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

4.8 MB·English

by  Davor Sudar

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
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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
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changing too. Here we have found a small asymmetry in rota-
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the nature and variation of solar rotation profile. Having more
Bulletinandonlinecatalogue
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Skokic´,I.,Brajsˇa,R.,Rosˇa,D.,Hrzˇina,D.,&Wo¨hl,H.2014,Sol.Phys.,289,
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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
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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
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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.
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