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Magnetic fields in galaxies are believed to be the result of dynamoamplification of initially weak seed fields, reaching equipartition strengthinside the interstellar medium. The small-scale dynamo appears to be a viablemechanism to explain observations of strong magnetic fields in present-day andhigh-redshift galaxies, considering the extreme weakness of seed fieldspredicted by battery mechanisms or primordial fields. Performinghigh-resolution adaptive mesh magneto-hydrodynamic simulations of a small mass,isolated cooling halo with an initial magnetic seed field strength well belowequipartition, we follow the small-scale dynamo amplification fromsupernova-induced turbulence up to saturation of the field. We find thatsaturation occurs when the average magnetic pressure reaches only 3 % to 5 % ofthe turbulent pressure. The magnetic energy growth transitions from exponentialto linear, and finally comes to halt. The saturation level increases slightlywith grid resolution. These results are in good agreement with theoreticalpredictions for magnetic Prandtl numbers of order $\mathrm{Pr_M} \sim 1$ andturbulent Mach numbers of order $\mathrm{M} \sim 10$. When we suppresssupernova feedback after our simulation has reached saturation, we find thatturbulence decays and that the gas falls back onto a thin disk with themagnetic field in local equipartition.  We propose a scenario in which galactic magnetic fields are amplified fromweak seed fields in the early stages of the Universe to sub-equipartitionfields, owing to the turbulent environment of feedback-dominated galaxies athigh redshift, and are evolved further in a later stage up to equipartition, asgalaxies transformed into more quiescent, large spiral disks.

A small-scale dynamo in feedback-dominated galaxies - II. The saturation phase and the final magnetic configuration