Evolution of magnetic fields in galaxies and future observational tests with the Square Kilometre Array

Aims. We investigate the cosmological evolution of large- and small-scale magnetic fields in galaxies in the light of present models of formation and evolution of galaxies. Methods. We use the dynamo theory to derive the timescales of amplification and ordering of magnetic fields in disk and puffy galaxies. Turbulence in protogalactic halos generated by thermal virialization can drive an efficient turbulent dynamo. Results from simulations of hierarchical structure formation cosmology provide a tool to develop an evolutionary model of regular magnetic fields coupled with galaxy formation and evolution. Results. The turbulent (small-scale) dynamo was able to amplify a weak seed magnetic field in halos of protogalaxies to a few muG strength within a few 10^8 yr. This turbulent field served as a seed to the mean-field (large-scale) dynamo. Galaxies similar to the Milky Way formed their disks at z~10 and regular fields of muG strength and a few kpc coherence length were generated within 2 Gyr (at z~3), but field-ordering on the coherence scale of the galaxy size required an additional 6 Gyr (at z~0.5). Giant galaxies formed their disks at z~10, allowing more efficient dynamo generation of strong regular fields (with kpc coherence length) already at z~4. However, the age of the Universe is short for fully coherent fields in giant galaxies larger than 15 kpc to have been achieved. Dwarf galaxies should have hosted fully coherent fields at z~1. After a major merger, the strength of the turbulent field is enhanced by a factor of a few. Conclusions. This evolutionary scenario can be tested by measurements of polarized synchrotron emission and Faraday rotation with the planned SKA. We predict an anticorrelation between galaxy size and ratio between ordering scale and galaxy size (abridged).