AstronomischeNachrichten,25January2016 Magnetic field reconstruction based on sunspot oscillations J.Lo¨hner-Bo¨ttcher,(cid:63),N.BelloGonza´lez,andW.Schmidt Kiepenheuer-Institutfu¨rSonnenphysik,Scho¨neckstrasse6,79104Freiburg,Germany ReceivedXXXX,acceptedXXXX PublishedonlineXXXX 6 Keywords Sun:chromosphere–Sun:magneticfields–Sun:oscillations–methods:observational–techniques:spec- 1 troscopic 0 2 The magnetic field of a sunspot guides magnetohydrodynamic waves toward higher atmospheric layers. In the upper photosphereandlowerchromosphere,wavemodeswithperiodslongerthantheacousticcut-offperiodbecomeevanescent. n Thecut-offperiodessentiallychangesduetotheatmosphericproperties,e.g.,increasesforlargerzenithinclinationsof a J themagneticfield.Inthiswork,weaimatintroducinganoveltechniqueofreconstructingthemagneticfieldinclination 2 onthebasisofthedominatingwaveperiodsinthesunspotchromosphereandupperphotosphere.On2013August21st, 2 we observed an isolated, circular sunspot (NOAA11823) for 58min in a purely spectroscopic multi-wavelength mode withtheInterferometricBidimensionalSpectro-polarimeter(IBIS)attheDunnSolarTelescope.Bymeansofawavelet ] poweranalysis,weretrievedthedominatingwaveperiodsandreconstructedthezenithinclinationsinthechromosphere R andupperphotosphere.TheresultsareingoodagreementwiththelowerphotosphericHMImagnetograms.Thesunspot’s S magneticfieldinthechromosphereinclinesfromalmostvertical(0◦)intheumbratoaround60◦ intheouterpenumbra. . Withincreasingaltitudeinthesunspotatmosphere,themagneticfieldofthepenumbrabecomeslessinclined.Weconclude h p thatthereconstructionofthemagneticfieldtopologyonthebasisofsunspotoscillationsyieldsconsistentandconclusive - results.Thetechniqueopensupanewpossibilitytoinferthemagneticfieldinclinationinthesolarchromosphere. o r Copyrightlinewillbeprovidedbythepublisher t s a [ 1 Introduction with the local speed of sound or atmospheric temperature. 1 The typical value for sunspot umbrae ranges around 192s. v Sunspot waves are one of the most prominent and dynam- AsproposedbyBel&Leroy(1977)andconfirmedby,e.g., 5 ical phenomena in the solar atmosphere. In the sunspot DePontieuetal.(2004),theinclinationofthemagneticfield 2 chromosphere, umbral flashes (Beckers & Tallant 1969) linesagainstthezenithstronglyimpactstheacousticcut-off 9 5 and running penumbral waves (Giovanelli 1972; Zirin & period.Theacousticcut-offperiod 0 Stein 1972) appear as unceasing brightness and velocity 4πc 1. oscillations. Numerous observational studies (e.g., Bloom- Tcut,ΦB = γg cosSΦ , (1) field et al. 2007; Centeno et al. 2006; Madsen et al. 2015) B 0 effectivelydependsonthesoundspeedc andthezenithin- 6 confirmed that sunspot waves are propagating slow-mode S clination Φ of the magnetic field. The constant adiabatic 1 magnetoacousticwaveswhichareguidedupwardalongthe B : magneticfieldlines.Fromtheumbratotheouterpenumbra, index γ = 5/3 (monoatomic gases) and the solar gravita- v tional acceleration g ≈ 274m/s enter the equation. In the i thewavecharacteristicschangeowingtotheincreaseinin- X power spectrum, those wave modes with periods slightly clinationofthemagneticwaveguidesagainstthezenith. r Asthetraveldistancetoadistinctchromosphericsam- shorterthanthecriticalcut-offvaluedominate.Theempir- a pling layer increases with the magnetic field inclination, ical formula Tcut,ΦB = m TPEAK with the factor m = 1.25 often describes a good indicator of the the cut-off period the penumbral waves delay and seem tofollow the umbral waves.Thesecondmajordifferencebetweenbothphenom- from the measured peak period TPEAK in the power spec- trum(Bogdan&Judge2006;Tziotziouetal.2006).Trans- enaisthewaveperiodicity(seeFig.1d).Whereastheum- posing and inverting Eq.(1), and substituting the adiabatic bral chromosphere is dominated by 2.5–3min waves, the sound speed yields the zenith inclination of the magnetic peakperiodsofpenumbralwavesincreaseasafunctionof fieldas radialdistancefrom3minattheumbral-penumbralbound-  (cid:113)  atircycTuupht-itosoffc8hlamanyigener.aitnWtwhaevaevoeumtpeorrodppeesangwuamittihobnrparee(rsJiouedlstssseflortonamlg.e2trh0te1ha3ac)n.outhse- ΦB =cos−1m4πγgTγPRMEϑAKK , (2) characteristic cut-off period become evanescent. For verti- with the peak periods T in seconds, the atmospheric calmagneticfields,thecut-offperiodscalesproportionally PEAK temperatureϑ inKelvin,andthespecificgasconstantR/M K (cid:63) Correspondingauthor:[email protected] withthemeanmolarmassMandgasconstantR. Copyrightlinewillbeprovidedbythepublisher 2 J.Lo¨hner-Bo¨ttcheretal.:Magneticfieldreconstructionbasedonsunspotoscillations Inthefollowing,thenovelmethodofreconstructingthe the umbral area is characterized by 2.5–3min periods, the magneticfieldinclinationfromtheatmosphericandoscilla- penumbra yields a filamentary radial increase of wave pe- torycharacteristicsisappliedtotheobservationswhichare riods up to 8min at the outer penumbra and beyond. The presentedinSection2.Thedeterminationofthetwocrucial three-dimensional evolution of wave periods is illustrated components,thedominatingwaveperiodT andtheat- inFig.2ofLo¨hner-Bo¨ttcher&BelloGonza´lez(2015). PEAK mospheric temperature ϑK, is described. In Section 3, the Besides the peak period TPEAK, which is the most sen- mostfundamentalresultsforupperphotosphericandlower sitiveparameterforthecomputationofthefieldinclination chromosphericzenithinclinationarediscussed.Theconclu- in Eq.(2), the local sound speed c is the second crucial S sionsaredrawninSection4. componenttobeevaluated.Asimpleapproachwaschosen to estimate the local temperature ϑ in the sunspot atmo- K sphere.First,areferencepositionwithinthesunspotregion 2 Observationsandanalysis is defined, either in the central core of the umbra or in the quiet sun surrounding the sunspot. According to the posi- The isolated fully-developed sunspot of active region tion,thecorrespondingsemi-empiricalatmospherictemper- NOAA11823 was observed on August 21st 2013 from ature model from Maltby et al. (1986) is selected. Then, 14:53UTC to 15:51UTC with the Dunn Solar Telescope the formation height of the spectral position is estimated (DST) at the National Solar Observatory in New Mexico. by means of spectral contribution functions (Cauzzi et al. In addition to the spectroscopic observations which were 2008;Leenaartsetal.2010).Themodeltemperatureisex- performedwiththeInterferometricBIdimensionalSpectro- tracted and averaged for a layer centered at the respective polarimeter (IBIS; Cavallini 2006), spectro-polarimetric estimated formation height (±100kms−1). Finally, accord- data were acquired from the Helioseismic Magnetic Im- ing to Plancks law and the Wien approximation, the atmo- ager (HMI) aboard the Solar Dynamics Observatory. The spherictemperatureiscalculatedonthebasisoftherelative sunspot in time-averaged continuum intensity is shown in spectral brightness across the sunspot region. Based on an Fig.1 (panel a) and Fig.2 (bottom left). The spot was lo- umbralandquietsunmodel,bothresultsareingoodagree- catedclosetothesolardiskcenterat(X,Y)=(63(cid:48)(cid:48),−222(cid:48)(cid:48)) mentandenterthereconstructionequationofthemagnetic withaheliocentricangleofθ = 14◦,hasacircularpenum- field inclination. This simple approach return a suited es- braandadiameterof24Mm. timation of the atmospheric temperature and local sound To gain knowledge and context information about the speed. To evaluate the atmospheric properties in an even photosphericmagneticfieldvector,theVeryFastInversion preciserway,apixel-wiseinversionofthespectrallinepro- of the Stokes Vector (VFISV; Borrero et al. 2011) was ap- filecanand,inthefuture,willbeappliedtothemethodol- pliedonthepolarimetricsignalsoftheFeI617.33nmline ogy. ofHMI.AsshowninFig.1(panelsbandc),theumbralcore yields an absolute magnetic field strength of up to 2.6kG and an inclination Φ against the line-of-sight of less 3 Resultsanddiscussion B,LOS than 20◦. According to the apparent displacement of the line-of-sight magnetic field toward the disc center, orien- Thezenithinclinationofthesunspot’smagneticfieldisre- tationintheumbracanbeassumedasvertical.Towardthe constructedsuccessfullybyEq.(2)onthebasisoftheatmo- outer penumbra, the magnetic field strength decreases al- spheric and oscillatory parameters. According to the pho- mostlinearly(seeFig.3b). tosphericHMImagneticfieldinclinationandanadditional The spectrometric multi-wavelength IBIS observations coronal magnetic field extrapolation with a Potential-Field sampled various non-equidistant line core and wing posi- Source-Surface(PFSS;Schrijver&DeRosa2003)model, tions of the NaID1 589.59nm and CaII 854.21nm lines, averticalmagneticfieldcanbeassumedforthecentralum- covering the photosphere and chromosphere up to an at- bra.Tomaintaintheverticalorientationofthecentralumbra mospheric formation height of around 1000km above the throughout the atmosphere, the peak-to-cut-off factor m of wavelength dependent optical depth unity. In addition, the Eq.(2)hastobeadaptedtotheatmosphericlayer,from1.1 FeI630.15nmlinewasobservedtogaininformationabout in the middle photosphere to 1.25 in the middle chromo- the lower photosphere. With an overall cadence of 13.2s, sphere. the Nyquist criterion enables the investigation of oscilla- The resulting three-dimensional distribution of the tions with periods as small as 26.5s. To obtain the dom- sunspot’s magnetic field inclination is illustrated in Fig.2 inating wave periods across the sunspot atmosphere, the on the right. The spectral intensities at the corresponding spectral intensities at the wavelength positions were ana- wavelength positions of the FeI, NaI D1, and CaII line lyzed with wavelet techniques (Torrence & Compo 1998). are ordered according to their estimated formation height Finally, the dominating wave period T was extracted and plotted on the left. Except for the lower photosphere PEAK from the global wavelet power spectra as the position of (two FeI line core positions) in which the acoustic cut-off the maximum below 10min. Exemplarily, the distribution not yet defines the dominating wave propagation, the re- of peak periods in the sunspot chromosphere (line core sultsespeciallyinthechromosphereandupperphotosphere of CaII 854.21nm) is shown in Fig.1 (panel d). Whereas are in good agreement with the lower photospheric HMI Copyrightlinewillbeprovidedbythepublisher asnaheaderwillbeprovidedbythepublisher 3 a) Continuum intensity I b) Field strength B [kG] c) Zenith angle (cid:92) [°] d) Peak period T [min] CONT 0 B, LOS PEAK 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 2.0 2.5 0 10 20 30 40 50 60 70 80 2.5 3.5 4.5 5.5 6.5 7.5 --224400 --223300 Y ["] ar- --222200 ol S --221100 --220000 DC 4400 5500 6600 7700 8800 4400 5500 6600 7700 8800 4400 5500 6600 7700 8800 4400 5500 6600 7700 8800 Solar-X ["] Solar-X ["] Solar-X ["] Solar−X ["] Fig.1 Time-averaged(1h)physicalquantitiesofsunspotNOAA11823.Thesunspotisdisplayedina)normalizedHMI continuumintensities I ataround617nm,b)absolutemagneticfieldstrengths B andc)line-of-sightmagneticfield CONT 0 inclinationsΦ ,bothfromHMIinversionsofthepolarimetricsignalsof FeI617.33nm.Thephotosphericinclination B,LOS anglesarescaledfromtheline-of-sightdirectionof0◦ (blue)toaroughlyperpendicularorientationof80◦ totheline-of- sight(red).d):ThechromosphericdistributionofdominantsunspotwavesisshownbythepeakperiodsT fromIBIS PEAK intensityoscillationsoftheCaII854.2nmlinecore.Theperiodsarescaledfrom2.5min(blue)to7.5min(red).Theblack a) (cid:92) (CaII, (cid:104) ) b) (cid:92) (CaII, (cid:104) ) c) (cid:92) (CaII, (cid:104) ) d) (cid:92) (H(cid:96)) contoB−uFirelsd mark the2, Cu−4m4pmbral (inneBr−)Fiealdn d penum3b, Cr−a22lpm(outer) boB−uFineldd aries fro5m, Corceontinuum intenBs−Fiitelyd . The arrow (in panel a) is −−224400 pointingtowarddiskcenter(DC). −−223300 Y ["] z! − ar −−222200 ~ 1000 km! Sol ere! −−221100 h p s Ca II : λ5, Core! mo −−220000 o hr e) (cid:92) (NaI, (cid:104) ) f) (cid:92) (NaI, (cid:104) ) g) (cid:92)C (NaI, (cid:104) ) h) (cid:92) (CaK) B−Field 2, C−12pm B−Field 3, C−6pm e B−Field 4, Core B−Field −−224400 Ca II : λ3, C-22pm! middl o −−223300 er t Y ["] Na I : λ4, Core! Low ar− −−222200 ~ 600 km! ol S −−221100 Na I : λ3, C-6pm! −−220000 i) (cid:92)Na I : λ(2F, Ce-12Ip,m (cid:104)! ) k) (cid:92) (FeI, V ) l) (cid:92)~ 300 (kNma! I, V ) m) (cid:92) (HMI, VFISV) (cid:92) [°] B−Field 4, C−4pm B−Field LOS B−Field LOS B, LOS B e! 70 −−224400 pher 60 −−223300 Fe I : λ4, C-4pm! otos 50 Y ["] Ph 40 − olar −−222200 Fe I : λ3, C-8pm! 30 S 20 −−221100 y! x! 10 −−220000 Continuum intensity! HMI Inversion! 0 4400 5500 6600 7700 8800 4400 5500 6600 7700 8800 4400 5500 6600 7700 8800 4400 5500 6600 7700 8800 Fig.2 SoSlaur−nXsp [o"]tNOAA11823inSaotlharr−eXe- [d"]imensionalviewofSoinlatre−nXs i[t"i]esandreconstructeSdozlaern−iXt h["]inclinationsΦB ofthe magneticfieldfromphotospherictochromosphericheights.Theintensitiesontheleftshowthesunspotat2013August21 at15:00:06UTCatseverallinecoreandwingpositionsof FeI630.15nm,NaI589.59nm,andCaII854.21nm.Abright umbralflashispresentinthecentralumbra.Theinferredzenithinclinationsontherightarescaledfrom0◦ (darkblue)to 70◦ (darkred).Thesunspotboundariesfromcontinuumintensity(bottomleft)arecontouredinblack.Thephotospheric line-of-sight inclination from the HMI inversion is added for comparison (bottom right). The image positions along the z-axisareorderedatanon-equidistantscaleaccordingtotheirestimatedheightabovetheopticaldepthunity. Copyrightlinewillbeprovidedbythepublisher 4 J.Lo¨hner-Bo¨ttcheretal.:Magneticfieldreconstructionbasedonsunspotoscillations a) b) c) a) 80 d) CaII, (cid:104) malized continuum intensity 00001.....24680 ICONT agnetic field strength [kG] 01122.....50505 BBLO0S Zenith inclination [°](cid:92)B 24680000Zenith angle [°](cid:92)B 123456700000000 CC(cid:92)aaIIBII, (cid:92),,P H(cid:104)(cid:104)OB235,T ,,,CO CCCHo−−Rr42e42OppMmmO Peak period T [min]PEAK 345678 TPPEAeKn, PuHmOTbOraTPEAK, CHROMO QS Nor 0.0 U PU QS M 0.0 U PU 0b) 80 UPmUbra QS 2 U PU QS NaI, (cid:104) 0 5 10 15 0 5 10 15QS 070U 5NaI, 1(cid:104)02, C−12p1m5 0 5 10 15 a) b) c) Distance X ["] d) Distance X ["] [°](cid:92)B 60 DNisataIn, c(cid:104)e34 ,, XCCo− r6e[p"m] Distance X ["] malized continuum intensity 00001.....24680 ICONT agnetic field strength [kG] 01122.....50505 BBLO0S Zenith inclination [°](cid:92)B 24680000 (cid:92)B, (cid:92)PHOB,T COHROMO Peak period T [min]PEAK 345678 TPEAK, PHOTO TPEAK, CHROMO FZenith angle ig.123454000000 0 ZenUitmhbirancl5inationDsisΦtancP1oee0f nXut h[m"e]brsaunspo1t5’s maQgSnetic Nor 0.0 U PU QS M 0.0 U PU 0 PU QS 2 U PU QS field from the photosphere toBthe chromosphere. The az- 0 5 10 15 0 5 10 15QS 0 U 5 10 15 0 5 10 15 imuthallyaveragedinclinationanglesareplottedasafunc- Distance X ["] Distance X ["] Distance X ["] Distance X ["] tion of radial distance X from the sunspot barycenter. The Fig.3 Azimuthally averaged sunspot parameters as a panels show the evolution of the inclination with increas- function of radial distance X from the sunspot barycenter: ingatmosphericheightfromthemiddlephotosphere(black a) the normalized continuum intensities at around 617nm, curves)tothelowertomiddlechromosphere(redandblue b) absolute (B , black curve) and line-of-sight (B , blue curves). The curves stem from distinct wavelength posi- 0 LOS curve)magneticfieldstrengthsfromphotosphericHMIin- tions:a)CaII854.21nmatthebluelinewing(blackcurve, versions, c) zenith inclinations Φ of the magnetic field ≈ 250km), blue line core (red curve, ≈ 900km), and line B in the lower photosphere (black curve) and chromosphere minimum (blue curve, ≈ 1000km); b) NaI 589.59nm at (bluecurve),andd)peakwaveperiodsT inthemiddle the blue line wing (black curve, ≈ 300km), blue line core PEAK photosphere (black curve) and chromosphere (blue curve). (red curve, ≈ 600km), and line minimum (blue curve, Theaveragesunspotboundariesaremarkedbythevertical ≈ 1000km).Theerrorbarstotheblackcurvearethestan- dashedlines.Thestandarddeviationsalongtheazimuthare darddeviationsalongtheazimuth.Theverticaldashedlines plottedaserrorbars. marktheaveragesunspotboundaries. 4 Conclusions line-of-sightmagneticfieldinclinationonthebottomright. The reconstruction of the magnetic field inclination on the The zenith inclinations of the sunspot’s magnetic field in- basis of sunspot oscillations from spectroscopic observa- creasessystematicallyfromaverticalorientation(0◦)inthe tions yields inherently consistent and conclusive results. umbra to around 60◦ in the outer penumbra. The penum- Sincetheeffectoftheacousticcut-offlayeronwavepropa- bralmagneticfieldinclinationdecreaseswithincreasingal- gationisemployed,thereconstructionyieldsthebestresults titude. It is best reflected in Fig.3c and Fig.4 in which in the chromosphere and upper photosphere. This novel theazimuthallyaveraged(includingsphericalprojectionef- technique opens up a new possibility to infer the mag- fects)magneticfieldinclinationsinthephotosphere(black netic field inclination in the solar chromosphere and pro- curves)andchromosphere(blueandredcurves)areplotted videsapromisingalternativetotheinvestigationofspectro- asafunctionofradialdistancefromthesunspotbarycenter. polarimetricfull-Stokessignalsinthehigheratmosphere. Therobustnessofthemethodologyisverifiedbytheconsis- Acknowledgements. Thedatawereacquiredinservicemodeop- tencyoftheresultsfrombothchromosphericspectrallines. eration within the transnational ACCESS program of SOLAR- Thedecreaseinmagneticfieldinclinationwithheightisin NET,anEU-FP7integratedactivityproject.TheIBISinstrument linewiththetopologyofamagneticfieldconfigurationthat at the DST (NSO) was operated by INAF personnel, with spe- fans out toward the less dense upper atmosphere (Westen- cial thanks to Gianna Cauzzi. 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