Orbital Decay of Hot Jupiters due to Weakly Nonlinear Tidal Dissipation

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⋆ ≲ 1.0 M_⊙ of nearly any age, we find that the orbital decay time is ≲100 Myr for orbital periods P_(orb) ≲ 1 day. For M⋆ ≳ 1.2 M_⊙, 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.