MNRAS000,000–000(0000) Preprint1March2017 CompiledusingMNRASLATEXstylefilev3.0 Kinetic and radiative power from optically thin accretion flows Aleksander Sa˛dowski1,(cid:63) & Massimo Gaspari2,† 1MITKavliInstituteforAstrophysicsandSpaceResearch,77MassachusettsAve,Cambridge,MA02139,USA 2DepartmentofAstrophysicalSciences,PrincetonUniversity,4IvyLane,Princeton,NJ08544,USA 1March2017 ABSTRACT 7 Weperformasetofgeneralrelativistic,radiative,magneto-hydrodynamicalsimulations(GR- 1 RMHD)tostudythetransitionfromradiativelyinefficienttoefficientstateofaccretionona 0 non-rotatingblackhole.WestudyiontoelectrontemperatureratiosrangingfromT/T =10 i e 2 to100,andsimulateflowscorrespondingtoaccretionratesaslowas10−6M˙ ,andashighas Edd b 10−2M˙Edd.Wehavefoundthattheradiativeoutputofaccretionflowsincreaseswithaccretion e rate,andthatthetransitionoccursearlierforhotterelectrons(lowerTi/Teratio).Atthesame F time,themechanicalefficiencyhardlychangesandaccountsto≈3%oftheaccretedrestmass energy flux, even at the highest simulated accretion rates. This is particularly important for 8 themechanicalAGNfeedbackregulatingmassivegalaxies,groups,andclusters.Comparison 2 withrecentobservationsofradiativeandmechanicalAGNluminositiessuggeststhattheion ] toelectrontemperatureratiointheinner,collisionlessaccretionflowshouldfallwithin10 < E T/T <30,i.e.,theelectrontemperatureshouldbeseveralpercentoftheiontemperature. i e H Keywords: accretion,accretiondiscs–blackholephysics–relativisticprocesses–methods: . h numerical p - o r t s 1 INTRODUCTION scope (mainly brightest cluster galaxies; BCGs) is Russell et al. a (2013). The radiative output is constrained via the nuclear X-ray [ Accreting black holes (BH) are behind some of most energetic luminosity,whilethekineticpowerisestimatedbymeasuringthe 2 and fundamental phenomena in the Universe. In the supermas- X-raybubbleenthalpydividedbythebuoyancytime.Thedatacor- siveregime(SMBH),theyareoftenknownasactivegalacticnu- v roboratesthatthemechanicaloutputalwaysdominateatlowand clei(AGN)andquasars.Whentherateatwhichgasislostbelow 3 intermediateaccretionrates(moreinSection1.1).Intermsofevo- theBHhorizonislow(normalizedtotheEddingtonunit),accre- 3 lution,inthenearbyUniverse,onlyafewpercentofsystemshosta 0 tionflowsareopticallythinandradiativelyinefficient(anextreme radiativelyefficientsource(orquasar).Inotherwords,belowred- 7 caseistheaccretionflowinthecenteroftheGalaxy).Radiatively shiftz∼2,AGNfeedbackisexpectedtoproceedatasub-Eddington 0 inefficient BHs do however inject significant amount of mechan- rate,i.e.,theAGNfeedback‘maintenance’phaseisdominatedby . ical energy into the environment, preventing catastrophic cooling 1 kineticinputofenergy–typicallyviamassiveoutflows(e.g.,see flowsandstarformationratesvialarge-scaleoutflows,cavitiesand 0 Gaspari2016forabriefreview). shocks(McNamara&Nulsen2012forareview),atthesametime 7 1 establishingthecelebratedBHmass-velocitydispersionrelation Inthiswork,weperformstate-of-the-art,3-dimensional(3D) : (Kormendy&Ho2013forareview).Theoutputmodeisexpected GR-RMHDsimulationsofaccretionflowsbelowandnearthetran- v tochangewhengasisaccretedatratesexceedingapercentofthe sitional regime, and calculate the corresponding mechanical and Xi Eddington rate. Under such conditions the previously radiatively radiativeefficiencies.Moreover,comparingtheobservedandsim- inefficientsourcesbecomequasarsdominatedbytheradiativeout- ulatedvaluesoftheluminosityatwhichtheradiativeefficiencybe- r a put. comes comparable with the mechanical one, we aim to constrain The transition from the radiatively inefficient to the efficient therangeofpossiblevaluesoftheelectrontoiontemperatureratio regimeisnotwellunderstood.Neitherthephysicsoftheelectron inaccretingsystems. heatinginopticallythincollisionlessplasmas.Ontheotherhand, In a parallel work, Gaspari & Sa¸dowski (2017), we apply thereisampleamountofobservationaldatawhichprobesaccreting the mechanical efficiency constrained here, to a model of self- systemsatverydifferentluminositiesandaccretionrates.Onekey regulatedAGNfeedbackwhichcouplesthesmall(horizon)scale observational study attempting to constrain the kinetic versus ra- to the large (kpc-Mpc) scale properties of cool-core systems (as diativeefficienciesinmassivegalaxiesdetectedwithChandratele- massive galaxies, groups, and clusters). The macro feeding properties are mediated by the recently probed chaotic cold accretion (CCA),i.e.,thecondensationofmultiphasecloudsoutofthetur- (cid:63) E-mail:asadowsk@mit.edu(AS);EinsteinFellow bulentplasmahalo,whichraintowardthenuclearregionandare † E-mail:mgaspari@astro.princeton.edu(MG);Einstein&SpitzerFellow efficientlyfunnelledviachaoticinelasticcollisionscancellingan- (cid:13)c 0000TheAuthors 2 A.Sa˛dowski&M.Gaspari gularmomentum(seeGasparietal.2013,2015,2017).Thepro- 2014)whichiscapableofevolvinggasandradiationinparallelfor posedunificationmodelprovidestheBHgrowthandAGNoutflow arbitrary optical depths. The most recent version of KORAL is ca- propertiesasafunctionofthemacroproperties(e.g.,hothalotem- pableofevolvingtwo-temperatureplasma(Sadowskietal.2016). perature),andcanbeusedasaneffectivesub-gridschemeinstruc- Thisapproach,however,isnotfreefromarbitrarychoicesandnu- tureformationsimulationsandanalyticstudies,withoutresorting mericalissues(seeDiscussionsectionbelow).Forthisreasonwe tothefine-tuningofafreeefficiency. decided to solve a simplified problem where we evolve only the Thepresentedworkisstructuredasfollows.Belowwereview mean temperature of the gas (mixture of electrons and ions), but theobservationalworkwebaseourcomparisonon.InSection2, forthepurposeofcalculatingradiativeemission,wesplitthegas weintroducethenumericalmethodandmainassumptions.InSec- temperatureintoelectronandiontemperatures,T andT,respec- e i tion 3, we discuss the performed 3D GR-RMHD simulations. In tively,followingtheprescribedratioT andT.Forpurehydrogen e i Section4,wediscussthekeyimplications.InSections5and6,we gasthespeciestemperaturesatisfy, discussthecaveatsandsummarizethemainresults,respectively. 1.1 Observationalconstraints Tgas=1/2(Te+Ti). (2) Accretingblackholesareknowntobothemitradiationandinject significantamountsofmechanicalenergyinthesurroundings.The latter effect often leads to the inflation of cavities in the medium Weaccountforfree-freeandsynchrotronemissionandabsorption, as well as Compton heating and cooling. The exact formulae for surroundingtheBH,andcouldhappenbothonparsecscales(for theopacitiesaregiveninSadowskietal.(2016).Inthisworkwe stellarmassBHs),aswellasonkpcscale(forAGN).Fromthevol- umeandpressureofagivencavity(E =4PV)anditsexpansion use only grey opacities and we do not calculate electromagnetic cav spectrumofgeneratedradiation. (sound-crossing)timeonemayinferthemechanicalluminosityof thecentralsource. Severalstudiesaimingatcomparingtheradiativeandkinetic properties have been recently performed (e.g., King et al. 2012; Mezcua&Prieto2014;Hlavacek-Larrondoetal.2015;Hoganet al. 2015; Shin et al. 2016) In this work, we mainly use results by Russell et al. (2013), one of the most comprehensive investi- gations based on observations of nuclear X-ray sources and the corresponding cavities in a large sample of 57 BCGs. These au- thorshavefoundthatthenuclearradiationexceedsthemechanical energy output of the outflow when the mean accretion rate rises aboveafewpercentoftheEddingtonluminosity,correspondingto 2.1 Problemsetup theonsetofthequasarmode.Thetwocomponentsbecomecom- parablealreadyat10−3−10−2L andtheradiativecomponentis Weperformedasetof9three-dimensionalsimulationsofaccretion Edd very weak, sometimes undetectable, for the lowest accretion and flowsonanon-rotatingBH.Thesimulationscoveraccretionrates emissionrates(cf.Fig.12inRusselletal.2013).Forallsuchrea- from10−6 to10−2M˙Edd -enoughtocoverboththelow-luminosity sons,belowweusetherange10−3−10−2L asreferencethreshold limitandtheobservedtransitiontoradiatively-efficientmode1.We belowwhichthemechanicalluminosityoEfdadnaccretingblackhole testedthreevaluesofiontoelectrontemperatureratios,Ti/Te=10, systemequalsorexceedsthecorrespondingradiativeoutput. 30and100.Thischoicereflectsthefactthattheexpectedelectron temperature is lower than the ion’s (only electrons cool emitting photons),and,asdiscussedbelow,iswideenoughtoputlimitson 1.2 Units thetemperatureratioconsistentwithobservations. Initially,weperformedasingle,non-radiative,simulationwith In this work we adopt the following definition for the Eddington anequilibriumtorus(sameasinNarayanetal.2012)threadedby massaccretionrate, a magnetic field forming set of poloidal loops (again, same as in L M˙ = Edd, (1) Narayanetal.2012,butflippingthepolarityalsoacrosstheequa- Edd ηc2 torialplane)onagridof336cellsinradiusandpolarangle,and32 whereL = 4πGMm c/σ = 1.25×1038M/M erg/sistheEd- cellsinazimuthspanningπ/2wedge.Suchasetupwasevolvedfor Edd p T (cid:12) 15000t , long enough for establishing a now-standard, scale-free dington luminosity for a BH of mass M, and η is the radiative g efficiency of a thin disk around a black hole with a given spin solution of a thick and hot accretion flow with converged region a∗ ≡ a/M. For a zero-spin BH, η ≈ 0.057 (Novikov & Thorne extendingupto∼25Rg. 1973) and M˙ = 2.48×1018M/M g/s. We denote the gravita- Wethenusedthefinalstateofthisnon-radiativesimulationas Edd (cid:12) tional radius and time as R ≡ GM/c2 and t ≡ GM/c3, respec- astartingpointfortheradiativerunsbeingthesubjectofthispaper. g g tively. Whenstartingaradiativerunwerescaledthedensitytoadesired value(whichultimatelydeterminedthefinalaccretionrate)keep- ingthemagnetictogaspressureratioandthegastemperaturefixed. Atthesametimeweturnedontheradiativeevolutionallowingfor 2 NUMERICALMETHOD emissionandabsorptionofradiationwithefficiencydeterminedby For the purpose of simulating optically thin and marginally opti- the choice of species temperature ratio. In such a way we simu- cally thin accretion flows we adopt the general relativistic, radia- lated the 9 models described in this work until the final time t end tivemagneto-hydrodynamicalsolverKORAL(Sa¸dowskietal.2013, (Table1),typically25000t . g MNRAS000,000–000(0000) Kineticandradiativeefficienciesinaccretionflows 3 Table1.Simulatedmodels Name Ti/Te M˙/M˙Edd Lrad/M˙c2 Ltot/M˙c2 Lkin/M˙c2 H/R tend/tg f2t10 10 9.7×10−7 0.0005 0.035 0.034 0.38 25000 f3t10 10 1.0×10−5 0.0026 0.025 0.022 0.36 29000 f4t10 10 2.7×10−4 0.033 0.065 0.032 0.35 26000 f5t10 10 2.9×10−3 0.033 0.067 0.034 0.20 27500 f4t30 30 1.9×10−4 0.0026 0.033 0.030 0.35 25000 f5t30 30 4.1×10−3 0.017 0.056 0.039 0.20 28000 f6t30 30 1.6×10−2 0.020 0.062 0.042 0.17 28000 f5t100 100 1.7×10−3 0.0016 0.032 0.030 0.38 20500 f6t100 100 1.0×10−2 0.014 0.055 0.041 0.16 27000 H/R-averagedensityscale-heightmeasuredatR=15Rg. Otherparameters:a∗=0.0,resolution:336x336x32,π/2wedgeinazimuth Figure1.Distributionsofgasdensity(leftpanels)andgastemperature(rightpanels)insimulatedaccretionflowscorrespondingroughlytotheaccretion rateof10−3M˙Edd andthreevaluesofiontoelectrontemperatureratio:(toptobottom)Ti/Te = 100(least-efficient,modelf5t100),30(f5t30),and10 (most-efficientradiativecooling,f5t10). 3 RESULTS opticallythinaccretionflows.Theinflowofmattertakesplacein thebulkofthediskwhereturbulentstressestakeangularmomen- 3.1 Generalproperties tumoutofthegas.Thebulkoftheflowisrelativelystronglymag- The simulations initialized as described in the previous section netized due to the non-zero radial component of the initial mag- evolve into turbulent, magnetorotational instability (MRI) driven, netic field at the equatorial plane, with magnetic pressure con- tributing ultimately to ∼30% of the total pressure in the region 10Lkin. ulatedaccretionflowsasafunctionofthenormalizedaccretionrate.Differ- entsymbolscorresponddodifferentiontoelectrontemperatureratios. intact dynamical properties (the total efficiency is determined by howboundsuchhorizoncrossinggasis).Forthelowestaccretion yetreachedsteadystate3.Numericalsimulationsofthetransitional ratesineachsubset,thiskineticenergyextractionratedominates regimewereperformed,althoughwithmuchsimplertreatmentof the total luminosity. In the case of the largest accretion rates, for radiation,alsobyDibietal.(2012)andWuetal.(2016). which the radiative output is significant, the kinetic and radiative ThebottompanelinFig.2showsthekineticefficiencycalcu- luminositieshavecomparablemagnitudes. latedfromthedifferencebetweenthetotalandradiativeluminosi- Thekineticandradiativeenergyextractionratesarecompared ties(Eq.6).Inallcasesthekineticefficiencyiscloseto3%.This inFig.3.Asalreadydiscussed,thekineticenergydominateswhen valueisconsistentwiththatobservedinthenon-radiativesimula- radiativeemissionisnegligible,i.e.,forthelowestaccretionrates. tiondescribedin-depthinSa¸dowskietal.(2016)4.Itisinteresting Oncemasstransferrateincreases,sodoestheradiativeefficiency, tonote,thatthekineticefficiencydoesnotgodownwithincreas- whichforthehottestelectroncasecanevenbecomecomparableor ingaccretionrateandradiativeluminosity.Thisisinpartdifferent exceedthekineticcomponent. frompreviousidealizedAGNmodels(Churazovetal.2005).Itre- Table2putstogethertheestimatesfortheluminosities,L trans flectsthefactthatradiationcomesfromtheinnermostpartofthe (eitherkineticorradiative),atwhichthetransitiontotheluminous accretionflowandtheunderlyinggascannotefficientlyrespondto regime(L ≈L )takesplace.Forthecoldestelectrons,wehave rad kin cooling in the last phase of accretion, crossing the horizon with shownthattheaccretionflowsremainradiativelyinefficientupto 10−2L andtheradiativeoutputneverreachestheleveloftheki- Edd netic one. The intermediate case behaves in similar way. For the 3 Ourownexperimentshaveshownthataxisymmetricaccretionflowsare hottest electron case (T/T = 10), however, the accretion flow i e characterized by significantly higher radiative efficiency than the three- starts generating radiative luminosity comparable to the mechan- dimensionalcounterparts–enforcingaxisymmetrychangesthenatureof icalonealreadyat10−4L .Wediscusstheimplicationsofthese Edd turbulenceleadingtotheformationofrapidlyradiating,highdensityfil- findingsinthenextSection. aments in the inner region which are not present in non-axisymmetrical solutions. 4 Weremindthis3%characterizesthickaccretionflowsonnon-rotating BHs.Fornon-zeroBHspinthisdisk-relatedefficiencymaygoup;ontop 4 IMPLICATIONS ofit,ageneratedrelativisticjetmayovercomethetotalenergybudget,albeit havingdifficultytoefficientlycouplewiththehosthaloduetotheveryhigh ObservationalstudiesofAGNradiativeluminositiesandmechan- collimation. ical output (Section 1.1) have shown that the radiative compo- MNRAS000,000–000(0000) 6 A.Sa˛dowski&M.Gaspari nent becomes comparable with the kinetic one at the luminosity transitiontothequasar-likeregime,andthusevenathighredshifts ∼ 10−3 −10−2L (e.g., Fig. 12 in Russell et al. 2013). In this (assuggestedbytheobservationalsampleinHlavacek-Larrondoet Edd workwehaveshownthatthiscriticalluminosityissensitivetothe al.2015). temperatureoftheelectrons,whichdeterminestheefficiencyofra- Finally,asanticipatedinSection1,therobustconstraintand diative cooling. Therefore, we can use the observational result to stabilityofthemechanicalefficiencyallowsustolinksuchmicro constrainthepropertiesoftheelectronpopulationinopticallythin valuetothemacropropertiesoftheself-regulatedAGNfeedback blackholeaccretionflows. loop(mediatedviaCCA),whichre-heatsandpreservesthecooling In Table 2 we listed the rough estimates of the critical lu- coresof galaxies,groups,and clustersin astateof quasi-thermal minositiesatwhichthekineticandradiativeluminositiesbecome equilibrium throughout the cosmic time (e.g., Gaspari 2015 and comparable. For the hottest electrons case we considered (ion to refs.within).Suchunificationmodelispresentedanddiscussedin- electrontemperatureratio,T/T =10),thistransitionoccurredfor depthinthecompanionwork,Gaspari&Sa¸dowski(2017). i e luminosityaslowas10−4L (seeFig.3),significantlybelowthe Edd observational constraint. For both the intermediate (T/T = 30) i e and the coldest (Ti/Te = 100) cases, the radiative output is sig- 5 CAVEATS nificantlybelowthemechanicaloneevenforkineticluminosities ∼10−2L ,wellabovetheconstraint. We base our work on simulations performed with a numerical Edd methodusingsomesimplifyingassumptions.Mostimportantly,we This argument implies that to satisfy the observational con- decidednottotracktheenergycontainedintheelectronfluidinde- straintsoneshouldexpectthetemperatureratiotofallbetweenthe pendentlyofions,buttofixtheiontoelectrontemperatureratio. hottestandintermediatecase,i.e.,10 < T/T < 30.Wetherefore i e Thisapproacheffectivelyarbitrarilyprescribesthebalancebetween suggestthatastrophysicalplasmasinopticallythinaccretionflows theelectronheatingandColoumbcouplingwhichdeterminesthe (atleastinthenuclearregion)produceelectronswithtemperature temperature ratio. We adopted this simplification to get a direct between3%and10%oftheiontemperature. handleontheelectrontemperaturesandtoavoidnumericalissues Thephysicsofelectronheatinginaccretionflowsdependson thatarisewhenidentifyingdissipationforthepurposeofelectron the phenomena taking place on the smallest lengthscales of col- evolution(seediscussioninSadowskietal.2016).Thetrade-offis lisionsless plasmas (see, e.g., Quataert & Gruzinov 1999) and is thatweforcethetemperatureratiotobespatiallyuniform–which stilldebated.Howes(2010)proposedaprescriptionforthefraction isnotthecaseinthewholevolume,butisclosetoconstantinside ofheatinggoingintotheelectronpopulationbasedontheoretical thebulkoftheaccretionflow(Ressleretal. 2015;Sadowskietal. modelsofthedissipationofMHDturbulenceinalmostcollision- 2016).Furthermore,wedonottracktheefficiencyofCoulombcou- lessplasmasandwhichhavebeenrecentlyappliedtosimulations pling,whichatthelargestaccretionrates(anddensities)cancouple oftwo-temperatureaccretionflows(Ressleretal. 2015;Sadowski etal.2016).Thismodelpredictsthattheefficiencyofelectronheat- electronsandionsstronglyenoughtopreventlargediscrepancybe- tweentheirtemperatures.Ontheotherhand,ifagiventemperature ing increases in highly magnetized regions, and the equilibrium ratioisfeasible,thentheaboveresultsapply,astheradiativeprop- species temperature ratio is determined by the magnetization of ertiesdependultimatelyontheelectrontemperature,andnotonthe local plasma. Putting the range of temperature ratios favored by processeswhichdetermineitsvalue. thiswork,10 < T/T < 30,intotheformulafortheequilibrium i e We limited our set of simulations to accretion flows on temperature ratio (Sadowski et al. 2016), one recovers the corre- spondingrangeofgas-to-magneticpressureratio,6(cid:46)β(cid:46)10.This non-rotating BHs. If the BH spin is non-zero, one may expect higher efficiency of extracting both radiative and mechanical en- levelofmagnetizationisinagreementwiththelevelexpectedfrom ergy(Tchekhovskoyetal.2011;McKinneyetal.2015;Sa¸dowski thesaturatedstateofmagnetorotationalinstability(e.g.,Davisetal. et al. 2016), and it is likely the transition luminosities identified 2010;Shietal.2010),whatfurthersupportstheargumentsmade, in this work will change6. However, if BH growth occurs mainly andsuggeststhattheaccretionflowsofinterestarenotthreadedby throughchaoticaccretion,asexpectedformostmassivegalaxies, significantnetpoloidalmagneticfluxeswhichwouldimplymuch groups,andclusters(Gasparietal.2013,2015,2017),oneshould strongermagnetization(Bai&Stone2013;Salvesenetal.2016). expecttheaveragevalueoftheBHspininAGNtobeclosetozero Akeyresultworthtoremarkistherobustnessofthekinetic efficiency,whichremainsstablearound3percentvalueregardless (King&Pringle2006).Inparticular,asampleasinRusselletal. (2013) should be biased toward the properties of a zero-spin BH oftheEddingtonratio,atmostvaryingby1percent.Whilebroadly population. accepted that the maintenance mode of AGN feedback resides in It has been understood recently that the level of magnetiza- thekineticregime,giventheubiquitousimprintsofAGNoutflows tion and the topology of magnetic field in an accretion flow are via X-ray cavities, shocks, and gas uplift (Section 1), the kinetic outputinthequasarregimeisstilldebated5.Previousmodelsas- not unique, and depend on the large scale properties of the field. Magneticfieldmaybeconsideredanotherdegreeoffreedominde- sumedastrongdecreaseofthekineticpoweratincreasingEdding- terminingtheflowproperties,whichweleavetofuturework.By tonratios(e.g.,Churazovetal.2005),howeverrecentobservational choosingaparticularconfigurationoftheinitialseedmagneticfield datahasstartedtodetectthepresenceofcavitieseveninsystems intheequilibriumtorus,wechosetostudyaccretionflowswhich withaquasarsource.E.g.,McDonaldetal.(2015)showthepres- arerelativelyweaklymagnetized,andwhichdonotleadtothesat- enceofX-raycavitiesinPhoenixclusterwhichalsohostsanX-ray urationofthefieldattheBHhorizon.Theoppositelimitwouldbe brightquasaremittingatafewpercentoftheEddingtonrate.Albeit themagneticallyarresteddisk(MAD,Narayanetal.2003),which theveryhighEddingtonratiosremaintobetested,ourworkcor- shows properties dramatically different from the weakly magne- roboratestheimportanceofmechanicalAGNfeedbackalsointhe tizedstate(SANE–usingthenomenclatureinNarayanetal.2012). 5 Wenotethateveninthequasar-likeregimetheradiativepowerhassevere 6 Anothercomplicationisthatitisuncertainhowefficientlythechaotic difficultyincouplingwiththegas,especiallyat>kpcscales. inflowwouldalignwiththeBHspinaxis. MNRAS000,000–000(0000) Kineticandradiativeefficienciesinaccretionflows 7 WhetherlowluminosityAGNaccretionflowsareSANEorMAD Gaspari,M.,&Sadowski,A.2017,ApJ,inpress,arXiv:1701.07030 isstilldebated.InthisworkwefocusedonlyontheSANEscenario. Hlavacek-Larrondo,J.,McDonald,M.,Benson,B.A.,etal.2015,ApJ,805, 35 Hogan,M.T.,Edge,A.C.,Geach,J.E.,etal.2015,MNRAS,453,1223 Howes,G.G.2010,MNRAS,409,L104 6 SUMMARY KingA.R.,PringleJ.E.2006,MNRAS,373,L90 We performed a set of general relativistic, radiative, magneto- King,A.L.,Miller,J.M.,&Raymond,J.2012,ApJ,746,2 KormendyJ.,&HoL.C.2013,ARAA,51,511 hydrodynamicalsimulationstostudythetransitionfromradiatively inefficienttoefficientstateofaccretiononanon-rotatingBH.We McKinney,J.C.,Dai,L.,&Avara,M.J.2015,MNRAS,454,L6 Mezcua,M.,&Prieto,M.A.2014,ApJ,787,62 studiedarangeofiontoelectrontemperatureratios,andsimulated McNamara,B.R.,&Nulsen,P.E.J.2012,NewJournalofPhysics,14,5 flowscorrespondingtoaccretionratesaslowas10−6M˙ ,andas Edd (id.055023) highas10−2M˙Edd.Wehavefoundthefollowing: McDonald,M.,McNamara,B.R.,vanWeeren,R.J.,Applegate,D.E.,et (i)Theradiativeefficiencyincreaseswithaccretionrate,and al.2015,ApJ,811,111 the increase occurs earlier for lower ion to electron temperature Narayan,R.,Igumenshchev,I.V.,&Abramowicz,M.A.2003,PASJ,55, ratios(i.e.,hotterelectrons).ForT/T = 10,theradiativeoutput L69 i e becomes significant (exceeding 1% of the rest mass energy flux) Narayan,R.,&Yi,I.1995,ApJ,452,710 alreadyat10−5-10−4M˙ .Forcolderelectrons,thistransitiontakes Narayan,R.,Sa¸dowski,A.,Penna,R.F.,&Kulkarni,A.K.2012,MNRAS, Edd place only at ∼10−3 and ∼10−2M˙ for T/T = 30 and T/T = 426,3241 Edd i e i e Novikov,I.D.,&Thorne,K.S.1973,BlackHoles(LesAstresOcclus),343 100,respectively(Fig.2). Quataert,E.,&Gruzinov,A.1999,ApJ,520,248 (ii)Themechanicaloutputoftheaccretionflowsisinsensitive Ressler,S.M.,Tchekhovskoy,A.,Quataert,E.,Chandra,M.,&Gammie, totheaccretionrate,withanefficiencyremainingstablenear3% C.F.2015,MNRAS,454,1848 of M˙c2.Suchmicroefficiencycanbeexploitedtocloseaunified Russell,H.R.,McNamara,B.R.,Edge,A.C.,etal.2013,MNRAS,432, self-regulatedAGNfeedbackmodelwhichshapesmassivegalax- 530 ies,groups,andclusters(seethecompanionGaspari&Sa¸dowski Ryan,B.R.,Dolence,J.C.,&Gammie,C.F.2015,ApJ,807,31 2017).Weremarkthisisalsovalidasenteringthequasarregime, Salvesen,G.,Armitage,P.J.,Simon,J.B.,&Begelman,M.C.2016,MN- corroboratingtheimportanceofmechanicalAGNfeedbackovera RAS,460,3488 largerangeofEddingtonratios(andthusredshifts). Sa¸dowski,A.,Narayan,R.,Tchekhovskoy,A.,&Zhu,Y.2013,MNRAS, (iii)Bycomparingthesimulatedradiativeandmechanicaleffi- 429,3533 Sa¸dowski,A.,Narayan,R.,McKinney,J.C.,&Tchekhovskoy,A.2014, ciencieswiththeobservationalresultsconstrainingtheluminosity MNRAS,439,503 at which the radiative output becomes comparable with the me- Sa¸dowski,A.,Lasota,J.-P.,Abramowicz,M.A.,&Narayan,R.2016,MN- chanicalpower(Russelletal.2013),weshowthatourmodelsare RAS,456,3915 consistentwithobservationswhentheiontoelectrontemperature Sadowski, A., Wielgus, M., Narayan, R., et al. 2016, arXiv:1605.03184, ratioiswithinarange10

Kinetic and radiative power from optically thin accretion flows

Similar Kinetic and radiative power from optically thin accretion flows