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

Context. Molecular clouds (MCs) exhibit supersonic turbulent velocity and density fluctuations on virtually all scales observed by modern telescopes. The origin and structural characteristics of this turbulence are, however, still poorly understood. Aims. To shed light on this subject, we study two extreme cases of turbulence forcing in numerical experiments: solenoidal (divergence-free) forcing, and compressive (curl-free) forcing. We compare our results to observational data reported in the literature. Methods. We solve the equations of isothermal hydrodynamics on periodic uniform grids with up to 10243 grid points. We compare results obtained with five different analysis techniques to observational data: density probability distribution functions (PDFs), centroid velocity increments, principal component analyses, Fourier spectra and ∆-variances. Results. Using Fourier spectra and ∆-variance analyses, we find that both compressive and solenoidal forcings yield velocity dispersion–size relations consistent with observations and independent numerical simulations. Compressive forcing yields stronger compression and rarefaction at the same RMS Mach number, resulting in roughly three times larger dispersions of volumetric and column density PDFs. Comparing these results with the column density PDFs obtained in the Perseus MC indicates the presence of a mainly compressive forcing agent within the Shell region investigated by Goodman and coworkers. The PDFs of both volumetric and column densities are typically close to log-normal distributions, but they nevertheless exhibit non-Gaussian higher-order moments (skewness and kurtosis) caused by intermittent fluctuations. We compare intermittency statistics of centroid velocity increments with observational studies by Hily-Blant et al., showing that the turbulence statistics of solenoidal forcing agree well with the statistics measured in the Polaris Flare. Furthermore, we compare results of principal component analysis with observational studies by Heyer et al., showing that G216-2.5 and most of the Rosette MC is in very good agreement with the statistics obtained in solenoidal forcing. On the other hand, the interior of an ionising shell within the Rosette MC displays clear signatures of compressive turbulence forcing. Additionally, we find a weak correlation between density and Mach number, such that the local Mach number decreases with increasing density on average. We speculate that this may naturally explain the observed transonic velocity dispersions typically measured for prestellar cores, if these cores formed close to the sonic scale in a supersonic turbulent medium. Conclusions. We conclude that both solenoidal and compressive forcings are compatible with observations. Depending on the subregion, observational data exhibit statistical signatures obtained for both solenoidal and compressive turbulence forcings, with compressive forcing primarily occurring in swept-up shells.