Direct N-body simulations of rotating and extremely massive Population III star clusters

¹ Astronomisches Rechen-Inst., Zentrum für Astronomie, Univ. of Heidelberg, Mönchhofstr. 12-14, 69120 Heidelberg, Germany
² Center for Information Science, Fukui Prefectural University, 4-1-1 Matsuoka Kenjojima, Eiheiji-cho, Fukui 910-1195, Japan
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, P.le Aldo Moro, 5, 00185 Rome, Italy
⁶ Inst. für Theoretische Astrophysik, Zentrum für Astronomie, Univ. Heidelberg, Albert Ueberle Str. 2, 69120 Heidelberg, Germany
⁷ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁸ Gran Sasso Science Institute (GSSI), 67100 Viale Francesco Crispi 7, L’Aquila, Italy
⁹ INFN, Laboratori Nazionali del Gran Sasso, 67100 Assergi, Italy
¹⁰ National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Rd., Chaoyang District, 100101 Beijing, China
¹¹ Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Lu 5, Haidian Qu, 100871 Beijing, China

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Received: 18 December 2025
Accepted: 24 March 2026

Abstract

Aims. We present eight direct N-body simulations with NBODY6++GPU of extremely massive, initially rotating Population III star clusters with 1.01 × 10⁵ stars.

Methods. Our models include primordial binaries, a continuous initial mass function, differential rotation, tidal mass loss, updated fitting formulae for extremely massive metal-poor Population III stars, and general-relativistic merger recoil kicks. We assess their impact on cluster dynamics.

Results. All runs form black holes below, within, and above the pair-instability gap, with multi-generation growth. Faster-rotating clusters core-collapse earlier; post-collapse clusters host a rotating, axisymmetric subsystem of intermediate-mass black holes (IMBHs) at the centre and an expanding halo of lower-mass objects. Pair-instability supernovae and compact-object formation at ∼2-3 Myr sharply reduce total mass and a large fraction of the cluster’s angular momentum. All Population III clusters in our simulations have the gravothermal-gravogyro catastrophe phase.

Conclusions. We confirm two of the hypothesized formation channels of galactic nucleus seed black holes: gravitational runaway mergers of black holes and of Population III stars, which core-collapse into IMBHs thereafter. A higher initial star cluster bulk rotation correlates with earlier core collapse and, in the event counts reported here, with more coalescences and collisions, as well as lower retained (compact) binary abundances. Initial bulk rotation is a primary control parameter of cluster evolution: faster rotation accelerates early angular-momentum transport, gravothermal collapse, mass segregation, and amplifies post-collapse expansion, which also favours the formation of a compact central IMBH subsystem.