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-Alfvénic 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, ρr ^-κ with κ ∼ 1.5-2.5, in agreement with observations. Studying velocity-size scalings, we find that all the simulations are consistent with the observed vℓ^1/2 scaling of supersonic turbulence and seem to approach Kolmogorov turbulence with vℓ^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 α of the density power spectrum, P₃D(ρ, k)k ^α, or equivalently the Δ-variance spectrum of the column density, σ² _Δ (Σ, ℓ) ℓ^-α, switches sign from α ≲ 0 for SFE ∼ 0 to α ≳ 0 when star formation proceeds (SFE > 0). We provide a relation to compute the SFE from a measurement of α. Studying the literature, we find values ranging from α = -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 α values, we infer SFEs and find good agreement with independent measurements based on young stellar object (YSO) counts, where available. Our SFE-α 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.