Selective Ion Acceleration in Impulsive Solar Flares

I. Roth and M. Temerin

Space Sciences Laboratory, University of California, Berkeley, CA 94720

ABSTRACT

The spectacular enrichment of ³He and the smaller enrichments of heavy ions in impulsive flares is discussed in the context of a resonant interaction with the same electromagnetic ion cyclotron waves. The observed abundances are used to delineate the coronal thermodynamic conditions, the scalings of the enhancements with the coronal parameters and the frequency range of the resonant waves.

INTRODUCTION

The classification of solar flares into gradual and impulsive events was established remotely in X-ray observations [Wild et al., 1963; Pallavicini et al., 1977], in radio emissions, event duration, intensity, [Reames et al., 1985], and directly in particle abundances (e.g. Reames et al, 1994]. In situ solar wind measurements [Coplan et al., 1984] as well as astrophysical spectroscopic observations [Geiss, 1993] deduce the cosmical isotopic ratio of ³He/⁴He as several times 10-4. In impulsive solar flares this ratio is increased by 3-4 orders of magnitude. Similarly, spectroscopic, meteoric and interplanetary measurements of the various elements determine their cosmical abundances [Anders and Grevesse, 1989]. Impulsive flares which enhance spectacularly the ³He abundance are also enriched in heavier ions above O up through Fe [Mason et al. 1986, 1994; Reames et al., 1994], however no clear correlation between both enrichments exists. In this Paper we describe the simultaneous increase of the ³He/⁴He isotopic ratio and the X/C elemental ratio (when X denotes elements heavier than oxygen) on coronal field lines due to resonant interaction with electromagnetic ion-cyclotron (EMIC) wave.

ELECTROMAGNETIC ION CYCLOTRON WAVES

EMIC waves are often observed in association with intense electron fluxes on the terrestrial auroral field lines. These waves were observed on board several satellites crossing the auroral acceleration regions: S3- 3 [Lysak and Temerin, 1983], Freja [Gustafsson et al, 1990], and Polar satellite, which is the first spacecraft with the ability to measure directly all the electric field components in interplanetary space. In a two-ion plasma these waves may propagate between the H+ ion gyrofrequency and the two-ion hybrid resonance. They are characterized by a nearly linear polarization, by a phase velocity nearly perpendicular to the magnetic field and a group velocity nearly parallel to the magnetic field.

Figure 1 shows the perpendicular and the parallel components of the electric field as well as the three magnetic components in a spinning frame during the Polar south pole traversal of the acceleration region. The parallel electric field was obtained by determining the background magnetic field and calculating scalar product with the observed electric data. From Figure 1 one observes that the waves are very oblique, they consist of a magnetic contribution and their main frequency mode is below 100 Hz, which for the measured field of 6000 nT are slighly below the hydrogen gyrofrequency. The measured fields indicate the existence of intense electromagnetic ion cyclotron wave fields at the acceleration region.

There exists an interesting analogy between physical processes on active auroral and flaring coronal field lines, as was suggested by Temerin and Roth [1992]. Both environments consist of very low b plasmas, are dominated by two majority species and are subjected to intense electron fluxes due to magnetic field reconfigurations. In the corona these electron fluxes are deduced from the X-ray emissions, while in the aurora they are measured directly by rockets or satellites. Therefore, it was argued that one can infer from the auroral in situ observations about coronal processes.

RESONANT ION ENHANCEMENT

Coronal ions are accelerated when their gyrofrequncy or its harmonic satisfy the Doppler-shifted resonant condition with an EMIC wave which propagates along the inhomogeneous magnetic field. ³He ions are unique among all the minority coronal ions in possessing a cyclotron frequency in the EMIC frequency range, such that when the ³He gyrofrequency approaches the wave frequency they are resonantly accelerated, while the heavier ions are accelerated at the higher harmonic of their cyclotron frequency. The waves are damped near the hydrogen and ⁴He gyrofrequencies; therefore ions with a charge-to-mass ratio of 0.5 (in units of H), like ⁴He or fully ionized CNO, are not affected by the waves [Roth and Temerin 1995; Temerin and Roth, 1995].

The acceleration rate of a coronal ion in the presence of monochromatic EMIC wave is given by \dot{W}_\perp = n q v_\perp \hat{e} \frac{J_n (k_\perp \rho)}{k_\perp \rho} cos [\int (n \Omega (z) / \gamma + k \nu - \omega) dt] where n=1 applies to ³He and n=2 or 3 to heavy ions, r = v^ / W is the gyroradius, and e^ denotes the amplitude of the perpendicular electric field. Equation 1 shows that the initial acceleration of the ³He ion is larger than that of the heavy ions, however the final energy is similar. This energy is determined by the balance between the maximun wave force and the mirror force, and is approximately given by the zeroes of the appropriate Bessel function. The mirror force, i.e. the inhomogeneity of the magnetic field is an important factor in the acceleration process, allowing an increase in the interaction time and the final energization. For insufficiently intense waves the mirror force will eject the heavy ion before it can reach high energy, and low energy ion may be removed from resonance by Coulomb colisions. Therefore the enrichment of heavy ions depends on wave amplitude, on background density and on thermal ion distribution.

Figure 2 shows the evolution of an ³He ion and of two heavy ions (²⁴Mg⁺⁹ and ⁵⁶Fe⁺²⁰) interacting with the same EMIC wave. Figure 2a shows the effect of varying the scale size L of the magnetic field: L= 1000, 2000, 4000 and 8000 km. For a larger L (smaller gradient) the mirror force decreases, the time scale of the resonance increases, and the final energy increases from 7 to almost 9 MeV as the balance between the mirror force and the parallel wave force allows k^ r to approach closer to the first zero of Bessel function Jn (k^ r) in agreement with equation (1).

Figure 3 depicts the abundances of the coronal ions as a function of their gyrofrequencies at a temperature of 4 MK. For completeness the coronal ³He abundance was added at half of its gyrofrequency. We have used the standard cosmic isotopic ratios; altogether we included around 300 different charge states. Due to the various combinations of ion charges and masses some of the gyrofrequencies are shared by different elements. An increase in temperature shifts the main abundance of the coronal ions to higher charge state. At lower temperature (~2MK) one finds a large population of O6 which is susceptible to acceleration. Since these ions are hardly enhanced in the impulsive flares, the flaring temperature for these flares should be above 2 MK. At higher temperatures (~8 MK) the large number of Fe charge states on both sides of the half ³He gyrofrequency would indicate a very large enhancenment of Fe vs all the other heavy elements, while observations give only factor of 3 for this ratio. Hence ~4 MK is the most favourable temperature as compared with the observed ion enhancements. Observations also indicate that Si and Mg are enhanced only by a factor ~3 vs C, hence the EMIC wave spectrum extends approximately over the frequency range w/WH = 0.6 - 0.8.

CONCLUSIONS

The selective acceleration of ³He and of heavy ions in impulsive solar flares by can be explained by resonant interaction with EMIC waves. These waves are deduced in analogy to auroral observations. The lower enhancement of the heavy ions is due to the lower acceleration rates at higher harmonic gyroresonance. Higher amplitude and lower density increase the relative enrichment of the heavy ions.

ACKNOWLEDGMENTS

We acknowledge the support of NSF grant ATM9224688, NASA contract NAS5-30367 and grant NAG5-3182.

REFERENCES

Anders, E. and H. Grevesse, Geochim. Cosmochim. Acta, 63, 197 (1989).
Coplan, M. A., Oglivie, K W, Bochsler P. and Geiss J , Solar Physics, 93, 415 (1984).
Geiss, J., in Origin and Evolution of Elements, ed. N. Prantzos, E. Vangioni-Flam and M. Casse, Cambridge University Press (1993).
Gustafsson, G., Andre, M., Matson, L., and Koskinen, H., J. Geophys. Res., 95, 5889 (1990).
Lysak, R. L., and Temerin, M., Geophys. Res. Lett., 10, 643 (1983).
Mason, G. M., Reames, D. V., Klecker, B., Hovestadt, D., and von Rosenvinge, T. T., Astrophys. J., 303, 849, (1986).
Mason, G. M., Mazur J. E., Hamilton, D. C., Astrophys. J., 425, 843 (1994).
Pallavicini, R., Serio, S., and Vaiana, G. S. , Astrophys. J., 216, 108 (1977).
Reames, D. V., von Rosenvinge, T. T., and Lin, R. P., Astrophys. J., 292, 716 (1985).
Roth, I., and Temerin, M., 24th Int. Cosmic Ray Conf., p.118 (1995).
Temerin, M., and Roth, I., Astrophys. J., 391, L105 (1992).
Temerin, M., and Roth, I., High Energy Solar Physics, Greenbelt, ed. R. Ramaty, N. Mandzhavidze and X. M. Hua, AIP Conf. Proc. (1996).
Wild, J. P., Smerd, S. F., and Weiss, A. A., Ann. Rev. Astron. Astrophys., 1, 291 (1963).

Figure 1. Perpendicular and parallel electric field components and three magnetic wave components as observed by the Polar satellite.

Figure 2. (i) Total energy, (ii) parallel trajectory of an ³He: effect of the magnetic field gradient. L= (a) 1000, (b) 2000, (c) 4000 and (d) 8000 km. k^ = 500 km-1, e^ = 80 V/m, Bo = 500 G , ne = 109 cm-3. (iii) total energy of ⁵⁶Fe+20 and ²⁰Mg+9 ions.

Figure 3. Abundances of the main coronal ions as a function of their gyrofrequencies at 4 MK, in units of H gyrofrequency.