Electron-Electron Bremsstrahlung Emission and the Inference of Electron Flux Spectra in Solar Flares

TL;DR

This paper demonstrates that including electron-electron bremsstrahlung in models of solar flare X-ray emission explains observed spectral features and affects the inferred electron spectra, especially above 300 keV.

Contribution

It introduces a comprehensive analysis of electron-electron bremsstrahlung's role in solar flare X-ray spectra and shows its impact on electron spectrum inference.

Findings

Electron-electron bremsstrahlung accounts for the spectral break around 400 keV.

Inclusion of both bremsstrahlung types yields a nearly constant electron spectral index from 200 keV to 1 MeV.

The analysis suggests the potential to diagnose electron beaming and cutoff energies.

Abstract

Although both electron-ion and electron-electron bremsstrahlung contribute to the hard X-ray emission from solar flares, the latter is normally ignored. Such an omission is not justified at electron (and photon) energies above $\sim 300$ keV, and inclusion of the additional electron-electron bremsstrahlung in general makes the electron spectrum required to produce a given hard X-ray spectrum steeper at high energies. Unlike electron-ion bremsstrahlung, electron-electron bremsstrahlung cannot produce photons of all energies up to the maximum electron energy involved. The maximum possible photon energy depends on the angle between the direction of the emitting electron and the emitted photon, and this suggests a diagnostic for an upper cutoff energy and/or for the degree of beaming of the accelerated electrons. We analyze the large event of January 17, 2005 observed by RHESSI and show that the upward break around 400 keV in the observed hard X-ray spectrum is naturally accounted for by the inclusion of electron-electron bremsstrahlung. Indeed, the mean source electron spectrum recovered through a regularized inversion of the hard X-ray spectrum, using a cross-section that includes both electron-ion and electron-electron terms, has a relatively constant spectral index $\delta$ over the range from electron kinetic energy $E = 200$ keV to $E = 1$ MeV. However, the level of detail discernible in the recovered electron spectrum is not sufficient to determine whether or not any upper cutoff energy exists.