A procedure to analyze nonlinear density waves in Saturn's rings using several occultation profiles

TL;DR

This paper presents a new, accurate procedure for analyzing nonlinear density waves in Saturn's rings using occultation data, enabling detailed reconstruction of wave parameters and insights into ring physics.

Contribution

It introduces an inversion method for wave profiles that accurately reconstructs kinematic parameters from occultation data, including in the nonlinear regime.

Findings

Successfully applied to Mimas 5:3 density wave data

Recovered wave kinematic parameters with high precision

Estimated ring opacity and velocity dispersion values

Abstract

Cassini radio science experiments have provided multiple occultation optical depth profiles of Saturn's rings that can be used in combination to analyze density waves. This paper establishes an accurate procedure of inversion of the wave profiles to reconstruct the wave kinematic parameters as a function of semi-major axis, in the nonlinear regime. This procedure is achieved from simulated data in the presence of realistic noise perturbations, to control the reconstruction error. By way of illustration we have applied our procedure to the Mimas 5:3 density wave. We were able to recover precisely the kinematic parameters from the radio experiment occultation data in most of the propagation region; a preliminary analysis of the pressure-corrected dispersion allowed us to determine new but still uncertain values for the opacity ($K\simeq 0.02$ cm$^2$/g) and velocity dispersion of ($c_o\simeq 0.6$ cm/s) in the wave region. Our procedure constitutes the first step in our planned analysis of the density waves of Saturn's rings. It is very accurate and efficient in the far-wave region. However, improvements are required within the first wavelength. The ways in which this method can be used to establish diagnostics of ring physics are outlined.