A radial limit on polar circumbinary orbits from general relativity

TL;DR

This paper investigates how general relativity influences the maximum radius at which a particle can maintain a stationary polar orbit around a binary system, revealing a critical limit relevant for planet formation and disk structures.

Contribution

It introduces the concept of a critical radius beyond which polar librating orbits cannot exist due to relativistic effects, extending previous Newtonian models.

Findings

A critical radius exists beyond which only circulating orbits are possible.

Relativistic apsidal precession increases the minimum inclination for libration.

The critical radius is within planet-forming regions for binaries with semi-major axis ≤ 1 au.

Abstract

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, the stationary inclination is inclined by 90 degrees to the binary angular momentum vector (aligned with the binary eccentricity vector) and does not depend on the particle semi-major axis. General relativity causes apsidal precession of the binary orbit. Close to the binary, the behaviour of the particle is not significantly affected, 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 semi-major 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 semi-major axis <= 1 au. This has implications for the search for misaligned circumbinary planets and the radial extent of polar circumbinary disks.