Secular dynamics of binaries in stellar clusters – III. Doubly averaged dynamics in the presence of general-relativistic precession

Chris Hamilton,Roman R Rafikov

doi:10.1093/mnras/stab1284

Abstract

ABSTRACT Secular evolution of binaries driven by an external (tidal) potential is a classic astrophysical problem. Tidal perturbations can arise due to an external point mass, as in the Lidov–Kozai (LK) theory of hierarchical triples, or due to an extended stellar system (e.g. galaxy or globular cluster) in which the binary resides. For many applications, general-relativistic (GR) apsidal precession is important, and has been accounted for in some LK calculations. Here, we generalize and extend these studies by exploring in detail the effect of GR precession on (quadrupole-level) tidal evolution of binaries orbiting in arbitrary axisymmetric potentials (which includes LK theory as a special case). We study the (doubly averaged) orbital dynamics for arbitrary strengths of GR and binary initial conditions and uncover entirely new phase space morphologies with important implications for the binary orbital evolution. We also explore how GR precession affects secular evolution of binary orbital elements when the binary reaches high eccentricity (e → 1) and delineate several different dynamical regimes. Our results are applicable to a variety of astrophysical systems. In particular, they can be used to understand the high eccentricity behaviour of (cluster) tide-driven compact object mergers – i.e. LIGO/Virgo gravitational wave sources – for which GR effects are crucial.

Highlights

The problem of the relative motion of two bound point masses has formed the basis of celestial mechanics since it was first successfully tackled mathematically by Newton in 1687
A century on, the LIGO/Virgo Collaboration has detected, and continues to detect, dozens of merging compact object binaries (The LIGO Scientific Collaboration et al 2018, 2020). These discoveries certainly warrant an astrophysical explanation, which is complicated by the fact that the timescale for an isolated compact object binary to merge via gravitational wave (GW) emission is often much longer than the age of the Universe
The resulting dynamics are significantly complicated by bifurcations that occur at Γ = ±1/5, 0, for Γ > 1/5 our qualitative results are intuitive, falling in line with those gleaned from previous LK (Γ = 1) studies that accounted for GR precession

Summary

Introduction

The problem of the relative motion of two bound point masses has formed the basis of celestial mechanics since it was first successfully tackled mathematically by Newton in 1687. In 1915 Einstein updated the solution, showing that the lowest order correction to Newton’s elliptical orbit (in the small parameter G(m1 + m2)/ac, with mi the constituent masses and a the binary semimajor axis) was an extra prograde apsidal precession at a rate ω GR =. A century on, the LIGO/Virgo Collaboration has detected, and continues to detect, dozens of merging compact object (black hole or neutron star) binaries (The LIGO Scientific Collaboration et al 2018, 2020). These discoveries certainly warrant an astrophysical explanation, which is complicated by the fact that the timescale for an isolated compact object binary to merge via gravitational wave (GW) emission is often much longer than the age of the Universe.

Objectives

Discussion

Conclusion