Clumpy shocks and the clump mass function

One possible mechanism for the formation of molecular clouds is large-scale colliding flows. In this paper, we examine whether clumpy, colliding, flows could be responsible for the clump mass functions that have been observed in several regions of embedded star formation, which have been shown to be described by a Salpeter-type slope. The flows presented here, which comprise a population of initially identical clumps, are modelled using smoothed particle hydrodynamics (SPH) and calculations are performed with and without the inclusion of self-gravity. When the shock region is at its densest, we find that the clump mass spectrum is always well modelled by a Salpeter-type slope. This is true regardless of whether the self-gravity is included in the simulations or not, and for our choice of filling factors for the clumpy flows (10, 20 and 40 per cent), and Mach number (5, 10 and 20). In the non-self-gravitating simulations, this slope is retained at lower Mach numbers (M = 5 and 10) as the simulations progress past the densest phase. In the simulations which include self-gravity, we find that low Mach number runs yield a flatter mass function after the densest phase. This is simply a result of increased coagulation due to gravitational collapse of the flows. In the high Mach number runs (M = 20) the Salpeter slope is always lost. The self-gravitating calculations also show that the subgroup of gravitationally bound clumps in which star formation occurs, always contain the most massive clumps in the population. Typically these clumps have a mass of order of the Jeans mass of the initial clumps. The mass function of these bound star-forming clumps is not at all similar to the Salpeter-type mass function observed for stars in the field. We conclude that the clump mass function may not only have nothing to do with gravity, but also nothing to do with the star formation process and the resulting mass distribution of stars. This raises doubt over the claims that the clump mass function is the origin of the stellar initial mass function (IMF), for regions such as ρ Oph, Serpens and the Orion B cloud