Molecular Cloud Evolution VI. Measuring cloud ages
  In previous contributions, we have presented an analytical model describing
the evolution of molecular clouds (MCs) undergoing hierarchical gravitational
contraction. The cloud's evolution is characterized by an initial increase in
its mass, density, and star formation rate (SFR) and efficiency (SFE) as it
contracts, followed by a decrease of these quantities as newly formed massive
stars begin to disrupt the cloud. The main parameter of the model is the
maximum mass reached by the cloud during its evolution. Thus, specifying the
instantaneous mass and some other variable completely determines the cloud's
evolutionary stage. We apply the model to interpret the observed scatter in
SFEs of the cloud sample compiled by Lada et al.\ as an evolutionary effect so
that, although clouds such as California and Orion A have similar masses, they
are in very different evolutionary stages, causing their very different
observed SFRs and SFEs. The model predicts that the California cloud will
eventually reach a significantly larger total mass than the Orion A cloud.
Next, we apply the model to derive estimated ages of the clouds since the time
when approximately 25\% of their mass had become molecular. We find ages from
$\sim 1.5$ to 27 Myr, with the most inactive clouds being the youngest. Further
predictions of the model are that clouds with very low SFEs should have massive
atomic envelopes constituting the majority of their gravitational mass, and
that low-mass clouds ($M \sim 10^3$-$10^4 \, M_\odot$) end their lives with a
mini-burst of star formation, reaching SFRs $\sim 300$-$500\, M_\odot$
Myr$^{-1}$. By this time, they have contracted to become compact ($\sim 1$ pc)
massive star-forming clumps, in general embedded within larger GMCs.
