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

2.2 Empirical Basis

2.2.1 THE GALAXY A number of observational attempts have been made to determine empirically the constant of proportionality relating H₂ masses to CO luminosities (or equivalently gas column densities to the integrated CO brightness temperature) in Galactic GMCs. The four general techniques that have been applied include (a) correlation of CO emission in nearby clouds with the visual extinction (A_V), (b) excitation analysis of ¹³CO and CO emission, (c) derivation of virial masses from the CO and ¹³CO cloud sizes and linewidths, and (d) comparison with -ray emission. The derived ratios of N (H₂ ) / I_CO range between 1-5 x 10²⁰ cm^-2 [K km s^-1]^-1 (see Table 1 in Scoville & Sanders 1987).

In our opinion, the virial theorem analysis provides the most reliable conversion factor, since it is free of uncertainties in the molecular excitation and the cosmic ray density. Figure 1 shows the correlation between the virial masses of Milky Way molecular clouds and their CO luminosities (Scoville et al 1987, Solomon et al 1987). The virial masses were derived for clouds with known sizes and linewidths, and for clouds with mass between 10⁵ and 2 x 10⁶ M, N (H₂) / I_CO 3.0 x 10²⁰ cm^-2 (K km s^-1)^-1 consistent with the -ray analysis (2.8 x 10²⁰ cm^-2 [K km s^-1]^-1) of Bloemen et al (1986). It is noteworthy that no significant large-scale variations in the conversion ratio are seen at radii 2-10 kpc in the inner Galaxy (Bloemen et al 1986, Scoville & Good 1989), and thus variations in metallicity and cloud properties cannot strongly affect the H₂ mass derivations. Throughout this review, we consistently adopt the value of N (H₂) / I_CO = 3.0 x 10²⁰ cm^-2 [K (T_R) km s^-1]^-1.

Figure 1. Comparison of CO luminosities and virial masses of molecular clouds in the Milky Way (Scoville et al 1987, Solomon et al 1987), M31 (Vogel et al 1987), M33 (Wilson & Scoville 1990), and in the low-metallicity galaxy IC 10 (Wilson & Reid 1991). In the Milky Way, the CO luminosity is closely correlated with the virial masses of the clouds, both with and without high mass star formation. This linear proportionality justifies the use of CO as a tracer of the mass of H2; the best fit to these data for clouds with masses between 105 and 2 x 106 M yields a constant of proportionality of 3.0 x 1020 H2 cm-2 (K km s-1)-1. The similarity of the clouds in M31, M33, and IC 10 to the Milky Way justifies the use of the same CO -> H2 proportionality in the external galaxies.

Most of the Galactic data used in the above studies are presented in units of T_R (Kutner & Ulich 1981), which does not correct for the coupling between the source and the telescope beam. Since giant molecular clouds have large angular sizes, the coupling efficiency, _c is close to unity, and T_R = T_{R c}^-1. For a galaxy filling only the primary diffraction beam, the coupling efficiency _c is ~ 0.8 on several of the telescopes used for extragalactic CO studies and the correction factors appropriate to this case are discussed by Sanders et al (1991). For more extended galaxies, a number of techniques have been used to compute the total CO emission (Stark et al 1986, Solomon & Sage 1988, Verter 1988, Kenney & Young 1988a) and one should be aware of the different assumptions when using these estimates.

2.2.2 EXTERNAL GALAXIES In some of the local group galaxies, several recent investigations have attempted to measure the sizes, linewidths, and CO luminosities of individual molecular clouds to check the applicability of the Galactic CO to H₂ conversion constant in other environments. In order to measure the sizes of individuals clouds, it is crucial to have a spatial resolution better than 40 pc, the ``typical'' size of a GMC.

The spiral galaxies M31 and M33 have both been observed with aperture synthesis in CO at 7" (20 pc) resolution (Vogel et al 1987, Wilson & Scoville 1989, 1990). The CO luminosities and virial masses for the M31, M33, and IC 10 molecular clouds are included in Figure 1 along with the Galactic clouds. The extragalactic molecular clouds are apparently similar to those in the Milky Way, even though they represent regions of lower metallicity (by a factor of 4 relative to the sun; Pagel & Edmunds 1981, Becker 1990, Wilson & Reid 1991) and are found in galaxies ranging from type Sb (M31) to Scd (M33) to irregular (IC 10).

Moderate resolution studies of the LMC and SMC [8.8' or 140 pc (Cohen et al 1988)] have also been made. Cohen et al (1988) suggest that the molecular clouds in the LMC have six times more mass per unit CO luminosity than molecular clouds in the Milky Way. It must be borne in mind, however, that their resolution of 140 pc is insufficient to resolve individual molecular clouds similar to Galactic GMCs and the emission may arise from unbound associations of clouds that are not virialized. Higher angular resolution maps of clouds in the LMC and SMC are essential for establishing the virial masses of individual clouds and to test further the accuracy of H₂ mass determinations in environments with low metallicity.

In addition to ascertaining the absolute accuracy of molecular mass determinations derived using the Galactic CO to H₂ conversion constant, establishing the relative accuracy of H₂ mass determinations from galaxy to galaxy is also important. Devereux & Young (1990b) have compared the inner disk gas masses (molecular plus atomic) with the warm dust masses derived from IRAS 60 µm and 100 µm flux densities for 58 luminous spiral galaxies in which the distributions of atomic and molecular gas have been measured. The dispersion of the gas/dust ratio computed from these three independently derived quantities is ± 0.19 dex, a value that is consistent with 30% uncertainties in each of the gas masses and a 10% uncertainty in the warm dust masses. In principle, this 1 uncertainty of ± 30% in global H₂ masses represents both measurement uncertainties and global variations from galaxy to galaxy in the CO -> H₂ conversion constant. Furthermore, Devereux & Young (1990b) point out that the similar scatter for the H I and H₂ dominated galaxies (see Figure 6b) indicates that global molecular gas masses in galaxies are apparently as accurately determined as the atomic gas masses for luminous spirals.