Two-dimensional spectroscopy of a sunspot. III Thermal and kinematic structure of the penumbra at 0.5" PDF
Preview Two-dimensional spectroscopy of a sunspot. III Thermal and kinematic structure of the penumbra at 0.5"
Astronomy&Astrophysicsmanuscriptno.bellot February5,2008 (DOI:willbeinsertedbyhandlater) Two-dimensional spectroscopy of a sunspot ′.′ III. Thermal and kinematic structure of the penumbra at 0 5 resolution L.R.BellotRubio1,2,R.Schlichenmaier2,andA.Tritschler3,2 6 1 InstitutodeAstrof´ısicadeAndaluc´ıa(CSIC),Apdo.3004,18008Granada,Spain 0 e-mail:[email protected] 0 2 Kiepenheuer-Institutfu¨rSonnenphysik,Scho¨neckstr.6,79104,Freiburg,Germany 2 3 NationalSolarObservatory/SacramentoPeak⋆,P.O.Box62,Sunspot,NM88349,USA n a Received/Accepted J 9 Abstract.Weinvestigatethethermalandkinematicconfigurationofasunspotpenumbrausingveryhighspectralandspatial 1 resolutionintensityprofilesofthenon-magneticFe557.6nmline.Thedatasetwasacquiredwiththe2Dsolarspectrometer TESOS.Theprofilesareinvertedusingaone-component model atmosphere withgradientsof thephysical quantities. From 1 this inversion we obtain the stratification with depth of temperature, line-of-sight velocity, and microturbulence across the v 3 penumbra. Ourresultssuggestthatthephysicalmechanism(s) responsibleforthepenumbralfilamentsoperatepreferentially 2 inthelowerphotosphere.Weconfirmtheexistenceofathermalasymmetrybetweenthecenterandlimb-sidepenumbra,the 4 formerbeinghotterby100-150Konaverage.Wealsoinvestigatethenatureofthebrightringthatappearsintheinnerpenumbra 1 when sunspots are observed in the wing of spectral lines. It is suggested that the bright ring does not reflect a temperature 0 enhancementinthemidphotosphericlayers.Theline-of-sightvelocitiesretrievedfromtheinversionareusedtodeterminethe 6 flow speed and flow angle at different heights inthe photosphere. Boththe flow speed and flow angle increase withoptical 0 depthandradialdistance.Downflowsaredetectedinthemidandouterpenumbra,butonlyindeeplayers(logτ ≤ −1.4). 500 / h Wedemonstratethatthevelocitystratificationsretrievedfromtheinversionareconsistentwiththeideaofpenumbralfluxtubes p channelingtheEvershedflow.Finally,weshowthatlargerEvershedflowsareassociatedwithbrightercontinuumintensities - intheinnercenter-sidepenumbra.Darkstructures,however,arealsoassociatedwithsignificantEvershedflows.Thisleadsus o tosuggestthatthebrightanddarkfilamentsseenat0′.′5resolutionarenotindividualflowchannels,butacollectionofthem. r t Ouranalysishighlightstheimportanceofveryhighspatialresolutionspectroscopicandspectropolarimetricmeasurementsfor s abetterunderstandingofsunspotpenumbrae. a : v Keywords.Line:profiles–Sun:photosphere–Sun:sunspots i X r a 1. Introduction characterizationofthepenumbracallsnotonlyfordiffraction- limited imaging observations, but also for more quantitative The fine structure of the penumbra is intimately connected spectroscopic and spectropolarimetric analyses at the highest to the Evershed flow, the most conspicuous dynamical phe- resolutionpossible.Byinterpretingtheshapeofspectrallines nomenonobservedinsunspots(e.g.,Solanki2003;Thomas& we can derive the thermal, magnetic, and kinematic configu- Weiss 2004). Therefore, a proper observational characteriza- ration of the penumbra via the Zeeman and Doppler effects. tionofthisfinestructureisessentialtounderstandtheEvershed Unfortunately,currentspectroscopicobservationsdonotattain flowand,moregenerally,thenatureofthepenumbraitself. resolutionsbetterthan∼ 0′.′5,andthislimitisoftenreachedat Studyingthefinestructureofthepenumbraisdifficultbe- thecostofpoorspectralresolution.Thesituationisevenworse cause of the very small scales involved. Recent imaging ob- in the case of spectropolarimetricmeasurements:the best an- servations with the Swedish 1-m Solar Telescope (Scharmer gularresolutionofexistingsolarpolarimetersisabout1′′. et al. 2003; Rouppe van der Voort et al. 2004) have revealed thatevenataresolutionof0′.′1someofthefilamentsthatform This paper is the third of a series devoted to the anal- the penumbramay be unresolved.Thatis, differentstructures ysis of 2D spectroscopic observations of a sunspot. The (each having different properties) may coexist in the resolu- data were acquired with the TElecentric SOlar Spectrometer tion element, and we are not able to separate them. A proper (TESOS; Kentischer et al. 1998; Tritschler et al. 2002) and the Kiepenheuer Adaptive Optics System (KAOS; Soltau et ⋆ Operated by the Association of Universities for Research in al. 2002; von der Lu¨he et al. 2003) at the German Vacuum Astronomy,Inc.(AURA),fortheNationalScienceFoundation Tower Telescope of Observatorio del Teide (Tenerife, Spain). 2 BellotRubioetal.:Thermalandkinematicstructureofthepenumbra These observations combine high spectral (λ/∆λ ∼ 250000) dI/dT [% K -1] andspatial(0′.′5)resolution(Tritschleretal.2004;hereafterre- 1 0.010 ferredtoasPaperI).InPaperIIofthisseries(Schlichenmaier etal.2004),weinvestigatedthepropertiesoftheEvershedflow 0 0.008 throughabisectoranalysisoftheobservedintensityprofiles. 0 50 -1 0.006 Here we perform a full inversion of the same data set in τg order to study the thermal and kinematic configurationof the lo -2 0.004 penumbra.Ouranalysisallowsustoexplainanumberoffind- -3 0.002 ingsreportedinPaperIandtoremovesomeoftheuncertainties associatedwiththemethodsemployedinPaperII.Atthesame -4 0.000 time, we gather new informationon the thermalpropertiesof -0.04 -0.02 0.00 0.02 0.04 thepenumbra.Thisisparticularlyimportantbecauseveryfew dI/dv [% (m /s)-1] thermal studies of sunspot penumbrae have been published LOS to date (del Toro Iniesta et al. 1994; Balasubramaniam 2002; 1 0.002 RouppevanderVoort2002;Sa´nchezCuberesetal.2005). 0 Abriefaccountoftheobservationsanddetailsoftheinver- 0.001 sion procedureare given in Sect. 2. In Sect. 3 we discuss the 00 -1 5 τ 0.000 maps of physical quantities inferred from the inversion. The g o -2 thermal and kinematic configuration of the penumbra is de- l -0.001 scribed in detail in Sects. 4 and 5. Some implications of the -3 resultsarepresentedinSect.6,andasummaryofourfindings -0.002 -4 isgiveninSect.7. -0.04 -0.02 0.00 0.02 0.04 ∆λ [nm] 2. Observationsanddataanalysis Fig.1. Response functions of the Fe 557.6 nm line to tem- perature (top) and line-of-sight velocity (bottom). The two 2.1.Observations plots indicate the percentage by which the specific intensity OnJuly5,2002,TESOSwasusedtomeasuretheintensitypro- atλchangeswhenthetemperature(resp.LOSvelocity)isin- filesofFe557.6nminthemainsunspotofNOAAAR10019 creased by 1 K (resp. 1 m s−1) in a layer of optical width (cf.PaperI).Atthetime ofthe observations,the spotwaslo- ∆logτ = 0.1 and optical depth τ . The thermal stratifi- 500 500 cated23ooffthediskcenter.Thelinewasscannedat100wave- cationofthepenumbralmodelofTTRhasbeenemployedfor lengthpointswithawavelengthstepof8.4pm,corresponding thesecalculations. toovercriticalspectralsampling.Thetimeneededtocomplete the scan was 37s. Operatedin highresolutionmode,TESOS yielded a pixel size of 0′.′089 × 0′.′089. During the scan, the 1Katagivenopticaldepthτ .Thefiguredemonstratesthat 500 KAOSsystemprovidedreal-timecorrectionofwavefrontdis- the line reacts to temperature changes. The sensitivity of any tortionsduetoturbulenceintheEarth’satmosphere. spectrallinetotemperatureperturbationsisdeterminedbytwo competingeffects: changesin the absorptionand in the emis- sion.Usually,onlyopacityvariationsareconsidered(e.g.,Gray 2.2.DiagnosticcapabilitiesofFe557.6nm 1988,Chapter13)but,aspointedoutbyCabreraSolanaetal. We use the intensity profiles of Fe 557.6 nm to derive the (2005),thedominantcontributionisthatofthesourcefunction. stratification of temperature and velocity in the penumbra. Neglect of this dominant factor is the likely cause of the line Therefore,itisimportanttoexaminethepropertiesofthisline beingquotedastemperatureinsensitiveinmostpublications. in some detail. Fe 557.6 nm is a fairly strong photospheric Figure 2 shows the temperature dependenceof the equiv- line with zero effective Lande´ factor,i.e., it doesnot undergo alent width for a set of neutral iron lines commonly used in anyZeemansplitting. The line is oftenquotedto be tempera- solar physics (adapted from Cabrera Solana et al. 2005). It is tureinsensitive,butthisistooasimplisticstatement.Figure5 apparentfromthisfigurethatFe557.6nmisoneofthemost of Paper I shows that the equivalent width of Fe 557.6 nm temperaturesensitivelines.Indeed,itshowsalargersensitivity changesbynon-negligibleamountswhengoingfromthequiet thanlinespresumedtobeappropriatefortemperaturemeasure- suntotheumbra,wherethetemperaturesareratherdifferent. mentssuchasFe524.7and525.0nm.Thelargevariationof In the following, we elaborate on the temperature sensi- theequivalentwidthof Fe557.6nmwithtemperatureiscon- tivity of Fe 557.6 nm by means of response functions(RFs; sistentwiththeobservedbehaviorofthelineinthequietsun, see Ruiz Cobo & del Toro Iniesta 1994 and del Toro Iniesta umbraandpenumbra(Fig.5ofPaperI). 2003).TheupperpanelofFig.1showstheRFofFe557.6nm LetusnowturnourattentiontothesensitivityofFe557.6 to temperature perturbations as evaluated in the penumbral nmtoline-of-sight(LOS)velocities.ThebottompanelofFig.1 model atmosphere of del Toro Iniesta et al. (1994; hereafter showstheRFoftheintensitytovelocityperturbationsaseval- TTR). This plot tells us how much the specific intensity at λ uatedinthepenumbralmodelofTTR.TheseRFs correspond changes when the temperature of the model is increased by to a modelwhere all velocities have been set to zero, so they BellotRubioetal.:Thermalandkinematicstructureofthepenumbra 3 -1.5 aboutthetemperatureinthedeepatmosphericlayers.Thetwo nodesused to inferthe thermalstructureallow forchangesin thegradientandabsoluteposition[e.g.,T(τ =1)]oftheini- 500 -1K)] -1.0 tialtemperaturestratification.Weassumelocalthermodynami- m calequilibrium(LTE).Sincenon-LTEeffectsmaybeimportant p 20 ( in the upper layers, our temperatures are reliable only up to, x1 say, logτ ∼ −3. Electron pressuresare computedfromthe T [ 500 W/d -0.5 inferredtemperaturesusingtheequationofhydrostaticequilib- d riumandtheidealgaslaw. Theinversionalsoyieldsthestratificationwithdepthofthe LOSvelocityandmicroturbulentvelocity.Inbothcasesweas- 0.0 524.7 525.0 537.9 557.6 617.3 630.25 709.0 1089.61564.8 sume linear variations with logτ500, i.e., two nodes for each Spectral line [nm] parameter. In the case of the LOS velocity, this choice seems tobeappropriateconsideringthatmostobservedbisectorspos- Fig.2. Variation of the equivalent width W of 9 neutral iron sessquitelinearshapes(PaperII).Fromtheinversionwealso lines when the temperature is increased by 1K in all photo- determinethe(height-independent)macroturbulenceneededto sphericlayers.Thecalculationshavebeencarriedoutusingthe reproducethe observedline widths.Thesyntheticprofilesare thermalstratificationofthepenumbralmodelofTTR. convolvedwiththeinstrumentalprofileofTESOSbeforebeing comparedwiththeobservedones.Todescribethebroadening aresymmetricaboutthelinecenter(modelsinwhichtheLOS of the line due to collisions with neutral hydrogen atoms we velocity varies with height would result in asymmetrical RFs use the quantummechanicalformulationofAnstee, Barklem, and slightly different sensitivities in the differentatmospheric &O’Mara(seeBarklemetal.2000).Thetotalnumberoffree layers). As can be seen, the line is sensitive to velocities in a parametersis7,whichcomparesfavorablywiththenumberof height range from about logτ500 = 0 to −3.5. The maximum observables(100). sensitivityis attainedin the midphotosphere.Inthe deepand Without additional spectral lines observed, or measure- highlayerswherethecontinuumandthelinecoreareformed, mentsofthe fourStokesparameters,itis notpossibleto esti- respectively,thesensitivitytovelocitiesismuchreduced.The matetheamountofstraylightcontamination.Weexpect,how- reasonhas beenexplainedby CabreraSolana etal. (2005):at ever, that stray light arising from seeing fluctuations is much agivenwavelength,theintensityvariationinducedbyDoppler reducedwithrespecttoearlierobservationsthatdidnotbenefit shifts is proportional to the slope of the line at that position. fromadaptiveoptics.Bycontrast,parasiticlightinsideTESOS Thus,the intensitychangesare maximumnear the line wings hasbeencorrectedfor.InPaperIwedeterminedthat∼ 5%of (which sample the mid photosphere) and minimum near the themeancontinuumintensitycontributestoeachfiltergramin continuum and the line core, where the slope of the intensity the formof ghostsand scatteredlight. Thisparasiticlighthas profile(dI/dλ)quicklygoestozero.ThelowerpanelofFig.1 been subtracted from the individual images before extracting also demonstratesthat the intensity observedat a fixed wave- theintensityprofiles. lengthissensitivetoLOSvelocitiesinabroadrangeofoptical Our inversion approachavoids importantshortcomingsof depths.Thatis,theDopplershiftsmeasuredfromlinebisectors simpler analyses. Since the complete radiative transfer prob- atagivenintensitylevelcontaininformationfromasignificant lemissolved,weeffectivelyseparatethecontributionoftem- fractionoftheatmosphere.Thus,itisdifficulttoascribethem peraturesandLOSvelocitiestotheobservedprofilesusingthe toanyparticularlayer.Thislimitationofbisectoranalyseshas information provided by the RFs. From Fig. 1 it is clear that longbeenrecognized(Maltby1964;Rimmele1995). theintensityatafixedwavelengthdependsonthetemperature and LOS velocity stratification along the atmosphere. Thus, we determine both parameters simultaneously in order not to 2.3.Inversionprocedure misinterpretthermaleffectsas velocityeffectsandvice versa. TheintensityprofilesobservedwithTESOShavebeeninverted Anotherimportantimprovementisthatwe canascribethe in- inordertodeterminethestratificationoftemperature,LOSve- ferredvelocitiesandtemperaturestospecificopticaldepths,be- locity, and microturbulence with optical depth. To this end, cause our proceduretakes into accountthe finite width of the we have used the SIR code (Ruiz Cobo & del Toro Iniesta intensitycontributionfunctions. 1992).Despitethehighspectralresolutionofourobservations, Thesimpleone-componentmodelatmosphereusedinthis the number of data points does not allow us to use complex investigationhasseverallimitations.First,itdoesnotallowfor atmospheric models. Hence, we have adopted a simple one- anyunresolvedstructureinthepixel.Althoughourspatialres- componentmodelwithgradientsofthephysicalparameters. olutionisoneofthehighesteverreachedinspectroscopicstud- We derive the temperature stratification by modifying the ies,wearestillfarfromresolvingtheindividualconstituentsof thermal structure of the penumbral model of TTR with two thepenumbra.Spectropolarimetricmeasurementssuggestthat nodes. For a better recovery of this parameter, the observed atleasttwomagneticcomponentsarenecessarytounderstand profiles are normalized to the continuum intensity of the av- thepenumbra(Schlichenmaier&Collados2002;BellotRubio eragequietsunprofile.Suchanabsolutenormalizationimplies et al. 2003, 2004; Borrero et al. 2004, 2005). One of the two thatthecontinuumoftheindividualprofilescarriesinformation componentscarriesmostoftheEvershedflow,whiletheother 4 BellotRubioetal.:Thermalandkinematicstructureofthepenumbra Center-side penumbra Limb-side penumbra 0′.′18 × 0′.′18, which is still sufficient to sample our seeing- 0.8 0.8 limited spatial resolution of about 0′.′5. After binning, we are 0.7 0.7 leftwith37000individualprofileswhichareinvertedindepen- 0.6 0.6 dently.Theinversionhas beenperformedusinga parallelized version of SIR in a 16-processor Linux Beowulf cluster. The I/Ic_QS00..45 00..45 inversionofthedatacubeisaccomplishedinabout2.5hours. Figure 4 displays maps of the temperature and LOS ve- 0.3 0.3 locity at two representative optical depths in the atmosphere 0.2 0.2 (logτ500 = 0 and −2). The fine structure of the penumbra is 0.1 0.1 apparent(bothintemperatureandvelocity)inthedeepphoto- -40 -20 0 20 40 -40 -20 0 20 40 sphere,wherehotpenumbralfilamentsandflow filamentsare ∆λ [pm] ∆λ [pm] seentoextendfromtheinnertotheouterpenumbralboundary. Fig.3.Examplesofobserved(dots)andbest-fit(solidlines)in- ThefluctuationsintemperatureandLOSvelocityaremuchre- tensity profilesemergingfrom the center-side (left) and limb- duced at logτ = −2; indeed, no fine-scale organization of 500 side (right) penumbra. The vertical dashed lines indicate the the penumbra is obvious at this optical depth. Consequently, positionofzerovelocities(seePaperI).Notethestrongasym- thephysicalmechanismsproducingthefilamentsmustoperate metries of the line, with an extendedblue wing in the center- preferentiallyinthedeeplayers. side penumbra and an extended red wing in the limb-side The right panels of Fig. 4 show maps of the microtur- penumbra. bulence at logτ = 0 and the macroturbulent velocity. 500 Accordingtoourresults,nomicroturbulenceisneededineither theumbraortheinnerpenumbra.Thisisincontrasttotheouter isessentiallyatrest.Iftheflowchannelsarehorizontallyunre- penumbra,wheremicroturbulentvelocitiesof1.8–2kms−1are solvedandwedonotaccountforthispossibility,theLOSve- common. Thus, the smaller line widths observed in the inner locities determined from the inversion would represent lower penumbra (Fig. 5 of Paper I) can be interpreted as being due limits to the real velocities. Second, we have chosen a very to a reducedmicroturbulence.Note that the map of microtur- simple functionaldependence to describe the run of the LOS bulenceshowsfinestructureinthemidpenumbra.Alsoimpor- velocitywith height.In an uncombedpenumbraconsisting of tantisthefactthatmicroturbulencedecreaseswithheight,until penumbralfluxtubesembeddedinabackgroundmagneticat- zerovaluesarereachedinthehighlayers(seeSect.5.3).Again, mosphere,linesof sightthatpierce the tubeswould’see’ dis- thisisconsistentwiththeideathatthemechanismsenhancing continuities in the LOS velocity as they encounter the upper the line width operate preferentiallyin deep atmospheric lay- andlowerboundariesofthetubes.Ourassumptionoflinearve- ers. The macroturbulence stays relatively constant across the locitystratificationswouldprovideonlyaveryroughdescrip- penumbra, with values of 1–1.2 kms−1. Only in the very in- tionofsuchdiscontinuousvelocitystratifications.Inthatcase, ner penumbraand the umbrais the macroturbulencereduced, it would be the magnitude and sign of the LOS velocity gra- perhapsasaconsequenceoftheirstrongermagneticfields. dientinferredfromtheinversionwhichwouldinformusabout Inthenextsections,wedescribeinmoredetailthethermal thevelocityinsidethefluxtubesandtheheightpositionofthe andkinematicconfigurationofthepenumbraasdeducedfrom flowchannels. theinversion. Despitetheseshortcomings,theadoptedmodelatmosphere doesanexcellentjobinexplainingtheobservedintensitypro- 4. Thermalstructure files.Onaverage,theresidualsofthefitareonlyslightlylarger thanthenoise(after2×2binning,theobservedprofileshavea First,letusexaminethereliabilityoftheinferredtemperatures. signal-to-noiseratioofabout120in thecontinuumintensity). Figure 5a shows the temperature at τ = cosθ = 0.92 re- 557.6 Figure3showsexamplesofprofilesrecordedinthecenter-and turned by the inversion code versus the observed continuum limb-side penumbra, along with the best-fit profiles resulting intensities.Thescatterofthepointsissmall,indicatinganex- fromthe inversion.Theveryasymmetricalshapesinducedby cellentcorrelationbetweenthetwoquantities.Thefactthatwe the photospheric Evershed flow are successfully reproduced, use an absolute normalizationforthe observedprofilesis one indicatingthattheassumptionoflinearLOSvelocitystratifica- ofthemainreasonswhytheinversioncodeisabletodetermine tionssufficestoexplaintheobservedDopplershiftsandlinebi- thetemperatureofthecontinuum-forminglayerssoaccurately. sectors.Thisistrueforallprofilesshowinglinearbisectors.In The solid line in Fig. 5a represents the temperatures ob- theveryouterpenumbra,bisectorkinksandreversalsarecom- tained from the Eddington-Barbier approximation I (θ) = λ mon(PaperII).Wecannotreproducetheseprofilessowell.In S (τ = cosθ), where I (θ) is the specific intensity observed λ λ λ thesecases,itseemsthatmorecomplexLOSvelocitystratifi- at an heliocentricangleθ, S is the source function(assumed λ cationsthantheoneusedherewouldapply. to be the Planck function), and τ is the continuum optical λ depth at the wavelength of the observation. As can be seen, theEddington-Barbierapproximationyieldsthesametemper- 3. Results aturesasthosededucedfromtheinversion.Onlyforsmallcon- The filtergrams have been binned by a factor of 2 before ex- tinuumintensitiesaretheinferredtemperaturesslightlylarger tracting the intensity profiles. This increases the pixel size to than those indicated by the Eddington-Barbier relation, but BellotRubioetal.:Thermalandkinematicstructureofthepenumbra 5 Temperature at log τ = 0 [K] LOS velocity at log τ = 0 [km s-1] Microturbulence at log τ =0 [km s-1] 500 500 500 5800 6000 6200 6400 -2 -1 0 1 0.0 0.5 1.0 1.5 2.0 Temperature at log τ = -2 [K] LOS velocity at log τ = -2 [km s-1] Macroturbulence [km s-1] 500 500 4200 4400 4600 4800 -0.5 0.0 0.5 1.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Fig.4.Mapsofphysicalquantitiesatlogτ = 0(top)andlogτ = −2(bottom).Depictedfromlefttorightarethetemper- 500 500 ature,theLOSvelocityandthemicroturbulence.NegativeLOSvelocitiesindicateredshifts.Thelowerrightpaneldisplaysthe macroturbulentvelocity,assumedtobeheightindependent.Contoursoutlinetheinnerandouterpenumbralboundaries. overalltheagreementisverysatisfactory.Thisimpliesthatthe ducedbytheEvershedflowandonthelinewidthvariationsdue observedcontinuumintensitiescanbereliablyusedtoestimate tomicroturbulentandmacroturbulentvelocities.Allthesefac- temperaturesindeepphotosphericlayers.Asimilarconclusion torscontributetothelargescatterofthepointsseeninFig.5b. hasbeenreachedbyTTRandRouppevanderVoort(2002). TheproblemhasbeenrecognizedbyBalasubramaniam(2002). Inanattempttocureit,Balasubramaniamintroducedthecon- In the line wing, the one-to-one correspondence between cept of flowless maps, i.e., intensity maps constructed by re- specific intensity and temperaturefoundbeforedoes nothold moving the global Doppler shift of the lines emerging from anylonger.ThisisdemonstratedinFig.5b,whereweplotthe eachindividualpixel.Unfortunately,flowlessmapsarestillaf- temperatures resulting from the inversion at logτ = −1.3 fectedbythelineasymmetriescausedbytheEvershedflow. 500 versustheintensitiesobservedat−5.2pmfromlinecenter.We use logτ = −1.3 because this is the optical depth of the Letusnowinvestigatetheradialvariationofthe tempera- 500 centroidofthecontributionfunctionforthelinedepressionat tureatdifferentopticaldepths.Tothisend,wehavecomputed ∆λ = −5.2pm,evaluatedinthemeanpenumbralmodelatmo- azimuthally averaged temperatures along elliptical paths cen- sphere.Itisimmediatelyapparentfromthefigurethatthesame teredonthespot(cf.Fig.6ofPaperI).Theaveragetempera- linewingintensitycanbeassociatedwithawiderangeoftem- turesareplottedinFig.6forfouropticaldepths.Atallheights peratures(uptoabout500K).Thus,linewingintensitiescan- intheatmosphere,thetemperatureisobservedtoincreaseradi- not be employed to infer temperaturesdirectly. The reason is allyfromthesunspotcentertotheouterpenumbralboundary. thattheintensitiescriticallydependonthelineasymmetriesin- Thisincreaseisratherlinearexceptforanobvioushumpinthe 6 BellotRubioetal.:Thermalandkinematicstructureofthepenumbra 6.5 log τ = 0 log τ500 = -1 log τ500 = -2 6.0 log τ500 = -3 500 K] 5.5 k e [ r u 5.0 at r e p 4.5 m e T 4.0 3.5 0.0 0.2 0.4 0.6 0.8 1.0 Normalized radial distance Fig.6. Radial variation of the azimuthally averaged tempera- turesatseveralopticaldepths.The shadedareasrepresentthe standarddeviationofthe temperaturesateachradialdistance. Theverticallinemarkstheinnerpenumbralboundary. (a) Mean temperature (b) CS and LS temperatures This work Center side 7 TTR - 200 K 7 Limb side K] Fig.5.(a) Temperatureatτ557.6 = cosθ = 0.92inferredfrom ure [k 6 6 at the inversion vs continuum intensity (normalized to the con- er p tinuum of the average quiet sun profile). The solid line rep- Tem 5 5 resentsthetemperaturesobtainedfromtheEddington-Barbier approximation using the observed continuum intensities. (b) 4 Temperature at logτ = −1.3 vs the intensity observed at 4 500 ∆λ = −5.2pmfromline center,normalizedto the continuum -4 -3 -lo2g τ500 -1 0 -4 -3 -lo2g τ500 -1 0 oftheaveragequietsunprofile. Fig.7. (a) Average temperaturestratification in the penumbra (solid).ThepenumbralmodelofTTR(shiftedby200K)isalso shownforcomparison(dashed).Theshadedareasrepresentthe innerpenumbra,wherethetemperatureseemstobeenhanced rms fluctuations of the temperature. (b) Average temperature by severalhundredsK. The amplitude of the hump decreases stratification in the center-sideand limb-sidepenumbra(solid as one moves towards the upper photospheric layers. In deep anddashed,respectively). layers (logτ = 0), the hump is so pronounced that the ra- 500 dialvariationofthetemperatureisalmostflatbetween0.6and 0.9 penumbral radii (i.e., the mid penumbra and most of the shiftedby200K(ourtemperaturesbeingcoolerthanthoseof outerpenumbra).Wealsonotethatthehumpislocatedincreas- TTR). We do notdeemthat the offset of 200K is significant, inglyclosertotheumbra/penumbraboundaryastheupperlay- asdifferentspotsmaycertainlyshowdifferenttemperatures.In ersareapproached.Thesetemperatureenhancementscouldbe addition,the two data sets may be affected by differentlevels due to the presence of hot penumbral tubes, as suggested by ofstraylightcontamination. thenumericalsimulationsofSchlichenmaieretal.(1998).The In Fig. 7b we plot the average temperature stratifications hot tubes would be more easily detected in the inner penum- forthecenter-sideandlimb-sidepenumbra.Again,thecurva- brabecausetheplasmaemergingfromsubphotosphericlayers tureofthetwostratificationsisverysimilar,butthelimb-side quicklycoolsoffbyradiationawayfromthetube’sinnerfoot- penumbraisobservedtobecoolerthanthecenter-sidepenum- point(Schlichenmaieret al. 1999).If the humpsexhibited by braatallheights.Thedifferenceislargerintheupperlayers(up the temperature curves of Fig. 6 are indeed produced by hot to150K).AsimilarasymmetryhasbeenreportedbyRouppe flux tubes, then it is clear that they must be located preferen- vanderVoort(2002)fromananalysisof CaKobservations. tiallyinthelowerlayers. RouppevanderVoortsuggeststhatthelargeraveragetemper- The mean temperaturestratification of the penumbracon- atureofthecenter-sidepenumbraisproducedbyanexcessof sidering all pixels is shown in Fig. 7a. For comparison, we brightstructuresintheoutercenter-sidepenumbra.Ourresults alsoplotthemeantemperaturestratificationobtainedbyTTR. support this idea. In Fig. 8, histograms of the temperature at Thetwocurveshavethesamecurvatureatallheights,butare logτ = 0 are presentedforthe innerand outerpartsof the 500 BellotRubioetal.:Thermalandkinematicstructureofthepenumbra 7 Outer penumbra (r/R>0.7) log τ = 0 500 200 500 Center side Limb side 100 400 els T [K] 0 pix 300 ∆ of -100 er b 200 -200 m u 100 200 300 N 100 log τ = -1 500 200 0 100 5400 5600 5800 6000 6200 6400 K] T [ 0 Inner penumbra (0.5>r/R<0.7) ∆ 200 -100 Center side Limb side -200 100 200 300 150 s el x log τ = -2 pi 500 ber of 100 120000 m Nu 50 T [K] 0 ∆ -100 0 -200 5400 5600 5800 6000 6200 6400 100 200 300 Temperature at log τ500 = 0 [K] Azimuthal angle [deg] Fig.8. Histogramsof temperatureat logτ = 0 in the outer Fig.9. Temperature fluctuations at different optical depths 500 (top) and inner (bottom) center-side and limb-side penumbra alonganazimuthalpathatr/R= 0.8.Theverticaldottedlines (solidanddashedlines,respectively). markanumberofselectedpositionsshowingenhancedtemper- atures.Azimuthalanglesaremeasuredcounterclockwise,with 90opointingtothelimband270otodiskcenter. centerandlimb side penumbra.Theinnerpenumbradoesnot showsignificantdifferencesbetweenthetwosidesofthespot. Pixelsintheouterpenumbra,bycontrast,aregenerallyhotter onthecenterside. found larger intensities in the limb-side penumbra for spots The fact that both sides of the penumbra show different closetothesolarlimb,i.e.,theoppositebehavior.Clearly,more temperatures might be related to the different viewing angle. observationsarerequiredtosettletheissue. Rouppe van der Voort (2002) suggests that the higher tem- Taking advantage of the high spatial resolution of our peratures of the outer center-side penumbra can be explained dataset, we conclude this section with a discussion of the by isotherms being tilted downwards away from the umbra. temperature fluctuations observed at different optical depths. The required tilt is opposite to what one would expect from Figure 9 displays such fluctuations along an azimuthal path the Wilson depression (inclined upwards away from the um- crossing the penumbraat a normalized radial distance of 0.8, bra, e.g., Mathew et al. 2004),but it may be real: it has been forlogτ = 0,−1,and−2.Thefluctuationsbecomesmaller 500 demonstrated that penumbralflux tubes dive down below the andsmallerastheupperlayersareapproached.Atlogτ =0, 500 solar surface in the mid penumbra and beyond (Westendorp thetemperaturefluctuatesbysome200K,whileatlogτ = 500 Plazaetal.1997,2001;BellotRubioetal.2004;Borreroetal. −2 the fluctuations are smaller than 50–100 K. The vertical 2004).Thatis,thefieldlinesareslightlyinclineddownwardsin linesmarka fewpositionswherethetemperatureisenhanced theouterpenumbra.Perhapsthisconfigurationofthemagnetic locally. Clearly, hot structures in the deep layers remain hot fieldiscapableofdeterminingtheinclinationoftheisotherms, intheupperlayers,butwithlowertemperaturecontrasts.This althoughtheexactmechanismhasnotbeenidentifiedyet. isinexcellentagreementwiththefindingsofRouppevander AspointedoutbyRouppevanderVoort(2002),otherau- Voort(2002)andBelloGonza´lezetal.(2005).Ourresultssug- thorsalsofindthatthecenter-sidepenumbraisgenerallyhotter gestthatthestructuresgivingrisetothebrightpenumbralfila- than the limb-sidepenumbra(e.g.,TTR; WestendorpPlaza et mentsseeninwhite-lightimages(probablyfluxtubes)arelo- al. 2001). To the best of our knowledge, only one discrepant catedmainlyinthelowerphotosphere.Thesmalltemperature analysis exists. Schmidt & Fritz (2004) have studied the az- fluctuations observed in high layers do not necessarily imply imuthal variation of the continuum intensity in a number of thatfluxtubesarepresentthere:ifthedeep-lyingtubesarehot, spots observed at different heliocentric angles. These authors itisverylikelythattheycanheatthelayersabovethem.Thus, 8 BellotRubioetal.:Thermalandkinematicstructureofthepenumbra 1.5 1.5 5.1.HeightvariationoftheLOSvelocity -1s] Rms difference: 0.054 km/s -1s] Rms difference: 0.07 km/s m 1.0 m 1.0 6 [k 0.5 8 [k 0.5 In Fig.11we show theazimuthallyaveragedLOSvelocityat = -0. 0.0 = -1. 0.0 fouropticaldepthsasafunctionofnormalizedradialdistance. τog 500-0.5 τog 500-0.5 Wbrae (cloenftsiadnedrrsiegphatrautpeplyerthpeanleimlsb,-rseisdpeecatnivdeclye)n.teTrh-seidceurpveensudme-- y at l -1.0 y at l -1.0 pictedinFig.11confirminamorequantitativewaytheimpres- ocit -1.5 ocit -1.5 sionfromFig.4thattheEvershedflowstronglydecreaseswith el el V -2.0 V -2.0 height. A velocity reversalis observed around logτ = −2. -2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 -2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 500 Bisector velocity at 60%-80% [km s-1] Bisector velocity at 2%-20% [km s-1] On the limb side, we infer redshifts in the deep photosphere andblueshiftsinthe upperlayers.Formostof thecenter-side Fig.10. Comparison of LOS velocities resulting from the in- penumbra,blueshiftsindeeplayersandredshiftsinhighlayers versionandbisectorvelocitiesatintensitylevelsof60%–80% areretrieved(anexceptionistheveryouterpartofthecenter- (left) and2%–20%(right).Thesolid linesrepresenta one-to- side penumbra).Interestingly,the LOS velocitystratifications onecorrespondence. displayed in Fig. 4 of TTR also feature sign reversals around logτ = −2. A possible explanation for the sign reversal is 500 offeredinSect.6.2. smalltemperaturefluctuationsinhighlayerscouldbeproduced ThelowerpanelsofFig.11showtheaveragevelocitystrat- bytubeslocateddeeperdown. ificationsattworadialdistances:r = 0.6Randr = 0.97R.On thelimbside,thegradientofv withlogτ issignificantly LOS 500 largerintheouterpenumbra.Onthecenterside,thesituationis 5. Kinematicstructure reversed,with slightlylargergradientsin theinnerpenumbra. Westartthissectionbyexamininghowwellthebisectorveloci- Thesegradientsreproducetheslopesoftheobservedbisectors tiesofPapersIandIIcomparewiththevelocitiesinferredfrom inthedifferentpartsofthepenumbra(Fig.1ofPaperII).Note theinversion.Suchacomparisonisimportanttostrengthenthe the occurrenceof negative velocities (blueshifts) in the upper conclusionsdrawninPaperIIfromtheanalysisoftheobserved layers except in the inner center-side penumbra, where posi- bisectors. Figure 10 shows scatter plots of the LOS velocities tive velocitiesare retrievedabovelogτ500 = −2. Theinferred deduced from the two different methods. As can be seen, the velocity stratifications, together with the various broadening agreement is very satisfactory in both deep and high layers. andsmearingmechanisms,explaintheline-coreblueshiftsob- Bisector velocities near the continuum(intensity levels 60%– servedalmosteverywhereinthepenumbra,aswellasthesmall 80%) are well correlated with the LOS velocities determined line-core redshifts detected in the inner center-side penumbra at logτ = −0.6, with an rms difference of only 55ms−1. (e.g.,bisectors#33and#34inPaperII).Atthispointitisim- 500 Bisectorvelocitiesnearthelinecore(intensitylevels2%–20%) portant to remark that the line-core blueshifts cannot be pro- arealsowellcorrelatedwiththeLOSvelocitiesreturnedbythe ducedbytheinverseEvershedflow.AccordingtoGeorgakilas inversion at logτ ∼ −1.8, the rms difference being about etal.(2003,hisFig.6),thespeedandanglewithrespecttothe 500 70ms−1.Wehavechosentheopticaldepthsthatyieldthebest localverticaloftheinverseEvershedfloware∼0.5kms−1and agreement,butitshouldberemarkedthattheycoincidealmost 100o in the inner penumbra,at the height where the intensity exactlywiththecentroidsoftheRFstovelocityperturbations, observed at 0.5 Å from the center of the Hα line is formed. evaluated in the average penumbral model atmosphere. The The flow speed and the flow angle near the outer penumbral centroidsare locatedatlogτ ∼ −0.8and∼ −1.6forinten- boundaryare ∼ 4.5kms−1 and 115o, respectively.With these 500 sitylevelsof60%–80%and2%–20%,respectively.Theagree- flow configurationsandthe heliocentricangleofourobserva- ment is not surprising: Ruiz Cobo & del Toro Iniesta (1994) tions,theinverseEvershedeffectwouldproducenon-negligible and Sa´nchez Almeida et al. (1996) have shown that physical Dopplershiftsonlyintheoutercenter-sidepenumbra,whereit parameters measured from spectral lines using simple tech- wouldshowupasaredshift,notasablueshift. niques(e.g.,Dopplershiftsfromlinebisectors)areanaverage oftheactualstratificationoftheparameterweightedbythecor- 5.2.Flowgeometryatdifferentheights respondingRF.Ifthestratificationislinearwithdepth,thenthe heightofformationofthemeasuredparameteristhebarycenter We have computedthe flow speed and flow angle at different oftheRF(delToroIniesta2003,Chapter10). opticaldepthsfromtheazimuthalvariationoftheLOSveloci- Figure 10 demonstrates that Doppler velocities derived tiesreturnedbytheinversioncode.Thecalculationshavebeen from bisectors near the line core should be ascribed to layers performedasexplainedinSect.5.4ofPaperI.Ifoneassumes significantlydeeperthanthe‘formationheight’ofthelinecore. that the flow field is axially symmetric, the azimuthally aver- ThisisbecauseoftheverylargewidthsoftheRFsofItov . aged LOS velocity reflects the vertical flow component, and LOS Suchwidthsimplythatawiderangeoflayerscontributetothe theamplitudeoftheazimuthalvariationoftheLOSvelocityre- observedDopplershift.AsshowninFig.1,thelinecorereacts flectsthehorizontalflowcomponent.Usingthesecomponents, only little to mass motions in the upper photosphere, and so themeanflowinclinationandtheabsoluteflowvelocitycanbe velocitiestherearedifficulttodetectunlessthecontributionof deduced.TheresultsoftheanalysisarepresentedinFig.12as deeperlayersisproperlyconsidered. afunctionofnormalizedradialdistance. BellotRubioetal.:Thermalandkinematicstructureofthepenumbra 9 Limb-side penumbra Center-side penumbra 2.0 1.0 log τ = 0 log τ = 0 log τ500 = -1 log τ500 = -1 log τ500 = -2 log τ500 = -2 1.5 log τ550000 = -3 log τ550000 = -3 1] 0.5 -s m 1.0 k y [ cit 0.5 0.0 o el v S 0.0 O -0.5 L -0.5 -1.0 -1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Normalized radial distance Normalized radial distance Limb-side penumbra Center-side penumbra 1.5 r/R = 0.60 1.5 r/R = 0.60 s] r/R = 0.97 r/R = 0.97 m/ 1.0 1.0 k y [ cit 0.5 0.5 o vel 0.0 0.0 S LO -0.5 -0.5 -1.0 -1.0 -4 -3 -2 -1 0 1 -4 -3 -2 -1 0 1 log τ log τ 500 500 Fig.11.Top:RadialvariationoftheazimuthallyaveragedLOSvelocityinthelimb-side(left)andcenter-sidepenumbra(right), for four different optical depths. The shaded areas represent the rms variation of the LOS velocities at each radial distance. PositiveLOSvelocitiesindicatemotionsawayfromtheobserver(i.e.,redshifts).Bottom:AverageLOSvelocitystratifications inthelimb-sidepenumbra(left)andcenter-sidepenumbra(right)atr=0.6Randr=0.97R. As mentioned in Sect. 2.3, our simple model atmosphere Inclination angle Flow velocity [km/s] doesnotaccountfor the possibilityof unresolvedstructurein 110 -0.0 theresolutionelement.Thus,theflowspeedsresultingfromthe -1.0 calculations are probably smaller than the real ones1. To first 3 100 -1.3 order,however,theflowanglesarenotinfluencedbythiseffect, -1.6 because they are derived from the ratio of the horizontal and 90 verticalcomponentsofthe flow,andbothare affectedequally bythelackofspatialresolution. 2 80 FromFig.12wenotethefollowingfeatures: 1. Theflowinclination(withrespecttothelocalvertical)in- 70 1 creases with optical depth. Downflows are present in the mid and outer penumbra,but only in deep layers. In high 60 layers,theflowisalwaysinclinedupward. 2. Theflowvelocitydecreaseswithdecreasingopticaldepth. 50 0 3. The radial position of maximum flow velocity and maxi- 0.6 0.8 1.0 1.2 0.6 0.8 1.0 1.2 mumflowinclination’migrate’outwardsaswegotohigher Radial distance Radial distance atmosphericlayers. Fig.12. Flow geometry at different optical depthsas deduced from the azimuthal variation of the observed LOS velocity. 1 FollowingBellotRubio(2004),wemayassumeforsimplicitythat Left:Flowinclination(withrespecttothelocalvertical).Right: atagivenradialdistancetheflowchannelsoccupyafraction0≤α≤ Absolutemagnitudeoftheflow. 1 of the resolution element, the remaining (1−α) being plasma at rest.Asaroughestimate,theLOSvelocityobservedintheresolution elementwouldbev ∼αv˜ ,withv˜ theintrinsicLOSvelocity In summary, the azimuthally averaged flow velocity in- LOS LOS LOS oftheflowchannel. creaseswithdepthandtheazimuthallyaveragedflowinclina- 10 BellotRubioetal.:Thermalandkinematicstructureofthepenumbra tion show downflows only in the deep layers. This strength- 2.0 log τ = 0 ens the conclusions of Paper II, where we inferred a similar log τ500 = -1 log τ500 = -2 flow configurationfromthe interpretationofindividualbisec- log τ500 = -3 1] 500 torshapes.Itisimportanttoremarkthatcalculationsusingthe -s 1.5 bisector velocities derived in Paper II lead to the very same m k flowanglesandflowspeeds(cf.Fig.6inBellotRubio2004), e [ ascouldhavebeenexpectedfromFig.10. c TheresultspresentedinFig.12areingoodagreementwith en 1.0 ul the flowinclinationsdeterminedbyBellotRubioetal. (2003, b r u 2004)fromatwo-componentinversionofinfraredStokespro- ot files.TheradialvariationoftheflowangledescribedbyBellot cr 0.5 Rubioetal.correspondsroughlytoourcurveforlogτ = 0, Mi 500 becausetheFe1565nmlinestheyusearesensitivetoveloc- itiesin verydeepandnarrowphotosphericlayers.Ourresults 0.0 arealsoconsistentwiththoseofSa´nchezCuberesetal.(2005), 0.0 0.2 0.4 0.6 0.8 1.0 whoinvertedspectropolarimetricmeasurementsofasunspotat Normalized radial distance diskcenterintermsofone-componentmodelatmosphereswith gradientsofvelocity.Theseauthorsfoundthatdownflowsoc- Fig.13. Radial variation of the azimuthally averaged micro- curpredominantlyindeeplayers(logτ500 <−1),disappearing turbulence at four optical depths. The shaded areas represent higher up in the atmosphere. The present analysis, however, thestandarddeviationofthemicroturbulentvelocitiesfoundat does not confirm the small downflows retrieved by Sa´nchez eachradialdistance.Theverticallinemarkstheinnerpenum- Cuberesetal.(2005)intheinnerpenumbra. bralboundary. 5.3.Microturbulence Foreachpixeltheinversionreturnstheheightvariationofthe microturbulence,assumedtobelinearwithlogτ .Figure13 500 showstheazimuthallyaveragedmicroturbulenceatfouroptical depthsversusnormalizedradialdistance.Fromthisfigureitis apparentthat: 1. Intheinnerpenumbra,uptoabout0.6penumbralradii,the microturbulenceiszeroatallheights. 2. Inthemidandouterpenumbra,themicroturbulenceisdif- ferentfromzeroandincreaseswithopticaldepthandradial distance. 3. The gradient with depth of the microturbulence increases withincreasingradialdistance. InPaperI(Fig.7)wedeterminedtheradialdependenceof Fig.14. LOS velocities determined from the inversion at the azimuthally averaged equivalent width (EW) and the full logτ = −1.5 versus the microturbulence at the same opti- 500 width at half maximum(FWHM) of the intensity profilesob- caldepth.The verticaldottedlines indicateLOSvelocitiesof servedinNOAA10019.Forbothparameterswefoundminima ±0.4kms−1. Larger velocities are always associated with en- in the inner penumbra (r ∼ 0.65R) and maxima in the outer hancedmicroturbulence.Thesamecorrelationisseenindeeper penumbra (r ∼ 0.95R). According to the present results, this layers,butlessclearly. radialincreaseoftheEWandtheFWHMisduetoamicrotur- bulencethatincreasesradially(item2above). What is the origin of the microturbulent velocities re- turnedbythe inversioncode?Onecanspeculatethatstronger forthemicroturbulence.Figure14showsthemicroturbulence Evershedflowsresultinincreasedshearattheboundarylayer determined from the inversion at logτ = −1.5 versus the 500 separatingtheflowchannelsfromthesurrounding(static)mag- LOS velocity at the same optical depth. From this figure, it netic atmosphere.Strong shearsmay producesmall-scale tur- is clear that large LOS velocities are always associated with bulence throughthe onset of instabilities. This would explain largemicroturbulences.ThefindingsofPaperIled ustocon- whywedetectenhancedmicroturbulenceinthemidandouter jecturethattheincreaseintheEWandtheFWHMassociated penumbra,wheretheflowspeedsarelarger. with large velocities may be due to the presence of strongly However, we also found in Paper I that both the EW and Doppler-shifted(butspectrallyunresolved)linesatellites.This theFWHMtendtobeslightlyenhancedintheregionsofmax- suggeststhatpartofthemicroturbulenceweinfermaynotrep- imum Doppler shifts (i.e., along the line connecting the disk resent real small-scale turbulence, but a convenient means to centerandthesunspotcenter).Asimilartendencyisobserved accountfortheeffectsoflinesatellites.
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