Assume an isothermal terminator, constant gravity and mean molecular weight, and use the stated nightside atmospheric scale height as the terminator value. Hydrostatic equilibrium gives . A band radius three atmospheric scale heights above a measured continuum at therefore corresponds toThis is the band's characteristic pressure, not automatically the top of an exoplanet cloud deck. The distinction matters because an opaque cloud generally raises the continuum and removes the lower part of a molecular feature; it does not cap the height of a strong molecular line above the cloud.
If the quoted is the actual observed continuum and the cloud dominates its opacity, the consistent estimate is insteadIf refers to a clear-atmosphere reference continuum, an additional clear band height is necessary. Let that height be . A cloud at height leaves a residual feature of when . Thus the cloud pressure degeneracy of a transmission feature givesFor example, a cloud estimate requires the extra assumption that the clear band spans six scale heights, so the cloud raises the continuum by three. Identifying the cloud with the level three scale heights above the original continuum gives the same numerical value, but is not justified by the observed band height alone. Without a clear-band opacity or equivalent reference radius, there is no unique cloud-top pressure. A strong dayside emission feature also does not supply that missing terminator information.
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.
Convection mixes material vertically where the Schwarzschild criterion or Ledoux criterion allows it. Its chemical effect is controlled by competition between transport and reaction, rather than by a direct alteration of the equilibrium constant. Parametrize vertical transport by a vertical eddy diffusion coefficient ; the eddy mixing time over a scale height isLet be the chemical relaxation time of the relevant interconversion. If reactions are faster, the gas follows local thermochemical equilibrium. If transport becomes faster, composition can be carried upward faster than it re-equilibrates. A chemical quench level is approximately where the two times match:For example, hot deep gas may contain abundant carbon monoxide. Strong mixing can maintain it in cooler layers where equilibrium would favour methane; this is carbon monoxide–methane quenching. Similar reasoning applies to nitrogen–ammonia quenching. The cooler nightside commonly has slower reaction rates and can preserve such quenched composition more readily, whereas sufficiently rapid dayside chemistry can restore local equilibrium. Neither statement is universal without the actual reaction network and temperature.
The observable atmosphere of a strongly irradiated hot Jupiter may be radiative and stable even if the deeper interior is convective. Deep convection influences the photosphere only if some mixing crosses the intervening radiative region, for example through overshoot or other dynamical transport. Moreover, transport from day to night is horizontal circulation, not vertical convection; its relevant competition is atmospheric advection time versus chemical relaxation time, giving horizontal chemical quenching. Convection can affect either hemisphere indirectly through connected vertical transport; strong deep convection alone does not guarantee a quenched observable composition.
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