Self-organized criticality in solar GeV flares

The Sun emits significant flares in X-ray, ultraviolet, and radio wavelengths. It is thought to originate from the magnetic reconnection activity, which is capable of accelerating particles to high energies. The magnetic process can be described by the avalanche model of self-organized criticality (SOC), and it is evidenced by the observation. Here, we study the frequency distribution of fluence, peak flux, and duration time for solar GeV flares detected first by Fermi-Large Area Telescope. Their cumulative distributions show a power-law behaviour. The exponents are also consistent with those derived from the observations at low-energy bands, and follow the predictions of the fractal-diffuse SOC model. In the meantime, the waiting time shows power-law distribution, and agrees a non-stationary Poission process. We then explore the correlation between energy (fluence) and duration time using a two-variable regression analysis. The correlation is found to be $T_{\rm Duration} \propto F_{\rm GeV}^{0.38\pm 0.08}$ with the solar GeV flare sample, which is comparable to that of the solar X-ray flares and gamma-ray bursts (GRBs) and could be understood in an SOC model. These facts suggest that, similar to the physical process accounting for the X-ray emission of solar flares and prompt emission of GRBs, magnetic reconnection may still dominate the energy-release process and particle acceleration for solar flares at GeV energies.