. 2004). Onescenario that has been proposed
2 NUMERICAL TECHNIQUES
tosolvethisprobleminvolvesfeedbackprocessesfromSuper
Massive Black Holes (SMBHs), usually referred to as AGN In this section we describe the numerical methods and the
feedback.Theoreticalconsiderations(Tabor & Binney1993; initialconditionsusedtomodeltheVirgo–likeclusterwewill
Ciotti & Ostriker1997;Silk & Rees1998)suggestthatthese study in this paper. We consider two numerical cosmologi-
processesshouldprovideenoughenergytopreventgasfrom cal simulations that have been presented by Teyssier et al.
accumulating in the central regions of galaxy clusters thus (2010). They were performed using the zoom-in technique
quenchingstarformation. Semi-analytical models including which allows us to obtain the required effective resolution
AGNfeedbackcoupledwithN-bodysimulationshaveshown in selected regions of the computational domain. We con-
that most of thestellar mass in present time BCGs was as- sideraperiodiccubicboxoftheuniverseofside100Mpc/h
sembled through dry minor mergers, following a phase of thathasthestandardΛCDMcosmologicalparameters,with
quiescent star formation influenced by feedback processes Ωm = 0.3, ΩΛ = 0.7, Ωb = 0.045, σ8 = 0.77 and H0 = 70
(Lucia & Blaizot 2007). The strongest evidence supporting km/s/Mpc. We used the Eisenstein & Hu (1998) transfer
the existence of AGN feedback is provided by observations function and the grafic package (Bertschinger 2001) in its
ofX-raycavitiesandradiocavitiesingalaxyclusters.These parallel implementation mpgrafic (Prunet et al. 2008) to
have been interpreted as buoyantly rising bubbles of high generate our initial conditions. We first ran a low resolu-
entropy material injected in the cluster core by jets of rela- tion dark matter only simulation, then we identified dark
tivistic particles. The success of numerical hydrodynamical matter halos at z = 0. From the original halo catalog we
simulations including AGNdriven buoyantlyrising bubbles constructed a set of candidate halos whose virial masses lie
in reproducing masses and colours of observed BCGs has in the range 1014 to 2×1014 M⊙/h. Finally, we identified
been shown by Sijacki & Springel (2006). Thus, AGN feed- ourfinalhalobasedonitsassemblyhistory:mostofitsmass
back is expected to play a significative role in shaping the is already in place at z = 1, therefore it can be considered
properties of BCGs. as relaxed at z=0. Itsfinal virial mass is Mvir ≃1014 M⊙,
In this paper we use two high resolution cosmological and M200c = 1.04×1014 M⊙ or M500c = 7.80×1013 M⊙,
simulations of a Virgo-like cluster, with and without AGN where indice c refers to the critical density. We stress that
feedback.ThesimulationswereperformedbyTeyssier et al. our aim is not to exactly reproduce the properties of the
(2010) using the AMR code RAMSES (Teyssier 2002). Virgo cluster, that is a relatively unrelaxed cluster, but to
Teyssier et al. (2010) showed that combining high spatial study the effect of AGN feedback on the formation of the
resolution and the effects of AGN feedback it is possible to central galaxy in a cluster with a similar mass. We select a
bringthestellarcontentintheclusterclosertotheobserved relatively relaxed halo: this allows usto focus on this effect
values, while a model without AGN feedback totally fails. withouthavingtodealwith averycomplex mergerhistory.
Here, we use the same simulations to study the effect of TheVirgo–likehalo wasthenre-simulated at higherresolu-
AGN feedback on the massive BCGs that form at the cen- tion includingdark matterand baryons.
ter of the cluster. The main questions we want to address
are:
2.1 The simulations
• What are the differences between the properties of the
The two cosmological hydrodynamical simulations consid-
BCG whenweincludeAGNfeedback andwhen wedonot?
ered in this paper were performed using the AMR code
We consider structural as well as kinematic quantities to
RAMSES (Teyssier 2002). The initial grid had an effective
addressthisproblem,includingellipticities,masses,velocity
size of 20483 and it has been used to extract a set of high
dispersions, rotational velocities and stellar surface density
resolution darkmatterparticlesonlyintheLagrangian vol-
profiles.
• What are the main ingredients that determine the ume of the halo, while a lower resolution has been used to
sample the rest of the periodic box. As a result we have
evolution of the BCG? Massive elliptical galaxies are ex-
22×106 particlesinthecosmological box,19×106 particles
pected to form through a long series of dry minor mergers
inthehighresolutionregionand8×106 particleswithinthe
(Naab et al.2007,2009),butprocessesconnectedtoSMBHs
virial radius of the halo at z = 0. This means that in the
and AGN feedback may also influencetheir evolution.
• Recent results showed that it is possible to repro- high resolution region we have a dark matter particle mass
duce some of the properties of massive elliptical galaxies of8.2×106 M⊙/handaresolutionelementmassof1.4×106
in the field and in galaxy groups neglecting AGN feedback M⊙/h for the baryoniccomponent.
TheAMRgridusedtosolvethehydrodynamicalequa-
(Naab et al.2009;Feldmann et al.2010).Isitpossibletodo
tions was initially refined to the same level as the particle
the same for BCGs in massive galaxy clusters? If not, can
grid (20483, level ℓ = 11), but 7 more levels of refinement
theproblem be solved by invokingAGN feedback?
were considered during the run (level ℓmax = 18). We used
The paper is organized as follows: the first section is a refinement criterion that allowed spatial resolution to be
dedicatedtothenumericalmethodsandthesub-gridrecipes nearly constant in physical units; in this way the minimum
adopted for our simulations (cooling, star formation and cell physical size was always close to ∆xmin = L/2ℓmax ≃
AGN feedback), while the second section presents our re- 500 pc/h. The grid was dynamically refined using a quasi-
sults, comparing our models with observational data and Lagrangianstrategy:whenthedarkmatterorbaryonicmass
The formation of the brightest cluster galaxies 3
Mass and spatial resolution supernovae: one M⊙ of metals per 10 M⊙ average progen-
itor mass is ejected in the ISM. This value for the metal
mcdm mgas m∗ ∆xmin
[106 M⊙/h] [106 M⊙/h] [106 M⊙/h] [kpc/h] yield has been chosen to match, on average, the metal en-
richmentfrom massivestars (Woosley & Weaver1995).Su-
8.2 1.4 0.3 0.38 pernovae feedback is modeled using the ”delayed cooling”
scheme (Stinson et al. 2006), i.e. we shut down gas cooling
for 50 Myr in the cells surrounding a star particle going
Table1.Massresolutionfordarkmatterparticles,gascellsand
supernova. Since regions where feedback acts are typically
star particles, and spatial resolution (in physical units) for our
verydense,thistechniquepreventsgasfromfastlyradiating
twosimulation.
awaythefeedbackenergy.SeeAgertz et al.(2011)formore
details.
inacellreaches8timestheinitialmassresolution,itissplit
It has been shown that these galaxy formation recipes
into 8 children cells.
are able to successfully reproduce the properties of spi-
ralgalaxies in thefield (Mayeret al. 2008; Governato et al.
2.2 Modelling the baryonic processes 2009, 2010; Agertz et al. 2011) as well as other observed
galaxy properties like the Kennicutt-Schmidt law, star
Gas dynamics is modeled using a second-order unsplit formation rates, galactic winds (Dubois & Teyssier 2008;
Godunov scheme (Teyssier 2002; Teyssier et al. 2006; Devriendtet al. 2010;Agertz et al. 2011).On galaxy group
Fromang et al. 2006) based on the HLLC Riemann solver scalesthesamerecipesarelesssuccessfulinreproducingthe
andtheMinModslopelimiter(Toro et al.1994).Weassume observedproperties(Feldmann et al.2010),whileongalaxy
aperfect gas equation ofstate (EOS)with γ =5/3. Part of cluster scales they fail (Borgani et al. 2004; Kravtsov et al.
thegalaxyformationprocesshasbeencalculatedusingsub- 2005; Borgani & Kravtsov 2009). In simulated galaxy clus-
grid models, since a correct modeling of the turbulent and ters similar sets of phenomenological models produce over-
multiphase interstellar medium (ISM) is beyond the reach coolingofgasthatleadstotheformationofahigherfraction
of present-day cluster simulations. In both simulations: ofstars thanobservedin realsystems(Borgani & Kravtsov
• The ISM has been modeled using a very simple EOS 2009).Ithasbeenarguedthatstarformationisquenchedin
for the gas halosmoremassivethanMc ≃6×1011 M⊙ (Cattaneo et al.
2006), and this mass threshold is thought to be related to
Tfloor =T∗(cid:18)nnH∗(cid:19)Γ−1 (1) tfrhoemstcaoblidlistaotihoontogfagsaascaccrectrieotnion(Bsihrnocbkosiman&dtDoetkheelt2r0a0n3s)it,iaoln-
thoughadditionalphysicalprocessesarerequiredtoprevent
where n∗ = 0.1 H/cc is the density threshold that defines overcooling. The favoured theoretical scenario proposed to
the star forming gas, T∗ = 104 K is a typical temperature solvetheovercoolingprobleminvolvestheroleofAGNfeed-
mimicking both thermal and turbulent motions in the ISM
andΓ=5/3 isthepolytropicindexcontrolling thestiffness backin halos ofmass M >Mc.Gas accretion favoursAGN
activityandtherelatedfeedbackonthegas(Cattaneo et al.
of the EOS. Gas cannot cool below the temperature floor,
2006). AGN feedback is expected to provide enough energy
while it can be heated above.
toheatupgasinhalosandpartiallyblowitaway,thuspre-
• Gas cooling is followed according to the
ventingfurtherstarformation.Theanalysisofcosmological
Sutherland & Dopita (1993) cooling function. We take
simulations of galaxy groups and clusters including AGN
into account H, He and metal cooling. Gas metallicity
feedbackliketheonesofPuchwein et al.(2008)supportthis
is advected as a passive scalar, and is self-consistently
scenario.
accounted for in the cooling function. We also considered
The two simulations of the Virgo–like cluster we are
the effect of the standard homogeneous UV background
considering differ substantially. The first run has been per-
of Haardt & Madau (1996), but we modified the starting
formed using only the galaxy formation recipes described
redshift, extrapolating the average intensity from zreion =6 above, without considering the presence of SMBHs and ne-
to zreion = 12. This extrapolation is justified by the fact glecting AGN feedback, therefore after much thought of a
that early reionization is expected in proto-cluster regions
clever acronymn, we call it the AGN-OFF run. In the sec-
(Iliev et al. 2008).
ond run we includeSMBHs and we take into account AGN
• Star formationisimplementedusingthefollowing sim-
feedback; we call it the AGN-ONrun.
plemodel.Wecreatenewstarparticlesincellswithgasden-
sity larger than n∗. The mass of the star particles depends
on resolution; in the present case we have chosen 3×105
2.3 SMBH growth and AGN feedback in the
M⊙/h. The formation rate of star particles is given by simulations
ρ˙∗ =ǫ∗ρtgas with tff =r323Gπρ (2) TheseedsforSMBHsformationarethoughttobeeitherPop
ff III stars (Madau & Rees 2001), or a result direct collapse
wheret isthelocalfree-falltimeofthegaseouscomponent of baryonic material within low angular momentum halos
ff
and ǫ∗ =0.01 is thestar formation efficiency. (Bromm & Loeb2003;Begelman et al.2006).Inbothcases
• Supernovaefeedbackisimplementedinthecode.A10% the seed SMBHs are expected to grow relatively quickly to
mass fraction of each star particle is ejected in supernovae MBH,s = 105 M⊙ when they will start to interact with the
explosions after 10 Myr.Weassume that thesupernovaen- environment and self-regulate their gas accretion rate. The
ergy is 1051 erg. We also include metal enrichment from fact that this black hole mass is at least one order of mag-
4 D. Martizzi et al.
nitude lower than the minimum SMBH mass observed in accountfor unresolvedmultiphaseturbulencein theSMBH
theMBH−σ relation (Gebhardt et al.2000;Gu¨ltekin et al. environment, and it’s value was originally chosen as con-
2009) allows us to consider MBH,s as the prototypical seed stant. Numerical studies by Booth & Schaye (2009) show
SMBH mass. that α should instead be considered as a function of
boost
Inourmodel,weusesinkparticlestosimulateSMBHs, the local density: it should be close to unity in low density
following the prescription of Krumholz et al. (2004). When regions, it should increase in high density regions, in order
thefollowing conditions aremet,wecreateanewSMBHin to match the subgrid model used for the unresolved turbu-
thesimulation: lence in the disks. As proposed by Booth & Schaye (2009),
we adopt
• The stellar density has to be greater than 0.1 H/cc
(s2te.4lla×r s1y0s6tMem⊙s.kpc−3). This ensures that SMBHs form in αboost = (cid:18)nnH∗(cid:19)2 if nH >n∗ =0.1 H/cc,
• Thestellar3Dvelocitydispersionhastobegreaterthan
α = 1 otherwise. (4)
boost
100 km/s. With this condition we require that the line–of–
sight velocity dispersion is σ1D > 60 km/s, in agreement We stress that the choice for this particular form of αboost
with theobserved MBH−σ relation. is strictly dependenton thechosen EOS for thegas.
• The gas density has to be greater than 1 H/cc. With Equation 3 does not provide any upper limit for the
thiscondition we are sure that seed black holes form in the accretionrate,howeveritcannotexceedtheEddingtonlimit
nuclear region of star forming disks.
• Noothersinkparticleispresentwithin10kpc.Nonew M˙ED = 4πGMBHmp with ǫr ≃0.1. (5)
ǫrσTc
seedSMBHwillbecreatedwithin10kpcfromanoldSMBH
residing at the centerof a galaxy. whereǫr isistheefficiencyatwhichaccretinggasrestmass
energy is converted into radiation. To enforce this upper
Each seed SMBH has a fixed mass MBH = 105 M⊙ and a limit we always set theaccretion rate to
fixed radius r = 4∆x ≃ 2 kpc, where ∆x is the spa-
tialresolutionsiinnkphysicalunits.WeassumethattheSMBH M˙acc =min(M˙BH,M˙ED) (6)
massishomogeneously distributedinsideasphereofradius At each time step, a total gas mass of M˙acc∆t is removed
r ,andweaddthisdensitydistributiontothetotalmass
sink from all cells within the sink radius, with the same weight-
densitywhensolvingthePoissonequation.Likedarkmatter
ing scheme as the one used to define average quantities
andstarparticles,sinkparticlesareadvancedintimebyin-
(Krumholzet al. 2004). In order to prevent the gas density
terpolating thegravitational force back tothesinkposition
from vanishing or becoming negative, we remove no more
using theinverse CIC scheme.
than 50% of thegas at each time step.
A key ingredient in our simulations is AGN feed-
In our simulations, AGN feedback is implemented
back from SMBHs. On the theoretical side, it is thought
in a way that allows self-regulated SMBH mass
that AGN feedback energy could be transported through
growth (Sijacki et al. 2007; Cattaneo & Teyssier 2007;
the gas by several processes, e.g. radiative feedback
Booth & Schaye2009),byinjectingthermalenergydirectly
(Ciotti & Ostriker 2001) or strong shocks (Begelman
into the gas surrounding the black hole. If the black hole
2004; Dubois et al. 2011; Gaspari et al. 2011). Additional
mass is too low, the amount of energy injected in the gas
feedback may come from production of cosmic rays
willnotbeabletoheatitup,soitwillremaincoldandwill
(Bru¨ggen et al. 2002; Chandran & Rasera 2007). On the
accrete onto the SMBH at rates close to Eddington limit.
theoretical side, all these processes are very complex to
In this case the SMBH growth can proceed exponentially
modelself-consistentlyandthereforeareverychallengingto
with time, with e-folding time scale equal to the Salpeter
be reproduced in hydrodynamical simulations. Additional
time
difficulties include the very high spatial resolution required
tostudytheseprocessesinadetailedway,althoughitisnot tS = ǫrσTc ≈45Myr (7)
4πGmp
onlyamatterofresolutionbutalsoofproperphysicalmod-
eling.Eveninstate-of-the-artcosmological hydrodynamical Feedback will become more efficient as long as the SMBH
simulations it is not possible to model these processes in a continues to grow, until the injected energy is enough to
self-consistentway,sothataphenomenologicaltreatmentof unbind the gas surrounding the black hole. In this regime
theproblem must be chosen. accretionwillbecomeBondi-Hoylelimitedandmassgrowth
MassaccretionontoSMBHsandAGNfeedbackareim- willproceedmoreslowly.Figure1showsthetimeevolution
plemented using a modified version of the Booth & Schaye oftheaccretion rateofthemost massiveSMBHinthesim-
(2009)modelwhichwasoriginally developedforSPHsimu- ulated region. Short bursts of Eddington limited accretion
lations.Thismodelisamodifiedversionofthatproposedby arefollowedbylongquiescentepochsofBondi-Hoylelimited
Springel et al. (2005). We compute the mass accretion rate accretion, self-regulated by SMBH feedback.
onto each SMBH using a modified Bondi-Hoyleformula At each time step we compute the thermal energy in-
jected in the gas surrounding each black hole as
4πG2M2 ρ
M˙BH =αboost(c2s +u2B)3H/2 (3) ∆E =ǫcǫrM˙accc2∆t. (8)
where ρ, cs and u are the average gas density, sound speed whereǫcisthecouplingefficiency,i.e.thefractionofradiated
and relative velocity within the sink radius, all computed energythatiscoupledwiththesurroundinggas.Thecorrect
following the approach of Krumholzet al. (2004). The pa- valueforǫ canbesetrequiringthesimulationstoreproduce
c
rameter αboost was introduced by Springelet al. (2005) to the observed MBH −σ relation; we use the fiducial value
The formation of the brightest cluster galaxies 5
an additional comparison with the BCG sample analysed
byBrough et al.(2011)toshowthatourresultsarerobust.
A final comparison is made with the cosmological hydro-
dynamical simulations performed by Naab et al. (2009) (a
massive early-typegalaxy) and Feldmann et al. (2010) (the
central galaxy of a group).
3.1 Identification of the BCGs
We identified galaxies in our simulations with the Adapta-
HOP algorithm (Aubertet al. 2004), using the version im-
plemented and tested by Tweed et al. (2009). This version
of the algorithm allows to use the Most Massive Substruc-
ture Method (MSM) to identify halos as well as their sub-
structures,alongwith theircenters,virial radiiandmasses.
Galaxy centers were identified by running the same halo
finderusingthestarparticles.Ineachoftheanalysedsnap-
shots, we defined the BCG as the object with the largest
stellar mass; we verified that such a definition of the BCG
also selects thegalaxy closest to thecluster halo center.
Inbothsimulations,theBCGsaresurroundedbyfairly
Figure 1. Timeevolution ofthe SMBHmassinred,andof its smooth stellar halos extending to beyond 50 kpc. Similar
instantaneous accretionrateinblack. stellar halos around BCGs have been found in numerical
simulationsbyotherauthors(Puchwein et al.2010),andare
similar to the intracluster light observed in galaxy clusters
ǫc ≃ 0.15 (Booth & Schaye 2009). The energy ∆E is not (Lin et al. 2003; Gonzalez et al. 2007; Giodini et al. 2009;
immediately injected in the gas, but its accumulated and
Rudicket al. 2010). There is no clear separation between
storedinanewvariableEAGN,sothatwecanavoidthegas the BCG and the intracluster stars, so just for accounting
instantlyradiatingawaythisenergyviaatomiclinecooling.
andcomparisonpurposes,acriterionshouldbechosentode-
Werelease this energy within thesink radius when
cidehowtoseparatethecentralgalaxyfromthestellarhalo.
3 We consider as part of the BCGs all the regions where the
EAGN > 2mgaskBTmin (9) stellardensityislargerthan2.5×106 M⊙/kpc3.Thischoice
where mgas is thegas mass within thesink radius and Tmin is justified by the fact that lowering the density threshold
is the minimum feedback temperature. Tmin should be cho- bya factor of twodoes not influencethevalues of themea-
sen to be at least 107 K, the temperature above which line suredstellarmassesbymorethan5%.Wealsocheckedthat
cooling is not very efficient, so that the resulting feedback themassestimatesweobtainusingthiscriterionarerobust
is independent of the value of Tmin. In our simulations we bycomparingthemwithestimatesobtainedusingtwoaddi-
adopt thefiducial valueTmin=107 K. tionalmethods:(i)wesubstitutedthe3Ddensitythreshold
This model allows us to phenomenologically reproduce with an equivalent surface density threshold; (ii) we use a
thetwoextremeregimesinwhichAGNfeedbackisthought criterion similar to that used by Naab et al. (2009), where
to work (Sijacki et al. 2007): theBCG isidentifiedastheset of starparticles enclosed in
asphericalregion offixedphysicalradius.Thevariationsin
(i) ”Quasarmode”:inthecaseofcolddensegasaccretion,
stellarmasswerealwayslessthan5%,thereforeweconsider
more energy is required to reach the energy threshold. A
themassesobtainedwiththestellardensitycriterionasour
large amount of energy is accumulated and released in a
fiducialvalues.
burst when theenergy threshold is reached. WefindthattheBCGmassatz=0isMstar =3.484×
(ii) ”Radio mode”: in the case of hot diffuse gas accre- 1012 M⊙ intheAGN-OFFrunandMstar =2.243×1011 M⊙
tion, less energy is required to reach the threshold. Energy in theAGN-ONrun.At z=1 wefindMstar =1.637×1012
is injected in thegas in a quasi-continuous fashion. M⊙ in the AGN-OFF run and Mstar =1.697×1011 M⊙ in
In the next section we will show how the presence or theAGN-ONrun.Atbothredshiftsthetotalstellarmassof
lack ofSMBHsandtheirfeedback can heavilyinfluencethe theBCG in theAGN-OFFsimulations are almost 10 times
structureof massive galaxies in clusters. larger. This fact implies that star formation quenching due
toAGNfeedbackprocessesisveryefficientinourmodeland
hassignificantly changedthestarformation historyalready
bya redshift z =1.
3 RESULTS
In Figure 2 we show the comparison of the stellar-vs-
In this section, we compare the properties of the BCGs in halo mass relation for the BCGs in our AGN-ON/OFF
our two simulations to show the strong differences between simulations with the predictions of abundance matching
the two models. We also compare our results with the two (Moster et al. 2010) (black solid line). The BCG mass pre-
observational samples of early-type galaxies at z ≈ 0 and dictedbytheAGN-OFFmodeldeviatesmorethan3σ from
z≈1 analysed byvan derWel et al. (2008). Westress that theaveragerelationobtainedthroughabundancematching.
BCGsareparticularkindsofearly-typegalaxies,sowemake Without feedback, the BCG forms stars at an efficiency of
6 D. Martizzi et al.
Figure 2. Comparison of the stellar-vs-halomass relation in 4 Figure3. StarformationrateintheBCGasafunctionoftime.
early-typegalaxiesfromdifferentcosmologicalsimulations(filled
and empty black dots). The red dotted line represents the rela-
tion expected for a 20% star formation efficiency from the uni- a factor 10, with the difference increasing towards z = 0.
versalbaryonfraction.Thesolidblacklineisthepredictionfrom Hirschmann et al. (2011) compare star formation rates of a
abundance matching (Mosteretal. 2010). The grey shaded ar-
widevarietyofsemi-analyticalmodelsandnumericalhydro-
eas representthe 1σ, 2σ and3σ scatter barsaroundthe average
dynamical zoom simulations: they also find that the differ-
relation.
ence between the star formation rates in models including
AGN and models do not including this effect is striking,
20% from the cosmic available baryon fraction, thus it lies howeversmaller than in our AGN-ONrun. A similar result
close to the dotted red line. On the contrary, the AGN-ON hasbeenfoundbyvan deVoort et al.(2011).Acomparison
modelpredictionisremarkablyclosetotheaveragerelation, withtheseresultssuggeststhatourAGNfeedbackmodelis
andwellinsidethe1σ scatterbars.Forcomparison withre- particularly efficient in quenching star formation. It should
cent simulations of massive early-type galaxies that do not bestressedthatthesuchhighfeedbackefficiencyisexpected
include AGN feedback, we show the results of Naab et al. because theresolution we reach is sufficient to resolve mas-
(2009) and Feldmann et al. (2010). The mass of the cen- sivegalaxieswhereSMBHresidealreadyatz &6,thusAGN
tralgroupgalaxysimulatedbytheseauthorsareboth∼3σ feedback starts playing its role in quenching star formation
abovetheaveragerelation;alsointhiscasetheresultisclose at very early times. It is interesting to note how in both
to the simplified model with 20% star formation efficiency. the simulations the star formation rate peaks before red-
This suggests that AGN feedback could well be the mecha- shift z = 1 and decreases toward z = 0. The fact that star
nism that reduces the star formation efficiencies in massive formation is extremely quenched between z = 1 and z = 0
galaxies. intheAGN-ONmodelisalso inagreementwith theresults
of recent semi-analytical models of BCGs (Lucia & Blaizot
2007).Somestarbursteventsareevidentaspeaksinthestar
3.2 Star formation rates formation rates at different times, while periods of strong
AGN activity appear as sudden decreases of the star for-
The star formation history of the BCG galaxy in our sim-
mation rate. This simple test shows how our simple AGN
ulations can be used to quantify the efficiency of the star
feedbackmodelisindeedabletoquenchstarformation, de-
formationquenchingproducedbyourAGNfeedbackmodel.
creasing thestellar mass observed in theBCG.
The difference between the star formation history between
the AGN-ON and AGN-OFFsimulations is striking. Fig. 3
shows the rate at which stars found in the BCG at z = 0
3.3 Ellipticity and velocity distribution of stars in
havebeenformedasafunctionoftime.Atthebeginningof
the BCGs
thesimulation(ageoftheUniverse<1Gyr),whenSMBHs
have not formed yet the star formation rates in the AGN- We constructed mock images of the central region of the
ON (blue line) and AGN-OFF (red line) galaxies are al- simulated galaxy clusters to detect further differences be-
most indistinguishable. Later on AGN feedback starts to tween the two models. Figure 4 shows a set of such images
play its role in quenchingstar formation: the difference be- at z=1 andz=0, wherethecolor of each pixelrepresents
tween the star formation rate in the two models is almost the flux in the g′ band. We have chosen the same spatial
The formation of the brightest cluster galaxies 7
BCG properties
Simulation Redshift Mstar[M⊙] Reff[kpc] σeff [km/s] ǫ v/σ
AGN-ON z=0 2.243×1011 10.286 292.96 [0.123,0.155] 0.08
AGN-OFF z=0 3.484×1012 6.858 652.83 [0.257,0.498] 0.65
AGN-ON z=1 1.697×1011 8.254 277.93 [0.201,0.424] 0.16
AGN-OFF z=1 1.637×1012 4.784 525.32 [0.120,0.721] 0.82
Table2. PropertiesoftheBCGs.(1)Typeofsimulation.(2)Redshiftz.(3)StellarmassMstar.(4)Half-massradiusReff.(5)Velocity
dispersionwithinReff,σeff.(6)EllipticityǫatReff.(7)Averagev/σ withinReff.
and color scales in all the pictures to show the remarkable at z=0, wemeasurea mean v/σ∼0.65 for theAGN-OFF
difference in sizes between the AGN-ON and OFF simula- BCG, and v/σ ∼0.08 for the AGN-ON BCG. At z =1 we
tions. The AGN-OFF BCG is much more extended than findv/σ ∼0.82fortheAGN-OFFBCG,andv/σ∼0.16for
the AGN-ON one, at z = 1 as well as at z = 0, i.e. the theAGN-ONBCG.
global size of the galaxies scales with their mass. However, It is interesting to compare the (ǫ,v/σ) values with
thehalf-light isophotes (black contours) show that thestel- those observed in early-type galaxies, despite the fact
lar light is more concentrated in the AGN-OFF BCG than that BCGs are a particular sub-category of these objects.
in the AGN-ON one. This implies that the surface density Cappellari et al. (2007) and Emsellem et al. (2007) used
profileoftheAGN-ONgalaxyisshallow whencomparedto 2D spectroscopy measurements from the SAURON survey
the AGN-OFF one; this is indeed the case as we will show (Bacon et al. 2001; deZeeuw et al. 2002) and analysed the
in 3.4. orbitalstructureof48nearbyS0andEgalaxies.Theydivide
the galaxies in their sample into two groups: slow rotators
To estimate the range of possible ellipticities an ob-
withǫ.0.3,v/σ.0.2andlowspecificangularmomentum,
serverwouldsee,weviewthesimulationsfrom differentan-
andfast rotators withǫ.0.7,v/σ&0.2andahighspecific
glesandmakethesamesurfacebrightnessimages. Wethen
angular momentum. Including the effects of AGN feedback
fit the half-light isophotes with ellipses and estimate their
ellipticityǫ=1−b/a,wherebandaarethesemi-minorand in our simulations moved our BCG from the class of fast
rotating early-typegalaxies tothat of the slow rotators.
semi-majoraxisoftheellipses.Inthiswaywegivetherange
The SAURON galaxies are not chosen to be central
of possible ellipticities for our galaxies. At z =0 the AGN-
cluster galaxies, so we can also directly compare our sim-
ON BCG has ǫ= [0.123,0.155], while the AGN-OFF BCG
ulations with the central galaxy in the Virgo Cluster, M87
has ǫ = [0.257,0.498]; both ranges are consistent with val-
(NGC 4486), that is also a slow rotator; according to
ues typical of spheroidal systems, but the AGN-ON galaxy
Cappellari et al.(2007),M87has(ǫ,v/σ)=(0.04,0.02),val-
isslightlymorespherical.Atz =1wehaveǫ=[0.201,0.424]
uesthatare consistent with theAGN-ONBCG simulation.
for the AGN-ONBCG, and ǫ=[0.120,0.721] for the AGN-
This close match with M87 is interesting, given that in our
OFF BCG; at this redshift, the AGN-ON galaxy is slightly
simulationsweonlyselectedtheVirgo-likehalobasedonits
more spheroidal than at z = 0, while the ellipticity of the
virial mass and merger history.
AGN-OFFgalaxyismoretypicalofflattenedellipsoidalsys-
tems.
Figure 5 shows the average line of sight velocity maps
3.4 Rotational velocity, velocity dispersion and
for the stars in the central region of the cluster at z = 0
stellar mass surface density profiles
and z =1. The AGN-OFFBCG hosts a rotating disk with
a rotational velocity of a few hundreds km/s, both at z = Hereweanalysethecircularvelocityandvelocitydispersion
1 and z = 0. Interestingly, in the AGN-ON case there is profiles of the two galaxies at z = 0 (Figure 7, left panel)
no evidence for rotation at z = 0, while at z = 1 there to further explore the structural and kinematic properties
is evidence for very slow rotation. These maps should be ofourBCGsimulations.Therotationalvelocity(filledsym-
compared with thoseinFigure 6thatshowthelineofsight bols)oftheAGN-ONBCGwithinReff (bluedashedline)is
velocity dispersion of the stars in the central region. The never larger than 25 km/s and its value is slightly growing
AGN-OFF velocity dispersion at z = 0 is highly peaked with the distance from the center. The line of sight veloc-
in the center, where it is larger than ∼ 750 km/s, and it ity dispersion profile is nearly constant within the BCG,
decreasesrapidlytowardstheexternalpartsoftheBCG.On 250.σ .300 km/s within R . Within this characteristic
eff
thecontrary,theAGN-ONvelocitydispersionatz=0does radius the galaxy is always dominated by random motions
notpeakinthecenter,butitincreasestowardstheoutskirts and has a very little rotation.
of the BCG (we will discuss this topic in greater detail in The AGN-OFF BCG has very different properties. Its
the next subsection). At z = 1 the velocity dispersion is velocity dispersion profileis maximum in thecentralregion
centrallypeakedinboththesimulations, butthevaluesare and decreases with radius; the rotational velocity increases
atleastafactoroftwolargerintheAGN-OFFcasethanin with distance from the center, peaking just before R is
eff
theAGN-ONcase.Ifwerotatethegalaxiesedge-onandwe reached, then decreases again. Within R the AGN-OFF
eff
account only for the regions within the half-light isophotes galaxy is stil dominated by random motions, however, the
8 D. Martizzi et al.
Figure4. Fluxesintheg′ bandoftheBCGprojectedalongthezaxisoftheperiodicbox.Wefilteredoutallpixelswithflux<10−17
erg/s/cm2.Top-left:z=0,AGN-OFF.Top-right:z=0,AGN-ON.Bottom-left:z=1,AGN-OFF.Bottom-right:z=1,AGN-ON.The
blackcontours representthehalf-lightisophotes.
rotational velocity is a significant fraction of the velocity spatial resolution limit is much larger: our AGN-ON model
dispersion (& 0.45). Whilst rotating disk-like structures in is not able to reproduce the velocity dispersion profile ob-
fastrotatorshavebeenobserved(Krajnovi´c et al.2008),the servedinM87forR<1kpc.However,whenweconsiderthe
peak vrot value of our AGN-OFF simulation is a factor ∼ resolvedregion,R>1kpc,thevelocitydispersionprofileof
2−3largerthanthetypicalvaluesmeasured forthefastest ourAGN-ONmodelandthatofM87(Emsellem et al.2004;
rotators. Murphyet al. 2011) are rathersimilar.
The velocity dispersion profiles measured for M87 OntherightpanelofFigure7weshowthestellarmass
(Murphyet al. 2011) are comparable with those of our surface density profiles at z =0 for ourtwo BCGs. Wefind
AGN-ONBCG,atleastbeyondthespatialresolutionlimit. thattheseprofilescanbefittedbyS´ersicprofilesforR>10
In SAURON the kinematic properties of M87 have been kpc for the AGN-ON BCG (blue line, S´ersic index n=10)
measureddownto∼0.1kpc(Emsellem et al.2004),butour andR>4kpcfortheAGN-OFFBCG(redline,S´ersicindex
The formation of the brightest cluster galaxies 9
Figure 5. Average velocity alongthe lineofsight. The projectionisalong the z axis of the periodicbox. Top-left:z =0, AGN-OFF.
Top-right:z=0,AGN-ON.Bottom-left:z=1,AGN-OFF.Bottom-right:z=1,AGN-ON.
n=10).Wefindthatthereisalmostanorderofmagnitude Virgo cluster and show that it is possible to fit them with
difference between the stellar mass surface density of our single light profiles to large radii. The fits are generally not
two models. It is also interesting to compare the measured satisfactory in the central regions; in particular, they find
profiles with theS´ersic functions at 1 kpc<R<10 kpc:in that most luminous elliptical galaxies have either light ex-
theAGN-OFFcasewefindthatthereisamassexcesswith cesses or deficiencies at there centres. Light deficiencies are
respect to the S´ersic function and in the AGN-ON case we preferably found in the most luminous objects like NGC
findamassdeficiency.Ontheobservationalside,similarre- 4472 andM87 andtheregionswheretheyarefoundextend
sults were described by several authors (Kormendy 1999; from the center to a distance . 10 kpc. If we assume that
Quillen et al. 2000; Laine et al. 2003; Trujillo et al. 2004; our surface density profiles can be mapped directly to sur-
Lauer et al. 2005; Cˆot´e et al. 2007; Kormendy et al. 2009; face brightnessprofiles, theobservations ofluminous galax-
Graham 2011). Kormendy et al. (2009) analyse the surface ies are a much closer match to the AGN-ONsimulation. In
brightnessprofilesofellipticalandspheroidalgalaxiesinthe