2013ApJ...778..182V

Although warm Jupiters are generally too far from their stars for tides to be important, the presence of an inner planetary companion to a warm Jupiter can result in tidal evolution of the system. Insight into the process and its effects comes form classical secular theory of planetary perturbations. The lifetime of the inner planet may be shorter than the age of the system, because the warm Jupiter maintains its eccentricity and hence promotes tidal migration into the star. Thus a warm Jupiter observed to be alone in its system might have previously cleared away any interior planets. Before its demise, even if an inner planet is of terrestrial scale, it may promote damping of the warm Jupiter's eccentricity. Thus any inferences of the initial orbit of an observed warm Jupiter must include the possibility of a greater initial eccentricity than would be estimated by assuming it had always been alone. Tidal evolution involving multiple planets also enhances the internal heating of the planets, which readily exceeds that of stellar radiation for the inner planet, and may be great enough to affect the internal structure of warm Jupiters. Secular theory gives insight into the tidal processes, providing, among other things, a way to constrain eccentricities of transiting planets based on estimates of the tidal parameter Q.