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Preview Multicomponent He I 10830 Å profiles in an active filament

AcceptedforpublicationinA&AonSep27th2010 i Multicomponent He 10830 Å profiles in an active filament C.Sasso1,2,A.Lagg1,andS.K.Solanki1,3 1 Max-Planck-Institutfu¨rSonnensystemforschung,Max-Planck-Str.2,Katlenburg-Lindau,Germany 2 INAF-OsservatorioAstronomicodiCapodimonte,SalitaMoiariello16,I-80131Napoli,Italy 3 SchoolofSpaceResearch,KyungHeeUniversity,Yongin,Gyeonggi446-701,Korea ABSTRACT 1 Aims.WepresentnewspectropolarimetricobservationsofthechromosphericHei10830Åmultipletobservedinafilamentduring 1 itsphaseofactivity. 0 Methods.ThedatawererecordedwiththenewTenerifeInfraredPolarimeter(TIP-II)attheGermanVacuumTowerTelescope(VTT) 2 on2005May18.WeinvertedtheHeStokesprofilesusingmultipleatmosphericcomponents. n Results.TheobservedHeStokesprofilesdisplayaremarkablywidevarietyofshapes.MostoftheprofilesshowverybroadStokes a I absorptions and complex and spatially variable Stokes V signatures. The inversion of the profiles shows evidence of different J atmosphericblue-andredshiftedcomponentsoftheHeilineswithintheresolutionelement(∼1arcsec),withsupersonicvelocities 8 ofupto∼ 100km/s.Uptofivedifferentatmosphericcomponentsarefoundinthesameprofile.Weshowthateventhesecomplex 2 profilescanbereliablyinverted. Keywords.Sun:chromosphere–Sun:magneticfields–Sun:infrared ] R S . 1. Introduction with three different methods, one of these being, as in our h case, Milne–Eddington inversions. They find the highest field p Filaments are typically elongated dark structures on the solar strengths measured in filaments so far, around600-700G, and - disk, characterized by additional absorption in strong chromo- o concludethatstrongtransversemagneticfieldsarepresentinac- spheric lines, like the Hα line. They are the on-disc counter- r tiveregionfilaments. t parts of prominences seen above the solar limb and represent s TheHei10830Åmultipletoriginatesbetweentheatomiclevels a denseandcoolchromosphericgassuspendedinthehotandthin 23S and23P .Itcomprisesacomponentat10829.0911Å [ corona. The strength and structure of the magnetic field plays 1 2,1,0 with J = 0(hereafterreferredtoasTr1),andtwocomponents a key role in keeping the prominence material from flowing u 1 at 10830.2501Å with J = 1 (Tr2) and at 10830.3397Å with down to normal chromospheric levels. It is therefore of con- u v J =2(Tr3)whichareblendedatsolarchromospherictempera- siderableinteresttodeterminethemagneticstructureassociated u 3 tures.Inthesubsequentdiscussionwecallthisblendedabsorp- with a prominence. A number of observations of the magnetic 6 tiontheTr2,3component. 5 vectorinprominenceshavebeencarriedout(e.g.,Leroy 1989; Weconcentrateondescribingtheobservationsandtheinversion 5 Casinietal. 2003; Linetal. 1998; TrujilloBuenoetal. 2002; oftheseprofiles.TheHeStokesprofilesintheactivatedfilament . Merendaetal. 2006;Kuckeinetal. 2009).Alltheseinvestiga- 1 revealaremarkablelevelofcomplexity,requiringuptofivein- tions, exceptfor the last one, have been restricted to quiescent 0 dependentmagneticcomponentstoreproduce.Inafollowingpa- prominences. 1 pertheobtainedmapsofthemagneticandvelocityfieldsinthe 1 In this paper we introduce spectropolarimetric observations in : theHei10830Åtripletofafilamentlocatedinanactiveregion filamentwillbepresented,criticallyanalyzedandinterpretedin v termsofprominencemodels. thathasbeenactivatedbyaflare.Filamentsalsoappearasdark i X absorptionfeaturesintheHei10830Åline. r Spectropolarimetry in the Hei triplet at 10830 Å is an impor- 2. Observations a tant tool to determine the magnetic field vector in the solar chromosphere(TrujilloBuenoetal. 2002;Solankietal. 2003). On 2005May 18we observedthe activeregionNOAA 10763, It is well suited for the measurement of the magnetic vector locatedat24◦ W,14◦ Sonthesolardisk,whichcorrespondsto near the base of the solar corona because these lines are of- a cosine of the heliocentric angle, µ = 0.9. During the obser- ten narrow, nearly optically thin, have a reasonable effective vationsa flare of GOES class C2.0 eruptedin the western part Lande´factor(seeTable1)andareeasilyobserved(Ru¨edietal. oftheactiveregion.Afilamentwaspresentintheactiveregion 1995). Measurements of the polarization of the Hei 10830 Å close to and partly overlyingthe flare ribbons,which was acti- vatedbytheflare. radiation are also indicated as a useful new tool for the di- The analyzed data were recorded with the second genera- agnostics of the magnetic field in filaments (Linetal. 1998; tionTenerifeInfraredPolarimeterTIP-II(Colladosetal. 2007) TrujilloBuenoetal. 2002). Recently, Kuckeinetal. (2009) mountedatthe70cmapertureVacuumTowerTelescope(VTT) studied the vector magnetic field of an active region filament byanalyzingspectropolarimetricdataintheHei10830Ålines at the Teide observatoryin Tenerife. The TIP-II instrument al- lows for a spectral window of 11 Å around the He10830 Å C.Sasso,e-mail:[email protected] line to be recorded with a wavelength dispersion of 11 mÅ 2 C.Sassoetal.:MulticomponentHei10830Åprofilesinanactivefilament a 3.6 b 3.5 5) ec] 30 33..24 10^5) ec] 30 3.0 Å (10^ rcs 20 3.0 nt ( rcs 20 2.5 0.3 a 2.8 o a 3 y [ 10 2.6 I c y [ 10 2.0 08 1 2.4 1.5 at 0 0 I 0 10 20 30 40 0 10 20 30 40 x [arcsec] x [arcsec] Fig.1. Intensity maps at different wavelengths of the scanned portion of active region NOAA 10763 (24◦ W, 14◦ S). Left (a): Continuum. Right (b): Hei line core of the Tr2,3 component. The four symbols overplotted on the right image refer to the line profilesshowninFig.2. Table 1.Spectrallinescontainedin the spectralwindowof the TIP-IIinstrument(10825-10836Å). Line Wavelength(Å) EffectiveLande´factor Sii 10827.09 1.5 Hei(Tr1) 10829.09 2.0 Cai 10829.27 1.00 Hei(Tr2) 10830.25 1.75 Hei(Tr3) 10830.34 1.25 H O(telluric) 10832.11 2 Cai 10833.38 1.00 H O(telluric) 10833.90 2 Nai 10834.85 1.03 per pixel. The wide wavelength range turned out to be abso- Fig.2.ObservedStokesIprofilesatdifferentlocations,indicated lutely necessary to cover the full range of possible He absorp- bythedifferentsymbolsinFig.1b.Solidline(starsymbol):quiet tion signatures observed during the evolution of the filament. As we shall show below in Sect. 4, some of the Hei profiles Sun profile. Dashed line (cross): Hei emission profile. Dash- dottedline(triangle):verybroadHeiprofileindicatingmultiple weobserveddisplayabsorptionatredshiftscorrespondingtoas redshifted atmospheric components.Dotted line (square):deep muchas100km/s.Thisisconsiderablyhigherthanthehighest absorption in the He lines, that is in part strongly blueshifted. redshiftsmeasuredbyAznarCuadradoetal. (2005),whoseex- haustiveanalysisofsupersonicdownflowsseenintheHeilines Thearrowsmarkthewavelengthsatwhichimagesareshownin Fig.4. waslimitedbythespectralrangeavailabletothemuchsmaller TIP-Idetector(Mart´ınezPilletetal. 1999). The spectralwindowof TIP-II (10825-10836Å) containspho- featuresinFig.1a.InFig.1bastrongabsorptionfromthefila- tospheric lines of Sii at 10827.09 Å, Cai at 10829.27 and mentmaterialisclearlyvisibleintheHeilinesat9”< x<33”, 10833.38ÅandNaiat10834.85Å,thechromosphericHeimul- scannedfrom∼14:43to14:53UT. tipletandtwotelluricblendsat10832.11Åand10833.90Å(see In the last part of the map (33” < x < 49”), at y ≈ 19”-28”, Table1). duringthescanofaflareribbon,theabsorptionintheHeilines Thefilamentwasscannedinstepsof0.35”perpendiculartothe is weaker than in quiet Sun regions and the spectra also show slitorientation(180.51◦withrespecttothesolarN-Sdirection), in part emission profiles (visible as brightenings in the image; from14:38:29to15:02:26UT,providingamapoftheregionof cf.Laggetal. 2007).InthisregiontheHαslit-jawimagesthat 36.5×25Mm2. were simultaneouslyrecordedat the VTT display flare ribbons Figure1showsStokesImapsoftheobservedregionobtainedin aswell. thecontinuumat10825.8Å(a)andinthecoreoftheTr2,3com- ponentoftheHeitriplet(b).Theslitisorientedalongthey-axis 3. AnalysisoftheStokesprofiles andthedirectionofthescanisalongthex-axis.Therefore,along the x-axis both spatial and temporal information are mixed. In InFig.2fourobservedStokesI profilesnormalizedtothecon- additionto a few small pores,Fig. 1a clearly shows the granu- tinuumintensityareplottedasanexampleoftheunusuallywide lationacrossthewholeimage,suggestingthattheseeingcondi- rangeofprofilesobserved.Thesespectraandallthespectrawe tionsduringthescanwereparticularlygoodandstable,allowing show here are binned over four spectral pixels (resulting in a onaveragearesolutionof1”.Theresolutionwasdeterminedby wavelength dispersion of 44 mÅ) and eight spatial pixels (re- performinga Fast FourierTransformofthe averagecontinuum sultinginaspatialpixelsizeof0.7×0.7arcsec2,asinglepixel image.Notethatthediffraction-limitedperformanceoftheVTT being0.35×0.18arcsec2)inordertoincreasethesignal-to-noise atthiswavelengthcorrespondstoaresolutionof0.39”.Atsome ratioto∼4000.Thesolidlinerepresentsaprofileobservedina locationsthe Hei profile is so broadthat no pure continuumis comparativelyquietregionofthemap(atthelocationoftheas- presentonthedetector.Theselocationsappearasdarkcloud-like terisk in Fig. 1b), the dashed spectrum shows a Hei profile in C.Sassoetal.:MulticomponentHei10830Åprofilesinanactivefilament 3 HeI Tr1 Tr2+3 telluric telluric SiI CaI HO CaIHONaI 2 2 6000 s) 5000 nt cou 4 000 I ( 3000 0.002 C Q/I 0. 000 −0.002 0.006 0.004 0.002 C U/I 0. 000 −0.002 −0.004 −0.006 0.04 0.02 C V/I 0 .00 −0.02 −0.04 108 26 108 28 108 30 108 32 108 34 108 36 Wavele ngth [Å] Fig.3.ExampleofanobservedaveragedStokesvector(dash-dottedprofileofFig.2).TheunusuallybroadStokesI profileandthe correspondingsignaturesoftheV profilesuggestthattheHetripletsamplesmultipleatmosphericcomponents.Theverticaldotted linesmarktherestwavelengthsofthedifferentlinesthatarepresentintheobservedwavelengthrangeandareidentifiedatthetop ofthefigureandlistedinTable1. emissionobservedinaflareribbon(crossinFig.1b).Notethat nearlytheentirewavelengthrangeoverwhichStokesI exhibits the Sii line is weakened at this location. The dash-dotted line astrongabsorption.ThecomplexityoftheStokesV profilecon- (triangle in Fig. 1b) shows a very broad absorption in the Hei firmsthatthebroadHeiabsorptionismostlikelycausedbymul- linesobservedinthefilament.Significantabsorptioncoversthe tipleatmosphericcomponentsharboringgasthatflowsatdiffer- wavelengthrangefrom10829Åto10835Å,withweakabsorp- entspeeds.Italsoindicatesthatatleastapartofthedownflow- tion to the very edge of the detector at 10836 Å. The Stokes I inggasislocatedinmagnetizedregionsofthesolaratmosphere. profile exhibits multiple minima that are not corresponding to Stokes Qand,toa lesserextent,StokesU alsodisplayasignal therestwavelengthsoflinesnormallyfoundintheSun’sspec- overabroadwavelengthrange,althoughthesignalisweakand trum, nor to telluric absorptions. The multiple absorption dips consequentlythesignal-to-noiseratioisfairlylow.InFig.3the intheprofilesuggestsmultipleatmosphericcomponentswitha wavelengthpositionsatrestofthe differentlinespresentin the shift in the Hei absorption caused by different velocities. For observedwavelength range are indicated by the vertical dotted thedash-dottedprofilethesecomponentsarenearlyatrestorare lines(seealsoTable1). redshifted(seealsoFig.3).Themaximumredshiftcorresponds Inorderto investigatehowthemultipleHe componentsarere- to a downflow velocity along the line-of-sight of ∼ 100 km/s. latedwiththemotionofthefilamentmaterial,weshowinFig.4 The dotted line (square in Fig. 1b) is an example of a particu- two intensity maps of the scanned active region at wavelength larly deep absorption in the Hei line, which becomes as deep positions−1.08Å(A)and+1.08Å(B)withrespecttotherest asthestrongSiilineinthequietSun.Inadditiontothisstrong wavelengthof theTr2,3componentofthe He lines. Thewave- unshiftedabsorptionthereisabroadblueshiftedabsorptionthat lengths at which the images are shown in Fig. 4 correspondto blendswiththeSii10827Ålineandextendsevenbluewardsof up-anddownflowsof30km/s,respectively,andaremarkedby it,revealingrapidlyupwardpropagatingchromosphericgas.The arrowsin Fig.2.Fromthesemapswecansee thatstrongblue- maximumblueshiftcorrespondstoavelocityalongtheline-of- orredshiftedlineprofilecomponentsarepresentoverpractically sightof∼60km/s.Aswealreadypointedout,theshownspectra thewholefilament,suggestingstrongdynamicsthroughoutthis arealwaysbinned,butmultiplecomponentsarealsoseeninthe active filament. These dynamicscan be very complex,because singleprofilesformingthecomposite. wenoteanumberoflocationsatwhichprofileswithstrongblue- InFig.3weplotthe(averaged)fullStokesvectorforthedash- andredshiftscoexistwithinaresolutionelement.Consequently, dotted profile of Fig. 2 (position x = 32”, y = 22” in Fig. 1). upflows and downflows are present at the same spatial posi- The polarized Stokes parameter displaying the highest signal- tion,althoughwiththissimpleanalysisalonewecannotruleout to-noise ratio is Stokes V. It displays a significant signal over thattheseprofilesaresimplystronglyturbulentlybroadened,or 4 C.Sassoetal.:MulticomponentHei10830Åprofilesinanactivefilament a strong Tr1 mimics a blueshift. Indeed, a similar anomalous needtodemonstratethatthesefitsarereliable.Additionally,we broadeningwas observed by Lo´pezAriste&Casini (2006) in needtodeterminethemaximumamountofinformationthatcan theHeiD lineinspicules.Theyfoundthatadistributionofve- bereliablygatheredfromthesecomplexinversions. 3 locitieswithFWHM=50km/swasrequiredtoreproducetheob- We have tested that we do not employ more components than servedbroadening. necessarybyfirstfittingeachprofilewithasmallernumberofat- InFig.5wepresentsomeexamplesofobservedaveragedStokes mosphericcomponentsandconsequentlyfreeparameters.Only I (A)andStokesV (B)profilesatdifferentpositionsmarkedby a significant improvementof the fitness function f (defined in thelettersa-finFig.4.Theystretchapproximatelyfromoneend Laggetal. 2004),whichgivesthegoodnessofthefit,warrants of the filament to the other and display a gradualchange from theuseofmorecomponentsorfreeparameters.Usually,anin- mainlyredshifted(a)tomainlyblueshifted(f)profiles.Allthese sufficientnumberoffreeparametersresultsinapoorfitforparts profiles are characterized by multiple atmospheric components oftheobservedlineprofile. of the Hei lines. In some of them, most prominently in c and Forsomeextremeprofileswefacetheproblemofahugenum- e,blueshiftedandredshiftedcomponentscoexist.Notealsothe ber of free parametersto be fitted. The spectralregioncovered changingratios of the Sii and the Hei Stokes V profile ampli- bytheHeabsorptionsignatureofstronglybroadenedorshifted tudes.Atsomelocations,notablybandc,thephotosphericand profiles also contains four photospheric lines of Sii, Cai (two chromosphericStokes V profiles have opposite polarities. This lines)andNaiandtwotelluricblends(seeTable1).Wehaveto indicatesthatthemagneticstructurechangesquitedramatically fittheselinesaswelltoobtainunbiasedfitsoftheHeiabsorp- between the photosphere and the chromosphere, which is not tion,whichoftenblendswithsomeoralloftheselines.Because unusual for filaments (Leroy 1989; Low&Zhang 2002). We thephotosphericmagneticandvelocityvectoringeneralsignifi- also have evidence of different He components showing emis- cantlydiffersfromthechromosphericparameters,thisincreases sion and absorption within the same profile (not shown in this thetotalnumberofatmosphericcomponentsandrequiresaddi- paper),whicharegenerallyco-locatedwiththebrightHαflare tionalline–specificparametersofeachlinetobedetermined.For kernels,butdonotnecessarilyappearbrightinFig.1b. simplicity,eachspectralline was assigneditsown atmospheric component.Thenumberoffreeparameterswaslimitedbycou- plingthemappropriately(seeSect.3.2).Toobtainagoodfitof 3.1.Stokesinversion the strongphotosphericSii line at10827.09Å, we hadto con- We analyze the spectropolarimetric observations with the nu- sider two atmosphericcomponents:a magneticcomponentand mericalcode HELIX1 for the synthesisandinversionof Stokes afield-freestray-lightcomponent.Onlythiscombinationcould profilesinaMilne-Eddingtonatmosphere(Laggetal. 2004)ex- satisfactorily reproduceboththe line coreand wingsof the Sii tended to include the Paschen-Back effect (Sassoetal. 2006; line. The two telluric blends result in eight additional free pa- Socas-Navarroetal. 2004). HELIX allows for inversions of a rameters, originating from fitting two Voigt profiles to the tel- singlespectrumusingmultipleatmosphericcomponents,sothat luriclines.Theparametersneededtofitthetelluricblendscould atmospheric parameters like the magnetic field vector and the bekeptinaverynarrowrangeoverthewholemap,introducing line-of-sight (LOS) velocity are retrieved for each component. nodecreaseinstabilityoftheconvergenceoftheinversion. ThefreeparameterstunedbythecodetofittheobservedStokes There are profiles in the scan where the He lines show emis- profilesarethemagneticfieldstrengthBanddirection(inclina- sion features. These profiles were excluded from further anal- tion angle γ and azimuthal angle χ), the line-of-sight velocity ysis. Even though the HELIX code can fit emission profilesby vLOS,theDopplerwidth∆λD,thedampingconstantΓ,theratio settingthegradientofthesourcefunctionS1toanegativenum- ofthelinecentertothecontinuumopacityη andthegradientof ber,the analysistechniqueis notoptimizedto producereliable 0 thesourcefunctionS .Formoreinformationontheseparame- results. Moreover, in some spatial pixels the He emission pro- 1 terswerefertoLaggetal. (2004).Arangeforeveryparameter filescoexistwithblue-orredshiftedHeabsorptions,makingthe tobe fittedis specifiedtoguaranteethatthe resultoftheinver- retrievalevenmorecomplicated.InthemapshowninFig.6,the sionstayswithintheregimeofphysicallyusefulsolutions. pixelscontainingprofilesthatwerenotinvertedareblack. The inversion includes a scattering polarization correction, a treatmentoftheHanleeffectforaspecialcase.Itisonlyvalidat diskcenterandforhorizontalfieldsanditonlyimprovestheaz- 3.2.Parametercoupling imuthretrieval(TrujilloBuenoetal. 2002). Indeed,in the par- ticular case of a LOS-direction perpendicular to the solar sur- In order to decrease the numberof free parametersand thus to face (disk center) and a magnetic field direction parallel to the enhancethe stabilityofthe fitting procedure,we coupledsome solar surface (horizontalfield) the polarization signal owing to atmospheric parameters between the atmospheric components, the Hanle effect is oriented along the magnetic field direction: so that a given atmospheric parameter was forced to have the tan(2χ)=(U/Q). same(butnotprescribed)valueinallatmosphericcomponents. ThedetailsoftheinputatmospheresdependonthenumberofHe Couplingbetweenparametersofdifferentcomponentswasalso componentsnecessary to reproduce the observed profiles. One used as a means to impose that all lines from the same atmo- parameter,thefillingfactorα,definesthecontributionofagiven sphericlayer(in particularthe photosphere)mustbe formedin i atmospheric componenti to the total observed He profile. The the same atmosphere.We also narrowedthe rangesof possible sumofthefillingfactorsofallatmosphericcomponentswithin solutionsforsomeotherparameters,whichalsohelpedtoensure aresolutionelementisrequiredtobeunity,P α =1.Themax- theuniquenessofthesolution. i i imumnumberofHeatmosphericcomponentsweneedtorepro- Inparticular,wecoupledthemagneticfieldvector(B,γandχ) ducetheprofilesinthescanisfive(seeFig.6).Thisisconsider- andthegradientofthesourcefunctionS1betweenthefourpho- ablymorethaninpreviousstudiesinvolvingtheHeline,andwe tosphericlines,assumingthattheirvaluesstayapproximatively constant. This is consistent with the assumption that the four 1 TheinversioncodeHELIXisfreelyavailableforthesolarcommu- lines are formed at similar heights and can be represented by nity.PleasecontactA.Laggtoobtainacopy. asingleatmosphere. C.Sassoetal.:MulticomponentHei10830Åprofilesinanactivefilament 5 1.0 1.0 A B 30 0.8 30 0.8 c] c] se 20 b a 0.6c se 20 b a 0.6c arc dc 0.4I/I arc dc 0.4I/I y [ 10 f e y [ 10 f e 0.2 0.2 0 0.0 0 0.0 0 10 20 30 40 0 10 20 30 40 x [arcsec] x [arcsec] Fig.4.IntensitymapsofthescannedactiveregionobtainedatdifferentwavelengthpositionsindicatedbyarrowsinFig.2.Left(A): At-30km/swithrespecttothecentralrestpositionoftheTr2,3componentoftheHetriplet.Right(B):At+30km/swithrespect tothecentralrestpositionoftheTr2,3componentoftheHetriplet.ThedifferentlettersrefertothelineprofilesshowninFig.5. A HeI B HeI SiI TCr1aITr2+3 teHllu2Oric CatIeHllu2OricNaI SiI TCr1aITr2+3 teHllu2Oric CatIeHllu2OricNaI a (28,19) a (28,19) b (21,17) b (21,17) c (19,15) c (19,15) I/Ic d V/Ic (16,12) d (16,12) e (13,9) e (13,9) f (9,8) f (9,8) ∆I/Ic=0.1 ∆V/Ic=0.01 10826 10828 10830 10832 10834 10836 10826 10828 10830 10832 10834 10836 Wavelength [Å] Wavelength [Å] Fig.5. ObservedaveragedStokes I (A) and V (B) profilesat the locationsmarkedby letters in Fig. 4. The dashed, verticallines mark the central position of the spectral lines in the wavelength field-of-view of the TIP-II instrument. The (x,y) coordinates in arcsecondsarewrittennexttoeachprofile. Amongthe photosphericlines, the Sii line is the strongestone ThedifferentHecomponentscertainlyhavedifferentLOSveloc- withthebestsignal-to-noiseratioandshowsclearsignaturesin ities,butitisnotaprioricleariftheysampledifferentmagnetic theStokesprofiles.Changesintheatmosphericparameterswill vectors(andiftheydo,whetherthereissufficientinformationin havealargerinfluenceontheStokesprofilesoftheSilinethan themeasuredStokesparameterstodistinguishbetweendifferent on the weaker photospheric lines. Therefore, the photospheric magnetic vectors affecting the various Hei absorption compo- parametersaremainlydeterminedbytheshapeandstrengthof nents). Therefore,we made severaltest runsto decide whether the Si Stokes profiles. Then, we made an inversion run for the tocouplethemagneticfieldvectorornot(seeSect.4). whole map, fitting only the photosphericand the telluric lines. WealsocoupledthegradientofthesourcefunctionS between 1 Fromtheresultsofthefit,assumingthattheselinesarenotdis- theHeatmosphericcomponents,andwecouldalsoassignarel- turbedbythefilamentactivityhappeningathigheratmospheric ativelynarrowinputrangeforv ofeachHecomponentfrom LOS layers, we could select a narrower input range for the Doppler the visual analysis of the observed profiles. Indeed, when the width∆λ ofthephotosphericlinesandthewidthandthedamp- velocity separation between the He profiles is distinct enough D ingoftheVoigtprofileforthetelluricblends.Thenarrowerin- (∼ 10km/s)wecanclearlydistinguishthepositionsofthe dif- putrangesarethenusedfortheinversiondoneincludingtheHe ferentminimaintheI profile. lines. This avoids that the code broadens and shifts these lines bylargeamountstomimiconeoftheHecomponents. 6 C.Sassoetal.:MulticomponentHei10830Åprofilesinanactivefilament 5s isobtainedbycouplingthewholemagneticfieldvectorbetween 30 nt the five components.The observedStokes Q, U and V profiles 4e cannotbereproducedbythisinversion(f = 0.89).Bycoupling n c] o Bandχ(longdashedlines)weobtainagoodfitonlyforIandV se 20 3mp (f = 1.26)andbycoupling Bandγ (dash-dot-dottedlines) we c o canfitI, Q,andU reasonablywell,butnotV (f = 1.02).Inno r [a 2e c casecanwereproducetheStokesvectorasawhole. y 10 H StokesQofthisobservedprofileshowsapredominantlysingle- 1 lobe signature that suggests resonance scattering polarization. f o The simple scattering polarization correction we used and de- 0 0# scribedinSect.3.1isnotsufficienttofitthestrongQpeak.An 0 10 20 30 40 improvedtreatmentofthescatteringpolarizationmayhelp. x [arcsec] We carriedoutthesameanalysisforanother25Stokesprofiles with 3, 4, and 5 He componentsin a region of 3.5×1.8 Mm2 Fig.6.NumberofHecomponentsneededtofittheobservedpro- aroundtheprofiledisplayedin Fig. 7. Thevaluesof thefitness filesforeachpixelofthemap.Inthemap,thepixelscontaining function f obtainedfromthreedifferenttypesoffits(leavingthe profilesthatwerenotinvertedareblack(mainlythoseinwhich magnetic field free, f1, coupling B, f2, and coupling B and χ, theHeprofileisinemission). f3)totheobservedprofilesaregroupedinTable2.Theprofiles are located at the spatial pixels listed at the top (x) and on the left(y)ofTable2.Theseobservedprofilescanbereproducedal- Table2.Valuesofthefitnessfunctions f returnedbythefitsto mostequallywelleitherbycouplingthemagneticfieldstrength 25observedaveragedprofiles. betweentheHecomponentsorbyleavingthefullmagneticfield vectorfree.SignificantlypoorerfitstothefullStokesvectorsare Pixelx/y 78-79 80-81 82-83 84-85 86-87 obtained by coupling B and χ. Indeed, f < f in 88% of the (arcsec) (27.3) (28.0) (28.7) (29.4) (30.1) 3 1 cases and f < f in 80% of the cases. f is higher than f in 104-107 f =1.44 1.42 1.53 1.54 1.29 3 2 1 2 1 56%of the cases, while in over40%of the cases f > f . The (17.7) f =1.48 1.71 1.75 1.58 1.17 2 1 2 difference between the two is insignificant and the marginally f =1.15 1.46 1.29 1.39 1.16 3 108-111 f1 =1.95 1.81 1.74 1.86 1.18 highervalueof f1isnotenoughtojustifyusingahighernumber (18.4) f =1.91 1.55 1.76 1.77 1.04 offreeparameters. 2 f =1.67 1.48 1.48 1.69 1.08 Anothertestisbasedontheanalysisoftheerrorsintheretrieval 3 112-115 f =1.89 1.68 1.73 1.25 1.50 of the atmosphericparameters.The convergenceof the genetic 1 (19.0) f =2.00 1.63 1.60 1.28 0.94 algorithmusedfortheminimizationofthemeritfunction,Pikaia 2 f3 =1.78 1.53 1.34 1.23 1.35 (Charbonneau 1995), does not depend on the choice of initial 116-119 f1 =1.59 1.76 1.41 1.58 1.56 guessesfortheatmosphericparameters.Theconvergencetothe (19.7) f =1.47 1.97 1.69 1.73 1.52 2 globalminimumoccursonarandompathafteraninfinitenum- f =1.32 1.80 1.36 1.46 1.40 3 berofiterations.Wesetanupperlimittothenumberofiterations 120-123 f =1.68 1.98 1.51 1.54 1.76 1 (700)inawaythatthenecessarycomputingtimeandthestabil- (20.4) f =1.66 1.88 1.51 1.38 1.60 2 ityoftheresultingfitness, f,areingoodbalance.Thevariations f =1.61 1.92 1.53 1.43 1.58 3 oftheparametervaluesresultingfromnumerousinversionruns withanupperlimittothenumberofiterationscanbeusedasa directmeasureoftheerrorintheretrievalofthisparameter.This 4. Results errorcontainstheintrinsicuncertaintyintheparameterretrieval, Test runs showed that the best fits to the observed Stokes pro- causedbythesimilarityofStokesprofilesfordifferentparameter files are obtained by coupling only the magnetic field strength values,andtheerrorintroducedbytheinversionprocessitself. BbetweentheHecomponents,leavingthetwoangles,γandχ, The mean retrieved values of the atmospheric parameters with free. InFig. 7 we show as an examplethe results of inversions their errors, as deduced from 100 inversion runs, are listed in oftheobservedaveragedStokesprofiles(solidlines)attheloca- Table3foreachoftheprofilesshowninFig.7.Thefivevalues tion(29”,19”)ofthemapinFig.1.InFigs.7(a-d)twofitstothe perparametercorrespondtothedifferentHeatmosphericcom- observedprofiles(dashed and dash-dottedlines) are displayed. ponents. As pointed out earlier both the dashed (no coupling) Bothareobtainedbyallowingfivedifferentatmosphericcompo- and the dash-dotted profiles (only B coupled) provide almost nentstodescribetheHeilines.Thedashedlinesrepresentafit equallygoodfits,butthelatterisobtainedbyaninversionwitha obtainedbyallowingthecodetofindadifferentmagneticfield lowernumberoffreeparameters.TheerrorswhenBiscoupled vectorforeachatmosphericcomponentusedtodescribetheHe are smaller than withoutcoupling,in particularthe errorson B profiles.Forthefitrepresentedbythedash-dottedlinesthough, andγ.Thismeansthatwithalowernumberoffreeparameters wecoupledthemagneticfieldstrengthbetweenthecomponents, thecodeismorestable.ThevLOS isalwayswellretrievedwitha whileleavingtheanglesdescribingthemagneticfielddirection significantlylowererrorthanthespecifiedrangeforthevLOS of uncoupled.Theaveragevaluesof f obtainedfrom100inversion anygivencomponent(∼ 10 km/s).Both themagneticfield an- runs of this particular observed profile are 1.62 for the dashed gles,γandχ,canbedeterminedfortheindividualcomponents. linefitand1.53forthedash-dottedlinefit.Bothfitsaregoodand Theerrorintheinclinationangle,γ,issufficientlylargethatnot thefitnessvaluesarecomparable,butforthedash-dottedprofile, allcomponentscanbeclearlydistinguishedfromeachother(e. thefitisobtainedwith4freeparametersless.Theslightlyhigher g. components2 and 3 in Table 3), butthe values obtainedare valueofthefitnessofthedashedprofileisnotenoughtojustify in generalgood enoughto deduce the polarity of the magnetic theuseofsomanymorefreeparameters.InFigs.7(e-h)thesame field. Regardingthe azimuth, the signal-to-noise ratio in the Q observedprofile(solidline)isplottedasin(a-d).Thedottedline and U profiles is barely high enough to reliably retrieve infor- C.Sassoetal.:MulticomponentHei10830Åprofilesinanactivefilament 7 mationonit. requires an additional fourth redshifted He component. The fi- ThefinalthreecolumnsofTable3listtheretrievedvalueswith nal fit shown in Fig. 12 requiresfive atmosphericcomponents. uncertainties for an increasing number of parameters that are Onlyfewotherprofiles(seeFig.6)needfivecomponentstobe forced to have the same value in all atmospheric components. reproduced,andthesearealllocatedaroundoneendpointofthe IrrespectiveofwhetherwekeepBandγ(dash-dot-dotted),Band observed filament. This is also the location where we measure χ (longdashes) or B, γ and χ (dotted)coupled,the fitness f is the highestdownflowvelocities(∼ 100km/s).Itis particularly significantlylowerthanifallparametersareuncoupled,oronly gratifyingtosee thatboththe fitness f andthe uncertaintiesof B is coupled. Furthermore, the spread (uncertainty) in the re- theretrievedparametersappeartobenearlyindependentofthe trievedparameterstendstobelargerinthelastthreecolumns,so number of atmospheric components. This is probably because thatcouplingadditionalparametersdoesnotleadtoanincrease profileswithmorecomponentstendto havea largerequivalent inthereliabilityoftheretrievedsolution,butexactlytheoppo- width and individual components are well separated in wave- site.Furthermore,theretrievedvaluesofthecoupledparameters length. areclosetotheα-weightedaveragesoftheuncoupledvaluesof the same parameter.The exceptionis B,for which the coupled valueisalwayslower.Basedontheabovetest(andsimilartests 5. Discussionandconclusions appliedtotheStokesprofilesinotherpixels)weinvertedallthe observedprofilesintheobservedmapbycouplingthemagnetic We focus on the analysis and the inversion of Stokes profiles fieldstrengthbetweentheHecomponents,andleavingχandγ of the Hei 10830 Å triplet observed in an active region fil- free(fitness f2 inTable2). ament during its phase of activity. We showed that even the Examples of the inversions of increasingly complex Hei most complex observed profiles can be well reproduced by 10830ÅStokesI,Q,U,andV profilesareshowninFigs.8–12. multi-componentatmospheres.Althoughwecannotcompletely Ineachplot,theblacklinesaretheaveragedobservedprofiles, exclude that the profiles could be simply strongly turbulently whiletheredlinesarethebestfitstotheobservationsobtained broadened,thefitsbasedonmultiplecomponentsareofclearly consideringone, two, three, four,and five atmosphericcompo- betterquality(seebelow).Wetestedtheresponseofthenumeri- nentsof the He I lines. These are the minimumnumbersof at- calcodeHELIXfortheinversionofStokesprofilestoworkwith mospheric componentsthat are needed to obtain a satisfactory ahighnumberofatmosphericcomponentsandfreeparameters. fit, both as judged by eye and from a decrease of f found by ThiswasnecessarytofitnotonlythedifferentobservedHecom- adding a further component. Also plotted are the different He ponents,butalsothephotosphericandtelluriclinesinthewave- components(magenta, light blue, yellow, green, and dark gray lengthrange.Wewereabletoretrievetheatmosphericparame- lines), whose sum gives the red lines. The plotted contribution ters for the individualHe componentsat differentlevels of ac- ofeachcomponentismultipliedbyitsfillingfactor.InTable 4 curacy. The values of the magnetic field strength, B, retrieved wegivethemeanretrievedvaluesoftheatmosphericparameters fromthefitpresentedhereareintherange100−250G.These B,γ,χ,v andα,togetherwiththeirerrors.Thevalueslisted valuesarelower thanthose foundbyKuckeinetal. (2009) for LOS inTable4areaveragesoftheparametervaluesreturnedfrom50 another active prominence.This difference could be caused by inversionruns,andtheuncertaintiesreflectthespread(standard the different methodsemployed,because unlike Kuckeinetal. deviation)ofthereturnedvalues.Whenmultiple-componentfits (2009) we invertedour profilesincludinga scattering polariza- totheHelinearerequired,suchasthosedisplayedinFigs.9–12, tioncorrection(seeSec.3.1)andthemagneticfieldstrengthwe theparametersretrievedforeachcomponentaregiven.Notethat retrievedisaresultofacouplingbetweenmanyHecomponents. the photospheric lines are simultaneously fitted by two atmo- Thedifferencecouldalsobemerelyareflectionofthedifferent sphericcomponents(onemagnetic,onefieldfree),asdescribed strengthsofthe two filaments’magneticfields,or theanalyzed in Sect. 3.1. For each fit we also give the value of the fitness profilespossiblydonotsamplethehighestfieldstrengthregion functionintheTable, f ±∆f. inthe observedfilament.Thev iswellretrievedforallpro- LOS Figure8displaysaone-He-componentfittotheobservedStokes fileswithasmallerror.Theinclinationangleγisretrievedwitha profiles.Similarquietprofilesarefoundintheregionofthescan somewhatlargererror,buttheinclinationsofthedifferentcom- outsidetheportionwiththefilamentorotheractivity(flare).In ponents of the magnetic field can often be distinguished. The Table 4 (first table) the mean values and the errors of the re- error bars on the azimuth angle, χ, are instead quite large, and trieved atmospheric parameters after 50 inversion runs are re- itisoftenimpossibletodistinguishbetweentheazimuthsofthe ported.Evenwith this simple profile we have difficultiesin re- different magnetic components. This is mainly because of the trievingthevaluesofthemagneticfieldangles,γandχ,inpar- complexity and the noise in the Q and U Stokes profiles. The ticularχwith highaccuracy.Thisismainlybecauseofthelow informationintheobservationsforretrievingtheazimuthislim- signal-to-noiseratio of the observed Q and U profilesand to a ited.Wethereforerefrainfromconclusionsabouttheazimuthal smallerextentbecauseofthealreadyhighnumberoffreeparam- directionofthemagneticfieldin thefilament.Thereisalsoin- eterstobefitted(theinversionincludestheHe,thephotospheric sufficientinformationin the profilesto distinguishbetweenthe andthetelluriclines).Figures9and10showatwo-andathree- field strength B of the differentcomponents.Note that because componentfittoother,morecomplexobservedprofiles.Thetwo Stokes V is generally much stronger than Q and U, Bcosγ is profiles,observedcloseinpositionandtime,aresomewhatsim- probablythemostreliablydeterminedquantity,althoughwedo ilar, with the difference of a deeper He blueshifted absorption notexplicitlytabulateit. in the latter profile. This additional absorption requires an ad- The analysis of the observed polarization of the Hei 10830 Å ditionalHecomponenttobefitted.ThepresenceofanotherHe multipletinthefilament,carriedoutbyinvertingtheStokespro- componentintheprofileofFig.10isalsoevidentfromthedif- files, reveals different unresolved atmospheric components of ferent shape of the negative lobe in the Sii V profile. In both the He lines, coexisting within each spatial resolution element profileswefindstronglysupersonicblueshiftedHecomponents (∼1arcsec).ThecomponentsaredistinguishedbytheirDoppler (speedsinexcessof-50km/s)coexistingwithaHecomponent shifts,whichgenerallydifferbymorethanthesoundspeed.For nearby at rest. The fit to the observedprofile shown in Fig. 11 morecomplexanalyzedprofileswealsotriedtofindasolution 8 C.Sassoetal.:MulticomponentHei10830Åprofilesinanactivefilament 1.0 1.0 0.8 0.8 c c I/I I/I 0.6 0.6 a e 0.4 0.4 0.002 0.002 0.001 0.001 0.000 0.000 c c Q/I−0.001 Q/I−0.001 −0.002 −0.002 b f −0.003 −0.003 0.003 0.003 0.002 0.002 0.001 0.001 c c U/I0.000 U/I0.000 −0.001 −0.001 g c −0.002 −0.002 0.008 0.008 0.006 0.006 0.004 0.004 c0.002 c0.002 V/I0.000 V/I0.000 −0.002 −0.002 −0.004 d −0.004 h −0.006 −0.006 10826 10828 10830 10832 10834 10836 10826 10828 10830 10832 10834 10836 Wavelength (Å) Wavelength (Å) Fig.7.InversionsoftheStokesI,Q,U,andVaveragedprofilesatthelocation(29”,19”)ofthemapinFig.1.Thefits(dashed,dash- dotted,dotted,dash-dot-dottedandlongdashedlines)totheobservedprofiles(solidlines)areobtainedbyallowingfivedifferent atmosphericcomponentstodescribetheHeItriplet.Left(a-d):thedashedprofileisobtainedbyleavingthemagneticfieldvector freebetweenthefiveHecomponentswhilethedash-dottedprofileisobtainedbycouplingonlythemagneticfieldstrength.Right (e-h):thedottedprofileisobtainedbycouplingthemagneticfieldvectorbetweenthefiveHecomponents,couplingthemagnetic fieldstrengthandtheinclinationgivesthedash-dot-dottedprofiles,while couplingthefield strengthandtheazimuthleadsto the longdashedprofiles. HeI Tr1Tr2+Tr3 SiI CaI HO CaIHONaI 2 2 6000 5000 I 4 000 3000 0.0015 0.0010 0.0005 C Q/I 0.0 000 −0.0005 −0.0010 −0.0015 0.0015 0.0010 0.0005 C U/I 0.0 000 −0.0005 −0.0010 −0.0015 0.006 0.004 0.002 V/IC 0. 000 −0.002 −0.004 −0.006 108 26 108 28 108 30 108 32 108 34 108 36 Wavele ngth [Å] Fig.8.ObservedspatiallyaveragedandinvertedStokes I, Q, U andV profilesatthe location(5”,13”)ofthemapin Fig.1.The solidblacklinesaretheobservedprofiles,whiletheredlinesarethefitstoallobservedlinesobtainedimposingoneatmospheric componenttodescribetheHeIlines(magentalines),andtwoforthephotosphericlines. C.Sassoetal.:MulticomponentHei10830Åprofilesinanactivefilament 9 Table3.MeanvaluesoftheatmosphericparameterswiththeerrorsreturnedbythefitsdisplayedinFig.7. Parameter/Fit-profile Dashed Dash-dotted Dash-dot-dotted Longdashes Dotted Nocoupling Bcoupled B,γcoupled B,χcoupled B,γ,χcoupled B±∆B(G) 478±330 228±53 250±134 234±55 222±123 264±215 403±285 307±159 632±376 γ±∆γ(◦) 47±25 33±22 122±23 31±26 124±22 122±22 110±4 110±5 108±24 102±7 102±7 131±21 141±17 143±17 141±22 170±10 169±12 χ±∆χ(◦) −29±34 −18±48 −30±43 30±42 27±44 46±70 52±62 60±53 58±28 48±32 50±32 7±16 0±13 1±13 8±33 −2±37 −3±37 v ±∆v (km/s) −38±3 −39±2 −31±2 −38±3 −31±2 LOS LOS 1±1 1.1±0.7 0.9±1.0 1±1 0.9±1.0 21±1 21±1 21±1 21±1 21±1 53±1 53±1 53±1 53±1 53±1 68±2 69±2 68±2 69±2 68±2 α±∆α 0.10±0.03 0.10±0.02 0.09±0.02 0.10±0.03 0.10±0.03 0.33±0.06 0.32±0.04 0.29±0.04 0.31±0.04 0.27±0.05 0.20±0.05 0.19±0.03 0.19±0.04 0.21±0.03 0.21±0.03 0.25±0.06 0.24±0.03 0.27±0.04 0.23±0.04 0.26±0.04 0.12±0.05 0.14±0.03 0.16±0.04 0.15±0.03 0.16±0.03 f ±∆f 1.62±0.19 1.53±0.16 1.02±0.06 1.26±0.09 0.89±0.04 considering a broadened profile with some emission contribu- dientsinvelocityalongtheLOScanaffecttheirshape.Thein- tionsdistributedattheappropriateplaces,butthefitstotheob- fluenceofthesegradientscannotbetreatedinthesimplemodel served profiles were not as good as the ones we present in the employedhere.A moregeneraltreatmentwithgradientsmight paper.Themainproblemisreproducingthe I andV profilesat leadtogoodfitswithareducednumberofcomponents. thesametime. The inversions supportthe idea that the He componentscorre- In this active filament we find profiles requiring up to five spondtoplasmatrappedindifferentmagneticfieldlines,which atmospheric components for a reasonable fit. Multiple un- may well be pointing in different directions along the LOS. resolved magnetic components are found not only in fila- Indeed, the coupling of the magnetic field vector between the ments, but also above pores and elsewhere in active regions individualcomponentsresultsinworsefitstotheobservedpro- (AznarCuadradoetal. 2005; Laggetal. 2007), but so far in files, whichsupportsthisinterpretation.Notethoughthatsome otherdatasetsnevermorethanthreecomponentswereneeded. He profiles do not show a significant signal in Stokes V. They AsLaggetal. (2007)pointedout,thegeometricalinterpretation describeintensityfeatureswithoutapolarizationcounterpart. of these multiple downflow components is not clear-cut in the Multiplemagneticcomponentsarefairlycommoninmostparts caseofalinesuchasHei10830Å,whichisgenerallyoptically of the observed filament and are often associated with strong thin. Thus the different components could be located at differ- blue- or redshifts corresponding to supersonic velocities. We enthorizontalpositionswithintheresolutionelement,implying measured downflow velocities of up to 100 km/s and upflows considerablefinestructureinthefilament.Thisfinestructurein of up to 60 km/s along the line-of-sight. These supersonic up- filaments at a sub-arc s scale has been reported earlier. See, e. and downflows always coexist with a He atmospheric compo- g., Tandberg-Hanssen (1995) or Heinzel (2007), for reviews. nentalmost at rest (−10 < vLOS < +10 km/s) within the same These fine structures show a random motion with velocities of resolutionelement.Sometimesstrongblue-andredshiftedcom- 5-10km/s,asdeducedmainlyfromobservationsintheHαline. ponents are found to coexist in the same profile. Velocities of Analternativeexplanationisthatthevariouscomponentsarelo- filament fine structures reported in the literature are low com- cated at differentheightsalong the LOS. It maybe arguedthat paredwiththeseobservedsupersonicdown-andupflows. the Hei line gets verystrong in the filamentand can hardlybe Strong motions and velocities in active region filaments were consideredtobeopticallythin,sothatoneshouldnotbeableto previously observed in the He I 10830 Å lines. Observations seethroughdifferentlayerssoeasily.Wenote,however,thatthe ofaneruptingactiveregionfilamentpresentedbyPenn (2000) line becomes optically thick only at wavelengths at which the revealed the He I absorption line blue-shifted to velocities be- absorption is large, whereas it remains optically thin at neigh- tween 200and 300km/s.Inthe same observation,the filament boringwavelengths.Consequently,ifthedifferentlayersabsorb alsoshowedinternalmotionswithmultipleDopplercomponents at wavelengths that are shifted by more than a Doppler width shifted by ±25 km/s. Redshifts of 30-60 km/s were reported relativeto eachother,thisexplanationremainspossible evenif byPenn&Kuhn (1995)inanactivefilamentduringthedecay individuallayersproduceopticallythickabsorption. phase of a flare in the He I 10830 absorption lines. We found Becauseinmanycasestheprofileshavesomeopticalthickness thehighestredshiftssofarmeasuredwiththeHei10830Åline. (theyareformedoverarangeofheights),itispossiblethatgra- In this respect, we emphasize the importance of the TIP-II in- 10 C.Sassoetal.:MulticomponentHei10830Åprofilesinanactivefilament HeI Tr1Tr2+Tr3 SiI CaI HO CaIHONaI 2 2 6000 5000 I 4 000 3000 2000 0.002 0.001 C Q/I 0. 000 −0.001 −0.002 0.003 0.002 0.001 C U/I 0. 000 −0.001 −0.002 −0.003 0.006 0.004 0.002 C V/I −00.. 000020 −0.004 −0.006 108 26 108 28 108 30 108 32 108 34 108 36 Wavele ngth [Å] Fig.9.ObservedandinvertedStokesI,Q,U,andV profilesatthelocation(27”,9”)ofthemapinFig.1.Thesolidblacklinesare theobservedprofiles,whiletheredlinesarethefitsobtainedimposingtwodifferentatmosphericcomponentstodescribetheHeI lines(theprofilesoftheindividualcomponentsaregivenbymagentaandlightbluelines). strument, which was used for the first time during this obser- Low,B.C.,&Zhang,M.2002,ApJ,564,53 vationcampaign.We were ableto observethe fullrangeof He Mart´ınez Pillet, V., Collados, M., Sa´nchez Almeida, J. et al. 1999, in High absorptionsignaturesandmeasurethehighestdownflowveloc- ResolutionSolarPhysics:Theory,Observations,andTechniques,eds.T.R. Rimmele,K.S.Balasubramaniam,&R.R.Radick,(AstronomicalSocietyof ities thanks to its wider range of wavelengths compared to the thePacific),ASPConf.Ser.,Vol.183,264 originalTIPinstrument. Merenda,L.,TrujilloBueno,J.,LandiDeglInnocenti,E.,&Collados,M.2006, ApJ,642,554 Acknowledgements. We thank Luca Teriaca for helpful discussions. We also Penn,M.J.2000,Sol.Phys.,197,313 thankRegina AznarCuadrado andManoloCollados fortheir helpduringthe Penn,M.J.,&Kuhn,J.R.1995,ApJ,441,51 observing run at the German Vacuum Tower Telescope at the Spanish obser- Ru¨edi,I.,Solanki,S.K.,&Livingston,W.C.1995,A&A,293,252 vatory in Tenerife. CS thanks the IMPRS on Physical Processes in the Solar Sasso,C.,Lagg,A.,&Solanki,S.K.2006,åp,456,367 SystemandBeyondfortheopportunitytocarryouttheresearchpresentedinthis Socas-Navarro, H.,TrujilloBueno,J.,&LandiDegl’Innocenti, E.2004,ApJ, paper.Thisworkwassupportedbytheprogram“AccionesIntegradasHispano- 612,1180 Alemanas”oftheGermanAcademicExchangeService(DAADprojectnumber Solanki,S.K.,Lagg,A.,Woch,J.,Krupp,N.,&Collados,M.2003,Nature,425 D/04/39952),bytheWCUgrantNo.R31-10016fromtheKoreanMinistryof Tandberg-Hanssen, E. 1995, The Nature of Solar Prominences (Dordrecht: Education,ScienceandTechnology,andbytheASI/INAFcontractI/05/07/0for KluwerAcad.Publ.) theprogram“StudiEsplorazioneSistemaSolare”. Trujillo Bueno, J., Landi Degl’Innocenti, E., Collados, M., Merenda, L., & MansoSainz,R.2002,Nature,415,403 References AznarCuadrado, R.,Solanki, S.K.,&Lagg,A.2005,inChromosphericand Coronal Magnetic Fields, eds. D. E. Innes, A. Lagg, S. K. Solanki, & D. Danesy,(ESAPublicationDivision),Vol.ESASP-596,49 Casini,R.,Lo´pezAriste,A.,TomczykS.,&Lites,B.W.2003,ApJ,598,67 Charbonneau,P.1995,ApJS,101,309 Collados, M., Lagg., A., D´ıaz Garc´ıa, J. J., et al. 2007, in The Physics of Chromospheric Plasmas, eds. P. Heinzel, I. Dorotovicˇ, & R. J. Rutten, (AstronomicalSocietyofthePacific),ASPConf.Ser.,Vol.368,611 Heinzel,P.2007,inThePhysicsofChromosphericPlasmas,eds.P.Heinzel,I. Dorotovicˇ,&R.J.Rutten,(AstronomicalSocietyofthePacific),ASPConf. Ser.,Vol.368,275 Kuckein,C.,Centeno,R.,Mart´ınezPillet,V.,etal.2009,A&A,501,1113 Lagg,A.,Woch,J.,Krupp,N.,&Solanki,S.K.2004,A&A,414,1109 Lagg,A.,Woch,J.,Solanki,S.K.,&Krupp,N.2007,A&A,462,1147 Leroy,J.L.1989,inDynamicsandStructureofQuiescentSolarProminences, ed.E.R.Priest,(Dordrecht:Kluwer),77 Lin,H.,Penn,M.J.,&Kuhn,J.R.1998,ApJ,493,978 Lo´pezAriste,A.,&Casini,R.2006,inSolarPolarization4,eds.R.Casini,& B.W.Lites,ASPConf.Ser.,Vol.358,443

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