X-ray flares reveal mass and angular momentum of the Galactic Center black hole

February5,2008

X-rayflaresrevealmassandangularmomentumoftheGalactic

Centerblackhole

B.Aschenbach1,N.Grosso2,D.Porquet1,andP.Predehl1

12

arXiv:astro-ph/04015v2 16 Feb 2004Max-Planck-Institutf¨urextraterrestrischePhysik,P.O.Box1312,GarchingbeiM¨unchenD-85741,GermanyLaboratoired’AstrophysiquedeGrenoble,Universit´eJoseph-Fourier,BP53,38041GrenobleCedex9,France

ReceivedDecember17,2003;AcceptedJanuary23,2004

Abstract.WehaveanalysedthelightcurveofthetwobrightestX-rayflaresfromtheGalacticCenterblackhole,oneflareobservedbyXMM-NewtononOctober3,2002(Porquetetal.2003),andtheotherflareobservedbyChandraonOctober26,2000(Baganoffetal.2001).Thepowerdensityspectrashowfivedistinctpeaksatperiodsof∼100s,219s,700s,1150s,and2250scommontobothobservationswithintheirestimatedmeasurementuncertainties.ThepowerdensityspectrumoftherecentlyreportedinfraredflareofJune16,2003(Genzeletal.2003)showsdistinctpeaksattwo,ifnotthree,periods(includingthe1008±120sinfraredperiod),whichareconsistentwiththeX-rayperiods.Theremainingtwoperiodscouldnotbecoveredbytheinfraredmeasurements.Eachperiodcanbeidentifiedwithoneofthecharacteristicgravitationalcyclicmodesassociatedwithaccretiondisks,i.e.eitherLense-Thirringprecession,Keplerorbitalmotionandtheverticalandradialepicyclicoscillation

.126

modes,insuchawaythataconsistentvaluefortheblackholemassofMBH=2.72+0−0.19×10M⊙andthe

.0026

angularmomentuma=0.9939+0−0.0074isobtained.TheavailabledataonMBHderivedfromstudiesoftheorbitalmotionoftheS2(S0-2)star(Sch¨odeletal.2002,Ghezetal.2003)agreewithourfindings.Finallywediscusssomeimplicationsofthefairlyhighvaluefortheangularmomentum.

Keywords.Galaxy:center–X-rays:individuals:SgrA*–X-rays:general–Radiationmechanisms:general

1.Introduction

TheregiontowardstheGalacticCenter(GC)hasbeenrecentlyresolvedinX-raysbyChandrameasurements(Munoetal.2003,Baganoffetal.2003).AsourcewasidentifiedasX-raycounterpartoftheGCblackholeSgrA*.ThequiescentX-rayluminosityturnsouttobeextraordinarylow(2.2×1033ergs−1,Baganoffetal.2003)foramassaccretingblackhole,givenitsmasswhichhasbeenmeasuredthroughthemotionoftheS0-2staror-bitingtheblackhole.Massvaluesrangefrom2.2×106M⊙(lowerlimitofSch¨odeletal.2002),3.6×106M⊙(Genzeletal.2003)to4.1±0.6×106M⊙foradistanceof8kpc(Ghezetal.2003).Variousmodelstoexplainthelowlu-minosityhavebeenproposedanddiscussedquitecontro-versiallyincludinglowaccretionratesandradiativelyin-efficientaccretionflows,forexample.ForabriefoverviewseeforinstanceMelia&Falcke(2001),Baganoffetal.(2001),Porquetetal.(2003)andYuanetal.(2003).Thequiescentstateisinterruptedbyoccasional,sometimesverybright,flares.Thefirstbrightflarewithapeaklu-minosityof1×1035ergs−1(Baganoffetal.2001)wasob-servedwiththeChandraACIS-IinstrumentonOctober

2Aschenbachetal.:MassandangularmomentumoftheGCblackhole

calculateanangularmomentumofa=0.5fortheblackhole.

Insection2weshowthelightcurvesofthetwobright-estX-flares,whichwehaveanalysedincludingbutsepa-ratedfromthetimesectionsbeforeandaftertheflareproper,aswellastwoverylong(11hoursand46hours)X-raylightcurvesrepresentingtheso-calledquiescentstate.LikethetwoflaresoneeventwasobservedbyXMM-NewtonandtheothereventwascoveredbyChandra.Thesetwoobservationswereprimarilyanalysedforcross-checkingwiththeflarecharacteristics.Section2alsocon-tainsthepowerdensityspectra(PDS)oftherelevantlightcurves.Fivegroupsofcharacteristicfrequencieswithatleasttwodetectionspergrouphavebeenfound.Insec-tion3wedescribetherelationoftheseperiodswiththecyclicgravitationalmodesthoughttobepossiblycreatedinaccretiondisks,i.e.theLense-Thirringprecessionfre-quency,theKeplerfrequencyandtheverticalandradialepicyclicfrequencies.Insection3wealsodescribehowwederivethevaluesforMBHandtheangularmomentuma(theKerrparameter)fromthefrequenciesmeasured.WeincludeinouranalysisthepowerdensityspectraofthetwoinfraredflarespublishedbyGenzeletal.(2003).Finallywediscussafewimplicationswhichresultfromthefairlyhighvalueofawehaveobtained.

2.Observationsandanalysis2.1.Lightcurves

Figure1ashowsthelightcurveoftheOctober3,2002flareobservedbyXMM-NewtonandpublishedbyPorquetetal.(2003)withaslightlydifferenttimebinning.Figure1bshowsthelightcurveofan∼11hoursquiescentperiodob-tainedbyXMM-NewtononFebruary26,2002.Figure2adisplaysthelightcurveoftheveryfirstflarereportedfromSgrA*datedOctober26,2000,observedwithChandraandpublishedbyBaganoffetal.(2001).Wechooseaslightlydifferentenergybandandadifferentbinning.SgrA*wasobservedfor46.5hoursonMay5/6,2002with-outabrightflareoccurring,andtheChandralightcurveisshowninFigure2b.Becauseofthenumerouspeaksthesourceisapparentlynotinatruequiescentstatebutex-hibitsquiteanumberofsmallerfluxincreasesorsmallflares.TheessentialobservationaldetailsaresummarizedinTable1.TheXMM-NewtondatahavebeenproprietaryPIdata,whichbynowarepubliclyavailable.TheChandradatahavebeenextractedfromthepublicChandraarchive(level2processedeventlist,providedbytheChandraX-rayCenter).Werestrictouranalysestojustthesefourdatasetsbecausetheycoverthetwobrightestflaresandtheothertwoobservationshavethelongestexposureoftheso-calledquiescentstate.ForthetiminganalysisweaddedPN,MOS1andMOS2datainonesetusingcounts,whichwereforXMM-Newtonextractedfromacircleof10′′radiuswithenergiesbetween2.6-10keV.FortheChandradatatheextractionradiuswas1.5′′aroundthe

Table1.Summaryofobservationsanalysed(c.f.Figs.1,2).Instr.IisEPICPN+MOS1+MOS2onXMM-Newton,andinstr.IIisACIS-IonChandra.Dateisinday/month/year.

I03/10/022.156.33197.82.6I26/02/02667.2––2.6II26/10/005.3115.3372.43.241II

25/05/02

2804.2

–

–

3.141

Aschenbachetal.:MassandangularmomentumoftheGCblackhole3

Fig.1.EPIClightcurves(MOS1+MOS2+PN)oftheXMM-NewtonobservationofOctober3,2002(upperpanel,Fig.1a)andtheFebruary26,2002observation(lowerthreepanels,Fig.1b).Errorbarsindicate1σun-certainties.Thehorizontallineinthelowerthreepanelscorrespondstothemeancountratelevel.Arrowsmarkpeaksassociatedwitha2178speriodicsignal.countrateforeachofthethreestates.Theseare:9.5µJy(EPICcounts/s)−1cent);0.5+1−0..1,47.6µJy(ACIS-Icounts/s)−13µJy(EPICcounts/s)−1

,2.8+6−2.(quies-.10µJy(ACIS-Icounts/s)−1(Chandraflare);12.3µJy(EPICcounts/s)−1,71.8µJy(ACIS-Icounts/s)−1(XMM-Newtonflare).TherelativelylargeuncertaintyoftheconversionfactorfortheChandraflareareduetotheuncertainspectrumandcol-umndensity.TheenergyfluxdensitiesaregivenforE=1keV.

2.2.Powerspectra

FromthelightcurvesshowninFigures1and2,powerden-sityspectra(PDS)havebeencreatedbyaFourieranal-ysisofsixdatasets.Twosetscoverthetimesectionofjusttheflare,oneeachforXMM-Newton(Fig.3a)andChandra(Fig.4a);anothertwosetscoverthetimesec-tionsbeforeandaftertheflare(Figs.3band4b).ForthesePDSthedataoftheflareproperhavebeenremoved

Fig.2.ACIS-IlightcurvesoftheChandraobservationofOctober26,2000(upperpanel,Fig.2a)andtheMay25,2002observation(lowerthreepanels,Fig.2b).Errorbarsindicate1σuncertainties.andreplacedbydatawithameanfluxidenticaltothatofthetimeprecedingtheflareassumingaPoissoniansta-tisticaldistribution.Thefinaltwosetscorrespondtothetwoobservationsofthequiescentlevel(Figs.5and6).Wedefinethepowerspectraldensitypsdnatafrequencyfandwavenumbernaspsdn=(a2n+b2n)/(2×∆t2

n

)×T;anandbnaretheFouriercoefficients,∆tisthesamplingorbinningtimeandTisthetotalobservingtime(Table1).TheFouriercoefficientsareinunitsofACIS-Icounts−1fortheChandraobservationsandEPICcounts−1fortheXMM-Newtonobservations.Becauseofthedifferenteffi-cienciesthepsdn’sareexpectedtogenerallydifferbyafactorof∼25±5forthesameluminositylevelgiventheenergyspectrumdescribedinsection2.1.

2.3.Frequencies

IngeneralthesixPDSlookverymuchalike.Thereisahighfrequencycomponentwhichismoreorlessrapidlygrowingwithincreasingfrequency,whichreflectsthenoiseintroducedbythelowcountingstatistics.Wenotethatthesmallestpossiblebinninghasbeenchosenso

4Aschenbachetal.:MassandangularmomentumoftheGCblackhole

Fig.3.PowerdensityspectraoftheOctober3,2002flare(upperpanel,Fig.3a)anditsprecursorsection(lowerpanel,Fig.3b);XMM-Newtonmeasurement.

thatwedealwithjustnooronecountperbin.AtlowfrequenciesthePDSaredominatedbyafewhighpeaks,whichsummarizethemeanshapeofthelightcurves,averagedoverperiodswhicharejustafewtimesshorterthanthewholetrack.Clearlyseparatedfromthesetworegimesisalownoisemid-frequencysectionbetween∼0.7mHzand∼7mHzfortheflareobservations(Fig.3aand4a),and0.7mHzand2.5mHzfortheflareprecursorsections(Figs.3band4b).InthisfrequencybandweseetwodistinctPDSpeaksat1.426mHzand4.562mHz(Fig.3a;labels3and1,respectively;XMM-Newtonflare)andsimilarlyat1.445mHzandat3.902mHz(Fig.4a;labels3and1,respectively;Chandraflare),standingwellabovethenoiselevelinthecorrespondingfrequencybands.IntheChandraflareweseeathirdpeakat10.41mHz(label0),which,however,islocatedatthebeginningoftheclimbinghighfrequencynoisesection(Fig.4a).TheXMM-NewtonflarePDSshowsasimilarclose-bypeakat9.12mHz(label0),althoughatafairlylowpowerlevel.LikeintheChandracasethisfrequency

Fig.4.PowerdensityspectrumoftheOctober26,2000flare(upperpanel,Fig.4a)anditsprecursorsection(lowerpanel,Fig.4b);Chandrameasurement.

isatthehighfrequencyedgeofthelow-noiseband.Theexistenceofthispairoffrequenciesmightbedoubtfulbuttheyshouldbenotedbasicallybecausetheyseemtoappearintwodifferentobservations.Thesearetheonlypairsintheflaresection.AbsentintheXMM-NewtonPDSbutfairlyprominentintheChandraPDS(Fig.4a)isapeakat∼2mHz(label2).

ThePDSofthedataprecedingtheflarealsoshowdis-tinctpeaksinthelownoiseregimeat0.853mHz(Fig.3b,label4;XMM-Newton)and0.5mHz(Fig.4b,label4;Chandra);afurtherpeakappearsintheXMM-NewtonPDSat0.459mHz(label5).Thepoweratthisfrequencyissohighthattheequivalentperiodof2178scanbeiden-tifiedbypeaksinthelightcurve(c.f.arrowsinFig.1a).APDSpeakassociatedwithorcloseto0.459mHzisclearlyabsentintheChandraflareprecursorobservationbutthereisapeakat0.434mHzintheChandraflare(label5).

Aschenbachetal.:MassandangularmomentumoftheGCblackhole5

Fig.5.PowerdensityspectrumoftheFebruary26,2002quiescentstate;XMM-Newtonmeasurement.Fig.6.PowerdensityspectrumoftheMay25,2002qui-escentstate;Chandrameasurement.

ThePDSisafunctionofdiscretefrequenciesgivenbyfn=ninprinciple2∆t)and∆tthebinningsize.Therefore,thereisa∆fsystematicrela-tivefrequencyuncertaintypossibleof(InTable2,wesummarizetheresultsincludingfrequencyn−1).f,wavenumbern,periodP,powerspectraldensitypsdandalabelID,whichhasthesamevalueforfrequenciesclosetoeachother.ThesameID’sareshownaslabelsinthePDSgraphs.WefindintheXMM-NewtonandtheChandraobservationsfivegroupsofperiods,eachofwhichisapairwithonememberfromXMM-NewtonandonefromChandra.Theperiodsofthemembersofeachpairarealmostidentical,i.e.110/96s(label0),219/256s(1),701/692s(3),1173/1117s(4),2178/2307s(5).They

Table2.Compilationofoutstandingfrequencies.1)Thepsdisgiveninunitsof(counts−1)2Hz−1.ForXMMEPICcountratesandforChandraACIS-I,countratesarequoted.na:notapplicable,i.e.,notcoveredbecausetheflaredidn’tlastlongenough.ThelowersectionofthetablecontainsthefrequenciesofhighpsdobservedinthetwoinfraredflaresbyGenzeletal.(2003).Thedatahavebeenreadofftheirfigure2c.

flare

XMM9.123321106.30Chandra10.4172960.780XMM4.5621621915.31Chandra3.902272560.781XMM-----Chandra2.023144940.462XMM1.426570116.43Chandra1.445106920.493XMMnananananaChandra0.4343

2307

1.6

5

appeartobenotexactlyidenticalbutconcedingthemax-imalpossibleuncertaintytheyareconsistentwitheachother.Thiscoincidencestronglysupportstheirexistenceandsuggeststhateachpairrepresentsthesameprocess.

Genzeletal.(2003)havepublishedthediscoveryofa16.8±2minperiodinthetwoinfraredflaresob-servedonJune15andJune16,2003.AlookatthetwopublishedPDSshowsthattherearemorepeaks,whichwehavereadofffromtheirfigure2candaddedtoTable2(IR/15,IR/16).Exceptthepeakat321sandwavenumbern=16,appearingintheJune16flare,eachfrequencyhasaclose-bycounterpartintheXMM-Newtonand/orChandraPDSaddinganotherfindingtogroups1,2,3and4.Ofcourse,thepsdat214sinIR/16isfairlylowbutitshowsupasalocalmaximum.Thereisnopeakatthefrequenciesofgroup5intheinfraredobservations,whichhoweverhavebeentooshorttosearchforit.Obviously,theinfrared

6Aschenbachetal.:MassandangularmomentumoftheGCblackhole

frequenciesarefullyconsistentwiththeX-rayfrequencies.Wenotethatatnoneofthefrequenciesselectedfromtheflaresorprecursorsaprominentpsdisevidentinthequiescentlevelobservations.ThePDSofthequiescentlevelobservationsareshowninFig.5(XMM-Newton)andFig.6(Chandra).TheXMM-NewtonPDSshowsasetofsixprominentPDSpeaksbetween0.65mHzand∼2mHzcenteredon∼1mHz.Thisfrequencybandembracesthe0.853/0.5mHzpeaksofboththeXMM-NewtonandChandraflareprecursors.Thepsd’satthesixfrequen-ciesvarybetween1.05and1.42(EPICcounts−1)2Hz−1whichisclosetowhatisobservedaspowerforthe1173speriodfortheflareprecursor(Table2).Apsdpeakattheperiodof2178sisnotpresentinthequiescentobser-vations.ThePDSoftheChandraquiescentlevelobser-vationsdoesn’tshowprominentpeaksaroundonemHz(Fig.6).ButextrapolatingtheXMM-Newtonpsdof∼1.2(EPICcounts−1)2Hz−1theequivalentChandrapsdisexpectedtobeclosetothenoiselevel.

Thelowestfrequenciesaccessibleforthisinvestiga-tionarecoveredbytheChandraMay25,2002obser-vation,withnobrightflarethough(Figure6).Startingat∼0.1mHzthepsddropsrapidlywithfrequencyreach-ingthenoiselevelminimumat∼0.4mHz.Theregionbe-tween0.18mHzand0.35mHzseemstoshowexcesspowerpeakingat∼0.24mHzor4100s.InthisbandtheXMM-NewtonPDSisverysimilartotheChandraPDSwithfairlyhighpeaksat0.225mHzand0.1mHz,butdetailslikeintheChandraobservationarenotresolvedbecauseoftheshorterexposure(Figure5).ThisPSDstructureisprobablynotrelatedtotheoccurrencerateofflares,whichhasbeenestimatedto1.2±0.6perdaybyBaganoff(2003),whichisafactorofabout17lowerinfrequency.Excludingthe0.18mHz–0.35mHzbandthePDS,with20singlepsdvaluesremaining,canbefittedbyapowerlawwithanindexofroughly−2.3.Westressthatthestatisticsarepoorandwedon’tclaimtheexistenceofaQPObuttheexcessbetween0.18mHzand0.35mHzlookslikeaQPOstructure.QPO’s(quasi-periodicoscillations),whichshowupasabandofincreasedpsdaboveanunder-lying,muchbroaderPDS,whichhastheshapeofapowerlaw,havebeenobservedinanumberofgalacticbinaries,containingacompactobjectlikeaneutronstarorblackhole.TheQPO’sareconsideredtobecreatedinassoci-atedaccretiondisks(e.g.,vanderKlis,2000).AsNowak&Lehr(1998)andothershavepointedout,QPOsaris-ingfromsupermassiveblackholesinAGNareexpectedtoshowperiodsbetweenthreehoursandyears,ifa0.1speriodistypicalforagalacticblackholeandifperiodsscalewithmass.Suchlongperiodsareverydifficulttomeasureforcurrentmissions.ButfortheGalacticCenterblackholewithitsfairlylowmassQPOperiodsmightbeshorter.Infact,ifwescalethe300Hz,whichisthehighestQPOfrequencyobservedinthe7M⊙blackholemicroquasarGROJ1655–40(Remillardetal.1999,Orosz&Bailyn1997)weexpectaQPOaround0.6mHzforthe

GalacticCenterblackhole,whichiswellwithinthelongdurationChandraandXMM-Newtonmeasurements.

2.4.Statisticalsignificance

Toquantifythesignificanceofameasuredpsdvaluewehaveapproximatedtherathererraticflarelightcurvesbysomesmoothfunctionswhichreproduceverywellthegen-eralshapebutdonotintroducehighfrequencyvariationsintheregimewhichcontainsthefrequenciestobeinves-tigated.Weareparticularlyinterestedinthefrequenciesofgroup0andgroup1.Thelowerfrequenciesmaybetoomuchbiasedbyrednoiseforwhichwedon’thaveamodel.ThemodellightcurveoftheXMM-Newtonflareconsistsofthreeexponentials,onefortherise,oneforthetopandthethirdforthedecay.ThemodellightcurvefortheChandraflareissetupbyafourpiecepolygon.Eachmodellightcurveisnormalizedtothetotalnumberofmeasuredcounts.Themodellightcurvesarebinnedwiththesamesamplingtimeasthemeasureddata,andthemodelcountsperbinaresubjecttoPoissonianstatistics.ForeachflareZ=3×105lightcurveshavebeenproduced,FourieranalysedandthePDScalculated.

Thesignificanceofapowerpeakisdefinedviaaconfi-dencelevelS,whichgivestheprobabilitythatthedetectedpowerpsdn,detectisnotproducedbythenoiseprocess,i.e.1-S=Ntrials×W(psdn≥psdn,detect)(vanderKlis,19).Wistheratioofthenumberofpowersexceedingpsdn,detectandZ.NtrialsisthenumberoffrequenciesforwhichthePDShasbeenmeasured,whichis674and1066fortheXMM-NewtonandChandraflare,respectively.WestressthatwehavenotmadeuseofafixedformforWlikeaχ2orGaussiandistribution,butwebuiltWbyMonteCarlosimulations(c.f.vanderKlis,19).Thesimula-tionsshowthattherearesomesignificantpeaks,i.e.forgroup0:S(96s)=0.9whereasthepsdat110softheXMM-Newtonflareisconsistentwithanoisecreatedpeak;forgroup1:S(219s)=0.993andS(256s)=0.947,whichmeansthatsignalswiththelatterperiodsquitelikelyex-ist.Thereisjustonemorepairofclose-byfrequencieseachofwhichshowsasignificantpsd,whichareataperiodof11.31swithS(11.31s)=0.634intheXMM-Newtonflareandof10.68swithS(10.68s)=0.968intheChandraflare.Thisveryshortperiodshouldbekeptinmindforfuturestudies.

WealsotriedquiteafewdifferentmodellightcurvesbuttheydonotchangesignificantlythevaluesforSgivenbefore.

3.Discussion

FivecharacteristicfrequencygroupshavebeendiscoveredintheX-rayflareswiththeirexistencebeingsupportedbythefactthattheyhavebeenfoundinmorethanoneob-servation.Wetrytoidentifyeachofthesefrequencieswithoneoftheoscillationmodeswhichcouldoccurinaccretiondiskssurroundingblackholes.AsNowak&Lehr(1998)forinstancepointouttherearefourcyclicmodeswhichcould

Aschenbachetal.:MassandangularmomentumoftheGCblackhole7

giverisetoperiodicorquasi-periodicchangesinaccretiondisks.Thesemodesarebasedongravitationbutitisanopenquestionwhethertheywouldcreatechangesofthelightoutputattheverysamefrequencies.However,Nowak&Lehr(1998)pointoutthatthemodefrequenciespre-dominantlydependuponfundamentalgravitationalfre-quenciesandarenotstronglyaffectedbyhydrodynamicprocessesforthindisks.

3.1.Characteristicaccretiondiskfrequencies

Therearefourcyclicgravitationalmodesassociatedwithblackholeaccretiondisks(Nowak&Lehr1998,equations1to3andMerlonietal.1999,equation4),whicharetheKeplerfrequency(ΩK),thediskperturbationfrequenciesinverticalandradialdirectioncalledvertical(ΩV)andra-dial(ΩR)epicyclicfrequencyandtheLense-Thirringpre-cessionfrequency(ΩLT).EachfrequencydependsonthecentralmassM,theangularmomentumaandtheradialdistancerfromthecenter.Equations1to4showtherela-tions,forwhichthestandardnotationofc=G=1isused.PhysicallengthscalesareinunitsofGM/c2andangularfrequenciesΩareinunitsofc3/GM.r=1isdefinedasthegravitationalradiusrg.ΩK=(r3/2+a)−1

2

Ω2V=ΩK(1−2Ω2R=ΩK(1−

4a

r2

(1)

)

3a2

(2)

6

r3/2

−

8Aschenbachetal.:MassandangularmomentumoftheGCblackhole

Fig.7.RelationofMBHversus(1−a).Eachcurverepre-sentsoneperiodassignedtoaspecificgravitationalmode,codedbyalabeldescribedinthetext.Theerrorregionisenclosedbythedashedpolygon.Thedottedpolygonisnarrowerbecauseoftheadditionalconstraintsimposedbythe321speriod(LT).

3.3.Thehighvalueofa

Thehighvalueofa≈1meansthattheemissionfromtheinnerpartsoftheaccretiondiskisquiteclosetotheblackhole.TheeventhorizonislocatedatrH=1.112.Withrms=1.371thedistancetothemarginallystableorbitisjust3.6lightseconds.Lightfrommattercross-ingthemarginallystableorbitisthereforeverylikelytodisappearinafairlyshorttime.IsthePDSpeakat∼11sthecharacteristictimescaleatwhichthelightisfad-ingaway?ThelightcurveoftheXMM-Newtonflare(fig-ure1a)showsadeep,veryshort(<100s)cutclosetomaximumlight,whichmightbesuchanevent.AsimilareventisalsoseenintheChandraflare(figure2a).Thearrowsplottedinfigure1apointtothemaximaofthe2178speriod,whichseemsomehowtosynchronizewiththedeepcutinthelightcurve.Accordingtoourarrange-mentschemethe2178speriodischaracteristicfortheradialepicyclicmodeanditlooksasifmatterispushedacrossthemarginallystableorbit.

Thehighvalueofa≈1andtheproximityofthein-nerregiontotheeventhorizonalsoimpliesthatfairlylow(<1)generalrelativisticboostfactorsghaveama-jorimpactontheemissionbecauseofincreasingbeaming(e.g.M¨uller&Camenzind2004).Theradiationisnotonlyshiftedinfrequencybuttheobservedfluxdensity(Fo)issignificantlydown-boostedcomparedtoitsrest-framevalue(Frf)withFo=

g3−α=

0.056,ortheradiationreceivedbytheobserverisreducedbyafactorof∼18comparedtoitsrestframevalue.Forlargerradiithereductionfactorapproachesunity,butatr=rRmax=2.5theradiationisstillreducedbyafac-torof1.7.Thereductionbecomesmuchmorepronouncedfordisksviewedalmostface-on.Fori=15◦0.133≤g≤0.265andg3−α<0.038.Radiationfromthe

innermostregionisonaveragedimmedbyafactorofsomehundred,dependingonthedetailsoftheradialbrightnessdistribution.Becauseofthelargereductionfactorstheobservationoftheinnerregionsofalmostface-onaccre-tiondiskssurroundingsupermassiveextragalacticblackholesinAGNbecomesprogressivelymoredifficultwithincreasingaand/ordecreasingi.MaybethatthiseffectcontributestosomeextenttothefaintnessoftheGCblackhole.

Althoughwehavenosuggestionwhichphysicalpro-cessgivesrisetotheflareweconstraintheregionfromwhereitcomes.Sinceweseethelightmodulatedwithfre-quenciesassociatedwiththemarginallystableorbitouttothemaximumfrequencyoftheradialepicyclicmodeandinbetweenthebulkoftheemissionarisesfromaregionof1.374.Conclusion

Wehavediscoveredfivedistinctperiodsinthepowerden-sityspectrumoftheXMM-NewtonX-rayflareofOctober3,2002.Onemaywonderaboutthestatisticalsignificance,butthesefiveperiods,withintheirmeasurementuncer-tainty,alsoappearinthepowerdensityspectrumoftheOctober26,2000X-rayflareobservedbyChandra,withperhapsoneadditionalperiodwhich,however,doesnotshowupintheXMM-Newtonflare.FurtherevidencefortheexistenceoftheseperiodscomesfromtheJune16,2003infraredflare(Genzeletal.2003).Thepowerden-sityspectrumshowsaclearincreaseforatleasttwooftheperiodsandpossiblyforathirdperiod;theremainingtwoperiodswerenotaccessibletotheinfraredobserva-tions.Eachoftheperiodscanbeidentifiedwithoneofthefourcharacteristicgravitationalmodesinaccretiondisks,i.e.Lense-Thirringprecession,Keplermotion,ver-ticalandradialepicyclicoscillation,insuchawaythatacommonvaluefortheblackholemassMBHandlarmomentumaemerges,i.e.,MBH=2.72+0−0..12theangu-19×106

M⊙

anda=0.9939+0−0..0026

0074.TheavailabledataonMBHderivedfromstudiesoftheorbitalmotionoftheS0-2starandthedarkmatterconcentrationinthecenteroftheMilkyWayareconsistentwithourresultconcerningMBH,which,bytheway,isindependentofthedistancetotheblackhole.Thereareindicationsofa∼100speriodicityintheX-raydata,bothinXMM-NewtonandChandra,butrightnow,

Aschenbachetal.:MassandangularmomentumoftheGCblackhole9

wearereluctanttoacceptitasfirmlyestablished.ForfurtherprogressintheX-raydomainaflareevenbrighterthantheXMM-Newtonflareisrequired,andinthein-fraredbandthetemporalresolutionshouldbeimprovedto∼10s.Thisisparticularlyimportantforsimultaneousmulti-wavelengthobservations.

Acknowledgements.B.A.likestothankWolfgangBrinkmann,MPEGarching,fornumerousinspiringdiscussionsandAndreasM¨uller,LSWHeidelberg,forprovidingtherelativis-ticboostfactors.WearegratefultoAndreaMerloni,MPAGarching,forpointingouttousthecorrectformulafortheLense-Thirringprecessionfrequency.D.P.issupportedbyaMPEfellowship.

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