Accurate determination of the total accelerated electron rate and power using solar flare hard X-ray spectra from RHESSI and FOXSI

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. Physically self-consistent warm-target 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. Using a solar flare observed in X-rays by the 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 determines the low-energy electron cutoff with ∼14% uncertainty at the 3\sigma level. We further show that using FOXSI imaging and spectroscopy data, the flare energetics can be determined more accurately than it was possible before.