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Magnetic fields have been included in cosmological simulations of galaxyformation only recently, due to advances in numerical techniques and a betterunderstanding of the galaxy formation physics. In this paper, we develop a newsubgrid model for the turbulent dynamo that takes place in the supersonicinterstellar medium in star-forming galaxies. It is based on a mean-fieldapproach that computes the turbulent kinetic energy at unresolved scales (theso-called subgrid scales) and modifies the induction equation to account forthe corresponding $\alpha$ dynamo. Our subgrid model depends on one freeparameter, the quenching parameter, that controls the saturation of the subgriddynamo. Thanks to this mean-field approach, we can now model the fastamplification of the magnetic field inside turbulent star-forming galaxies,without relying on artificially strong initial fields or without usingprohibitively expensive high-resolution simulations. We show that the evolutionof the magnetic field in our zoom-in Milky Way-like galaxy is consistent with asimple picture, in which the field is in equipartition with the turbulentkinetic energy inside the star-forming disc, with a field strength around 10$\mu$G at low redshift, while at the same time strong galactic outflows fillthe halo with a slightly weaker magnetic field, whose strength (10 nG) isconsistent will the ideal MHD dilution factor. Our results are in goodagreement with recent theoretical and numerical predictions. We also compareour simulation with Faraday depth observations at both low and high redshift,seeing overall good agreement with some caveats. Our model naturally predictsstronger magnetic fields at high redshift (around 100 $\mu$G in the galaxy and1 $\mu$G in the halo), but also stronger depolarisation effects due to strongerturbulence at early time.

A Subgrid Turbulent Mean Field Dynamo Model for Cosmological Galaxy Formation Simulations