Measurement prospects for the pair-instability mass cutoff with gravitational waves

Pair-instability supernovae leave behind no compact remnants, resulting in a predicted gap in the distribution of stellar black-hole masses. Gravitational waves from binary black-hole mergers probe the relevant mass range and analyses of the LIGO–Virgo–KAGRA catalog (GWTC-4) indicate a possible mass cutoff at <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>40</a:mn> <a:mo>−</a:mo> <a:mn>50</a:mn> <a:msub> <a:mi>M</a:mi> <a:mo stretchy="false">⊙</a:mo> </a:msub> </a:mrow> </a:math> . However, the robustness of this result remains unclear. To this end, using full Bayesian parameter estimation, we simulate gravitational-wave catalogs with and without such a mass cutoff and then test whether its presence or absence is correctly inferred with parametric population models. For catalogs similar to GWTC-4, confident identification of a cutoff is not guaranteed, but the best constraints among our simulations are compatible with results from GWTC-4 when the model includes a cutoff. Conversely, spurious identification of a cutoff is unlikely. For catalogs expected by the end of the O4 observing run, uncertainty in the cutoff mass is reduced by <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mo>≳</d:mo> <d:mn>20</d:mn> <d:mo>%</d:mo> </d:math> , but a cutoff at <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mrow> <f:mn>40</f:mn> <f:mo>−</f:mo> <f:mn>50</f:mn> <f:msub> <f:mi>M</f:mi> <f:mo stretchy="false">⊙</f:mo> </f:msub> </f:mrow> </f:math> yields only a lower bound on the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mmultiscripts> <i:mi mathvariant="normal">C</i:mi> <i:mprescripts/> <i:none/> <i:mrow> <i:mn>12</i:mn> </i:mrow> </i:mmultiscripts> <i:mo stretchy="false">(</i:mo> <i:mi>α</i:mi> <i:mo>,</i:mo> <i:mi>γ</i:mi> <i:msup> <i:mo stretchy="false">)</i:mo> <i:mn>16</i:mn> </i:msup> <i:mi mathvariant="normal">O</i:mi> </i:math> reaction rate, our most stringent constraints on the S factor at 300 keV being <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>S</o:mi> <o:mn>300</o:mn> </o:msub> <o:mo>≳</o:mo> <o:mn>125</o:mn> </o:math> keV b at 90% credibility. Relative uncertainties on the Hubble parameter <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>H</q:mi> <q:mn>0</q:mn> </q:msub> </q:math> from gravitational-wave data alone can still be up to 100%. We also analyze GWTC-4 with the nonparametric population model, finding that some mass features are more prominent than in parametric models but a sharp cutoff is not required. However, the parametric model passes a likelihood-based predictive test in GWTC-4 and the results are consistent with those from our simulated catalogs with a cutoff. Such tests are necessary to make astrophysical claims from gravitational-wave catalogs.