Gareth "Indy" Jones

I am a Physics undergraduate at Trinity. My research this summer will focus on the structure and composition of the dense rings (A and B) of Saturn. In order to determine the maximum mass that could be contained in the regions with high optical depth, N-body simulations of A and B ring particles in environments with different surface and volume densities will be run. In addition, the amount of silicates in the rings will be examined by performing photometric analysis of N-body simulations of B-ring particles with different percentages of silicates. For reference, our observer theta will go from -PI to PI, our light theta will go to 2*PI, our observer phi will go from -1.4 to 1.4, and out light phi will go from 0.1 to 0.5.

## Overview of Procedure

For this study, we produced sets of particles that had different surface densities, size ranges, and distances from Saturn via N-body simulations. Because we were studying the hiding of silicates, each simulation contained 0.5, 1, or 2% silicates by number of particles. The surface density we used was determined before the addition of silicates. Because of this, for a surface density of 30g/cm

^{2}, the effective surface density after silicate addition was 30.75 for 0.5%. 31.5 for 1%, and 33g/cm

^{2}for 2%. Our distances from Saturn were those of the middle of the A and B ring, and our particle radius range was 9E-10—9E-9 that of Saturn. Because of time constraints, we only performed photometry on simulations with 30g/cm

^{2}. Once we had those files, we used the program SwiftVis to perform photometry and other processes. Photometry was done by tracking the path of around two million photons as they interacted with the particles.

Using a spherical surface with 400 bins, we recorded the total light intensity received by each bin and the amount of reflected light from silicates received. After repeating this process for 100 permutations of horizontal and vertical lighting angle, we made a plain text file that contained the lighting angles, the observation angles, and information about received light. In order to glean a truer sense of the properties of each system, we averaged the text files from three times in the N-body simulation. From there, we performed two procedures on the averaged files.

The first was to plot the ratio of reflected silicate light to total incoming light as a function of each of the four angles (ref RelIntensVAng). No clear relationship was evident on any of the plots we produced, with the exception of the vertical angle of the observer, where a marked difference between the light ratio above and below the plane of particles was present. To quantify this difference, we separated the plot into three sections, took the average of each, and found the ratios.

The second procedure was to make a plot of reflected silicate light as a function of total received light, or the relative intensity. and find the slope of the line of best fit (ref RelIntens). Once we had the best fit slope, we could plot the difference between the slope of the best fit line and the slope of a line from the origin to all points as a function of the phase angle. We did this for total, horizontal, and vertical phase angle (ref Phase). Again, a marked relationship was present in the slope difference as a function of the vertical phase angle, but not the horizontal. We found the slope and error of the line of best fit for this plot.

Additional operations we could perform with the light ratio data were to plot the residual and slope difference as functions of the angles(ref Residual & SlopeDiff. In order to display the four angles and the additional value, we used the main axes to represent two angles and colored by the additional value. Instead of a point at each value of the two major angles, we displayed a small plot whose axes were the two other angles. In this way, we displayed the values of the residual or slope difference across all applicable values of the four-dimensional parameter space of the angles. We then found interesting angles that were above and below the plane (for the observer) or in the plane and above it (for the incoming light). Our selection criteria was to acquire a diverse range of behaviors. We then performed photometry on the original N-body simulation data with these angles over a period of two orbits, which we made into movies in order to observe the temporal evolution of the system.

page revision: 30, last edited: 28 Jul 2011 17:27