1. Collisional formation of ringlets in high M resonances
By Amy West

2. Objective We were looking to find how ringlets formed in resonance.
Ringlet formation in 2:1 mean motion resonances had previous been explored by Haenninen and Salo.
We looked at higher order resonances such as the 100:99 resonance that might be seen with embedded moonlets or shepherds.

3. Methodology
We ran several different simulations varying the M value of resonance, particle size, optical depth, and moon size.
Our simulations included particle collisions using a velocity dependent normal coefficient of restitution.
The simulations ignored spin, transverse friction, and particle self-gravity.
Simulations ran for ten synodic periods.

4. Wakes and Guiding Center Migration

5. Wakes and Guiding Center Migration at Lower M

6. Ringlet Formation
Tau from
E from 0-1e-5

7. Eccentricity
Graph shows eccentricity for both in resonance and out of resonance.
Ringlets stared to form in the third synotic period corresponding with the decrease in eccentricity.
The straight lines before the third synotic period show that there's very little damping due to collisions before the ringlet forms.

8. Eccentricity Graphs Compared

9. Difference in Tau and Eccentricity compared with Optical Depth

10. Streamlines

12. Streamlines
Top plot shows where streamlines start to intercept is where the ringlets starts to form.
Bottom plot has the bottom two streamlines start to intercept and this caused the two ringlets to start to merge.

13. Results
Simulations show that lower optical depth, larger moon mass, and higher M values produce stronger ringlet formation.
Preliminary results shows that particle size does not have a significant effect on ringlet formation.
Eccentricity plots shows that ringlet formation corresponds with drops in eccentricity.
Particle streamlines show that ringlets tend to form when wakes reach a point where their stream lines intercept.