On the role of AGN feedback on the thermal and chemodynamical properties of the hot intracluster ...

22 Pages·2013·2.43 MB·English

MNRAS438,195–216(2014) doi:10.1093/mnras/stt2141
AdvanceAccesspublication2013December13
On the role of AGN feedback on the thermal and chemodynamical
properties of the hot intracluster medium
S. Planelles,1,2‹ S. Borgani,1,2,3 D. Fabjan,3,4,5 M. Killedar,1,2 G. Murante,2
G. L. Granato,2 C. Ragone-Figueroa2,6 and K. Dolag7,8
1AstronomyUnit,DepartmentofPhysics,UniversityofTrieste,viaTiepolo11,I-34131Trieste,Italy
2INAF,OsservatorioAstronomicodiTrieste,viaTiepolo11,I-34131Trieste,Italy
3INFN–NationalInstituteforNuclearPhysics,ViaValerio2,I-34127Trieste,Italy D
4SPACE-SI,SlovenianCentreofExcellenceforSpaceSciencesandTechnologies,Asˇkercˇeva12,1000Ljubljana,Slovenia ow
5FacultyofMathematicsandPhysics,UniversityofLjubljana,Jadranska19,1000Ljubljana,Slovenia nlo
6InstitutodeAstronom´ıaTeo´ricayExperimental(IATE),ConsejoNacionaldeInvestigacionesCient´ıficasyTe´cnicasdelaRepu´blica a
d
Argentina(CONICET),ObservatorioAstrono´mico,UniversidadNacionaldeCo´rdoba,Laprida854,X5000BGRCo´rdoba,Argentina ed
7Universita¨tssternwarteMu¨nchen,Scheinerstr.1,D-81679Mu¨nchen,Germany fro
8Max-Planck-Institutfu¨rAstrophysik,POBox1317,D-85741Garching,Germany m
h
ttp
Accepted2013November4.Received2013November4;inoriginalform2013September20 s://a
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ABSTRACT ic
Wepresentananalysisofthepropertiesoftheintraclustermedium(ICM)inanextendedsetof .ou
p
cosmologicalhydrodynamicalsimulationsofgalaxyclustersandgroupsperformedwiththe .c
o
TREEPM+SPHGADGET-3code.Besidesasetofnon-radiativesimulations,wecarriedouttwosets m/m
ofsimulationsincludingradiativecooling,starformation,metalenrichmentandfeedbackfrom n
ra
supernovae(SNe),oneofwhichalsoaccountsfortheeffectoffeedbackfromactivegalactic s
/a
nuclei(AGN)resultingfromgasaccretionontosupermassiveblackholes.Thesesimulations rtic
areanalysedwiththeaimofstudyingtherelativeroleplayedbySNandAGNfeedbackonthe le-a
b
generalpropertiesofthediffusehotbaryonsingalaxyclustersandgroups:scalingrelations, s
temperature, entropy and pressure radial profiles, and ICM chemical enrichment. We find trac
thatsimulationsincludingAGNfeedbackproducescalingrelationsbetweenX-rayobservable t/43
8
quantitiesthatareingoodagreementwithobservationsatallmassscales.Observedpressure /1
/1
profilesarealsoshowntobequitewellreproducedinourradiativesimulations,especiallywhen 9
5
AGNfeedbackisincluded.However,oursimulationsarenotabletoaccountfortheobserved /10
3
diversity between cool-core and non-cool-core clusters, as revealed by X-ray observations: 0
3
3
unlikeforobservations,wefindthattemperatureandentropyprofilesofrelaxedandunrelaxed 2
b
clustersarequitesimilarandresemblemoretheobservedbehaviourofnon-cool-coreclusters. y g
u
As for the pattern of metal enrichment, we find that an enhanced level of iron abundance is e
s
producedbyAGNfeedbackwithrespecttothecaseofpurelySNfeedback.Asaresult,while t o
n
simulations including AGN produce values of iron abundance in groups in agreement with 2
6
observations,theyover-enrichtheICMinmassiveclusters.TheefficiencyofAGNfeedback N
o
v
in displacing enriched gas from haloes into the intergalactic medium at high redshift also e
m
creates a widespread enrichment in the outskirts of clusters and produces profiles of iron b
e
abundance whose slope is in better agreement with observations. By analysing the pattern r 2
0
oftherelativeabundances ofsiliconand ironandthefractionofmetalsinthestellarphase, 18
ourresultsclearlyshowthatdifferentsourcesofenergyfeedbackleavedifferentimprintsin
the enrichment pattern of the hot ICM and stars. Our results confirm that including AGN
feedbackgoesintherightdirectionofreconcilingsimulationpredictionsandobservationsfor
severalobservationalICMproperties.Stillanumberofimportantdiscrepancieshighlightthat
(cid:2)
E-mail:[email protected]
(cid:2)C 2013TheAuthors
PublishedbyOxfordUniversityPressonbehalfoftheRoyalAstronomicalSociety
196 S.Planellesetal.
the model still needs to be improved to produce the correct interplay between cooling and
feedbackincentralclusterregions.
Key words: methods: numerical–galaxies: clusters: general–cosmology: miscellaneous–
X-rays:galaxies.
Yepes2000;Borganietal.2001;Springel,White&Hernquist2001;
1 INTRODUCTION
Kayetal.2002).
The sensitivity reached by X-ray observations with the existing Thesesimulationshavehaddifferentdegreesofsuccessinrepro-
generationofsoftX-raytelescopes(Chandra,XMM–Newtonand ducingthethermodynamicalpropertiesofthehotICM.Itiswell
SUZAKU)hasprovideduswithadetailedanalysisofthethermo- establishedthatsimulationsthatincludeonlytheeffectsofradiative
and chemodynamical properties of the hot intracluster medium cooling form too many stars relative to observational results (see
D
(ICM) for significant samples of galaxy clusters. These observa- Baloghetal.2001,forfurtherdiscussionofthis‘coolingcrisis’). o
w
tionshavenowestablishedsomeofthemainICMproperties:out- Thesolutiontothisproblemshouldbeprovidedbyasuitablemech- nlo
side cluster core regions, observations report negative gradients anismcombiningtheactionofheatingandcoolingprocessesina ad
e
in the temperature profiles of galaxy clusters (e.g. De Grandi & self-regulated way (e.g. Voit 2005, fora review). Different forms d
Molendi2002;Vikhlininetal.2005;Zhangetal.2006;Baldietal. of energy feedback from supernova (SN) explosions have been fro
m
2007;Prattetal.2007;Leccardi&Molendi2008b);gasentropyin proposed to generate a self-regulated star formation (Springel & h
poorclustersandgroupsishigherthanpredictedfromtheICMself- Hernquist 2003). However, models based on the action of stellar ttp
s
similarscalingrelations(seeGiodinietal.2013,forarecentreview feedback are not able to regulate star formation to the low levels ://a
on observational scaling relations and references therein); galaxy observedinthemostmassivegalaxieshostedatthecentreofrich c
a
clustersshowaglobalmetalenrichmentatalevelofabout0.3ZFe,(cid:3) galaxyclusters,theso-calledbrightestclustergalaxies(BCGs;e.g. dem
(DeGrandietal.2004;Vikhlininetal.2005;dePlaaetal.2006; Borganietal.2004andreferencestherein).Withinthisscenario,it ic
Leccardi & Molendi 2008b; Snowden et al. 2008; Werner et al. isbecomingincreasinglyclearthatAGNfeedbackisthemostplau- .ou
p
2008);centralvaluesofZFe closetothesolarvalue,strongnega- siblesourceofheatingtocounteractgascoolingwithinthemassive .c
o
tivegradientsintheradialprofilesoftheironabundanceandlow darkmatter(DM)haloesofgroupsandclusters.Itisonlyrelatively m
amountsofgaswithtemperaturelowerthanaboutonethirdofthe recentlythatstudiesoftheeffectofAGNfeedbackincosmological /m
n
virialtemperature(e.g.Petersonetal.2001;Bo¨hringeretal.2002; simulationsofgalaxyclustershavebeenundertakenbyanumberof ra
s
Sanderson,Ponman&O’Sullivan2006)havebeenfoundincore independentgroups(e.g.Sijackietal.2007;Puchwein,Sijacki& /a
regionsofrelaxedcool-core(CC)clusters;etc. Springel2008;Fabjanetal.2010;McCarthyetal.2010;Puchwein rtic
le
ComplementarytoX-rayobservations,clustersobservedinlarge et al. 2010; Short et al. 2010; Dubois et al. 2011; Battaglia et al. -a
b
Sunyaev–Zel’dovich (SZ) surveys offer an additional channel to 2012b;Martizzi,Teyssier&Moore2012).Duetoitscentralloca- s
analyse the properties of the hot ICM (see Carlstrom, Holder & tionanditsabilitytoprovideenoughenergy,anincreasingnumber tra
c
Reese2002,forareview).WhiletheX-raysignalisproportionalto ofauthorshavearguedthatgasaccretionontosupermassiveblack t/4
3
thesquareofthegasdensity,theSZeffect(Sunyaev&Zeldovich holes (SMBHs) plays a crucial role in regulating the star forma- 8
/1
1972) depends on the integrated pressure along the line of sight, tionratesofmassivegalaxies(e.g.Granatoetal.2004;Springel, /1
9
whichdecreasesmoregentlywithradius(e.g.Arnaudetal.2010). DiMatteo&Hernquist2005;Boweretal.2006;Bower,McCarthy 5
/1
It is thanks to the larger dynamic range in gas density accessible &Benson2008)andsuppressingovercoolingingroupsandclusters 0
3
0
and the redshift independence of the signal that SZ observations (e.g.Churazovetal.2001),apicturethatisbroadlysupportedby 3
3
aretheidealcomplementtoX-rayobservations.Newgenerations alargebodyofobservationalevidence(e.g.McNamara&Nulsen 2
b
ofmillimetreinstrumentsarenowroutinelydetectingtheSZsignal 2007,forareview). y
g
ofgalaxyclusters,sometimesouttolargeradii,therebyopeninga Motivatedbythisidea,Springeletal.(2005)developedanovel u
e
newwindowonthestudyofthethermodynamicsofthehotbaryons scheme to follow the growth of SMBHs and the ensuing feed- st o
ingalaxyclusters(e.g.Hasselfieldetal.2013;Plaggeetal.2013; backfromAGNincosmologicalsmoothedparticlehydrodynam- n
2
PlanckCollaborationetal.2013;Reichardtetal.2013). ics (SPH) simulations (see also Sijacki & Springel 2006; Booth 6
N
Giventherangeofscalesinvolvedbygalaxyclusters,theirob- &Schaye2009,forsubsequentmodificationsofthismodel).Us- o
v
servational properties arise from a non-trivial interplay between ingthisoriginalimplementationofAGNfeedbackasareference, em
gravitationalprocesses,whichshapethelarge-scalestructureofthe Sijacki & Springel (2006), Sijacki et al. (2007), Puchwein et al. be
Universe,andanumberofastrophysicalprocessesthattakeplace (2008),Bhattacharya,DiMatteo&Kosowsky(2008)andFabjan r 2
0
onmuchsmallerscales[e.g.radiativecooling,starformationandits et al. (2010) went one step further and modified the original im- 1
8
associatedenergyandchemicalfeedbackandactivegalacticnuclei plementationtoincludeboth‘quasar’and‘radio’feedbackmodes.
(AGN)heating].Withinthiscontext,itisonlywithcosmological Theformerischaracterizedbyisotropicthermalheatingofthegas
hydrodynamicalsimulationsthatonecancapturethefullcomplex- whenaccretionratesarehigh,whilethelatter,characteristicwhen
ity of the problem (see Borgani & Kravtsov 2009; Kravtsov & accretionratesarelow,consistsofthermalheatingmeanttomimic
Borgani 2012, for recent reviews). In the last two decades, much ‘bubbles’observedinmanynearbyclusters,whicharethoughtto
progresshasbeenmadeinthenumericalmodellingoftheforma- beinflatedbyrelativisticjetscomingfromthecentralBH.1Asfor
tionandevolutionofgalaxyclustersandgroups,thankstotheever
evolvingefficiencyofsophisticatedcosmologicalhydrodynamical
simulation codes, that include now advanced descriptions of the 1OnlythemodelsbySijacki&Springel(2006)andSijackietal.(2007)
astrophysical processes shaping galaxy formation, and the rapid wereexplicitlymodifiedtoincludethepossibilitytoinflatehigh-entropy
increase of accessible supercomputing power (e.g. Evrard 1990; bubblesintheICMwheneveraccretionontothecentralBHentersina
Navarro,Frenk&White1995;Bryan&Norman1998;Kravtsov& quiescent‘radio’mode.
ThermalandchemodynamicalICMproperties 197
Eulerian adaptive mesh refinement (AMR) simulations, an alter- 2 THE SIMULATED CLUSTERS
nativewayofimplementingtheAGNenergyinjectionisthrough
AGN-drivenwinds,whichshockandheatthesurroundinggas(e.g. 2.1 Initialconditions
Duboisetal.2011;Gasparietal.2011;seealsoBaraietal.2013
Thesample ofgalaxyclusters andgroups that weanalyse inthis
foranSPHimplementationofkineticAGNfeedback).
work has been extracted from high-resolution re-simulations of
As a result of these analyses, AGN feedback was generally
29 Lagrangian regions taken around the massive haloes recog-
foundtoreproducebetteranumberofobservablepropertiesofthe
nizedwithinalargevolume,low-resolutionN-bodyparentcosmo-
ICM(seealsoMcCarthyetal.2010)togetherwithreducedstellar
logical simulation (see Bonafede et al. 2011, for details). These
massfractions.Inthisregard,theAGNsimulationsperformedby
simulations have been performed assuming a flat (cid:3) cold dark
Puchwein et al. (2008) reproduced the luminosity and gas mass
matter ((cid:3)CDM) cosmological model: matter density parameter
fraction–temperature relations of groups and clusters. In addition
(cid:4) = 0.24, baryon density parameter (cid:4) = 0.04, Hubble con-
totheseresults,thesimulationsperformedbyFabjanetal.(2010) m b
stant H = 72 km s−1 Mpc−1, primordial power spectral index D
alsoobtainedtemperatureprofilesingoodagreementwithgalaxy 0 o
n =0.96andpowerspectrumnormalizationσ =0.8.Following w
groupsobservations. thsezoomedinitialconditiontechnique(Tormen8,Bouchet&White nlo
Less attention has been paid so far to analyse the interplay 1997),eachLagrangianregionhasbeenre-simulatedbyincreasing ade
between AGN and chemical enrichment by including a detailed d
chemodynamical description of the ICM (e.g. Moll et al. 2007; the mass resolution and by including the relevant high-frequency fro
modes of the power spectrum. In order to maintain a proper de- m
SMijeaacskuireemteanl.ts20o0f7t;heFaebnjrainchemteanlt. 2p0a1tt0e;rnMocfCtahrethyICeMt arle.p2r0es1e0n)t. scription of the large-scale tidal field, outside these re-simulated http
regions, particles with masses increasing with distance from s
a unique means towards a unified description of the thermo- the considered halo were employed. Within each high-resolution ://a
dynamical properties of the diffuse gas and of the past his- c
Lagrangian region there are not low-resolution particles, at least ad
tory of star formation within the population of cluster galaxies out to 5 virial radii,2 contaminating the central halo at z = 0. em
(aen.agl.ysReesnozifnitheetIaClM. 19m9e3t;alBeonrrgiacnhimeetntalf.ro2m00c8o).smInolfoagcitc,alresciemn-t Csiognnsifieqcaunetnthlya,loeawchithroeguitolnowis-rleasrgoeluetinoonugpharttoiclheasveoumtotoretthheanviorinael ic.oup
ulations including the effect of AGN feedback show that this radius. .co
mechanism can actually displace a large amount of highly en- m
riched gas that is already present inside massive haloes at the Theinitialconditionswerecreatedbyaddingagascomponent /m
onlyinthehigh-resolutionregion.Inordertodoso,bychoosingthe n
redshift z ∼ 2–3, at which SMBH accretion peaks. The resulting ra
massratiotoreproducethecosmicbaryonfraction,eachdarkmatter s
widespreadenrichmentoftheintergalacticmediumleadstoasensi- /a
tivechangeoftheamountanddistributionofmetalswithinclusters particle was split into two, one standing for the gas and another rtic
for the DM component. The initial mass of each gas particle is le
a2n0dT11hg)er.oauipmsaotflothwisrepdaspheifrti(se.tgo.Fparebsjaenntetaadl.e2ta0i1le0d;MancaClyasritshyofettahle. misgmasD=M1=.583.4×71×0810h8−1hM−1(cid:3)M,(cid:3)w.hereasthemassofeachDMparticle -abstra
c
properties of the ICM for an extended set of cosmological hy- t/4
3
drodynamical simulations of galaxy clusters, which have been 2.2 Thesimulationmodels 8/1
performed with the TREEPM+SPH GADGET-3 code (Springel 2005). /1
Wecarriedoutonesetofnon-radiativesimulations,andtwosets The simulations were performed using the TREEPM–SPH GADGET-3 95
of simulations including metallicity-dependent radiative cooling, code,animprovedversionoftheGADGET-2code(Springel2005). /10
3
Thegravitationalforceinthehigh-resolutionregionsiscomputedby 0
star formation, metal enrichment and feedback from SNe, one of 3
which also accounts for the effect of an efficient model of AGN assumingaPlummer-equivalentsofteninglengthof(cid:6)=5h−1kpc 32
feedback. The scheme of AGN feedback implemented in these in physical units below z = 2, and kept fixed in comoving units by
simulations is a modification of the original model presented in at higher redshift (see Borgani et al. 2006, for an analysis of the gu
e
Ftoabtjhaenwetayal.in(2w01h0ic)hwBitHhssoamreesiemepdreodveamndenatsrereallaltoewde,destpoecgiraollwy,, ecoffmecptuoteftshoeftheyndinrgodoynnaramdiicaatilvfeorscimesu,ltahteiomnisnoimfguamlavxayluceluasctceerss)s.ibTloe st on
with their positioning within their host galaxy and with the way bytheSPHsmoothinglengthoftheB-splinekernelisassumedto 26
be half of the corresponding value of the gravitational softening N
in which the thermal energy is distributed. We will show results o
ontheeffectthatthedifferentfeedbackmechanismsimplemented length.Wecarriedoutthreedifferentsetsofsimulations,thatwe vem
in our simulations have on the ICM thermodynamical proper- tag as NR, CSF and AGN, whose description is provided here be
tiesofoursystemsandonthecorresponding patternofchemical below. r 2
0
enrichment. (i) NR.Non-radiativehydrodynamicalsimulations,basedonthe 18
Thepaperisorganizedasfollows:inSection2,wedescribeour entropy-conservingSPH(Springel&Hernquist2002),withcompu-
setofsimulatedgalaxyclusters,thenumericalimplementationof tationcarriedoutusingtheB-splinekernelwithadaptivesmoothing
thedifferentphysicalprocessesincludedinoursimulations,andthe constrainedtoattainaminimumvalueequaltohalfofthegravita-
definitionsoftheobservablequantitiescomputedfromthesimula- tionalsofteningscale.Theadoptedartificialviscosityfollowsthe
tions.InSection3,wepresenttheresultsobtainedfromthissetof scheme introduced by Monaghan (1997), with the inclusion of a
simulationsongeneralX-raypropertiesoftheICMandwecompare
themwithdifferentobservationalresults.Section4isdevotedtothe
descriptionofthemetalenrichmentoftheICMinoursimulations. 2Thevirialradius,Rvir,isdefinedastheradiusenclosingtheoverdensity
Finally,wediscussourresultsandsummarizeourmainconclusions ofvirialization,aspredictedbythesphericalcollapsemodel(e.g.Ekeetal.
inSection5. 1996).
198 S.Planellesetal.
viscosity limiter, as described by Balsara (1995) and Steinmetz limited.3 For each BH, the corresponding Bondi accretion rate is
(1996). estimatedusingthelocalgasdensityassignedattheBHposition
(ii) CSF. Hydrodynamical simulations including the effect of by the same SPH spline kernel used for the hydrodynamic com-
cooling, star formation and SN feedback. We follow the proce- putations. The BH dynamical mass is updated according to the
dure described in Wiersma, Schaye & Smith (2009) to compute accretion rate, but the corresponding mass is not subtracted from
the radiative cooling rates. In addition, the contributions of the the surrounding gaseous component. This generates a mass non-
cosmic microwave background and of UV/X-ray background ra- conservation of the order of at most a fraction of percent of the
diationprovidedbyquasarsandgalaxiesistakenintoaccountas clustercentralgalaxystellarmass,butimprovesthepositioningof
introduced by Haardt & Madau (2001). In order to compute the theSMBHparticleand,moreimportant,avoidsthegasdepletion
contributionstocoolingfromeachoneofthe11elementsthatwe intheBHsurroundings,that,attheresolutionofoursimulations,
consider(H,He,C,N,O,Ne,Mg,Si,S,CaandFe),wemakeuse wouldtakeplaceonexceedinglylargescales.
oftheCLOUDYphotoionizationcode(Ferlandetal.1998)assuming (b) SMBHadvection.AsrecentlyalsodiscussedbyWurster& D
anopticallythingasin(photo)ionizationequilibrium.Oncemetals Thacker(2013)andNewton&Kay(2013),numericaleffectscan ow
aredistributedfromstarstosurroundinggasparticles,noprocess drift BHs, originally seeded in DM haloes, outside such haloes. nlo
is included in the simulations to diffuse metals to neighbour gas InordertopinBHsatthecentreofgalaxies,ateachtimestepwe ad
e
particles. As a consequence, the metallicity field is quite noisy, repositiontheBHparticlesatthepositionoftheneighbourparticle, d
sinceheavilyenrichedgasparticlesmayhaveneighbourparticles ofanytype(i.e.DM,gasorstar),whichhastheminimumvalueof fro
m
which are instead characterized by low metallicity. This could in thegravitationalpotential.Weperformthesearchofsuchaparticle h
turninduceanoisypatterninthecomputationofthecoolingrates. withinthegravitationalsofteningoftheSMBH.WhentwoBHsare ttp
s
In order to prevent such a spurious noise in the computation of withinthegravitationalsofteningandtheyhavearelativevelocity ://a
radiative losses, we decided to smooth the metallicity field, for smallerthan0.5ofthesoundvelocityofthesurroundinggas,they ca
d
the only purpose of computing cooling rates, by using the same are merged and the resulting BH is placed at the position of the e
m
kernel used for the SPH computations (see also Wiersma et al. mostmassiveone. ic
2010). Notethatweuseasasearchinglength,forboththeadvectionandthe .ou
p
Thissetofsimulationsaccountsforstarformationandtheeffectof mergingalgorithms,thegravitationalsofteningratherthantheBH .c
o
galacticoutflowstriggeredbySNexplosions.Followingthemodel smoothinglength.Giventhegravitationalnatureofthenumerical m
originally described by Springel & Hernquist (2003), in order to processesresponsiblefordriftingtheBHsawayfromgalaxies,and /m
n
provideasub-resolutiondescriptionoftheinterstellarmedium,gas thephysicalprocessesleadingtomergersofBHs,thislength-scale ra
s
particlesaboveathresholddensityof0.1cm−3 andbelowatem- is the most appropriate to be used. In addition, at the resolution /a
peraturethresholdof2.5×105 Karetreatedasmultiphase.Each ofoursimulations,theBHsmoothinglengthissignificantlylarger rtic
le
multiphasegasparticlesharesacold(thereservoirofstarforma- thanthegravitationalsofteningand,therefore,quitelargeforthese -a
b
tion) and a hot phase in pressure equilibrium. As described by purposes. In this sense, if we use the BH smoothing length to s
Tornatoreetal.(2007),thecontributionsfromSNe-II,SNe-Iaand lookfortheparticlehavingtheminimumpotential,BHslivingin trac
lowandintermediatemassstarsareconsideredinordertodescribe satellitehaloescouldoftenbespuriouslydisplacedtothecentreof t/4
3
the production of heavy elements. We assume a Chabrier initial amoremassiveDMhalo,andimmediatelywouldmergewiththe 8/1
massfunction(IMF;Chabrier2003)todistributestarsofdifferent BHsittingthere.Asaconsequenceofthisnumericalovermerging, /1
9
masses,whichreleasemetalsoverthetime-scaleasdeterminedby thereisaspuriousincreaseinthenumberofhigh-massBHsand, 5/1
Padovani&Matteucci(1993).Weimplementkineticfeedbackfol- correspondingly, a depletion in the number of BHs with low and 03
0
lowingtheprescriptionbySpringel&Hernquist(2003),inwhicha intermediatemasses.WeverifiedthatnumericalBHovermerging 3
3
mouutlfltiopwhsas(ewsetaarspsaurmticelevhwa=sa5p0r0okbmabsil−it1yftoorbteheupolouatfldoewdinveglaolcaictyti)c, issofstiegnninifigclaenntglythr.educed by repositioning within the gravitational 2 by g
whichisproportionaltoitsstarformationrate(weassumeafactor (c) ThermalEnergydistribution.Inourimplementation,aparam- ue
ofproportionalityof2). eter(cid:6)r providesthefractionoftheaccretedmassthatisconverted st o
(iii) AGN. Radiative simulations including the same physical inenergyasaresultoftheSMBHgrowth.Anadditionalparameter n 2
processesasintheCSFcase,butalsotheeffectofAGNfeedback. (cid:6)f givesthefractionofextractedenergythatisthermallycoupled 6 N
OurmodelforthegrowthofSMBHandrelatedAGNfeedbackis to the surrounding gas. In our implementation, both of these pa- o
v
based on the original scheme presented by Springel et al. (2005) rameters, (cid:6)r and (cid:6)f, are given a value of 0.2. Finally, when the em
(tosetehealosnoeDpireMseanttteeod,iSnpFrianbgjaenl&etHale.r(n2q0u1i0s)t.2H0e0r5e),abnedloqwuiwteesbimrieifllayr aactcrraentisoitniornatefrgoomesabe‘qlouwastahre’lpimhaisteM˙tBoHa/M‘˙raEdddio=’ m10o−d2e,wofetahsesuBmHe ber 2
0
describe the BH feedback model used for our simulations, while feedback(seealsoSijackietal.2007;Fabjanetal.2010).Inthis 18
werefertotherecentlysubmittedpaperbyRagone-Figueroaetal. case,thefeedbackefficiency(cid:6) isincreasedbyafactorof4.Inthe
f
(2013)foramoredetaileddescription. originalimplementationbySpringeletal.(2005),thethermalen-
ergyfromtheBHswassimplyaddedtothespecificinternalenergy
(a) SMBHseedingandgrowth.WerepresentSMBHswithcolli- ofgasparticles.Asaconsequence,wheneverthisexternalenergy
sionlessparticles,interactingonlyviagravitationalforces.During wasgiventoastar-forminggasparticle,itwasalmostcompletely
the simulation, we periodically perform the identification of DM lost.Thishappensbecauseintheeffectivemodelofstarformation
haloesusinganon-the-flyFriends-of-Friends(FoF)algorithm.Ifa andfeedback(Springel&Hernquist2003),theinternalenergyof
DMhalodoesnotalreadyhostanSMBHandithasamasslarger
thanagiventhresholdM ,weseeditwithanewBHwithaninitial
th
smallmassofMseed=5×106h−1M(cid:3).WesetMth=2.5×1011h−1 3As explained in the appendix of Ragone-Figueroa et al. (2013), the
M(cid:3).TheSMBHgrowthproceedsaccordingtotheaccretionrate α-modified Bondi accretion rate employed in our model is characterized
given by the Bondi formula (Bondi 1952), and it is Eddington byadimensionalfactorofα=100.
ThermalandchemodynamicalICMproperties 199
star-forming particles converges to the equilibrium energy of the
interstellarmediumonaveryshorttime-scale,andtheequilibrium
energyisindependentonthespecificinternalenergyofthegas(see
discussioninRagone-Figueroaetal.2013).Topreventthis,when
astar-forminggasparticleobtainsenergyfromanSMBH,thetem-
peratureatwhichitwouldheatthecoldgasphaseiscalculated.4
Ifthistemperatureislargerthantheaveragetemperaturethatthe
gasparticlehadbeforereceivingtheAGNenergy,theparticleisnot
consideredmultiphaseanymoreandispreventedfromstarforma-
tion.Theparticleis,however,subjecttonormalradiativecooling.
Wealsoaddatemperaturethresholdof5×104Kasafurthercon-
dition,besidesdensity,foragasparticletobecomemultiphaseand
D
formstars.Thisisneededbecauseinournewschemeadensegas o
w
particlecanbeveryhot:ifitbecamestar-formingagain,itwould nlo
immediatelyloseallofitsinternalspecificenergyinexcesstothe ad
e
equilibriumone. d
fro
m
2.3 Identificationofclusters http
s
Toidentifyoursampleofclusters,inafirststepweemployanFoF ://a
algorithm (with a linking length of 0.16 times the mean particle ca
d
separation)inthehigh-resolutionregions.TheDMparticlewithin e
m
eachFoFgroupwiththeminimumvalueofthegravitationalpoten- ic
tialrepresentsthecentreofthehalo.Afterthisfirststep,aspherical gFrioguuprse1id.enCtuifimeudlaintivtehediAstGribNutsioetnooffmsimasusleastiMonvisr.fSoorltihdebselatcokf,ctlruipstleer–sdaontd– .oup
oarvoeurdnednesaitcyhaclegnotrriethemncilsosuisnegdatomiedaenntdifeynsthiteysepqhuearletsoo(cid:8)frtaidmiuesstRh(cid:8)e dreasspheecdtibvleulye.anddashedredlinescorrespondtoredshiftsz=0,0.5and1, .com
criticalcosmicdensityattheconsideredredshift,ρ (z).Inthefol- /m
c n
lbt(cid:8)ohewevicriv(onzingr)isρ,ailcvd(arezalr)ude,ediaus.ssIonddfeesdtfiohunmecineeogdvsetbihtryudeaetstnhpiosehintesysrp,5ehwte(cid:8)hreaict=waelinl2clc5ola0olll0ssaoe,pss5teta0hk0meevaoinindrdteioal.1la8Fdc0eocnrowsutihitnlyelt vmbcuoaenlltaudatml.eldieTcidhutVesyi-inde=gnepetmrehgniey/dρ-pediln.eatpsFmeeumnratdiheseesnmritvmiisetosymrioeic,nsos(cid:3)mimv(piTotuy,dtZeefl)dobirswyetihtaRhecaihntyemmpaaopgrnetiivdrcaelt&neureieSsn-mecaraigntlydh- ras/article-a
acnodsm≈o1lo5g1icaatlzm=od1e(lBarsysuanm&edNinoormurasnim19u9la8t)i.ons,(cid:8)vir≈93atz=0 (e1n9e7rg7y).iTnhteervspalesc,trsaoaarsectoomhapvueteadnbyenbeirngnyinrgestohleuetimoniss(cid:8)ivEity=w0it.h0i1n. bstrac
Afterthisprocess,weterminatewithasampleofabout160clus- Luminositieswithinagivenenergybandarethencomputedbyin- t/43
tersandgroupswithMvir >3×1013h−1M(cid:3)atz=0.Thisnumber tegrating this energy-dependent emissivity within the appropriate 8/1
islargerathigherredshift:∼240systemsatz=0.5and∼200at energy interval. We point out that the assumed cooling function /19
z=1.InFig.1,weshowthecumulativenumberofclusterswithin adopted for the computation of X-ray luminosity depends on a 5/1
the AGN set of simulations as a function of their mass Mvir at globalmetallicity,ratherthanaccountingforthecontributionsfrom 03
z=0,0.5and1. allthechemicalspeciesfollowedinoursimulations.Inthefollow- 033
2
ing,wewillpresentresultsontheX-rayluminosityascomputed b
2.4 Computingtheobservablequantities withinthe[0.1−2.4]keVenergyband. y g
u
(ii) Temperature. Different proxies to the X-ray observational e
s
Inordertoanalysetheresultsofoursimulations,wewillstudysev- definition of temperature have been proposed in the literature. t o
eral thermodynamical and chemodynamical properties which can Ingeneral,theICMtemperaturecanbeestimatedas n 2
bedirectlycomparedwithobservationaldata,andwhichhavebeen (cid:3) 6 N
widelystudiedbydifferentsimulations.Here,webrieflydescribe wiTi ov
howthesequantitieshavebeencomputedfromoursimulations. T = i(cid:3) , (2) em
w b
i e
(i) X-rayluminosity.Thisquantityiscomputedbysummingthe i r 2
contributions to the emissivity, (cid:6)i, carried by all the gas particles whereT isthetemperatureofthei-gaselement,whichcontributes 01
withintheregionR(cid:8)whereLXiscomputed: withtheiweightw.Themass-weighteddefinitionoftemperature, 8
(cid:2) (cid:2) i
LX= (cid:6)i = ne,inH,i(cid:3)(Ti,Zi)dVi, (1) Tmw,isrecoveredforwi=mi,whichalsocoincideswiththeelec-
trontemperatureforafullyionizedplasma.Theemission-weighted
i i
temperaturewouldbeinsteadrecoveredforw =(cid:6).Incontrast,the
where n and n are the number densities of electrons and of i i
e,i H,i spectroscopic-like estimate of temperature, T , is recovered from
hydrogenatoms,respectively,associatedwiththeithgaselement equation(2)byusingtheweightw =ρmTαsl−3/2 withα=0.75
of given density ρi, temperature Ti, mass mi, metallicity Zi and (Mazzottaetal.2004).IntheBremssitrahluingiregime(T(cid:2)2–3keV),
thistemperatureestimatorprovidesaclosematchtotheactualspec-
4TheAGNenergyisgiventothehotandcoldphaseinproportiontotheir troscopictemperature,derivedbyfittingX-rayspectraofsimulated
mass. clusterswithasingle-temperatureplasmamodel.Whenmeasuring
5Thecorrespondingradiiapproximatelyrelatetothevirialradiusas(R2500, the spectroscopic-like temperature Tsl of our systems, we follow
R500,R180)≈(0.2,0.5,0.7)Rvir(e.g.Ettorietal.2006). theproceduredescribedbyVikhlinin(2006),whichgeneralizesthe
200 S.Planellesetal.
analyticformulaoriginallyintroducedbyMazzottaetal.(2004)to 3 GENERAL X-RAY PROPERTIES
includerelativelycoldclusterswithtemperaturebelow3keV.
Before presenting the general X-ray properties of our sample of
(iii) Entropy.Thisisanotherusefulquantitytocharacterizethe
galaxyclusters,wehighlightresultsfrompreviousworksthatanal-
thermodynamicalstatusoftheICM(Voit2005).Weusethestandard
ysedifferentaspectsofthesamesuiteofsimulations.Together,these
definition of entropy usually adopted in X-ray studies of galaxy
resultsestablishareasonablelevelofconsistencywithobservations
clusters:
withregardstothebaryoniccontentoftheclusters,emphasizethe
K(cid:8) = kBT(cid:8)ne−,(cid:8)2/3, (3) ipmorptoanrttacnatlrioblreatoiofnrasdfioartiovbesaenrvdafteioendablatcekstpsr.ocessesandprovideim-
wherene,(cid:8)istheelectronnumberdensitycomputedatR(cid:8),andkB Generallyspeaking,asshowninPlanellesetal.(2013),including
istheBoltzmannconstant. theeffectofAGNfeedbackhelpstoalleviatetensionwithobserva-
(iv) Total thermal content. A useful proxy to the total thermal tionsforthestellar,thehotgasandthetotalbaryonmassfractions.
gcoasntmenatssofanthdeTICoMneiessttihmeaqtouranotfittyheYXgl=obMalgITCM,wtiethmMpegrabtuerineg(et.hge. Hthoewsteevlelar,rbmoathssoffraocutriornadwiaitthivcelusismteurlmatiaosnstsheatstipsrewdeiacktearttrheanndofbo-r Down
Kravtsov,Vikhlinin&Nagai2006).Inourcase,wewillusetwo served. On the other hand, this tension depends on the particular loa
slightly different definitions of YX, the mass-weighted, YX,mw= setofobservationaldataconsidered.Formassiveclusters,theratio ded
aMamplrpsaogorsTcoseamxshwrysoa,ebsoasunfaisdntthlctomehlwueatdosssetspcadpealicrttntotherxetorhyrsame,cnwosadiphlmioiccsuos-ellnaailtsktmecienoa,otnlYsisontXf(g,iKsntlrhder=eaelavpItMtCeisonoMgndvTe,asenlgY,ttaXeaioslntt.nusi2mtrt0nthao0sett6eaop;slu.hSctBylttuaseonsiictnebeakgerl dplbYuerebtoct,iwcorweeneash.essenAeensstt,hcisbenomycmclalauuplndlsueatetreemdrdroaabadnuatidnriyRt,coti5hhn.0eaa0.cr,taoRdicnse2tt5pene0rene0in,aztdreatlhsdnyeodbintnytyhdtphaeeiepccnpeoaenlhsgmdylviesagiinclicutbsbeloaienforyrcftelhoudYendsbhfeprsidhafliytcignstehiivotctholnaye-l, from https://ac
etal.2010;Fabjanetal.2011).Inordertominimizethecontribution simulations,whileitsscatterincreasesbyafactorof2.Theseresults ad
e
tothescatterfromtheclustercentralregions,Kravtsovetal.(2006) haveinterestingimplicationsforthecosmologicalapplicationsof m
showed that the temperature should be estimated by excising the thebaryonfractioninclusters. ic.o
regions within 0.15R . We will also adopt this procedure in the Someofthetensionswithobservationsmaybeduetodifficulties up
following. 500 in accounting for the diffuse stellar content, distinct from clus- .com
(v) Pressure. By assuming an ideal gas equation of state, we termembergalaxies.Cuietal.(2013)havecarriedoutadetailed /m
computethevolume-weightedestimateofthegaspressureas analysis of the performance of two different methods to identify nra
the diffuse stellar light. One of the methods separates the BCG s
(cid:3) /a
pidVi fromthe‘diffusestellarcomponent’(DSC)viaadynamicalanaly- rtic
P = i(cid:3)id Vi , (4) smbirsoi.gcThkthnimeesaosgthleiesmraiirtse(SgineBsnpLei)rraeitsdeadbsyfsruotmhmeesdsitmtaonuddlaaistriedonnotasb,nsagenlredvatahtiseotanBnaCdlGaterdcfrhsonumirqfauthceee: le-abstra
wherepi =(kB/μmp)ρiTianddViarethecontributionstopressure itnhteraICclLusatenrdlDigShCt(fIrCaLct)i.oSnsigcnoifimcpauntteddiwffeitrhenthceesseatrweofomuentdhobdestw.Teehne ct/438
andvolume,respectively,ofeachconsideredgasparticle(μandmp useofabrighterSBLcanreconciletheICLandDSCfractionsbut /1/1
beingthemeanatomicweightandtheprotonmass,respectively). theexactvalue,ascalibratedbythesimulations,isquitesensitive 9
5
(vi) MetallicityoftheICM.Fromanobservationalpointofview, tofeedback. /1
0
this quantity is computed through a spectral fitting procedure, by Moreover,Ragone-Figueroaetal.(2013)investigatedsomeprob- 30
3
measuringtheequivalentwidthofemissionlinesassociatedwitha lemsthatarecommonthroughouttheliteratureofnumericalsim- 3
2
transitionbetweentwoheavilyionizedstatesofagivenelement.The ulations of galaxy clusters that also include the effect of AGN b
y
simplestproxytothisspectroscopicmeasureoftheICMmetallicity feedback. For example, the inclusion of AGN feedback helps to g
u
is,therefore,theemission-weighteddefinition, reduce the stellar mass content of BCG galaxies, yet their stellar es
(cid:3) massesremainthreetimeshigherthanobserved.Correspondingly, t o
Zew = i(cid:3)Ziimmiiρρii(cid:3)(cid:3)((TTii,)Zi), (5) tthheersetriuscsttuirllalsopmroepetertniesisoonfbBeCtwGese,nnapmreedliyc,tliaorngseranhdalfo-blisgehrvtaratidoinisanodf n 26 N
o
indications of a flattening of the stellar density profiles on scales v
whereZi,mi,ρiandTiarethemetallicity,mass,densityandtemper- (cid:2)10kpc,muchlargerthanobserved.Inaddition,theBCGsstellar em
b
agtausrepaorftitchleesi-glyaisneglewmitehnitn,wthiethctlhuestseurmexbteraincgtiopnerrfeogrimoned.Rovaesiraaellttahle. velocity dispersions are too large, but the implementation of the er 2
AGNfeedbackhaslittleimpacthere. 0
(2008) showed that the emission-weighted estimator of equation 18
(5)providesvaluesofmetallicitythatarequiteclosetotheactual
spectroscopicones,atleastforironandsilicon,whileabundance 3.1 Self-similarscalingrelations
ofoxygencanbeseverelybiasedinhigh-temperature,T(cid:2)3keV,
The simplest model to describe the properties of the ICM is the
systems.
self-similarmodeloriginallyderivedbyKaiser(1986).Thismodel
Since both simulated and observed metallicity radial profiles are
assumesanEinstein-deSitterbackgroundcosmology,thattheshape
characterizedbysignificantnegativegradients,weexpectthe‘true’
of the power spectrum of fluctuations is strictly a power law and
mass-weightedmetallicity,
thatnocharacteristicscalesareintroducedinthecollapseprocess
(cid:3)
Zm thatleadstoclusterformation.Thefirsttwoassumptionsamount
Z = (cid:3)i i i , (6)
mw m toassumethatnocharacteristicscaleispresentintheunderlying
i i
cosmological model. The third assumption is naturally satisfied
tobelowerthanthe‘observed’emission-weightedestimate. in the case that gravity is the only process driving halo collapse
ThermalandchemodynamicalICMproperties 201
and gas heating. The self-similar model further assumes clusters aprobeofthestarformationandfeedbackprocessesoperatingin
to be spherically symmetric and in hydrostatic equilibrium (HE). clustergalaxies.
Afurtherkeyassumptionofthismodelisthatthelogarithmicslopes
of gas density and temperature profiles, which enter in the HE
equationtoprovidethemasswithinagivenradius,areindependent 3.2 Scalingrelationsatz=0
of the cluster mass (see Kravtsov & Borgani 2012, for a recent
In this section, we analyse the scaling relations for our sample
review).Insuchself-similarmodelseveralsimplerelationsbetween
of simulated clusters and groups, paying special attention to the
different X-ray properties of the gas in clusters can be predicted.
effectthatthedifferentphysicalmodelshaveonthem.Inparticular,
Here,weprovidesomeofthescalingrelationsthatwillberelevant weanalysetheL −T,K−T,Y −MandT−Mrelationsatz=0.
forouranalysis. OnlyclusterswithXM (cid:2)3×10X13h−1M(cid:3)withinourNR,CSFand
If,atredshiftz,M(cid:8) isthemasscontainedwithintheradiusR(cid:8), AGNsimulationsetsvairreincludedinouranalysis.Unlessotherwise
enclosingameanoverdensity(cid:8)timesthecriticalcosmicdensity,6 stated,wecomputethesescalingrelationsadopting(cid:8)=500and, D
thetotalenclosedmassscaleswithtemperatureas o
therefore,allquantitiesareevaluatedwithinR .Thereasonforthis w
500 n
M(cid:8) ∝ T(cid:8)3/2E−1(z), (7) choiceisthat,typically,R500correspondstothemostexternalradius loa
outtowhichdetailedX-rayobservations(e.g.Maughan2007;Pratt de
bwehtwereeenT(cid:8)maisssthaendgtaesmtpeemrapteurraetucraenmbeeatsuurnreeddianttoRs(cid:8)c.alTinhgisrerelalatitoionns ectomalb.in2a0t0io9n; SwuitnheStZaol.bs2e0r0v9a;tioVniskh(eli.ngi.nPleatnaclk.C20o0ll9a)b,opraotsiosinbleytailn. d from
amongotherobservablequantities. 2011),areprovided. h
butAiosnsuamndintghathtatthethtehegramsadlisBtrriebmutsisotnrathrlaucnegspthreocdeasrskdmomatitneartdesistthrie- parWiseonwsiwlliuthseXt-hreayTsdlaetsat.iHmoawtoervfeorr,itthiestwemelplekrnaotuwrnetihnaat,llctohmepcaormed- ttps://a
c
emissionfromtheICMplasma,theX-rayluminosityscalesas withthemass-weightedtemperature,theTslproduceslargerscatter ad
e
LX,(cid:8) ∝M(cid:8)ρcT(cid:8)1/2∝T(cid:8)2E(z). (8) iintythtoetshcealcionngtrreiblauttiioonnso(fe.tgh.eFcaobljdancoemtapl.o2n0e1n1t)o,fotwheinggatsoteitmsspeenrsaittuivre- mic.o
Within the self-similar model, the entropy computed at a fixed distribution.Inordertoanalysetheintrinsicscatterintheserela- up
overdensity(cid:8)(seeequation3),scaleswithtemperatureandredshift tionsandtheirbehaviourasmassproxies,wewillcomputethem .co
accordingto by using both estimates of the ICM temperature, that is, Tsl and m/m
T .Correspondingly,wewillshowtheY −M relationforboth n
K(cid:8)∝T(cid:8)E−4/3(z). (9) esmtwimates of YX (YX,sl and YX,mw). In additXion, in order to reduce ras/a
AsforYX,itsself-similarscalingagainstmasscomputedwithinR(cid:8) thescatterinthescalingrelationsinvolvingtemperature(e.g.Pratt rtic
ispredictedtobe etal.2009,andreferencestherein)andtobetterreproducethepro- le
YX,(cid:8)∝M(cid:8)5/3E2/3(z). (10) cre<du0r.e15oRf5o0b0,seinrvtahteiocnoamlpauntaaltyisoens,ofwteheextecmlupdeerathtuerec.entral regions, -abstra
A number of observations of representative samples of galaxy (MF,oYr e)aacnhdse(Mt ,ofT)c,luwsteerfitprtoopeorutriessa,m(Xpl,eFo)f=si(mTu,lLatXed),c(lTu,stKer)s, ct/43
clustersinthelocalUniversehaveestablishedthatscalingrelations X 8
atz=0apower-lawscalingrelationoftheform /1
predictedbytheself-similarmodeldonotmatchtheobservational (cid:6) (cid:7) /1
results. For instance, the relation between X-ray luminosity and X α 95
mass is steeper than the self-similar prediction (e.g. Chen et al. F =C0 X , (11) /10
2007). Consistently with the L –M relation, the observed L –T 0 30
X X 3
scalingisalsosteeperthanpredicted(e.g.Markevitch1998;Arnaud byminimizingtheunweightedχ2 inlogspace.Here,X0 =6keV 32
T&αEwvriathrdα19(cid:7)992;.5O−sm3ofnodr&cluPsotenrmsa(nT2(cid:2)0024;kPeVra)ttaentdal.p2o0ss0i9b)l,yLeXve∝n pifaXram=eTterasnαdXan0d=C50.f0o×re1ac0h14rhe−la1tiMon(cid:3)ariefXsu=mmMa.riTzhedebinesTt-afibtltein1g. by gu
steeper for groups (T (cid:3) 1keV). Furthermore, the measured gas FollowingasimilarapproachtothatpresentedinShortetal.(2010), es
e2n0t0r9o;pPyrainttceetnalt.ra2l0r1e0g)i,oensspeiscihalilgyhfeorrtphoaonrecxlupsetcetresdan(ed.gg.roSuupns,ewtiatlh. ttihoensocfatltoegr1i0nFthfreosmertehleatmioenasn,σrleolga10tiFo,ni:sestimatedasthermsdevia- t on 26
respecttotheK∝Tpredictedscaling.Thisextraentropyprevents (cid:8) (cid:6) (cid:7) (cid:9) N
1 (cid:2)N X 2 ov
tehmeigssaisvfitryomcobmepinagrecdomtoptrheessseedlf-tosimhiiglhardpernesditiicetsio,nre.ducingitsX-ray σl2og10F = N−2 i=1 log10Fi−αlog10 X0 −log10C0 , embe
Thesediscrepanciesbetweentheself-similarmodelandtheob- r 2
servationshavemotivatedtheideathat,besidesgravity,someim- (12) 01
8
portantphysicsrelatedwiththebaryoniccomponentismissingin whereNisthenumberofindividualdatapoints.Thescatterabout
themodel.Themainnon-gravitationalphysicalprocessesthought eachrelationisalsolistedinTable1.
toberesponsibleforboostingtheentropyoftheICMareheating Inordertocomparewithobservationaldata,weuseaselection
fromastrophysicalsources,suchasSNeandAGN,andtheremoval of representative observational samples, mainly from Pratt et al.
of low-entropy gas via radiative cooling (e.g. Voit 2005). Lower (2009,2010),Sunetal.(2009),Mahdavietal.(2013)andEckmiller,
masssystemsareaffectedmorethanmassiveobjects,thusbreak- Hudson&Reiprich(2011).To‘scale’theseobservationaldatato
ingtheself-similarityofthescalinglawsandproviding,therefore, z = 0 for comparison with our simulated clusters, the correction
factor E(z)n is included, thus removing the self-similar evolution
predictedbyequations(8)–(10).
6M(cid:8)=(cid:8)ρc(z)(4π/3)R(cid:8)3,where(cid:4)ρc(z)=3H02E(z)2(cid:5)/8πGisthecritical Beforepresentingtheresultsofouranalysis,webrieflydescribe
densityandE(z) ≡ H(z)/H0 = (1+z)3(cid:4)m+(cid:4)(cid:3) 1/2inaspatiallyflat themaincharacteristicsofeachoftheobservationaldatasetswe
(cid:3)CDMcosmologicalmodel. comparewith.Prattetal.(2009)andPrattetal.(2010)examinethe
202 S.Planellesetal.
Table1. Best-fittingparameters(with1σ errors)fortheX-rayscal- of scaling relations, they found that gas mass is the most robust
ingrelationsforoursampleofclustersintheNR,CSFandAGNsetsat estimatorofweaklensingmass,yielding15±6percentintrinsic
z=0.OnlyclusterswithMvir(cid:2)3×1013h−1M(cid:3)havebeenconsid- scatteratr5W00L,whereasthepseudo-pressureYX yieldsaconsistent
ered.AllquantitieshavebeencomputedwithinR500.Foreachsetof scatterof22±5percent.
clusterproperties,apower-lawscalingrelationgivenbyequation(11)
In order to test local scaling relations for the low-mass range,
isfittooursampleofsimulatedclusters.Accordingtothisfitting,C0, Eckmilleretal.(2011)compiledastatisticallycompletesampleof
αandσlog10F(seeequation12)representthenormalization,theslope 112galaxygroupsfromtheX-rayselectedHIFLUGCS,NORAS
andthescatterofthedifferentrelations,respectively.Thenormaliza-
tionC0 hasunitsof1044ergs−1,keVcm2,1014h−1M(cid:3) keV,and andREFLEXcatalogues(Reiprich&Bo¨hringer2002;Bo¨hringer
keVforLX−T,K−T,YX−MandT−M,respectively. etal.2000,2004,respectively).Groupswereselectedbyapplying
anupperlimittotheX-rayluminosity,whichwasdeterminedho-
Relation C0 α σlog10F mogeneouslyforallthreeparentcatalogues,plusalowerredshift
cuttoexcludeobjectsthatweretooclosetobeobservedouttosuffi-
D
NRsimulation cientlylargeradii.Inthiswork,onlyasub-sampleof26localgroups o
TYTsmXl,−ws−lM–MM 342...283494±±±000...000766 001...565153±±±000...000111 000...000739 s(mufefidciiaenntreedxsphoifstu0re.0t2im5)e,o(b(cid:2)s1er0vkesd),wwitahsthinevCeshtaignadtread.teTleemscpoepreatwuirteh, wnloade
LYXX,,m[0w.1−−2M.4]keV−Tsl 631..5038±±04..0563 21..2697±±00..0014 00..0156 m26etgarloliucpitsy,aannddussuerdfatcoedbertiegrhmtnineessthperomfialeinspwheyrseiccarleaqtueadntfiotiresthaensde d from
LKX−,[T0.s1l−2.4]keV−Tmw 252838.1.360±±19.295.21 11..1875±±00..0032 00..1058 scalingrelations. https
K−Tmw 1550.44±52.64 0.93±0.02 0.09 3.2.1 Massscalingrelations ://a
c
CSFsimulation a
Tsl−M 4.80±0.08 0.55±0.01 0.05 Fig. 2 shows the Tmw−M and Tsl−M relations (left- and right- dem
TYmX,ws−l–MM 52..4505±±00..0086 01..6606±±00..0011 00..0058 ihnanodurpaNnRel,sC, SreFspaencdtivAeGlyN) wruitnhsi.nRRe5s0u0ltfsoronthtehesaTmmpwl−eMof rcelulasttieorns ic.ou
YX,mw−M 2.87±0.06 1.71±0.01 0.07 arecomparedwiththeself-similarprediction,whileresultsonthe p.c
LX,[0.1−2.4]keV−Tsl 7.49±0.61 2.17±0.05 0.22 Tsl−M relation are compared with observational data from Pratt om
LX,[0.1−2.4]keV−Tmw 5.80±0.43 2.00±0.05 0.21 etal.(2009)andSunetal.(2009). /m
K−Tsl 2027.88±42.16 1.02±0.01 0.06 In agreement with previous analyses (e.g. Stanek et al. 2010; nra
KAG−NTmsiwmulation 1787.95±37.55 0.94±0.01 0.06 aFasbljoapneeitnacl.lo2s0e1a1g),retehmeeTnmtww−itMh trheelastieolnf-siinmitlhaer sNcRalincgas,eαha∼s s/artic
TTsml−w−MM 55..0223±±00..0077 00..5545±±00..0011 00..0044 0w.h6e5re±as0a.0t1t,healssocawleitohfahtiigghh-tmsacsasttesyrs(tseemesTtahbilser1e)l.atIinonadisdirtieolan-, le-abs
YX,sl–M 3.19±0.08 1.73±0.01 0.08 tivelyinsensitivetobaryonphysics,atthescaleofgroups,M (cid:3) tra
LLYXXX,,,m[[00w..11−−−22M..44]]kkeeVV−−TTsmlw 983...453862±±±000...760778 221...447634±±±000...000551 000...220327 1ti0o1n4ihs−p1rMes(cid:3)en,tainsigthneifircaadniattdiveevisaitmiounlafrtioomnst.hTehseeldf-esvimiaitliaorneixsp5me0c0otare- ct/438/1
K−Tsl 1686.51±33.27 0.94±0.01 0.05 significant for the AGN simulations due to the heating from the /19
K−Tmw 1619.83±31.76 0.93±0.01 0.06 BHenergyfeedback,whichisrelativelymoreefficientinlow-mass 5/1
groups. 0
3
Asforthecomparisonwithobservationaldata,weconsiderthe 03
3
mass–temperaturerelationusingthespectroscopic-likeestimatorof 2
b
X-raypropertiesof31nearbygalaxyclustersfromtheRepresenta- temperature.Asawordofcautioninperformingthiscomparison, y
g
tiveXMM–NewtonClusterStructureSurvey(REXCESS;Bo¨hringer we remind that we use here true cluster masses for simulations, u
e
etal.2007).Thissample,whichincludesclusterswithtemperatures while masses for the observational data shown in the right-hand st o
intherange2–9keV,hasbeenselectedinX-rayluminosityonly, panelofFig.2arebasedonX-raydataandtheapplicationofHE. n
2
withnobiastowardsanyparticularmorphologicaltype.According While itis beyond the scope ofthis paper to carryout a detailed 6
N
to their central densities, clusters in this sample have been clas- analysisofbiasesinX-raymassestimates,theevidencefromsimu- o
v
sified as relaxed, CC systems or as morphologically disturbed or lationanalysesindicatesthatX-raymassesmaybeunderestimated e
m
non-cool-core(NCC)systems.Thesedataareparticularlysuitable by ∼20 per cent (e.g. Nagai, Vikhlinin & Kravtsov 2007a; Rasia b
e
foracomparisonwithoursimulatedclustersamplesbecausespec- etal.2012,andreferencestherein). r 2
traltemperatures,luminosities,massesandentropiesaretabulated We note that in the T −M relation, for a given mass, clusters 01
sl 8
withinR . in the NR runs are much cooler than observed, by an amount
500
Sunetal.(2009)presentananalysisof43nearbygalaxygroups that is definitely larger than in the T −M relation. In addition,
mw
(kT =0.7–2.7keVorM =1013–1014h−1 M(cid:3),0.012<z< the scatter around the mean relation is larger than in the radia-
500 500
0.12), based on Chandra archival data. They trace gas properties tive runs. By definition (see Section 2.4), the spectroscopic-like
outtoatleastR forall43groups.For11groups,gasproperties temperaturetendstogivemoreweighttotherelativelycoldercom-
2500
arerobustlyderivedtoR and,foranadditional12groups,they ponentofthegastemperaturedistribution(seealsoMazzottaetal.
500
derivepropertiesatR fromextrapolation. 2004).Inordertoshowthedifferentdegreeofthermalcomplexity
500
InarecentworkwithintheCanadianClusterComparisonProject, oftheICMgeneratedbythedifferentmodels,weshowinFig.3the
Mahdavietal.(2013)presentastudyofmultiwavelengthX-rayand temperaturemapsofamassiveclusterfortheNR,CSFandAGN
weaklensingscalingrelationsforasampleof50clustersofgalaxies cases.Quiteapparently,intheNRsimulationsthereismoregasin
intheredshiftrange0.15<z<0.55.Afterconsideringanumber relativelysmallcoldclumpsthatbiasT lowandcontributetothe
sl
ThermalandchemodynamicalICMproperties 203
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Figure2. Mass-weighted(left-handpanel)andspectroscopic-like(right-handpanel)temperatureasafunctionoftotalmasswithinR500atz=0.Resultsfor ://aca
oursampleofclusterswithintheNR,CSFandAGNrunsarerepresentedbyblackcircles,bluetrianglesandredstars,respectively.Ontheleft-handpanel, d
e
ourresultsarecomparedwiththeself-similarscaling(blackcontinuousline).Ontheright-handpanel,observationalsamplesfromPrattetal.(2009)andSun m
ic
etal.(2009)areusedforcomparison. .o
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.c
o
m
/m
n
ra
s
/a
rtic
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-a
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t/4
3
8
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/1
9
5
/1
0
3
0
3
3
2
b
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Figure3. TemperaturemapscentredonamassiveclusterhavingM200(cid:7)1.3×1015h−1M(cid:3).Fromlefttoright,panelsshowmapsfortheNR,CSFand gu
AGNsimulations.Eachpanelencompassesaphysicalscaleof6.25h−1Mpcaside.Colderregionsareshownwithbrightercolours. es
t o
n
2
increaseinscatter.7Asmalleramountofcoldgasisinsteadpresent mass,withrespecttothenon-radiativecase,anddecreasesthescat- 6
N
intheradiativesimulations.FortheCSFsimulations,thisismostly terduetothepresenceofcoldclumps,thusbringingthesimulated o
v
due to gas removal by overcooling. As a result, only relatively mass–temperature relation in better agreement with observations. em
hot gas, having longer cooling time, is present in sub-structures. Quite interestingly, the effect of AGN feedback in haloes below be
In this case, a smaller amount of cold gas characterizes not only 1014h−1M(cid:3) is that of slightly increasing Tsl with respect to the r 20
thesub-clumps,butalsotheram-pressurestrippedgasthatforms CSFsimulations,thusproducingashallowerslopeofthisscaling 18
thecomet-likefeaturesassociatedwithmergingevents.Asforthe relation,inbetteragreementwithobservations.Despitethediffer-
AGNsimulation,inthiscaserelativelycoldgasisremovedfrom ent manner in which cooling/heating processes remove gas from
sub-clumpsbyatwofoldeffectofBHfeedback.First,thisfeedback sub-clumpsineachcase,theTsl−M relationsobtainedinbothof
heats gas before a sub-structure is merged into the main cluster ourradiativerunshavesimilarnormalizationsandslopes.Thefact
halo.Secondly,themorediffusegasdistributionmakessub-haloes thattheslopeweobtainforthisrelationisprettysimilarinallcases
morepronetoberam-pressurestrippedastheymovethroughthe (α ∼0.5)indicatesthattheTsl−M relationisweaklysensitiveto
hotpressurizedatmosphereofthecluster.Thesmoothertempera- baryonicphysics(e.g.Shortetal.2010).However,weseethatnone
turedistributionintheradiativesimulationsincreasesTsl atfixed ofoursimulationsreproducetheself-similarscalingfortheTsl−M
relation.
AsfortheY −Mrelation,weremindthatbothsimulations(e.g.
X
7We note that the coldest gas particles, those with temperature below Kravtsovetal.2006;Shortetal.2010;Staneketal.2010;Fabjan
0.3keV,arenottakenintoaccountinthecomputationofTsl. etal.2011)andobservations(e.g.Arnaud,Pointecouteau&Pratt
204 S.Planellesetal.
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Figure4. RelationbetweenYX andtotalmasswithinR500 atz=0.Intheleft-handpanel,ourresultsontheYX,mw−M relationarecomparedwiththe ://aca
self-similarscaling(blackcontinuousline).Intheright-handpanel,wecompareourresultsontheYX,sl–MrelationwiththeobservationalresultsfromPratt de
etal.(2009)andMahdavietal.(2013).Inbothpanels,resultsforoursampleofclusterswithintheNR,CSFandAGNrunsarerepresentedbyblackcircles, m
ic
bluetrianglesandredstars,respectively. .o
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p
.c
2007;Maughan2007;Vikhlininetal.2009)indicatethatYX isa TheincreaseofTsl whenpassingfromtheNRtotheCSFandthe om
low-scattermassproxy,eveninthepresenceofsignificantdynam- AGNsetsalsocausesacorrespondingprogressiveincreaseofY , /m
X n
icalactivity.Furthermore,X-rayobservationshaveshownthatthe thusimprovingtheagreementwithobservationalresults. ra
mtioenasαur=ed5s/l3op(esefeoreqthuiastiroenla1ti0o)n.agreeswiththeself-similarpredic- ourTrhaedisaitmivielarruitnysowfitthheeaYchX−otMherraenladtiwonitshothbetasinelefd-sifmroimlarbsoctahlinogf s/artic
Fig.4showsthelocalYX−Mrelationobtainedforoursampleof suggeststhatYX isonlyslightlyaffectedbythenon-gravitational le-a
clusterswithintheNR,CSFandAGNsimulations.Intheleft-hand physicsincludedinthesesimulations.InthecaseoftheAGNrun, bs
panel,weshowourresultsontheYX,mw−M relationandcompare thisarisesbecauseAGNfeedbackremovesgasfromcentralcluster trac
itwiththeself-similarscaling.Basedonthisplot,weconfirmthat regions,decreasingthegascontentwithinR500,butthisispartially t/43
thetotalthermalcontentoftheICMistightlyconnectedtocluster compensatedbyanincreaseinthegastemperatureproducedbythe 8
/1
massinawaythatisweaklysensitivetotheinclusionofdifferent continuousinjectionofenergyfromtheBHfeedback. /1
9
physicalprocessesaffectingtheevolutionoftheintraclusterplasma 5
/1
(e.g.Kravtsovetal.2006;Shortetal.2010;Fabjanetal.2011;Kay 0
etal.2012,andreferencestherein).ResidualvariationsfortheCSF 3.2.2 LX−T relation 303
3
simulationswithrespecttotheNRonesareduetotheremovalofgas Fig.5showstheL –T relationforthesampleofclustersinour 2
X sl b
fromthehotphaseasaconsequenceofovercooling,whichcauses NR, CSF and AGN sets. Here X-ray luminosities are computed y
adecreaseofYX atfixedmass.Themass-dependentefficiencyof inthe[0.1–2.4]keVenergyband.Wecomparewithobservational gue
coolinginthiscasecausesasmalldeviationfromtheself-similar data on the scale of galaxy clusters and groups from Pratt et al. st o
slopeoftheNRsimulations.Conversely,includingAGNfeedback (2009)andEckmilleretal.(2011),respectively.Inthiscase,there n
2
hastheeffectofpartiallypreventinggasremovalfromcooling,thus is no special reason to compare our results to predictions of the 6
sligYhXt,lmywiniscraeakseinygpthhyesnicoarlmqaulaiznattiitoynsoinfcteheitYiXs,mthwe−XM-rareylaatnioanlo.gue saeslfa-sciomnisleaqrumenocdeelo.fIncofamcpt,uvtiinoglaLtioXninofasseplfe-csiifimcileanrietrygyisbeaxnpdecatnedd Novem
oftheintegratedComptonparametery,ameasureofthegaspres- usingTslinsteadofTmw. be
sureintegratedalongthelineofsight(e.g.Kravtsovetal.2006). WenotethattheNRrunsfailtoreproducetheobservedLX−Tsl r 20
The total SZ signal, integrated over the cluster extent, is propor- relationandproduceclustersthataremoreluminousthantheob- 1
8
tionaltotheintegratedComptonparameterYSZ,whichrelatestoYX served ones. On the contrary, both of our radiative runs produce
as YSZDA∝YX, where DA is the angular distance to the system. asignificantreductionofX-rayluminosityatallscalesobtaining,
Therefore,understandingthescalingandevolutionofYX,mwisim- therefore, results that are closer to the observational data. In the
portantnotonlyasaprobeoftheICMphysics,butalsotoexploit CSF simulations the reduction of X-ray luminosity is the conse-
thecombinationofX-rayandSZdata(e.g.Arnaudetal.2010). quenceofovercooling,whichcausesanexceedinglyhighremoval
In the right-hand panel of Fig. 4, our results for the YX,sl–M of hot gas from the X-ray emitting phase and forces a too large
relation are compared with the observational relation from Pratt fractionofgastobeconvertedintostars(e.g.Kravtsov,Nagai&
etal.(2009)andfromMahdavietal.(2013).Weremindthereader Vikhlinin2005;Fabjanetal.2010;Puchweinetal.2010;Planelles
herethatPrattetal.(2009)estimatedmassesfromtheapplication et al. 2013; Sembolini et al. 2013, and references therein). Quite
ofHEtoX-raydata,whileMahdavietal.(2013)measuredclus- interestingly,boththeCSFandAGNmodelsyieldalmostidentical
termassesfromweaklensingdata.TheYX,sl–Mrelationobtained LX,[0.1−2.4]keV−Tsl relations,despitethefactthatthelatterreduces
fromtheNRsimulationsisshallowerthantheobservedrelations. theamountofstarstolevelsconsistentwithobservationalresults