Indexing of exoplanets in search for potential habitability: application to Mars-like worlds

Abstract

Study of exoplanets is one of the main goals of present research in planetary sciences and astrobiology. Analysis of huge planetary data from space missions such as CoRoT and Kepler is directed ultimately at finding a planet similar to Earth—the Earth’s twin, and answering the question of potential exo-habitability. The Earth Similarity Index (ESI) is a first step in this quest, ranging from 1 (Earth) to 0 (totally dissimilar to Earth). It was defined for the four physical parameters of a planet: radius, density, escape velocity and surface temperature. The ESI is further sub-divided into interior ESI (geometrical mean of radius and density) and surface ESI (geometrical mean of escape velocity and surface temperature). The challenge here is to determine which exoplanet parameter(s) is important in finding this similarity; how exactly the individual parameters entering the interior ESI and surface ESI are contributing to the global ESI. Since the surface temperature entering surface ESI is a non-observable quantity, it is difficult to determine its value. Using the known data for the Solar System objects, we established the calibration relation between surface and equilibrium temperatures to devise an effective way to estimate the value of the surface temperature of exoplanets.

ESI is a first step in determining potential exo-habitability that may not be very similar to a terrestrial life. A new approach, called Mars Similarity Index (MSI), is introduced to identify planets that may be habitable to the extreme forms of life. MSI is defined in the range between 1 (present Mars) and 0 (dissimilar to present Mars) and uses the same physical parameters as ESI. We are interested in Mars-like planets to search for planets that may host the extreme life forms, such as the ones living in extreme environments on Earth; for example, methane on Mars may be a product of the methane-specific extremophile life form metabolism.

Appendix: Calculation of Mars ESI as an example

$\mathrm{ESI}_{x}$ calculations for Mars are performed using Eq. (10), with weight exponents from Table 1, by using the following values for the input parameters,

$$\begin{aligned} &R=0.53 \times 6371~\mbox{km} = 3376.63~\mbox{km},\\ & \rho=0.71 \times 5.51~\mbox{g}/\mbox{cm}^{3} = 3.9121~\mbox{g}/\mbox{cm}^{3},\\ &V_{e}= 0.45 \times 11.19~\mbox{km}/\mbox{s} = 5.0355~\mbox{km}/\mbox{s} , \\ &T_{s}= 240~\mbox{K} . \end{aligned}$$

The ESI for each parameter are, accordingly,

$$\begin{aligned} & \mathrm{ESI}_{R}= \bigl(1- \vert 3376.63~\mbox{km}-6371~\mbox{km} \vert / \vert 3376.63~\mbox{km} \\ &\phantom{\mathrm{ESI}_{R}=\,\,}{} +6371~\mbox{km} \vert \bigr)^{0.57} = 0.8124 ,\\ & \mathrm{ESI}_{\rho} = \bigl(1-|3.9121~\mbox{g}/\mbox{cm}^{3} - 5.51~\mbox{g}/\mbox{cm}^{3}| /|3.9121~\mbox{g}/\mbox{cm}^{3}\\ &\phantom{\mathrm{ESI}_{R}=\,\,}{} +5.51~\mbox{g}/\mbox{cm}^{3}| \bigr)^{1.07} = 0.8218 ,\\ & \mathrm{ESI}_{v_{e}} = (1-|5.0355~\mbox{km}/\mbox{s}-11.19~\mbox{km}/\mbox{s}| /|5.0355~\mbox{km}/\mbox{s}\\ &\phantom{\mathrm{ESI}_{R}=\,\,}{} +11.19~\mbox{km}/\mbox{s}| )^{0.7} = 0.7162 ,\\ & \mathrm{ESI}_{T_{s}} = (1-|240~\mbox{K}-288~\mbox{K}| /|240~\mbox{K}+288~\mbox{K}| )^{5.58}\\ &\phantom{\mathrm{ESI}_{R}}{} =0.5875 . \end{aligned}$$

Interior ESI from Eq. (14) is:

$$\mathrm{ESI}_{I} = \sqrt{0.8124\times0.8218} \approx 0.8171. $$

Surface ESI from Eq. (15) is:

$$\mathrm{ESI}_{S} = \sqrt{0.7162 \times 0.5875} \approx 0.6487. $$

And the global ESI for Mars (Eq. (16)) is:

$$\mathrm{ESI} = \sqrt{0.8171 \times 0.6487} \approx 0.728. $$