Saturn's main ring particle size distribution: An analytic approach

An analytic theory for Saturn's ring particle size distribution is developed using the so-called “dynamic ephemeral bodies” (or DEBs) model of ring particles (S.J. Weidenschilling, C.R. Chapman, D.R. Davis, and R. Greenberg, 1984, in Planetary Rings, pp. 367–416, Univ. of Arizona Press, Tucson). Accretion and erosion criteria are defined, and the fundamental integrodifferential equation describing the collisional evolution of the mass distribution function of ring particles is derived in the approximation that the ring velocity dispersion is independent of the particle size. A simple stationary solution of this equation is developed, which reproduces all the main features of the distributions determined from the Voyager I radio data (H.A. Zebker, E.A. Marouf, and G.L. Tyler, 1985, Icarus 64, 531–568). The main results of this work are the following: (i) the upper cutoff of the distribution can be explained by a relative enhancement of the erosion of the large particles; (ii) the power-law index of the distribution can be related to parameters characterizing the particle collisional properties; (iii) the model yields estimates for the particle life times and for the dispersion velocity in various unperturbed regions of the rings; (iv) “hard-sphere” ring particle models are most probably ruled out, because they lead to stationary distribution functions in disagreement with the Voyager results