Numerical resolution effects on simulations of massive black hole seeds

We have performed high-resolution numerical simulations with the hydrodynamical adaptive mesh refinement code enzo to investigate the formation of massive seed black holes in a sample of six dark matter haloes above the atomic cooling threshold. The aim of this study is to illustrate the effects of varying the maximum refinement level on the final object formed. The virial temperatures of the simulated haloes range from T ∼ 10 000 to ∼16 000 K and they have virial masses in the range M ∼ 2 × 107 to ∼7 × 107 M⊙ at z ∼ 15. The outcome of our six fiducial simulations is both generic and robust. A rotationally supported, marginally gravitationally stable, disc forms with an exponential profile. The mass and scale length of this disc depends strongly on the maximum refinement level used. Varying the maximum refinement level by factors between 1/64 and 256 times the fiducial level illustrates the care that must be taken in interpreting the results. The lower resolution simulations show tentative evidence that the gas may become rotationally supported out to 20 pc while the highest resolution simulations show only weak evidence of rotational support due to the shorter dynamical times for which the simulation runs. The higher resolution simulations do, however, point to fragmentation at small scales of the order of ∼100 au. In the highest resolution simulations a central object of a few times 102 M⊙ forms with multiple strongly bound, Jeans unstable, clumps of ≈10 M⊙ and radii of 10–20 au suggesting the formation of dense star clusters in these haloes.