An upper limit on the spins of merging binary black holes formed through isolated binary evolution

¹ Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium
² University of Oxford, St Edmund Hall, Oxford OX1 4AR, UK
³ School of Physics and Astronomy, Monash University, Clayton, VIC 3800, Australia
⁴ The ARC Centre of Excellence for Gravitational Wave Discovery – OzGrav, Clayton, VIC 3800, Australia

^⋆ Corresponding author; pablo.marchant@kuleuven.be

Received: 7 October 2023
Accepted: 19 August 2024

Abstract

Context. As the sensitivity of ground-based gravitational wave detectors progressively increases, observations of black hole mergers will provide us with the joint distribution of their masses and spins. This will be a critical benchmark to validate different formation scenarios.

Aims. Merging binary black holes formed through the evolution of isolated binary systems require both components to be stripped of their hydrogen envelopes before core-collapse. The rotation rates of such stripped stars are constrained by the critical rotation limit at their surface, including its deviation from the Keplerian value owing to the outward force provided by radiation. This sets a restriction on their angular momentum content at core-collapse. We aim to determine if this restriction plays a role in the spins of binary black hole mergers.

Methods. We used detailed calculations of stripped stars with the MESA code at low metallicities (Z = Z_⊙/10, Z_⊙/50, and Z_⊙/250) to determine the dimensionless spins of black holes produced by critically rotating stellar progenitors. To study how such progenitors can arise, we considered their formation through chemically homogeneous evolution (CHE) in binary stars. We used a semi-analytical model to study the physical processes that determine the final angular momentum of CHE binaries, and compared our results against available population synthesis models that rely on detailed binary evolution calculations.

Results. We find that above black hole masses of ≃25 M_⊙, the dimensionless spin parameter of critically rotating stripped stars (a = Jc/(GM²)) is below unity. This results in an exclusion region at high chirp masses and effective spins that cannot be populated by isolated binary evolution. CHE can produce binaries where both black holes hit this limit, producing a pileup at the boundary of the excluded region. High-spin black holes arise from very low-metallicity CHE systems with short delay times, which merge at higher redshifts. On the other hand, the contribution of CHE to merging binary black holes detected in the third observing run of the LVK collaboration is expected to be dominated by systems with low spins (χ_eff < 0.5) that merge near redshift zero. Owing to its higher projected sensitivity and runtime, the fourth observing run of the LVK collaboration can potentially place constraints on the high-spin population and the existence of a limit set by critical rotation.