Ocean Tidal Dissipation and its Role in Solar System Satellite Evolution
The history of satellites in the Solar System is quite diverse. For example, satellites like Io and Enceladus exhibit active volcanism currently, while satellites like Ganymede and Tethys show signs of geologic activity in the deep past, but not at present. The energy dissipated by tides has been identified as a major heat source for satellites, but calculations for satellite tidal dissipation primarily focus on dissipation in a solid layer, such as the ice shell. An exciting discovery of the NASA spacecraft missions Galileo and Cassini is that global-scale, deep, liquid water oceans are present on many of the outer Solar System satellites. Tyler (2008) suggested that tidal dissipation due to flow in these oceans could potentially be a significant and previously neglected source of heat. However, a critical free parameter in Tyler's model is the effective turbulent viscosity in the ocean. The value of the effective viscosity is unconstrained and because the amount of tidal dissipation scales with this parameter, the amount of ocean tidal dissipation is also unconstrained.
In order to address this uncertainty, we developed a numerical model that solves the shallow-water equations on a spherical shell and includes a nonlinear bottom friction parameterization for viscous dissipation. The bottom friction coefficient has a well-established value in the terrestrial literature; however, the nonlinearity of this term in the equations of motion make the model far more computationally expensive than a model that includes turbulent viscosity. Thus, we provide numerically-derived scalings that map the bottom friction coefficient and satellite parameters to an equivalent effective turbulent viscosity. Because tides depend on both the thermal structure of a satellite as well as characteristics of the satellite's orbit, models that couple thermal and orbital evolution are required to understand the history of a satellite. We use our numerically-derived scalings to adapt a coupled thermal-orbital model to include the effects of ocean tides on satellite evolution.
We applied these methods to explore whether or not ocean tidal dissipation was significant in the evolution of satellites of the Solar System. In the case of the outer Solar System satellites, we find that the dominant contributors to the present thermal budgets are radiogenic heating and solid-body eccentricity tidal heating. The one notable exception, where ocean tidal heating may be important, is Neptune's satellite Triton. Because Triton's orbit is evolving inwards toward Neptune, ocean tides are growing over time. The dissipation of these tides could have led to the recent geologic activity on Triton.
A global magma ocean was present on the early Moon. By including the effects of tidal dissipation in this ocean in the orbital evolution of the early Earth-Moon system, we find that for consistency with the present day Earth-Moon system configuration, our models require that the global lunar magma ocean solidify prior to an orbital semi-major axis of ∼30 Earth radii. The timing of this orbital configuration is controlled by dissipation in the Earth and suggests that the Hadean Earth was significantly less dissipative than the present Earth.