Long period slow MHD waves in the solar wind sourc

1LONGPERIODSLOWMHDWAVESINTHESOLARWINDSOURCEREGIONLongperiodslowMHDwavesinthesolarwindsourceregionB.N.Dwivedi*,A.K.Srivastava**DepartmentofAppliedPhysics,InstituteofTechnology,BanarasHinduUniversity,Varanasi-221005,India_______________________________________________________________________AbstractWeconsidercompressiveviscosityandthermalconductivitytostudythepropagationanddissipationoflongperiodslowlongitudinalMHDwavesinpolarcoronalholes.Wediscusstheirlikelyroleinthelineprofilenarrowing,andintheenergybudgetforcoronalholesandthesolarwind.WecomparethecontributionoflongitudinalMHDwaveswithhighfrequencyAlfvénwaves.PACS:96.50.Tf;96.60.pc;96.60.VgKeywords:MHDwaves;solarwind;coronalholes.*CorrespondingauthorE-mailaddress:[e-mail](B.N.Dwivedi)**PresentAddress:ArmaghObservatory,CollegeHill,NorthernIrelandBT619DG.1.IntroductionThebroadeningoflineprofilewithradialheightisthelikelysignatureoftheundampedAlfvénwavepropagation(Hassleretal.,1990;Wilhelmetal.,2004,2005;andreferencescitedtherein).Thenarrowingoflineprofileis,however,attributedtothepropagatingdampedAlfvénwaves(Harrisonetal.,2002;O’Sheaetal.,2005).Spectroscopicstudies,bothonthediskandoff-limb,alsoshowthepresenceofcompressionalwavesinplumesandinter-plumeregionsofpolarcoronalholesandtheirpossibleroleinthesolarwindacceleration(GurmanandDeForest,1998;Ofmanetal.,1997,1998;Banerjeeetal.,2001).Recently,O’Sheaetal.(2006,2007)havealsoinferredthepresenceoffastandslowmagnetoacousticwavesinthepolaroff-limbregion.LinearMHDmodelofAlfvénwavedissipationintheequatorialcoronahasbeenreportedbyHarrisonetal.(2002).ThesameexplanationisgivenbyPekünlüetal.(2002)2LONGPERIODSLOWMHDWAVESINTHESOLARWINDSOURCEREGIONinthenorthernpolarcoronalholes,invokinglinearMHDmodelcorrelatingwiththeobservedlineprofilenarrowingintheseregions.DwivediandSrivastava(2006)havealsostudiedtheoutwardlypropagatingAlfvénwavesandtheirdissipationincoronalholes,supportingthesolarwindoutflowstartingbetween5Mmand20MmasreportedbyTuetal.(2005a,b).Thequasi-periodicdisturbancesintheoff-limbabovethepolarcoronalholeshavebeeninterpretedastheslowmagnetosonicwavesbyOfmanetal.(2000b).UsingExtreme-UltravioletImagingTelescope(EIT)onboardtheSOHOspacecraft,Ofmanetal.(1999)havealsofoundthesignaturesofquasi-periodiccompressionalwaveswithperiodsof1015minutesinsouthernpolarplumes,andinterpretedthemasslowmagnetosonicwaves.Thesewavespropagatewiththesubsonicspeedof75150kms-1andsteepeninthecoronanonlinearly.Thesteepeningmayleadtotheformationofshockshigherinthecorona,andmaycontributesignificantlytothesolarwindaccelerationbytransferringmomentumtotheflow.Ofmanetal.(2000a)havefoundthatnonlinearsteepeningoftheslowmagnetosonicwavesleadstoenhanceddissipationowingtocompressiveviscosityatthewavefronts.Theefficientdissipationoftheslowwavebycompressiveviscosityleadstodampingofthewaveswithinthefirstsolarradiiabovethelimb.ThesphericallysymmetricAlfvénwavesarealsosubjectedtothenonlinearsteepeningastheymoveupinthehighercorona(Nakariakovetal.,2000).SuzukiandInutsuka(2005)havealsofoundthataftertheattenuationofthe85%oftheinitialenergyfluxinthechromosphere,theoutgoingAlfvénwavesenterthecoronaandcontributetotheheatingandaccelerationoftheplasmamainlybythenonlineargenerationofcompressivewavesandshocks.Hence,thestudyofbothlinearandnonlinearMHDwavesareimportanttodescribetheheatingofcoronalholesandaccelerationofthefastsolarwind.ThesignatureofslowwaveoscillationsanditsdissipationhasalsobeenstudiedinhotcoronalloopsbyOfmanandWang(2002).Mendoza-Bricenoetal.(2002,2005)havealsostudiednumericallytheresponseofthecoronalplasmatomicroscaleheatingpulsesinloops.Inthispaper,weconsiderthermalconductivityandcompressiveviscosityasdissipatingagentstoinvestigateslowlongitudinalMHDwaveswithperiods60s,180s,and300srespectively.WeconsiderthesolarwindsourceregionanditsupperpartinsidepolarcoronalholesforthepropagationofslowlongitudinalMHDwavesalongthebackgroundmagneticfielddirection.Ourfirstaimistoexplorewhetherornotthe3LONGPERIODSLOWMHDWAVESINTHESOLARWINDSOURCEREGIONdissipationofMHDwavescausesobservedlineprofilenarrowing(O’Sheaetal.,2005).Inthelightofspectroscopicsignatureofline-widthvariationinpolarcoronalholes,oursecondaimistocomparetheroleofhigh-frequencyAlfvénwaves(SrivastavaandDwivedi,2007;DwivediandSrivastava,2006)withtheslowlongitudinalMHDwavesintheinnercorona.ThenonlinearityandbackgroundplasmaflowcanaffectthepropertiesoftheseMHDwaves,e.g.,cut-offfrequencies,dissipationrates,andphasespeedsetc(e.g.,Terra-Homemetal.,2003).However,weconsiderthelinearapproximationinordertoexploreourprimarygoalofexplainingtheobservation.WeestimateenergyfluxdensityofMHDwavesinthelinearapproximationtocalculatetheoreticallinewidth.Sinceobservedspectrallinewidthvariationisalongoutwardradialdirectiononly,weconsideronlytheradialoutwardpropagationofMHDwaves,neglectingresonantabsorptionandphasemixing.InSection2,wedescribeMHDequationsandtheoreticalconsiderations.InSection3,wedescribetheoreticallinewidths,estimatedasaresultofAlfvénwaves,andslowlongitudinalMHDwavesinpolarcoronalholes.Resultsanddiscuss