Crosby Burdon

I'm an undergraduate physics major astronomy minor about to enter my senior year at Trinity University. For the summer of 2010, I worked with Dr. Mark Lewis on an analysis of his Saturn ring simulations. This is a running commentary on the progress I have made in the last 8 weeks, broken up into categories of major projects.

Small Particles

These simulations compared the photometry of different sized particles each having the same total surface density/mass. The purpose of these analyses is to illustrate the importance of choosing the correct size distribution of particles in simulations of the rings in order to match observations before making strong conclusions about other properties of the ring particles , e.g coefficient of restitution (how much energy is conserved in their collisions) and particle density. It turns out that the radius is a much more important property than the two listed previously , and even with everything else remaining constant changing the radius of the particles changes the physical appearance of the rings (photometry) significantly.

  • ran comparison photometry for angle phi ranging from 0 to pi/2 and angle theta 0-2pi for particle size 0.2, 0.4, and 0.8.
  • used movie filter to export frames of each photo plot and input collection filter to make text file of the photo info, saved files and used them as general data for comparison plot
  • found that smaller particles reflect more light because they have a greater surface area, and lower surface density. This is a result of the 1/r surface area dependence( sims preserve surface density, keeping same total mass but smaller particles, translates into more particles and larger surface area as r decreases. More surface area = more scattering of light = more reflected intensity.
  • used albido formula 0.7
  • varied angles using trig functions in photo filter for binning and sources
  • observed azimuthal brightness asymmetry(theta dependent brightness variations)
  • note the troughs for each particle size intensity variations(y-axis also included phi) were not at the same angle and hence did not line up.
  • designed to contest the assertions that a fixed particle size is OK to use in Azimuthal brightness asymmetry simulations while adjusting other parameters to match observations. Found that particle size does matter in these considerations.


The primary purpose of the Moonlet analysis was to explore possible causes of the propeller shaped bright structures (propellers) observed by the Cassini probe orbiting Saturn. While there is a consensus among researchers that there are larger particles than those in the ring background (moonlets: as their name implies, they are smaller than Saturn's moons but bigger than anything else in the ring background by at least a factor of 10) at the centre of the structures, there are still conflicting hypotheses as to why they are so bright regardless of whether they are on the lit side of the rings or the dark side. The plots of moonlet simulations (ray tracing photometry) also indicate a dark area around the moonlet caused by its gravity wake, which does not appear in any Cassini images of propeller structures. This raises the question of why they appear bright, prompting an investigation of possible vertical structure caused by the smaller particles getting thrown out of the ring plane (above or below) by the gravitational forces of the moonlet. The vertical structure, if present, could scatter the smaller particles over a large surface area and reflect more light than do the clumped, higher density particles, resulting in an increase in reflected light from those areas and possibly hiding the dark gravity wakes from view. A big problem that we face is the lack of sufficient resolution in the Cassini propeller images as compared to our ray tracing photometry, as well as the lack of instrument or environmental noise in the simulations (which leads to problems comparing the two sets of images).

This image has a scatter plot colored by standard deviation in z (in other words, how far apart vertically these particles are spread) on the left and a photometry plot of a propeller structure on the right.
Note the darkened area that makes up the wake around the moonlet. This is what isn't visible in the Cassini images. Go to the Moonlet page for more images related to this experiment.
  • Ran similar photometry to what was done with the small particles sims, but without the multiple frames due to the increased amount of photons being thrown at the moonlets and surrounding particles (108 as compared to 105) and the increased workload for the cores (processors) involved in the photometry computation. Rendering single frames from various angles, we were able to match to some degree the available propeller images from the Cassini probe with our photo plot.
  • The first plots were scatter plots colored by height on the Z axis, and they confirmed that the moonlets throw large amounts of smaller (beach ball sized, 1e-8*R0 or 2.6m diameter) particles above and below the ring plane immediately adjacent to the moonlet in a propeller-like shape. The consequent photometry seems to indicate that a moonlet of the right size is capable of creating the bright structures visible in the lower-resolution Cassini images, but the dark gaps in the ring particles created by these smaller moonlets could possibly be washed out by the lack of resolution and the vastly decreased SNR (signal to noise ratio) of the real data versus the noiseless simulation data.
  • Subsequent plots colored by total intensity of light received for each bin location on the plot (which is essentially a 2-dimensional grid overlaid on the plot containing a specified number of bins in each dimension) indicate a large amount of light being reflected by the elevated smaller particles adjacent to the moonlet. Another plot was made colored by standard deviation in Z, which revealed a semi-periodic (but decreasing) distribution of particles on the Z axis, the lower density regions having a larger deviation because of the small number of particles distributed over a large area in z. The higher density regions were almost exclusively concentrated on the ring plane, with maybe a few outliers above and below.
  • Also worth noting is the sinusoidal nature of the gravity wake borders, especially for the larger radius moonlets.
  • Direction of light source is important in these ray tracings, because the nature of the vertical structures revealed by the photometry varies significantly depending on the angle of incoming light and also the phase angle of the photon source with the camera location. The edge of the propeller structures (moonlet wakes) are asymmetrically lit depending again on the angle of incoming light, and viewing geometry.
  • Continued examination of moonlet photometry (movies made with scatter/photo plots) has revealed the relative frequency of shedding events (trails of material shed from the moonlet after it builds up enough particles to fill its Hill Radius and collides with other groups of particles) after the moonlet has gained enough material to acquire a characteristic “tail” pattern on each side. The collision of gravity wakes near and adjacent to the moonlet as well as shedding events along the moonlet wake (happens with larger moonlets as the wake is carved out of the surrounding gravity wakes) scatter a considerable amount of material above and below the moonlet, but more examination of the data is required (statistical correlation of z distribution with shedding events) for conclusive hypothesis.
  • The most recent moonlet simulations have revealed interesting results. The moonlets, which were just a group of particles of the same density but only held together by their self-gravity, were abrupted (torn apart) by collisions with the self-gravity wakes. This is an unexpected result, and thus far we believe it is indicative of a critical density the moonlet constituents must reach in order to stick together. The density in the simulations currently running is now surpassing the density of ice, which is a slight problem because ice is what largely makes up the rings. We currently believe this problem will be resolved by adjusting the radius of the particles as well as the density, but are waiting for further simulation data before making any conclusions about it.
  • With the help of the binned filter in SwiftVis, we have been able to investigate further the possible correlations between moonlet size and amount of particles thrown out of the ring plane/height of particles outside the ring plane. Using guiding center coordinates (specifically inclination (i), a unitless way to take into account both the current position of the particle and the orbit it will follow as time progresses) we now have some evidence that the average (RMS) inclination value of particles within the self gravity wake of the moonlet is close to the radius value of the moonlet. Unfortunately this relationship seems to break down with the larger radius moonlets. The particles in these simulations were truncated by a selection filter which only allowed particles above a certain inclination to be included in the scatter plots. This was done based on a graph of count of particles vs inclination, which indicated that the vast majority of the particles (the ones permanently in the ring plane) had below a certain inclination value, 1e-7*r0. Since the particles we are interested in are above the ring plane and have a much smaller population, culling the particles in the ring plane was the best way to gain any information about them. No true conclusions can be made with certainty at this time.
  • Additionally, my research partner Cameron Swords and I managed to write a new filter for SwiftVis called a Distribution Difference filter, which given two binned data sets allows the user to normalize one by the other (either by max or by sum) and then flag the stream that contains data that was in one but not the other. This new ability has been instrumental in gaining insight on the vertical structure on the moonlets, via looking at average inclination of particles present in the moonlet wake but not in the background distribution. Given this data set, we then found average inclinations of the top 50%, 25% 10% and 5% of them. Our goal is to do photometry on two sets for each, one including the top X% and one without those particles, to observe when the moonlet structure becomes invisible. This should give us some clue as to what the threshold for visibility of the vertical structure is. The table below lists the statistics so far (NOTE: these averages are only for the 2e-7*r0 moonlet simulation (frame 8520), and only for a single set of selection data given to the Distribution Dfference filter. More data will be posted later, with standard deviation included):
Top Percentage Average Inclination
50% 9.89E-8
25% 1.47E-7
10% 2.06E-7
5% 2.5E-7

The top 10% of these particles appear to be in the range of inclination on the order of the moonlet radius, which is a nice correlation but still a tenuous one. Current data runs utilizing a few frames of the 1e-7 moonlet simulation indicate a possibility of this relationship between moonlet radius and average inclination of normalized wake particles becoming stronger as the radius decreases, but sufficient data has yet to be gathered to substantiate this. More moonlet simulations utilizing a larger size distribution are necessary for such a substantiation to be possible.

  • A new experiment has been proposed to further explore moonlet abruption. Details are here.

Hide Silicates

The hide silicates project is an examination of the reflected light of the ring particles when the simulations include a small percentage of silicates (rocks of various types), so as to further investigate reasons for the bright appearance of the "propeller" structures. While the consensus is that the ring particles consist mostly of ice, the presence of particles of a different density may change the physical profile of the rings in terms of how much light is reflected.

  • ran photometry for A ring simulations with 0.5%, 1%, 2%, and 4% silicates, similar setup to Small Particles sims but more focused on total amount of received photon intensity from the silicate particles, plots colored by Z axis location
  • most interesting is the fairly constant 25% rule for silicates: however large the percentage of silicates present in the simulation sample, 25% of those silicates are the last to reflect light back to the camera.
  • might pursue the significance of scattered light versus direct light in these ray tracings.
  • New photometry on the B ring suggests that the 25% rule only applies to the A ring, given that the direct reflected intensity for a 4% mix of silicate particles comes from a silicate particle considerably more than 1% of the time (but results are so inconsistent that trying to find an analogue to the 25% rule is proving difficult). Only preliminary analysis has been made, however, so any further conclusions would just be guesswork.
  • Further analysis of the B ring photometry has revealed something surprising. It seems that the amount of light directly reflected by silicates is not a constant fraction of the percent mix of silicates, but in fact it varies for different percent mixtures. The close to 50% fraction for the 4% mix contrasts sharply with the 1% mix that has a <~20% direct silicate reflectance rate. In other words, only 20% of the silicates reflect light directly back to the camera. This is peculiar because not only is it inconsistent across silicate percentage variations, but considerably lower than expected (at least for the 1% case). Further photometry will be done with the 2% silicate mix sims to attempt to shed more light on this new development.

This is a scatter plot (meaning simply a plot of the particles, not taking into account photometry at all) of the 1% silicate simulation file, the left hand side has particles drawn in order of appearance (the silicates appear in red) and the right side has all of the silicates drawn on top and highlighted to get a sense of how much of them are hidden.

AAS Poster on Silicate Hiding

This is the poster that was shown at the January 2011 AAS meeting on this work.

Crosby Research Plan