The CO-to-H₂ conversion factor across the Perseus molecular cloud

We derive the CO-to-H₂ conversion factor, X _CO = N(H₂)/I _CO, across the Perseus molecular cloud on sub-parsec scales by combining the dust-based N(H₂) data with the I _CO data from the COMPLETE Survey. We estimate an average X _CO ∼ 3 × 10¹⁹ cm^–2 K^–1 km^–1 s and find a factor of ∼3 variations in X _CO between the five sub-regions in Perseus. Within the individual regions, X _CO varies by a factor of ∼100, suggesting that X _CO strongly depends on local conditions in the interstellar medium. We find that X _CO sharply decreases at A_V ≲ 3 mag but gradually increases at A_V ≳ 3 mag, with the transition occurring at A_V where I _CO becomes optically thick. We compare the N(H I), N(H₂), I _CO, and X _CO distributions with two models of the formation of molecular gas, a one-dimensional photodissociation region (PDR) model and a three-dimensional magnetohydrodynamic (MHD) model, tracking both the dynamical and chemical evolution of gas. The PDR model based on the steady state and equilibrium chemistry reproduces our data very well but requires a diffuse halo to match the observed N(H I) and I _CO distributions. The MHD model matches our data reasonably well, suggesting that time-dependent effects on H₂ and CO formation are insignificant for an evolved molecular cloud like Perseus. However, we find interesting discrepancies, including a broader range of N(H I), likely underestimated I _CO, and a large scatter of I _CO at small A_V . These discrepancies most likely result from strong compressions and rarefactions and density fluctuations in the MHD model.