Spin-Orbit Resonances of Rigid Triaxial Super-Earths

Abstract

The spins of exoplanets can affect their atmospheric dynamics, which can in turn affect their habitability. There exist numerous spin-orbit resonances that can drastically alter the trajectory of a planet’s spin evolution. The majority of previous studies on spin-orbit resonances among exoplanets have adopted a fluid-body model for the planet, but this model may not be accurate for Super-Earths up to a few Earth masses, as these can have rocky, Earth-like compositions. Moreover, it is possible that such planets can possess three different moments along their three principal axes. Consequently, it is important to study spin-orbit resonances with rigid planets to gain an understanding of the spin dynamics of these planets. We present a new spin integrator in REBOUNDx that treats bodies as perfectly rigid and allows up to three distinct moments of inertia about a body’s three principal axes. Unlike previous works studying rigid-body spin dynamics, we do not use secular equations of motion or assume principal axis rotation about the body’s shortest axis. We use our implementation to study spin-orbit resonances of rigid planets. We find three resonances for both triaxial and oblate planets: 1:1, 2:1, and 90◦. Previous works have found similar resonances at 1:1 and 2:1, though it is not clear whether the mechanisms of capture into these resonances are the same as for the resonances we found. On the other hand, we are not aware of any other works that have reported a resonance at 90◦.