The Critical Dark Matter Halo Mass for Population III Star Formation: Dependence on Lyman-Werner Radiation, Baryon-dark Matter Streaming Velocity, and Redshift

A critical dark matter halo mass (M (crit)) for Population III stars can be defined as the typical minimum halo mass that hosts sufficient cold-dense gas required for the formation of the first stars. The presence of Lyman-Werner (UV) radiation, which can dissociate molecular hydrogen, and the baryon-dark matter streaming velocity both delay the formation of Population III stars by increasing M (crit). In this work, we constrain M (crit) as a function of Lyman-Werner flux (including self-shielding), baryon-dark matter streaming, and redshift using cosmological simulations with a large sample of halos utilizing the adaptive mesh refinement code enzo. We provide a fit for M (crit) as a function of these quantities, which we expect to be particularly useful for semi-analytical models of early galaxy formation. In addition, we find (i) the measured redshift dependence of M (crit) in the absence of radiation or streaming is (1 + z)(-1.58), consistent with a constant virial temperature; (ii) increasing the UV background increases M (crit) while steepening the redshift dependence, up to (1 + z)(-5.7); (iii) baryon-dark matter streaming boosts M (crit) but flattens the dependence on redshift; (iv) the combination of the two effects is not simply multiplicative.