Size-density relations in dark clouds: Non-LTE effects

One of the major goals of molecular astronomy has been to understand the physics and dynamics of dense interstellar clouds. Because the interpretation of observations of giant molecular clouds is complicated by their very complex structure and the dynamical effects of star formation, a number of studies have concentrated on dark clouds. Leung, Kutner and Mead (1982) (hereafter LKM) and Myers (1983), in studies of CO and NH3 emission, concluded that dark clouds exhibit significant correlations between linewidth and cloud radius of the form delta v varies as R(0.5) and between mean density and radius of the form n varies as R(-1), as originally suggested by Larson (1981). This result suggests that these objects are in virial equilibrium. However, the mean densities inferred from the CO data of LKM are based on an local thermodynamic equilibrium (LTE) analysis of their 13CO data. At the very low mean densities inferred by LKM for the larger clouds in their samples, the assumption of LTE becomes very questionable. As most of the range in R in the density-size correlation comes from the clouds observed in CO, it seems worthwhile to examine how non-LTE effects will influence the derived densities. One way to assess the validity of LTE-derived densities is to construct cloud models and then to interpret them in the same way as the observed data. Microturbulent models of inhomogeneous clouds of varying central concentration with the linewidth-size and mean density-size relations found by Myers show sub-thermal excitation of the 13CO line in the larger clouds, with the result that LTE analysis considerbly underestimates the actual column density. A more general approach which doesn't require detailed modeling of the clouds is to consider whether the observed T sub R*(13CO)/T sub R*(12CO) ratios in the clouds studied by LKM are in the range where the LTE-derived optical depths (and hence column densities) can be seriously in error due to sub-thermal excitation of the 13CO molecule.