Simulations of the polarized radio sky and predictions on the confusion limit in polarization for future radio surveys

Numerical simulations offer the unique possibility to forecast the results of surveys and targeted observations that will be performed with next generation instruments like the Square Kilometre Array. In this paper, we investigate for the first time how future radio surveys in polarization will be affected by confusion noise. To do this, we produce 1.4 GHz simulated full-Stokes images of the extra-galactic sky by modelling various discrete radio sources populations. The results of our modelling are compared to data in the literature to check the reliability of our procedure. We also estimate the number of polarized sources detectable by future surveys. Finally, from the simulated images we evaluate the confusion limits in I, Q, and U Stokes parameters, giving analytical formulas of their behaviour as a function of the angular resolution.