On the shape of the mass-function of dense clumps in the Hi-GAL fields . I : Spectral energy distribution determination and global properties of the mass-functions

Context. Stars form in dense, dusty clumps of molecular clouds, but little is known about their origin and evolution. In particular, the relationship between the mass distribution of these clumps (also known as the clump mass function or CMF) and the stellar initial mass function (IMF), is still poorly understood. Aims: To discern the ''true'' shape of the CMF and to better understand how the CMF may evolve toward the IMF, large samples of bona-fide pre- and proto-stellar clumps are required. The sensitive observations of the Herschel Space Observatory (HSO) are now allowing us to look at large clump populations in various clouds with different physical conditions. Methods: We analyze two fields in the Galactic plane mapped by HSO during its science demonstration phase (SDP), as part of the more complete and unbiased Herschel infrared GALactic Plane Survey (Hi-GAL). These fields underwent a source-extraction and flux-estimation pipeline, which allowed us to obtain a sample with thousands of clumps. Starless and proto-stellar clumps were separated using both color and positional criteria to find those coincident with MIPS 24 $m sources. We describe the probability density functions of the power-law and lognormal models that were used to fit the CMFs. For the lognormal model we applied several statistical techniques to the data and compared their results. Results: The CMFs of the two SDP fields show very similar shapes, but very different mass scales. This similarity is confirmed by the values of the best-fit parameters of either the power-law or lognormal model. The power-law model leads to almost identical CMF slopes, whereas the lognormal model shows that the CMFs have similar widths. Conclusions: The similar CMF shape but different mass scale represents an evidence that the overall process of star formation in the two regions is very different. When comparing with the IMF, we find that the width of the IMF is narrower than the measured widths of the CMF in the two SDP fields. This may suggest that an additional mass selection occurs in later stages of gravitational collapse.