Tracing star formation with non-thermal radio emission

Understanding the evolution of galaxies and in particular their star formation history is a central challenge of modern cosmology. Theoretical scenarios will be constrained by future ultra deep radio surveys. In this paper we present an analytical tool for analyzing radio data. Our physical model, based on an analytical description of the steady-state cosmic ray spectrum, explains the correlation between the non-thermal radio flux and the star formation rate (SFR). As cosmic rays are produced in supernova remnants, their injection rate is proportional to the supernova rate and thus also to the SFR. When these highly energetic charged particles travel in the magnetized interstellar medium they emit synchrotron radiation. As a result there is a relation between the SFR and the non-thermal radio emission. A crucial point is that synchrotron emission can be absorbed again by the free-free mechanism. This suppression becomes stronger with increasing number density of the gas, more precisely of the free electrons, and with decreasing frequency. We present an estimate of the critical frequency above which radio emission can be used as a tracer for the SFR. If the observed galaxy is redshifted, this critical frequency moves along with other spectral features to lower values in the observing frame. The method can therefore be successfully applied at high redshift. However, for high redshift, i.e. > 5 , and observations at high radio frequency bands, i.e. > 50 GHz, special caution should be paid, as the observed flux might be dominated by free-free emission or the thermal contribution.