Heavy black hole seed formation in high-z atomic cooling halos

¹ Centre for Astrophysics and Space Science Maynooth, Department of Theoretical Physics, Maynooth University, Maynooth, Ireland
e-mail: lewis.prole@mu.ie
² Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Straße 2, 69120 Heidelberg, Germany
³ Universität Heidelberg, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
⁴ Cardiff University School of Physics and Astronomy, Cardiff, UK

Received: 11 December 2023
Accepted: 15 February 2024

Abstract

Context. Halos with masses in excess of the atomic limit are believed to be ideal environments in which to form heavy black hole seeds with masses above 10³ M_⊙. In cases where the H₂ fraction is suppressed, this is expected to lead to reduced fragmentation of the gas and the generation of a top-heavy initial mass function. In extreme cases this can result in the formation of massive black hole seeds. Resolving the initial fragmentation scale and the resulting protostellar masses has, until now, not been robustly tested.

Aims. We run zoom-in simulations of atomically cooled halos in which the formation of H₂ is suppressed to assess whether they can truly resist fragmentation at high densities and tilt the initial mass function towards a more top-heavy form and the formation of massive black hole seeds.

Methods. Cosmological simulations were performed with the moving mesh code AREPO, using a primordial chemistry network until z ∼ 11. Three haloes with masses in excess of the atomic cooling mass were then selected for detailed examination via zoom-ins. A series of zoom-in simulations, with varying levels of maximum spatial resolution, captured the resulting fragmentation and formation of metal-free stars using the sink particle technique. The highest resolution simulations resolved densities up to 10⁻⁶ g cm⁻³ (10¹⁸ cm⁻³) and captured a further 100 yr of fragmentation behaviour at the centre of the halo. Lower resolution simulations were then used to model the future accretion behaviour of the sinks over longer timescales.

Results. Our simulations show intense fragmentation in the central region of the halos, leading to a large number of near-solar mass protostars. Even in the presence of a super-critical Lyman-Werner radiation field (J_LW > 10⁵J₂₁), H₂ continues to form within the inner ∼2000 au of the halo. Despite the increased fragmentation, the halos produce a protostellar mass spectrum that peaks at higher masses relative to standard Population III star-forming halos. The most massive protostars have accretion rates of 10⁻³–10⁻¹ M_⊙ yr⁻¹ after the first 100 years of evolution, while the total mass of the central region grows at 1 M_⊙ yr⁻¹. Lower resolution zoom-ins show that the total mass of the system continues to accrete at ∼1 M_⊙ yr⁻¹ for at least 10⁴ yr, although how this mass is distributed amongst the rapidly growing number of protostars is unclear. However, assuming that a fraction of stars can continue to accrete rapidly, the formation of a sub-population of stars with masses in excess of 10³ M_⊙ is likely in these halos. In the most optimistic case, we predict the formation of heavy black hole seeds with masses in excess of 10⁴ M_⊙, assuming an accretion behaviour in line with expectations from super-competitive accretion and/or frequent mergers with secondary protostars.