The Pair-instability Mass Gap for Black Holes

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 o˙ and M high ≈ 130 M o˙. These calculations have been challenged by recent LIGO observations that show many black holes merging with individual masses M low ⪆ 65 M o˙. 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 o˙ and M high as large as 161 M o˙. Rapid rotation could further increase M low to ∼70 M o˙, 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.