Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2016/iii/paper-315/4/i/solution

A thermal inversion is outward-increasing temperature over part of an atmosphere. In an irradiated radiative model, an upper absorber that captures incoming stellar energy efficiently compared with its infrared cooling can create an inversion. Early hot-Jupiter models proposed titanium monoxide/vanadium monoxide as strong visible absorbers, and an irradiation-based division between hotter titanium monoxide/vanadium monoxide-rich inverted atmospheres and cooler non-inverted atmospheres followed.
The simple temperature classification needed refinement. Condensation and vertical or day-night atmospheric cold traps can remove Ti/V even when the observed dayside is hot; settling competes with vertical mixing. Bulk C/O and metallicity determine whether oxygen-bearing absorbers are available, so irradiation alone does not specify their abundance. Photochemistry, stellar UV activity and alternative absorbers were also proposed to affect inversion formation or destroy an absorber; such correlations were hypotheses rather than a unique established cause.
Observationally, molecular bands in emission rather than absorption can diagnose an inverted contribution region, but sparse broadband eclipse measurements are degenerate with chemistry. By 2016, spectroscopic constraints had weakened some early inversion claims and supported the need for planet-specific opacity, abundance and transport models. The key development is from a single irradiation threshold to a composition- and transport-dependent visible/infrared opacity balance, tested by spectra rather than assuming every very hot planet must have the same inversion.

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