Probing the Cold Deep Depths of the California Molecular Cloud: The Icy Relationship between CO and Dust

We study the relationship between molecular gas and dust in the California Molecular Cloud over an unprecedented dynamic range of cloud depth (A V = 3-60 mag). We compare deep Herschel-based measurements of dust extinction with observations of the 12CO, 13CO, and C18O J = 2 - 1 lines on sub-parsec scales across the cloud. We directly measure the ratio of CO integrated intensity to dust extinction to derive the CO X-factor at over 105 independent locations in the cloud. Confirming an earlier study, we find that no single 12CO X-factor can characterize the molecular gas in the cold (T dust ≤ 20) regions of the cloud that account for most of its mass. We are able to derive a single-valued X-factor for all three CO isotopologues in the warm (T dust > 25 K) material that is spatially coincident with an H ii region surrounding the star LkHα 101. We derive the LTE CO column densities for 13CO and C18O since we find both lines are relatively optically thin. In the warm cloud material, CO is completely in the gas phase and we are able to recover the total 13CO and C18O abundances. Using CO abundances and deep Herschel observations, we measure lower bounds to the freeze-out of CO onto dust across the whole cloud, finding some regions having CO depleted by a factor of >20. We construct the first maps of depletion that span the extent of a giant molecular cloud. Using these maps we identify 75 depletion-defined cores and discuss their physical nature.