Prestellar Cores in Turbulent Clouds: Properties of Critical Cores

A fraction of the dense cores within a turbulent molecular cloud will eventually collapse to form stars. Identifying the physical criteria for instability and analyzing critical core properties is therefore necessary to star formation theory. Here we quantify the characteristics of an ensemble of "critical cores" on the verge of collapse. This critical epoch was identified in a companion paper, which followed the dynamical evolution of prestellar cores in numerical simulations of turbulent, self-gravitating clouds. We find that radial profiles of density and turbulent velocity dispersion in individual critical cores are consistent with our new model for turbulent equilibrium spheres (TESs). While a global linewidth-size relation exists for a cloud with given size and Mach number, the turbulent scaling relations around each core exhibit significant variations. As a result, there is no single density threshold for collapse; instead, cores collapse at a range of densities determined by the local sonic scale and gravitational potential environment. The critical cores in our simulations are mostly transonic; we do not find either purely thermal or highly turbulent cores. In our low Mach number model which better resolves the characteristic mass and sonic scales, we find marginal evidence that the core mass function (CMF) of critical cores peaks around a characteristic mass scale associated with the large-scale cloud properties. We highlight the importance of constructing the CMF at the critical time for the purpose of testing gravoturbulent fragmentation theories, and derive the resolution requirements to unambiguously identify the peak of the CMF.