Properties of the cavity half-widths to check the model validity. The left panel shows a comparison between the half-width of the outflow cavity and the location radius of a BH r _cav/R _BH. The right panel shows the wind stand-off radius r _sta/r _cav, and shows by contour lines the cavity maximum half-width dominated by the shear motion of the AGN disk gas r _shear/r _cav.