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We study the star formation efficiency (SFE) in simulations and observationsof turbulent, magnetized, molecular clouds. We find that the probabilitydensity functions (PDFs) of the density and the column density in oursimulations with solenoidal, mixed, and compressive forcing of the turbulence,sonic Mach numbers of 3-50, and magnetic fields in the super- to thetrans-Alfvenic regime, all develop power-law tails of flattening slope withincreasing SFE. The high-density tails of the PDFs are consistent withequivalent radial density profiles, rho ~ r^(-kappa) with kappa ~ 1.5-2.5, inagreement with observations. Studying velocity-size scalings, we find that allthe simulations are consistent with the observed v ~ l^(1/2) scaling ofsupersonic turbulence, and seem to approach Kolmogorov turbulence with v ~l^(1/3) below the sonic scale. The velocity-size scaling is, however, largelyindependent of the SFE. In contrast, the density-size and column density-sizescalings are highly sensitive to star formation. We find that the power-lawslope alpha of the density power spectrum, P(rho,k) ~ k^alpha, or equivalentlythe Delta-variance spectrum of column density, DV(Sigma,l) ~ l^(-alpha),switches sign from alpha < 0 for SFE ~ 0 to alpha > 0 when star formationproceeds (SFE > 0). We provide a relation to compute the SFE from a measurementof alpha. Studying the literature, we find values ranging from alpha = -1.6 to+1.6 in observations covering scales from the large-scale atomic medium, overcold molecular clouds, down to dense star-forming cores. From those alphavalues, we infer SFEs and find good agreement with independent measurementsbased on young stellar object (YSO) counts, where available. Our SFE-alpharelation provides an independent estimate of the SFE based on the columndensity map of a cloud alone, without requiring a priori knowledge ofstar-formation activity or YSO counts.

On the Star Formation Efficiency of Turbulent Magnetized Clouds