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In the absence of H 2 molecules, the primordial gas in early dark matter haloes with virial temperatures just above T vir 10 4 K cools by collisional excitation of atomic H. Although it cools efficiently, this gas remains relatively hot, at a temperature near T 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 threedimensional hydrodynamical adaptive mesh refinement (AMR) simulations of gas collapse in three different protogalactic haloes with T vir 10 4 K, irradiated by a UV flux with various intensities and spectra. We determined the critical specific intensity, J crit 21 , 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 crit 21 < 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 crit 21 < 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 crit 21 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 10 5 M may form at the centre of these haloes, compared to the M 10 2 M stars forming when H 2 cooling is efficient.
Shang et al. (Tue,) studied this question.