Tidal Heating Models for the Radii of the Inflated Transiting Giant Planets WASP-4b, WASP-6b, WASP-12b, and TrES-4

TL;DR

This study models tidal heating to explain the inflated radii of certain transiting giant planets, highlighting the degeneracy between core mass and tidal dissipation, and emphasizing the need for precise eccentricity measurements.

Contribution

It introduces a method to estimate the combined effects of core mass and tidal heating on planetary radii, accounting for degeneracies and applying it to multiple exoplanets.

Findings

Tidal heating can account for inflated radii with specific core mass and eccentricity combinations.

Degeneracy exists between core mass and tidal dissipation factor, complicating radius predictions.

Improved eccentricity measurements could help constrain planetary interior parameters.

Abstract

In order to explain the inflated radii of some transiting extrasolar giant planets, we investigate a tidal heating scenario for the inflated planets WASP-4b, WASP-6b, WASP-12b, WASP-15b, and TrES-4. To do so, we assume that they retain a nonzero eccentricity, possibly by dint of continuing interaction with a third body. We calculate the amount of extra heating in the envelope that is then required to fit the radius of each planet, and we explore how this additional power depends on the planetary atmospheric opacity and on the mass of a heavy-element central core. There is a degeneracy between the core mass $M_{\rm core}$ and the heating $\dot{E}_{\rm heating}$. Therefore, in the case of tidal heating, there is for each planet a range of the couple $\{M_{\rm core},e^2/Q'_p\}$ that can lead to the same radius, where $Q'_p$ is the tidal dissipation factor and $e$ is the eccentricity. With this in mind, we also investigate the case of the non-inflated planet HAT-P-12b, which can admit solutions combining a heavy-element core and tidal heating. A substantial improvement of the measured eccentricities of such planetary systems could simplify this degeneracy by linking the two unknown parameters $\{M_{\rm core},Q'_p\}$. Further independent constraints on either of these parameters would, through our calculations, constrain the other.