Supermassive black hole formation by direct collapse: keeping protogalactic gas H2 free in dark matter haloes with virial temperatures Tvir ≳ 104 K

In the absence of H-2 molecules, the primordial gas in early dark matter haloes with virial temperatures just above T-vir greater than or similar to 10(4) K cools by collisional excitation of atomic H. Although it cools efficiently, this gas remains relatively hot, at a temperature near T similar to 8000 K, and consequently might be able to avoid fragmentation and collapse directly into a supermassive black hole. In order for H-2 formation and cooling to be strongly suppressed, the gas must be irradiated by a sufficiently intense ultraviolet (UV) flux. We performed a suite of three-dimensional hydrodynamical adaptive mesh refinement (AMR) simulations of gas collapse in three different protogalactic haloes with T-vir greater than or similar to 10(4) K, irradiated by a UV flux with various intensities and spectra. We determined the critical specific intensity, J(21)(crit), required to suppress H-2 cooling in each of the three haloes. For a hard spectrum representative of metal-free stars, we find (in units of 10(-21) erg s(-1) Hz(-1) sr(-1) cm(-2)) 10(4) < J(21)(crit) < 10(5), while for a softer spectrum, which is characteristic of a normal stellar population, and for which H-dissociation is important, we find 30 < J(21)(crit) < 300. These values are a factor of 3-10 lower than previous estimates. We attribute the difference to the higher, more accurate H-2 collisional dissociation rate we adopted. The reduction in J(21)(crit) exponentially increases the number of rare haloes exposed to supercritical radiation. When H-2 cooling is suppressed, gas collapse starts with a delay, but it ultimately proceeds more rapidly. The infall velocity is near the increased sound speed, and an object as massive as M similar to 10(5) M-circle dot may form at the centre of these haloes, compared to the M similar to 10(2) M-circle dot stars forming when H-2 cooling is efficient.