An Analytical Model for the Propagation of Thermal Runaway Electrons in Solar Flares

Abstract

The nature of the hard X-ray emission from solar flares is well known. The observed emission in both the corona and the chromosphere consists of two components: nonthermal and thermal. The non-thermal and thermal components are attributable to the bremsstrahlung of accelerated electrons and heated plasma electrons, respectively. Since the nonthermal and thermal hard X-ray emission spectra partially overlap, their proper interpretation directly depends on the accuracy of the kinetic models describing the propagation of thermal and nonthermal runaway electrons in the solar atmosphere. The evolution of the distribution function for the latter, i.e., the electrons accelerated in the magnetic reconnection region, is accurately described in the approximation of present-day thick-target models with a reverse current. Here we consider a model for the thermal runaway of electrons and find an analytical solution of the corresponding kinetic equation in which the Coulomb collisions are taken into account. The degree of polarization of the emission has been estimated to be no greater than ∼5%. The derived distribution function can also be used to calculate the thermal X-ray emission spectrum and, as a consequence, to interpret the observations of the thermal component in the X-ray spectrum of a solar flare.