Abstract

Atomic cooling haloes with virial temperatures T$_{vir}$ {\ge} 10$^{4}$ K are the most plausible sites for the formation of the first galaxies and the first intermediate-mass black holes. It is therefore important to assess whether one can obtain robust results concerning their main properties from numerical simulations. A major uncertainty is the presence of turbulence, which is barely resolved in cosmological simulations. We explore the latter both by pursuing high-resolution simulations with up to 64 cells per Jeans length and by incorporating a subgrid-scale turbulence model to account for turbulent pressure and viscosity on unresolved scales. We find that the main physical quantities in the halo, in particular the density, temperature and energy density profile, are approximately converged. However, the morphologies in the central 500 au change significantly with increasing resolution and appear considerably more turbulent. In a systematic comparison of three different haloes, we further found that the turbulence subgrid-scale model gives rise to more compact central structures and decreases the amount of vorticity. Such compact morphologies may in particular favour the accretion on to the central object.