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

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