The formation of star clusters - II. 3D simulations of magnetohydrodynamic turbulence in molecular clouds

We present a series of decaying turbulence simulations that represent a cluster-forming clump within a molecular cloud, investigating the role of magnetic fields on the formation of potential star-forming cores. We present an exhaustive analysis of numerical data from these simulations that include a compilation of all of the distributions of physical properties that characterize bound cores-including their masses, radii, mean densities, angular momenta, spins, magnetizations and mass-to-flux ratios. We also present line maps of our models that can be compared with observations. Our simulations range between 5 and 30 Jeans masses of gas, and are representative of molecular cloud clumps with masses between 100 and 1000M(circle dot). The field strengths in the bound cores that form tend to have the same ratio of gas pressure to magnetic pressure, beta, as the mean beta of the simulation. The cores have mass-to-flux ratios that are generally less than that of the original cloud, and so a cloud that is initially highly supercritical can produce cores that are slightly supercritical, similar to that seen by Zeeman measurements of molecular cloud cores. Clouds that are initially only slightly supercritical will instead collapse along the field lines into sheets, and the cores that form as these sheets fragment have a different distribution of masses than what is observed. The spin rates of these cores ( wherein 20-40 per cent of cores have Omega(tff)>= 0.2) suggests that subsequent fragmentation into multiple systems is likely. The sizes of the bound cores that are produced are typically 0.02-0.2 pc and have densities in the range 104-105 cm(-3) in agreement with observational surveys. Finally, our numerical data allow us to test theoretical models of the mass spectrum of cores, such as the turbulent fragmentation picture of Padoan & Nordlund. We find that while this model gets the shape of the core mass spectrum reasonably well, it fails to predict the peak mass in the core mass spectrum.