# Beyond the Drake Equation: A Time-Dependent Inventory of Habitable Planets and Life-Bearing Worlds in the Solar Neighborhood

**Authors:** Piero Madau  
**arXiv:** [2309.11927](https://arxiv.org/abs/2309.11927)  
**Date:** 2023-09-21  
**Summary page:** https://www.summarizepaper.com/en/paper/2309.11927v1/

## Key points

- Mathematical framework for statistical exoplanet population and astrobiology studies
- Formation of exoplanets in the solar vicinity was episodic
- Thick disk emerged approximately 11 billion years ago
- 11,000 Earth-size planets in the habitable zone of K-type stars within 100 parsecs from the Sun
- Our solar system is younger than the median TTP (temperate terrestrial planet)
- Occurrence rate of giant planets is modulated by metallicity
- TTPs are more abundant at early times compared to giant planets
- Possibility of a life-harboring Earth-like planet within 20 parsecs from us if microbial life arose as soon as it did on Earth in more than 1% of TTPs around K stars
- Older Earth analogs are more likely to have developed complex life capable of altering their environment and producing detectable oxygenic biosignatures
- Rate-equation approach provides a more informative framework compared to previous approaches like Drake equation and its 'Biosignature' version
- Study expands upon previous research in Galactic habitability field

## Summary

In this study, the authors present a mathematical framework for statistical exoplanet population and astrobiology studies that aims to provide a time-dependent mapping between star formation, metal enrichment, and the occurrence of exoplanets and potentially life-harboring worlds in the solar neighborhood. The existing summary highlights several key findings from their research. Firstly, the authors find that the formation of exoplanets in the solar vicinity was episodic, with the emergence of the thick disk occurring approximately 11 billion years ago. This suggests that planet formation is not a continuous process but rather occurs in bursts. Secondly, within 100 parsecs from the Sun, there could be as many as 11,000 Earth-size planets in the habitable zone of K-type stars. The authors refer to these planets as "temperate terrestrial planets" (TTPs). Interestingly, they note that our own solar system is younger than the median TTP and was formed during a star formation surge that peaked around 5.5 billion years ago. This surge was likely triggered by an external agent. The authors also discuss how the occurrence rate of giant planets is modulated by metallicity. They find that this modulation leads to a later typical formation time for giant planets compared to TTPs; in other words, TTPs are more abundant at early times. Furthermore, based on their calculations they suggest that if microbial life arose as soon as it did on Earth in more than 1% of TTPs around K stars (assuming simple life is abundant), then there could be a life-harboring Earth-like planet within 20 parsecs from us. Additionally, they propose that if simple life is indeed abundant and emerged more than 8 billion years ago on about one third of all life-bearing planets today older Earth analogs are more likely to have developed complex life capable of altering their environment and producing detectable oxygenic biosignatures. The authors emphasize the limitations of previous approaches such as Drake equation and its 'Biosignature' version which do not incorporate temporal structure or evolutionary effects; they argue that their rate-equation approach based on a system of first order differential equations provides a more informative and modern framework for understanding the formation history of Earth like and giant planets in our galaxy. Overall this study expands upon previous research in field Galactic habitability and offers new insights into time varying incidence exoplanets and potentially habitable worlds in our solar neighborhood; emphasizing importance incorporating detailed calculations based on evolving astrophysical biological processes estimate relative biosignature yields among potential target stars.