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 halos at high redshift. The resulting radiative cooling by HD can lower the gas temperature to that of the cosmic microwave background, T_CMB=2.7(1+z)K, significantly below the temperature of a few 100 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 UV irradiation in the Lyman-Werner (LW) bands. We include photo-dissociation of both H_2 and HD, and explicitly compute the self-shielding and shielding of both molecules by neutral hydrogen 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 = 1e-22 erg/cm^2/sr/s/Hz is able to suppress HD cooling and thus prevent collapsing primordial gas from reaching temperatures below 100 K. The main reason for the lack of HD cooling for J>J_crit is the partial photo-dissociation of H_2, which prevents the gas from reaching sufficiently low temperatures (T<150K) for HD to become the dominant coolant; direct HD photo-dissociation is unimportant except for a narrow range of fluxes and column densities. Since the prevention of HD-cooling requires only partial H_2 photo-dissociation, the critical flux J_crit is modest, and is below the UV background required to reionize the universe at redshift z=10-20. We conclude that HD-cooling can reduce the masses of typical stars only in rare halos forming well before the epoch of reionization.