# Sharp gap edges in dense planetary rings: An axisymmetric diffusion model

## TL;DR

This paper presents an axisymmetric diffusion model incorporating angular momentum flux reversal to explain the sharp edges of gaps in Saturn's rings, supported by observations and viscosity estimates.

## Contribution

It revises previous models using granular flow to define viscosities and applies the model to real ring gaps for viscosity estimation.

## Key findings

- Sharp gap edges occur over the rings' thickness.
- The model successfully explains the observed edge sharpness.
- Viscosity estimates near the gaps are obtained.

## Abstract

One of the most intriguing facets of Saturn's rings are the sharp edges of gaps in the rings where the surface density abruptly drops to zero. This is despite of the fact that the range over which a moon transfers angular momentum onto the ring material is much larger. Recent UVIS-scans of the edges of the Encke and Keeler gap show that this drop occurs over a range approximately equal to the rings' thickness. Borderies et al. (1982, 1989) show that this striking feature is likely related to the local reversal of the usually outward directed viscous transport of angular momentum in strongly perturbed regions. In this article we revise the Borderies et al. (1989) model using a granular flow model to define the shear and bulk viscosities and incorporate the angular momentum flux reversal effect into the axisymmetric diffusion model we developed for gaps in dense planetary rings (Gr\"atz et al. 2018). Finally, we apply our model to the Encke and Keeler division in order to estimate the shear and bulk viscosities in the vicinity of both gaps.