Numerical Simulations of Density Waves in Saturn’s A-Ring

In this work, we report on the use of various cell simulation methods to model density waves in Saturn’s A-Ring using three different boundary conditions, with and without particle self-gravity. The boundary conditions used are 1) global, 2) a cell that matches the azimuthal extent of a single synodic period of drift relative to the moon, and 3) a local cell that preserves external moon perturbations. All simulations model resonant encounters with Prometheus and we use a surface density of 45 g/cm². Each boundary condition uses a different set of particle sizes and optical depths to make the simulations computationally feasible. In simulations without particle self-gravity, no true density waves form, only wake-like structures formed by compression of streamlines. When the self-gravitational effects of the particles are taken into account, however, our simulation produces density waves propagating toward the perturbing moon whose wavelength decreases as we move radially farther from the location of the Lindblad Resonance. This occurs across all three boundary conditions. Evidence of straw-like features is seen in the wave peaks of the density waves in the local cell simulation, which is the only one with sufficient resolution to model such structures.