Long-lived Planetary Obliquities of Close-in Exoplanets: The Tricky Story for Rocky Bodies

A planet sufficiently close to its host star is generally thought to rapidly evolve into a tidally locked configuration. In this state, the planet’s spin period becomes synchronized to its orbital period, and the planet’s “obliquity”, the angle between its axis of rotation and its orbital normal, damps to zero. Recent work has suggested that tidal locking may not be the only possible configuration in multiplanetary systems: certain secular spin-orbit resonances can counteract tidal alignment of the planet’s spin axis and trap the planetary obliquity at large values nearing 90 degrees. However, these works assume a fluid planet model, where the planet’s rotation state and shape are simply related. In practice, planets less massive than a few Earth masses appear to be most consistent with predominantly rocky compositions, which are likely to retain permanent shapes that are not straightforwardly related to their present-day rotation. The effect of spin-orbit resonances for such rocky planets has not been well-studied. We extend the spin-orbit resonance dynamics to rocky planets and present numerical and analytical results characterizing a class of previously-undiscovered resonances. We discuss the impact of these new results on the prospect of oblique exoplanets.