̊m M _⊙ and sizes of ∼ 1, ̊m pc, as has recently been revealed by James Webb Space Telescope observations at z∼ 10. Sufficiently high compactness can provide a time window for early-formed stellar black holes (BHs) to accrete primordial gas. We developed a semi-analytic model to follow BH spin-up and determine the final spin distribution of stellar BHs that grow in mass via gas accretion within compact gaseous proto-stellar clusters. The velocity shear within a BH's sphere of influence induces the formation of an accretion disk that is repeatedly disrupted by stochastic perturbations to the BH motion. We assumed low initial BH spins of a_ *, ̊m ini = 0. 01, consistent with stellar-evolution models with efficient angular-momentum transport, and we restricted initial BH masses to values below the upper BH mass gap, m_ ̊m BH, ini < 55, ̊m M _⊙. Our analysis shows a strong BH spin-mass correlation, obtained within ∼ 10, ̊m Myr when gas is depleted. Low-spin BHs, a_ * łeq 0. 3, are predominantly low-mass, m_ ̊m BH łesssim 25, ̊m M _⊙, in contrast to high-spin BHs, a_ * ≥ 0. 7, which are predominantly high-mass, m_ ̊m BH ≳ 65, ̊m M _⊙. Notably, there exist also low-spin, high-mass outliers with ∼ 1 mass-gap BH per cluster expected to have a_ * ∼ 0. 1. The general trend, however, expressed by the median spin as a function of final BH mass, is well fit by a high-spin saturating exponential with a transition mass of ∼ 50, ̊m M _⊙. For m_ ̊m BH ≥ 100, ̊m M _⊙ the median spin is bar a _ * ∼ 0. 90, with the central 68% of the distribution spanning a_ * ∼ 0. 70 - 0. 96, in striking agreement with the estimated spins of the BH components of the gravitational-wave signal GW231123. These spin values persist up to the highest masses generated by our mechanism, m_ ̊m BH ∼ 10³, ̊m M _⊙.
Zacharias Roupas (2026) studied this question.