OH in the diffuse interstellar medium: physical modelling and prospects with upcoming SKA precursor/pathfinder surveys

Hydroxyl ($\rm OH$) is known to form efficiently in cold gas ($T\sim 100$K) along with the molecule $\rm H_2$ and can be used as an efficient tracer of the diffuse molecular gas in the interstellar medium (ISM). Using a simple formalism describing the $\rm H\,I/H_2$ transition and a reduced network of major chemical reactions, we present a semi-analytical prescription to estimate the abundances of O-bearing molecules in the diffuse ISM. We show that predictions based on our prescription are in good agreement with the estimates obtained using the MEUDON PDR code which utilizes the full reaction network. We investigate the dependence of the relative abundances of $\rm OH/H\,I$ and $\rm OH/H_2$ on the variations of physical conditions i.e., the metallicity, number density ($n$), cosmic ray ionization rate ($\zeta$) and strength of UV field ($\chi$) in the medium. We find that the $\rm OH/H\,I$ abundances observed in the Galactic ISM can be reproduced by models with $n\sim 50$cm$^{-3}$, $\chi\sim 1$ (Mathis field) and $\zeta\sim3\times10^{-17}$s$^{-1}$, with a variation of about one dex allowed around these values. Using the constrained $\rm H_2$ column density distribution function at $z\sim3$, we estimate the $\rm OH$ column density distribution function and discuss future prospects with the upcoming large radio absorption line surveys.