Galactic synchrotron emission and the FIR-radio correlation at high redshift

Galactic magnetic fields in the local Universe are strong and omnipresent. There is mounting evidence that galaxies were magnetized already in the early Universe. Theoretical scenarios including the turbulent small-scale dynamo predict magnetic energy densities comparable to the one of turbulence. Based on the assumption of this energy equipartition, we determine the galactic synchrotron flux as a function of redshift z. The conditions in the early Universe are different from the present day, in particular the galaxies have more intense star formation. To cover a large range of conditions we consider models based on two different systems: one model galaxy comparable to the Milky Way and one typical high-z starburst galaxy. We include a model of the steady state cosmic ray spectrum and find that synchrotron emission can be detected up to cosmological redshifts with current and future radio telescopes. Turbulent dynamo theory is in agreement with the origin of the observed correlation between the far-infrared (FIR) luminosity L_FIR and the radio luminosity L_radio. Our model reproduces this correlation well at z=0. We extrapolate the FIR-radio correlation to higher redshift and predict a time evolution with a significant deviation from its present-day appearance already at z~2 for a gas density that increases strongly with z. In particular, we predict a decrease of the radio luminosity with redshift which is caused by the increase of cosmic ray energy losses at high z. The result is an increase of the ratio between L_FIR and L_radio. Simultaneously, we predict that the slope of the FIR-radio correlation becomes shallower with redshift. This behavior of the correlation could be observed in the near future with ultra-deep radio surveys.