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We conduct numerical experiments in which we systematically vary the initialdensity over four orders of magnitude and the turbulent velocity over a factorten. In a companion paper, we investigate the dependence of this distributionon the gas thermodynamics. We performed a series of hydrodynamical numericalsimulations using adaptive mesh refinement, with special attention to numericalconvergence. We also adapted an existing analytical model to the case ofcollapsing clouds by employing a density probability distribution function(PDF) $\propto \rho^{-1.5}$ instead of a lognormal distribution. Simulationsand analytical model both show two support regimes, dominated by either thermalenergy or turbulence. For the first regime, we infer that $dN/d \log M \proptoM^0$, while for the second, we obtain $dN/d \log M \propto M^{-3/4}$. This isvalid up to about ten times the mass of the first Larson core, as explained inthe companion paper, leading to a peak of the mass spectrum at $\sim 0.2M_\odot$. From this point, the mass spectrum decreases with decreasing mass.Although the mass spectra we obtain for the most compact clouds qualitativelyresemble the observed initial mass function, the distribution exponent isshallower than the expected Salpeter exponent of -1.35. Nonetheless, we observea possible transition toward a slightly steeper value that is broadlycompatible with the Salpeter exponent for masses above a few solar masses. Thischange in behavior is associated with the change in density PDF, which switchesfrom a power-law to a lognormal distribution. Our results suggest that whilegravitationally induced fragmentation could play an important role for lowmasses, it is likely the turbulently induced fragmentation that leads to theSalpeter exponent.

Stellar mass spectrum within massive collapsing clumps I. Influence of the initial conditions