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We present a model for the seeding and evolution of magnetic fields inprotogalaxies. Supernova (SN) explosions during the assembly of a protogalaxyprovide magnetic seed fields, which are subsequently amplified by compression,shear flows and random motions. We implement the model into the MHD version ofthe cosmological N-body / SPH simulation code GADGET and we couple the magneticseeding directly to the underlying multi-phase description of star formation.We perform simulations of Milky Way-like galactic halo formation using astandard LCDM cosmology and analyse the strength and distribution of thesubsequent evolving magnetic field. A dipole-shape divergence-free magneticfield is injected at a rate of 10^{-9}G / Gyr within starforming regions, giventypical dimensions and magnetic field strengths in canonical SN remnants.Subsequently, the magnetic field strength increases exponentially on timescalesof a few ten million years. At redshift z=0, the entire galactic halo ismagnetized and the field amplitude is of the order of a few $\mu$G in thecenter of the halo, and 10^{-9} G at the virial radius. Additionally, weanalyse the intrinsic rotation measure (RM) of the forming galactic halo overredshift. The mean halo intrinsic RM peaks between redshifts z=4 and z=2 andreaches absolute values around 1000 rad m^{-2}. While the halo virializestowards redshift z=0, the intrinsic RM values decline to a mean value below 10rad m^{-2}. At high redshifts, the distribution of individual starforming, andthus magnetized regions is widespread. In our model for the evolution ofgalactic magnetic fields, the seed magnetic field amplitude and distribution isno longer a free parameter, but determined self-consistently by the starformation process occuring during the formation of cosmic structures.

Strong magnetic fields and large rotation measures in protogalaxies by supernova seeding