Magnetic field formation in the Milky Way-like disk galaxies of the
  Auriga project
  The magnetic fields observed in the Milky~Way and nearby galaxies appear to
be in equipartition with the turbulent, thermal, and cosmic ray energy
densities, and hence are expected to be dynamically important. However, the
origin of these strong magnetic fields is still unclear, and most previous
attempts to simulate galaxy formation from cosmological initial conditions have
ignored them altogether. Here, we analyse the magnetic fields predicted by the
simulations of the Auriga Project, a set of 30 high-resolution cosmological
zoom simulations of Milky~Way-like galaxies, carried out with a moving-mesh
magneto-hydrodynamics code and a detailed galaxy formation physics model. We
find that the magnetic fields grow exponentially at early times owing to a
small-scale dynamo with an e-folding time of roughly $100\,\rm{Myr}$ in the
center of halos until saturation occurs around $z=2-3$, when the magnetic
energy density reaches about $10\%$ of the turbulent energy density with a
typical strength of $10-50\,\rm{\mu G}$. In the galactic centers the ratio
between magnetic and turbulent energy remains nearly constant until $z=0$. At
larger radii, differential rotation in the disks leads to linear amplification
that typically saturates around $z=0.5$ to $z=0$. The final radial and vertical
variations of the magnetic field strength can be well described by two joint
exponential profiles, and are in good agreement with observational constraints.
Overall, the magnetic fields have only little effect on the global evolution of
the galaxies as it takes too long to reach equipartition. We also demonstrate
that our results are well converged with numerical resolution.
