198 9ApJ. . .337. .568L from strong“magnetizedstreams” whichlastforseveralrota- average flareoccurrencerate, described byBai(1987a).and (1987), equivalenttothesuperactive zonesofhigherthan ferent rates.Ichimotaetal. (1985) suggestthatitoriginates charts. Thesestreamsare, according toBaiandSturrock active regionsorCarringtonlongitudes,rotatingat dif- period. BogartandBai(1985)attributeittotheinteraction of with sphericalharmonicsl=2and3maygenerate this tions andareeasilyrecognized inmagneticfieldsynoptic ling ofactivebandsgeneratedbythesolar0-modeoscillations of solarorigin,theassociatedphysicalmechanismsare still especially thosewithlargesunspots. being debated.Wolff(1983)hassuggestedthatrotationcoup- predominantly, butnotexclusively,withactivecomplexes, stronger incycle21than20andwhichisassociated emerged isofaperiodbetween152and158dayswhich was and ground-basedmicrowaveHadata(Bogart Bai analysis ofSMMandGOESsatellitedata(Riegeretal.1984; Kiplinger, Dennis,andOrwig,1984;BaiSturrock1987) which measuredirectly,orinfer,flareoccurrence.Fromthe nature ofthiscyclehavecontinuedtoutilize,primarily,records 1985; Ichimotaetal.1985),thepicturewhichhasthus far days (~75nHz)intheoccurrenceofflares,firstreportedby Rieger etal.(1984).Subsequenteffortscharacterizingthe the mechanismsofsolarvariability. data haslongbeenofinterest,forthecluesthismayprovideto periods, otherthanat11yrand27days,insolarobservational at Earthbysolarrotation.Establishingtheexistenceofreal the latterreflectingmodulationimposedonsolarflux the formerbeingrelatedtosolarmagneticactivitycycle, periods ofapproximately11yrand27daysiswellestablished, The AstrophysicalJournal,337:568-578,1989February1 © 1989.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. While itisgenerallyagreedthatthe155dayperiodindeed Recently, attentionhasfocusedontheperiodicitynear155 That variationsinthesolaroutputmeasuredatEarthhave Subject headings:Sun:activity—flaresradioradiationsunspots period. However,thisperiodisaprominentfeatureonlyinsolarcycle21. span eachhasapeaknear323days,whichsupportsprevioussuggestionsthatthis,too,mayberealsolar tunction, 10.7cmradioflux,sunspotnumber,andplageindexdailydataduringtheentirethree-cycletime 21, thoughitisweakerincycle20thantheothertwocycles.Theperiodogramofsunspotblocking m thesunspotblockingfunctionand10.7cmradiofluxduringeachofthreesolarcycles,19,20 areas, suchasinsunspots,butnotwheretheyaremoredispersed,plages.Powerat155daysispresent suggests thatitisassociatedwiththoseregionsontheSunwheremagneticfieldsareconcentratedintosmall index. Thisindicatesthatthe155daysolarperiodicityisnotsimplyafeatureofflareactivityaloneand present inthesunspotblockingfunction,10.7cmradioflux,andnumber,butnotplage confirm thatapenodicitynear155days,originallydetectedintheoccurrencerateofmajorsolarflaresisalso © American Astronomical Society • Provided by the NASA Astrophysics Data System Penodogram analysesoftimeseriesground-basedsolarobservationsduringthepastthreecycles I. INTRODUCTION INTERMEDIATE-TERM SOLARPERIODICITIES:100-500DAYS E. O.HulburtCenterforSpaceResearch,NavalResearchLaboratory Received 1987July14;accepted1988June23 Applied ResearchCorporation G. E.Brueckner ABSTRACT J. L.Lean 568 AND area andnumbersofsunspot groupsfrom1969to1986, solar diameterrecordduring cycle21.Intheiranalysisofthe peak isalsopresentinDelarche etal.'spowerspectrumofthe (36 nHz)intheZürichsunspot numbervariations,andthis Laclare, andSadsaoud(1985) detectedapeaknear320days based solaractivitydata.Both Wolff(1983)andDelarche, considerable nonoscillatorypower(Hudson1987),although their existencehasbeenspeculated fromtheanalysisofground because ofthebrevitytimeseriesandpresence of intermediate-term solarperiodicitieslongerthanat155days, optic magneticdata. that displayactiveregionsclearly,suchastheKittPeak syn- according toHudson(1987),isitstrikinginthesynopticdata analysis ofthedaily10.7cmradiofluxfrom1947to1978.Nor, Kestevan (1981)makenomentionofsuchaperiodintheir sunspot numbersduringcycle21.However,Hughes and observed thisperiodinthesolardiameterrecordandZürich among amultitudeofpeakswithsimilarpower,peaknear sunspot numbersfrom1874to1979Wolff(1983)diddetect, the flarerecords.Inpowerspectrumofmonthlymean indicators ofsolaractivityis,todate,lessconvincinglythanin 155 days.Delarche,Laclare,andSadsaoud(1985) also which, itwasnoted,maybeaharmonicofthatat155days. near 155days.Rather,thedominantperiodicitywasat51days prehensive flareindex(CFI>5),didnotexhibitaperiodicity occurrence ofmajorflares,asdeterminedfromthecom- report byBai(1987b)that,duringcycle19,theglobal Bai’s superactivezones.Additionallyconfusingistherecent characteristic offlaresproducedbothinsideandoutside non, occurringindependentlyinbothsolarhemispheres,and slightly differentratesandclaimthatitisaglobalphenome- period isduetotheinteractionofactivezonesrotatingat Sturrock (1987)disagreethatthe155dayflareoccurrence There is,generally,evenlessconfidenceinthereality of Evidence forarealsolarperiodicitynear155daysinother 198 9ApJ. . .337. .568L which maycorrespondtothe320dayperiodicity.Theyalso for exampleat36nHz,maybepartlyartifactsofrunningmean reported a17month(~510day)periodicity.Hudson(1987), Akioka etal(1987)detectedapeaknear12solarrotations, however, cautionsthatpowerspectrumpeaksatlongperiods, used inWolffsanalysis. smoothing andnormalizationofthetimeseries,suchaswere ground-based recordsofsolaractivityduringthepastthree period insolarflareoccurrenceis,asspeculatedbyBogartand index. Ourprimaryfocusistheperiodnear155days.Ifthis solar cycles.Weanalyzethesunspotblockingfunction, mena suchassunspots,plages,andhotcoronalloops,thenthe form anactivitycomplexmanifestavarietyofsolarpheno- based solaractivitytimeseries,unlessitisafeatureofflare then itshouldbedetectableinatleastsomeoftheground- Bai (1985),associatedwithcomplexesofsolaractiveregions, phenomena mayyieldphysicalinsightastoitsorigin. detection ofthiscycleinoneorothertheseactiveregion activity alone.Furthermore,sincethemagneticfieldswhich indicators givegreaterconfidencethatthecorresponding periods between100and500days.Presumably,peakswhich cycles maybeintrinsicsolarvariability,ratherthanartifactsof are commontothepowerspectraofavarietysolaractivity solar periodicitiesotherthanat155days,concentratingon 10.7 cmradioflux,theZürichsunspotnumber,andplage the analysis. blocking function(P),the10.7cmradioflux(F Zürich sunspotnumber(R)andtheCanKplageindex(PJ), light onthesolardiskandisthusaproxyforregionswhere portional totheprojectedareaofsunspotsobservedinwhite reflects differentsolaractiveregionphenomena.Pispro- index reflectstheweaker,averagemagneticfieldsassociated more ofthesolardiskarea,andaredispersedlonger with chromosphericCanKemissionfromplages,whichcover spatially averagedmagneticfieldisverystrong.Theplage lived thansunspots.The10.7cmfluxisemittedfromtheupper Tapping (1987),solarcentimetricemissioncomprisestwo chromosphere-transition regionandcorona.Accordingto primary components:gyroemissionfromcompact,bright more orlesscoincidewithplages(seealsoLang,Willson, and from fainter,morediffuse“halo”regions,which “ cores,”associatedwithsunspots,andthermalbremsstrahlung which weusehereareactuallycorrectedforflare-related Gaizauskas, 1983).Notethatthedaily10.7cmradiofluxdata bursts. TheZürichsunspotnumberisthetraditionalindicator s10 interpret itsvariationsphysicallybecauseitisanumericalcon- z of theelevenyearsolaractivitycycle.Itis,however,difficult to s the numberofindividualsunspots.Weincludeitin our struction, equaltotentimesthenumberofsunspotgroups plus periodicities. analyzed previouslyforthepresenceofintermediate-termsolar analysis because,asdiscussedabove,thisrecordhasbeen and 21,fromtheWorldData CenteroftheNationalOceanic tional dataareavailableforthe pastthreesolarcycles,19,20, communication). Thedailydata from1954to1984areshown data after1982whichwere providedbyD.Hoyt(private and AtmosphericAdministration (WDC/NOAA),exceptforP s In thispaperweinvestigatetheexistenceofperiodicitiesin We alsoexamine,intheground-baseddata,realityof Each ofthefourrecordssolarvariability,sunspot Daily valuesofeachthese fourdifferentsolarobserva- © American Astronomical Society • Provided by the NASA Astrophysics Data System II. SOLARACTIVITYTIMESERIES INTERMEDIATE-TERM SOLARPERIODICITIES in Figure1.Overthistotaltimeintervalof11323days,data cients whicharegiveninTable1forboththeraw,dailydata, demonstrated bythehighvaluesoflinearregressioncoeffi- relation betweeneachofthesetimeseriesiswellknownand 98.6%, 92.9%,and77.5%ofalldays.Thatthereisalinear are availableforP,F.7RandPIon,respectively,92.0%, from thedailyvalues.Noneoffourtimeseriesare, however, identical(see,forexample,Donnelly,Hinteregger, and thedatadetrendedbyremovinga365dayrunningmean and Heath1986). using, first,datafortheentiretimespanofthreesolarcycles, procedures isgiveninthissection,andtheresultsof and thenthedataforeachseparatecycle.Anoverviewof analysis aregivenin§IV. unevenly sampleddata.Missingdatainthetimeseriesofdaily on Scargle(1982),tocalculatethemodifiedperiodogramfor points arefilledinorthedatabinnedintowidertime tions directlyfromthetimeseries,unlessmissingdata solar observationsshowninFigure1precludetheuseof may, however,altertheperceivedfrequencyandsignificanceof intervals. Interpolatingmissingdatapointsandbinning Fast FourierTransformforcalculatingspectraldensityfunc- unevenly sampledobservationsontoanevenlygrid is calculatedat100equallyspacedfrequenciesoverthetwo daily data,transformedtozero-meantimeseries,butwithout a periodicsignal(HorneandBahúnas1986). s10z variance ofthedataset.Wethenestimateprobabilitythat and 22-59nHz(-200-500days),normalizedtothetotal separate frequencyintervals,55-129nHz(~100-200days) smoothing, binningorremovinglong-termtrends.Thepower (FAP) describedbyHorneandBahúnas(1986). a peakinthepowerspectrumoccursassumingthatdata leakage arisingfromthespacingofdataandfinite are pure(Gaussian)noisebyusingthefalsealarmprobability cient forestablishingwhetherornotastrongpeakinperiod- length ofthetimeseries),FAPcriterion,alone,isinsuffi- other phenomenanotpresentinGaussiannoise(e.g.,spectral tapering 25%ofthedataatendstimeinterval by spurious peaksbyrecomputingtheperiodogramafter (1) ogram isindeedarealperiodicityinthetimeseries.Wetestfor removing long-termtrendsfromthetimeseriesbysubtracting applying asplitbellcosinewindow(Bloomfield1976), (2) We usethetechniqueofHorneandBahúnas(1986),based Initially, theperiodogramsaredeterminedfromraw Since peaksinaperiodogrammayarisefromaliasingor Each ofthefourdatasetsareanalyzedforperiodicities series. Thevaluesbelowthediagonal weredeterminedfrom tracted fromtherawdailyvalues. 7873 daysofmutualdata,witha365 dayrunningmeansub- 8015 dayswhendataareavaiablefor eachofthefourtime / 0.8310.950.87 P 10.860.80 PI 0.59 0.68 1 R \0.77 0.84 10.87 10 7 z Linear RegressionCoefficientsforP,FRand sl01z Note.—Values abovethediagonalwere determinedfrom PI duringSolarCycles19,20,and21 III. PERIODOGRAMANALYSIS TABLE 1 P Flo.i&ZRI s 569 198 9ApJ. . .337. .568L period ofinterest.Additionally, weremove,priortothisfilter- equal toalllargepeaksinthe periodogramotherthanthe Horne andBahúnas1986) (2)sinecurveshavingperiods of interest(Ferraz-Mello1981; DelarcheandScherrer1983; removing fromthetimeseries (1)asinecurvewiththeperiod the windowfunction,werecalculate theperiodogramafter result ofaliasinganotherperiodinthepowerspectrum by gested byastrongpeakintheperiodogramisnotsimply the and noisecharacteristics.Finally,totestthataperiod sug- coherent signalsinthetimesseries,butpreserveswindow procedure (Delarche,Laclare,andSadsaoud1985),destroys and (4)randomizingthedataontimegrid.Thislatter the dailydataintofirstdifferences(JenkinsandWatts1968), from thedailyvaluea365dayrunningmean,(3)transforming 570 © American Astronomical Society • Provided by the NASA Astrophysics Data System a. <0 v i. — o >- o 2 c 0.1 0.2 0.3 0.4 54 56586062646668707274767880828486 0 - cl)PI LEAN ANDBRUECKNER 1—I—I—T an near 155,270,287,and323days, andweaker,butstillpromi- 7^10.7’ dRareremarkably similar.Eachhasstrongpeaks this figurethattheoverallshape oftheperiodogramsP, cation exceptconversiontoa zeromeanseries.Itisevidentin days, usingthedailydatafrom theWDCwithoutanymodifi- sets inFigure1,calculatedover atotaltimeintervalof11323 z moving-average detrendedtimeseries. s the recalculatedperiodogramwiththatfor365 day ing, theperiodcorrespondingto11yrcycleandcompare YEAR Figure 2showstheperiodograms foreachofthefourdata ,wbing ” *•“—•»- a) SolarCycles19,20,and21,Combined IV. RESULTS Vol. 337 198 9ApJ. . .337. .568L No. 1,1989 periods, 323days,isthereastrongpeakinthePIperiodogram, nent, peaksnear116and162days.Atonlyoneofthese which has,overall,adifferentshapefromtheotherperiodo- grams. estimate theprobabilitythatpeaksinperiodograms in number ofindependentfrequencies,Nsampledbytheperi- measurements, N,inthetimeseries.Usingtheirformula, the relationship forderivingNifromthenumberofindependent odogram. HorneandBaliunas(1986)provideanempirical Figure 2areduetochancealone,itisnecessaryestimate the height for1%probabilityisshownbythedashedlines in a peakofheight16,and10%for14.The FAP fortheperiodogramsinFigure2isapproximately1% for caused bynoisealoneis,according totheFAP,lessthan1%. of thesixpeaksat115,155,162,270,287,and323days is Figure 2.ThusforthePperiodogram,chancethatany one is, inthePIperiodogram Figure2d,asmallpeaknear cannot reliablydistinguishthis peakfromnoise.Wenotethat at 155and323daysaredueto noiseisalsolessthan1%.There For theFandRperiodograms, thechancethatpeaks because ofmissingdatainthe timeseries,iV,maybesmaller i9 0 155 days,butsinceforapeak heightof8,theFAPis1,we s 10z In ordertocalculatethefalsealarmprobability(FAP) to © American Astronomical Society • Provided by the NASA Astrophysics Data System INTERMEDIATE-TERM SOLARPERIODICITIES PERIOD (days) Fig. 2.—Periodogramsofthedailydatain1 modifying thetimeseriesasdescribedin§III.Thisfigure the strongpeaksareduetonoisealone. than ourestimatedvalue,inwhichcaseitisevenlesslikelythat demonstrates thatneithertaperingthetimeseries,norremov- ing a365dayrunningmean,norfirstdifferencingcauses the peak near155daystobeeliminated,norcausesitsperiod be shifted. Neitheraretheotherstrongpeaksnear115,162, 270, is, however,evidentinFigures3band3cthat,althoughall six nificantly bythevariousmodificationstoPtimeseries. It 287, and323daysremoved,noraretheirperiodsaltered sig- peaks intheoriginalperiodogram(Fig.2a)arepresent,power enhanced anddiminished.Thisisbecausewhenatimeseries is at thelongerperiods,200-500days,hasbeen,respectively, encing atimeseriesfiltersoutlowfrequencies(i.e.,long transformed itsfrequencycontentandthetotalvariance are altered (see,forexample,Gottman1981).Inparticular,differ- encing detrending,respectively, isconfirmedbysimulations is indeedaconsequenceofthe movingaverageandfirstdiffer- That thisredistributionofpower, evidentinFigures3band3c, periods) andamplifieshigh frequencies (i.e.,shortperiods). known amplitudes. using atesttimesserieshaving sinusoidalperiodicitiesof s Figure 3showstheperiodogramsforP,recalculatedafter s PERIOD (days) 571 198 9ApJ. . .337. .568L peak forwhichtheFAPisless than1,butbothhavingsmall similar tothatoftherandomized Pdata,neitherhavingany series arerandomized,therecalculated periodogramsarequite than intheoriginalperiodogram. WhentheFandRtime in Figure3.However,afterdetrendingtheRtimeseries, the recalculatedperiodograms, theyaremuchlessprominent although thepeaksnear155 and 162daysarestillpresentin lated aftermodifyingtheFdataarequitesimilartothose R timeseries.Althoughnotshown,theperiodogramsrecalcu- reflect anannualfeatureinthedatasampling. domizations ofthetimeseries;peaknear350days may persist intheperiodogramsrecalculatedforthreedifferent ran- The small,broadpeaksnear160and350daysinFigure 3d periodogram correspondtocoherentsignalsinthetimeseries. s periodogram oftherandomizeddata,whichfurthersubstan- tiates thelikelihoodthatprimarypeaksinoriginal According totheFAP,therearenosignicantpeaksin the 10z z the Pdataonitstimegrid,canbecompareddirectlywith that oftheoriginaltimeseries,andsameFAPisapplicable. 10 and thetimegridofrandomizedseriesisidenticalto periodogram oftherawdailydata(Fig.2a),sincevariance z removing thelong-termtrendbysubtractinga365dayrunningmean,(c)differencingadjacentdatapoints,and(d)randomizingondaily timegrid. s 572 We alsotapered,detrendedandrandomizedtheF The periodograminFigure3d,calculatedafterrandomizing 10 Fig. 3.—Comparisonofperiodogramsforthedailysunspotblockingfunctioncalculatedafter(a)applyingasplitbellcosinetaperto25%time interval,(b) © American Astronomical Society • Provided by the NASA Astrophysics Data System 100 120140160180200 115d PERIOD (days) 155d LEAN ANDBRUECKNER filtering boththeFandR timeseries.Theseresultsfurther ing allotherpeaks(including a26daypeakcorrespondingto solar rotationmodulation).Similar resultswereobtainedfrom is affectedwhentheperiodograms arerecalculatedafterfilter- 287, and323days.Ontheother hand,noneofthesefivepeaks that inthisperiodogramonly noiseremainsat155,162,270, than 8.Sinceforapeakheight of8,theFAPequals1,itisclear power attheperiodofeachcyclewhichwasremovedis less gram calculatedafterremovingallsixcycles(Fig.4/), the (Fig. 3b);asexpected,theyarequitesimilar.Intheperiodo- day runningmeanwhicheffectivelyremovesthe11yrcycle culated afterdetrendingthetimeseriesbysubtractinga 365 10z only the11yrcycle(Fig.4a)canbecomparedwiththatrecal- and 323days.Theperiodogramrecalculatedafterremoving activity cycle),then,successively,cyclesat155,162,270, 287, recalculated afterfiltering,first,acycleat4085days(the11 yr cycles fromtherawPtimeseries.Theperiodogramswere spurious. having aFAPoflessthan1%,indicatingthatthepeaknear ized PItimeseriesthepeaknear350daysismuchlarger, 350 daysintheperiodogramofPIdata(Fig.2d)maybe broad peaksnear350days.Intheperiodogramofrandom- s Figure 4illustratestheiterativeprocessofremovingspecific PERIOD (days) 300 400 198 9ApJ. . .337. .568L (6) twoperiodsat4085and155days,(c)three4085,155, 162 days,(d)fourperiodsat4085,155,162,and270(e)five4085,155,162, 270, and287days,(/)sixperiodsat4085,155,162,270,287,323days. Fig 4.—Comparisonofperiodogramsforthedailysunspotblockingfunction datainFig.1calculatedafterremoving(a)aperiodat4085days(»11-2,yr), © American Astronomical Society • Provided by the NASA Astrophysics Data System PERIOD (days) 155d 573 270d 323d 198 9ApJ. . .337. .568L remained approximately constant,at12%-15%. Theampli- of the155daycyclerelative tothatofthe11yrcyclehas suggests thatduringthepast three solarcycles,theamplitude cycle alsovariesfromto cycle,from~0.12%ofSincycle and 0.011%ofSincycle21. Since theamplitudeof11yr total irradiance(S)insolarcycle 19,to0.007%ofSincycle20, the amplitudeof155daycyclevariedfrom0.016% the (1985), thiswassoforcycles20and21.ForthePtimeseries, 19, to0.06%ofSincycle20 and0.075%ofSincycle21, coherent throughallthreecycles.AccordingtoBogartand Bai assuming thatthephaseof155dayperiodhasremained day periods,fittedtothedataduringeachseparatesolarcycle, Instead, wecomparetheamplitudesofsinecurveshaving 155 solar cyclesdoesnotresolvethepeakat155daysfromthat at s resolution oftheperiodogramscalculatedforindividual based P,Fio.7,orRdatabecausethepoorerfrequency periodicity fromonesolarcycletothenextinground- 162 days(whichisapparentlynotpresentinflareoccurrence). ized Pdata. that thispeakisnotpresentintheperiodogramofrandom- differencing, doesnoteliminatethepeaknear159days,and P timeseriesduringcycle21,bytapering,detrending,and odograms incycle19.Figure8illustratesthatmodifyingthe but cannotreliablybedistinguishedfromnoiseintheperi- in boththeFandRperiodogramsduringcycles2120, sz clotted lineinthesefigures.Apeaknear159daysisalsopresent s noise. ThepeakheightforaFAPof1%isindicatedbythe periodograms inFigures5,6,and7,peaksofheight14 cycle periodogram(Fig.2).AccordingtotheFAPfor at 155and162days(andpossible173days)inthethree- s peak near159dayswhichcorrespondstotheunresolvedpeaks 10 7: 11.6 have,respectively,a1%and10%chanceofarisingfrom identical. of thetimeseries,areperiodogramsfordifferentsolarcycles similar toeachother,butnotthePIperiodogram;fornone solar cycle,theperiodogramsofP,F-j,andRarequite Figures 5,6,and7illustratesthefollowing:foreachindividual periodicities ismoredifficult.Qualitativecomparisonof those inFigure2forthreesolarcycles,anddiscerningreal resolution oftheseperiodogramsisreduced,comparedwith shorter timeintervalofasinglesolarcycle,thefrequency (Harvey 1984),forreasonsdiscussedbelow.Becauseofthe for theHelium1083nmequivalentlinewidthincycle21 and 7,respectively.IncludedinFigure5,istheperiodogram sl0z data insolarcycles21,20,and19areshownFigures5,6, cycles 20and21. icity inflaresduringtheintervalofsolarminimumbetween Bogart andBai(1985)foundnoevidenceofthe152dayperiod- likely presentduringtimesofhighsolarmagneticactivity. manifest themselvesinsolaractivitytimeserieswillbemost We assumethattheexistenceofsolarperiodicitieswhichmay 2922 days)nearthemaximumofsolaractivityineachcycle. cycles 19,20,and21,using8yrofdailydata(atimeinterval each ofP,FRandPI,separateperiodogramsforsolar peaks fromonesolarcycletothenext,wehavecalculated,for time series. spurious, but,rather,thattheyidentifyrealperiodicitiesinthe indicate thatthesepeaksintheoriginalperiodogramsarenot 574 s10/!z It isdifficulttoassesstherelativestrengthof155day There is,inthePperiodogramforeachofthreecycles,a s The periodogramscalculatedfromzero-mean,raw,daily To investigatethestatisticalregularityofperiodogram © American Astronomical Society • Provided by the NASA Astrophysics Data System b) SolarCycles19,20,and21,Individually LEAN ANDBRUECKNER is alsoprominentintheperiodogramsof10.7cmradioflux amplitude isapproximately12%ofthatofthe11yrcycle,and in theperiodogramofsunspotblockingfunction,whereits at 155and323days.Apeakdaysisthestrongestfeature between 100and500daysintheground-basedsolardataare parison. data asinusoidwithperiodof4085days,isgivenforcom- amplitude ofthe11yrsolarcycle,obtainedbyfittingto curve withtheperiodofpeak(cf.Ferraz-Mello1981).The obtained byfitting,totheentirethree-cycletimeseries,asine this tableareestimatesofthecorrespondingcycleamplitude, during thepastthreesolarcycles,19,20,and21.Includedin grams (FAP<10%)ofeachground-basedsolartimeseries the two(unresolved)peaksat270and287daysinFigure2. 21) isthepeaknear277days,corresponding,presumably,to and Rperiodogramsforallthreecycles(butstrongestincycle evident intheheliumequivalentlinewidthdata. present onlyintheperiodogramsforcycle21,whereitisalso three-cycle periodogramsforallfourtimeseries(Fig.2),is equivalent linewidth. near 155daysintheperiodogramofhelium1083nm ing functionor10.7cmradioflux.Notethatthereisnotapeak z during solarcycle21,muchweakerthaninthesunspotblock- icity near155daysmayhavebeenpresentintheplageindex peak issomewhatreduced.Thissuggeststhataweakperiod- culated afterremovingaperiodicityat155,theheightofthis is asmallpeaknear159days.Whentheperiodogramrecal- in cycle21than19. other cycles,butinthesedatatheamplitudewasslightlyhigher are alsoconsiderablysmallerincycle20thaneitherofthe tudes ofthe155daycyclesinbothFcmandRdata 10 7z The twomostprominentintermediate-termperiodicities Table 2liststhepeakswhicharepresentinperiodo- Finally, anotherfeaturewhichiscommontotheP,F The peaknear323days,whichisadominantfeatureofthe s10 7 In theperiodogramofplageindexdataincycle21,there comparison. peak-to-peak amplitude ofthe11yrcycleisincluded for series, sinecurveshavingtheperiodof interest.Thenominal from least-squaresfittingtoeachof thethree-cycletime amplitudes (inunitsoftherespective timeseries)obtained 4085 (0.086)(133) (142)4085(58.5) 323 (0.008) 287 (0.009) 270 (0.009) 162 (0.008) 155 (0.01) 115 (0.005) Note.—Numbers inparenthesesare thepeak-to-peak Summary ofthePeriods(indays)PeaksDetected in PeridogramsofGround-basedSolarTimeSeries during SolarCycles19,20,and21forWhichthe False AlarmProbabilityIsLessThan10% 323 (9.1) 287 (9.5) 270 (8.4) 155 (7.3) 11 YearCycle V. SUMMARY TABLE 2 349 335 323 (10.2) 155 (8.9) 390 351 336 324 (6.8) 149 (2.9) PI Vol. 337 198 9ApJ. . .337. .568L No. 1,1989 data sets.Thatthesepeaksareseenindifferentsolarobserva- and thesunspotnumber.Apeakat323daysoccursinall four cations tothetimeseries,suggeststhattheyarerealfeatures of tional data,andthattheyarenotdestroyedbyvariousmodifi- these ground-basedsolarrecords. following discussionconcentratesonthesetwoperiodicities. periodicity inflareoccurrence,reportedrecently,whilethat at 323 dayshasbeendetectedinvariouspreviousstudies. The (Rieger etal1984),153to160 days(Ichimotoetal1985),155 days (BogartandBai1985; andSturrock1987),154days days (Wolff1983) and158days(Kiplinger,Dennis, andOrwig 155 days.Otherpublications have identifiedthisperiodas152 The periodat155dayscorresponds,presumably,tothe We havereferredthroughout thispapertoaperiodicityat F. 5.—PeriodogramsforthedailydatainFig.1duringcycle21(1977-1984), only,andfortheheliumequivalentlinewidthduringsameperiod IG © American Astronomical Society • Provided by the NASA Astrophysics Data System VI. DISCUSSION INTERMEDIATE-TERM SOLARPERIODICITIES PERIOD (days) because thedatacorrespondtodifferenttimeintervals,with different overalllevelsofsolaractivity. flare occurrenceisalsopresentinthePdata.Thissunspot projected areasofallsunspotsonthesolardisk.Itis well blocking functionisdirectlyproportionaltothesumof the known thatthemagneticfluxinasunspotisapproximately lated withthetotalmagnetic energyofanactiveregion.That proportional toitsarea(Allen1976),andMayfield and blocking functionissimplybecause thisisamoredirectindica- this periodicityismostconclusively detectedinthesunspot Lawrence (1985)haveshownthatflareproductioniscorre- 1984). Presumably,theidentificationofthisperioddiffers tor oftheamountmagnetic fluxonthediskthaniseither day periodicityissomewhat lessprominentinthe10.7cm s 10.7 cmradioemissionorthe sunspotnumber.Thatthe155 It isnotsurprisingthatthenominal155dayperiodicityin 575 198 9ApJ. . .337. .568L the moredispersedmagnetic fieldswhichcharacterizeplages. concentrated magneticfields typical ofsunspots,butnotwith icity maybeassociatedwiththe presence,onthesolardisk,of include largesunspots.Thissuggests thatthe155dayperiod- duction ismorehighlycorrelated withactiveregionswhich more, MayfieldandLawrence (1985)notedthatflarepro- feature oftheglobalmagneticfieldsynopticdata.Further- cycle 21.Nor,accordingtoHudson(1987),isitaprominent absent inthehelium1083nmequivalentlinewidthdata in plage indexdatathroughoutthethreesolarcycles.Itis also producing moreactiveregions. icity bymakingactiveregionsmoreflare-rich,ratherthan by day periodicity,whateverthemechanism,itcausesperiod- consistent withtheobservationbyBai(19876)thatfor 51 ponent. Thatitisalsolessprominentinthesunspotnumber is “core” emissioncomponent,dilutedbythe“halo”com- radio fluxdataisbecauseitmostlikelyassociatedwith the 576 The 155dayperiodicityisabsent,orextremelyweak,inthe © American Astronomical Society • Provided by the NASA Astrophysics Data System Fio. 6.—PeriodogramsforthedailydatainFig.1,calculatedusingduringcycle20(1966-1973)only PERIOD (days) LEAN ANDBRUECKNER field. periodogram analysistoshorter periodswedonotdetecta the emergingfluxondisk,asdistinctfromglobalmean can beinvestigatedinthefuturebyusingtemporalrecords of inferred flaredataduringsolar cycle19.Whenweextendour does report,however,astrong peakat51daysintheCFI- (19876), wherethisperiodwas notdetectedincycle19.Bai of thetotalamountfluxpresentonsolardisk.This idea day periodicitymaybeapropertyofemergingflux,ratherthan N. Sheeley(privatecommunication)hassuggestedthatthe 155 indicate thepresenceof155 dayperiodicityinsolarcycle from themicrowaveandHadata.However,thatthey also icity insolarcycle20than21agreeswiththeresults these ground-baseddataallindicateaweaker155dayperiod- periodicity waslessinsolarcycle20than21.That 19 doesnotagreewiththerecent analysisofCFIdatabyBai that themodulationofflareoccurrencerateby155 day Both BogartandBai(1985)Ichimotoetal.agree Vol. 337 198 9ApJ. . .337. .568L (1987), havealsoused,primarily, dataduringcycle21, peak at51daysintheperiodogramsofanyfour time feature oftheplageindexvariations butthe155dayperiodicity is indeedofsolarorigin,then itsphysicalmechanismmaybe prominent onlyincycle21.Otherreportsofthisperiodicity, by confidence thatitis,indeed,real.However,thisperiodicity was different solartimeseriesduringthepastthreecyclesgives periodicity remainsuncertain.Thatitispresentineachof four cycle 21sunspotnumberandsolardiameter. Delarche, Laclare,andSadsaoud(1985)powerspectrum of F, andRdata.Apeakatthisperiodisalsopresentin the 20. Thereis,however,apeakat~52daysinthecycle21 P, series, foreitherthethreecyclescombined,norin19 or different fromthatofthe155day periodicity,sinceitisastrong although Wolff(1983)alsoreports it.Ifthe323dayperiodicity Delarche, Laclare,andSadsaoud (1985)andAkiokaetal No. 1,1989 10 7z s Whether ornottheperiodicitynear323daysisarealsolar © American Astronomical Society • Provided by the NASA Astrophysics Data System tr (XÍ o u a. O £ U O Ui 0. £ CL £ £L o £ LxJ a: Fig. 7.—Periodogramsforthedailydatain1,calculatedusingduringcycle19(1955-1962)only 30 50 30 35 30 50 30 35 20 40 20 25 20 40 20 25 10 10 15 10 10 15 100 120140160180200 0 0 5 0 0 5 INTERMEDIATE-TERM SOLARPERIODICITIES PERIOD (days) and othersatNRLforcomments onthiswork. period. evaluate, usingcomplexdemodulationtechniques,thetempo- 86-C-2230. WethanH.Hudson, N.Sheeley,M.VanHoosier, ral stabilityofboththeamplitude andphaseofthe155day daily dataareavailablesince1874.Inparticular,weplan to of theseperiodicities,especiallythatat155days,andforwhich P data,whichhaveproventobeaparticularlyusefulindicator term periodicitiestosolarcyclespriorcycle19byusing the both periodicities. these timeseriesofactiveregionswouldbeexpectedtoreflect ent physicalorigins,thenneitherislikelytobetheproduct of is not.Andifthe155dayand323periodicitieshavediffer- the ¿/-modebeatinghypothesizedbyWolff(1983),sinceboth s This workwassupportedatARC byNRLcontractN00014- We intendtoextendourinvestigationofsolarintermediate- PERIOD (days) 577 198 9ApJ. . .337. .568L 578 data onthedailytimegrid. to 25%ofthetimeinterval,{b)removinglong-termtrendbysubtractinga365dayrunningmean,(c)differencingadjacentdatapoints,and{d) randomizingthe .19876,Ap.J.{Letters),318,L85. 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