Physical Constraints on, and a Model for, the Active Regions in Seyfert Galaxies

7991 yaM 03 1v4525079/hp-ortsa:viXraPhysicalConstraintson,andaModelfor,theActive

RegionsinSeyfertGalaxies

SergeiNayakshin∗andFulvioMelia∗†1

∗

PhysicsDepartment,UniversityofArizona,Tucson,AZ85721†

StewardObservatory,UniversityofArizona,Tucson,AZ85721

ABSTRACT

WediscussseveralphysicalconstraintsonthenatureoftheActiveRegions(AR)inSeyfert1Galaxies,andshowthataplausiblemodelconsistentwiththeseconstraintsisoneinwhichtheARsaremagneticallyconfinedand“fed”.TheuniqueX-rayin-dexofthesesourcespointstoalargecompactnessparameter(l≫1).This,togetherwiththeconditionsrequiredtoaccountfortheobservedopticaldepthbeingclosetounity,suggeststhatthemagneticenergydensityintheARshouldbecomparabletotheequipartitionvalueintheaccretiondisk,andthatitshouldbereleasedinaflare-likeeventabovethesurfaceofthecoldaccretiondisk.Weconsiderthevariousissuespertain-ingtomagneticflaresandattempttoconstructacoherentpicture,includingareasonfortheopticaldepthintheARbeing∼1,andanunderstandingofthecharacteristicsoftheX-rayreflectioncomponentandthepowerdensityspectraassociatedwiththishigh-energyemission.

Subjectheadings:accelerationofparticles—blackholephysics—magneticfields—plasmas—radiationmechanisms:non-thermal—galaxies:Seyfert

1.Introduction

X-rayemissionisamajorcontributortotheob-servedspectrumofSeyfertGalaxies,andyetthephysicsoftheemittingregionisstillnotwellunder-stood.Themostcommonand(thusfar)successfulapproachtothisproblem,towhichweshallreferasthe‘spectralapproach’(SA),makesverysimpleassumptionsaboutthegeometryand/ortheparticleheatingmechanisms,butusesadetailedmicrophysi-calapproachtoaccountfortheparticle-photoninter-actionsandtoderivethespectrum.Thisspectrumisthencomparedwiththeobservationsinordertoplaceconstraintsontheparametersoftheemittingregions.Theearlymodelsassumedanon-thermalpairdominatedplasma.(Foracomprehensivereviewofnon-thermalmodelsseeSvensson1994.)However,withthemorerecentsubstantialprogressmadeintheX-rayobservationofSeyfertGalaxies(e.g.,Jourdainetal.1992;Johnsonetal.1993),itisnowevidentthatthermalmodelsarestronglyfavoredbythedata.Accordingly,muchofthecurrentattentionisfocusedonthermalmodels(Svensson1996a).

Asidefromthequestionconcerningthenatureoftheparticledistribution,thereisalsotheissuere-gardingtheemitter’sgeometry.Haardt&Maraschi(1991,1993)arguedthatifmostoftheenergyisdissi-patedinahotcoronaoverlyingacoldaccretiondisk,thentheresultingspectrumnaturallyexplainsmanyoftheobservedfeaturesinthesesources.Inpar-ticular,roughlyhalfofthecoronalX-rayemissionisdirectedtowardsthecolddisk,whereitgetsab-sorbedandre-emittedasUVradiation,whichthenre-entersthecoronaandcontributestothecoolingoftheelectrons.Thus,theleptoncoolingratebe-comesproportionaltotheheatingrate.Inthiscase,theinverseComptonup-scatteringoftheUVradia-tionleadstoanalmostuniversalX-rayspectralindex,consistentwiththeobservations(e.g.,accordingtoNandra&Pounds1994,α≃1.95±0.15forasampleofSeyfertGalaxies).Thehardeningofthespectrumaboveabout10keV(Nandra&Pounds1994)andabroadhumpat∼50keV(e.g.,Zdziarskietal1995)areaccountedforbyreflectionofthehardX-raysinthecolddisk.

However,observationallythehardX-rayluminos-ity,Lh,canbeafewtimessmallerthanthelumi-nosity,Ls,inthesoftUV-component.Thisisin-consistentwiththeuniformtwo-phasediskcoronalmodel,becausethelatterpredictsaboutthesame

luminosityinbothX-raysandUV(duetothefactthatalltheUVradiationarisesasaconsequenceofreprocessingofthehardX-rayflux,whichisaboutequalintheupwardanddownwarddirections).Toovercomethisapparentdifficulty,Haardt,Maraschi&Ghisellini(1994)introducedapatchydisk-coronalmodel,whichassumesthattheX-rayemittingregionconsistsofseparate‘activeregions’(AR)independentofeachother.Inthiscase,aportionoftherepro-cessedaswellasintrinsicradiationfromthecolddiskescapestotheobserverdirectly,ratherthanenteringARs,thusallowingforagreaterratioofLs/Lh.

Recently,Sternetal.(1995)andPoutanen&Svensson(1996a)carriedoutstateoftheartcalcula-tionsoftheradiativetransportoftheanisotropicpo-larizedradiation,forarangeofARgeometries.TheyshowedthatthistypeofmodelindeedreproducestheobservedX-rayspectralslope,thecompactness,andthehigh-energycutoff.Themodelhasveryfewpa-rameters,namely,thecompactnessandthetemper-atureoftheintrinsic/reprocessedradiationfromthecolddisk.Therefore,itappearsthatthemodelisveryrobustinitspredictions.

Ontheotherhand,anothersomewhatlesscommonapproachtoexplainingtheX-raysfromGalacticblackholecandidates(GBHC)andSeyfertGalaxies,whichweshallcallthe‘magneticflare’(MF)approach,isbe-ingdevelopedbyanalogywiththestrong,energetic(X-rayemitting)flaresobservedontheSun.Apio-neeringpaperinthisfieldwasthatofGaleev,Rosner&Vaiana(1979),whoshowedthatthephysicalcondi-tionsinanaccretiondisksurroundingablackholearesuchthatmagneticfieldsarelikelytogrowtoequipar-titionvalues.Thismagneticfieldisthentransportedtothesurfaceofthediskbybuoyancyforceswhereitsenergyisreleasedinaflare-likeevent.Themag-neticflareapproachis,inasense,complementarytothespectralapproach,inthatitattemptstoin-cludealltherelevantphysicsself-consistently(e.g.,deVries&Kuijpers1992;vanOss,vandenOord&Kuperus1993;Volwerk,vanOss&Kuijpers1993).Unfortunately,thephysicsinvolvedisquitecomplexandstillsomewhatopentodebate.Theresultingspectrumisacombinationoftime-averagedcompo-nentsfrommanydifferentflares,andissubjecttomanyuncertainties—clearlytheMFmodelmustin-vokemanymoreparameters,orassumptionsaboutthemagneticfieldreconnection,thandoestheSAapproach.Therefore,nodetailedspectrafromtheseevents(inthecaseofSeyfertGalaxies)haveyetbeen2

computed.

Onemayarguethattomakesubstantialprogress,thesetwoapproachesneedtofindanoverlapofself-consistency.Inparticular,theSAmodeldoesnotspecifythemechanismbywhichthegravitationalen-ergydissipatedwithinthecolddiskistransportedouttotheopticallythincorona.Itisassumedthatsomeprocesscanprovidetheneededelectronheat-ing,andoftenareferenceismadetomagneticfields.Moreover,theparticledynamicsisignored,impos-inginsteadtheartificialconstraintthattheparticlesareconfinedtoaclosedbox.Thus,eventhoughtheSAmodelcanreproducetheobservedspectrumquitewell,thesituationisunsatisfactoryfromabroadertheoreticalperspective.

Correspondingly,itappearsthatthemostimpor-tantresultsobtainedwithintheframeworkoftheSAmodelhavenotbeenfullyincorporatedintothemag-neticflarescenarios.Forexample,itiswellknownthattheuniversalX-rayspectralindexinSeyfertGalaxiesisbestexplainedbytheinverseComptoniza-tionofsoftUVphotons.Thisrequiresarelativelyhighvalueofthecompactnessparameter(seediscus-sionbelow)intheemittingregion.Asfaraswecantell,noworkhasyetbeendonetoshow(basedonthephysicsofreconnectionorsomeothermechanismforthetransferofenergyfromthemagneticfieldtotheparticles)thataspecificMFmodelcanindeedpro-videtheneededhighcompactnessduringtheactivephase,thoughHaardt,Maraschi&Ghisellini(1994,hereafterHMG94)didusethephysicsofmagneticflarestoaccountfortheheatingratesandtherequiredconfinementoftheARs.Theyshowedthatthecom-pactnesscanbehighenoughduringtheactivephaseifoneassumesthattheentiremagneticfieldenergyistransferedtotheparticlesduringafewlight-crossingtimescales.Theydidnot,however,explicitlycon-siderthequestionofhowthespectrumfromthesehighlytransientphenomenaisformed.

Morerecently,Nayakshin&Melia(1997b)consid-eredtheissueofpressurebalancewithintheplasmatrappedinsidetheflareduringtheactivephase.Theyfoundthatundercertainconditions,apressureequi-libriumcanbemaintainedinthesourceifitsThom-sonopticaldepthisτT=1−2.Theyalsoshowedthatthecurrentdatacannotdistinguishbetweenaspectrumcomprisedofasingleflarecomponentandoneformedfrommanydifferentflareswitharange∼0.5−2inτT.Inotherwords,onecanalwaysfindaτTforthespectrumassumingasingleflarethat

representsthecompositespectrumquitewellouttoabout100keV,wherethequalityofthedatadeteri-orates.Inaddition,Nayakshin&Melia(1997c)haveconsideredtheimplicationsofatime-dependentX-rayreflectionandreprocessingbythecolddiskun-derneaththeflare.Theyfindthatduetotheshortlived,butveryintenseX-rayfluxfromtheAR,theupperlayerofthediskiscompressedtoadensityinexcessofthatfoundinthedisk’smid-plane.Un-dertheseconditions,theX-rayreprocessingleadstoatemperatureoftheemittedUVradiationthatisroughlyindependentoftheX-rayluminosityandtheoverallbolometricluminosityofthesource,assug-gestedbytheEUV-softX-rayobservations(Walter&Fink1993;Finketal.1994;Zhouetal.1997).Duetotheincreasedgasdensityinthecompressedlayer,theionizationparameterissmallerthanthatarisingintime-independentX-rayreflection(i.e.,whentheX-raysourceisassumedtobestationary—acondi-tionthatisclearlyviolatedinmagneticflares).ThismayexplainthoseobservationsofSeyfertGalaxiesthatsuggestthepresenceofanearlyneutralreflector(Zdziarskietal.1996).

TheseresultsstrengthentheMFmodelandmoti-vateusheretoattempttoassemblethevariouscom-ponentsofthispicture.Wefirstdiscussthediffer-entphysicalconstraintsimposedontheARsbyboththespectralobservationsandthephysicsofthecorre-spondingprocesses,withoutnecessarilyconfiningourdiscussiontotheMFmodel.WewillthenshowthatmagneticflaresabovethecolddiskareprobablythebestcandidatesforproducingtheseARs,andwedis-cussthephysicsoftheMFmodelingreaterdepth.Weconcludebylistingsomeoftheunresolvedissues.2.

PhysicalConstraintsontheActiveRe-gions

OurfirsttaskherewillbetoassemblethevariousconstraintsimposedontheARsinSeyfertGalaxiesfromobservationsandtheoreticalconsiderations.Insodoing,weshallfirstsummarizethebetterknownresults,andthendiscusstheadditionalconstraintsthatfollowfromvariousattemptstoconstructreal-isticARsbasedontheideathatthesemaybemag-neticstructures,characterizedbyawell-definedcon-finementandenergysupply.

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2.1.CompactnessoftheActiveRegions

ThemostimportantparameteroftheARisthecompactnessl≡FγσT∆R/mec3,whereFγisthera-diationenergyfluxatthetopoftheARand∆Risitstypicalsize.Notethatthisdefinitionisforthelocalcompactness,i.e.,theonethatcharacterizesthelocalpropertiesoftheplasma,unliketheglobalcom-pactnesslg≡LσT/R′mec3,whereListhetotallu-minosityoftheobjectandR′isthetypicalsizeoftheregionthatemitsthisluminosity.Itisthelatterthatshouldbecomparedtotheobservedcompactnessratherthantheformer.

Considerthefollowingexample.Assumethattheemittingregionisafulldisk-likecorona.Inthiscasethelocalandglobalcompactnessesarerelatedinthisway:

l≃lg

Hc

X-rayfluxoftheAR,atleastduringtheactivephase(Poutanen&Svensson1995).Assumingthatafrac-tion(∼1)ofthetotalenergycontentinthesurfaceareaofthediskimmediatelybelowtheARistrans-ferredintotheAR,thetimescaleforthereleaseofthisenergymustthenbemuchshorterthantth,dur-ingwhichtimethedisk’sinternalenergyisradiated.Ourcalculationsshowthatifthisconditionisnotsatisfied,thenthelocalizedARsactuallyproduceasteeperspectrumthanthatofafullcorona,duetotheenhancedinternalemissionfromregionsofthediskthatsurroundtheAR.Thisisaneffectthatisneglectedinthetwo-phasecorona-diskmodel.Phys-ically,theinternaldiskemissionprovidestoomuchcoolinginthiscase,unlesstheX-rayemittingregionsomehowsnatchesheatingpowerevenfromdiskre-gionsthatarenotdirectlybelowit,whichappeartobeunrealistic.

TheplasmaintheARsshouldbeconfineddur-ingtheactivephase,otherwisetheenergywillbelosttotheexpansionoftheplasmaratherthanproduc-ingtheX-rays.Notconfined,thesourcewouldex-pandatthesoundspeed(whichturnsouttobeafractionofcfortheseconditions).ThelifetimeoftheARwouldthenbelimitedtoafewlightcrossingtimes.Itisnotclearthatthespectrumfromsuchanexpandingandshortlivedsourcecanresembleany-thingstudiedthusfarintheliterature.Thefamil-iargravitationalconfinement,operatinginthemainpartoftheaccretiondisk,doesnotworkhereduetoseveralreasons.Firstofall,thelocallylimitedEddingtoncompactnesslisatmost∼50/(1+2z)forARswitharoughlysemi-sphericalshape,wherezisthepositronnumberdensityn+dividedbythatoftheprotonsnp,whiletherelativelylargeThom-sonopticaldepthτT≡σTnp(1+2z)∼1obtainedbyZdziarskietal.(1996)requiresacompactnessofafewhundred(ifnomagneticfieldisinvolvedandthepar-ticlesareconfinedtoarigidbox).Second,thereisnomechanismforcounterbalancingaside-waysexpan-sionoftheplasma.Therefore,sincethereseemstobenootherreasonablepossibilityforconfinementoftheARplasma,itmaybearguedthatamagneticfieldisrequiredtoprovidetheboundingpressure.Anycon-finementmechanismwillfailtoconfinetheplasmaforatimelongerthanaboutonedynamicaltimescaleforthedisk,sinceadjacentpointswithslightlydifferentradiiaretornapartonthistimescaleduetothedisk’sdifferentialrotation.

Inaddition,ifthepairsareimportantforthe

model,thenthelifetimeoftheARshouldbelargeenoughtoallowestablishmentofthepairequilibrium.Toputitanotherway,thereshouldbeenoughtimetocreateenoughpairsiftheplasmaisinitiallyopti-callythinandproton-dominated.Weexperimentedwithtime-dependentcodesinwhichradiationtrans-feristreatedinthefrequency-dependentEddingtonapproximation,andfoundthatthisconditionleadstotherequirementthatthelifetimeoftheregionshouldberoughlyanorderofmagnitudelongerthanthelightcrossingtimefortheAR.Inthethindiskapproxima-tiononecanalwayssatisfybothrequirementsaslongasthesize∆RoftheARisoftheorderofthediskscaleheightHd,sinceth≡Hd/csshould≫alsoHd/c,wherecsisthelocalsoundspeed.Wenotethattherecanbeotherthanpaircreationmechanismsfortheplasmatoadjustitsopticaldepth(see§3.3),sothisconstraintisonlyimportantwhentheopticaldepthisdominatedbypairs.

Tobeconsistentwiththeobservationsandthephysicsofthetwo-phaseaccretiondisk-coronamodel,oneneedsveryshortlivedphenomenatooccurabovethedisk’satmosphere.Infact,thewholeevolutionoftheARshouldhappenfasterthanthedisk’shy-drostatictimescale.Toconfinetheplasmawithahighcompactnessparameterl≫1,oneneedsmecha-nismsotherthangravitationalconfinement.Wesug-gestthatthispointstomagneticflaresasthemostlikelymechanismfortheARformation.3.

MagneticFlaresandAccretionDisks

Galeev,Rosner&Vaiana(1979)showedthatmag-neticflaresarelikelytooccuronthesurfaceofanaccretiondisk,sincetheinternaldissipativeprocessesareineffectiveinlimitingthegrowthofmagneticfieldfluctuations.Asaconsequenceofbuoyancy,magneticfluxshouldbeexpelledfromthediskintoacorona,consistingofmanymagneticloops,wheretheenergyisstored.IthasalsobeenspeculatedthatjustasintheSolarcase,themagneticallyconfined,loop-likestructures(whichweshallcollectivelycallmagneticflares;see,e.g.,Priest1982)producethebulkoftheX-rayluminosity.TheX-raysareassumedtobecre-atedbyupscatteringoftheintrinsicdiskemission.Sincethen,severalSolarmagneticflareworkershaveelaboratedonthissubject(e.g.,Kuperus&Ion-son1985;Burm1986;Burm&Kuperus1988;Stepin-ski1991;deVries&Kuijpers1992;Volwerk,vanOss&Kuijpers1993;vanOss,vanOord&Kuperus1993).

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Unfortunately,thesemodelsareverymuchmorecom-plicatedthansimplerplasmamodelsthattakeintoaccountthedetailedinteractionofparticlesandradi-ationbutleaveoutthequestionofhowtheplasmaisconfinedandenergyissupplied.Thus,althoughthemodelsinvokingmagneticflaresabovethecoldac-cretiondiskhavebeenviable,thedetailedspectrumfromsuchaflarecouldnotbecomputed,andthemodelhasremainedsomewhatofanabstraction.AnimportantstepforwardwasthatbyHaardt,Maraschi&Ghisellini(1994),whoforthefirsttimeattemptedtoconnectthephysicsofmagneticflareswiththeobservationalneedforlocalizedactivere-gionsabovethedisk.However,theactualconsid-erationofthemagneticfieldstructurethatconfinestheplasmatotheARwasstillmissing.Further-more,theamountofenergystoredinthemagneticfieldhasbeentreatedasjustaparameter,dependingonhowlongandatwhatratetheenergyissuppliedtotheAR.Inreality,thefieldvalueislimitedbytheequipartitionfieldinthedisk(Galeev,Rosner&Vaiana1979).Thequestionofhowthepressureequi-libriumintheAR(importantwhendiscussingτTofthesource)issetuphasnotbeendiscussed.

OneofthepurposesofthispaperistopaymoreattentiontothemagneticflaremodelfortheX-rayemissionfromaccretiondisksinblackholesystemsingeneral,andinSeyfertGalaxiesinparticular.Intherestofthepaper,wepointoutthattheMFmodelcanaccountformany,ifnotall,oftheobservedX-rayandUVspectralfeaturesofSeyfertGalaxies.Veryimpor-tantly,weshallalsodemonstratethattheseflaresarephysicallyconsistentwiththeconstraintsimposedontheARsdiscussedabove.3.1.

PossibleFlareGeometry

Inthestandardaccretiondisktheory,thegasden-sityhasanapproximatelyGaussianverticalprofile,andthusitdecreasesveryfastwithincreasingheight.Letusalsoassumethatthemagneticfluxtubeisrootedinthemidplaneofthedisk.The“flarere-gion”,i.e.,thatpartofthefluxtubeabovetheac-cretiondisksurface,isthendominatedbymagneticfieldpressure.Itiswellknownthatamagneticfield,lefttoitsowndevices,tendstofillalltheavailablespace(e.g.,Parker1979,§8.4).Forthemagneticfluxtuberootedinthemidplaneofthedisk,thismeansthatthetubecrosssectionexpands;thetubeisthickinthesensethatthecrosssectionalradiusisoftheorderofthetubelength.Thewholestructurehasa

roughlysemi-sphericalshape(Fig.1).

WenotethattheobservationsactuallyrequirethemagneticfluxtubestobethickiftheyaretoexplaintheX-rayemissionfromSeyferts.Indeed,ifthetubesareslim,thenmostofthephotonsreflectedfromthediskwillnotre-entertheAR,butleavesystem.TheamountofcoolingoftheARduetothesephotonsisthennotenoughtoexplaintheX-rayindexesofSeyfertgalaxies—fromspectralmodeling,itisknownthatthefractionofphotonsre-enteringtheARshouldberelativelylarge,∼1/2(e.g.,Svensson1996a).

∆RHdRFig.1.—Schematicofthemagneticflaregeome-tryabovethesurfaceofanaccretiondiskwithscaleheightHd.TheradiusRismeasuredfromtheblackhole,andthefluxtubeishereshownwithaverticalsize(∆R)comparabletoHd.3.2.

MaximumCompactness

Wewillnowassumethatbysomeprocess(e.g.,bymagneticreconnectionordissipationofmagneticwaves)themagneticfieldenergyisbeingtransferredtotheparticles.Wecanestimatethemaximumcom-pactnessoftheARbythefollowingconsiderations.Themagneticfieldislimitedbytheequipartitionvalueinthemidplaneofthedisk.ThesizeoftheAR,∆R,isoftheorderofoneturbulentcell,whichisatbestoftheorderofthediskscaleheightHd.Letusassumethatthefieldannihilation(whichprovidestheenergytransfertotheparticles)occursonatimescaletlequaltothelightcrossingtimeHd/ctimessomenumberb>∼afew.Wewillalsoassumethat

6

theflareoccursat6gravitationalradii,wheremostofthebolometricluminosityisproduced.UsingtheresultsofSZ94,weobtain:

l≤

󰀂1∆RΣcr

/2

Σ=C×(mcr

p/me)α−1r−33

LJ(4)

wherer3≡3R/Rgistheradiusinunitsof3gravi-tationalradii,Rghole),αis≡the2GM/c2(Misthemassoftheblackstandardviscosityparameter,andListhedimensionlessluminosity,L≡L/LEdd,whereLEdd=2π(mpc2/σTRg)istheEddingtonlu-minosity.Finally,J≡1−(1/r3)1/2accountsfortheassumedstress-freeboundaryconditionattheedge.TheconstantChasthevalue

󰀁disk’sinner6ifthe

dominantpressureisduetoradiation.Takingr3=2asanexample,weget

l<∼400

L

εdH(5)

d

whereεmisthemagneticenergydensitysuggestedαare10and0.1,respectively.Wecanalsoassumethatεm0.1εd.Itisthenseenthatl≫1,butitisnotlikely∼tobeashighasafewhundred.3.3.

SpectrumFromEnergeticMagneticFlares

Thetwo-phasemodelisoftencriticizedforalackofself-consistency:oneofthemostimportantquanti-tiesdeterminingthespectrum—theThomsonopticaldepthoftheAR—iseitherfixedinanadhocman-ner,orissaidtobegivenbypairequilibrium.ThelattermaybeviableifthepairsarestronglyconfinedinsidetheARandifthecompactnessoftheregionis∼severalhundred.However,aphysicaldescrip-tionofhowthishappenisneededinordertoval-idatethebasicassumptionsofthemodel.Haardt,Maraschi&Ghisellini(1994)havemadeanattemptinthisdirection,buttheirdescriptionofmagneticflareswasrathersimplisticanddidnotprovideanexplanationfortheobservedopticaldepth.Toad-dressthisissueingreaterdepth,Nayakshin&Melia

(1997b)consideredtheroleplayedbypressurebal-anceinestablishinganequilibriumopticaldepthdur-ingtheactivephaseofamagneticflare.ThemaindifferencewiththeSolarcaseisthatherethecom-pactnessoftheflareismuchlargerthanunity,andthusradiationpressuredominatesoverparticlepres-sure(iftheprotontemperatureisthesameasthatoftheelectrons).TheconditionsprovidingapressurebalancearethereforedrasticallydifferentfromthoseintheSun,wheretheparticlesdictatethenatureoftheequilibrium.Nayakshin&Melia(1997b)assumedthattheenergyissuppliedtothegasbymagnetohy-drodynamicwaves.UndertheconditionstypicalforSeyfertGalaxies,thegroupvelocityofthesewaves(va)isexpectedtobeclosetothespeedoflightc.Becausemomentumistransferredtothegas,aswellasenergy,acompressionalforceisimposedontheplasma.Theradiationpressurewithintheactivere-gionisapproximatelyτTFx/c,whereFxistheX-rayfluxleavingthesource.Inquasi-equilibriumtheen-ergyinfluxisequaltotheenergyoutflux,andradi-ationpressureisequaltothemomentuminfluxduetothemagneticwaves.ThisthenrequiresthattheThomsonopticaldepthτTbeintherange0.5−2,dependingontheactualgeometryoftheflare.TheAlfv´envelocitycanbeusedasanestimateforthegroupvelocityofthemagnetohydrodynamicwaves.Takingthediskstructuretobethatofastan-dardShakura-Sunyaevmodelinitsradiationpressuredominatedregion,onecanshowthattheAlfv´enve-locityva(atadistanceof6gravitationalradiifromtheblackhole)is

va

󰀄εm2

similartothatofastaticactiveregionofthesamesizeandcompactness,aslongasthelifetimeoftheflareexceedsseverallight-crossingtimescales.Thisiscer-tainlytrueifpairsarenotimportant,sincethetimescalesforotherprocessesthatmayinfluencethespec-trum(e.g.,Poutanen&Svensson1996a)areoftheorderofalightcrossingtime.However,thelifetimeofonesingleflareisshortcomparedwiththetypicalintegrationtimeofcurrentX-rayinstruments.More-over,itisverylikelythattherearemanymagneticflarespresentatanygivenmomentoftime.There-fore,itbecomesclearthatifmagneticflaresarere-sponsiblefortheX-rayemissionfromSeyfertGalax-ies,thespectrummustbeacompositeofthecon-tributionsfrommanydifferentflares.Nayakshin&Melia(1997b)testedthispossibility,assumingthattheenergybalanceisfixedbyrequiringtheComptony-parametertobeconstantforalltheflares(whichisreasonable,giventhatyisfixedbythegeometryofthetwo-phasemodel),andtheysummedoverthespectrafromflareswithdifferentτT.Forillustrativepurposes,thedistributionofflareswastakentobeaGaussianoverτT,centeredon1.14withadispersionof0.7.Theresultingspectrumispracticallyindistin-guishablefromthatofasingleflarewithτT=1.14uptoaphotonenergyofaboutahundredkeV.TheOSSEerrorbarsaremuchlargerthanthedeviationsofthecompositeandsingleflarespectra,andsothecurrentobservationscannotdistinguishbetweenthesetwopossibilities.Thus,magneticflarescanconceiv-ablyaccountfortheobservedX-ray/γ-rayspectraofSeyfertGalaxies.3.4.

ExplanationoftheBBBTemperature

Nayakshin&Melia(1997c)consideredtheX-rayreflection/reprocessingduetoatransient,energeticflareabovetheaccretiondisktocomparewithotherstudiesreportedintheliteraturethatassumeasta-tionarystate.Themaindifferencebetweenthetwoisthestructureoftheemitting(i.e.,reprocessing)layer.Inparticular,sincetheflarelifetimeisshorterthanthediskthermaltimescale,apressureandenergyequilibriumbetweentheincidentX-rayfluxandtheunderlyingdiskisnotestablished.Atypicalpho-tondoesnothavesufficienttimetodiffusetothemidplaneofthediskduringonelifetimeoftheflare.How-ever,theX-rayskin,i.e.,thelayerthatabsorbsandreprocessestheX-rays,isonlyatinyfractionofthewholedisk,andthusaquasi-equilibriumisestablishedwithinit.Asaresultoftheincidentflux,theX-ray

skiniscompressedtomuchhigherdensitiesthanthedensityoftheundisturbedaccretiondisk.ItturnsoutthatthepressureandenergyequilibriumofthisX-rayskinyieldsauniquetemperature∼few×105Kindependentlyofthemassofthecentralengine.ThisseemstoaccountwellfortheobservedindependenceoftheBigBlueBumptemperatureontheluminosityofthesource(Walter1994;Zhouetal.1997).Bycomparison,astationary,timeindependentreflectioncannoteasilyexplaintheseobservations.

AnadditionalattractivefeatureoftheMFmodelisthatduetoamuchlargergasdensityinthereflectinglayer,theionizationparameter(ξ∼20)remainsrel-ativelysmall,inwhichcasethereflected/reprocessedspectrumisindistinguishablefromthatofaneutralreflector,whichappearstobefavoredbycurrentob-servations(Zdziarskietal.1996).StaticX-rayreflec-tion/reprocessing,ontheotherhand,mayhavediffi-cultiescomplyingwiththeobservedlowionizationpa-rameterofthereflectingmatter,sinceinthiscasetheX-rayskindensityismuchlower.Summarizing,manyoftheattractivefeaturesofreflection/reprocessinginastaticlayerbelowtheARarepreservedinthecaseofatime-dependent,short-livedmagneticflare,butthelatterhastheadditionaladvantageofbeingabletoaccountfortheapproximateuniversalityoftheBBBtemperatureandthelowionizationfractioninthere-flector.3.5.

PairEquilibriumwithintheMagneticFlares

OneofthecentralquestionsinthemodelingofSeyfertGalaxieshasalwaysbeenwhetherapairequi-libriumisestablishedwithinthesource,sincethishassomeseriousobservationalconsequences.However,pairshavesuccessfullyeludeddetectioninSeyfertGalaxies.Withthediscoveryofahigh-energybreakabove∼100keVandthenon-detectionofapre-dictedannihilationline,ithasbecomeapparentthatthenon-thermalpowerinSeyfertGalaxies,ifatallpresent,isquitesmall(e.g.,Svensson1996a;Zdziarskietal.1996,andreferencestherein).Thus,itwasconcludedthattheplasmaismostlythermal(e.g.,Haardt&Maraschi1991;Fabian1994).Thisinfer-encewassupportedbythefindingthatanannihila-tionlinewouldnotbeobservedfromathermalplasmabecauseitisalwayshiddeninthebroadComptonizedspectrum(Zdziarski&Coppi1995).

Recentworkby(Zdziarskietal.1996)suggeststhatinthecontextofathermalpairequilibrium,

8

anopticaldepthofroughlyunityisthenthecon-sequenceofalargecompactness(∼severalhundred).We,however,suggestthatthissituationisachievedbypressureequilibrium,asdiscussedin§3.3.Inthiscase,theplasmaconsistsprimarilyoftheelectronsandprotonsstrippedfromthedisk,atleastatthebeginningoftheflare,sinceduringthemagneticen-ergystoragephasetheplasmaisnotsufficientlyhottoprovideenoughhardphotonsthatwouldcreateelectron-positronpairs.Thus,inthisframework,thepairsarenotimportantindeterminingthespectrumfromtheflare,andthisisagainconsistentwiththelackofanyobservedpairsignature.

Ofcourse,adetailedmodelingofamagneticflareeventmusttakeintoaccountthepaircreationprocesswhichcontinuouslyproducesnewpairswhenl>Itisthetotalopticaldepth(i.e.,thesumoftheThom-∼10.sonopticaldepthsofelectronsandpairs)thatmat-tersforthepressureequilibrium.Ifthispressurebal-ancefixestheopticaldepthtosomeparticularvalue∼plasma1,thenmustclearly,expandcomparedtoaccommodatetotheno-pairthenewcase,parti-thecles.Letusassumethatthetotalenergysuppliedtotheplasmaisaconstant,whichmeansthatthelu-minosityLremainsconstant.Then,astheplasmaexpands,itscompactnessdecreasesas1/∆Rsincel∼L/∆R.Sincethepaircreationrateispropor-tionaltol2,anequilibriumisreachedatsome∆Rsuchthatthepairsarenowresponsibleforafrac-tionofthetotalopticaldepthτT.Thisfractionturnsouttobequitesmallunlesstheinitialcompactnessisashighasseveralhundred.Itisinterestingtonotethatevenflareswithaninitialvalueoflthatwouldleadtoapairrunaway(e.g.,Svensson1982)findanequilibriumconfigurationwithasourcecompactnessbelowthiscriticalvalue.Weintendtoquantifythecharacterofthepairequilibriuminthissituationinafuturepublication,butwemayalreadyanticipatethatacompactnessashighasseveralhundredisonlybarelypermittedbyEquation(5),andthatthereforepairsshouldbeofrelativelylowimportancetothedynamicsandenergeticsofmagneticflares.3.6.

MagneticFlaresandAGNLightCurves

Severalauthorshavesuggestedthatmagneticflaresabovetheaccretiondiskareresponsiblefortheob-servedvariationsintheAGNandGBHCluminos-ity(e.g.,Galeev,Rosner&Vaiana1979;deVries&Kuijpers1992;Volwerk,vanOss&Kuijpers1993;vanOss,vandenOord&Kuperus1993,andoth-ers).Thepowerdensityspectrum(PDS)fromthesesourcesistypicallyapower-law(Lawrenceetal.1987;McHardy&Czerny1987;Kroliketal.1991).InthecaseoftheSun,Dmitruk&Gomez(1997)haveshownthatmagneticflarescannaturallyaccountforapower-lawshapeinthePDSwithanindex≃1.5.Sinceinprincipletheflaresinblackholesystemsmayhavedifferentspatialsizes,andthusdifferentdura-tionsandoverallpower,onecanreasonablyexpectthatasimilarPDSmaybeproducedbythesetran-sienteventsabovetheaccretiondisksinAGNsandGBHCs.

Wenoteherethatthepower-lawPDSshouldbeex-plainedbylocalvariationsofthemagneticflareprop-erties,ratherthanvariationsoccurringsystematicallywithachanginglocationoftheflare(comparewiththerotatingbright-spotsmodel,e.g.,Abramoviczetal.1991).TheobservedX-rayPDSspansawiderangeinfrequencies,typically10−5-10−3Hz.Thisrangecorrespondstotherangeinradius∼30,sinceΩ−1∼R3/2,whereΩistherotationalfrequencyoftheKepleriandisk.ButthelocalcontributiontotheoverallluminositygoesasJ/R2,andthusthesmall-estfrequenciescontributelessthanthelargestones,incontradictiontotheobservedpowerspectrum.Onlyifoneassumesthattheluminosityoftheflareisin-dependentofitslocationdoesoneobtaintherightpowerspectrum.However,suchanassumptionisun-physical,sinceweknowthattheX-rayluminosityisamajorcomponentofthebolometricluminosity,andthusitshouldscaleinthesamewayasthelocalgrav-itationaldissipationinthedisk.

Therefore,sincetheemissioncomesfromarela-tivelynarrowrangeinradii,itshouldbetheflaresizethatvariesandproducestheobservedPDS.Alterna-tively,sincedisturbancespropagatealongmagneticfieldlinesinastrongmagneticfield,andsincethemagneticfluxtubeisthick,therecanbeawiderangeincharacteristicscalesDeveninonesource(Disessentiallythelengthofthegivenmagneticfieldline[seeFig.1]).Moreover,theenergydensityofthemagneticfieldwillscaleroughlyas1/D2(thatwouldbesoforapotentialfieldthathasnocurrentsevenattheboundary,i.e.inthefootpoints).Thus,onemightexpecttoseeapower-lawPDSevenfromasingleeventinthiscase.Weintendtoinvestigatethisquestioninfuturework,butwecautionthattheanalysisofthePDSisunlikelytoprovideanyvaluableinformationaboutonesinglemagneticflare,sinceatanygiveninstantoftimethereshouldbeanumber

9

ofsuchevents.Theseflaresoccurroughlyatrandom,andthusinformationaboutasingleflareiswashedout.

Thecompleteannihilationofthemagneticfielden-3

ergyεm(≈εd)withinavolumeHdduringatimebHd/cprovidesanestimateofthesingleflarelumi-nosity:

L1

4b,

(7)

wherewehaveusedtheSZ94accretiondiskparam-eterswiththeirfsetequalto1/2.Basedonsim-ilarconsiderations,HMG94estimatedtherequirednumberofmagneticflarestobeabout10.Wearethereforeinagreementwiththisestimate,althoughinprinciplethenumberoflessenergeticorsmallerflaresmaystillbelarger,sinceEquation(7)isonlyanupperlimitonL1.3.7.

GravityConstraints

Animplicitassumptionthusfarhasbeenthatthemagneticflarecanindeedsustainasufficientnum-berofprotonsroughlyonediskheightHdabovethedisk.Forthistobeviable,weneedtodemon-stratethatthegravitationalenergyoftheprotonstrappedinsidethefluxtubeisverymuchsmallerthanthemagneticfieldenergy.Thelatterisatmostthetotalthermalenergyofthediskimmediatelybe-lowtheflare,whiletheformermaybeestimatedas

2

Egrav∼3−1(τT/3r3)(mpc2/σT)(Hd/R)2Hd.UsingexpressionsfromSZ94forr3=2,weseethat

Egrav

4.Conclusions

Inthispaperwehaveattemptedtoaddresstheproblemsthatarisewhenphysicalconstraintsareim-posedontheactiveregionsthoughttoexistinthetwo-phasecorona-accretiondisksinSeyfertGalax-ies.Weshowedthattheseregionsshouldnecessarilybehighlytransient,i.e.,evolvefasterthanonether-maldisktimescaleduetospectrumformationcon-straints.AconsiderationoftheplasmaconfinementleadustorequireanoverallmagneticfieldwithastressmuchlargerthantheX-rayradiationpressure.Furthermore,puttingtheseconstraintstogether,weconcludedthatthemagneticflaremodelappearstobeconsistentwiththetypeoftransientactiveregionsrequiredbytheobservations.Wethenproceededtoshowthatthemodelisprobablycapableofexplain-ingtheobservedopticaldepth,X-rayreflectionandUVreprocessingimpliedbythedata,andtheob-servedpower-lawpowerdensityspectra.Finally,wediscussedtheunresolvedissuesthatneedtobeinves-tigatedinfuturework.5.

Acknowledgments

ThisworkwaspartiallysupportedbyNASAgrantNAG5-3075.Wehavebenefittedfrommanydiscus-sionswithRandyJokipiiandEugeneLevy.REFERENCES

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