The Mass-Size Relation and the Constancy of GMC Surface Densities in the Milky Way

Abstract: We use two existing molecular cloud catalogs derived from the same CO survey and two catalogs derived from local dust extinction surveys to investigate the nature of the GMC mass-size relation in the Galaxy. We find that the four surveys are well described by $M_{GMC} \sim R^2$ implying a constant mean surface density, $\Sigma_{GMC}$, for the cataloged clouds. However, the scaling coefficients and scatter differ significantly between the CO and extinction derived relations. We find that the additional scatter seen in the CO relations is due to a systematic variation in $\Sigma_{GMC}$ with Galactic radius that is unobservable in the local extinction data. We decompose this radial variation of $\Sigma_{GMC}$ into two components, a linear negative gradient with Galactic radius and a broad peak coincident with the molecular ring and superposed on the linear gradient. We show that the former may be due to a radial dependence of X${CO}$ on metallicity while the latter likely results from a combination of increased surface densities of individual GMCs and a systematic upward bias in the measurements of $\Sigma{GMC}$ due to cloud blending in the molecular ring. We attribute the difference in scaling coefficients between the CO and extinction data to an underestimate of X${CO}$. We recalibrate the CO observations of nearby GMCs using extinction measurements to find that locally X${CO}$ $=$ 3.6$\pm$0.3 $\times$ 10$^{20}$ cm$^{-2}$ (K-km/s)$^{-1}$. We conclude that outside the molecular ring the GMC population of the Galaxy can be described to relatively good precision by a constant $\Sigma_{GMC}$ of 35 M$_\odot$ pc$^{-2}$.