a) Circularly averaged radial surface brightness profiles of B68 at 70, 160, 250, 350, 500 μm derived from Herschel/SPIRE and PACS data (after adding Planck offsets). b) Logarithmic slopes of the circularly averaged column density profile (solid black curve) and 500 μm intensity profile (solid blue curve) of B68 as a function of radius. The horizontal dotted line is the logarithmic slope s = −1 expected for the column density profile of a core with a ρ ∝ r^-2 density profile. The vertical dashed line marks the integration upper bound adopted when integrating the right-hand side of Eq. (2) to perform the Abel reconstruction of the density and temperature profiles (see Sect. 3). The vertical dot-dashed line shows the radius of the footprint automatically derived for B68 by the getsources source-finding algorithm.