Collisional Formation Of Ringlets In High M Resonances

Astronomy and Astrophysics – Astronomy

Scientific paper

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Scientific paper

Numerical, N-body simulations were run of ring particles in various mean motion resonances with a single moon to observe the formation of ringlets. In these simulations the M value of the resonances, moon mass, particle size, and optical depth were varied. The simulations include particle collisions using a velocity dependent normal coefficient of restitution. Transverse friction, spin, and particle self-gravity were ignored. The simulations were run for ten synotic periods and many clearly showed formation of ringlets in resonance over that time scale. It was found that lower optical depths resulted in more defined ringlet formation relative to higher optical depths. Also, higher moon masses and higher M values all showed stronger ringlet formation. In general, ringlets were shown to form with optical depths significantly lower than unity in any system where the moon could excite forced eccentricities on the order of 10^-5 or higher. Preliminary results show that particle size does not have a significant effect on this process.
The simulations display the formation of moon induced wakes, similar to those seen near the embedded moon Pan in the Encke gap. Analysis of the particle streamlines indicates that ringlets tend to form when the wakes reach the critical point such that the streamlines intersect. Plots of the eccentricity of the particles over the ten synotic periods show that the ringlet formation is accompanied by significant decreases in eccentricity. This is consistent with earlier results indicating that particle orbits can be systematically altered by collisions when streamlines are compressed sufficiently. The drops in eccentricity are a direct result of the changes the must occur in the orbits to prevent the streamlines from crossing. The eccentricities in these simulations show very little damping due to collisions prior to the critical point where streamlines intersect.

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