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Abstract We study tidal dissipation in hot Jupiter host stars due to the nonlinear damping of tidally driveng-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 withM_⋆≲ 1.0M_⊙of nearly any age, we find that the orbital decay time is ≲100 Myr for orbital periodsP_orb≲ 1 day. ForM_⋆≳ 1.2M_⊙, the orbital decay time only becomes short on the subgiant branch, where it can be ≲10 Myr forP_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. 

Abstract High-eccentricity tidal migration is a potential formation channel for hot Jupiters. During this process, the planetary f-mode may experience a phase of diffusive growth, allowing its energy to quickly build up to large values. In Yu et al., we demonstrated that nonlinear mode interactions between a parent f-mode and daughter f- and p-modes expand the parameter space over which the diffusive growth of the parent is triggered. We extend that study by incorporating (1) the angular momentum transfer between the orbit and the mode, and consequently the evolution of the pericenter distance; (2) a prescription to regulate the nonlinear frequency shift at high parent mode energies; and (3) dissipation of the parent’s energy due to both turbulent convective damping of the daughter modes and strongly nonlinear wave-breaking events. The new ingredients allow us to follow the coupled evolution of the mode and orbit over ≳10⁴yr, covering the diffusive evolution from its onset to its termination. We find that the semimajor axis shrinks by a factor of nearly 10 over 10⁴yr, corresponding to a tidal quality factor $\mathit{}\sim 10$. The f-mode’s diffusive growth terminates while the eccentricity is still high, at arounde= 0.8–0.95. Using these results, we revisit the eccentricity distribution of proto-hot Jupiters. We estimate that less than 1 proto-HJ with eccentricity >0.9 should be expected in Kepler's data once the diffusive regime is accounted for, explaining the observed paucity of this population.