Efficient black hole seed formation in low-metallicity and dense stellar clusters with implications for JWST sources

¹ Astronomisches Rechen-Institut, Zentrum für Astronomie, University of Heidelberg, Mönchhofstrasse 12-14, 69120 Heidelberg, Germany
² Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, 00-716 Warsaw, Poland
³ Department of Physics, New York University Abu Dhabi, PO Box 129188 Abu Dhabi, UAE
⁴ Center for Astrophysics and Space Science (CASS), New York University Abu Dhabi, PO Box 129188, Abu Dhabi, UAE
⁵ Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Rome, Italy
⁶ Departamento de Astronomía, Facultad Ciencias Físicas y Matemáticas, Universidad de Concepción, Av. Esteban Iturra s/n Barrio Universitario, Casilla 160-C, Concepción, Chile
⁷ Departamento de Astronomía, Universidad de Chile, Casilla 36-D, Santiago, Chile
⁸ National Astronomical Observatories and Key Laboratory of Computational Astrophysics, Chinese Academy of Sciences, 20A Datun Rd., Chaoyang District, Beijing 100012, China
⁹ Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Lu 5, Haidian Qu, 100871 Beijing, China
¹⁰ OzGrav: The ARC Centre of Excellence for Gravitational Wave Discovery, Hawthorn, VIC 3122, Australia
¹¹ Centre for Astrophysics and Supercomputing, Department of Physics and Astronomy, John Street, Hawthorn, Victoria 3122, Australia
¹² Gran Sasso Science Institute, Viale F. Crispi 7, 67100 L’Aquila, Italy
¹³ Physics and Astronomy Department Galileo Galilei, University of Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy
¹⁴ INFN – Laboratori Nazionali del Gran Sasso, 67100 L’Aquila, (AQ), Italy
¹⁵ INAF – Osservatorio Astronomico d’Abruzzo, Via M. Maggini snc, 64100 Teramo, Italy
¹⁶ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany

^★ Corresponding authors: This email address is being protected from spambots. You need JavaScript enabled to view it. ; This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 15 August 2025
Accepted: 16 December 2025

Abstract

Context. Recent observations with the James Webb Space Telescope (JWST) have revealed the presence of young massive clusters (YMCs) as building blocks of the first galaxies during the first billion years of the Universe. They are not only important constituents of the galaxies, but also potential birthplaces of very massive stars (VMSs) and black hole (BH) seeds.

Aims. In this paper, we investigate whether runaway stellar collisions in extremely dense clusters inevitably lead to the formation of VMSs and BH seeds. We focus on clusters with initial half-mass densities of ρ_h ≳ 10⁸ M_⊙ pc⁻³ at very low metallicity (Z = 10⁻⁴), using idealized initial conditions that assume a fully formed, gas-free, monolithic stellar system. Our goal is to follow their early internal evolution and quantify the efficiency of collisional growth.

Methods. We use NBODY6++GPU and MOCCA, including the latest updates of the single stellar evolution (SSE) and binary stellar evolution (BSE), along with specific routines to handle the formation, growth through collisions, and dynamical evolution of VMSs.

Results. Our direct N-body and Monte Carlo simulations show that VMSs form rapidly and unavoidably through repeated collisions, reaching final masses of ~5 × 10³ to 4 × 10⁴ M_⊙, before collapsing into BH seeds of similar mass in less than 4 Myr. These results confirm the existence of a critical mass scale at which collisional growth becomes highly efficient, enabling the formation of VMSs and potentially intermediate-mass BHs.

Conclusions. We identify a critical mass–density threshold beyond which clusters undergo runaway collisions, leading to efficient BH-seed formation. For YMCs detected with JWST, we expect efficiencies up to ~10%, corresponding to BH masses as large as 10⁵ M_⊙. We predict a BH mass–cluster mass scaling relation of log(M_BH / M_⊙) = −0.76 + 0.76 log(M / M_⊙). Frequent VMS formation in this regime may also provide a natural explanation for the strong nitrogen enrichment observed in some high-redshift galaxies.