  Recent studies seem to suggest that the stellar initial mass function (IMF)
in early-type galaxies might be different from a classical Kroupa or Chabrier
IMF, i.e. contain a larger fraction of the total mass in low-mass stars. From a
theoretical point of view, supersonic turbulence has been the subject of
interest in many analytical theories proposing a strong correlation with the
characteristic mass of the core mass function (CMF) in star forming regions,
and as a consequence with the stellar IMF. Performing two suites of smoothed
particles hydrodynamics (SPH) simulations with different mass resolutions, we
aim at testing the effects of variations in the turbulent properties of a
dense, star forming molecular cloud on the shape of the system mass function in
different density regimes. While analytical theories predict a shift of the
peak of the CMF towards lower masses with increasing velocity dispersion of the
cloud, we observe in the low-density regime the opposite trend, with high Mach
numbers giving rise to a top-heavy mass distribution. For the high-density
regime we do not find any trend correlating the Mach number with the
characteristic mass of the resulting IMF, implying that the dynamics of
protostellar accretion discs and fragmentation on small scales is not strongly
affected by turbulence driven at the scale of the cloud. Furthermore, we
suggest that a significant fraction of dense cores are disrupted by turbulence
before stars can be formed in their interior through gravitational collapse.
Although this particular study has limitations in its numerical resolution, we
suggest that our results, along with those from other studies, cast doubt on
the turbulent fragmentation models on the IMF that simply map the CMF to the
IMF.
