Evidence of the pair-instability gap from black-hole masses.

Abstract

Stellar theory predicts a forbidden range of black-hole masses between approximately 50 M_⊙ and 130 M_⊙ owing to pair-instability supernovae^1-7, but evidence for such a gap in the mass distribution from gravitational-wave astronomy has proved elusive. Early hints of a cut-off in black-hole masses at about 45 M_⊙ disappeared with the subsequent discovery of more massive binary black holes^8,9. Here we report evidence of the pair-instability gap in LIGO-Virgo-KAGRA's fourth Gravitational-Wave Transient Catalog (GWTC-4), with a lower boundary of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn> <msubsup><mrow><mn>4</mn></mrow> <mrow><mo>-</mo> <mn>4</mn></mrow> <mrow><mo>+</mo> <mn>5</mn></mrow> </msubsup> <mspace></mspace> <msub><mrow><mi>M</mi></mrow> <mrow><mo>⊙</mo></mrow> </msub> </math> (90% credibility). Although the gap is not present in the distribution of primary masses m₁ (the bigger of the two black holes in a binary system), it appears unambiguously in the distribution of secondary masses m₂, in which m₂ ≤ m₁. The location of the gap lines up well with a previously identified transition in the binary black-hole spin distribution; binaries with primary components in the gap tend to spin more rapidly than those below the gap. We interpret these findings as evidence for a subpopulation of hierarchical mergers: binaries in which the primary component is the product of a previous black-hole merger and thus populates the gap. Our measurement of the location of the pair-instability gap constrains the S-factor for ¹²C(α, γ)¹⁶O at 300 keV to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>26</mn> <msubsup><mrow><mn>0</mn></mrow> <mrow><mo>-</mo> <mn>108</mn></mrow> <mrow><mo>+</mo> <mn>190</mn></mrow> </msubsup> <mspace></mspace> <mrow><mrow><mi>keV</mi></mrow> </mrow> <mspace></mspace> <mrow><mrow><mi>barns</mi></mrow> </mrow> </math> .