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Fig. 4


PDF of the normalized mass surface density Xn in case of spheres (top figure) and the asymptotic PDF in case of cylinders (bottom figure) with a truncated radial density profile given by Eq. (1) for various assumptions of the power n. The thin lines show at which mass surface density Xn at given density ratio q = ρ(rcl) /ρc the PDF corresponding to a certain power n truncates (for spheres) or has a pole (for cylinders). The lines are labeled with log 10q. The dashed lines show the asymptotic behavior at large and small Xn.

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