The Structure and Evolution of Early Cosmological H II Regions

We study the formation and evolution of H II regions around the first stars formed at redshifts z = 10-30. We use a one-dimensional Lagrangian hydrodynamics code that self-consistently incorporates radiative transfer and nonequilibrium primordial gas chemistry. The star-forming region is defined as a spherical dense molecular gas cloud with a Population III star embedded at the center. We explore a large parameter space by considering, as plausible early star-forming sites, dark matter halos of mass Mhalo = 105-108 M☉, gas density profiles with a power-law index w = 1.5-2.25, and metal-free stars of mass Mstar = 25-500 M☉. The formation of the H II region is characterized by initial slow expansion of a weak D-type ionization front near the center, followed by rapid propagation of an R-type front throughout the outer gas envelope. We find that the transition between the two front types is indeed a critical condition for the complete ionization of halos of cosmological interest. In small-mass (≲106 M☉) halos, the transition takes place within a few 105 yr, yielding high escape fractions (>80%) of both ionizing and photodissociating photons. The gas is effectively evacuated by a supersonic shock, with the mean density within the halo decreasing to ≲1 cm-3 in a few million years. In larger mass (≳107 M☉) halos, the ionization front remains to be of D-type over the lifetime of the massive star, the H II region is confined well inside the virial radius, and the escape fractions are essentially zero. We derive an analytic formula that reproduces well the results of our simulations for the critical halo mass below which the gas is completely ionized. We discuss immediate implications of the present results for the star formation history and early reionization of the universe.