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In hot hydrogen-rich thermochemical equilibrium, much carbon can be bound in carbon monoxide, consuming oxygen that is unavailable for water. At a C/O ratio near or above one, water can be strongly depleted. Cooler methane-dominated chemistry can release more oxygen for water at the same elemental inventory. Pressure, quenching, dissociation and atmospheric photochemistry can modify this temperature-dependent partition.

At fixed temperature and pressure, a closed reacting system reaches thermochemical equilibrium by minimizing Gibbs free energy over nonnegative species amounts subject to conserved elemental abundances. For an allowed stoichiometric vector $\nu$, an interior minimum has ${\sum }_i{\nu }_i{\mu }_i=0$. More generally the chemical potential vector lies in the row span of the elemental conservation matrix at positive concentrations, with the appropriate one-sided inequalities for absent species. The first law of thermodynamics gives the thermodynamic differential, while the Second law of thermodynamics supplies the minimization direction.

Atmospheric advection time shorter than the chemical relaxation time allows winds to carry a composition into regions where it differs from local thermochemical equilibrium. In a hot Jupiter, this can transport dayside carbon chemistry into the cooler nightside.

The usual major carbon/oxygen reservoirs in a hydrogen-rich hot Jupiter are water, carbon monoxide and methane, with their relative importance set by thermochemical equilibrium. This is not a universal ranking for every temperature and composition: nitrogen molecules or carbon dioxide can exceed a strongly depleted member of this trio.

At about one bar, the useful net reaction isThe rightward reaction is exothermic. Cooler gas favors methane and water; warming favors carbon monoxide and suppresses methane. The CO/CH4 crossover is of order $10^3\mathrm{K}$ and shifts with pressure, elemental inventory and metallicity; it is not a universal temperature. Water remains an important oxygen reservoir for oxygen-rich compositions but can dissociate at sufficiently high temperature.

Increasing the atmospheric metallicity of a giant planet raises the available carbon and oxygen. In a dilute, H2-dominated regime, major CO and H2O abundances roughly increase with the enrichment factor, and cool-regime CH4 does likewise. CO2 can rise faster, approximately quadratically in suitable warm regimes. At very high enrichment, the H2 fraction and mean molecular weight also change, invalidating simple linear scalings.

At high temperature and atmospheric carbon-to-oxygen ratio below unity, CO binds much of the carbon, leaving excess oxygen for H2O. As C/O approaches or exceeds one, CO consumes nearly all available oxygen and H2O is strongly depleted; excess carbon enhances CH4, hydrogen cyanide and acetylene. Cooler CH4-dominated chemistry uses less oxygen in CO and can leave more water even at the same elemental ratio. These trends are carbon partition and atmospheric water abundance, and assume equilibrium rather than vertical or horizontal quenching.

These are three distinct ways to maintain disequilibrium chemistry in an exoplanet atmosphere; each compares chemistry with a different transport or irradiation process.

For a representative hydrogen-rich hot Jupiter, increasing altitude lowers pressure, slows collision-driven chemistry, and increases exposure to stellar UV. Three principal regimes follow.

At high pressures, illustratively $P\gtrsim 1$--$10$ bar, collisions and sufficiently high temperature make thermochemical equilibrium a useful approximation. Molecular abundances minimize the free energy subject to elemental conservation. Condensation and atmospheric condensate rainout can remove selected elements from the gas.

At intermediate pressures, illustratively $10^{-3}\lesssim P\lesssim 1$ bar, vertical mixing and horizontal winds can outrun chemical relaxation time. The chemical quench level is defined by ${\tau }_{\mathrm{chem}}\sim {\tau }_{\mathrm{mix}}$; above it, some abundances retain values from a deeper or hotter region. Horizontal chemical quenching similarly occurs when chemical adjustment is slower than advection between the day and night hemispheres.

At low pressures, illustratively $P\lesssim 10^{-3}$ bar, atmospheric photochemistry becomes important: photodissociation and radical reactions change equilibrium abundances and can produce hydrocarbons and atmospheric hazes. At still lower pressures, roughly $10^{-6}$ bar and above in altitude, photoionization and an escaping thermosphere can become important.

These pressures label a representative sketch, not universal interfaces. UV optical depth, stellar spectrum, gravity, metallicity, reaction rates and eddy diffusivity determine the transitions; quenching is species-dependent.

Assume a hydrogen-rich gas with approximately solar elemental ratios and local thermochemical equilibrium when identifying the limiting compositions. At $T\lesssim 500\mathrm{K}$, a representative set of dominant molecules is ${\mathrm{H}}_2,{\mathrm{H}}_{2}O,{\mathrm{CH}}_4,{\mathrm{NH}}_3$. In the deeper $T\gtrsim 1300\mathrm{K}$ regime, it is ${\mathrm{H}}_2,{\mathrm{H}}_{2}O,\mathrm{CO},{\mathrm{N}}_2$. Helium is an abundant atom, not a molecule. The carbon and nitrogen switches, carbon monoxide–methane quenching and nitrogen–ammonia quenching when frozen by mixing, are represented byLow temperature and high pressure favor the right-hand sides, while hotter gas favors carbon monoxide and ${\mathrm{N}}_2$. Exact boundaries depend on pressure and composition; ${\mathrm{CO}}_2$ can become important at high metallicity. If mixing is strong, the cool upper atmosphere need not retain its local-equilibrium four-species ordering.

To preserve the hot-region reactant $A_1$ aloft, require transport to beat its conversion at the quench region. With a mixing length $\ell$ and vertical eddy diffusivity $K_{zz}$,For the simplest use of the supplied atmospheric scale height reference, assume the same temperature and mean molecular weight as the reference atmosphere and take $\ell =H$. Since $H\propto 1/g$, $H\simeq 30/0.4=75\mathrm{km}$, giving $K_{zz}\gtrsim 5.6\times 10^4{\mathrm{m}}^2{\mathrm{s}}^{-1}=5.6\times 10^8\mathrm{c}{\mathrm{m}}^2{\mathrm{s}}^{-1}$.

The hotter quench layer requires a temperature correction if the reference is ordinary Jupiter; the temperature of that scale-height reference was not specified. An explicit estimate using $T_q=1300\mathrm{K}$, dimensionless mean molecular weight $\mu =2.3$, and $g\simeq 0.4\times 25=10\mathrm{m}{\mathrm{s}}^{-2}$ givesThus a scale-height-based estimate using the hot layer is of order $10^{10}\mathrm{c}{\mathrm{m}}^2{\mathrm{s}}^{-1}$. Both estimates state their assumptions: the reference scaling alone does not include the temperature ratio. Choosing $\ell =0.1H$ lowers the threshold by a factor of $100$, and a full quench calculation needs the reaction timescale along the profile. The dependence of a quench diffusivity on mixing length shows why the stated reaction timescale supplies a mixing constraint, not a unique measured coefficient.

Let the closed atmospheric parcel exchange heat and volume work with reservoirs at fixed temperature $T$ and pressure $P$, while reactions rearrange its conserved elemental inventory. For a reversible differential between equilibrium states, the first law of thermodynamics, with chemical work included, isThe Gibbs free energy $G=U+PV-TS$ therefore obeysThe first law of thermodynamics supplies this differential but does not alone choose the direction of a reaction. The Second law of thermodynamics does: for the parcel plus its reservoirs, at fixed $T,P$ and with no non-volume work,Thus spontaneous reactions decrease Gibbs free energy, and stable thermochemical equilibrium is its constrained minimum. For an allowed reaction of extent $d\xi$, let $d{N}_i={\nu }_{i}d\xi$, with positive stoichiometric vector entries for products and negative entries for reactants. At an interior minimum,The condition must hold for every independent allowed reaction, with fixed total atoms of each element and any relevant charge constraint. At a boundary with absent species, only feasible one-sided variations are permitted. These are the hypotheses of constrained Gibbs minimization for chemical equilibrium.

For an ideal gas mixture, ${\mu }_i={\mu }_i^{\circ }(T)+\mathcal{R}T\log (x_{i}P/P^{\circ })$, where $x_i$ is the volume mixing ratio and $\mathcal{R}$ the molar gas constant. ThereforeThis is a dimensionless activity-based equilibrium constant, not a bare product of dimensional pressures.

Convection mixes material vertically where the Schwarzschild criterion or Ledoux criterion allows it. Its chemical effect is controlled by competition between transport and reaction, rather than by a direct alteration of the equilibrium constant. Parametrize vertical transport by a vertical eddy diffusion coefficient $K_{zz}$; the eddy mixing time over a scale height isLet ${\tau }_{\mathrm{chem}}$ be the chemical relaxation time of the relevant interconversion. If reactions are faster, the gas follows local thermochemical equilibrium. If transport becomes faster, composition can be carried upward faster than it re-equilibrates. A chemical quench level is approximately where the two times match:For example, hot deep gas may contain abundant carbon monoxide. Strong mixing can maintain it in cooler layers where equilibrium would favour methane; this is carbon monoxide–methane quenching. Similar reasoning applies to nitrogen–ammonia quenching. The cooler nightside commonly has slower reaction rates and can preserve such quenched composition more readily, whereas sufficiently rapid dayside chemistry can restore local equilibrium. Neither statement is universal without the actual reaction network and temperature.

The observable atmosphere of a strongly irradiated hot Jupiter may be radiative and stable even if the deeper interior is convective. Deep convection influences the photosphere only if some mixing crosses the intervening radiative region, for example through overshoot or other dynamical transport. Moreover, transport from day to night is horizontal circulation, not vertical convection; its relevant competition is atmospheric advection time versus chemical relaxation time, giving horizontal chemical quenching. Convection can affect either hemisphere indirectly through connected vertical transport; strong deep convection alone does not guarantee a quenched observable composition.

The two measurements sample different atmospheric regions and different radiative transfer geometries. An exoplanet emission spectrum probes the dayside; an exoplanet transmission spectrum probes the morning and evening limbs of the day-night terminator. Several alternatives to an exoplanet cloud deck can therefore suppress the transmission feature.

Temperature, mean molecular weight, limb chemistry, continuum opacity and the dayside temperature gradient are alternatives or degeneracies to test. In particular, the three-scale-height amplitude alone cannot establish different CO abundances between the hemispheres.

The three parameter groups are local temperature, local pressure, and elemental composition. The elemental composition includes both atmospheric metallicity of a giant planet and atmospheric carbon-to-oxygen ratio; these are independent compositional controls, so a specification by $T$ and $P$ alone is incomplete. Given these inputs, thermochemical equilibrium minimizes Gibbs free energy with element conservation.

Three useful chemical observables in a hydrogen-rich hot Jupiter are:

CO/CH4, H2O, and CO2 bands provide complementary temperature and elemental-abundance diagnostics, but their observed strengths also depend on the atmospheric pressure-temperature profile, exoplanet clouds and observing geometry. A spectral feature is not by itself a direct equilibrium abundance.

Three routes away from local thermochemical equilibrium are:

Vertical mixing, horizontal advection, and photochemistry supply three mechanisms and examples in both exoplanets and Solar-System atmospheres. A photochemical steady state balances production and loss; it is different from a Gibbs free energy minimum. These examples describe mechanisms and model expectations rather than asserting unique observational attribution for every planet.

Four mechanisms that can produce disequilibrium chemistry in an exoplanet atmosphere are:

The exoplanet transport and photochemical examples follow kinetic atmosphere calculations and models including horizontal transport; the condensate example is examined in cold-trap calculations.

Take the logarithm to base ten and write pressure in units of $1\mathrm{bar}$, so its argument is dimensionless. Continuity of the atmospheric pressure-temperature profile givesThusIf the logarithm means $\ln$, the equivalent constant is $C=900/\ln 100\simeq 195.4\mathrm{K}$. A plot of temperature against logarithmic pressure is vertical in each isothermal region and straight between the two endpoints.

The processes can be organized by the supplied pressure ranges, although the exact boundaries require reaction rates, irradiation and mixing information:

The profile identifies plausible chemical regimes, but does not fix their transition pressures by itself. In particular, cloud formation depends on the species-specific condensation curve, and ultraviolet processing depends on shielding.

At fixed temperature and pressure, a closed reacting system is in thermochemical equilibrium when its Gibbs free energy is minimal subject to elemental-abundance constraints. For every independent reaction,with a positive second variation in every allowed direction.

An atmosphere can be driven into disequilibrium chemistry in an exoplanet atmosphere by vertical mixing faster than chemical conversion, which causes chemical quenching; ultraviolet atmospheric photochemistry; and atmospheric escape. Lightning, energetic particles, horizontal transport, condensation, and rainout provide further mechanisms.

At fixed temperature and pressure, thermochemical equilibrium minimizes the Gibbs free energy subject to elemental conservation. For every independent reaction with stoichiometric coefficients ${\nu }_i$,Equivalently, forward and reverse rates satisfy detailed balance. For ideal gases,

For $A+B\rightleftharpoons C+D$, the forward and reverse rates areAt thermochemical equilibrium, $r_f=r_r$ by detailed balance, whileafter the appropriate standard-concentration factors are included. The standard reaction Gibbs free energy isConsequentlyFor other stoichiometries, the same argument uses the corresponding activity product and its standard-state factors.