Supernova Driving. IV. The Star Formation Rate of Molecular Clouds
  We compute the star formation rate (SFR) in molecular clouds (MCs) that
originate {\it ab initio} in a new, higher-resolution simulation of
supernova-driven turbulence. Because of the large number of well-resolved
clouds with self-consistent boundary and initial conditions, we obtain a large
range of cloud physical parameters with realistic statistical distributions, an
unprecedented sample of star-forming regions to test SFR models and to
interpret observational surveys. We confirm the dependence of the SFR per
free-fall time, $SFR_{\rm ff}$, on the virial parameter, $\alpha_{\rm vir}$,
found in previous simulations, and compare a revised version of our turbulent
fragmentation model with the numerical results. The dependences on Mach number,
${\cal M}$, gas to magnetic pressure ratio, $\beta$, and compressive to
solenoidal power ratio, $\chi$ at fixed $\alpha_{\rm vir}$ are not well
constrained, because of random scatter due to time and cloud-to-cloud
variations in $SFR_{\rm ff}$. We find that $SFR_{\rm ff}$ in MCs can take any
value in the range $0 \le SFR_{\rm ff} \lesssim 0.2$, and its probability
distribution peaks at a value $SFR_{\rm ff}\approx 0.025$, consistent with
observations. The values of $SFR_{\rm ff}$ and the scatter in the $SFR_{\rm
ff}$--$\alpha_{\rm vir}$ relation are consistent with recent measurements in
nearby MCs and in clouds near the Galactic center. Although not explicitly
modeled by the theory, the scatter is consistent with the physical assumptions
of our revised model and may also result in part from a lack of statistical
equilibrium of the turbulence, due to the transient nature of MCs.
