Black hole mass function shift in proto-stellar clusters driven by gas accretion

¹ Dipartimento di Fisica “G. Occhialini”, Universitá degli Studi di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
² Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy

^★ Corresponding author: zacharias.roupas@unimib.it

Received: 16 July 2025
Accepted: 10 September 2025

Abstract

The James Webb Space Telescope (JWST) has observed compact, massive proto-stellar clusters of low metallicity in the Cosmic Gems arc galaxy at high redshift, which represent likely precursors to globular clusters. We model the mass growth of stellar black holes (BHs) during the first few million years of the life of a massive, compact, gaseous stellar cluster before stellar feedback expels the primordial gas. At high redshift, in a lower-metallicity environment stellar winds get weaker, allowing for larger gas-depletion timescales in the cluster despite energetic pair-instability supernova (PISN) feedback for sufficiently compact clusters. Mass segregation drives the massive stellar progenitors of BHs in the center of the cluster, where gas is densest. We estimate the conditions for which the initial black hole mass function (BHMF), with a PISN-induced cutoff of <55 M_⊙, gets shifted to values within the upper BH mass gap, ~60–130 M_⊙, or higher, as observed by the LIGO-Virgo-KAGRA gravitational wave (GW) experiments. We find that the BHs are shifted by the end of gas depletion to values within and above the mass gap, well within the range of BH components of the recent GW-signal GW231123, depending on the total mass, star formation efficiency, metallicity, and compactness. The individual BH mass increase approximately follows a surprisingly steep power law with respect to the initial BH mass with an exponent in the range of ≈4–6. This occurs in gaseous proto-stellar clusters that are sufficiently massive and compact, with typical values for the total mass of ~10⁶ M_⊙ and size of ~1 pc. Our analysis suggests that proto-stellar clusters at high redshift such as Cosmic Gems arc clusters have generated through early gas accretion, BHs as heavy as ~10²−10³ M_⊙.