Tidal Dissipation in WASP-12

TL;DR

This paper investigates the tidal dissipation in the hot Jupiter system WASP-12, proposing that the observed orbital decay is consistent with the star being a subgiant, which enhances tidal dissipation and explains the planet's inspiral.

Contribution

It introduces the idea that the star's evolutionary state affects tidal dissipation, providing a model that matches observed orbital decay in WASP-12.

Findings

Tidal dissipation is too weak if the star is on the main sequence.

Enhanced dissipation occurs if the star is a subgiant due to nonlinear wave breaking.

The subgiant model's parameters align with observed orbital decay rates.

Abstract

WASP-12 is a hot Jupiter system with an orbital period of $P= 1.1\textrm{ day}$, making it one of the shortest-period giant planets known. Recent transit timing observations by Maciejewski et al. (2016) and Patra et al. (2017) find a decreasing period with $P/|\dot{P}| = 3.2\textrm{ Myr}$. This has been interpreted as evidence of either orbital decay due to tidal dissipation or a long term oscillation of the apparent period due to apsidal precession. Here we consider the possibility that it is orbital decay. We show that the parameters of the host star are consistent with either a $M_\ast \simeq 1.3 M_\odot$ main sequence star or a $M_\ast \simeq 1.2 M_\odot$ subgiant. We find that if the star is on the main sequence, the tidal dissipation is too inefficient to explain the observed $\dot{P}$. However, if it is a subgiant, the tidal dissipation is significantly enhanced due to nonlinear wave breaking of the dynamical tide near the star's center. The subgiant models have a tidal quality factor $Q_\ast'\simeq 2\times10^5$ and an orbital decay rate that agrees well with the observed $\dot{P}$. It would also explain why the planet survived for $\simeq 3\textrm{ Gyr}$ while the star was on the main sequence and yet is now inspiraling on a 3 Myr timescale. Although this suggests that we are witnessing the last $\sim 0.1\%$ of the planet's life, the probability of such a detection is a few percent given the observed sample of $\simeq 30$ hot Jupiters in $P<3\textrm{ day}$ orbits around $M_\ast>1.2 M_\odot$ hosts.