Collapsing molecular clouds with tracer particles: Part 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 behavior 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, $t_{\rm{sing}}$, and examine how it transitions to high density. We find that the time to collapse is uniformly distributed between $0.25 t_{\rm{ff}}$ and the end of the simulation at $\sim 1 t_{\rm{ff}}$, and that the duration of collapse is universally short, $\Delta t \sim 0.1 t_{\rm{ff}}$, where $t_{\rm{ff}}$ 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 over density in $\sim 0.1 t_{\rm{ff}}$.