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[en] We present results of an extinction-CO line survey of the southeastern part of the California molecular cloud (CMC). Deep, wide-field, near-infrared images were used to construct a sensitive, relatively high resolution (∼0.5 arcmin) (NICEST) extinction map of the region. The same region was also surveyed in the 12CO(2–1), 13CO(2–1), and C18O(2–1) emission lines at the same angular resolution. These data were used to investigate the relation between the molecular gas, traced by CO emission lines, and the dust column density, traced by extinction, on spatial scales of 0.04 pc across the cloud. We found strong spatial variations in the abundances of 13CO and C18O that were correlated with variations in gas temperature, consistent with temperature-dependent CO depletion/desorption on dust grains. The 13CO-to-C18O abundance ratio was found to increase with decreasing extinction, suggesting selective photodissociation of C18O by the ambient UV radiation field. The effect is particularly pronounced in the vicinity of an embedded cluster where the UV radiation appears to have penetrated deeply (i.e., ≲ 15 mag) into the cloud. We derived the cloud-averaged X-factor to be X = 2.53 × 1020 , a value somewhat higher than the Milky Way average. On sub-parsec scales we find there is no single empirical value of the 12CO X-factor that can characterize the molecular gas in cold (T ≲ 15 K) cloud regions, with X ∝ for ≳ 3 mag. However, in regions containing relatively hot (T ≳ 25 K) molecular gas we find a clear correlation between W(12CO) and over a large (3 ≲ ≲ 25 mag) range of extinction. This results in a constant X = 1.5 × 1020 for the hot gas, a lower value than either the average for the CMC or the Milky Way. Overall we find an (inverse) correlation between X and T in the cloud with X ∝ T . This correlation suggests that the global X-factor of a giant molecular cloud may depend on the relative amounts of hot gas contained within the cloud.