2021MNRAS.503.1051D

More than 200 supermassive black holes (SMBHs) of masses ≳10⁹M_☉ have been discovered at z >= 6. One promising pathway for the formation of SMBHs is through the collapse of supermassive stars (SMSs) with masses ∼10³-10⁵ M_☉ into seed black holes which could grow upto few times 10⁹M_☉ SMBHs observed at z ∼ 7. In this paper, we explore how SMSs with masses ∼10³-10⁵ M_☉ could be formed via gas accretion and runaway stellar collisions in high-redshift, metal-poor nuclear star clusters (NSCs) using idealized N-body simulations. We explore physically motivated accretion scenarios, e.g. Bondi-Hoyle-Lyttleton accretion and Eddington accretion, as well as simplified scenarios such as constant accretions. While gas is present, the accretion time-scale remains considerably shorter than the time-scale for collisions with the most massive object (MMO). However, overall the time-scale for collisions between any two stars in the cluster can become comparable or shorter than the accretion time-scale, hence collisions still play a crucial role in determining the final mass of the SMSs. We find that the problem is highly sensitive to the initial conditions and our assumed recipe for the accretion, due to the highly chaotic nature of the problem. The key variables that determine the mass growth mechanism are the mass of the MMO and the gas reservoir that is available for the accretion. Depending on different conditions, SMSs of masses ∼10³-10⁵ M_☉ can form for all three accretion scenarios considered in this work.