The influence of magnetic fields, turbulence, and UV radiation on the formation of supermassive black holes

Context. The seeds of the supermassive black holes with masses of ~10⁹ M_⊙ observed already at z ~ 6 may have formed through the direct collapse of primordial gas in T_vir ≳ 10⁴ K halos, whereby the gas must stay hot (~10⁴ K) in order to avoid fragmentation. 
Aims: The interplay between magnetic fields, turbulence, and a UV radiation background during the gravitational collapse of primordial gas in a halo is explored; in particular, the possibilities for avoiding fragmentation are examined. 
Methods: Using an analytical one-zone model, the evolution of a cloud of primordial gas is followed from its initial cosmic expansion through turnaround, virialization, and collapse up to a density of 10⁷ cm^-3. 
Results: It was found that in halos with no significant turbulence, the critical UV background intensity (J₂₁^crit) for keeping the gas hot is lower by a factor ~10 for an initial comoving magnetic field B₀ ~ 2 nG than for the zero-field case, and even lower for stronger fields. In turbulent halos, J₂₁^crit is found to be a factor ~10 lower than for the zero-field-zero-turbulence case, and the stronger the turbulence (more massive halo and/or stronger turbulent heating), the lower J₂₁^crit. 
Conclusions: The reduction in J₂₁^crit is particularly important, since it exponentially increases the number of halos exposed to a supercritical radiation background.