  Turbulence is a critical ingredient for star formation, yet its role for the
initial mass function (IMF) is not fully understood. Here we perform
magnetohydrodynamical (MHD) simulations of star cluster formation including
gravity, turbulence, magnetic fields, stellar heating and outflow feedback to
study the influence of the mode of turbulence driving on IMF. We find that
simulations that employ purely compressive turbulence driving (COMP) produce a
higher fraction of low-mass stars as compared to simulations that use purely
solenoidal driving (SOL). The characteristic (median) mass of the sink particle
(protostellar) distribution for COMP is shifted to lower masses by a factor of
~ 1.5 compared to SOL. Our simulation IMFs capture the important features of
the observed IMF form. We find that turbulence-regulated theories of the IMF
match our simulation IMFs reasonably well in the high-mass and low-mass range,
but underestimate the number of very low-mass stars, which form towards the
later stages of our simulations and stop accreting due to dynamical
interactions. Our simulations show that for both COMP and SOL, the multiplicity
fraction is an increasing function of the primary mass, although the
multiplicity fraction in COMP is higher than that of SOL for any primary mass
range. We find that binary mass ratio distribution is independent of the
turbulence driving mode. The average specific angular momentum of the sink
particles in SOL is a factor of 2 higher than that for COMP. Overall, we
conclude that the turbulence driving mode plays a significant role in shaping
the IMF.
