Formation Criteria and the Mass of Secondary Population III Stars
  We explore the formation of secondary Population III (Pop III) stars under
radiation hydrodynamic (RHD) feedback by a preformed massive star. To properly
treat RHD feedback, we perform three-dimensional RHD simulations incorporating
the radiative transfer of ionizing photons as well as H_2 dissociating photons
from a preformed star. A collapsing gas cloud is settled at a given distance
from a 120Msun Pop III star, and the evolution of the cloud is pursued
including RHD feedback. We derive the threshold density depending on the
distance, above which the cloud can keep collapsing owing to the shielding of
H_2 dissociating radiation. We find that an H_2 shell formed ahead of an
ionizing front works effectively to shield the H_2 dissociating radiation,
leading to the positive feedback for the secondary Pop III star formation.
Also, near the threshold density, the envelope of gas cloud is stripped
significantly by a shock associated with an ionizing front. By comparing the
mass accretion timescale with the Kelvin-Helmholtz timescale, we estimate the
mass of secondary Pop III stars. It turns out that the stripping by a shock can
reduce the mass of secondary Pop III stars down to \approx 20Msum.
