Biermann Mechanism in Primordial Supernova Remnant and Seed Fields

We have studied the generation of magnetic fields by the Biermann mechanism in the pair-instability supernovae explosions of the first stars. The Biermann mechanism produces magnetic fields in the shocked region between the bubble and interstellar medium (ISM), even if magnetic fields are absent initially. We have performed a series of two-dimensional magnetohydrodynamic simulations with the Biermann term and estimate the amplitude and total energy of the produced magnetic fields. We find that magnetic fields with amplitude $10^{-14}-10^{-17}$ G are generated inside the bubble, though the amount of magnetic fields generated depend on specific values of initial conditions. This corresponds to magnetic fields of $10^{28}-10^{31}$ ergs per each supernova remnant, which is strong enough to be the seed magnetic field for a galactic and/or interstellar dynamo.