  We propose a simple analytical method for estimating the central volume density of prestellar molecular cloud cores from their column density profiles. Prestellar cores feature a flat central part of the column density and volume density profiles of the same size indicating the existence of a uniform density inner region. The size of this region is set by the thermal pressure force which depends only on the central volume density and temperature of the core, and can provide a direct measurement of the central volume density. Thus a simple length measurement can immediately yield a central density estimate independent of any dynamical model for the core and without the need for fitting. Using the radius at which the column density is 90% of the central value as an estimate of the size of the flat inner part of the column density profile yields an estimate of the central volume density within a factor of 2 for well resolved cores. 
A New Recipe for Obtaining Central Volume Densities of Prestellar Cores   from Size Measurements