The $\chi_\mathrm{eff}-z$ correlation of field binary black hole mergers and how 3G gravitational-wave detectors can constrain it

TL;DR

This paper predicts a correlation between the effective spin parameter and redshift in binary black hole mergers if they originate from isolated binary evolution, and discusses how future third-generation detectors can test this.

Contribution

It introduces a model linking the $ ext{chi}_ ext{eff}$-$z$ correlation to isolated binary evolution and shows current data favor this correlation, which can be tested with future detectors.

Findings

Current data favor a positive $ ext{chi}_ ext{eff}$-$z$ correlation.

Third-generation detectors can distinguish between formation models.

The model explains the correlation through metallicity-dependent stellar evolution.

Abstract

Understanding the origin of merging binary black holes is currently one of the most pressing quests in astrophysics. We show that if isolated binary evolution dominates the formation mechanism of merging binary black holes, one should expect a correlation between the effective spin parameter, $\chi_\mathrm{eff}$, and the redshift of the merger, $z$, of binary black holes. This correlation comes from tidal spin-up systems preferentially forming and merging at higher redshifts due to the combination of weaker orbital expansion from low metallicity stars given their reduced wind mass loss rate, delayed expansion and have smaller maximal radii during the supergiant phase compared to stars at higher metallicity. As a result, these tightly bound systems merge with short inspiral times. Given our fiducial model of isolated binary evolution, we show that the origin of a $\chi_\mathrm{eff}-z$ correlation in the detectable LIGO--Virgo binary black hole population is different from the intrinsic population, which will become accessible only in the future by third-generation gravitational-wave detectors such as Einstein Telescope and Cosmic Explorer. Finally, we compare our model predictions with population predictions based on the current catalog of binary black hole mergers and find that current data favor a positive correlation of $\chi_\mathrm{eff}-z$ as predicted by our model of isolated binary evolution.