The Relationship Between the Dust and Gas-Phase CO Across the California Molecular Cloud

A deep, wide-field, near-infrared imaging survey was used to construct an extinction map of the southeastern part of the California Molecular Cloud (CMC) with $\sim$ 0.5 arc min resolution. The same region was also surveyed in the $^{12}$CO(2-1), $^{13}$CO(2-1), C$^{18}$O(2-1) emission lines at the same angular resolution. Strong spatial variations in the abundances of $^{13}$CO and C$^{18}$O were found to be correlated with variations in gas temperature, consistent with temperature dependent CO depletion/desorption on dust grains. The $^{13}$CO to C$^{18}$O abundance ratio was found to increase with decreasing extinction, suggesting selective photodissociation of C$^{18}$O by the ambient UV radiation field. The cloud averaged X-factor is found to be $<$X$_{\rm CO}$$>$ $=$ 2.53 $\times$ 10$^{20}$ ${\rm cm}^{-2}~({\rm K~km~s}^{-1})^{-1}$, somewhat higher than the Milky Way average. On sub-parsec scales we find no single empirical value of the X-factor that can characterize the molecular gas in cold (T$_{\rm k}$ $\lesssim$ 15 K) regions, with X$_{\rm CO}$ $\propto$ A$_{\rm V}$$^{0.74}$ for A$_{\rm V}$ $\gtrsim$ 3 magnitudes. However in regions containing relatively hot (T$_{\rm ex}$ $\gtrsim$ 25 K) gas we find a clear correlation between W($^{12}$CO) and A$_{\rm V}$ over a large (3 $\lesssim$ A$_{\rm V}$ $\lesssim$ 25 mag) extinction range. This suggests a constant X$_{\rm CO}$ $=$ 1.5 $\times$ 10$^{20}$ ${\rm cm}^{-2}~({\rm K~km~s}^{-1})^{-1}$ for the hot gas, a lower value than either the average for the CMC or Milky Way. We find a correlation between X$_{\rm CO}$ and T$_{\rm ex}$ with X$_{\rm CO}$ $\propto$ T$_{\rm ex}$$^{-0.7}$ suggesting that the global X-factor of a cloud may depend on the relative amounts of hot gas within it.