Context : The seeds of the supermassive black holes ( SMBHs ) with masses of \mathord { \sim } \SI e9 M _ { \odot } observed already at z \sim 6 may have formed through the direct collapse of primordial gas in T _ { \mathrm { vir } } \gtrsim \SI { e 4 } { K } halos , whereby the gas must stay hot ( \mathord { \sim } \SI e4K ) 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 \SI e7cm^-3 .

Results : It was found that in halos with no significant turbulence , the critical UV background intensity ( J _ { \mathrm { 21 } } ^ { \mathrm { crit } } ) for keeping the gas hot is lower by a factor \mathord { \sim } 10 for an initial comoving magnetic field B _ { \mathrm { 0 } } \sim \SI { 2 } { nG } than for the zero-field case , and even lower for stronger fields .
In turbulent halos , J _ { \mathrm { 21 } } ^ { \mathrm { crit } } is found to be a factor \mathord { \sim } 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 J _ { \mathrm { 21 } } ^ { \mathrm { crit } } .

Conclusions : The reduction in J _ { \mathrm { 21 } } ^ { \mathrm { crit } } is particularly important , since it exponentially increases the number of halos exposed to a supercritical radiation background .