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
$\rm{z\,\sim\,1}$.
