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

¹ Département d’Astronomie, Université de Genève, Chemin Pegasi 51, 1290 Versoix, Switzerland
e-mail: Simone.Bavera@unige.ch
² Gravitational Wave Science Center (GWSC), Université de Genève, 1211 Geneva, Switzerland
³ Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern University, 1800 Sherman Ave, Evanston, IL 60201, USA
⁴ Kavli Institute for Cosmological Physics, The University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA
⁵ Enrico Fermi Institute, The University of Chicago, 933 East 56th Street, Chicago, IL 60637, USA
⁶ IAASARS, National Observatory of Athens, Vas. Pavlou and I. Metaxa, Penteli 15236, Greece

Received: 6 April 2022
Accepted: 19 June 2022

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, χ_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 χ_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. Given the limited horizon of current gravitational-wave detectors, z ≲ 1, highly rotating black hole mergers in the LIGO–Virgo observed χ_eff − 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 χ_eff − z as predicted by our model of isolated binary evolution.