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Astronomy&Astrophysicsmanuscriptno.bewsher4November10,2004(DOI:willbeinsertedbyhandlater)ComparisonofBlinkersandExplosiveEvents:ACaseStudyD.Bewsher1,D.E.Innes2,C.E.Parnell3,andD.S.Brown31ESAResearchandScienticSupportDepartment,NASA/GSFC,Mailcode682.3,Greenbelt,MD20771,USA2Max-Planck-Institutf¨urAeronomie,Katlenburg-LindauD-37191,Germany3MathematicalInstitute,UniversityofStAndrews,NorthHaugh,StAndrews,Fife,KY169SS,ScotlandReceived/AcceptedAbstract.BlinkersarebrighteningsatnetworkcelljunctionsthataretraditionallyidentiedwithSOHO/CDSandexplosiveeventsorhighvelocityeventsareidentiedinhighresolutionUVspectraobtainedfromHRTSandSOHO/SUMER.CriteriaaredeterminedtofacilitateobjectiveautomaticidenticationofbothblinkersandexplosiveeventsinbothSOHO/CDSandSOHO/SUMERdata.BlinkersareidentiedinSUMERdata,ifthetemporalresolutionofthedataisreducedtothatofCDS.Otherwiseshortlived,localisedintensityenhancementsthatmakeuptheblinkerareidentied.ExplosiveeventsareidentiedinCDSdatawhenthelinewidthissignicantlyincreased,andoccasionallyifthereisanenhancementinthewingofthelineprole.Atheoreticalstatisticalmodelispresentedwhichhypothesisesthatblinkersandexplosiveeventsarerandomandnotconnectedinanyway.TheresultsgiveninthispapersuggestthatthishypothesiscannotberejectedandourprobabilityinterpretationoftherecentresultsofBrkovi´c&Peter(2004)areinconclusive.Keywords.Sun:SOHO,SUMER,CDS,transitionregion,blinkers,explosiveevents1.IntroductionTherehasbeenmuchdiscussionastotherelationshipbetweenblinkersandexplosiveevents(Harrisonetal.,2003;Peter&Brkovi´c,2003;Brkovi´c&Peter,2004).Blinkersaresmall-scaleintensityenhancementsthatwererstobservedbyHarrison(1997)usingtheSOHO/CDSinstru-ment(Harrisonetal.,1995).Morerecently,anumberofau-thorshaveusedautomatedidenticationmethodstoobserveblinkersinthequiet-Sun(QS)(Brkovi´c,Solanki&R¨uedi,2001;Bewsher,Parnell&Harrison,2002)andinactive-regions(AR)(Parnell,Bewsher&Harrison,2002).BothSOHO/CDSandSOHO/SUMERdatahavebeenusedtodeterminethedynamicsofblinkers.Bewsheretal.(2003)usedSOHO/CDSOV,formedatatemperatureof2:5105K,toshowthatblinkersarepreferentiallymorered-shiftedthanthewholeofthetransitionregionandhaveamaximumlineshiftof30kms1intheQSand40kms1inARs.Theyalsofoundthelinewidthsofblinkerstobepreferentiallylargerthanthewholeofthetransitionregionwithamaximumlinewidthof45kms1inbothQSandARs.Madjarska&Doyle(2003)usedSOHO/SUMERNVdata,formedatatemperatureof2:0105K,tocalculatetheDopplershiftofthreeblinkersandfoundthattheywerepredominantlyred-shifted,rangingfrom5-25kms1,whichagreeswiththeresultsofBewsheretal.(2003).UsingSOHO/SUMEROVIdata,Peter&Brkovi´c(2003)foundthatthelinewidthofasingleblinkerdecreasedSendoprintrequeststo:D.Bewshere-mail:dbewsher@esa.nascom.nasa.govovertheblinker'slifetime,reachingaminimumatthepeakoftheblinker'sintensity,incontrasttothelineshiftwhichreachesitsmaximumatthistime.Anumberofmechanismshavebeensuggestedtoex-plainblinkers(Harrisonetal.,1999;Priest,Hood&Bewsher,2002;Bewsher,Parnell&Harrison,2002;Parnell,Bewsher&Harrison,2002;Madjarska&Doyle,2003;Peter&Brkovi´c,2003;Bewsheretal.,2003),butasyet,noneofthesuggestedmechanismshavebeenveried.Explosiveeventshavebeencharacterisedbystrongnon-Gaussianenhancementsinthewingsoftheirlineprolesre-sultingfromahighvelocitycomponentrangingfrom50to200kms1.Detectionofsatellitecomponentsshiftedtotheredorbluefromthecentreofalineprolehavealsobeenusedtoidentifyexplosiveevents.Dere(1994)foundthatbrighten-ingswerenotassociatedwithexplosiveeventsinallcases.Likeblinkers,explosiveeventshavebeenidentiedinthequietSunandactiveregions.Theyhavealsobeenfoundincoronalholes(Dere,Bartoe&Brueckner,1989;Dereetal.,1991).TheywererstobservedusingHRTS,butarecommonlyidentiednowwithSOHO/SUMER(Wilhelmetal.,1995).Explosiveeventshavebeenfoundtobeassociatedwithre-gionsofcomplexweakeldorontheedgesofunipolareld(Porter&Dere,1991).Dereetal.(1991)andDere(1994)as-sociatedexplosiveeventswithmagneticreconnectionthatoc-curredduringthecancellationofmagneticuxandInnesetal.(1997)presentedamodelofthemagneticreconnectioncon-gurationrequiredforanexplosiveeventtooccur.Innes&T´oth(1999)usedacompressibleMHDsimulationtorepro- 2D.Bewsheretal.:ComparisonofBlinkersandExplosiveEvents:ACaseStudyTable1.PropertiesofblinkersandexplosiveeventsQSExplosivePropertyBlinkersEventsGlobalfrequency(s1)7.51443,6004Meanintensity%increase801605Meanarea(Mm2)2912.04Meanlifetime(minutes)16.411.04MaximumLineShift(kms1)3021104MaximumLineWidth(kms1)452-1Bewsher,Parnell&Harrison(2002)2Bewsheretal.(2003)3Cooketal.(1987)4Dere,Bartoe&Brueckner(1989)5Brkovi´c&Peter(2004)ducemanyexplosiveeventfeaturesseeninobservationaldata,includingthehighDopplershiftedlineproles.Asuiteof6pa-pers(Roussevetal.,2001a,b,c;Roussev,Galsgaard&Judge,2002;Galsgaard&Roussev,2002;Roussev&Galsgaard,2002)havepresentedtheresultsofvariouscongurationsof2Ddissipativenumericalmagnetohydrodynamicsmodelsofexplosiveevents.Themodelshowsthebi-directionaljetasso-ciatedwiththeexplosiveeventtohaveavelocitywhichisoftheorderoftheAlfv´enspeed,aswouldbeexpectedfromthereconnectionthatisthoughttocausetheseevents.Themod-elsalsoincludednon-equilibriumionisationcalculationsofthespectraresultingfromthenumericalsimulations.Theyfoundthatthetransitionregionresponsetothereconnectioneventswasdependentontheinitialconditions,butthedynamicsoftheeventsdidnotvarythatmuch.Table1showsthegeneralpropertiesofblinkers(Bewsher,Parnell&Harrison,2002;Bewsheretal.,2003)andexplosiveevents(Cooketal.,1987;Dere,Bartoe&Brueckner,1989;Brkovi´c&Peter,2004).Comparingtheresultsfromthistable,weseethatblinkersare60timeslessfrequentthanexplosiveevents,20timeslargerinarea,and20timeslongerinlifetime.Theintensityenhancementfactorsofbothphenomena,how-ever,areapproximatelythesame.Oneshouldbecarefulwhenmakingsuchcomparisons,however,astheresolutionofthein-strumentsandtheobservationalmethodusedtoidentifytheeventsarevastlydierent.Thepropertiesanddynamicsofblinkersandexplosiveeventsappeartobeverydierent,whichleadsustosuggestthateither(i)thetwophenomenareallyaredierentor(ii)thedierencesininstrumentresolutionandsensitivitycausethemtoappeardierent.Speculationwhetherblinkersandexplosiveeventsarethesamephenomenaornotcontinueseventhoughmuchresearchhasbeencarriedoutoneachindividualphenomenon.Wheninvestigatingexplosiveeventsandtwo`blinker-likeregions',Chaeetal.(2000)suggestedthatblinkersweremadeupofmanySUMERunitbrightenings,andwere`closelyrelated'toexplosiveevents.Madjarska&Doyle(2003),however,havesuggestedthatblinkersarenotrelatedtoexplosiveevents,butarethe`on-disk'signatureofspicules.TheresearchofPeter&Brkovi´c(2003)leadthemtoclaimthat`explosiveeventsaremostprobablynotrelatedto...transitionregionblinkers'.AnalysisofvequietSunSUMERdatasets,whereeventsinSUMERcalledblinkerswereidentiedautomaticallyandexplosiveeventswereidentiedbyeye,ledBrkovi´c&Peter(2004)toconcludethat`blinkersandexplosiveeventsaretwoindependentphenomena'.Itisunclear,however,whetherblinkersobservedinCDScanalsobeidentiedinSUMER(Madjarska&Doyle,2003).Brkovi´c,Solanki&R¨uedi(2002),however,haveshownthatthevariabilityinintensityinSUMERandCDSissimilariftheresolutionoftheSUMERdataisre-ducedtothatofCDS.Inallofthestudiesabove,noneoftheauthorshavecom-paredblinkersautomaticallyidentiedinSOHO/CDSdatawithexplosiveeventsautomaticallyidentiedinaco-alignedSOHO/SUMERdataset.Inthispaper,wedojustthat.InSection2,wedescribethedatausedandtheautomaticiden-ticationtechniques.InSection3,theblinker/explosiveeventexamplesareshown.Section4discusseswhetherwingen-hancementsareactuallyobservableinCDSdataandSection5providesasimpletheoreticalstatisticalmodeltodeterminewhetherourresultsandthoseofBrkovi´c&Peter(2004)areasonewouldexpectifthephenomenaarerandomanduncon-nected.FinallywemakeourconcludingremarksinSection6.2.DataThedatausedinthispaperaretakenfromtwoSolarandHeliosphericObservatory(SOHO)instruments;theCoronalDiagnosticSpectrometer(CDS;Harrisonetal.,1995)andtheSolarUltravioletMeasurementsofEmittedRadiation(SUMER;Wilhelmetal.,1995)andfromtheTransitionRegionandCoronalExplorer(TRACE;Handyetal.,1999).TheCDSdatausedareaseriesofOVfeature-trackingrasteredimagesformedatatemperatureof2:5105K.Therunstartedat12:30UTon19thJune1998andlastedforeighthours.Thedatacoversanareaof400012400,haspixelsofsize4001:600,a10secondexposuretimeandacadenceof151seconds.Thecoordinatesofthecentreoftherstrasterare22000Eand25000N.AfulldescriptionofthepreparationofthedatacanbefoundinBewsher,Parnell&Harrison(2002).TheSUMERdataareaseriesofSiIVsingle-slitlinepro-lesformedatatemperatureof6:6104K.Theobservationrunstartedat12.32UTandlastedfor4hoursuntil16:32UT.The10030000slitwasused,buttheonlythecentral24000wastelemetered,afterbinningovertwospatialpixels.Thedatahasa15secondcadenceandapixelsizeof100200.Thecoordi-natesofthecentreoftherstsingleslitare22000Eand26000N.TheSUMERdatatracksthesamepartoftheSunwithin100throughoutthetimesequence.AfulldescriptionofthedataandthepreparationusedcanbefoundinInnes(2001).AseriesofTRACE1550,1600and1700ÅimageswerealsotakensimultaneouslywiththeSUMERandCDSdata,whichenabledaseriesofCIVimagestobesimulated.ThisdataisthesameasthatanalysedbyInnes(2001).ThealignmentoftheCDSandSUMERdataisnotmadesolelybyusingtheheadersofbothdatasets,sincethisalign-mentisknowntohaveanerrorofapproximately500.AbetteralignmentwasachievedbyrstaligningtheSUMERdatato D.Bewsheretal.:ComparisonofBlinkersandExplosiveEvents:ACaseStudy3theTRACECIVdataandthenaligningtheTRACEdatatotheCDSdata.Theestimatednalalignmenterrorisapproxi-mately200300.Weanalyse3.5hoursofcoincidentSUMERandCDSS11484datafrom12:30UTuntil15.49UT.Inthesubsequentsubsections,weexplainthecriteriathatwesettoautomaticallyandidentifyblinkersandexplosiveeventsinbothCDSandSUMER.Ourcriteriaenablecompar-isonstobemadebetweenbothphenomenaasseeninbothdatasets.Eventhough,wehavebeencarefultoaligntheCDSandSUMERdataveryclosely,itispossiblethatthedierentspatialresolutionsoftheinstrumentsledthemtoseedierentthings.SinceCDShasabroadpointspreadfunction(600inSolar-Xand800inSolar-Y)(Pauluhnetal.,1999),itispossiblefortheSUMERslittobesittinginapositionwhereCDSseesafea-ture,butSUMERdoesnot.Forthisreason,wedonotassumeanythingaboutthefeaturesthatweseeuntilwehavetestedthemwithourcriteria.WeuseCDSdatasothatweidentifywholeblinkersandnotjustasmallsliceofthem.2.1.BlinkerIdenticationProcedure(BLIP)BLIPisanautomatedmethodofidentifyingblinkersfromase-riesofCDSrasteredimages.FulldetailsofthealgorithmcanbefoundinBewsher,Parnell&Harrison(2002)andBewsher(2002).Thealgorithmndsgroupsofpixelsthathavesigni-cant(intensityjumpgreaterthann,whereisthevaluebe-lowwhich99%ofthePoissonerrorsexist)temporalpeaks.Tobeclassiedasablinker,theremustbenpadjacentpixelsthatpeaksimultaneously.Inthispaper,weshowexamplesofblinkersidentiedwithn=5andnp=3.Theseparametershavebeenshown(Bewsher,Parnell&Harrison,2002)toiden-tifyblinkersthatmeettheestablishedmeanpropertiessetbyHarrison(1997)andHarrisonetal.(1999).FortheCDSandSUMERdatasets,theerrorthresholds(cands)arecalculatedtoequal3.5photons/pixel/second(p/p/s)and4.9counts/pixel/second(c/p/s),respectively.2.2.ExplosiveEventIdenticationWefollowtheexampleofWinebargeretal.(1999)andsettwocriteriafortheidenticationofexplosiveevents.Apositivetestfromeithercriteriaimpliestheexistenceofanexplosiveevent.First,welookforasignicantlinewidth;denedasthevalue,v,belowwhich95%ofthelinewidthsoccur.Ifthelinewidthisgreaterthanthisvalue,thenanexplosiveeventissaidtohaveoccurred.FortheCDSdata,thesignicantlinewidth,vcisfoundtobe34.4kms1andfortheSUMERdataset,thesignicantlinewidth,vs,isequalto25.0kms1.Sincewedeterminethelinewidthcriteriafromalloftheindividualpixelsinthedataset,andthencomparewithasummedgroupofpixels(theblinkerortheexplosiveevent)ourcriteriaisanupperlimit.Sincesummingoveranumberofpixelsreducesthenoiseandthespreadofthedata.TherelativelineshiftsandwidthsoftheCDSdataandblinkersarecalculatedusingthemethodofBewsheretal.(2003).TheactualvelocitiesgivenaredeterminedusingthetypicaltransitionregionbackgroundDopplershiftandwidthasdeterminedinBewsheretal.(2003)whichusesstandardresultsfromanumberofauthors(Achouretal.,1995;Chae,Yun&Poland,1998;Teriaca,Banerjee&Doyle,1999;Peter&Judge,1999;Hansteen,Betta&Carlsson,2000;Mariska,Feldman&Doschek,1978;Dere&Mason,1993;Chae,Sch¨uhle&Lemaire,1998),i.e.,thebackgroundOVDopplershiftis7kms1,andthebackgroundOVlinewidthis28kms1.The2noiseassociatedwiththeCDSDopplershiftsandlinewidthsare9.0and3.6kms1,respectively.Since,thereisalsonocalibrationlineintheSUMERdataset,wecalculaterelativeDopplershiftsinthesamewayaswedotheCDSdata,i.e.,withrespecttoareferencelinecen-trepositioncalculatedfromthewholedataset.WedeterminetheactualvelocitiesbyusingatypicaltransitionregionSiIVDopplershiftof7kms1(seeBewsheretal.(2003)fordetailsofhowthetypicalvelocitywascalculated).Wecalculaterela-tivelinewidthswithrespecttoareferencewidthof21kms1fortheSUMERdataandatimevaryingreferencewidthwhichisthemodalvaluefromeachrasterfortheCDSdata.Theref-erencelinecentrepositionisalsousedwhencalculatingthelinewidthvelocity.The2(orfullwidthofthet)erroras-sociatedwiththeSUMERDopplershiftsandlinewidthswerecalculatedusingaMonteCarlosimulationandfoundtobeoftheorderof1-2kms1.ThisisconsistentwithPeter&Judge(1999)whofoundtheerroronSiIVDopplershiftmeasure-mentstobe1.7kms1.Second,weconsidertheskewnessofthelinewhichisusedtodeterminewhetheranenhancementinthewingofthelineproleispresent.Skewnessisadimensionlessquantitywhichismathematicallydenedasameasureofasymmetryofadis-tribution.Inthiscase,thelineprole.HowtocalculatetheskewnessandexamplesofskewedGaussiansandskewnessval-uesaregiveninAppendixA.Herethesignicantskewnesslimitiscalculatedbyconsideringtheskewnessesofthelineprolesofallthepixelsinthedatasetanddetermininganon-signicantrangethatexcludesthetopandbottom2%ofval-ues.FortheCDSdata,thenon-signicantskewnessrangeis[-0.58,0.40].Thenon-signicantskewnessrangefortheSUMERdatais[-0.92,0.27].Aswiththecriteriaforthelinewidth,thesenon-signicantboundsaremaximumlimits,sincesumminganumberofpixelsreducesthenoiseandthespreadofthedata,i.e.,ifanythingisfoundintheblinker(orexplosiveevent),thenitisverylikelytoberealandpresentinallthepixelsthatmakeuptheblinker(orexplosiveevent).UnlikeWinebargeretal.(1999)andInnes(2001),wedonotsetalimitontheuxthatmustbepresentinthewingforapositiveexplosiveeventtest.Thecriteriawerechosensothataminimumofthe8eventsidentiedbyInnes(2001)weredetected.Infact,atotalof12eventswereidentied(seeSection3.5).Moreim-portantly,however,bysettingspeciccriteria,theautomatedmethodcanbeusedonbothSUMERandCDSdatasets,andenablesatruecomparisonoftheresultsfrombothdatasets.3.ResultsIntheco-alignedCDSOVdata,wend58blinkersusingBLIP,butonly11liebelowtheSUMERslit.IntheSUMER 4D.Bewsheretal.:ComparisonofBlinkersandExplosiveEvents:ACaseStudy(a)(b)Fig.1.(a)SUMERSiIVsingleslitimageand(b)CDSOVraster.The'sontheCDSrasterarethemid-pointsofblinkersidentiedwithn=5andnp=3andtheverticaldashedlineindicatesthepositionoftheSUMERslit.BothCDSandSUMERimagesareshowninfalsecolourwhereadarkregioncorrespondstoabrightening.SiIVdata,weobserveapproximately80brighteningsand8explosiveevents.Thedierenceinthenumberofbrighteningsobservedisaselectioneectduetotheresolutionofthedif-ferentinstruments.Aftercomparingthelocationsofbothwithrespecttoeachother,wendthatduringthis3.5hourdatasetthreedierentscenariosoccur:co-spatialandco-incidentblinkerandexplosiveevent(1example);blinkerwithnoasso-ciatedexplosiveevent(10examples);andexplosiveeventswithnoassociatedblinker(7examples).Weinvestigateoneexam-pleofeachofthethreescenariosinmoredetailinthefollowingsubsections.3.1.BlinkerandexplosiveeventFigure1shows(a)aSUMERSiIVsingleslitimageand(b)thecorrespondingCDSOVrastertakenat12:46UT.ThedashedlineontheCDSdatamarksthepositionoftheSUMERslitandthesmarkthemid-pointsofthen=5andnp=3blinkers.BothSUMERandCDSimagesareshowninfalsecolourwhereadarkregioncorrespondstoabrightening.TheSUMERimageisanintensityplotofwavelength(x-axis)versuspositionalongtheslit(y-axis).AtthetopoftheSUMERSiIVframe,anex-plosiveevent(S1)canbeseen,butitsfullspatialextentcannotbegaugedduetotheobservationaldataavailable;thisfactshouldbekeptinmindthroughoutthispaper.InthislocalityintheCDSOVraster,threeblinkers,C1,C2andC3arealsoobserved.Themiddleblinker(C2)isthenearestspatiallytotheexplosiveevent.Thisistheonlyexample,withinour3.5hoursequenceofco-alignedCDSandSUMERdata,ofablinkerandanexplosiveeventtogether.Figure2(a)showsthelightcurveoftheexplosiveevent,S1,whilstFigure2(b)showsthelightcurveofthewholeblinker,C2(solid)andthelightcurveoftheCDSpixelsthatcorresponddirectlytotheSUMERregionS1(dashed).Thestartandendoftheblinkeraremarkedwiths.Thedotted,dashedanddot-(a)(b)(c)(d)Fig.2.(a)SUMERSiIVlightcurvefortheexplosiveevent,S1.(b)CDSOVlightcurveforblinker,C2(solid)andthelightcurveoftheCDSpixelsthatreferdirectlytoSUMERregionS1(dashed).Thesmarkthestartandendoftheblinker.(c)SUMERSiIVlineprolesand(d)CDSOVlineprolesattimes,t1(dashed),t2(dotted)andt3(dot-dash).TheSUMERandCDSreferenceGaussiansattimet2areplottedwithasolidlinedashedverticallinesrefertothetimesoftheframeshowninFigure1(t2,thetimenearestthemaximumvelocityoftheex-plosiveevent),theCDSframebefore(t1)andtheCDSframeafter(t3),respectively.LineprolesareshowninFigures2(c)and(d)fromSUMERSiIVfortheexplosiveevent,S1,andfortheCDSblinkerC2,respectively,attimest1(dashed),t2(dotted)andt3(dot-dash).TheSUMERandCDSreferenceGaussiansfortimet2areplottedforcomparison(solid).Inthiscase,itappearsthatweareseeingthesamebright-eningeventwithbothCDSandSUMER,asthelightcurvesfollowthesamegeneralpattern.Asexpected,however,thebet-terspatialresolutionoftheSUMERinstrumentprovidesmorevariationintheintensity(Brkovi´c,Solanki&R¨uedi,2002).TheSUMERlightcurveisanalysedusingBLIPtodeter-minewhetheritmeetsthen=5criteriaforbeingablinker.Thepeak(shownwitha)nearesttotimet3,isidentiedasablinker.Thestartandendofthiseventaremarkedwithaanda+,respectively.TheSUMEReventthatBLIPactuallyidenti-esasablinkerisjustasmalllocalisedintensitychange,andisonlyasmallpartofthelarger,longer-livedCDSblinkerthatisseen.ThereasonforthisisthehighertemporalresolutionoftheSUMER.Indeed,iftheSUMERdataisreducedtothetem-poralresolutionoftheCDSdatathenaneventwithasimilarlifetimetotheCDSblinkerisfoundinSUMER.AllthepropertiesofblinkerC2arecomparablewiththeaveragecharacteristicsforblinkers,exceptforitspeakfactor. D.Bewsheretal.:ComparisonofBlinkersandExplosiveEvents:ACaseStudy5Table2.Dopplershiftsandlinewidths(kms1)ofexplosiveeventS1andblinkerC2.RegionVelocitiesWholelineproleWingenhancement(kms1)t1t2t3t1t2t3S1(Dopplershift)-3.5-7.3-10.0-80.3,66.0S1(Linewidth)22.226.925.517.5,20.1C2(Dopplershift)15.20.42.8C2(Linewidth)34.534.840.4C2hasthehighestpeakfactorofallthe131blinkeridentiedinthisCDSdataset.TheexampleshownhereisdierentfromtheblinkeranalysedinPeter&Brkovi´c(2003)whichledthemtosuggestthatthesmaller,shorter-livedblinkersareactuallyexplosiveevents.Table2showstheDopplershiftsandthelinewidthsofthewholelinesandwhereappropriate,anysignicantwings.WetesttheblinkerC2lineprolesforthepresenceofanexplosiveeventusingthecriteriastatedinSection2.2.TheCDSlinewidthsofC2attimest1,t2andt3aregreaterthanvc,andtherefore,meettheexplosiveeventcriteria.TheskewnessesoftheC2lineproles,however,fallinthenon-signicantrange(-0.049,-0.076and0.027attimest1,t2andt3,respectively)andthereforefailtheskewnesstestatalltimes.Sincetheblinkerlineprolesmetoneofthecriteria,wesaythatCDShaspossiblyfoundanexplosiveevent.Incomparison,wingenhancementscanclearlybeseenonbothsidesoftheexplosiveevent,S1lineprole.Theexplosiveeventwasidentiedbecauseattimest2andt3ithassigni-cantbroadenings.S1alsohasasignicantskewness(0.28)attimet3,buttheskewnessesattimest1andt2(-0.10and0.05,respectively)failourcriteria.Thus,inthiscase,ouranalysisindicatesthatapossibleex-plosiveeventisvisibleintheCDSlineprolesattimest1,t2andt3,butintheSUMERlineprolesattimet2andt3only!TheidenticationofexplosiveeventswithCDSmustbeap-proachedwithcare,andthecriteriamayneedtobeadapted.Inthiscase,theCDSexplosiveeventcriteriaappeartobetoolenient.ThesensitivityandresolutionofCDSandSUMERareleadingustoidentifyanexplosiveeventinCDSwhenitisnotpresentinthebetterresolutionSUMERdata.Sucientspec-tralresolutionisalsonecessarytodistinguishbetweenaloneblinker,orinthiscase,anexplosiveeventbrighteningandablinker.3.2.BlinkerandnoexplosiveeventThesecondscenarioisasituationinvolvingablinker,butnoexplosiveevent.Figure3showsthesametwotypesofframesasthoseshowninFigure1,buttheseframesaretakenattime13:33UT.Twoblinkers,C4andC5,observedintheCDSOVdata,liealongtheSUMERslit.IntheSUMERSiIVdata,thetworegionsthatcorrespondtoC4andC5arelabelledS2andS3,butneitherregionappearstocontainanexplosiveeventthatcanbedetectedbyeye.Theseexamplesaretwooutoftenobservedinthisdataset,wherethereareblinkerspresentintheCDSdataalongtheSUMERslit,butnoexplosiveevents(a)(b)Fig.3.AsFigure1,butwith(a)SUMERSiIVand(b)CDSOVframestakenattime13:33.(a)(b)(c)(d)Fig.4.AsforFigure2,butforSUMERregionS2,andblinkerC4.seenintheSUMERdata.WeinvestigateblinkerC4andthecorrespondingSUMERregion,S2inmoredetail.Figure4issimilartoFigure2andshowsthelightcurvesandlineprolesofSUMERregionS2andblinkerC4.Asintheprevioussection,theCDSandSUMERlightcurvesshowthesamegeneralpattern,butthereismorevariationintheSUMERintensities.Weanalysethefulltem-poralresolutionSUMERlightcurvewithBLIP,andndthatnoblinkerwithn�5isidentied.IfweanalyseareducedtemporalresolutionSUMERlightcurve(withintensitiesonlytakenatthetimesnearesttotheCDStimes),thenagain,BLIPdoesnotndablinkerwhichmeetsthe5criteria.So,eventhoughthelightcurvesshowthesamepatternofvariations,the 6D.Bewsheretal.:ComparisonofBlinkersandExplosiveEvents:ACaseStudyTable3.Dopplershiftsandlinewidths(kms1)ofSUMERregionS2andblinkerC4.RegionVelocitiesWholeregionWingenhancements(kms1)t1t2t3t1t2t3S2(Dopplershift)2.70.4-2.3S2(Linewidth)19.519.618.8C4(Dopplershift)7.68.84.1C4(Linewidth)30.532.032.1(a)(b)Fig.5.AsFigure3,butSUMERSiIVandCDSOVframestakenattime15:00magnitudeofthoseuctuationsisnotsucientforablinkertobeidentiedinSUMER.AllpropertiesofblinkerC4,arecomparablewiththemeanpropertiesshowninTable1.Table3showstheDopplershiftsandlinewidthsofblinkerC4andSUMERregionS2.ThelinewidthandskewnessofblinkerC4failtomeetourcriteriaforanexplosiveevent.Similarly,SUMERregionS2failstheexplosiveeventtests.Similarly,ifweinvestigatetheSUMERS3regionandtheCDSblinker,C5,wendthesamestory.Indeed,intotalwefound10suchexamplesinourdataset.InallcasesblinkerscouldbeidentiedinCDSbutnotinSUMERandneithershowedanyevidenceofanexplosiveevent.3.3.ExplosiveeventandnoblinkerFigure5issimilartoFigures1and3.AtthetopoftheSUMERSiIVframe(Figure5(a)),abi-directionalexplosiveeventcanbeseen;itislabelledS4.InFigure5(b),thecorrespond-ingCDSOVregion,C6,showsnoblinker.ThisisoneofsevencasesfoundwhereanexplosiveeventisobservedintheSUMERdata,butnoassociatedblinkerisseenintheCDSdata.Figure6showsthelightcurvesandlineprolesofSUMERregionS4andCDSregionC6.Inthiscase,thelightcurvesofSUMERregionS4andCDSregionC6donotcorrelatepar-ticularlywell.ThereisclearevidenceofanexplosiveeventintheSUMERspectra,however,withenhancementsseenonbothsidesofthelineprole.Asbefore,weanalysetheSUMERlightcurvewithBLIPtodeterminewhetheranyblinkersarepresent.TheSUMERpeakintensitynearesttotimet2,meets(a)(b)(c)(d)Fig.6.AsinFigure2,butforexplosiveeventS4,andforCDSregionC6Table4.Dopplershiftsandlinewidths(kms1)ofSUMERregionS4andCDSregionC6.RegionVelocitiesWholeregionWingenhancement(kms1)t1t2t3t1t2t3S4(Dopplershifts)8.87.59.1S4(Linewidths)22.025.722.9C6(Dopplershifts)9.712.69.2C6(Linewidths)33.832.932.0then=5criteriaforablinker,andthestart,peakandendofthe`blinker'aremarkedwitha,anda+,respectively.AsinthecaseoftheSUMERlightcurveS1,BLIPidentiesalo-calisedintensityenhancementwhichismuchshorterthanthelarger,longer-livedbrighteningthatisclearlypresent.AblinkerisnotidentiedintheCDSdata,becausenotallofthepixelsthatmakeuptheregionhavesignicantpeaksatthesametime.TheblinkerseeninFigure5(b)totherightofregionC6,isnotassociatedwiththeexplosiveeventsinceitdoesnotliebeneaththeSUMERslitduringitslifetime.Asinprevioussections,weanalyseboththeSUMERandCDSlineproleswiththeexplosiveeventtests.Table4showstheDopplershiftsandlinewidthsoftheSUMERregionS4,andtheCDSregion,C6.TheCDSlineprolesfailthelinewidthandskewnesscriteriaatalltimes.Thereis,therefore,noevidenceofanexplosiveeventintheCDSlineproles.TheSUMERlineproles,however,meetthelinewidthtestattimet2,butliketheCDSlineproles,failtheskewnesstestatalltimes.Eventhoughtheproleslookskewed,thepresenceofwingsonbothsidesoftheprolereducestheoverallskew-nessintheline,henceitdoesnotmeettheskewnesscriteria. D.Bewsheretal.:ComparisonofBlinkersandExplosiveEvents:ACaseStudy7Table5.Propertiesofblinkersidentiedinfullandreducedtimeres-olutionSUMERdataandinasingleslitoftheCDSdata.PropertySUMERSUMERCDSFullReducedSingleslitNoofblinkers163511Meanintensity%increase9010070Meanarea(Mm2)2.42.821.3Meanlifetime(minutes)2.816.817.3Inthiscase,therefore,thereisevidenceofbothablinkerandanexplosiveeventintheSUMERdata,butnoevidenceofeithereventintheCDSdata.Wehavefoundanother6caseswhereaSUMERexplosiveeventoccurswithoutaCDSblinker,ofwhichwecouldidentify2asblinkersinSUMERand3showedsignsofanexplosiveeventinCDS.3.4.SUMERBlinkersWehaveshownexampleswhereblinkersinCDSandexplo-siveeventsinSUMERarepresenteithertogetheroralone.Forallexamples,wehaveinvestigatedwhetherthereisevidenceofblinkersinSUMERorexplosiveeventsinCDS.Howsuc-cessfulareweatidentifyingblinkersinSUMERorexplosiveeventsinCDSwithouttheotherdatasetsforcomparison?WeuseBLIPtoidentifyblinkersintheSUMERdata.Firstly,weusethefullresolutionSUMERdataandthenare-ducedtimeresolutionversionoftheSUMERdata.ToachievethereducedSUMERtimeresolution,wejustpickthedataatthetimesthatareclosestintimetotheCDSrasters.SincetheSUMERdataisonlyasingleslit,forcomparison,wealsoanal-yseasingleslitoftheCDSdataforblinkers.Thepropertiesoftheblinkersidentiedwithn=5andnp=3fromall3ofthesedatasetsareshowninTable5.Themeanintensityenhancementfactorsoftheblinkersfoundinallthreerunsarecomparable.Asexpected,theareaoftheblinkersfoundwiththeSUMERdataaresmallerthanthoseblinkersidentiedinCDS.ThisisduetothesmallersizeoftheSUMERpixelswithrespecttotheCDSpixelsizeandthelimitedspatialextentoftheSUMERdata.ThelifetimesoftheblinkersfoundinCDSandinthereducedtimeresolu-tionSUMERdataarecomparable,butagainthefulltempo-ralresolutionoftheSUMERdataleadstotheidenticationofshorterlivedevents.ThefrequencyofeventsidentiedinSUMERisalsohigherthanthatfoundwiththeCDS,asmanysmallershorterlivedeventsareidentied.Also,astheSUMERdatahasagreaternumberofpixels,andeventsidentiedaresmaller,agreaternumberofeventscanbeidentied.Allofthe11blinkersfoundintheCDSdatahadsomecounterpartinthereducedSUMERdata,i.e.therewassomeintensityenhancementthatspatiallyoverlappedwiththeCDSblinkerthatmetthecriteriaforablinkeratsomepointdur-ingthelifetimeoftheCDSblinker.Ofthe35blinkersiden-tiedintheSUMERreducedresolutiondata,18weresmalllocalisedbrighteningsthatmadeupthe11blinkersidentiedinCDS.Theremaining17blinkersdidnothaveacounterpartinCDS.AlloftheSUMERfullresolutionblinkershavecoun-terpartsintheSUMERreducedblinkers.Ofthe16fullreso-lutionSUMERblinkers,11arepartof5largerCDSblinkers,theother5aresmalllocalisedbrighteningsthatdidnothaveacounterpartinCDS.3.5.CDSExplosiveeventsHere,weasktheanalogousquestionofwhetherexplosiveeventscanbeidentiedinCDSwithoutusingtheSUMERdataforcomparison.UsingthecriteriastatedinSection2.2,weidentifyexplosiveeventsinasinglecolumnoftheCDSdatathatalignswiththeSUMERslitandinthefullresolutionSUMERdataforcomparison.Wendthat80%ofSUMERandCDSpixelsrecordthesameresult,i.e.thatthereisasignicantlinewidth,asignicantskewnessorboth.ThisclearlyshowsthatourexplosiveeventcriteriaisfairlygoodatproducingthesameresultwithbothCDSandSUMERdataWealsoadd2furthercriteriaforexplosiveevents,namelythat(i)theexplosiveeventmustoccurin3ormorepixels,andthat(ii)itmustbevisiblefor3ormoretimesteps.Wedothissothatwecanbemorecondentinouridenticationofrealeventsratherthananomaliesinthedata.ItshouldbenotedthatthesefurthercriteriawerenotusedbyInnes(2001).Usingtheseextracriteria,wend3explosiveeventsintheCDSdatawhichconsideringthelargersizeoftheCDSpixelsandthelowerspectralandtemporalresolutionofCDS,iscom-parablewiththe8explosiveeventsidentiedbyInnes(2001).These3explosiveeventshaveameanlifetimeof10.7minutesandameanareaof20Mm2.Bothofthesepropertiesarehigherthantypicalforexplosiveevents.Bothofthesecharacteristics,however,aresmallerthanthoseforblinkers,suggestingthatblinkersandexplosiveeventsaredierentclassesofevents.Ofthe3explosiveeventsfoundinthesingleslitofCDSdata,1oftheexplosiveeventswasidentiedpurelyusingtheskew-nesscriteria,theother2wereidentiedbytheirincreasedlinewidth.OnlyoneoftheexplosiveeventsidentiedinCDSwiththeextracriteriacoincideswiththosefoundbyInnes(2001).Obviouslyoureventsizeandlifetimecriteriastopusfromiden-tifyingtheeventsthatInnes(2001)did.Asafurthertest,wealsoidentifyexplosiveeventsinthefullresolutionSUMERdata.12explosiveeventsarefoundwithameanareaandlifetimeof2.1Mm2and2.3minutes,re-spectively,whichiscomparabletothetypicalexplosiveeventcharacteristicsshowninTable1.Ofthe12explosiveeventsfoundintheSUMERdata,3wereidentiedusingtheskew-nesscriteriaandtheother9wereidentiedusingthelinewidthcriteria.Ofthe12explosiveeventsidentied,4arethesameasthoseidentiedbyInnes(2001).AgainitappearsthatthegroupingofpixelstomeettheextraexplosiveeventcriteriacanruleoutsomeshortlivedorsmalleventsfoundbyInnes(2001).ItmaybenecessarytoincludealternativeexplosiveeventcriteriathatsetlimitsontheamountofuxinthewingsasWinebargeretal.(1999)andInnes(2001)did. 8D.Bewsheretal.:ComparisonofBlinkersandExplosiveEvents:ACaseStudyFig.7.ContourplotofthefractionoftheCDSprolemadeupofthewingGaussianwhentheamplitudeandthevelocityofthewingGaussianarevaried.Thesolidlinemarksthe80kms1velocityoftheSUMERexplosiveeventS1,andthedottedanddashedlinesmarktheamplitudeexpectedfromthewholeand2%oftheSUMERexplosiveeventproducingthe80kms1velocityobserved,respectively.4.CanwingenhancementsbedetectedinCDSdata?OnlyoneoftheexplosiveeventsidentiedinCDSwasidenti-edwiththeskewnesscriteria.ButwouldweexpecttoidentifyexplosiveeventsinCDSwiththiscriteria,giventheresolutionofCDS?Ifso,whatsizeofwingcouldwedetect?Todeterminethis,weassumethatatheoreticallinepro-leiscomprisedoftwoGaussianproles:onecoreGaussianwithamplitudeA1,linecentre1andwidth;andonewingGaussianwithamplitudeA2,linecentre2andthesamewidth.Foragivenlineshift(velocity)andamplitudeofthewingGaussian,wecancalculatethefractionofthewholelineprolethatismadeupofthewingcomponent.Figure7showsacontourplotofthefractionofthelineprolethatismadeupofthewingcomponentgiventheve-locityandamplitudeofthewingcomponent.Inthecaseoftheexplosiveevent,S1andblinker,C2,theareaoftheSUMERexplosiveeventis0.12timestheareaoftheCDSblinker.IfweassumethatthewholeoftheplasmaintheSUMERregionisgivingrisetotheexplosiveevent,thenavelocityof80kms1(Figure7solidline)wouldshowupasawingwhichhasbe-tweenonefthandonetenththeuxofthewholeCDSprole.ThewholeoftheSUMERregion,however,willnotcontributetotheexplosiveevent,andifweassumethatonly2%oftheplasma(asourdatasuggests)intheSUMERregiongivesrisetotheexplosiveevent(i.e.0.0024oftheCDSblinker),thenthewingwillcontributelessthanafourtiethofthewholeCDSprole.Itisnosurprise,therefore,thatwehavebeenunabletoidentifywingenhancementsintheCDSlineproles,andfur-thermoreitisunlikelythatthismethodwouldbesuccessfulinidentifyingexplosiveeventsinCDSdata.5.Canblinkersandexplosiveeventsrandomlycoincide?Letusmakethehypothesisthatblinkersandexplosiveeventsarenotphysicallyrelatedandtheoccurrenceofablinkerhasnobearing(eitherpositiveornegative)onwhetheranexplosiveeventwilloccurthere.Then,ifwehaveobservationscontainingaknownsetofblinkers,thecasethatanexplosiveeventwillcoincidewithoneoftheseblinkerscanberepresentedasaBernoullitrialwithparameterP=probabilityofcoincidence.Therefore,multipleexplosiveeventswillhaveabinomialdistributionwithparame-tersne=numberofexplosiveeventsandP.Themeannumberofcoincidencesis=neP(1)andthestandarddeviationis=pneP(1P)(2)TheprobabilityPisdependentontheblinkercoverageintheobservations.Thisprobabilityexperimentissimilartothefollowing.Supposewehaveamatonwhichwehavedrawnseverallargecircles(theblinkers),nowsupposewetossacoin(explosiveevent)randomlyontothemat.Whatistheprobabilitythatthecoinlandsinsideoneofthecircles?Thesimplestprobabilitytocalculateistheprobabilitythatthecentreofthecoin(explosiveevent)occurswithinthecircle(blinker).Thisisequaltotheareaofthecirclesdividedbytheareaofthemat.Notethatiftheradiusofthecoinismuchsmallerthantheradiiofthecircles,thenthisisapproximatelytheprobabilitythat50%ofthecoinoverlapsthecircle.Forourblinkerobservations,wecancalculatethepercent-agevolume(areatime)ofblinkersintheCDSdataanalysedinSection3is6.7%.WeassumethatthisisalsorepresentativeoftheSUMERdata,whichiscontainedwithintheCDSeldofview.Wenotethatthispercentagevolumefoundishigherthanthe4%and5%giveninBewsher,Parnell&Harrison(2002)andBrkovi´c,Solanki&R¨uedi(2001),respectively.Brkovi´c&Peter(2004)provideduswithabreakdownoftheirresults(privatecommunication)foreachdatasetanalysed.Inthefollowing,datasetsA-Erefertotheirdatafrom97-04-22,97-04-25,98-05-12,98-05-16and97-04-23,respectively.ThepercentagecoverageofblinkersinSUMERdatasetsA-Ewere23.1%,18.7%,19.6%,11.5%and35.5%,respectively.Assumingthattheexplosiveeventsaresmallerthantheblinkers,wedenethreeprobabilities;P100istheprobabilitythatanexplosiveeventiscompletelyenclosedbyablinker;P50istheprobabilitythatthecentreofanexplosiveeventcoincideswithablinker(i.e.approximately50%ofanexplosiveeventoverlapsablinker);andP0istheprobabilitythat(0,100]%ofanexplosiveeventoverlapsablinkeroratleasttheedgesoftheexplosiveeventandblinkertouch.Iftheareaofanexplosiveeventisgreaterthantheareaofablinkerthen;P100istheprobabilitythattheexplosiveeventcompletelycoversablinker;P50istheprobabilitythatthecen-treoftheexplosiveeventcoincideswiththetheblinker;andP0remainsthesame.Itmayalsobeusefultodeneafourthprobability;Pc,whichistheprobabilitythattheexplosiveeventcoincideswiththecentreoftheblinker.ThederivationsandequationfortheseprobabilitiesaregiveninAppendixB. D.Bewsheretal.:ComparisonofBlinkersandExplosiveEvents:ACaseStudy9ThevaluesofP100andP0givesusarangeofprobabilitieswhichmaybevaliddependingonthedenitionofcoincidence.Forexample,doesa2%overlapcountasacoincidence?Allofthedenedprobabilitiesaredependentontheratiooftheexplosiveeventandtheblinkerareas.ThearearatioforthedierentdatasetsisgiveninTable6.Thearearatioofexplosiveeventsandblinkersidentiedinthispapersuggeststhatblink-ersareconsiderablylargerthanexplosiveevents.ThreeoutofthevedatasetsanalysedbyBrkovi´c&Peter(2004)havethemeanexplosiveeventareagreaterthanthemeanblinkerarea(i.e.arearatioisgreaterthan1)andtheothertwodatasetshaveexplosiveeventsbeingsmallerthanblinkers(i.e.arearatiolessthan1).Butinmanycases,thearearatiosofBrkovi´c&Peter(2004)areverynearto1(i.e.theareaofexplosiveeventsandblinkersaresimilar).Table6showsthepercentageblinkercoveragecalculatedfromthenumberofblinkersidentiedinCDSdatainthispa-perandinSUMERdatabyBrkovi´c&Peter(2004).Italsoshowstheratioofexplosiveeventareatoblinkerareacalcu-latedfromthemeanpropertiesofexplosiveeventsandblink-ersidentiedinSUMERbyBrkovi´c&Peter(2004)andfrommeanpropertiesofexplosiveeventsidentiedinSUMERandblinkersinCDSgiveninSections3.4and3.5.Theexpectednumberofexplosiveeventscoincidingwiththeblinkerscalcu-latedfromtheprobabilityanalysisfortheobservationalresultsgiveninthispaper(BIPB)andgiveninBrkovi´c&Peter(2004)(BPA-E)arealsogiveninTable6.Thenumberofexplosiveeventsobserved(ne),thenumberofexplosiveeventscoincidentwithblinkers,themeannumberofexplosiveeventsexpectedandthestandarddeviationfromthemeanforthethreedier-entvaluesofParealsoallgiven.Giventhesevaluesandatwostandarddeviation(approx95%)condenceinterval,wealsostatewhetherwecanrejectourhypothesis(R)oracceptit(A).Brkovi´c&Peter(2004)gavethenumberofpixelsthatshowedblinkerorexplosiveeventcharacteristicsintheirpa-per,butwereabletoprovideuswiththenumberofblinkerandexplosiveevents(i.e.groupsofadjacentpixelsthatallshowablinkerorexplosiveeventcharacteristic)sothatwecouldmakeatruecomparison.Thesearethenumberofblinkersandexplo-siveeventsinTable6.Unfortunately,theywerenotabletopro-videuswithhowmanyoftheseexplosiveevent`groups'werecoincidentwithblinker`groups'andviceversa.Therefore,wehaveassumedthatthepercentageofexplosiveeventsthatarecoincidentwithblinkersisthesamepercentageofexplosiveeventpixelsthatarecoincidentwithblinkerpixels.Thisgivesusalowerboundtothenumberofexplosiveeventsthatoccurwithblinkers,thetruenumbermaybehigher.IntheP0casefortheBrkovi´c&Peter(2004)datasetE,wendthatthecalculationinAppendixAbreaksdown.Thisisbecausetheextendedannuli(whereexplosiveeventspartiallyoverlapablinker)aroundblinkersmayintersectgivinganareagreaterthanthetotalarea.Thismayhappenwhenthereisahighpercentagecoverageofblinkers,andexplosiveeventsarelarge.ThuswetakeamaximumprobabilityofP0=0:99inTable6forcomparison.Thedatapresentedinthispapersuggeststhatwecannotrejectourhypothesisforanyoftheprobabilities.FormostoftheBrkovi´c&Peter(2004)cases,thehypothesisisrejectedforTable6.Meannumberofexplosiveeventsexpectedtocoincidewiththeblinkersandthestandarddeviationfromthemean.R(N)indicateswhetherthehypothesiscanberejected(ornot).Inthecasesmarked*,theprobabilityiseithergreaterthan1.0andhencehasbrokendown,ortheprobabilityislessthan0.01.BIPBP0P50P100%blinkercoverage6.76.76.7Arearatio0.10.10.1P0.120.070.03NoofEE's(ne)888NoofCoincidentEE's111Mean()0.90.50.3StandardDeviation()0.950.70.5Hypothesis(R/A)AAABPAP0P50P100PC%blinkercoverage23.123.123.123.1Arearatio0.90.90.90.9P0.890.230.01*0.22NoofEE's(ne)18181818NoofCoincidentEE's13131313Mean()164.10.03.9StandardDeviation()1.31.80.01.7Hypothesis(R/A)RRRRBPBP0P50P100PC%blinkercoverage18.718.718.718.7Arearatio1.21.21.21.2P0.830.190.01*0.23NoofEE's(ne)68686868NoofCoincidentEE's37373737Mean()56.212.70.115.4StandardDeviation()3.13.20.43.5Hypothesis(R/A)RRRRBPCP0P50P100PC%blinkercoverage19.619.619.619.6Arearatio1.31.31.31.3P0.900.200.01*0.26NoofEE's(ne)5555NoofCoincidentEE's4444Mean()4.51.00.01.3StandardDeviation()0.70.90.11.0Hypothesis(R/A)ARRRBPDP0P50P100PC%blinkercoverage11.511.511.511.5Arearatio1.01.01.01.0P0.450.120.01*0.11NoofEE's(ne)43434343NoofCoincidentEE's15151515Mean()19.34.90.04.7StandardDeviation()3.32.10.12.0Hypothesis(R/A)ARRRBPEP0P50P100PC%blinkercoverage35.535.535.535.5Arearatio1.21.21.21.2P0.99*0.360.01*0.41NoofEE's(ne)54545454NoofCoincidentEE's29292929Mean()53.519.20.122.0StandardDeviation()0.73.50.33.6Hypothesis(R/A)RRRR 10D.Bewsheretal.:ComparisonofBlinkersandExplosiveEvents:ACaseStudyTable7.Comparisonofthetheoreticalprobabilitiessuggestedbythemodelandanidealprobabilitycalculatedfromtheobservations.P0P50P100PidealBIPB0.120.070.030.13BPA0.890.230.010.72BPB0.830.190.010.54BPC0.900.200.010.80BPD0.450.120.010.35BPE0.990.360.010.54thegivenprobabilitiesbecausethenumberofexplosiveeventscoincidingwithablinkerisgreaterthantwostandarddevia-tionsawayfromthemeangivenbythebinomialdistribution.ThetwocaseswhentheresultsofBrkovi´c&Peter(2004)leadustoacceptourhypothesisareintheP0case,wheretheeventscanbeanythingfromtouchingtocompletelyoverlapping.However,ifwereversethisprocessandcalculatewhattheidealprobabilitywouldbefromtheobserveddata(Table7),weseethatinalloftheBrkovi´c&Peter(2004)cases,theidealprobabilityliesbetweenP50andP0.Thismayreectthese-lectioncriteriausedtodecidewhetheranexplosiveeventcoin-cideswithablinker.Thecalculationusingthedatapresentedinthispapersug-geststhatwecannotrejectourhypothesis.ThecalculationsusingdatafromBrkovi´c&Peter(2004)arelessconclusive.Inordertocometoaconclusion,twothingsarerequired;(i)spe-cicvaluesofhowmanyexplosiveeventswerecoincidentwithblinkersand(ii)amorerigorousdenitionofwhenexplosiveeventscoincidewithblinkers-howmuchmusttheyoverlapinordertobeclassedascoinciding?6.ConclusionsWehaveanalysedco-alignedSUMERandCDSdatasetsandautomaticallyidentiedbothblinkersandexplosiveeventsinbothdatasets.Itisclearthatusingourcriteria,blinkersareonlyidentiedinSUMERdatawhenthetemporalresolutionofthedatahasbeenreducedtothatofCDS.Elsesmalllocalisedbrighteningsthatmakeuptheblinkerareidentiedortheblinkermayevenbemissed(e.g.SUMERregionS2).CDSdataisneededforidentifyingblinkers,however,becauseofthespatialcoverageoftheinstrument.IdentifyingblinkerswithSUMERmeansthatonlyasmallareaoftheselargeeventsaresampled.SUMERisnecessary,however,forcompletingdetailedspectralstudiesofblinkers.Itisalsoclearthatour2criteriamethodforautomaticallyidentifyingexplosiveeventssuccessfullyidentiesexplosiveeventinbothSUMERandCDS.Infact,80%ofSUMERandCDSpixelsregisterthesameresulttothe2explosiveeventtests.ItismorelikelythatCDScansuccessfullyidentifyanexplosiveeventswhenthereisasignicantincreaseinthelinewidth,butcannotberelieduponforsuccessfulidenticationifawingenhancementispresent.SUMERisessential,therefore,forsuccessfulidenticationofexplosiveevents.Wehypothesisedthatblinkersandexplosiveeventsareran-domandnotphysicallyrelatedinanyway.Wethenusedabino-mialprobabilitymodeltodeterminewhethertheresultsfromthispaperandthoseofBrkovi´c&Peter(2004)supportedourhypothesisornot.UsingthepercentagecoverageofblinkersandthemeanpropertiesofblinkersidentiedinCDSandexplosiveeventsinSUMERgiveninthispaper,wesupportthehypothesisstated.However,theresultsofBrkovi´c&Peter(2004)arelessconclu-sive.Thehigherblinkercoverageandlargerexplosiveeventtoblinkerarearatiohasgivenussomeextremeprobabilitiesandhavebrokensomeoftheassumptionsmade.However,ineachcase,theidealprobabilityliesinthe[P50;P0]range.ItisunclearwhethertheeventsthatBrkovi´c&Peter(2004)haveidentiedinSUMERareactuallythecounterpartsofblinkersobservedinCDS.Madjarska&Doyle(2003)raisedsomeconcernsaboutidentifyingblinkersinSUMER,suggest-ingthatCDSwasnecessaryforsuccessfulidentication.Itisalsounclearwhethertheblinkersidentiedusingtheauto-matedroutinesdetailedinBrkovi´c,Solanki&R¨uedi(2001)andBewsher,Parnell&Harrison(2002)actuallyidentifythesameevents.Soareblinkersandexplosiveeventsthesamephe-nomenon?Ourresultsshowthatitisunlikely,whichourprob-abilityanalysisalsosupports.ArecentpaperbyHarrisonetal.(2003),alsoraisesdoubtsastoalinkbetweenblinkersandex-plosiveevents.Infact,inmostrecentpapersreferringtolinksbetweenblinkersandexplosiveevents(e.g.Peter&Brkovi´c,2003;Brkovi´c&Peter,2004),thecurrentfeelingisthatthereisnolinkbetweentheevents.Thedynamicsofthetransitionregionareverycomplex,fastandonsmallscalesand,unfortunatelybeyondthecapabil-itiesofSUMERandCDS.Werequirethenextgenerationofsolarspectrometerswithfasthighresolutionspectralimagingbeforewecanbegintounderstandthesourceofthevariabilityandthetruelinkbetweenblinkersandexplosiveevents.Acknowledgements.SOHOisamissionofinternationalcoopera-tionbetweenESAandNASA.CDSwasbuiltandisoperatedbyaconsortiumledbytheRutherfordAppletonLaboratoryandin-cludingtheMullardSpaceScienceLaboratory,theNASAGoddardSpaceFlightCenter,OsloUniversityandtheMax-Planck-InstituteforExtraterrestrialPhysics,Garching.TheSUMERprojectisnanciallysupportedbytheDARA,CNES,NASAandtheESAPRODEXpro-gramme.DBissupportedbyanEuropeanSpaceAgency(ESA)ExternalFellowshipatNASA/GSFC.CEPandDSBwouldliketothanktheUK'sParticlePhysicsandAstronomyResearchCouncilfornancialsupport.Thisworkstartedatthe`Smallscaletransientactivity'workshopattheInstitutd'AstrophysiqueSpatiale,Orsay,FranceinDecember2001.Thediscussionsofworkinggroup2:`Blinkerandexplosiveeventjointanalysis'providedvaluableinputtothispaper.AppendixA:SkewnessasacriteriaforexplosiveeventsForarandomsampleofvalues,x1;:::;xn,skewness(sk)isde-nedassk=m3(m2)1:5(A.1) D.Bewsheretal.:ComparisonofBlinkersandExplosiveEvents:ACaseStudy11Fig.A.1.Gaussianproleswithvaryingwingenhancementsandskewnessvalueswherem1=nXj=1xjnandmi=nXj=1xjm1in;i=2;3;4(A.2)FigureA.1(a)showsaGaussianfunctionthathasawidthof0.2units,centredat1.25units(solid).Tothis`core'proleweaddenhancementstothewingsthatcontain10%oftheuxofthecoreandhavethesamewidth.Thewingsarecentredat0.25(dotted),0.5(dashed)and0.75(dash-dot)unitstotheleftofthecentreofthecore.TheskewnessofeachoftheseprolesarecalculatedandareplottedonFigureA.1.Asthewingmovesfurtherfromthecentreofthecoreofthelineprole,theskewnessincreases.InthecasesgiveninFigureA.1(a),alltheskewnessvaluesarenegative.Ifthewingswereplacedatthesamepositionbutontherighthandsideofthecoreprole,theskewnesswouldbethesamemagnitude,butthesignwouldbereversed,i.e.allthenegativeskewnesseswouldbecomepositive.Next,weconsiderproleswith2wings.Ifwingprolesofequalsizeareplacedatequaldistancesoneithersideifthecentreofthecore,thentheskewnesswillequal0,sincethesymmetryofthelineisnotaected.Ifthesizeofthewingsorthedisplacementofthecentreofthewingfromthecoreisnotequal,theskewnesswillbenonzero.FigureA.1(b)showsasymmetriclineprolewithnowingsand2proleswithequallysizedwingsplacedat0.25unitstotheleftand0.5unitstotherightofthecentreofthecore(dotted).Afurtherprolewhichhasequallysizedwingsplacedat0.5unitstotheleftand0.75unitstotherightofthecentreofthecoreisalsoplotted(dashed).Againtheskewnessvaluescalculatedfortheprolesaregivenonthegraphs.Inthecaseswherethereare2wings,theskewnessvaluesarelowerthanwhentherewasasinglewing.Thisisbecausethewingspartiallybalancethesymmetryofthelineproleandhencethelinesaremoresymmetricthanthecasesshownwherethereisasinglewing.Therefore,theskewnesscriteriawillbemoreusefulforidentifyingexplosiveeventscharacterisedwithasinglejet,ratherthanabi-directionaljet.AppendixB:OverlappingblinkersandexplosiveeventsAssumeblinkersandexplosiveeventscanbeapproximatedbycircleswithradiusrb,andre,respectively.Also,assumethatablinkerislargerthananexplosiveevent(rbre).Ifthecentreoftheexplosiveeventisontheedgeoftheblinker(adistancerbfromtheblinkercentre),thenapproxi-mately50%oftheexplosiveeventcoincideswiththeblinker.Fortheexplosiveeventtobecompletelyenclosedbytheblinker,thecentreoftheexplosiveeventmustbeatmostrbrefromthecentreoftheblinker.Similarly,explosiveeventsthathaveanykindofoverlapwiththeblinkermusthaveacentrethatisatmostrb+refromthecentreoftheblinker.Wherethecentresoftheblinkerandexplosiveeventareexactlyrb+reaparttheiredgestouch,butthetwodon'tactuallyoverlap.Thecasewherethecentreoftheexplosiveeventcoincideswiththeblinker(approximately50%overlap),P50isequaltoP50=Pb100;(B.1)wherePbisthepercentagecoverageofblinkers.Thecasewheretheexplosiveeventisenclosedwithintheblinker(100%overlap)P100isequaltoP100=P50(rbre)2rb2=P500BBBBB@12rerb+ rerb!21CCCCCA(B.2)Ifweset, rerb!2=AeAb=Ar;(B.3)whereAeandAbaretheareasoftheexplosiveeventandblinkerrespectively,thenP100=P5012pAr+Ar(B.4)Similarly,thecasewhereatleasttheedgesoftheexplosiveeventandblinkeraretouching,P0isequaltoP0=P501+2pAr+Ar(B.5)However,ifre�rbthen;P100istheprobabilitythattheblinkeriscompletelyoverlappedbytheexplosiveevent.Wecandeneafourthprobability,Pc,theprobabilitythattheex-plosiveeventoverlapsthecentreoftheblinker(orthecentreoftheblinkeriscontainedwithintheexplosiveevent),isequaltoPc=P50r2er2b=P50Ar(B.6) 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