# In Search of the Thermal Eccentricity Distribution

## TL;DR

This paper challenges the assumption that star cluster dynamics quickly thermalize binary star eccentricities, showing instead that initial conditions are likely preserved and significantly impact binary evolution predictions.

## Contribution

The authors develop a rapid semi-analytic model and compare it with detailed simulations to demonstrate that dynamical encounters do not thermalize binary eccentricities within cluster lifetimes.

## Key findings

- Dynamical encounters rarely convert uniform to thermal eccentricity distributions.
- Observed thermal distributions likely reflect formation conditions, not dynamical evolution.
- Models assuming initial thermal distributions may overestimate binary merger rates.

## Abstract

About a century ago, Jeans (1919) discovered that if binary stars reach a state approximating energy equipartition, for example through many dynamical encounters that exchange energy, their eccentricity distribution can be described by : dN/de = 2e. This is referred to as the thermal eccentricity distribution, and has been widely used for initial conditions in theoretical investigations of binary stars. However, observations suggest that the eccentricity distributions of most observed binaries, and particularly those with masses < 5 Msun, are flatter than thermal and follow more closely to a uniform distribution. Nonetheless, it is often argued that dynamical interactions in a star cluster would quickly thermalize the binaries, which could justify imposing a thermal eccentricity distribution at birth for all binaries. In this paper we investigate the validity of this assumption. We develop our own rapid semi-analytic model for binary evolution in star clusters, and also compare with detailed N-body and Monte Carlo star cluster models. We show that, for nearly all binaries, dynamical encounters fail to convert an initially uniform eccentricity distribution to thermal within a star cluster's lifetime. Thus, if a thermal eccentricity distribution is observed, it is likely imprinted upon formation rather than through subsequent long-term dynamical processing. Theoretical investigations that initialize all binaries with a thermal distribution will make incorrect predictions for the evolution of the binary population. Such models may overpredict the merger rate for binaries with modest orbital separations by a factor of about two.