An Empirical Estimation of the Galaxy Radio Number Counts model at 3~GHz
  and the Effect of Gravitational Lensing
  We analyzed the evolution of 3GHz luminosity function of radio selected
galaxies through cosmic time, up to about 1 Gyr after Big Bang, with making use
of the VLA-COSMOS3GHz large project. We estimated the luminosity function for
SFGs and AGNs in the VLA-COSMOS field respectively with two independent
methods, the non-parametric C-method for accuracy to avoid the effect of cosmic
variance and parametric MCMC method assuming pure luminosity evolution. We
obtained pure luminosity evolution parameter as L*=(1+z)(3.36-0.31)z for SFG
and L* = (1+z)(2.91-0.99)z for AGN. The resultant model agreed well with
observed number counts down to sub-muJy level. Additionally, we compared the
model with cosmic star formation rate density history with multiple
observations in various wavelength and confirmed that our result is consistent
with literature up to z=3. We further analyzed the statistical effect of
gravitational lensing due to the dark matter halos and found that the effect is
maximized at S_3GHz = 100muJy with about 1% contribution for SFG and less than
0.5% for AGN for the flux range considered in this study. In order to evaluate
the effect of lensing magnification on parameter estimation in the SKA
observations, we performed Fisher analysis and find that while the bias is
limited, there is a distinguishable effect on SFG LF evolution parameter with
SKA I MID wide survey, and all-sky and wide survey for AGN LF evolution
parameters.
