Supermassive Black Hole Formation by Direct Collapse: Keeping Protogalactic Gas H2–Free in Dark Matter Halos

In the absence of H2 molecules, the primordial gas in early dark matter halos with virial temperatures just above Tvir > ∼ 10K 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 (SMBH). In order for H2–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 halos with Tvir > ∼ 10K, irradiated by a UV flux with various intensities and spectra. We determined the critical specific intensity, J 21 , required to suppress H2 cooling in each of the three halos. For a hard spectrum representative of metal–free stars, we find (in units of 10 erg s Hz sr cm) 10 < J 21 < 10, 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 < 300 . These values are a factor of 3–10 lower than previous estimates. We attribute the difference to the higher, more accurate H2 collisional dissociation rate we adopted. The reduction in J 21 exponentially increases the number of rare halos exposed to super–critical radiation. When H2 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 M⊙ may form at the center of these halos, compared to the M ∼ 10 2 M⊙ stars forming when H2–cooling is efficient.