One of the projects we are working on is to look at the impact of particle size on the results of simulations. This work is being done with an undergraduate student, Crosby Burdon under an NSF AAG grant. A number of conclusions have been drawn from comparisons between simulations and observations in regards to the internal density of particles and their coefficients of restitution. Out of necessity, those simulations have to limit the smallest particles used to keep particle counts and simulation times reasonable. This work is aimed at determining how much of an impact the lack of small particles might have on the conclusions that are drawn. This is a work in progress and many aspects are currently incomplete.
In this work we are looking at different behaviors in the systems. One of the keep observables that we want to compare to is the azimuthal brightness asymmetry in the A ring. All simulations were done at 130,000 km from the center of Saturn assuming an internal density of 0.7 g/cm^3, a surface density of 30 g/cm^2, and the velocity dependednt coefficient of resitution from Bridges, et al. With those assumptions locked in, particle sizes were varied to see what impact it had.
The first set of simulations that were done use particles of a single size.
We have also performed a set of simulations with a size distribution. We use a power-law distribution with a differential slope of -3.
There are a few different types of analysis we are performing on the simulation output to determine how significant the use of a proper particle size is for drawing various conclusions. Since the other work involves comparisons to observations, we have focused on photometry and elements of the dynamics that would be significant to observations which can't resolve the individual particles.
Ray Tracing - Comparisons between simulations and observations are best done by throwing photons into the system and tracking the photons as they scatter then seeing what light would be seen by observations from different directions. This type of analysis can be used, for example, to compare with the observed azimuthal brightness asymmetry. This set of figures shows some results from that type of analysis.
Figures from Crosby go here.
Vertical Splatter - The light that we see from a patch of particles is impacted by the spatial distribution of the particles. The vertical distribution of particles can be particularly significant as any particles well above or below the plane are less likely to be shadowed by other particles. In addition, the vertical extent of gravity wakes has a strong influence on how much light is reflected or gets through low incidence angles. For this reason, we have rendered the systems using color to indicate the vertical displacement of particles from the ring plane. The midplane is green. Moving upward it goes through yellow, orange, and saturates at red 19.5 meters above the midplane. Similarly, it moves to blue and purple below the plane before saturating at black 19.5 meters below the plane.
These movies show that when gravity wakes collide with one another, they tend to splash particles out of the plane. The magnitude to which this happens depends on the size of the particles involved.