Saturn's Rings II: Particle Sizes Inferred from Stellar Occultation Data

We derive power-law particle size distributions for each of Saturn's main ring regions, using observations of the 3 July 1989 stellar occultation of 28 Sgr from Palomar, McDonald, and Lick observatories. We use the Voyager PPS δ Sco optical depth profile to estimate and then remove the directly transmitted signal from the 28 Sgr observations, leaving high SNR scattered light profiles at wavelengths of 3.9, 2.1, and 0.9 μm. The angular distribution of this diffracted signal depends on the ring particle size distribution: the sharpness of the forward lobe is set by the largest particles, while the overall breadth and amplitude of the scattered signal reflect the abundance of smaller, cm-sized particles. From a simple one-dimensional scattering model, we estimate characteristic particle sizes in the A, B, and C rings, and obtain a good match to the detailed structure of the observed scattered light profiles. To accommodate more realistic particle size distributions and to take proper account of the geometry of the occultation, we then develop a two-dimensional forward-scattering model. We assume for simplicity a single power law particle size distribution for each major ring region, and we determine the index q and lower and upper size cutoffs a min and a max that provide the best match to all three data sets in each region. Our results in the A and C rings are fairly consistent with values of q and a max derived from Voyager radio occultation (RSS) measurements (Zebker et al. 1985). We extend their results by determining lower limits to the particle size distributions and by probing the B Ring. We find a rather flat ( q=2.75) and narrow size distribution for both the inner A Ring and the B Ring, with a surprisingly large a min=30 cm. From the detailed shape of the scattered signal in the A and B rings, we find a max=20 m, a factor of two larger than the RSS result. The fraction of cm-sized particles increases between the inner and outer A Ring and is greatest in the C Ring, where a min=1 cm and q=3.1. Our upper size cutoffs are in excellent agreement with Showalter and Nicholson's (1990) estimates based on the statistical properties of the Voyager PPS occultation data, but the implied surface mass densities significantly exceed those derived from studies of density and bending waves, if the ring particles are made of solid ice.