A MIGHTEE robust measurement of the star formation rate-radio correlation
Determining the relationship between star-formation rate (SFR) and the radio luminosity ($L_{1.4}$) is critical if we are to trace the star-formation history of the Universe dust-agnostically using current and future radio facilities. However, until now, such work has relied on potentially biased binary classifications of sources to remove contaminating active galactic nuclei (AGN). We present a new, statistically-driven methodology for deriving the SFR -- $L_{1.4}$ relation, removing the need for problematic cuts. We use a Bayesian hierarchical mixture model fit to the radio-detected sources in the deep MIGHTEE COSMOS DR1 catalogue, incorporating the full SFR posterior probability distributions generated by state-of-the-art spectral energy distribution fitting code \texttt{GRAHSP}. This allows us to probabilistically determine a mean SFR -- $L_{1.4}$ relation for the SF dominated galaxies, whilst accounting for changing fractions of SF dominated sources across redshift, radio luminosity and stellar mass ranges. We find that the SFR -- radio luminosity correlation exhibits a significant dependence on redshift, but a stellar mass dependence that is weaker than previous studies. Our resultant SFR-radio correlation is $\log_{10}(\text{SFR}/M_{\odot}\,\text{yr}^{-1}) = 0.790\times(\log _{10}(L_{1.4}/\text{W\,Hz}^{-1})-23) + 1.244 \times(1+z)^{0.122} -0.033 \times (\log_{10}(M_*/M_{\odot})-10)$, with an intrinsic scatter of 0.178 dex. We show that this redshift evolution could be explained by a moderate evolution in the radio spectral index of SF galaxies. We attribute the lack of observed strong dependence on stellar mass, compared to recent studies, to the novel statistical approach that does not rely on cuts to remove AGN.