Chemical Rates on Small Grains and PAHs: C⁺ Recombination and H₂ Formation

We use observations of the C I, C II, H I, and H₂ column densities along lines of sight in the Galactic plane to determine the formation rate of H₂ on grains and to determine chemical reaction rates with polycyclic aromatic hydrocarbons (PAHs). Photodissociation region models are used to find the best-fit parameters to the observed columns. We find the H₂ formation rate on grains has a low rate (R ∼ 1 × 10⁻¹⁷ cm³ s⁻¹) along lines of sight with low column density (A_V≲ 0.25) and low molecular fraction (f_H2≲ 10⁻⁴). At higher column densities (0.25 ⩽ A_V ⩽ 2.13), we find a rate of R ∼ 3.5 × 10⁻¹⁷ cm³ s⁻¹. The lower rate at low column densities could be the result of grain processing by interstellar shocks, which may deplete the grain surface area or process the sites of H + H formation, thereby inhibiting H₂ production. Alternatively, the formation rate may be normal, and the low molecular fraction may be the result of lines of sight that graze larger clouds. Such lines of sight would have a reduced H₂ self-shielding compared to the line-of-sight column. We find the reaction C⁺ + PAH⁻→ C + PAH⁰ is best fit with a rate 2.4 × 10⁻⁷Φ_PAHT^−0.5₂ cm³ s⁻¹ with T₂ = T/100 K, and the reaction C⁺ + PAH⁰→ C + PAH⁺ is best fit with a rate 8.8 × 10⁻⁹Φ_PAH cm³ s⁻¹. In high-column-density gas, we find Φ_PAH ∼ 0.4. In low-column-density gas, Φ_PAH is less well constrained, with Φ_PAH ∼ 0.2–0.4.