Predicting the Heaviest Black Holes below the Pair Instability Gap

TL;DR

This study uses detailed stellar evolution models to explore the potential for stars to produce black holes heavier than the traditional pair instability gap, especially at low metallicity, challenging previous assumptions.

Contribution

It provides a comprehensive grid of models showing that stars can form black holes above the traditional pair instability mass gap, influenced by stellar interior physics and envelope retention.

Findings

Maximum BH mass below PI is about 93.3 solar masses.

Stars at low metallicity can produce heavier BHs than previously thought.

Distribution of BHs above the PI gap depends on stellar physics, not just initial mass.

Abstract

Traditionally, the pair instability (PI) mass gap is located between 50\,and 130\,$M_{\odot}$, with stellar mass black holes (BHs) expected to "pile up" towards the lower PI edge. However, this lower PI boundary is based on the assumption that the star has already lost its hydrogen (H) envelope. With the announcement of an "impossibly" heavy BH of 85\,$M_{\odot}$ as part of GW\,190521 located inside the traditional PI gap, we realised that blue supergiant (BSG) progenitors with small cores but large Hydrogen envelopes at low metallicity ($Z$) could directly collapse to heavier BHs than had hitherto been assumed. The question of whether a single star can produce such a heavy BH is important, independent of gravitational wave events. Here, we systematically investigate the masses of stars inside the traditional PI gap by way of a grid of 336 detailed MESA stellar evolution models calculated across a wide parameter space, varying stellar mass, overshooting, rotation, semi-convection, and $Z$. We evolve low $Z$ stars in the range $10^{-3} < Z / Z_{\odot} < Z_{\rm SMC}$, making no prior assumption regarding the mass of an envelope, but instead employing a wind mass loss recipe to calculate it. We compute critical Carbon-Oxygen and Helium core masses to determine our lower limit to PI physics, and we provide two equations for $M_{\text{core}}$ and $M_{\text{final}}$ that can also be of use for binary population synthesis. Assuming the H envelope falls into the BH, we confirm the maximum BH mass below PI is $M_{\text{BH}} \simeq 93.3$ $M_{\odot}$. Our grid allows us to populate the traditional PI gap, and we conclude that the distribution of BHs above the traditional boundary is not solely due to the shape of the initial mass function (IMF), but also to the same stellar interior physics (i.e. mixing) that which sets the BH maximum.