The Radio-FIR Correlation in the Context of Deep Radio Source Counts
Increasingly deep, confusion-limited radio surveys have pushed direct radio source-count measurements down to tens of $μ$Jy at 1.4 GHz. Confusion-noise P(D) analyses extend the statistical counts to below $1\,\mathrm{μJy}$. Radio source counts have allowed for constraints on the radio-derived star formation rate density (SFRD) history through models of the backwards evolution of the local radio luminosity function, using the radio-FIR correlation, $q \propto \log(L_{\mathrm{FIR}}/L_{1.4})$, to convert radio luminosities to FIR luminosities and hence star-formation rates. Recent deep radio source counts from MeerKAT suggest a potential tension in the SFRD history between radio and UV/IR measurements at $1\lesssim z\lesssim 2$. This corresponds to a $\gtrsim 3σ$ discrepancy between the predicted and measured source counts near the star forming galaxy source count $S^2n(S)$ peak of ${\sim}30\,\mathrm{μJy}$ under both a pure luminosity (PLE) and combined luminosity and density evolution (LADE). We consider what the requirement of agreement between radio source counts and the observed UV/IR SFRD indicates about the redshift evolution of the radio-FIR correlation and its intrinsic scatter out to $z=3$. We introduce a radio-luminosity based parameterization to $q_{\mathrm{FIR}}(z)$ based on changing thermal radio fractions alone that agrees with the observed stellar-mass dependent $q_{\mathrm{FIR}}(z)$ better than a non-evolving or decreasing $q_{\mathrm{FIR}}(z)$. Despite this, we find that a decreasing $q_{\mathrm{FIR}}(z)$ at fixed radio luminosity provides better agreement between source counts and the observed SFRD, while a $q_{\mathrm{FIR}}(z)$ that breaks down due to cosmic ray losses requires an intrinsic scatter up to $σ_q\approx 0.3\,\mathrm{dex}$.