We present the results of three-dimensional radiation-hydrodynamics simulations of the formation and evolution of early H ii /He iii regions around the first stars .
Cooling and recollapse of the gas in the relic H ii region is also followed in a full cosmological context , until second-generation stars are formed .
We first carry out ray-tracing simulations of ionizing radiation transfer from the first star .
Hydrodynamics is directly coupled with photo-ionization heating as well as radiative and chemical cooling .
The photo-ionized hot gas is evacuated out of the host halo at a velocity of \sim 30 km/sec .
This radiative feedback effect quenches further star-formation within the halo for over tens to a hundred million years .
We show that the thermal and chemical evolution of the photo-ionized gas in the relic H ii region is remarkably different from that of a neutral primordial gas .
Efficient molecular hydrogen production in the recombining gas enables it to cool to \sim 100 K , where fractionation of HD/H _ { 2 } occurs .
The gas further cools by HD line cooling down to a few tens Kelvin .
Interestingly , at high redshifts ( z > 10 ) , the minimum gas temperature is limited by that of the cosmic microwave background with T _ { CMB } = 2.728 ( 1 + z ) .
The gas cloud goes run-away collapse when its mass is \sim 40 M _ { \odot } , which is significantly smaller than a typical clump mass of \sim 200 - 300 M _ { \odot } for early primordial gas clouds .
We argue that massive , rather than very massive , primordial stars may form in the relic H ii region .
Such stars might be responsible for early metal-enrichment of the interstellar medium from which recently discovered hyper metal-poor stars were born .