Simulating the effect of AGN feedback on the metal enrichment of galaxy clusters

22 Pages·2009·0.63 MB·English

Mon.Not.R.Astron.Soc.000,000–000(0000) Printed3September2009 (MNLATEXstylefilev2.2)
Simulating the effect of AGN feedback on the metal enrichment of
galaxy clusters
9
D. Fabjan1,2,3, S. Borgani1,2,3, L. Tornatore1,2,3, A. Saro1,2,3, G. Murante4 & K. Dolag5
0
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2 1DipartimentodiAstronomiadell’Universita` diTrieste,viaTiepolo11,I-34131Trieste,Italy(fabjan,borgani,tornatore,[email protected])
2INAF–IstitutoNazionalediAstrofisica,viaTiepolo11,I-34131Trieste,Italy
p 3INFN–IstitutoNazionalediFisicaNucleare,Trieste,Italy
e 4INAF–IstitutoNazionalediAstrofisica–OsservatorioAstronomicodiTorino,Str.Osservatorio25,I-10025,PinoTorinese,Torino,Italy([email protected])
S
5Max-Planck-Institutfu¨rAstrophysik,Karl-SchwarzschildStrasse1,GarchingbeiMu¨nchen,Germany([email protected])

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3September2009
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ABSTRACT
p
We presentastudyoftheeffectofAGNfeedbackonmetalenrichmentandthermalproper-
-
o tiesoftheintraclustermedium(ICM)inhydrodynamicalsimulationsofgalaxyclusters.The
r simulationsare performedusing a version of the TreePM-SPH GADGET-2code, which also
t
s followschemo-dynamicalevolutionby accountingfor metalenrichmentcontributedbydif-
a
ferentstellarpopulations.Wecarryoutcosmologicalsimulationsforasetofgalaxyclusters,
[ coveringthemassrangeM200 ≃(0.1−2.2)×1015h−1M⊙.Besidesrunsnotincludingany

1 efficientformofenergyfeedback,wecarryoutsimulationsincludingthreedifferentfeedback
v schemes:(i)kineticfeedbackintheformofgalacticwindstriggeredbysupernovaexplosions;
4 (ii)AGNfeedbackfromgasaccretionontosuper-massiveblackholes(BHs);(iii)AGNfeed-
6 backinwhicha ’radiomode’isincludedwithanefficientthermalcouplingoftheextracted
6
energy,wheneverBHsenterinaquiescentaccretionphase.Besidesinvestigatingtheresulting
0
thermalpropertiesoftheICM,weanalyseindetailtheeffectthatthesefeedbackmodelshave
.
9 ontheICMmetal-enrichment.WefindthatAGNfeedbackhasthedesiredeffectofquenching
0 starformationinthebrightestclustergalaxiesatz <4andprovidescorrecttemperaturepro-
9 filesinthecentralregionsofgalaxygroups.However,itseffectisnotyetsufficienttocreate
0
“coolcores”inmassiveclusters,whilegeneratinganexcessofentropyincentralregionsof
:
v galaxygroups.Asforthepatternofmetaldistribution,AGN feedbackcreatesa widespread
i enrichmentintheoutskirtsofclusters,thankstoitsefficiencyindisplacingenrichedgasfrom
X
galactichalostothe inter-galacticmedium.ThisturnsintoprofilesofIronabundance,ZFe,
r whichareinbetteragreementwithobservationalresults,andintoamorepristineenrichment
a
oftheICMaroundandbeyondtheclustervirialregions.Followingthepatternoftherelative
abundancesofSiliconandIron,weconcludethatasignificantfractionoftheICMenrichment
is contributed in simulations by a diffuse population of intra-cluster stars. Our simulations
alsopredictthatprofilesoftheZSi/ZFeabundanceratiodonotincreaseatincreasingradii,at
leastoutto0.5Rvir.Ourresultsclearlyshowthatdifferentsourcesofenergyfeedbackleave
distinct imprints in the enrichment pattern of the ICM. They further demonstrate that such
imprints are more evident when looking at external regions, approaching the cluster virial
boundaries.
Key words: Cosmology: Theory – Methods: Numerical – X–Rays: Galaxies: Clusters –
Galaxies:Abundances–Galaxies:IntergalacticMedium
1 INTRODUCTION gions of relaxed clusters show little evidence of gas cooler than
about a third of the virial temperature (e.g., Petersonetal. 2001;
High quality data from the current generation of X–ray satel- Bo¨hringeretal.2002;Sandersonetal.2006);temperatureprofiles
lites(XMM-Newton, Chandra andSuzaku) have now established have negative gradients outside core regions, a trend that ex-
anumberofobservationalfactsconcerningthethermo-dynamical tendsout tothelargestradii coveredsofar byobservations (e.g.,
andchemo-dynamicalpropertiesoftheintra-clustermedium(ICM) DeGrandi&Molendi 2002; Vikhlininetal. 2005; Zhangetal.
for statistically representative sets of galaxy clusters: core re- 2006; Baldietal. 2007; Prattetal. 2007; Leccardi&Molendi
2 Fabjanet al.
2008b); gas entropy is higher than expected from simple self- print of the conversion of mechanical energy associated to AGN
similarscalingpropertiesoftheICM,notonlyincoreregions,but jets into thermal energy (and possibly in a non–thermal content
alsoouttoR5001(e.g.,Sunetal.2009,andreferencestherein);ra- ofrelativisticparticles)throughshocks(e.g.,Mazzottaetal.2004;
dialprofilesoftheIronabundanceshownegativegradients,more Fabianetal.2005;McNamaraetal.2006;Sanders&Fabian2007;
pronounced for relaxed “cool core” clusters, with central values seeMcNamara&Nulsen2007 forareview).Although analytical
of ZFeapproaching solar abundance and with a global enrich- argumentsconvincinglyshowthattheenergyradiatedfromgasac-
mentatalevelofabout1/3–1/2ZFe,⊙(e.g.,DeGrandietal.2004; cretionontoacentralsuper-massiveblackhole(BH)isenoughto
Vikhlininetal. 2005; dePlaaetal. 2006; Snowdenetal. 2008; suppress gas cooling, it is all but clear how this energy is ther-
Leccardi&Molendi 2008a; see Mushotzky 2004; Werneretal. malisedanddistributedinthesurrounding medium. Alikelysce-
2008forrecentreviews). nario is that bubbles of high entropy gas are created at the ter-
Galaxy clusters arise from the collapse of density perturba- minationofjets.Buoyancy ofthesebubblesintheICMthendis-
tions over a scale of ∼ 10h−1 comoving Mpc. As such, the tributesthermalenergyoverlargerscales(e.g.,DallaVecchiaetal.
aboveobservationalpropertiesoftheICMcomefromanon-trivial 2004; Cattaneoetal. 2007). Crucial in this process is the stabil-
interplay between the underlying cosmological scenario, which ityofthebubblesagainstgasdynamicalinstabilitieswhichwould
shapes thelarge-scalestructureof theUniverse, andanumber of tendtodestroythemquiterapidly.Indeed,detailednumericalsim-
astrophysical processes (e.g., star formation, energy and chemi- ulations have demonstrated that gas circulation associated to jets
cal feedback from supernovae and AGN) taking place on much (e.g., Ommaetal. 2004; Brighenti&Mathews 2006; Heinzetal.
smaller scales. Cosmological hydrodynamical simulations repre- 2006),gasviscosity,magneticfields(e.g.,Ruszkowskietal.2007)
sent the modern instrument withwhichsuch complexities can be andinjectionofcosmicrays(e.g.,Ruszkowskietal.2008)areall
described as the result of hierarchical assembly of cosmic struc- expectedtocooperateindeterminingtheevolutionofbuoyantbub-
tures(e.g.,Borgani&Kravtsov2009,forarecentreview).Indeed, bles.Although highly instructive, allthesesimulationshavebeen
simulationsofgalaxyclustersreachnowadaysahighenoughres- performedforisolatedhalosand,assuch,theydescribeneitherthe
olution, whileincluding a realisticdescription of theabove men- cosmologicalgrowthandmergingofblackholes,northehierarchi-
tioned astrophysical processes, for them to provide a coherent calassemblyofgalaxyclusters.
interpretative framework for X-ray observations. Quite remark- Springeletal. (2005) and DiMatteoetal. (2005) have pre-
ably, simulation predictions for the thermodynamical properties sentedamodelthatfollowsinacosmologicalsimulationtheevolu-
of the ICM are in good agreement with observations, at least tionoftheBHpopulationandtheeffectofenergyfeedbackresult-
outside the core regions: simulated profiles of gas density and ingfromgasaccretionontoBHs.Inthismodel,BHsaretreatedas
temperature match the observed ones at cluster-centric distances sinkparticleswhichaccretefromthesurroundinggasaccordingto
∼>0.1R500 (e.g.,Lokenetal.2002;Borganietal.2004;Kayetal. aBondiaccretionrate(e.g.,Bondi1952),withanupperlimitpro-
2004; Roncarellietal. 2006; Prattetal. 2007; Nagaietal. 2007; videdbytheEddingtonrate(seealsoBooth&Schaye2009).This
Crostonetal.2008);theobservedentropylevelatR500iswellre- modelwasusedbyBhattacharyaetal.(2008),whoruncosmolog-
produced by simulations including radiative cooling and star for- ical simulations to study the effect of AGN feedback on galaxy
mation (e.g., Nagaietal. 2007; Borgani&Viel 2009). The situa- groups.Theyfoundthatthisfeedbackiseffectiveinreducingstar
tion is quite different within cluster cores, where simulations in- formationincentralregionsandtodisplacegastowardsouterre-
cluding only stellar feedback generally fail at producing realistic gions.However,theresultingentropylevelwithinclustercoresis
coolcores.Thetwoclearestmanifestationsofthisfailurearerep- higher thanobserved. Initsoriginalversion, theenergy extracted
resented by the behaviour of temperature and entropy profiles at fromBHaccretionislocallydistributedtothegasaroundtheBHs
small radii, ∼<0.1R500. Observations of cool core clusters show accordingtoaSPH-kernelweightingscheme.Thismodelhasbeen
thattemperatureprofilessmoothlydeclinetowardthecentre,reach- modifiedbySijacki&Springel(2006)whoincludedthepossibil-
ingtemperaturesofabout1/3–1/2ofthemaximumvalue,whilethe itytoinflatehigh-entropybubblesintheICMwheneveraccretion
entropylevelatthesmallestsampledscalesisgenerallyverylow ontothecentralBHentersinaquiescent“radiomode”.Theunder-
(e.g.,Sunetal.2009;Sandersonetal.2009a).Onthecontrary,ra- lying idea of injecting bubbles with this prescription was to pro-
diativesimulationsincludingavarietyofmodelsofstellarfeedback vide a more realistic description of the effect of jet termination
predictsteepnegativetemperaturegradientsdowntotheinnermost ontheICM,althoughtheeffectofthejetitselfwasnotincluded.
resolvedradiiandcentralentropylevelsmuchhigherthanobserved Puchweinetal. (2008) simulated a set of clusters and groups to
(e.g., Valdarnini 2003; Tornatoreetal. 2003; Borganietal. 2004; showthatthisfeedbackschemeisabletoreproducetheobserved
Nagaietal.2007;cf.alsoKayetal.2007).Thisfailureofsimula- slope of the relation between X–ray luminosity and temperature.
tions is generally interpreted as due to overcooling, which takes Sijackietal.(2007)showedinasimulationofasinglepoorgalaxy
place in simulated clusters even when including an efficient su- clusterthattheinjectionof bubblesisquiteeffectiveinsuppress-
pernova(SN)feedback,andcausesanexcessofstarformationin ingstarformationincentralregions.However,alsointhiscasethe
thesimulatedbrightestclustergalaxies(BCGs;Romeoetal.2005; temperatureprofileinthecoreregionsdoesnotmatchtheobserved
Saroetal.2006). slope,whilemorerealistictemperatureprofilescanbeproducedif
Thegenerallyacceptedsolutiontotheseshortcomingsofsim- bubbleinjectionisassociatedtotheinjectionofanon–thermalpop-
ulationsisrepresentedbyAGNfeedback.Indeed,thepresenceof ulationofrelativisticparticles(Pfrommeretal.2007;Sijackietal.
cavitiesintheICMattheclustercentreisconsideredasthefinger- 2008).Althoughtheseauthorspresentedresultsconcerningtheef-
fectofAGNontheICMthermodynamics,nodetailedanalysishas
been so far carried out to study the interplay between AGN and
1 HereandinthefollowingwewillindicatewithR∆ theradiusencom- chemicalenrichment,byincludingadetailedchemo-dynamicalde-
passingameandensityequalto∆ρcr,beingρcr =3H2/8πGthecritical scriptionoftheICM.
cosmicdensity.Inasimilarway,wewillindicatewithM∆themasscon- Indeed,theamountanddistributionofmetalsintheICMpro-
tainedwithinR∆. videanimportantdiagnostictoreconstructthepasthistoryofstar
AGNfeedbackand metalenrichmentofclusters 3
formationandtheroleofgas-dynamicalandfeedbackprocessesin
Table1.Characteristicsofthesimulatedclusters.Column1:clustername.
displacingmetalsfromstarformingregions(e.g.,Mushotzky2004; Column 2: mass contained within R200 (units of 1014h−1M⊙). Col-
Borganietal.2008;Schindler&Diaferio2008,forreviews).Cos- umn 3: value of R200 (units of h−1Mpc). Column 4: value of the
mological chemo-dynamical simulations of galaxy clusters gen- spectroscopic-liketemperaturewithinR500,T500.Columns5and6:mass
erally show that the predicted profiles of Iron abundance are ofthecentralBHhostedintheBCGfortheAGN1andAGN2runs(unitsof
steeperthanobserved(e.g.,Valdarnini2003;Tornatoreetal.2004; 1010h−1M⊙),respectively.Fortheg51cluster,thetwoadditionalvalues
Romeoetal. 2005; Tornatoreetal. 2007; Dave´etal. 2008), with reportedforthemassofthecentralBHrefertotheAGN2(0.8)andAGN2W
runs(seetext)andareindicatedwiththe†and‡symbol,respectively.
anexcessofenrichmentinthecoreregions.Thisisgenerallyinter-
pretedasduetothesameexcessofrecentstarformationinsimu- Cluster M200 R200 T500 MBH
latedBCGs.However, Fabjanetal.(2008)showed thatanexcess AGN1 AGN2
of recent star formation has also the effect of efficiently locking
g1.a 12.69 1.76 9.71 56.22 15.74
recently-produced metals into stars, thereby preventing a too fast
g1.b 3.64 1.16 3.39 7.96 2.52
increaseofthemetallicityofthehotdiffusemedium.
g1.c 1.36 0.84 2.03 4.63 1.32
All the above analyses are based on different implementa- g1.d 1.04 0.76 1.82 1.59 0.46
tionsofSNenergyfeedback, whileonlymuchlessdetailedanal- g1.e 0.62 0.64 1.44 0.84 0.30
yses of ICM metal enrichment have been so far presented by
also including AGN feedback in cosmological simulations (e.g., g8.a 18.51 2.00 12.82 113.50 27.73
Sijackietal.2007;Molletal.2007).Forinstance, Roedigeretal. g8.b 0.65 0.65 1.41 2.58 0.88
(2007)showedfromsimulationsofisolatedhalosthatbuoyancyof g8.c 0.52 0.61 1.42 1.74 0.63
bubblescanactuallydisplacealargeamountofthecentralhighly
g51 10.95 1.68 7.55 43.38 16.50
enriched ICM, thus leading toa radical change of the metallicity
6.18†
profiles,oreventoadisruptionofthemetallicitygradients.
15.02‡
Theaimofthispaperistopresentadetailedanalysisofcos-
g72.a 10.57 1.66 8.67 48.74 13.87
mological hydrodynamical simulations of galaxy clusters, which g72.b 1.48 0.86 2.18 3.79 1.34
havebeencarriedoutwiththeGADGET-2code(Springel2005),by
combining the AGN feedback model described by Springeletal. g676 0.87 0.72 1.91 3.03 0.95
(2005)withtheSPHimplementationofchemo-dynamicspresented g914 0.88 0.72 2.03 2.89 1.13
byTornatoreetal.(2007).Besidesshowingresultsontheeffectof g1542 0.83 0.71 1.79 2.54 0.79
combining metallicity–dependent cooling and AGN feedback on g3344 0.92 0.74 2.03 3.15 1.29
g6212 0.89 0.73 2.02 2.57 0.99
theICMthermodynamics,wewillfocusourdiscussiononthedif-
ferent effects that SNe and AGN feedback have on the chemical
enrichmentoftheICM.Althoughwewillshortlydiscusstheeffect Table2.Resolutionofthedifferentruns.Column2-3:massoftheDMpar-
ofdifferentfeedbacksourcesonthepatternofstarformationinthe ticlesandinitialmassofthegasparticles(unitsof108h−1M⊙).Column
BCG, the results presented in this paper will mainly concern the 4:valueofthePlummer-equivalentgravitationalforcesofteningatz = 0
enrichmentofthehotdiffuseintra-clustergas.Wedefertoaforth- (unitsof h−1kpc).Column5:clusterssimulatedateachresolution.
comingpaperadetailedanalysisoftheeffectofAGNfeedbackon
MDM mgas ε Clusters
the population of cluster galaxies. The scheme of the paper is as
follows.WepresentinSection2thesimulatedclusters,andbriefly Lowres. 11.0 2.03 5.00 g1,g8,g51,g72,g676
describe the implementation of the chemical evolution model in Highres. 1.69 0.31 2.75 g676,g914,g1542,g3344,
g6212
the GADGET-2codealongwiththeSNandAGNfeedbackmod-
els.InSection3weshowourresultsonthethermalpropertiesof
theICMandtheir comparison withobservational results.Section 18clusterswithM200∼>5×1013h−1M⊙,whosebasiccharacter-
4isdevoted tothepresentation of theresultsontheICMchemi- isticsarereportedinTable1.
calenrichmentfromoursimulationsandtheircomparisonwiththe Eachregionwasre-simulatedusingthezoomedinitialcondi-
mostrecentobservations.Wediscussourresultsanddrawourmain tion(ZIC)techniquebyTormenetal.(1997).Therelativemassof
conclusionsinSection5. thegasanddarkmatter(DM)particleswithinthehigh–resolution
regionofeachsimulationissetsothatΩ = 0.045fortheden-
bar
sityparametercontributedbybaryons.ForeachLagrangianregion,
initialconditionshavebeengeneratedatabasicresolutionandat
2 THESIMULATIONS 6.5timeshighermassresolution.Atthishigherresolution,themass
2.1 Thesetofsimulatedclusters mofgtahseD=M2.a8nd×g1as07phar−ti1cMles⊙arreesmpeDctMive≃ly,1w.9it×h P1l0u8mhm−e1rMeq⊙uiavnad-
Our set of simulated clusters is obtained from nine Lagrangian lentsofteninglengthforthecomputationofthegravitationalforce
regions extracted from a simulation containing only dark matter set to ε = 2.75h−1kpc in physical units below z = 2 and
(DM)withaboxsizeof479h−1 Mpc(Yoshidaetal.2001),per- to ε = 8.25h−1kpc in comoving units at higher redshifts. In
formed for aflat Λcold darkmatter (CDM) cosmological model the lower resolution runs, these values are rescaled according to
with relevant parameters Ωm = 0.3, h100 = 0.7, σ8 = 0.9. m−D1M/3.WedecidedtosimulatethenineLagrangianregionswith
ThissetofsimulatedclustersisdescribedindetailbyDolagetal. massiveclustersatthelowerresolution,whileweusedthehigher
(2008).Theregionsarecentredonninegalaxyclusters:fiveofthem resolutionforthefivelow-massclusters.Onlythelow-massg676
havemassesM200 ≃1.0×1014h−1M⊙,whiletheremainingfour clusterwassimulatedatbothresolutions.WeprovideinTable2a
haveM200 ≃ (1.0−2.2)×1015h−1M⊙. Theregionsof three descriptionoftheparametersforthetwodifferentresolutions,also
largestobjectsalsocontainotherclusters,sothatwehaveintotal listingtheclusterssimulatedateachresolution.
4 Fabjanet al.
2.2 Thesimulationcode centralBHofmass105h−1M⊙,providedthehalodoesnotcon-
tainanyBHyet.Fortherunsatthelowerresolutionthevalueof
OGuArDGsEimT-u2latcioodnes (wSperreingepler2fo0r0m5e).d AullsinsgimutlhaetionTsreeinPcMlu-dSePHa thehalomassassumedtoseedBHsisMth = 5×1010h−1M⊙,
so that it is resolved with about 40 DM particles. At the higher
metallicity-dependent radiative cooling (Sutherland&Dopita
resolution the halo mass threshold for BH seeding decreases to
1g9ro9u3n)d, he(Hatainagrdtfr&omMaaduaunifo1r9m96t)imaen-ddeptheendeenfftecutlitvraevimoloetdeblacbky- Mth = 1010h−1M⊙, so astoresolve it withapproximately the
same number of particles. We verified that using in the higher-
Springel&Hernquist(2003)forthedescriptionofstarformation.
resolutionrunsthesamevalueofM asinthelow-resolutionruns
In this model, gas particles above a given density are treated as th
causes theeffect of BHaccretion tobeshiftedtoward lower red-
multiphase, so as to provide a sub–resolution description of the
shift, since its onset has to await the formation of more massive
inter-stellar medium. In the following, we assume the density
halos, whileleavingthefinalpropertiesof galaxyclustersalmost
thresholdfortheonsetofstarformationinmultiphasegasparticles
unaffected.
to be n = 0.1cm−3 in terms of number density of hydrogen
H Onceseeded,eachBHcanthengrowbylocalgasaccretion,
atoms.Oursimulationsalsoincludeadetailedmodelofchemical
witharategivenby
evolution by Tornatoreetal. (2007, T07 hereafter). We address
the reader to T07 for a more detailed description of this model. M˙BH = min(cid:0)M˙B,M˙Edd(cid:1) (1)
Metals are produced by SNe-II, SNe-Ia and intermediate and
low-mass stars in the asymptotic giant branch (AGB hereafter). orbymergingwithotherBHs.HereM˙B istheaccretionrateesti-
We assume SNe-II to arise from stars having mass above 8M⊙. matedwiththeBondi-Hoyle-Lyttletonformula(Hoyle&Lyttleton
As for the SNe-Ia, we assume their progenitors to be binary 1939;Bondi&Hoyle1944;Bondi1952),whileM˙Edd istheEd-
systems, whose total mass lies in the range (3–16)M⊙. Metals dington rate. The latter is inversely proportional to the radiative
and energy are released by stars of different mass by properly efficiencyǫr,whichgivestheradiatedenergyinunitsoftheenergy
accounting for mass–dependent lifetimes. In this work we as- associatedtotheaccretedmass:
sume the lifetime function proposed by Padovani&Matteucci L
ǫ = r . (2)
(1993),whileweassumethestandardstellarinitialmassfunction r M˙ c2
BH
(IMF) by Salpeter (1955). We adopt the metallicity–dependent
FollowingSpringeletal. (2005), weuse ǫ = 0.1 as areference
stellar yieldsby Woosley&Weaver (1995) for SNe-II, theyields r
value, which istypical for a radiatively efficient accretion onto a
by vandenHoek&Groenewegen (1997) for the AGB and by
Schwartzschild BH (Shakura&Syunyaev 1973). The model then
Thielemannetal.(2003)forSNe-Ia.Theversionofthecodeused
assumes that a fraction ǫ of the radiated energy is thermally
forthesimulationspresentedhereallowedustofollowH,He,C, f
O,Mg,S,SiandFe.Onceproducedbyastarparticle,metalsare coupled to the surrounding gas, so that E˙feed = ǫrǫfM˙BHc2
is the rate of provided energy feedback. In standard AGN feed-
thenspreadtothesurroundinggasparticlesbyusingtheB-spline
backimplementationweuseǫ =0.05followingDiMatteoetal.
kernelwithweightscomputedover64neighboursandtakentobe f
(2005), who were able with this value to reproduce the observed
proportional to the volume of each particle (see T07 for detailed
M −σrelationbetweenbulgevelocitydispersionandmassof
tests on the effect of choosing different weighting schemes to BH
thehostedBH(e.g.,Magorrianetal.1998).Thischoicewasalso
spreadmetals).
found to be consistent with the value required in semi-analytical
modelstoexplaintheevolution ofthenumber densityof quasars
(Wyithe&Loeb2003).
2.3 Feedbackmodels
GasswallowedbytheBHisimplementedinastochasticway,
Inthesimulationspresentedinthispaperwemodeltwodifferent by assigning to each neighbour gas particle a probability of con-
sources of energy feedback. The first one is the kinetic feedback tributingtotheaccretion,whichisproportionaltotheSPHkernel
modelimplementedbySpringel&Hernquist(2003),inwhichen- weightcomputedattheparticleposition.DifferentlyfromSDH05,
ergy released by SN-II triggers galactic winds, with mass up- weassumethateachselectedgasparticlecontributestotheaccre-
load rate assumed to be proportional to the star formation rate, tionwith1/3ofitsmass,insteadof beingcompletelyswallowed.
M˙ = ηM˙ .Therefore,fixingtheparameterη andthewindve- Inthisway,alargernumberofparticlescontributetotheaccretion,
W ⋆
locity v amounts to fix the total energy carried by the winds. whichisthenfollowedinamorecontinuousway.Weremindthat
W
Inthefollowing,weassumeη =2forthemass-uploadparameter intheSDH05scheme,thisstochasticaccretionisusedonlytoin-
andv =500kms−1forthewindvelocity.IfeachSN-IIreleases creasethedynamicmassoftheBHs,whiletheirmassenteringin
W
1051ergs,theabovechoiceofparameterscorrespondstoassuming the computation of the accretion rateis followed in acontinuous
thatSNe-IIpowergalacticoutflowswithnearlyunityefficiencyfor way,byusingtheanalyticexpressionforM˙ .Oncetheamount
BH
aSalpeterIMF(seeSpringel&Hernquist2003). of energy to be thermalised is computed for each BH at a given
Furthermore, we include in our simulations the effect of time-step,onehastodistributethisenergytothesurroundinggas
feedback energy released by gas accretion onto super-massive particles.Intheiroriginalformulation,SDH05distributedthisen-
blackholes(BHs),followingtheschemeoriginallyintroducedby ergyusingtheSPHkernel.
Springeletal. (2005, SDH05 hereafter; see also DiMatteoetal. Besides following thisstandard implementation of the AGN
2005,2008;Booth&Schaye2009).WerefertoSDH05foramore feedback, wealsofollow analternativeprescription, whichdiffer
detailed description. In thismodel, BHsare represented by colli- fromtheoriginaloneintwoaspects.
sionlesssinkparticlesofinitiallyverysmallmass,thatareallowed Firstly,followingSijackietal.(2007),weassumethatatran-
tosubsequently grow viagasaccretionandthroughmergerswith sitionfroma“quasar”phaseto“radio”modeoftheBHfeedback
otherBHsduringcloseencounters.Duringthegrowthofstructures, takes place whenever the accretion rate falls below a given limit
weseedeverynewdarkmatterhaloaboveacertainmassthreshold (e.g.,Churazovetal.2005,andreferencestherein),corresponding
M ,identifiedbyarun-timefriends-of-friendsalgorithm,witha toM˙ /M˙ < 10−2,whichimpliesanincrease of thefeed-
th BH Edd
AGNfeedbackand metalenrichmentofclusters 5
backefficiencytoǫ =0.2.AthighredshiftBHsarecharacterised (d) Modified version of the AGN feedback (AGN2 hereafter),
f
byhighaccretionratesandpowerveryluminousquasars,withonly withfeedback efficiencyincreasingfromǫ = 0.05toǫ = 0.2
f f
asmallfractionoftheradiatedenergybeingthermallycoupledto whenM˙ /M˙ <10−2,anddistributionofenergyaroundthe
BH Edd
the surrounding gas. On the other hand, BHs hosted within very BHwithatop-hatkernel.
massive halos at lower redshift are expected to accrete at a rate
wellbelowtheEddingtonlimit,whiletheenergyismostlyreleased Inordertofurtherexploretheparameterspaceoftheconsid-
in a kinetic form, eventually thermalised in the surrounding gas ered feedback models we also carried out one simulation of the
throughshocks.Secondly,insteadofdistributingtheenergyusing g51clusterbasedontheAGN2scheme,butwiththefeedbackeffi-
aSPHkernel,wedistributeitusingatop-hatkernel,havingradius ciencyincreasedtoǫ =0.8(AGN2(0.8)hereafter).Wealsonote
f
givenbytheSPHsmoothinglength.Inordertoavoidspreadingthe that our simulations include either winds triggered by SN explo-
energywithinatoosmall sphere, weassume aminimum spread- sionsorAGNfeedback.Whilethischoiceisdonewiththepurpose
ing length of 2h−1kpc. The rationale behind the choice of the ofseparatetheeffectsofthesetwofeedbacksources,weexpectin
top-hatkernelistoprovideamoreuniformdistributionofenergy, realisticcases that both AGN and SN feedback should cooperate
thus mimicking the effect of inflating bubbles in correspondence in determining the star formation history of galaxies. In order to
of thetermination of the AGN jets. It iswell known that a num- verify the effect of combining the two feedback sources, we car-
berofphysicalprocessesneedtobeadequatelyincludedforafully riedout one simulation of theAGN2 scheme for the g51 cluster,
self-consistentdescriptionofbubbleinjectionandbuoyancy: gas- inwhichalsogalacticwindswithavelocityv =300kms−1are
w
dynamicaleffectsrelatedtojets,magneticfields,viscosity,thermal included(AGN2Whereafter).
conduction,injectionofrelativisticparticles. Beforestartingthepresentationoftheresultsonthethermal
Inparticular,anumberofstudiesbasedonsimulationsofiso- andenrichmentpropertiesoftheICM,webrieflycommentonthe
lated halos (e.g., Ommaetal. 2004; Brighenti&Mathews 2006) resultsconcerningthemassofthecentralblackholesinthesimu-
havepointedoutthatgascirculationgeneratedbyjetsprovidesan lationsincludingAGNfeedback,andthestarformationrate(SFR)
important contribution for the stabilization of cooling flows (see historyofthebrightestclustergalaxies(BCGs).
alsoHeinzetal.2006,foracosmologicalsimulationofclusterfor- Looking at Table 1, we note that our simulations predict
mationincludingjets).Initscurrentimplementation,themodelof ratherlargemassesforthesuper-massiveBHshostedinthecentral
BHfeedbackincludedinoursimulationsneglectsanykineticfeed- galaxies.Quiteinterestingly,theAGN2runsgenerallyproduceBH
backassociatedtojets.Basedonananalyticalmodel,Pope(2009) masseswhicharesmaller,byafactor3–5,thanfortheAGN1runs.
computed the typical scale of transition from kinetic to thermal Thisdemonstrates that including themoreefficient “radiomode”
feedback regime for AGN in elliptical galaxies and clusters. As for the feedback and distributing the energy in a more uniform
aresult,hefoundthattheeffectofmomentumcarriedbyjetscan wayhasasignificant effect inregulating gasaccretion. Although
beneglectedonscales∼>20kpc,theexactvaluedependingonthe BCGs are known to host BHs which are more massive than ex-
localconditionsofthegasandontheinjectionrateofkineticand pected for normal early type galaxies of comparable mass (e.g.,
thermal energy. In order to compare such a scale to that actually Laueretal.2007),theBHmassesfromour simulationsseemex-
resolvedinoursimulations,weremindthereaderthatSPHhydro- ceedingly large, also for the AGN2 model. For instance, the BH
dynamicsisnumericallyconvergedonscalesabout6timeslarger mass hosted by M87, within the relatively poor Virgo cluster, is
thanthePlummer–equivalentsofteningscaleforgravitationalforce mBH ≃ (3 −4) ×109M⊙ (e.g., Raffertyetal. 2006). This is
(e.g.,Borganietal.2002).Owingtothevaluesofthegravitational aboutafactor3–5smallerthanfoundinourAGN2runsforclus-
softeningreportedinTable2,thescalesresolvedinoursimulations tersofcomparablemass,M200 ≃2×1014h−1M⊙.Wenotethat
arenotintheregimewherekineticfeedbackisexpectedtodomi- increasingtheradio-modefeedbackefficiencyfromǫ =0.2to0.8
f
nate,thusjustifyingtheadoptionofapurelythermalfeedback.As (AGN2(0.8)run)reducesthemassofthecentralblackholeinthe
afurther test,wehave computed theradius of thetop–hat kernel g51clusterfrommBH ≃16.5×109M⊙to≃6.2×109M⊙(see
within which energy is distributed around the central BHsin our Table1).Thissuggeststhatahighlyefficientthermalizationofthe
simulatedclusters.Asafewexamples,wefoundatz = 0thisra- energyextractedfromtheBHisrequiredtoregulategasaccretion
diustobe21kpcand23kpcfortheAGN2runsoftheg72andg676 totheobservedlevel.Quiteinterestingly,wealsonotethatadding
clusters,respectively. Thisimpliesthat weareinfactdistributing the effect of galactic winds in the AGN2 scheme (AGN2W run)
thermal energy over scales where kinetic feedback should not be onlyprovidesamarginalreductionofthefinalmassofthecentral
dominant. BH.Therefore,althoughgalacticwindscanplayasignificantrole
Inviewofthedifficultyofself–consistentlyincludingtheco- in regulating star formation within relatively small galaxies, they
operative effect of all the physical processes we listedabove, we arenotefficientindecreasinggasdensityaroundthelargestBHs,
preferheretofollowarathersimplifiedapproachandseetowhat soastosuppresstheiraccretionrate.
extent[resultson]thefinalresultsofoursimulationsaresensitive As for the comparison with previous analyses, Sijackietal.
tovariationsintheimplementationoftheBHfeedbackmodel. (2007)performed asimulationofthesameg676 cluster included
Insummary,weperformedfourseriesofruns,corresponding in our simulation set at the lower resolution, for their feedback
toasmanyprescriptionforenergyfeedback. schemebasedontheinjectionofAGNdrivenbubbles.Theyfound
thatthefinalmassofthecentralBHismBH ≃6×109h−1M⊙.
(a) Nofeedback(NFhereafter):neithergalacticwindsnorAGN This value is about 30 per cent lower than what we find for the
feedbackisincluded. AGN2 runs of g676. In order to compare more closely with the
(b) Galacticwinds(Whereafter)includedbyfollowingthemodel result by Sijackietal. (2007), we repeated the run of the g676
bySpringel&Hernquist(2003),withv =500kms−1andη=2 cluster by switching off the metallicity-dependence of the cool-
w
forthewindmassupload. ing function. As a result, BH accretion proceeds in a less effi-
(c) Standard implementation of AGN feedback from BH accre- cientway,andtheresultingcentralBHmassinthiscasedropsto
tion(AGN1hereafter),usingǫf =0.05forthefeedbackefficiency. ≃3.5×109h−1M⊙.
6 Fabjanet al.
AsfortheSFRhistoryoftheBCG,thisisestimatedbyidenti- DMparticles,usingalinkinglengthof0.15intermsofthemean
fyingfirstallthestarsbelongingtotheBCGatz=0.Thishasbeen inter-particleseparation. Withineach FOFgroup, weidentify the
donebyrunningtheSKIDgroup-findingalgorithm(Stadel2001), DMparticlehavingtheminimumvalueofthegravitationalpoten-
usingthesameproceduredescribedbySaroetal.(2006).Aftertag- tialandtakeitspositiontocorrespondtothecentreofthecluster.
gingallthestarparticlesbelongingtotheBCG,wereconstructthe Allprofilesarethencomputedstartingfromthiscentre.Thesmall-
SFRhistorybyusingtheinformationontheredshiftatwhicheach estradiusthatweusetocomputeprofilesencompassesaminimum
starparticlehasbeenspawnedbyaparentgasparticle,according number of 100 SPH particles, a criterion that gives numerically
tothestochasticalgorithmofstarformationimplementedintheef- converged results for profiles of gas density and temperature in
fectivemodelbySpringel&Hernquist(2003).TheresultingSFR non–radiative simulations (e.g., Borganietal. 2002). As we shall
historiesfortheBCGoftheg51clustersareshownintheleftpanel seeinthefollowing,profilescomputedwiththiscriterionwillex-
ofFigure1. tendtosmallerradiiforthoserunswhichhaveahighergasdensity
Asexpected,therunwithnoefficientfeedback(NF)produces atthecentre,whilestoppingatrelativelylargerradiifortherunsin-
thehigheststarformationatallepochs:SFRhasapeakatz ≃ 4 cludingAGNfeedback,whicharecharacterisedbyalowercentral
andthendropsasaconsequenceoftheexhaustionofgaswithshort gasdensity.
cooling time. Despite this fast reduction of the SFR, its level at
z = 0 is still rather large, ≃ 400h−1M⊙ yr−1. As for the run
3.1 Theluminosity-temperaturerelation
withwinds,ithasareducedSFRsincetheverybeginning,owing
to the efficiency of thisfeedback scheme in suppressing star for- Therelationbetween bolometricX–rayluminosity, L andICM
X
mationwithinsmallgalaxieswhichformalreadyathighredshift. temperature, T, provided one of the first evidences that non–
Alsointhiscase,thepeakofstarformationtakesplaceatz ∼ 4, gravitationaleffectsdeterminethethermo-dynamicalpropertiesof
butwithanamplitudewhichisabout40percentlowerthanforthe the ICM (e.g., Voit 2005, for a review). Its slope at the scale of
NFrunsandwithamoregentledeclineafterwards.Asfortheruns clustersisobservedtobeL ∝Tαwithα≃2.5–3(e.g.,Horner
X
withAGNfeedback,theirSFRhistoryisquitesimilartothatofthe 2001;Prattetal.2009),andpossiblyevensteeperorwithalarger
Wrundowntoz ≃ 5.Starformationisthensuddenlyquenched scatter at the scale of galaxy groups (e.g., Osmond&Ponman
at z∼<4. We note in general that SFR for the AGN1 model lies 2004).Theseresultsareatvariancewithrespecttotheprediction,
slightlybelowthatoftheAGN2model,asaconsequenceofboth α = 2,ofself-similarmodelsbasedonlyontheeffectofgravita-
thedifferentwayofdistributingenergyand,atlowredshift,ofthe tionalgasaccretion(e.g.,Kaiser1986).Attemptstoreproducethe
inclusionoftheradiomodeassumedinthequiescentBHaccretion observed L –T relationwithhydrodynamic simulations of clus-
X
phase. Suppression of the SF at relatively low redshift is exactly tershavebeenpursuedbyseveralgroups(seeBorganietal.2008,
thewelcomeeffectofAGNfeedback.Atz =0,theresultingSFR forarecentreview).Simulationsofgalaxyclustersincludingtheef-
isofabout70M⊙yr−1forbothmodels,avaluewhichiscloserto, fectofstarformationandSNfeedbackintheformofenergy–driven
althoughstillhigherthanthetypicalvaluesofSFRobservedinthe galactic winds produce results which are close to observations
BCGsofclustersofcomparablemass.(e.g.,Raffertyetal.2006). at the scale of clusters, while generally producing too luminous
Quiteinterestingly,increasingthefeedbackefficiencytoǫf =0.8 galaxygroups(e.g.,Borganietal.2004).Althoughacloseragree-
intheAGN2(0.8)rundoesnotsignificantlyaffecttheleveloflow- ment withobservations atthescaleofgroups canbeobtained by
redshiftstarformation,whileitsuppressesstarformationbyonly using SN–triggered momentum–driven winds (Dave´etal. 2008),
∼ 10 per cent around the peak of efficiency. Therefore, while a thereisageneralconsensusthatstellarfeedbackcannotreproduce
higher efficiency is indeed effective in suppressing gas accretion atthesametimeboththeobservedL –T relationandthelowstar
X
onto thecentral BH,a further reduction of star formation associ- formationrateobservedincentralclustergalaxies.Puchweinetal.
atedtotheBCGshouldrequireadifferentwayofthermalizingthe (2008)presented resultsontheL –T relationfor simulationsof
X
radiatedenergy.AsfortheAGN2Wrun,itsSFRathighredshiftis galaxy clusters which included the bubble–driven AGN feedback
lowerthanfortheAGN2run,duetotheeffectofwinds,whileno scheme introduced by Sijackietal. (2007). They concluded that,
significantchangeisobservedatz∼<3. while simulations not including any efficient feedback (in fact,
IntherightpanelofFig.1weplotthestellarmassfoundinthe quitesimilartoourNFruns)produceoverluminousobjects,their
BCG at z = 0that isformed before agiven redshift. According mechanismforAGNfeedbackisefficientinsuppressingtheX–ray
tothisdefinition,thisquantityistheintegraloftheSFRplottedin luminosityofclustersandgroupsattheobservedlevel.
therightpanel,computedfromagivenredshiftz toinfinity.This We present here our results on the L –T relation, keeping
X
plot clearly shows the different effect that winds and AGN feed- inmindthat our simulationsdiffer fromthose by Puchweinetal.
backhaveinmaking theBGCstellarpopulation older.IntheNF (2008)bothinthedetailsoftheimplementationoftheAGNfeed-
and W runs, theredshift at which 50per cent of theBCG stellar backschemeandinthetreatmentofthemetallicitydependenceof
masswasalreadyinplaceisz50 ≃ 2.Thisindicatesthatevenan thecoolingfunction.IntheleftpanelofFigure2weshowthere-
efficientSNfeedbackisnotabletomakethestellarpopulationof sultsforourrunsbasedonSNgalacticwinds(Wruns)andforthe
theBCGolder.Onthecontrary,theeffectofAGNfeedbacktakes runs not including any efficient feedback (NF runs). Filled sym-
placemostlyatrelativelylowreshift.Asaconsequencetheageof bols refer to the main halo of each simulated Lagrangian region,
theBGCstellarpopulationincreases,withz50 ≃3.0−3.6,almost while open circles are for the “satellites”. Although we find sev-
independentofthedetailoftheAGNfeedbackscheme. eralsatelliteshavingatemperaturecomparabletothoseofthelow-
massmainhalos(seealsoTable1),weremindthatthesesatellites
aredescribedwithamassresolutionsixtimeslowerthanthatofthe
low-massmainhalos.WenotethattheNFrunsprovideaL –T re-
3 THERMALPROPERTIESOFTHEICM X
lationwhichisnotfarfromtheobservedone,especiallyatthescale
Galaxy clusters are identified in each simulation box by running ofgroups.Thereasonforthiscloseragreement,withrespecttothe
firstafriends-of-friends(FOF)algorithmoverthehighresolution resultbyPuchweinetal.(2008)liesinthefact thattheseauthors
AGNfeedbackand metalenrichmentofclusters 7
7000
AGN1 2.5e+13
NF AGN1
W NF
6000 AGN2 W
AGN2W AGN2
AGN2(0.8) AGN2W
2e+13 AGN2(0.8)
5000 ]⊙
M
s [
M/yrs]⊙ 4000 ar masse 1.5e+13
SFR [ 3000 ve Stell 1e+13
ati
2000 mul
u
C
5e+12
1000
0 0
0 2 4 6 8 10 0 2 4 6 8 10
redshift redshift
Figure1.Leftpanel:thehistoryofstarformationrateofthebrightestclustergalaxy(BCG)intheg51clusterfortherunswithnofeedback(NF,blueshort-
dashed),withgalacticwinds(W,greendashed),withstandardAGNfeedback(AGN1,reddot-dashed)andwithmodifiedAGNfeedback(AGN2,light-blue
solid).AlsoshownaretheresultsfortheAGN2runwithhigherradio-modeBHfeedbackefficiency(AGN2(0.8),purplelong-dashed)andfortheAGN2run
alsoincludinggalacticwinds(AGN2W,magentadotted).Rightpanel:thestellarmassfoundintheBCGatz=0thatwasformedbeforeagivenredshift.
adoptedacoolingfunctioncomputedforzerometallicity.Includ- indeedabletoproducearealisticL –T relation,almostindepen-
X
ingthecontributionofmetallinestotheradiativelossesincreases dentofthedetailofhowtheenergyisthermalisedinthesurround-
coolingefficiencyand,therefore,gasremovalfromthehotX–ray ingmedium.
emittingphase.However,thepricetopayforthisreductionofX–
rayluminosity isthat a far too largebaryon fraction isconverted
intostarswithinclusters(seebelow).Quiteparadoxically,wealso 3.2 TheentropyoftheICM
note than including an efficient feedback in the form of galactic
Entropy level in central regions of clusters and groups isconsid-
windsturnsintoanincreaseofX–rayluminosity.Thisisduetothe
ered another fingerprint of the mechanisms which determine the
fact that this feedback prevents a substantial amount of gas from
thermodynamical history of the ICM. Early observational results
cooling,withoutdisplacingitfromthecentralclusterregions,thus
on the presence of entropy cores (e.g., Ponmanetal. 1999) have
increasingtheamountofX-rayemittingICM.
been more recently revised, in the light of higher quality data
Inordertoassestheeffectofthedifferentresolutionusedfor from Chandra (e.g., Cavagnoloetal. 2009) and XMM–Newton
largeand smallclusters, wecarried out runsof g676 at thesame (e.g.,Johnsonetal.2009)observations. Thesemorerecentanaly-
lowerresolutionofthemassiveclusters.Theresultsareshownin sesshowthatentropylevelofclustersandgroupsatR500ishigher
Fig. 2 with black diamonds connected with arrows to the corre- thanpredictedbynon–radiativesimulations,withentropyprofiles
sponding higher resolution result. We note that resolution effects forrelaxedsystemscontinuouslydecreasingdowntothesmallest
go in opposite directions for the NF and W runs. In fact, in the resolvedradii(seealsoSunetal.2009).
absenceofwinds,therunawayofcoolingwithresolutionremoves Whileradiativesimulationsofgalaxyclustershavebeengen-
fromthehotphasealargeramountofgas,thusdecreasingX–ray erally shown to reproduce observationalr results at R500 (e.g.,
luminosity. On the contrary, higher resolution allows a more ac- Nagaietal.2007;Dave´etal.2008),theygenerallypredicttoolow
curatedescriptionofkineticfeedback,whichstartsheatinggasat entropylevelsatsmallerradii.Forinstance,Borgani&Viel(2009)
higherredshift.Asaconsequence,radiativelossesarecompensated have shown that the entropy at R2500 can be reproduced by re-
athigherresolutionforalargeramountofdiffusebaryons,which sortingtoafairlystrongpre-heatingatz = 4.However,thispre-
remaininthehotphase,therebyincreasingtheX–rayluminosity. heatingmusttargetonlyrelativelyoverdenseregions,topreventthe
As for the runs with AGN feedback, it is quite efficient in creationoftoolargevoidsinthestructureoftheLyman-αforestat
decreasing X–ray luminosity at the scale of galaxy groups, thus z∼2(seealsoShangetal.2007).
wellrecoveringtheobservedL –T relation.Thisconclusionholds In the following we use the standard definition of entropy,
X
forbothimplementationsoftheAGNfeedback,whichhaverather whichisusuallyadoptedinX–raystudiesofgalaxyclusters(e.g.,
smalldifferences. Therefore,althoughtheAGN2schemeismore Sunetal.2009):
efficientinregulatingthegrowthofthecentralBHshostedwithin T∆
theBCGs,ithasamarginaleffectontheX–rayluminosity.These K∆ = n2/3 , (3)
resultsareinlinewiththosefoundbyPuchweinetal.(2008),who e,∆
however usedtheinjectionofheatedbubblestodistributetheen- whereT∆andne,∆arethevaluesofgastemperatureandelectron
ergyextractedfromtheBHaccretion.Thiswitnessesthatthefeed- numberdensitycomputedatR∆.Asforthetemperature,itiscom-
backenergyassociatedtogasaccretionontosuper-massiveBHsis puted by following theprescription of spectroscopic liketemper-
8 Fabjanet al.
100 100
Horner 2001 Horner 2001
Arnaud&Evrard 99 Arnaud&Evrard 99
Osmond&Ponman 04 Osmond&Ponman 04
Pratt et al. 09 Pratt et al. 09
NF AGN-1
W AGN-2
s] 10 s] 10
g/ g/
er er
4 4
4 4
0 0
1 1
) [0 1 ) [0 1
0 0
5 5
R R
< <
(ol (ol
b b
X, X,
L 0.1 L 0.1
0.01 0.01
1 10 1 10
T (< R ) [keV] T (< R ) [keV]
sl 500 sl 500
Figure2.RelationbetweenX–rayluminosityandtemperatureforsimulated(colouredsymbols)andobserved(greypointswitherrorbars)clustersandgroups.
ObservationaldatapointsarefromArnaud&Evrard(1999)(greydiamonds)andPrattetal.(2009)(greysquares)forclusters,fromOsmond&Ponman(2004)
(greycircles)forgroupsandfromHorner(2001)(greytriangles).DatafromsimulationswerecomputedinsideR500.Leftpanel:resultsforthenofeedback
case(NF,bluetriangles)andforthecasewithgalacticwinds(W,greensquares).Rightpanel:resultsfortherunswithstandardAGNfeedback(AGN1,red
circles)andwiththemodifiedAGNfeedbackscheme,wherealsoaradio-moderegimeisincluded(seetext,AGN2;cyancircles).Foreachseriesofruns,
filledandopensymbolsrefertothemainhalowithineachresimulatedLagrangianregionandto“satellite”halosrespectively.Blackdiamondsrefertothe
runsat1×resolution,witharrowspointingtoresultsat6×higherresolutionfortheg676cluster.
atureintroducedbyMazzottaetal.(2004).Thisdefinitionoftem- withtheresultontheL –T relation,thisresultshowsthatarather
X
peraturehasbeenshowntoaccuratelyreproduce, withinfewper- tunedenergyinjectionisrequired,whichmustbeabletosuppress
cents,theactualspectroscopictemperatureobtainedbyfittingspec- X–rayluminositybydecreasinggasdensity,whileatthesametime
traofsimulatedclusterswithasingle–temperatureplasmamodel, reproducingthelowentropylevelmeasuredatsmallradii.
withinthetypicalenergybandswheredetectorson-boardofpresent
X–raysatellitesaretypicallysensitive.
3.3 Temperatureprofiles
WeshowinFigure3thecomparisonbetweenoursimulations
andobservationaldataongroups(Sunetal.2009)andonclusters Anumberofcomparisonsbetweenobservedandsimulatedtemper-
(Vikhlininetal. 2009) for the relation between entropy and tem- atureprofilesofgalaxyclustershaveclearlydemomnstratedthata
peratureatR500andR2500(upperandlowerpanels,respectively). remarkableagreementexistsatrelativelylargeradii,R∼>0.2R180,
Inorder toreproduce theprocedure adopted bySunetal.(2009), wheretheeffectofcoolingisrelativelyunimportant.Whilethisre-
wecomputethespectroscopic–liketemperatureofsimulatedclus- sult, which holds almost independently of the physical processes
tersbyexcludingthecoreregionswithin0.15R500.Asfortheruns includedinthesimulations(e.g.,Lokenetal.2002;Borganietal.
withnoefficientfeedback(NF)wenotethattheyproduceentropy 2004;Kayetal.2007;Prattetal.2007;Nagaietal.2007),should
levels, at both R500 and R2500, which are close to the observed be regarded as a success of cosmological simulations of galaxy
ones. Thisresult can beexplained inthesameway asthat found clusters, the same simulations have much harder time to predict
for the LX–T relation: overcooling, not balanced by an efficient realisticprofileswithincool-coreregions(e.g.,Borganietal.2008,
feedbackmechanism,removesalargeamountofgasfromtheX– forarecentreview). Inthisregime,radiativesimulationssystem-
rayemittingphase,whileleavinginthishotphaseonlyrelatively atically produce steep negative temperature profiles, at variance
highentropygas,whichflowsinfromlargerradiiasaconsequence with observations, as a consequence of the lack of pressure sup-
oflackofcentralpressuresupport. portcausedbyovercooling. Thisfurtherdemonstratesthatasuit-
Including winds (W runs) has the effect of increasing the ablefeedbackmechanismsisrequiredtopressurisethegas,soas
amountoflow-entropygas,whichisnowallowedtoremaininthe topreventovercoolingandturningthetemperaturegradientsfrom
hotphasedespiteitsformallyshortcoolingtime,thankstothecon- negativetopositiveinthecoreregions.Whilefeedbackassociated
tinuousheatingprovidedbywinds.Asaresult,entropydecreases toSNehasbeenprovednottobesuccessful,AGNfeedbackisgen-
atbothradii,forthesamereasonforwhichX–rayluminosityin- erallyconsideredasalikelysolutionforsimulationstoproducere-
creases. As for the runs with AGN feedback, its effect is almost alisticcoolcores.Basedonsimulationsofonerelativelylow–mass
negligibleformassiveclusters.Ontheotherhand,AGNfeedback cluster,Sijackietal.(2008)foundthatAGNfeedbackcanprovide
providesasignificantincreaseoftheentropylevelinpoorsystems, reasonabletemperatureprofilesonlyifapopulationofrelativistic
aneffectwhichislargeratsmallercluster-centricradii.Theresult- particlesisinjectedalongwiththermalenergyininflatedbubbles.
ingentropyishigherthanindicatedbyobservationaldata.Together WepresentinFigure4thecomparisonbetweensimulatedand
AGNfeedbackand metalenrichmentofclusters 9
2] 2]
m m
c c
V 1000 V 1000
e e
k k
[0 [0
0 0
5 5
K K
3 3
4/ 4/
z) z)
E( E(
NF AGN1
W AGN2
Sun et al. 2006 Sun et al. 2006
Vihlinin et al. 2009 Vihlinin et al. 2009
100 100
1 10 1 10
T (T ) (< R ) [keV] T (T ) (< R ) [keV]
spec sl 500 spec sl 500
2] 2]
m 1000 m 1000
c c
V V
e e
k k
[0 [0
0 0
5 5
2 2
K K
3 3
4/ 4/
z) z)
E( E(
100 100
NF AGN1
W AGN2
Sun et al. 2006 Sun et al. 2006
Vihlinin et al. 2009 Vihlinin et al. 2009
1 10 1 10
T (T ) (< R ) [keV] T (T ) (< R ) [keV]
spec sl 2500 spec sl 2500
Figure3.Relationbetweenentropyandtemperatureforoursimulatedclusters(colouredcirclesandsquares)andfortheobservationaldatapointsatR500
(upperpanels)andR2500 (lowerpanels)fromSunetal.(2009)(blackfilleddiamonds)andVikhlininetal.(2009)(blackopendiamonds).Leftandright
panelsshowresultsfortheninecentralclustersfortherunswithout(NF:bluesquares;W:greencircles)andwithAGNfeedback(AGN1:redsquares;AGN2:
cyancircles),respectively.Forafaircomparisonwithobservations,spectroscopic-liketemperaturesofthesimulatedclustersarecomputedbyexcludingthe
regionswithin0.15R500.
observed temperatureprofilesfor galaxyclusters withT∼>3 keV andtheAGN2feedbackschemespressurisetheICMinthecentral
(leftpanel)andforpoorerclustersandgroupswithT∼<3keV(right regions, thus preventing adiabatic compression in inflowing gas.
panel). Observational results are taken from Leccardi&Molendi From the one hand, this result confirms that a feedback scheme
(2008b) and Sunetal. (2009) for rich and poor systems, respec- not relatedto star formation goes indeed inthe right direction of
tively. As for rich clusters, none of the implemented feedback regulatingthethermalpropertiesoftheICMincoolcoreregions.
schemeiscapabletoprevent thetemperaturespikeatsmallradii, Ontheotherhand, italsodemonstratesthattheschemesofAGN
whileallmodelsprovideatemperatureprofilequitesimilartothe feedbackimplementedinoursimulationsdoanexcellentjobatthe
observedoneatR∼>0.3R180.Thesituationisdifferentforgroups. scaleof galaxygroups, whiletheyarenot efficient enough at the
Inthiscase,bothschemesofAGNfeedbackprovideresultswhich scaleofmassiveclusters.
gointherightdirection.Whilegalacticwindsarenotabletosignif-
icantlychangethesteepnegativetemperaturegradients,theAGN1
10 Fabjanet al.
2 2
AGN-1 NF
W W
AGN-2 AGN-1
1.8 1.8
NF AGN-2
Leccardi&Molendi 2008 Sun et al. (2009)
1.6 1.6
R)180 1.4 R)2500 1.4
< 1.2 < 1.2
T(mean 1 T(mean 1
T / sl 0.8 T / sl 0.8
0.6 0.6
0.4 0.4
0.2 0.2
0 0.2 0.4 0.6 0.8 1 0 0.5 1
R/R R/R
180 500
Figure4.ComparisonbetweenthetemperatureprofilesforsimulatedandobservedclusterswithT∼>3keV(leftpanel)andforgroupswithT∼<3keV(right
panel).Ineachpanel,differentlinescorrespondstotheaveragesimulatedprofilescomputedoverthefourmainmassiveclustersintheleftpanelandover
thefivemainlow-massclustersintherightpanel,forthedifferentsetsofruns:nofeedback(NF,blueshortdashed),galacticwinds(W,greenlongdashed),
standardAGNfeedback(AGN1,reddot-dashed),modifiedAGNfeedback(AGN2,cyansolid).Forreasonsofclarity,weshowwitherrorbarsther.m.s.scatter
overtheensembleofsimulatedclustersonlyfortheAGN1runs.ObservationaldatapointsforclustersintheleftpanelaretakenfromLeccardi&Molendi
(2008b),whilethoseforgroupsintherightpanelarefromSunetal.(2009).
0.18 0.18
0.16 0.16
0.14 0.14
0.12 0.12
) 00 0.1 ) 00 0.1
5 5
R R
< <
(as 0.08 (as 0.08
g g
f f
0.06 0.06
0.04 0.04
Vikhlinin et al. 2006 Vikhlinin et al. 2006
0.02 0.02
NF AGN-1
W AGN-2
cosmic baryon fraction cosmic baryon fraction
0 0
0 2 4 6 8 10 12 0 2 4 6 8 10 12
T (T ) [keV] T (T ) [keV]
spec sl spec sl
Figure5.ComparisonofthegasfractionwithinR500insimulations(colouredcircles)andobservationaldatafromChandradata(diamondswitherrorbars)
analysedbyVikhlininetal.(2006).Leftpanel:resultsforthenofeedback(NF)runs(darkblue)andfortherunswithgalacticwinds(W,lightgreen).Right
panel:resultsfortherunswiththestandardAGNfeedback(AGN1,darkred)andwithmodifiedAGNfeedback(AGN2,lightcyan).Thehorizontaldottedline
marksthecosmicbaryonfractionassumedinthesimulations.