  The mass fraction of dense gas within giant molecular clouds (GMCs) of the
Milky Way is investigated using 13CO data from the FCRAO Galactic Plane Surveys
and the Bolocam Galactic Plane Survey (BGPS) of 1.1 mm dust continuum emission.
A sample of 860 compact dust sources are selected from the BGPS catalog and
kinematically linked to 344 clouds of extended (>3') 13CO J=1-0 emission. Gas
masses are tabulated for the full dust source and subregions within the dust
sources with mass surface densities greater than 200 M_solar/pc^2, which are
assumed to be regions of enhanced volume density. Masses of the parent GMCs are
calculated assuming optically thin 13CO J=1-0 emission and LTE conditions. The
mean fractional mass of dust sources to host GMC mass is 0.11 (-0.06, +0.12).
The high column density subregions comprise 0.07 (-0.05, +0.13) of the mass of
the cloud. Owing to our assumptions, these values are upper limits to the true
mass fractions. The fractional mass of dense gas is independent of GMC mass and
gas surface density. The low dense gas mass fraction suggests that the
formation of dense structures within GMCs is the primary bottleneck for star
formation. The distribution of velocity differences between the dense gas and
the low density material along the line of sight is also examined. We find a
strong, centrally peaked distribution centered on zero velocity displacement.
This distribution of velocity differences is modeled with radially converging
flows towards the dense gas position that are randomly oriented with respect to
the observed line of sight. These models constrain the infall velocities to be
2-4 km/s for various flow configurations.
