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The magnetic fields observed in the Milky~Way and nearby galaxies appear tobe in equipartition with the turbulent, thermal, and cosmic ray energydensities, and hence are expected to be dynamically important. However, theorigin of these strong magnetic fields is still unclear, and most previousattempts to simulate galaxy formation from cosmological initial conditions haveignored them altogether. Here, we analyse the magnetic fields predicted by thesimulations of the Auriga Project, a set of 30 high-resolution cosmologicalzoom simulations of Milky~Way-like galaxies, carried out with a moving-meshmagneto-hydrodynamics code and a detailed galaxy formation physics model. Wefind that the magnetic fields grow exponentially at early times owing to asmall-scale dynamo with an e-folding time of roughly $100\,\rm{Myr}$ in thecenter of halos until saturation occurs around $z=2-3$, when the magneticenergy density reaches about $10\%$ of the turbulent energy density with atypical strength of $10-50\,\rm{\mu G}$. In the galactic centers the ratiobetween magnetic and turbulent energy remains nearly constant until $z=0$. Atlarger radii, differential rotation in the disks leads to linear amplificationthat typically saturates around $z=0.5$ to $z=0$. The final radial and verticalvariations of the magnetic field strength can be well described by two jointexponential profiles, and are in good agreement with observational constraints.Overall, the magnetic fields have only little effect on the global evolution ofthe galaxies as it takes too long to reach equipartition. We also demonstratethat our results are well converged with numerical resolution.

Magnetic field formation in the Milky Way-like disk galaxies of the Auriga project