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 _ { * } \leq 0.8 M _ { \odot } ) and extremely metal-poor ( Z \leq 4.5 \times 10 ^ { -5 } Z _ { \odot } ) star in the Galactic halo by Caffau et al .
( 7 ) .
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 a 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 } { cm } ^ { -3 } .
The cloud core then becomes unstable and fragments again .
We argue that early SNe can trigger the formation of low-mass stars in the extremely metal-poor environment as Caffau et al .
( 7 ) discovered recently .