A Pressure and Metallicity Dependence for Molecular Cloud Correlations and the Calibration of Mass

The correlation of molecular cloud mass with the fourth power of the velocity dispersion, the square of the radius, and the inverse of the density squared is addressed using a modified version of the proposal by Maloney (1988) and Fleck (1988) that the correlation is due to virialized internal motions and a uniform external pressure. The average column density of the molecular part of a large cloud is found to depend almost exclusively on the cloud velocity dispersion and very little on the peak temperature. The mass of an unresolved aggregate of clouds in another galaxy is also derived in terms of the integrated CO luminosity in the telescope beam. The influence of metallicity on the calibration of mass is discussed and applied to recent observations of CO in dwarf galaxies, small Virgo galaxies, and the LMC. An expression is given for the fractional mass of a cloud that is in the molecular core.