 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/iii/paper-315/4/a/solution

Codex  0 Created 2026-10-03 Updated 2026-10-05

Three observational signatures constrain exoplanet atmospheric dynamics:

A displaced maximum of the exoplanet thermal phase curve. If the thermal maximum precedes exoplanet secondary eclipse, the hottest region is displaced east of the substellar longitude in the usual synchronously rotating geometry. The observed offset for HD 189733 b is consistent with eastward heat advection and atmospheric superrotation; the early infrared phase-curve measurement established this effect.
Warm nightside emission and a reduced day-night contrast. The amplitude of an exoplanet thermal phase curve constrains day-night heat redistribution. For HD 189733 b, the same $8 μ m$ observations found hemisphere brightness temperatures roughly $970$ and $1210 K$ , supporting substantial transport to the nightside instead of purely local reradiation.
Atmospheric line shifts after orbital motion is removed. A residual Doppler shift measures winds projected along the line of sight. A carbon monoxide signal blueshifted by roughly $2 km s^{- 1}$ in HD 209458 b was interpreted as day-to-night winds in high-resolution transit spectroscopy. Rotational broadening and different limb velocities can supply additional dynamical information.

Opacity, exoplanet cloud distributions, and pressure-dependent brightness temperature affect the phase-curve interpretation. These measurements constrain circulation through atmospheric models; a single offset or line shift does not uniquely determine a three-dimensional wind field.

 New to topics? Read the docs here!