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

Abstract: 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.