Earth Similarity Index
The Earth Similarity Index (ESI) is a proposed characterization of how similar a planetary-mass object or natural satellite is to Earth. It was designed to be a scale from zero to one, with Earth having a value of one; this is meant to simplify planet comparisons from large databases. It has no quantitative meaning for habitability.
The ESI, as proposed in 2011 by Schulze-Makuch et al. in the journal Astrobiology, incorporates a planet's radius, density, escape velocity, and surface temperature into the index. Thus the authors describe the index as having two components: (1) associated with the interior which is associated with the mean radius and bulk density, and (2) associated with the surface which is associated with the escape velocity and surface temperature. A paper on the preprint server arxiv.org attempts to reproduce the ESI using only the temperature and mass of the planet. ESI was also referenced in a paper published in Revista Cubana de Física.
For exoplanets, in almost every case only the planet's orbital period along with either the proportional dimming of the star due to the planet's transit or the radial velocity variation of the star in response to the planet is known with any degree of certainty, and so every other property not directly determined by those measurements is speculative. For example, while surface temperature is influenced by a variety of factors including irradiance, tidal heating, albedo, insolation and greenhouse warming, as these factors are not known for any exoplanet, quoted ESI values use planetary equilibrium temperature as a stand-in.
A webpage maintained by one of the authors of the 2011 Astrobiology paper, Abel Méndez at the University of Puerto Rico at Arecibo, lists his calculations of the index for various exoplanetary systems. Méndez's ESI is calculated as
where and are properties of the extraterrestrial body and of Earth, respectively, is the weighted exponent of each property, and is the total number of properties. It is comparable to, and constructed from, the Bray–Curtis Similarity Index. The weight assigned to each property, , are free parameters that can be chosen to emphasize certain characteristics over others or to obtain desired index thresholds or rankings. The webpage also ranks what it describes as the habitability of planets and moons according to three criteria: the location in the habitable zone, ESI, and a speculation as to a capacity to sustain organisms at the bottom of the food chain, a different index collated on the webpage identified as the "Global Primary Habitability scale".
The 2011 Astrobiology paper and the ESI values found in it received press attention at the time of paper's publication. As a result, Mars was reported to have the second-highest ESI in the solar system with a value of 0.70. A number of exoplanets listed in that paper were reported to have values in excess of this with Kepler-438b reported to have the highest ESI of confirmed exoplanets at 0.88.
Other ESI values that have been reported by third parties include:
|Gliese 581 g||0.89||unconfirmed|
|Gliese 581 d||0.74|
|Gliese 581 c||0.70|
|HD 69830 d||0.60|
|55 Cnc c||0.56|
|Gliese 581 e||0.53|
Relation to habitability
Although the ESI does not characterize habitability, given the point of reference is the Earth, some of its functions match those used by habitability measures. As with the definition of the habitable zone, the ESI uses surface temperature as a primary function (and the terrestrial point of reference). A 2016 paper uses ESI as a target selection scheme and obtains results showing that the ESI has little relation to the habitability of an exoplanet, as it takes no account of the activity of the star, planetary tidal locking, nor the planet's magnetic field (i.e. ability to protect itself) which is one of the keys to surface conditions.
Planets with an Earth-like size
The classification of exoplanets is difficult in that many methods of exoplanet detection leave several features unknown. For example, with the transit method, one of the more successful, measurement of radius can be highly accurate, but mass and density are often estimated; likewise with radial velocity methods, which can provide accurate measurements of mass but are less successful measuring radius. Planets observed via a number of different methods therefore can be most accurately compared to Earth.
Similarity of non-planets to Earth
The index can be calculated for objects other than planets, including natural satellites, dwarf planets and asteroids. The lower average density and temperature of these objects give them lower index values. Only Titan (a moon of Saturn) is known to hold on to a significant atmosphere despite an overall lower size and density. While Io (a moon of Jupiter) has a low average temperature, surface temperature on the moon varies wildly due to geologic activity.
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