Modeling the Rate of Occurrence of Solar Flares

Dimensional considerations are used to analyze the distribution of times between solar flares (the flare waiting-time distribution). An analytical estimate for the mean flaring rate λ0 is obtained, based on the idea that the rate reflects a balance between the processes of energy input into the corona and energy dissipation by flaring. The estimate is shown to be in good agreement with observations of flares by Geostationary Operational Environmental Satellite detectors. The analytic result is confirmed using the master equation (probability balance equation) formalism. Analysis of time variation leads to a differential equation describing how the free energy in the corona changes when the rates of driving of the system and of flaring vary. This equation may be used to describe the global energy balance in the corona over the solar cycle