High Energy Limit of Particle Acceleration in Solar Flares
In several intense γ-ray flares, a broad line-shaped spectral component peaking at about 70 MeV has been observed. This component is interpreted as π0 decay emission produced with GeV protons. In the case of the largest flares like June 3, 1982 event, we have to assume a power-law spectrum for the accelerated protons. It would be important to determine the highest cut-off energy E cut in the proton spectrum in order to decide the depth of the acceleration region if the acceleration is due to a shock. On the other hand, the p-p collision cross-section for π0 production has a sharp low energy cutoff at around 300 MeV. Considering both high and low energy cutoffs in the energy distribution for protons, virtually a mono-energetic distribution of high energy protons might be responsible for the π0 production. In this paper, we have calculated the line width of π0 emission with various E cut of the incident protons. In this calculation of γ-ray spectrum, the energy distribution of the is needed. The most important finding in this calculation is that the calculated 70-MeV line width varies very sensitively with the E cut in the energy range 300MeV–3GeV. Within this energy range, the line width varies more than a factor of two. We can thus determine the unique energy (the peak energy in a narrow distribution between the high and low energy cutoffs) of the accelerated protons by comparing the line width for each energy to the observed line width. Consequently we can determine the actual E cut in the energy spectrum of accelerated protons by using the above obtained unique energy. The high energy cutoff thus obtained is about 1 GeV for the June 3, 1982 flare.