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

Abstract

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 $40$-$50M_{\odot }$. 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, 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 $\gtrsim 20\%$, but a cutoff at 40-50$M_{\odot }$ yields only a lower bound on the ${}^{12}\mathrm{C}(\alpha ,\gamma {)}^{16}\mathrm{O}$ reaction rate, our most stringent constraints on the S-factor at $300\mathrm{keV}$ being $S_{300}\gtrsim 125\mathrm{keV}\mathrm{b}$ at $90\%$ credibility. Relative uncertainties on the Hubble parameter $H_0$ from gravitational-wave data alone can still be up to $100\%$. We also analyze GWTC-4 with the nonparametric PixelPop 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 PixelPop results are consistent with those from our simulated catalogs with a cutoff. Such tests are necessary to make astrophysical claims from gravitational-wave catalogs.

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