How Cassini can constrain tidal dissipation in Saturn

Abstract

Tidal dissipation inside giant planets is important for the orbital evolution of their natural satellites. It is conventionally treated by parameterized equilibrium tidal theory, in which the tidal torque declines rapidly with distance, and orbital expansion was faster in the past. However, some Saturnian satellites are currently migrating outward faster than predicted by equilibrium tidal theory. Resonance locking between satellites and internal oscillations of Saturn naturally matches the observed migration rates. Here, we show that the resonance locking theory predicts dynamical tidal perturbations to Saturn's gravitational field in addition to those produced by equilibrium tidal bulges. We show that these perturbations can likely be detected during Cassini's proximal orbits if migration of satellites results from resonant gravity modes, but will likely be undetectable if migration results from inertial wave attractors or dissipation of the equilibrium tide. Additionally, we show that the detection of gravity modes would place constraints on the size of the hypothetical stably stratified region in Saturn.

Tidally trapped pulsations in binary stars

“…Because the density and sound speed drop sharply near the surface, the amplitude of a propagating acoustic wave increases, with the radial displacement, scaling as ξ r ∝(ρr 2 c s ) −1/2 in the WKB limit. The surface flux perturbation of a mode scales as F/F∝ T/T, which approximately scales as T/T ∼ k r ξ r (Luan, Fuller & Quataert 2018). So, if pulsation energy is independent of latitude, we expect the mode visibility to scale approximately as…”

Excitation mechanisms for Jovian seismic modes

“…One possibility is that the effective Q is actually determined by the interaction of modes with each other rather than intrinsic dissipation. However, these interactions are probably negligible [37], so for the moment we will focus on intrinsic processes. Much work has already been done estimating Jupiter's tidal Q [28].…”

“…As a simplifying assumption, assume ζ ∼ η. Now compare the relative importance of the the first and second bracketed terms on the right hand side of Equation 37. Noting κ(1/c V −1/c p ) = κ/c p (γ −1) and plugging in typical values for hydrogen, the second term is ∼ 10 −12 in cgs units, compared to viscosity which is ∼ 10 −3 .…”

The complex interplay between tidal inertial waves and zonal flows in differentially rotating stellar and planetary convective regions

“…Tidal dissipation at a given frequency may then alter each orbital and spin element of the two-body systems differently, as postulated, for instance, by Lai (2012) to explain the survival of hot Jupiters with completely damped spin-orbit angles; this idea was revisited by Damiani & Mathis (2018) with an improved treatment of dynamical tides in the convective region. Additionally, in the context of the Jupiter and Saturn moon systems, Fuller et al (2016) and Luan et al (2018) also investigated the dependence of tidal dissipation on frequency to explain the rapid outward migration of the moons through the resonant locking of tidally forced internal modes in the giant gaseous planets. This concept could, for example, explain the high dissipation observed in Saturn as derived from astrometric measurements at the frequency of Rhea (Lainey et al 2017) and at the frequency of Titan (Lainey et al 2020).…”