ON THE STAR FORMATION EFFICIENCY OF TURBULENT MAGNETIZED CLOUDS

We study the star formation efficiency (SFE) in simulations and observations of turbulent, magnetized, molecular clouds. We find that the probability density functions (PDFs) of the density and the column density in our simulations with solenoidal, mixed, and compressive forcing of turbulence, sonic Mach numbers of 3-50, and magnetic fields in the super-to the trans-Alfvenic regime all develop power-law tails of flattening slope with increasing SFE. The high-density tails of the PDFs are consistent with equivalent radial density profiles, rho proportional to r(-kappa) with kappa similar to 1.5-2.5, in agreement with observations. Studying velocity-size scalings, we find that all the simulations are consistent with the observed upsilon proportional to l(1/2) scaling of supersonic turbulence and seem to approach Kolmogorov turbulence with upsilon proportional to l(1/3) below the sonic scale. The velocity-size scaling is, however, largely independent of the SFE. In contrast, the density-size and column density-size scalings are highly sensitive to star formation. We find that the power-law slope a of the density power spectrum, P-3D(rho, k) proportional to k(alpha), or equivalently the Delta-variance spectrum of the column density, sigma(2)(Delta)(Sigma, l) proportional to l(-alpha), switches sign from alpha less than or similar to 0 for SFE similar to 0 to alpha greater than or similar to 0 when star formation proceeds (SFE > 0). We provide a relation to compute the SFE from a measurement of 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, over cold molecular clouds, down to dense star-forming cores. From those alpha values, we infer SFEs and find good agreement with independent measurements based on young stellar object (YSO) counts, where available. Our SFE-alpha relation provides an independent estimate of the SFE based on the column density map of a cloud alone, without requiring a priori knowledge of star formation activity or YSO counts.