2012ApJ...754..105H

We model the production of OH⁺, H₂O⁺, and H₃O⁺ in interstellar clouds, using a steady-state photodissociation region code that treats the freezeout of gas species, grain surface chemistry, and desorption of ices from grains. The code includes polycyclic aromatic hydrocarbons (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 (χ ≲ 1000; χ = 1 = local interstellar value), the columns of OH⁺ and H₂O⁺ scale roughly as the cosmic-ray primary ionization rate ζ_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⁺) ∼4x10¹³/cm2 independent of ζ_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 ζ_crp/n, χ/n and A_V in them. We compare our models to Herschel observations of these two ions, and estimate ζ_crp ∼4-6x10^–16(n/100/cm3)/s and χ/n = 0.03 cm3 for diffuse foreground clouds toward W49N.