The Influence of General Relativity on the Spins of Celestial Bodies in Inclined Orbits

Abstract

Through the Rossiter-McLaughlin effect, several hot Jupiters have been found to exhibit spin-orbit misalignment, and even retrograde orbits. The high obliquity observed in these planets can be attributed to two primary formation mechanisms, as summarized in the existing literature. First, the host star's spin becomes misaligned with the planetary disk during the late stages of star formation, primarily due to chaotic accretion and magnetic interactions between the star and the planetary disk. Second, the orbital inclination of an individual planet can be excited by dynamical processes such as planet-planet scattering, the Lidov-Kozai cycle, and secular chaos within the framework of Newtonian mechanics. This study introduces a third mechanism, where, within the framework of general relativity, the post-Newtonian spin-orbit coupling term induces precession of the host star's spin around the orbital angular momentum. The orbital inclination, relative to a reference plane, can expand the range of deviation in the spatial orientation of the bodies' spins from the plane's normal. The varying amplitude and period of spin precession for both the star and the planet are derived theoretically, and the results, which can be applied without restriction, agree well with numerical simulations.