Dust-Gas Scaling Relations and OH Abundance in the Galactic ISM

Observations of interstellar dust are often used as a proxy for total gas column density $N_\mathrm{H}$. By comparing $\textit{Planck}$ thermal dust data (Release 1.2) and new dust reddening maps from Pan-STARRS 1 and 2MASS (Green et al. 2018), with accurate (opacity-corrected) HI column densities and newly-published OH data from the Arecibo Millennium survey and 21-SPONGE, we confirm linear correlations between dust optical depth $\tau_{353}$, reddening $E(B{-}V)$ and the total proton column density $N_\mathrm{H}$ in the range (1$-$30)$\times$10$^{20}$cm$^{-2}$, along sightlines with no molecular gas detections in emission. We derive an $N_\mathrm{H}$/$E(B{-}V)$ ratio of (9.4$\pm$1.6)$\times$10$^{21}$cm$^{-2}$mag$^{-1}$ for purely atomic sightlines at $|b|$$>$5$^{\circ}$, which is 60$\%$ higher than the canonical value of Bohlin et al. (1978). We report a $\sim$40$\%$ increase in opacity $\sigma_{353}$=$\tau_{353}$/$N_\mathrm{H}$, when moving from the low column density ($N_\mathrm{H}$$<$5$\times$10$^{20}$cm$^{-2}$) to moderate column density ($N_\mathrm{H}$$>$5$\times$10$^{20}$cm$^{-2}$) regime, and suggest that this rise is due to the evolution of dust grains in the atomic ISM. Failure to account for HI opacity can cause an additional apparent rise in $\sigma_{353}$, of the order of a further $\sim$20$\%$. We estimate molecular hydrogen column densities $N_{\mathrm{H}_{2}}$ from our derived linear relations, and hence derive the OH/H$_2$ abundance ratio of $X_\mathrm{OH}$$\sim$1$\times$10$^{-7}$ for all molecular sightlines. Our results show no evidence of systematic trends in OH abundance with $N_{\mathrm{H}_{2}}$ in the range $N_{\mathrm{H}_{2}}$$\sim$(0.1$-$10)$\times$10$^{21}$cm$^{-2}$. This suggests that OH may be used as a reliable proxy for H$_2$ in this range, which includes sightlines with both CO-dark and CO-bright gas.