SIMULATION OF VARIATIONS OF ABSORPTION-LINE PROFILES IN CLUMPY MOLECULAR CLOUDS

We have carried out numerical simulations of spectral line optical depth profiles along narrow lines of sight in a clumpy molecular cloud. The cloud is modeled to have uniform excitation temperature and intraclump velocity dispersion, a clump size spectrum dN/dL is-proportional-to L(-(D+1)), where D is the fractal (Hausdorff) dimension and L is the clump size, and intraclump density n is-proportional-to L-1. Optical depth profiles are generated for successive lines of sight, each separated by the minimum clump size. These profiles are compared with the theoretical (i.e., corresponding to an infinite number of clumps along the line of sight) and best-fit Gaussian profiles. Analytical expressions are obtained to relate the mean square deviation from the best-fit Gaussian to the intraclump velocity dispersion and the mean number of clumps along each line of sight as well as the expected change in equivalent width across adjacent lines of sight. The results of this study can be used to interpret observations of variations of absorption-line profiles toward compact continuum sources that lie behind interstellar clouds. The variations reported in the literature require a steeper value of the fractal dimension on AU scales, D greater-than-or-equal-to 1.5, than observed on parsec scales.