The Maximum Mass Ratio of Hierarchical Binary Black Hole Mergers May Cause the <i>q</i> – <i>χ</i> _eff Correlation

Abstract Regardless of their initial spins, the merger of two roughly equal mass black holes (BHs) produces a remnant BH of dimensionless spin 0.69. Such remnants can merge with other BHs in dense stellar environments and produce hierarchical mergers. Analyzing the latest catalog binary black hole (BBH) mergers from the LIGO–Virgo–KAGRA detectors, we identify a subpopulation with primary spins consistent with such hierarchical mergers. Consistent with astrophysical expectations for mergers of second-generation BHs with first-generation BHs, we find that this subpopulation has mass ratios below <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0.5</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>9</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.23</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.18</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> . We also infer that 19%–88% of the BBH population below this mass ratio is consistent with belonging to the hierarchically merged population. Our results offer a natural explanation for the narrowing of the effective inspiral spin distribution with mass ratio observed in other studies.