Gravitational Waves in the Circular Restricted Three Body Problem

TL;DR

This paper analyzes gravitational wave emission in a modified three-body system, providing analytic formulas and revealing that the third body can slow down binary coalescence, impacting gravitational wave signal interpretation.

Contribution

It introduces analytic expressions for gravitational wave emission in the circular restricted three-body problem, a novel extension of binary systems.

Findings

Third body slows binary coalescence

Effective rescaling of the binary's chirp-mass

Analytic expressions for emitted power and frequency variation

Abstract

The prospect of unprecedented high-quality data of gravitational waves in the upcoming decades demands a theoretical effort to optimally study and analyze the signals that next generation detectors will provide. Here we study the gravitational wave emission and related dynamics during the inspiralling phase of the Circular Restricted Three Body Problem, a modification of the conventional binary scenario in which a small third object co-rotates with the parent binary system. Specifically, we obtain analytic expressions for the emitted power, frequency variation and other dynamical variables that describe the evolution of the system. As a key highlight, we find that the presence of the third body actually slows down the coalescence of the binary, which can be partially interpreted as an effective rescaling of the binary's chirp-mass. Our analysis assumes semi-Keplerian orbits for the particles and a highly mass asymmetric parent binary needed for the stability of orbits.