Past exam of the mathematics course of the University of Cambridge 2022 iii Paper 315 4 b Solution 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.
Past exam of the mathematics course of the University of Cambridge 2022 iii Paper 315 4 e Solution 2026-09-28
Exoplanet clouds and atmospheric haze add scattering and absorption opacity to an exoplanet transmission spectrum. A high opaque deck truncates the slant path and mutes molecular bands, while small aerosol particles can produce a blue scattering slope; patchiness creates mixtures of clear and cloudy limbs. In an exoplanet emission spectrum, aerosols move the photosphere to lower pressure, weaken or reshape molecular features, alter the geometric albedo, and can heat or cool layers depending on their shortwave and longwave absorption.
Observed aspects of exoplanet atmospheric dynamics include eastward equatorial atmospheric superrotation inferred from shifted thermal hot spots, day-night heat transport measured by phase-curve amplitude, and high-altitude winds measured from Doppler shifts of resolved spectral lines. Time-variable phase curves and eclipse maps also reveal changing cloud patterns and storms.