Without any doubt, searching for ocean planets, which may harbor life by providing a habitat for biological evolution, is one of the main goals of exoplanetary studies. Such doctrine, absolutely understandably, based on our knowledge about Earth, the exponentially growing understanding of the Solar system (e.g., the putative paleocean on Mars, and the subsurface oceans of icy satellites in the outer Solar system), and the fact that science, to avoid speculations, tend to use examples with clear explanations, which can be used further comparisons as archetypes of a certain phenomenon, processes and so on.
The discovery of the new type of exoplanets, including the ones with putative oceans on their surface, teaches us, that the applied key parameters, which have been used as potential indicators of surface oceans and based on the comparative planetary concept (i.e., comparison to Earth, the only planet with surface ocean and life on it) need continuous development and update. In addition, due to the (technical) limitation in exoplanet research, the number of measurable parameters, which directly indicate certain planetary characteristics related to ocean formation (e.g., detailed information about the atmosphere of an exoplanet) are relatively low (to be exposed to statistical or big data analysis), compared to the parameters, which may indicate ocean planets, but not exclusively, and the use of those parameters may result in speculation.
1.1 Diagnostic exoplanet parameters and exoplanet classifications
Despite the limitation in the use of those basic measurable parameters, there have been numerous approaches, building theories about the connection of certain parameters and various planetary processes, and using the basic parameters and/or creating various proxies to characterize the exoplanet (Table 1).
Table 1
Examples of some parameters and observable parameter-based indices commonly applied in the classification of exoplanets. *warm ice: exoplanets with very high surface temperature, but ice surface due to their extremely high mass compared to other planets (e.g., hot Neptune GJ 436 b; Gillon et al. 2007)
Applied parameter(s) and indices (proxies) | Background information | References |
Mass-radius relationship, built on parameters of constructed, theoretical planet models | Distribution curves for pure iron, pure rock (olivine - Mg2SiO4), and, pure (warm* and cold) water ice exoplanets on the MP plot | Fortney et al. (2007) |
Generic mass-radius relationship | Target: solid exoplanets, made primarily of iron, silicates, water, and carbon, up to about 20 ME | Seager et al. (2007) |
Mass-radius relationship plot | Target: Earth-like exoplanets and ocean planets with 50 wt% of H2O, up to 15 ME | Sotin et al. (2007) |
Mass-radius relationship plot | Target: solid exoplanets with massive atmospheres | Adams et al. (2008) |
Mass, radius, and stellar insolation (ternary and quaternary diagram) | Uncertainties; relative contributions of the core, mantle, ice layer, and gas layer to the structure of a differentiated exoplanet | Rogers and Seager (2010) |
Earth Similarity Index (ESI): mass, radius, and temperature | Earth similarity; assessing the habitability of exoplanets; | Schulze-Makuch et al. (2011) |
Planetary Habitability Index (PHI): the presence of a stable substrate, available energy, appropriate chemistry, and the potential for holding a liquid solvent |
Mass-radius plot | Short review of various planet types, based on the application of MR and FR plots | Spiegel et al. (2013) |
Flux (irradiation) - radius plot |
Mass-radius plot | Target: the composition of Rexoplanets < 4REarth | Weiss and Marcy (2014) |
Density - radius plot |
Mass-radius plot, hierarchical Bayesian approach; about adding additional parameters | Target: sub-Neptune size planets, trans. between rocky exoplanets (comprised of iron and silicates) and planets with voluminous layers of volatiles (H/He and ices); study the underlying population of similar planet groups | Rogers (2015) |
Mass-radius plot uncertainties | Targeting sub-Neptune-sized planets; displays the uncertainties in the M–R relation parameters | Wolfgang et al. (2016) |
Mass-radius plot (“Forecaster”) | New insights about MR plot-based exoplanet classification (e.g. about super-Earth type exoplanets) | Chen and Kipping (2017) |
Stellar flux range | radius | occurrence rate per bin (η) | New classification scheme based on the relationship between radius and stellar flux range | Koppararu et al. (2018) |
Mass-radius plot | Description of four exoplanet classes based on MR plot; main focus on super-Earths and sub-Neptunes; | Zeng et al. (2019) |
Surface area/volume ratio - internal heating plot | Focusing on volcanic activity, the appearance of oceans, and planet types | Quick et al. (2020) |
As shown in Table 1, the most common parameters used in the classification of exoplanets are planetary mass and radius. These two observable parameters do not simply represent what their name indicates but may carry information about e.g., the composition and inner structure of the planet (mass) and the characteristics of the atmosphere (radii or radius). Reaching that information ultimately led to a more detailed description and classification of the exoplanets.
One way to get that information is the construction of theoretical planets with various characteristics, included in their mass and atmosphere parameters (using the equation of state – EOS for various planetary components such as iron, water, olivine, hydrogen, and so on). Using the parameters of various types of modeled planets, curves, representing the planet types can be drawn on the mass vs. radius (MR) plot. Based on their mass and radius data, the observed exoplanets are placed in various regions of the plot, along various theoretical curves indicating the type of the planet (Table 1; Fortney et al. 2007; Saeger et al. 2007; Sotin et al. 2007). Regarding the MR relation-based identification of ocean planets, one of the potential target types of the ExTerrO research, it was confirmed that “identification of water worlds based on the mass-radius relationship alone is impossible unless a significant gas layer can be ruled out by other means” (Adams et al. 2008, p. 1160). The same, given the MR relationship, may indicate a planet with substantial water ice content, or an exoplanet with a larger rocky/iron core and a H and/or He envelops around the planet.
Following the early models, the exponentially increasing number of discovered exoplanets allowed to test the results of the early works on MR relations (Fortney et al. 2007; Saeger et al. 2007; Sotin et al. 2007, and Adams et al. 2008), and lead to the classification of the planets. Spiegel et al. (2013) reviewed the structure of exoplanets and based on the MR and FR (flux vs. radius) plot classified and characterized the planets as i) gas giants, ii) Neptunes, iii) terrestrial planets, and iv) ocean planets. In one of the latest works, following the early MR relations studies, Zeng et al. (2019) described four exoplanet classes, namely, i) rocky worlds, ii) water worlds, iii) transitional planets, and iv) gas giants.
Along the commonly applied MR plots, there have been other approaches to characterize and classify (exo)planets. The study of Kopparapu et al. (2018) used radius and stellar flux as key parameters and defined fifteen various planetary types. Five types of exoplanet classes (Earths, Super Earths, Sub-Neptunes, Neptunes/Sub-Jovians, and Jovians) with three subtypes (cold, warm, and hot) are described in a planetary radius – stellar flux plot/matrix, from the category of Cold Earths to Hot Jovians.
One of the newest approaches investigates the relationship between the surface area/volume ratio and the value of internal heating to identify volcanic activity and oceans on planetary bodies and attempt to determine whether the planet is an ocean planet, a cold ocean planet/icy moon, or a rocky planet/moon (Quick et al. 2020).
The approach of Schulze-Makuch et al. (2011) points toward the necessity of more complex proxies in the identification of various, ocean-bearing and habitable, planetary environments. Their goal is to assess the ability of exoplanets, based on their similarity to Earth, the only known planet which harbors life and allows biological evolution. The study applies the so-called Earth Similarity Index (ESI), an index built-in available parameters, such as mass, radius, and temperature, and the more complex Planetary Hability Index (PHI), which allows the discovery of exoplanets with a possible more exotic environment, which may harbor life but different to Earth. From the view of extraterrestrial oceanography, PHI considers key index components, regarding surface ocean formation (referred to e.g., atmosphere and liquids) (Schulze-Makuch et al. 2011).
One of the ways to search for liquid water on the surface of stars would be the definition of the Habitable (or Goldilocks) zone (HZ) (Huang 1959; Kopparapu et al. 2013). The equation that allows the calculation of HZ was originally applied for F, G, K, and M-type stars (Kasting et al. 1993), and, although one of the components in the equation (Seff) can be calculated for different planet conditions, it is advised to use Venus and Earth (Kasting 1988; Kasting 1991). Based on such conditions, the determination of HZ works well in the case of a certain type of stars and planets but may have some uncertainty if it is applied for newly discovered non-Earth (terrestrial) type ocean-bearing planets and solar systems with non-main sequence host stars.
The work of Gupta et al. (2022), focuses on the mass, composition, and orbital parameter of the exoplanets, and provide a detailed review of exoplanet types, including main types, such as sub-Earth, terrestrial, super-Earth, mega-Earth, mini-Neptune, gas giant, and super-Jupiter based on mass, size and composition, and hot super-Earth, hot-Neptune, cold Neptune/Ice-Giant, hot-, and cold-Jupiter based on mass, composition, and orbit. It also introduces so-called “super-puff”, or “cotton-candy” planets, and hycean worlds, potentially habitable ocean planets, covered by oceans and has a hydrogen-rich atmosphere (Madhusudhan et al. 2021).
It seems there are numerous ways, in which ocean worlds are expected to be found, using various observable parameters (referring to the state of art technic and the open, accessible data). Assuming the number of parameters and indices, which may suggest a surface ocean on an exoplanet, ocean formation is a complex process, influenced by various conditions, e.g., vital conditions in the solar system and on the planetary body which need to be fulfilled. The use of a limited number of parameters may increase the potential of analytical bias and uncertainty during the search of ocean planets (e.g. certain parameters may represent not only one type of planet; Adams et al. 2008; Rogers and Seager, 2010).
Finding a key parameter that individually can indicate the surface ocean, and/or create a more complex surface ocean proxy may be one of the next challenges in exoplanetology and extraterrestrial oceanography, which requires interdisciplinary collaboration between all fields involved in planetary studies.
The focus of the ExTerrO (Extraterrestrial Oceanography) framework, our initiative to find an established extraterrestrial ocean formation probability proxy, is the joint astronomical and geological evaluation of (some of) the basic (and potentially key) parameters found in existing datasets, including i) the influence of those parameters in surface ocean formation, and ii) their possible role as surface ocean formation probability proxy, standing individually or as a part of a more complex index.