Induced Ellipticity for Inspiraling Binary Systems

TL;DR

This paper introduces a semi-analytical approach to determine the eccentricity distribution of binary black holes influenced by surrounding matter, accounting for complex dynamical effects near galactic centers.

Contribution

It presents a novel semi-analytical method for calculating eccentricity in binary black holes affected by matter and generalizes Kozai-Lidov dynamics for more comprehensive angular momentum exchange.

Findings

Analytical eccentricity determination considering tidal forces and evaporation.

Generalization of Kozai-Lidov dynamics to non-perturbative regimes.

Framework for understanding black hole environments in galactic centers.

Abstract

Although gravitational waves tend to erase eccentricity of an inspiraling binary system, ellipticity can be generated in the presence of surrounding matter. We present a semi-analytical method for understanding the eccentricity distribution of binary black holes in the presence of a supermassive black hole in a galactic center. Given a matter distribution, we show how to determine the resultant eccentricity analytically in the presence of both tidal forces and evaporation up to one cutoff and one matter-distribution-independent function, paving the way for understanding the environment of detected inspiraling black holes. We furthermore generalize Kozai-Lidov dynamics to situations where perturbation theory breaks down for short time intervals, allowing more general angular momentum exchange, such that eccentricity is generated even when all bodies orbit in the same plane.