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What Does Exoplanet Equilibrium Temperature Really Mean?

I will start by saying that it is not currently possible to directly measure the temperature of the surface of an exoplanet (and the matter below the surface is even less accessible). What you see in the literature and in the popular media is known as the equilibrium temperature. This temperature is an inferred quantity, derived under highly idealized assumptions, and may in fact have nothing to do with the actual temperature of the planet. In general, temperature is determined by balancing all heating and cooling processes, and one of the assumptions in the context of exoplanets is that the only source of heating is radiation from the host star, and the only source of cooling is re-radiation of some of the received energy back into space. Venus is a good example of how such a naively calculated equilibrium temperature may not even be anywhere close to the actual temperature because when the same method that is used to estimate the temperature of exoplanets is applied to Venus we get an error of 1150% (that's not a typo: over a thousand-percent error). We know this because Venus is close enough to get an independent and more reliable measurement of the temperature. The predicted equilibrium temperature of Venus is about −40 degrees Celsius (about −40 degrees Fahrenheit), but the actual temperature is 462 degrees Celsius (864 degrees Fahrenheit).

The particular assumptions made in calculating the equilibrium temperature (sometimes known as the effective temperature) are that the planet is naked (has no atomosphere), and its only interaction with the star light incident upon it is to absorb some and reflect some back into space. The catch is that the amount that is reflected, charcaterized by a quantity called the albedo is not possible to reliably measure yet, and is usually just guessed without much justification. The albedo depends on many factors, some of which are geometry, composition, atmospheric properties, and even the activity of lifeforms on a planet.

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Usually, the albedo is simply set equal to that of Earth, even if a planet is clearly nothing like Earth. This was done in the Kepler data analysis paper by Borucki et al. (2011, ApJ, 736, 19). The authors state that the uncertainties in their equilibrium temperatures amount to 22%. Even this is an underestimate because it does not account for the fact that the assumed albedo may be completely wrong, and it does not account for the assumption that no other heating and cooling mechanisms are considered. (To be fair, the Borucki et al. paper does state that, “The uncertainties associated with the effect of an atmosphere could dwarf the uncertainties discussed here.” The calculation of equilibrium temperature also depends on what fraction of a planet receives heat from the host star, how heat is redistributed by the planet (and therefore its rotation rate), and what the radiant energy re-emission properties are. These factors have to be guessed. The equilibrium temperature also depends on the radius and surface temperature of the host star, and the planet-star distance, and each of these quantities have their own margins of error. The case of Venus amply illustrates that a blanket uncertainty of 22% is clearly not a true assessement of how meaningful the equilibrium temperatures might be. (Advanced readers: there are works that try to account for redistribution of heat and other effects but these are still parameterizations based on guesses; see for example Kane and Gelino 2011).

The bottom line is that exoplanet temperatures should be interpreted with extereme caution, even those in the scientific literature. Whilst the latter type of reporting usually is very clear about the limitations and usefulness of equilibrium temperatures, popular media may not be so clear. Certainly, it is meaningless to quote exoplanet temperatures to one degree accuracy, and such misleading figures really have been quoted in the popular media.

Day/Night Temperature Differences and Thermal Inversions

For some exoplanets it has been claimed from observations that there are significant differences between the “day side” (star-facing) and the “night side” of a planet. It is usually argued that planets very close to their host star would be “tidally-locked,” meaning that gravitational forces cause a planet to slow down and stop spinning. But the claims have been made for hot Jupiters and these are gaseous planets but we know very little about atmospheric circulation and the redistribution of heat on these planets.

The term vertical thermal inversion refers to the temperature in the upper atmosphere increasing with height instead of decreasing. The inference of thermal inversion has been made for several exoplanets based on infrared observations, but the inference is not a direct consequence of the observations. The inference of thermal inversion involves modeling complex physics that relies on many assumptions, some of which may not be have a firm basis. The subject is rather tentative at the moment. (For advanced readers: a good review of the issues, problems, and assumptions involved in studying both day/night temperature differences and thermal inversions has been given by Seager and Deming (2010), ARA&A, 48, 631.)

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File under: Equilibrium temperature of exoplanets; Effective temperature of exoplanets; Assumptions made for deriving exoplanet temperatures; Effect of albedo on exoplanet temperatures. Day/Night differences in exoplanet temperatures; Thermal inversions in exoplanet atmospheres.

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