SUPER III. Broad Line Region properties of AGN at z$\sim$2

The SINFONI survey for Unveiling the Physics and Effect of Radiative feedback (SUPER) was designed to conduct a blind search for AGN-driven outflows on X-ray selected AGN at redshift z$\sim$2 with high ($\sim$2 kpc) spatial resolution, and correlate them to the properties of the host galaxy and central black hole. The main aims of this paper are: a) to derive reliable estimates for the BH mass and accretion rates for the Type-1 AGN in this survey; b) to characterize the properties of the AGN driven winds in the BLR. We analyzed rest-frame optical and UV spectra of 21 Type-1 AGN. We found that the BH masses estimated from H$\alpha$ and H$\beta$ lines are in agreement. We estimate BH masses in the range Log(M$\rm_{BH}/M_{\odot}$)=8.4-10.8 and Eddington ratios $\rm\lambda_{Edd}$ =0.04-1.3. We confirm that the CIV line width does not correlate with the Balmer lines and the peak of the line profile is blue-shifted with respect to the [OIII]-based systemic redshift. These findings support the idea that the CIV line is tracing outflowing gas in the BLR, with velocities up to $\sim$4700 km/s. We confirm the strong dependence of the BLR wind velocity with the UV-to-Xray continuum slope, L$\rm_{Bol}$ and $\rm\lambda_{Edd}$. We inferred BLR mass outflow rates in the range 0.005-3 M$_{\odot}$/yr, showing a correlation with the bolometric luminosity consistent with that observed for ionized winds in the NLR and X-ray winds detected in local AGN, and kinetic power $\sim$10$^{[-7:-4]}\times$ L$\rm_{Bol}$. Finally, we found an anti-correlation between the equivalent width of the [OIII] line with respect to the CIV shift, and a positive correlation with [OIII] outflow velocity. These findings, for the first time in an unbiased sample of AGN at z$\sim$2, support a scenario where BLR winds are connected to galaxy scale detected outflows, and are capable of affecting the gas in the NLR located at kpc scale.