Amplification of magnetic fields in a primordial H ii 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.