Combining Physical galaxy models with radio observations to constrain the SFRs of high-z dusty star forming galaxies

We complement our previous analysis of a sample of z~1-2 luminous and ultra-luminous infrared galaxies ((U)LIRGs), by adding deep VLA radio observations at 1.4 GHz to a large data-set from the far-UV to the sub-mm, including Spitzer and Herschel data. Given the relatively small number of (U)LIRGs in our sample with high S/N radio data, and to extend our study to a different family of galaxies, we also include 6 well sampled near IR-selected BzK galaxies at z~1.5. From our analysis based on the radiative transfer spectral synthesis code GRASIL, we find that, while the IR luminosity may be a biased tracer of the star formation rate (SFR) depending on the age of stars dominating the dust heating, the inclusion of the radio flux offers significantly tighter constraints on SFR. Our predicted SFRs are in good agreement with the estimates based on rest-frame radio luminosity and the Bell (2003) calibration. The extensive spectro-photometric coverage of our sample allows us to set important constraints on the SF history of individual objects. For essentially all galaxies we find evidence for a rather continuous SFR and a peak epoch of SF preceding that of the observation by a few Gyrs. This seems to correspond to a formation redshift of z~5-6. We finally show that our physical analysis may affect the interpretation of the SFR-M* diagram, by possibly shifting, with respect to previous works, the position of the most dust obscured objects to higher M* and lower SFRs.