Determination of the Total Accelerated Electron Rate and Power Using Solar Flare Hard X-Ray Spectra

Solar flare hard X-ray (HXR) 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, 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 that involves the use of both HXR spectroscopy and imaging data. This 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 RHESSI, we demonstrate that using the standard cold-target methodology, the low-energy cutoff (hence the energy content in electrons) is essentially undetermined. However, the warm-target methodology can determine the low-energy electron cutoff with ~7% uncertainty at the 3σ level, hence it permits an accurate quantitative study of the importance of accelerated electrons in solar flare energetics.