The Earth Similarity Index (ESI), or the "easy scale," is a multiparameter first assessment of Earth-likeness for solar and extrasolar planets as a number between zero (no similarity) and one (identical to Earth). Such similarity indices are used in many fields and provide a powerful tool for categorizing and extracting patterns from large and complex datasets. The ESI can be used to prioritize exoplanets observations, perform statistical assessments and develop planetary classifications. It is used as a way to sort the objects of interest of the Habitable Exoplanets Catalog. The basic ESI expression is
where xi is a planetary property (e.g. surface temperature), xio is the corresponding terrestrial reference value (e.g. 288 K), wi is a weight exponent, n is the number of planetary properties, and ESI is the similarity measure. The weighting exponents are used to adjust the sensitivity of the scale and equalize its meaning between different properties. In practice, a simpler and more limited form of the ESI formulation is used for exoplanets (using only stellar flux, mass or radius) since this is the only data available of them.
Earth-like planets can be defined as any planetary body with a similar terrestrial composition and a temperate atmosphere. As a general rule, any planetary body with an ESI value over 0.8 can be considered and Earth-like planet. This means that the planet might have a rocky in composition and temperate atmosphere. Planets with ESI values in the 0.6 to 0.8 range (e.g. Mars) might still be habitable since habitability depends on many other factors.
The parameters for the ESI equation for mean radius, bulk density, escape velocity, and surface temperature are shown in Table 1. Sample calculations for solar and extrasolar planets (assuming different mass, radius, and surface temperatures) are shown in Figure 1. They are also divided for convenience into an Interior ESI, based on the mean radius and bulk density, and a Surface ESI, based on the escape velocity and surface temperature. Both the interior and surface ESI are combined into a global ESI. The ESI is more a surface than a subsurface indirect indicator of habitability due to its Earth-centric definition (Table 1).
A similarity formulation can be constructed for other planetary bodies using different reference values (e.g. jovian-like planets). One of the most practical applications of the ESI is in studies about the distribution and diversity of Earth-like planets (Figure 2). Sample ESI values of the Kepler planets candidates are shown in Figure 3. Complete data table for the solar, extrasolar and Kepler planets ESI values and IDL code is available in the resources section below.
Table 1. Reference values and weight exponents for the four planetary properties used to define the ESI. The scale is much more sensitive to surface temperature than to the other planetary properties.
Note: Eu = Earth’s units
Figure 1. ESI for 47 Solar System bodies with radius greater than 100 km (orange) and 258 known extrasolar planets (blue). Only some of the most notable bodies are labeled. The ESI scale makes a distinction between those rocky interior (light red area) and temperate surface (light blue area) planets. Only planets within these two categories can be considered Earth-like planets (light green area). The dotted lines represent constant ESI values. If confirmed, only Gliese 581 g is in the Earth-like category together with Earth.
Figure 2. Distribution of ESI values based on a theoretical statistical prediction (yellow), for 47 Solar System bodies with radius greater than 100 km (orange), and 258 known extrasolar planets (blue). Our Solar System match the prediction but the bars for the known extrasolar planets show the bias of current observational techniques toward large planetary bodies (ESI values between 0.2 and 0.4). This type of analysis with the ESI can be used to predict the number of expected Earth-like planets within a sample of stars.
Figure 3. ESI for 47 Solar System bodies with radius greater than 100 km (orange), 258 known extrasolar planets (blue) and Kepler's 1235 planet candidates (green). The mass for the ESI calculations was estimated using generic mass-radius relationships for gas, ocean, and rocky planets (there was no mass in the dataset). The surprising result in the Kepler data is the potential abundance of rocky bodies and the presence of two Earth-like planets candidates, plus a few more close to this category. The information on this planetary candidates is very limited and further observations will be necessary to confirm them.