Supermassive Black Hole Formation at High Redshifts Through a Primordial Magnetic Field

It has been proposed that primordial gas in early dark matter halos, with virial temperatures above 10⁴ K, can avoid fragmentation and undergo rapid collapse, possibly resulting in a supermassive black hole (SMBH). This requires the gas to avoid cooling and to remain at temperatures near T=10⁴ K. We show that this condition can be satisfied in the presence of a sufficiently strong primordial magnetic field, which heats the collapsing gas via ambipolar diffusion. If the field has a strength above B = 3. 6 (comoving) nG, the collapsing gas is kept warm (T=10⁴K) until it reaches the critical density ncrit=10³ cm^-3 at which the roto-vibrational states of H₂ approach local thermodynamic equilibrium. H₂-cooling then remains inefficient, and the gas temperature stays near 10⁴K, even as it continues to collapse to higher densities. The critical magnetic field strength required to permanently suppress H₂-cooling is somewhat higher than upper limit of approx. 2 nG from the cosmic microwave background (CMB). However, it can be realized in the rare (2-3) -sigma regions of the spatially fluctuating B-field; these regions contain a sufficient number of halos to account for the z=6 quasar BHs.