Radio Continuum Emission from Evolving Star-Forming Galaxies -- I. Correlations Involving the Total Synchrotron Luminosity
Synchrotron radiation dominates the continuum emission of star-forming galaxies in the frequency range from a few $\rm MHz$ to about $30\,\rm{GHz}$. We model the total synchrotron emission of a large population of evolving star-forming galaxies using the semi-analytic galaxy formation model GALFORM combined with the dynamo simulation code MAGNETIZER. Assuming local energy equipartition between cosmic rays and magnetic fields, we calculate the specific synchrotron luminosity $L_ν$ for each simulated galaxy at various frequencies and find strong positive correlations between $L_ν$ and both the star formation rate ($\rm SFR$) and characteristic galaxy rotation speed $V_{\rm rot}$ for redshifts up to $z\simeq 3$. At low redshifts, the turbulent magnetic field is found to dominate in the synchrotron luminosity, but the contribution of the large-scale magnetic field increases with redshift and becomes important for $z\gtrsim 1$. The correlation between $L_ν$ and $\rm SFR$ arises from the tight correlation between the disc gas mass $M_{\rm gas}$ and $\rm SFR$, and the correlation between $L_ν$ and $V_{\rm rot}$ is additionally a consequence of the stellar mass Tully--Fisher relation for main-sequence galaxies. At low redshifts, the model predictions and observational data compiled for this work show remarkable agreement, but a discrepancy arises at higher redshifts, where modelled $\rm SFR$ values are systematically smaller than those previously inferred from observations. These theoretical models will aid the interpretation of next-generation radio surveys with the Square Kilometre Array and other telescopes.