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The effect of Compton scattering on gamma-ray spectra of the 2005 January 20 flare

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The effect of Compton scattering on gamma-ray spectra of the 2005 January 20 flare

ResearchinAstron.Astrophys.2012Vo1.12No.10,14391450http//www.raajourna1.orghttp//www.iop.org/journals/raaResearchinAstronomyandAstrophysicsTheeffectofComptonscatteringongammarayspectraofthe2005January20flareWeiChenandWeiQunGanKeyLaboratoryofDarkMatterandSpaceAstronomy,PurpleMountainObservatory,ChineseAcademyofSciences,Nanjing210008,Chinaw.chenpmo.ac.Received2012March23accepted2012April11AbstractGammarayspectroscopyprovidesawealthofinformationaboutacceleratedparticlesinsolarflares,aswellastheambientmediumwithwhichtheseenergeticparticlesinteract.Theneutroncaptureline2.223MeV,thestrongestinthesolargammarayspectrum,forN1sinthedeepatmosphere.TheenergyofthesephotonscallbereducedviaComptonscattering.WiththefullyrelativisticGEANT4toolkit,wehavecarriedoutMonteCarlosimulationsofthetransportofaneutroncapturelineinsolarflares.andappliedthemtotheflarethatoccurredon2005January20X7.1/2B,oneofthemostpowerfulgammarayflaresobservedbvR丑ESIduringthe23rdsolarcycle.BycomparingthefittingresultsofdifferentmodelswithandwithoutComptonscatteringoftheneutroncapture1ine,wefindthatwhenincludingtheComptonscatteringfortheneutroncaptureline.theobservedgammarayspectrumcanbereproducedbyapopulationofacceleratedparticleswithaveryhardspectrums2.3.TheComptoneffectofa2.223MeVlineonthespectraisthereforeproventobesignificant,whichinfluencesthetimeevolutionoftheneutroncapturelinefluxaswel1.Thestudyalsosuggeststhatthemeanverticaldepthforneutroncalltureinhydrogenforthiseventisabout8gcm_。.KeywordsSunflaresSungammaraysscatteringComptonscattering1INTRoDUCTIoNInsolarflares,bothionsandelectronsareacceleratedtohighenergiestheinteractionsbetweenthemandambientnucleiproducegammarays,positrons,neutrons,andmesonse.g.,ChuppRyan2009.Observationsofgamma.rayemissiongiveinformationaboutthenatureofacceleratedionsseeKienereta1.2006Murphyeta1.2007andaboutthephysicalpropertiesoftheambientmediumfGall2005.ThefirstobservationChuppeta1.1973ofgammarayspectrafirmlyestablishedgammarayspectroscopyasatooltostudytheactiveSunforexampleRamatyeta1.1977Murphyeta1.1987.1991.Gawlma.raylineemissionsinsolarflarescovertheenergybandrangingfrom0.4to8MeV.includinglinesfromdeexcitationofnuclei,the2.223MeVlinefromneutroncaptureinhydrogen,andthe0.5llMeVlinefrompositron.annihilation.NarrowdeexcitationlinesareproducedbySuppoaedbytheNationalNaturalScienceFoundationofChina.1440、Chen&Q.Ganacceleratedprotons,alphaparticlesr口,and0Hejnteractingwithambientheaviernuclei,whilebroadlinesresultfrominteractionsofacceleratedC,N,OandotherheaviernucleiwiththeambientHandHe.Therearealsomanyunresolvedlinesthatareblendedwiththegammaraycontinua.DetailedtheoreticalcalculatioasofaneutroncaDturelineHua&Lingenfelter1987Huaeta1.2002andgammaraylinesRamatyeta1.1979RamatyMurphy19871producedbyinteractionswithacceleratedionswerecarriedoutbefore.Recently,Murphyeta1.2009extendedthegamma.raylineproductionmodelbyincorporatingthecrosssectionscomputedfromtheTALYScodeKoning&Duijvestijn2006.ThiscodewasintroducedintoastrophysicalcalculationsofnuclearreactionratesfGorielyeta1.2008Spyroueta1.2008andradioactivenucleiyieldsinsolarflaresTatischeffetal。2006.Thetraditionalmethodusedforstudyingthespectrumofacceleratedionsinsolarflaresistoestimatethefluenceratioofthe47MeVbandtotheneutroncapturelineMurphyRamaty1984HHaLingenfelter1987Murphyeta1.2007.Gan1998developedamethodwhichusesthetimeprofilesof47MeVandtheneutroncapturelinetodeducethespectralevolutionofacceleratedions.However.weshouldpointoutthattheapproachtakeninourworkisdifferent.Firstandforemost,thewholesolarde.excitationlinespectrumwascalculatedundertheassumptionofvarioussolaratmosphereabundancesandacceleratedioncompositionsforasetofspectralindicesofacceleratedions.Thenbyuseofthesetemplatespectra,wefittheobservedspectrumtodeterminethebestparametersoftheacceleratedionspectrum.Comptonscatteringhasbeenstudiedbysevera1authorsfBai&Ramaty1978Kontareta1.2006,whoshowedthatthisprocesscansignificantlymodifythebremsstrahlungspectra.However,theseinitialstudiesfocusedonsubMeVenergies.Kotokueta1.2007,Oiltheotherhand,studiedtheComptonscatteringofgammaraysproducedbyenergeticelectronsviathebremsstrahlungprocess.Inthepresentwork,wefoCUSonthepropagationofhighenergyphotonsexperiencingasexesofComptonscatterings.Forthispurpose,weemployedaMonteCarlosimulationtoolkitnamedGEANT4.whichiswidelyusedinexperimentalhighenergyphysics,tosimulatetheeff.ectofComptonscatteringonphotonsinasolaratmosphere.InSection2wepresentthecalculationsoftheComptonscatteredcontinuumofthe2.223MeVneutroncapturelineasafunctionofdepth.InSection3.weapplytheseresultsinRHESSIobservationstoseewhethertheComptonscatteringonthe2.223MeVlinehasasignificanteffectonthegammarayspectra.WealsopresenttimeprofilesoftheneutroncaDturedepthandthecorrectedneutroncapturelineflux.W_esummarizeourconclusionsinSection4.2S玎ULATIoNoFCoMPToNSCA1TERINGItiswellknownthatnucleardeexcitationlinesareproducedinopticallythinregions,wheretheattenuationinthetranspoprocessisnegligible.However,the2.223MeVneutroncapturelineismostlyproducedinthedeeperchromosphereorevenmephotosphereHuaLingenfelter1987,andtheComptonscatteringcanmodifytheresultingemissioncharacteristics.TheGEometryANdTrackingversion4fGEANT4MonteCarlosimulationtoolkitAgostinellieta1.2003isaplatformforsimulationsofthepassageofparticlesthroughmatter.DevelopedatCERNbvexpefimenthigh.energyphysicists,GEANT4hasthefollowingimportantfeaturesfirstly,itallowsaveryflexibleconstructionofthegeometryinwhichparticlesinteractsecondly,itcantrackanindividualparticlewhilemonitoringitsphysicalquantities,suchastheenergy,momentum,position,andtimelagthirdly,itallowsustoincorporatethedeskedinteractions,inmepresentcase.includingmultiplescatteringandcaptureofneutrons,andComptonscatteringofphotons.Thepairproductionisneglectedbecauseat2.223MeVinhydrogenplasma,thetotalpairproductionCROSSsectionisapproximatelythreeordersofmagnitudesmallerthanthetotalComptoncrosssection.Thephotoelectriceffectisalsoneglectedbecauseitisonlydominantatlowerenergyf100keV.TheEffectofComptonScatteringonGammaraySpectra1441UsingtheGEANT4toolkit,wesimulatedtheeffectsofComptonscatteringonisotropic2.223MeVphotonspassingthroughasphericalshel1ofthesolaratmospherewithaseriesofdepths,andrecordedtheescapingphotonsenergiestodeterminetheexpectedspeca.1henwecomparedtheseresultswithobservationstoconstrainthedepthorneutroncaptureprocesses.ThedependenceoftheComptoneffectonthedepthofneutroncapturephotonproductionwasexaminedbycarryingoutaseriesofsimulationsinwhich2.223MeVlinephotonswerereleasedatspecificatmosphericdepthswiththeHe/Hratioof0.1.Figure1showstheComptonscatteredspecaofthe2.223MeVlinefordifferentdepthsrangingfrom1.0to50.0gcm_。.WecanseethattheComptoneffectofthe2.223MeVlinedecreasessharplywithdecreasingneutroncapturedepth.Moreover,theComptonscatteredcontinuumhasarelativelyflatspectrumatenergiesbetweenthe2.223MeVlineand1MeVandbecomessteepbelow一1MeVAsameasureoftherelativestrengthoftheComptonscatteredspectrumforVarlOUSdepths,weassumethattheComptonscatteredcontinuum1sauniformspectrumwhlchextendsfrom0to2.223MeVAlsoweconsidertheaveragenumberofphotonsperkeVofthescatteredcomponentatthel一2_22MeVbandasthatofthewholeComptonscatteredcontinuum.Hereweneglecttheslopeofthecontinuumbelowthe1MeVbandbecausepositronannihilationphotonsandbremsstrahlungphotonstendtodominatethecountingratesattheseenerglesinHarespectra.OnecanthendefinetheComptonEfficiencyastheratiooftheComptonscatteredcontinuumintensitytotheintensityofthe2.223MeVline.WehaveapproximatedtheseresultsbytheexpressionD14.53CE0.621HereCE/isComptonEfficiency,isthe2.223MeVlineintensityand厶istheComptonscatteredcontinuumintensity.Thisequationcanbeusedtoestimatethedepthofproductionoftheneutroncapture1ine.Forflareanalysis,itshouldbenotedthatDinEquation1isthelineofsightdepthinunitsofgcm一2.Sincetheheightandsizeofaflareistypicallysmal1whencomparedtothesolarradius,thetransformationofthelineofsightdepthtotheverticaldepthisjustmultipliedbyacosineofheliocentricangle.Anaccuratecalculationmusttakeintoaccountthedependenceofdepthonthedensityofthesolaratmospheresinceithasasongup/downasymmetry.However,thepreliminarysimulationshowsthatthereisnosignificantdifferenceamongscatteredspectraresultingfrombackscatteringatdifferentdepths,exceptasmalleffectthatlowerstheenergyofthescatteredspectrum.Vestrand1990developedaMonteCarlocodeforphotontransportationtosimulatetheneutroncapturephotonsinasemiinfiniteplaneparallelatmosphere.ThecalculationindicatedthattherelativestrengthoftheComptontai1increasedwiththedepthofphotonproduction.BasedontheadvancedMonteCarlosimulationcode,GEANT4,weobtainedsimilarresults.TherelmivestrengthsOfthescatteredcontinuumarequantitativelyconsistentwitheachother.ByincorporatingthedepthandComptonefficiencyintoEquation1,itiseasiertodeterminetheneutroncapturedepth.3APPLICATIoNANDDISCUSS10NToinvestigatetheroleofComptonscatteringinthegammarayspectra、westudyindetailtheX7.1/2Beventon2005January20.whichoccurredinactiveregion10720atcoordinatesN14W61rwithaheliocentricangleof一65。1.ThisflarewaswellobservedbyR.ThelightcurvesaredisplayedinFigure2.ThebackgroundsubtractionwasdonewiththesamemethodasSmitheta1.2003.taking15orbitsbeforeandaftertheflare.Thetemporalevolutionoftheflare1ookssimple,withonlyonedominantDeakingammarayenergYbands.Thelightcurvesinthisperiodconsistofthreephasesrise.peak.anddecay.W_ehavechosenthetimeinterval064310070010UTasourperiodofinterest.anddividedthisperiodinto16intervalsforlatercalculations.RHESSIobservationswithahighspectra1resolutioningammarayenableustoanalyzeitscontinuumandlineprofiles.Afu11countspectrumfrom250keVtol6MeVtheupperlimitofenergyTheEffectofComptonScatteringonGammaraySpectra1443fChenGan2012.TheabundancesofbothacceleratedparticlesandambientelementsarecoronalReames1995exceptfortheambientHe/Hratioof0.1andtheaccelerated/pratiorangingfrom0.0tO1.0.A11nuclearcrosssectionsarecalculatedfromtheTALYScode,whichhasbeenverifiedbymanyauthors.Wlehavetwoassumptionsinourcalculation.First,weassumeadownwardisotropicangulardistributionoftheacceleratedions.Shareeta1.2003showedthatanisotropicdistributioninthedownwarddirectionisbetterthanasimpledownwardbeam.Second,consideringtheeffectofbothangulardistributionofionsanddiversificationofthenuclearreactions,weassumetheisotropicgammarayemissionsareintheexcitednuclerrestflame.Inaddition,weconsidertheeffectoftheflare1ocationonthedeexcitationlinespectrum.Sincetheflarelocationisaknownquantityofmeasurement,thedeexcitationgammarayspectrum,therefore,dependsonthespectralindexofacceleratedionsandthealphatoprotonratiooL/P.Thecontinuousemissioninthegammaraybandismainlyfromelectronbremsstrahlungand7r.decay.Becansetheshapeof7rdecayemissionapproximatesapowerlawdistributionatenergiesbelow16MeVweassumethebrokenpowerlawshaperepresentsthecontinuousemissionwhichblendstheelectronbremsstrahlungemissionand丌一decayemission.ThefittingwasdonebyusingtheSPEXpackagefSchwartzeta1.2002withdifferentmodels.WdidnotconsidertheComptonscatteringofthe2.223MeVlineinourfirstfittingmode1.Thebestfittingresultofthetimeinterval064310070010UTforthiseventisshowninFigure3。inwhichthegreencurverepresentsthecontinuousemissioncomponentwithabrokenpowerlawshape.theyellowcurveandthepinkcurverepresentthepositronannihilation1ine0.5l1MeVandtheneutroncaptureline2.223MeVrespectively,andthecVancurvere,resentsthetotaldeexcitationlineswhichincludethenarrowlinesandthecontinua.Thesumofallthesecontributionsispresentedbytheredcurve.TheComptonscatteringofthe2.223MeVlinewasintroducedinoursecondfittingmodelwithanextraparameterofComptonscatteredcontinuumintensity.Figure4showsthebestfitresult.Inthiscase.wecanseealargecontributioninthelowerenergyspectrumresultingfromtheComptonscatteredcontinuumofthe2.223MeVlinerpurplecurve.ComparingboththebestfitresultswithoutandwithComptonscatteringinFigures3and4respectively.wenotethattheshapeandintensityofthe0.511MeVlinehashardlychangedinbothcases.Asimilarsituationispresentedinthe2.223MeVline.However,theacceleratedionspectrumofthelatterfittingmodelismuchflatterthanthatoftheformer.Todeterminethequalityoffit,weusethestatisticx。∑ct一zt/。。2asdefinedinMurphyeta1.1990,wherecisthenumberofobservedcountsinchanneli,miisthenumberofcountspredictedbythemodelandoistheuncertaintyofthemeasurementinchanneli.Theminimumvaluesare1291and1237forthesetwomodels,respectively.WethenplotaAXAX一m2incontourmapinthebottomrightpanelofFigures3and4whichcanbeusedtoestimatethespectra1indexofionsandthealphatoprotonratio.ByusingaMonteCarlosimulation,theestimatedAvalueswith1盯uncertaintyare8.9and10forthesetwocases,respectively.Inadditiontheresidualsoffittingresultsarealsoimprovedwithasmallerchi.squarevalueinthesecondmode1.especiallynear2MeVBothsetsofevidenceimplythatthesecondmodelisbetter.Moreover,sincetheneutroncapturephotonsareemittedataverticaldepthcorrespondingtoacolumndensityofabout10一10Hcm一HuaLingenfelterl987.theComptoneffectof2.223MeVphotonsisnaturallyexpectedfromaphysicalpointofview.A11resultssupportthatthesecondmodelismorereasonableinthisevent.ThecorrespondingComptoneficiencyisabout1.4forthebestfittingresultofthesecondmode1.W_ethusinferfromEquationfl1thatthe1ine.ofsightdepthDisabout20gcm.DHetotheoffdiagonalresponsefromtheneu仃oncapturelinebeingsignificantfortheRHESSI,wethenestimatedthattheintensityoftheComptonscatteredcontinuumhaschangedbyabout20%foranuncertaintyofinstrumentalresponsechanging10%inmagnitude.Sotheverticaldepthforneutroncaptureonhydrogeninthiseventis8.5土0.3『土1.91gcmz.Here1446量1.0藏毯4,iiij1.5ChenQ.GanPhotonEnergyMeV02468PhotonEnergyMeVFig.5Calculateddeexcitationgammarayspectraversustheacceleratedionpowerlawindex.Theleftpanelshowsthespectrumfromacceleratedionswithpowerlawindexs2.0.Therightpanelshowsthespectrumfromacceleratedionswithpowerlawindexs5.0.Thesolidcurvesshowtotaldeexcitationgammarayspectraofthesolarflareataheliocentricangleof60。,whilethedashedcurveandthedottedcurveshowthebroadlinesandtheunresolvedcomponents,respectively..J。}J。\..uhIinenuH二二二....J。_。。_。。。。。....~Btrhlugnuat25。k一Nuden砒I。nlinen唧H『_}.L}.TTs一o¨。IⅢI』I06440.6§仉麟0.13z差{.2.31.5...J\.二utenenu1。『.。AnnihnIim二工_J一Bremsstrahlungflat250keV一~\二二_二pIctralind06480652065607呻0644StartTime20Jan050643100648065206560700StartTime20Jan05064310Fig.6Timeevolutionoftheneutroncaptureline2.223MeVflux,positronannihilationline0.511MeVflux,bremsstrahlungfluxat250kenucleardeexcitationlineflux,andpowerlawindexofacceleratedionspectrum.Thestartingtimeofthefigureis064310UT.TheteftandrightsidesarebestfittingresultswithoutandwithComptonscattering,respectively.Besidesthetimeprofilesoflinefluxandspectralindex,wealsoderivethetimeevolutionoftheComptonscatteredcomponent.InFigure7weshowthetimeprofilesoftheneutroncapturelineflux,theComptonscatteredcontinuumintensity,andtheComptonefficiencyfortheflare.Ascanbeseen,thereisastrongcorrelationbetweenneutroncapturelinefluxandtheComptonscattered目0l0qd54j{2蛊10TheEffectofComptonScatteringonGammaraySpectra一.f}~。。nnuⅧltensity一eC二omr。pntocnEffirceie。necytlhStartTime2OJan05064310Fig.7Timeprofilesoftheneutroncapturelinefluxtoppane1,theComptonscatteredcontinuumintensitymiddlepane1,andtheComptonefficiencyandtheneutroncapturedepthbottompane1fortheflare.Thediamondsymbolinthetoppanelrepresentsthecorrectedneutroncapturelineflux.1447continuumintensityofthe2.223MeVlineduringsometimeperiod.However,thelatterrisesfasterandlastsonlyseveralminutes.TheComptoneffectlooksimportant,atleastaroundthepeakoftheflare.WlecanalsoseefromFigure7thattheComptone伯ciencyrisesrapidlyattheearlyphase.andthendeclinesgradually.CombiningthediscussionwithEquationf11,wecandeducehowmuchco1.umndensityisrequiredforneutroncaptureonhydrogeninasolarflare.Mostneutroncapturephotonsareproducedfromthedeeperatmospherewiththehighestdepthabout15gcm一1duringtheearlyphase.Subsequently.tl1ephotonsproducedfromneutroncaptureareemittedfromthehigheratmosphere1owerdepthorformedwithinamoredi肌sespacerelativetothatattheearlytime.Themosteffecfiveneutronsforproducingthe2.223MeVlinearethosewithenergybelow50MeV.whichneedtopassthroughagrammageof10gcm一forthermalizationTroitskaiaeta1.2009.Consequently.ourresultof15gcm一2impliestheexistenceofhigherenergyneutronsattheearlyphase.Inotherwords,italsoindicatestheexistenceofharderionspectrumresultsinhigherenergyneutronsinthisevent.ThecorrectedneutroncapturefluxbyincludingtheComptonscatteredcontinuumisalsoshowninthetoppanelbyadiamondsymbo1.Sincemanyneutroncapturephotonsareconvertedto1owenergyphotonsattheearlyphase.wecanseethatthepeakofcorrectedneutroncapturefluxisabout1minuteearlierthanthatoftheuncorrectedflux.Therefore,theComptonscatteringonthe2.223MeV1ineisimportantforallaccuratemeasurementoftheneutroncapturelineflux.Thedepthdistributionofneuuoncaptureonhydrogendependsprimarilyonneutronpropagation.W_euseGEANT4tofindadecaytimeseries.Themonoenergyneutronsiniectdownwardfromthebottomofthechromosphere.TheSunisassumedtobeawellmixedplasmasphereofhydrogenandhelium、havingaseriesofshellsstackedintheverticaldirectionwithadensitygradient.Thisassumptionisbasicallyreasonable,becausetheenergYlossesofneutronsareprimarilydeterminedbythecolumndensityofmatteralongitspath.Asaresult.thehistogramofneutroncapturetimereflects.toacertainextent.thedepthdistributionofneutroncapturelineproduction.321032l0.菖I.s∞鲁qd笛曙田鲁苣目0u

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