Utilizing multiwavelength dust emission maps acquired with Herschel, we reconstruct local volume density and dust temperature profiles for the prestellar cores B68 and L1689B using an inverse-Abel transform-based technique. We present intrinsic radial dust temperature profiles of starless cores directly from dust continuum emission maps disentangling the effect of temperature variations along the line of sight, which were previously limited to the radiative transfer calculations. The reconstructed dust temperature profiles show a significant drop in the core center, a flat inner part, and a rising outward trend until the background cloud temperature is reached. The central beam-averaged dust temperatures obtained for B68 and L1689B are 9.3 ± 0.5 K and 9.8 ± 0.5 K, respectively, which are lower than the temperatures of 11.3 K and 11.6 K obtained from direct SED fitting. The best mass estimates derived by integrating the volume density profiles of B68 and L1689B are 1.6 M and 11 M , respectively. Comparing our results for B68 with the near-infrared extinction studies, we find that the dust opacity law adopted by the HGBS project, κ λ = 0.1 × agrees to within 50% with the dust extinction constraints.

Context. For the project Galactic cold cores, Herschel photometric observations were carried out as a follow-up of cold regions of interstellar clouds previously identified with the Planck satellite. The aim of the project is to derive the physical properties of the population of cold sources and to study its connection to ongoing and future star formation. Aims. We build a catalogue of cold sources within the clouds in 116 fields observed with the Herschel PACS and SPIRE instruments. We wish to determine the general physical characteristics of the cold sources and to examine the correlations with their host cloud properties. Methods. From Herschel data, we computed colour temperature and column density maps of the fields. We estimated the distance to the target clouds and provide both uncertainties and reliability flags for the distances. The getsources multiwavelength source extraction algorithm was employed to build a catalogue of several thousand cold sources. Mid-infrared data were used, along with colour and position criteria, to separate starless and protostellar sources. We also propose another classification method based on submillimetre temperature profiles. We analysed the statistical distributions of the physical properties of the source samples. Results. We provide a catalogue of ∼4000 cold sources within or near star forming clouds, most of which are located either in nearby molecular complexes ( 1 kpc) or in star forming regions of the nearby galactic arms (∼2 kpc). About 70% of the sources have a size compatible with an individual core, and 35% of those sources are likely to be gravitationally bound. Significant statistical differences in physical properties are found between starless and protostellar sources, in column density versus dust temperature, mass versus size, and mass versus dust temperature diagrams. The core mass functions are very similar to those previously reported for other regions. On statistical grounds we find that gravitationally bound sources have higher background column densities (median N bg (H 2 ) ∼ 5 × 10 21 cm −2 ) than unbound sources (median N bg (H 2 ) ∼ 3 × 10 21 cm −2 ). These values of N bg (H 2 ) are higher for higher dust temperatures of the external layers of the parent cloud. However, only in a few cases do we find clear N bg (H 2 ) thresholds for the presence of cores. The dust temperatures of cloud external layers show clear variations with galactic location, as may the source temperatures. Conclusions. Our data support a more complex view of star formation than in the simple idea of a column density threshold. They show a clear influence of the surrounding UV-visible radiation on how cores distribute in their host clouds with possible variations on the Galactic scale.