Solution (source code)

= Solution

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 $P\gtrsim1$--$10$ 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 $10^{-3}\lesssim P\lesssim1$ bar, vertical mixing and horizontal winds can outrun <chemical relaxation time>. The <chemical quench level> is defined by $\tau_{\rm chem}\sim\tau_{\rm mix}$; 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 $P\lesssim10^{-3}$ 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.

\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2016/iii/paper-315-chemistry-regimes.png]
{title=Nominal deep-equilibrium, transport-quenching and photochemical regimes in a hydrogen-rich irradiated atmosphere}

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.