Dynamics of Self-Gravity Wakes in Dense Planetary Rings I. Pitch Angle

TL;DR

This study uses N-body simulations to analyze how the pitch angle of self-gravity wakes in dense planetary rings varies with ring parameters, confirming observed trends and providing new insights into their dependence on distance from Saturn.

Contribution

It presents a detailed analysis of the pitch angle dependence on ring parameters, especially Saturnicentric distance, using autocorrelation functions in N-body simulations.

Findings

Inner pitch angle increases with Saturnicentric distance.

Outer pitch angle remains roughly constant around 10-15 degrees.

Results are consistent with observations of the A ring and spiral arm characteristics.

Abstract

We investigate the dynamics of self-gravity wakes in dense planetary rings. In particular, we examine how the pitch angle of self-gravity wakes depend on ring parameters using N-body simulations. We calculate the pitch angles using the two-dimensional autocorrelation function of the ring surface density. We obtain the pitch angles for the inner and outer parts of the autocorrelation function separately. We confirm that the pitch angles are 15 to 30 degrees for reasonable ring parameters, which are consistent with previous studies. We find that the inner pitch angle increases with the Saturnicentric distance, while it barely depends on the optical depth and the restitution coefficient of ring particles. The increase of the inner pitch angle with the Saturnicentric distance is consistent with the observations of the A ring. The outer pitch angle does not have the clear dependence on any ring parameters and is about 10 - 15 degrees. This value is consistent with the pitch angle of spiral arms in collisionless systems.