Earth Similarity Index

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Though differing in size and temperature, terrestrial planets of the Solar System tend to have high Earth Similarity Indexes – Mercury (0.596), Venus (0.444), Earth (1.00) and Mars (0.697). In true colors, sizes to scale.[1]

The Earth Similarity Index (ESI or "easy scale") is a measure of how physically similar a planetary-mass object is to Earth. It is a scale from zero to one, with Earth having a value of one. The ESI was designed to measure planets, but the formula can also be applied to large natural satellites and other objects. The ESI is a function of the planet's radius, density, escape velocity, and surface temperature.[2][3] These parameters are often estimated based on one or more known variables. Such variables depend greatly on the method of observation used. For example, surface temperature is influenced by a variety of factors including irradiance, tidal heating, albedo, insolation and greenhouse warming. Where these are not known, planetary equilibrium temperature is frequently used, or the variable is inferred from other known attributes.

A planet with a high ESI (values in the range from 0.8 and 1.0) is likely to be of terrestrial rocky composition.

ESI is not a measure of habitability, though given the point of reference being Earth, some of its functions match closely to those used by habitability measures. The ESI and habitable zone share in common the use of surface temperature as a primary function (and the terrestrial point of reference).

According to this measure there are no other Earth-like planets or moons in the Solar System (second-ranked Mars is 0.697), though a number of exoplanets have been found with values in this range. Kepler-438b has the highest Earth Similarity of confirmed exoplanets at 0.88. Further, the candidate exomoon HD 222582 b m of a confirmed exoplanet, and several candidate exomoons (KOI 375.01 m, KOI-2933.01 m, KOI-422.01 m) of unconfirmed exoplanets, all have an ESI of 0.86.[1]

On November 4, 2013, astronomers reported, based on data gathered by the Kepler spacecraft, that there could be as many as 40 billion Earth-sized planets orbiting in the habitable zones of Sun-like stars and red dwarfs within the Milky Way.[4][5] 11 billion of these estimated planets may be orbiting sun-like stars.[6] The nearest such planet may be 12 light-years away, according to the scientists.[4][5]

Formulation[edit]

The ESI is defined by the expression

 ESI = \prod_{i=1}^n \left(1 - \left| \frac{x_i - x_{i_0}}{x_i + x_{i_0}} \right| \right)^\frac{w_i}{n}

where  x_i is one of the planetary properties (e.g. surface temperature),  x_{i_0} is the corresponding terrestrial reference value (e.g. 288 K) for the property,  w_i is a weight exponent for the property, and n is the total number of planetary properties. The weight exponents adjust the sensitivity of the scale and equalize their meanings across the different properties. The set of properties, their reference values, and their weight exponents are found in the following table.

Property Reference value Weight exponent
Mean radius 1.0 Earth 0.57
Bulk density 1.0 Earth 1.07
Escape velocity 1.0 Earth 0.70
Surface temperature 288 K 5.58

ESI has been split into two components to measure different aspects of physical similarity: the Interior ESI and the Surface ESI. The mean radius and bulk density constitute the Interior ESI, while the escape velocity and surface temperature constitute the Surface ESI. Global ESI is typically cited as the global measure.

Planets with relatively high ESI[edit]

Comparison of the sizes of planets Kepler-69c, Kepler-62e (0.82), Kepler-62f (0.69), and the Earth. All planets except the Earth are artists' conceptions.

Extrasolar planets dominate the list of known Earth-like objects. However, the classification is made difficult in that many methods of extrasolar planet detection leave ESI parameters unquantified. 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 provide accurate measurements of mass but are less successful measuring radius. Planets observed via a number of different methods therefore have the most accurate measures of ESI, though this is not possible in many situations.

The following exoplanets have been determined to have higher ESI than 0.80 (Venus, Mars, and Mercury have been added for comparison purposes):

Name ESI SPH HZD HZC HZA pClass hClass Distance (ly) Status Year of
discovery
0N/A !Earth 1.00 0.72 −0.50 −0.31 −0.52 warm terran mesoplanet 0 non-exoplanet prehistoric
1 Kepler-438b 0.88 0.88 −0.93 −0.14 −0.73 warm terran mesoplanet 470 confirmed 2015
2 Gliese 667 Cc 0.84 0.64 −0.62 −0.15 +0.21 warm superterran mesoplanet 23.6 confirmed 2011
3 KOI-3010.01 0.84 0.63 −0.88 −0.16 −0.06 warm superterran mesoplanet 1213.4[7] Kepler candidate 2011
4 Kepler-442b 0.83 0.98 −0.72 −0.15 +0.28 warm superterran mesoplanet 1291.6 confirmed 2015
5 Kepler-62e 0.83 0.96 −0.70 −0.15 +0.28 warm superterran mesoplanet 1199.7 confirmed 2013
6 Kepler-452b[8][9] 0.83 ??? −0.49 ??? ??? warm superterran mesoplanet 1,400 confirmed 2015
7 Gliese 832 c 0.81 0.96 −0.72 −0.15 +0.43 warm superterran mesoplanet 16.1 confirmed 2014
@2N/A ~Mars 0.70 0.00 +0.33 −0.13 −1.12 warm subterran hypopsychroplanet .000008 non-exoplanet prehistoric
@3N/A ~Mercury 0.60 0.00 −1.46 −0.52 −1.37 hot mercurian non-habitable .000010 non-exoplanet prehistoric
@1N/A ~Venus 0.44 0.00 −0.93 −0.28 −0.70 warm terran hyperthermoplanet .000004 non-exoplanet prehistoric

Key[edit]

The planets listed above are evaluated on seven different criteria:

  • Earth Similarity Index (ESI)—Similarity to Earth on a scale from 0 to 1, with 1 being the most Earth-like. ESI depends on the planet's radius, density, escape velocity, and surface temperature.
  • Standard Primary Habitability (SPH)—Suitability for vegetation on a scale from 0 to 1, with 1 being best-suited for growth. SPH depends on surface temperature (and relative humidity if known).
  • Habitable Zone Distance (HZD)—Distance from the center of the star's habitable zone, scaled so that −1 represents the inner edge of the zone, and +1 represents the outer edge. HZD depends on the star's luminosity and temperature and the size of the planet's orbit. Note that even though many planets have an HZD value similar to Venus (−0.93), including Kepler-438b, the HZD is not used to rule on whether a planet has suffered a runaway greenhouse effect or not, and therefore, Kepler-438b is currently assumed to be a mesoplanet rather than a hyperthermoplanet.
  • Habitable Zone Composition (HZC)—Measure of bulk composition, where values close to zero are likely iron–rock–water mixtures. Values below −1 represent bodies likely composed mainly of iron, and values greater than +1 represent bodies likely composed mainly of gas. HZC depends on the planet's mass and radius.
  • Habitable Zone Atmosphere (HZA)—Potential for the planet to hold a habitable atmosphere, where values below −1 represent bodies likely with little or no atmosphere, and values above +1 represent bodies likely with thick hydrogen atmospheres (e.g. gas giants). Values between −1 and +1 are more likely to have atmospheres suitable for life, though zero is not necessarily ideal. HZA depends on the planet's mass, radius, orbit size, and the star's luminosity.
  • Planetary Class (pClass)—Classifies objects based on thermal zone (hot, warm, or cold, where warm is in the habitable zone) and mass (asteroidan, mercurian, subterran, terran, superterran, neptunian, and jovian).
  • Habitable Class (hClass)—Classifies habitable planets based on temperature: hypopsychroplanets (hP) = very cold (< −50 °C); psychroplanets (P) = cold; mesoplanets (M) = medium-temperature (0–50 °C; not to be confused with the other definition of mesoplanets); thermoplanets (T) = hot; hyperthermoplanets (hT) = very hot (> 100 °C). Mesoplanets would be ideal for complex life, whereas class hP or hT would only support extremophilic life. Non-habitable planets are simply given the class NH.

ESIs of non-planets[edit]

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 resulting in relatively high ESIs. It is theoretically possible for Earth-sized extrasolar moons and other non-planets to have high ESIs.

The ESI can be applied to objects other than planets, including natural satellites, dwarf planets and asteroids, though comparisons typically draw lower global ESI due to the lower average density and temperature of these objects, at least for those known in the Solar System.[10]

The following non-planetary objects have relatively high global ESIs:

Name ESI SPH HZD HZC HZA pClass hClass Distance (ly) Status Year of
discovery
0N/A !Earth 1.00 0.72 -0.50 -0.31 -0.52 warm terran mesoplanet 0 non-exoplanet prehistoric
1 KOI-433.02 m 0.93 ?? -0.45 ?? ?? warm terran mesoplanet  ?? Kepler Candidate
2 HD 222582 b m 0.86 ?? -0.75 ?? ?? warm subterran mesoplanet 136.8 Unconfirmed
3 Moon 0.559 ?? ?? ?? ?? warm? subterran? 0 non-exoplanet prehistoric
4 Io 0.362 ?? ?? ?? ?? cold? subterran? 0 non-exoplanet 1610
5 Callisto 0.338 ?? ?? ?? ?? cold? subterran? 0 non-exoplanet 1610
6 Ganymede 0.289 ?? ?? ?? ?? cold? subterran? 0 non-exoplanet 1610
7 Ceres 0.271 ?? ?? ?? ?? warm? asteroidan or subterran? 0 non-exoplanet 1801
8 Europa 0.262 ?? ?? ?? ?? cold? subterran? 0 non-exoplanet 1610
9 4 Vesta 0.256 ?? ?? ?? ?? warm? asteroidan 0 non-exoplanet 1807
10 Titan 0.242 ?? ?? ?? ?? warm? subterran? 0 non-exoplanet 1655
11 2 Pallas 0.222 ?? ?? ?? ?? warm? asteroidan 0 non-exoplanet 1802
12 Iapetus 0.211 ?? ?? ?? ?? cold? subterran? 0 non-exoplanet 1671
13 Titania 0.104 ?? ?? ?? ?? cold? subterran? 0 non-exoplanet 1787
14 Enceladus 0.094 ?? ?? ?? ?? cold? subterran? 0 non-exoplanet 1789
15 Pluto 0.094 ?? ?? ?? ?? cold? subterran or asteroidan? 0 non-exoplanet 1930
16 Triton 0.074 ?? ?? ?? ?? cold? subterran? 0 non-exoplanet 1846

Of these, only Titan is known to hold on to a significant atmosphere despite an overall lower size and density.

See also[edit]

References[edit]

  1. ^ a b "HEC: Data of Potential Habitable Worlds". 
  2. ^ "Earth Similarity Index (ESI)". Planetary Habitability Laboratory. 
  3. ^ Schulze-Makuch, D., Méndez, A., Fairén, A. G., von Paris, P., Turse, C., Boyer, G., Davila, A. F., Resendes de Sousa António, M., Irwin, L. N., and Catling, D. (2011) A Two-Tiered Approach to Assess the Habitability of Exoplanets. Astrobiology 11(10): 1041–1052.
  4. ^ a b Overbye, Dennis (November 4, 2013). "Far-Off Planets Like the Earth Dot the Galaxy". New York Times. Retrieved November 5, 2013. 
  5. ^ a b Petigura, Eric A.; Howard, Andrew W.; Marcy, Geoffrey W. (October 31, 2013). "Prevalence of Earth-size planets orbiting Sun-like stars". Proceedings of the National Academy of Sciences of the United States of America. arXiv:1311.6806. Bibcode:2013PNAS..11019273P. doi:10.1073/pnas.1319909110. Retrieved November 5, 2013. 
  6. ^ Khan, Amina (November 4, 2013). "Milky Way may host billions of Earth-size planets". Los Angeles Times. Retrieved November 5, 2013. 
  7. ^ "The New Potential Habitable Exoplanets Candidates of NASA Kepler – Planetary Habitability Laboratory @ UPR Arecibo". upr.edu. 
  8. ^ Pelmorex Inc. "News - Astronomers discover Earth's 'bigger, older cousin' - The Weather Network". The Weather Network. 
  9. ^ "No, Kepler-452b is not the most Earth-like planet found so far". cnnhit.com. 
  10. ^ pg 143. Multivariate and other worksheets for R (or S-Plus): a miscellany P.M.E.Altham, Statistical Laboratory, University of Cambridge. January 10, 2013

External links[edit]