Abstract

Context. Observations of galaxies up to z {\tilde} 2 show a tight correlation between far-infrared and radio continuum emission, suggesting a relation between star formation activity and magnetic fields in the presence of cosmic rays. Aims: We explain the far-infrared - radio continuum correlation by relating star formation and magnetic field strength in terms of turbulent magnetic field amplification, where turbulence is injected by supernova explosions from massive stars. We assess the potential evolution of this relation at high redshift, and explore the impact on the far-infrared - radio correlation. Methods: We calculate the expected amount of turbulence in galaxies based on their star formation rates, and infer the expected magnetic field strength due to turbulent dynamo amplification. We calculate the timescales for cosmic ray energy losses via synchrotron emission, inverse Compton scattering, ionization and bremsstrahlung emission, probing up to which redshift strong synchrotron emission can be maintained. Results: We find that the correlation between star formation rate and magnetic field strength in the local Universe can be understood as a result of turbulent magnetic field amplification. The ratio of radio to far-infrared surface brightness is expected to increase with total field strength. A continuation of the correlation is expected towards high redshifts. If the typical gas density in the interstellar medium increases at high z, we expect an increase of the magnetic field strength and the radio emission, as indicated by current observations. Such an increase would imply a modification, but not a breakdown of the far-infrared - radio correlation. We expect a breakdown at the redshift when inverse Compton losses start dominating over synchrotron emission. For a given star formation surface density, we calculate the redshift where the far-infrared - radio correlation will break down, yielding z {\tilde} ({$\Sigma$}$_{SFR}$ / 0.0045 M$_{⊙}$ kpc$^{-2}$ yr$^{-1}$)$^{1 / (6 - α / 2)}$. In this relation, the parameter {$\alpha$} describes the evolution of the characteristic ISM density in galaxies as (1 + z)$^{α}$. We note that observed frequencies of 1-10 GHz are particularly well-suited to explore this relation, as bremsstrahlung losses could potentially dominate at low frequencies. Conclusions: Both the possible raise of the radio emission at high redshift and the final breakdown of the far-infrared - radio correlation at a critical redshift will be probed by the Square Kilometre Array (SKA) and its pathfinders, while the typical ISM density in galaxies will be probed with ALMA. The combined measurements will thus allow a verification of the model proposed here.