High mass but low spin: an exclusion region to rule out hierarchical black-hole mergers as a mechanism to populate the pair-instability mass gap

TL;DR

This paper identifies an exclusion region in black hole mass-spin space that hierarchical mergers cannot easily populate, providing a way to distinguish alternative formation mechanisms for massive black holes beyond the pair-instability mass gap.

Contribution

It introduces an exclusion region in the mass-spin parameter space that challenges hierarchical merger models for black holes above 50 solar masses.

Findings

Hierarchical mergers cannot easily produce black holes with mass >50 M_ and spin 0.2.

Detection of such black holes would suggest alternative formation channels.

Fine-tuned hierarchical mergers are required to explain outliers in this region.

Abstract

The occurrence of pair-instability supernovae is predicted to prevent the formation of black holes with masses $\gtrsim 50 M_\odot$. Recent gravitational-wave detections in this mass range require an explanation beyond that of standard stellar collapse. Current modeling strategies include the hierarchical assembly of previous generations of black-hole mergers as well as other mechanisms of astrophysical nature (lowered nuclear-reaction rates, envelope retention, stellar mergers, accretion, dredge-up episodes). In this paper, we point out the occurrence of an exclusion region that cannot be easily populated by hierarchical black-hole mergers. A future gravitational-wave detection of a black hole with mass $\gtrsim 50M_\odot$ and spin $\lesssim 0.2$ will indicate that the pair-instability mass gap is polluted in some other way. Such a putative outlier can be explained using hierarchical mergers only with considerable fine-tuning of both mass ratio and spins of the preceding black-hole merger -- an assumption that can then be cross-checked against the bulk of the gravitational-wave catalog.