Comparing the statistics of interstellar turbulence in simulations and observations: Solenoidal versus compressive turbulence forcing

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We study two limiting cases of turbulence forcing in numerical experiments: solenoidal (divergence-free) forcing, and compressive (curl-free) forcing, and compare our results to observations reported in the literature. We solve the equations of hydrodynamics on grids with up to 1024³ cells for purely solenoidal and purely compressive forcing. Eleven lower-resolution models with mixtures of both forcings are also analysed. We find velocity dispersion--size relations consistent with observations and independent numerical simulations, irrespective of the type of forcing. However, compressive forcing yields stronger turbulent compression at the same RMS Mach number than solenoidal forcing, resulting in a three times larger standard deviation of volumetric and column density probability distributions (PDFs). We conclude that the strong dependence of the density PDF on the type of forcing must be taken into account in any theory using the PDF to predict properties of star formation. We supply a quantitative description of this dependence. We find that different observed regions show evidence of different mixtures of compressive and solenoidal forcing, with more compressive forcing occurring primarily in swept-up shells.