Detecting stochastic gravitational waves with binary resonance

TL;DR

This paper introduces a novel formalism for detecting stochastic gravitational waves by analyzing their subtle effects on binary systems' orbits, offering new tools for data analysis in GW astronomy.

Contribution

It develops a first-principles secular Fokker-Planck equation for binary orbital evolution under stochastic GWs and provides practical methods for data analysis.

Findings

Derived a comprehensive Fokker-Planck equation for binary orbital elements.

Created numerical tools for integrating the orbital evolution equations.

Established statistical methods for GW detection using binary pulsar data.

Abstract

LIGO and Virgo have initiated the era of gravitational-wave (GW) astronomy; but in order to fully explore GW frequency spectrum, we must turn our attention to innovative techniques for GW detection. One such approach is to use binary systems as dynamical GW detectors by studying the subtle perturbations to their orbits caused by impinging GWs. We present a powerful new formalism for calculating the orbital evolution of a generic binary coupled to a stochastic background of GWs, deriving from first principles a secularly-averaged Fokker-Planck equation which fully characterises the statistical evolution of all six of the binary's orbital elements. We also develop practical tools for numerically integrating this equation, and derive the necessary statistical formalism to search for GWs in observational data from binary pulsars and laser-ranging experiments.