PDF of the mass surface density of Bonnor-Ebert spheres embedded in a medium with p_ext/k = 2 × 10⁴ K cm^-3 for different gravitational states (solid black curves). The curves correspond to overpressures with i = −1,0,1 where is the overpressure of a critically stable Bonnor-Ebert sphere. The PDFs are directly compared with those of spheres with a simple density profile (Eq. (1)) with n = 3 (dotted curves). The black dashed lines are asymptotes of the PDF Σ₃P_sph(Σ₃) in the limit of high mass surface densities (Eq. (39)). The PDF of a Bonnor-Ebert sphere in the limit of infinite overpressure is shown as a gray curve and is derived assuming a sphere with an analytical density profile with n = 2. The gray dashed lines are the corresponding power-law asymptotes in the limit of low (Eq. (34)) and high (Eq. (40)) mass surface densities.