The gas-to-extinction ratio and the gas distribution in the Galaxy
  We investigate the relation between the optical extinction ($A_V$) and the
hydrogen column density ($N_H$) determined from X-ray observations of a large
sample of Galactic sightlines toward 35 supernova remnants, 6 planetary
nebulae, and 70 X-ray binaries for which $N_H$ was determined in the literature
with solar abundances. We derive an average ratio of
${N_H}/{A_V}=(2.08\pm0.02)\times10^{21}{\rm H\, cm^{-2}\, mag^{-1}}$ for the
whole Galaxy. We find no correlation between ${N_H}/{A_V}$ and the number
density of hydrogen, the distance away from the Galactic centre, and the
distance above or below the Galactic plane. The ${N_H}/{A_V}$ ratio is
generally invariant across the Galaxy, with
${N_H}/{A_V}=(2.04\pm0.05)\times10^{21}{\rm H\, cm^{-2}\, mag^{-1}}$ for the
1st and 4th Galactic quadrants and ${N_H}/{A_V}=(2.09\pm0.03)\times10^{21}{\rm
H\, cm^{-2}\, mag^{-1}}$ for the 2nd and 3rd Galactic quadrants. We also
explore the distribution of hydrogen in the Galaxy by enlarging our sample with
additional 74 supernova remnants for which both $N_H$ and distances are known.
We find that, between the Galactic radius of 2 kpc to 10 kpc, the vertical
distribution of hydrogen can be roughly described by a Gaussian function with a
scale height of $h=75.5\pm12.4\,{\rm pc}$ and a mid-plane density of
$n_{H}(0)=1.11\pm0.15\,{\rm cm^{-3}}$, corresponding to a total gas surface
density of ${\sum}_{gas}{\sim}7.0\,{M_{\bigodot}}\,{\rm pc^{-2}}$. We also
compile $N_H$ from 19 supernova remnants and 29 X-ray binaries for which $N_H$
was determined with subsolar abundances. We obtain
${N_H}/{A_V}=(2.47\pm0.04)\times10^{21}{\rm H\, cm^{-2}\, mag^{-1}}$ which
exceeds that derived with solar abundances by $\sim$20%. We suggest that in
future studies one may simply scale $N_H$ derived from subsolar abundances by a
factor of $\sim$1.2 when converting to $N_H$ of solar abundances.
