Spin dynamics of close-in planets exhibiting large transit timing variations

We study the spin evolution of close-in planets in compact multi-planetary systems. The rotation period of these planets is often assumed to be synchronous with the orbital period due to tidal dissipation. Here we show that planet-planet perturbations can drive the spin of these planets into non-synchronous or even chaotic states. In particular, we show that the transit timing variation (TTV) is a very good probe to study the spin dynamics, since both are dominated by the perturbations of the mean longitude of the planet. We apply our model to KOI-227  b and Kepler-88  b , which are both observed undergoing strong TTVs. We also perform numerical simulations of the spin evolution of these two planets. We show that for KOI-227  b non-synchronous rotation is possible, while for Kepler-88  b the rotation can be chaotic.