MICROWAVE MODE COUPLING ABOVE ACTIVE REGIONS AS A

MICROWAVEMODECOUPLINGABOVEACTIVEREGIONSASACORONALDENSITYDIAGNOSTICJeongwooLee,StephenM.WhiteandM.R.KunduAstronomyDepartment,UniversityofMaryland,CollegePark,MD20742ZoranMikicScienceApplicationsInternationalCorporation,SanDiego,CA92121A.N.McClymontInstituteforAstronomy,UniversityofHawaii,Honolulu,HI96822Abstract.Itiswellrecognizedthatthephenomenonofdepolarization(theconversionofpolarizedradioemissionintounpolarizedemission)ofmicrowavesoversolaractiveregionscanbeusedtoinferthecoronalelectrondensityoncethecoronalmagneticeldisknown.Inthispaperweexplorethistechniqueusinganactiveregionforwhichwehaveexcellentradiodatashowingdepolarizationattwofrequencies,andforwhichwehaveanexcellentmagneticeldmodelwhichhasbeentestedagainstobservations.Weshowthatthistechniqueforobtainingcoronaldensitiesisverysensitivetoanumberoffactors.WhenCohen’s(1960)theorywheredepolarizationisduetomagneticeldrotationaloneisused,theresultisparticularlysensitivetothelocationofthesurfaceonwhichthemagneticeldisorthogonaltothelineofsight.Dependingonwhetherwetakeintoaccountthepresenceofelectriccurrentsinthephotosphereornot,theirextrapolationintothecoronacanresultinverydierentheightsbeingdeducedforthelocationofthedepolarizationstrip,andthischangesthedensitywhichisthendeducedfromthedepolarizationcondition.Suchextremesensitivitytothemagneticeldmodelrequiresthateldextrapolationsbeabletoaccuratelypredictthepolarityofmagneticeldsuptocoronalheightsashighas105kminordertoexploitdepolarizationasadensitydiagnostic.Keywords:Corona,MagneticFields,Polarization,ModeCoupling1.IntroductionTheabilitytomeasurethefundamentalphysicalpropertiesofthesolaratmosphere,suchastemperature,densityandmagneticeld,isessentialtoprogressinunder-standingtheprocesseswhichoccurthere.Inthispaperweinvestigateamethodformeasuringelectronnumberdensitiesinthesolarcorona.Atpresent,theonlyviabletechniqueformeasuringelectrondensitiesinthenon{aringcoronadirectlyinvolvesradioemission,sinceothertechniques(opticalforbiddenlines,EUVandX{raylines)actuallymeasurethenumberdensityofaparticularchargestateofaparticularelement,ratherthantheelectronnumberdensity(thenon{aringcoronadoesnotproduceenoughcontinuumemissionatshortwavelengthsforittobeuse-ful),andthe(unknownandpossiblyspatiallyvariable)abundanceofthisparticularstatemustbeassumedinordertoconvertthemeasurementstoelectrondensities.Radioobservationsprovideseveraldiagnosticsofelectrondensity.Thesimplestinvolvesthemeasurementoffree{free(bremsstrahlung)emission,whichisproducedbythecollisionsofelectronswithprotonsandparticles.Theobservedfree{free2Leeetal.emissionisthusgenerallydominatedbyregionsofhighdensitywhichoccuratlowaltitudesinactiveregions.Asecondtechniquecan,inprinciple,beexploitedatsomewhatgreaterheightswherethefree{freeemissionistooweaktobeveryuseful,andthisisthetechniqueaddressedinthispaper.Thistechniqueinvolvesobservationofthelocationsatwhichradioemissionfromtheunderlyingactiveregionbecomesdepolarized.InanionizedplasmasuchastheSun’scorona,thetwonaturalmodesoftheplasmaarecircularlypolarizedeverywhereexceptforanarrowrangeofpropagationanglesorthogonaltothelocalmagneticeld.Sinceelectronsinteractmorestronglywithonemode(themodewhichispolarizedinthesamesensethattheelectrongyratesaboutthemagneticeld,labeledtheXmode)thantheother(theOmode),theemissionisgenerallypreferentiallycircularlypolarizedinoneparticularsense(Xmode)whenitleavestheemissionregion.TheXandOmodesgenerallypropagateindependentlyofoneother,andhencethepolarizationisunchangedduringpropagation,ifthemediumisuniform.However,duetotheinhomogeneousnatureofthecorona,couplingbetweenthetwomodesmayoccuriftheirrefractiveindicesbecomesimilar(whichdependsonthefrequency,magneticeldanddensity;e.g.,Cohen,1960).Oneparticularoutcomeofmodecouplingisthecompletedepolarizationoftheemission,andthiscasehasthepotentialtobeavaluablediagnostic.KunduandAlissandrakis(1984)exploitedthisdiagnosticusing5GHzpolariza-tionobservationsmadewiththeWesterborkSynthesisRadioTelescopeonseveralconsecutivedays.Depolarizationcorrespondstoaspecicrelationshipbetweenden-sityandmagneticeldbeingsatised.KunduandAlissandrakis(1984)assumedanelectrondensityof108cm3,andforadipolecongurationforthemagneticeldtheyderivedamagneticeldstrengthof10{20Ginthedepolarizationlayer.Gelfreikh,Peterova,andRyabov(1987)usedmultiplefrequenciesandwereabletoderivethecoronaleldstrengthasafunctionofheight.Mostrecently,Alissandrakisetal.(1996)makeuseofapotentialeld(PF)extrapolationtodeterminethemag-neticeld,andthenusedepolarizationobservationstoderivethecoronaldensity.Themodelpredictsamagneticeldstrengthof16Gandheight105kmatthepositionofdepolarization,andtherequireddensitytherewas6:4107cm3.TheauthorsconsidertheresultingdensitytoolowtobecompatiblewithsimultaneousFaradayrotationobservations(AlissandrakisandChiuderiDrago,1994)andcon-cludedthattheerrorcouldbeduetotheuncertaintyinvolvedinextrapolatingeldstrengthsallthewayfromthephotosphereuptosuchhighcoronalheights.Otherstudieshavepointedoutthatsomepolarizationobservationsappeartobeincompatiblew