Obliquity Tides May Drive WASP-12b's Rapid Orbital Decay

Abstract

Recent analyses have revealed a mystery. The orbital period of the highly inflated hot Jupiter, WASP-12b, is decreasing rapidly. The rate of inspiral, however, is too fast to be explained by either eccentricity tides or equilibrium stellar tides. While dynamical stellar tides are possible, they require a subgiant structure for the star, whereas stellar models point toward a main sequence host. Here, we show that these hitherto irreconcilable observations might be explained by planetary obliquity tides if planet b's spin vector is trapped in a high-obliquity state maintained by a secular spin-orbit resonance with an unseen exterior perturbing planet. We derive constraints on the obliquity ($\epsilon\gtrsim50^{\circ}$), reduced tidal quality factor ($Q^{\prime}\sim10^{6}-10^{7}$), and perturbing planet parameters ($M_{2}\sim10-20M_{\oplus}$, $a_2\lesssim0.04\,{\rm AU}$) required to generate the observed orbital decay. Direct N-body simulations that include tidal and spin dynamics reinforce the plausibility of the scenario. Furthermore, we show that the resonance could have been captured when planet b's obliquity was small, making the proposed sequence of events easy to explain. The hypothetical perturbing planet is within the limits of current radial velocity constraints on the system yet is also detectable. If it exists, it could provide evidence in favor of the in situ formation hypothesis for hot Jupiters.