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

Context. Stars constitute the building blocks of our Universe, and their formation is an astrophysical problem of great importance. Aims. We aim to understand the fragmentation of massive molecular star-forming clumps and the effect of initial conditions, namely the density and the level of turbulence, on the resulting distribution of stars. For this purpose, we conduct numerical experiments in which we systematically vary the initial density over four orders of magnitude and the turbulent velocity over a factor ten. In a companion paper, we investigate the dependence of this distribution on the gas thermodynamics. Methods. We performed a series of hydrodynamical numerical simulations using adaptive mesh refinement, with special attention to numerical convergence. We also adapted an existing analytical model to the case of collapsing clouds by employing a density probability distribution function (PDF) proportional to rho(-1.5) instead of a lognormal distribution. Results. Simulations and analytical model both show two support regimes, a thermally dominated regime and a turbulence-dominated regime. For the first regime, we infer that dN/d log M proportional to M-0, while for the second regime, we obtain dN/d log M proportional to M-3/4. This is valid up to about ten times the mass of the first Larson core, as explained in the companion paper, leading to a peak of the mass spectrum at similar to 0.2 M-circle dot. From this point, the mass spectrum decreases with decreasing mass except for the most diffuse clouds, where disk fragmentation leads to the formation of objects down to the mass of the first Larson core, that is, to a few 10(-2) M-circle dot. Conclusions. Although the mass spectra we obtain for the most compact clouds qualitatively resemble the observed initial mass function, the distribution exponent is shallower than the expected Salpeter exponent of -1.35. Nonetheless, we observe a possible transition toward a slightly steeper value that is broadly compatible with the Salpeter exponent for masses above a few solar masses. This change in behavior is associated with the change in density PDF, which switches from a power-law to a lognormal distribution. Our results suggest that while gravitationally induced fragmentation could play an important role for low masses, it is likely the turbulently induced fragmentation that leads to the Salpeter exponent.