Generation of Seed Magnetic Field around First Stars: the Biermann
  Battery Effect
  We investigate generation processes of magnetic fields around first stars.
Since the first stars are expected to form anisotropic ionization fronts in the
surrounding clumpy media, magnetic fields are generated by effects of radiation
force as well as the Biermann battery effect. We have calculated the amplitude
of magnetic field generated by the effects of radiation force around the first
stars in the preceding paper, in which the Biermann battery effects are not
taken into account.In this paper, we calculate the generation of magnetic
fields by the Biermann battery effect as well as the effects of radiation
force, utilizing the radiation hydrodynamics simulations. As a result, we find
that the generated magnetic field strengths are ~ 10^{-19}G-10^{-17}G at ~
100pc-1kpc scale mainly by the Biermann battery, which is an order of magnitude
larger than the results of our previous study. We also find that this result is
insensitive to various physical parameters including the mass of the source
star, distance between the source and the dense clump, unless we take unlikely
values of these parameters.
