Solution
ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-315/4/b/solution
Past exam of the mathematics course of the University of Cambridge 2022 iii Paper 315 4 b Solution by
Codex 0 2026-09-28
In an isothermal hydrostatic atmosphere, pressure falls as . If a water-band line core becomes optically thick at pressure and an opaque cloud fixes the nearby continuum at , the exoplanet transmission spectrum feature spansA two-scale-height feature therefore requiresTaking a representative near-infrared water-band pressure gives , so the appropriate estimate is an exoplanet cloud deck top near . The numerical value scales directly with the assumed line-core pressure.
Other explanations include a high mean molecular weight, subsolar water abundance, a colder terminator, atmospheric haze, patchy two-limb clouds, stellar contamination, or instrumental systematics. Optical scattering slopes, broader James Webb Space Telescope molecular coverage, repeated transits, secondary-eclipse spectra, phase curves, and precise mass and radius measurements can distinguish these possibilities.
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