1D Photochemical–Thermochemical Kinetics Model

• 1D Photochemical–Thermochemical Kinetics Model is a unified simulation framework that couples deep thermochemical equilibrium with photochemistry and transport-driven disequilibrium in planetary atmospheres.
• The model employs time-dependent continuity equations, explicit reaction rate expressions, and vertical mixing parameters to accurately map atmospheric chemical profiles.
• Application to Jupiter and similar bodies constrains key abundances like water and cloud compositions, guiding future observational and theoretical studies.

A one-dimensional (1D) photochemical–thermochemical kinetics model represents the state-of-the-art approach for simulating the chemical composition and vertical distribution of gaseous species in planetary and substellar atmospheres, as well as their response to both thermal processes and incident radiation. This modeling framework self-consistently couples thermochemical equilibrium deep in the atmosphere—where high temperatures enforce rapid kinetics—with photochemistry and transport-induced disequilibrium at lower pressures and temperatures. The result is a predictive tool capable of mapping the full atmospheric column, yielding insights on chemical abundances, cloud formation, and observable species from the deep troposphere to the high stratosphere.

1. Fundamental Principles of 1D Photochemical–Thermochemical Kinetics Models

The 1D photochemical–thermochemical kinetics model consists of a set of time-dependent continuity equations describing the vertical evolution of species concentrations. For a species $i$ at altitude $z$ (or equivalently, pressure level), the continuity equation takes the general form: $$\frac{\partial n_i}{\partial t} = P_i - L_i + \frac{\partial}{\partial z} \left[ K_{zz} \frac{\partial n_i}{\partial z} \right]$$ where $n_i$ is number density, $P_i$ and $L_i$ are chemical production and loss rates (including both thermal and photochemical processes), and $K_{zz}$ is the eddy diffusion coefficient characterizing vertical mixing (Moses, 2013). The model discretizes the atmosphere into vertical layers, integrating this system (often semi-implicitly, due to stiffness) until steady state is achieved.

Thermal (thermochemical) kinetics employ bidirectional, temperature-dependent rate coefficients for all significant reactions: $$k(T) = A \, T^\beta \exp\left(-\frac{E_a}{RT}\right)$$ where $A$, $\beta$, and $E_a$ are reaction-specific constants (Line et al., 2011). Forward and reverse rates are maintained via thermochemical data (exploiting detailed balance), enforcing relaxation to equilibrium at depth (Visscher et al., 2010).

Photochemistry is included through wavelength-dependent photolysis rates: $$J = \int_\lambda \sigma(\lambda)\,\phi(\lambda)\,I(\lambda) \, d\lambda$$ with $\sigma(\lambda)$ the cross-section, $\phi(\lambda)$ the quantum yield, and $I(\lambda)$ the incident spectral irradiance (Moses, 2013). Photodissociation produces radicals that engage in catalytic or chain processes far from thermal equilibrium.

2. Application to Jovian and Giant-Planet Atmospheres

Such models have been applied to Jupiter with exceptional vertical coverage ($1.1 \times 10^3$ to $7.4 \times 10^{-11}$ bar), incorporating updated gas-phase and condensate chemistry for major (C, H, O, N, S) volatiles and their cloud-forming processes (Knížek et al., 4 Sep 2025). Thermochemistry dominates the deep ($>10$ bar) regions, where reaction networks maintain equilibrium compositions. Vertical mixing—parameterized with $K_{zz}$—transports material upward; when the chemical destruction timescale for a given species equals the mixing timescale, “quenching” occurs and the abundance becomes fixed above that level.

For carbon monoxide (CO), the key reaction is: $\ce{CH4 + H2O <=> CO + 3H2}$ In Jupiter, the tropospheric CO abundance observed by Bezard et al. (2002) directly constrains the deep H$_2$O abundance. By requiring the model to match $q_{\rm CO} \sim 1.0 \times 10^{-9}$ in the upper troposphere, the water mole fraction is tightly constrained to $(0.25-6.0) \times 10^{-3}$, or $0.3$–$7.3$ times the solar value (Visscher et al., 2010). This rules out formation scenarios needing $>8$ times solar water enrichment.

For nitrogen and sulfur, the model simultaneously predicts a mixed NH$_3$--NH$_4$SH cloud deck in the 0.1–1 bar region, explicitly modeling condensate formation via

$\ce{NH3 + H2S <=> NH4SH}$

and employing temperature-dependent Antoine equations for volatile vapor pressures (Knížek et al., 4 Sep 2025).

3. Kinetics, Quenching, and Modeling of Disequilibrium Species

Critical to the 1D model is the treatment of kinetic pathways departing from local equilibrium. Quenching is evaluated by comparing each species’ chemical interconversion timescale $\tau_{\rm chem}$ to the vertical mixing timescale $\tau_{\rm mix}$: $\tau_{\rm mix} = \frac{L^2}{K_{zz}}$ with $L$ a fraction of the pressure scale height $H$ (Line et al., 2011). When $\tau_{\rm chem} = \tau_{\rm mix}$, further chemical equilibration is precluded above that pressure.

For example, the CO–CH$_4$ quenching is controlled by the rate-limiting step: $\ce{CH3OH + H -> CH3 + H2O}$ with kinetics, for a dominant path at high $T$, of

$$k = 9.41 \times 10^{-9}\,\exp(-124000/T) \text{ cm}^3\text{s}^{-1}$$

(Liggins et al., 2022). Above the quench level, the observed mole fraction of CO is governed by equilibrium at the quench point, and can be used as a proxy for constraining deep water abundance (Visscher et al., 2010).

Methane (CH$_4$) and ammonia (NH$_3$) interconversion with CO and N$_2$, respectively, proceeds similarly, with quenching and subsequent photochemistry dictating upper-tropospheric and stratospheric abundances. In Jupiter’s model, a near-uniform N$_2$ mixing ratio of 490 ppm is maintained up to 10$^{-6}$ bar, with the onset of radical-driven HCN photochemistry at lower pressures, peaking at 33 ppb near 3 × 10$^{-7}$ bar (Knížek et al., 4 Sep 2025).

4. Coupling of Photochemistry and Thermochemistry

Photochemical processes dominate in regions where incident UV photons can drive photodissociation. In Jupiter, as well as in giant exoplanets and brown dwarfs, the model includes radical production by photolysis of CH$_4$, NH$_3$, H$_2$O, H$_2$S, etc., with subsequent catalytic cycles leading to small hydrocarbons, nitriles (HCN), and oxygenated species. Representative pathways include: ${\rm H_2O + h\nu \rightarrow OH + H}$

${\rm H + CH_4 \rightarrow CH_3 + H_2}$

with radical–radical recombination and photodissociation chains giving rise to species such as C$_2$H$_2$, HCN, and C$_2$H$_6$ above the methane homopause (Dobrijevic et al., 2020, Knížek et al., 4 Sep 2025).

A key finding is that photochemical production of these minor species in the stratosphere—normally negligible with only thermochemistry—can explain observed abundances, such as the predicted HCN “production zone” between $10^{-6}$ and $10^{-7}$ bar in Jupiter’s high stratosphere (Knížek et al., 4 Sep 2025).

5. Methodological Advances and Innovations

The Jupiter full-atmosphere model implements several technical advances over previous approaches:

• Unified Deep/Tropospheric/Stratospheric Coverage: Extends the modeled region from deep (1.1 × 10³ bar) thermochemical equilibrium to extremely low pressures (7.4 × 10⁻¹¹ bar), unifying layers previously modeled independently (Knížek et al., 4 Sep 2025).
• Comprehensive Reaction Network: Incorporates an expanded version of the STAND network, including thousands of reversible and irreversible reactions across C/H/O/N/S chemistry, and new or updated rate coefficients for key kinetic bottlenecks.
• Sulfur Condensation Chemistry: First consistent sulfur chemistry across full vertical extent, including NH$_4$SH formation/dissociation with temperature-dependent Antoine constants.
• Third-Body Collisions: Modern treatment of three-body associations, where collisional stabilization rates depend explicitly on the total number density, improving deep atmosphere accuracy.
• Cloud and Quench Layer Self-Consistency: Simultaneous computation of cloud formation (e.g., mixed NH$_3$–NH$_4$SH layer), gas phase depletion, and chemical quenching, thus closely linking observable cloud features with underlying chemistry.

Model validation is achieved by benchmarking mixing ratios and cloud properties against probe data (Galileo), previous model predictions, and remote sensing, demonstrating agreement for major species (e.g., CH$_4$, C$_2$H$_2$, HCN, H$_2$O, CO, N$_2$) (Knížek et al., 4 Sep 2025, Visscher et al., 2010).

6. Observational Implications and Future Directions

The predictive capacity of this class of models has direct consequences for interpretation of spectroscopic data and for constraining planetary formation scenarios. For Jupiter, fitting the observed $q_{\rm CO}$ fixes the deep water enrichment to $0.3$–$7.3$ times solar, excluding high-water formation scenarios such as those invoking extensive clathrate hydrates (Visscher et al., 2010). The predicted structure and composition of cloud layers, quenched N$_2$ values, and stratospheric HCN maxima allow upcoming missions (e.g., JUICE) and ground-based millimeter/submillimeter observations (e.g., ALMA) to test and refine the model.

Extension to other planetary atmospheres—including exoplanets and brown dwarfs—follows directly, with adaptation of chemical networks and temperature–pressure profiles. For example, the kinetic and photochemical behavior described for Jupiter applies, mutatis mutandis, to the more extreme regimes of ultra-hot Jupiters and cool Neptunes, where the balance of thermal and photochemical processes shifts (Line et al., 2011, Kopparapu et al., 2011, Moses, 2013, Molaverdikhani et al., 2020).

Ongoing and future improvements rely on inclusion of additional heterogeneous cloud microphysics, refinement of vertical mixing and condensation/evaporation boundary treatments, and expansion of the reaction network as new kinetic and thermodynamic data become available. Increased resolution of the interplay between transport, photolysis, and equilibrium chemistry across planetary environments promises more robust constraints on elemental abundances, atmospheric dynamics, and planetary formation pathways.

---

In summary, the 1D photochemical–thermochemical kinetics model provides a unified, physically grounded description of vertical atmospheric chemistry—spanning equilibrium, quenching, and radical-driven disequilibrium regimes. In application to Jupiter, such models robustly connect observable molecular mixing ratios and cloud layers to deep elemental inventories and dynamical processes, and remain essential to understanding atmospheric composition across the spectrum of hydrogen-rich planets (Knížek et al., 4 Sep 2025, Visscher et al., 2010).