The Pair-Instability Mass Gap for Black Holes

Abstract

Stellar evolution theory predicts a "gap" in the black hole birth function caused by the pair instability. 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.

Hierarchical mergers of stellar-mass black holes and their gravitational-wave signatures

“…Similarly, Renzo et al 42 found a threshold of 48M , robust against the treatment of convection in the stellar evolutionary models. Additional pieces of the puzzle include potential correlations of the location of the pair-instability gap with the BH spin 43,44 which might the impact edge of the gap by ∼ 15%, uncertainties in current stellar-wind prescriptions, 45,46 as well as dredge-up episode during the helium-burning phase 47 which can also push the lower edge of the mass gap all the way to ∼ 90M . GW observations from the first two observing runs of Advanced LIGO and Virgo provided observational evidence for a dearth of BHs heavier than ∼ 45M , [48][49][50][51] widely thought to be a consequence pair instabilities in supernovae.…”

“…The pair-instability process immediately translates into a promising signature of hierarchical mergers in GW observations: if BHs with 50M m 120M cannot be produced by stars, they might well be the remnants of previous BH mergers. Possible caveats to this statement include envelope retention in low-metallicity population III stars, [52][53][54] stellar mergers prior to BH formation, 37,[55][56][57] evolution in detached binaries, 44 as well as accretion in either molecular clouds, 58 minihalos, 59 dense clusters, 60,61 or isolated binaries. 62…”

A Long-term Study of Ultraluminous X-ray Sources in NGC 891

“…Using Chandra's high spatial resolution, we find the unabsorbed luminosity at 9 Mpc for ULX-1 to be approximately (5.8 ± 0.5) × 10 39 erg s −1 and for ULX-2 to be (9 ± 1) × 10 39 erg s −1 . Assuming isotropic emission and Eddington-limited accretion, these luminosities would correspond to ∼ 50 − 80 M black holes, placing these sources in the upper stellar black hole mass gap [77]. This would reinforce the interpretation of ULXs as simply an extension in the population of stellar mass black holes [78].…”

High mass but low spin: an exclusion region to rule out hierarchical black-hole mergers as a mechanism to populate the pair-instability mass gap

“…Di Carlo et al 2019;Marchant et al 2019), as well as lowered nuclear-reaction rates and stellar rotation (e.g. Marchant & Moriya 2020;Costa et al 2021;Woosley & Heger 2021).…”

“…The mass of a stellar-origin BH strongly depends on the details of the evolution of its progenitor star and many evolutionary processes are still uncertain. Recent studies have shown that one can populate the mass gap by exploiting uncertainties in the 12 C(α, γ) 16 O reaction rate (Takahashi 2018;Belczynski 2020;Farmer et al 2020;Costa et al 2021;Woosley & Heger 2021), as well as by reviewing stellar-wind prescriptions (Leung et al 2019;Belczynski et al 2020b) and including stellar rotation (Marchant & Moriya 2020;Woosley & Heger 2021). The presence of stellar companions and/or gaseous environments might also aid the formation of heavier BHs via either stellar mergers (Di Carlo et al 2019, 2020Spera et al 2019;Renzo et al 2020a;Kremer et al 2020;González et al 2021) or accretion episodes (Marchant et al 2019;Roupas & Kazanas 2019;van Son et al 2020;Safarzadeh & Haiman 2020;Rice & Zhang 2021;Natarajan 2021).…”