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Astronomy&Astrophysicsmanuscriptno.zhangetal2014 (cid:13)c ESO2015 January13,2015 LettertotheEditor Solar surface rotation: N-S asymmetry and recent speed-up L.Zhang1,2 ,K.Mursula1,andI.Usoskin1,3 1 ReSoLVECentreofExcellence,DepartmentofPhysics,UniversityofOulu,Finland,e-mail:[email protected] 2 KeyLaboratoryofSolarActivity,NationalAstronomicalObservatories,ChineseAcademyofSciences,Beijing,China 3 Sodankyla¨GeophysicalObservatory,UniversityofOulu,Finland Preprintonlineversion:January13,2015 5 ABSTRACT 1 0 Context.Therelationbetweensolarsurfacerotationandsunspotactivitystillremainsopen.Sunspotactivityhasdramaticallyreduced 2 insolarcycle24andseveralsolaractivityindicesandfluxmeasurementsexperiencedunprecedentedlylowlevelsduringthelastsolar n minimum. a Aims.Weaimtorevealthemomentaryvariationofsolarsurfacerotation,especiallyduringtherecentyearsofreducingsolaractivity. J Methods.Weusedadynamic,differentiallyrotatingreferencesystemtodeterminethebest-fitannualvaluesofthedifferentialrotation 2 parametersofactivelongitudesofsolarX-rayflaresandsunspotsin1977-2012. 1 Results.The evolution of rotation of solar active longitudes obtained with X-ray flares and with sunspots is very similar. Both hemispheres speed up since the late1990s, withthe southern hemisphere rotating slightlyfaster than the north. Earlier, in1980s, ] rotationinthenorthernhemispherewasconsiderablyfaster,butexperiencedamajordecreaseintheearly1990s.Ontheotherhand, R littlechangewasfoundinthesouthernrotationduringthesedecades.Thisledtoapositiveasymmetryinnorth-southrotationratein S theearlypartofthetimeintervalstudied. Conclusions.Therotationofbothhemispheres hasbeenspeedingupatroughly thesameratesincelate1990s, withthesouthern . h hemisphere rotating slightly faster than the north. This period coincides with the start of dramatic weakening of solar activity, as p observedinsunspotsandseveralothersolar,interplanetaryandgeomagneticparameters. - o Keywords.Sun:activelongitudes—flares—sunspots—rotation r t s a 1. Introduction convincingly that the ALs are persistent structures that sustain [ forseveraltensofyears,andpossiblyevenlonger.Alargefrac- 1 A number of solar activity indices and flux measurements tion of various forms of solar activity are produced by regions v reached abnormally low values during last solar minimum, whichare themselvesdifferentiallyrotating.Thepersistenceof 8 which was also exceptionally long. The activity level in the ALs is clearly demonstrated in this reference frame, and the 9 ongoing cycle 24 dramatically reduced compared to previous level of longitudinal asymmetry increases significantly higher 6 few solar cycles. The remarkably long and deep solar mini- than in any rigidly rotating system. Moreover, the stronger 2 mum and the weak cycle 24 have caused intensive attention formsofsolaractivityaremoreasymmetricallydistributedthan 0 . in the solar and space physics community (Jianetal. 2011; theweaker,morediffusiveforms(Zhangetal.2011a). 1 Clette&Lefe`vre 2012; Wangetal. 2009; Solomonetal. 2010, Solar surface rotation has been studied for a long time us- 0 2011;Cliver&Ling2011). ing various forms of solar activity (Balthasar&Wo¨hl 1980; 5 Here we study the changes in solar surface rotation during Pulkkinen&Tuominen 1998; Wangetal. 1988; Brajsˇaetal. 1 : thelastfewdecades,includingtheperiodofactivityweakening, 2000).Theseculardecelerationofsolarrotationwassuggested v by analyzing the rotation of solar active longitudes. Sunspots by Brajsˇaetal. (2006) and Lietal. (2014), while a secular ac- Xi andotherformsofsolarmagneticactivityarenotuniformlydis- celerationtrendwasfoundbyHeristchi&Mouradian(2009).A tributedin solar longitude,butare centeredaroundcertain lon- north-south(N-S)asymmetryinsolarrotationhasbeenreported r a gitude bands, which are called active longitudes (ALs). Active bymanyauthors(Brajsˇaetal.2000;Javaraiah&Komm1999). longitudes have been observed in several studies using differ- Veryrecently,bystudyingtherotationofALsofsunspotsinthe ent data bases (Temmeretal. 2006; Chenetal. 2011; Li 2011; lasttwelvesolarcyclesitwasfoundthatthelong-termevolution Murako¨zy&Ludmańy2012). ofthesolarsurfacerotationhasaquasi-periodicityabout80-90 Typically the ALs can be seen clearly only during a few years (Zhangetal. 2013). Rotation was also found to be N-S solar rotations. The longitudinal distribution of active regions asymmetric duringmost of this time period.The consistent N- becomes rather symmetric after a moderately long time inter- SasymmetryofsolarsurfacerotationwasconfirmedbySuzuki val, typically a few years. Accordingly, a simple way of cal- (2014). culating the longitudinaldistribution of solar activity using the The level of non-axisymmetrywas found to increase when Carringtonlongitudeoftheactiveregionsdoesnotyieldaper- using shorter fit lengths (Zhangetal. 2013). The average non- sistentlyinhomogeneousdistribution. axisymmetry of sunspots increased from 0.280 for the 5-year A few recent studies (Berdyugina&Usoskin 2003; runningmethodto0.464forthe1-yearmethod.Sincetherota- Usoskinetal. 2005; Zhangetal. 2011a,b) using a dynamic, tionratesvaryatatimescaleofoneyear,therotationparameters differentiallyrotatingcoordinatesystemhavebeenabletoshow obtainedfortheshorterintervalsrepresentthemomentaryrota- 1 L.Zhang,K.Mursula,andI.Usoskin:RotationofALsofsolarX-rayflares tionrate valuesofALsmoreclosely.Accordingly,theALsare We studied both the weighting method and no-weight moreaccuratelydeterminedfromshorterintervals. method.Theresultsobtainedwiththetwomethodsareverysim- However,veryshortintervalfitsofafewsolarrotationsonly ilar.Thus,onlytheresultsofno-weightmethodarepresentedin may lose the continuous evolution of the rotational phase and thispaper. therebycauseincreaseduncertaintywhendeterminingtherota- tionparameters.Thethree-yearfitintervallengthhasbeenfound tobetheoptimumlengthwhenbothsatisfactoryrepresentation andcontinuousevolutionaremet(Zhangetal.2013). 3. Results Herewestudythevariationofsolarrotationinrecentyears bystudyingtherotationparametersofALsofsolarX-rayflares 3.1.N-Sasymmetryandrecentspeed-upofsolarrotation in 1977-2012. To compare the results of flares with those of sunspots, we also study the rotation parameters determined by WehavecalculatedtheyearlyrotationratesΩ ofALsdefined 17 sunspotsforthecommonperiod.Wepresenttheyearlyrotation byformula(1)atthereferencelatitude17◦ forX-rayflaresand rates at the average latitude of flares and of sunspots, respec- sunspots, separately. The values of Ω are presented in Fig. 17 tively. 1 (left-hand panels for X-ray flares and right-hand panels for sunspots;toppanelsfornorthernhemisphereandbottompanels forsouthernhemisphere).Opencirclesdepicttheyearlyvalues 2. Dataandanalysismethod of Ω for the central year of each 3-year fit interval. The 1σ 17 errorforeachΩ valueiswithin ±0.015deg/daywhich istoo We study the solar X-ray flares of class-B and higher ob- 17 small to be shown in the figure. To demonstrate the long-term served by the NOAA GOES satellites during the period of variation pattern more clearly, the 11-point running mean (av- 1977-2012. Most X-ray flares were identified by simulta- erage over one solar cycle) is shown in the figure as red filled neous optical flare observations in the data prior to 2006. circles. However, a large fraction of the X-ray flares are without an accompanying optical flare since 2007. No X-ray flare is The rotation rates of Ω17 in the two hemispheres obtained observed together with an optical flare in 2011. Fortunately, with X-ray flares depict little correlation from 1977 until pre- the flare location can be identified during the whole time 2000. In the 1980s the north rotates faster than the south but periodusingtheNOAA/USAFsunspotregionnumber.Tokeep slows down in the 1990s even below the southernrate. During the treatment consistent throughout the entire study period, thistimethesouthernrotationrateremainsratherconstant.The we use the location of the sunspot region where the flare rotation rate has been speeding up in both hemispheres since occurred as the location of the flare. GOES X-ray flare data pre-2000,with thesouthernhemisphererotatingfasterthanthe (ftp://ftp.ngdc.noaa.gov/STP/space-weather/solar-data/solar-featurenso/srothla.rT-flhaerreost/axt-iroanyse/vgooleust/i)onobtainedforsunspotsdepictsano- provides the NOAA/USAF sunspot group number where tablysimilarpatternasflares.However,therecentrotationofthe the flare is observed, but no location information for northern hemisphere according to sunspots is somewhat faster the sunspot groups. The location information of sunspot than thataccordingto flares. Therefore,the hemisphericasym- groups can be retrieved from NOAA/USAF sunspot data metry in the rotation rate is smaller for sunspots. This is prob- (http://solarscience.msfc.nasa.gov/greenwch.shtml). For ably caused by a few large and flare productive active regions sunspots we study the NOAA/USAF sunspot groups for whichrotateratherslowlyinthenorthernhemisphere.Figure2 thecommonperiodofsolarflares. depictstheN-Sasymmetry((N-S)/(N+S))ofsolarrotationat the latitude of 17◦ obtained for X-ray flares (open circles) and The analysis method can be found in earlier studies sunspots(filledcircles).Theevolutionofthehemisphericasym- (Usoskinetal. 2005; Zhangetal. 2011a, 2013), and is briefly describedhere.Differentialrotationof the solar surfaceis usu- metry of solar rotation is quite similarly depicted by flares and sunspots:whiletheasymmetryhasbeenfairlyconstantandneg- allydescribedas ative since the late 1990s,it was stronglypositivein the 1980s anddecreasedrapidlyfrommid-1980stomid-1990s. Ω =Ω −Bsin2φ, (1) φ 0 The fact that the southern hemisphere rotates faster than whereΩ standsforthesidereal(allrotationratesaretakenhere the north can also be seen in the migration of ALs in the two φ to be sidereal) angular velocity at latitude φ, Ω (deg/day) de- hemispheres.Figure3demonstratesthemigrationofALsinthe 0 notestheequatorialangularvelocity,and B(deg/day)describes Carrington reference frame in the northern (top) and southern the differential rotation rate. The active longitudes are also as- (bottom) hemispheres in 2004. Black dots denote the B-flares, sumed to follow the same form of differential rotation at their trianglesC-flares,reddotsM-flaresandstarsX-flares.Thetwo ownspecificvaluesfortheparametersΩ andB. solid lines in each panel depict the migration of the two ALs 0 from the beginningto the end of 2004.The dotted lines on ei- Assuming that the two ALs are at Carrington longitudeΛ and Λ ±180◦ and follow the differentialrotation of solar sur0- thersideofthetwosolidALlinesdenotethe90◦(±45◦)regions 0 aroundthetwoALs. face, one can measure the distance between the longitude of a flare or sunspot group and the nearest AL. The merit func- One can see that in the northern hemisphere the longitudi- tioncanbedefinedasthemeansquareofthesedistanceseither nal location of one AL increases graduallyfrom 120◦ to 180◦- withoutanyweightingonflaresorsunspots(Zhangetal.2011a) 190◦ intheCarringtonreferenceframein2004yieldingtheto- or by weighting the flares with their normalized peak intensity tal increase of 60-70◦ in one year, while in the southern hemi- andthesunspotswiththeirnormalizedarea.Themeritfunction spherethetotalincreaseinthisyearisabout160◦-170◦.Thisin- ǫ(Λ ,Ω ,B)dependsonthethreeparametersΛ ,Ω ,and Bof dicatesthatbothhemispheresrotateconsistentlyfasterthanthe 01 0 0 0 theactivelongitudes.We usetheleast-squaremethodtosearch Carringtonreferenceframe(asshowninFig.1)andthesouthern forthebest-fitparameters.The3-yearrunningfitintervalisused hemisphererotatessignificantlyfasterthanthenorth(asdepicted here,yieldingtherotationparametersforthemiddleyear. bythenegativevaluesinFig.2). 2 L.Zhang,K.Mursula,andI.Usoskin:RotationofALsofsolarX-rayflares Fig.1.Left-handpanels:YearlyvaluesofΩ inthenorth(top)andsouth(bottom)forX-rayflares.Opencirclesstandfortheyearly 17 best-fitvaluesand red filled circles demonstratethe 11-pointrunningmeanvalues. Solid horizontalline denotesthe averageΩ 17 overtheentirestudyperiod,anddashedlinethesiderealCarringtonrotationrate.Right-handpanels:thesameasintheleft-hand butforsunspots. axisymmetryofflaresinthesouthernhemisphereincreasessys- tematically with flare class from 0.422 (71.1%) of B-flares to 0.679 (83.9%) of X-flares. In the northern hemisphere, the in- creaseofnon-axisymmetrywithflareclassislessdramaticand lesssystematic.Thenon-axisymmetry0.488(74.4%)ofX-flares isslightlylowerthanthenon-axisymmetry0.506(75.3%)ofM- flares. This indicates that the rotation rates of these active re- gionsinthenorthernhemispherethatproduceX-classflaresand those that produce other flares of other classes have somewhat largerdifferencesthaninthesouthernhemisphere.Allthenon- axisymmetryvaluesofflaresinbothhemispheresarelargerthan the non-axisymmetryof sunspot.Thisis in agreementwith the earlierfindingthatmorepowerfulsolaractivityattendstoappear closertothetwoALs(Zhangetal.2011a,b). Fig.2.YearlyvaluesofN-Sasymmetryof solar rotationat latitude 17◦ obtained for X-ray flares (open circles) and sunspots (filledcircles). 4. Discussionandconclusion The relationship between solar rotation and sunspot activity 3.2.Non-axisymmetryofALs is a foundamental problem. It is known that sunspot activity presents a secular increase during the 20th century leading to Wedefinethemeasureofnon-axisymmetryΓasfollows the so-called Modern Maximum (MM) (Solankietal. 2004). N −N Brajsˇaetal. (2006) and Kitchatinovetal. (1999) found a sec- Γ= 1 2, (2) ular decelerationof solar rotation,implyinga negativecorrela- N +N 1 2 tion between solar rotation rate and sunspot activity. However, whereN andN denotethenumberofsolarflaresthatappeared a secular acceleration in solar rotation has also been pro- 1 2 within(N )oroutside(N )thetwoALregions,whicharetaken posed(Heristchi&Mouradian2009;Lietal. 2014).Moreover, 1 2 hereasthetwo90◦-longitudebands,depictedinFig.3. Ribes&Nesme-Ribes(1993)claimedthatthe solarsurfacero- The averaged yearly values of Γ for sunspots and for each tationat20◦ latitudewas6%slowerduringMaunderMinimum flare class are listed in Table 1 (online). The asymmetries for thaninmoderntimes.Theselatterstudiessuggestthatthecorre- the different flare classes were calculated using the same rota- lationbetweensolarrotationrateandsunspotactivityispositive. tionparametersofthe(common)ALs.Thecorrespondingfrac- We find that the northern and southern hemispheres both tions of flares in the ALs are also listed in Table 1. The non- have been speeding up since late 1990s - the ending phase of 3 L.Zhang,K.Mursula,andI.Usoskin:RotationofALsofsolarX-rayflares The recent speed-up of solar rotation coincided with the breakdown of the mutual relationships among several solar activity and geo-activity indices. A large diver- gence was observed at about 2001-2002 between the sunspot numbers and several UV/EUV flux proxies, including the F10.7 radio flux (Floydetal. 2005; Lefe`vre&Clette 2011; Lukianova&Mursula 2011; Kane 2003; Leanetal. 2011; Liuetal. 2011). These changes can be understood in terms of the changesin sunspotdistribution and the recent vanishingof smallsunspots(Clette&Lefe`vre2012). Tosummarize,wefindthatbothsolarhemisphereshavein- creasedtheirrotationratesincethelate1990suntilrecentyears. Also,therateofincreaseisfairlysimilarinthetwohemispheres so that the hemispheric asymmetry in rotation rates has been roughly constant, with southern rotation being slightly faster. Thisperiodof recentsolar speed-upcoincideswith the decline oftheModernMaximum(periodofexceptionallyhighactivity duringmostofthe20thcentury),whichisevidencedbytheover- allreductionofsunspotactivity,vanishingofsmallsunspots,de- creasingsolarwinddensityandmagneticfieldetc.Wealsonote thatsimilar,althoughshorterandlesssignificantperiodsofboth hemispheresspeedingupwereonlyfoundduringthetwolowest solarcycles12and14atthe turnof the19thand20thcentury. These results strongly suggest that there is, at least momentar- ily,anegativecorrelationbetweensolarsurfacerotationrateand sunspot activity. However, the causes to these results and their possible implications to, e.g., solar dynamo, remain for subse- quentstudiestobesolved. Fig.3. Migration of ALs in northern (top) and southern hemi- Acknowledgements. Theresearchleadingtotheseresultshasreceivedfunding spheres(bottom)in2004.BlackdotsstandforB-flares,triangles fromtheEuropeanCommission’sSeventhFrameworkProgramme(FP7/2007- 2013)underthegrantagreementeHeroes(projectn◦284461,www.eheroes.eu). C-flares,reddotsM-flaresandstarsX-flares.Thetwosolidlines Wealsoacknowledge thefinancial supportbytheAcademyofFinlandtothe depict the migration of the two ALs from the beginningto the ReSoLVECentreofExcellence(projectno.272157). endof2004with45◦ extensionsoneachsidedenotedbydotted lines. References MM. The activity level in cycle 23 significantly reduced com- Balthasar,H.&Wo¨hl,H.1980,A&A,92,111 pared with other cycles during the space era. The recent mini- Berdyugina,S.V.&Usoskin,I.G.2003,A&A,405,1121 Brajsˇa,R.,Ruzˇdjak,D.,&Wo¨hl,H.2006,Sol.Phys.,237,365 mum between cycles 23-24 lasted exceptionally long, and var- Brajsˇa,R.,Ruzˇdjak,V.,Vrsˇnak,B.,etal.2000,Sol.Phys.,196,279 ious solar activity measurements reached abnormally low val- Chen,A.Q.,Wang,J.X.,Li,J.W.,Feynman,J.,&Zhang,J.2011,A&A,534, ues. Solar wind density and the heliosphericmagnetic field in- A47 tensityreducedbynearly1/3,bothreachinguniquelylowlevels Clette,F.&Lefe`vre,L.2012,JournalofSpaceWeatherandSpaceClimate,2, A260000 sincethemeasuredtimeofabout50years(Cliver&Ling2011; Cliver,E.W.&Ling,A.G.2011,Sol.Phys.,274,285 Jianetal. 2011). The sunspotactivity in cycle 24 is even more Floyd,L.,Newmark,J.,Cook,J.,Herring,L.,&McMullin,D.2005,Journalof dramaticallyreducedandmatchesthelowlevelinthebeginning AtmosphericandSolar-TerrestrialPhysics,67,3 of the 20th century. This supports the negative correlation be- Heristchi,D.&Mouradian,Z.2009,A&A,497,835 tweensolarrotationrateandsunspotactivity. Javaraiah,J.&Komm,R.W.1999,Sol.Phys.,184,41 Jian,L.K.,Russell,C.T.,&Luhmann,J.G.2011,Sol.Phys.,274,321 Therecentspeed-upofsolarrotationwasalso foundin our Kane,R.P.2003,JournalofGeophysicalResearch(SpacePhysics),108,1455 earlier study of sunspots. Zhangetal. 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K., Usoskin, I. G., Kromer, B., Schu¨ssler, M., & Beer, J. 2004, dayswereobservedwithoutsunspots.Duringtheminimumbe- Nature,431,1084 tweencycles14-15morethanonethousanddayswererecorded Solomon, S. C.,Qian, L.,Didkovsky, L.V.,Viereck, R. A.,&Woods, T.N. asspotless(Clette&Lefe`vre2012). 2011,JournalofGeophysicalResearch(SpacePhysics),116,0 4 L.Zhang,K.Mursula,andI.Usoskin:RotationofALsofsolarX-rayflares Table1.Averagenon-axisymmetriesofsunspotsandthediffer- ent flare classes obtained with the best-fit parameters of ALs. PercentageofflaresandsunspotswithinthetwoALs,N /(N + 1 1 N ),aregiveninparenthesis. 2 north south Γ Γ sunspots 0.313(65.7%) 0.330(66.5%) B-flares 0.422(71.1%) 0.422(71.1%) C-flares 0.474(73.7%) 0.425(71.2%) M-flares 0.506(75.3%) 0.572(78.6%) X-flares 0.488(74.4%) 0.679(83.9%) Solomon,S.C.,Woods,T.N.,Didkovsky,L.V.,Emmert,J.T.,&Qian,L.2010, Geophys.Res.Lett.,37,16103 Suzuki,M.2014,Sol.Phys.,289,4021 Temmer, M., Veronig, A., Ryba´k, J., Brajsˇa, R., & Hanslmeier, A. 2006, AdvancesinSpaceResearch,38,886 Usoskin,I.G.,Berdyugina,S.V.,&Poutanen,J.2005,A&A,441,347 Wang,Y.-M.,Robbrecht,E.,&Sheeley,Jr.,N.R.2009,ApJ,707,1372 Wang,Y.-M.,Sheeley,Jr.,N.R.,Nash,A.G.,&Shampine,L.R.1988,ApJ, 327,427 Zhang,L.,Mursula,K.,&Usoskin,I.2013,A&A,552,A84 Zhang,L.,Mursula,K.,Usoskin,I.,&Wang,H.2011a,JournalofAtmospheric andSolar-TerrestrialPhysics,73,258 Zhang,L.,Mursula,K.,Usoskin,I.,&Wang,H.2011b,A&A,529,A23 5