Herschel Survey of Galactic OH+, H2O+, and H3O+: Probing the Molecular
  Hydrogen Fraction and Cosmic-Ray Ionization Rate
  In diffuse interstellar clouds the chemistry that leads to the formation of
the oxygen bearing ions OH+, H2O+, and H3O+ begins with the ionization of
atomic hydrogen by cosmic rays, and continues through subsequent hydrogen
abstraction reactions involving H2. Given these reaction pathways, the observed
abundances of these molecules are useful in constraining both the total
cosmic-ray ionization rate of atomic hydrogen (zeta_H) and molecular hydrogen
fraction, f(H2). We present observations targeting transitions of OH+, H2O+,
and H3O+ made with the Herschel Space Observatory along 20 Galactic sight lines
toward bright submillimeter continuum sources. Both OH+ and H2O+ are detected
in absorption in multiple velocity components along every sight line, but H3O+
is only detected along 7 sight lines. From the molecular abundances we compute
f(H2) in multiple distinct components along each line of sight, and find a
Gaussian distribution with mean and standard deviation 0.042+-0.018. This
confirms previous findings that OH+ and H2O+ primarily reside in gas with low
H2 fractions. We also infer zeta_H throughout our sample, and find a log-normal
distribution with mean log(zeta_H)=-15.75, (zeta_H=1.78x10^-16 s^-1), and
standard deviation 0.29 for gas within the Galactic disk, but outside of the
Galactic center. This is in good agreement with the mean and distribution of
cosmic-ray ionization rates previously inferred from H3+ observations.
Ionization rates in the Galactic center tend to be 10--100 times larger than
found in the Galactic disk, also in accord with prior studies.
