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.
