AVALANCHE MODELS OF SOLAR-FLARES AND THE DISTRIBUTION OF ACTIVE REGIONS

Avalanche models of solar hares successfully reproduce the power-law d istribution of flare frequency as a function of energy. However, the m odel distributions have been produced for a single numerical grid, rep resenting a single active region on the Sun. Here we convolve the dist ribution owing to an avalanche grid with each of two observationally d etermined active region size distributions. The resulting energy distr ibutions are power laws (with index alpha approximate to 1.5) below ab out 10(31) ergs, but they gradually steepen with energy. The resulting distributions are compared with a flare energy distribution derived f rom International Cometary Explorer satellite observations. Qualitativ e agreement is found between the model and observed distributions, alt hough the observations favor a simple power-law model distribution wit h a somewhat steeper index (approximate to 1.71).