Which Molecular Cloud Structures Are Bound?
  We analyze surveys of molecular cloud structures defined by tracers ranging
from CO $J = 1-0$ through $^{13}$CO $J = 1-0$ to dust emission together with
NH$_3$ data. The mean value of the virial parameter and the fraction of mass in
bound structures depends on the method used to identify structures. Generally,
the virial parameter decreases and the fraction of mass in bound structures
increases with the effective density of the tracer, the surface density and
mass of the structures, and the distance from the center of a galaxy. For the
most complete surveys of structures in the Galaxy defined by CO $J = 1-0$, the
fraction of mass that is in bound structures is 0.19. For catalogs of other
galaxies based on CO $J = 2-1$, the fraction is 0.35. These results offer
substantial alleviation of the fundamental problem of slow star formation. If
only clouds found to be bound are counted and they are assumed to collapse in a
free-fall time at their mean cloud density, the sum over all clouds in a
complete survey of the Galaxy yields a predicted star formation rate of 46
solar masses per year, a factor of 6.5 less than if all clouds are bound.
