Collapsing molecular clouds with tracer particles - II. Collapse histories

In order to develop a complete theory of star formation, one essentially needs to know two things: what collapses and how long it takes. This is the second paper in a series, where we query how long a parcel of gas takes to collapse and the process it undergoes. We embed pseudo-Lagrangian tracer particles in simulations of collapsing molecular clouds, identify the particles that end in dense knots, and then examine the collapse history of the gas. We find a nearly universal behaviour of cruise-then-collapse, wherein a core stays at intermediate densities for a significant fraction of its life before finally collapsing. We identify time immediately before each core collapses, t(sing), and examine how it transitions to high density. We find that the time to collapse is uniformly distributed between 0.25 t(ff) and the end of the simulation at similar to 1 t(ff), and that the duration of collapse is universally short, Delta t similar to 0.1 t(ff), where t(ff) is the free-fall time at the mean density. We describe the collapse in three stages: collection, hardening, and singularity. Collection sweeps low-density gas into moderate density. Hardening brings kinetic and gravitational energies into quasi-equipartition. Singularity is the free-fall collapse, forming an envelope in rough energy balance and central overdensity in similar to 0.1 t(ff).