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Supermassive Black Hole Formation by Direct Collapse: Keeping Protogalactic Gas H_2--Free in Dark Matter Halos with Virial Temperatures T_vir >~ 10^4 K

In the absence of H_2 molecules, the primordial gas in early dark matter halos 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 (SMBH). 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 halos with T_vir >~ 10^4 K, irradiated by a UV flux with various intensities and spectra. We determined the critical specific intensity, Jcrit, required to suppress H_2 cooling in each of the three halos. 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<Jcrit<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<Jcrit<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 Jcrit exponentially increases the number of rare halos exposed to super--critical 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 solar mass may form at the center of these halos, compared to the M ~ 10^2 solar mass stars forming when H_2--cooling is efficient.