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We investigate the formation of extremely metal-poor (EMP) stars that areobserved in the Galactic halo and neighboring ultra-faint dwarf galaxies. Theirlow metal abundances (${\rm [Fe/H]} < -3$) indicate that their parent cloudswere enriched by a single or several supernovae (SNe) from the first (Pop III)stars. In this study, we perform numerical simulations of the entire formationsequence of a EMP star through the feedback effects of photo-ionization andmetal-enrichment by a Pop III SN. We for the first time employ a metal/dustproperties calculated consistently with the progenitor model, and solve allrelevant radiative cooling processes and chemical reactions including metalmolecular formation and grain growth until the protostar formation. In aminihalo (MH) with mass $1.77\times 10^{6} \ {\rm M}_{\bigodot}$, a Pop IIIstar with mass $13 \ {\rm M}_{\bigodot}$ forms at redshift $z=12.1$. After itsSN explosion, the shocked gas falls back into the central MH internallyenriching itself. The metallicity in the recollapsing region is $2.6\times10^{-4} \ {\rm Z}_{\bigodot}$ (${\rm [Fe/H]} = -3.42$). The recollapsing cloudundergoes cooling by HD, CO, and OH molecules and heating along with H$_2$formation. Eventually by grain growth and dust cooling, knotty filaments appearin the central 100 au region with the help of turbulence driven by the SN,leading to the formation of low-mass EMP stars surviving until the present day.

Seeding the Second Star: enrichment from population III, dust evolution, and cloud collapse