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%.