The far-infrared/radio correlation and radio spectral index of galaxies in the SFR-M$_∗$ plane up to z2

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 stellar-mass-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 the Herschel Space Observatory. Their radio luminosities and radio spectral indices (i.e. α, where Sν ∝ ν−α) are estimated using their stacked 1.4 GHz and 610 MHz flux densities from the Very Large Array and Giant Metre-wave Radio Telescope, respectively. Our far-infrared and radio observations include the most widely studied blank extragalactic fields – GOODS-N, GOODS-S, ECDFS, and COSMOS – covering a total sky area of ~2.0 deg2. Using this methodology, we constrain the radio spectral index and FRC index of star-forming galaxies with M∗ > 1010 M⊙ and 0 <z< 2.3. We find that α1.4 GHz610 MHz 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. Δlog (SSFR)MS = log  [ SSFR(galaxy) /SSFRMS(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 the FRC index, 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 Δlog (SSFR)MS, though a weak positive trend, as observed in one of our redshift bins (i.e. Δ [ qFIR ]/Δ [ Δlog (SSFR)MS ] = 0.22 ± 0.07 at 0.5 <z< 0.8), cannot be firmly ruled out using our dataset.