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

Abstract

In Lammer et al. 2024, we defined Earth-like Habitats (EH) as rocky planets in the habitable zone of complex life (HZCL) on which Earth-like N$_2$-O$_2$-dominated atmospheres with minor amounts of CO$_2$ can exist and derived a formula for estimating their maximum number in the Galaxy. Here, we apply this formula by considering only requirements that are already scientifically quantifiable. By implementing models for star formation rate, initial mass function, and galactic mass distribution, we calculate the spatial distribution of disk stars as functions of stellar mass and birth age. We apply models for the GHZ and evaluate the thermal stability of Earth-like atmospheres with various CO$_2$ mixing ratios by implementing the newest stellar evolution and upper atmosphere models. In addition, we include the rocky exoplanet frequency, the availability of oceans and subaerial land, and the potential large moon requirement by evaluating their importance and implementing these criteria from minima to maxima values. We also discuss factors that are not yet scientifically quantifiable but may be requirements for EHs to evolve. We find that EHs are rare by obtaining maximum numbers of $2.5^{+71.6}_{-2.4}\times10^{5}$ and $0.6^{+27.1}_{-0.59}\times10^{5}$ planets that can potentially host N$_2$-Earth-like atmospheres with maximum CO$_2$ mixing ratios of 10\% and 1\%, respectively, implying that a minimum of $\sim 10^3 - 10^6$ rocky HZCL planets are needed for 1 EH to evolve. Their actual number, however, may be substantially lower as several requirements are not included in our model; this also implies ETIs are significantly rarer still. Our results illustrate that neither every star can host EHs, nor that each rocky HZCL planet evolves such that it may be able to host complex animal-like life. The Copernican Principle therefore cannot be applied to infer that such life is common in the Galaxy.