The formation of molecular hydrogen (H2) is a critical step in the conversion of interstellar gas into stars, yet the physical processes involved still remain unclear. We present two studies of H2 in the Perseus molecular cloud on sub-pc scales. In the first study, we derive the atomic hydrogen (HI) and H2 surface density images and compare the observed H2-to-HI ratio of several dark and star-forming regions to the analytic model by Krumholz et al. (2009; KMT09). To derive the H2 surface density image, we use the dust column density measured by far-infrared data from IRAS in combination with the HI data from the GALFA-HI survey. We find a uniform HI surface density of 6-8 solar mass/pc2 for both dark and star-forming regions, in agreement with KMT09's prediction for the minimum HI surface density to shield H2 against photodissociation. In addition, we find that H2 linearly increases with the total gas surface density. Both results are consistent with KMT09's steady-state model for equilibrium H2 formation and suggest that turbulence may play a secondary role in H2 formation.
In the second study, we investigate how XCO (the ratio of the H2 column density to the CO integrated intensity) varies with environmental conditions. We find XCO ~ 3 x 1019 cm-2 K-1 km-1 s in Perseus, with a factor of ~3 variations across the cloud. In addition, XCO has the lowest value at Av ~ 2 mag and gradually increases up to 10 mag. The photodissociation region model by Wolfire et al. (2010) reproduces the observed XCO versus Av profile reasonably well, while the MHD simulation by Shetty et al. (2011) predicts the minimum XCO at Av ~ 8 mag, suggesting that turbulence allows UV photons to penetrate much deeper into the cloud due to a less effective shielding. However, both models have difficulties producing the observed CO integrated intensity in the lowest column density regions in Perseus.