Using three-dimensional cosmological simulations , we study the assembly process of one of the first galaxies , with a total mass of \sim 10 ^ { 8 } ~ { } M _ { \odot } , collapsing at z \simeq 10 .
Our main goal is to trace the transport of the heavy chemical elements produced and dispersed by a pair-instability supernova exploding in one of the minihalo progenitors .
To this extent , we incorporate an efficient algorithm into our smoothed particle hydrodynamics code which approximately models turbulent mixing as a diffusion process .
We study this mixing with and without the radiative feedback from Population III ( Pop III ) stars that subsequently form in neighboring minihalos .
Our simulations allow us to constrain the initial conditions for second-generation star formation , within the first galaxy itself , and inside of minihalos that virialize after the supernova explosion .
We find that most minihalos remain unscathed by ionizing radiation or the supernova remnant , while some are substantially photoheated and enriched to supercritical levels , likely resulting in the formation of low-mass Pop III or even Population II ( Pop II ) stars .
At the center of the newly formed galaxy , \sim 10 ^ { 5 } ~ { } M _ { \odot } of cold , dense gas uniformly enriched to \sim 10 ^ { -3 } ~ { } Z _ { \odot } are in a state of collapse , suggesting that a cluster of Pop II stars will form .
The first galaxies , as may be detected by the James Webb Space Telescope , would therefore already contain stellar populations familiar from lower redshifts .