Simulations of the Sunyaev-Zeldovich Effect from Quasars

发布时间：2024-11-25

Mon.Not.R.Astron.Soc.000,000–000(0000)Printed2August2008

A(MNLTEXstyle lev2.2)

SimulationsoftheSunyaev-ZeldovichE ectfromQuasars

1212

SuchetanaChatterjeeTizianaDiMatteo,ArthurKosowsky&IntiPelupessy1

DepartmentofPhysicsandAstronomy,UniversityofPittsburgh,Pittsburgh,PA15260USA

CenterforCosmology,CarnegieMellonUniversity,Pittsburgh,PA15213USA

arXiv:0808.0268v1 [astro-ph] 2 Aug 2008

2McWilliam’s

2August2008

ABSTRACT

Quasarfeedbackhasmostlikelyasubstantialbutonlypartiallyunderstoodimpactontheformationofstructureintheuniverse.ApotentialdirectprobeofthisfeedbackmechanismistheSunyaev-Zeldoviche ect:energyemittedfromquasarheatsthesur-roundingintergalacticmediumandinduceadistortioninthemicrowavebackgroundradiationpassingthroughtheregion.Hereweexaminetheformationofsuchhotquasarbubblesusingacosmologicalhydrodynamicsimulationwhichincludesaself-consistenttreatmentofblackholegrowthandassociatedfeedback,alongwithradiativegascoolingandstarformation.Fromthissimulation,weconstructmicrowavemapsoftheresultingSunyaev-Zeldoviche ectaroundblackholeswitharangeofmassesandredshifts.Thesizeofthetemperaturedistortionscalesapproximatelywithblackholemassandaccretionrate,withatypicalamplitudeuptoafewmicro-Kelvinonangularscalesaround10arcseconds.Wediscussprospectsforthedirectdetectionofthissignalwithcurrentandfuturesingle-dishandinterferometricobservations,in-cludingALMAandCCAT.Thesemeasurementswillbechallenging,butwillallowustocharacterizetheevolutionandgrowthofsupermassiveblackholesandtheroleoftheirenergyfeedbackongalaxyformation.

Keywords:cosmicmicrowavebackground–intergalacticmedium–galaxies:active.

1INTRODUCTION

Thetemperature uctuationsinthecosmicmicrowavebackground,asmeasuredbytheWilkinsonMicrowaveAnisotropyProbe(WMAP)satellite(Bennettetal.2003)andnumerousothermicrowaveexperiments(e.g.,Dawsonetal.2002;Rajguruetal.2005;Reichardtetal.2008)haveproventobethesinglemostpowerfultoolinconstrainingcosmology(Spergeletal.2007).Thetemperatureanisotropyhasbeenmappedwithlargestatisticalsigni canceonangu-larscalesdowntoaroundaquarterdegree,wherethedom-inantphysicalmechanismscontributingtothe uctuationsarisefromdensityperturbationsattheepochofrecombina-tion.Attentionisnowturningtoarcminuteangularscales,wheretemperature uctuationsariseduetointeractionofthemicrowavephotonswithmatterinthelow-redshiftuni-verse(forabriefreview,seeKosowsky2003).Theselow-redshiftandsmall-angleanisotropiesarecollectivelyknownas“secondaryanisotropies”inthemicrowavebackground.ThemostprominentamongthemistheSunyaev-Zeldovich(SZ)e ect(Sunyaev&Zeldovich1972)fromtheinverseComptonscatteringofthemicrowavephotonsduetohotelectrons.TheSZe ectprovidesapowerfulmethodfordetectingaccumulationsofhotgasintheuniverse(Carl-stromHolder&Reese2002).Galaxyclusters,whichcon-tainthemajorityofthethermalenergyintheuniverse,

providethelargestSZsignal;clusterswere rstdetectedthiswaythroughpioneeringmeasurementsoverthepastdecade(e.g,Marshalletal.2001)andthousandsofthemwillbedetectedbytheupcomingSZsurveysliketheAta-camaCosmologyTelescope(ACT)(Kosowskyetal.2006)andtheSouthPoleTelescope(SPT)(Ruhletal.2004).However,anumberofotherastrophysicalprocesseswillalsocreateSZdistortions.ThisincludesSZdistortionfrompe-culiarvelocitiesduringreionization(McQuinnetal.2005,Illievetal.2006),supernova-drivengalacticwinds(Majum-dar,Nath,&Chiba2001),blackholeseededproto-galaxies(Aghanim,Ballad&Silk2000),kineticSZfromLymanBreakGalaxyout ow(Babich&Loeb2007),e ervescentheatingingroupsandclustersofgalaxies(Roychowdhury,Ruszkowski&Nath2005)andsupernovafrom rstgenera-tionofstars(Oh,Cooray,&Kamionkowski2003).TheSZdistortioningalacticscales(hotprotogalacticgas)havebeenstudiedbydi erentauthors(e.g,deZottietal.2004,Rosa-Gonz’alezetal.2004,Massardietal.2008).HereweinvestigateonegenericclassofSZsignals:thehotbubblesurroundingaquasarpoweredbyasupermassiveblackhole.ProbingblackholeenergyfeedbackviaSZdistortionsisonedirectobservationalroutetounderstandingthegrowthandevolutionofsupermassiveblackholesandtheirroleinstruc-tureformation.Analyticstudiesofthissignalhavebeendonebyseveralauthors(e.g.,Natarajan&Sigurdsson1999;

2Chatterjeeetal.

D6(BHCosmo)33.7533.75

2×21632×48632.75×1082.75×1074.24×1074.24×106

6.252.730.001.00

QuasarSZSimulations

Figure1.Simulatedy-distortionmapsaroundtwomassiveblackholes,atthreedi erentredshifts;left,middle,andrightcolumnsareforz=3,z=2,andz=1.Thetoptworowsareforthemostmassiveblackholeinthesimulation,withmass7.35×108M⊙,2.76×109M⊙and4.26×109M⊙atredshifts3,2,and1respectively.Thetoprowshowsyina5Mpcsquareregioncenteredontheblackhole;thesecondrowshowszoomsintoasmallerregion200kpcsquare.Notethetworowshavedi erentcolorscales.Thethirdandfourthrowsarethesameasthe rsttworows,foradi erentblackhole(thesecondmostmassiveblackholeatredshift3.0)withmass7.15×108M⊙,8.2×108M⊙and2.11×109M⊙atredshifts3,2,and1.Forbothblackholes,thepeakvalueofyisbetween10 7and10 6,correspondingtoane ectivemaximumtemperaturedistortionbetweenafewtenthsofaµKtoafewµK.

lationbetweenblackholemassandSZdistortion.Thecon-cludingSectionestimatesdetectabilityofthesesignalsandsummarizesfutureprospects.Throughoutweuseunitswithc=kB=1.

2SIMULATION

ThenumericalcodeusesastandardΛCDMcosmologicalmodelwithcosmologicalparametersfromthe rstyear

WMAPresults(Spergeletal.2003).Thecosmologicalpa-rametersare m=0.3, Λ=0.7,H0=70km/sMpc 1andGaussianinitialadiabaticdensityperturbationswithaspectralindexns=1andnormalizationσ8=0.9.(Whilethecurrentlowervalueofσ8willa ectthetotalnumberofblackholesinagivenvolume,itshouldhavelittleimpactontheresultsforindividualblackholespresentedhere.)Thesimulationusesanextendedversionoftheparallelcos-mologicalTreeParticleMesh-SmoothedParticleHydrody-

4Chatterjeeetal.

Mostmassiveblackhole

Secondblackhole

Table2.Theaccretionratesandthenumberofneighboringblackholeswithinaradiusof100kpc,forthetwoblackholesinFig.1.

namicscodeGADGET2(Springel2005).GasdynamicsaremodeledwithLagrangiansmoothedparticlehydrodynamics(SPH)(Monaghan1992);radiativecoolingandheatingpro-cessesarecomputedfromtheprescriptiongivenbyKatz,Weinberg,&Hernquist(1996).Therelevantphysicsofstarformationandtheassociatedsupernovafeedbackhasbeenapproximatedbasedonasub-resolutionmultiphasemodelfortheinterstellarmediumdevelopedbySpringel&Hern-quist(2003a).

AdetaileddescriptionoftheimplementationofblackholeaccretionandtheassociatedfeedbackmodelisgiveninDiMatteoetal.2008.Blackholesarerepresentedascolli-sionless“sink”particlesthatcangrowinmassbyaccretinggasorbymergerevents.TheBondi-Hoylerelation(Bondi1952;Bondi&Hoyle1944;Hoyle&Lyttleton1939)isusedtomodeltheaccretionrateofgasontoablackhole.Theac-223/2˙BH=4π[G2MBHcretionrateisgivenbyMρ]/(c2,s+v)

whereρandcsaredensityandspeedofsoundofthelo-calgas,visthevelocityoftheblackholewithrespecttothegas,andGisthegravitationalconstant.Theradiated

˙BHc2)whereη=0.1luminosityistakentobeLr=η(M

isthecanonicale ciencyforthindiskaccretion.Itisas-sumedthatasmallfractionoftheradiatedluminositycou-plestothesurroundinggasasfeedbackenergyEf,suchthat˙f= fLTwiththefeedbacke ciency ftakentobe5%.E

Thisfeedbackenergyisputdirectlyintothegassmoothingkernelatthepositionoftheblackhole(DiMatteoet.al2008).Thee ciency fistheonlyfreeparameterinourquasarfeedbackmodel,andischosentoreproducetheob-servednormalizationoftheMBH σrelation(DiMatteo,Springel&Hernquist2005).ThisnumberisalsoconsistentwiththepreheatingingroupsandclustersthatisrequiredtoexplaintheirX-rayproperties(Scannapieco&Oh2004).Thefeedbackenergyisassumedtobedistributedisotropi-callyforthesakeofsimplicity;howevertheresponseofthegascanbeanisotropic.Thismodelofquasarfeedbackasisotropicthermalcouplingtothesurroundinggasislikelyagoodapproximationtoanyphysicalfeedbackmechanismwhichleadstoashockfrontwhichisotropizesandbecomeswellmixedoverphysicalscalessmallerthanthoserelevanttooursimulationsandontimescalessmallerthanthedy-namicaltimeofthegalaxies(seeDiMatteoetal.2008andHopkins&Hernquist2006formoredetaileddiscussions).Inactualactivegalaxies,theaccretionenergyisoftenreleasedanisotropicallythroughjets.Asradiogalaxylobescanhavesubstantialseparations,itisconceivablethatactualhotgasbubblemorphologycoulddi ersomewhatfromthatinthesimulations.Thisdi erenceneedstobeinvestigatedwithfurthersimulations,buttheoveralldetectabilityofthesig-naldependsprimarilyonitsamplitudeandcharacteristic

angularscale,whicharedeterminedmainlybythetotalen-ergyinjectionasafunctionoftime.Theresultsforthesig-nalsanddetectabilitypresentedhereareunlikelytodi ersigni cantlyduetomoredetailedmodelingoftheenergyinjectionmorphology.

Theformationmechanismfortheseedblackholeswhichevolveintotheobservedsupermassiveblackholestodayisnotknown.Thesimulationcreatesseedblackholesinhaloeswhichcrossaspeci edmassthreshold.Atagivenredshift,haloesarede nedbyafriends-of-friendsgroup nderalgorithmrunonthe y.ForanyhalowithmassM>1010h 1M⊙whichdoesnotcontainablackhole,thedensestgasparticleisconvertedtoablackholeofmassMBH=105h 1M⊙;theblackholethengrowsviatheaccre-tionprescriptiongivenaboveandbye cientmergerswithotherblackholes(DiMatteoetal.2008).Thesimulationsusedinthispaperhaveaboxsizeof33.75h 1Mpcwithpe-riodicboundaryconditions.Thecharacteristicsofthesim-ulationarelistedinTable1,whereNpisthetotalnumberofdarkmatterplusgasparticlesinthesimulation,mDMandmgasaretheirrespectivemasses, givesthecomovingsofteninglength,andzendisthe nalredshiftoftherun.Forredshiftslowerthan1,thefundamentalmodeintheboxbe-comesnonlinear,solarge-scalepropertiesofthesimulationareunreliableafterz=1.ThecurrentresultsarederivedfortheD4runwith2×2163particles;wewillpresentbriefcomparisonswiththehigher-resolutionD6(BHCosmo)runtodemonstratethatourresultsarereasonablyindependentofresolution.

Adi erentsimulationandfeedbackmodelhaverecentlybeenusedbyScannapieco,Thacker&Couchman(2008)tostudythesameissues.Theyassociatetheremnantcircularvelocitywithinapostmergereventwithblackholemass.ThetimescaleonwhichtheblackholeshinesatitsEd-dingtonluminosityisassumedtobea xedfractionofthedynamicaltimescaleofthesystem;thetimescaleandblackholemassscaleareusedtoestimatetheenergyoutputfromablackhole.Theirfeedbackenergye ciencyintotheinter-galacticmediumis5%,consistentwiththeassumptioninoursimulation.Incontrast,oursimulationtracksthetime-varyingfeedbackfromagivenblackholeduetochanginglocalgasdensityasthesurroundingcosmologicalstructureevolves.Thissimulationo ersthepossibilityoftrackingtheaccretionhistoryanddutycycleofblackholeemissionforindividualblackholes,whichweplantoaddressinfuturework.

QuasarSZSimulations

Figure2.Thedi erenceiny-distortionbetweenasimulationwithblackholefeedbackandasimulationwithout,forthesameregionofspaceshowninFig.1.Thetwosimulationshaveidenticalresolutionandinitialconditions.The rstrowcorrespondstothemostmassiveblackholeatz=3,thesecondrowatz=1;thethirdrowcorrespondstotheotherblackhole(secondmostmassiveblackholeatredshift3.0)inFig.1atz=3,thefourthrowatz=1.Theleftcolumnshowsy,themiddleshowsthelogofthemass-weightedaveragetemperatureinunitsofKelvin.Therightcolumnshowsthelogoftheelectronnumbersurfacedensityinunitsofcm 2.

3RESULTSFROMTHESIMULATIONS

y=2

dlσTne

3.1TheSunyaev-ZeldovichDistortionandMaps

TheComptony-parametercharacterizingthenon-relativisticthermalSZspectraldistortionisproportionaltotheline-of-sightintegraloftheelectronpressure:

6Chatterjeeetal.

Figure3.Theangularpro lesoftheydistortionforthetwoblackholesshowninFig.1atthreedi erentredshifts.Thesolid,dot-dashedanddashedlinesareforredshifts3,2,and1respectively.Theleftpanelshowsthemostmassiveblackholeandtherightpanelistheotherblackhole(secondmostmassiveblackholeatredshift3.0).Althoughthecentralamplitudeataparticulartimedependsstronglyontheinstantaneousstateoftheblackholeaccretion,thedistortionamplitudeincreasesmonotonicallywithtimeata20arcsecondangulardistance.

Figure4.Thedi erenceinthey-distortionradialpro lewithandwithoutblackholefeedback,forthetwoblackholesshowninFig.1.Theleftpanelisforthemostmassiveblackholeandtherightpanelisforthesecondblackhole(secondmostmassiveblackholeatredshift3.0).Foreach,thedashedlineisthefractionalchangeintheydistortionwithrespecttothenoblackholecaseatz=1;thesolidlineisatz=3.

3.02.01.0237831103404127336404logy=0.56log(MBH/M⊙) 9.8logy=1.00log(MBH/M⊙) 14logy=1.90log(MBH/M⊙) 22log(dMBH/dt)=0.74log(MBH/M⊙) 8.1log(dMBH/dt)=0.65logMBH/M⊙) 8.4log(dMBH/dt)=1.4log(MBH/M⊙) 15

QuasarSZSimulations

Figure5.Thetoprowshowsthemeanydistortionwithinacomoving200kpcregionaroundtheblackholeasafunctionofblackholemass,forredshifts3,2,1fromlefttoright;atz=1theangularsizeoftheboxisaround25arcseconds.Thebottomrowshowsthemassaccretionrateasafunctionofblackholemass,forthesameredshifts.Thepointsarethenumericaldataandthesolidlinesarepower-law ts.Allblackholesintheplottedmassrangeareincluded.Thequalitativesimilaritybetweenthetopandthebottompanelshowstheassociationofthey-distortionwithaccretionrates.

Chatterjeeetal.

3.2

AngularPro les

ForthetwoblackholesshowninFigure1weseeanover-allenhancementintheSZsignalduetoquasarfeedback.ThisagreeswiththesimulationsinScannapieco,Thacker&Couchman2008.Tofurtherquantifythee ectsofquasarfeedbackweaveragetheSZsignalinannuliaroundtheblackholeandexaminetheangularpro leoftheresultingyfromthehotbubbleinFigure3and4.

Figure3showstheaverageangularpro lesofthetotalydistortionaroundthetwoobjectsinthemapsinFigure1.Theblackdashed,bluedot-dashedandredsolidlinesareforz=1,z=2,andz=3respectively.Inbothcasestheyincreaseswithtimebetween～10to25arcsecondseparationfromtheblackhole.ygetssteadilylargerasthefeedbackenergyspreadsoverthisvolume(seealsoFig.4).Atz=3theypro leissteeperinthecentralregionswithasigni cantpeak(inparticularforthesecondquasar)atscalesbelow5arcseconds.Thebumpsinthepro lesareduetoconcentrationsofhotgasoroccasionalotherblackholeswhichareincludedinthetotalaveragesignal.ytypicallyreachesitshighestcentralpeaksattimewhenthequasarismostactive(theblackholeaccretionrateishigh-seeTable2),andhencelargeamountsofenergyarecoupledtothesurroundinggasaccordingtoourfeedbackprescription.Forexample,thez=3curveintherightpanelshowstheblackholeataparticularlyactivephase;thecentralydistortioncorrespondstoatemperaturedi erenceofover4µK.Atz=2thiscentraldistortionissmallerbyafactorof20,whileitislargerbyafactorof10atanangularseparationof10arcseconds.Figure3showsthetotalSZe ectinthedirectionofaquasarresultingfromthesuperpositionoftheSZsignaturefromquasarfeedbackplustheSZdistortionfromtherestofthelineofsightduetothesurroundingadiabaticgascompression,whichisexpectedtoformanaveragebackgroundlevelintheimmediatevicinityofthebackhole.

Inordertoclearlydisentanglethecontributionduetoquasarfeedback,inFigure4,weplotthefractionalchangeinydistortionbetweenthesimulationwithandwithoutblackholemodeling,attwodi erentredshifts.Thesearethepro lescorrespondingtothemapsshowninFigure2.ItisclearthatthelocalSZsignatureislargelydominatedbytheenergyoutputfromtheblackhole,givingafactorbetween300toover3000(forthesecondblackholeatz=3inrightpanel)increaseinyneartheblackhole.Ourre-sultsarealsoconsistentwiththeexpectedydistortionfromthethermalizedgasinthehosthaloscontainingtheseblackholes(whichareontheorder1012M⊙to1013M⊙)andistherange10 9to10 7(seealsoKomatsu&Seljak2002).Thelargestpeakinydistortionenhancementduetoquasarfeedbackgenerallylieswithin5arcsecondsoftheblackhole.

3.3BlackHoleMassScalingRelations

SincetheSZe ectfromtheregionaroundtheblackholesweanalyzedintheprevioussectionisdominatedbythequasarfeedback,weinvestigatewhetheracorrelationbetweenblackholemassandydistortionexistsforthepopulationasawhole(seealsoColberg&DiMatteo2008forotherscalingrelationsbetweenMBHandhostproperties).ThetoprowofFigure5plotsthemeanydistortion,computedovera

sphereofradius200kpc/h(i.e.thesameasinthemaps,correspondingto20arcseconds)versusblackholemassforallblackholesinthesimulationswithMBH>107M⊙atz=1,2and3(fromrighttoleftrespectively).Thesizeoftheregionischosentosampletheentireregionofdistortionduetothequasarfeedback,whileminimizingbiasfromthelocalenvironment(Fig.3and4).Themasscut-o ischosento(a)minimizee ectsduetolackofappropriateresolutioninthesimulationsaswellas(b)produceSZdistortionsthatmaybedetectablebycurrentorupcomingexperiments.

Simplepowerlaw tstotheydistortionasafunctionofblackholemassshowaredshiftevolutionwiththescal-ingbecomingsteeperwithdecreasingredshift.Table3sum-marizesourresultsfromthe ts.Thetrendsshowaclosecorrespondencebetweenthemeanyparameterandtheto-talfeedbackenergyasmeasuredfromy.Inordertofurtherinvestigatethereasonfory MBHrelations,inthebottomrowofFigure5weplottheaccretionrateversusblackholemassatredshifts3,2,and1forthesamesampleasinthetoppanelandperformsimilarpower-law ts(seeTable3).ThetrendsinaccretionrateversusMBHarequalitativelysimilartothetoppanel,demonstratingtheconnectionoftheydistortionduetoquasarfeedbackwiththeblackholeaccretionrateandblackholemass.Inparticular,atz=1therelationsgetsteeperasexpectedifthelargestfractionofblackholesareaccretingaccordingtotheBondiscal-ing(e.g.,m˙∝MBH2

)andshallowerwithincreasingredshiftwhenmostblackholesareaccretingclosetothecriticalEd-dingtonvalue(e.g.,m˙∝MBH).Ofcourse,theaccretionratedependsnotonlyonblackholemassbutalsoontheprop-ertiesofthelocalgasandisalsoregulatedbythelargescalegasinfalldrivenbymajormergers,whichpeakathigherredshifts(DiMatteoetal.2008).Theratiooftheslopes(accretionratetoydistortion)forthe tsshownintable3are1.32,0.65and0.73atredshifts3.0,2.0and1.0respec-tively.ThisshowstheagreementofthetopandthebottompanelsinFigure5,andthecloseconnectionbetweenaccre-tionhistoryandSZdistortion:theSZe ecttrackscloselyquasarfeedbackandispromisingprobeofblackholeac-cretion.ThelargestamplitudesofSZsignalfromquasarisexpectedfromz～2 3atatimeclosetothepeakofthequasarphaseingalaxies.3.4

ResolutionTest

IntheprevioussectionwehavemadeuseoftheD4(Ta-ble1)simulationsfromouranalysis.Atthisresolutionwehavetwoidenticalrealizations,withandwithoutblackholemodeling,allowingustocarryoutdetailedcomparisonsofthee ectsofthequasarfeedback.Wenowwishtoassesspossiblee ectsduetonumericalresolutionbymakinguseoftheD6(BHCosmo)run(seealsoDiMatteoetal.2008,Croftetal.2008andBhattacharyaDiMatteo&Kosowsky2008foradditionalresolutionstudies).Figure6showstheydistortionmapsforthemostmassiveblackholeatredshifts3,2,and1.Thetoprowisforthehigher-resolutionBH-Cosmorunandthebottomrowisforthelower-resolutionrun(D4).Ourresultsatthelowerresolutionappearrea-sonablywellconverged,thoughwithsomedi erences.Thecentralblackholemassesinthetworunsdi ersomewhat.Atz=1,2,and3,theblackholemassesintheD4andBH-Cosmorunare(4.29×109M⊙,2.96×109M⊙),(2.76×109M⊙,

QuasarSZSimulations

Figure6.Thetoprowshowsy-distortionmapsofthemostmassiveblackholeatz=3(left),z=2(center)andz=1(right)inahigher-resolution(D6)simulation.Thebottomrowshowsthesamethingforalower-resolution(D4)run.Theblackholemassesinthetwosimulationsareslightlydi erentfromeachother:forz=1masses4.29×109M⊙(D4)and2.96×109M⊙(D6),forz=2masses2.76×109M⊙(D4)and1.83×109M⊙(D6),andforz=3masses7.35×108M⊙(D4)and8.56×108M⊙(D6).Theboxsizeis200kpcsquare.Thedi erenceinpeakyvalueforD4andD6variesfrom22%(z=3)to6%(z=2)anditishigherforthehigher-resolutionsimulationatallthreeredshifts.

1.85×109M⊙)and(7.35×108M⊙,8.56×108M⊙)respec-tively.Itclearthatthedi erenceinresolutionisa ectingtheblackholemassasexpectedfrommodestchangesinmassaccretionrate(whichissensitivetothegaspropertiesclosetotheblackhole).Also,moresmallscalestructureinthegasdistributionisevidentathigherresolution,asexpected.Thisa ectstheamplitudeofthetotalSZ uxwhichisen-hancedbyabout6%atz=2andbyabout22%atz=3(whenitismostpeakedaroundtheblackhole)inthehigherresolutionrun.

4DETECTABILITYANDDISCUSSION

Observationally,quasarfeedbackisdirectlydetectablebyresolvingSunyaev-ZeldovichpeaksonsmallangularscalesoftensofarcsecondswithamplitudesofuptoafewµKabovetheimmediatelysurroundingregion.Thecombinationofangularscaleandsmallamplitudemakedetectingthisef-fectverychallenging,atthemarginsofcurrentlyplannedexperiments.Thenecessarysensitivityrequireslargecol-lectingareas,whiletheangularresolutionneededpointstoaninterferometerinacompactcon guration,oralargesingle-dishexperiment.SincetheSZsignalismanifestedasapeakoverthesurroundingbackgroundlevel,aregionsub-stantiallylargerthantheSZpeakmustbeimaged.Thisrequiresatelescopehavingsu cientresolutiontoresolvethecentralpeakintheSZdistortioninanSZimageandenough eldofviewsothatthepeakcouldbeidenti ed.AnexampleisthecompactALMAsubarrayknownastheAtacamaCompactArray(ACA),composedof127-meter

dishes.TheALMAsensitivitycalculatorgivesthatthesyn-thesizedbeamforthisarrayisabout14arcseconds,andtheintegrationtimerequiredtoattain1µKsensitivityperbeamatafrequencyof145GHzandamaximumbandwidthof16GHzisontheorderof1000hours(ALMAsensitivitycalculator).AverydeepsurveywiththisinstrumentcoulddetecttheSZe ectfromindividualblackholes.The50-meterLargeMillimeter-WaveTelescopeinstrumentedwiththeAzTECbolometerarraydetectorwillhaveasomewhatsimilarsensitivitybutdetectibilitywouldrequireaverydeep(thousandsofhours)integrationtime.TheCornell-CaltechAtacamaTelescope(CCAT),a25-metertelescope,estimatesapossiblepixelsensitivityforSZdetectionat150GHzof310µKs1/2for26arcsecondpixels,soa30hourobserva-tioncouldgive1µKpixelnoise.Thesepixelswouldnotbesmallenoughtoresolvethehothaloaroundablackhole,butmightbeabletodetectthedi erenceinasinglepixelduetoblackholeemissioncomparedtothesurroundingpixels.Asidefromrawsensitivityandangularresolution,aseriousdi cultywithdirectdetectionistheconfusionlimitfrominfraredpointsourceemission;http://ATestimatesshowthattheirone-source-per-beamconfusionlimitwillbearound6µKat150GHz(Golwala2006).Thiswillpresentsubstantialdi cultiesfordetectinga1µKtemperaturedistortionifaccurate.Itisnotedthattheobservationsinthesub-millimeterbandislimitedbyconfusionnoiseandsoanotherpossibilityofdirectdetec-tionofthesignalthroughradiofrequencytelescopescouldbeconsidered.Massardietal.2008showsthattheconfusion

10Chatterjeeetal.

duetodustygalaxiesislowerat10GHzthenat100GHz.TheauthorsshowthatforgalacticscaleSZe ecttheopti-malfrequencyrangefordetectionisbetween10to35GHz.Howeversubstantialconfusionfromradiogalaxiesattheselowfrequencyobservationswouldstillbeachallengingissueinthedirectdetectionofthesignal.

Giventhesesubstantialdi cultiesassociatedwithdi-rectdetection,analternateroutemaybenecessary.Cross-correlationofarcminute-resolutionmicrowavemapswithop-ticallyselectedquasarormassivegalaxiesisasecondpossi-bledetectionstrategy(ChatterjeeandKosowsky2007,Scan-napieco,Thacker,andCouchman2008).Byaveragingoverlargenumbersofobjects,wecanhaveanestimateofasmallmeanblackholedistortionsignalfromthenoiseinthemaps.Theprimarychallengewiththistechniqueisthedirectemis-sionfromquasarinthemicrowaveband.Itmaybepossibletoselectasampleofquasarwhichissu cientlyradio-quietthatthecross-correlationisnotdominatedbytheintrin-sicemission.Anotherpossibilityistoselectmassive eldgalaxiesundertheassumptionthattheyharboracentralmassiveblackholewhichatonetimewasactive;thehotbubbleproducedhasacoolingtimecomparabletotheHub-bletime,soformerlyactivegalaxiesshouldstillhaveanSZsignature.Finally,theSZe ectfromblackholesisinadditiontotheSZemissionfromanyhotgasinwhichtheblackhole’shostgalaxyisembedded.Massivegalaxiestracelarge-scalestructure,andanycross-correlationwillalsode-tectthissignal.Althoughtheobservationalrequirementsforthecross-correlationmethodareplausiblethescopesfordetectibilitywiththismethodisstilllimitedbycon-fusionnoise.Stackingmicrowave(SZ)mapsinthedirectionofknownquasarswouldalsoserveasanindependentrouteindetectingthesignal(Chatterjee&Kosowsky2007).Thiscanimprovethesignaltonoisebyasubstantialamountal-thoughthismethodwouldstillbelimitedbytheuncertain-tiesdescribedabove.Quantifyingindetailtheobservablesignal(whichwillneedtobedisentangledfromothercon-fusionssuchasdustygalaxies,radiogalaxiesetc.)forthepossibledirectdetectionsmethodsorfromcross-correlationanalysisthatwehavediscussedisbeyondthescopeofthispaperandwedeferittoafuturework.Thesimulationsandmapspresentedhereprovideabasisforfurthermodelingofallthesee ects.

Themainconclusionsdrawnfromthisworkaresum-marizedasfollows.Wehaveusedthe rstcosmologicalsim-ulationstoincorporaterealisticblackholegrowthandfeed-backtoproducesimulatedmapsoftheSunyaev-Zeldovichdistortionofthemicrowavebackgroundduetothefeedbackenergyfromaccretionontosupermassiveblackholes.Thesesimulationsaddresstherapidaccretionphasesofblackholes:periodsofstrongemissionaretypicallyshort-livedandre-quiregalaxymergerstoproducestronggravitationaltidalforcingnecessaryforsu cientnucleargasin owrates(Hop-kins,Narayan&Hernquist2006;DiMatteoetal.2008).Theresultisheatingofthegassurroundingtheblackhole,sothatthelargestblackholesproduceasurroundinghotregionwhichinducesay-distortion(relatedtoatempera-turedistortion)withacharacteristicamplitudeofafewµK.WehaveobtainedascalingrelationbetweentheblackholemassandtheirSZtemperaturedecrement,whichinturnisameasureoftheamountoffeedbackenergyoutput.Thecorrespondencebetweentheydistortionandtheaccretion

ratesisnotexactbutthereisacloseassociationwhichshowsthecorrelationbetweenfeedbackoutputandblackholeac-tivity.FromourresultswehaveshownthatwiththeturnonofAGNfeedbackthesignalgetsenhancedlargelyandtheenhancementispredominantatangularscalesof5arcsec-onds.Finallywehaveshownthatthereisafairprobabilityofdetectingthissignalevenfromtheplannedsubmillimetermissions.

Theroleofenergyfeedbackfromquasarsandfromstarformationisknowntohavesubstantialimpactonthepro-cessofgalaxyformationandevolutionoftheintergalacticmedium,butthedetailsofthisprocessarenotwellunder-stood.ProbesbasedonSunyaev-Zeldovichdistortionsarechallenging,butaneventualdetectioncanbeusedtoputusefulconstraintsandchecksonmodelsofAGNfeedback.

5ACKNOWLEDGMENTS

SCwouldliketothankBrucePartridgeandJamesMoranforhelpfuldiscussionsonexperimentalcapabilitiesofvar-ioustelescopes.SpecialthankstoMarkGurwellforhelp-ingwiththesensitivitycalculationforSMA.SCandAKwouldalsoliketothankChristophPfrommerforsomeini-tialdiscussionsontheproject.ThankstoJonathanLasFargeaswhohelpedwiththeanalysis,supportedbyNSFgrant0649184totheUniversityofPittsburghREUpro-gram.Wewouldalsoliketothanktherefereeforvaluablesuggestionsonimprovementofthepaper.Thisworkwassup-portedattheUniversityofPittsburghbytheNationalSci-enceFoundationthroughgrantAST-0408698totheACTproject,andbygrantAST-0546035.AtCMUthisworkhasbeensupportedinpartthroughNSFAST06-07819andNSFOCI0749212.SCwasalsopartlyfundedbytheZaccheusDanielFellowshipattheUniversityofPittsburgh.

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