Anatomy of a slow merger: dissecting secularly-driven inspirals of LIGO/Virgo gravitational wave sources

TL;DR

This paper provides an analytical framework for understanding how external tidal perturbations, including cluster tides and Lidov-Kozai dynamics, drive compact binaries to merge via gravitational waves, considering relativistic effects.

Contribution

It offers the first analytical description of the evolutionary stages of binaries under cluster tides, including relativistic precession and GW emission, enhancing population synthesis models.

Findings

Analytical model of binary evolution stages under cluster tides.

Inclusion of relativistic precession and GW emission effects.

Insights into the phase space structure leading to mergers.

Abstract

The dozens of compact object mergers detected by LIGO/Virgo raise a key theoretical question: how do initially wide binaries shrink sufficiently quickly that they are able to merge via gravitational wave (GW) radiation within a Hubble time? One promising class of answers involves secular driving of binary eccentricity by some external tidal perturbation. This perturbation can arise due to the presence of a tertiary point mass, in which case the system exhibits Lidov-Kozai (LK) dynamics, or it can stem from the tidal field of the stellar cluster in which the binary orbits. While these secular tide-driven mechanisms have been studied exhaustively in the case of no GW emission, when GWs are included the dynamical behavior is still incompletely understood. In this paper we consider compact object binaries driven to merger via high eccentricity excitation by (doubly-averaged, test-particle quadrupole level) cluster tides - which includes LK-driven mergers as a special case - and include the effects of both general relativistic precession and GW emission. We provide for the first time an analytical understanding of the different evolutionary stages of the binary's semimajor axis, secular oscillation timescale, and phase space structure all the way to merger. Our results will inform future population synthesis calculations of compact object binary mergers from hierarchical triples and stellar clusters.