Cosmic evolution of star-forming galaxies to $z \simeq 1.8$ in the faint low-frequency radio source population

We study the properties of star-forming galaxies selected at 610 MHz with the GMRT in a survey covering $\sim$1.86 deg$^2$ down to a noise of $\sim$7.1\,$\mu$Jy / beam. These were identified by combining multiple classification diagnostics: optical, X-ray, infrared and radio data. Of the 1685 SFGs from the GMRT sample, 496 have spectroscopic redshifts whereas 1189 have photometric redshifts. We find that the IRRC of star-forming galaxies, quantified by the infrared-to-1.4 GHz radio luminosity ratio $\rm{q_{IR}}$, decreases with increasing redshift: $\rm{q_{IR}\,=\,2.86\pm0.04(1\,+\,z)^{-0.20\pm0.02}}$ out to $z \sim 1.8$. We use the $\rm{V/V_{max}}$ statistic to quantify the evolution of the co-moving space density of the SFG sample. Averaged over luminosity our results indicate $\rm{\langle V/V_{max} \rangle}$ to be $\rm{0.51\,\pm\, 0.06}$, which is consistent with no evolution in overall space density. However we find $\rm V/V_{max}$ to be a function of radio luminosity, indicating strong luminosity evolution with redshift. We explore the evolution of the SFGs radio luminosity function by separating the source into five redshift bins and comparing to theoretical model predictions. We find a strong redshift trend that can be fitted with a pure luminosity evolution of the form $\rm{L_{610\,MHz}\,\propto\,(\,1+\,z)^{(2.95\pm0.19)-(0.50\pm0.15)z}}$. We calculate the cosmic SFR density since $\rm{z \sim 1.5}$ by integrating the parametric fits of the evolved 610\,MHz luminosity function. Our sample reproduces the expected steep decline in the star formation rate density since $\rm{z\,\sim\,1}$.