Stellar evolution theory predicts a “gap” in the black hole birth function caused by the pair instability. Many presupernova stars that have a core mass below some limiting value, M _low, after all pulsational activity is finished, collapse to black holes, while more massive ones, up to some limiting value, M _high, explode, promptly and completely, as pair-instability supernovae. Previous work has suggested M _low ≈ 50 M _⊙ and M _high ≈ 130 M _⊙. These calculations have been challenged by recent LIGO observations that show many black holes merging with individual masses M _low ≳ 65 M _⊙. Here we explore four factors affecting the theoretical estimates for the boundaries of this mass gap: nuclear reaction rates, evolution in detached binaries, rotation, and hyper-Eddington accretion after black hole birth. Current uncertainties in reaction rates by themselves allow M _low to rise to 64 M _⊙ and M _high as large as 161 M _⊙. Rapid rotation could further increase M _low to ∼70 M _⊙, depending on the treatment of magnetic torques. Evolution in detached binaries and super-Eddington accretion can, with great uncertainty, increase M _low still further. Dimensionless Kerr parameters close to unity are allowed for the more massive black holes produced in close binaries, though they are generally smaller.

恒星演化理论预测了由这对不稳定性引起的黑洞诞生函数的“缺口”。许多核心质量低于某个极限值M _{低 的前超}新星恒星，在所有脉动活动结束后，坍缩成黑洞，而质量更大的，达到某个极限值M _高，迅速而完全地爆炸，成对-不稳定性超新星。以前的工作建议中号 _低≈50中号 _⊙和中号 _高≈130中号 _⊙。这些计算受到了最近 LIGO 观测的挑战，这些观测显示许多黑洞与单个质量M _低合并≳ 65 M _⊙ . 在这里，我们探讨了影响这种质量差距边界理论估计的四个因素：核反应速率、分离双星的演化、旋转和黑洞诞生后的超爱丁顿吸积。当前反应速率本身的不确定性使得M _low上升到 64 M _⊙，M _high上升到161 M _⊙。快速旋转可能进一步增加中号 _低到约70中号 _⊙，取决于磁转矩的治疗。分离双星和超级爱丁顿吸积的演化可以在很大的不确定性下增加M _再低。接近统一的无量纲克尔参数允许用于在接近双星中产生的更大质量的黑洞，尽管它们通常更小。