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A key for understanding the evolution of galaxies and in particular theirstar formation history will be future ultra-deep radio surveys. While starformation rates (SFRs) are regularly estimated with phenomenological formulasbased on the local FIR-radio correlation, we present here a physicallymotivated model to relate star formation with radio fluxes. Such a relationholds only in frequency ranges where the flux is dominated by synchrotronemission, as this radiation originates from cosmic rays produced in supernovaremnants, therefore reflecting recent star formation. At low frequenciessynchrotron emission can be absorbed by the free-free mechanism. Thissuppression becomes stronger with increasing number density of the gas, moreprecisely of the free electrons. We estimate the critical observing frequencybelow which radio emission is not tracing the SFR, and use the threewell-studied local galaxies M 51, M 82, and Arp 220 as test cases for ourmodel. If the observed galaxy is at high redshift, this critical frequencymoves along with other spectral features to lower values in the observingframe. In the absence of systematic evolutionary effects, one would thereforeexpect that the method can be applied at lower observing frequencies for highredshift observations. However, in case of a strong increase of the typical gascolumn densities towards high redshift, the increasing free-free absorption mayerase the star formation signatures at low frequencies. At high radiofrequencies both, free-free emission and the thermal bump, can dominate thespectrum, also limiting the applicability of this method.

Tracing star formation with non-thermal radio emission