We carried out a comprehensive far-ultraviolet ( UV ) survey of ^ { 12 } CO and H _ { 2 } column densities along diffuse molecular Galactic sight lines in order to explore in detail the relationship between CO and H _ { 2 } .
For this survey we measured new CO abundances from absorption bands detected in Hubble Space Telescope spectra for 62 sight lines , and new H _ { 2 } abundances from absorption bands in Far Ultraviolet Spectroscopy Explorer data for 58 sight lines .
In addition , high-resolution optical data were obtained at the McDonald and European Southern Observatories , yielding new abundances for CH , CH ^ { + } , and CN along 42 sight lines to aid in interpreting the CO results .
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 ( \leq 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 denser gas , where C _ { 2 } and CN molecules also reside , reactions involving C ^ { + } and OH are the dominant factor leading to CO formation via equilibrium chemistry .
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 .