Localization of electron acceleration in solar flares based on the spectrum analysis of hard X-ray time delays

Abstract

Data on hard X-rays of solar flares recorded by the BATSE spectrometer are analyzed. Time delays were determined and their spectra were constructed for X-ray profiles at different energies. The X-ray emission of 82 flares was analyzed, and three types of time delay spectra were identified, i.e., decaying spectra, U-shaped spectra, and spectra that grow with increasing photon energy. In order to interpret delay spectra, the kinetic model of accelerated electrons that propagate in the plasma of the flare loop with a converging magnetic field was considered. Two cases of electron injection were investigated, i.e., isotropic injection and injection in a pitch-angle cone. Of particular note is that delay spectra that decay with increasing energy can be explained only in the case of the spatial diversity of areas of injection and acceleration and a small change in the magnetic field with altitude or if magnetic inhomogeneities is present. Calculations have also shown different types of delay spectra at the top and footpoints of the loop, which are determined by the dynamics of electrons in the loop when selecting different initial conditions, loop geometry, and spatial localization of the areas of acceleration and injection.