A Two-Stage Fragmentation Model for Star Cluster Formation
We extend the linear analysis of the non-ideal magnetohydrodynamic equations for a model planar molecular cloud (Ciolek & Basu 2006) to apply to the context of clustered star formation. The linear analysis has shown that the time and length scales for the collapse of a cloud depend strongly upon the ambient cloud properties, including density, ionization fraction, and mass-to-flux ratio. We propose and show that the collapse times and length scales for substructures (subclumps) within a collapsing macro structure (clump) can be dramatically smaller than that for the macro structure itself. This analysis accounts for the transition from the ultraviolet dominated ionization regime to the cosmic ray dominated ionization regime of the cloud. The varying collapse times and lengths for the clumps versus subclumps implies that cluster formation can be achieved through a hierarchical two-stage fragmentation within a molecular cloud.