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

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.

Three solar-system effects illustrate chemical disequilibrium. First, vertical mixing carries carbon monoxide from hot deep regions into cooler observable layers of giant planets, where its local-equilibrium abundance would be small. Second, phosphine survives in the observable atmospheres of Jupiter and Saturn because deep supply competes with its destruction, making it a tracer of transport. Third, methane photolysis creates hydrocarbons such as ethane and acetylene, and can help form upper-atmospheric atmospheric hazes in giant planets and Titan.

Three exoplanet effects are complementary. First, carbon monoxide–methane quenching can keep carbon monoxide abundant and methane depleted in cool observable gas, including hot-Neptune/giant atmospheres that would locally favor methane. Second, atmospheric photochemistry dissociates methane/ammonia and produces radicals, hydrogen cyanide, hydrocarbons and possibly atmospheric hazes, changing spectral bands from their equilibrium strengths. Third, horizontal chemical quenching can preserve hot-dayside carbon chemistry on the cooler nightside/terminator and reduce the abundance contrast expected from separate local-equilibrium columns.

Transport, photon-driven reactions and finite chemical adjustment times change the observable composition. The effects are conditional on the species' chemical timescale relative to mixing, advection and irradiation; they do not imply that every molecule is out of equilibrium everywhere.

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 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.

Four possible molecular signatures of disequilibrium chemistry in an exoplanet atmosphere, measured through an exoplanet transmission spectrum or exoplanet emission spectrum, are:

The first two signatures can be consequences of the same process and are not independent evidence for two mechanisms. Changes in atmospheric carbon-to-oxygen ratio, atmospheric metallicity of a giant planet, exoplanet cloud coverage, and the atmospheric pressure-temperature profile can mimic abundance changes. A convincing inference compares several molecular bands with a chemically consistent equilibrium model rather than identifying one unusual band alone.

Assume a hydrogen-helium perfect gas with mean particle mass $2.3m_H$, Jupiter gravity $g\simeq 24.8\mathrm{m}{\mathrm{s}}^{-2}$, and mixing over one atmospheric scale height. At $T=1000\mathrm{K}$,The eddy mixing time is ${\tau }_{\mathrm{mix}}\simeq H^2/K_{zz}$. A chemical quench level at one bar requires ${\tau }_{\mathrm{mix}}\lesssim {\tau }_{\mathrm{chem}}=10^5\mathrm{s}$, hence the vertical eddy diffusion coefficient must be of orderThe number depends quadratically on the assumed mixing length; using a fraction of $H$ reduces it accordingly.

Above the chemical quench level, neglect photochemistry, condensation, and molecular diffusion. The quenched atmospheric mixing ratio $f_A=n_A/n$ is approximately constant, while the number density isThus the abundance fraction is frozen, but the absolute number density falls with pressure and altitude. Examples are carbon monoxide–methane quenching, through $\mathrm{CO}+3{\mathrm{H}}_2\rightleftharpoons {\mathrm{CH}}_4+{\mathrm{H}}_2\mathrm{O}$, and nitrogen–ammonia quenching, through ${\mathrm{N}}_2+3{\mathrm{H}}_2\rightleftharpoons 2{\mathrm{NH}}_3$.

Approximate the atmosphere above $R_p$ as isothermal with constant gravity and atmospheric scale height $H$, soVertical transport over one scale height has eddy mixing timeThe chemical quench level satisfies ${\tau }_{\mathrm{chem}}(z_q)={\tau }_{\mathrm{mix}}$. Since ${\tau }_{\mathrm{chem}}=\eta z$,Above this level, mixing is faster than reaction and freezes the deeper abundance of A. Larger $K_{zz}$ moves the quench level deeper and raises $P_q$. Important examples are carbon monoxide–methane quenching and nitrogen–ammonia quenching; phosphine destruction is another tracer of vertical quenching.