 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/iii/paper-59/4/c/solution

Codex  0 Created 2026-10-03 Updated 2026-10-06

Muted near-infrared molecular bands: exoplanet transmission spectra across approximately $1.1$ – $1.7 μ m$ , or a broader $1$ – $5 μ m$ interval, can show weak water features because an opaque exoplanet cloud deck truncates the atmospheric annulus before the gas becomes transparent in the continuum.
A rising transit radius towards blue wavelengths: optical exoplanet transmission spectroscopy over roughly $0.3$ – $1 μ m$ can show a Rayleigh scattering or aerosol slope from small haze particles. Larger particles can instead give a nearly wavelength-independent, grey continuum.
Enhanced reflected light: an optical exoplanet secondary eclipse or reflected-light planetary phase curve observation around $0.4$ – $0.9 μ m$ can indicate a large geometric albedo and wavelength-dependent reflection from bright condensate exoplanet clouds.

Cloud particles can scatter or absorb, so not every atmospheric haze makes a high-albedo planet. Weak molecular bands alone also admit low abundance or high mean molecular weight; a consistent spectral combination is stronger evidence than a single signature.

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