Impacts of zonal winds on planetary oscillations and Saturn ring seismology

Abstract

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

arXiv comment15 pages, 14 figures. Published in MNRAS. Update includes minor corrections made while in press

References in corpus (21)

• Acoustic oscillations of rapidly rotating polytropic stars. II. Effects of the Coriolis and centrifugal accelerations
• Saturn Ring Seismology: Evidence for Stable Stratification in the Deep Interior of Saturn
• Concentric Maclaurin spheroid models of rotating liquid planets
• Kronoseismology: Using density waves in Saturn's C ring to probe the planet's interior
• Oscillations of rapidly rotating stratified neutron stars
• An algorithm for computing the 2D structure of fast rotating stars
• Cassini Ring Seismology as a Probe of Saturn's Interior I: Rigid Rotation
• Pulsation modes in rapidly rotating stellar models based on the Self-Consistent Field method
• The landscape of Saturn's internal magnetic field from the Cassini Grand Finale
• Combined magnetic and gravity measurements probe the deep zonal flows of the gas giants
• Mode visibilities in rapidly rotating stars
• Non-radial Oscillations in Rotating Giant Planets with Solid Cores: Application to Saturn and its Rings
• Gravity and Zonal Flows of Giant Planets: From the Euler Equation to the Thermal Wind Equation
• Dynamical tidal Love numbers of rapidly rotating planets and stars
• Linear Stability Analysis of Differentially Rotating Polytropes -- New results for the m = 2 f-mode dynamical instability --
• Kronoseismology IV. Six previously unidentified waves in Saturn's middle C ring
• Oscillations of 2D ESTER models. I. The adiabatic case
• The intimate relation between the low T/W instability and the co-rotation point
• Kronoseismology V: A Panoply of Waves in Saturn's C Ring Driven by High-Order Internal Planetary Oscillations
• Covariant model for proton-proton bremsstrahlung: Comparison with high-precision data
• Importance of Perturbed Gravitational Potentials in Differentially Rotating Newtonian Stars

Cited by in corpus (4)

• Dynamical tides in Jupiter and other rotationally flattened planets and stars with stable stratification
• Setting the Stage for Uranian Seismology from Rings and Radial Velocities
• Tidal synchronization trapping in stars and planets with convective envelopes
• Excitation and Damping of Oscillation Modes in Gaseous Planets