Resonant-plane locking and spin alignment in stellar-mass black-hole binaries: a diagnostic of compact-binary formation

TL;DR

This paper investigates how the formation scenarios of stellar-mass black-hole binaries influence their spin dynamics, proposing that spins tend to align in a resonant plane detectable by gravitational-wave observatories, thus linking observations to astrophysical models.

Contribution

It introduces the concept of a resonant plane for black-hole spins, providing a diagnostic tool to infer binary formation mechanisms from gravitational-wave data.

Findings

Black-hole spins are likely to lie in a resonant plane at detection.

The distribution of spin angles constrains formation models.

Measurement of spin angles can reveal the efficiency of tidal interactions.

Abstract

We study the influence of astrophysical formation scenarios on the precessional dynamics of spinning black-hole binaries by the time they enter the observational window of second- and third-generation gravitational-wave detectors, such as Advanced LIGO/Virgo, LIGO-India, KAGRA and the Einstein Telescope. Under the plausible assumption that tidal interactions are efficient at aligning the spins of few-solar mass black-hole progenitors with the orbital angular momentum, we find that black-hole spins should be expected to preferentially lie in a plane when they become detectable by gravitational-wave interferometers. This "resonant plane" is identified by the conditions \Delta\Phi=0{\deg} or \Delta\Phi=+/-180{\deg}, where \Delta\Phi is the angle between the components of the black-hole spins in the plane orthogonal to the orbital angular momentum. If the angles \Delta \Phi can be accurately measured for a large sample of gravitational-wave detections, their distribution will constrain models of compact binary formation. In particular, it will tell us whether tidal interactions are efficient and whether a mechanism such as mass transfer, stellar winds, or supernovae can induce a mass-ratio reversal (so that the heavier black hole is produced by the initially lighter stellar progenitor). Therefore our model offers a concrete observational link between gravitational-wave measurements and astrophysics. We also hope that it will stimulate further studies of precessional dynamics, gravitational-wave template placement and parameter estimation for binaries locked in the resonant plane.