Formation of supermassive stars in the first stellar clusters: Dependence on the gas temperature

¹ Hamburg Observatory, Hamburg University, Gojenbergsweg 112, 21029 Hamburg, Germany
² Departamento de Astronomía, Facultad Ciencias Físicas y Matemáticas, Universidad de Concepción, Av. Esteban Iturra s/n, Concepción, Chile
³ Department of Physics, Gustaf Hällströmin katu 2, FI-00014 University of Helsinki, Finland
⁴ Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120 Heidelberg, Germany
⁵ Universität Heidelberg, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany

^⋆ Corresponding author: paulo.solar.vera@uni-hamburg.de

Received: 29 May 2024
Accepted: 1 May 2025

Abstract

Context. The origin of supermassive black holes is an open question that has been explored considering gas- and collision-based formation channels to explain the high number of quasars observed in the early Universe. According to numerical simulations, supermassive stars can be formed in atomic cooling halos when protostars reach accretion rates greater than ∼10⁻² M_⊙ yr⁻¹ and fragmentation is inhibited on parsec scales. It remains uncertain, however, whether fragmentation on smaller scales leads to the formation of a star cluster instead of a supermassive star in the presence of possible cooling mechanisms.

Aims. We explored the formation of a central massive object through collisions and the accretion of Population III stars in a primordial gas cloud in a gravitationally unstable system by varying the gas temperature and thus the degree of gravitational instability. We explored the impact of disk fragmentation and compared our results with theoretical accretion rates.

Methods. We evolved a small Population III star cluster embedded in a primordial gas cloud on subparsec scales considering a gravitationally unstable initial configuration with different gas temperatures. We performed multiphysics simulations in the AMUSE framework with a hydrodynamical gas treatment through smoothed-particle hydrodynamics and N-body dynamics for the protostars represented through sink particles. To do this, we incorporated physically motivated accretion recipes. We also included a realistic mass-radius relation and solved the collisions with the sticky-sphere approximation.

Results. Our results show that central massive objects with masses ∼10⁴ M_⊙ can be formed by accretion and collisions at different temperatures and that the most massive object can reach efficiencies of ∼0.61 for atomic cooling conditions and ∼0.95 for more unstable conditions. We observe a quasi-disk formation for warmer temperatures and a higher contribution through collisions to the mass of a central massive object. Our results show that the embedded cluster is in a supercompetitive accretion regime in which it obtains mass by accretion that is regulated by self-gravity at the beginning and via Bondi–Hoyle accretion at later times in simulations with higher temperatures.

Conclusions. Our results suggest that in more unstable conditions with lower gas temperatures the seed of a more massive supermassive black hole can form. This corresponds to a higher efficiency in the formation of the central object.