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# Earth Similarity Index - ESI

The Earth Similarity Index, or ESI, is a proposed prescription to quantify the notion of Earth-like planet. The index was proposed by the Planetary Habitability Laboratory (PHL) but there is no concensus yet as to whether it should be universally applied. The ESI is a single number that is the result of plugging certain exoplanet parameters into a specially constructed formula. The idea is that the ESI is a number between 0 and 1, where a value of 1 would correspond to an exoplanet being identical to Earth. The ESI uses four parameters of an exoplanet (and implicitly of the host star), namely the mass, density, escape velocity, and a theoretical quantity called the equilibrium surface temperature of the planet. The latter three parameters require the radius of the exoplanet to be known.

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There are several problems with the PHL prescription of the ESI. For confirmed exoplanets, the planet mass often only has a lower limit. For the Kepler mission exoplanet candidates, there is often no mass estimate, only a radius. On the other hand, most confirmed exoplanets do not have a radius estimate (on 17 August, 2012, only about 32% of confirmed exoplanets had a size measurement or estimate). As explained in the article on surface temperature estimates, the theoretical temperature is based on such simple assumptions that it could be wrong by hundreds of degrees Celsius. Moreover, this temperature parameter comes into the ESI formula with a very high exponent (power), so any deviations of the “predicted” temperature parameter from the (unknown) actual temperature are significantly amplified. Thus, between one and three parameters that are used to calculate the ESI have to be guessed, and those guesses may be wild, based only on assumptions and not direct observational evidence. Moreover, for the Kepler mission exoplanet candidates (and very often for confirmed planets too), one of the key parameters used to calculate the theoretical temperature (the albedo) is simply assumed to be equal to the value for Earth (without justification). Clearly there is some circularity here. Given these considerations, the usefulness of the ESI is questionable.

At the very least, a plausible range in ESI should be calculated, as opposed to a single value. However, in the PHL plot the ESI values are shown only as single points with no indication of the large range in uncertainty. Note that this plot splits the ESI into an interior ESI (based only on the planet's radius and density), and a surface ESI, based only on the escape velocity and the theoretical surface temperature. The PHL plot shows one ESI versus the other. There is again some circularity here because a planet's density is related to the escape velocity squared divided by its radius squared.

File under: A critical assessment of ESI, the Earth Similarity Index.