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

¹ Instituto de Física Fundamental (CSIC). Calle Serrano 121–123, 28006, Madrid, Spain
² LUX, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS, 92190 Meudon, France
³ Chalmers University of Technology, Onsala Space Observatory, Onsala, Sweden
⁴ Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse, CNRS, CNES, Toulouse, France

^★ Corresponding author: javier.r.goicoechea@csic.es

Received: 6 June 2025
Accepted: 20 September 2025

Abstract

The likely JWST detection of vibrationally excited H₃⁺ 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 H₃⁺ 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 H₂ that lead to the formation of H₃⁺ in the PDR, including detailed state-to-state dynamical calculations of reactions H₂(v ≥ 0) + HOC⁺ → H₃⁺ + CO and H₂(v ≥ 0) + H⁺ → H₂⁺ + H. We also consider the effects of photoionization of vibrationally excited H₂(v ≥ 4), a process not previously included in PDR or disk models. We find that these FUV-driven reactions dominate the formation of H₃⁺ in the PDR of strongly irradiated disks, largely independently of cosmic-ray ionization. The predicted H₃⁺ abundance in the disk PDR peaks at x(H₃⁺) ≳ 10⁻⁸, coinciding with regions of enhanced HOC⁺ and water vapor abundances, and is linked to the strength of the external FUV field (G₀). The predicted H₃⁺ column density (≲10¹³ cm⁻²) agrees with the presence of H₃⁺ in the PDR of d203-506. We also find that formation pumping, resulting from exoergic reactions between excited H₂ and HOC⁺, drives the vibrational excitation of H₃⁺ in these regions. We expect this photochemistry to be highly active in disks where G₀ > 10³. The H₃⁺ 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.