Amplification of Magnetic Fields in a Primordial HII Region and
  Supernova
  Magnetic fields permeate the Universe on all scales and play a key role
during star formation. We study the evolution of magnetic fields around a
massive metal-free (Population III) star at $z \sim 15$ during the growth of
its HII region and subsequent supernova explosion by conducting three
cosmological magnetohydrodynamic simulations with radiation transport. Given
the theoretical uncertainty and weak observational constraints of magnetic
fields in the early universe, we initialize the simulations with identical
initial conditions only varying the seed field strength. We find that magnetic
fields grow as $\rho^{2/3}$ during the gravitational collapse preceding star
formation, as expected from ideal spherical collapse models. Massive Population
III stars can expel a majority of the gas from the host halo through radiative
feedback, and we find that the magnetic fields are not amplified above the
spherical collapse scaling relation during this phase. However, afterwards when
its supernova remnant can radiatively cool and fragment, the turbulent velocity
field in and around the shell causes the magnetic field to be significantly
amplified on average by $\sim$100 in the shell and up to 6 orders of magnitude
behind the reverse shock. Within the shell, field strengths are on the order of
a few nG at a number density of 1 cm$^{-3}$. We show that this growth is
primarily caused by small-scale dynamo action in the remnant. These
strengthened fields will propagate into the first generations of galaxies,
possibly affecting the nature of their star formation.
