Re-Examining Larson's Scaling Relationships in Galactic Molecular Clouds

The properties of Galactic molecular clouds tabulated by Solomon et al. (SRBY) are re-examined using the Boston University-FCRAO Galactic Ring Survey of ¹³CO J = 1-0 emission. These new data provide a lower opacity tracer of molecular clouds and improved angular and spectral resolution compared with previous surveys of molecular line emission along the Galactic Plane. We calculate giant molecular cloud (GMC) masses within the SRBY cloud boundaries assuming local thermodynamic equilibrium (LTE) conditions throughout the cloud and a constant H₂ to ¹³CO abundance, while accounting for the variation of the ¹²C/¹³C with galactocentric radius. The LTE-derived masses are typically five times smaller than the SRBY virial masses. The corresponding median mass surface density of molecular hydrogen for this sample is 42 M _sun pc^-2, which is significantly lower than the value derived by SRBY (median 206 M _sun pc^-2) that has been widely adopted by most models of cloud evolution and star formation. This discrepancy arises from both the extrapolation by SRBY of velocity dispersion, size, and CO luminosity to the 1 K antenna temperature isophote that likely overestimates the GMC masses and our assumption of constant ¹³CO abundance over the projected area of each cloud. Owing to the uncertainty of molecular abundances in the envelopes of clouds, the mass surface density of GMCs could be larger than the values derived from our ¹³CO measurements. From velocity dispersions derived from the ¹³CO data, we find that the coefficient of the cloud structure functions, v _° = σ _v /R ^1/2, is not constant, as required to satisfy Larson's scaling relationships, but rather systematically varies with the surface density of the cloud as ~Σ^0.5 as expected for clouds in self-gravitational equilibrium.