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We use a suite of 3D simulations of star-forming molecular clouds, with andwithout stellar feedback, magnetic fields, and driven turbulence, to study thecompression and expansion rates of the gas as functions of density. We showthat, around the mean density, supersonic turbulence promotes rough equilibriumbetween the amounts of compressing and expanding gas, consistent withcontinuous gas cycling between high and low density states. We find that theinclusion of protostellar jets produces rapidly expanding and compressinglow-density gas. We find that the gas mass flux peaks at the transition betweenthe lognormal and power-law forms of the density probability distributionfunction (PDF). This is consistent with the transition density tracking thepost-shock density, which promotes an enhancement of mass at this density(i.e., shock compression and filament formation). At high densities, the gasdynamics are dominated by self-gravity: the compression rate in all of our runsmatches the rate of the run with only gravity, suggesting that processes otherthan self-gravity have little effect at these densities. The net gas mass fluxbecomes constant at a density below the sink formation threshold, where itequals the star formation rate. The density at which the net gas mass fluxequals the star formation rate is one order of magnitude lower than our sinkthreshold density, corresponds to the formation of the second power-law tail inthe density PDF, and sets the overall star formation rates of thesesimulations.

What Sets the Star Formation Rate of Molecular Clouds? The Density Distribution as a Fingerprint of Compression and Expansion Rates