Orbital Decay of Hot Jupiters due to Weakly Nonlinear Tidal Dissipation

Abstract

We study tidal dissipation in hot Jupiter host stars due to the nonlinear damping of tidally driven g-modes, extending the calculations of Essick & Weinberg to a wide variety of stellar host types. This process causes the planet’s orbit to decay and has potentially important consequences for the evolution and fate of hot Jupiters. Previous studies either only accounted for linear dissipation processes or assumed that the resonantly excited primary mode becomes strongly nonlinear and breaks as it approaches the stellar center. However, the great majority of hot Jupiter systems are in the weakly nonlinear regime in which the primary mode does not break but instead excites a sea of secondary modes via three-mode interactions. We simulate these nonlinear interactions and calculate the net mode dissipation for stars that range in mass from 0.5M ⊙ ≤ M ⋆ ≤ 2.0M ⊙ and in age from the early main sequence to the subgiant phase. We find that the nonlinearly excited secondary modes can enhance the tidal dissipation by orders of magnitude compared to linear dissipation processes. For the stars with M ⋆ ≲ 1.0M ⊙ of nearly any age, we find that the orbital decay time is ≲100 Myr for orbital periods P orb ≲ 1 day. For M ⋆ ≳ 1.2M ⊙, the orbital decay time only becomes short on the subgiant branch, where it can be ≲10 Myr for P orb ≲ 2 days and result in significant transit time shifts. We discuss these results in the context of known hot Jupiter systems and examine the prospects for detecting their orbital decay with transit timing measurements.

TESS Giants Transiting Giants. IV. A Low-density Hot Neptune Orbiting a Red Giant Star

“…However, at the shortest orbital periods (<5 days), even planets around evolved stars appear to have largely circular orbits. Constraints on orbital eccentricities will constrain both planet engulfment and stellar structure models (Weinberg et al 2017;Sun et al 2018;Soares-Furtado et al 2021;Grunblatt et al 2023;Weinberg et al 2024). We find no evidence for significant eccentricity in the orbit of TIC 365102760 b based on our current set of observations.…”

Doomed Worlds. I. No New Evidence for Orbital Decay in a Long-term Survey of 43 Ultrahot Jupiters

“…The orbital period decrease for this planet was measured as P 131 22  =  ms yr −1 by Vissapragada et al (2022). The evolved host star is probably key to explaining the rapid rate of decay: although Weinberg et al (2024) found that g-mode dissipation is too weak to explain it, Vissapragada et al (2022) argued that inertial wave dissipation, combined with rapid stellar rotation, could. On the other hand, recent results from Barker et al (2024) find that the time the star spends with Q 10 4  ¢ < may be too short, potentially requiring nonsynchronous rotation if tidal dissipation is to explain the rate of orbital decrease.…”

“…The resulting theoretical estimates for Q  ¢ are listed as Q th ¢ in Table 3, and we computed the theoretical decay time τ th and rate of period decrease P th  as in Equation (15) in Weinberg et al (2024). For stellar models with radiative cores and convective envelopes, Weinberg et al (2024) found values that range from Q 10 th 5…”

Damping Obliquities of Hot Jupiter Hosts by Resonance Locking

“…The full calculation of k abb¢ is challenging (e.g., Van Beeck et al 2023). For a ∼4 Gyr solar-mass star, using the WKB scaling for how parent and child modes behave close to the star's center, Weinberg et al (2012Weinberg et al ( , 2024 show that k abb¢ may be approximated as E E thr,sw , which does not depend on Δ α . To demonstrate how parametric instability and the spawning of child modes can suppress the resonant response of the parent, we solve Equations (B1) using the following model.…”