A One-Dimensional Energy Balance Model Parameterization for the Formation of CO2 Ice on the Surfaces of Eccentric Extrasolar Planets

Eccentric planets may spend a significant portion of their orbits at large distances from their host stars, where low temperatures can cause atmospheric CO2 to condense out onto the surface, similar to the polar ice caps on Mars. The radiative effects on the climates of these planets throughout their orbits would depend on the wavelength-dependent albedo of surface CO2 ice that may accumulate at or near apoastron and vary according to the spectral energy distribution of the host star. To explore these possible effects, we incorporated a CO2 ice-albedo parameterization into a one-dimensional energy balance climate model. With the inclusion of this parameterization, our simulations demonstrated that F-dwarf planets require 29% more orbit-averaged flux to thaw out of global water ice cover compared with simulations that solely use a traditional pure water ice-albedo parameterization. When no eccentricity is assumed, and host stars are varied, F-dwarf planets with higher bond albedos relative to their M-dwarf planet counterparts require 30% more orbit-averaged flux to exit a water snowball state. Additionally, the intense heat experienced at periastron aids eccentric planets in exiting a snowball state with a smaller increase in instellation compared with planets on circular orbits; this enables eccentric planets to exhibit warmer conditions along a broad range of instellation. This study emphasizes the significance of incorporating an albedo parameterization for the formation of CO2 ice into climate models to accurately assess the habitability of eccentric planets, as we show that, even at moderate eccentricities, planets with Earth-like atmospheres can reach surface temperatures cold enough for the condensation of CO2 onto their surfaces, as can planets receiving low amounts of instellation on circular orbits.

Eta-Earth Revisited II: Deriving a Maximum Number of Earth-Like Habitats in the Galactic Disk

In Lammer et al. (2024), we defined Earth-like habitats (EHs) as rocky exoplanets within the habitable zone of complex life (HZCL) on which Earth-like N2-O2-dominated atmospheres with minor amounts of CO2 can exist, and derived a formulation for estimating the maximum number of EHs in the galaxy given realistic probabilistic requirements that have to be met for an EH to evolve. In this study, we apply this formulation to the galactic disk by considering only requirements that are already scientifically quantifiable. By implementing literature models for star formation rate, initial mass function, and the mass distribution of the Milky Way, we calculate the spatial distribution of disk stars as functions of stellar mass and birth age. For the stellar part of our formulation, we apply existing models for the galactic habitable zone and evaluate the thermal stability of nitrogen-dominated atmospheres with different CO2 mixing ratios inside the HZCL by implementing the newest stellar evolution and upper atmosphere models. For the planetary part, we include the frequency of rocky exoplanets, the availability of surface water and subaerial land, and the potential requirement of hosting a large moon by evaluating their importance and implementing these criteria from minima to maxima values as found in the scientific literature. We also discuss further factors that are not yet scientifically quantifiable but may be requirements for EHs to evolve. Based on such an approach, we find that EHs are relatively rare by obtaining plausible maximum numbers of 2.5 - 2.4 + 71.6 × 10 5 and 0.6 - 0.59 + 27.1 × 10 5 planets that can potentially host N2-O2-dominated atmospheres with maximum CO2 mixing ratios of 10% and 1%, respectively, implying that, on average, a minimum of ∼ 10 3 - 10 6 rocky exoplanets in the HZCL are needed for 1 EH to evolve. The actual number of EHs, however, may be substantially lower than our maximum ranges since several requirements with unknown occurrence rates are not included in our model (e.g., the origin of life, working carbon-silicate and nitrogen cycles); this also implies extraterrestrial intelligence (ETI) to be significantly rarer still. Our results illustrate that not every star can host EHs nor can each rocky exoplanet within the HZCL evolve such that it might be able to host complex animal-like life or even ETIs. The Copernican Principle of Mediocrity therefore cannot be applied to infer that such life will be common in the galaxy.

Carbonate-silicate cycle predictions of Earth-like planetary climates and testing the habitable zone concept

In the conventional habitable zone (HZ) concept, a CO₂-H₂O greenhouse maintains surface liquid water. Through the water-mediated carbonate-silicate weathering cycle, atmospheric CO₂ partial pressure (pCO₂) responds to changes in surface temperature, stabilizing the climate over geologic timescales. We show that this weathering feedback ought to produce a log-linear relationship between pCO₂ and incident flux on Earth-like planets in the HZ. However, this trend has scatter because geophysical and physicochemical parameters can vary, such as land area for weathering and CO₂ outgassing fluxes. Using a coupled climate and carbonate-silicate weathering model, we quantify the likely scatter in pCO₂ with orbital distance throughout the HZ. From this dispersion, we predict a two-dimensional relationship between incident flux and pCO₂ in the HZ and show that it could be detected from at least 83 (2σ) Earth-like exoplanet observations. If fewer Earth-like exoplanets are observed, testing the HZ hypothesis from this relationship could be difficult.

In the habitable zone concept, a planet’s carbon dioxide-water greenhouse maintains surface liquid water. Here, the authors estimate how many Earthlike exoplanets are needed to detect a relationship between stellar flux and the atmospheric carbon dioxide predicted by carbon cycle modeling.

Albedos, Equilibrium Temperatures, and Surface Temperatures of Habitable Planets

The potential habitability of known exoplanets is often categorized by a nominal equilibrium temperature assuming a Bond albedo of either ∼0.3, similar to Earth, or 0. As an indicator of habitability, this leaves much to be desired, because albedos of other planets can be very different, and because surface temperature exceeds equilibrium temperature due to the atmospheric greenhouse effect. We use an ensemble of general circulation model simulations to show that for a range of habitable planets, much of the variability of Bond albedo, equilibrium temperature and even surface temperature can be predicted with useful accuracy from incident stellar flux and stellar temperature, two known parameters for every confirmed exoplanet. Earth's Bond albedo is near the minimum possible for habitable planets orbiting G stars, because of increasing contributions from clouds and sea ice/snow at higher and lower instellations, respectively. For habitable M star planets, Bond albedo is usually lower than Earth's because of near-IR H2O absorption, except at high instellation where clouds are important. We apply relationships derived from this behavior to several known exoplanets to derive zeroth-order estimates of their potential habitability. More expansive multivariate statistical models that include currently non-observable parameters show that greenhouse gas variations produce significant variance in albedo and surface temperature, while increasing length of day and land fraction decrease surface temperature; insights for other parameters are limited by our sampling. We discuss how emerging information from global climate models might resolve some degeneracies and help focus scarce observing resources on the most promising planets.

Habitable Climate Scenarios for Proxima Centauri b with a Dynamic Ocean

The nearby exoplanet Proxima Centauri b will be a prime future target for characterization, despite questions about its retention of water. Climate models with static oceans suggest that Proxima b could harbor a small dayside surface ocean despite its weak instellation. We present the first climate simulations of Proxima b with a dynamic ocean. We find that an ocean-covered Proxima b could have a much broader area of surface liquid water but at much colder temperatures than previously suggested, due to ocean heat transport and/or depression of the freezing point by salinity. Elevated greenhouse gas concentrations do not necessarily produce more open ocean because of dynamical regime transitions between a state with an equatorial Rossby-Kelvin wave pattern and a state with a day-night circulation. For an evolutionary path leading to a highly saline ocean, Proxima b could be an inhabited, mostly open ocean planet with halophilic life. A freshwater ocean produces a smaller liquid region than does an Earth salinity ocean. An ocean planet in 3:2 spin-orbit resonance has a permanent tropical waterbelt for moderate eccentricity. A larger versus smaller area of surface liquid water for similar equilibrium temperature may be distinguishable by using the amplitude of the thermal phase curve. Simulations of Proxima Centauri b may be a model for the habitability of weakly irradiated planets orbiting slightly cooler or warmer stars, for example, in the TRAPPIST-1, LHS 1140, GJ 273, and GJ 3293 systems.