${\rm{H}}_3^ + $ in irradiated protoplanetary disks: Linking far-ultraviolet radiation and water vapor

The likely JWST detection of vibrationally excited H 3 + emission in Orion’s irradiated disk system d203-506 raises the important question of whether cosmic-ray ionization is enhanced in disks within clustered star-forming regions, or whether alternative mechanisms contribute to H 3 + formation and excitation. We present a detailed model of the photodissociation region (PDR) component of a protoplanetary disk – comprising the outer disk surface and the photoevaporative wind – exposed to strong external far-ultraviolet (FUV) radiation. We investigate key gas-phase reactions involving excited H 2 that lead to the formation of H 3 + in the PDR, including detailed state-to-state dynamical calculations of reactions H 2 ( v ≥ 0) + HOC + → H 3 + + CO and H 2 ( v ≥ 0) + H + → H 2 + + H. We also consider the effects of photoionization of vibrationally excited H 2 ( v ≥ 4), a process not previously included in PDR or disk models. We find that these FUV-driven reactions dominate the formation of H 3 + in the PDR of strongly irradiated disks, largely independently of cosmic-ray ionization. The predicted H 3 + abundance in the disk PDR peaks at x (H 3 + ) ≳ 10 −8 , coinciding with regions of enhanced HOC + and water vapor abundances, and is linked to the strength of the external FUV field ( G 0 ). The predicted H 3 + column density (≲10 13 cm −2 ) agrees with the presence of H 3 + in the PDR of d203-506. We also find that formation pumping, resulting from exoergic reactions between excited H 2 and HOC + , drives the vibrational excitation of H 3 + in these regions. We expect this photochemistry to be highly active in disks where G 0 > 10 3 . The H 3 + formation pathways studied here may also be relevant in the inner disk region (near the host star), in exoplanetary ionospheres, and in the early Universe.