Disequilibrium chemistry in an exoplanet atmosphere

Atmospheric chemistry is out of equilibrium when reaction times exceed transport or photochemical times. Vertical quenching, ultraviolet photochemistry, and atmospheric escape can then maintain abundances far from local thermochemical equilibrium.

Atmospheric photochemistry begins when a molecule absorbs a photon and dissociates or ionizes. The products can drive reaction networks whose steady abundances differ strongly from thermochemical equilibrium.

A photochemical steady state has production and loss rates balanced for each short-lived species even though individual photochemical reactions continue.

The Chapman ozone mechanism combines oxygen photodissociation, three-body ozone formation, ozone photodissociation, and the reaction between atomic oxygen and ozone. Under local steady state and dominant photolytic ozone loss,

An ozone layer is an atmospheric altitude range with enhanced ozone abundance. Oxygen-dissociating ultraviolet radiation is strongest aloft while three-body formation is fastest at greater density, so their competition can concentrate ozone at intermediate altitude.

The eddy mixing time over one atmospheric scale height is ${\tau }_{\mathrm{mix}}\simeq H^2/K_{zz}$, where $K_{zz}$ is the vertical eddy diffusion coefficient.

The vertical eddy diffusion coefficient parametrizes turbulent transport in an atmosphere by a diffusive flux proportional to an abundance gradient. Over distance $L$, the corresponding eddy mixing time is $L^2/K_{zz}$. Its units are area per time, so $1{\mathrm{m}}^2{\mathrm{s}}^{-1}=10^4\mathrm{c}{\mathrm{m}}^2{\mathrm{s}}^{-1}$.

A chemical quench level is where a reaction time equals the atmospheric transport time. Above it, transport is faster and carries an approximately fixed deeper abundance faster than local chemistry can restore equilibrium.

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.

Above a chemical quench level, rapid eddy mixing can keep a species' number mixing ratio $f_A$ approximately fixed at its deeper value, provided condensation, photochemical loss, and molecular diffusion remain negligible. The species' number density is then $n_A=f_{A}p/(k_{B}T)$; constant mixing ratio does not imply constant number density. In an isothermal atmosphere, $n_A$ decreases exponentially with altitude on the atmospheric scale height.

Carbon monoxide–methane quenching freezes the CO-to-CH4 abundance ratio near the level where their interconversion time first exceeds the vertical mixing time.

Nitrogen–ammonia quenching similarly preserves a deeper N2-to-NH3 ratio above the level where chemical conversion becomes slower than atmospheric mixing.