Spin–Orbit Misalignment of Merging Black Hole Binaries with Tertiary Companions

Abstract

We study the effect of an external companion on the orbital and spin evolution of merging black hole (BH) binaries. A sufficiently nearby and inclined companion can excite Lidov–Kozai (LK) eccentricity oscillations in the binary, thereby shortening its merger time. During such LK-enhanced orbital decay, the spin axis of the BH generally exhibits chaotic evolution, leading to a wide range (0°–180°) of the final spin–orbit misalignment angle from an initially aligned configuration. For systems that do not experience eccentricity excitation, only modest ( ) spin–orbit misalignment can be produced, and we derive an analytic expression for the final misalignment using the principle of adiabatic invariance. The spin–orbit misalignment directly impacts the gravitational waveform and can be used to constrain the formation scenarios of BH binaries and dynamical influences of external companions.