Simultaneous evolution of the virial parameter and star formation rate in star forming molecular clouds

We study the evolution of the virial parameter, $\alpha$, and the star formation activity of a star forming region in a numerical simulation and two observational samples likely to be at different evolutionary stages, the Pipe and the G14.225 clouds. We consider a numerical simulation of turbulence in the warm atomic gas, in which clouds form by a combination of thermal instability and turbulent compressions. In this simulation we select a region with physical properties similar to those of the Pipe in both its global physical properties and the dense cores it contains, and show that this region evolves to become similar to the G14.225 cloud and its substructure in the course of $\sim$1.5 Myr. Within this region, we follow the evolution of $\alpha$ and the star formation activity of the cores over this time interval, during which they grow in mass by accretion and develop further substructure of higher density. We find that the individual cores evolve by exhibiting first a mild decrease in $\alpha$ followed by a rapid increase when star formation begins. We suggest this evolution is due to an early loss of external compressive kinetic energy followed by an increase of the gravitationally driven motions. Nevertheless, collectively, the ensamble of clumps and cores reproduces the recently observed trend of decreasing $\alpha$ for objects of higher mass. We also find that the star formation rate and star formation efficiency increase monotonically as the region evolves. Thus, we propose that the energy balance, $\alpha$, and the star formation activity determine the evolutionary stage of a star forming region, and that a star forming region like the Pipe may evolve into a G14.225-like stage over the course of a few megayears if it is allowed to accrete from its environment. This evolution is consistent with the recently proposed scenario of hierarchical gravitational collapse.