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), $^{1
3}$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.
The deuterium fraction [N$_2$D$^+$]/[N$_2$H$^+$], may provide information about the ages of dense, cold gas structures, important to compare with dynamical models of cloud core formation and evolution. Here we introduce a complete chemical network wi
th species containing up to three atoms, with the exception of the Oxygen chemistry, where reactions involving H$_3$O$^+$ and its deuterated forms have been added, significantly improving the consistency with comprehensive chemical networks. Deuterium chemistry and spin states of H$_2$ and H$_3^+$ isotopologues are included in this primarily gas-phase chemical model. We investigate dependence of deuterium chemistry on model parameters: density ($n_{rm H}$), temperature, cosmic ray ionization rate, and gas-phase depletion factor of heavy elements ($f_{rm D}$). We also explore the effects of time-dependent freeze-out of gas-phase species and dynamical evolution of density at various rates relative to free-fall collapse. For a broad range of model parameters, the timescales to reach large values of $D_{rm frac}^{rm N_2H^+} gtrsim 0.1$, observed in some low- and high-mass starless cores, are relatively long compared to the local free-fall timescale. These conclusions are unaffected by introducing time-dependent freeze-out and considering models with evolving density, unless the initial $f_{rm D} gtrsim$ 10. For fiducial model parameters, achieving $D_{rm frac}^{rm N_2H^+} gtrsim 0.1$ requires collapse to be proceeding at rates at least several times slower than that of free-fall collapse, perhaps indicating a dynamically important role for magnetic fields in the support of starless cores and thus the regulation of star formation.
