Simultaneous evolution of the virial parameter and star formation rate
  in molecular clumps undergoing global hierarchical collapse
  We compare dense clumps and cores in a numerical simulation of molecular
clouds (MCs) undergoing global hierarchical collapse (GHC) to observations in
two MCs at different evolutionary stages, the Pipe and the G14.225 clouds, to
test the ability of the GHC scenario to follow the early evolution of the
energy budget and star formation activity of these structures. In the
simulation, we select a region that contains cores of sizes and densities
similar to the Pipe cores, and find that it evolves through accretion,
developing substructure similar to that of G14.225 cloud after $\sim 1.6$ Myr.
Within this region, we follow the evolution of the Larson ratio $\mathcal{L}
\equiv \sigma_{\rm v}/R^{1/2}$, where $\sigma_{\rm v}$ is the velocity
dispersion and $R$ is the size, the virial parameter $\alpha$, and the star
formation activity of the cores/clumps. In the simulation, we find that as the
region evolves: $i)$ its clumps have $\mathcal{L}$ and $\alpha$ values first
consistent with those of the Pipe substructures and later with those of
G14.225; $ii)$ the individual cores first exhibit a decrease in $\alpha$
followed by an increase when star formation begins; $iii)$ collectively, the
ensemble of cores/clumps reproduces the observed trend of lower $\alpha$ for
higher-mass objects, and $iv)$ the star formation rate and star formation
efficiency increase monotonically. We suggest that this evolution is due to the
simultaneous loss of externally-driven compressive kinetic energy and increase
of the self-gravity-driven motions. We conclude that the GHC scenario provides
a realistic description of the evolution of the energy budget of the clouds'
substructure at early times, which occurs simultaneously with an evolution of
the star formation activity.
