Tiscareno, Matthew S., Perrine, R. P., Richardson, D. C., Hedman, M. M., Burns, J. A., Weiss, J. W., Porco, C. C. (2008). "An Analytic Parameterization of Self-Gravity Wakes" American Astronomical Society, DPS meeting #40, #21.06.

Saturn's dense A and B rings are pervaded by a microstructure dubbed "self-gravity wakes," which arise due to a rough balance between the clumping together of particles under their mutual self-gravity and their shearing apart again due to tidal forces (Julian and Toomre 1966; Salo 1995). This effect causes azimuthal variations in the rings' brightness as seen in images (Franklin et al. 1987; Dones and Porco 1989; Salo et al. 2004; Porco et al. 2008) and in the optical depth as probed by occultations (Colwell et al. 2006; Hedman et al. 2007).

The latter papers explain the occultation observations with models that assume widely separated elongated structures that have an optical-depth dichotomy, with nearly-opaque wakes (with optical depth τwake) and a low but relatively constant optical depth in the spaces between the wakes (τgap). However, it is not known whether simulated wakes (not to mention real ones) can be so characterized, nor, if they can, how τwake and τgap respond to environmental parameters such as optical depth and coefficient of restitution. What do observed values of τgap (Colwell et al. 2006; Hedman et al. 2007) tell us about the conditions under which wakes occur?

To this end, we determine the distribution of densities in simulated wake cells. Our method uses an adaptive bin size to simultaneously accommodate low-density regions, where particles are sparse (large bins required), and the sharp boundaries between high- and low-density regions (small bins required). The result is a histogram of the local densities within simulated patches of the ring. We apply this method to a suite of simulated wake cells, and will present our results. We further plan to use our results to address the question of whether local disruption of self-gravity wakes can explain the observed brightness of "propeller" structures (Tiscareno et al. 2008, AJ).