Pair instability should prevent the direct formation of black holes above about 50 M⊙, creating a ‘pair-instability’ mass gap. Yet gravitational-wave observations have detected black holes in this mass range. These systems can be explained with uncertainties in massive-star evolution, or hierarchical mergers in stellar clusters, which are expected to produce large spins with isotropic orientations. Here we present evidence for the pair-instability mass gap in the LIGO–Virgo–KAGRA fourth transient catalogue, with a lower edge at <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$44.{3}_{-3.5}^{+5.9}\,{M}_{\odot }$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>44</mn> <mo>.</mo> <msubsup> <mrow> <mn>3</mn> </mrow> <mrow> <mo>−</mo> <mn>3.5</mn> </mrow> <mrow> <mo>+</mo> <mn>5.9</mn> </mrow> </msubsup> <mspace width="0.25em" /> <msub> <mrow> <mi>M</mi> </mrow> <mrow> <mo>⊙</mo> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation>. We also obtain a measurement of the 12C(α, γ)16O reaction rate, yielding an S-factor of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$26{8}_{-116}^{+195}\,{\rm{keV\; b}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>26</mn> <msubsup> <mrow> <mn>8</mn> </mrow> <mrow> <mo>−</mo> <mn>116</mn> </mrow> <mrow> <mo>+</mo> <mn>195</mn> </mrow> </msubsup> <mspace width="0.25em" /> <mi mathvariant="normal">keV b</mi> </mrow> </math></EquationSource> </InlineEquation>, a parameter critical for modelling helium burning and stellar evolution. The data reveal two populations: a low-spin group with no black holes above the gap, and a high-spin, isotropic group that extends across the full mass range and occupies the gap, consistent with hierarchical mergers. These findings are consistent with pair instability playing a role in shaping the black hole mass spectrum, point to a connection between gravitational-wave astronomy and nuclear astrophysics, and highlight dense stellar clusters as key environments in the growth of black holes.

Gravitational-wave constraints on the pair-instability mass gap and nuclear burning in massive stars

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2026年5月7日

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Fabio Antonini,
Isobel M. Romero-Shaw,
Thomas Callister,
Fani Dosopoulou,
Debatri Chattopadhyay,
Yonadav Barry Ginat,
Mark Gieles,
Michela Mapelli

摘要

Pair instability should prevent the direct formation of black holes above about 50 M_⊙, creating a ‘pair-instability’ mass gap. Yet gravitational-wave observations have detected black holes in this mass range. These systems can be explained with uncertainties in massive-star evolution, or hierarchical mergers in stellar clusters, which are expected to produce large spins with isotropic orientations. Here we present evidence for the pair-instability mass gap in the LIGO–Virgo–KAGRA fourth transient catalogue, with a lower edge at $44.{3}_{-3.5}^{+5.9}\,{M}_{\odot }$ $44 . 3_{- 3.5}^{+ 5.9} M_{⊙}$ . We also obtain a measurement of the ¹²C(α, γ)¹⁶O reaction rate, yielding an S-factor of $26{8}_{-116}^{+195}\,{\rm{keV\; b}}$ $26 8_{- 116}^{+ 195} keV b$ , a parameter critical for modelling helium burning and stellar evolution. The data reveal two populations: a low-spin group with no black holes above the gap, and a high-spin, isotropic group that extends across the full mass range and occupies the gap, consistent with hierarchical mergers. These findings are consistent with pair instability playing a role in shaping the black hole mass spectrum, point to a connection between gravitational-wave astronomy and nuclear astrophysics, and highlight dense stellar clusters as key environments in the growth of black holes.