Magnetohydrodynamic effect on first star formation: prestellar core
  collapse and protostar formation
  Recent theoretical studies have suggested that a magnetic field may play a
crucial role in the first star formation in the universe. However, the
influence of the magnetic field on the first star formation has yet to be
understood well. In this study, we perform three-dimensional
magnetohydrodynamic simulations taking into account all the relevant cooling
processes and non-equilibrium chemical reactions up to the protostar density,
in order to study the collapse of magnetized primordial gas cores with
self-consistent thermal evolution. Our results show that the thermal evolution
of the central core is hardly affected by a magnetic field, because magnetic
forces do not prevent the contraction along the fields lines. We also find that
the magnetic braking extracts the angular momentum from the core and suppresses
fragmentation depending on the initial strength of the magnetic field. The
angular momentum transport by the magnetic outflows is less effective than that
by the magnetic braking because the outflows are launched only in a late phase
of the collapse. Our results indicate that the magnetic effects become
important for the field strength $B> 10^{-8}(n_{\rm H}/1\ \rm cm^{-3})^{2/3}\
\rm G$, where $n_{\rm H}$ is the number density, during the collapse phase.
Finally, we compare our results with simulations using a barotropic
approximation and confirm that this approximation is reasonable at least for
the collapse phase. Nevertheless, self-consistent treatment of the thermal and
chemical processes is essential for extending simulations to the accretion
phase, in which radiative feedback by protostars plays a crucial role.
