The χeff − z correlation of field binary black hole mergers and how 3G gravitational-wave detectors can constrain it

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, χeff, 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 χeff − 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. Given the limited horizon of current gravitational-wave detectors, z ≲ 1, highly rotating black hole mergers in the LIGO–Virgo observed χeff − z correlation are dominated by those formed through chemically homogeneous evolution. This is in contrast to the subpopulation of highly rotating black holes in the intrinsic population, which is dominated by tidal spin up following a common evolve event. The different subchannel mixture in the intrinsic and detected population is a direct consequence of detector selection effects, which allows for the typically more massive black holes formed through chemically homogeneous evolution to be observable at larger redshifts and dominate the LIGO–Virgo sample of spinning binary black holes from isolated evolution at z > 0.4. 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 χeff − z as predicted by our model of isolated binary evolution.