Gravitational collapse and the thermal evolution of low-metallicity gas
  clouds in the early Universe
  We study gravitational collapse of low-metallicity gas clouds and the
formation of protostars by three-dimensional hydrodynamic simulations. Grain
growth, non-equilibrium chemistry, molecular cooling, and chemical heating are
solved in a self-consistent manner for the first time. We employ the realistic
initial conditions for the abundances of metal and dust, and the dust size
distribution obtained from recent Population III supernova calculations. We
also introduce the state-of-the-art particle splitting method based on the
Voronoi tessellation and achieve an extremely high mass resolution of ~10^{-5}
Msun (10 earth masses) in the central region. We follow the thermal evolution
of several early clouds with various metallicities. We show that the condition
for cloud fragmentation depends not only on the gas metallicity but also on the
collapse timescale. In many cases, the cloud fragmentation is prevented by the
chemical heating owing to molecular hydrogen formation even though dust cooling
becomes effective. Meanwhile, in several cases, efficient OH and H2O cooling
promotes the cloud elongation, and then cloud "filamentation" is driven by dust
thermal emission as a precursor of eventual fragmentation. While the filament
fragmentation is driven by rapid gas cooling with >10^{-5} Zsun, fragmentation
occurs in a different manner by the self-gravity of a circumstellar disk with
<10^{-5} Zsun. We use a semi-analytic model to estimate the number fraction of
the clouds which undergo the filament fragmentation to be a several percents
with 10^{-5}--10^{-4} Zsun. Overall, our simulations show a viable formation
path of the recently discovered Galactic low-mass stars with extremely small
metallicities.
