# Earth Similarity Index

Though differing in size and temperature, terrestrial planets of the Solar System tend to have high Earth Similarity Index values – Mercury (0.596), Venus (0.444), Earth (1.00) and Mars (0.697)[citation needed]. Sizes to scale.[1]

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.

## Formulation

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.[2] 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. An article on the preprint server arxiv.org attempts to reproduce the ESI using only the temperature and mass of the planet.[3] ESI was also referenced in an article published in Revista Cubana de Física.[4]

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.[2]

A webpage maintained by one of the authors of the 2011 Astrobiology article, Abel Méndez at the University of Puerto Rico at Arecibo, lists his calculations of the index for various exoplanetary systems.[5] Méndez's ESI is calculated as

${\displaystyle {\mathsf {ESI}}=\prod _{i=1}^{n}\left(1-{\Big \vert }{\frac {x_{i}-x_{i0}}{x_{i}+x_{i0}}}{\Big \vert }\right)^{\frac {w_{i}}{n}}}$,

where ${\displaystyle x_{i}}$ and ${\displaystyle x_{i0}}$ are properties of the extraterrestrial body and of Earth, respectively, ${\displaystyle w_{i}}$ is the weighted exponent of each property, and ${\displaystyle n}$ is the total number of properties. It is comparable to, and constructed from, the Bray–Curtis Similarity Index.[5][6] The weight assigned to each property, ${\displaystyle w_{i}}$, 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".[7]

The 2011 Astrobiology article and the ESI values found in it received press attention at the time of the article's publication. As a result, Mars was reported to have the second-highest ESI in the Solar System with a value of 0.70.[8] A number of exoplanets listed in that article were reported to have values in excess of this, with Teegarden b reported to have the highest ESI[9] of confirmed exoplanets at 0.95.

Other ESI values that have been reported by third parties include:[8][5]

In next table, planets marked with * represents unconfirmed planet or planet candidate. Distances are from Earth Star system.

Planet ESI Distance (ly) Notes
Earth 1.00 0
KOI-4878.01* 0.98 1075 unconfirmed but surface pressure may be 10atm at 292K, G4V-type Sun-like star
TRAPPIST-1e 0.95 40 likely tidally locked to star, surface pressure may be as little as 6atm at 285K, one of the most habitable known planets
Teegarden b 0.95 12
Gliese 581 g* 0.92 20 unconfirmed, tidally locked to star, surface pressure may be 18atm at 284K
Luyten b 0.91 12.2 tidally locked to star, surface pressure may be 25atm at 294K
TRAPPIST-1 d 0.91 40 innermost habitable planet in TRAPPIST-1 system
Kepler-438b 0.88 640 temperature 276 K, likely tidally locked, habitability is uncertain
Proxima Centauri b 0.87 4.2 closest potentially habitable planet
Ross 128 b 0.86 11 host star is inactive and quiet, it is habitable if has an Earth-like atmosphere
LHS 1723 b 0.86 17.5 lack of planet density or atmospheric data
Kepler-296 e 0.85
Gliese 667 Cc 0.85 23.62 likely tidally locked to star, temperature is 277.4 K (4.3°C), based on black body temperature calculation
Kepler-442b 0.84 1206 it is in center of the habitable zone, temperature 233 K
Kepler-452b 0.83 1402 surface pressure may be 16-56atm at 288K with Helium if strong 587.5nm line.
Kepler-62e 0.83 1200 surface pressure may be 35atm at 288K with Helium if strong 587.5nm line.
Gliese 832 c 0.81 16 tidally locked, no plate tectonics, it is habitable if have an Earth-like atmosphere
Kepler-283c 0.79 temperature is 238.5 K
HD 85512 b 0.77 36 if has an Earth-like atmosphere, without greenhouse effect
Wolf 1061c 0.76 13.8
Gliese 667 Cf* 0.76 23.6 controversial existence
Kepler-440b 0.75 850 it has an elliptical orbit, temperature 273 K
HD 40307 g 0.74 42
Mars 0.73 lacks global plate tectonics, too small for atmospheric water vapour
Mercury 0.73 in 3:2 spin-orbital resonance to Sun
Kepler-61b 0.73 1100
Gliese 581 d* 0.72 20.4 tidally locked to star
Kepler-22b 0.71 587
Kepler-443b 0.71 2540 it has 89.9% chance of habitability, yet only 4.3% to be rocky
Gliese 422 b* 0.71 unconfirmed
TRAPPIST-1 f 0.70 39 temperature is 230 K, small chance to be rocky
Gliese 3293 c* 0.70 unconfirmed
Kepler-62f 0.69 990 surface pressure may be 10atm at 288K with Helium if strong 587.5nm line
Teegarden c 0.68 12
Kepler-298d 0.68 1545
Kapteyn b 0.67 12.8 oldest known potentially habitable planet
Kepler-186f 0.64 582 potentially colder climate than Mars, but still habitable planet
Kepler-174d 0.61
Kepler-296f 0.60
Gliese 667 Ce* 0.60 23.6 controversial existence
HD 69830 d 0.60 40.7 lack of planet density or atmospheric data
TRAPPIST-1 g 0.59 39 largest planet in system, too cold to be habitable
Gliese 682 c* 0.59 unconfirmed
55 Cnc c 0.56 lack of planet density or atmospheric data
Moon 0.56 too small for surface or atmospheric water, lacks plate tectonics
55 Cnc f 0.53 41 lack of planet density or atmospheric data
KOI-4427b* 0.52 unconfirmed
Gliese 581b 0.48 it orbits within inner edge of habitable zone
Venus 0.44 solar flux > Komabayasi-Ingersoll limit, slow retrograde orbit induced by Sun.
Kepler-20f 0.44 929
Gliese 1214b 0.42 48 it is probably ocean planet, temperature 390-552 K
Kepler-11b 0.30
Kepler-20e 0.29
Mu Arae e 0.27
Gliese 581 c 0.24 20.37 tidally locked to star
Kepler-20b 0.24
Neptune 0.18 Gas giant, blue color
Gliese 581 e 0.16 20.4 tidally locked to star
Jupiter 0.12 Gas giant
KOI-55c* 0.03

## No 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 article 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 are among the keys to habitable surface conditions.[9]

It has been noted that ESI fails to differentiate between Earth similarity and Venus similarity, as can be seen in the table above, where planets with a lower ESI have a greater chance at habitability[10].

## Planets with an Earth-like size

Comparison of the sizes of planets Kepler-69c, Kepler-62e (0.83), Kepler-62f (0.69), and the Earth. All planets except the Earth are artists' conceptions.

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 Moon, Io and Earth shown to scale. Although significantly smaller, some of the Solar System's moons and dwarf planets share similarities to Earth's density and temperature.

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.[11]

## References

1. ^ "HEC: Data of Potential Habitable Worlds".
2. ^ a b Schulze-Makuch, D.; Méndez, A.; Fairén, A. G.; von Paris, P.; Turse, C.; Boyer, G.; Davila, A. F.; Resendes de Sousa António, M.; Catling, D. & Irwin, L. N. (2011). "A Two-Tiered Approach to Assess the Habitability of Exoplanets". Astrobiology. 11 (10): 1041–1052. Bibcode:2011AsBio..11.1041S. doi:10.1089/ast.2010.0592. PMID 22017274.
3. ^ Suresh Chandra; Subas Nepal; Mohit K. Sharma (July 2015). "Earth Similarity Index with two free parameters". arXiv:1507.06293v1 [astro-ph.EP].
4. ^ Gonzalez, A.; Cardenas, R. & Hearnshaw, J. (2013). "Possibilities of life around Alpha Centauri B.". Revista Cubana de Física. 30 (2): 81. arXiv:1401.2211. Bibcode:2014arXiv1401.2211G.
5. ^ a b c "Earth Similarity Index (ESI)". Planetary Habitability Laboratory.
6. ^ Rushby, A. (2013). "A multiplicity of worlds: Other habitable planets". Significance. 10 (5): 11–15. doi:10.1111/j.1740-9713.2013.00690.x.
7. ^ Sample, I. (December 5, 2011). "Habitable exoplanets catalogue ranks alien worlds on suitability for life". The Guardian. Retrieved April 9, 2016.
8. ^ a b "Most liveable alien worlds ranked". BBC. November 23, 2011. Retrieved April 10, 2016.
9. ^ a b Armstrong, D. J.; Pugh, C. E.; Broomhall, A.-M.; Brown, D. J. A.; Lund, M. N.; Osborn, H. P.; Pollacco, D. L. (2016). "The host stars of Kepler's habitable exoplanets: superflares, rotation and activity". Monthly Notices of the Royal Astronomical Society. 5 (3): 3110–3125. arXiv:1511.05306. Bibcode:2016MNRAS.455.3110A. doi:10.1093/mnras/stv2419.
10. ^ Elizabeth Tasker (July 9, 2014). "No, that new exoplanet is not the best candidate to support life". The Conversation. Retrieved November 5, 2018.
11. ^ Keszthelyi, L.; et al. (2007). "New estimates for Io eruption temperatures: Implications for the interior". Icarus. 192 (2): 491–502. Bibcode:2007Icar..192..491K. doi:10.1016/j.icarus.2007.07.008.