Formation of Population III Stars in Fossil HII Regions: Significance of   HD
  We study the evolution of gas in HII regions around the first stars after the death of the exciting stars. 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 of the gas on subsequent star formation within small halos 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 halos. The low temperature circumstances produced by the H_2 cooling is suitable for 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 Galactic halo. 
Takanori Nagakura, Kazuyuki Omukai