Avalanche models of solar flares and the distribution of active regions

Avalanche models of solar hares successfully reproduce the power-law distribution of flare frequency as a function of energy. However, the model distributions have been produced for a single numerical grid, representing a single active region on the Sun. Here we convolve the distribution owing to an avalanche grid with each of two observationally determined active region size distributions. The resulting energy distributions are power laws (with index alpha approximate to 1.5) below about 10(31) ergs, but they gradually steepen with energy. The resulting distributions are compared with a flare energy distribution derived from International Cometary Explorer satellite observations. Qualitative agreement is found between the model and observed distributions, although the observations favor a simple power-law model distribution with a somewhat steeper index (approximate to 1.71).