Using a large set of high resolution numerical simulations incorporating non-equilibrium molecular hydrogen chemistry and a constant source of external radiation , we study gas collapse in previously photo-ionized mini-galaxies with virial temperatures less than 10 ^ { 4 } K in the early universe ( redshifts z = 10 - 20 ) .
We confirm that the mechanism of positive feedback of ionizing radiation on star formation in mini-galaxies proposed by Ricotti , Gnedin , & Shull ( 25 ) can be efficient despite a significant flux of metagalactic photo-dissociating radiation .
We derive critical fluxes for the Lyman-Werner background radiation sufficient to prevent the collapse of gas in mini-galaxies as a function of the virial mass of the halo and redshift .
In our model , the formation of mini-galaxies in defunct H ii regions is most efficient at large redshifts ( z \gtrsim 15 ) and/or for large local gas overdensity \delta \gtrsim 10 .
We show that non-equilibrium chemistry plays an important dynamical role not only during the initial evolutionary phase leading to the gas becoming gravitationally unstable inside the mini-halo , but also at the advanced stages of the core collapse , resulting in efficient gas accretion in the core region .
We speculate on a possible connection between our objects and metal-poor globular clusters and dwarf spheroidal galaxies .