Evolution Of Binary Supermassive Black Holes In Rotating Nuclei

TL;DR

This paper develops a comprehensive model for how rotating galactic nuclei influence the orbital evolution of binary supermassive black holes, affecting their orientation and eccentricity, with implications for gravitational wave signals.

Contribution

It introduces a Fokker-Planck based framework incorporating nuclear rotation effects on binary black hole evolution, including new analytic and numerical diffusion coefficients.

Findings

Binary orbit orientation aligns with nuclear rotation plane

Eccentricity decreases for aligned binaries, increases for counter-aligned

Rotation reduces the diffusive component of orbital evolution

Abstract

Interaction of a binary supermassive black hole with stars in a galactic nucleus can result in changes to all the elements of the binary's orbit, including the angles that define its orientation. If the nucleus is rotating, the orientation changes can be large, causing large changes in the binary's orbital eccentricity as well. We present a general treatment of this problem based on the Fokker-Planck equation for f, defined as the probability distribution for the binary's orbital elements. First- and second-order diffusion coefficients are derived for the orbital elements of the binary using numerical scattering experiments, and analytic approximations are presented for some of these coefficients. Solutions of the Fokker-Planck equation are then derived under various assumptions about the initial rotational state of the nucleus and the binary hardening rate. We find that the evolution of the orbital elements can become qualitatively different when we introduce nuclear rotation: 1) the orientation of the binary's orbit evolves toward alignment with the plane of rotation of the nucleus; 2) binary orbital eccentricity decreases for aligned binaries and increases for counter-aligned ones. We find that the diffusive (random-walk) component of a binary's evolution is small in nuclei with non-negligible rotation, and we derive the time-evolution equations for the semimajor axis, eccentricity and inclination in that approximation. The aforementioned effects could influence gravitational wave production as well as the relative orientation of host galaxies and radio jets.