Fokker‐Planck Modeling of Asymmetric Footpoint Hard X‐Ray Emission in Solar Flares

Abstract

Chromospheric hard X-ray emission in a solar flare generally occurs in two magnetically connected "footpoint" regions. Recent spatially resolved hard X-ray observations carried out using the RHESSI spacecraft have shown that the ratio of total X-ray fluxes from the two footpoints is time dependent and demonstrates a weak but detectable photon energy dependence. A Fokker-Planck code is used to identify possible scenarios that could reproduce the observed dependence of footpoint asymmetry on time and energy. The code, which is benchmarked against analytical results in the limit of collisionless precipitation from a symmetric flaring loop, includes collisional friction and pitch-angle scattering, asymmetric magnetic mirroring, and a source term that can be prescribed arbitrarily. This model is used to demonstrate that the observed dependence of hard X-ray asymmetry on photon energy can be attributed to an energetic electron source that is isotropic at low energy (presumed to be due to Coulomb collisions) and at high energy (presumed to be due to resonant wave-particle scattering) and strongly anisotropic at intermediate energies.