We construct the average radio spectral energy distribution ( SED ) of highly star-forming galaxies ( HSFGs ) up to z \sim 4 .
Infrared and radio luminosities are bound by a tight correlation that is defined by the so-called q parameter .
This infrared-radio correlation provides the basis for the use of radio luminosity as a star-formation tracer .
Recent stacking and survival analysis studies find q to be decreasing with increasing redshift .
It was pointed out that a possible cause of the redshift trend could be the computation of rest-frame radio luminosity via a single power-law assumption of the star-forming galaxies ’ ( SFGs ) SED .
To test this , we constrained the shape of the radio SED of a sample of HSFGs .
To achieve a broad rest-frame frequency range , we combined previously published Very Large Array observations of the COSMOS field at 1.4 \mathrm { GHz } and 3 \mathrm { GHz } with unpublished Giant Meterwave Radio Telescope ( GMRT ) observations at 325 \mathrm { MHz } and 610 \mathrm { MHz } by employing survival analysis to account for non-detections in the GMRT maps .
We selected a sample of HSFGs in a broad redshift range ( z \in [ 0.3 , 4 ] , \mathrm { SFR } \geq 100 \mathrm { M _ { \odot } } / \mathrm { yr } ) and constructed the average radio SED .
By fitting a broken power-law , we find that the spectral index changes from \alpha _ { 1 } = 0.42 \pm 0.06 below a rest-frame frequency of 4.3 \mathrm { GHz } to \alpha _ { 2 } = 0.94 \pm 0.06 above 4.3 \mathrm { GHz } .
Our results are in line with previous low-redshift studies of HSFGs ( \mathrm { SFR } > 10 \mathrm { M _ { \odot } } / \mathrm { yr } ) that show the SED of HSFGs to differ from the SED found for normal SFGs ( \mathrm { SFR } < 10 \mathrm { M _ { \odot } } / \mathrm { yr } ) .
The difference is mainly in a steeper spectrum around 10 \mathrm { GHz } , which could indicate a smaller fraction of thermal free-free emission .
Finally , we also discuss the impact of applying this broken power-law SED in place of a simple power-law in K-corrections of HSFGs and a typical radio SED for normal SFGs drawn from the literature .
We find that the shape of the radio SED is unlikely to be the root cause of the q - z trend in SFGs .