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

The occurrence of pair-instability supernovae is predicted to prevent the formation of black holes with masses ⪆50 M o˙. 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 ⪆50 M o˙ and spin ≲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.