Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 315 / 2 / a / 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 $P\gtrsim 1$--$10$ 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.