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Steps toward a high precision solar rotation profile: Results from SDO/AIA coronal bright point data PDF

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Astronomy&Astrophysicsmanuscriptno.Rotation (cid:13)c ESO2015 January7,2015 Steps toward a high precision solar rotation profile: Results from SDO/AIA coronal bright point data D.Sudar1,I.Skokic´2,R.Brajsˇa1,andS.H.Saar3 1 HvarObservatory,FacultyofGeodesy,UniversityofZagreb,Kacˇic´eva26,10000Zagreb,Croatia 2 CybrotechLtd,Bohinjska11,10000Zagreb,Croatia 3 Harvard-SmithsonianCenterforAstrophysics,60GardenStreet,Cambridge,MA02138,USA ReleaseJanuary7,2015 5 1 ABSTRACT 0 2 Context.Coronalbrightpoints(CBP)areubiquitoussmallbrighteningsinthesolarcoronaassociatedwithsmallmagneticbipoles. Aims.WederivethesolardifferentialrotationprofilebytracingthemotionsofCBPsdetectedbytheAtmosphericImagingAssembly n (AIA)instrumentaboardtheSolarDynamicsObservatory(SDO).Wealsoinvestigateproblemsrelatedtodetectionofcoronalbright a J pointsresultingfrominstrumentanddetectionalgorithmlimitations. Methods.Todeterminethepositionsandidentificationofcoronalbrightpointsweusedasegmentationalgorithm.Alinearfitoftheir 6 centralmeridiandistanceandlatitudeversustimewasutilisedtoderivevelocities. Results.Weobtained906velocitymeasurementsinatimeintervalofonly2days.Thedifferentialrotationprofilecanbeexpressed R] asωrot = (14.47±0.10+(0.6±1.0)sin2(b)+(−4.7±1.7)sin4(b))◦day−1.Ourresultisinagreementwithotherworkanditcomes withreasonableerrorsinspiteoftheveryshorttimeintervalused.Thiswasmadepossiblebythehighersensitivityandresolutionof S theAIAinstrumentcomparedtosimilarequipmentaswellashighcadence.Thesegmentationalgorithmalsoplayedacrucialroleby h. detectingsomanyCBPs,whichreducedtheerrorstoareasonablelevel. p Conclusions.Data and methods presented in this paper show a great potential to obtain very accurate velocity profiles, both for - rotationandmeridionalmotionand,consequently,Reynoldsstresses.Theamountofcoronalbrightpointdatathatcouldbeobtained o fromthisinstrumentshouldalsoprovideagreatopportunitytostudychangesofvelocitypatternswithatemporalresolutionofonly r afewmonths.OtherpossibilitiesarestudiesofevolutionofCBPsandpropermotionsofmagneticelementsontheSun. t s a Keywords.Sun:rotation-Sun:corona-Sun:activity [ 1 1. Introduction used 19.4 nm SOHO/EIT channel. Kariyappa(2008) also used v 5 Hinode/XRT full-disk images to determine the solar rotation We present a new solar rotation profile obtained by trac- 8 profile. ing the motions of coronal bright points (CBPs) observed by 2 Other tracers are used as well: magnetic fields 1 Atmospheric Imaging Assembly (AIA) instrument on board (Wilcox&Howard 1970; Snodgrass 1983; Kommetal. 0 the Solar Dynamics Observatory (SDO) satellite (Lemenetal. 1993)andHαfilaments(Brajsˇaetal.1991).Apartfromtracers, 1. 2012). Doppler measurements can also be used (Howard&Harvey 0 Themostfrequentlyusedandoldesttracersofthesolardif- 1970;Ulrichetal.1988;Snodgrass&Ulrich1990). 5 ferential rotation profile are sunspots (Newton&Nunn 1951; Helioseismic measurements also show differential rotation 1 Howardetal.1984;Balthasaretal.1986b;Brajsˇaetal.2002a). below the photosphere all the way down to the bottom of : Oneoftheadvantagesofusingsunspotsisverylongtimecov- theconvectivezone(Kosovichevetal.1997;Schouetal.1998). v i erage. On the other hand, there are numerous disadvantages: Furtherdown,the rotationprofilebecomesuniformforall lati- X sunspotshavecomplexandevolvingstructure,theirdistribution tudes(cf.eg.Howe2009). r inlatitudeishighlynon-uniformanditdoesnotextendtohigher For further details about solar rotation, its importance for a solar latitudes. The number of sunspots is also highly variable solar dynamo models, and comparison of rotation measure- duringthesolarcyclewhichmakesmeasurementsofsolardiffer- ments between different sources, see the reviews by Schro¨ter entialrotationprofilealmostimpossibleduringsolarminimum. (1985); Howard (1984); Beck (2000); Ossendrijver (2003); CBPsaremoreuniformlydistributedinlatitudeandarenu- Ru¨diger&Hollerbach (2004); Stix (2004); Howe (2009); merousinallphasesofthesolarcycle.Theyalsoextendoverall Rozelot&Neiner(2009). solarlatitudes.Theyhavebeenusedastracersofsolarrotation In this work we use CBP data obtained by SDO/AIA over sincethebeginningofthespaceage(Dupree&Henze1972).In onlytwodaystoassessthequalityofthedata,identifysourcesof recentyearstherearenumerousstudiesinvestigatingsolardiffer- errorsandcalculatethesolardifferentialrotationprofile.Wewill entialrotationbyusingCBPsastracers.Kariyappa(2008);Hara alsoinvestigatethepossibilityofusingCBPdatafromSDO/AIA (2009)usedYohkoh/SXTdatawhileBrajsˇaetal.(2001,2002b, forfurtherstudiesofotherrelatedphenomena(meridionalflow, 2004); Vrsˇnaketal. (2003); Wo¨hletal. (2010) used SOHO- rotationvelocityresidualsandReynoldsstress). EITobservationsin28.4nmchannelandKarachiketal.(2006) CBP data from SDO/AIA were also used in other works. Lorencetal.(2012)discussedrotationofthesolarcoronabased Sendoffprintrequeststo:D.Sudar,e-mail::[email protected] on 69 structures from 674 images detected in 9.4 nm channel 1 D.Sudaretal.:Stepstowardahighprecisionsolarrotationprofile:ResultsfromSDO/AIAcoronalbrightpointdata usinganinteractivemethodofdetection.Dorotovicˇetal.(2014) presentedahybridalgorithmfordetectionandtrackingofCBPs. McIntoshetal. (2014b) used detection algorithm presented in 1500 their previous paper (McIntosh&Gurman 2005) to identify CBPsinSDO/AIA19.4nmchannelandcorrelatetheirproper- 1000 tieswiththoseofgiantconvectivecells.UsingmoreSDO/AIA dataand extendinganalysisbacktoSOHO era,McIntoshetal. 500 (2014a) concluded that CBPs almost exclusively form around els] theverticesofgiantconvectivecells. pix 0 y [ 2. Dataandreductionmethods −500 We haveuseddatafromtheAIAinstrumentonboardtheSDO −1000 satellite(Lemenetal.2012).Thespatialresolutionoftheinstru- ment is ≈0.6”/pixel. For comparison, SOHO/EIT resolution is −1500 2.629”/pixelwhileHinode/XRThasaresolutionof1.032”/pixel. −2000 −1000 0 1000 2000 Toobtainpositionalinformationforthecoronalbrightpoints x [pixels] (CBPs),weemployedasegmentationalgorithmwhichusesthe 19.3nmAIAchanneldatatosearchforlocalized,smallintensity enhancementsintheEUVcomparedtoasmoothedbackground intensity. More details about the detection algorithm, which is similartothealgorithmbyMcIntosh&Gurman(2005),canbe foundinMartensetal.(2012). Thisresultedinmeasurementsof66842positionsof13646 individual CBPs covering two days (1st and 2nd of January 2011).Thetimeintervalbetweentwosuccessiveimageswas10 minutes. In top panelof Fig. 1 we show the distribution of de- tected CBPs and compare it to the full disk image of the Sun in the 19.3 nm channel obtained on 1st of January 2011 (bot- tom panel of the same Figure). In the bottom panel, white cir- cles show CBPs that were detected on one image by the seg- mentationalgorithm.WecanseethatCBPsarescarceinactive regions, partly because of difficultiesin detecting them against suchbrightandvariablebackgrounds. The segmentation algorithm provides coordinates in pixels (centroidsofCBPsontheimage)andweconvertedthemtohe- liographiccoordinatestakingintoaccountthecurrentsolardis- tance given in FITS files (Rosˇaetal. 1995, 1998). Positions of objects near the solar limb are fairly inaccurate. Limiting the data to ±58◦from the centre of the Sun or ≈0.85R of the pro- ⊙ jectedsolardiskremovesthisproblem(cf.Stark&Wo¨hl1981; Balthasaretal.1986a). Fig.1.DistributionofCBPsdetectedbythesegmentationalgo- As can be seen from Fig. 2, the calculated velocities show rithm (top panel) and image of the Sun in the 19.3 nm chan- some scatter. This scatter arises because the shifts are fairly nelobtainedbySDO/AIAon1stofJanuary2011.Whitecircles smallatour10mincadence,andtherecanbesignificantvaria- showdetectedCBPsonthisimage(bottompanel). tionsin brightnessandstructureofCBPs whichinfluencescal- culationofthecentroidpoints.Nevertheless,trendsarevisible, especially in azimuthal motion which is known to be a signif- islatitudeofeachmeasurementforasingleCBP.Wehavealso icantly larger effect. The dominant azimuthal motion led us to removedallCBPswhichhadlessthan10measurementsofpo- approximate the CBP motion with a linear fit to calculate the sitioninorderforlinearfitstobemorerobust.Thisisequivalent velocities: to100minutesorabout1◦attheequator.Toobtainthetruerota- N N N tionofCBPsontheSunweconvertsynodicvelocitiestosidereal N lt − l t i i i i usingEq.7fromSkokic´etal.(2014). ωsyn = iP=1 iP=1 iP=12 , (1) Tryingtoidentifythesameobjectonsubsequentimageswith N N an automatic method is bound to result in some misidentifica- N t2− t i=1 i i=1 i! tion.Theresultingvelocitiesareusuallyverylargeandcaneas- P P ilyberemovedbyapplyingasimplevelocityfilter.Eventhehu- N N N N bt − b t manfactorcan introducesuch errors.For example,Sudaretal. i i i i ωmer = iP=1N iP=1N iP=21 , (2) (ti2o0n1s4o)fasnuanlsypsoedtgsrooluaprsrfortoamtiotnhereGsriedeunawlsicahndPhmoteorhideiloiongarlapmhoic- NiP=1ti2− iP=1ti! Rfoersruolttastaionndaflovuenlodctihtaytitnheoyrdheardtotoeluismeianafitletethre8s<eωerrrootn<e1o9u◦sdmaye−a1- whereω isasynodicrotationalvelocity,ω isameridional surements.TheGreenwichPhotoheliographicResultscatalogue syn mer angular velocity, l is central meridian distance (CMD) and b isbeinginvestigatedandrevisedpartlyinordertoremovesuch i i 2 D.Sudaretal.:Stepstowardahighprecisionsolarrotationprofile:ResultsfromSDO/AIAcoronalbrightpointdata -81.8 3 -81.9 2.5 -82.0 ay] 2 b [deg] deg/d 1.5 -82.1 ) [ ot ωr ( 1 σ -82.2 0.5 -82.3 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0 t [days] 0 200 400 600 800 1000 25.0 Coronal bright point no. Fig.3.Errorsofrotationalvelocity,σ(ω ),foreachofthe906 24.5 rot measurements. 24.0 g] 23.5 de 2.2 D [ 23.0 40 M 2 C 22.5 1.8 g] 20 22.0 de 1.6 e [ ud 1.4 21.5 c latit 0 1.2 hi 21.0 ap 1 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 ogr−20 t [days] eli 0.8 H 0.6 Fig.2.MotionofasingleCBP.Toppanel:latitude,b,overtime, −40 t;bottompanel:centralmeridionaldistance,CMDovertime,t. 0.4 0.2 −60 problems(Willisetal.2013a,b;Erwinetal.2013).Inthiswork 180 200 220 240 260 280 300 Heliographic longitude [deg] we havealso useda 8< ω <19◦day−1 filter forrotationalve- rot locitiestoremovesuchoutliers.Inaddition,weappliedamerid- Fig.4. Distribution of rotation velocity errors (ω ) in helio- rot ionalvelocityfilterof-4<ωmer <4◦day−1toremovefurtherout- graphiccoordinates.Errorscaleisin◦ day−1. liers. Aftercompletingalltheproceduresdescribedabove,weob- tained 906 velocity measurements by tracing CBPs over just In Fig. 3 we show errorsof the calculated rotationalveloc- twodays.Olemskoy&Kitchatinov(2005)pointedoutthatnon- ities, σ(ωrot), for each CBP, which resulted from errors in the uniformdistributionoftracerscanresultinfalseflows.Thisef- linear fitting of longitude vs time measurements. Although the fect is most notable for meridional motion and rotation veloc- errors can go up to 3◦day−1, the majority is below 1◦day−1. In ityresiduals,butcaneasilyberemovedbyassigningthecalcu- Fig.4weshowtheseerrorsinheliographiccoordinatestocheck latedvelocitytothelatitudeofthefirstmeasurementofposition their spatial distribution on the solar surface. Larger errors are (Olemskoy&Kitchatinov 2005; Sudaretal. 2014). Although shown with brighter shades and we can see that these roughly theeffectisnegligibleforsolarrotation,weneverthelessapplied correspondtothepositionsofactiveregionsshowninthebottom thecorrectioninthiswork. panelofFig.1.Thiscorrelationwithactiveregionisprobablya Itisimportanttokeepinmindthatevenwhenthetracersare consequenceofthedetectionalgorithmdesignanddifficultiesin uniformlydistributed over the solar surface, the distribution of detectionofCBPsoverabright,variablebackground. tracersinlatitudewillbenon-uniform.Aswemovefromequator In Fig. 5 we show the distribution of CBPs in heliographic tothepole,theareaofeachlatitudebinbecomessmaller,sowe coordinates with arrows indicating the velocity vector. As ex- observeprogressivelyfewertracers(∼cosb). pected,thedominanteffectisthatofsolarrotation. The latitudinal dependence of rotational velocity is usually expressedas(Howard&Harvey1970;Schro¨ter1985): 3. Results ω (b)=A+Bsin2b+Csin4b, (3) rot Inthiswork,wepresentananalysisofthemotionofCBPsob- servedby theSDO/AIA instrument.Fora betterunderstanding where b is the latitude. Parameter A represents equatorial ve- oftheresultsandthepotentialoffuturestudiesalongtheselines, locity, while B and C depict the deviation from rigid body ro- itisveryusefultoanalysetheaccuracyanderrorsofthedataset. tation. The problem with Eq. 3 is that the functions in this 3 D.Sudaretal.:Stepstowardahighprecisionsolarrotationprofile:ResultsfromSDO/AIAcoronalbrightpointdata 60 20 40 18 20 Heliographic latitude [deg]−200 ω (deg/day)1146 12 −40 −60 10 −80 160 180 200 220 240 260 280 300 320 340 8 Heliographic longitude [deg] 0 10 20 30 40 50 60 70 b (degrees) Fig.5.DistributionofCBPsinheliographiccoordinateswithar- Fig.6.Solardifferentialrotationprofileobtainedwithdatafrom rowsshowingthedirectionandstrengthofthevelocityvector. SDO/AIA.Opencirclesareindividualmeasurements,whilethe solidlineisthebestfitdefinedbyEq.3fortheA, B,Ccase. expression are not orthogonal, so the parameters are not in- Table1.Coefficientsofthesolarrotationprofile. dependent of each other (Duvall&Svalgaard 1978; Snodgrass 1984; Snodgrass&Howard 1985; Snodgrass&Ulrich 1990). Type A[◦day−1] B[◦day−1] C[◦day−1] n This crosstalk among the coefficients is particularity bad for B A,B,C 14.47±0.10 +0.6±1.0 -4.7±1.7 906 andC.Theeffectofcrosstalkdoesnotaffecttheactualshapeof A,B=C 14.59±0.07 -1.35±0.21 -1.35±0.21 906 the fit (ω (b)),butit createsconfusionwhendirectlycompar- A,B,C=0 14.62±0.08 -2.02±0.33 0 906 rot Northernhemisphere ing coefficients from different authors or obtained by different A,B,C 14.43±0.13 +0.8±1.5 -5.6±3.0 461 indicators. A,B=C 14.55±0.10 -1.35±0.35 -1.35±0.35 461 There are various methods to alleviate this problem. A,B,C=0 14.57±0.10 -1.92±0.52 0 461 Frequently C is set to zero since its effect is noticeable only Southernhemisphere at higherlatitudes. Thisis almosta standardpractise when ob- A,B,C 14.50±0.15 +0.7±1.4 -4.8±2.3 445 serving rotationby tracing sunspotsor sunspotgroupsbecause A,B=C 14.65±0.11 -1.39±0.28 -1.39±0.28 445 their positions do not extend to high latitudes (Howardetal. A,B,C=0 14.69±0.12 -2.14±0.45 0 445 1984; Balthasaretal. 1986b; Pulkkinen&Tuominen 1998; Brajsˇaetal.2002a;Sudaretal.2014). average values of ω in bins 5◦ wide in latitude, b, with their Anothermethodtoreducethecrosstalkproblemistosetthe rot respectiveerrors. C/Bratiotosomefixedvalue.Scherreretal.(1980)settheratio C/B = 1 whileUlrichetal. (1988),aftermeasuringthe covari- anceofBandC,settheratiotoC/B=1.0216295. 4. Discussion InFig.6weshowindividualmeasurementsofrotationalve- locities,ω ,withrespecttolatitude,b,asopencircles.Wein- InTable2weshowacomparisonofthesolardifferentialprofile rot (Eq.3)fromanumberofdifferentsources,includingtheresults dicate, with a solid line, the best fit to the data using a func- tional form given in Eq. 3. Coefficients of the fit are given in fromthispaper(Table1).Sincewefoundnostatisticallysignif- icantdifferencebetweenNorthernandSouthernhemispherewe Table 1. We also fitted the rotation profile for Northern and onlyincludetheresultsforbothhemispherescombined.Results Southernsolarhemisphereseparatelybecauseofpossibleasym- inTable2comefromawidevarietyofdifferenttechniques,trac- metry(cf.eg.Wo¨hletal.2010)andshowtheresultsinthesame table.Coefficient A showsa largervaluein the Southernhemi- ersandinstruments. sphere for all 3 fit functions. Jurdana-Sˇepic´etal. (2011) re- Snodgrass(1984) suggested that the rotation profile should beexpressedintermsofGegenbauerpolynomialssincetheyare portedthatcoefficientAislargerwhensolaractivityissmaller. orthogonalon the disk. This eliminates the cross-talk problem According to the SIDC data (SILSOWorldDataCenter 2011) between coefficients in Eq. 3. Using the expansion in terms of we cansee thatNorthernhemisphereismoreactivebothwhen Gegenbauerpolynomialssolarrotationprofilebecomes: lookingatthemonthlysmoothedmeansanddailysunspotdata, consistentwithJurdana-Sˇepic´etal.(2011).However,judgingby ω (b)=A T1(sinb)+B T1(sinb)+C T1(sinb), (4) rot G 0 G 2 G 4 the errorsof the coefficients,the differencebetween South and Northisstatisticallylowandthehypothesisthatthisisaresultof whereA ,B andC arecoefficientsofexpansionandT1(sinb), G G G 0 asymmetricsolaractivityneedstobeverifiedwithalargerdata T1(sinb) and T1(sinb) are Gegenbauerpolynomialsas defined 2 4 sample. bySnodgrass&Howard(1985)intheirequation(2). In Fig. 7 we show a comparison between different fitting AsSnodgrass&Howard(1985);Snodgrass&Ulrich(1990) techniques: A , B , C (solid line), A , B = C (dashed line) pointed out, the relationship between coefficients A, B and C andA, B,C =0(dottedline).Inthesamefigurewealsoshow from standard rotation profile (Eq. 3) and coefficients A , B G G 4 D.Sudaretal.:Stepstowardahighprecisionsolarrotationprofile:ResultsfromSDO/AIAcoronalbrightpointdata Table2.Comparisonwithsomeotherresults. Method/object timeperiod A[◦day−1] B[◦day−1] C[◦day−1] A [◦day−1] B [◦day−1] C [◦day−1] Ref G G G CBPs 1967 14.65±0.2 14.65 (1) CBPs 1994-1997 14.39±0.01 -1.91±0.10 -2.45±0.17 13.80 -0.709 -0.117 (2) CBPs 1998-1999 14.454±0.027 -2.22±0.07 -2.22±0.07 13.82 -0.740 -0.106 (3) CBPs 1998-2006 14.499±0.006 -2.54±0.06 -0.77±0.09 13.93 -0.611 -0.037 (4) CBPs 1-2Jan2011 14.47±0.10 +0.6±1.0 -4.7±1.7 14.19 -0.507 -0.224 (5) CBPs 1-2Jan2011 14.59±0.07 -1.35±0.21 -1.35±0.21 14.20 -0.450 -0.064 (5) CBPs 1-2Jan2011 14.62±0.08 -2.02±0.33 14.22 -0.404 (5) sunspotgroups 1853-1996 14.531±0.003 -2.75±0.05 13.98 -0.550 (6) sunspotgroups 1874-1976 14.551±0.006 -2.87±0.06 13.98 -0.574 (7) sunspotgroups 1878-2011 14.499±0.005 -2.64±0.05 13.97 -0.528 (8) sunspotgroups 1880-1976 14.37±0.01 -2.59±0.16 13.85 -0.518 (9) sunspots 1921-1982 14.522±0.004 -2.84±0.04 13.95 -0.568 (10) sunspotgroups 1921-1982 14.393±0.010 -2.95±0.09 13.80 -0.590 (10) Hαfilaments 1972-1987 14.45±0.15 -0.11±0.90 -3.69±0.90 14.11 -0.514 -0.176 (11) magneticfeatures 1967-1980 14.307±0.005 -1.98±0.06 -2.15±0.11 13.73 -0.683 -0.102 (12) magneticfeatures 1975-1991 14.42±0.02 -2.00±0.13 -2.09±0.15 13.84 -0.679 -0.100 (13) Doppler 1966-1968 13.76 -1.74 -2.19 13.22 -0.640 -0.104 (14) Doppler 1967-1984 14.05 -1.49 -2.61 13.53 -0.646 -0.124 (15) Helioseismology 1996 14.16 -1.63 -2.52 13.62 -0.662 -0.120 (16) Helioseismology Apr2002 14.04 -1.70 -2.49 13.49 -0.672 -0.119 (17) References. (1) Dupree&Henze (1972); (2) Hara (2009); (3) Brajsˇaetal. (2004); (4) Wo¨hletal. (2010); (5) this paper; (6) Pulkkinen&Tuominen (1998); (7) Balthasaretal. (1986b); (8) Sudaretal. (2014); (9) Brajsˇaetal. (2002a); (10) Howardetal. (1984) (11)Brajsˇaetal.(1991);(12)Snodgrass(1983);(13)Kommetal.(1993);(14)Howard&Harvey(1970);(15)Snodgrass(1984);(16)Schouetal. (1998);(17)Kommetal.(2004) thatwithAIA/SDOCBPdatawecouldreach50000datapoints 15 withonly4monthsofdataandachievesimilaraccuracyinsolar rotationprofilecoefficients.ThismeansthatwithAIA/SDOdata 14.5 itshouldbepossibletomeasurerotationprofileseveraltimesper yearandtrackpossiblechangesinsolarsurfacedifferentialrota- 14 tiondirectlywithaverysimpletracermethod.Thisisalsotrue formeridionalmotionandReynoldsstress,bothofwhichprob- ablyvaryoverthesolarcycle(cf.e.gSudaretal.2014). 13.5 13 5. SummaryandConclusion A, B, C 12.5 B=C Using 19.3nm data from the SDO/AIA instrument at 10 min C=0 cadence we have identified a large number of CBPs, resulting in 906 rotation velocity measurements. We obtained a fairly 12 0 10 20 30 40 50 60 70 good differential solar rotation profile in spite of the fact that weuseddataspanningonlytwodays.Thelargedensityofdata Fig.7. Comparison of three different fitting procedures for the pointsintimeisaresultofseveralfactors.Theinstrumentitself solar differential rotation profile. Average values of ω in 5◦ (SDO/AIA) has better spatial resolutionand is capable of high rot cadence(<5min).Forcomparison,SOHO/EIT28.4nmchannel binsinlatitude,b,arealsoshownwiththeirrespectiveerrors. hada cadenceoftwo imagesevery6 hours(Wo¨hletal. 2010). In this work, the high cadence enabled us to track and mea- sure velocities of short lived CBPs which couldn’tbe detected and CG from Eq. 4 is linear. Therefore, it is not necessary to or accurately tracked by the comparatively large time interval recalculatethefitsusingGegenbauerpolynomials,wecancom- betweensuccessiveimagesintheSOHO/EIT28.4nmchannel. pute A , B andC directlyfrom A, BandC. We usedthere- Coupled with the fact that short lived CBPs are more numer- G G G lationshipgivenin Snodgrass&Howard(1985)(theirequation ous than long lived ones (Brajsˇaetal. 2008), this resulted in a (4))sincethereseemstobeatypoforasimilarrelationshipfor very high density of data points in time. High data density ne- coefficientsC andC inSnodgrass&Ulrich(1990).InTable2 cessitatedtheuseofanautomaticproceduretodetectandtrack G wealsoshowthevaluesofcoefficientsA ,B andC . CBPs.Thesegmentationalgorithmusedhereprovedtobecom- G G G Ourrotationalprofileresultsareroughlyconsistentwithall pletely adequate for the task, as similar algorithms have else- the previously published work we surveyed (Table 2). The ac- where(McIntosh&Gurman2005;McIntoshetal.2014a,b). curacy of our coefficients is lower when compared with other Thesurfacerotationprofileanditsaccuracyobtainedbyhe- results,aconsequenceofourfairlysmallnumberofdatapoints lioseismologyisseldomgiveninaformsuitableforcomparison (n=906).Wo¨hletal.(2010),forexample,hadmorethan50000 with those obtained by tracer measurements. We can estimate data points spanning a time interval of 8 years. We have used from the number of published significant digits in the results data spanning only 2 days. It is therefore reasonable to expect Schouetal. (1998); Kommetal. (2004), given in Table 2, that 5 D.Sudaretal.:Stepstowardahighprecisionsolarrotationprofile:ResultsfromSDO/AIAcoronalbrightpointdata the accuracy is of the same order as better quality tracer mea- Brajsˇa,R.,Wo¨hl,H.,Vrsˇnak,B.,etal.2001,A&A,374,309 surements. Zaatrietal. (2009) publishedthe errorfor the coef- Brajsˇa,R.,Wo¨hl,H.,Vrsˇnak,B.,etal.2002b,A&A,392,329 ficient B(see Eq.3)andthevalueof0.01fromthatpaperisin Brajsˇa,R.,Wo¨hl,H.,Vrsˇnak,B.,etal.2004,A&A,414,707 Brajsˇa,R.,Wo¨hl,H.,Vrsˇnak,B.,etal.2008,CentralEuropeanAstrophysical agreementwithourestimateabove. Bulletin,32,165 It isquite conceivablethaterrorsin the differentialrotation Dorotovicˇ,I.,Shahamatnia,E.,Lorenc,M.,etal.2014,SunandGeosphere,9, profile coefficientswould drop significantly when more data is 81 used. From our analysis, we can expect to obtain 400-500 ve- Dupree,A.K.&Henze,Jr.,W.1972,Sol.Phys.,27,271 locity measurements per day from CBPs using SDO/AIA. A Duvall,Jr.,T.L.&Svalgaard,L.1978,Sol.Phys.,56,463 Erwin,E.H.,Coffey,H.E.,Denig,W.F.,etal.2013,Sol.Phys.,288,157 time interval of 4 months seems adequate to obtain 50000 ve- Hara,H.2009,ApJ,697,980 locity measurements, which should be sufficient to match the Howard,R.1984,ARA&A,22,131 most accurate results obtained by tracer methods (for example Howard,R.,Gilman,P.I.,&Gilman,P.A.1984,ApJ,283,373 Wo¨hletal.(2010)). Howard,R.&Harvey,J.1970,Sol.Phys.,12,23 Howe,R.2009,LivingReviewsinSolarPhysics,6,1 CBPs are also verygoodtracerssince theyextendto much Jurdana-Sˇepic´,R.,Brajsˇa,R.,Wo¨hl,H.,etal.2011,A&A,534,A17 higherlatitudesthansunspots.Theyarealsoquitenumerousin Karachik,N.,Pevtsov,A.A.,&Sattarov,I.2006,ApJ,642,562 all phases of the solar cycle while sunspotsare often absent in Kariyappa,R.2008,A&A,488,297 theminimumofthecycle. Komm,R.,Corbard,T.,Durney,B.R.,etal.2004,ApJ,605,554 Komm,R.W.,Howard,R.F.,&Harvey,J.W.1993,Sol.Phys.,145,1 This opens up an intriguing possibility of measuring the Kosovichev,A.G.,Schou,J.,Scherrer,P.H.,etal.1997,Sol.Phys.,170,43 solar rotation profile almost from one month to the next over Lemen,J.R.,Title,A.M.,Akin,D.J.,etal.2012,Sol.Phys.,275,17 an entire cycle. Such studies could provide new insight into Lorenc,M.,Rybansky´,M.,&Dorotovicˇ,I.2012,Sol.Phys.,281,611 mechanisms responsible for solar rotation. We already know Martens,P.C.H.,Attrill,G.D.R.,Davey,A.R.,etal.2012,Sol.Phys.,275,79 thatmeridionalmotionexhibitssomechangesduringthecourse McIntosh,S.W.&Gurman,J.B.2005,Sol.Phys.,228,285 McIntosh,S.W.,Wang,X.,Leamon,R.J.,etal.2014a,ApJ,792,12 of the solar cycle, and the same is probably true for Reynolds McIntosh,S.W.,Wang,X.,Leamon,R.J.,&Scherrer,P.H.2014b,ApJ,784, stress. Sudaretal. (2014) foundbyaveragingalmost150years L32 ofsunspotdatathatmeridionalmotionchangesslightlyoverthe Newton,H.W.&Nunn,M.L.1951,MNRAS,111,413 solar cycle and hinted that the Reynolds stresses are probably Olemskoy,S.V.&Kitchatinov,L.L.2005,AstronomyLetters,31,706 Ossendrijver,M.2003,A&ARev.,11,287 changing too. Here we have found a small asymmetry in rota- Pulkkinen,P.&Tuominen,I.1998,A&A,332,755 tion profile for two solar hemispheres and suggested that this Rosˇa,D.,Vrsˇnak,B.,&Bozˇic´,H.1995,HvarObservatoryBulletin,19,23 mightberelatedtodifferentsolaractivitylevelsinthetwohemi- Rosˇa,D.,Vrsˇnak,B.,Bozˇic´,H.,etal.1998,Sol.Phys.,179,237 spheres. This needsto be verified with a largerdataset though, Rozelot,J.-P.&Neiner,C.,eds.2009,LectureNotesinPhysics,BerlinSpringer asthedifferenceinrotationprofileswasoflowstatisticalsignif- Verlag,Vol.765,TheRotationofSunandStars Ru¨diger,G.&Hollerbach,R.2004,TheMagneticUniverse,byG.Ru¨digerand icance. R.Hollerbach.ISBN3-527-40409-0. WileyInterscience,2004. TheplannedSDOmissiondurationof5–10yearswillcover Scherrer,P.H.,Wilcox,J.M.,&Svalgaard,L.1980,ApJ,241,811 a large portion of the solar cycle which should result in enor- Schou,J.,Antia,H.M.,Basu,S.,etal.1998,ApJ,505,390 mous amountof velocity data to assist in the understandingof Schro¨ter,E.H.1985,Sol.Phys.,100,141 SILSO World Data Center. 2011, International Sunspot Number Monthly the nature and variation of solar rotation profile. Having more Bulletinandonlinecatalogue detailedtemporalresolutionanddirectresults(withouttheneed Skokic´,I.,Brajsˇa,R.,Rosˇa,D.,Hrzˇina,D.,&Wo¨hl,H.2014,Sol.Phys.,289, to average many solar cycles) could prove to be very informa- 1471 tive. Snodgrass,H.B.1983,ApJ,270,288 A time interval of 10 minutes between successive images Snodgrass,H.B.1984,Sol.Phys.,94,13 Snodgrass,H.B.&Howard,R.1985,Sol.Phys.,95,221 also offers a good opportunity to study the evolution of CBPs Snodgrass,H.B.&Ulrich,R.K.1990,ApJ,351,309 andpossibleeffectthismighthaveonthedetectedsurfaceveloc- Stark,D.&Wo¨hl,H.1981,A&A,93,241 ityfields.Forexample,Vrsˇnaketal.(2003)reportedthatlonger Stix,M.2004,Thesun:anintroduction,2nded.,byMichaelStix.Astronomy lastingCBPsshowdifferentresultsthanshort-livedCBPs. andastrophysicslibrary,Berlin:Springer,2004. ISBN:3540207414 Sudar,D.,Skokic´,I.,Ruzˇdjak,D.,Brajsˇa,R.,&Wo¨hl,H.2014,MNRAS,439, Based on the promising results here, we will use larger 2377 datasets to further exploit the potential of SDO/AIA CBP data Ulrich,R.K.,Boyden,J.E.,Webster,L.,Padilla,S.P.,&Snodgrass,H.B.1988, to determine meridional motions, rotation velocity residuals, Sol.Phys.,117,291 Reynoldsstressesandpropermotionsinsubsequentpapers. Vrsˇnak,B.,Brajsˇa,R.,Wo¨hl,H.,etal.2003,A&A,404,1117 Wilcox,J.M.&Howard,R.1970,Sol.Phys.,13,251 Acknowledgements. This work has received funding from the European Willis,D.M.,Coffey,H.E.,Henwood,R.,etal.2013a,Sol.Phys.,288,117 Commission FP7 project eHEROES (284461, 2012-2015) and SOLARNET Willis,D.M.,Henwood,R.,Wild,M.N.,etal.2013b,Sol.Phys.,288,141 project(312495,2013-2017)whichisanIntegratedInfrastructureInitiative(I3) Wo¨hl,H.,Brajsˇa,R.,Hanslmeier,A.,&Gissot,S.F.2010,A&A,520,A29 supported by FP7 Capacities Programme. It was also supported by Croatian Zaatri,A.,Wo¨hl,H.,Roth,M.,Corbard,T.,&Brajsˇa,R.2009,A&A,504,589 ScienceFoundationundertheproject6212SolarandStellarVariability.SSwas supported by NASA Grant NNX09AB03G to the Smithsonian Astrophysical Observatory and contract SP02H1701R from Lockheed-Martin to SAO. We wouldliketothankSDO/AIAscienceteamsforprovidingtheobservations.We wouldalsoliketothankVeroniqueDelouilleandAlexanderEngellforvaluable helpinpreparationofthiswork. References Balthasar,H.,Lustig,G.,Woehl,H.,&Stark,D.1986a,A&A,160,277 Balthasar,H.,Va´zquez,M.,&Wo¨hl,H.1986b,A&A,155,87 Beck,J.G.2000,Sol.Phys.,191,47 Brajsˇa, R., Vrsˇnak, B., Ruzˇdjak, V., Schroll, A., & Pohjolainen, S. 1991, Sol.Phys.,133,195 Brajsˇa,R.,Wo¨hl,H.,Vrsˇnak,B.,etal.2002a,Sol.Phys.,206,229 6

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