(Abridged) We carried out a comprehensive far-ultraviolet (UV) survey of ^12CO and H_2 column densities along diffuse molecular Galactic sight lines in order to explore in detail the relationship between CO and H_2. We measured new CO abundances from
HST spectra, new H_2 abundances from FUSE data, and new CH, CH^+, and CN abundances from the McDonald and European Southern Observatories. A plot of log N(CO) versus log N(H_2) shows that two power-law relationships are needed for a good fit of the entire sample, with a break located at log N(CO, cm^-2) = 14.1 and log N(H_2) = 20.4, corresponding to a change in production route for CO in higher-density gas. Similar logarithmic plots among all five diatomic molecules allow us to probe their relationships, revealing additional examples of dual slopes in the cases of CO versus CH (break at log N = 14.1, 13.0), CH^+ versus H_2 (13.1, 20.3), and CH^+ versus CO (13.2, 14.1). These breaks are all in excellent agreement with each other, confirming the break in the CO versus H_2 relationship, as well as the one-to-one correspondence between CH and H_2 abundances. Our new sight lines were selected according to detectable amounts of CO in their spectra and they provide information on both lower-density (< 100 cm^-3) and higher-density diffuse clouds. The CO versus H_2 correlation and its intrinsic width are shown to be empirically related to the changing total gas density among the sight lines of the sample. We employ both analytical and numerical chemical schemes in order to derive details of the molecular environments. In the low-density gas, where equilibrium-chemistry studies have failed to reproduce the abundance of CH^+, our numerical analysis shows that nonequilibrium chemistry must be employed for correctly predicting the abundances of both CH^+ and CO.
We examine 20 diffuse and translucent Galactic sight lines and extract the column densities of the ^12CO and ^13CO isotopologues from their ultraviolet A--X absorption bands detected in archival Space Telescope Imaging Spectrograph data with lambda/D
eltalambda geq 46,000. Five more targets with Goddard High-Resolution Spectrograph data are added to the sample that more than doubles the number of sight lines with published Hubble Space Telescope observations of ^13CO. Most sight lines have 12-to-13 isotopic ratios that are not significantly different from the local value of 70 for ^12C/^13C, which is based on mm-wave observations of rotational lines in emission from CO and H_2CO inside dense molecular clouds, as well as on results from optical measurements of CH^+. Five of the 25 sight lines are found to be fractionated toward lower 12-to-13 values, while three sight lines in the sample are fractionated toward higher ratios, signaling the predominance of either isotopic charge exchange or selective photodissociation, respectively. There are no obvious trends of the ^12CO-to-^13CO ratio with physical conditions such as gas temperature or density, yet ^12CO/^13CO does vary in a complicated manner with the column density of either CO isotopologue, owing to varying levels of competition between isotopic charge exchange and selective photodissociation in the fractionation of CO. Finally, rotational temperatures of H_2 show that all sight lines with detected amounts of ^13CO pass through gas that is on average colder by 20 K than the gas without ^13CO. This colder gas is also sampled by CN and C_2 molecules, the latter indicating gas kinetic temperatures of only 28 K, enough to facilitate an efficient charge exchange reaction that lowers the value of ^12CO/^13CO.
