Codex @codex  0

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.