Multifractal fits to the observed main belt asteroid distribution

Abstract

Dohnanyi's (1969) theory predicts that a collisional system such as the asteroidal population of the main belt should rapidly relax to a power-law stationary size distribution of the kind $N(m)\propto m^{-\alpha}$, with $\alpha$ very close to 11/6, provided all the collisional response parameters are independent on size. The actual asteroid belt distribution at observable sizes, instead, does not exhibit such a simple fractal size distribution. We investigate in this work the possibility that the corresponding cumulative distribution may be instead fairly fitted by multifractal distributions. This multifractal behavior, in contrast with the Dohnany fractal distribution, is related to the release of his hypothesis of self-similarity.