We use the distance probability density function ( DPDF ) formalism of Ellsworth-Bowers et al .
( 24 , 23 ) 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 _ { { } _ { \sun } } and 50 % complete above 70 M _ { { } _ { \sun } } .
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 \pm 0.1 for sources nearer than 6.5 kpc and \alpha = 1.9 \pm 0.1 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 % .