Kinetic and radiative power from optically thin accretion flows

0.63 MB·

by  A. Sadowski

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 prop-
erties are mediated by the recently probed chaotic cold accretion
(CCA),i.e.,thecondensationofmultiphasecloudsoutofthetur-
(cid:63) E-mail:[email protected](AS);EinsteinFellow bulentplasmahalo,whichraintowardthenuclearregionandare
† E-mail:[email protected](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
10<R/R <20.Themagnetocentrifugalforcesdriveoutflowfrom
g
1 Althoughtempting,simulatingaccretionflowswithaccretionrateshigher thesurfacelayersofthedisk.Duetoitslowdensity,theoutflowing
than10−2M˙Edd isextremelychallengingbecausesuchflowscollapsetoa gasdoesnotcontributesignificantlytothetotalradiativeemission.
geometricallythindiskwhichaccretesveryslowly,and,therefore,obtain-
ingconvergedsolutioninareasonablevolumerequiresbothextremenu- Differentdensitiesattheonsetofthesimulationsdetermined
mericalresolutionandlongsimulationtime. theefficiencyofradiativecooling–thelargerthedensity,thehigher
MNRAS000,000–000(0000)
4 A.Sa˛dowski&M.Gaspari
the relative bremsstrahlung cooling rate. Similarly, the larger the However,becauseradiativeenergyisnotconserved(radiationcan
electrontemperatureforagivengastemperature,themoreefficient begeneratedandabsorbedbythegas),weneedtocarefullychoose
is the cooling. The latter effect is clearly visible in Fig. 1 which the radius at which to perform the integration. Ideally, we would
showsthepoloidalsliceofthegasdensity(leftpanels)andtemper- liketomeasuretheluminosityatinfinity.However,wearelimited
ature(rightpanels)forthreemodelswithroughlythesameaccre- bytheregionwheretheaccretionflowhassettledtotheconverged
tionrateofafew10−3M˙ :f5t100,f5t30,andf5t10.Whilethe solution.WedecidedtoperformtheintegralsatR=20R ,whichis
Edd g
densitiesareofthesameorder,thetemperaturesarenot.Thesimu- notinfinity,butencompassedtheregionwheremostoftheradiation
lationwiththecoldestelectrons(f5t100,T/T =100,toppanel) inopticallythindisksisformed.
i e
isashotasitgetswithgastemperatureclosetothevirialtempera- Assumingthattheenergyliberatedinanaccretingsystemcan
ture,asexpectedforanon-radiativeaccretionflow.Assoonaselec- ultimatelyescapeonlyeitherbyradiationormechanicalenergy,we
tronsgethotterrelativetoions(modelf5t30,middlepanel),the cancalculatethekineticcomponentas,
radiativelossesaresignificantenoughtoaffectthegasproperties–
thegastemperature(themeanofelectronandiontemperatures)no- Lkin=Ltot−Lrad. (6)
ticeablydecreases.Gasattheequatorialplane,atR=15R isnow
g
at∼ 1010K,comparedto∼ 1011Kformodelf5t100.Increasing
the electron relative temperature increases further the cooling ef-
3.3 Radiativeandkineticluminosities
fect.Forthelowestion-to-electrontemperatureratio(T/T = 10,
i e
bottompanel,modelf5t10),thegastemperatureatthislocation Theefficiencyassociatedwithgivenluminosityisdefinedas,
fallsdownto∼ 109K.Inadditiontothegastemperature,thera-
L
diativecoolinghaveaneffectonthediskthickness-thetworuns η= , (7)
affectedbycoolinghavenoticeablysmallerthickness(seeTable1), M˙c2
buttheyarefarfromcollapsingtoathindisk.2 Atthelowestac- whereM˙ istheaccretionratethroughtheBHhorizonandcisthe
cretionrates,theradiativeemissionisdominatedbysynchrotron, speedoflight.
while at the largest, for which the radiative cooling has signifi- Table1liststheninesimulationsweperformedandgivesthe
cantimpactongasproperties,itispredominantlyComptoncool- accretionratesandefficienciesobtainedbyapplyingformulaefrom
ing(contributing,e.g.,to∼95%ofcoolingattheequatorialplane theprevioussectiontotime-andazimuth-averageddataspanning
for model f5t30) and, to lesser extent, bremsstrahlung (see, e.g. thelast8000t ofeachsimulation.Theseefficienciesarepresented
g
Narayan&Yi1995;Esinetal.1997). graphicallyinFigs.2and3.
The top panel in Fig. 2 shows the radiative efficiencies as a
function of the accretion rate normalized to the Eddington value
3.2 Massandenergytransferrates (Section1.2).Thesquares,circlesandtrianglescorrespondtoion
totemperatureratiosofT/T =10(hottestelectrons),30,and100
Quasi-stationary,i.e.,accretingatonaverageconstantrate,accre- i e
(coldestelectrons),respectively.Withineachsubgroup,theradia-
tionflowsshowmassandtotalenergytransportratesindependent
tiveefficiencyincreaseswithaccretionrate–growinggasdensity
ofradius.Undersuchcondition,neithergasorenergyaccumulates
resultsinincreasedefficiencyofbremsstrahlungemission.Theac-
atanyradius,butpreservestheiraverageradialprofiles.Wemea-
cretionrateatwhichanaccretionflowdepartsfromtheradiatively
suretheaccretionrateandluminosityintotalenergyinsimulated
inefficientstate(η (cid:28)1)isdifferentfordifferentelectrontemper-
accretionflowsbyintegratingthemassandenergyfluxesoverthe rad
atures.Forthehottestelectronscase(T/T = 10,squarepoints),
BHhorizon. i e
alreadyat∼10−4M˙ (modelf4t10)theamountoftheproduced
Themeanaccretionrateisthereforedefinedthrough, Edd
radiationaccountsto3%oftheaccretedrest-massenergy-roughly
(cid:90) π(cid:90) 2π √ theamountthatthestandard,radiativelyefficientthindisk(Shakura
M˙ = −g(cid:104)ρur(cid:105)dφdθ, (3)
& Sunyaev 1973; Novikov & Thorne 1973) would generate in-
0 0
sideradius20R .Forcolderellectrons,thistransitiontakesplace
whereρstandsforgasdensity,ur denotestheradialvelocity,and g
√ atsignificantlyhigheraccretionrates:∼10−3M˙ forT/T =30,
−gisthemetricdeterminant. Edd i e
∼ 10−3−10−2M˙ forT/T = 100.Inthosecases,theradiative
The luminosity in total energy (binding, kinetic, radiative, Edd i e
efficiency does not exceed 2% even for the highest simulated ac-
magnetic,andthermal,seeSa¸dowskietal.2016fortherelateddis-
cretionrates.Suchadiscrepancyinthecriticalaccretionratecor-
cussion)isgivenas,
responding to the transition to the luminous regime is not unex-
(cid:90) π(cid:90) 2π √ pected–thehottertheelectrons(withrespecttogasorions),the
Ltot=− −g(cid:104)Ttr+Rrt +ρur(cid:105)dφdθ, (4) more efficient is radiative emission, and lower gas densities (and
0 0
corresponding accretion rates) are required for the same amount
whereTr andRr arecomponentsofthematterandradiationstress
t t of emission. Comparable results were obtained by Xie & Yuan
energytensors,respectively. (2012)whocalculatedradiativeefficienciesusingsemi-analytical,
The radiative-only luminosity is given by the integral of the
one-dimensionalsolutionsparametrized,however,bytheelectron
latter,
heatingparameter,δ,notthetemperatureratio.Similarcalculations
(cid:90) π(cid:90) 2π √ werealsoperformedinthecontextofM87byRyanetal.(2015)
Lrad=− −g(cid:104)Rrt(cid:105)dφdθ. (5) whosimulatedGRMHDaccretionflowsaffectedbyradiativecool-
0 0 ing effects tracked with a Monte Carlo radiative transport solver.
Forequalionandelectrontemperatures(T/T =1)andaccretion
i e
2 Theirpropertiesresembletolargeextenttheluminoushotaccretionflow rate∼10−5M˙Edd theyobtainedradiativeefficiencyLrad = 0.51M˙c2
(LHAF)solutionsproposedbyYuan(2001).Detailedstudyofthecollapse – as authors note, surprisingly high even for their choice of BH
wouldrequireprecisetreatmentofCoulombcoupling(seeDiscussion). spinvalue,a∗=0.9375,andpresumablyduetotheflowhavingnot
MNRAS000,000–000(0000)
Kineticandradiativeefficienciesinaccretionflows 5
Figure3.Ratiooftheradiativetokineticluminositiesasafunctionofthe
totalluminosity(sumofthetwo).Thehorizontallinecorrespondstothetwo
equalinvalueandseparatestheradiativelyinefficientregime(below)from
theluminousstate(abovetheline).Theshadedregionreflectstherange
ofluminositiesatwhichtheobservedAGNstartproducingradiativeand
kineticoutputsofcomparablemagnitude(Russelletal.2013).
Table2.Transitiontotheluminousstate
Ti/Te Ltrans/LEdd
100 (cid:38)10−2
30 (cid:38)10−2
10 ∼10−4
Luminousstatedefinedas
Figure2.Radiative(top)andkinetic(bottompanel)efficienciesofthesim- satisfyingLrad>Lkin.
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<Ti/Te<30. MNRAS,inpress
Shakura,N.I.,&Sunyaev,R.A.1973,A&A,24,337
Shi,J.,Krolik,J.H.,&Hirose,S.2010,ApJ,708,1716
Shin,J.,Woo,J.-H.,&Mulchaey,J.S.2016,ApJS,227,31
7 ACKNOWLEDGMENTS
Tchekhovskoy,A.,Narayan,R.,&McKinney,J.C.2011,MNRAS,418,
TheauthorsthankSeanResslerforcommentsonthemanuscript. L79
ASandMGacknowledgesupportforthisworkbyNASAthrough Xie,F.-G.,&Yuan,F.2012,MNRAS,427,1580
Yuan,F.2001,MNRAS,324,119
EinsteinPostdoctotralFellowshipsnumberPF4-150126andPF5-
Wu,M.-C.,Xie,F.-G.,Yuan,Y.-F.,&Gan,Z.2016,MNRAS,
160137,respectively,awardedbytheChandraX-rayCenter,which
is operated by the Smithsonian Astrophysical Observatory for
NASAundercontractNAS8-03060.Supportforthisworkwasalso
providedbyNASAChandraawardnumberG07-18121X.Theau-
thors acknowledge computational support from NSF via XSEDE
resources(grantTG-AST080026N),fromthePL-GridInfrastruc-
ture,andtheNASA/AmesHECProgram(SMD-16-7251).
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