Clump mass function at an early stage of molecular cloud evolution - I. A statistical approach

We derive the mass function of condensations (clumps) which were formed through a turbulent cascade over a range of spatial scales L= 20 pc during early, predominantly turbulent evolution of a molecular cloud. The approach rests upon the assumption of a statistical clump massdensity relationship n?mx with a scale dependence of the exponent x obtained from equipartition relations between various forms of energy of clumps. The derived clump mass function (ClMF) could be represented by series of two or three power laws, depending on the chosen equipartition relation, the velocity scaling index and the type of turbulent forcing. The high-mass ClMF exhibits an average slope G?-1, typical for fractal clouds, whereas its intermediate-mass part is shallower or flattened, in agreement with some observational studies.