Investigations of turbulent motions and particle acceleration in solar flares

Adv, Space Res. Vol. 6 No. 6. pp. 191—19.t, Lg86 Pnntcd in Great Britain. All ngl~tsrescr~ed.

‘)~3—l ~6 SI) 00 ~0 Copright © COSPAR.

INVESTIGATIONS OF TURBULENT MOTIONS AND PARTICLE ACCELERATION IN SOLAR FLARES J. Jakimiec,~A. FIudra,~J. R. Lemen,*~ B. R. Dennis*** andJ. Sylwester± *Astronomical Institute, Wroclaw University, Poland *~ivIt11IardSpace Science Laboratory, Dorking, U. K. ~~NASA/Goddard

Space Flight Center, Greenbelt, MD, U.S.A.

~Space Research Center, Wroclaw, Poland ABSTRACT Investigations of X—ray spectra of solar flares show that intense random (turbulent) motions are present in hot flare plasma. Here we. argue that the turbulent motions are of great importance for flare development. They can efficiently enhance flare energy release and accelerate particles to high energies. INTRODUCTION Investigations of X—ray spectra of solar flares show significant line broadening by random (turbulent) mass motions /1,2/. In this paper we suggest that the random motions can be strong enough to play an important role in the flare energy release, as well as in the acceleration of particles to high energies. Recently, efforts have been made /3/ to improve the investigation of the line profiles in the SNN Bent Crystal Spectrometer spectra. Intense random motions have been found for all investigated flares. For a sample of 15 class N and X flares the maximu.~values of the turbulent velocity v~ fall withi~ the limits of 100—190 km s and their distribution peaks at vt = 140 km s . Assuming that the random motions ar~~asi-isotropic, the r.rn.s turbulet4 velocity can be calculat~d: v = V(v2~> = 1.22 V~ • Taking v~ = 140 km s we obtain v = 170 km s as a typical value for big flares.. In order to estimate the energy in the turbulent motions it is necessary to know the density of the flare plasma. A method for determining the hot plasma density N and the rate of flare heating ER is 1~iven3in /4/. For big flares we ob~ined.~hotplasma densities of up to 5 x 10 cm . Here we take N = 3 x 10 om~ as a value typically achieved near the time of maximum turbulent velocity. Combining the abov~values of v an~N, we obtain a typical turbulent energy density e~ ~ v /2 ~ 75 ergsmcm . This energy density is sufficient to disturb signif~cantlymagnetic fields with strength H~H = 5 (~T ~40 G. There are at least two reasons, however, why the investigated turb~.lent motions can significantly disturb much stronger magnetic fields: (1) The turbulent velocities have some distribution. Assuiaing that the dis— 2 tribution is quasi—Gaussian for each velocity component, f(v1)o~.exp -(v./v,~j, we estimate, for example, th9 about 0.1 % of the turbulent plasma elem~nt~ have energies .~ 400 ergs cm , which is su.fficient to modify magnetic fields with H”lOO G. (2) The estimated turbulent energy density et is the mean value averaged over the whole volume of hot flare plasma (the BCS observations have no spatial resolution). It is very probable that in the flare volume there are places where the turbulent energy density is significantly higher than the overall mean value. Therefore, it is probable that the observed turbulent motions can efficiently disturb the magnetic fields in the upper parts of the flare magnetic structure, so that the observed turbulence may be a i91

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developed magnetohydrodynamic (~‘~) turbulence. The development of the 1~ turbulence will, in turn, significantly i~luence the flare energy release. The tangling of the magnetic lines of force and the collisions of the turbulent plasma elements should produce transient, small scale regions of effective magnetic field dissipation (current sheets). The courlintz of the magnetic field dissipation and turbulent motions can be summarized in the following scheme: plasma heating ~

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The hypothesis that i’U-~turbulence developes in large flare volumes exolains the free energy of big flares, for which it i~ 3necessary to annihilate the magnetic field over very large volumes, V”-’lO INVESTIGATION OF TII~VARIATION OF THE TUR31J1~TTMOTIONS The 305 observations permit investigations of the time variations of the turbulent velocities v.~ which relate to the whole volume of hot plasma. A sample of 15 flares was considered from which the following conclusions were drawn: 1 • ~e compared the time variations of the turbulent energy density e (t) with the variations of the rate of thermal energy release EH(t) as derives from 30S data. ‘;Te have found that these time variations show close similarities. In particular, both Guantities increase during the beginning of flare growth and peak at about the same time. In Figure 1 the heating function is compared with the turbulent velocity v and not with the turbulent energy density et, since the values of e~a~ead~itionally affected by the errors of density determination, Ltheir between time variations noisier. 1,’Te suggest that and the thus, similarity the andaree~ (or v÷) time variations confirms the close coupling between the turbtdent motions ~.ndthe flare energy release.

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2. During the flare growth the plasma flows up into the flare volume (chromes— pheric evaporation) and blue components of the spectral lines are observed in the X—ray spectra /2/. If the turbulent region developes in the upper part of flare magnetic structure, the kinetic energy of the inflowing plasma streams will be transferred into the turbulent motions. The improved method of analysis of the BOS spectra /3/ allows a more reliable investigation of the time variations of the plasma inflow velocity v 1. For six appropriate flares showing intense blue components in the X—ray spectra, we have found a close similarity of the time variation of the inflow velocity v1(t) and the turbulent velocity vt(t). An example is shown in Figure 2. ~Te sug~est that this confirms the coupling of the plasma inflow and the turbulent motions, i.e. the energy transfer from the plasma streams to the turbulent notions. PARTICLE ACC~ERATION BY TURBUlENT IIOTIONS Prom the above estimates (cf. Introduction) it seems very probable that in some big quickly developing- flares the turbulent motions may produce large magnetic field fluctuations (5H/H~1, where ~H is the turbulent magnetic field fluctuation and H is the mean magnetic field strength). Such turbulent motions can efficiently accelerate ions and electrons to high energies via stochastic Fermi acceleration. The theory as developed by Nelrose /5/ gives the acceleration time =

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Turbulent \lotions and Particle Acceleration

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and c is the light velocity. When applied to the turbulent volume of hot flare plasma, equation (1) gives a very short acceleration tine, T’~1 s. This short acceleration time is very important, because it explains the quick acceleration of ions and electron3 to high energies as observed for some impulsive solar ~‘—ray flares /6/. Furthermore, we have estimated the total energy contained in the turbulent motions:

io28

2 5 x ergs e 4. E/~r where V is the hot plasma volume and E is its emission measure. These estimates have been made for the big flare of 1 July 1980, for which ~‘—ray line emission was recorded. It is more difficult to estimate the rate of energy supply to the turbulence, St V, where E~ is the rate of energy supply per unit volume. ‘iie have estimated from the model calculations /7/ that during the filling of the flare loops about 10 % of the released thermal energy is transformed into the kinetic energy of the inflowing plasma. Bulk of the kinetic energy should be transferred to the turbulent motions, as discussed in point 2 of the preceding section. Moreover, the energy release in the transient current sheets will produce large temperature gradients, which should generate additional turbulent motions. The intense magnetic field reconnection itself may produce turbulence as a result of a current sheet instabilit~ 7(cf. /8/~’. Therefore, we have taken E~~ 0.2 This gives E~V 2 x 10 ergs s

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On the other hand, from the hard X-ray spectra recorded by the HIRES we have calculated the rate of energy gain by electrons with energies E > E1, assuming a standard power law electron spectrum and a thick—target emission ‘model. We have found that the turbulent motions contain at least enough energy to produce all the particles of energies greater than ~ 80—100 keV. Similar estimates for the big flare of 14 October 1980 give E~~ 50—60 keV. The simplest explanation for the particles of intermediate energies, 20—100 heX, is to assume that the turbulent9magnetic field dissipation produces a small amount of very hot plasma (T ‘~ 10~X) near the magnetic field reconnection regions. A0KNOUl~GEI-iENTS The BUS is part of the X—ray polychromator built by a collaboration involving’ Lockheed Palo Alto Laboratory, 1-lullard Space Science Laboratory and Rutherford Appleton Laboratory. -J.J. acknowledges financial support from the Uh Science and Engineering Research Council. A.F. gratefully acknowledges a Scholarship from the IlK Foreign and Commonwealth Office. REFEREUCNS 1. (2.A. Doschek, U. Feldman, R.W. Freplin, and L. Cohen, kstrophys. 5. 259, 725 (1980) 2. 5. Antonucci, A.H. Gabriol, L.W. Acton, J.L. Cuihane, J.U. Boyle, 5.’.’. Leibacher, 11.5. Yachado, 1.5. Orwig, nod 0.0. F.apiey, Solar Pligs. 78, 107 (1982) 5. A. Fhudra, 5.5. Lemen, .J. Jakimiec, S.D. Bentley, and 5. Syl~’rester, to be submitted (1985) 4. 5. Jakimieo, 3. Sylwester, 5. Sylwester, s. Me~e, ‘H. Ceres, 3. Serio, and 5. Schrijver, this issue 5. 0.8. i’ielrose, 3-iar 7hys. 37, 353 (1974) 5. E.L. Ohupp, Ann. Rev. Astron. Astrophys. 22, 359 (1954) 7. 5. Fallavicini, 0-. Beres, S. Serio, U. Taiana, L. gcton, 5.1’. Leibacher, and 5. Rosnor, ~strophys. 5.270, 27~) (19.83) U. S.F. Uriest, in: Froc. SA l’iorkshop on SOlO and .21us5~, 1905