Early Cosmological HII/HeIII Regions and Their Impact on Second-Generation Star Formation

(Abridged) We present the results of three-dimensional radiation-hydrodynamics simulations of the formation and evolution of early HII/HeIII regions around the first stars. Cooling (by H2 and HD) and recollapse of the gas in the relic HII region is also followed in a full cosmological context, until second-generation stars are formed. A large HII region with a few kiloparsec diameter is formed, within which a smaller HeIII region is embedded. Radiative feedback effect quenches further star-formation within the halo for a hundred million years. Accretion onto remnant blackholes will be inefficient. Recombination radiation within the HII region is weak, but persists for 50 million years. We also follow the thermal and chemical evolution of the photo-ionized gas in the relic HII region. The gas cools by HD line cooling down to a few tens Kelvin. At high redshifts (z>10), the minimum gas temperature is limited by T_CMB. Because of its low temperature, the characteristic mass of a Jeans-unstable gas clump is ~ 40 Msun, and is significantly smaller than a typical clump mass for early primordial gas clouds. We find no evidence of fragmentation by this epoch. Together with the small cloud mass, this result indicates that massive, rather than very massive, primordial stars may form in the relic HII region. Such stars might be responsible for early metal-enrichment of the interstellar medium from which recently discovered hyper metal-poor stars were born.