On the effect of coronal outflow on spectra formation in galactic black hole systems

A(MNLTEXstylefilev1.4)

Ontheeffectofcoronaloutflowonspectraformationin

galacticblackholesystems

˙A.Janiuk,B.Czerny,P.T.Zycki

NicolausCopernicusAstronomicalCenter,Bartycka18,00-716Warsaw,Poland

arXiv:astro-ph/0007070v1 6 Jul 20001February2008

ABSTRACT

Wepresenttheresultsofbothanalyticalandnumericalcalculationsoftheamplitude

ofthereflectioncomponentinX-rayspectraofgalacticblackholesystems.WetakeintoaccounttheanisotropyofComptonscatteringandthesystematicrelativisticbulkmotionofthehotplasma.InthecaseofsinglescatteringapproximationthereflectionfromthediscsurfaceissignificantlyenhancedduetotheanisotropyofComptonscattering.OntheotherhandthecalculationsofmultiplescatteringobtainedusingtheMonteCarlomethodshowthattheanisotropyeffectismuchweakerinthatcase.Therefore,theenhancedbackscatteredfluxmayaffecttheobservedspectraonlyifthediscsurfaceishighlyionized,whichreducestheabsorptionintheenergybandcorrespondingtothefirstComptonscattering.

Keywords:accretion,accretiondiscs–blackholephysics–galaxies:active–X-rays:galaxies–X-rays:stars

1INTRODUCTION

HardX-rayspectraofthegalacticblackholesystemsarewelldescribedbyapowerlawprimaryemissionalongwiththepronouncedreflectedcomponent,whichcausestheob-servedflatteningofthespectrum.TheprimaryemissionislikelytobeproducedbyComptonupscatteringofsoftpho-tonsonthermalelectronsinhot,opticallythinmediumclosetoarelativelycoldaccretiondisc,beingthesourceofseedphotonsforComptonization(seee.g.reviewinPoutanen1998).Afractionoftheupscatteredphotonsisdirectedto-wardsthediskandcanbereflectedfromitssurface,giv-ingtherisetoreflectedcontinuumandfluorescentironlineemission(Lightman&White1988;George&Fabian1991).ObservationaldataforCygX-1andotherblackholesystemsintheirhard/lowstateshowoftenratherhardspec-tra(photonspectralindexΓ∼1.5−1.9;Poutanenetal.1997;Gierli´nskietal.1997;Doveetal.1997;seealsoPouta-nen1998),whiletheamplitudeofreflectionRcoversthebroadrangeofvaluesbetween0and2.Moreover,RandΓarecorrelated(Zdziarski,Lubi´nski&Smith1999;Revnivt-sev,Gilfanov&Churazov1999),inthesensethattheharderthespectrum,thesmallertheamplitudeofreflection.Thecorrelationexistsbothwithinthelow/hardstateandwhen

˙sourceschangetheirspectralstate(Zycki,Done&Smith

1998).

Theseobservationscannotbeexplainedbythemodelinwhichstatic,continuouscoronacoversthecoldaccretiondisc,asitpredictsthepowerlawslopeΓ󰀂2(i.e.rathersoft

c0000RAS󰀁

spectra)andthereflectionamplitudeR∼1.0.Amongthe

possiblemodels,whichcouldreproducethereflectionam-plitudeintherangeR=0−1therearetwocompetitive:(i)colddiscdisruptedintheinnerpart(e.g.Poutanen,Krolik&Ryde1997;Esin,McClintock&Narayan1997)and(ii)ahighlyionized,non-disrupteddisc(Nayakshin,Kazanas&Kallman2000;Ross,Fabian&Young1999).Detailedshapeofthereflectedcontinuumdependsonthegeometry,ion-izationstateandabundancesofelementsinthescatteringmedium.However,spectralfittingdoesnotalwaysallowtoconstraintheseparametersindependently.ItispossibletoexplaintheobservedspectraofGBHintermsofweaklyion-ized,orneutralreflectionfromthediscwhichinnerradius

˙isoftheorderof50Rg(e.g.Done&Zycki1999forthehard

stateofCygX-1),aswellaswithhighlyionizedreflectionfromthediscextendingtothemarginallystableorbit(assuggestedbyRossetal.1999forthehardstateofCygX-1;seealsoDone&Nayakshin2000).

Thethirdpossiblemodel,inwhichboththereflectionamplitudesR>1andR<1arepossible,isamildlyrel-ativisticoutflow/inflowinthecorona(Beloborodov1999).RelativisticaberrationreducesthehardX-rayfluxscatteredtowardsthedisc,whichleadstoreductionofthereflectedcomponentandthesoftfluxfromreprocessingenteringthecorona.Inordertoobtainquantitativeagreementwithob-servedspectralindicesandreflectionamplitudes,themodelrequiresadditionalreductionofthesoftfluxinterceptedbythehotplasma.Thisleadstothe’activeregions’geome-try(e.g.magneticflaresabovethedisc;Haardt,Maraschi&

2

A.Janiuk,B.Czerny,P.T.Zycki

˙Ghisellini1994)ratherthanacontinuouscorona.However,thecoronaloutflowmayreproducethereflectionamplitudeR<1andinordertoobtainR>1aninflowoftheplasmamustbepostulated.

Inthisarticlewereanalyzethenon-staticcoronamodel,withplasmamovingatrelativisticspeedinthedirectionper-pendiculartothediscsurface.Westudythedependenceoftheamplitudeofthereflectioncomponentonthebulkmo-tionvelocity,takingintoaccountthethermalmotionofelec-tronswithintheplasmadeterminedbytheelectrontemper-atureTeandwediscusstheresultingshapeofthespectra.Wealsocheckifhighreflectionamplitudes(R>1)mightbeexplainedintheframeoftheoutflowmodelbuttak-ingintoaccountpossiblehighionizationofthediscsurfaceandtheanisotropyofComptonscattering.WeemphasizetheimportanceofthefirstComptonscattering,whichplayscrucialroleatlowerenergies.Forhighlyionizeddiscsurfacetheeffectofabsorptionbyheavyelementsisreducedandthereflectedspectrummakesasubstantialcontributiontothetotalspectruminthe∼0.5−5keVband.Thereforewepresentfirstlythesemi-analyticalcalculationsintheap-proximationofsinglescattering,andafterthatweperformnumericalsimulationsofmultiplescattering,whichisre-sponsibleforthepowerlawshapeofthehardX-raytail.

Thecontentsofthepaperisasfollowing.InSection2weanalyzesemi-analyticallytheamplitudeofthereflectioninasinglescatteringapproximation(afterGhisellinietal.1991)buttakingintoaccountanisotropyofscatteringwithintherestframeoftheelectron,describingthethermalmotionwithouttheassumptionofhighlyrelativisticbeamingandincorporatingthesystematicbulkmotion(outflow)ofthecorona.Sincetheeffectofmultiplescatteringisessentialinarealsituation,inSection3werepeatthecomputationsforacoronaofagivenopticaldepthandanelectrontemperatureusingaMonteCarlomethodforbothoutwardsandinwardsdirectionsofbulkvelocity.ThedependenceofthereflectionamplitudeontheoutflowvelocityispresentedinSection3.1.ThespectraresultingfromMonteCarlocomputationsarepresentedinSection3.2.ThediscussionoftheresultsisgiveninSection4.

2

SINGLESCATTERINGAPPROXIMATIONFORTHEAMPLITUDEOFREFLECTION

Inthissectionwegeneralizethedeterminationoftheampli-tudeofthereflectioncomponentderivedbyGhisellinietal.(1991)foraslabgeometryofahotcoronaandanisotropicsoftphotoninputfromunderlyingdisc.Thoseresultswereobtainedassumingisotropicelectronscatteringintherestframeofanelectronandrelativisticchaoticmotionofelec-trons.WeintroducesubsequentlytheanisotropyoftheThomsoncross-section(Section2.1),werelaxtheassump-tionthatthethermalmotionoftheplasmaisrelativistic(Section2.2),andfinallyweintroducethesystematicbulkmotionofthecorona(Section2.3).

Weshow,thatincludingtheeffectofanisotropicsoftphotondistributioninComptonscatteringprocessthere-flectionamplitudeR󰀂2canbeobtained.It’svalueissomewhatlargerwhentheangulardependenceofThom-soncross-sectionistakenintoaccount.Ontheotherhandforlowelectronvelocities(γ<2)theangulardistributionof

scatteredradiationbecomesimportantandthevalueofRis

reduced.Addingthesystematiccoronaloutflowreducestheanisotropyeffectonlyintherangeofhighbulkvelocities.Howeveralltheseresultsstandmostlyforthefirstscatter-ing,whileforthemultiplescatteringinthecloudofopticaldepthτ∼1thereflectionisweaker(seeSection3).

2.1

TheeffectofangulardependenceoftheThomsoncross-section

InthissectionwecalculatethepowerofComptonradia-tionscatteredbyelectronswithisotropicrelativisticveloc-ityfieldv=βc,β∼1.Thisapproachisappropriateforanon-thermalplasma.Theradiationfieldisanisotropicandincomingphotonssubtendarestrictedsolidangle.Weas-sumethegeometryisthesameasinGhisellinietal.(1991).However,inourcalculationswetakeintoaccounttheangu-lardependenceofThomsoncross-section(Rybicki&Light-man,1979).Thereforetheemittedpowerisgivenby

3

2π−φmin

P(α,γ)=

(1+β2/3)

dφ

󰀄

φmin

θmax

󰀄

(1−βcosθ)2(1+cos2θ)sinθdθ

(1)

θmin

HerePisoisthepowerofisotropicemissionandP(α)isthepowerofradiationscatteredbyelectronoftheangleαbetweenitsvelocityandtheaxisofsymmetryofincomingphotons.Thelimitsθmin,θmaxandφminarefunctionsofαandaregivenbyequations(seeGhisellinietal.,1991):θmin=max(0,α−π/2)θmax=min(α+π/2,π)

(2)

for0<θ<π/2−αφmin=

󰀇

0

or3π/2−α<0<πarccos[(tanθtanα)−1]otherwise

HerewefollowtheassumptionofGhiselliniet.al(1991),thatallphotonsareemittedinthedirectionofelectron’svelocity.Thisisjustifiedinthecaseofγ≫1,whenthedirectionofthemotionofanelectron(i.etheangleα)canbeidentifiedwiththeviewingangle.InFigure1weplottheratioofthetotalpoweremittedbyelectronsmovingdownwardstothatofelectronsmovingupwards:R(γ)=

󰀆π

π/2

P(α)sin(α)dα

Ontheeffectofcoronaloutflowonspectraformationingalacticblackholesystems3

Figure1.Theratioofthetotalpoweremittedbyelectronsmov-ingdownwardstothatofmovingupwardsasafunctionofelec-tron’sLorentzfactorγ.

Figure2.Theratioofthetotalpoweremittedbyelectronsmov-ingdownwardstothatofelectronmovinginoneparticulardirec-tion,asafunctionofelectrontemperaturekT[keV],foranincli-nationangleα=30◦,undertheassumptionofefficientbeaming

(dashedline),andforthesameinclinationangle(i=30◦)butav-eragedoverthewholerangeofelectron’svelocitydirection(solidline).

π

R(α,kT)=

󰀆π/2

P(α)sin(α)dα

󰀁

c0000RAS,MNRAS000,000–0002γ4(1+βcosΘout)3

(5)

whereΘout=πmeansscatteringinthedirectionofelec-tron’smovement.Theaccretiondiscreceivesafractionofscatteredradiationthatdependsonthedirectionandveloc-ityofelectron

Pdisc(󰀄

α,γ)=

Θmaxout

φminout

P(α,γ,Θout)sinΘoutdΘoutdφout(6)

Θminout

󰀄

2π−φminout

whereΘmaxout,Θminoutandφmin

outaregivenbyequations(2).

Theviewingangleiinthiscasecannotbeidentifiedwiththedirectionofelectronmotiongivenbyα.Instead,wehavearelation

cosΘout=−(sinisinϕsinα+cosicosα).(7)

Hereαandϕdeterminetheelectron’svelocityvectordirec-tion:

󰀤v=v(cosϕsinα,sinϕsinα,cosα)

(8)

InFigure3weshowtheassumedgeometryscheme.Note,thattheangleΘoutismeasuredfromthevector−󰀤vtothedirectionofemittedphoton,andthereforewekeepthein-tegrationlimitsgivenbyequations(2)unchanged(seealsoFig.1andFig.2inGhisellinietal.1991).

Wecalculatethereflectionamplitudeaveragedoverthewholerangeofαandϕasafunctionofelectronvelocityandviewingangle,accordingtotheformulaR(γ,i)=

1

InFigure4we󰀆πplot󰀆2π

0

0

P(α,γ,Θout(α,ϕ,i))sinαdαdϕ

.(9)

thereflectionamplitudeasafunctionofγforthreedifferentvaluesofviewingangle.Theplotforaninclinationi=60oroughlycorrespondstothevalueaver-agedoverallinclinations,aspresentedinFigure1fornon-thermalplasma.Weseethattheanisotropyisonlyslightlyreducedifthetotalcollimationassumptionisrelaxed.ThiseffectismostlyseeninFigure2wherewepresentwiththesolidcurvelowvelocity(moderatetemperature)tailofthedistribution.2.3

Mildlyrelativisticbulkmotion

Inthissectionweassumethatbulkvelocityvectorisperpen-diculartothediscsurfaceanddirectedoutwards.Wecalcu-latethenetelectronvelocityasasumofthermalchaoticmo-tionandsystematic(bulk)outflow.Theanglebetweenthenetvelocityvectorandverticalaxis,α′,isconnectedwithangleαviarelativisticvelocitytransformation.ThereforethenetLorentzfactor,γ′,dependsontheangleα′aswell

4

A.Janiuk,B.Czerny,P.T.Zycki

˙zivayQoutjx-vFigure3.Theassumedgeometryscheme.Theelectronisinthe

centerofthereferenceframeandhasthevelocity󰀍vatthein-clinationαtothesymmetryaxisofthediscandattheangleϕmeasuredinthediscplane.Thephotonisemittedattheangleitothediscaxis,andattheangle(Θout−π)totheelectron’svelocityvector.

Figure4.Thereflectionamplitudefortheviewinganglei=0(solidline),30◦(short-dashedline)and60◦(long-dashedline)asafunctionofelectron’sLorentzfactorγincaseofpurethermalmotion.

asonbulkandthermalvelocities.Inthiscasetheamountofreflectionisgivenby:R(β1

bulk,βtherm,i)=

In󰀆πFigure󰀆2π

0

0

P(α′,βbulk,βtherm,Θout(α′,i))sinα′dα′dϕ′

(.10)

5weplotthedependenceoftheamountofreflectiononthebulkvelocitytothelightvelocityratio,βbulk,fordifferentvaluesofelectrontemperatureβthermand

Figure5.Thereflectionamplitudefortheviewinganglei=0◦(boxes)andi=45◦(triangles)asafunctionofβbulkforelectrontemperatureβtherm=0.63(toppanel)andβtherm=0.72(bottompanel).

viewinganglei.Theelectrontemperaturecorrespondstoasinglevalueofelectronvelocity,asforvelocitydistributiontheanalyticapproximationwouldnotwork.

Inthecaseofvtherm=0weobtainthesamesolutionasinBeloborodov(1999).InFigure6weplotthissolution,calculatedfordifferentviewingangles.

ThecomparisonofFigures6and5showsthatsinglescatteringapproachpredictsverystrongdependenceoftheamplitudeofreflectionontheplasmatemperatureduetoanisotropyoftheComptonscattering.Whenthethermalmotionsareimportant(vtherm/c≈βbulk)thefirstreflectionissignificantlyenhanced,byafactorofatwo,andthehigherthetemperaturethestrongertheeffect.Thevaluesoftheamplitudeofreflectioncoverthewholerangebetween0and∼2foroutflowsolutions(βbulk>0).

Theeffectofreflectionenhancementdropsrapidlywhenthebulkvelocityisdominant(βbulk>vtherm/c).Inthiscasethemaximumangleα′ismuchsmallerthanπandtheintegrationlimitsintheequation(10)mustbechanged.Thereflectionamplitudeincreasesthenwiththevalueofassumedviewinganglei,whileinthecaseofmoresignificantthermalmotionthetrendisopposite.

3

REFLECTEDSPECTRAFROMMONTE

CARLOSIMULATIONS

Theroughlypowerlawshapeoftheprimaryemissioncom-ponentinX-rayspectrainGBHismostlikelyduetotheeffectofmultiplescatteringswithinthehotplasma.

ItiswellknownfromanalyticalsolutionsandMonte

󰀁

c0000RAS,MNRAS000,000–000Ontheeffectofcoronaloutflowonspectraformationingalacticblackholesystems5

Figure6.Thereflectionamplitudefortheviewinganglei=0◦(solidline),30◦(short-dashedline)and60◦(long-dashedline)asafunctionofβbulkforpurebulkmotion.

Carlosimulationsthatthecontributionofthefirstscat-teringtothetotalspectrumisratherspecific(seeSternetal.1995,Svensson1996,Haardt,Maraschi&Ghisellini1997).Itmeans,thatwhenthehardX-rayspectrumformsviamultiplescatterings,onlythefirstoneisinfluencedbytheanisotropyofseedphotondistribution.Thisistherea-sonwhyanyanisotropyeffectsarepresentinthelowen-ergypartofthespectrum.Inthethermalmedium,evenforsmallopticaldepths,thepowerlawspectrumisshapedbymultiplescatterings.Thereforethesemi-analyticalcompu-tations,dealingwiththefirstscatteringprocess,inthecaseofboththermalandsystematicbulkmotionoftheelectronswithinthecoronacanonlyserveasaguideandahelptounderstandthenumericalresults.ThefullyreliableanswercanonlybeprovidedbyfullMonteCarlosimulationsoftheComptonizationprocesswithinthecorona.

InthisSectionwecomputetheamplitudeoftheComp-tonreflectedcomponentusingaMonteCarlocomptoniza-tioncodeandweshowthecorrespondingspectra.Wecon-centrateonhighlyionizedreflector,astheapproximationsusedinBeloborodov(1999)maynotbevalidinthatcase.ThecodeemploysstandardalgorithmsforsimulatingtheinverseComptonscattering,anditwaswrittenfollowingdescriptionsbyPozdnyakov,Sobol&Sunyaev(1983)andG´orecki&Wilczewski(1984).Modificationstothecodenec-essarytoimplementthebulkmotionaredescribedinAp-pendixA.FollowingBeloborodov(1999)weassumethatthecomptonizingregionasawholeisstationaryanditsgeom-etryisthatofaslab.3.1

Reflectionamplitude

Thebulkvelocityvectorisassumedperpendiculartotheplaneofthediscbutthedirectionofthevelocitycanbebothoutwardsandtowardsthedisc.Thediscisasourceofsoftphotonsforthecomptonization.Photonsbackscat-teredfromthecloudformradiationilluminatingthedisc.TheusualComptonreflectionprocessisthensimulatedanotherMonteCarloroutine(Zycki˙by

&Czerny1994),as-sumingtheabundancesgiveninMorrison&McCammon

(1983).Theopacitieswerecomputedusingthecodede-

Figure7.AmplitudeoftheCompton-reflectedcomponentasafunctionofthebulkoutflowvelocity,βbulk,computedusingtheMonteCarlomethodformultiplescatteringintheplasmaofopticaldepthτes=0.8andelectrontemperaturekTe=100keV.Opentrianglesindicatetheresultsfortheinclinationanglecosi=0.3,starsmarktheresultsforcosi=0.9,andsolidsquaresresultfromtheangleaveragedspectrum.

scribedinDoneetal.(1992)fortheionizationparameterξ≡FX/(ner2)=104.Furtherscatteringofthereflectedphotonsinthehotcomptonizingcloudisnotconsidered,sincetheinterceptedfractionwouldbegeometry-dependent(e.g.factorµsinBeloborodov1999).

ThereflectionamplitudeRisdefinedhere(cf.Be-loborodov1999andSection2.3),astheratiooftheenergyintegratedfluxes:R(βFbulk)=

back(βbulk)

6

A.Janiuk,B.Czerny,P.T.Zycki

˙Figure8.ComptonizedspectraresultingfromtheoutflowingcoronamodelobtainedbyMonteCarlosimulations.Parameterswerechosensothatthespectracorrespondtotypicalspectraoflow/hardstateofGBH:kTe=100keV,τes=0.8.Thebulkve-locityisβbulk=0.3.Thedashedlinerepresentsthesoftphotoninput,solidlineshowsthecomptonizedcontinuumscatteredto-wardstheobserver(angleaveraged),theshort-dashedlineshowsthebackscatteredspectrumandtheshort-long-dashedlinerep-resentsthereflectedspectrumforionizationparameter,ξ=104.

wardsthediscarestillnecessaryinsomecasesinordertoexplainfullrangeoftheΓ–RrelationfoundbyZdziarskietal.(1999),astheenhancementoffluxtowardsthediscduetoplasmabulkmotionisrequiredtoexplainR>1seeninsomesources.3.2

Radiationspectraofoutflowingcorona

InFigure8wepresentanexampleoftheoverallspec-trumcalculatedfromthemodeloftheoutflowingcorona.Wechoosethefollowingvaluesforthemodelparameters:kTe=100keV,τ=0.8,kT0=0.1keVandthebulkvelocityβbulk=0.3.Adoptedsoftphotontemperaturecorrespondstoatypicalvalueforgalacticblackholes.Suchaparameteri-zationisconvenientifwedonotconsidertheenergybalancewithinthecorona.Weassumethatthecoronaisacontin-uousmedium,i.e.weneglecttheclumpinessofthecoronadescribedbytheparameterµsinthemodelofBeloborodov(1999)sincewealsoneglectthesecondaryreprocessingofthereflectedcomponentthroughthecorona.

Thecontinuouslineshowstheradiationemittedto-wardsanobserver(averagedovertheentirehemisphere,roughlycorrespondingtoaninclinationof60◦)whiletheshort-dashedlineshowsthecomponentbackscatteredto-wardsthedisk.SincethefirstscatteringdominatessoftX-raybandforgalacticsources,thebackscatteredradiationinthisbandisenhanced,aspredictedbyanalyticalresultspre-sentedinSection2.However,hardX-raypartisdominatedbymultiplescatteredphotons,anisotropyeffectissmearedoffandthebackscatteredcomponentisnotenhancedinthisband.Theneteffectisthereforethesystematicdifferencebetweenthespectralslopeoftheback-scatteredradiation

andforward-scatteredradiation.Thiseffectwasdiscussed

foracoronawithoutabulkmotioninanumberofpapers(e.g.Sternetal.1995).Therefore,thecontinuumformedinthecoronaandemittedtowardsanobserverisslightlycurved,particularlyinthesoftX-rayband,insteadofbeingasimplepowerlawwithahighenergycut-off,asfrequentlyassumedinspectralanalysisofthedata.

Thebackscatteredcontinuumissubsequentlyreflectedbythedisksurfacewhichinourcalculationsisassumedtobeionized(ξ=104).WeshowthisspectralcomponentintheFigure8.

Thereflectedcomponentintheoutflowingcoronamodelisagainpartiallyreprocessedbythecorona.Theef-fectdependsonthecoronaclumpinesssinceonlyafractionofradiationµs(followingthenotationofBeloborodov,1999)wouldpassagainthroughthehotplasma.Inthepresentpa-perweneglectthissecondaryreprocessingsinceitisessen-tialonlyifµsiscloseto1andtheopticaldepthiscloseto1.However,indetailmodelingthiseffectshouldberathertakenintoaccount.

4DISCUSSION

ItisgenerallyassumedthatingalacticX-raysourcesandactivegalacticnucleisoftX-rayradiationoriginatesfromthegeometricallythinandopticallythickaccretiondiscwhilethehardfluxisproducedbyComptonizationinopticallythinplasmaoutsidethedisc.PartofthehardX-rayfluxthatisdirectedtowardstheobserverisdetectedintheformofpowerlawcontinuumandthepartofthefluxscatteredbacktothediscsurfaceproducessocalled’reflectionhump’inthespectrumover10keV(Lightman&White1988;Poundsetal.1990;Doneetal.1992)aswellastheironKαlinenear

6.4keV(Zycki˙&Czerny1994).

Theobservedvaluesoftheamplitudeofthereflec-tioncomponentcoverbroaderrangethaninitiallyexpected(R∼1forAGNinPoundsetal.1990).ForsomeX-raysourcestheobservedreflectionseemstobeweak,whichwasmodelledeitherbythedisruptionoftheinnerdiscandX-rayirradiationofitsouterparts,orbythehighionizationstateofilluminatedmedium,whichresultsinsteepeningofthereflectedcontinuumandmakesitindistinguishablefromtheprimarypowerlaw(Rossetal.1999).

Bothinterpretationscanexplaintheobservedcorrela-tionbetweenRandΓ.Inthemodelwithadisruptedcolddiscpartiallyoverlappingtheinnermosthotflowtheob-servedcorrelationisduetoradiativecouplingofthetwocomponents,astheamountofoverlapvaries(Zdziarskietal.1999).Inthemodelwithstronglyionizeddiscsurfacethecorrelationisgovernedbythevariableopticaldepthoftheionizedscatteringlayer(Nayakshinetal.2000),whichdeterminestheeffectivealbedoofthediscandthesoftfluxfromthermalizedfractionoftheilluminatingX-rays.BothmodelscanexplainthereflectionamplitudevaluesR󰀁1.

However,thestrengthofreflectionwasforsomesourcesfoundtobeR>1,whichmayeitherindicatethatreflectingmediumsubtendsasolidanglelargerthan2π,orthattheradiationdirectedtowardsthediscisenhanced.Thelatterispossiblewhenthescatteringprocessisanisotropicormaybeduetothevelocityofsystematicbulkmotiondirectedtowardsthedisc.

󰀁

c0000RAS,MNRAS000,000–000Ontheeffectofcoronaloutflowonspectraformationingalacticblackholesystems

7

Inthisarticleweshowthattheanisotropyeffectisim-portantmostlyforthefirstscatteringandweakensinnumer-icalMonteCarlosimulationsperformedformultiplescatter-ingintheplasmaparameterizedbyopticaldepthandelec-trontemperature.ThemaximumamplitudereachedinthecaseofhighlyionizedreflectorisonlyR∼1.1.Therefore,thesystematicmildly-relativisticmotiontowardsthedisc,orthe’coronalinflow’,isrequiredtoexplainthehighervaluesofR.Ontheotherhand,inordertoproduceR>1inthedisrupteddiscmodelitwouldbenecessarytoallowforre-flectionfromouterregionsofathickeneddisc(e.g.Shakura&Sunyaev1973)and/orfromthedusty/moleculartorusaroundcentralblackholesofAGN.SincetheabsorptionofirradiatingX-raysbelow∼5keVisreducedforahighlyionizeddiscsurface,thereflectedphotonsmaycontributetothesoftX-rayexcessesobservedinthespectraofGBHinthehard/lowstate(CygX-1;DiSalvoetal.1999,andinpreparation).Weshowthatthiscontributionishigherwhentheradiationbackscatteredtothediscisenhancedasaresultoftheanisotropyofthefirstscattering.

Thehardtolowstatetransitioncharacteristicformanyaccretingblackholesystemsisinthe’discplussphere’modelconnectedwiththechangeoftheinnerradiusofthecolddisc.Inthehardspectralstatethecolddiscispushedout-wardwhilethehotinnerplasmaisresponsibleforhardX-rayradiation.Inthesoftstatethethermaldiscemissiondominatesasthecolddiscextendsalmosttothemarginallystableorbit.However,thephysicalmechanismofsuchbe-haviouriscurrentlyunclear.Intheoutflowingcoronamodeltheoutflowvelocityisthebasiccontrolparameter.Thehardspectralstatewouldthencorrespondtorapidcoronalex-pansion,whilethespectrumwithdominatingsoftcompo-nentwouldbeproducedduringtheverticalcollapseofthehotgas.Againthephysicalmechanismofsuchdependenceisunclear,andinparticularitisunclearhowtherequiredchangesofeitherRinorβbulkcouldbedrivenbychangingaccretionrate.

Inconclusion,thebasicpredictionsofalltheproposedmodelsaresimilarandonlydetailedcomputationsofspec-tralandtemporalbehaviourandcomparisonwiththehighqualitydata,asexpectedfromChandraandXMM,mayallowforadistinctionbetweenthem.

ACKNOWLEDGMENTS

Thisworkwassupportedinpartbygrant2P03D01816,2P03D01718and2P03D01519ofthePolishStateCommit-teeforScientificResearch.

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APPENDIXA:THEMONTECARLOCODEOurinitialcomptonizationcodewaswrittenfollowingcloselydescriptionsgivenbyPozdnyakov,Sobol&Sunyaev(1983)andG´orecki&Wilczewski(1984),andappliedtomodelX-rayspectraofaccretiondiscwithaccretingtivecoronabyJaniuk,Zycki˙advec-&Czerny(2000).Inorderto

includetheeffectofbulkmotionoftheplasma,weneededtomaketwomajormodifications.

Firstly,theaveragescatteringcrosssectionhastobemodified.Theescapeprobabilityofaphotonisgivenbyd

P(d)=exp󰀅−

Ne󰀂σ󰀁dl,

󰀆

󰀄0

󰀈

(A1)

whereNe=N(v)d3vistheelectrondensity,N(v)isthe

electronvelocitydistribution,disthedistancetothecloudboundaryalongthedirectionofphotonmotion,Ω,and󰀂σ󰀁=

1

m(1−v·Ω/c)(A3)

ec2

γ8

A.Janiuk,B.Czerny,P.T.Zycki

˙istheenergyofanincomingphotonintheelectronrest

frame,γistheLorentzfactorandσ(x)istheKlein-Nishinacrosssection.ForanisotropicN(v)e.g.Maxwelldistribu-tion,󰀂σ󰀁isafunctionofphotonenergyonly(foragivenkTe).

Withthenon-zerobulkvelocitywecannotusethemethodpresentedbyPozdnyakovetal.(1983)toevaluatetheintegralinEq.(A2),sinceN(v)isnolongerisotropic.Thepresenceofthespecificdirection–thebulkvelocityvectorβ–introducesanadditionalangulardependenceof󰀂σ󰀁.WenowhavetocomputetheintegralasinEq.(A2)butwithvinthedot-productv·Ωreplacedbytotalelectronvelocity,u.Hereuisthesum(inthesenseofLorentztrans-formation)ofthethermalvelocityandthebulkvelocity.Wecomputethis3-Dintegralnumerically.Introducingacoor-dinatesystemwiththez-axisalongthebulkvelocityandthex-axisalongthedirectionofphotonmotionweobtainΩ=(sinθ,0,cosθ),whereθistheanglebetweenΩandβ.ApplyingtheLorentztransformationweobtaintheelectronvelocity󰀉

inthediscframe,u=

vx

c

withγ=(1−β2)−󰀃1/,

vy

z+βc

,(A4)

c

2,andvx,v󰀃y,

vc

󰀂

andvz–componentsoftheelectron’sthermalvelocity.Thisenablestocomputeu·Ωandcalculatetherequiredintegral,whichisnowadditionallyafunctionofphoton’sdirectionofmotion,θ.Weusedtheprocedurequad3dfromPressetal.(1992)toevaluatetheintegral.

Thesecondmodificationconcernsthescatteringevent.Sincethisismodeledintheelectronrestframe,weintro-ducedapairofadditionalLorentztransformationsofapho-ton’smomentum:fromthedisc/coronaframetotheframecomovingwiththebulkvelocitybeforesimulatingthescat-teringevent,andthereversetransformationafterthescat-teringevent.

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󰀁

c0000RAS,MNRAS000,000–000