This paper is available on arxiv under CC 4.0 license. Authors: (1) Eleonora Alei, ETH Zurich, Institute for Particle Physics & Astrophysics & National Center of Competence in Research PlanetS; (2) Björn S. Konrad, ETH Zurich, Institute for Particle Physics & Astrophysics & National Center of Competence in Research PlanetS; (3) Daniel Angerhausen, ETH Zurich, Institute for Particle Physics & Astrophysics, National Center of Competence in Research PlanetS & Blue Marble Space Institute of Science; (4) John Lee Grenfell, Department of Extrasolar Planets and Atmospheres (EPA), Institute for Planetary Research (PF), German Aerospace Centre (DLR) (5) Paul Mollière, Max-Planck-Institut für Astronomie; (6) Sascha P. Quanz, ETH Zurich, Institute for Particle Physics & Astrophysics & National Center of Competence in Research PlanetS; (7) Sarah Rugheimer, Department of Physics, University of Oxford; (8) Fabian Wunderlich, Department of Extrasolar Planets and Atmospheres (EPA), Institute for Planetary Research (PF), German Aerospace Centre (DLR); (9) LIFE collaboration, www.life-space-mission.com. Table of Links Abstract & Introduction Methods Results Discussion Conclusions Next Steps & References Appendix A: Scattering of terrestrial exoplanets Appendix B: Corner Plots Appendix C: Bayes’ factor analysis: other epochs Appendix D: Cloudy scenarios: additional figures ABSTRACT Context. An important future goal in exoplanetology is to detect and characterize potentially habitable planets. Concepts for future space missions have already been proposed: from a large UV-Optical-Infrared space mission for studies in reflected light, to the Large Interferometer for Exoplanets (LIFE) for analyzing the thermal portion of the planetary spectrum. Using nulling interferometry, LIFE will allow us to constrain the radius and effective temperature of (terrestrial) exoplanets, as well as provide unique information about their atmospheric structure and composition. Aims. We explore the potential of LIFE in characterizing emission spectra of Earth at various stages of its evolution. This allows us (1) to test the robustness of Bayesian atmospheric retrieval frameworks when branching out from a Modern Earth scenario while still remaining in the realm of habitable (and inhabited) exoplanets, and (2) to refine the science requirements for LIFE for the detection and characterization of habitable, terrestrial exoplanets. Methods. We perform Bayesian retrievals on simulated spectra of 8 different scenarios, which correspond to cloud-free and cloudy spectra of four different epochs of the evolution of the Earth. Assuming a distance of 10 pc and a Sun-like host star, we simulate observations obtained with LIFE using its simulator LIFEsim, considering all major astrophysical noise sources. Results. With the nominal spectral resolution (R = 50) and signal-to-noise ratio (assumed to be S/N = 10 at 11.2 µm), we can identify the main spectral features of all the analyzed scenarios (most notably CO2, H2O, O3, CH4). This allows us to distinguish between inhabited and lifeless scenarios. Results suggest that particularly O3 and CH4 yield an improved abundance estimate by doubling the S/N from 10 to 20. Neglecting clouds in the retrieval still allows for a correct characterization of the atmospheric composition. However, correct cloud modeling is necessary to avoid biases in the retrieval of the correct thermal structure. Conclusions. From this analysis, we conclude that the baseline requirements for R and S/N are sufficient for LIFE to detect O3 and CH4 in the atmosphere of an Earth-like planet with an abundance of O2 of around 2% in volume mixing ratio. Doubling the S/N would allow a clearer detection of these species at lower abundances. This information is relevant in terms of the LIFE mission planning. We also conclude that cloud-free retrievals of cloudy planets can be used to characterize the atmospheric composition of terrestrial habitable planets, but not the thermal structure of the atmosphere. From the inter-model comparison performed, we deduce that differences in the opacity tables (caused by e.g. a different line wing treatment) may be an important source of systematic errors. Methods: statistical – Planets and satellites: terrestrial planets – Planets and satellites: atmospheres Keywords. 1. Introduction Temperate terrestrial exoplanets are predicted to be very abundant in our galaxy (Bryson et al. 2021). These planets are ideal candidates when searching for life beyond our Solar System. A powerful way to characterize a terrestrial exoplanet in the context of its habitability is by detecting and studying its atmosphere with the goal to constrain its surface conditions. Atmospheric spectra are influenced by many parameter and processes, such as the chemical composition, the temperature structure of the atmosphere, the presence of clouds, as well as emission and scattering from the surface. The detection and characterization of potentially habitable, rocky exoplanets is challenging with current facilities. For this reason, there is a widespread interest in the community to build new instruments for the search of life in the universe, as reported in the White Paper series in the context of the ESA “Voyage 2050” process[1] , as well as the US Astro 2020 Decadal survey (National Academies of Sciences, Engineering, and Medicine 2021). Space missions that aim at characterizing terrestrial exoplanets have been proposed, such as HabEx (Gaudi et al. 2020) and LUVOIR (Peterson et al. 2017) focusing on the reflected (visible and near-infrared) portion of the planetary spectrum, as well as LIFE (Large Interferometer for Exoplanets, Quanz et al. 2021, hereafter Paper I), which will characterize terrestrial planets in the thermal (mid-infrared), emitted portion of the planetary spectrum. Using nulling interferometry, LIFE will allow us to constrain the radius and effective temperature of (terrestrial) exoplanets, as well as provide unique information about their atmospheric structure and composition (Dannert et al. 2022; Konrad et al. 2021, hereafter Paper II and III, respectively). Due to the current lack of high-quality observational data, we must rely momentarily on simulated observations of terrestrial planets to create and improve the analyses algorithms, but also to provide scientific and technical requirements when planning a mission. This effort is currently ongoing within the LIFE Initiative and in a previous study (Paper III), we built a Bayesian retrieval routine to estimate the planetary and atmospheric parameters of a simulated Modern Earth twin at 10 pc distance as it would be observed by LIFE. In this work, we extend this exercise to other stages in the evolution of Earth’s atmosphere. Our planet has been habitable for about 4.4 billion years (see e.g. Heller et al. 2021, and references therein). In this context, we define a planet as habitable if its physical and chemical conditions would allow water, if present, to be liquid on the surface. In the prebiotic stage of Earth’s evolution, the atmosphere lacked O2 (currently about 21% of the atmospheric composition by volume). It was instead a CO2-N2-H2O-rich atmosphere, with traces of CH4 from volcanism. The early forms of life developed under a reducing environment and survived under anaerobic conditions (Olson et al. 2018, and references therein). Methanogenesis was thought to be a dominant metabolism at this stage (around 3.5 Ga), which would explain the increase in CH4 in the atmosphere (see e.g. Wolfe & Fournier 2018). Around 3 Ga, life forms that could use carbon dioxide to produce oxygen (via oxygenic photosynthesis) appeared (Marais 2000). These eventually led to a significant increase of O2 maximally up to ∼ 1% PAL[2] (see Gregory et al. 2021; Lyons et al. 2014, 2021, and references therein) around 2.33 Ga (Luo et al. 2016), during the so-called "Great Oxygenation Event" (GOE). There is also evidence pointing to a second increase in the O2 abundance (up to ∼ 10% PAL) occurred around 0.8 Ga, in the "Neoproterozoic Oxygenation Event" (NOE) (Shields-Zhou & Och 2011; Campbell & Squire 2010). The high abundance of carbon dioxide in the early Earth would have enhanced the atmospheric greenhouse effect, allowing Earth to be habitable despite the fainter solar irradiation (see e.g. Feulner 2012, and references therein). The positive feedback between the carbon-silicate cycle and the increase in irradiation would have then allowed to maintain temperatures conducent to liquid water over the last 4 Ga. The increase in irradiation from the Sun over the eons has made the weathering of CO2 more efficient, decreasing the amount of carbon dioxide in the atmosphere and thus dampening the atmospheric greenhouse effect (see e.g. Graham 2021, and references therein). The appearance of photosynthetic life forms and the onset of plate tectonics also contributed to the depletion of atmospheric CO2. Numerous processes including biology and geology have driven the wide-ranging evolution of Earth’s atmosphere during the various epochs of its development. Our modern atmosphere represents however only a small fraction of Earth’s evolutionary states. It is therefore important to simulate a suitable range of different atmospheric epochs from Earth’s history when in vestigating Earth-like atmospheres. For this study, we simulated observations obtained by LIFE starting from theoretical spectra of 4 distinct epochs of Earth’s atmospheric evolution, produced from a self-consistent 1D climate and photochemistry model coupled with a line-by-line radiative transfer model (Rugheimer & Kaltenegger 2018). The observed spectra were simulated using the LIFE noise simulator LIFEsim (for details on the simulator see Paper II). We then used the Bayesian retrieval routine presented in Paper III to characterize the different atmospheres. We aim to address the following research questions: – science-driven questions: How well could LIFE characterize atmospheres of habitable planets? Could LIFE differentiate between different atmospheres, and with what confidence? What is the impact of clouds on this assessment? What are the most promising (combinations of) detectable biosignatures? – technology- and computationally-driven questions: Is the combination of spectral resolution (R = λ/∆λ), signal to noise ratio (S/N) and wavelength range defined in Paper III still adequate for this case study? What are the caveats and limitations of the Bayesian retrieval routine? What systematics may arise when comparing two different models (e.g. in terms of differences in line lists, scattering treatment, identification of biomarkers)? We discuss how we adapted the input spectra to simulate LIFE observations and describe the grid of scenarios in Section 2. We show and describe the results in Section 3. A thorough discussion of our findings and of the potential systematic uncertainties of the retrieval routine is provided in Section 4. In Section 5 we report the main takeaway points from this study, and in Section 6 we trace an outlook of the ongoing and future studies. [1] https://www.cosmos.esa.int/web/voyage-2050 [2] Present Atmospheric Level This paper is available on under CC 4.0 license. arxiv

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