Orbital precession in short-period hot Jupiter exoplanet systems

In several exoplanet systems the stellar rotation axis is not aligned with the normal to the orbital plane. For the class of 'hot Jupiters', a significant fraction of total angular momentum resides in the orbit. Orbit precessional motion has been observed in several such systems. We expect the tides raised by the orbiting exoplanet to induce normal mode oscillations in the host star, with the possibility of normal mode-orbit resonance. Gravity modes possess frequencies in the range of typical orbital Keplerian frequencies and their overtones. These resonances, confined to very narrow ranges of frequency space, would be highly improbable unless 'resonance locking' occurs, driven, for example, by structural and spin rate changes of the host star, operating on nuclear evolutionary time-scales. Resonance locking amplifies the amplitude of tidally driven oscillations, possibly by orders of magnitude, compared to the equilibrium tide displacements. We address the problem of precession and nutation in a system with a single exoplanet, with non-aligned spin and orbit axes, coupling the gravitational perturbations of normal mode distortions with orbital motion. Resonant modes are expected to have large amplitudes, contributing significantly to the gravitational perturbation already present due to rotational distortion of the star that gives rise to uniform orbital precession. The relative magnitude of rotational distortion and normal-mode perturbations is estimated. For Kepler-13Ab, estimates of their influence on transit time variations are given, and suggest they may be discernible with modern space telescope missions.