The thermodynamics of stellar multiplicity: dynamical evolution of binary star populations in dense stellar environments

TL;DR

This paper develops a self-consistent analytic model based on statistical mechanics to describe the dynamical evolution of binary star populations in dense stellar environments, focusing on orbital energy and eccentricity distributions.

Contribution

It introduces a novel steady state eccentricity distribution and compares analytic predictions with N-body simulations, advancing understanding of binary evolution.

Findings

Steady state eccentricity distribution with depletions at high and low eccentricities

Good agreement between analytic model and N-body simulations for initial conditions

Model captures the dominant gravitational physics in dense stellar environments

Abstract

We recently derived, using the density-of-states approximation, analytic distribution functions for the outcomes of direct single-binary scatterings (Stone & Leigh 2019). Using these outcome distribution functions, we present in this paper a self-consistent statistical mechanics-based analytic model obtained using the Fokker-Planck limit of the Boltzmann equation. Our model quantifies the dominant gravitational physics, combining both strong and weak single-binary interactions, that drives the time evolution of binary orbital parameter distributions in dense stellar environments. We focus in particular the distributions of binary orbital energies and eccentricities. We find a novel steady state distribution of binary eccentricities, featuring strong depletions of both the highest and the lowest eccentricity binaries. In energy space, we compare the predictions of our analytic model to the results of numerical N-body simulations, and find that the agreement is good for the initial conditions considered here. This work is a first step toward the development of a fully self-consistent semi-analytic model for dynamically evolving binary star populations in dense stellar environments due to direct few-body interactions.