Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-315/4/d/solution

Three observable signatures of disequilibrium chemistry in an exoplanet atmosphere are vertically quenched carbon monoxide in methane-favored cool layers or methane in carbon-monoxide-favored hot layers; quenched ammonia-nitrogen chemistry; and photochemical products such as hydrogen cyanide, sulfur dioxide, hydrocarbons, or hazes. Their abundances constrain mixing, ultraviolet irradiation, reaction kinetics, and atmospheric escape.
Solar-System methane and gravity-field measurements imply that Jupiter is enriched in heavy elements by a few times solar, Saturn by roughly an order of magnitude, and Uranus and Neptune by tens of times solar. This motivates an inverse planetary mass-metallicity trend: lower-mass planets acquire a larger heavy-element fraction from solids relative to hydrogen-helium gas. Carbon-to-oxygen and nitrogen abundances also constrain ice lines, planetesimal accretion, core erosion, and migration.
Uniform exoplanet transmission and emission surveys can test whether this trend is universal across mass, equilibrium temperature, age, and host metallicity. Measurements of water, methane, carbon monoxide, carbon dioxide, ammonia, and sulfur species can separate bulk enrichment from carbon-to-oxygen ratio, clouds, and disequilibrium, thereby constraining where and how planets formed.

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