Population III Star Formation in an X-ray background: I. Critical Halo
  Mass of Formation and Total Mass in Stars
  The first luminous objects forming in the universe produce radiation
backgrounds in the FUV and X-ray bands that affect the formation of Population
III stars. Using a grid of cosmological hydrodynamics zoom-in simulations, we
explore the impact of the Lyman-Warner (LW) and X-ray radiation backgrounds on
the critical dark matter halo mass for Population III star formation and the
total mass in stars per halo. We find that the LW radiation background lowers
the H$_2$ fraction and delays the formation of the Population III stars. On the
other hand, X-ray irradiation anticipates the redshift of collapse and reduces
the critical halo mass, unless the X-ray background is too strong and gas
heating shuts down gas collapse into the halos and prevents star formation.
Therefore, an X-ray background can increase the number of dark matter halos
forming Population III stars by about a factor of ten, but the total mass in
stars forming in each halo is reduced. This is because X-ray radiation
increases the molecular fraction and lowers the minimum temperature of the
collapsing gas (or equivalently the mass of the quasi-hydrostatic core) and
therefore slows down the accretion of the gas onto the central protostar.
