High-energy gamma-ray emission from solar flares: Constraining the accelerated proton spectrum

Abstract

Using a multi-component model to describe the γ-ray emission, we investigate the flares of December 16, 1988 and March 6, 1989 which exhibited unambiguous evidence of neutral pion decay. The observations are then combined with theoretical calculations of pion production to constrain the accelerated proton spectra.

The detection of π⁰ emisson alone can indicate much about the energy distribution and spectral variation of the protons accelerated to pion producing energies. Here both the intensity and detailed spectral shape of the Doppler-broadened π⁰ decay feature are used to determine the spectral form of the accelerated proton energy distribution. The Doppler width of this γ-ray emission provides a unique diagnostic of the spectral shape at high energies, independent of any normalisation. To our knowledge, this is the first time that this diagnostic has been used to constrain the proton spectra. The form of the energetic proton distribution is found to be severely limited by the observed intensity and Doppler width of the π⁰ decay emission, demonstrating effectively the diagnostic capabilities of the π⁰ decay γ-rays.

The spectral index derived from the γ-ray intensity is found to be much harder than that derived from the Doppler width. To reconcile this apparent discrepancy we investigate the effects of introducing a high-energy cut-off in the accelerated proton distribution. With cut-off energies of around 0.5–0.8 GeV and relatively hard spectra, the observed intensities and broadening can be reproduced with a single energetic proton distribution above the pion production threshold.