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 _ { \ast } ) plane up to z \sim 2 .
We start from a stellar-mass-selected sample of galaxies with reliable SFR and redshift estimates .
We then grid the SFR - M _ { \ast } plane in several redshift ranges and measure the infrared luminosity , radio luminosity , radio spectral index , and ultimately the FRC index ( i.e . q _ { FIR } ) of each SFR– M _ { \ast } – z bin .
The infrared luminosities of our SFR– M _ { \ast } – 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 . \alpha , where S _ { \nu } \propto \nu ^ { - \alpha } ) 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 \sim 2.0 deg ^ { 2 } .
Using this methodology , we constrain the radio spectral index and FRC index of star-forming galaxies with M _ { \ast } > 10 ^ { 10 } M _ { \odot } and 0 < z < 2.3 .
We find that \alpha ^ { 1.4 GHz } _ { 610 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 _ { \ast } plane ( i.e . { \Delta log ( SSFR ) _ { MS } = log [ SSFR ( galaxy ) / SSFR _ { MS } } ( M _ { \ast } ,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 , q _ { FIR } , displays a moderate but statistically significant redshift evolution as q _ { FIR } ( z ) = ( 2.35 \pm 0.08 ) \times ( 1 + z ) ^ { -0.12 \pm 0.04 } , consistent with some previous literature .
Finally , we find no significant correlation between q _ { FIR } and \Delta log ( { SSFR } ) _ { MS } , though a weak positive trend , as observed in one of our redshift bins ( i.e . \Delta [ q _ { FIR } ] / \Delta [ \Delta log ( { SSFR } ) _ { MS } ] = 0.22 \pm 0.07 at 0.5 < z < 0.8 ) , can not be firmly ruled out using our dataset .