PDF of the mass surface density of isothermal self-gravitating pressurized cylinders for various overpressures. The vertical line marks the pole position of the PDFs and is labeled with the corresponding pressure ratio q^-1. The asymptotes at high and low mass surface density are shown as black dashed lines. The gray curves are the corresponding asymptotic PDFs (Eq. (43)) where the pole is removed. The power-law asymptotes at high mass surface densities are shown as gray dashed lines.