We study the evolution of gas in H II regions around the first stars after the exciting stars end their lives. If the first star in a small halo dies without supernova (SN), subsequent star formation is possible in the same halo. We thus investigate the effect of ionization on subsequent star formation within small haloes in the early Universe using one-dimensional hydrodynamics with spherical symmetry along with non-equilibrium primordial gas chemistry. We find that the enhanced electron fraction facilitates the formation of molecular hydrogen at the cores of these haloes. The low temperature circumstances produced by the H2 cooling is favourable to HD formation and the resultant cooling further drops the temperature below 100 K. Consequently, low-mass stars with primordial abundances can form even in a small halo. After accreting the interstellar metals, these stars might resemble low-mass ultra metal-poor stars discovered in the present-day Galactic halo.
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