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

Aims. In the context of models of galaxy formation and evolution, we investigate the cosmological evolution of large-and small-scale magnetic fields inside 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 mu G 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 approximate to 10 and regular fields of mu G strength and a few kpc coherence length were generated within 2 Gyr (at z approximate to 3), but field-ordering on the coherence scale of the galaxy size required an additional 6 Gyr (at z approximate to 0.5). Giant galaxies formed their disks at z approximate to 10, allowing more efficient dynamo generation of strong regular fields (with kpc coherence length) already at z approximate to 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 approximate to 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 Square Kilometre Array (SKA). We predict an anticorrelation between galaxy size and ratio between ordering scale and galaxy size. Weak regular fields (small Faraday rotation) in galaxies at z less than or similar to 3 are signatures of major mergers. Undisturbed dwarf galaxies should host fully coherent fields, giving rise to strong Faraday rotation signals. Radio observations may serve as a clock for measuring the time since the last major merger.