Collisional relaxation of electrons in a warm plasma and accelerated nonthermal electron spectra in solar flares

TL;DR

This paper develops an analytic method to more accurately infer the spectrum of accelerated electrons in solar flares by accounting for collisional effects and thermalization, improving upon the cold-target model.

Contribution

It introduces a new analytic approach that considers the finite volume of hot plasma and electron thermalization, refining the estimation of nonthermal electron spectra from X-ray data.

Findings

Thermalization effects can eliminate the need for a low-energy cutoff in the electron spectrum.

The method yields more realistic estimates of injected non-thermal electron energies.

Considering the hot plasma volume improves the interpretation of hard X-ray observations.

Abstract

Extending previous studies of nonthermal electron transport in solar flares which include the effects of collisional energy diffusion and thermalization of fast electrons, we present an analytic method to infer more accurate estimates of the accelerated electron spectrum in solar flares from observations of the hard X-ray spectrum. Unlike for the standard cold-target model, the spatial characteristics of the flaring region, especially the necessity to consider a finite volume of hot plasma in the source, need to be taken into account in order to correctly obtain the injected electron spectrum from the source-integrated electron flux spectrum (a quantity straightforwardly obtained from hard X-ray observations). We show that the effect of electron thermalization can be significant enough to nullify the need to introduce an {\it ad hoc} low-energy cutoff to the injected electron spectrum in order to keep the injected power in non-thermal electrons at a reasonable value. Rather the suppression of the inferred low-energy end of the injected spectrum compared to that deduced from a cold-target analysis allows the inference from hard X-ray observations of a more realistic energy in injected non-thermal electrons in solar flares.