Beyond the Drake Equation: A Time-dependent Inventory of Habitable Planets and Life-bearing Worlds in the Solar Neighborhood

We introduce a mathematical framework for statistical exoplanet population and astrobiology studies that may help direct future observational efforts and experiments. The approach is based on a set of differential equations and provides a time-dependent mapping between star formation, metal enrichment, and the occurrence of exoplanets and potentially life-harboring worlds over the chemo-population history of the solar neighborhood. Our results are summarized as follows: (1) the formation of exoplanets in the solar vicinity was episodic, starting with the emergence of the thick disk about 11 Gyr ago; (2) within 100 pc from the Sun, there are as many as 11,000( η _⊕ /0.24) Earth-size planets in the habitable zone (“temperate terrestrial planets” or TTPs) of K-type stars. The solar system is younger than the median TTP, and was created in a star formation surge that peaked 5.5 Gyr ago and was triggered by an external agent; (3) the metallicity modulation of the giant planet occurrence rate results in a later typical formation time, with TTPs outnumbering giant planets at early times; and (4) the closest, life-harboring Earth-like planet would be ≲20 pc away if microbial life arose as soon as it did on Earth in ≳1% of the TTPs around K stars. If simple life is abundant (fast abiogenesis), it is also old, as it would have emerged more than 8 Gyr ago in about one-third of all life-bearing planets today. Older Earth analogs are more likely to have developed sufficiently complex life capable of altering their environment and producing detectable oxygenic biosignatures.