The MOSDEF Survey: Calibrating the relationship between H$\alpha$ star-formation rate and radio continuum luminosity at $1.4 < z < 2.6$

The observed empirical relation between the star-formation rates (SFR) of low-redshift galaxies and their radio continuum luminosity offers a potential means of measuring SFR in high redshift galaxies that is unaffected by dust obscuration. In this study, we make the first test for redshift evolution in the SFR-radio continuum relation at high redshift using dust-corrected H$\alpha$ SFR. Our sample consists of 178 galaxies from the MOSFIRE Deep Evolution Field (MOSDEF) Survey at $1.4 < z < 2.6$ with rest-frame optical spectroscopy and deep 1.5 GHz radio continuum observations from the Karl G. Jansky Very Large Array (VLA) GOODS North field. Using a stacking analysis we compare the observed radio continuum luminosities with those predicted from the dust-corrected H$\alpha$ SFR assuming a range of $z\sim0$ relations. We find no evidence for a systematic evolution with redshift, when stacking the radio continuum as a function of dust-corrected H$\alpha$ SFR and when stacking both optical spectroscopy and radio continuum as a function of stellar mass. We conclude that locally calibrated relations between SFR and radio continuum luminosity remain valid out to $z\sim 2$.