Abstract
Abstract Normal mode oscillations in Saturn excite density and bending waves in the C ring, providing a valuable window into the planet’s interior. Saturn’s fundamental modes (f-modes) excite the majority of the observed waves, while gravito-inertial modes (rotationally modified g-modes) associated with stable stratification in the deep interior provide a compelling explanation for additional density waves with low azimuthal wavenumbers m. However, multiplets of density waves with nearly degenerate frequencies, including an m = 3 triplet, still lack a definitive explanation. We investigate the effects of rapid and differential rotation on Saturn’s oscillations, calculating normal modes for independently constrained interior models. We use a non-perturbative treatment of rotation that captures the full effects of the Coriolis and centrifugal forces, and consequently the mixing of sectoral f-modes with g-modes characterized by very different spherical harmonic degrees. Realistic profiles for differential rotation associated with Saturn’s zonal winds can enhance these mode interactions, producing detectable oscillations with frequencies separated by less than 1%. Our calculations demonstrate that a three-mode interaction involving an f-mode and two g-modes can feasibly explain the finely split m = 3 triplet, although the fine-tuning required to produce such an interaction generally worsens agreement with seismological constraints provided by m = 2 density waves. Our calculations additionally demonstrate that sectoral f-mode frequencies are measurably sensitive to differential rotation in Saturn’s convective envelope. Finally, we find that including realistic equatorial antisymmetry in Saturn’s differential rotation profile couples modes with even and odd equatorial parity, producing oscillations that could in principle excite both density and bending waves simultaneously.
Highlights
The interiors of gas giants remain enigmatic, even within our own solar system
We present examples of three-mode interactions that could in principle explain the observed m = 3 triplet of density waves with finely split frequencies, producing these interactions still requires fine-tuning
We focus on fundamental modes and gravito-inertial modes with super-inertial frequencies |ω| > 2ΩS
Summary
The interiors of gas giants remain enigmatic, even within our own solar system. Cassinis Grand Finale facilitated precise measurement of the planet’s nonspherical gravitational field (Iess et al 2019), but even knowledge of high-order harmonic coefficients (through J12) leaves room for significant degeneracy in deep-interior density profiles (Movshovitz et al 2020). Saturn’s rings present a rare opportunity to place seismological constraints on the planet’s interior. Analyzing occultation data obtained by Cassini, Hedman & Nicholson (2013) validated a decades-old prediction (Marley 1991; Marley & Porco 1993) that Saturn’s “fundamental” oscillation modes ( fmodes) excite density waves at Lindblad resonances in the C ring. Continued analysis of Cassini observations has revealed a wealth of additional density (and bending) waves, thought to be excited by planetary oscillations with even (odd) equatorial symmetry
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