The Chemistry of Interstellar OH+, H2O+, and H3O+: Inferring the Cosmic
  Ray Ionization Rates from Observations of Molecular Ions
  We model the production of OH+, H2O+, and H3O+ in interstellar clouds, using
a steady state photodissociation region code that treats the freeze-out of gas
species, grain surface chemistry, and desorption of ices from grains. The code
includes PAHs, which have important effects on the chemistry. All three ions
generally have two peaks in abundance as a function of depth into the cloud,
one at A_V<~1 and one at A_V~3-8, the exact values depending on the ratio of
incident ultraviolet flux to gas density. For relatively low values of the
incident far ultraviolet flux on the cloud ({\chi}<~ 1000; {\chi}= 1= local
interstellar value), the columns of OH+ and H2O+ scale roughly as the cosmic
ray primary ionization rate {\zeta}(crp) divided by the hydrogen nucleus
density n. The H3O+ column is dominated by the second peak, and we show that if
PAHs are present, N(H3O+) ~ 4x10^{13} cm^{-2} independent of {\zeta}(crp) or n.
If there are no PAHs or very small grains at the second peak, N(H3O+) can
attain such columns only if low ionization potential metals are heavily
depleted. We also model diffuse and translucent clouds in the interstellar
medium, and show how observations of N(OH+)/N(H) and N(OH+)/N(H2O+) can be used
to estimate {\zeta}(crp)/n, {\chi}/n and A_V in them. We compare our models to
Herschel observations of these two ions, and estimate {\zeta}(crp) ~ 4-6 x
10^-16 (n/100 cm^-3) s^-1 and \chi/n = 0.03 cm^3 for diffuse foreground clouds
towards W49N.
