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.