The Bolocam Galactic Plane Survey. XIII. Physical Properties and Mass
  Functions of Dense Molecular Cloud Structures
  We use the distance probability density function (DPDF) formalism of
Ellsworth-Bowers et al. (2013, 2015) to derive physical properties for the
collection of 1,710 Bolocam Galactic Plane Survey (BGPS) version 2 sources with
well-constrained distance estimates. To account for Malmquist bias, we estimate
that the present sample of BGPS sources is 90% complete above 400 $M_\odot$ and
50% complete above 70 $M_\odot$. The mass distributions for the entire sample
and astrophysically motivated subsets are generally fitted well by a lognormal
function, with approximately power-law distributions at high mass. Power-law
behavior emerges more clearly when the sample population is narrowed in
heliocentric distance (power-law index $\alpha = 2.0\pm0.1$ for sources nearer
than 6.5 kpc and $\alpha = 1.9\pm0.1$ for objects between 2 kpc and 10 kpc).
The high-mass power-law indices are generally $1.85 \leq \alpha \leq 2.05$ for
various subsamples of sources, intermediate between that of giant molecular
clouds and the stellar initial mass function. The fit to the entire sample
yields a high-mass power-law $\hat{\alpha} = 1.94_{-0.10}^{+0.34}$. Physical
properties of BGPS sources are consistent with large molecular cloud clumps or
small molecular clouds, but the fractal nature of the dense interstellar medium
makes difficult the mapping of observational categories to the dominant
physical processes driving the observed structure. The face-on map of the
Galactic disk's mass surface density based on BGPS dense molecular cloud
structures reveals the high-mass star-forming regions W43, W49, and W51 as
prominent mass concentrations in the first quadrant. Furthermore, we present a
0.25-kpc resolution map of the dense gas mass fraction across the Galactic disk
that peaks around 5%.
