Stability criteria for hierarchical triple systems

TL;DR

This paper reviews various stability criteria for hierarchical triple systems, including analytical, numerical, and chaos-based approaches, discussing their advantages, disadvantages, and comparisons.

Contribution

It provides a comprehensive summary and comparison of existing stability criteria for hierarchical triple systems, highlighting their derivations and applicability.

Findings

Criteria based on zero velocity surfaces are useful but have limitations.

Numerical integration methods offer detailed stability insights.

Chaos-based criteria help identify unstable configurations.

Abstract

In this paper, we give a summary of stability criteria that have been derived for hierarchical triple systems over the past few decades. We give a brief description and we discuss the criteria that are based on the generalisation of the concept of zero velocity surfaces of the restricted three body problem, to the general case. We also present criteria that have to do with escape of one of the bodies. Then, we talk about the criteria that have been derived using data from numerical integrations. Finally, we report on criteria that involve the concept of chaos. In all cases, wherever possible, we discuss advantages and disadvantages of the criteria and the methods their derivation was based on, and some comparison is made in several cases.