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A chemical system is out of local chemical equilibrium when reaction adjustment cannot keep pace with transport, imposed changes or external driving. Comparing the chemical relaxation time with transport and irradiation times identifies plausible departures. Disequilibrium chemistry in an exoplanet atmosphere combines this principle with mixing, horizontal advection and atmospheric photochemistry.

For a vertical eddy diffusivity $K_{zz}$, mixing over a length $\ell$ takes ${\tau }_{\mathrm{mix}}\sim {\ell }^2/K_{zz}$. The condition that transport outrun a chemical relaxation time therefore gives $K_{zz}\gtrsim {\ell }^2/{\tau }_{\mathrm{chem}}$. Taking $\ell =0.1H$ instead of one atmospheric scale height $H$ changes this estimate by a factor of one hundred. The atmospheric scale height itself depends on both temperature and gravity.

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.

Eliminate cis using $[\mathrm{cis}]=C_{\mathrm{tot}}-[\mathrm{trans}]$:ThusBoth directions restore the perturbed distribution: an excess of trans both increases its reverse consumption and reduces cis available for forward formation. This explains why the chemical relaxation time is $1/(k_1^{\prime }+k_{-1}^{\prime })$, rather than the reciprocal of only one rate constant.

Subtract the new equilibrium concentration and divide by the initial displacement:At the halfway concentration this ratio is $1/2$, soThis is the half-time of the displacement from equilibrium. It is not the time for the absolute trans concentration to fall to half its initial value; that value lies far below the attainable new equilibrium plateau. The corresponding chemical relaxation time is $671$ s.

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.

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.

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.

Use the standard local chemical quench level approximation: carbon monoxide-rich gas from the hot deep region is transported upward, and conversion becomes slower as the gas enters the cooler layers. Assume that neither a faster loss process nor strong compositional fractionation removes carbon monoxide above the quench level. For an effective mixing length $L$, the eddy mixing time is ${\tau }_{\mathrm{mix}}\simeq L^2/K_{zz}$, so outrunning conversion near $1\mathrm{bar}$ requiresThe usual order-of-magnitude choice is $L\simeq h_b$, the local atmospheric scale height at $T_b=1400\mathrm{K}$. Equal planetary mass and radius give the same gravity as Jupiter; with the same mean molecular weight, the atmospheric scale height scales linearly with temperature. To use the supplied $30\mathrm{km}$ reference, additionally adopt a representative Jovian reference temperature $T_J=150\mathrm{K}$. ThenUsing $k_{B}T/(\mu m_{H}g)$ directly with $\mu \simeq 2.3$ and Jovian $g\simeq 25\mathrm{m}{\mathrm{s}}^{-2}$ gives $h_b\simeq 200\mathrm{km}$ and $K_{zz}\gtrsim 4\times 10^5{\mathrm{m}}^2{\mathrm{s}}^{-1}$, the same order of magnitude. The supplied Jovian height is approximate and does not specify its reference temperature. Inserting $30\mathrm{km}$ unchanged for the hot gas would instead give $9\times 10^3{\mathrm{m}}^2{\mathrm{s}}^{-1}$ and neglect this temperature scaling.

The pressure separation is relevant to a stronger, whole-column transport estimate. With constant gravity and mean molecular weight, the profile givesIf one additionally requires diffusion through the entire column within $10^5\mathrm{s}$, a sufficient conservative condition is $K_{zz}\gtrsim \Delta z^2/{\tau }_{\mathrm{chem}}\sim 10^7{\mathrm{m}}^2{\mathrm{s}}^{-1}$. It is not a necessary local quench condition: the chemical relaxation time is expected to become much longer in the cooler gas, so a longer total transit time can still preserve carbon monoxide.

The usual quench estimate is $K_{zz}$ of order $10^6{\mathrm{m}}^2{\mathrm{s}}^{-1}$ under the stated scale-height assumptions. A unique bound for survival to $10^{-3}\mathrm{bar}$ cannot be inferred from one reaction time without assumptions about its variation, the mixing length and upper-atmospheric losses.

Here is an explicitly stipulated elementary kinetic model, not experimental data. A well-mixed ideal closed system has constant temperature and volume. Alongside an uncatalysed elementary reaction, allow an illustrative catalytic encounter that returns C immediately:Both channels obey the law of mass action. In the second, the forward reaction rate is ${\alpha }_f[\mathrm{A}][\mathrm{C}]$ and the reverse reaction rate is ${\alpha }_r[\mathrm{B}][\mathrm{C}]$. C cancels in each encounter, so its free concentration $c_C$ stays constant without an external supply. This toy elementary reaction encodes regeneration without binding; it is not a claim that real catalytic cycles universally consist of one encounter. A binding cycle can accumulate a reaction intermediate, in which case constant total C does not imply constant free $c_C$.

Adding the parallel reaction rates gives effective first-order reaction rate constantsBecause $k_f^u/k_r^u={\alpha }_f/{\alpha }_r=3$, each channel balances at the same $[\mathrm{B}]/[\mathrm{A}]=3$, and so does their sum. At $c_C=0$ the pair is $(0.030,0.010){\mathrm{s}}^{-1}$; at $c_C=0.001\mathrm{mol}{\mathrm{L}}^{-1}$ it is $(0.300,0.100){\mathrm{s}}^{-1}$. Both give $K=3$ with ideal thermodynamic activities and a common concentration standard state. At $T=300\mathrm{K}$ their compatible standard reaction change in Gibbs free energy is ${\Delta }_r{G}^{\circ }=-RT\ln 3\approx -2.7403\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$. Choosing an unrelated reverse rate constant would break this consistency.

Let $S=[\mathrm{A}]+[\mathrm{B}]$ be the conserved concentration, and define the dimensionless quantity $x=[\mathrm{B}]/S$. ThenSolving this first-order linear differential equation givesThe chemical relaxation time is $25\mathrm{s}$ without C and $2.5\mathrm{s}$ with the chosen C. From either $x_0=0$ or $x_0=1$, the exponential decay of the deviation leads to the same chemical equilibrium $x=3/4$. Reducing that deviation to one percent takes $\ln (100)\tau$: about $115.13\mathrm{s}$ versus $11.51\mathrm{s}$.

At this chemical equilibrium, conversion continues in both directions. For $S=1\mathrm{mol}{\mathrm{L}}^{-1}$, the uncatalysed channel has equal forward and reverse reaction rates $0.0075\mathrm{mol}{\mathrm{L}}^{-1}{\mathrm{s}}^{-1}$. Adding C gives total directional reaction rates $0.075\mathrm{mol}{\mathrm{L}}^{-1}{\mathrm{s}}^{-1}$ each, yet zero net reaction rate. Faster molecular exchange and unchanged composition coexist. This exact calculation explains how catalysis can matter enormously within an observation window while leaving the final equilibrium constant intact.