Resolving The Peak Of The Black Hole Mass Spectrum

Gravitational wave detections of binary black hole (BH) mergers have begun to sample the cosmic BH mass distribution. The standard theory of stellar evolution predicts a gap in the BH mass distribution due to pair-instability supernova (PISN). Determining the upper and lower edges of the BH mass gap can be useful for interpreting gravitational wave detections from merging BHs and constraining uncertain nuclear physics. We use the MESA stellar evolution code to evolve massive helium cores until they either collapse to form a BH or explode as a PISN without leaving a compact remnant. We calculate the boundaries of the lower BH mass gap for nuclear cross-sections in the range S(300 keV) = (77,203) keV b, corresponding to the ±3σ uncertainty in new high resolution tabulated ¹²C(α,γ)¹⁶O reaction rate probability distribution functions. We extensively test the temporal and mass resolution to resolve the peak of the BH mass spectrum across the BH mass gap. We explore the convergence with respect to convective mixing and nuclear burning, finding that significant time resolution is needed to achieve convergence. We establish a new lower edge of the upper mass gap as M_lower ≃ 60 (+32,-14) M_⊙ from the ±3σ uncertainty in the ¹²C(α,γ)¹⁶O rate. We explore the effect of a larger 3-α rate on the lower edge of the upper mass gap, finding M_lower ≃ 69 (+34,-18) M_⊙. We compare our results with BHs reported in the Gravitational-Wave Transient Catalog.