T. G. Forbes- A review on the genesis of coronal mass ejections

8/3/2019 T. G. Forbes- A review on the genesis of coronal mass ejections

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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. A10, PAGES 23,153-23,165, OCTOBER 1, 2000

A review on the genesis f coronalmassejectionsT. G. ForbesInstitute or the Studyof Earth, Oceans, ndSpace,Universityof New Hampshire,Durham

Abstract. This paperprovidesa short eview of someof the basicconceptselated o the originof coronalmassejections CMEs). The various deaswhich have beenput forward o explainthe initiation of CMEs are categorized n termsof whether hey are force-freeor non-force-freeand deal or nonideal. A few representative odelsof eachcategoryare examined o illustratethe principles nvolved. At the present ime there s no modelwhich s sufficientlydeveloped oaid forecastersn their efforts o predictCMEs, but given he currentpaceof research,his situa-tion could mprovedramatically n the near uture.

1. IntroductionFigure 1 illustrates hreedifferent ypesof large-scale ruptive

phenomena ccurring n the solar atmosphere, pecificallycoro-nal mass ejections (CMEs), prominenceeruptions,and largeflares. They are all closely elated and may, in fact, be differentmanifestations f a singlephysicalprocess.Let us first considerthe CME.

Here we will use the term "CME" to indicate the entire pro-cess hat leads o the ejectionof massand magnetic lux into in-terplanetary pace. Traditionally,observers ave defineda CMEas the outward ravelingbright arc seen n coronagraphsFigurel a) and the dark cavity (also Figure l a), prominencematerial(Figure lb), and X-ray loops (Figure ld) that appearbehind hisarc are not considered s the CME even though hey are associ-atedwith it. The bright arc s thought o result rom the pileup ofthe helmet streamerwhich typically overlies he erupting egion[Hundhausen, 1988; Low, 1996], but most of the models we dis-cuss here do not include a helmet streamer. Since there is nofeature in these models which can be associatedwith the brightarc, they are not modelsof CMEs according o the standard efi-nition of many observers.However, for a general heoretical is-cussionwe need to have a term which refers not just to an iso-lated featureseenby a particular nstrument ut to the underlyingphysical reality of the entire phenomenon. Already many re-searchers se the term CME in just this way. Even though hiscreates certaindegreeof confusion,t is natural or the defini-tion of a phenomenono evolve from one that s basedpurely onobservational spects o one that is basedon an understanding fthe physicalphenomenontself.

CMEs constitute arge-scaleejectionsof massand magneticflux from the lower corona into the interplanetary medium.Measurementsrom spacecraft nd coronagraphshow hat a typ-icalCME njectsoughly 023Maxwells f magneticlux and1016 of plasmanto nterplanetarypaceGosling,990;Webbet al., 1994]. During the quiet phaseof the solarcycle thereareapproximately wo CMEs per week, but during the active phasethe rate can exceed one per day. Although most CMEs are notassociatedwith large flares, if a large flare does occur, it isinevitably associatedwith a CME.Historically,lareshavebeendefined s he ocalized right-eningsof the chromosphere ver the courseof a few minutesasCopyright 000 by the AmericanGeophysical nionPapernumber2000JA000005.0148- 0227/00/2000JA000005509.00

observedn Hot mages Zirin, 1988]. TheseHotbrighteningsnthechromospherereknown s lare ibbonssee igurec), andthey ypically ccurn pairs, lthough ore omplexormationsare not uncommon. More recently, he term "flares"hasbeenused o describehe apidonset f X-rayandUV emissionsn thecorona.The softerX-ray andUV emissionsppearn the ormof oopssee igured)withemperaturesangingrom 05o3x 107 K and with the UV loopsnested elow the X-ray ones.CoolHot oops, orrespondingo a temperaturef 104K, appearunderneath he UV loops, and it is generallyaccepted hat theyare formed rom the hot oopsby a thermalcondensationrocess[Parker, 1953; Cox, 1972]. The outermost dgeof the hot X-rayloops maps to the outer edge of the ribbons [Schmiederet al.,1996], while the nnermost dgeof the cool Hot oopsmaps o theinner edge of the ribbons [Rust and Bar, 1973]. During thecourseof the flare the separationbetween he ribbons ncreases,and both hot and cool oopsappear o grow argerwith time.

Figure 2 shows he temporalbehaviorat variouswavelengthsfor a very large flare which occurredon August 28, 1966. Thisevent had intense Hot, X-ray, and radio emissions,and it pro-duced a high-speedshock wave which manifested tself in thechromosphere s a "Morton wave." The Morton wave s thoughtto be the chromosphericootprintof a fast mode MHD shock nthe corona,and t is causedby a slightdisturbance f the chromo-sphere at the location where the fast mode wave intersects hesolar surface [Dodson and Hedeman, 1968; Zirin and Lacknet,1969; Uchida, 1970, 1974].

The Hot emission n Figure 2a comes rom the two chromo-spheric ribbons whose appearance s the classicalsignatureofflare onset. The Hot emission ecomes uite ntensewithin 5 minafter onsetbut takes a long time to decay. Even after 6 hours, tstill exceeds the preflare emission by almost a factor of 2.During the rapid rise phaseof the Hot emission he flare ribbonsmove part t a rateof more han100km s 1, butassoon s hepeak s reached, hey quickly slow o a speedof the orderof 4 kms 1. Anevent f this ype,astingormany ours,sknownsa"Long Duration Event" or LDE, for short. To the extent that itcan be determinedwith imperfectobservations, DEs are alwaysassociated with a CME.

The soft X rays, which are thermal n origin, are produced ythehot> 107K flare oopswhoseootpointsap o theHot ib-bons. Both the Hot ribbons and the soft X-ray loops persist ormany hours, sometimesas long as 2 days after a really largeevent qvestka,976]. HardX rays > 20 keV) appearnlydur-ing the impulsive phasewhen the Hot and the soft X-ray emis-sions are rapidly increasing n intensity. The hard X rays are

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23,154 FORBES: CORONAL MASS EJECTIONS REVIEW

(a)

(d)

Figure . Solar ruptivehenomena:a)whiteight oronagraphmage f a coronal assjectionCME) ontain-inganeruptedrominence.hewhite ircularine n heupperight-handomerndicateshe ocationf heSun'ssurfaceehindheoccultingiskof the nstrumentAugust8,1980,SMM archive, igh-Altitudebservatory).(b)Hotmage f he arge rominenceruption,nowns granddaddy"June, 1946, igh-Altitudebservatory).(c)Hot ibbonsroducedya flare ssociatedith CME July 9,1973, igBear olar bservatory).d)Cusp-shaped-rayoop ystem,sseen n he imb f heSun fter neruptiveventMarch, 1999, ohkohrchive,Institutef SpacendAstronauticalcience).uch osteruptionoop ystemsre ommono he hree henomenaof CMEs,erupting rominences,nd arge lares.

generallyhoughto be producedy nonthermallectrons,ndtheyareaccompaniedy radioemissionshichsupporthis n-terpretationvestka ndSimon, 969]. Duringhe mpulsivephase, 'rays ndneutronslsoappear, hich ndicateshepres-enceof high-energyrotons ithenergiesn excess f 100MeV.More thanhalf of all CMEs are associated ith the eruption fprominences.argequiescentrominenceshich xistoutsideof active egions an be quite spectacular hen hey erupt,asshown n Figure lb, and they nearly alwayscreatea CME.However, he muchsmallerprominenceshatexistwithin activeregions analsoerupt, suallyn associationith lares, ut t isnot knownhow well they correlatewith CMEs. In manycasesthese mallprominencesredifficult o identify,and heir ate soften difficult to determine.

As observationsave mproved, t hasbecome ncreasinglyclear haterupting rominencesutside ctive egions avemanyfeaturesypicalof large lares.Like arge lares, rupting romi-nences roduceoops nd ibbons hichmoveapartn time,butunlike arge lares, he ibbons reusuallyoo aint o be seennHa. However,he ibbonsan ften eseenn theHe 10830line, which s a moresensitivendicator f chromosphericxcita-

tion [Harveyand Recely,1984]. The eruption f a largequies-centprominenceoesnotusuallyproduce ignificant ardX-rayor y-ray emissions,robably ecauset occursn a regionwherethe field is relativelyweak (< 10 G).High-resolutionmagesobtained y the soft X-ray telescopeon Yohkoh in 1992 have made t clear that all CMEs and promi-nence ruptions reate aint X-ray loopswhichare sometimesreferredo as"giant rches"e.g.,qvestkat al., 1997].Thesegiantarches re he CME counterpartsf the flare oopsoccur-ring n two-ribbonlares, ut heyoftenexhibit pattern f mo-tion different from that of the flare oops. Insteadof continuallyslowingwith time, he archesmoveupward t a ratewhich e-mainsnearlyconstant r whichmay even ncreasewith time[qvestka,996]. However,hisdifferenceanbe explainedythe variationof the coronalAlfv6n speedwith height Lin andForbes, 2000].The interrelationshipetweenhe various eatureswhichonecan associate ith CMEs is shown n Figure3. It shouldbe keptin mind that these features are not necessarilypresent n allCMEs. Not all CMEs containa prominence, or do all CMEshavedetectablehromosphericibbons ndshockwaves.


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FORBES' CORONAL MASS EJECTIONS REVIEW 23,155

ia).............6 Hot-0.40.2

,--, evelntevel.0 , ,lO 103

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o15 16 17 18 19 20 21

UTFigure 2. Time evolutionof the radiationproduced y a flare onAugust28, 1966, which was associated ith both a two-ribbonflare and a prominence eruption: (a) Hot ribbon intensity[Dodsonand Hedeman, 1968], (b) thermal, soft X-ray emission[Zirin and Lackner, 1969], and (c) nonthermal, ard X-ray emis-sion Arnoldyet al., 1968].

photospheresweaklyonized,avingesshan 0-4 hargedar-riers per neutral particle, compared o the fully ionized corona.These models nvoke the sameprocess hat occurs n laboratoryMHD generatorswhen a weakly ionized plasma lows acrossastationarymagnetic ield. However, Melrose and McClymont[ 1987] have shown hat the conceptof a photospheric ynamoofthis type is grossly nconsistentwith the observedpropertiesofthe photosphere nd the way it is coupled o the regionsaboveand below it.

A related flux injection model has been proposedby Chen[1989] which impulsively injects magnetic lux and power fromthe convection zone into the corona at CME onset. This modelrequiresa rapid increase n the magneticenergy of the coronaduring the eruption,rather than a decrease s n the storagemod-els, and it does not address he reasonwhy the convectionzoneshould suddenly nject flux into the corona. An analysisbyMcClymontand Fisher [ 1989] finds that the flux injectionmodelrequires arge-scale horizontal motions that are not consistentwith those hat are observed. Although the photospheres onlyweakly ionized, it is still an excellent conductor,and field linesthere are frozen to the plasma. Thus any sudden njectionof fluxfrom the convection zone to the corona must necessarilymovethe photospheric lasma.Models basedon the storage f magnetic nergyprior to CMEonsetalso ransferenergy rom the convective one o the corona,but this processoccursover a long time period of the order ofhours o days prior to the CME. The photosphericmotionsaredirectly observed,while the buildupof currentwhich results romthem can be inferred from vector magnetograms nd changes nfield-alignedplasmastructurese.g., filamentsand ibrils).How muchenergy s required o drivea CME canbe discernedfrom Table 1, which shows he estimated nergyoutputof a veryfast CME of moderately arge size (valuesare from Canfield et

2. EnergeticsWhen CMEs were first clearly identified by Skylab in 1973,many researchersssumedhat they were caused y the outwardexpansionof hot plasmaproducedby a large flare. We nowknow that this is not the case, for several reasons. First, less than

20% of all CMEs are associated ith large lares Gosling,1993].Second, CMEs that are associatedwith flares often appear tostart before the onsetof the flare [Wagner et al., 1981; Simnettand Harrison, 1985]. Finally, the thermalpressure roduced y aflare is too small to blow open the strongmagnetic ield of thecorona.

At the present ime, the mostgenerallyaccepted xplanationfor the causeof CMEs is that they are produced y a lossof sta-bility or equilibrium of the coronal magnetic ield [cf. Low,1996]. The continual mergence f new flux from the convectionzone and the shuffling of the footpointsof closedcoronal ieldlines causestresseso build up in the coronal ield. Eventually,thesestresses xceeda thresholdbeyondwhich a stableequilib-rium cannotbe maintained,and the field erupts. The eruptionreleases he magneticenergystored n the fields associated ithcoronal currents, so models based on this mechanism can bethoughtof as "storagemodels."

However, from time to time, various researchershave consid-ered the possibility hat the energy sourcewhich drives CMEsand flares ies within or below the photosphere.Sen and White[1972], Heyvaerts 1974], Hdnoux 1986], and Kan et al. [1983]have proposed lectricdynamomodelsbasedon the fact that the

Figure 3. Schematicdiagramshowing he relationship etweenvarious eaturesassociatedwith a CME. The shaded egion a-beled "plasma pileup" refers to the outer circular arc seen ncoronagraphs.


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23,156 FORBES: ORONAL ASSEJECTIONSEVIEWTable1. Energy equirementsora ModeratelyargeCME

Parameter ValueKineticenergy CME, prominence,ndshock)Heating and radiationWork doneagainstgravityVolume involvedEnergy ensity

1032 rgs1032 rgs1031 rgs1030cm3100 rgsrn3

Table 2. Estimates f Coronal nergySourcesFormof Energy Observedverage alues

EnergyDensityergs rn3Kinetic(mpnV2)/2)= 109m3,V = 1km 1 105ThermalnkT) T = 106 0.1Gravitationalmpngh) h = 105m 0.5MagneticB2/8r) B = 100G 400

al. [1980] ndWebb tal. [1980]).By dividinghe otal nergyrequirementy thevolumef thecorona hich rupts, ecandeducehat he sourcemusthavean energy ensity f theorderof 100 rgs m3. Now etuscomparehis alue ith he inetic,thermal, ravitational,ndmagneticnergy ensitiesn thecorona as shown n Table 2. The kinetic energy density(mpnV2/2,hereps he rotonest ass)s 105ergsm3assuminghathe oronalensitys 109 m3andhathe e-locity isof theorder f 1 kms 1 (the onvectiveelocityfstructuresn thephotosphere).he hermalnergyensitynkT,where is Boltzmann'sonstant)s -0.1 ergs m3 sincehetemperatureis-106K, and hegravitationalnergyensity(mpngh,heres he olarurfaceravityf .47104m 2)is of theorder f 0.5ergs m3, assuminghat heaverage assheight is -1010cm. Finally,hemagneticnergy ensity(B2/8r)s 400ergs m3 foranaverageield trengthf 100G,aswould e appropriateor aneruptionnvolvingnactivee-gion.Thus nly hemagneticnergyensityxceedshe e-quirednergyensityf100 rgsm3. For easonsewilldis-cuss hortlyotallof themagneticnergyensitysavailableodrive neruption,ut he xtractionfonly quarterf t isstillamplenoughoaccountorevenhemostnergeticfCMEs.Becausehe magnetic nergy ensity reatly xceedshethermalndgravitationalnergy ensityn thecorona,hecur-rents ssociatedith hemagneticnergytoredheremust itherbe force-free, s llustratedn Figure4a, or confinedo currentsheets, s llustratedn Figure b. In otherwords,heenergycannot e stored sa distributed,on-force-freeurrentn theab-sencef any ignificantas ressurergravitationalorce hichcould ounterbalancemagneticx B force.Thus torage od-els or lares ndCMEsaregenerallyividednto hose ased nforce-free urrents nd hosebasedon current heets, lthough swe will discussn section .4, it is possiblehatsmalldeviationsfroma perfectlyorce-freetatemight laya role n triggeringsomeruptions.well-knownxamplef a storageodel ti-

lizing currentheets he mergingluxmodelor lareshownin Figureb. Asnew luxemergesrom hephotosphere,tforms currentheets t pressesgainstieldstructureshat realreadyresent.s he urrentn he heetrows,t mayhenreach critical hresholdor the onset f a micro-instability.Althoughhismodeleleasesagneticnergy,t doesot jectanymassrmagneticlux, o t cannotxplainMEs rpromi-nenceruptions,utt may eapplicableosmallompactlaresnotassociatedithCMEs. MostCME models ssumehat heinitial onfigurations a force-freeieldsuch s heshearedr-cade hownnFigurea. Variousroposalsorhow uchfieldmight rupt illbediscussedn section.An mportantonstraintorCMEmodelss heobservationthat henormal omponentf thephotosphericagneticieldremainsirtuallynchangeduringhe oursef he vent. heslowmovementsf sunspotsndothermagneticeaturesn thephotospherereunaffectedy heoccurrencef theCMEbe-causehe lasman he hotospheresalmost09imesenserthanhe lasman he oronaherelaresriginate.his nor-mous ifferencen density eanshat t is verydifficultordis-turbancesn the enuousoronao havemuch ffecton heex-tremely assivelasmaf thephotosphericayer.Fieldinesmappingrom hecoronao thephotosphereresaido be"inertiallyine-tied,"hich eanshathe ootpointsfcoronalfield ines reessentiallytationaryver he imescalef theeruption.hereforehe omponentf he oronalield ueophotosphericield ourcesemainsnvarianturingneruptionanddoesnot contributeo theenergy elease.Althoughhecoronal agneticield annotedirectlyb-servedn thecorona,t is possibleo estimatets strengthndform y akingdvantagef he acthat lasmatructuresn hecoronand hromospherere tronglynfluencedy hemagneticfield. By using magnetogramf thesurfaceieldat thephotospherend ssuminghat ontoursfconstantensityndtemperatureie alongoronalield ines,t ispossibleocon-

reconnection x whenj>Jcriticjl

/


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FORBES:CORONAL MASS EJECTIONSREVIEW 23,157

. .V..--'': '. :'-:'..i... :::: ':'::'-" ' .,i:'::'.i" ,er

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-1.0 -0.5 0.0 0.5 1.0(a) (b)

Figure 5. (a) Hot mageof prominencesbserved y theOttawaRiver SolarObservatoryn July22, 1979,and b) alinear force-freemodelof the field obtained y extrapolatinghe normalcomponent f the photospheric agneticfield [from Mackay etal., 1997].

struct orce-freemodels f the field as shown n Figure5. Usingthis method,Mackay etal. [ 1997] have ound hat the ratio of thetotal magnetic nergy including othcoronal ndphotosphericsources) o the potential magnetic energy (the photosphericsources lone) s -1.3 [Mackay and Longbottom, rivatecom-munication].Duringa CME, magneticield inesmappingrom heejectedplasma o the photosphere re stretched utward o form an ex-tended, pen-field tructure. hisopening f the ield creates napparent aradox,since he stretching f the field lines mpliesthat the magneticenergyof the system s increasing,whereas

storagemodels equire t to decreaseSturrock tal., 1984]. Aly[1991] andSturrock1991]haveestablishedhat or a simplyconnectedield, the ully openedield configurationlwayshasahighermagnetic nergy han he correspondingorce-free ield.Aly hasalsoshown hat for a simplyconnected agneticieldthe ratio of the total magnetic nergy o the potentialmagneticenergy s necessarilyess han 2. For example, he maximumratio for a Sun-centeredipole s 1.66 [Low and Smith,1993].The Aly-Sturrock onstraint asworriedmanyproponentsfstoragemodelsbecauset seems o imply that suchmodels reenergeticallympossible.However, hereare severalpossiblewaysaround he constraint.First, he magneticield may not besimplyconnected ndmay contain notted ield lines. Second,tmay contain ield lines hat are completely isconnectedrom thesurface.Third, an dealMHD eruption anstill extend ield inesas ongas t doesnot open hemall the way to infinity. Fourth,an dealMHD eruptionmaybepossiblef it onlyopens portionof theclosedield ines. Fifth, smalldeviationsroma perfectlyforce-freenitial statemightmakea difference.Finally,a non-idealprocess, pecificallymagneticeconnection,ightbe im-portant.

3. Origin of the Fields and CurrentsThe magnetic ields observed t the photosphere re quitecomplex,and the areas hat eventuallygenerateCMEs do notnecessarilynclude ctive egions ontaining unspotsndstrong

magnetic ields. The coronal ield that eruptsoutwardduringaCME has ts origin n the Sun'smagnetic ynamo egion,which

is thought o be located at the base of the convectionzone (seeGlatzmaier 1985] for references).Althoughmany aspects f thedynamo region remain poorly understood, here is a consensusamong esearchershat it leads o the formationof large magneticflux ropes hat rise to the surfaceof the Sun because f magneticbuoyancy Browningand Priest, 1986; Low, 1996]. As the fluxropes ise, they expandand are disrupted y the turbulent low inwhich they are imbedded, so that much of the magnetic fieldwhich reaches the surface is contained in fine-scale structuresconcentrated ithin the boundaryayersbetweensupergranualconvectioncells. (The boundary ayers are often referred o asthe "network.") Thesecells have a characteristicengthof 3 x104 m,whichmaybedue o he act hathelium ecomesullyionizedat a depthbelow the photosphere hich s equal o thislength. (Similarly, t hasbeenproposedhat he onization f hy-drogenand he single onizationof heliumgive rise o the smallercharacteristicength calesssociatedith hegranulationndthemeso-granulation,espectivelyPriest, 982].) It is nowpossiblewith the adventof helioseismologyo detect he arger-scalestructures efore hey reach he photosphereKosovichevtal., 2000]. Once he nterior ield emergeshroughhe surfaceinto the corona, t is no longerbuoyant,so t remains ransfixedbetween he corona nd he convectionone or a periodof daysto weeksbeforedisappearing. arge-scale tructuresisappearby breakingup into increasinglysmaller scalestructureswhicheventuallybecome oo small to see with existing elescopes.Thus the eventual fate of the surface field remains unknown.

Exactly what the preeruptivemagnetic ield structures re inthe coronaand how they get that way is a subjectof active re-searche.g.,Krall etal., 1998;Fan etal., 1999]. Fromplasmastructures bservedat variouswavelengths,t appears hat thefield s n the ormof a shearedrcade rhalf-emergedlux ope.The two possibilitiesre essentiallyndistinguishablenlessheaxis of the flux roperisesabove he surface.From measurementsof the magnetic ield and lows n prominences,t is inferred hatthe amountof twist n the field is not arge,so hat f the structureis a flux rope, henumber f tumswithin t is somethingetweenone and two [Leroy etal., 1983; Gaizauskas,1979; Antiochosetal., 1994]. Low [1993] andGibson nd Low [2000]havearguedpersuasively hat the region of strongmagnetic ield within the


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23,158 FORBES' CORONAL MASS EJECTIONS REVIEWflux rope shouldbe identified with the dark cavity that is typi-cally observedboth before and after the onset of a CME (seeFigures 1a and 3).Perhaps he most mportantquantity o consider or any stor-age model is the coronal currentdensity n the preeruptivecon-figuration. The distribution of the current density determineshow muchenergy s storedand whetheror not the field is stable.Unfortunately,because he currentdensity s the derivativeof themagnetic field, it is even more difficult to measureaccuratelythan the field itself.

As for the origin of the current density, here are essentiallytwo possibilities:One is that t is createdby the observed urfaceflows which stress he field. The other s that the currentdensityis transported longwith the field as t emergesrom the convec-tion zone [Low, 1996]. It is not always easy o distinguish e-tween these wo processes ince he motion of the photosphericfootpointsof the field line may be part of the emergence rocess.Many storagemodelsassume hat the corona s initially current-free and that the buildup of magneticenergy s entirely due tostressing f the coronal field by the observedphotosphericmo-tions. Thesemotions re of the orderof 1 km s l or less,andover a time period of a few days they are sufficient o store he1032 rgs eededor a largeCME. However,ery argeCMEshave sometimes een observedn regionswhere he photosphericmotions are too slow and of too short a duration to store 1032ergs. Theseevents mply that the magnetic ieldsemerging romthe convection one may not be current ree and may alreadybein a stressed tate McClymontand Fisher, 1989]. (This conclu-sion appears o confirm a statement hat was once made to theauthorby H. Zirin that "big flaresare bornbad.")4. Illustrative Models

In this sectionwe discuss ome epresentative odelswhichare all based n the principle hatCMEs arepowered y the sud-den elease f magnetic nergy toredn thecorona.Fourdiffer-ent classes f modelscan be distinguished:First is a classofforce-freemodelswhichattempt o explain he eruption olely ntermsof an dealMHD process.Seconds a class f modelshatinvoke esistiveMHD processesuchas magneticeconnectionto trigger heeruption.Third s a class f hybridmodelswhichinitiate he eruption y a purely deal MHD process ut requirethe nonideal rocess f magneticeconnectionn order o sustainthe eruption.Finally s a fourthclassof modelswhichsupposesthat the small deviations rom a completely orce-free ield,caused y gravityor gaspressure, ayplaya significantole nthe initiation of an eruption.4.1. Ideal MHD ModelsThe classof ideal MHD modelsdealswith processeshatrequireno dissipation r diffusion of the magnetic ield to operate.Although dissipativerocessike reconnection ayoccur, t isassumedo play no role n the eruption f the field. Modelsofthis type are severely estricted y the Aly-Sturrock onstraintdiscussedn section2, namely, that a completelyopenedmag-netic field alwayshas a highermagnetic nergy han he corre-sponding losed tate. However,oneway aroundhisconstraintis to supposehat duringa CME eruptiononly a portionof thetotal field is opened, while the remainder remains closed[Wolfson,1993].Wolfson nd Low [1992] have shownexplicitly hat a partlyopened tatecanexistwhichhasa lowermagnetic nergy hananinitial fully closedstatewith the samephotosphericoundary

(a) (b)Figure 6. Two force-freemagneticconfigurations aving hesamemagnetic oundary ondition. a) The field within he hickline is unsheared ndpotential,but the field outsidet is shearedandnonpotential.b) The field s everywhere otential xcept oranequatorialurrent heet xtending utwardrom hecusp.Thecompletely losed onfigurationn Figure6a hasa highermag-netic energy han he partly opened onfigurationn Figure6b[after Wolfson nd Low, 1992].

condition. Their initial and final configurationswith this prop-erty are shown n Figure 6. Unfortunately, heir methodof solu-tion does not allow them to determine whether a transition fromthe closedstate o the open state s possiblen the absence f re-connection,so at the present ime there is still no model whichdemonstrateshat a partly open magnetic ield can be achievedsolelyby a lossof ideal MHD equilibriumor stability. Perhapsfurtherexplorationof the configurations onsidered y WolfsonandLow couldbe carriedout usingnumericalmethods.4.2. Resistive MHD Models

Another way to get around he Aly-Sturrock constraints toappeal to a nonideal process,such as magnetic reconnection,since the constraintonly applies to strictly ideal MHD. Howsucha processmight work is shown n Figure 7, which s takenfrom a numerical alculation y Miki6 and Linker [ 1994]. From= 0 to 540 :A he arcade s shearedwith the resistivity s near ozero as possible where 'A s the Alfv6n scale ime of the globalstructure).After 540 :A he shearings stopped, nd heresistiv-ity is instantaneouslyncreased o a value which givesan effec-tivemagnetic eynoldsumber f-104. This ncreaseeadsoreconnection nd the formationof a flux rope which s expelledoutward,away from the Sun. If the resistivitydoesnot ncrease,then the configuration radually i.e. quasi-statically)pensupwithoutany sudden ruptionof the field.The magnetic orce which drives he flux rope outwardorigi-nates rom two differenteffects' The first is the compressionfthe magnetic ield between he flux rope and the solarsurface.This force s due o the nertial ine-tying t thephotosphere,ndit is sometimes eferred o as the diamagnetic orce [Yeh, 1983].The second s the curvature orce causedby the pinchingofpoloidal field at the inner edge of the curved flux rope[Shafranov,1966]. Of these wo forces, he curvature orce s themore mportant ecauset actsover a much onger ange han he


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t=0 t = 540 :A

t = 900 r

t = 563 *A

(a)

1.71.6 --1.5 -1.4 -1.3 -1.2 _

1.1

1.0 s,0

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200 400 600 800t/

1000

(b)Figure 7. (a) Quasi-staticvolution f an axiallysymmetricrcadewhich s sheared y rotatingheNorthern ndSouthern emispheresf the Sun n opposite irections. he nitial ield at t = 0 is a Suncentered ipolewhichevolvesnto he orce-freeieldshown t t = 540:A.Aftera rotation f 126o, he ieldbecomeslly openedt t =900 :/t, f themagneticesistivity/remains ero. However, neruption ccurs t t = 563 :Af r/is suddenlyn-creased. b) The correspondingvolution f totalenergydividedby the potential nergy afterMiki and Linker,1994].

diamagneticorce,whichquicklydiesawayas the flux ropemoves away from the Sun.In order orMiki andLinker's1994]modelo explain MEs,the reconnectionatemustundergo suddenransition.Prior othe eruption t must be much slower than the timescaleof thephotospheric otions o hatenergy anbe storedn the coronalcurrents.After the eruptiont mustbe fastso hatenergy anbereleasedapidly.Thusa complete odelof theeruption rocessmustexplainwhy the reconnectionatesuddenly hangest thetime of the eruption. There are severalpossiblemechanismswhich ould o his. Forexample,f thecurrent heets subjectto the tearingmode nstability, henreconnection ill not occuruntil the lengthof the currentsheetbecomesonger han -2r

timestswidth Furth t al., 1963].Alternatively,s hecurrentsheet uilds p, tscurrent ensity ayexceedhe hresholdf amicro-instability,hich reatesnanomalousesistivityGaleevandZelenyi, 975;HeyvaertsndPriest,1976]. The anomalousresistivityubsequentlyriggersapid econnectionnd heejec-tion of a flux rope.Anotherxamplef a model hichequiresnonidealrocessis themodel evelopedy Antiochost al. [1999]which as hesphericaluadrupolareometryhownn Figure . As hecen-tralarcadetraddlingheequators sheared,t pushespwardagainsthex line abovet andcreates curved, orizontalurrentlayer. n theabsencef gas ressurerresistivityhis ayersaninfinitely thin sheet,and it confines he centralarcadeso that it


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(a) (b)Figure . Magneticield onfigurationsn themodelyAntiochostal. [1999] t a)anearlyime nd b)a atetime.Becausehe ield s symmetricboutheaxis f rotation,nlyone ides shown. force-freeurrents cre-ated yshearinghe rcadeield thickines) t he quator,ut currentayer orizontalo he olar urfacesalsocreateds heshearedegionulgesutward. econnectionf the ield inesn thisayer llowsheshearedieldlineso open utwardo nfinityfigureemplatesourtesyf S.Antiochos).

cannot pen. Whengaspressurend econnectionre ncluded,the currentwhichdevelops t the x line is initially quitediffuse,so rapid reconnection oesnot occurat first. However,as theshear increases, he diffuse current evolves into a thin currentsheetwhicheventually ndergoesapid econnection.Antiochos t al. [1999] have rigorouslyshown hat the mag-neticenergy toredn the inal,partlyopened tates ess han hemagnetic nergystored n the preeruptivetate. This result ssimilar to the one of Wolfson nd Low [ 1992] discussed bove,except hathere here s a cleardescriptionf the ransitionromthe closedstate o the partly opened tate. The precisenatureofthe transitionrom slowreconnectiono rapid econnectionn themodel still remains to be determined.

4.3. Ideal ResistiveHybridsThe resistive model of Mikid and Linker [1994] described n

section .2 utilizesa sudden hangen the rateof reconnectionoproducea dynamiceruption. If sucha changedoesnot occur,then he systemust evolves uasi-staticallyt the ratesetby theslowevolution f the photosphericield. Although he onsetof amicro-instability s one way to change he reconnection aterapidly,anotherway is to havean ideal MHD process uddenlycreate a current sheet.

An example how this processwould work is illustrated nFigures9 and 10, which showan dealized lux ropemodelwiththe sameaxial symmetryas that assumed y Mikid and Linker[ 1994]. The particularmodelshown n Figures and 10 wasde-rived by Lin et al. [1998], but the basicconceptwasdevelopedearlier by Van Tend and Kuperus 1978], Molodenskii andFillipov [1987], and van Ballegooijenand Martens [1989],amongothers. nitially, the flux rope s suspendedn the coronaby a balance between magnetic tension, compression,andcurvature orces the latter caused y the pinchingof the

poloidal ield at the inner edgeof the flux rope). However, hisbalancecannotbe maintained f the photospheric ourceof thecoronal field is reduced below a critical value. When the balanceis lost, he flux rope umps o an equilibrium t a higherheightasshownn Figure 10, anda relativelysmall raction < 10%) of thestoredmagnetic nergys released. he newequilibrium ontainsa vertical currentsheet ocatedbelow the flux rope (see.Figure9), and unless reconnectionoccurs n this sheet, he flux ropecannot scapento interplanetary pace.Justhow fast he recon-nection ate has to be in order for a smoothescape o occurhasbeenestimated y Lin and Forbes [2000] for a two-dimensionalconfigurationwith translational ymmetry i.e., a Cartesian ys-tem). They show hat a smoothescape s possible f the inflowAlfv6n Mach number into the current sheet exceeds -0.005. Theactual value of this number inferred from the observations is-0.025 [Polettoand Kopp, 1986], soa smooth scapes to be ex-pected.

The quasi-static volution n Figures and 10 beforeeruptionoccurss accomplishedn a highly dealizedmanner y reducingthe strength f the photosphericield (in this casea simpleSun-centered ipole). This reduction equires he footpoints f fieldlines in the Northern and SouthernHemispheres o migrate to-ward the equatorandreconnect o that he work done n movingthese footpoints is transferred to the coronal currentsvia aPoynting flux. Although colliding polarities which reconnectmight conceivably e a sourceof someeruptions Zirin, 1988],any photospheric oundary onditionwhich changeshe relativestrength f the repulsiveand attractive orcesactingon the fluxrope will suffice. For example, n the two-dimensional nalysisby Forbesand Priest [ 1995] a lossof equilibriums triggered ysimply moving the photospheric ources loser o one anotherwithout econnection r a reduction f the photosphericield.Becauseof the assumed ymmetry, he flux rope n Figure 9is a toms which encircles the Sun, and thus it contains ield lines


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FORBES:CORONAL MASS EJECTIONSREVIEW 23,161

(a)

I I I

(b)Figure 9. Axially symmetric lux ropemodelshowing he dealMHD transitionrom (a) the high-energy quilibrium tatebeforeeruption o (b) the low energyequilibriumstateafter eruption.The difference n scalebetween he figures9a and9b is indicatedby the differencen the sizeof the Sun. Initially, theradiusof theflux rope s assumedo be -104 km. The field ines emainclosed hroughout, ut the configurationormedafterwardcon-tainsa currentsheet. The flux rope can only escapen a smoothmanner f the reconnection rocess n the sheet s fast enough[after Lin et al., 1998].

which are not attached o the solarsurfaceas shown n Figure 9.It has been arguedby Antiochoset al. [1999] that the flux ropemodel will not work once its ends are anchored i.e., line-tied) tothe photosphere.However, their argument ssumeshat the umpin the flux rope model involves a violation of the Aly-Sturrockconstraintwhich, as originally formulated,doesnot includecon-figurationswith unattachedield lines. In fact, onecanshow ig-orously hat for this particularmodel he energyof the openstateexceeds ll otherstates seeLin et al., 1998], a resultwhichsug-gests hat the Aly-Sturrock imit may also apply to at least someconfigurationswith detached ield lines. The importantaspectofLin et al. 's [1998] model, which is not present n the modelsofMikM andLinker [1994] or Antiochos t al. [1999], s thatslowlychanging he photosphericield can ead to the sudden ormationof a currentsheet. (A process ftenreferred o as a "catastrophe"according o the usage ntroduced y Thom [1972].)The maximum total magneticenergy which can be stored nthis flux rope model before equilibrium s lost is 1.53 times theenergyof the potential ield, less han the limiting value of 1.66for the fully opened ield. The way the model gets around heAly-Sturrockconstraint s by invoking the nonidealprocess fmagneticreconnection. The only role of the ideal MHD transi-tion is the sudden reationof a currentsheet,and this processreplaces he onsetof a micro-instability hat hasbeen nvoked nother esistiveMHD models e.g.,Mikt and Linker, 1994].Whether the catastrophicprocesswhich creates he currentsheetwill still work when he endsof the flux rope are tied to thephotosphere emains an unansweredquestion. However, it islikely that t will for the followingreason:When the endsof theflux ropeare ied, an upwarddisplacementf a middleportionofthe flux rope constitutes n ideal MHD kink. Thus the relevant

question o consider s whether the configuration an becomekink unstable. Since the kink instability is an inherently three-dimensional rocess,t can be quite difficult to obtain stabilitycriteria or it in a complexconfigurationnvolvinga curved luxrope,a line-tyingboundary, nd a nonuniform xternal ield. Inthe absence f line-tyingor external ields, a straight lux rope salwaysunstableno matter what the currentdistribution s inside t[Anzer, 1968]. A straight, solated lux rope of finite length canbe stabilizedby anchoring ts endsat fixed boundaries ut only ifthe twist is less han a critical value [Hood and Priest, 1981 . Fora force-free lux rope with a uniform twist the critical value s 3.3r corresponding o 1.7 turns of the flux rope between the twoboundaries Hood and Priest, 1979], but this number may behigher or lower dependingon the distributionof current withinthe flux rope.

If the flux rope is twisted beyond he critical numberof turns,it becomesunstableand dynamically umps to a lower energystate [Arber et al., 1999] which necessarilycontains a currentsheet Bhattacharjee nd Wang, 1991 . It seems nreasonableosuppose hat curving the flux rope and addingan externalback-ground field would cause he line-tying to become so efficientthat the flux rope would becomeunconditionally tableno matterhow much t is twisted. If this were true, thengradually educingthe curvature and external field to zero would not recover theresult of Hood and Priest [ 1979].

Titov and Dgmoulin [1999] have recentlyanalyzed he specialcaseof a circular flux rope which is imbedded n a line-tying sur-face as shown n Figure 11a. The outwardcurvature orce actingon the rope is counterbalanced y the field from two point mag-netic charges uriedat a depthz =-d below he surface nd o-cated at x = +_Las indicated n Figure 11. In addition o the ex-ternal field generated y the point charges, here s also a contri-bution from an infinitely long line currentwhich coincideswiththe x axis. The field producedby this line currentexertsno force

h 2

0 I '0.0 0.5 2.0" currentheetorm1.0 1.5

Figure10. Theequilibriumeight of the lux ope hownnFigure in units f thesolaradiuss unctionf hestrength,',of theSun enteredipolen normalizednits.Thedottedor-tionof thecurvendicatesnextrapolationetweenheasymp-totic solution upperportionof curve)and he no-current-sheetsolutionlower ortion).When he ieldstrength' s slowlye-ducedo 0.95, he lux ope ndergoesdynamicump o a newstatecontaining current heet. Upon further eduction f cr o0.74 dashedine), he ieldevolvesuasi-staticallyo theopenstate afterLin et al., 1998].


10/13


,"" t" / '' :::::::::::::::::::::::::::::::::::::::::::::::::::::::::...::-$

::F.,..."*'%-.r:' - :''*""'"'*o*:;: :::::::::::::::::::::::

:;":::*%% ..... .:.. :.::..----:**:::**:**:.,:::.:...-,

...........*'*'a ....... """'"'"''""""'"'"'"'""':*",............................ ........ .. _ ...-50 0 50Figure 11. Line-tied flux rope modelof Titov and Ddmoulin 1999]: (a) three-dimensionaliew showing he rela-tion of the flux rope shaded oms) to the backgroundield sources t a depthd below the surface.Thesesources repoint magneticcharges q locatedat x = + L and a line current unningalong he x axis. (b) normal components fthe surfacemagnetic ield with regionsof opposite olarity ndicatedby dark and ight tones.The polarity nversionline is indicatedby a thin black ine, while the bald-patch egion s indicated y a thick black ine. The photospherictracesof the magnetic eparatricesre ndicated y the white ines.

on the flux rope,and ts purposes to make he overall ield struc-ture more nearly resemble hat occurring n the corona. Withoutthe field from the line current the field lines at the surface of theflux ropeare purelypoloidal,and heyhavean nfinitenumber fturns n a finite length. This is quiteunrealistic ecause varietyof observations indicate that the maximum number of turns onany field line is probably less than two (see section 3).Incorporating he line current ield eliminates his problembycreating strong oroidal ield whichensureshat no field linesare highly twisted. By adjusting he strength f the line currentone can achieve a reasonable amount of twist everywhere asshown n Figure 1 b.

Figure12. Magneticieldconfigurationormed y reconnectingthe photosphericootpoints f a fully three-dimensionalmade(from the simulation y Amari et al. [2000]).

Titovand Ddmoulin 1999] havealsoconsideredhe stabilityof theirconfigurationndasserthat t is unstablef the arge a-dius, ,of helux opeFigure1 )exceedsL in heimitthatd is small. Althoughheydo notprove his esult igorously,they are able o establishhat the configuration asequilibriumproperties imilar to the completelysymmetric onfigurationshown n Figure9.There s alsoa fully three-dimensionalimulation y Amarietal. [2000]whichshows owa flux ropecanbe formed y recon-necting he photosphericootpoints f a sheared rcade. Suchaprocesswas suggested 0 years ago by van BallegooijenandMartens [1989] and later simulated n two dimensions yInhester et al. [1992]. In the simulation of Amari et al. the re-

connection f the photosphericield leads o the sudden orma-tionof a flux ropewith a vertical urrent heet elow seeFigure12). However, it is not at all clear if the transition to this stateconstitutestruecatastrophe,ecausehephotosphericoundaryconditionn thesimulations Changedt a ratewhich s too apidto be considereduasi-static. hus hem s still no convincingdemonstrationt the presentime hata realistic ruption anbemodeled singa line-tied lux ropeconfigurationike thatshownin Figure 11.Even f it shouldurnout hata simple urvedlux ropecannotproduce realisticeruption, hereare otherclosely elatedcon-figurationshat may be able o do so. Gibsonand Low [1998,2000] have shown hat the overall appearance f CMEs bothbeforeand after eruption an be modeled uitewell using hesame ype of force-free ields as occurs n spheromaks,ut theequilibrium ndstability ropertiesf these ields n thepresenceof a line-tyingsurface emain o be determined.4.4. Non-Force-Free Models

Therestrictionmposed y theAly-Sturrockonstraintanbesidesteppedf the nitial onfigurationsnot orce-free.t isgen-erallysupposedhat hecoronal agneticield s nearlyorce-freebecausef thedominancef themagneticnergy verall


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FORBES: CORONAL MASS EJECTIONS REVIEW 23,163

other forms (see Table 2), but it is possible hat small deviationsfrom a purely force-free ield might play a role in triggeringaneruption.

Low [1999] has pointedout that total magneticenergy n thecoronacanbe expressed s

dV= Br- Bo - B -pdS> Ro8zr = Ro8zr

Ii pGMoRo r 37 dV ,whereB is the total coronalmagnetic ield with spherical ompo-nents , BO, ndBe,p is thecoronalaspressure,is thecoro-nal density,G is the universalconstantof gravitation,Mo is thesolarmass,dV is the differentialvolumeelement,Ro s the solarradius, and dS is the differential surface element. The above ex-pression is obtained from the MHD virial theorem (seeChandrasekhar 1961] or Priest [1982]), and it expresseshecoronalmagneticenergy n terms of the surfacemagnetic ieldand gas pressureand the volumetric gravitational and thermalenergy n the corona.

If the gravitational nd hermalenergyare gnored, he field isforce-free,and the magneticenergy s given entirely n termsofan integral over the components f the surface ield. From theform of the integrandone sees hat the value of this ntegralhasan upper bound given by integratingover the radial componentBr. Since he line-tying of the field at the surfacemakesBr in-variant there, the amountof total magneticenergymustbe lessthan that obtainedby integrating he radial component f the po-tential field over all space. In other words, the maximum totalmagnetic energy of a force-free field in the corona cannot bemore than about double hat of the potential ield, one of Aly'sresults (see section 2).If gravity is importantbut pressures not, then the magneticfield is no longer force-free, and it is possible o increase hemagneticenergystored n the coronaabove ts force-free imit byan amount qual o the gravitational otential nergy:

JiGMoV-McMor gowhereM c is the coronalmasssupported y the field. This gravi-tational energy s essentially he same as that listed in Table 1,but it is a factorof Ro/h (-7) greater han hat consideredn Table2, which s the energygained f an object alls to the surface roma coronal scale height h rather than infinity. Thus the gravita-tional energy could allow the storedmagneticenergy o exceedits maximum orce-freevalueby as muchas 10%.

Some of the cool plasma n an eruptingprominence s oftenseen o fall back o the surface,which suggestshat a CME mightbe triggered if the magnetic field slowly evolves to a criticalpointwhere t canno longersupporthe prominenceLow, 1999].In otherwords, he weightof the prominence ctsas a lid whichallows he magnetic nergy o increase bove he open imit, andwhen the lid is suddenly emoved, the field springsoutward.Even if the drainingof the material s not sufficient o open hefield, it could, nevertheless, lead to the formation of a currentsheet. However, many CMEs do not appear to contain anyprominencematerial,so t seems nlikely hat sucha mechanismcould account for all CMEs.

The effectsof both pressure nd gravity have beenconsideredby Low and Smith [ 1993], Wolfsonand Dlamini [ 1997], andWolfson nd Saran [ 1998]. As can be seen rom the virial theo-rem, pressure educes he magneticenergy hat can be stored nthe corona,but unlike gravity,pressure an tself propelmaterialoutwardgiven the appropriate radient. However, the problemstill remains hat the thermal energydensityassociated ith pres-sure in the lower corona is so small that it is difficult for it tohave a significanteffect.5. Summary

Many modelshave been developed o explain the appearanceor propagationof CMEs, but very few have been developedwhich really explain he exactnatureof the mechanismor mech-anisms)which triggers hem. For example,severalof the modelswe have discussed ere propose hat CMEs are triggeredby theonsetof a micro-instabilitywhich eads o a sudden nhancementof the resistivity n a currentsheet,but they do not actuallypre-scribe he processwhich produceshe micro-instability.What isrequired s a mechanism hat will causea sudden ransition romthe preonsetquasi steady state to the postonsetdynamic state.The mechanismwhich triggers he eruptionneed not involve amicro-instability. There are models,suchas the flux rope modeldiscussedn section4.3, which use an ideal MHD catastropheoform a current sheet on a timescale of the same order as theAlfv6n timescale of the system (typically 10-100 s in thecorona).

At the present ime, there s a general but not universal)con-sensus that the onset mechanism involves the release of the freemagneticenergy associatedwith currents lowing in the corona.However, there is no consensus about the mechanism which re-leases his energy. Nevertheless, s observationsnd general n-terest n CMEs increase, here s every reason o hope hat the is-suemay be resolvedwithin a few years.

Acknowledgments. The author thanks Boon-Chye Low and SpiroAntiochos or their helpful comments n the originalmanuscript nd alsoNancy Crooker and Janet Luhmann for their invitation to present hiswork at the Solar andHeliospheric Nterplanetary nvironment SHINE)meeting held June 14-17, 1999, in Boulder, Colorado. This work wassupported by NASA grants NAG5-4856 and NAG5-1479 to theUniversity of New Hampshireand NAS 8-37334 to the Lockheed-MartinCorporation.Janet G. Luhmann thanks Richard Wolfson and Spiro K. Antiochosfor their assistancen evaluating his paper.ReferencesAly, J. J., How much energycan be stored n a three-dimensionalorce-free field?,Astrophys. ., 375, L61-L64, 1991.Amari, T., J. F. Luciani, Z. Mikic, and J. Linker, A twisted flux ropemodel or coronalmassejections nd wo-ribbon lares,Astrophys. .,529, L49-L52, 2000.Antiochos,S. K., R. B. Dahlburg,and J. A. Klimchuk, The magnetic ieldof solarprominences, strophys. ., 420, L41-L44, 1994.Antiochos, S. K., C. R. DeVore, and J. A. Klimchuk, A model for solarcoronalmassejections,Astrophys. ., 510, 485-493, 1999.Anzer, U., The stability of force-free magnetic ields with cylindricalsymmetry n the contextof solar lares,Sol. Phys.,3, 298-315, 1968.Arber,T. D., A. W. Longbottom,ndR. A. M. vanderLinden,Unstablecoronal oops:Numericalsimulations ith predicted bservationalsignatures, strophys. ., 517, 990-1001, 1999.Arnoldy,R. L., S. R. Kane,andJ. R. Winkler,Theobservationf 10-50key solar lareparticles,n Structure ndDevelopmentf SolarActive

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T. G. Forbes, nstitute or the Study of Earth, Oceans,and Space,39College Road, University of New Hampshire,Durham, NH 03824.([email protected])

(ReceivedJanuary , 2000; revisedMarch 13, 2000;accepted arch13, 2000.)

T. G. Forbes- A review on the genesis of coronal mass ejections

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Transcript of T. G. Forbes- A review on the genesis of coronal mass ejections