in irradiated protoplanetary disks: Linking far-ultraviolet radiation and water vapor

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Volume 703 (November 2025)

A&A, 703 (2025) A189

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Table 1

Rate constants discussed in this work.

Reaction	α	β	γ
	(cm³ s⁻¹)		(K)
$H_{2} (v = 0) H^{+} \to H_{2}^{+} + H$ ${{\rm{H}}_2}\left( {v = 0} \right){{\rm{H}}^ + } \to {\rm{H}}_2^ + + {\rm{H}}$	2.70e–10		22 000
$H_{2} (v = 1) H^{+} \to H_{2}^{+} + H$ ${{\rm{H}}_2}\left( {v = 1} \right){{\rm{H}}^ + } \to {\rm{H}}_2^ + + {\rm{H}}$	4.00e–10		16 500
$H_{2} (v = 2) H^{+} \to H_{2}^{+} + H$ ${{\rm{H}}_2}\left( {v = 2} \right){{\rm{H}}^ + } \to {\rm{H}}_2^ + + {\rm{H}}$	3.20e–10		10 500
$H_{2} (v = 3) H^{+} \to H_{2}^{+} + H$ ${{\rm{H}}_2}\left( {v = 3} \right){{\rm{H}}^ + } \to {\rm{H}}_2^ + + {\rm{H}}$	5.74e–11	+0.76	4254
$H_{2} (v = 4) H^{+} \to H_{2}^{+} + H$ ${{\rm{H}}_2}\left( {v = 4} \right){{\rm{H}}^ + } \to {\rm{H}}_2^ + + {\rm{H}}$	3.74e–10	+0.75	–126
$H_{2} (v = 5) H^{+} \to H_{2}^{+} + H$ ${{\rm{H}}_2}\left( {v = 5} \right){{\rm{H}}^ + } \to {\rm{H}}_2^ + + {\rm{H}}$	2.28e–10	+0.77	–182
$H_{2} (v = 6) H^{+} \to H_{2}^{+} + H$ ${{\rm{H}}_2}\left( {v = 6} \right){{\rm{H}}^ + } \to {\rm{H}}_2^ + + {\rm{H}}$	7.58e–10	+0.37	–92
$H_{2} (thermal) H^{+} \to H_{2}^{+} + H$ ${{\rm{H}}_2}\left( {{\rm{thermal}}} \right){{\rm{H}}^ + } \to {\rm{H}}_2^ + + {\rm{H}}$	1.32e–09	+0.42	21 993

$H_{2}^{+} + H \to H_{2} {+H}^{+}$ ${\rm{H}}_2^ + + {\rm{H}} \to {{\rm{H}}_2}{\rm{ + }}{{\rm{H}}^ + }$	6.64e–10	+0.21	–2.0

${HOC}^{+} + H_{2} (v = 0) \to H_{3}^{+} +CO$ ${\rm{HO}}{{\rm{C}}^ + } + {{\rm{H}}_2}\left( {v = 0} \right) \to {\rm{H}}_3^ + {\rm{ + CO}}$	1.25e–11	+1.07	–80.5
${HOC}^{+} + H_{2} (v = 1) \to H_{3}^{+} +CO$ ${\rm{HO}}{{\rm{C}}^ + } + {{\rm{H}}_2}\left( {v = 1} \right) \to {\rm{H}}_3^ + {\rm{ + CO}}$	3.44e–10	+0.06	3.4
${HOC}^{+} + H_{2} (v = 2) \to H_{3}^{+} +CO$ ${\rm{HO}}{{\rm{C}}^ + } + {{\rm{H}}_2}\left( {v = 2} \right) \to {\rm{H}}_3^ + {\rm{ + CO}}$	4.77e–10	–0.01	7.1
${HOC}^{+} + H_{2} (v = 3) \to H_{3}^{+} +CO$ ${\rm{HO}}{{\rm{C}}^ + } + {{\rm{H}}_2}\left( {v = 3} \right) \to {\rm{H}}_3^ + {\rm{ + CO}}$	5.34e–10	–0.01	–1.9
${HOC}^{+} + H_{2} (v = 4) \to H_{3}^{+} +CO$ ${\rm{HO}}{{\rm{C}}^ + } + {{\rm{H}}_2}\left( {v = 4} \right) \to {\rm{H}}_3^ + {\rm{ + CO}}$	5.40e–10	+0.01	–12.2

HOC⁺ + H₂(v=0) → HCO⁺ + H₂	2.37e–10	–0.37	20.0
HOC⁺ + H₂(v=1) → HCO⁺ + H₂	2.16e–10	–0.35	20.0
HOC⁺ + H₂(v=2) → HCO⁺ + H₂	1.66e–10	–0.33	20.0
HOC⁺ + H₂(v=3) → HCO⁺ + H₂	1.47e–10	–0.37	20.0
HOC⁺ + H₂(v=4) → HCO⁺ + H₂	1.19e–10	–0.29	20.0

HOC⁺ +H → CO⁺ +H₂	5.10e–10		7125
HCO⁺ + H → CO⁺ + H₂	1.30e–09		24 500
$H_{3}^{+} + H \to H_{2}^{+} + H_{2}$ ${\rm{H}}_3^ + + {\rm{H}} \to {\rm{H}}_2^ + + {{\rm{H}}_2}$	2.10e–09		20000

Notes. Rate constants from fitting the Arrhenius-like form k (T) = α (T/300 K)^β exp(–γ/Τ) to reaction rates computed in this study, and valid in the T ≃ 100–2000 K range. For the last three endoergic reactions, see footnote ¹⁰.

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