A Radial Limit on Polar Circumbinary Orbits from General Relativity

A particle orbiting a misaligned eccentric orbit binary undergoes nodal precession either around the binary angular momentum vector (a circulating orbit) or around a stationary inclination (a librating orbit). In the absence of general relativity (GR), the stationary inclination is inclined by 90° to the binary angular momentum vector (aligned with the binary eccentricity vector) and does not depend on the particle semimajor axis. GR causes apsidal precession of the binary orbit. Close to the binary, the behavior of the particle is not significantly affected, and a librating particle precesses with the binary. However, we find that the stationary inclination and the minimum inclination required for libration both increase with the particle semimajor axis. There is a critical radius beyond which there are no librating orbits, only circulating orbits, and therefore there is a maximum orbital radius for a stationary polar-orbiting body. The critical radius is within planet-forming regions around binaries with a semimajor axis ≲1 au. This has implications for the search for misaligned circumbinary planets and the radial extent of polar circumbinary disks.