Impacts of zonal winds on planetary oscillations and Saturn ring seismology

The excitation of density and bending waves in Saturn's C ring by planetary oscillation modes presents a unique opportunity to learn about gas giant interiors rotation. However, theoretical complications related rapid differential rotation pose barrier the full utilization wave detections. We calculate using complete, non-perturbative treatment modelled after zonal winds self-consistently computed, polytropic equilibria. find that previous, approximate treatments effects Saturn overestimate shifts frequencies fundamental (f-modes) thought be responsible for majority detected ring, due an omitted modification equilibrium shape structure planet bias introduced these frequency overestimates is small, but significant relative uncertainties afforded Cassini data. additionally consider Saturn-like on rotational mixing f-modes internal gravity (g-modes), which relevant detections multiple with very closely split pattern speeds. higher order can produce orders-of-magnitude enhancements surface gravitational perturbations g-modes dominated large spherical harmonic degrees $\ell$, regardless separation from sectoral f-mode. Despite this enhancement, we observed fine-splitting unlikely involve $\ell\gtrsim 10$. This restriction may aid inference possible structures Saturn.