2025ApJ...983..167L

Observations of hierarchical triple-star systems show that misalignments are common both between the angular momentum vector of the inner binary and the outer companion orbit, and between the outer binary orbit and a circumtriple gas disk. With analytic methods and n-body simulations, we explore the dynamics of circumtriple orbits around a misaligned hierarchical triple star. Circumtriple test-particle orbits nodally precess either about the outer binary angular momentum vector (circulating orbits) or about a stationary inclination that depends upon the binary properties (librating orbits). For a coplanar (or retrograde coplanar) triple star, the apsidal precession rate is maximal and the critical orbital radius outside of which all orbits are circulating is minimal. Polar alignment of a circumtriple gas disk requires nodal libration, and therefore it can be more likely if there is a large misalignment between the inner and outer binary orbits. There are two values of the mutual misalignment, i_c and 180° - i_c, for which the apsidal precession rate of the triple star is zero and polar alignment is possible at all orbital radii. For a circular inner binary orbit i_c = 55°, and it changes with the eccentricity of the inner binary while being insensitive to other triple-star parameters.