Gravitational Ionization: A Chaotic Net in the Kepler System

TL;DR

This paper explores the complex nonlinear dynamics of a binary system influenced by gravitational radiation and external tidal forces, revealing chaotic behavior and resonance phenomena that affect system stability and ionization.

Contribution

It introduces a detailed analysis of the interplay between damping and external perturbations in Kepler systems, highlighting conditions for chaos and resonance capture.

Findings

Chaotic behavior occurs when damping and perturbations nearly balance.

Periodic orbits can exist with small damping.

Resonance capture phenomena are investigated using averaging methods.

Abstract

The long term nonlinear dynamics of a Keplerian binary system under the combined influences of gravitational radiation damping and external tidal perturbations is analyzed. Gravitational radiation reaction leads the binary system towards eventual collapse, while the external periodic perturbations could lead to the ionization of the system via Arnold diffusion. When these two opposing tendencies nearly balance each other, interesting chaotic behavior occurs that is briefly studied in this paper. It is possible to show that periodic orbits can exist in this system for sufficiently small damping. Moreover, we employ the method of averaging to investigate the phenomenon of capture into resonance.