The far-infrared/radio correlation and radio spectral index of galaxies
  in the SFR-M* plane up to z 2
  [Abridged] We study the evolution of the radio spectral index and
far-infrared/radio correlation (FRC) across the star-formation rate-stellar
masse (i.e. SFR-M*) plane up to z 2. We start from a M*-selected sample of
galaxies with reliable SFR and redshift estimates. We then grid the SFR-M*
plane in several redshift ranges and measure the infrared luminosity, radio
luminosity, radio spectral index, and ultimately the FRC index (i.e. qFIR) of
each SFR-M*-z bin. The infrared luminosities of our SFR-M*-z bins are estimated
using their stacked far-infrared flux densities inferred from observations
obtained with Herschel. Their radio luminosities and radio spectral indices
(i.e. alpha, where Snu nu^-alpha) are estimated using their stacked 1.4GHz and
610MHz flux densities from the VLA and GMRT, respectively. Our far-infrared and
radio observations include the most widely studied blank extragalactic fields
-GOODS-N/S, ECDFS, and COSMOS- covering a sky area of 2deg^2. Using this
methodology, we constrain the radio spectral index and FRC index of
star-forming galaxies with M*>10^10Msun and 0<z<2.3. We find that
alpha^1.4GHz_610MHz does not evolve significantly with redshift or with the
distance of a galaxy with respect to the main sequence (MS) of the SFR-M* plane
(i.e. Delta_log(SSFR)_MS=log[SSFR(galaxy)/SSFR_MS(M*,z)]). Instead,
star-forming galaxies have a radio spectral index consistent with a canonical
value of 0.8, which suggests that their radio spectra are dominated by
non-thermal optically thin synchrotron emission. We find that qFIR displays a
moderate but statistically significant redshift evolution as
qFIR(z)=(2.35+/-0.08)*(1+z)^(-0.12+/-0.04), consistent with some previous
literature. Finally, we find no significant correlation between qFIR and
Delta_log(SSFR)_MS, though a weak positive trend, as observed in one of our
redshift bins, cannot be firmly ruled out using our dataset.
