Supermassive black hole formation by direct collapse: keeping protogalactic gas H2free in dark matter haloes with virial temperatures Tvir>rsim 104K

Abstract

In the absence of H2 molecules, the primordial gas in early dark matter haloes with virial temperatures just above Tvir≳ 104 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 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 haloes with Tvir≳ 104 K, irradiated by a UV flux with various intensities and spectra. We determined the critical specific intensity, Jcrit21, required to suppress H2 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) 104 < Jcrit21 < 105, while for a softer spectrum, which is characteristic of a normal stellar population, and for which H− dissociation is important, we find 30 < Jcrit21 < 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 Jcrit21 exponentially increases the number of rare haloes exposed to supercritical 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∼ 105 M⊙ may form at the centre of these haloes, compared to the M∼ 102 M⊙ stars forming when H2 cooling is efficient.