1988ApJ. . .330. .474P 8_1 -27 - 10 -2_1 7 7-21 6 2 10-3 9 10 2 8 Noyes 1977),mostofwhichislostbyradiationasEUVandX- waves, andmagnetohydrodynamicwaveswhichpropagate tially force-free. Alfvén speedis2x10cms.Themagneticfieldessen- is then6-9dyncm,thespeedofsound2-3x10 s \ with apressurescaleheightof1-1.5x10cm;thedensity cm stheformationofcoronaisstraightforward:The Golub etal.1980),andgivenasourceofheatabout10ergs elusive. Thereisadirectequationbetweenmagneticfield confining bipole(Rosner,Tucker,andVaiana1978)fromthe ray coronaisessentiallyindependentofthedimensions rays. ItisobservedthatthesurfacebrightnessofactiveX- by aheatinputofabout10ergscms(Withbroeand The hightemperature(2-3x10K)ofthegasismaintained primarily Alfvénwavesthatreach theactiveX-raycorona.The visible surfaceoftheSunproducessoundwaves,gravitational the magneticpressure(10G)istypically4x10dyn,and the point radiativelossesbalancetheheatinput.Thegaspressure the risinggasincreasestoabout10atomscm,atwhich heated gasexpandsupwardfromthetopofchromosphere bright pointsat10cm,andinsomecasesevendowntothe normal activeregionwithascaleof10cmdowntotheX-ray of hotgasenclosedinstrong(10G)bipolarmagneticfields. Administration underNASAgrantNGL 14-001-001. problem isthatAlfvénwaves are disinclinedtodissipateinthe rock andUchida1981;Priest 1982).Presumably,then,itis Whitaker 1963).Morerecentlyithasbecomeclearthatall but and deposittheirenergyasheatintheambientgas(Bierman upward intotheoverlyingatmospherewheretheydissipate strength andheatinput(Rosner,Tucker,Vaiana1978; small bipolesof2x10cmatthelimitresolutionpresent the corona(Osterbrock1961; SteinandLeibacher1974;Stur- Alfvén wavesaredissipatedand/orrefractedbeforereaching observational instruments. The AstrophysicalJournal,330:474-479,1988July1 © 1988.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. 1946, 1948;Alfvén1947;SchwarzschildParker1958; 1 The traditionalviewhasbeenthattheconvectionbelow The heatsourcethatcausestheX-raycoronahasproved The X-raycoronaoftheSuniscomposedtenuouswisps Thisworkwassupportedinpartby theNationalAeronauticsandSpace from smallisolatedmagneticbipolesisintermittentandimpulsive,whilethesteadieremissionlarger characteristics oftheprocessareinferredfromobservedcoronalheatinput. continuities arisingspontaneouslyinthebipolarfieldsofactiveregionsSunasaconsequence bipoles appearsasthesumofmanyindividualimpulses.Werefertobasicunitimpulsiveenergyrelease random continuousmotionofthefootpointsfieldinphotosphericconvection.Thequantitative a swarmofnanoflares. as ananoflare.Theobservationssuggest,then,thattheactiveX-raycoronaofSunistobeunderstood Subject headings:hydromagnetics—Sun:coronaflares © American Astronomical Society • Provided by the NASA Astrophysics Data System This interpretationsuggeststhattheX-raycoronaiscreatedbydissipationatmanytangentialdis- Observations oftheSunwithhightimeandspatialresolutioninUVX-raysshowthatemission I. INTRODUCTION Enrico FermiInstituteandDepartmentsofPhysicsAstronomy,UniversityChicago 1 NANOFLARES ANDTHESOLARX-RAYCORONA Received 1987October12;acceptedDecember29 E. N.Parker ABSTRACT 474 _1 corona. Indeed,itisjustthatdisinclinationallowsthemto with magneticreconnection(Parker1983d,1986c). entire space(Glencross1975,1980;Parker1981a,b;Sturrock fibril movesindependentlyofitsneighbors,producingtangen- individual magneticfibrilsatthephotosphere,each mixing ofthefootpointsfieldinphotosphericcon- (Cheng, Doschek,andFeldman1979)theAlfvénwavemust corona. Variousideashavebeenproposedtofacilitatedissi- penetrate thechromosphereandtransitionregiontoreach netic fieldbythephotospheric convection.Thus,far,observa- input tothecoronaismechanical workdoneonthemag- tangential discontinuities(currentsheets)becomeincreasingly between localregionsofdifferentwindingpatterns. The appear intheinitiallycontinuousfieldatboundaries Tsinganos 1982;Tsinganos,Distler,andRosner1984;Moffatt tangential discontinuities(Syrovatsky1971,1981;Parker1972, continuous mappingofthefootpointsspontaneouslyproduces and Uchida1981).Thereis,however,amorebasiceffect,viz., a at higherlevelswheretheyexpandagainsteachothertofillthe tial discontinuities(currentsheets)betweenneighboringfibrils vection. Insofarasthefieldisconcentratedintoseparate regions asaconsequenceofthecontinuousshufflingandinter- the manysmallcurrentsheetsforminginbipolarmagnetic disintegration ofaturbulenteddy(Hollweg1984,1986). dissipate withinaboutoneperiod,whichisreminiscentofthe provide thenecessaryheatinputwithoutviolating pation (cf.HayvaertsandPriest1983;Hollweg1984,1986, resolve theindividualmagnetic fibrils[withdiametersofabout principal observationaldifficulty isthecontinuinginabilityto the expectedshufflingandintermixing ofthefootpoints.The tions havefailedtodetecteither theexpectedwavemotionor tually producingintensemagneticdissipationinassociation severe withthecontinuingwindingandinterweaving,even- observed upperlimitof25kmsonthewaveamplitudes Roberts 1986;Davila1987).Thebasicpointisthatinorderto 1986c, 1988)thattheX-raycoronaisheatedbydissipationat 1985, 1986;VainsteinandParker1986).Thediscontinuities 1979, 1982,1983a,b,c,d,1986a,h,1987a;Yu1973; 1987; Kuperus,lonson,andSpicer1981;lonson1984;Lee Now, fundamentaltoanytheoretical ideaontheenergy Alternatively ithasbeensuggested(Parker1979,1983d, 1988ApJ. . .330. .474P -1 2 8 21 27_15 126 _1 3 26_14- 2 3 1023 21 5 27 4-2_1 27-1 ening. Porteretal.suggestthat thesebrighteningsmayperhaps rapid successionofnanoflares, producingcontinualbright- 27 bright. Thelargerandstronger thebipole,morelikely perhaps 10%ofthebipoles being continuouslybutvariably bipoles exhibitmorefrequent nanoflaresthanothers,with jets appearatarateofabout20s,withanindividuallife of lived (~10s),occurringinthe smallerbipoles.Somemagnetic minutes toanhour,butthemostcommoneventsareshort 24 2-4 x10cm.Afractionofthebrighteningslastseveral occurring inthesmallmagneticbipoles,withdimensions of represent localizedimpulsiveheatingevents(nanoflares) brightenings, observedmosteffectivelyinthelinesofC iv, localized brighteningsthroughoutthemagneticnetwork. The cm “s~averagedoverthesurfaceofSun. time. Thetotalenergyisthen6x10ergss,or ergs 0.4 x10gofgasandakineticenergy3ergs. The with velocitiesof400kms,eachjetapproximately 50 ssothatthereare10jetspresentovertheentireSunat any tions alsodiscoveredintensepinpointjetsdirectedupward averaged overthesurfaceofSun.ThesameEUVobserva- up toabout6x10ergssorcms“,when ergs. Thelifeofanindividualeventistypically10s.Thereare about 10neweventseachsecondovertheentireSun,sothat involves 10gofgas,withakineticenergyabout7x gas atspeedsof10kms“.Thetypicalturbulentevent intense “turbulentevents”involvinglocalizedchurningofthe (1983; Brueckneretal.1986),observingintheEUV,discovered 10 eventsareinprogressatanytime.Thetotalenergyadds (Parker 1987h)thatflaresofallsizesaremadeupclusters nanoflares (seealsotheinterestingparallelideasproposedby Sturrock etal.1984). position ofmanynanoflares.Indeed,wehavesuggested event). Evidently,then,themicroflareismadeupofasuper- in thesequeltoreferanylocalizedimpulsiveenergyrelease below thelevelofconventionalmicroflare(>10ergsper flaring. Thesmallenergyofeacheventsuggeststhattheterm nanoflare isanappropriateapellation,whichtermweshalluse the individualspike,indicatingverysmall,frequent flare withadurationof5-100s.Theextraordinaryfeatureis 2 X10ergscms.Atrandomintervalsoftheorder 300 sthereappeardenseclustersofspikes,suggestingamicro- of theSuninthesehardspikesisabout10ergss,or spikes belowthisinstrumentalcutoff.Thetotalenergyoutput numerous smallerspikesdowntothedetectionlimitofabout (>20keV) withindividualdurationsof1-2s.Thelarger Sun, butmostoftheemittedenergyappearsinmore spikes representindividualenergyemissionsof10ergsatthe orbit ofEarth.TheyobserveintermittentspikeshardX-rays an X-raydetectorlookingattheSunfromaposition 10 ergsperspike.Onesuspectsthattheremaybemanymore bursts ofenergy,whichwerefertoasnonoflares. show aheatinputcomposedofmanylocalizedimpulsive transition region,employinghighspaceandtimeresolution, precise. X-rayandUVobservationsoftheactivecorona aspect ofthecorona,dealingdirectlywithheatinput.Tobe determination oftheirmotions. 200 km(0'.'2)atphotosphericlevels]whichprecludesaprecise A recentpaperbyPorteretal.(1987)reportsthediscoveryof To continuewiththeobservations,BruecknerandBartoe Consider firsttheobservationsofLinetal.(1984)employing The presentwritingisdirectedtoobservationsofanother © American Astronomical Society • Provided by the NASA Astrophysics Data System II. OBSERVATIONS NANOFLARES ANDSOLARX-RAYCORONA 23_ 124 7 -21 162 162 8 27 24 27 8 4 x10ergssor8 ergsin20s.Ifasinglenanoflare The totalemission(at10ergs cms)fromtheregionis estimate thecharacteristicenergy ofthatindividualnanoflare. 9 total brightnessoftheregion (4x10cm),itispossibleto to theindividualnanoflare,producing a20%fluctuationinthe times of20-60s.Ifweattribute theshortesttimescaleof20s (4 x10cm)fluctuatesby20%-100%oncharacteristic (1984). Theyfindthataregionwithdimensionsof2x10 cm from thefluctuationsreportedbyPorter,Toomre,andGebbie active X-raycoronaistobeunderstoodonthisbasis. cause thehardX-rayburstsobservedbyLinetal.(1984). The velocity jetsobservedbyBruecknerandBartoe(1983) and ing 10ergs,producetheisolatedturbulenteventsand high X-ray corona.Theaveragenanoflareprobablyhasanenergy of 10ergsorless,whereasthelargestnanoflares,approach- about 10ergsmakesupthephenomenonthatwecall the of nanoflaresrangingdownwardinindividualenergyfrom number ofnanoflares.Thatistosay,astatisticaldistribution X-ray coronaissimplythesuperpositionofaverylarge collectively, theobservationssuggestthatwhatweseeas solar activeregions. ubiquitous bursts,scintillations,andflickeringsassociatedwith a convenientlistofreferencestoearlierpapersreportingthe just thisconditionwhichleadstotheremarkableobservational random small-scalemagneticreconnection.Theyalsoprovide remark thatthecontinualflickeringsuggestsheatingby 20%-100% oncharacteristictimescalesof20-60s.They dimensions. Theyfoundthatthebrightnessvariedtypicallyby found theimpulsivebrighteningtobemuchsameas observed (Porteretal.1987)inisolatedsmallbipolesofsimilar spatial resolutionof2x10cm)inanormalactiveregion, emission linesofSiivandOfromUV-brightpoints(witha regions. Porter,Toomre,andGebbie(1984),observingthe fact, notedintheIntroduction,thatsurfacebrightnessof dependent onthedimensionsoflocalmagneticbipole.Itis sions oftheassociatedmagneticbipole. the X-raycoronadependsonlyweakly,ifatall,ondimen- flares thatoccuratarate(perunitarea)isnotstrongly to beunderstoodasadirectresultofthestatisticsnano- together withtheobservedbehaviorofsmallerbipoles,is shorter livedthanthelargerX-ray-brightpoints.Thisfact, points aremorenumerous,rapidlyfluctuating,and and Withbroe(1981)foundthatthesmallerX-ray-bright et al.1977).Golub,Krieger,andVaiana(1976a,b)Habbal Vaiana, andVanSpeybroeck1971;Golubetal.1911;Moore microflares, sothattheX-raybrightpointseemstobeascaled down versionofthelargernormalactiveregion(Krieger, Occasional enhancementsintheemissionrisetolevelof Golub 1979;Nolte,Solodyna,andGerassimenko1979). loops varyontimescalesoftheorder400s(Sheeleyand variable EUVandX-rayemission.Theindividualemitting which individuallyturnonandofftoprovideacontinuingbut points andwithephemeralactiveregions.Theessentialpointis istic dimensionsof10cm,associatedwithX-ray-bright that theseregionsaremadeupofmanysmallbrightloops from theobservationsisthatheatinputtomagnetic bipole consistsofmanysmalltransientburstsenergy. Brueckner andBartoe(1983).Theessentialpointtobeinferred be associatedwiththeturbulenteventsandjetsfoundby A crudeestimateofthecharacteristicnanoflarecanbemade The purposeofthepresentwritingistoemphasizethat, This conditionextends,evidently,tothenormalactive Consider, then,thesomewhatlargerbipoleswithcharacter- 475 1988ApJ. . .330. .474P 24 _1/2 8 2 2/32 1/3 2 2422 27- nanoflare, deducedfromobservationsofthelocalflickeringdiscontinuitycausesmagneticenergytodegrade contributes 20%ofthis,thenanoflareinvolvesapproximatelypropertiesmagneticfieldembeddedinaninfinitelycon- a normalregionoftheactiveX-raycorona.throughdynamicalnonequilibriumandconsequentrapid observed fluctuationsof20%-100%andwiththe10ergsperParker1987a;Moffatt1987;LowWolfson1988).Each time, suggestingfluctuationsinbrightnessbyatypicalfractionmagneticlinesofforcearewoundandwrappedabouteach about fivenanoflaresinprogresstheregionatanygivenjectedtocontinuousbutcomplexdeformation,sothat from theirobservationofthesmall-scaleflickeringUV is createdbyalargenumberofsmall-scalemagneticreconnec- collection ofnanoflares,thenitwouldappearthatthecorona emission fromthetransitionregion.Wesuggestedidea 5, orabout44%.Thisisinroughagreementwiththeothercomplicatedpatterns(seediscussionandreferences based onacriticalreviewofthetheoreticalpossibilities(Parker tions. Porter,Toomre,andGebbie(1984)madethissuggestion 476 from eithergranulemotions(withcharacteristictime waves atsuchshortperiodswouldbearevelationinthem- longer, thenthepassageofwaverepresentsonlyaslow dimensions ofthebipole.Forifwavelengthissignificantly periods of1-10sifthewavelengthistobeassmall regions ofX-rayemission,requiringstrongAlfvénwaveswith accounting forthebrightnessofverysmall(2-10x10cm) gating upfromthephotosphererunsintogravedifficultyin the X-raycoronaisheatedbydissipationofwavespropa- factor of10-50thanthewaveswith10speriod.Theat characteristic lifeist=l/v(l)oc/.Henceipv(l)t(/),and with acharacteristicscale/isproportionalto,whilethe T «300s)orfromobservedoscillationswithperiodsof10s. selves. Theycouldnotbeunderstoodasaturbulentcascade quasi-static deformationofthemagneticfield(seediscussionin mixing, thentherearetangentialdiscontinuitiesproducedin increase withthepassageoftime(seediscussionin§IV).Even- but thewavesat2-10swouldbeentirelyinadequate. smaller indirectproportionaltotheirperiods,i.e.,bya such short-periodwaveswouldhavekineticenergydensity For theKolmogorovspectrumpredictsthatvelocityv(l) Parker 1986c,1988),producinglittleornoheating.Strong 1.6 x10ergsor8s.Thereare,onthisbasis,ductingfluid.Thediscontinuitiesarisewhenthefieldissub- the bipolarfields.Thenumberofdiscontinuities(current of thebipolarfieldsaresubjecttorandomshufflingand picture seemstobesubstantiatednowbytheaccumulating principal causeoftheactiveX-raycorona.Thistheoretical nanoflares. Wesuggestedsomeyearsago(Glencross1975, to befilledwithsmall-scalereconnectionevents,i.e., Hence, weexpectthebipolefieldsabovesurfaceof Sun as fasttheyarecreatedbythemotionsoffootpoints. netic fieldacrosstheindividualdiscontinuitiesdestroysthem tually apointisreachedwhererapidreconnectionofthemag- sheets) andtheindividualamplitudesofeachdiscontinuity convection. Thespontaneous formationoftangentialdiscon- X-ray coronasofsimilarsolitary, late-type,main-sequence the shufflingoffootpoints ofthefieldinphotospheric uities formedspontaneously in thesurfacemagneticfieldsby stars, areprimarilyaconsequence ofthetangentialdiscontin- observations citedabove. 1979, 1983c,d,1986c).Inparticular,thetraditionalviewthat tinuities isapeculiarconsequence ofthestaticequilibrium 10 smayperhapscarrysufficientenergy(~10ergscm), 1980; Parker1979,1981a,b,1983d,1986c,1988)thatthisis the If observationsindicatethattheX-raycoronaisprimarilya If, ontheotherhand,weacceptideathatfootpoints It appears,then,thattheX-raycoronaofSun,andhence © American Astronomical Society • Provided by the NASA Astrophysics Data System III. IMPLICATIONS PARKER -1 -1 (1977, 1982);Biskamp(1982,1984,1986);VanHoven,Tachi, (1976, 1979,1981);Tajima,Brunei,andSakai(1982);Spicer ford 1973;Kadomtsev1975,1984;Waddelletal1976;Finn has beenreducedtoaform withuniformtorsiona(where et al.(1986);andChiuehZweibel(1987)forapresentation Tajima andSakai(1986);PriestForbesDahlberg Taylor (1974,1975,1976,1986);Vasyliunas(1975);VanHoven burg etal.1986)andleadingtoreconnectionbetweentheinner magnetically confined,current-carryingplasmasinthelabor- which furtherenhancesthereconnection.Therapidreconnec- overall meanvalueofaisclose tozero. that hasbeenwoundandinterwoven atrandomsothatthe accordance withTaylor’shypothesis (Taylor1974,1975,1976, \ •B=otBfortheforce-free field B)throughouttheregionin ture thattherapidreconnectionmaycutoffonlywhen field tion phenomenon.Dixon,Browning,andPriest(1988)conjec- of somethemoresalienttheoreticalfacetsreconnec- and Steinolfson(1984);VanHoven and externalfields.Thereaderisreferredtosuchworks as and Kaw1977;Montgomery1982;Lichtenberg1984;Dahl- atory apparentlyinitiatedbytheonsetofaninternalinstability ruptive magnetohydrodynamicalactivityobservedin tion phaseisnotunliketheindividuallarge-scaleburstofdis- producing bothhydromagneticandplasma“turbulence,” cal instabilityleadingtoanexplosivereconnectionphase, continuity exceedssomethreshold,thereisarunawaydynami- of theplasmaandfield(cf.Rosenbluth,Dagazian,Ruther- ive calculationoftheratedissipationataspecifiedtangen- input totheX-raycorona.Weshallassume,forsakeof Matthaeus andLamkin(1985,1986);LeeFu(1986); increases fromzerowiththepassageoftimeonlyavery granule radius.Hopefully,withinthenextdecadeaproper km sandwithacorrelationlength/comparableto at randomwithachracteristicvelocityvoftheorder0.5 km s,thefootpointsofmagneticfieldareshuffledabout discussion, that,inkeepingwiththegranulemotionsof1-2 and wanderingofthosefibrilsthatprovidesmosttheenergy not presentlyavailablefromobservation,sinceitisthejiggling reconnection ofthefieldacrossdiscontinuity. discontinuity |A/?|.Thenwhenthestrength|A/?|ofdis- theoretical numericalsimulations)indicatesthatthestrength nonlinear dynamicalcharacterofthereconnection.However, observational determinationofvand/willbecomeavailable. slow reconnectionoccurring,presumablyproportionaltothe of theindividualtangentialdiscontinuity,orcurrentsheet, some ofthemainfeaturesprocess. using presentobservationsasaguide,itispossibletoinfer tial discontinuityisnotforthcoming,becauseofthecomplex 1986). Itisnotentirelyclear how toapplythisideaafield It isunfortunatethatthemotionsofmagneticfibrilsare To begin,then,experience(bothinthelaboratoryand On thetheoreticalside,weshouldbeawarethataquantitat- IV. DISCUSSION Vol. 330 1988ApJ. . .330. .474P 721 footpoint. is progressivelyextendedtransversely bythemotionof The powerinput,then,increases linearlywithtime,asthefield 2 21/_ field atarate with astressBB/4nsothatthefootpointdoesworkon the footpoint opposestheonwardrandommarchof The tensioninthefluxbundletrailingoutbehindmoving the transverse(horizontal)componentBistan0(i),sothat ’ at leastfor0(t)<1.Iftheverticalcomponentoffieldis B, footpoints oftheneighboringverticalfluxbundles.Thebundle has amoreorless,uniformdeviation0(i)tothevertical,where at z=Lasthemovingfootpointloopsinandoutaround connects themovingfootpointatz=0withfixed ± sphere movesaboutwitharandomvelocityv.Thefluxbundle given elementalfluxbundle,whosefootpointatthephoto- L plane (z=L)inwhichthefootpointsarefixed.Thenconsidera photosphere (z=0)extendingadistanceLstraightupto field isinitiallyuniformandperpendicular(vertical)tothe footpoints. motions ofthefootpointsatphotosphere(cf.Parker1983d, readily deduced,giventhescale/andvelocityvof mutual windingandwrappingofthemagneticlinesforceis ing isoftheorder10ergscm“s“inbipolarfields that theenergyreleasethroughreconnectionandnanoflar- are subjecttointerweaving. there areextendedfluxsurfacesinafieldwhoselinesofforce where thewavesmayleakaway,anditisnotobviousthat 1986c, 1988).Toprovidethesimplestmodel,supposethat itself toformatubeofsomesortifitisavoidhavingedges, 10 gsubjecttocontinuousdeformationbythemotionvof although itrequiresthattheresonantfluxsurfacebeclosedon effect. However,thebuildupofalarge-amplituderesonance oscillation isatleastatheoreticalpossibility(cf.Davila1987), obvious thatthisbackgroundnoisewouldhaveaninteresting is