  Using a suite of 3D hydrodynamical simulations of star-forming molecular
clouds, we investigate how the density probability distribution function (PDF)
changes when including gravity, turbulence, magnetic fields, and protostellar
outflows and heating. We find that the density PDF is not lognormal when
outflows and self-gravity are considered. Self-gravity produces a power-law
tail at high densities and the inclusion of stellar feedback from protostellar
outflows and heating produces significant time-varying deviations from a
lognormal distribution at the low densities. The simulation with outflows has
an excess of diffuse gas compared to the simulations without outflows, exhibits
increased average sonic Mach number, and maintains a slower star formation rate
over the entire duration of the run. We study the mass transfer between the
diffuse gas in the lognormal peak of the PDF, the collapsing gas in the
power-law tail, and the stars. We find that the mass fraction in the power-law
tail is constant, such that the stars form out of the power-law gas at the same
rate at which the gas from the lognormal part replenishes the power-law. We
find that turbulence does not provide significant support in the dense gas
associated with the power-law tail. When including outflows and magnetic fields
in addition to driven turbulence, the rate of mass transfer from the lognormal
to the power-law, and then to the stars, becomes significantly slower,
resulting in slower star formation rates and longer depletion times.
