Normalized mass surface density Xn as function of 1 − yn for truncated density profiles as given in Eq. (1) for various power indices n ranging from 0 to 10. The thicker lines correspond to n = 0, 1, and 3. For a fixed pressure ratio q the mass surface densities for a given power index n vary from the central value at 1 − yn = q2 /n to zero at the edge of the cloud where 1 − yn = 1. The central values of the normalized mass surface density for various pressure ratios q are shown as thin gray lines.
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