The Collisional Evolution of the Asteroid Belt and Its Contribution to the Zodiacal Cloud

Abstract

We present a number of results from a numerical model of asteroid collisional evolution. Our results verify those of Dohnanyi (1969,J. Geophys. Res.74,2531–2554) and allow us to place constraints on the impact strengths of asteroids. The slope of the equilibrium size–frequency distribution is found to be dependent upon the shape of the size–strength scaling law. We find that pure size-independent and strain-rate scaling laws yield model size distributions which fail to match the observed mainbelt size distribution. An empirical modification has been made to the size–strength scaling law which allows us to match the observed asteroid size distribution and indicates a more gradual transition from strain-rate to gravity scaling. This result is not sensitive to the mass or shape of the initial asteroid population, but rather to the form of the strength scaling law: scaling laws have definite observational consequences. Asteroid families with material properties that differ from that of the average background population may evolve a size distribution with a different equilibrium slope than that of the background. Wave-like deviations from a strict power-law equilibrium size distribution result if the smallest particles in the population are removed at a rate significantly greater than that needed to maintain a Dohnanyi equilibrium slope. We find, however, that the observed small particle cutoff in the interplanetary dust complex is too gradual to support a significant wave. We suggest that any deviations from an equilibrium size distribution in the asteroid population are the result of stochastic cratering and fragmentation events which must occur during the course of collisional evolution. By determining the ratio of the area associated with the mainbelt asteroids to that associated with the prominent Hirayama asteroid families, our analysis indicates that the entire mainbelt asteroid population produces 3.4 ± 0.6 times as much dust as the prominent families alone. This result is compared with the ratio of areas needed to account for the zodiacal background and the IRAS dust bands as determined by analysis of IRAS data. We conclude that the entire asteroid population is responsible for at least one third of the dust in the entire zodiacal cloud.