Suppression of HD cooling in protogalactic gas clouds by Lyman-Werner radiation

It has been shown that HD molecules can form efficiently in metal-free gas collapsing into massive protogalactic haloes at high redshift. The resulting radiative cooling by HD can lower the gas temperature to that of the cosmic microwave background (CMB), T-CMB = 2.7(1 + z) K, significantly below the temperature of a few x100 K achievable via H-2 cooling alone, and thus reduce the masses of the first generation of stars. Here we consider the suppression of HD cooling by ultraviolet (UV) irradiation in the Lyman-Werner (LW) bands. We include photodissociation of both H-2 and HD, and explicitly compute the self-shielding and shielding of both molecules by neutral hydrogen, H i, as well as the shielding of HD by H-2. We use a simplified dynamical collapse model, and follow the chemical and thermal evolution of the gas, in the presence of a UV background. We find that a LW flux of J(crit,HD) approximate to 10-22 erg cm-2 sr-1 s-1 Hz-1 is able to suppress HD cooling and thus prevent collapsing primordial gas from reaching temperatures below similar to 100 K. The main reason for the lack of HD cooling for J > J(crit,HD) is the partial photodissociation of H-2, which prevents the gas from reaching sufficiently low temperatures (T < 150 K) for HD to become the dominant coolant; direct HD photodissociation is unimportant except for a narrow range of fluxes and column densities. Since the prevention of HD cooling requires only partial H-2 photodissociation, the critical flux J(crit,HD) is modest, and is below the UV background required to re-ionize the Universe at z similar to 10-20. We conclude that HD cooling can reduce the masses of typical stars only in rare haloes forming well before the epoch of re-ionization.