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 ($M_{\rm crit}$) for Population III (Pop 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 Pop III stars by increasing $M_{\rm crit}$. In this work, we constrain $M_{\rm crit}$ 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 (AMR) code ENZO. We provide a fit for $M_{\rm crit}$ 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 $M_{\rm crit}$ in the absence of radiation or streaming is $(1+z)^{-1.58}$, consistent with a constant virial temperature; (ii) increasing the UV background increases $M_{\rm crit}$ while steepening the redshift dependence, up to $(1+z)^{-5.7}$; (iii) baryon-dark matter streaming boosts $M_{\rm crit}$ but flattens the dependence on redshift; (iv) the combination of the two effects is not simply multiplicative.