Thermal and non-thermal traces of AGN feedback: results from cosmological AMR simulations

23 Pages·2012·4.69 MB·English

MNRAS428,2366–2388(2013) doi:10.1093/mnras/sts213
Thermal and non-thermal traces of AGN feedback: results
from cosmological AMR simulations
F. Vazza,1,2,3‹ M. Bru¨ggen1,2 and C. Gheller4
1JacobsUniversityBremen,CampusRing1,D-28759Bremen,Germany
2HamburgerSternwarte,Gojenbergsweg112,D-21029Hamburg,Germany
3INAF/IstitutodiRadioastronomia,viaGobetti101,I-40129Bologna,Italy
4SwissNationalSupercomputingCentre,ViaCantonale,CH-6928Lugano,Switzerland
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Accepted2012October12.Received2012October12;inoriginalform2012July8 n
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ABSTRACT fro
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Weinvestigatetheobservableeffectsoffeedbackfromactivegalacticnuclei(AGN)onnon- h
thermal components of the intracluster medium (ICM). We have modelled feedback from ttp
s
AGNincosmologicalsimulationswiththeadaptivemeshrefinementcodeENZO,investigating ://a
c
threetypesoffeedbackthataresometimescalledquasar,jetandradiomode.Usingasmall ad
e
set of galaxy clusters simulated at high resolution, we model the injection and evolution of m
ic
cosmicrays,aswellastheireffectsonthethermalplasma.Bycomparingboththeprofilesof .o
u
thermalgastoobservedprofilesfromtheACCEPTsampleandthesecondaryγ-rayemission p.c
o
to the available upper limits from Fermi, we discuss how the combined analysis of these m
/m
twoobservablescanconstraintheenergeticsandmechanismsoffeedbackmodelsinclusters.
n
ThosemodesofAGNfeedbackthatprovideagoodmatchtoX-rayobservationsyieldaγ-ray ras
/a
luminosity resulting from secondary cosmic rays that is about 10 times below the available rtic
upperlimitsfromFermi.Moreover,weinvestigatetheinjectionofturbulentmotionsintothe le
-a
ICMfromAGN,andthedetectabilityofthesemotionsviatheanalysisoflinebroadeningof b
s
theFeXXIIIline.Inthenearfuture,deeperobservations/upperlimitsofnon-thermalemissions trac
from galaxy clusters will yield stringent constraints on the energetics and modes of AGN t/4
2
feedback,evenatearlycosmicepochs. 8/3
/2
3
Key words: methods: numerical–galaxies: clusters: general–intergalactic medium–large- 6
6
scalestructureofUniverse. /1
0
7
0
9
8
5
b
y
centralsupermassiveblackhole(BH),tothe∼10–100kpccooling g
1 INTRODUCTION radius.Verysimilarproblemsareencounteredinellipticalgalaxies ues
Radiativecoolingofgasingalaxyclustersissoefficientthatmost (e.g.Sarazin&White1987;Ciotti&Ostriker1997;Brighenti& t o
n
ofthehotgasphaseintheircoreoughttoberemovedonatime- Mathews2000;Ciotti&Ostriker2012).Forclusters,animportant 0
4
scalesmallerthanthelifetimeofthesystem,producinganinward issue is whether most of the energy input from AGN (or galac- M
a
motion of the cooling gas, a ‘cooling flow’ (e.g. Fabian, Nulsen ticwinds)totheICMhas occurred muchbeforetheassemblyof y
2
& Canizares 1984). However, dramatic cooling flows are not ob- the clusters via ‘pre-heating’ (e.g. Bialek, Evrard & Mohr 2001; 0
1
served in real clusters, and additional non-gravitational heating Brighenti & Mathews 2001; Tozzi & Norman 2001; McCarthy 9
mechanismsarelikelytokeepgasonahigheradiabat(e.g.Kaiser etal.2004),oratalowredshiftwithinalreadyformedclusters(e.g.
1991;Ponman,Cannon&Navarro1999;Lloyd-Davies,Ponman& Binney & Tabor 1995; Churazov et al. 2001; Bru¨ggen & Kaiser
Cannon2000).Itislargelyagreedthatactivegalacticnuclei(AGN) 2002). The first mechanism requires a lower energy budget, with
are a viable source of energy available for the self-regulation of totalenergies≤1062erg(McCarthyetal.2008),whilethesecond
galaxyclusters.Observationsshowthattheenergyassociatedwith possibilityrequiresenergiesinexcessof∼1063–1064erg(Mathews
AGN in clusters is in most cases sufficient to balance radiative &Guo2011b).However,thereisampleevidenceforstrongAGN
lossesintheintraclustermedium(ICM;e.g.McNamara&Nulsen outflows in cool-core clusters (e.g. McNamara & Nulsen 2007,
2007,andreferencestherein).However,itislessclearhowtheen- 2012).
ergyisreleasedfromthecompact((cid:2)kpc)regionsurroundingthe Theoretical work suggests that the real evolution of heating in
clusters might be a combination of both (Brighenti & Mathews
2006;McCarthyetal.2008;Vazza2011;Duboisetal.2012;Short,
(cid:3) Thomas&Young2012).
E-mail:[email protected]
(cid:5)C 2012TheAuthors
PublishedbyOxfordUniversityPressonbehalfoftheRoyalAstronomicalSociety
Thermalandnon-thermaltracesofAGNfeedback 2367
Quasar-induced outflows at high redshift, possibly following sionfromgalaxyclusterscanofferacomplementarywayoftesting
mergers of gas-rich galaxies, have been observed (e.g. Nesvadba andfalsifyingfeedbackmodels.Onceaccelerated,CRhadronscan
et al. 2006; Bhattacharya, Di Matteo & Kosowsky 2008; Dunn accumulateingalaxyclusters(Berezinsky,Blasi&Ptuskin1997)
etal.2010).Atlowerredshift,themechanicalworkdonebyX-ray andproduceanon-thermalcomponentthatcouldbedetectedbyγ-
cavities on the surrounding ICM may represent another viable rayobservations(e.g.Ackermannetal.2010).Secondaryparticles
mechanismforheatingandmixingtheICM(e.g.Davidetal.2001; arecontinuouslyinjectedintotheICMviaproton–protoncollisions,
McNamara & Nulsen 2007, 2012). Additional mechanisms can possiblyleadingtodetectablesynchrotronradiation(e.g.Blasi&
modify the energy requirements of AGN feedback, by providing Colafrancesco1999;Dolag&Enßlin2000).Thecombinedanalysis
complementary heating/mixing on various scales. The heating ofradioobservationsandγ-upperlimits,however,presentlysug-
from Alfve´n waves in cosmic rays (CRs) enriched bubbles, and geststhatmostoftheobservedlarge-scaleradioemissioninclusters
heatingfromCoulomblossesofCRsandthesurroundingthermal cannotbeduetosecondaryelectrons,basedontheoreticalestimates
ICM, is an additional interesting topic of research (Loewenstein, oftherequiredtotalenergyinCRs(Brunettietal.2007;Brunetti
Zweibel&Begelman1991;Colafrancesco,Dar&DeRu´jula2004; 2009;Donnertetal.2010b),andtotherequiredvaluesofthemag- D
o
Guo&Oh2008;Sijackietal.2008;Fujita&Ohira2011;Mathews neticfieldintheICM,inconflictwithobservations(Brunettietal. w
n
&Guo2011a). 2009;Bonafedeetal.2010;Donnertetal.2010a;Bonafedeetal. lo
a
Thermalconductioncansomewhatreducetheenergybudgetthat 2011;Jeltema&Profumo2011). d
e
cBeenrttrsaclhAinGgeNr &havMeetiokspirnov1i9d8e6;inBorerdgemratno&steDmavcoidol1in9g88fl;oNwasra(ey.agn. cluTstheerrecfeonrter,esthemdayeteinctfioornmoruslaacbkoouft nthoen-ethneerrmgyalbeumdgisestioonffnroonm- d fro
m
& Medvedev 2001). Magnetorotational instabilities and heat-flux thermalparticles,andofthehistoryandmodalityofpreviousheat- h
driven instabilities in the weak and anisotropic cluster magnetic ing episodes in the ICM. In addition, CR particles may have an ttp
s
fieldhavebeenproposedtoreducethecoolingofgas(e.g.Quataert importantdynamicaleffectontheICM(e.g.Brunetti&Lazarian ://a
c
2008;McCourtetal.2011).Finally,alsomajormergershavebeen 2011b;Ruszkowski&Oh2011),andtheycanalsoaffecttheevo- a
d
suggestedasaviablemechanismtoreducethecoolingcatastrophe, lution of X-ray cavities powered by AGN jets (e.g. Mathews & e
m
eveniftherealefficiencyofthismechanismiscontroversial(Poole Brighenti2007;Guo&Oh2008;Sijackietal.2008;Mathews& ic
.o
etal.2006;Burnsetal.2008). Guo2011a). u
p
Cosmologicalsimulationswithradiativecooling,starformation Inthisworkwestudytheobservablenon-thermalfeaturesrelated .c
o
andgalacticwindsareunabletoreproducetheobservedprofilesof to AGN feedback models in a cosmological framework. A few m
/m
gastemperature,metallicityandentropyintheICM(e.g.Kravtsov single-objectsimulationshavebeenusedtoinvestigatetheroleof n
&Borgani2012,forarecentreview).Themostpowerfulfeedback CRfeedbackinstoppingcoolingflows(Guo&Oh2008;Fujita& ra
s
frreocmentApGaNst.hSaesvbeeraelngsrtouudpiesdswucicthescsofusmllyoliomgpicleamlseinmteudlataiotnresaitnmtehnet OofhiCraR2s0a1t1,sh2o0c1k2s).tHriogwgeerveedr,bthyeAacGceNle,raastiowne(lalnadsrea-tacmceerlgereartiaonnd) /article
ofthermalAGNfeedbackincosmologicalGADGETsimulations(e.g. accretionshocks,hasbeenneglectedinpreviousworks. -ab
DallaVecchia etal.2004;Sijacki&Springel2006;Sijackietal. To our knowledge, the present study is the first in which stra
2007; Fabjan et al. 2010; McCarthy et al. 2010). In the afore- such detailed CR physics (e.g. particle acceleration, reduced c
mentionedpapers,thegrowthofBHsatthecentresofgalaxiesis thermalization at the sub-shock, pressure feedback of CRs and t/42
8
followedusingsinkparticles,andtheenergyreleasefromeachBH effective adiabatic index of the baryon gas) as well as variety of /3
followsfromtheBondi–Hoyleaccretionrate(‘quasar’mode).The AGN feedback models (quasar, jet and bubble modes) have been /23
6
energyemittedbytheAGNisreleasedbyheatingupsmoothedpar- appliedtocosmologicalsimulations. 6
/1
ticle hydrodynamics (SPH)particles surroundingthe surrounding 0
7
ICM. Similar methods have been implemented in adaptive mesh 0
9
2 NUMERICAL METHODS 8
refinement(AMR)gridsimulationsbyCattaneo&Teyssier(2007) 5
andTeyssieretal.(2011)intheRAMSEScode.Thecreationof‘bub- WehaveproducedcosmologicalclustersimulationswiththeAMR by
g
bles’inflatedbyAGNduringtheir‘radiomode’wassimulatedby codeENZO.Onthebasisofthepublic1.5versionofENZOwehave ue
DallaVecchiaetal.(2004)andSijacki&Springel(2006)inGADGET. implementedourmethodstomodeltheevolutionandfeedbackof st o
Inthiscase,theenergyreleasedbytheBHisdepositedwithinpairs CRparticlesinjectedatshockwaves(Vazzaetal.2012a),aswell n
0
ofbubblesintheformofthermalenergyorCRenergy,andexerts asour(simplified)implementationsofenergyreleasefromAGN. 4
mechanicalworkPdVonthesurroundingICMwhilebuoyantlyris- ENZO is a grid and AMR code using the piecewise parabolic Ma
ingintheclusteratmosphere.Othermodelsofmechanicalfeedback method(PPM)tosolvetheequationsofhydrodynamics,originally y 2
0
fromAGNhavealsobeenimplemented,byassigninga‘wind’drift writtenbyBryanetal.(1995)anddevelopedbytheLaboratoryfor 1
9
velocitytogasparticlessurroundingtheBH,withvelocitiesinthe ComputationalAstrophysicsattheUniversityofCaliforniainSan
rangeof∼103–104kms−1(DallaVecchia&Schaye2008;Fabjan Diego(Normanetal.2007;Collinsetal.2010).1
etal.2010).Duboisetal.(2010,2011)implementedaschemeto ThedetaileddescriptionofourmodulesforCRphysicsandAGN
followbipolarkineticoutflows(‘jet’mode)fromsimulatedAGN feedbackarepresentedinSection2.1.Inallrunsinthispaper,we
inRAMSES,monitoringthegrowthofBHsusingthesameset-upof adoptedradiativecoolingforafullyionizedH–Heplasmawitha
Teyssieretal.(2011).Intheframeworkofgalaxyformationstud- constantmetallicityofZ=0.3Z(cid:6),andacoolingfunctionwitha
ies,run-timemodelsofradiativeandkineticfeedbackfromAGN cut-offatT=104K(Sarazin&White1987),asinthepublicversion
ingalaxysimulationshavebeendevelopedbyKimetal.(2011)in ofENZO,whilethere-ionizationbackgroundduetotheultraviolet
ENZOsimulations,andbyOppenheimer&Dave´ (2006)andGabor (UV)radiationfromearlystarsandAGNismodelledbykeepinga
etal.(2011)inGADGETsimulations. gastemperaturefloor(∼2×104K)intheredshiftrange4≤z≤7
Todate,however,littleattentionhasbeenpaidtotheamountof (asinVazzaetal.2010a).
non-thermalenergydepositedintheICMbythevariousfeedback
mechanisms.Thisisanimportantaspect,sincenon-thermalemis- 1http://lca.ucsd.edu
2368 F.Vazza,M.Bru¨ggenandC.Gheller
Wedidnotincludestarformationandfeedbackthroughwinds
orsupernovaeintheseruns,therebyreducingthecomplexityand
memory usage of the code. Hydrodynamical simulations suggest
thatwhilesupernovaeareimportanttoreproducetheobservedmetal
distribution of the ICM, they do not have a significant impact on
the thermal history of the ICM on large scales (e.g. Short et al.
2012).
For the simulations presented here, we assumed a ‘concor-
dance’ (cid:4) cold dark matter ((cid:4)CDM) cosmology with (cid:5) = 1.0,
0
(cid:5)B=0.0441, (cid:5)DM=0.2139, (cid:5)(cid:4) = 0.742, Hubble parameter
h = 0.72 and a normalization for the primordial density power
spectrumσ =0.8.
8
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2.1 Cosmicrayphysics a
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e
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TfeheedbbaacskicomfeCtRhosdisntooumrEoNdZeOltrhuensinajreecteioxnp,laaidnvedecitniodneatanidlipnreVsaszuzrae Figure1. AccelerationefficiencyofCRsasafunctionofMachnumberfor from
ecMte,laelwr.a(ht2iic0oh1n2iesaf)fig.ciWvieeennacsbys,yuηmd(iMeff)tuh,satihvtaeCtRsohnsolaycrkedieanpcjceeencldteesrdaotanitotsnhheo(ecM.kgsa.cwBhietnlhlua1mn9b7aec8r-;, td=oif0rf.ee0dr6e,,nt=htep0rd.e1i-f2ef,ex0ries.1nti8tn,lgi=nre0ast.i2so4hsoaownfdtPh=cer0/a.Pc3cg.eilnertahteiopnree-ffishcoiecnkcryegfoiornP.cFr/rPomg=bl0a.c0k, https://a
c
Blandford & Ostriker 1978; Drury & Voelk 1981; Kang & Jones a
d
1990;Ellison,Baring&Jones1995;Malkov&O’CDrury2001; 2.1.1 Shockre-acceleration em
Kang & Jones 2007; Caprioli 2012). New CR energy is injected ic
Wemodelatrun-timetheshockre-accelerationofCRs,byshocks .o
inthesystembymultiplyingtheenergyfluxthrougheachshocked u
cellbythetimestepandthecellsurface(ateachAMRlevel): rinujnencitniognosv.eTrhaismceadniubmeaplarretaicduylaernlryicrheeledvoafntCiRnethneercgaysebyopfrsehvoiockuss p.com
ρ v3 (cid:9)t causedbyAGNfeedback,whereatlateredshifttheICMisalready /m
Ecr=η(M)· u2s · (cid:9)xll, (1) teonrtihceherdeswulittshiCnRKsa(nPgcr&/PJgo∼nes10(2−020to7)1t0h−e1partesze≤nc0e.5o)f.CARccsoirnditnhge nras/a
whereρ isthepre-shockdensity,v istheshockvelocity,(cid:9)t and pre-shock region mimics an increased injection efficiency of CR rtic
(cid:9)resxpleacretivtuheelyt.imToeesntespuraendentehregyspcaotinaslesrrevsaotliuotniotnheatththeermAaMleRnelergvlyel-iln, eunsienrggyadinifftehreenptoasnta-slyhtoicckal.fTuhnicstiodnynfoamrηic(Me)f,fedcetpecnandebnetotnretahteedratbiyo le-abs
the post-shock region is reduced proportionally at run-time. The Pcr/Pginthepre-shock.Inourcase,wecalculateη(M)viaalinear trac
1dthy)eengato+mtai(clγsecforf−fectht1ie)veemcrp]i,rxewtsuhsrueerreoefγogf=atsh5ea/nt3wd,oγC,cRrP=sefwf4=i/t3hP,inegge+iasctPhhcecreg=lalsρfeo[nl(leγorwg−ys cainnatsdeerPpthcore/laPetfigfio=nci0ebn.e3ctwy(beηoe(tnMhtt)ahikeseiendxeftrnroetmimcaeKlatconasgthe&esooJnofenEeocsfr/2VE0a0gz7z=)a.Fe0tiga[i.ln.12sw0h1ho2iwcahs] t/428/3/23
densityandecr istheCR-energydensity.Thedynamicalfeedback the acceleration efficiency, based on the interpolation of Kang & 66
of CR pressure is treated in the Riemann solver by updating the Jones(2007),asafunctionofthepressureratiobetweenCRsand /10
gas matter fluxes in the in 1D sweeps along the coordinate axes thermalgasinthepre-shockregion.Thepost-shockthermalization 70
and using the effective gamma factor (γeff = (γPPg++γPcrPcr)), for the isthenreducedatrun-timeaccordingly,asinVazzaetal.(2012a). 985
computationofthelocalsoundspeedincells. g cr BasedonourtestsinVazzaetal.(2012a),therun-timemodelling by
4/3AesvienryVwazhzearee,twalh.i(c2h0c1o2rare),spwoenudssetothteherefllaattitveissttpicosvsailbuleeomfoγmcren=- othfeshfioncakldreis-atrcicbeulteiorantioofnCoRfCeRnserdgoyesthnaottishaovneaavderraamgeatiinccirmeapsaecdtboyn gues
tfuomrγscpre=ctr4u/m3]o.fFCixRinsg,tthhreouvgalhuγecorf=γqcr/w3i[twhiinththfe(ps)im∝upl−atqeadnvdoqlu=m4e ∼r(aSt1ei0octipboeenrtw3c.ee2ne)nt,aiCnnsRdidstheaetnrhedefotvhrieerritamhlearliamdgpiausasc.itnTohaflirwse-aiasycsbceeticlneayruastieendstihCdeeRpcsrleousnsstutehrrees t on 04 M
isanunavoidableassumptionofthetwo-fluidmodeladoptedhere.
a
However,oncetheCR-energydensityisspecified,theCRpressure finalbudgetofCRenergyoftheICMissmall. y 2
0
dependsonlyweaklyonthespectralshapeoff(p)andonthecut-off 1
9
ofthespectrum(e.g.Jones&Kang1993;Jubelgasetal.2008).
2.1.2 HadronicandCoulomblosses
To model the injection of CRs at each shocked cell, we devel-
opedarun-timeshockfinderbasedonpressurejumps,similarto CRscanloseenergyviabinaryinteractionswiththermalparticles
Ryuetal.(2003).Ateachtimestep,weflagcellswithanegative of the ICM. This channel of energy exchange between thermal
3Ddivergence,∇·v<0,andwithconcordantlocalgradientsof and relativistic particles in the ICM is important for the high gas
temperatureandentropy,∇S·∇T>0(e.g.Ryuetal.2003).The density]ρ/(μm )>10−2cm−3]ofcoolcores.Relativisticprotons
p
local Mach number is computed by inverting standard Rankine– transferenergytothethermalgasviaCoulombcollisionswiththe
Hugoniot jump conditions for gas pressure. This method can run ionizedgas.Theycanalsointeracthadronicallywiththeambient
in either fixed grid resolution or AMR mode in ENZO runs, and thermalgasandproducemainlyπ+,π−andπ0,providedthattheir
compares very well with the shock-finding methods we develop kineticenergyexceedsthethresholdof282MeVforthereaction.
elsewhere (Vazza, Brunetti & Gheller 2009b). Compared to our The neutral pions decay after a mean lifetime of ≈9 × 10−17s
firstpaperonthissubject(Vazzaetal.2012a),weaddthetreatment intoγ-rays.ToestimatethetotalenergytransferratebetweenCRs
ofseveraladditionalphysicalprocessesthatarelistedbelow. and thermal gas in both mechanisms, we need to determine the
Thermalandnon-thermaltracesofAGNfeedback 2369
CR-energyspectrum.Sincethisinformationisnotreadilyavailable andgroups(e.g.Sijackietal.2007;Teyssieretal.2011;Martizzi
inthetwo-fluidmodel,wemustassumeanapproximatesteady-state etal.2012).3
spectrumfortheCR-energydistribution.Wefixedaspectralindex Inthefollowing,wewillrefertothecellsexceedingthisdensity
ofα=2.5fortheparticleenergy2andcomputedthetotalCoulomb thresholdandpoweringenergyfeedbackas‘AGNcells’.
andhadroniclossratesasafunctionoftheICMdensityandofE WehaveimplementedthreemodesofAGNfeedback:a‘quasar’
cr
foreachcell,asinGuo&Oh(2008): mode (i.e. thermal output of energy from AGN, Section 2.2.1), a
n E ‘jet’mode(i.e.kineticenergyoutputfrombipolarjetsaroundAGN,
(cid:12)coll=−ζccme−3ergccmr−3 ergs−1cm−3, (2) Section2.2.2)anda‘radio’mode(i.e.creationofbuoyantbubbles
inpressureequilibriumwiththeICM,Section2.2.3).
wheren ≈nistheelectronnumberdensity,andζ =7.51×10−16 Once the feedback mode is specified, the only parameters that
e c
isthecoefficientforallcollisionalenergylossterms.Inhadronic mustbesetare(a)theinitialredshiftforthestartofAGNfeedback
collisions, only ∼1/6 of the inelastic energy goes into secondary (z )and(b)theenergyreleaseofeachsingleAGNevent,E .
AGN AGN
electrons(Colafrancescoetal.2004;Guo&Oh2008).Theenergy- Inthecaseof‘quasar’and‘jet’modesthisdirectlymeasuresthe D
dominating region of CR electrons (γ ∼ 102) will heat the ICM energyweprovideforeachburstofeitherthermalorkineticenergy, ow
n
through Coulomb interactions, plasma oscillations and excitation whileforthe‘bubble’feedbackthisrepresentstheestimatedtotal lo
a
ofAlfve´nwaves(e.g.Guo&Oh2008).Therefore,wecanassume energyreleasedtotheICMbythecreationofbubbleswithinternal d
e
tthhaetrmthaeliszeatsieocnoannddartyhueslehcetraotntsheloIsCeMm.oSsitmoiflatrhteoireqenueartigoynt(h2r)o,utghhe p&reBssruu¨gregePnbb2a0n0d8)v.olumeVbb,EAGN≈3PbbVbb/2(e.g.Scannapieco d from
heatingrateoftheICMthroughCoulombandhadroniccollisions Evenifjetsandradiobubblesareassociatedwiththesametype h
canbecomputedas ofAGNfeedback(e.g.McNamara&Nulsen2007,2012),inour ttp
s
n E studytheyareconsideredasalternative scenarios.Thisallows us ://a
(cid:12) =ξ e cr ergs−1cm−3, (3) to distinguish the CR effects of buoyancy and impulsive kinetic ca
heat ccm−3ergscm−3 d
feedbackinaclearerway. e
m
whereξ =2.63×10−16(Guo&Oh2008).Inoursimulationswith Inapreliminarysetoftests(seeAppendixA)weexploredvarious ic
c .o
radiativecoolingandAGNfeedback,therateofenergylossdueto recipesfortheimplementationoffeedbackmodesinonereference u
p
thesecollisionsisextremelysmall,typically∼10−3to10−4ofE cluster,beforevaryingtheefficienciesinthewholesetofclusters. .c
cr o
ore duringthetimestepateachAMRlevel.Thisallowsustouse Here,however,wewilldiscussonlythe‘fiducial’subsetofpa- m
g /m
asimplefirst-orderintegrationtocomputetheenergylossesofCRs rametersforwhicheachimplementationoffeedbackmodesshowed n
(andthecorrespondinggasheatingrate)atrun-time. thebestperformance.Whiletherangeofspatialresolutionachieved ras
hadInroonuicrapnrdevCioouuslowmobrklo(sVseasz.zIanegteanle.ra2l0,1m2oa)d,ewlliengditdhinsoptroincecslusdaet ifneaotuurrersuansssoiscipartoedbawbliythneoatcshuAffiGciNenmttoodestu(ed.yg.stpheecimficorspmhoallol-gsycaolef /article
run-timedecreasestheCRenergybyafactorof∼10withinclus- jetsorrisingbubbles),ourresolutionandphysicalset-uparesuitable -a
tercores,whileyieldingidenticalresultsfortheremainingcluster for"studyingthelarge-scalefeaturesofCRsintheICM. bstra
volumecomparedtorunsthatneglectlosses. c
t/4
2.2.1 ThermalfeedbackfromAGN 2
8
/3
2.2 ModelsoffeedbackfromAGN AsignificantfractionoftheenergyemittedfromAGNcanthermally /2
3
coupletothesurroundinggas.Onecandefineefficienciessuchthat 6
InVazza(2011),weimplementedasimplemodelofAGNfeedback theenergyaddedintime(cid:9)tis 6/1
inENZO,viainjectionofthermalenergyattheoppositesidesofthe 07
coolingregionofgalaxyclusters.Here,weexploremorecomplex (cid:9)EAGN,g=(cid:15)r(cid:15)fM˙BHc2(cid:9)t, (4) 098
recipesofenergyfeedbackbetweenthecoldgasandthesurrounding where (cid:15) ∼ 0.1 is the bolometric radiative efficiency for a 5 b
ICM,allowingalsoforadirectinputofCRenergyfromAGN. SchwarzsrchildBH(Shakura&Sunyaev1973),M˙ ,and(cid:15) isthe y g
Ateachtimestep,theidentificationofasuitablelocationofthe BH f ue
couplingefficiencywiththethermalgas,whichisusuallyassumed s
cgeanstoravlersduepnesrimtya.sFsiirvset,BwHeflisagbacseeldlsohnostthinegsaimgpalsedmenesaistyureexcoefeldoicnagl tMo bevienrstuhseσranregleatoiofn(cid:15)(fe≈.g.0D.0i5M–a0t.t1e5oeintaolr.d2e0r05to;Bfiotoththe&obSscehrvayede t on 0
agiventhreshold,n≥nBH,andthenweselectasactive‘AGNcells’ 20B0H9;Yangetval.2012).ThisthermalcouplingbetweentheAGN 4 M
onlythemaximawithincubicregionsofsize≈1Mpch−1.Basedon a
moredetailedmodellingofBHgrowthusingsinkparticles(Sijacki andthesurroundingICMisusuallycalled‘quasar’feedback,which y 2
maybeamechanismforpre-heatingoftheICM(McCarthyetal. 0
etal.2007;Teyssieretal.2011;Martizzietal.2012),wetunedthe 19
2004, 2008; Lapi, Cavaliere & Menci 2005; Sijacki, Springel &
thresholdvaluetoexciteAGNfeedbackton ≈10−2cm−3.The
min Haehnelt2009;Lapi,Fusco-Femiano&Cavaliere2010).Inaddi-
use of this threshold is motivated by the fact that in our fiducial
tion, quasar-induced outflows at high redshift, possibly following
set-up(peakresolutionof25kpch−1percell)themassenclosedin
mergers of gas-rich galaxies, have been observed in many cases
acellwithn=10−1to10−2cm−3is≈1010to1011M(cid:6).Thisisthe
(e.g. Nesvadba et al. 2006; Bhattacharya et al. 2008; Dunn et al.
typicalgasmasssurroundingBHsofM ∼108 to5×109M(cid:6),
BH
which are commonly hosted inside the masses of galaxy clusters
3Thechoiceofrelyingonlyonthegasdensityasaproxymaytriggeralso
feedbackfromcoldfilamentsconnectinggalaxies,whereAGNfeedbackof
2ThischoiceofαcorrespondstoaMachnumberofM=3attheparticle thetypeconsideredhereisunlikely.However,oursimulationshavesufficient
injection.Onaverage,thisrepresentsthetypicalinjectionspectraofparticles highresolutiononlyingalaxyclusters.Thisseemstoexcludeanyspurious
acceleratedatpowerfulmergershocksincosmologicalsimulations,which releaseoffeedbackenergyfromcoldfilaments,asindeedwefind.Tofully
are dominant sources of thermalization and CR injection within clusters avoidthispossibility,onewouldhavetoresorttomorecomplexmodels
(e.g.Vazzaetal.2011b,andreferencestherein). (e.g.sinkparticles).
2370 F.Vazza,M.Bru¨ggenandC.Gheller
2010).SimilartoMcCarthyetal.(2010)andTeyssieretal.(2011), in our cosmological runs. For this reason, we created already
whenwedetectcellswithn≥n ,wereleasethethermalenergy, formedevacuatedbubblesaroundcellshostinganAGN,similarto
min
E ,addingtothetotalandinternalgasenergyinsidecellsatthe Scannapieco&Bru¨ggen(2008).Thebubblesarecreatedin(approx-
AGN
highestavailableAMRlevel. imate)pressureequilibriumwiththesurroundingICM,bydecreas-
Thisimplementationofquasarfeedbackisonlyanapproximation ingthegasdensityinsidethecellsbyρ(cid:12)=δ ρ,andcorrespondingly
bb
ofthetruephysicalprocessesatplay,i.e.thelaunchingofstrong increasingthethermalenergyinordertoconservetheoriginalgas
windsduetotheradiationpressureofphotonsfromtheaccretion pressure. During run-time, this modification is performed over a
disc.Thisisunavoidable,giventhatourbestresolutionisordersof single time step of the simulation, at the highest available AMR
magnitudelargerthanthetheoreticalaccretiondiscregion,andalso level. This obviously leads to a loss of gas mass in these cluster
giventhedifficultyofmodellingtheradiativetransferofphotons runs. The simulations show that on average this loss amounts to
fromtheaccretionregion. ∼5–10percentofthegasmassbytheendofthesimulation.
Ourchoiceofaminimumgasdensityn =10−2cm−3 selects Theinitialunderdensityofthebubblesissetbyenergyconser-
min
thetypicalenvironmentofmassiveBHswithinclustersandgroups. vationinsidethebubbles,afterthatEAGN isaddedtothegasand D
o
Furthermore,weassumeanenergyoutputsimilartomosttheoretical CRenergywithinthesamevolume.FortherangeofEAGNandnmin w
n
models,withoutactuallymeasuringtheaccretionpowerofBHsat adopted inthiswork,theunderdensityinsidethebubblesistypi- lo
a
run-time.Thisisdifferentfromsimulationswherethemassgrowth cally0.1–0.01.Thebubblesaregeneratedasapairofcubicblocks d
e
orefcBonHsstriuscmtioondeolfletdheusBinHgmsinatktepraartciccrleetsi,ownhriactheeantarubnle-stiamnea.cTchuirsaties iosfa23vecreyllsc,ruadtethaepdpirsotaxnimceatoifontwaondceilslsexfrpoemctethdetoclulesatedrtcoeenxtrpee.dTiehnist d fro
m
notpossibleinourcase.Ourapproachisonlyafirststeptoinclude numericallymixingofthethermalenergy. h
theeffectsofAGNfeedbackinourversionofthecode,anditallows Inprinciple,wecanalsoallowforthepresenceofCRsinjectedby ttp
s
usafastandefficientstudyofAGNmodes. theAGN,parametrizedbyφcr=Ecr,AGN/EAGNofthetotalinjected ://a
c
energy,similartoSijackietal.(2008).Inthiscasetheenergyofthe a
d
2.2.2 KineticfeedbackfromAGN bubblesisconservedalsobymodifyingtheeffectiveadiabaticindex em
ofthemixtureofgas+CRs(asinVazzaetal.2012a).However,inthe ic
TheinnermostICMcanbeaffectedbytheinjectionofkineticenergy mainbodyofthispaperweonlyrefertopurelythermalbubbles.We .ou
p
throughbipolarjetsoriginatingfromtheAGN(e.g.Binney&Tabor presentafewresultswithgas+CRsinflatedbubblesinAppendixA .c
o
1995;Ciotti&Ostriker2012).Thisenergycanbethermalizedby (theresults,however,arenotsignificantlydifferent). m
impactingontheICMafterashortdistancefromtheclustercentre /m
n
(10–100kpc;Pope2009).Gasparietal.(2011a,b)andDuboisetal. ra
s
(2010,2011)recentlysimulatedthemechanicalcouplingbetween 3 RESULTS /a
purelykineticjetsfromtheAGNandthesurroundingICMinthe rtic
The results discussed in the main part of this paper have been le
coolingregion. -a
producedconsideringthefollowingphysicalmechanisms:(a)pure b
Inthismodeleachofthetwojetsisinitializedasapureinputof s
kineticenergydensityE =1/2ρv2 ,withvelocity,v ,pointing cooling; (b) cooling and thermal feedback by AGN from z ≤ 4, tra
radiallyoutwardsfromtAhGeNclustercenjettre.Evenifinourjevtersionof withafixedenergyreleasepereventofEAGN =1059erg(oralso ct/4
1060erginthecaseofE1andE5A);(c)coolingandkineticenergy 2
ENZOthelaunchingdirectionofthejetsissetbyarandomselection feedbackbyAGNfromz≤4,withafixedenergyreleaseperevent 8/3
ofcoordinateaxes,inthisworkwekeepthejetaxisfixed.Inthis ofE =1059erg;(d)coolingandenergyfeedbackfrombuoyant /23
way, velocity effects related to the direction of jet launching can AGN 6
easilybedetected(Section3.4).Everytimeajetisgenerated,we bubblesinjectedbyAGNfromz≤4,withanapproximateenergy 6/1
modifythegasvelocity,thetotalandinternalenergyatthehighest preesrimveunltatoefdEfoAGuNrc∼lus1t0e5r9seinrgt.hWeimthastsheraanbgoeve10i1m4p≤lemMe≤nta1t0io1n5sM,w(cid:6)e. 0709
available AMR level in a pair of cells on opposite sides of the 8
gasdensitypeak.Thewidthandtheinitialextensionofthejetare Thelistofthemostimportantparametersofall‘fiducial’models 5 b
set by the maximum resolution, which is ∼10 times larger than investigatedinthearticleisgiveninTable1.Thefirstmodel(pure y g
thebestresolutionavailablein‘single-object’runs(Gasparietal. cooling) obviously produces strong cooling flows in all systems. ues
2011a).Atourresolution,theequivalentopeningangleofeachjetis In this work, this model is therefore regarded only as a standard t o
∼30◦–40◦withrespecttotheclustercentre.Thisisanunavoidable referencetoassesstheroleofeachfeedbackmodel. n 0
drawback of the fact that in such cosmological runs achieving a Inordertoachieve thelargest possibledynamical rangeinside 4 M
thevolumewhereeachclusterforms,thefourclusterswereresim- a
muchlargerresolutioniscomputationallyveryexpensive.However, y
ulatedathighspatialandDMmassresolutionstartingfromparent 2
forthedynamicalfeedbackofjetsthemostimportantquantityis 0
theinjectedkineticenergy,whichissimilartosimulationsathigher simulationsatlowerresolutionandaddingnestedinitialconditions 19
resolution,oncethedifferentmassloadofthejetsandlaunching
velocityareconsidered.Alsotheinitialvelocityofourjets(which Table1. Listofthephysicalmodelsadoptedinourruns.Column1:identi-
depends on the typical density of AGN cells, through the total ficationname.Column2:cooling.Column3:energyperevent.Column4:
kinetic energy released in the AGN burst) is ∼500–1000kms−1, detailsonfeedbackmode(withapproximatevaluesofheatingtemperature,
jetvelocityandinitialbubbleunderdensity).
about one order of magnitude lower than the typical velocity of
jetsinsingle-objectsimulationsatmuchhigherresolution(Gaspari
eta"l.2011a,b). ID Cooling EAGN(erg) Feedbackmode
Cooling Yes 0 No
Quasars Yes 1059 Thermal,TAGN∼5×107K
2.2.3 BubblefeedbackfromAGN Quasars2 Yes 1060 Thermal,TAGN=5×108K
ThecreationofbuoyantbubblesintheICMinflatedbyjetsrequires Jets Yes 1059 Kinetic,vjet∼750kms−1
a spatial resolution (∼0.1–1 kpc) beyond what can be achieved Bubbles Yes 1059 Buoyant,δbbl∼0.05
Thermalandnon-thermaltracesofAGNfeedback 2371
Table 2. Main parameters of the clusters simulated in shocksandintenseturbulentmotionsintheICMouttotheclusters
this work. Column 1: identification name. Column 2: to- outskirts.Shocksandturbulenceareanalysedinthenextsections
tal(gas+DM)massatz=0.Column3:virialradius(Rv). (Sections3.2–3.4).Inaddition,ourtestwithENZOhasshownthat
Column4:dynamicalstateatz=0.Theidentificationname
thiscompositeAMRcriterionbettercapturesphysicalmixingmo-
ofeachclusterischosentobeconsistentwithotherworks
tionsintheICM,andreducestheamountofnumericalmixing,with
ofours(Vazzaetal.2010a,2012a).Theclusterparameters
importantconsequencesintheamountofcoldgaswithintheclus-
arereferredtothesimplenon-radiativesimulationofeach
tervolume(Vazza2011).However,thismethodiscomputationally
object.
muchmoreexpensivewithrespecttothegas/DMoverdensitycri-
ID Mtot(×1014M(cid:6)) Rv(Mpc) Dynamicalstate teriaalone,andwecouldaffordtorunitonlyinthe‘fiducial’AGN
models(Table1).
E1 11.2 2.67 Post-merger InAppendixAweshowtheeffectsofdifferentimplementations
E5A 8.2 2.39 Merging andenergiesbudgetinAGNfeedbackinthesmallestofthesesys-
H5 2.4 1.70 Post-merger tems,usingthestandardAMRcriterionwhichworksongas/DM D
H10 1.2 1.20 Relaxed o
overdensity.Inthemainpaperwewillstudytheobservablether- w
n
mal and non-thermal features of the ‘fiducial’ implementation of lo
a
of increasing spatial and mass resolution (e.g. Abel et al. 1998). eachfeedbackmodeinourversionofENZO.Theparametersofthe de
Tcewnotrleedveolnsothfenecsltuesdteinrictieanltcroesn.dTitihoensbowxeraetptlhaecefidrsint lceuvbeilchreagdiothnes sfemeadlblacclkusitsergisvaemnpilneTreasbilmeu2l.atedwiththedifferentrecipesofAGN d from
sizeof≈95Mpch−1(withm ≈5.4×109M(cid:6)h−1andconstant Theevolutionofgastemperaturebetweenz=2and0incluster h
spatialresolutionof(cid:9)1≈425dmkpch−1).Thesecondboxhadasize H5 (quasar mode) is shown in the panels of Fig. 2. Blast waves ttps
of ≈47.5Mpch−1 (with mdm ∼ 6.7 × 108M(cid:6)h−1 and constant triggeredbyAGNfeedback(highlightedbyarrows)inthethermal ://a
spatialresolutionof(cid:9) ≈212kpch−1).Foreveryclusterrun,we modedrivepowerfulshocksthroughtheICM,addingtothepattern ca
1 d
identifiedcubicregionswiththesizeof∼6Rv(whereRvisthevirial ofmergerandaccretionshockwaves.Weobservethatingeneral em
radiusofclustersatz=0,calculatedinlowerresolutionruns),and only two to three AGN cells are located inside forming clusters ic
.o
allowed for three additional levels of mesh refinement, achieving at a high redshift, while at a lower redshift only one AGN cell u
p
apeakspatialresolutionof(cid:9)≈25kpch−1 (inthefollowing,we is usually found inside the virial volume. The shocks triggered .c
o
willrefertothissubvolumeastothe‘AMRregion’).Fromz=30 byAGNfeedbackareefficientinremovingthecoldgasphaseat m
(theinitialredshiftofthesimulation)toz=2,meshrefinementis z>1,whileproducingsignificantamountsofCRsintheforming /mn
triggeredbygasorDMoverdensity.Fromz=2anadditionalre- cluster.Blastwavesalsocausetheexpulsionofasignificantfraction ras
fiisnsewmietcnhtecdritoenr.ioTnhbisasseedcoonnd1ADMveRloccriittyerjiuomnpiss(dVeasizgznaeedttaol.c2a0p0t9uare) oetfatlh.e(2h0o1t0)g.as from the cluster volume, in line with McCarthy /article
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Figure2. Timesequenceofgastemperature[inunitsof(K)inthecolourcoding]forasliceof5×5comovingMpch−1andwidth25kpch−1forrunH5
with‘quasar’feedback.Thearrowspointtothelocationsofrecent‘quasar’eventsinthevolume.The‘coarse’resolutionofthefirstsnapshotsisduetothe
factthatweturnonAMRbasedonvelocityjumpsatz=2.
2372 F.Vazza,M.Bru¨ggenandC.Gheller
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Figure3. Timesequenceofmass-weightedaveragegastemperatureforacomovingvolumeof∼(5Mpch−1)3intheformationregionofclusterH5.Weshow 85
theresultsofthethreeresimulationsemployingAGNfeedback,alwayswithanenergypereventofEAGN=1059erg.Horizontalarrowssuggestthelocation by
ofinterestingepisodesofAGNfeedbackwithinthevolume. g
u
e
s
Fig.3showsacomparisonofprojectedgastemperatureacross ofclusterE5AinrunsemployingAGNfeedback.Jetsandquasars t o
n
theentireAMRregionofthesamecluster,atthreedifferentcosmic arenotactiveanymoreatz=0inthisrun,andnoclearfeatures 0
4
epochs.Whilethelarge-scalemorphologyoftheclusterissimilar relatedtotheiractivitycanbeseenintheinnermostclusterregion M
a
inallrunstowardstheendofthesimulation,eachfeedbackmode atthisredshift.Apairofbubbles,ontheotherhand,hasrecently y
2
locallyperturbstheICMinadifferentway,drivingpowerfulout- beeninjectedandcanbeseenasacoupleofunderdenseblobson 0
1
bursts (or buoyant bubbles) whenever strong cooling causes n > oppositesidesoftheclustercentre(shownbygreencirclesinthe 9
n . image).OtherimagesofactivejetsandbubblescanbeseeninFig.
min
Inthequasarmode,thefinallarge-scalemorphologyofthecluster A1ofAppendixA.
isalsoaffectedbytheoverallactionofpowerfulthermalbursts,and Weusephasediagramsforthecellsinsidethevirialvolumein
presents a large amount of ejected hot gas outside of the cluster order to characterize relevant differences. In Fig. 5 we show the
volume. In the jet mode, prominent jets are launched along the example of phase diagrams for an early cosmic epoch before the
horizontalaxis,drivingpowerfulshocks(M∼5–10)intothe∼106– cluster formation, z = 2 (top panels), and after the formation of
107Kcoolinggasaswellasgasmotionsalongtheiraxis.Thebubble thecluster,z=0.2(bottompanels)forthefourdifferentfeedback
mode,ontheotherhand,hasbarelydetectableeffectsonthelarge modes.Themostevidentdifferencebetweentherunsistheabsence
scale, and is globally similar to a simple pure cooling run (not ofthe‘coolingflow’phaseonthelowerrightpartofthediagram,
shown). in all runs employing AGN feedback. In the bubble mode, the
Fig. 4 presents a zoomed image of the gas density maps for a feedbackfrombuoyantbubblesonlyaffectsthehigh-densityregions
sliceof2×2Mpc2anddepth25kpch−1forthefinalconfiguration aroundtheclustercore.Athighredshift,thephasediagramisvery
Thermalandnon-thermaltracesofAGNfeedback 2373
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Figure4. Gasdensity(toppanels)forasliceof2×2Mpch−2 andwidth25kpch−1 acrossresimulationsofclusterE5Aatz=0.Thecolourcodingis m
[ρ/ρcr,b](whereρcr,bisthebaryoncriticaldensity).Thegreencirclesshowtheprojectedlocationoftwobubblespreviouslyinjectedintheclustercentre. http
s
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Figure5. PhasediagramsofcellswithinthevirialvolumeoftheresimulationsofclusterE1atz=2(toppanels)andatz=0.2(bottompanels).Thecolour
codingshowsthecell-wisepressureratiobetweenCRandgaswithincells;thethicklineshowstheaveragetrendwithineachphasediagram.
similartothepurecoolingrun,withtheexceptionoftheselective phasehasalmostdisappearedinjetandquasarfeedback,duetothe
removalofgaswithn >10−2cm−3cells,whichareheatedtohigh efficientandvolume-fillingnatureoftheheatingeventsdrivenby
min
temperatures(>5×107K)bytheinjectionofbubbles.Ontheother such powerful mechanisms. In the bubble run the phase diagram
hand,inthequasarandjetmodestheactionoffeedbackdrastically is similar to the pure cooling run, with the exception of the n ∼
altersthephasediagramswithrespecttothepurecoolingrun.This 10−2cm−3regime,wherebubblesareinjectedalmostcontinuously
isparticularlyevidentinthequasarmodeatz=2,wherea‘cloud’of andovercoolingisbalancedbymixing.Thisleavesasignificant
high-temperaturecells(T>107Kandn∼10−4cm−3)isleftafter portionof‘cold’(<106K)anddensecellsinthesimulatedvolume,
thepassageofanAGN-drivenblastwave.Atz=0.2,the‘cooling’ characterizedbylargevaluesofP /P .
cr g
2374 F.Vazza,M.Bru¨ggenandC.Gheller
if the power per event is 10 times larger. In Fig. 7 we show the
3.1 X-rayproperties
total energy released by AGN in the formation region of cluster
WecompareoursimulationswiththecollectionofChandracluster E1,intheredshiftrange0≤z≤1.Bytheendofthesimulation,
observationsofCavagnoloetal.(2009),publiclyavailableviathe allfeedbackmodesusedatotalamountofenergyintherangeof
ACCEPT catalogue (http://www.pa.msu.edu/astro/MC2/accept). ∼2–9×1061erg,correspondingto∼0.01–0.09ofthetotalthermal
The catalogue consists of 241 clusters mostly located in the red- energyoftheclusteratz=0.
shiftrange0.05≥z≥0.5andwithaveragecentraltemperaturesin Interestingly,bytheendofthesimulationthehigherpowerAGN
therangeof0.5–10keV.Forourcomparisonweselectedasubsam- mode(EAGN=1060erg)usedabout∼30percentlessenergythan
pleof∼60objectsfromtheACCEPTcatalogue,withredshiftsand thelowerpowerrun(EAGN=1059erg),whichis∼1/3ofthetotal
averagecentraltemperaturescompatiblewithourclusterdataset: energy used in the kinetic feedback mode at a lower power. The
z≤0.2and0.2≤T≤5keVinside0.2R .Forfurtherdetailson totalenergybudgetusedinthebubblemodeissimilartothequasar
200
theACCEPTcatalogueandsetofobservations,wereferthereader modeatthesamepowerperevent.Wenotethatinthissystemthe
toCavagnoloetal.(2009). useofAGNfeedbackissignificantlyreducedforz>0.6,duetothe D
o
In Fig. 6, we show the radial profile of reduced gas entropy4 onsetoflarge-scalemergersandpowerfulshockheatingwithinthe w
(K/TSL, where K = TSL/n2/3 and TSL is the spectroscopic-like cluster volume. However, episodes of AGN feedback are present nloa
temperature; Rasia et al. 2005), gas number density, n, and even at later epochs. Overall, a smaller amount of energy from d
e
sTpheectsriomscuolaptiecd-lipkreofitelmespaerreatucroemfpoarrethdetodiftfheerepnrtofifeleedsboafckobmseordveesd. ApuGreNlyfethederbmacaklfiesendebcaecsksa,royrtboubbabllaensc,ecothmepcaarteadsttroopkhinicetciocofeliendgbwacitkh. d from
clusters, divided by the colour coding into ‘cool-core’ systems if This is consistent with analytical results of Pope (2009, fig. 1), h
theircentralentropyis<30keVcm2 (inblue),or‘non-cool-core’ whereitisshownthatahigherinjectionrateofkineticenergy,with ttps
systemsotherwise(red). respecttothermalenergy,isnecessarytobalancethecoolingflow ://a
As expected, none of the pure cooling runs can reproduce the forclustermasses>1015M(cid:6).Thisisbecauseinamassivecluster ca
d
observed profiles. In these runs, steep gas density profiles with thecriticalmomentuminjectionrateneededtoovercomethepull em
centralvaluesof∼0.1–1cm−3 andreducedcentralentropybelow of gravity and the surrounding gas pressure in the cluster core is ic
.o
∼10cm2 are found, at odds with observations and in agreement more difficult to reach than the critical injection rate of thermal u
p
with standard radiative runs (e.g. Li & Bryan 2012, for a recent energyrequiredtoovercomethecoolingflowviathermalfeedback. .c
o
review).OnlyclusterE1ismarginallywithintherangeallowedby Inaddition,theenergyreleasefromjetsclosetotheclustercoreis m
/m
observationsfordensityandentropy.However,consideringthatthis veryanisotropic,anditbecomesmoreisotropic(duetothedriving n
systemhasjustgonethroughastrongmajormergerat(z∼0.25), ofshocks)onlyatadistanceof∼100–200kpcfromthecore. ras
ibtycaitnsngoatsbedecnlasistsyifiaenddatsemacplearsastiucraelpcoroofil-lceo.rOencltuhseteor,thaesrsuhgangdes,taeldl obsOevrveeradlll,otwhe-tXem-rpayerpartuorpeerntioens-ocofoolu-rcoclruesctelursstseeresmsicnocnestihsteentytpwicitahl /article
runs employing AGN feedback yield a much better comparison internaldropintemperatureofcool-coreclustersisnotobserved. -a
b
withobservations.Jetandbubblefeedbackmodesproduceroughly On the other hand, in the epoch in which the AGN feedback is stra
similarprofilesforallclusters:aratherflatentropyprofilewithin triggeredinoursimulations,thethermalstructureoftheinnermost c
clustercores(compatiblewiththehighentropyfloorofnon-cool- clusterregionsisnotcompatiblewiththeappearanceoftypicalcool t/42
8
coreclustersinCavagnoloetal.2009),ashallowdensityprofileand cores either, because the internal drop in temperature is typically /3
analmostisothermaltemperatureprofileinsidethecentral∼Mpc muchstrongerthanwhatisobserved.Alackofresolutioncompared /23
6
fromthecentre.Lessclearresultsarefoundinthecaseofquasar toobservationscouldberesponsibleforthat. 6
/1
feedback. While in clusters E1, H5 and H10 a reasonable match However,wefindnoevidenceofbimodalityinthedistribution 0
7
with observations is found with the ‘fiducial’ energy budget of of clusters entropy or gas density in our resimulations, at odds 09
E =1059ergperevent,thisisinsufficienttoquenchthecooling withobservations(Cavagnoloetal.2009;Prattetal.2010;Eckert 85
caAtGaNstrophe in cluster E5A, where a rather standard cooling flow et al. 2012). This might be connected to our coarse sampling of by
g
takesplacebytheendofthesimulation.Byincreasingtheavailable theparameterspaceofAGNfeedback,ormayinsteadcallforthe u
e
energypereventbyoneorderofmagnitude,EAGN =1060erg,the implementationofmorecomplexphysicsinoursimulations.How- st o
coolingflowisstoppedalsoinclusterE5A(lowerrowofFig.6). ever,theinvestigatedsampleistoosmalltoaddressthisimportant n
0
Interestingly,thesameistrueforaresimulationofclusterE1using issueindetail,andwewillleavethisforfuturework. 4
M
thesamehigherenergybudget.However,inthecaseoftheother We illustrate the effects of AGN feedback on the radial distri- a
smallerclustersthehigherenergybudgetistoolargeandthethermal bution of baryon fraction by referring to the relevant example of y 2
structure of both is destroyed, leading to a gas-poor cluster (see cluster H5 at z = 0, shown in Fig. 8. As expected, the onset of 01
9
AppendixA). thecoolingflowcausestoostrongaconcentrationofbaryonsin-
This may simply suggest that different cluster masses must be sidethecoolingradius,clearlyatoddswithobservation(e.g.Ettori
characterizedbydifferenttypicalpowersperevent,mirroringthe etal.2009;Sun2012,andreferencestherein).Ontheotherhand,
factthatalargerpowerpereventisneededtobalancethegravityand allfeedbackrunsproduceafinaldistributionofgasmasswhichis
thepressureofthecoolinggaseousatmosphere(e.g.Pope2009). moreinagreementwithobservations,showingincreasingprofiles
However,itisinterestingtonotethattheself-regulatingnatureof towardstheclusterouterregions(e.g.Ettorietal.2009;Sun2012).
AGNfeedback(evenwiththissimpleimplementation)yieldsvery Approaching R200 the enclosed gas mass fraction is 90–100 per
similarfinalprofilesinthemostmassiveobjectofoursample,even cent of the cosmological baryon fraction. However, the different
implementations of feedback produce significantly different and
time-dependentfeaturesintheprofile.Inparticular,themechanical
4Weusethe‘reduced’entropy,ratherthantheusualentropy,K=T/n2/3, action of jets changes the shape of the enclosed baryon fraction
sincethisremovesthedependenceonthehostclustermass(Borganietal. in this low-mass system, due to a more recent feedback episode.
2008). Similar trends are found in the other systems, provided that the
Thermalandnon-thermaltracesofAGNfeedback 2375
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Figure6. Profilesofreducedgasentropy,gasnumberdensityandspectroscopic-liketemperatureforthesimulatedclusters(thicklineswithdifferentstyles)
andforobservedclustersintheACCEPTcatalogue(Cavagnoloetal.2009,theredlinesarefornon-cool-coreclustersandtheblueareforcool-coreclusters).
Eachrowshowstheprofilesofadifferentfeedbackmode.Thelastrowshowstheprofilesforthequasarmode,withEAGN=1060ergperevent(onlythetwo
mostmassiveclustersareshown).