We study the formation of low-mass and extremely metal-poor stars in the early universe. Our study is motivated by the recent discovery of a low-mass (M < 0.8 Msun) and extremely metal-poor (Z <= 4.5 x 10^{-5} Zsun) star in the Galactic halo by Caffau et al. We propose a model that early supernova (SN) explosions trigger the formation of low-mass stars via shell fragmentation. We first perform one-dimensional hydrodynamic simulations of the evolution of an early SN remnant. We show that the shocked shell undergoes efficient radiative cooling and then becomes gravitationally unstable to fragment and collapse in about ten million years. We then follow the thermal evolution of the collapsing fragments using a one-zone code. Our one-zone calculation treats chemistry and radiative cooling self-consistently in low-metallicity gas. The collapsing gas cloud evolves roughly isothermally, until it cools rapidly by dust continuum emission at the density 10^{13}-10^{14} /cc. The cloud core then becomes thermally and gravitationally unstable and fragments. We argue that early SNe can trigger the formation of low-mass stars in the extremely metal-poor environment as Caffau et al. discovered recently.
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