  The origin and evolution of magnetic fields in the Universe is still an open
question. Their observations in galaxies suggest strong magnetic fields already
at high redshift as well as at present time. However, neither primordial
magnetic fields nor battery processes can account for such high field
strengths, which implies the presence of a dynamo process with rapid growth
rates in high-redshift galaxies and subsequent maintenance against decay. We
investigate the particular role played by feedback mechanisms in creating
strong fluid turbulence, allowing for a magnetic dynamo to emerge. Performing
magnetohydrodynamic simulations of isolated cooling gas halos, we compare the
magnetic field evolution for various initial field topologies and various
stellar feedback mechanisms. We find that feedback can indeed drive strong gas
turbulence and dynamo action. We see typical properties of Kolmogorov
turbulence with a $k^{-5/3}$ kinetic energy spectrum, as well as a small-scale
dynamo, with a $k^{3/2}$ magnetic energy spectrum predicted by Kazantsev dynamo
theory. We also investigate simulations with a final quiescent phase. As
turbulence decreases, the galactic fountain settles into a thin, rotationally
supported disk. The magnetic field develops a large-scale, well-ordered
structure with even symmetry, which is in good agreement with magnetic field
observations of nearby spirals. Our findings suggest that weak initial seed
fields were first amplified by a small-scale dynamo during a violent,
feedback-dominated early phase in the galaxy formation history, followed by a
more quiescent evolution, where the fields have slowly decayed or were
maintained via large-scale dynamo action.
