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Stars form in dense, dusty clumps of molecular clouds, but little is knownabout their origin and evolution. In particular, the relationship between themass distribution of these clumps (also known as the "clump mass function", orCMF) and the stellar initial mass function (IMF), is still poorly understood.In order to discern the "true" shape of the CMF and to better understand howthe CMF may evolve toward the IMF, large samples of bona-fide pre- andproto-stellar clumps are required. The sensitive observations of the HerschelSpace Observatory (HSO) are now allowing us to look at large clump populationsin various clouds with different physical conditions. We analyse two fields inthe Galactic plane mapped by HSO during its science demonstration phase, aspart of the more complete and unbiased Herschel infrared GALactic Plane Survey(Hi-GAL). These fields undergo a source-extraction and flux-estimationpipeline, which allows us to obtain a sample with thousands of clumps. Starlessand proto-stellar clumps are separated using both color and positional criteriato find those coincident with MIPS 24 micron sources. We describe theprobability density functions of the power-law and lognormal models that areused to fit the CMFs, and we then find their best-fit parameters. For thelognormal model we apply several statistical techniques to the data and comparetheir results. The CMFs of the two SDP fields show very similar shapes, butvery different mass scales. This similarity is confirmed by the values of thebest-fit parameters of either the power-law or lognormal model. The power-lawmodel leads to almost identical CMF slopes, whereas the lognormal model showsthat the CMFs have similar widths. The similar CMF shape but different massscale represents an evidence that the overall process of star formation in thetwo regions is very different.

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