Geometry-Independent Determination of Radial Density Distributions in
  Molecular Cloud Cores and Other Astronomical Objects
  We present a geometry-independent method for determining the shapes of radial
volume density profiles of astronomical objects whose geometries are unknown,
based on a single column density map. Such profiles are often critical to
understand the physics and chemistry of molecular cloud cores, in which star
formation takes place. The method presented here does not assume any geometry
for the object being studied, thus removing a significant source of bias.
Instead it exploits contour self-similarity in column density maps which
appears to be common in data for astronomical objects. Our method may be
applied to many types of astronomical objects and observable quantities so long
as they satisfy a limited set of conditions which we describe in detail. We
derive the method analytically, test it numerically, and illustrate its utility
using 2MASS-derived dust extinction in molecular cloud cores. While not having
made an extensive comparison of different density profiles, we find that the
overall radial density distribution within molecular cloud cores is adequately
described by an attenuated power law.
