Alfvenic Turbulence in the Extended Solar Corona K

arXiv:astro-ph/0305134v18May2003Astrophys.J.(2003),inpressAlfv´enicTurbulenceintheExtendedSolarCorona:KineticEffectsandProtonHeatingS.R.CranmerandA.A.vanBallegooijenHarvard-SmithsonianCenterforAstrophysics,60GardenStreet,Cambridge,MA02138ABSTRACTWepresentamodelofmagnetohydrodynamic(MHD)turbulenceintheextendedsolarcoronathatcontainstheeffectsofcollisionlessdissipationandanisotropicparticleheating.Recentobservationshaveshownthatpreferentialheatingandaccelerationofpositiveionsoccursinthefirstfewsolarradiiofthehigh-speedsolarwind.MeasurementsmadebytheUltravioletCoronagraphSpectrometeraboardSOHOhaverevivedinterestintheideathationsareenergizedbythedissipationofioncyclotronres-onantwaves,butsuchhigh-frequency(i.e.,smallwavelength)fluctuationshavenotbeenobserved.Aturbulentcascadeisonepossiblewayofgeneratingsmall-scalefluctuationsfromapre-existingpopula-tionoflow-frequencyMHDwaves.Wemodelthiscascadeasacombinationofadvectionanddiffusioninwavenumberspace.Thedominantspectraltransferoccursinthedirectionperpendiculartotheback-groundmagneticfield.Asexpectedfromearliermodels,thisleadstoahighlyanisotropicfluctuationspectrumwitharapidlydecayingtailintheparallelwavenumberdirection.Thewavepowerthatde-caystohighenoughfrequenciestobecomeioncyclotronresonantdependsontherelativestrengthsofadvectionanddiffusioninthecascade.Forthemostrealisticvaluesoftheseparameters,though,thereisinsufficientpowertoheatprotonsandheavyions.Thedominantobliquefluctuations(withdispersionpropertiesofkineticAlfv´enwaves)undergoLandaudamping,whichimpliesstrongparallelelectronheating.Wediscusstheprobablenonlinearevolutionoftheelectronvelocitydistributionsintoparallelbeamsanddiscretephase-spaceholes(similartothoseseenintheterrestrialmagnetosphere)whichcanpossiblyheatprotonsviastochasticinteractions.Subjectheadings:MHD—plasmas—solarwind—Sun:corona—turbulence—waves1.IntroductionInordertoproducethehot(106K)solarcorona,afractionofthemechanicalenergyintheSun’sinternalconvectivemotionsmustbeconvertedintoheatabovethephotosphere.Despitemorethanahalfcenturyofin-vestigation,though,theprecisephysicalprocessesthatleadtocoronalheatingandthesubsequentaccelerationofthesolarwindarenotknown.Atthecoronalbase,differentcombinationsofmechanisms(e.g.,magneticreconnection,turbulence,wavedissipation,andplasmainstabilities)areprobablyresponsibleforthevariedap-pearanceofcoronalholes,quietregions,loops,andX-raybrightpoints(Priestetal.2000).Intheopenmag-neticfluxtubesthatfeedthesolarwind,additionalheat-ingatheliocentricdistancesgreaterthanabout2solarradii(R⊙)isbelievedtobeneeded(e.g.,Leer,Holzer,&Fl˚a1982;Parker1991).Thispaperinvestigatesthecon-sequencesofapromisingmechanismforextendedcoro-nalheating:thekineticdissipationofdrivenmagnetohy-drodynamic(MHD)turbulenceinthestrongbackgroundmagneticfieldoftheacceleratingsolarwind.–2–Thenecessityforgradualenergydepositionatlargedistancesfromthecoronalbasecomesfromthreesetsofempiricalconstraints(seealsoCranmer2002).First,pressure-drivenmodelsofthehigh-speedcomponent(v&750kms−1)ofthesolarwindcannotbemadeconsistentwiththerelativelylowinferredelectrontem-peraturesincoronalholes(Te1.5×106K)with-outadditionalenergyormomentumdeposition.Second,spacecraftintheinterplanetarymediumhavemeasuredradialgradientsinprotonandelectrontemperaturesthataresubstantiallyshallowerthanpredictedfrompureadi-abaticexpansion(Phillipsetal.1995;Richardsonetal.1995).Similarmeasurementsofradialgrowthofthepro-tonmagneticmomentbetweentheorbitsofMercuryandtheEarth(Schwartz&Marsch1983;Marsch1991)pointtospecificformsofgradualenergyaddition.Third,theUltravioletCoronagraphSpectrometer(UVCS)aboardtheSolarandHeliosphericObservatory(SOHO)mea-suredextremelyhighheavyiontemperatures,fasterbulkionoutflowcomparedtoprotons,andstronganisotropies(withT⊥≫Tk)inionvelocitydistributionsintheex-tendedcorona(Kohletal.1997,1998,1999;Nocietal.1997;Cranmeretal.1999b;Giordanoetal.2000).ThelistofpossiblephysicalprocessesresponsibleforextendedcoronalheatingislimitedseverelybythefactthatCoulombcollisionsareextremelyweakabove2to3R⊙andthationsreceivemoreenergythanelec-trons(withTion≫Tp&Te).Also,mostsuggestedmechanismsinvolvethetransferofenergyfrompropa-gatingfluctuations—suchaswaves,shocks,orturbulenteddies—totheparticles.Thisbroadconsensushasarisenbecausetheultimatesourceofenergymustbesolarinorigin,andthusitmustsomehowbetransmittedouttothedistanceswheretheheatingoccurs(see,e.g.,Holl-weg1978;Tu&Marsch1995).Themostcommonwavedampingmechanismsproposedforthecoronalbase(re-sistivity,viscosity,andthermalconductivity)seemtoberuledoutintheextendedcoronabecauseoftherelativeunimportanceofcollisions.Wave-particleinteractionsarenaturalalternativestocollisionalprocessesandhavebeenstudiedinasolarwindcontextforseveraldecades(Barnes1968;Toichi1971;Abraham-Shrauner&Feldman1977;Hollweg&Turner1978;Marsch,Goertz,&Richter1982;Isenberg&Hollweg1983;Hollweg1986;Tu1987,1988;Ax-ford&McKenzie1992).TheSOHOobservationsdis-cussedabovehavegivenrisetoaresurgenceofinter-estinthecollisionlessdissipationofioncyclotronwavesasapotentiallyimportantmechanism