Formation and Fractionation of CO (carbon monoxide) in diffuse clouds observed at optical and radio wavelengths

We modelled \HH\ and CO formation incorporating the fractionation and selective photodissociation affecting CO when \AV\ $\la2$mag. UV absorption measurements typically have N(\cotw)/N(\coth) $\approx 65$ that are reproduced with the standard UV radiation and little density dependence at n(H) $\approx32-1024\pccc$: Densities n(H) $\la256\pccc$ avoid overproducing CO. Sightlines observed in mm-wave absorption and a few in UV show enhanced \coth\ by factors of 2-4 and are explained by higher n(H) $\ga256\pccc$ and/or weaker radiation. The most difficult observations to understand are UV absorptions having N(\cotw)/N(\coth) $>$100 and N(CO)$\ga10^{15}\pcc$. Plots of \WCO\ vs. N(CO) show that \WCO\ remains linearly proportional to N(CO) even at high opacity owing to sub-thermal excitation. \cotw\ and \coth\ have nearly the same curve of growth so their ratios of column density/integrated intensity are comparable even when different from the isotopic abundance ratio. For n(H)$\ga128\pccc$, plots of \WCO\ vs N(CH) are insensitive to n(H), and \WCO/N(CO)$\approx1\Kkms/(10^{15}~{\rm CO}\pcc)$: This compensates for small CO/\HH\ to make \WCO\ more readily detectable. Rapid increases of N(CO) with n(H), N(H) and N(\HH) often render the CO bright, ie a small CO-\HH\ conversion factor. For n(H) $\la64\pccc$ CO enters the regime of truly weak excitation where \WCO $\propto$n(H)N(CO). \WCO\ is a strong function of the average \HH\ fraction and models with \WCO=1\Kkms\ fall in the narrow range \mfH2\=0.65-0.8, or \mfH2\=0.4-0.5 at \WCO\=0.1\Kkms. The insensitivity of easily-detected CO emission to gas with small \mfH2\ implies that even deep CO surveys using broad beams may not discover substantially more emission.