Viscoelastic tidal dissipation in giant planets and formation of hot jupiters through high-eccentricity migration

Abstract

We study the possibility of tidal dissipation in the solid cores of giant planets and its implication for the formation of hot Jupiters through high-eccentricity migration. We present a general framework by which the tidal evolution of planetary systems can be computed for any form of tidal dissipation, characterized by the imaginary part of the complex tidal Love number, Im[K̃2(ω)], as a function of the forcing frequency ω. Using the simplest viscoelastic dissipation model (the Maxwell model) for the rocky core and including the effect of a non-dissipative fluid envelope, we show that with reasonable (but uncertain) physical parameters for the core (size, viscosity and shear modulus), tidal dissipation in the core can accommodate the tidal-Q constraint of the Solar system gas giants and at the same time allows exoplanetary hot Jupiters to form via tidal circularization in the high-e migration scenario. By contrast, the often-used weak friction theory of equilibrium tide would lead to a discrepancy between the Solar system constraint and the amount of dissipation necessary for high-e migration. We also show that tidal heating in the rocky core can lead to modest radius inflation of the planets, particularly when the planets are in the high-eccentricity phase (e~0.6) during their high-e migration. Finally, as an interesting by-product of our study, we note that for a generic tidal response function Im[K̃2(ω)], it is possible that spin equilibrium (zero torque) can be achieved for multiple spin frequencies (at a given e), and the actual pseudo-synchronized spin rate depends on the evolutionary history of the system. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.