Magnetically-Dominated Accretion Flows (MDAFs) and Jet Production in the LowHard STate

DavidL.Meier

JetPropulsionLaboratory,CaliforniaInstituteofTechnologyOctober22,2004

Abstract.InthispaperIproposethattheinnerpartofablackholeaccretioninflow(<100rg)mayenteramagnetically-dominated,magnetosphere-likephaseinwhichthestrong,well-orderedfieldsplayamoreimportantrolethanweak,turbulentfields.Inthelow/hardstatethisflowisinteriortothestandardADAFusuallyinvokedtoexplaintheobservedhot,opticallythinemission.PreliminarysolutionsforthesenewMDAFsarepresented.

Time-dependentX-rayandradioobservationsgiveconsiderableinsightintothesepro-cesses,andanewinterpretationoftheX-raypowerspectrum(asarisingfrommanydiskradii)maybeinorder.WhileanevaporativeADAFmodelexplainsthenoisepowerabove0.01Hz,aninnerMDAFisneededtoexplainthehighfrequencycutoffnear1Hz,thepresenceofaQPO,andtheproductionofajet.TheMDAFscenarioalsoisconsistentwiththedata-based,phemonenologicalmodelspresentedatthismeetingbyseveralauthors.Keywords:blackholes,accretion,magneticfields,jets

1.Introduction:The‘BlackHoleProblem’

Ageneric,robustelectrodynamicmodelforproducingmostastrophysicaljetsisnowwellunderstood.Ithastwobasicrequirements:

−Astrongmagneticfield(VA≡B/(4πρ)1/2>>CS≡(Γp/ρ)1/2,where

VAistheAlfvenspeedandCSisthesoundspeed)thatrotatesfairlyrapidly(Ω󰀁ΩK,whereΩKistheKeplerianangularvelocity).−Somemeansofloadingthisrotatingmagneticfieldwithplasmaatfairly

highelevations(Z∼Rinacylindrical[R,Z,θ]coordinatesystem).Earlymodelsaccomplishedthisloadingbycentrifugalactionfromathindisk,butmorerecentstudiessuggestthattheprimarymeansisthermal,(heatingtheplasmatoroughlythevirialtemperature;Meier,2001).ThemeansbywhichthisconfigurationproducesajetwasfirstproposedbyBlandford(1976)andLovelace(1976)andhasbeenreviewedrecentlybytheauthor(Meieretal.,2001;Meier,2004).Therotationofthemagneticfieldlinesisretardedbytheinertiaoftheplasmaload,creatingarotatinghelicalfieldconfiguration.Lorentzforcessimultaneouslypushplasmaupandoutofthesystemalongtherotationaxisandcollimatetheflowwithmagnetichoopstressbysqueezingittowardtherotationaxis,convertingrotationalenergyofthecentralengineintodirectedkineticoutflowenergyalongtherotationaxis.

󰀁

c2008KluwerAcademicPublishers.PrintedintheNetherlands.Meier.tex;2/02/2008;17:48;p.1

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DavidMeier

ThejetisacceleratedtothelocalAlfvenspeedbytherotationalAlfvenwaveandbeyondthattothelocalmagnetosonicspeedbythetoroidalmagneticpressuregradient.Theterminalvelocityofthejetisapproximatelyequaltotheescapespeedatthefootpointofthemagneticfieldintherotatingcentralengine.

1.1.SPECIFICMODELS

FOR

STELLARJETS

Whilethismodelgivesageneraldescriptionofhowastrophysicaljetsform,itdoesnotanswerthequestionofhoweachsourceproducestheabovetwomainingredients—theglobalrotatingmagneticfieldandtheplasmaload-ing.Forstellarsourcesthefirstrequirementisstraightforward:theglobalmagneticfieldisthatproducedbythestar’smagnetosphereitself.Thediscov-eryofstrongmagneticfieldsinpulsarsandprotostarsystemsisconsideredconfirmationoftheMHDjetproductionmodel.

Theplasmaloadingismoreproblematical.Inpulsarsithasbeenshownthatpairproductioncanoccurin‘sparkgaps’intheverystrongmagneticfield(1011−13G),producingtheneededplasmainsidethemagnetosphereitself(Goldreich&Julian,1969;Ruderman&Sutherland,1975).Inprotostarsystems,however,thefieldisnotnearlyasstrong,sopairproductioncannotoperate.Instead,theprotoplanetaryaccretiondiskisusedtopinchthefieldneartheequator,creatingan“X-point”(Shuetal,1994),whereplasmaisallosedtoflowfreelyfromthediskontotherotatingstellarfield.

Finally,forjetsproducedincollapsingsupernovacores(Wheeleretal,2002),theplasmacomespre-loaded,sincethemagneticfieldofthecol-lapsingcorehasbecomethreadedintotheprogenitormantleduringthelatestagesofstellarevolution.Itistherapidrotationofthecorethatissuddenlyandrapidlygenerated,bythecollapseofthatironcoretoproto-neutronstardensities.

1.2.THEBLACKHOLEPROBLEM

Whileitisclearthatblackholesystemsoftenproducefastandpowerfuljets,theypresentaseriouschallengetotheelectromagnetictheoryofjetproduction.Theplasmaloadingitselfisarelativelyeasyproblemtosolve.Thefactthatblackholesystemsthatproducejetsareassociatedwithhotaccretionflows(Fenderetal.,1999)indicatesthattheplasmamustbeloadedontothefieldlinesfromtheaccretionflowbysomethermalmeans.

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However,bythemselves,blackholescannotsupportamagneticfield1.Theycanhavesuchafieldonlyifthereisanexternalsupplyofplasmainwhichcurrentsgeneratemagneticfluxthatcanthenthreadtheblackhole.Intheabsenceofasignificantamountofexternalplasma,ablackholelosesitsfieldinafewlight-crossingtimes(Thorne,Price,&MacDonald,1986).Thefield,therefore,mustbesupportedbycurrentsintheblackholeaccretionflow.Thisconclusionitselfpresentsaproblem,however.Accretiondisksarebelievedtobeweakly-magnetizedplasmasinhighlyturbulent,orbitalflowabouttheblackhole(Balbus&Hawley,1998).Howdoesaglobal,well-orderedrotatingmagnetospheredevelopnaturallyfromaturbulentaccretiondisk?

Inaddition,evenifaglobalmagnetospherecanbeconstructed,thereisaquestionastohowthatmagnetospherecancoupletoblackholerotationtoproduceastrongjet.Whiletheaccretiondiskitselfcanproducerotationofthemagneticfield,itcannotbethemainsourceofjetpowerinmanyjet-producingsupermassiveblackholesystems.Radiogalaxiesandquasarsthathavesimilaropticalproperties,andthereforesimilaraccretiondisks,candifferintheirradiojetluminositiesbyfactorsof105−6.Thisismosteasilyexplainedbytyingjetproductiontorotationofthecentralobject,justasitisdoneinstellarjet-producingsystems.Inaddition,blackholesystemsareknowntoproducejets∼30timesstrongerthanthosefromneutronstarswithsimilaraccretionrates(Migliarietal.,2003).Whilethiscomparisonmaybecomplicatedbyeffectsoftheneutronstars’magneticfield,astrongcouplingofjetproductiontotheblackholespinalsomaybeatwork.

Tosolvethisproblemwewillassumeherethatthe“magneticPenrose”mechanismofextractingrotationalenergyisatwork(Koideetal.,2002):ifplasmathreadedwithamagneticfieldenterstheergosphere,thenthatplasmacanbeacceleratedinadirectionoppositetotheblackhole’sspin,acquiringnegativeenergyandangularmomentumintheprocess.Positiveenergyandangularmomentumthenistransferredtotherotatingmagneticfield,whichusesthattoaccelerateandcollimatethejet.

Thepurposeofthispaperistoexploreanswerstothetworemainingquestions:1)howdoesaturbulent,magnetizeddiskcreateaglobal,well-orderedmagneticfieldthatcancoupletotheblackholerotationand2)howdoestheaccretiondiskloadthefieldlineswithplasma?

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2.BasicsofMagnetically-DominatedAccretionFlows

2.1.WHATIS

AN

MDAF?

AnMDAFisanaccretionflowinwhichthemagneticforcesdominateoverthethermalandradiationforces.Inanormalaccretiondiskmodel,theweakmagneticfieldcreatesa“magneto-rotationalinstability”(MRI)(Balbus&Hawley,1998)inwhichturbulencedominatestheangularmomentumtrans-portandtheeddyturnovertimeτturbisshorterthantheinflowtimeτinflow≡R/VR.AsteadydiskstructuredevelopsinwhichmagneticfieldcomponentsBR∼Bφ∝R−5/4andpressurescalesasp∝R−3/2.Theratioofmagnetictothermalforcesα∝BRBφ/premainsconstantat∼0.01−1.0.

Werecognizetwotypesofmagnetically-dominatedaccretionflows.Thefirstisstillturbulent,butnowtheratioofthetimescalesisreversed:τinflow<τturb.Smalleddiescontinuetotransportangularmomentum,butthelargeronesarestretchedoutintheRdirectionbeforetheyhaveachancetoturnover.Inthiscase,BR∝R−5/2andBφ∝R−1/2decoupleandp∝R−3/2,sothatmagneticstressesincreaseasRdecreases:α∝R−3/2.Wecallthistypeofflow“transitional”,becauseitconnectsaturbulentflowwithα<1toonewithα>1andtheMRIturnedoff.Ifα0isthevalueatR0,andR1istheradiuswhereαattainsunitvalue,then

R1/R0=α0−2/3

(1)

Ifα0∼0.3,asisexpectedinadvection-dominatedaccretionflows(Narayanetal.,1998),thenR1/R0∼0.5.So,iftheinteriorofanADAFbecomesmagneticallydominated,thetransitionregionwillberathernarrowinradius.InthesecondtypeofMDAF,whichisasolutionto“Gammieflow”(Gam-mie,1999),MRIturbulencehasceasedandtheinflowislaminaralongstrongmagneticfieldlines.BR∝R−3/2andBφ∝R−1arestilldecoupled.Thether-malpressurescalingdependscriticallyontheenergybalanceinthegasnow,butsimplemodelsindicatep∝R−1/2.Soα∝R−2continuestoincreaseinward,andtheflowcontinuestobecomemoremagneticallydominatedasitapproachestheblackhole.Figure1showsaschematicofourlow-statemodelandwillbediscussedmorefullybelow.

MDAF-typesolutionsareseeninMRIsimulationsonlyintheplungingregionveryneartheblackhole,notouttodistancesaslargeas∼100rg.Why?Thereasonmaybetheassumptionimplicitinthesimulationsthattheflowisradiativelyinefficient.ThismaybethecaseforR󰀂100rg(whererg≡GM/c2);inthiscasethetemperatureremainsT󰀁5×109K.However,insidethisradiuselectronsradiatecopiouslybysynchrotron,pairproduction,andotherrelativisticprocesses.WhileADAFmodelsassumethattheiontemperaturecanremainhot(Ti∼1012K(R/rg)−1),ifthereisstrongcouplingbetweenionsandelectrons,theionswillcooltothe󰀂109Ktemperatureas

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Figure1.SchematicdiagramoftheMDAFmodelforGRS1915+105.PowerspectrumdataaretakenfromMorganetal.(1997).Acooldiskfitsthepowerspectruminthehighstate(left)whennojetisproduced.Inthehardstate(right)wenotonlyneedanADAF(extendedcorona)butalsoanMDAF(inward-facingmagnetosphere)toproducethefewHzcutoffandQPO,andanoutward-facingmagnetospheretoproducethejet.Thejetwillbelaunchedfromthetransitionradiusnear∼100rg.TheinputandoutputpowersPi,jcorrespondtothoseintheMalzacetal.model.AnMDAFisalsoexpectedinsomeintermediateaccretionstateswhenthecooldiskisstilltruncatedataradius>rg.

well.Itisoftenassumedthatsuchcoolingwouldleadonceagaintoageo-metricallythin,opticallythickdisk.However,thesemodelsshowthatthereisanothersolution:cool,butstillopticallythinflowalongstrongmagneticfieldlines.It,therefore,isextremelyimportanttobeginperformingMRIsimulationswitharealenergyequation,includingseparateevolutionoftheionsandelectrons.2.2.WHATARE

THE

PROPERTIES

OF

MDAFS?

TheinnerMDAFisanextraordinarilyinefficientflow.Itisanearly-radialin-spiral,geometricallythickbecauseofmagneticpressuresupport(Meier,2004).VirtuallyallorbitalangularmomentumistransferredouttoR1alongthestrongfieldlines.Theplasmaexperiencesonlycompressionalheatingandradiativecoolingbyelectronsandcouldremainquitecool;themajorityofthe

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gravitationalenergyreleasedisconvertedintoradialinfallkineticenergy,notheat.

Becausethemagneticradialchannelsarepotentiallydistinct,theflowmaybreakupintoinhomogeneous“spokes”.AsignatureofanMDAFmaybeaquasi-periodicoscillationatoneormoreoftwotransitionradiusfrequencies:1)theorbital/Alfvenfrequency

νA=VA/2πR1=1.1Hz(M•/10M⊙)−1

and2)theMHDslowmode(“organpipe”)frequency

νS=VS/2πR1≈CS/2πR1=0.02−0.13νA

(3)(2)

or∼20−140mHzfora10M⊙blackhole,dependingontheazimuthallengthoftheresonatingmagnetictubes.BecauseνSisexcitedacousticallynearR1alongthelengthofthesetubes,itmaybecharacterizedbymultipleharmon-ics,whereastheorbital/Alfvenmodeshouldberatherpure.

Themagneticfieldlinesextendinginwardtowardtheblackholemaytapthehole’srotationalenergyiftheypenetratetheergosphere.However,ingen-eraltheholerotationratewillnotmatchthe,usuallyslower,νA.Onethereforemightexpectanepisodicinteraction,wherethefieldenterstheergosphere,iswounduprapidly,reconnectsinaseriesofrapidflaresseparatedbytheergosphererotationtime,andfinallypullsbackfromtheholeforaseculartime.ThebehaviorofSgrAattheGalacticcenter(Genzeletal.,2003)isverysimilartowhatmightbeexpectedfromarotatingblackhole/MDAFinteraction.

Inadditiontoaninnermagnetosphereofclosedfieldlinesreachingtowardtheblackhole,therealsomaybeopenfieldlinesextendingfromR1toinfinity(seeFig.1andMeier,2004).Thetransitionradius,therefore,hasallthepropertiesnecessarytolaunchajet:thebaseoflarge-scale,open,rotatingmagneticfieldlinesbeingloadedwithhotADAFmaterial.ExcessangularmomentumisdepositedatR1bytheradialfieldlinesthatconnectperiodicallytotheblackholeergosphere.AnoutflowingMHDwind/jetwouldbeagoodcandidateforcarryingoffthisexcessangularmomentum.

3.Discussion

3.1.MDAFS

ANDTHE

LOW/HARD(PLATEAU)STATE

OF

XRBS

WhenthetransientX-raybinary(XRB)sourceGRS1915+105isinthesoftstateandnotproducingajet,itsphotonspectrumisdominatedbyacoolthermalspectrum,anditspowerspectrumisaratherfeaturelesspowerlawofdP/dν∝ν−4/3.Whenthesourcebeginstoproduceasteadyjet,itenters

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alow/hardstateinwhichthephotonemissionisdominatedbyanon-thermalspectrum.Andthepowerspectrumdevelopsbandwidth-limitednoise(aflat(dP/dν∝ν0shoulderwithasteepcutoffabove∼3Hz)andaQPOat1-3Hz.Itisnaturaltoassociatethenon-thermalphotonspectrumandbandwidth-limitednoisewiththeopticallythin,turbulentADAFthathasformedinthecenterofthedisk.ButwhatproducestheQPO,andwhywouldtheADAFbebandwidth-limited?Whydoesitsturbulencenotextendallthewaytothenaturalfrequenciesneartheblackhole(∼100Hz)?

TheinnerMDAFmodelprovidesnaturalanswerstothesequestions.WhilethethinaccretiondiskistruncatedbytheADAFat,perhaps,∼1000rg,theADAFitselfistruncatedatR1∼100rgbytheMDAF,cuttingofftheADAFturbulenceaboveafewHz.TheslopeofthiscutoffmayrepresentthehighfrequencytailoftheturbulencespectrumnearR1.TheQPOisproducedbythemagneticfluxtubesthatstretchtowardtheblackholeandrotateatroughlytheorbitalR1frequency—againafewHz.

Thepowerspectrumateachdiskradiusshouldbedominatedbyarathernarrowly-peakedlocalspectrum(Maron&Blackman,2002).Wethereforecanapproximatethetotaldiskpowerspectrumbyassumingthelocalspec-trumtobeadeltafunctionandsimplyplottingthevariationoftheturbu-lencestrengthwithradiusagainstthevariationoftheprincipallocal(orbital)frequencywithradius:

P[r(ν)]=(2π∆RδH)ρVturb(R)2

(4)

where∆R∼RistheannulusoverwhichρandVturbremainroughlyconstant,andδHistheskindepthoverwhichtheturbulenteddiescanbeseenbytheobserver(roughlytheopticaldepth).Foranα-disk(Shakura&Sunyaev,1973),wefindP(r)∝R1/2∝ν−1/3,ordP/dν∝ν−4/3,inagreementwithGRS1915+105inthehighstate.However,inthelowstate,forasimple

˙∝R−1)(Esinetal.,1997),wefindthatdP/dν∝evaporativeADAFmodel(M

ν−2/3,whichisnotflat.InordertoobtaindP/dν∝ν0,weneedtoassumea

˙∝R−2.DetailedsteeperrateofevaporationofthethindiskintotheADAF:M

modelingofthepowerspectrumasdiskturbulenceatdifferentradiimay,therefore,becomeanimportantdiagnosticofconditionsintheopticallythinportionoftheaccretionflow,ADAFandMDAFalike.

Figure1showsaschematicpictureofGRS1915+105inthesoftandhardstates,thecorrespondingpowerspectra,andenergyinputstoandoutputsfromthetransitionregion.3.2.RELATION

TO

PRESENTATIONS

ON

XRBS

ATTHIS

MEETING

Fenderetal.(2004)haveproposedaphenomenologicalmodelforjetproduc-tioninwhichthejetspeedincreasesastheinnerdiskradiusdecreases.Thismodelexplainswhystrongjetoutburstsareseenwhenthedisktransitions

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DavidMeier

tothehigh/softstateandnotwhenittransitionstothelow/hardstate:thejetspeeddecreaseswithtimeinthelattercase,resultinginnoformationofashock.

ThismodelfitswellwiththeMDAFscenario.Weidentifythelow/hardstateasoneinwhichthecoolaccretiondiskcompletelyevaporatesbeforetheADAFtransitionsintoanMDAF,i.e.forR>R1.Inthiscase,nearthecentralengine,thejetspeedissimplytheescapespeedfromthetransitionradius,or

Vjet∼2GM/R1

(5)

whichgivesanon-relativisticjetofVjet∼0.1c.Eventually,astheaccretionrateisincreased,thecooldiskbeginstoextendinside∼100rg,andtheADAFchangesfromanaccretionflowinitsownrighttosimplyacoronaaboveadensecooldisk.TheADAFnolongerextendsinsidethetruncatedcooldisk;thatregionisfilledwiththeMDAFonly,extendingfromtheADAFcoronainward.Thisbeginsthemovetowardthehighstatealongtheupperhorizontalbranchintheintensity/hardnessplane:thehardADAFemissionbeginstobesuppressed,thethermalemissionfromthecooldiskgainsinstrength,theradiusR1wherethetransitiontoMDAFoccursnowfollowsthecooldisktruncationradius.Thejetvelocityfromequation(5)increasesasthedisktruncationradiusdecreases.EventuallyR1reachesallthewaytotheblackholehorizon,andtheMDAFisswallowed.Thisturnsoffthejet,butnotbeforeitsvelocityreachesclosetocasR1→rH,thehorizonradius.Itisthisfastjetthatcreatestheshockandoutburstthatweobserve.

Malzacetal.(2004)alsohaveinterpretedthevariabilityofXTEJ1118+480ascouplingbetweenthecoronaandthejetthroughacommonreservoirwherelargeamountsofaccretionpowerarestored.IntheMDAFmodelweidentifythetransitionregionatR1asthisreservoir.Energyandangularmomentuminputintothisregioncomesfromtwosources:theaccretionflowfromoutsideandthemagneticcouplingtotheblackholefrominsideR1.Theoutputpoweristhejetproductionthatoccursatthisradius.Itisimportanttonotethatthepredictedtemperatureatthistransitionregionisoforderafew×109K,anditliesat∼100rginthelowstate,butcanmoveinwardastheaccretionrateincreases(seeabove).3.3.MDAFS

AND

LOW-LUMINOSITYAGN

Blackholeaccretioninactivegalacticnuclei(AGN)isexpectedtoactsimi-larlytothatinXRBsystems:brightSeyfertandquasarobjectsarebelievedtobeinasoftstatewhilethoseAGNwithoutstrongopticallineemission(low-luminosityAGN[LLAGN],FRIradiogalaxies,SgrA)arebelievedtobeinalow/hardstate.Whilethereissometimingdataavailableontheselatterobjectes,adetailedcomparisonwiththeMDAFmodelisnotpossible

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atthistimeasaQPO-producingplateaustatehasnotyetbeenidentified.OurdiscussionofMDAFsinAGNthereforewillbemorespeculative.

LLAGNdoindeedshowbandwidth-limitednoise,andthecutoff/breakathighfrequencysometimesisusedasanindicatorofblackholemass,withτbr≈7.7d(M•/107M⊙),whereτbristhetimescale,indays,wherethebreakoccursintheAGNX-raypowerfluctuationspectrumPapadakis(2004).TheMDAFmodelprovidesaphysicalreasonwhythisadhocscalingofthebreakindifferentsystemsisareasonableblackholemassindicator.Inthemodelthefrequencyofthisbreakwillbeequalto,orslightlygreaterthan,νA(equation2),soτbr=1/νA≈10d(M•/107M⊙).

AGNalsodisplayanotherpropertysimilartothatshownbyX-raybi-naries,andtheMDAFmodelprovidesthesameexplanationthereaswell.JetsproducedbyquasarsandmanySeyfertstendtobequiterelativistic,evenwithinonlyaparsecfromtheblackholecore.Theythereforemaybelaunchedandacceleratedratherclosetothecentralblackhole.Thissugges-tionissupportedbysemi-analyticjetaccelerationmodels,whichsuggestamagneticfootpointonlyafewgravitationalradiifromtheholefor3C345(Vlahakis&Konigl,2004).However,jetsproducedbyLLAGNandFRIs(andtheircounterparts,theBLLacertaeobjects)areeitherlessrelativisticorshownomotionatall.AsimilarmodelforaccelerationoftheNGC6251jetyieldsaninnerfoot-pointof∼34rgfora6×108M⊙blackhole(Vlahakis&Konigl,2004).Furthermore,M87showssignificantcollimationonscalesof60−200rg(Birettaetal.,2002),anditsjetspeedatadistanceof0.16pcfromthecoreisonly0.1c.Yet,atkiloparsecdistances,M87showssuperluminalmotionsupto6c.JetsinAGNsystemsidentifiedwiththelow/hardstateappeartobelaunchedwithsmallervelocitiesandatlargerdistancesfromthecentralblackhole.

Itappearspossible,then,thatthejet-productionregioninLLAGNandFRIobjectsalsomaylooklikethatinFigure1,withthelaunchpointlyingmanytensofgravitationalradiifromtheblackhole.Onlythroughcontinual,andpersistentaccelerationbytheblackholeoverlargeverticaldistances(manyparsecstokiloparsecs)dojetsinlow/hardstateAGNachievetherelativisticspeedsobservedveryfardownstreamoftheaccretiondisk.

4.Conclusions

InterpretationofthephotonandpowerspectraofblackholesystemslikeGRS1915+105leadstoanewmagnetically-dominatedaccretionflow(MDAF)modelforthelow/hardstatewiththreedistinctdiskregions:

1.Asinpreviousmodels,theouterregionofthediskisageometricallythin,opticallythick,andcoolturbulentdisk,drivenbytheMRI.

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2.Likewise,atintermediateradii(∼100−1000rg)thereisaone-temperature,advection-dominated,turbulentaccretionflow(ADAF)disk/coronathatisgeometricallythick,opticallythin,andhot.Anevaporationrateinto

˙∝R−2ismoreconsistentwiththepowerthiscoronathatscalesasM

spectrumthanothermodels.3.Thestructureinside∼100rgdistinguishesthismodelfromothers:attheradiuswherecoolingbyrelativisticelectronsbecomesimportant,theADAFtransitionstoanMDAFwithα>>1.Theinflowisextremelyinefficient,non-turbulentandnearlyradialalongstrongmagneticfieldlines—essentiallyaninward-facingmagnetosphere.ThenarrowannuluswheretheflowtransitionsfromADAFtoMDAFisanidealsiteforopenfieldlinesandthelaunchinganMHD-poweredjet.Weidentifythebandwidth-limitednoisethatappearsinthelow/hardstateastheADAF’sMRIturbulenceviewedthroughtheopticallythinflow.TheMDAFmodelpredictstheobservedtruncationofthatnoiseatafewHzandtheappearanceofastrongQPOatthesameplace,aswellastheverylowfrequencyQPOsat0.01-0.1Hz.Finally,theMDAFmodelisconsistentwiththepheomenologicalmodelsofFenderetal.(2004)andMalzacetal.(2004)andprovidesaphysicalconnectionbetweenthemandblackholeaccretiontheory.Inparticular,extensionofthismodeltoincludeanMDAFinsidealltruncateddisksnaturallypredictsthevariationinjetspeedwithinnerradiusdeducedbyFenderetal.(2004).

Themodelsuggestsanewinterpretationofthepowerspectrumofblackholecandidates:likethephotonspectrum,eachsmallrangeinfrequency∆νiscontributedbyagivenannulus∆Rintheaccretiondisk,withthecentralfre-quencycorrespondingtotheKeplerianfrequencyatthatradius.Thespectralslopesareduenottothephysicsoftheturbulenceitselfbutrathertovariationsindiskstructurewithradius.OnlythecutoffatafewHzisindicativeofthe(highfrequencyendofthe)localpowerspectrumthere.

Acknowledgements

TheauthorisespeciallygratefultoT.MacaroneandR.Fenderfororganizingthisconferenceonblackholeaccretiononallmassscales.Emphasizingthesimilaritiesandscalingofblackholesystemscontributesgreatlytotheirover-allunderstanding.Theauthorissupported,inpart,byaNASAAstrophysicsTheoryProgramgrant.ThisresearchwasperformedattheJetPropulsionLaboratory,CaliforniaInstituteofTechnology,undercontracttoNASA.

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