Few-Body Modes of Binary Formation in Core Collapse

TL;DR

This paper investigates the formation of binary stars during the core collapse of star clusters, revealing that traditional models based on three-body encounters are incomplete, especially regarding resonant interactions like democratic resonances.

Contribution

It refines the understanding of binary formation by analyzing the limitations of conventional three-body encounter models, emphasizing the role of resonant scattering and perturbations.

Findings

Conventional three-body scattering models are valid for direct encounters.

Resonant scattering, especially democratic resonances, cannot be approximated as isolated.

Strong perturbations often occur after resonant interactions, affecting binary formation.

Abstract

At the moment of deepest core collapse, a star cluster core contains less than ten stars. This small number makes the traditional treatment of hard binary formation, assuming a homogeneous background density, suspect. In a previous paper, we have found that indeed the conventional wisdom of binary formation, based on three-body encounters, is incorrect. Here we refine that insight, by further dissecting the subsequent steps leading to hard binary formation. For this purpose, we add some analysis tools in order to make the study less subjective. We find that the conventional treatment does remain valid for direct three-body scattering, but fails for resonant three-body scattering. Especially democratic resonance scattering, which forms an important part of the analytical theory of three-body binary formation, takes too much space and time to be approximated as being isolated, in the context of a cluster core around core collapse. We conclude that, while three-body encounters can be analytically approximated as isolated, subsequent strong perturbations typically occur whenever those encounters give rise to democratic resonances. We present analytical estimates postdicting our numerical results. If we only had been a bit more clever, we could have predicted this qualitative behaviour.