Orbital decay of hot Jupiters due to nonlinear tidal dissipation within solar-type hosts

TL;DR

This paper investigates how nonlinear tidal interactions in solar-type stars lead to rapid orbital decay of hot Jupiters, explaining their scarcity and predicting observable effects.

Contribution

It demonstrates that nonlinear mode interactions significantly enhance tidal dissipation, resulting in faster orbital decay than previously estimated.

Findings

Nonlinear tidal dissipation rates are much higher than linear estimates.

Orbital decay timescales are less than a Gyr for certain hot Jupiters.

Approximately 10 known systems may be undergoing rapid orbital decay.

Abstract

We study the orbital evolution of hot Jupiters due to the excitation and damping of tidally driven $g$-modes within solar-type host stars. Linearly resonant $g$-modes (the dynamical tide) are driven to such large amplitudes in the stellar core that they excite a sea of other $g$-modes through weakly nonlinear interactions. By solving the dynamics of large networks of nonlinearly coupled modes, we show that the nonlinear dissipation rate of the dynamical tide is several orders of magnitude larger than the linear dissipation rate. We find stellar tidal quality factors $Q \approx 10^5-10^6$ for systems with planet mass $M_p \geq 0.5 M_\mathrm{J}$ and orbital period $P \leq 2$ days, which implies that such systems decay on timescales that are small compared to the main-sequence lifetime of their solar-type hosts. According to our results, there are $\approx 10$ currently known exoplanetary systems, including WASP-19b and HAT-P-36-b, with orbital decay timescales shorter than a Gyr. Rapid, tidally induced orbital decay may explain the observed paucity of planets with $M_p \ge M_\mathrm{J}$ and $P < 2$ days around solar-type hosts and could generate detectable transit-timing variations in the near future.