Where is OH and Does It Trace the Dark Molecular Gas (DMG)?

Hydroxyl (OH) is expected to be abundant in diffuse interstellar molecular gas as it forms along with $H_2$ under similar conditions and within a similar extinction range. We have analyzed absorption measurements of OH at 1665 MHz and 1667 MHz toward 44 extragalactic continuum sources, together with the J=1-0 transitions of $^{12}$CO, $^{13}$CO , and C$^{18}$O, and the J=2-1 of $^{12}$CO. The excitation temperature of OH were found to follow a modified log-normal distribution, $f(T{\rm_{ex}}) \propto \frac{1}{ \sqrt{2\pi}\sigma } \rm{exp}\left[-\frac{[ln(\textit{T}_{ex})-ln(3.4\ K)]^2}{2\sigma^2}\right]$, the peak of which is close to the temperature of the Galactic emission background (CMB+synchron). In fact, 90% of the OH has excitation temperature within 2 K of the Galactic background at the same location, providing a plausible explanation for the apparent difficulty to map this abundant molecule in emission. The opacities of OH were found to be small and peak around 0.01. For gas at intermediate extinctions (A$\rm_V$ $\sim$ 0.05-2 mag), the detection rate of OH with detection limit $N(\mathrm{OH})\simeq 10^{12}$ cm$^{-2}$ is approximately independent of $A\rm_V$. We conclude that OH is abundant in the diffuse molecular gas and OH absorption is a good tracer of `dark molecular gas (DMG)'. The measured fraction of DMG depends on assumed detection threshold of the CO data set. The next generation of highly sensitive low frequency radio telescopes, FAST and SKA, will make feasible the systematic inventory of diffuse molecular gas, through decomposing in velocity the molecular (e.g. OH and CH) absorption profiles toward background continuum sources with numbers exceeding what is currently available by orders of magnitude.