A simple model of the radio-infrared correlation depending on gas surface density and redshift

We introduce a simple parametric model of the radio-infrared correlation (i.e., the ratio between the IR luminosity and the 1.4 GHz radio luminosity, $q_{\mbox{\tiny IR}}$) by considering the energy loss rate of high-energy cosmic ray (CR) electron governed by the radiative cooling (synchrotron, bremsstrahlung, inverse Compton scattering), ionization, and adiabatic expansion. Each process of CR electron energy loss is explicitly computed and compared to each other. We rewrite the energy loss rate of each process to be dependent on the gas surface density and redshift using the relevant scaling relations. By combining each energy loss rate, the fraction of the synchrotron energy loss rate is computed as a function of gas surface density and redshift, and used to extrapolate the well-established `local' radio-infrared correlation to the high-redshift universe. The locally established $q_{\mbox{\tiny IR}}$ is reformulated to be dependent upon the redshift and the gas surface density and applied for understanding the observed distribution of the radio-infrared correlation of high-redshift galaxies in \cite{delvecchio_etal_2021}. Our model predicts that $q_{\mbox{\tiny IR}}$ value is anti-correlated with gas surface density and the redshift dependency of $q_{\mbox{\tiny IR}}$ value changes by gas surface density of galaxies, which captures the observed trend of $q_{\mbox{\tiny IR}}$ values for stellar mass selected star forming galaxies with a minimal impact of radio-infrared selection bias.