Studying Binary Formation under Dynamical Friction Using Hill's Problem

TL;DR

This study uses Hill's problem with added dynamical friction to analyze binary formation in gaseous disks and stellar clusters, revealing a linear relationship between friction strength and binary formation rate across scales.

Contribution

It introduces a scale-free model incorporating dynamical friction into Hill's problem, providing broad insights into binary formation mechanisms.

Findings

Binary formation rate is linearly proportional to friction coefficient under weak friction.

The model's results are generalizable across different astrophysical scales.

Simulations show how eccentricity and inclination affect binary formation.

Abstract

Using the equations of motion from Hill's problem, with added accelerations for different forms of dynamical friction, we provide the (to-date) broadest scale-free study of friction-driven binary formation in gaseous disks and stellar clusters. We focus mainly on binary formation between stellar-mass black holes in active galactic nuclei (AGNi), considering both gas dynamical friction from AGN disks and stellar dynamical friction from the nuclear star cluster. We first find simple, dimensionless friction coefficients that approximate the effects of standard models for gas and stellar dynamical friction. We perform extensive simulations of Hill's problem under such friction, and we present a picture of binary formation through encounters between single stars on nearby orbits, as a function of friction parameter, eccentricity, and inclination. Notably, we find that the local binary formation rate is a linear function of the friction coefficient so long as the friction is weak. Due to the dimensionless nature of our model problem, our findings are generalizable to binary formation at all scales (e.g., intermediate-mass black holes in a star cluster, planetesimals in a gaseous disk).