Dependence of the star formation efficiency on global parameters of molecular clouds

We investigate the response of the star formation efficiency (SFE) to the main parameters of simulations of molecular cloud formation and evolution (growth and star formation) by the collision of warm diffuse medium [warm neutral medium (WNM)] cylindrical streams, and compare our results with theoretical predictions for this dependence. The parameters we vary are the Mach number of the inflow velocity of the streams, M-s,M-inf, the rms Mach number, M-s,M-bgd, of the initial background turbulence in the WNM and the total mass contained in the colliding gas streams, M-inf, which is eventually deposited in the forming clouds. Because the SFE is a function of time, we define two estimators for it, the 'absolute' SFE, measured at t = 25 Myr into the simulation's evolution (SFEabs,25), and the 'relative' SFE, measured 5 Myr after the onset of star formation in each simulation (SFErel,5). The latter is close to the 'SFE per free-fall time' for gas at n = 100 cm(-3). Our simulations suggest that the dominant parameter controlling the SFE is M-inf. The SFE in general decreases as this parameter is decreased, presumably because, with the other parameters being equal, smaller fragments are more weakly gravitationally bound. In terms of the initial virial parameter (alpha equivalent to 2E(kin)/vertical bar E-grav vertical bar) of the clouds, our results are qualitatively consistent with the theoretical prediction by Krumholz & McKee that the SFE decreases with increasing alpha. However, quantitatively, their prediction lies beyond the 1 sigma error of our observed trend. This may be due to the fact that the simulated clouds develop significant gravitational contraction motions, which overwhelm the initial turbulent motions, contrary to Krumholz & McKee's assumption of stationary turbulent support. We also observe that the SFE decreases (moderately) with increasing M-s,M-inf, although the SFR increases. The decrease of the SFE with M-s,M-inf is thus a consequence of the cloud mass accretion rate from the WNM increasing more steeply with this parameter than the SFR. Finally, we find that increasing levels of background turbulence (injected at scales comparable to the streams' transverse radius) similarly reduce the SFE, because the turbulence disrupts the coherence of the colliding streams, fragmenting the cloud and producing small-scale clumps, which again have lower SFEs.