Viscoelastic Tidal Dissipation in Giant Planets and Formation of Hot Jupiters Through High-Eccentricity Migration

TL;DR

This paper investigates how tidal dissipation in the solid cores of giant planets influences the formation of hot Jupiters via high-eccentricity migration, using a viscoelastic model to reconcile Solar system constraints with exoplanet observations.

Contribution

It introduces a general framework for tidal evolution considering complex tidal responses and demonstrates that core dissipation can explain hot Jupiter formation consistent with Solar system data.

Findings

Core dissipation can match Solar system tidal-Q constraints.

Tidal heating can cause modest planetary radius inflation.

Multiple spin equilibrium states are possible depending on system history.

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, ${\rm Im}[{\tilde k}_2(\omega)]$, as a function of the forcing frequency $\omega$. Using the simplest viscoelastic dissipation model (the Maxwell model) for the rocky core and including the effect of a nondissipative 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 ($e\sim 0.6$) during their high-e migration. Finally, as an interesting by-product of our study, we note that for a generic tidal response function ${\rm Im}[{\tilde k}_2(\omega)]$, 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.