The Steep Redshift Evolution of the Hierarchical Binary Black Hole Merger Rate May Cause the <i>z</i> - <i>χ</i> _eff Correlation

Abstract There is growing evidence from gravitational-wave (GW) observations that some merging black holes (BHs) are created from previous mergers. Using the prediction that these hierarchically merged BHs have dimensionless spin magnitudes of χ ≈ 0.69, we identify a subpopulation in the GW data consistent with a hierarchical-merger origin in dense star clusters. This subpopulation’s primary mass distribution peaks at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>17</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>0</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4.4</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>18.3</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:math> , which is approximately twice as large as its secondary mass distribution’s mode ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>10</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>5</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4.7</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>29.7</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:math> ), and its spin tilt distribution is consistent with isotropy. Our inferred secondary mass distributions imply that isolated binary evolution may still be needed to explain the entirety of the 9 M ⊙ peak. Surprisingly, we find that the rate of hierarchical mergers may evolve more steeply with redshift than the rest of the population (98.0% credibility): the fraction of all binary BHs that are hierarchically formed at z = 0.1 is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0.0</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.02</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.05</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , compared to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0.0</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>9</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.07</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.11</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> at z = 1. This provides an explanation for the previously discovered broadening of the effective spin distribution with redshift. Our results have implications for star cluster formation histories, as they suggest the potential existence of a high-redshift population of massive, compact clusters.