Retrograde-rotating Exoplanets Experience Obliquity Excitations in an Eccentricity-enabled Resonance

Previous studies have shown that planets that rotate retrograde (backward with respect to their orbital motion) generally experience less severe obliquity variations than those that rotate prograde (the same direction as their orbital motion). Here, we examine retrograde-rotating planets on eccentric orbits and find a previously unknown secular spin-orbit resonance that can drive significant obliquity variations. This resonance occurs when the frequency of the planet's rotation axis precession becomes commensurate with an orbital eigenfrequency of the planetary system. The planet's eccentricity enables a participating orbital frequency through an interaction in which the apsidal precession of the planet's orbit causes a cyclic nutation of the planet's orbital angular momentum vector. The resulting orbital frequency follows the relationship f = 2 pi -omega, where pi and omega are the rates of the planet's changing longitude of periapsis and longitude of ascending node, respectively. We test this mechanism by simulating cases of a simple Earth-Jupiter system and confirm the predicted resonance. Over the course of 100 Myr, the test Earths with rotation axis precession rates near the predicted resonant frequency experienced pronounced obliquity variations of the order of 10 degrees-30 degrees. These variations can be significant and suggest that while retrograde rotation is a stabilizing influence most of the time, retrograde rotators can experience large obliquity variations if they are on eccentric orbits and enter this spin-orbit resonance.