A close-in giant is often in <synchronous rotation> after <tidal locking>, giving persistent dayside heating and nightside cooling. Its contrast is controlled by the competition between <radiative relaxation time in a planetary atmosphere>, wind transport characterized by the <atmospheric advection time>, wave adjustment, and drag. When heat transport is fast compared with radiation, <day-night heat redistribution> lowers the contrast; when radiation is fast, each hemisphere stays closer to its local radiative balance.

For a rough atmospheric column estimate,
$$
\tau_{\rm rad}\sim\frac{c_pp}{4g\sigma_{\rm SB}T^3},\qquad
\tau_{\rm adv}\sim\frac{R_p}{U}.
$$
At comparable <pressure>, higher <planetary equilibrium temperature> sharply shortens radiative relaxation, tending to increase the day-night contrast. Wind speeds, rotation, and magnetic drag can modify this trend; dissociation and recombination can carry additional heat in very hot atmospheres.

At higher altitude, lower <pressure> generally means shorter radiative relaxation and a larger contrast. Infrared bands with larger <opacity> probe these higher layers, while lower-opacity windows sample deeper layers with longer cooling times and more effective redistribution. A wavelength-dependent <exoplanet thermal phase curve> can therefore reveal how the contrast and hot-region displacement change with pressure.

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 315 / 4 / a / Solution

Synchronous rotation has spin period equal to orbital period. A synchronously rotating <exoplanet> on a circular orbit has a persistent illuminated hemisphere and a persistent dark hemisphere, making <day-night heat redistribution> crucial.

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