Adv. Space Res.Vol. 13,No.9,pp. (9)259—(9)262,1993 0273—1177/93$24.00Printedin Great Britain. All rightsreserved. Copyright t~1993COSPAR

INTERPRETATION OF SOLAR FLAREy-RAY CONTINUUM OBSERVATIONS

DavidAlexander*and AlexanderL. MacKinnon*** DepartmentofPhysicsandAstronomy,Universityof Glasgow,GlasgowG128QQ, U.K.** DepartmentofAdultandContinuingEducation, UniversityofGlasgow,GlasgowG128QQ, U.K.

ABSTRACT

The 7-ray spectrometeron board the Solar Maximum Mission detecteda large numberof solarflares with 7-ray emissionin the 10-100 MeV range. A smallernumberof theseeventsdisplayedevidenceof ahardeningof thephotonspectrumaround70 MeV indicating the presenceof neutralpion decay7-rays. We considerthick-targetcalculationsof the interactionof acceleratedprotonswith the ambientsolaratmosphereto addressthe productionof this pion decayradiation.

INTRODUCTION

Rich spectraof nuclearde-excitationlines in the energy range 4-7 MeV from solar flares wereobtainedby the SMM GammaRay Spectrometer,signifyingthe existenceof protonswith energiesin excessof 100MeV. In additionto these7-raylines, thestrongneutroncaptureline at 2.223MeVand the positronannihilation line at 0.511MeV, evidencefor 7-ray continuumand broad-bandemissionin excessof 10MeV wasalso recordedin severalflare events(/1/). The mostenergeticoftheseemissionsproduced7-ray photonswith energiesgreaterthan100MeV (/2/). A small numberof thesevery high energyeventsare observedto exhibit adistinct spectralhardeningat energiesaround100MeV (/2,3/) characteristicof the decayof neutralpionsand it is this sortof emissionwe wish to addresshere. Thus,the investigationof the subsequent7-ray emissionfrom ir° decayobservedat energiesaround100MeV is important for our understandingof the highestenergyprocessestaking placein solar flares. In particular,while the productionof nuclearde-excitationlines is dominatedby protonswith energies<100MeV, the close studyof the piondecayradiationhas potential for constrainingthe form of the proton distribution at higher energies.Murphy etal. (/2/) havecarriedout a comprehensivestudy of the eventof June3 1982 which exhibitedneutralpion decayemission(/4/). They constructedaself-consistentinteractionmodel for thisflare in which the time-dependentfluxesof the 7-radiationare producedby two distinct particlepopulationswith differentinteractiontime historiesaswell asdifferentbut time-independentenergyspectra.The resultsof Murphy et al. (/2/) were foundto be consistentwith theobservedspectralshapesof the nuclearline and pion decay emissionandwith the neutronsand chargedparticlesobservedin space. Recently, Mandzhavidzeand Ramaty (/5/) havecarriedout more detailedcalculations,which include the productionof 7-raysfrom the decayof chargedpions, investigatingthe effects of particletrappingandpitch anglescatteringon the characteristicsof the pion decayemission. A comparisonwith the 1982 June3 eventdemonstratedthat asinglephaseaccelerationmodel could bemadeconsistentwith observationsby varying the propertiesof the scattering.

An alternativeto the two-phaseaccelerationmodel wasalso proposedby Ryan andLee (/6/), whoconsideredthe diffusion of particles in real and momentumspaceby MilD turbulence. In thisapproachtheparticlesresponsiblefor thenuclearline emissionandthe pion productionare partofthe sameinitial particle population. The time delaybetweenthe impulsiveline emissionand thehigherenergypion-relatedemission,observedin theeventof June3 1982, is due in thismodel tothegradualaccelerationof protonsto pion-producingenergies(>300MeV) by diffusion in momentum

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(9)~ D. AlexanderandA. L. MacKinnon

space.This model is ableto reproducethe temporalandspectralbehaviourof the June3 19827-ray emissionextremelywell. The successof the modelof Ryanand Lee(/6/) in explainingsomeof the characteristicsof the June3 1982 event,togetherwith the resultsof /2/ and /5/, suggeststhat current observationsare not adequateto specify uniquely the particle accelerationprocess~fl 7-ray flares. The acceleratedproton spectra,resultingfrom the two-stepaccelerationprocessassumedand the spectralfitting of the data, shouldnot, therefore,be regardedas definitivebutasauseful measureof the energydistribution requiredby the acceleratedparticles.

The apparentsuccessof severaldistinct accelerationmechanismsin producingan energeticprotonspectrumwhich leadsto 7-rayemissionconsistentwith observationssuggeststhat aless restrictiveapproachis required. In this paperwe will considera simple form for the acceleratedprotonspectrumat high energieswith no specific referenceto an accelerationmechanism.This enablesusto addressthe energydistribution of the protons in a fairly model-independentway, allowingthe datato place constraintson the numberof protonsabovethe pion-productionthresholdandon the generalshapeof the spectrumat theseenergies.

ir07-RAY PRODUCTIONIN SOLAR FLARES

We only considerthe production of secondary~.0 from thick-target interactionsof high energyprotons with the protonsof the ambientsolaratmosphere.The neglectof interactionsinvolvingheaviernuclei meansthat our resultsfor the radiationfluxeswill underestimatethe solarfluxes bysomesmall factor (cf. /7/). The productionspectrumof secondary~r

0producedin p-H collisionsin solar flares is given by

2 (°° dE5. !°° ~ do(T’,T11.)T’

F~H(e~)= 1~JE,r,m,,, (E~— m~)1/2JTp,m.~ dT~.

3~(T~)JTp,m,,, dT1. -~dT~ (1)

(photons/cm2/GeV/s)where the integral over expressesthe pion production rate per unit

proton kinetic energy,T~j~(T~)[protons/s/GeV] is theincident proton spectrum;R is the earth-sun distance,1.5x1013cm,Tp,mjn is the minimumkinetic energyrequiredby a proton to producea pion of kinetic energyT,r, E,~is the pion energy, Eir,min is given by relativistic considerations

(cf. /8/), K = 2ire~(2mV2/m~)Aand A is the Coulomblogarithm relevant to protons (/9/).The differentialcross-sectionfor the productionof apion with energyT,~dueto a collision of anacceleratedprotonof energyT~with the ambientsolarplasmacanbe expressedas

da(T~,T,~)— T dN(T~,T4 2

dT~ — ((t~7( ~ dT,~ ( )(/10/) where ((a(T~))denotesthe inclusive cross-sectionfor the reactionp + p —+ lr°+ anythingand (dN/dT~)is the normalisedproductionspectrumof secondary~r°such that

1 dT dN(T~,T,~)— 1 3J0 dT,. — ()

An empirical basis for the fit to the inclusive cross-sectionjust above the threshold energy,T~’=28OMeV,is given in /10/.

The proton spectrumincidentupon thetargetregion,j~(T~),is chosensuchthat it hastheform ofa Besselfunction spectrum,obtainedin some stochasticaccelerationprocessesandcharacterisedby a hardnessparameter,ctT, (ci. /2/), up to a proton kinetic energy,1’,,~,which is typically ofthe order 100MeV. Sincewe intend to concentrateon pion productionand decay,which requiresprotonswith energiesgreaterthan300 MeV, we choosethe Bessel function form to representtheproton spectrumat lower energiesas a convenienceand becauseit hasbeen shownto providegood fits to nuclearde-excitationline data(cf. /11/). AboveT~oour spectrumadoptsthe simpleform of a power-law. This choiceof proton spectrumenableslimits to be placedon the numberof protons acceleratedto energiesgreaterthan the pion productionthresholdwithout restrictive

DRay Continuum Observations (9)261

~ ~

0 ~

Fig. 1: a) Adoptedproton spectra,Jp (protons/GeV/s)for a rangeof spectralindex, 6 b) Piondecay7-ray spectra(photons/cm2/s/GeV) resulting from the photonspectraof Figure la.

assumptionsaboutthe accelerationmechanism.Thus the spectrumwe useto describeour singlepopulationof acceleratedprotonsis given by

j~(T~)= ANK2[2(3p~/m~cczT)”

2} T~<T~o (4)

= ANK2[2(3p~o/m~cctT)’

12](T~/T~o)6T~> T~0

[protons/GeV/s] where AN is a normalisationfactor to be determinedfrom comparisonwithobservations;K2 is the modified Bessel function (ci. /11/); ct is the accelerationefficiency; T isthe particleescapetime from the accelerationregion;Pp is the totalproton momentum;T~0is theturn-overenergyfrom Besselfunction to power-lawwith p7,o being the correspondingmomentum.Spectraof this form areshownin Figure la for a rangeof the spectralindex, 6.

Equation(1), then,is the photonenergyspectrumexpectedfrom adistributionof energeticprotonswith spectralform (4), acceleratedduring the intial energyreleasein a flare andinteractingwiththeambientsolaratmosphere.Wehaverestrictedour attentionto 7-raysproducedvia thedecayofneutralpions. To completethe solution of our problemthe form of the pion productionspectrumdN/dT~is required.This is takenfrom /10/.

The 7-ray spectraresultingfrom the decayof secondaryir0 producedin thick-targetinteractionsof

protonsacceleratedto high energiesin solarflares with the ambientsolaratmosphereare showninFigure lb. In this Figure the energyspectrumof the injectedprotonsis characterisedby equation(4) with aT=0.04and T~o=10OMeV.ctT=0.04 is typical of the valuesinferred from nuclearde-excitation line observationsby Murphy et a!. (1987) andT~=l00MeVis a typical uppercut-offfor protons contributing significantly to the nuclear line production(/11/). The 7-ray spectraillustratedcorrespondto the different valuesof the spectralindex,6, of the power-lawconsideredin the thick-targetapproximation.We seethat the ~r°decayemissionis sharplypeakedaroundaphotonenergyof 67.5MeV andis very sensitiveto the form of theinjectedproton spectrum.Asexpectedthe harderthe proton spectrumthe broaderthe 7r0 decayfeature. In light of the recentresults by Dunphy and Chupp(/3/) where the ir°-decayfeatureis found to be quite narrow incontrastto the broaderfeatureof the 1982June3 eventit is importantto considerthe consequencesof the shapeand intensityof the ir°-decayfeatureto the spectrumof protonsacceleratedin solarflares.

CONCLUSIONS

Our theoretical calculationsshow that the detailed structureof the 70MeV pion decay featuredependsstrongly upon the form of the acceleratedproton spectrumat energiesfrom 300MeV to

(9)262 D. Alexander andA. L MacKinnon

a few GeV. Dependingupon the valueof 6, the intensitiesandenergydistribution of the 7-rayemissioncan vary quite substantially. In general,the harderthe proton spectrumthe wider andmore intensethe pion decayfeature as one would expect. It was argued in /2/ that a singletime-independentpopulationof acceleratedprotons could not producethe observed7-rayline andcontinuumemissionin the June3 1982 event. This was due mainly to the restrictionsimposedby the accelerationmechanismsassumed.However,recently Ryan and Lee(/6/) havedevelopeda model in which the diffusive transportin momentumspaceof a singlepopulationof particlescanexplain the observedtemporalandspectralcharacteristicsof the line andcontinuumemissionobserved. Thus, it is clear that the acceleratedproton spectrumis not definitively determinedby the observed7-ray emission. In the presentwork, the particlesresponsiblefor the 7 raysareassumedto belongto a singletime-independentpopulation,the sourceof which is not addressed.

The primary motivationfor this work is as follows. The beststudied(and morecomplex) regionof the flare 7-ray spectrumis the region between1 and 8 MeV, where the nuclearde-excitationand neutroncapturelines are found. Theselines yield definitive information about protons ofenergiesless than about 100MeV but are fairly insensitiveto higher energy protons. To inferthe propertiesof theseprotons we must turn to ir° decay 7-radiation(wherethis is observed)and we hope here to havedemonstratedthe usefulnessof such an investigation. Our assumedcompositeBesselfunction/power-lawproton energydistributionis contrivedandlacking physicaljustification. However,all of the ir°decayspectrain Figure lb would be consistentwith the sameset of de-excitationlines. Thus our resultsemphasisethe potentialof the~r°decayspectralfeaturefor yielding information on the proton populationabovethe ~r°productionthresholdof 280MeV.

A detailed comparisonof our results with observationsis requiredbefore our conclusionscanbe fully realised. Many solar eventsexhibit >10MeV emission. However, in most cases thisemissionis dominatedby relativistic electronbremsstrahlung(/12/). Only a very few of theseobservationsdemonstrateunambiguouslya strong (possiblydominant)pion emission. The SMMeventsof June3 1982 (studiedin detail by /2/), December16 1988 and March 6 1989 (Rieger-

privatecommunication;/3/) allow us someevidencefor aneutralpion decayfeatureat -‘-~70MeV.However,theseeventsalso display the steepphotonspectraassociatedwith relativistic electronbremsstrahlung. Although, the distinctive flattening of the spectrumaround 70MeV signifiesthe dominanceof the ir°emission at theseenergies,the bremsstrahlungcontributionwill not benegligible and shouldbe considered(cf. /2/).

ACKNOWLEDGEMENTS

We would like to thank Prof. JohnBrown and Drs. Chuck Dermer, Phil Dunphy and ErichRiegerfor helpful commentsandsuggestions.This work wassupportedby the awardof an SERCPost-doctoralFellowship(DA).

REFERENCES

1. E.L.Chupp,Ann. Rev. Astrori. Astrophys.,22, 359 (1986)Mihalas andR.K. Ulrich (Reidel,Dordrecht)1986,p291.

2. R.J., Murphy, C.D., Dermer andR., Ramaty,Astrophys.J., 263, 721 (1987)3. P., Dunphy andE.L., Chupp, Proc. 22nd InternationalCosmicRayConf.,3, 65 (1991)4. D.J., Forrestetal., Proc. 19th InternationalCosmicRay Con!.,4, 146 (1985)5. N.Z., Mandzhavidzeand R., Ramaty,Astrophys.J., 389,739 (1992)6. J.M., Ryan andM.A., Lee, Astrophys. J., 368,316 (1991)7. C.D., Dermer, Astrophys. J., 307, 47 (1986)8. F.W., Stecker,Cosmic GammaRays,MonoBook Co., Baltimore, 1971.9. A.G., Emslie, Astrophys. J., 224, 241 (1978)10. C.D., Dermer, Astron. Astrophys.,157,223 (1986)11. R., Ramaty andR.J.,Murphy,SpaceScienceRev.,45, 213 (1987)12. R., Ramatyet al., Solar Phys.,86, 395 (1983)