1105.3936 (Michael Efroimsky)

Tidal dissipation compared to seismic dissipation: in small bodies, in earths, and in superearths    [PDF]

Michael Efroimsky

While the seismic quality factor and phase lag are defined solely by the bulk properties of the mantle, their tidal counterparts are determined both by the bulk properties and the size effect (self-gravitation of a body as a whole). For a qualitative estimate, we model the body with a homogeneous sphere, and express the tidal phase lag through the lag in a sample of material. Although simplistic, our model is sufficient to understand that the lags are not identical. The difference emerges because self-gravitation pulls the tidal bulge down, thereby reducing strain and the damping rate, and making tidal damping less efficient in larger objects. Being negligible for small terrestrial planets and moons, the difference between the seismic and tidal lagging (and likewise between the seismic and tidal damping) becomes very considerable for large exoplanets (superearths). In those, it is much lower than what one might expect from using a seismic quality factor. The tidal damping rate deviates from the seismic damping rate especially in the zero-frequency limit, and this difference takes place for bodies of any size. So the equal in magnitude but opposite in sign tidal torques, exerted on one another by the primary and the secondary, go smoothly through zero as the secondary crosses the synchronous orbit. We describe the mantle rheology with the Andrade model, allowing it to lean towards the Maxwell model at the lowest frequencies. To implement this additional flexibility, we reformulate the Andrade model by endowing it with a free parameter which is the ratio of the anelastic timescale to the viscoelastic Maxwell time of the mantle. Some uncertainty in this parameter's frequency-dependence does not influence our principal conclusions.

View original: http://arxiv.org/abs/1105.3936