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.