Saturnian Ring N-Body Simulations

Introduction

The purpose of this website is to provide supporting materials for visualization of our ring simulation results. For detailed information about how the code works, a discussion of our results, and the implications for Saturn's rings, please see our paper:

• Robbins, S.J., Stewart, G.R., Lewis, M.C., Colwell, J.E., and M. Sremčević. (2009). "Estimating the Masses of Saturn's A and B Rings from High-Optical Depth N-Body Simulations and Stellar Occultations." Submitted to Icarus.

We have run nearly 200 different simulations spanning a large range of parameter space. The parameters we explored were:

• Simulations in the C, B, and A rings, located at 85 Mm, 100 Mm, and 130 Mm from Saturn, respectively.
• Particles with an internal density of 0.45 g·cm^-3 and those with 0.85 g·cm^-3.
• Uniform-sized particles with a radius R=1 m and those with a particle size distribution with a power-law slope of -3, with a range of particle sizes from 0.256 m < R < 2.56 m (chosen to have the same surface density as the R=1 m simulations).
• Initial geometric/classic optical depth between 0.0884 all the way to 4.000 in multiplicative intervals of 2^1/4.

The cell size for all simulations was chosen based upon the Toomre Critical Wavelength λ_crit. We initially planned on running simulations with N=100,000 particles, but this became computational overkill for many of the easier simulations. So we set a cap such that the length of the square cell L was an upper bound L = 100λ_crit. For the more computationally intensive simulations, 100,000 particles would result in a cell size L << 100λ_crit, and so we set a lower limit such that L = 6λ_crit. Hence, our constraint on the cell size was 100λ_crit ≤ L ≤ 6λ_crit. We chose this lower limit because we think it is the minimum size required such that structure is not suppressed by the mirror boundary conditions.

We have not made movies of every simulation, but we have made movies of many of them. They are linked in the tables below. It is recommended that you download the movies to your computer before starting to play them because of their size - they are between 100 and 200 MB each. They span 5 orbital periods with each frame being 1/100 of an orbit. They are 20 seconds long at 25 frames per second (1 orbit in 4 seconds). They are MOV (QuickTime) format.

Parameters of ρ = 0.45 g·cm^-3, R = 1m Simulations
Click to download tab-separated TXT file of this table.

Note: This set of parameters were the easiest in terms of CPU time requirements, and they also best-match the Cassini UVIS data for the B ring stellar occultations at 100 Mm from Saturn. Because of this, the widest range of τ were run for this parameter set, including a few additional B ring locations (105, 110, and 115 Mm from Saturn).

Parameters of ρ = 0.85 g·cm^-3, R = 1m Simulations
Click to download tab-separated TXT file of this table.

Parameters of ρ = 0.45 g·cm^-3, 0.256m < R < 2.56m Simulations
Click to download tab-separated TXT file of this table.

Parameters of ρ = 0.85 g·cm^-3, 0.256m < R < 2.56m Simulations
Click to download tab-separated TXT file of this table.

Note: This set of parameters were the most difficult in terms of CPU time requirements. Because of this, the smallest range of τ were run for this parameter set.

C Ring (85 Mm from Saturn, orbital period ~7.02 hours)

B Ring, Inner (100 Mm from Saturn, orbital period ~8.96 hours)

B Ring, Middle (105 Mm from Saturn, orbital period ~9.64 hours)

B Ring, Middle (110 Mm from Saturn, orbital period ~10.3 hours)

B Ring, Outer (115 Mm from Saturn, orbital period ~11.1 hours)

A Ring (130 Mm from Saturn, orbital period ~13.3 hours)