In diffuse interstellar clouds the chemistry that leads to the formation of the oxygen bearing ions OH ^ { + } , H _ { 2 } O ^ { + } , and H _ { 3 } O ^ { + } begins with the ionization of atomic hydrogen by cosmic rays , and continues through subsequent hydrogen abstraction reactions involving H _ { 2 } .
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 _ { H _ { 2 } } ) .
We present observations targeting transitions of OH ^ { + } , H _ { 2 } O ^ { + } , and H _ { 3 } O ^ { + } made with the Herschel Space Observatory along 20 Galactic sight lines toward bright submillimeter continuum sources .
Both OH ^ { + } and H _ { 2 } O ^ { + } are detected in absorption in multiple velocity components along every sight line , but H _ { 3 } O ^ { + } is only detected along 7 sight lines .
From the molecular abundances we compute f _ { H _ { 2 } } in multiple distinct components along each line of sight , and find a Gaussian distribution with mean and standard deviation 0.042 \pm 0.018 .
This confirms previous findings that OH ^ { + } and H _ { 2 } O ^ { + } primarily reside in gas with low H _ { 2 } fractions .
We also infer \zeta _ { H } throughout our sample , and find a log-normal distribution with mean \log ( \zeta _ { H } ) = -15.75 , ( \zeta _ { H } = 1.78 \times 10 ^ { -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 H _ { 3 } ^ { + } 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 .