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

## TL;DR

This paper proposes that obliquity tides, maintained by a secular spin-orbit resonance with an unseen planet, can explain the rapid orbital decay of WASP-12b, a phenomenon not accounted for by previous models.

## Contribution

It introduces a novel explanation involving planetary obliquity tides and a hidden perturbing planet to account for WASP-12b's rapid orbital decay.

## Key findings

- Obliquity of planet b likely exceeds 50 degrees.
- Perturbing planet estimated to be 10-20 Earth masses within 0.04 AU.
- Resonance capture scenario consistent with system's evolution.

## 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.