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.
