Cluster Formation in Contracting Molecular Clouds

We explore, through a simplified, semianalytic model, the formation of dense clusters containing massive stars. The parent cloud spawning the cluster is represented as an isothermal sphere. This sphere is in near-force balance between self-gravity and turbulent pressure. Self-gravity, mediated by turbulent dissipation, drives slow contraction of the cloud, eventually leading to a sharp central spike in density and the onset of dynamical instability. We suggest that, in a real cloud, this transition marks the late and rapid production of massive stars. We also offer an empirical prescription, akin to the Schmidt law, for low-mass star formation in our contracting cloud. Applying this prescription to the Orion Nebula Cluster, we are able to reproduce the accelerating star formation previously inferred from the distribution of member stars in the HR diagram. The cloud turns about 10% of its mass into low-mass stars before becoming dynamically unstable. Over a cloud free-fall time, this figure drops to 1%, consistent with the overall star formation efficiency of molecular clouds in the Galaxy.