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Incoming links: Exoplanet thermal phase curve
Past exam of the mathematics course of the University of Cambridge 2018 iii Paper 315 4 a Solution 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 observations found hemisphere brightness temperatures roughly and , 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 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.
Past exam of the mathematics course of the University of Cambridge 2018 iii Paper 315 4 e Solution Created 2026-10-03 Updated 2026-10-05
Three major research directions, appropriate to the scientific questions posed in 2018, are:
- Characterizing small-planet atmospheres and habitability. Measure an exoplanet transmission spectrum and an exoplanet emission spectrum to establish whether rocky planets retain atmospheres, determine their composition and climate, and test exoplanet habitability. Interpreting an exoplanet biosignature requires a planetary and stellar context: photochemical false positives, exoplanet cloud obscuration and atmospheric escape can all affect apparently promising molecules.
- Connecting atmospheres and interiors to planet formation. Combine planetary mass-radius relations with ages, host-star abundances, atmospheric metallicity of a giant planet and atmospheric carbon-to-oxygen ratio to test growth and migration histories. Exoplanet interior-composition degeneracy, chemical processing and atmospheric condensate rainout prevent a molecular abundance or bulk radius from being a unique record of birth conditions.
- Understanding atmospheric circulation and thermal evolution across populations. Combine exoplanet thermal phase curves, Doppler spectroscopy and pressure-dependent spectra to test day-night heat redistribution, exoplanet cloud formation and disequilibrium chemistry in an exoplanet atmosphere. Relate these measurements to hot-Jupiter radius inflation, internal cooling and atmospheric escape, using comparative observations to distinguish mechanisms instead of fitting each planet in isolation.
These are research goals rather than claims that the relevant mechanisms or habitable atmospheres have already been established.
Past exam of the mathematics course of the University of Cambridge 2019 iii Paper 315 4 a Solution Created 2026-10-03 Updated 2026-10-05
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,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.
Past exam of the mathematics course of the University of Cambridge 2019 iii Paper 315 4 e Solution Created 2026-10-03 Updated 2026-10-05
First refine the ephemeris, planetary mass, stellar radius, and stellar variability using exoplanet transit photometry and the radial-velocity method. Then combine observations that probe different regions rather than relying on one spectrum. A present-day programme could use the following complementary measurements; in the 2019 setting of the paper, James Webb Space Telescope observations would have been a future capability.
- Exoplanet transmission spectrum at roughly – with the Hubble Space Telescope or optical ground-based spectroscopy: constrain exoplanet clouds, atmospheric haze, the scattering slope of a transmission spectrum, and sodium or potassium absorption.
- Near-infrared exoplanet transmission spectrum with NIRISS at – and NIRSpec modes covering roughly –: measure water, carbon monoxide, carbon dioxide, and methane bands, then constrain atmospheric metallicity of a giant planet and atmospheric carbon-to-oxygen ratio through a joint atmosphere model.
- Exoplanet secondary eclipses at near- and mid-infrared wavelengths with NIRSpec and MIRI, especially about – for the latter's time-series low-resolution mode: infer brightness temperatures, the vertical pressure-temperature structure, and whether an atmospheric thermal inversion turns bands into emission.
- A full-orbit exoplanet thermal phase curve in one or more infrared bands with the James Webb Space Telescope: constrain day-night heat redistribution, nightside emission, and the offset of the hottest region, with different bands probing different pressures.
- High-resolution near-infrared spectroscopy around molecular bands such as carbon monoxide near using CRIRES on the Very Large Telescope: resolve the planetary Doppler shift and seek wind velocities or rotation broadening after accounting for the orbital velocity.
- Ultraviolet transit spectroscopy with the Hubble Space Telescope, or ground-based near-infrared helium spectroscopy at : search for atmospheric escape and an extended upper atmosphere.
Together these address aerosols, molecular composition, elemental enrichment, vertical thermal structure, horizontal heat transport, winds, and escape. Repeat key events and monitor stellar activity, since stellar contamination and instrumental trends can imitate atmospheric signals. Use actual brightness, saturation limits, and predicted feature amplitudes to choose observing modes and exposure times.
The wavelength ranges and time-series capabilities are documented in the NIRISS SOSS guide, NIRSpec overview, MIRI spectroscopy guide, and ESO's CRIRES description.