Profiles of the normalized mass surface density X_n of a truncated density profile as given in Eq. (1) for three assumptions of the pressure ratio q = p_ext/p_c. The maxima or the curves are labeled with the corresponding power index n. The profiles for n = 1 and n = 3 are enhanced with a thicker line. The dashed lines are Gaussian approximations (Eq. (A.21)) where the variance is obtained using Eq. (A.20). The profile for n = 0 need to be considered as an asymptote.