A procedure to analyze nonlinear density waves in Saturnʹs rings using several occultation profiles

Cassini radio science experiments have provided multiple occultation optical depth profiles of Saturnʹs 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 established using simulated data in the presence of realistic noise perturbations, to control the reconstruction error. It is then applied to the Mimas 5:3 density wave. There are two important concepts at the basis of this procedure. The first one is that it uses the nonlinear representation of density waves, and the second one is that it relies on a combination of optical depth profiles instead of just one profile. A related method to analyze density waves was devised by Longaretti and Borderies [Longaretti, P.-Y., Borderies, N., 1986. Icarus 67, 211–223] to study the nonlinear density wave associated with the Mimas 5:3 resonance, but the single photopolarimetric profile provided limited constraints. Other studies of density waves analyzing Cassini data [Colwell, J.E., Esposito, L.W., 2007. Bull. Am. Astron. Soc. 39, 461; Tiscareno, M.S., Burns, J.A., Nicholson, P.D., Hedman, M.M., Porco, C.C., 2007. Icarus 189, 14–34] are based on the linear theory and find inconsistent results from profile to profile. Multiple cuts of the rings are helpful in a fundamental way to ensure the accuracy of the procedure by forcing consistency among the various optical depth profiles. 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 ≃ 0.02 cm 2 / g ) and velocity dispersion of ( c 0 ≃ 0.6   cm/s ) in the wave region. Our procedure constitutes the first step in our planned analysis of the density waves of Saturnʹs 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.