Astronomy & Celestial Mechanics
the sky, computed
Concept

Abundance degeneracy — where it appears

The trade-off in which a spectral feature can be matched by more of an absorber or by a different atmospheric structure. In transmission the reference radius trades against abundance; in emission the temperature gradient does, and only features at many wavelengths separate them.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Three planets that are the same spectrum. A model transmission spectrum, in scale heights of apparent radius, drawn three times: once as it is, once with the reference radius raised by 0.45 scale heights and the abundance reduced to compensate, and once with a cloud deck truncating the features. The three differ by 0.21 scale heights root-mean-square against features of 2.1, which is well inside the error bars of any real observation. The reason is structural rather than observational: a transmission spectrum measures a difference in apparent radius with wavelength and never an absolute radius, so the level is a free parameter, and shifting the level trades against the abundance almost exactly. Adding a cloud deck adds a third parameter that flattens features and trades against both. Three unknowns and one curve is why the quoted abundance uncertainties from transmission spectroscopy are so much larger than the photometric precision suggests.

A spectrum flattened by cloud, or by nothing

A transmission spectrum measures how a planet's apparent radius changes with wavelength, and never the radius itself. That missing level is a free parameter, it trades almost exactly against the abundance of whatever is absorbing, and a cloud deck adds a third unknown to a curve that constrains two.

exoplanets · Exoplanet atmospheres Brightness temperature across the infrared, for three profiles. The brightness temperature of the planet's emission against wavelength from 1 to 12 microns, for the three temperature profiles, with water and carbon monoxide bands in the opacity. In a band the opacity is high, so the light comes from higher, lower-pressure layers; in the windows between bands it comes from deeper. Over a profile falling outward the bands are cooler than the windows: at 6.3 microns 1457 K against 1570 K at 3.6. Over the inverted profile they are hotter: 1851 against 1538. Over the isothermal profile every wavelength has the same brightness temperature and the spectrum is a blackbody, whatever molecules are present.

Molecules seen only through a change of temperature

The heat a planet gives off, measured colour by colour as it disappears behind its star, carries the fingerprints of the molecules in its atmosphere — but only because the atmosphere's temperature changes with height. Water absorbs where the air cools upward and emits where it warms, and in an atmosphere at one temperature every molecule vanishes from the spectrum, however much of it there is. An emission spectrum is a sounding of a temperature gradient, and the molecules are what it is taken with.

exoplanets · Exoplanet atmospheres

Named alongside it

The objects these essays reach for when they reach for this one.

Bayesian inferenceBrightness temperatureCloud deckContribution functionEmission spectrumGrey opacityMean molecular weightRayleigh scatteringReference radiusRetrievalScale heightSecondary eclipse

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