Excitation and Damping of Oscillation Modes in Gaseous Planets

TL;DR

The paper investigates how oscillation modes in gas giants are damped and excited, combining analytic theory, numerical models, and solar calibration to predict f- and p-mode amplitudes in Jupiter, Saturn, and Uranus. It identifies differential rotation as a key amplifier of convective viscosity, suggesting damping times of $t_{ m damp} \,\sim\, 10^4$--$10^7$ years for f and low-order p modes, with radiative diffusion governing higher-frequency p modes, and ring interactions damping only a subset of Saturn’s low-ℓ f modes. Excitation is dominated by non-convective sources: storms and cometary impacts, with storms capable of larger energy transfer than ordinary convection and impacts potentially exciting p modes to detectable levels. The study provides predictions for surface velocities and gravitational perturbations, guides observational strategies (Doppler tracking, RV monitoring, ring seismology), and highlights large uncertainties in storm energetics, wind shear, and impact rates. This work lays groundwork for planetary seismology, offering testable hypotheses for future missions and measurements, while acknowledging that robust amplitude estimates require further detailed physics and simulations.

Abstract

The excitation and damping mechanisms for oscillation modes of gas giant planets are undetermined. We show that differential rotation may greatly enhance convective viscosity in giant planets, resulting in damping times of $t_{\rm damp} \sim 10^5-10^6 \, {\rm years}$ for f modes and low-order p modes. Radiative diffusion damps p modes on time scales of $t_{\rm damp} \sim 10^3-10^7 \, {\rm years}$. While the lethargic convective motions cannot effectively excite f mode or p modes, storms driven by condensation of water and/or silicates may play a role. High-order p modes are most effectively excited by cometary/asteroid impacts. Applying these calculations to solar system planets, water storms, rock storms, and impacts may all contribute to exciting the observed f modes amplitudes of Saturn via ring seismology. Similar f mode amplitudes with fractional gravitational perturbations of $δΦ/Φ\sim 10^{-10}-10^{-9}$ are expected for Jupiter and Uranus, apart from their lowest $\ell$ f modes which could have larger gravitational perturbations of $δΦ/Φ\sim 10^{-7}$. Rock storms may contribute to mode driving in Jupiter, while water storms are more important for Uranus. The highest-amplitude p modes are predicted to have periods of $\sim$10-30 minutes, with surface velocities of $\sim$10 cm/s for Jupiter and Saturn, and $\sim$1 cm/s for Uranus. These oscillation modes may be detectable with radial velocity measurements, ring seismology, or spacecraft Doppler tracking. However, both the damping and excitation physics are uncertain by orders of magnitude, so more careful examination of the relevant physics is required for robust estimates.

Figures (17)

• Figure 1: Oscillation mode frequencies of our Uranus model as a function of angular number $\ell$. Symbol sizes indicate surface gravitational potential perturbations, while symbol colors indicate surface radial velocities, for modes normalized to have equal energies. The f modes typically have larger gravitational perturbations than low-order p modes by a factor of $\sim$100, but smaller radial velocity perturbations by a similar factor. Modes of Jupiter and Saturn models have similar behavior, but with frequencies proportional to $\sqrt{GM/R^3}$ in each case.
• Figure 2: Damping time of $\ell=m$ f modes in Saturn, as a function of angular number $\ell$, due to different models of convective viscosity. The blue line shows the simple estimate of equation \ref{['eq:nucon_sup']}, while the green line accounts for enhancement due to zonal winds (equation \ref{['eq:nuconrotef']}).
• Figure 3: Damping time of $\ell=m$ f modes of Saturn as a function of $\ell$. The green line is damping due to convective viscosity (equation \ref{['eq:tdampcon']}), the maroon line accounts for damping via interaction with the rings (equation \ref{['eq:tdampring']}), and the black line is the combined effect of both.
• Figure 4: The damping time of $\ell=2$ p modes of Saturn, as a function of mode frequency. The green line shows damping due to convective viscosity (equation \ref{['eq:tdampcon']}), the orange line accounts for damping due to radiative diffusion, and the purple line accounts for wave damping above the acoustic cutoff frequency (equation \ref{['eq:edampac']}). Modes with frequencies larger than $f \gtrsim f_{\rm ac} \sim 1.5 \, {\rm mHz}$ are strongly damped due to the latter effect.
• Figure 5: Similar to Figures \ref{['fig:tdamprot']} and \ref{['fig:tdamp-p']}, now showing the damping time of modes in Jupiter. Top: Damping time of $\ell=m$ f modes as a function of $\ell$ due to different models of convective viscosity. Bottom: Damping time of $\ell=2$ p modes as a function of angular frequency.