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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mrow><mml:mn>2.5</mml:mn></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>2.4</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>71.6</mml:mn></mml:mrow></mml:msubsup><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mn>5</mml:mn></mml:msup></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mrow><mml:mn>0.6</mml:mn></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.59</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>27.1</mml:mn></mml:mrow></mml:msubsup><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mn>5</mml:mn></mml:msup></mml:mrow></mml:math>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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>∼</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mn>3</mml:mn></mml:msup><mml:mo>-</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mn>6</mml:mn></mml:msup></mml:mrow></mml:math>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 (<i>e.g.</i>, 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.