Annu. Rev. Astron. Astrophys. 1991. 29: 581-625 Copyright © 1991 by Annual Reviews. All rights reserved

2.1 Theoretical Basis

If I_CO is the CO brightness temperature integrated over the line profile (I_CO T_CO dV), one can define the CO luminosity of a cloud as

1.

where D is the distance of the cloud. For a uniform, spherical cloud of radius R, the CO luminosity is given by

2.

where T_CO is the peak brightness temperature in the CO line and V the linewidth. Numerous studies of Galactic molecular clouds have shown that they are self-gravitating. For a cloud of mass M in virial equilibrium, V = sqrt(GM / R) and

3.

To the extent that the ratio / T_CO does not vary in the mean from galaxy to galaxy and the emission of separate clouds along each line of sight is not overlapped in velocity, Eq. (3) indicates that the total CO luminosity of a galaxy (summing over all individual clouds in the antenna beam) is directly proportional to the total mass of molecular clouds.

In Galactic GMCs, typical mean densities and CO brightness temperatures are 100-300 H₂ cm^-3 and 5-10 K (Scoville & Sanders 1987). In the nearby starburst galaxy M82, observations of CO J = 3 -> 2., 2 -> 1, and 1 -> 0 (Wild et al 1989, Turner et al 1990) indicate the presence of two cloud populations: a cool one (T ~ 10-20 K) with low density [n (H₂) < 10³ cm^-3], and a warm one (T ~ 75 K) with high density [n (H₂) ~ 5 x 10⁴ cm^-3]. In spite of the markedly different cloud properties in these two components, the difference in / T between these two populations and the clouds in the Milky Way is only a factor of ~ 1.5. Therefore, even in the extreme conditions encountered in M82, the assumption of a constant conversion factor between CO luminosity and H₂, mass can lead to global molecular gas mass estimates that are reasonably accurate.

Maloney & Black (1988) and Elmegreen (1989) have considered the effects of metallicity variations on the H₂ masses derived from the CO luminosities, and in particular the case of very low metallicity in irregular galaxies in which a reduction in the UV shielding may lead to smaller molecular cores.