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Incoming links: Two-limb transmission spectrum
Past exam of the mathematics course of the University of Cambridge 2017 iii Paper 315 2 c ii Solution Created 2026-10-03 Updated 2026-10-06
The two measurements sample different atmospheric regions and different radiative transfer geometries. An exoplanet emission spectrum probes the dayside; an exoplanet transmission spectrum probes the morning and evening limbs of the day-night terminator. Several alternatives to an exoplanet cloud deck can therefore suppress the transmission feature.
- A cooler terminator has a smaller atmospheric scale height , so the same change in slant optical depth produces a smaller transit-area change. A larger mean molecular weight has the same geometric effect. The assumption that the nightside temperature sets both limbs may itself be wrong.
- Genuine chemical heterogeneity can reduce terminator carbon monoxide. At lower temperature, thermochemical equilibrium can favour methane through , if local reaction times are sufficiently short. Atmospheric photochemistry, elemental abundance differences, and horizontal chemical quenching can modify this simple picture.
- The feature depends on a band-to-continuum opacity ratio, not abundance alone. A continuum enhanced by other gas absorption or a partly covered heterogeneous limb can mute the feature; the two-limb transmission spectrum illustrates this averaging. Stellar surface heterogeneity and measurement systematics can also bias an inferred feature amplitude.
- A strong CO emission feature can be amplified by an atmospheric thermal inversion, because the line forms in hotter gas than the continuum. It is consequently not an unambiguous abundance measurement without a simultaneous atmospheric pressure-temperature profile fit.
Temperature, mean molecular weight, limb chemistry, continuum opacity and the dayside temperature gradient are alternatives or degeneracies to test. In particular, the three-scale-height amplitude alone cannot establish different CO abundances between the hemispheres.