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Incoming links: Coronagraph
Past exam of the mathematics course of the University of Cambridge 2015 iii Paper 59 4 i Solution Created 2026-10-03 Updated 2026-10-06
Three detection methods are exoplanet transit photometry, the radial-velocity method, and exoplanet direct imaging. Transits detect obscuration of the star; radial velocities detect stellar reflex motion; imaging separates the planet's own reflected or thermal light from the star.
Exoplanet transit photometry supports wavelength-dependent exoplanet transmission spectra, while the same orbital geometry supports exoplanet secondary eclipses and phase-resolved planetary spectra. Exoplanet direct imaging provides resolved light for atmospheric spectroscopy. Stellar radial-velocity discovery alone does not measure an atmosphere, although high-resolution follow-up can separate a moving planetary molecular spectrum through its changing Doppler effect.
- Resolvable projected separation: the angular separation is , so a wide orbit around a nearby star places the planet beyond the instrument's inner working angle, related to and the coronagraph design.
- Sufficient planet-star contrast: young, massive planets remain intrinsically hot and bright in the infrared, improving contrast against the star; starlight suppression and favorable observing wavelengths further help.
A wide orbit improves separation but weakens reflected-light illumination and lengthens the orbital period. These conditions therefore describe imaging sensitivity, not an assertion that every detection method becomes easier at large separation.
Past exam of the mathematics course of the University of Cambridge 2017 iii Paper 315 3 a ii Solution Created 2026-10-03 Updated 2026-10-06
Assume the planet and present-day Jupiter have the same mass, comparable composition and initial cooling normalization, and both can be described by the supplied power-law planetary cooling over the relevant ages. Take the age of present-day Jupiter to be and the young planet's age to be . The normalization cancels:The 5-AU orbit is used to regard stellar irradiation as modest compared with a hot-Jupiter orbit; the ratio is specifically intrinsic cooling, not the sum of intrinsic and reradiated luminosity. Initial entropy and irradiation can change the assumed normalization, so this estimate is not independent of formation conditions.
Such a young self-luminous giant is a favourable target for near-infrared exoplanet direct imaging. The increased intrinsic luminosity improves its contrast with the host star, and a wide physical orbit is more readily separated on the sky than a hot-Jupiter orbit. Two essential observing considerations are:
- Angular separation: at distance parsecs, a projected 5-AU separation is at most roughly arcseconds. It must exceed the instrumental inner working angle; orbital projection can make it smaller. Nearby targets and adaptive optics help.
- Planet-star contrast and wavelength: the band must balance the young planet's thermal radiation, stellar leakage, detector sensitivity and thermal background. Suppression with a coronagraph and stable calibration are required; a large intrinsic bolometric ratio to old Jupiter is not itself the measured contrast with the star.
Thus direct imaging of a nearby young system, with sufficient angular resolution and contrast, is the natural discovery method, subject to the actual stellar brightness and instrumental limits.