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The mass function of clumps observed in molecular clouds raises interestingtheoretical issues, especially in its relation to the stellar initial massfunction. We propose a statistical model of the mass function of prestellarcores (CMF), formed in self-gravitating isothermal clouds at a given stage oftheir evolution. The latter is characterized by the mass-density probabilitydistribution function ($\rho$-PDF), which is a power-law with slope $q$. Thevariety of MCs is divided in ensembles according to the PDF slope and eachensemble is represented by a single spherical cloud. The cores are consideredas elements of self-similar structure typical for fractal clouds and aremodeled by spherical objects populating each cloud shell. Our model assumesrelations between size, mass and density of the statistical cores. Out of thema core mass-density relationship $\rho\propto m^x$ is derived where$x=1/(1+q)$. We found that $q$ determines the existence or non-existence of athreshold density for core collapse. The derived general CMF is a power law ofslope $-1$ while the CMF of gravitationally unstable cores has a slope $(-1 +x/2)$, comparable with the slopes of the high-mass part of the stellar initialmass function and of observational CMFs.

Statistical mass function of prestellar cores from the density distribution of their natal clouds