What is the maximum mass of a Population III galaxy?

We utilize cosmological hydrodynamic simulations to study the formation of Population III (Pop III) stars in dark matter halos exposed to strong ionizing radiation. We simulate the formation of three halos subjected to a wide range of ionizing fluxes, and find that for high flux, ionization and photoheating can delay gas collapse and star formation up to halo masses significantly larger than the atomic cooling threshold. The threshold halo mass at which gas first collapses and cools increases with ionizing flux for intermediate values, and saturates at a value approximately an order of magnitude above the atomic cooling threshold for extremely high flux (e.g. ≈5×108 M⊙ at z≈6). This behavior can be understood in terms of photoheating, ionization/recombination, and Lyα cooling in the pressure-supported, self-shielded gas core at the center of the growing dark matter halo. We examine the spherically-averaged radial velocity profiles of collapsing gas and find that a gas mass of up to ≈106 M⊙ can reach the central regions within 3 Myr, providing an upper limit on the amount of massive Pop III stars that can form. The ionizing radiation increases this limit by a factor of a few compared to strong Lyman-Werner (LW) radiation alone. We conclude that the bright HeII 1640 Å emission recently observed from the high-redshift galaxy CR7 cannot be explained by Pop III stars alone. However, in some halos, a sufficient number of Pop III stars may form to be detectable with future telescopes such as the James Webb Space Telescope (JWST).