MNRAS437,1456–1475(2014) doi:10.1093/mnras/stt1977 AdvanceAccesspublication2013November13 Kinetic or thermal AGN feedback in simulations of isolated and merging −σ disc galaxies calibrated by the M relation Paramita Barai,1‹ Matteo Viel,1,2 Giuseppe Murante,1 Massimo Gaspari3 and Stefano Borgani1,2,4 1INAF–OsservatorioAstronomicodiTrieste,ViaG.B.Tiepolo11,I-34143Trieste,Italy 2INFN/NationalInstituteforNuclearPhysics,ViaValerio2,I-34127Trieste,Italy 3MaxPlanckInstituteforAstrophysics,Karl-Schwarzschild-Strasse1,D-85741Garching,Germany 4DipartimentodiFisicadell’Universita`diTrieste,SezionediAstronomia,ViaTiepolo11,I-34131Trieste,Italy D o w n lo a Accepted2013October12.Received2013October11;inoriginalform2013July19 de d fro m ABSTRACT http We investigate two modes of coupling the feedback energy from a central active galactic s://a nucleus (AGN) to the neighbouring gas in galaxy simulations: kinetic – velocity boost and c a thermal – heating. We formulate kinetic feedback models for energy-driven wind (EDW) de m aAnGdNmwominednvtuelmoc-ditryivven.wAinndov(eMlnDuWm)e,riucsailnaglgtworoitfhrmeeispaimrapmleemteersn:tefdeeidnbtahceksmeffioocitehnecdyp(cid:2)arftiacnlde ic.ou w p hydrodynamics code GADGET-3, to prevent the expansion of a hole in the gas distribution .co m around the black hole (BH). We perform simulations of isolated evolution and merger of /m disc galaxies, of Milky Way mass as well as lower and higher masses. We find that in the nra isolated galaxy BHkinetic feedback generates intermittentbipolar jet-likegas outflows. We s/a infer that current prescriptions for BH subgrid physics in galaxy simulations can grow the rtic le BH to observed values even in an isolated disc galaxy. The BH growth is enhanced in a -a b gthaalanxaynmiesorglaetre,dwhcaicshe.cConosmeqpuaerinntglytrheequ[MireBsHd−ifσfe(cid:4)r]ernetlmatioodnelopbatraainmeedteirnstooufirtstihmeuolabtsieornvsatwioinths stract/4 observational data, we conclude that it is possible to find parameter sets for a fit in all the 3 7 models (e.g. v = 10000kms−1 and (cid:2) = 0.25 for BH kinetic EDW), except for the case /2 w f /1 with MDW feedback in a galaxy merger, in which the BH is always too massive. The BH 45 6 thermalfeedbackimplementationofSpringeletal.withinthemultiphasestarformationmodel /1 1 is found to have negligible impact on gas properties, and the effect claimed in all previous 03 0 studiesisattributedtogasdepletionaroundtheBHbythecreationofanartificialhole.The 82 b BHmassaccretionrateinoursimulationsexhibitheavyfluctuations.Thestarformationrateis y g quenchedwithfeedbackbyremovalofgas.Thecircumgalacticmediumgasatgalactocentric u e distances (20–100)h−1 kpc is found to give the best metallicity observational diagnostic to st o n distinguishbetweenBHmodels. 0 6 A Keywords: blackholephysics–methods:numerical–galaxies:active–galaxies:evolution– p galaxies:interactions–cosmology:theory. ril 2 0 1 9 (e.g.Silk&Rees1998;King2003;Granatoetal.2004;Begelman 1 INTRODUCTION &Nath2005;Barai&Wiita2006;Crotonetal.2006;Barai2008; Supermassiveblackholes(SMBHs)arebelievedtoexistatthecen- Fabian2012;Wagner,Umemura&Bicknell2013),generatingob- tresofactivegalaxies(e.g.Kormendy&Richstone1995;Ferrarese servationaltrendssuchasthecentralSMBH–hostgalaxystellar & Ford 2005), powered by the accretion of matter and liberating bulgecorrelations(e.g.Magorrianetal.1998;Gebhardtetal.2000; enormousamountsofenergy.Activegalacticnuclei(AGN)influ- Shankaretal.2006).TheenergyoutputisoftenobservedasAGN encetheformationandevolutionofgalaxiesintheformoffeedback outflows in a wide variety of forms (see Crenshaw, Kraemer & George2003;Everett2007forreviews),e.g.collimatedrelativistic jets and/or huge overpressured cocoons in radio (Nesvadba et al. (cid:4)E-mail:[email protected] 2008), blueshifted broad absorption lines in the UV and optical (cid:2)C 2013TheAuthors PublishedbyOxfordUniversityPressonbehalfoftheRoyalAstronomicalSociety KineticAGNfeedback 1457 (Reichard et al. 2003; Rupke & Veilleux 2011), warm absorbers 2011)togetherwiththeirownmodelingalaxymergersimulations, (Krongoldetal.2007)andultrafastoutflows(Tombesietal.2013) and found wide variation in accretion behaviours. Among these, inX-rays,moleculargasinfar-IR(Feruglioetal.2010;Sturmetal. inDebuhretal.(2011)thefeedbackisreturnedasmomentumor 2011). inthekineticform,whiletheothershavethermalfeedback.How- Concordance galaxy formation models in the cold dark matter ever,themodelbyDebuhretal.(2011)alsohasadistinctaccretion (DM)cosmologywidelyincorporatefeedbackfromAGNinsim- prescriptionbasedontheviscoustransportofangularmomentum; ulationsofisolatedgalaxiesandmergers(e.g.Springel,DiMatteo therefore,comparingitwithe.g.Springeletal.(2005,whichuses & Hernquist 2005; Johansson, Burkert & Naab 2009b), and cos- themodifiedBondiaccretionrate)makesithardtodisentangleif mologicalvolumes(e.g.Sijackietal.2007;Booth&Schaye2009; the differential effects are because of various accretion methods Dubois et al. 2010; Fabjan et al. 2010; Barai, Martel & Germain orvaryingfeedbackmodels.Inourstudy,weusethesameaccre- 2011b; Di Matteo et al. 2012; Hirschmann et al. 2013) as well tionmethodologyandthencomparebetweenthermalversuskinetic assemi-analyticalstudies(e.g.Saluccietal.1999;Shankaretal. modesoffeedback. 2004).SimulationsgenerallyinvokeAGNfeedbackinthenegative This paper is organized as follows: we describe our numerical D o formwhichquenchesstarformation(SF)andlimitstheformationof code and simulation setup in Section 2, in Section 3 we present w n massivestellarsystems(e.g.Scannapieco,Silk&Bouwens2005; and analyse our results, some important outcomes are discussed lo a van de Voort et al. 2011; Dubois et al. 2013b), as supported by in Section 4, while in Section 5 we give a summary of the main d e sAotmtheeosbasmeervtaimtioen,As(GeN.g.feSecdhbaawcikncskaniebteaplo.s2i0ti0v6e;oWccaansgioentaallly.2w0h0i7c)h. findingsanddiscusspossiblefutureapplications. d from alsoplaysanimportantroleinthecosmologicalcontext.AGNout- h flows have been shown to overpressure, compress and fragment ttp s clumpygasclouds,triggeringstarbursts,intheoreticalandnumer- 2 NUMERICAL METHOD ://a c icalstudies(e.g.DeYoung1989;Silk2005;Zubovasetal.2013), We use a modified version of the TreePM (particle mesh) – a d and observed in jet-induced SF and radio–optical alignment (e.g. smoothedparticlehydrodynamics(SPH)codeGADGET-3(Springel em Chambers,Miley&vanBreugel1987;Zinnetal.2013). 2005), which includes a more efficient domain decomposition to ic.o Weinvestigate,inthispaper,differentmodelsandimplementa- improve the work-load balance over the public version GADGET-2. up tionofAGNfeedbackingalaxysimulations.Ourgoalistocompare Someofthesubgrid1physicsincludedinthesemipublicversionof .co andcontrasttwomodesofcouplingofthefeedbackenergyfrom GADGET-3codeweuseareoutlinedbelow.TheBHmodulesinclud- m/m black hole (BH)to the surroundinggas:thermal – where the gas ingournewkineticfeedbackmodelaredescribedinSections2.1, n temperature(or,internalenergy)isincreasedandkinetic–where 2.2and2.3.TheinitialgalaxymodelsarepresentedinSection2.4, ras tihneeagcahscvaesleocwithyicishbfiotsosreteledv.aWnteoabismervtoatfiionndalthdeatma,oadnedlepxapralomreettehres andThoeurnsoinm-AulGatNionsusbagrreidmmenotdioenlse:draindiSateicvteiopnhy2s.5ic.s,SFandchemi- /article signatures of various feedback models on the BH growth, galaxy calevolutionaresameasintheworkofBaraietal.(2013).Radiative -a b and circumgalactic medium (CGM) properties. In this work, we coolingandheatingiscomputedbyaddingmetal-linecoolingfrom stra performsimulationsofisolatedandmergingdiscgalaxies,before Wiersma, Schaye & Smith (2009), considering 11 different ele- c applyingourmodelstocosmologicalvolumesinthefuture. ments:H,He,C,Ca,O,N,Ne,Mg,S,SiandFe.Aphotoionizing t/43 7 GalaxyformationsimulationshaveinvestigatedbothAGNfeed- backgroundradiationfromthecosmicmicrowavebackgroundand /2 backmechanisms:thermal(e.g.DiMatteo,Springel&Hernquist theHaardt&Madau(2001)modelfortheUV/X-raybackground /14 5 2005;Sijackietal.2007;Booth&Schaye2009;Fabjanetal.2010; areconsidered. 6 /1 Gaspari et al. 2011b) and kinetic (e.g. Germain, Barai & Martel SF is implemented following the multiphase effective subreso- 1 0 2009;Duboisetal.2010;Ostrikeretal.2010;Gaspari,Brighenti& lution model by Springel & Hernquist (2003). Gas particles with 30 Temi2012a;Vazza,Bruggen&Gheller2013).Gasparietal.(2011a) densityabovealimitingthreshold,ρ =0.13cm−3(unitsofnum- 82 SF b exploredseveralfeedbackmechanismsingalaxyclusters,including berdensityofhydrogenatoms),containcoldandhotphases,and y g cold gas accretion and massive subrelativistic outflows, that self- arestarforming.Collisionlessstarparticlesarespawnedfromgas u e regulatethemechanicalpowerfromAGNoutflowheating.These particlesundergoingSF,basedonthestochasticschemebyKatz, st o modelswereextendedbyGasparietal.(2011b)togalaxygroups. Weinberg&Hernquist(1996).Weallowagasparticletospawnup n 0 Gasparietal.(2012a)studiedtheroleofmechanicalAGNfeedback tofourgenerationsofstars. 6 A incontrollingthethermodynamicalevolutionofisolatedelliptical Stellar evolution and chemical enrichment feedback are incor- p galaxies.Gaspari,Ruszkowski&Sharma(2012b)exploredthefor- poratedfollowingthechemicalevolutionmodelofTornatoreetal. ril 2 mation of multiphase gas via thermal instability in cluster cores (2007).Productionof11species(H,He,C,Ca,O,N,Ne,Mg,S, 01 9 heatedbycollimatedbipolarAGNjets. SiandFe)areaccountedforusingdetailedyieldsfromTypeIaSN There have been two contemporary studies of BH feedback in (SN-Ia),TypeIISN(SN-II),alongwithlow-andintermediate-mass isolated galaxy systems, the distinction of our work from those stars (LIMS) in the thermally pulsating asymptotic giant branch is outlined below. Newton & Kay (2013) simulated isolated and phase.BothSN-IaandSN-IIcontributetothermalfeedback.There mergingdiscgalaxiestoinvestigatetheeffectoffeedbackfromboth aremass-dependenttimedelayswithwhichdifferentstellarpopu- AGNandsupernovae(SNe)ongalaxyevolution,andtoisolatethe lationsreleasemetals,adoptingthelifetimefunctionbyPadovani& most important factors of these feedback processes. They utilize Matteucci(1993).Differentstellaryieldsareused:forSN-Iataken differentmethodsfordistributingthefeedbackenergyinthesame from Thielemann et al. (2003), SN-II from Woosley & Weaver thermalform,anddonothavekineticfeedback.Ourworkconsiders (1995)andLIMSfromvandenHoek&Groenewegen(1997).The thekineticmodeinadditiontothermal. Wurster&Thacker(2013b)comparedtheAGNfeedbackalgo- rithms of four authors (Springel et al. 2005; Okamoto, Nemmen 1Bysubgridwemeansubresolution,referringtophysicalprocessesoccur- & Bower 2008; Booth & Schaye 2009; Debuhr, Quataert & Ma ringatlength-scalessmallerthantheresolvedscalesinoursimulations. 1458 P.Baraietal. massrangeforSN-IIisconsideredtobeM/M(cid:3)>8,whilethatfor 2010).Booth&Schaye(2009)usedanα factordependentonthe SN-Iaoriginatingfrombinarysystemsis0.8<M/M(cid:3)<8witha gasdensity. binaryfractionof10percent. TheidealizedassumptionsoftheoriginalBonditheory:spher- Weincludeafixedstellarinitialmassfunction(IMF)according ically symmetric, non-rotating, adiabatic, steady and unperturbed totheformalismgivenbyChabrier(2003),whichisapowerlaw gasflowwithconstantboundaryconditions,hasledtorecentcriti- atM/M(cid:3) >1andhasalog-normalformatmassesbelow.How- cismsoftheadoptedBondiaccretionmodelingalaxysimulations. ever,weusepower-lawIMFswithdifferentslopesoverthewhole Usinganalyticalargumentsandsimulatingsphericalgasdistribu- massrangeof0.1to100M(cid:3),whichmimicsthelog-normalform tion within the length-scales (0.001–1)kpc, Hobbs et al. (2012) ofChabrier(2003)atlowermasses,astestsindicate.Thefunctional showed that in free-falling gas due to efficient cooling and grav- form:φ(M)=KM−y,iscomposedofthreeslopesandnormaliza- ity of the surrounding halo, the Bondi–Hoyle formalism can be tions:y=0.2andK=0.497forstellarmasses0.1≤M/M(cid:3)<0.3, erroneousbyordersofmagnitudeineitherdirection.Insub-pcres- y = 0.8 and K = 0.241 for 0.3 ≤ M/M(cid:3) < 1, and y = 1.3 and olutionsimulationswherethegasiscooling,Gasparietal.(2013) K = 0.241 for 1 ≤ M/M(cid:3) < 100. Stars within a mass interval andBaraietal.(2012)sawtheformationofamultiphasemedium, D o [8–40]M(cid:3)becomeSNefirstbeforeturningintoBHsattheendof composed of thermal-instability-driven cold clouds and filaments w theirlives,whilestarsofmass>40M(cid:3)areallowedtodirectlyend within the hot gas, which makes the accretion cold and chaotic. nlo a inBHs. Gasparietal.(2013)inferredthattheaccretionrateisboostedup d e steTllhaerwchinedmsiacnadl eSvNoeluetxiopnlomsioondse,lwinhciochrpaorreatseeslf-mcoasnss-ilsotessnttlhyrcooumgh- tSouctwhoonogrdoeinrsgostfumdiaegsnairteudaettecmomptpinargedtowimithprtohveeBthoendBiHpraecdcircettiioonn. d from puted for a given IMF and lifetime function. A fraction of a star prescription in intermediate-scale simulations resolving the sonic h particle’smassisrestoredasdiffusegasduringitsevolution,and radius(alsoBarai,Proga&Nagamine2011a).Alternatemethods ttp s distributedtothesurroundinggasparticles.Thereisnokineticfeed- have also been prescribed recently to estimate the BH accretion ://a c backfromSNe-drivengalacticoutflowsinoursimulations.Thisis rateongalaxyscales:useviscoustransportofangularmomentum a d because we want to decouple AGN-driven from SNe-driven out- (Debuhr et al. 2010) and accretion disc particle method (Power, em flowing gas, and aim to explore uncontaminated outflows driven Nayakshin&King2011;Wurster&Thacker2013a).Incorporating ic .o solelybythermalorkineticAGNfeedback. suchmodifiedaccretionschemesinfullcosmologicalsimulations u p makeupavenuesforfuturework. .c o Nevertheless despite the limitations, the Bondi model for BH m /m 2.1 BHaccretionandenergyfeedback accretioniswidelyusedingalaxy-scalenumericalstudies,aswe n dointhiswork.Theaccretionrateestimatedfromthesimulations ras OotoruigirnisnculaubldgperrideksimcnreoitpditceilosfnefseodrbbByaHcSkpa.rcTicnhrgeeetilmoenatsaasnld.in(ffl2eo0ewd0b5a)r,actkweahoriefchbsuawsrreeodueonxndteitnnhdge micnauntshtbeaelUlaonnwiavlteyhrtesiceaBltHloydsastyho,ogwwrniotwhtihnfartoamafeBsweHe,GdeymmrabosersdetdsheetdoHitnhuabstbtaolerb-sfteoimrrvmea.ibnlIget /article-a gasontoacentralSMBHofmassM isparametrizedbytherate b given by Hoyle & Lyttleton (1939),BHBondi & Hoyle (1944) and gas(havingρ>ρSF)governedbytheSpringel&Hernquist(2003) stra effectiveequationofstate(Section2),accretingviaequation(1)has c Bondi(1952): amassgrowthtimetg∝1/α.Thetimetg islessthantheHubble t/43 M˙Bondi=α(cid:2)4cπs2,G∞2+MvB2H2(cid:3)ρ3∞/2. (1) ttmiimmaseesewasnh.deFnothlαleon≥wiit1ni0gs0tnh.eeWvseeitrahrpgaoussmsmibeanlleltestrtooαgmvroaimwluiect,httehgeBeaxHpcpetreoodptshriteahteoebHgsrueorbwvbetldhe 7/2/1456 IntheoriginalBondi–Hoyle–Lyttletonparametrization,ρ∞ isthe of BHs in our simulations, we adopt the Bondi–Hoyle–Lyttleton /110 gasdensityfarfromtheBH(or,atinfinity),cs,∞isthesoundspeed formulationwithaconstantmultiplicativefactorα=100. 30 inthegasfarfromBH,v isthevelocityoftheBHrelativetothe Furthermore,accretionislimitedtotheEddingtonrate,making 82 far-off gas, and the parameter α is analytically dependent on gas theresultantBHmassaccretionrate, by adiabaticindex(γ)withα=1/4forγ =5/3.Itwasoriginallyused (cid:2) (cid:3) gu toformulatecriticalastrophysicalaccretion,wheregasissubsonic M˙BH=min M˙Bondi,M˙Edd . (2) est o faraway,passesthroughasonicpointandaccretesontothecentral n objectwithasupersonicvelocity. Here,M˙EddistheEddingtonmassaccretionrate,expressedinterms 06 Theissueofcomputationalresolutionappears:currentstandard oftheEddingtonluminosity Ap gsucanalraleexssyo,lvhfoeedrnm.ceaTtthihoeengBsaiosmnudpliraortpiaoednritusiesrseasn(oρdl∞vseo,ncksip,c∞cp)toouins1te0d(0∼’isn10oe’fsqpuocaftiploecnn)ga(th1re-) LEdd = 4πGMσTBHmpc =(cid:2)rM˙Eddc2. (3) ril 2019 are estimated by smoothing on the resolution scale (smoothing Afractionoftheaccretedrest-massenergyisconsideredtobe length > a few 100pc) at the BH location. This results in arti- radiatedawaybytheBH,assumingradiativelyefficientaccretion. ficially low densities compared to spatially resolving the Bondi Theradiationluminosityis radiusscale.Furthermore,smallerscalesimulations(Barai,Proga & Nagamine 2012; Gaspari, Ruszkowski & Oh 2013) show that L =(cid:2)M˙ c2, (4) r r BH thecoolinggasismultiphase,withavariableaccretionrate.This cold phase of the ISM is not resolved in galaxy simulations. As with(cid:2) beingtheradiativeefficiencyfraction.Weadoptthemean r a numerical correction, the Bondi–Hoyle–Lyttleton accretion rate valueforradiativelyefficientaccretionontoaSchwarzschildBH inferredfromsimulationsisenhancedbysettingthemultiplicative (Shakura&Sunyaev1973):(cid:2) =0.1,whichiskeptfixed.Thisis r factor to α ∼ 100 (e.g. Springel et al. 2005; Sijacki et al. 2007; supported by recent sub-pc resolution simulations of Maio et al. DiMatteoetal.2008;Khalatyanetal.2008;Johansson,Naab& (2013), who found that possible values of radiative efficiencies Burkert 2009a; Sijacki, Springel & Haehnelt 2009; Dubois et al. shouldbebetween0.09−0.15. KineticAGNfeedback 1459 Afraction(cid:2) oftheradiatedenergyiseventuallyfedbacktothe Thisgivestheoutflowrateas f neighbouringgasasfeedbackenergyfromtheBH: c2 M˙ =2(cid:2)(cid:2)M˙ . (8) E˙ =(cid:2)L =(cid:2)(cid:2)M˙ c2. (5) w f r BHv2 feed f r f r BH w Using(cid:2) =0.05,DiMatteoetal.(2005)foundconsistentcorrelation f of BH mass and galaxy stellar velocity dispersion (the MBH−σ(cid:4) 2.2.2 Momentum-drivenwind relation),betweengalaxymergersimulationsandobservations.We considerthefeedbackefficiency(cid:2) asafreeparameterinourmodels. EnergyoutputisrelatedtothemomentumofradiationviaE=pc. f TherateofmomentumoutflowintheAGNwindisp˙ =M˙ v . WeexaminetwowaysinwhichtheBHfeedbackenergyiscou- w w w Equatingp˙ totheradiationmomentumfromAGNweget pledtothesurroundinggas. w E˙ (i) Thermal. We adopt the default scheme from Springel et al. p˙ =M˙ v = feed =(cid:2)(cid:2)M˙ c. (9) (2005).TheenergyE˙ isdistributedthermallytoheatupthegas w w w c f r BH feed D isotropicallyaroundtheBH.Thetemperatureoftheneighbouring ThisexpressesthemassoutflowrateintermsoftheBHaccretion o w gas particles (those contributing to equation 11 in Section 2.3) is rate nlo iFnocrreamgeanstpedartbicyleandeanmseoeunnotusgchalteodbbeymtuhletiirphSaPseHstkaerrnfoerlmwinegig,hthtse. M˙w=(cid:2)f(cid:2)rM˙BHvc . (10) aded excessspecificthermalenergydecaystoattainthespecificenergy w fro The main difference between energy-driven wind (EDW) and m oeqfuthaetieofnfe1c2tivoefSeqpuriantgioenl&ofsHtaetren,qounisatr2e0la0x3a)t:iontime-scaleτh(from m(c/ovme)n2tuanmd-d(cri/vven)iwnitnhdem(MasDsWou)tflioswtrhaeteoecqcuuartrioenncse(8)ofanfdac(1to0r)s. https τh= β(At(cid:4)+ρh1)ρc. (6) Hisennecweed,etdoihnavMeDthWwes:a(cid:2)mf,MeDMW˙w=in2b(cid:2)of,tEhDWca(sce/sv,wa)l.argerefficiencyfactor ://acade Hρeareret(cid:4)thisetdheenSsFititeimsoef-shcoatleaminbtiheenetfgfaesctaivnedmcoulldticplhoausdesm,roedspeel,cρtihvaenlyd, feeTdhbearcek:ar(cid:2)eftawnodfvrewe. TpyarpaimcaelteArsGNinwouinrdsuvbegloricditmyovdaeluleosfskeiennetiinc mic.o βcisthemassfractionofstarswhichareshortlivedandinstantly Qobusaetraveartti&onMsaare(2b0e1tw2)eceonnvsiwde=readfwewin1d0v0e0lo–c1i0ti0es00ofk3m00s−01,.7D00e0buahnrd, up.co dreiteuarnseSdNtoe,tAheishothtephefafisecidenuceytoofSeNveapfeoeradtbioacnko.fIfcothldelcolocauldcsotooinbge 10000kms−1 in their simulations of kinetic AGN feedback. The m/m radiativeefficiency(cid:2) (equations3,4)isheldatafixedvalue.We n BtiismHshetoh(rcetoremmratphluaftneeedτdhab,sasncuokmrmeinnaeglrgraayldl.itahteivpeacrtoioclleinmgaisssuissedintothdeishsoitpaptheatshee) vaacrlyotsheestfrmeeatpcahraomfethtererssi(m(cid:2)fu,lvawti)onwivtherinsurseaosbosnearbvaletiroannagle[sMtoBHo−btσai(cid:4)n] ras/artic relation(Section3.1),anddiscussthebest-fittingparameters. le (ii) Kinetic.Thegasvelocityisincreased,asdescribednext. -a b s tra 2.3 ImplementationintheGADGET-3code c 2.2 KineticAGNfeedback t/4 A BH is represented as a collisionless particle in the GADGET-3 37 Ionftvheelofcoiltlyowvinagn,dwmecaosnssoiudteflrothwatraBteHMf˙eed.Tbahcekednreirvgeys-acognasseoruvtafltioown code,havingadynamicalmassmBH,dyn,givenbysimulationres- /2/1 w w olution(Section2.4,Table1).Owingtothenumericsoflow-and 45 equationscanbewrittenusingthekineticenergyormomentumof 6 medium-resolutionsimulations(whereonemightneedtotrackBHs /1 theoutflowinggas,eachofwhichgivesoneAGNwindformalism. 1 ingalaxiescontainingsomehundredsofparticles),thereisanother 0 We consider one fixed value for v (a free parameter), which is 3 w variabledescribingtheBHmassinasmoothfashion,whichwecall 08 a simplified assumption of our models (intended to be applied to 2 cosmologicalsimulationsinthefuture),althoughmorephysically thesubgridmass,MBH.ThevaluemBH,dynisusedforthenon-AGN by theAGNwindvelocityshouldbeself-regulated(e.g.Gasparietal. physicsinthecode(e.g.gravitationalinteractions).MBHisusedto gu computetheAGNphysics(e.g.Bondirate,equation1),whichis e 2011a,b). s hencethetrueBHmass. t o Att=0inoursimulations,thecollisionlessparticleisseededwith n 0 2.2.1 Energy-drivenwind aBHhavinganinitialsubgridmassMBH =MBH,seed =105M(cid:3). 6 A The kinetic energy carried away by the wind is equated to the (Aetqueaactihonti2m)e,iststespub(cid:11)gtr,iditmgaroswsisncarcecaosredsinbgytaontahmeoBuHntaMc˙cre(cid:11)tiotn,wraitthe pril 2 BH 0 feedbackenergyfromBH: mBH,dyn remaining the same. The initial growth from MBH,seed to 19 1 mBH,dyn occurs in that way, without altering the surrounding gas 2M˙wvw2 =E˙feed=(cid:2)f(cid:2)rM˙BHc2. (7) distribution. After a BH has grown such that MBH ≥ mBH,dyn, it Table1. Galaxyinitialconditions.Column2:virialvelocity.Column3:totalmass(darkmatter+gas+stars).Column4:gasmass(disc).Column5:stellar discmass.Column6:stellarbulgemass.Column7:DMparticlemass.Column8:gasparticlemass.Column9:discstarparticlemass.Column10:BHparticle dynamicalmass.Column11:disc(gas+stars)scalelength. Series v200 Mtot Mgas M(cid:4),disc M(cid:4),bulge mDM mgas m(cid:4),disc mBH,dyn d name (kms−1) (M(cid:3)) (M(cid:3)) (M(cid:3)) (M(cid:3)) (M(cid:3)) (M(cid:3)) (M(cid:3)) (M(cid:3)) (kpch-1) Lowmass 75 1.40×1011 1.12×109 4.47×109 1.40×109 4.42×105 2.23×104 1.79×105 6.98×105 1.49 Fiducial 150 1.12×1012 8.93×109 3.57×1010 1.12×1010 3.53×106 1.79×105 1.43×106 5.58×106 2.99 Highmass 300 8.93×1012 7.15×1010 2.86×1011 8.93×1010 2.83×107 1.43×106 1.14×107 4.47×107 5.98 1460 P.Baraietal. mightaccrete(so-calledswallow)neighbouringgasparticles,using ThemergercriterionoftwoBHsiswhentheycomeinsidethe astochasticmethodology.Whenagasparticleisswallowed,itis s ofeachother,andtheirrelativevelocityissmallerthanthelocal BH removed from the simulation and m increases by the swal- soundspeed. BH,dyn lowed particle mass m . This conserves dynamical mass within gas thecomputationalvolume.Theprobabilityofswallowinggasisset 2.3.1 Detectholeingasdistributionandpreventitsgrowth toensurethatM andm trackseachotherclosely. Sucha BH BH,dyn proceduregrowstheBHinacontinuousfashionwithtime,increas- We implement a novel numerical algorithm in the GADGET-3code todetectandpreventtheexpansionofholeinthegasdistribution ingthemassM smoothly.ItalsoallowstotrackBHslessmassive BH around the BH. In the original version, there was a problem of thanm .HavingjustasingleBHmasswouldcreatesignificant BH,dyn holecreation,classicallydemonstratedbyaBHaccretinggaswith fluctuationsinm attheepochswhendiscretegasparticlesare BH,dyn no feedback at the centre of a rotationally supported disc galaxy. accreted,andwouldrenderimpossibletohaveacorrectBHmass TheBHwoulddepletethecentralgas,insideitssmoothinglength, inlessmassivegalaxies. by swallowing particles. In order to have a constant number of WedonotincorporateanyschemeforBHadvection(whichis D neighbours,s increasesaftersometimeencompassinggasfurther o done in some studies by e.g. reposition BH at minimum gravita- BH w out.Thenewgasisdepletedinturn,turningtheBHmoremassive, n tionalpotential),sinceourtestsobtainaBHdynamicsexpectedfor lo and creating an enlarging hole at the galaxy centre. The process a isolatedsystems.Inanisolatedgalaxytheseparationbetweenthe d BsoHfteannidngthleenmgitnhism,uwmhigleradvuirtaintigonaamlpeorgteenrttihaeliBsHalswdaeyvsilaetsesftrhoamntthhee tchoengtiansuoefstahdewinhfionlietugmal,awxyi,thunslBeHsseaxnteunpdpinerglifmuritthiesrimmoproesetodoacncsrBeHte. ed from potentialminimabyafewtimessofteningsomeofwhichisdueto Here,gasisartificiallyaccretedbecauseofthenumericalscheme, h mergerdynamics. andnotphysicallybecauseithasflowninward.Observedgalaxies ttp s Kernel-weighted quantities are computed smoothing over gas donotshowanyholeinthegasdistributionaroundtheircentralBHs, ://a thereforethecreationofsuchartificialholesaffectsthesimulated c particles in the local environment around the BH, using a kernel a havingthesameshapeasthatusedinSPHcalculations.However, evolutionofthegalaxyandAGNfeedbackinunwantedways. dem four times more neighbours are used for the BH particle, than in ThisissuehasbeenpresentinallthestudiesusingtheBHnu- ic the SPH (which has 32 ± 4 neighbours). The kernel size, or the mericalmethodologyofSpringeletal.(2005),demonstratedbythe .ou BHsmoothinglengths ,isdetermined(inanalogytofindinggas BHgrowingtoMBH>109M(cid:3)(theirfig.10)inano-feedbackrun. p.c particlesmoothinglengBtHh)byimplicitsolutionoftheequation Avisualexampleoftheholecanbeseeninfig.13ofWurster& om Thacker(2013b). /m 4πs3 ρ =M . (11) OnesolutionistosetamaximumsBHmanually,whichhowever nra 3 BH BH ngb isnotelegantbecausethevaluewouldvarywithresolution,galaxy s/a Here,ρ isthekernelestimateofthegasdensityatthepositionof massandadditionallytheenvironmentinacosmologicalsimula- rtic theBHaBnHdMngbisthemassof∼4×32neighbouringgasparticles. tion.Wehaveratherworkedoutacomputationalsolution,toprevent le-a preWsceriipmtipolnesmiennGtAaDpGrEoTb-3a)btiolisdtiicstrcirbiutetreiothne(ksiimneitliacrfteoeodtbhaecrkseunbegrrgiyd theOluimrintulemsseriinccarlemaseethoofdsoBHloignydeapsseunmdeensttohfatsitmheuBlaHtiolniecsoantdtihtieongas.s bstrac fromtheBHtotheneighbouringgas,i.e.particleswhosemasses density peak, or minimum SPH smoothing length (ssml) location. t/43 contributedtothetotalneighbourmassMngbinequation(11).Gas The existence of a hole around the BH is detected using the ssml 7/2 particlesarestochasticallyselectedfromtheneighboursandkicked distributionofneighbours.Withnohole,theminimumssmloccurs /1 4 intoAGNwind,byimpartingaone-timevwboost.Aprobabilityfor attheBHposition.Whenthereisahole,apreferentialboundaryis 56 beingkickediscalculatedinatimestep(cid:11)tforeachneighbouring createdatsBH,withafewerthanexpectednumberofgasparticles /11 ithgasparticle: inside.Thiscausesasmallincreaseinthessmlofneighboursnearest 03 0 wM˙ (cid:11)t totheBH,andtheminimumssmloccursatafinitedistancefromthe 82 pi = iρBwH . (12) BmHinilmocuamtiosnsm.lAolfsonesiBgHhbisouthrse.nmorethantwotimeslargerthanthe by gu Here, w = W(|r − r|, s ) is the SPH kernel weight of the Inourcodeimplementation,wedetectjustwhenaholeiscreated es gas partiicle relatiBvHe to thie BBHH, and M˙w is the mass outflow rate aroundaBHandcontrolit.Gasparticleslyingwithinamultipli- t on expressedbyequation(8)or(10)forEDWorMDW,respectively. cationfactordhtimessBHaresearchedtofindthenearestparticle’s 06 Notethatpiissimilartotheprobabilityforswallowinggasparticles smoothinglengthsnear,andtheminimumsmoothinglengthsmin.If Ap udunrifinogrmBlyHdaisctcrriebtuitoend(iSnptrhienginelteertvaall.[02,010]5,)i.sAdrraawnndoamndncuommbpearrexdi, erhit:herofthefollowingratioofsmoothinglengthsexceedsavalue ril 201 withp.Forx <p,thegasparticleisgivenawindvelocitykick.If s s 9 v isiparticlieveloicityandφ itsgravitationalpotential,thenafter sBH >rh, or, snear >rh, (14) old min min receivingAGNwindkick,itsvelocityisupdatedto thenaholeexists.Whenthisexistence-of-holeconditionismetfora vnew=vold+vwxˆ. (13) BH,itssBHisheldfixed,andnotallowedtoenlargefurther.Testing withasingleBHinanisolatedgalaxywefindtheworkingvaluesof Thedirectiongivenbytheunitvectorxˆissetalong(vold×∇φ)or− factorsas:d =4andr =1.7.Theholeislimitedtoasize∼(0.7– (vold×∇φ), randomly selected between the two. This makes the 0.8)h−1kpchsuccessfullhy.Allourisolatedandmergersimulations windparticlestobepreferentiallyejectedalongtherotationaxisof aredoneusingthesevaluesinthehole-detectionalgorithm. thegalaxyorperpendiculartothegalaxydisc.Someotherstudies (e.g.Tescarietal.2011;Baraietal.2013)implementhydrodynamic 2.4 Initialgalaxymodels decouplingofthewindparticles.Unlikethosewedonotallowany decoupling, i.e. in this work the AGN wind particles are always The initial isolated galaxy models are constructed following the coupledandundergohydrodynamicinteractions. approachdescribedinSpringel&White(1999)andSpringeletal. KineticAGNfeedback 1461 (2005).ThetotalgalaxymassM =v3 /(10GH )isexpressed (iv) kinM1–kinM4.FourrunsofkineticfeedbackfromBHwith tot 200 0 intermsofthecircularvirialvelocityv200.AHubbleparameterof MDWprescription(Section2.2.2),usingcombinationsof(cid:2)f=0.25, H0=70.3kms−1Mpc−1,orh=0.703(e.g.Komatsuetal.2011), 1.0,andvw=1000,2500,5000kms−1. isadopted.EachgalaxyiscomposedofaDMhalo,arotationally Thefiducialgalaxy(v =150kms−1)issimulatedusingallthe supported gaseous and stellar disc comprising of a fraction f = 200 d aboveparametercasesforbothisolatedgalaxyevolution(indicated 0.04ofthetotalmass,andacentralstellarbulgeofmassfraction byletter‘I’inTable2,columns5,6,7)andgalaxymerger(indicated f =0.01.ThemassdistributionoftheDMhaloismodelledwith b byletter‘M’inTable2).Theparametersetofeachcategorywhich theHernquist(1990)profile,andhasaspinparameterofλ=0.04. generatesaclosestfittoobservationsisalsorunwiththelowermass The disc has a mass fraction fgas = 0.2 as gas, and the rest as (v = 75kms−1) and higher mass (v = 300kms−1) galaxy stars; both components are modelled with an exponential surface 200 200 models.Theisolatedgalaxiesareevolveduptoatime2Gyrand densityprofileofradialscalelengthdandradiallyconstantvertical thegalaxymergersupto3Gyr. scaleheightz =0.2d.Thesphericalstellarbulgeismodelledwith 0 aHernquist(1990)profilehavingascalelengthb=0.2d. D o We simulated galaxies of three masses. Our fiducial galaxy 3 RESULTS AND ANALYSIS w n iMs ge=nera1t.e1d2 u×sin1g012v2M00(cid:3)=, a1s5i0mkimlars−m1,aswshaicshthceorMresilpkoyndWsatyo. WecomparetheBHmass(MBH)versusgalaxystellarvelocitydis- load Fv2ut0or0tth=erm75okrem, sw−e1 asnimdualahtieghgearlmaxaisesswhiatvhinvg200a=lo3w0e0rkmmass−s1.wTihthe pcoerrrseiolanti(oσn(cid:4),)urseisnugltasmobatnauinaeldchini-boyu-reysiemauplpartiooancsh.wTithhisthceomobpsaerrivsoedn ed from numberofparticlesofvarioustypesintheinitialconditionofeach isconsideredasthefigureofmeritinordertoobtainthebest-fitting h galaxy are: 3 × 105 DM, 5 × 104 gas, 25 × 103 disc stars and parameters for each AGN feedback model. The fiducial galaxy ttps 25×103 bulgestars.Table1liststherelevantmasscomponents (v200=150kms−1)issimulatedusingseveralparametervariations ://a and particle masses of all the galaxies. New star particles form inaseriesofruns(Section2.5),eachforisolatedandmergerevolu- ca d tion.Theparametersetofeachcategorywhichgenerateaclosestfit e during the simulation (via SF in the gas), which are less mas- m spiavreticthleasn(tDhMei,ngitaisalasntdelslatarrsp)arftoilclloewsicnoltlhiesiodnislcesasngdrabvuiltgatei.onAallldthye- taorethseeloebctseedrv.aTtihoensaelc[hMoBseHn−cσa(cid:4)s]ersealarteioanlsaotrtuhnefiwdituhcitahleglaolwaxeyrmmaassss ic.ou namics,whileinadditionthegasparticlesundergohydrodynamical (v200 = 75kms−1) and higher mass (v200 = 300kms−1) galaxy p.co models. m ginetnAeerarcacottleilodisniasot.ntlheesscternatcreeropfaratigclaelaoxfymtoascsafrraryctitohnefSBMHB=H5.×Th1i0s−c6oirs- galAaxllytmheorrpuhnoslopgeirefsorimneSdecatiroenp3r.e2s,ewnteedchionosSeecmtioodnel3s.g1e.nFeorartitnhge /mnras fimredsaupscsoi.naTdlhsgeatoBlaaHxydp)yanwrathimcicliehcaisilstBh∼Hu1s.pe6axrtptiiemccleteesdmhtiaogshstrea(r5c.te5ht8ahne×tmh1ei0n6DimMMu(cid:3)mpaionrftiotchuleer asbaemctwoemerepengartihoabenrleomfaBtlhHaen[mdMkaBsinHs,e−tiiσ.ce(cid:4).f]etdehdieabgaBrcaHkmsw.iCinthotndhsieefsfqeeureecnnattsle(cid:2)ysf,,webxeeicscatoumisnepttahhreee /article-a respectivebest-fitting(cid:2) areunequal.Resultsinremainingsections bs gtiroanv.iItantitohneaAlGpoNtesnitmiaullcaltoiosenlsy,,amBinHimofiziinnigtiaalrtsiufibcgiarilddmynaasms1ic0a5lMm(cid:3)o- onlyshowtheclosestfiftmodels,plusafewcaseswithvarying(cid:2)f trac andv .Notethatourapproachexploresparameterswhichfitthe t/4 isseededinthistracerparticle. w 3 ThePlummer-equivalentsofteninglengthforgravitationalforces [MBH−σ(cid:4)] relation. This however renders difficult to perform an 7/2 ifsorsethtetoDLMsofatn=d0B.5H/hpakrpticclfeosr.tThheegmasinanimdusmtarSpPaHrtiscmleoso,tahnidng1/lehnkgpthc arebsspoelcuttievecoomutppaurtispoonwoefrsthaerremdaiflfevreernsut,saksidneesticcrifbeeeddbinacSke,cstiinocne3t.h3e. /1456 issettoafraction0.001ofL . Weanalysethecarboncontentofthegasinthegalaxies,since /11 soft 0 Astheinitialconditionsforthemergersimulations,twoequal- itisoneofthemostabundantheavyelementintheUniverse,and 30 massisolatedgalaxiesaregeneratedusingafixedv .Theorbital the spectral lines produced by ionized carbon are relatively easy 82 200 to observe. The carbon metallicity, Z , is computed as the ratio b planes of the two discs are kept the same, and they are set on a C y of carbon mass to the total particle mass for each gas particle. g paraboliccollisioncourseinthediscplane.Aminimumseparation u e amtawssheisc)histhteakgeanlaaxsie2s.5w/ohu,ld5/phasasndat1p0e/rhickepnctr,ere(isfpethcetiyvewlye,refoprotihnet AwhbuicnhdiasnZceC,(cid:3)rat=ios0a.0re02e1x7p7re(smseadssifnratcetrimonsooffcathrbeosnoilnarSmune)tadlelriciviteyd, st on fromthecompilationbyAsplund,Grevesse&Sauval(2005). 0 lowermass,fiducialandhighermasscases. 6 A p 2.5 Simulations 3.1 [MBH−σ(cid:3)]correlation ril 201 Table 2 lists the series of simulations we perform. The different Thegalaxystellarvelocitydispersionσ(cid:4)iscomputedbyconsider- 9 ingallthestars:thosenewlyformedduringthesimulationevolution runsincorporatethesamenon-AGNsubgridphysicsdescribedin bySFfromgas,thediscandbulgestellarcomponentspresentfrom Section2andinvestigatedifferentAGNfeedbackmodels.Theyare theinitialcondition(Section2.4,Table1).ThepositionoftheBH chosen from four broad categories, as given below, exploring the is taken as the galaxy centre, and the distances (or radii) of star modelparameterspace. particlesareestimatedfromit.Inthecaseofmerginggalaxiesthe (i) SF.OnerunwithSF,stellarevolutionandchemicalenrich- calculationsaredoneatatimewhentheBHshavemergedtopro- mentonly(noBH). duceasingleBH,definingauniquegalaxycentre.Thecumulative (ii) th1–th3. Three runs of thermal feedback from BH (Sec- sumofallstar’smassversusradiusisfound,aswellastheradius tion2.1),using(cid:2)f =0.002,0.01and0.05. R1/2containing1/2ofthetotalstellarmass.Thisstellarhalf-mass (iii) kinE1–kinE6. Six runs of kinetic feedback from BH with radius is considered as the effective radius in estimating σ(cid:4). 100 EDWprescription(Section2.2.1),usingcombinationsof(cid:2) =0.01, randomline-of-sight(LOS)directionsarechosenaroundthecentre f 0.05,0.25,andvw=5000,10000kms−1. (or,BHposition).AllthestarslyingwithinR1/2fromthecentreare 1462 P.Baraietal. Table 2. Simulation parameters. Column 1: name of simulation run. Column 2: feedback efficiency,(cid:2)f =fractionoftheradiatedenergyfromBHwhichiscoupledtothesurrounding gas.Column3:vw=outflowvelocityinkineticfeedbackprescription.Column4:specifications ofAGNfeedbackmodel.Columns5,6,7:letters‘I’(isolatedgalaxyevolution)and/or‘M’ (galaxymerger)arewrittenbelowlowermass(v200=75kms−1),fiducial(v200=150kms−1) andhighermass(v200=300kms−1)galaxymodels,wherevertheparametersetintherowhas beenrunwiththecolumninitialconfiguration. Run (cid:2)f vw AGNfeedback Lowermass Fiducial Highermass name (kms−1) SF NoBH I,M th1 0.002 BHthermal I,M th2 0.01 BHthermal I I,M I D o th3 0.05 BHthermal M I,M M w n lo kinE1 0.01 5000 BHkinetic:EDW I,M a d kinE2 0.05 5000 BHkinetic:EDW I I,M I e d kinE3 0.25 5000 BHkinetic:EDW M I,M M fro kinE4 0.01 10000 BHkinetic:EDW I,M m kinE5 0.05 10000 BHkinetic:EDW I,M h kinE6 0.25 10000 BHkinetic:EDW I,M I,M I,M ttps kinM1 0.25 5000 BHkinetic:MDW I,M ://a c kinM2 1.0 5000 BHkinetic:MDW I,M ad e kinM3 1.0 2500 BHkinetic:MDW I I,M I m kinM4 1.0 1000 BHkinetic:MDW M ic.o u p .c pickedandtheLOSvelocitycomponentofeach,vLOS,isfound.The kineticEDW),alsowhenvwisdecreased(kineticEDW).However, om stellar velocity dispersion along each LOS direction is computed thereisareversaloftrendswithkineticMDW;atv =5000kms−1 /m w bysummingoverallrelevantstars MBH decreases as the efficiency rises from (cid:2)f = 0.25 to 1, but nra σ(cid:4)=(cid:2)(cid:10)vL2OS(cid:11)−(cid:10)vLOS(cid:11)2(cid:3)1/2. (15) wMhBeHnin(cid:2)cfreisasseestratothe1r,atshevwsmisarleldesutceBdHfumrthaessrtpor2o5d0u0cekdmiss−M1.BEHve∼n s/artic The same is done for the 100 LOS directions. The median and 2.5×108M(cid:3)withvw=5000kms−1inafiducialgalaxyrun.With le-a v =1000kms−1theBHgrowsdrasticallytoM ∼2×109M(cid:3). b percentile of the 100 random direction σ(cid:4) values are found and TwhishappensbecauseinthemergingsystemsucBhHavelocityisnot stra shownasourresults. c Fig.1presentstheMBHversusσ(cid:4)diagramobtainedinoursim- hniegahrtehneoBugHh(sto)arnedmiosvaectchreetgeads.Tawhuasy,,wbuetfithnedkthicakteitdigsansoftapllossbsiabclke t/437 uevlaotliuotnios.nTtihmeele2fGt-hyar.nTdhpearnieglhst-hhoawndstphaeneisloslhaotewdsgthaleagxaylacxaysemseartgaenr tofind(cid:2)fandvwvaluestofittheobservational[MBH−σ(cid:4)]relation /2/14 with MDW prescription of BH kinetic feedback in the case of a 5 runsatatime2.5Gyr,anepochbywhenthetwoBHsmergeinall 6 the cases. The median σ(cid:4) is depicted by the plotting symbol and galaxymerger. /110 70thpercentilesaroundthemedianareindicatedbythelowerand 30 8 uppererrorbars.ObservationaldataareoverplottedinFig.1asthe 2 3.2 Galaxymorphologyandoutflow b straightlines.Thesolidanddashedlinesdisplaythebest-fittingre- y g lationsanderrorbarsobtainedbyTremaineetal.(2002)areshown Thegalaxymorphologyandoutflowstructureofthreerepresenta- u e inblackandGultekinetal.(2009)inorange. tiveisolatedcasesareplottedinFig.2atanevolutiontime1.73Gyr. st o Thebest-fittingparametersthatweobtainfortheisolatedgalaxy Itisafiducialgalaxywithdifferentfeedbackmodels:SF(lefttwo n nevvewotil=cutiE1oD0nW0a0r0ef:kemefodrsb−aB1ckHwivtthhwer(cid:2)=mfa=l50f00e.e02d5kb;maacsnk−d1(cid:2)ffwo=ritBh0H.(cid:2)0f1k;i=nfeot0ric.0BM5HDaknWid- cfbeoaecldukbmwanciskt)hE–(cid:2)DfSWF=ow0n.il0ty0h,2t(cid:2)hfa1n=d(m0k.ii0dn1dE,l1evwt(wri=goh5cto0tl0wu0mokncmos)lsu–−m1B.nHIsn)tt–hheeBrmlHatatkleirfneteewtdioc- 06 April 2 nfeeeadrbnaecsskovfwth=e 2si5m0u0lkamtiosn−1rewsuilttht(cid:2)oft=he1o.bEsesrtvimataiotinnaglb[My-BeHye−σth(cid:4)e] (rufrnosmthFeigB.H1)s.grow to a comparable mass MBH ∼ 1.5 × 107M(cid:3) 019 relation at a given galaxy mass, we find mass dependence of the Thegasdiscofthegalaxyretainsitsidentityinalltheruns,visible relativefitgivenbyasetofparameters,moreprominentlyforthe as a well-defined rotating disc in the central r = (10–20)h−1kpc isolatedgalaxythanthemergercase.ThefinalBHmassesofthe regions.ThereisnooutflowintheSFcase.Thermalfeedback(run fourbest-fittingcasestendtoberelativelysmallerthantheobser- th1) produces a weak outflow with some gas going out to (30– vationsforthehighermassgalaxyandlargerthantheobservations 40)h−1kpc,butlaterintimemostoftheoutflowinggasfallback forthelowermassgalaxy. to the disc. Kinetic feedback (edge-on plane of kinE1) produces We obtain the following best-fitting parameters for the galaxy a well-developed bipolar gas outflow propagating perpendicular merger: for BH thermal feedback (cid:2) = 0.05; and for BH kinetic to the galaxy disc, escaping to r > 100kpc from the central BH f EDW feedback v = 5000 or 10000kms−1 with (cid:2) = 0.25. For position,seeninthetopmost-rightpanel,astheredarrowsupward w f BHkineticMDWfeedback,noneoftheparametersweexploredfit anddownwarddirected. theobservations;theBHmassisalwaystoolarge.Inthecaseof Thegasdensity,temperatureandcarbonmetallicityareplottedin otherfeedbackmodels,M reduceswhen(cid:2) isincreased(thermal, thesecond,thirdandfourthrowsofFig.2,respectively.Alltheruns BH f KineticAGNfeedback 1463 D o w n lo a d e d fro m h ttp s ://a c a d e m ic .o u Figure1. BHmassversusgalaxystellarvelocitydispersionalongLOS.Thesingleisolatedgalaxymodels,shownatanevolutiontimeof2Gyr,arein p .c theleft-handpanel.Themergersimulations,shownatanevolutiontimeof2.5Gyr,areintheright-handpanel.Thedifferentcoloursandplottingsymbols o m distinguishtheAGNmodelsaslabelledineachpanel.Eachofthefourbroadcategoriesoffeedbackisdenotedbyadifferentcolour:[th1–th3]thermal–red, /m g[krieneEn1.–TkhienEp3a]rakmineetetirccEhDoiWceswairtehrvewpr=ese5n0t0ed0kbmytsh−e1p–lobttliuneg,[skyimnEb4o–lsk:in(cid:2)Ef6=]0k.i0n0e2tic–EaDstWeriswki,t(cid:2)hfv=w0=.0110–0t0r0iaknmgles−,(cid:2)1f–=cy0a.0n5,[–kifinlMle1d–ckiirncMle4,](cid:2)fki=ne0ti.c25M–DoWpe–n nras sbqeusta-rfiet,ti(cid:2)nfg=re1lat–ioonpseanncdirecrlreo,r(cid:2)bfa=rso1batnaidnevdwf=rom25o0b0skemrvast−io1n–sfibylleTdredmiaaminoenedt,a(cid:2)lf.=(20102an)d–vbwlac=k1an0d00Gkumltesk−i1n–etcarlo.s(s2.0T0h9e)s–oolirdanagned.dashedlinesdisplaythe /artic le -a b haveacentraloverdenseregion,theouterhalfofwhichcorresponds thediscplaneandoutflow,inallthemodelsincludingtheSFcase. s to a cold, annular ring composed of gas cooling in the disc, on BHfeedbackinducesenhancedgasoutflow:moreinrunth3than trac the way to SF. There is a large central concentration of metals, SF,andhighestinrunkinE3.Eachmerginggalaxyinalltherunsex- t/4 3 originatingfromSF,inalltheruns.Themetallicitydistributionis hibitspiralpatternscomposedofoverdensegas.Thespiralpatterns 7/2 morecentrallyconcentratedinSFandth1cases.Kineticfeedback aresomewhatdisturbedwithkineticBHfeedback.Thestellardis- /1 4 carriessomemetalsoutfromtheSFregionsandenrichtheCGM tributionisalmostindistinguishablebetweenthefeedbackmodels 56 andIGMto>100kpc.Aremarkablespiralpatternisvisibleinthe hereat1.59Gyr. /11 face-onZ distributioninthefourthrow,fifthcolumnpanel. Thebottomtworows(t=2.31Gyr)ofFig.3showtheresulting 03 C 0 ThebottomrowofFig.2depictstheprojectedstellarmass,where mergedgalaxyatanepochduringcoalescence.Itconsistsofacen- 82 allstars(disc,bulge,newlyformedinsimulationfromgasparticles tralcompactspheroidandtwotidaltailsofoverdensegas(visible by byactiveSF)havebeencounted.Theedge-onplaneshowstheco- asredinthethirdrow,tailsmoreprominentinSFandth3runs). gu e existence of a disc-like and a bulge-like stellar components. The Thereisadiffusegaseoushalolargerinsize,whichismorespheri- s stardistributionisindistinguishablebetweenthethreeruns. callyshapedintheSFcase,andquitedisturbedgivinganirregular t on Fig.3presentstheprojecteddistributionsofgasandstarsinthe appearancewithkineticfeedback.Thestellardistributiondisplaya 06 fiducial galaxy merger with three representative models: SF (left fewdifferencesbetweenthemodelsat2.31Gyr:central30h−1kpc A p twocolumns)–SFonly,th3(middletwocolumns)–BHthermal radiusoftheface-onpanelsexhibitmoresphericallyshapedstruc- ril 2 feedbackwith(cid:2) =0.05andkinE3(righttwocolumns)–BHkinetic tureintheSFcase,thenth3,andmoreellipticallyshapedinkinE3. 0 f 1 feedbackEDWwithv =5000kms−1and(cid:2) =0.25.Inthelatter 9 w f tworunstheBHsgrowtoacomparablemassM ∼7×106M(cid:3) BH 3.3 Blackholeaccretionrate,feedbackpower (fromFig.1).TheintermittentgasoutburstsproducedbyBHkinetic andstarformationrate feedback,whichwereclearlydistinguishableintheisolatedgalaxy, are difficult to disentangle in a merger, because other dynamical TheBHmassaccretionrateisanimportantquantityinthemodels, processes related to the merger process cause substantial gas to whichgovernsBHgrowthaswellasprovidesfeedbackenergyin outflow. a self-regulated manner. It is measurable in observations, which The top two rows (t = 1.59Gyr) of Fig. 3 depict an epoch canbecomparedtosimulationresults.ThetimeevolutionofBlack whenthegalaxiesareapproachingeachother,onthewaytotheir Hole Accretion Rate (BHAR) in our fiducial isolated galaxy is second pericentre passage and subsequent coalescence. Earlier at presentedinFig.4,top-leftpanel.Att=0,wefindanaccretion t∼0.4Gyrthemerginggalaxypairgoesthroughafirstpericentre surgeof0.002M(cid:3)yr−1becauseofoursimulationinitialcondition. passageduringwhichthereisagrazingcollisionoftheouterdiscs. Embedding a 105M(cid:3) BH in the gas-rich environment of a disc Theresultingshocksandtidalinteractionscausesomegastoleave galaxycentresuddenly,resultsinahighaccretionrate.Itreduces 1464 P.Baraietal. D o w n lo a d e d fro m h ttp s ://a c a d e m ic .o u p .c o m /m n ra s /a rtic le -a b s tra c Figure2. Projectionofgaskinematics(topfourrows)andstars(bottomrow)inisolatedfiducialgalaxysimulationwithdifferentfeedbackmodels:SF(left t/4 3 tt(cid:2)rwfao=cecr0op.l0ua1rm,tivncwsle)=i–n5Sth0Fe0o0SnFklmyr,ustnh−)11a.(tTmthiimeddeplaten=2el1sco.s7lh3uomGwnytsrh.)eF–fiarBsctHer-ootwhne(drlmeefpati)lcaftsenedthdeebdavgceekl-oowcniitt(yhrivg(cid:2)ehfct=t)opr0lsa.0on0fe2s20oafnpader(k1ci0ne0Enth1o−(f1riakglplhctth)t3ewvgooalcsuopmlauermticcnelsne)tsr–ewdBitaHhrionkuitnnhdeettiphcreofBejeeHcdtbe(aodcrvkcooEllulDmisWieo,nwwleiistthhs 7/2/145 6 theoutflowing(vr>0)particlesdenotedasredandtheinflowing(vr<0)asblack.Secondrowshowsgasdensity,thirdrowisgastemperatureandfourthrow /1 1 isgascarbonmetallicity,allprojectedvalues,colourcodedfromredasthehighestandblackasthelowest.Bottomrowpresentstheprojectedstellarmass, 0 3 countingallstars(disc+bulge+newlyformedinsimulation). 0 8 2 b by100timessoonafter,becauseofreducedcentralgas,whichhas toBHAR,att=0thereisaninitialburstofSFRof6M(cid:3)yr−1.It y g u depletedbytheinitialburstofaccretionandSF.From0.02Gyr,the reducesafterwardviadepletionofcentralgas,andthenincreases e s BHARriseslinearlyuptoatime(0.5−0.7)Gyrtoreachafewtimes again. The SFR decreases linearly after 0.5Gyr, as more gas in t o 0.001−0.01M(cid:3)yr−1,thedurationcoincidingwiththeexponential the galaxy is converted to stars, to reach 1.5M(cid:3)yr−1 at 2Gyr. n 0 6 massgrowthoftheBH(Section3.4,Fig.5top-leftpanel).Thereare ThereareperiodicfluctuationsintheSFR,whenitwoulddecrease A hbeyaavyfaflcutoctruoaftiounpstion1th0e0BinHA0.R02,wGhyer.reTbhyeitBiHncAreRasienstoerrmdescroefasthees sbtyelalafraecvtoorluotfio(n1.m1−od2e),l.oAccllurtrhiengAbGeNcaumsoedoeflsSsNheowfeethdebsaeckgeinnetrhael pril 2 0 Eddingtonmassaccretionrate(equation3)alsodisplayssignificant trendssimilarly.ThermalfeedbackproducesalmostthesameSFR 19 variability, especially at t > 0.5Gyr. M˙BH/M˙Edd varies between astheSFrun.Kineticfeedback,moreprominentlytheEDWmodels, 10−3−1forthethermalfeedbackmodels,whilebetween10−5−1 produceupto1.5timeslowerSFRthantheSFandthermalcases forkinetic. att>0.9Gyr. Thefeedbackenergyrate(E˙feed,equation5)isplottedinFig.4, Thetop-rightpanelofFig.4depictstheBHmassaccretionrate middle-leftpanel.Asexpectedthefeedbackpowerhassametrends timeevolutioninthefiducialgalaxymerger,withtheratessummed asBHAR;however,theabsolutevalueofE˙feedisdifferentdepend- overeachofthetwomergingBHsinitiallywhentheyareseparate. ing on (cid:2)f. At t < 0.5Gyr, when the BH mass is small, higher (cid:2)f Notethattheparametervaluesoftheplottedlinestylesarediffer- producesalargerpower.Forthesamefeedbackmodel,theimpact entbetweenisolatedandmergercases.Mostofthefeaturesofthe ofvarying(cid:2)freducesatt>0.5Gyr,astheBHsgrow,andtheBHAR BHARinthemergeraresameasthatoftheisolated.Theamplitude becomesadominatingfactorinE˙feed. of fluctuations (change by a factor of up to 1000 in 0.02Gyr) is Thetotalstarformationrate(SFR)inthefiducialisolatedgalaxy larger in a merger than isolated case, because of extra dynamical versustimeisdisplayedinthebottom-leftpanelofFig.4.Similar processes(tidalforces,shocks)actingonthetwomerginggalaxies. KineticAGNfeedback 1465 D o w n lo a d e d fro m h ttp s ://a c a d e m ic .o u p .c o m /m n ra s /a rtic le -a b s tra c Figure3. Projectionofgasdistributionandstarsinfiducialgalaxymergersimulationwithdifferentfeedbackmodels:SF(lefttwocolumns)–SFonly,th3 t/4 (Tmhiedpdalenetwlsoschoolwumthnes)fa–cBe-Honth(elerfmt)aalnfedeeddbgaec-kowni(trhig(cid:2)hft=)p0la.0n5esanodfaki(n1E030(hr−ig1hktptwc)o3cvoolluummnesa)t–tiBmHek1i.n5e9tiGcyfereidnbtahcektoEpDtWwowriothwvswan=d5a0(02000kmh−s1−k1pacn)d3(cid:2)vfo=lum0.e25at. 37/2/1 t=2.31Gyrinthebottomtworows.Projectedgasdensityisplottedinthefirstandthirdrows,andprojectedtotalstellarmassinthesecondandfourthrows. 45 6 /1 1 0 The vertical dashed and solid black lines in the right-hand pan- startingfrom0.9Gyr;thereductionfactorswithrespecttotheSF 3 0 (etls∼o1f.8F6igG.y4r)mpaerrkicethnetreeppoacshsasgoefsofifrstthe(ttw∼o0g.a3l6axGieysr,)wahnidchseoccocnudr caansdeianreM:D5−W30mtoimdeelssi(ngEreDenW),m10o−de1l0s0wtiitmhevswf=or5E0D0W0kmmosd−e1ls(bwluiteh) 82 by ataconcurrenttimeforthedifferentfeedbackmodels.Thegalaxies vw=10000kms−1(cyan). gue mergeatthesecondpericentreepoch,whiletheBHsundergoathird s andsomesubsequentpericentresbeforemerging. t on ThefeedbackpowerinthemergerisinFig.4,middle-rightpanel. 06 Its dependence on BHAR and (cid:2)f is similar to that in an isolated 3.4 Galaxymasscomponents Ap galaxy. ThemassesofBHandgascomponentsintheisolatedfiducialgalaxy ril 2 Thebottom-rightpanelofFig.4showsthetotalSFRinthefidu- modelsversusevolutiontimeisplottedinFig.5.Theleft-handpanel 01 9 cial merger versus time, with the rates summed over each of the presentstheBHmass,whereallthefeedbackmodelshavetheBH two galaxies. The initial features of the SFR in the merger case growinginaqualitativelysimilarmanner.Startingfromaseedmass arethesameasthatoftheisolated.Thestellarevolutioninduced of105M(cid:3),eachBHfirstundergoesaslowgrowth.Itthenhasan fluctuations have larger amplitudes at t> 1Gyr in a merger than exponentialgrowthoverthetimerange(0.5−1)Gyr,whenitsmass an isolated galaxy. The SFR decreases linearly from 0.9Gyr to increases by a factor of 10 to a few 100. After 1Gyr it comes to (1.6−1.7)GyrreachingalocalminimumdependingontheAGN analmoststeadystate,havingaveryslowsubsequentgrowth.The model. It rises subsequently because of additional gas inflow to finalBHmassreachedat2GyrdependsontheAGNmodel,and densecentralregionsofthemerginggalaxies,andpassesthrough is inversely proportional to (cid:2) and directly proportional to v . A f w alocalpeakatt=1.86Gyrduringthesecondpericentrepassage. higher (cid:2) imparts a stronger feedback affecting more central gas, f Itreachesanotherpeakat(2.1−2.2)Gyr,anddecreaseshenceforth andyieldsalessmassiveBHthanalower(cid:2) .Onincreasingv ,M˙ f w w bygasdepletion.Att>2Gyr,thermalfeedback(redcurves)pro- decreases(inverseproportionalityinequation(8)forEDWand(10) duceslowerSFRthantheSFrun(blackcurve)byafactorbetween forMDW),thereisreducedkineticfeedbackandlessgasisejected (1.5−10). Kinetic feedback causes a greater suppression of SFR, out,makingmoregasavailableforaccretingontoBHwhichgrows