# Determination of the total accelerated electron rate and power using solar flare hard X-ray spectra

## TL;DR

This paper introduces a self-consistent warm-target method combining X-ray spectroscopy and imaging to precisely determine the low-energy cutoff of accelerated electrons in solar flares, improving energy estimates over traditional cold-target models.

## Contribution

The study develops and applies a novel warm-target approach that accurately constrains the low-energy cutoff and energetics of accelerated electrons using combined spectral and imaging data.

## Key findings

- Warm-target method determines electron cutoff with ~7% uncertainty.
- Standard cold-target approach cannot constrain low-energy cutoff.
- Accurate electron energetics are crucial for understanding solar flare energy release.

## Abstract

Solar flare hard X-ray spectroscopy serves as a key diagnostic of the accelerated electron spectrum. However, the standard approach using the collisional cold thick-target model poorly constrains the lower-energy part of the accelerated electron spectrum, and hence the overall energetics of the accelerated electrons are typically constrained only to within one or two orders of magnitude. Here we develop and apply a physically self-consistent warm-target approach which involves the use of both hard X-ray spectroscopy and imaging data. The approach allows an accurate determination of the electron distribution low-energy cutoff, and hence the electron acceleration rate and the contribution of accelerated electrons to the total energy released, by constraining the coronal plasma parameters. Using a solar flare observed in X-rays by the {\em RHESSI} spacecraft, we demonstrate that using the standard cold-target methodology, the low-energy cutoff (and hence the energy content in electrons) is essentially undetermined. However, the warm-target methodology can determine the low-energy electron cutoff with $\sim$7\% uncertainty at the $3\sigma$ level and hence permits an accurate quantitative study of the importance of accelerated electrons in solar flare energetics.