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M. C. Lewis, G. R. Stewart (University of Colorado)
We simulate wake evolution in the Encke Gap forced by a nearby moon. The N-body calculations run on a single processor, include a few hundred thousand particles, and explicitly include collisions. The motivation for these simulations is to explain the morphology and the persistence of the wakes seen in the Voyager PPS data. Showalter et al. (1986, Icarus 66, 297) proposed that the oscillatory patterns observed in the radial profiles around this gap in the A Ring were due to the perturbations of a small moon. This small moon, Pan, was later located by Showalter (1991, Nature 351, 709). From the analytic work of Showalter et al. in 1986, which describes the evolution of the wake without self-gravity, the wakes should essentially disappear 20-30 degrees downstream from the moon. However, Showalter noted in 1991 that the wakes were still visible in the data ~330 degrees downstream. More recent analysis has shown that the wakes persist well beyond re-encountering Pan and can be found superimposed over the more recent perturbations. To better understand how collisions affect the evolution of these wakes, we use the collisional model of Bridges et al. (1984, Nature 309, 333) for a velocity dependent coefficient of restitution. Our simulations differ from previous work in that we have tried to keep the parameters in the simulation as close as possible to those at the actual Encke Gap. We preserve the satellite to planet mass ratio and run the simulations for a full synodic period to determine damping rates for the wakes. We have run simulations with particles ranging from 133 meters in radius down to 6.7 meters in radius at an optical depth of 0.3. For lower optical depths we have used particles as small as 1 meter in radius. Our simulations show how cell size, particle size, and optical depth affect the results. Preliminary results are that with particle sizes of several meters and optical depths around 0.3, collisions can sustain the wakes further downstream than the collisionless theory would predict. Also, we find that the collisions produce a phase shift in the wake near the ring edge.
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The author(s) of this abstract have provided an email address for comments about the abstract: ml@colorado.edu