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 which self-consistently incorporates radiative transfer and non-equilibrium 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 M _ { halo } = 10 ^ { 5 } -10 ^ { 8 } { M } _ { \odot } , gas density profiles with a power-law index w = 1.5 - 2.25 , and metal-free stars of mass M _ { star } = 25 - 500 { M } _ { \odot } .
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 ( \lesssim 10 ^ { 6 } { M } _ { \odot } ) halos , the transition takes place within a few 10 ^ { 5 } 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 \lesssim 1 { cm } ^ { -3 } in a few million years .
In larger mass ( \gtrsim 10 ^ { 7 } { M } _ { \odot } ) 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 .