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

TL;DR

This work addresses whether gravitational-wave inferences of the pair-instability–induced mass gap are robust to modeling choices and data limitations. It uses full Bayesian parameter estimation on simulated GW catalogs and compares parametric and nonparametric population models (including PixelPop) to GWTC-4 data, assessing both current constraints and future O4 prospects. The findings indicate that GWTC-4 data are compatible with a lower-edge cutoff near $40$--$50\,M_\odot$ under certain population models, while nonparametric analyses favor a declining secondary-mass density without requiring a sharp cutoff; predictive checks support overall consistency but reveal model-dependence. Projections for the end of O4 suggest substantial improvements in the precision of the cutoff mass and modest gains in GW-only cosmology, though intrinsic limitations remain, underscoring the need for robust validation of astrophysical claims drawn from GW catalogs.

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 is yet to be tested. To this end, we simulate a comprehensive suite of gravitational-wave catalogs with full Bayesian parameter estimation and analyze them with parametric population models. For catalogs similar to GWTC-4, confident identification of a cutoff is not guaranteed, but GWTC-4 results are compatible with the best constraints among our simulations. Conversely, spurious false 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 $\gtrsim20\%$, but a cutoff at $40$-$50M_\odot$ yields only a lower bound on the $^{12}\mathrm{C}(α,γ)^{16}\mathrm{O}$ reaction rate, which in terms of the S-factor at $300\,\mathrm{keV}$ may be $S_{300}\gtrsim125\,\mathrm{keV}\,\mathrm{b}$ at $90\%$ credibility by the end of O4. 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 where a cutoff is present. We use the simple focus of this study to emphasize that such tests are necessary to make astrophysical claims from gravitational-wave catalogs going forward.

Figures (12)

• Figure 1: Mass distributions of BHs in merging binaries inferred from GWTC-3 (blue) and GWTC-4 excluding GW231123 (orange) using three parametric models (top three rows) and a nonparametric model (bottom row). The masses for GW231123 (green) are included for reference. The left column shows central 90% posterior credible regions, with population constraints in terms of the probability density of logarithmic BH mass. The right column shows the posteriors of the maximum-mass parameters for the parametric models and three upper mass percentiles (99%, 99.9%, and 99.99%) for the nonparametric model. Primary ($m_1$) and secondary ($m_2$) BH masses are distinguished by filled and unfilled regions, respectively.
• Figure 2: Self-consistent data-level PPC showing the cumulative distribution of highest-likelihood secondary BH masses for: events in GWTC-4 (black); central 50%, 90%, and 99% posterior credible regions for simulated observations based on the Single Power Law + 2 Peaks + Cutoff fit to GWTC-4 (darker to lighter blue); and the highest-likelihood population prediction (red). Central 50%, 90%, and 99% posterior credible intervals for the astrophysical maximum secondary mass (darker to lighter gray) are included for reference.
• Figure 3: Posterior distributions for the source masses of GW190521 inferred from the original LVK PE results (blue) and population-informed measurements using the PixelPop (purple) and Single Power Law + 2 Peaks + Cutoff (red) models. The lower left panel shows the 50%, 90%, and 99% credible regions for the joint posteriors of primary ($m_1$) and secondary ($m_2$) masses, with the gray region excluded by the definition $m_1 \geq m_2$, and the diagonal panels show the individual marginal posteriors.
• Figure 4: Constraints on the mass cutoff for secondary BHs ($m_2$) inferred from GWTC-4 without GW231123 (black) and from simulated catalogs containing 150 O4-like GW events (blue). The true simulated values for the maximum $m_2$ are marked with dashed gray lines. Each column represents a different simulated population indicated in the column titles, with 10 catalog realizations for each. The top row shows posteriors on the maximum $m_2$ when the real and simulated catalogs are analyzed with the parametric Single Power Law + 2 Peak + Cutoff population model. The bottom rows show the posterior 99%, 99.9%, and 99.99% population-level $m_2$ percentiles inferred from each catalog with the nonparametric PixelPop model.
• Figure 5: Posterior distributions for the maximum secondary BH mass (left panel) and the S-factor for the $^{12}\mathrm{C}(\alpha,\gamma)^{16}\mathrm{O}$ reaction at a temperate 300 k eV (right panel), assuming this maximum mass is the lower edge of the PISN mass gap, inferred using the Single Power Law + 2 Peaks + Cutoff model. Results from GWTC-4 (solid black) are used to select a simulated population for this model (dashed gray), from which 10 catalogs and analyzed, each of 150 (blue) and 300 (red) O4-like events.