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 $40$-$50M_\odot$. 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.

💡 Research Summary

This paper investigates how well current and near‑future gravitational‑wave (GW) observations can detect and measure the low‑mass edge of the pair‑instability supernova (PISN) mass gap, a predicted absence of black holes (BHs) in the ∼40–50 M⊙ range. The authors combine a thorough re‑analysis of the latest LIGO‑Virgo‑KAGRA catalog (GWTC‑4) with an extensive suite of simulated GW catalogs that include full Bayesian parameter estimation, and they compare results from several parametric population models as well as a non‑parametric PixelPop model.

Data analysis (GWTC‑4).
Using 69 confident binary‑BH events (excluding the outlier GW231123), three phenomenological models are fit: (i) a single power‑law with two Gaussian peaks plus an independent cutoff for the secondary mass (m₂), (ii) the same without a cutoff, and (iii) a broken power‑law with two peaks. Bayesian evidence strongly favors model (i), with a Bayes factor ≈ 200 over model (ii) and ≈ 600 over the broken‑power‑law baseline. The posterior for the secondary‑mass cutoff peaks at 45 +7 −5 M⊙ (90 % credible interval), a substantial tightening compared with GWTC‑3 (53 +46 −13 M⊙). The primary‑mass maximum remains loosely constrained (> 100 M⊙ at 99 % credibility). Translating the m₂ cutoff into the astrophysical S‑factor for the 12C(α,γ)16O reaction (S₃₀₀) yields S₃₀₀ = 233 +193 −108 keV·b, consistent with nuclear‑physics priors but still broad.

Simulation‑based validation.
To test robustness, the authors generate thousands of mock catalogs that mimic GWTC‑4’s detection efficiency and noise, with and without an intrinsic PISN cutoff. Each mock catalog is analyzed with the same parametric model. For catalogs of GWTC‑4 size, the probability of correctly identifying a true cutoff is only ∼60–70 %, while the false‑positive rate (identifying a cutoff when none exists) is < 5 %. For a future O4‑scale catalog (≈ 200–300 events), the relative uncertainty on the cutoff mass shrinks by > 20 %, and, assuming a true cutoff, the inferred lower bound on S₃₀₀ improves to S₃₀₀ ≳ 125 keV·b (90 % credibility). This demonstrates that O4 will be able to place meaningful nuclear‑physics constraints, even though the cutoff itself may still be statistically modest.

Non‑parametric PixelPop analysis.
PixelPop treats the (m₁, m₂) plane as a set of bins and infers the merger rate density in each bin without imposing hard edges. The resulting secondary‑mass distribution shows a pronounced decline between 30 and 50 M⊙, with 99 %/99.9 %/99.99 % percentile masses of ≈ 33 M⊙, 49 M⊙, 82 M⊙ for GWTC‑4. These percentiles align with the parametric cutoff but PixelPop does not require a strict step‑function; instead it favors a steep but continuous drop. Consequently, high‑mass secondary BHs (> 50 M⊙) are not ruled out, highlighting the limited discriminating power of the current data.

Predictive checks and cosmology.
The authors perform posterior predictive checks by drawing synthetic catalogs from the best‑fit parametric model and comparing the cumulative distribution of the highest‑likelihood secondary masses to the observed GWTC‑4 distribution. The simulated envelopes encompass the data, confirming model adequacy. Using the “spectral‑sirens” approach with a flat ΛCDM prior (Ωₘ fixed), they infer the Hubble constant H₀. Models that include the m₂ cutoff modestly reduce the 90 % credible interval width (≈ 60 km s⁻¹ Mpc⁻¹ for GWTC‑4 vs. ≈ 80 km s⁻¹ Mpc⁻¹ for GWTC‑3), a ∼10 % improvement, indicating that GW‑only H₀ measurements remain limited by sample size and mass‑distribution uncertainties.

Conclusions and outlook.

1. The GWTC‑4 catalog hints at a secondary‑mass cutoff near 45 M⊙, but the evidence is not decisive; the result is sensitive to the chosen parametric form.
2. Simulations show that a true cutoff would be identified with ≈ 60–70 % confidence in a GWTC‑4‑sized catalog, while false detections are rare.
3. By the end of O4, the cutoff mass uncertainty should shrink by > 20 %, enabling a lower bound on the 12C(α,γ)16O S‑factor (S₃₀₀ ≳ 125 keV·b) that is competitive with laboratory extrapolations.
4. Non‑parametric PixelPop confirms a steep decline in the secondary‑mass distribution but does not require a hard edge, underscoring the importance of model‑agnostic checks.
5. Inclusion of a cutoff yields only modest gains for H₀ inference, suggesting that substantial improvements will require many more events or external redshift information.

Overall, the paper demonstrates that robust claims about the PISN mass gap must be backed by predictive validation and that upcoming O4 data will substantially sharpen astrophysical and nuclear‑physics constraints derived from GW observations.