Rapid formation of a very massive star (>50000 M_⊙), and subsequently, of an IMBH, from runaway collisions

Direct N-body and Monte Carlo simulations of dense star clusters

¹ Astronomisches Rechen-Institut, Zentrum für Astronomie, Mönchhofstrasse 12-14, 69120 Heidelberg, Germany
² Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, 00-716 Warsaw, Poland
³ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁴ National Astronomical Observatories, 20A Datun Rd., Chaoyang District, 100101 Beijing, China
⁵ Kavli Institute for Astronomy and Astrophysics, Peking University, 5 Yi He Yuan Road, Haidian District, Beijing 100871, China
⁶ Department of Physics, New York University Abu Dhabi, PO Box 129188 Abu Dhabi, UAE
⁷ Center for Astrophysics and Space Science (CASS), New York University Abu Dhabi, PO Box 129188, Abu Dhabi, UAE
⁸ Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Rome, Italy
⁹ Departamento de Astronomía, Facultad Ciencias Físicas y Matemáticas, Universidad de Concepción, Av. Esteban Iturra s/n Barrio Universitario, Casilla 160-C, Conc epción, Chile
¹⁰ Gran Sasso Science Institute, Viale F. Crispi 7, 67100 L’Aquila, Italy
¹¹ Physics and Astronomy Department Galileo Galilei, University of Padova, Vicolo dell’Osservatorio 3, 35122, Padova, Italy
¹² INFN – Laboratori Nazionali del Gran Sasso, 67100 L’Aquila, (AQ), Italy
¹³ INAF – Osservatorio Astronomico d’Abruzzo, Via M. Maggini snc, 64100 Teramo, Italy
¹⁴ Faculty of Mathematics and Computer Science, A. Mickiewicz University, Uniwersytetu Poznariskiego 4, 61-614 Poznari, Poland
¹⁵ OzGrav: The ARC Centre of Excellence for Gravitational Wave Discovery, Hawthorn, VIC 3122, Australia
¹⁶ Centre for Astrophysics and Supercomputing, Department of Physics and Astronomy, John Street, Hawthorn, Victoria, Australia
¹⁷ Main Astronomical Observatory, National Academy of Sciences of Ukraine, 27 Akademika Zabolotnoho St, 03143 Kyiv, Ukraine
¹⁸ Departamento de Astronomía, Universidad de Chile, Casilla 36-D, Santiago, Chile
¹⁹ Donostia International Physics Center, Paseo Manuel de Lardizabal 4, 20118 Donostia-San Sebastián, Spain
²⁰ Universität Heidelberg, Seminarstrasse 2, 69117 Heidelberg, Germany
²¹ Department of Physics, Xi’an Jiaotong-Liverpool University, 111 Ren’ai Road, Dushu Lake Science and Education Innovation District, Suzhou 215123, Jiangsu Province, PR China
²² Shanghai Key Laboratory for Astrophysics, Shanghai Normal University, 100 Guilin Road, Shanghai 200234, PR China
²³ Department of Earth Science and Astronomy, College of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8902, Japan
²⁴ Center for Information Science, Fukui Prefectural University, 4-1-1 Matsuoka Kenjojima, Eiheiji-cho, Fukui, 910-1195, Japan
²⁵ Center for Cosmology and Computational Astrophysics, Institute for Advanced Study in Physics, Zhejiang University, Hangzhou 310027, China
²⁶ Institute of Astronomy, School of Physics, Zhejiang University, Hangzhou 310027, China
²⁷ Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, 85741 Garching, 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: 26 April 2025
Accepted: 19 October 2025

Abstract

Context. We present simulations of a massive young star cluster using the codes Nbody6++GPU and MOCCA. The cluster is initially more compact than previously published models. It contains one million stars and has a total mass of 5.86 × 10⁵ M_⊙ and a half-mass radius of 0.1 pc.

Aims. We analyzed the formation and growth of a very massive star (VMS) through successive stellar collisions and investigated the subsequent formation of an intermediate-mass black hole (IMBH) in the core of a dense star cluster.

Methods. We used direct N-body and Monte Carlo simulations that incorporated updated stellar evolution prescriptions for single and binary stellar evolution (SSE and BSE) tailored to massive stars and VMSs. These include revised treatments of stellar radii, rejuvenation, and mass loss during collisions. While the prescriptions represent reasonable extrapolations into the VMS regime, the internal structure and thermal state of VMSs that formed through stellar collisions remain uncertain, and future work may require further refinement. Results. Runaway stellar collisions in the cluster core produce a VMS that exceeds 5 × 10⁴ M_⊙ within 5 Myr that subsequently collapses into an IMBH. We stress that further work on stellar astrophysics is needed, particularly in the context of VMS formation. The VMS formation currently represents strong uncertainties.

Conclusions. Our model suggests that dense stellar environments may enable the formation of VMSs and massive black hole seeds through runaway stellar collisions. These results provide a potential pathway for early black hole growth in star clusters and offer a theoretical context for interpreting recent observations with the James Webb Space Telescope of young compact clusters at high redshift.