Supernova Driving. IV. The Star-formation Rate of Molecular Clouds

Abstract

We compute the star-formation rate (SFR) in molecular clouds (MCs) that originate 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, which is 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 ff , on the virial parameter, α vir , found in previous simulations, and compare a revised version of our turbulent fragmentation model with the numerical results. The dependences on Mach number, , gas to magnetic pressure ratio, β , and compressive to solenoidal power ratio, χ at fixed α vir are not well constrained, because of random scatter due to time and cloud-to-cloud variations in SFR ff . We find that SFR ff in MCs can take any value in the range of 0 ≤ SFR ff  ≲ 0.2, and its probability distribution peaks at a value of SFR ff  ≈ 0.025, consistent with observations. The values of SFR ff and the scatter in the SFR ff – α 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.