Retrograde-rotating exoplanets experience obliquity excitations in an eccentricity-enabled resonance

Previous studies show that planets that rotate retrograde (backwards with respect to their orbital motion) generally experience less severe variations of their axial tilt, or obliquity, than those that rotate prograde. The reason for this is that retrograde rotators often get to avoid the secular spin-orbit resonances that are conventionally responsible for driving large obliquity variations. Specifically, this 1:1 spin-orbit resonance requires the frequency of the precession of the planet's rotation axis to become commensurate with an orbital eigenfrequency of the planetary system, which doesn't usually work out for retrograde rotators in the small-eccentricity regime due to their flipped direction of axial precession. Here we examine retrograde rotators in the large-eccentricity regime, and study a particular spin-orbit resonance in which 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 ˙ϖ - ˙Ω, where ˙ϖ and ˙Ω are the rates of the planet's changing longitude of periapsis and 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 order 10°-30°. These variations can be significant in terms of the prospects of potential habitability for exoplanets, and express 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.