The far-infrared/radio correlation for a sample of strongly lensed dusty star-forming galaxies detected by Herschel

We investigate the radio-far infrared (FIR) correlation for a sample of $28$ bright high-redshift ($1 \lesssim z \lesssim 4$) star-forming galaxies selected in the FIR from the Herschel-ATLAS fields as candidates to be strongly gravitationally lensed. The radio information comes either from high sensitivity dedicated ATCA observations at $2.1$ GHz or from cross-matches with the FIRST survey at $1.4$ GHz. By taking advantage of source brightness possibly enhanced by lensing magnification, we identify a weak evolution with redshift out to $z\lesssim 4$ of the FIR-to-radio luminosity ratio $q_{\rm FIR}$. We also find that the $q_{\rm FIR}$ parameter as a function of the radio power $L_{1.4\,\rm GHz}$ displays a clear decreasing trend, similarly to what is observed for optically/radio selected lensed quasars found in literature, yet covering a complementary region in the $q_{\rm FIR}-L_{1.4\,\rm GHz}$ diagram. We interpret such a behavior in the framework of an in-situ galaxy formation scenario, as a result of the transition from an early dust-obscured star-forming phase (mainly pinpointed by our FIR selection) to a late radio-loud quasar phase (preferentially sampled by the optical/radio selection).