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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 Appendix D: Cloudy scenarios: additional figures In this section, we provide additional plots for the cloudy scenarios. In Figures D.1 and D.2 we show the retrieved exoplanet parameters and abundances for the different scenarios with varying R and S/N values. Finally, we plot in Figure D.3 the maximum difference ∆ between the cumulative posteriors for the different model parameters, for each combination of the cloudy scenarios and different R-S/N pairs. This paper is available on under CC 4.0 license. arxiv

The Finale of Our Exoplanet LIFE Study: Cloudy Scenarios

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 Appendix C: Bayes’ factor analysis: other epochs As described in Section 2, the theoretical spectral model was updated with respect to Paper III and it now takes into account additional physical processes. For the results presented in Section 3, we ran retrievals using the most updated version of the Bayesian framework. The additional flexibility of petitRADTRANS now allows us to quantify the impact of CIA and scattering in retrievals. We ran additional retrievals on the clear sky scenarios for R = 50 and S/N = 10. In these retrievals, we altered the number of physical processes that were treated in the petitRADTRANS theoretical spectral model as follows: – Including both CIA and scattering (setup used in Section 3); – Excluding both CIA and scattering; – Including scattering and excluding CIA; – Including CIA and excluding scattering. In the runs where scattering is included, we consider selfscattering, surface scattering of the thermal radiation, and gaseous Rayleigh scattering (see Table 5 for references). We do not include aerosol and cloud scattering in the calculation. Since our theoretical spectral model neglects clouds, in this analysis we considered only the cloud-free scenarios. The effect of modeling cloudy spectra using a cloud-free retrieval model will be discussed in detail in the Section 4.2. To determine the theoretical spectral model configuration that best reproduces the input spectra we performed a Bayes’ factor analysis. The Bayes’ factor is defined as: The results for the remaining epochs exhibit similar behaviour. In Figure C.2, we show the results for the NOE Earth, Figure C.3 shows the ones for the GOE Earth, and the results for the prebiotic Earth are shown in Figure C.4. This paper is available on under CC 4.0 license. arxiv

Baye's Factor Analysis - Other Epochs: A Deeper Look Into Our Exoplanet Study

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 Appendix B: Corner Plots Corner plots for the retrieval runs at the reference R and S/N are shown in this section. We grouped both the cloudy and the clear sky retrievals for each epoch in the same figure, in order to compare the results. Namely: Figure B.1 shows the corner plots of the two Modern Earth scenarios (MOD-CF and MODC); Figure B.2 shows the NOE Earth scenarios (NOE-CF and NOE-C); the GOE Earth scenarios (GOE-CF and GOE-C) are in Figure B.3; finally, the prebiotic scenarios (PRE-CF and PRE-C) are shown in Figure B.4. The models are color-coded according to Table 1. Also, the results for the clear sky retrievals are shown using dashed contour lines, while the cloudy models are represented using solid lines. The table on the top right of each figure shows the expected values for each parameter, together with the estimates and the 1- σ uncertainty for the two scenarios. This paper is available on under CC 4.0 license. arxiv

How We Used Corner Plots in Our Astrophysics Study

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 Appendix A: Scattering of terrestrial exoplanets As discussed in Mollière et al. (2020), petitRADTRANS was updated to treat scattering. This was done using the Feautrier method (Feautrier 1964). This is a third-order method that allows the treatment of the radiative transfer equation in the diffusive regime. The Feautrier method solves the angle- and frequencydependent radiative transfer equation for both the planetary and the stellar radiation field. These can be treated separately, since the radiative transfer equation (Eq. A.1) depends only linearly from the intensity I. Here, µ = cos θ where θ is the angle between a light ray and the surface normal, τ is the optical depth, I is the intensity, and S is the source function. Conceptually, for any direction µ of a ray, there also exists a ray in direction −µ, where µ ∈ [−1, 1]. It is possible to instead let µ run from 0 to 1 only, and define rays I+ and I− parallel and antiparallel to this direction. For one of these, the projection onto the atmospheric normal vector (defined by the scalar product) will be positive (going upward), while for the other one it will be negative (that is, going downward). Eq. A.1 can be therefore rewritten as: To solve these, it is convenient to define other two variables: So that Eqs. A.2 and A.3 become: In this paper, we only take into account thermal scattering, i.e. scattering of the planetary radiation. We therefore neglect the scattering of the direct stellar contribution. However, since the radiative transfer equation depends only linearly on Iν, the contribution of the stellar radiation can be treated as an additional term in the calculation (see Mollière et al. 2017). This term is also included in the latest version of petitRADTRANS and we refer to the online documentation for a more detailed description [10] . Purely considering the planetary radiation, we define the boundary conditions at the top of the atmosphere: meaning that there is no planetary radiation coming downwards from the top of the atmosphere, and at the surface: there is no dependence from the (N − 1)th layer in the boundary condition A.13; bN, as a consequence, will be equal to 1. The iterations stop once the estimate of the flux has reached a convergence value. [10] https://petitradtrans.readthedocs.io/en/ latest/content/notebooks/emis_scat.html# Scattering-of-stellar-light This paper is available on under CC 4.0 license. arxiv

The Scattering of Terrestrial Exoplanets: What This Means

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 6. Next Steps Several new interesting questions and opportunities for more detailed studies arise from this work. First of all, we plan to work on a study that will take advantage of the model selection potential that Bayesian retrievals have to offer, for example by comparing retrievals including and excluding non-retrieved parameters (e.g. the CO abundance). We are also performing retrievals assuming various cloud models (Konrad et al., in prep.). Retrievals of hazy planets (see e.g. Arney et al. 2016), as well as ocean worlds, might also help us further quantify the science potential of LIFE for a variety of different planet types. Another interesting study would be to increase S/N and R to even higher values. This will not only evaluate the extreme limits of a concept like LIFE, but also help us better understand if retrievals are limited by R rather than S/N (e.g. due to unresolved narrow features at low R). It would also be useful to compare different R-S/N combinations, this time fixing the observing time. This would help us quantify the best R-S/N combination needed to optimize the characterization of a terrestrial atmosphere. Further work is needed to optimize the yield in the characterization phase of the LIFE mission concept. The estimates of the observation time needed to establish knowledge about the habitability and the presence of biologically relevant molecules in the atmosphere that we derived here are a crucial piece of information for these follow-up studies. In this work, we only used simulated data obtained with the LIFE mission. However, in the future there will likely be more information available to each system and planet. Therefore, it will be important to put this study in context with other observations. For instance, joint retrievals of reflected light data obtained with LUVOIR/HabEx at optical/near-infrared wavelengths and thermal emission spectra as obtained by LIFE would provide useful insight on the synergies between the various missions. One of the most important open questions regarding the ultimate goal of detecting extrasolar life will require to put our results in context with life detection frameworks (e.g. Green et al. 2021; Catling et al. 2018; Walker et al. 2018). Our ongoing retrieval efforts could be useful for the fine-tuning of such frameworks. These, in turn, would provide insight on the meaning and the likelihood of a potential biosignature detection, which would allow us to infer and justify the presence of life forms on another planet. This work has been carried out within the framework of the National Center of Competence in Research PlanetS supported by the Swiss National Science Foundation. S.P.Q. and E.A. acknowledge the financial support from the SNSF. P.M. acknowledges support from the European Research Council under the European Union’s Horizon 2020 research and innovation program under grant agreement No. 832428. J.L.G. thanks ISSI Team 464 for useful discussions. Acknowledgements. 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N. & Tennyson, J. 2014, MNRAS, 440, 1649 [7] http://www.astropy.org [8] https://matplotlib.org/3.1.1/index.html [9] https://seaborn.pydata.org This paper is available on under CC 4.0 license. arxiv

What Are the Next Steps in Exoplanet Research?

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 5. Conclusions The Bayesian retrieval framework introduced in Paper III and extended here has delivered insightful answers to the questions introduced in Section 1. These can be summarized as follows: This paper is available on under CC 4.0 license. arxiv

The Conclusion to Our Exoplanet Study: The Future of Astrophysics

Discussing the Impact of Our Exoplanet Study: How This Impacts Everything

The Results of Our Research: Our Exoplanet Study

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 2. Methods We start by discussing the details of the input spectra that were used in this study (Section 2.1). We then discuss the updates on the Bayesian retrieval routine (Section 2.2). We describe the assumptions that our model takes into account and the main potential source of systematic errors in the retrievals in Section 2.3. 2.1. Input spectra and scenarios We consider spectra corresponding to four different evolutionary epochs of Earth: the prebiotic Earth (3.9 Ga), the Earth shortly after the Great Oxygenation Event (2.0 Ga), the Neoproterozoic Oxygenation Event (0.8 Ga), and Modern Earth. All considered Earth spectra were produced by Rugheimer & Kaltenegger (2018). These self-consistent spectra were produced using a 1D convective-radiative transfer model loosely coupled with a 1D climate model and a 1D photochemistry model. The authors accounted for the thermal chemistry and the photochemistry of more than 55 species. The atmospheres were modeled up to 10−4 bar and split into 100 layers. The radiative forcing of clouds is included by adjusting the surface albedo of the planet. The results of the photochemistry-climate-radiative model were then fed to a line-by-line radiative transfer model to produce emission spectra. The line lists and the pressure broadening coefficients were from to the HITRAN 2016 database (Gordon et al. 2017). Surface scattering was included in the calculations, assuming 70% ocean, 2% coast, and 28% land. In some scenarios, a partial cloud coverage was directly included in the calculation of the emission spectrum. In these cloudy cases, the authors assumed a 60% cloud coverage (split into 40% water clouds at 1 km altitude, 40% water clouds at 6 km altitude, and 20% ice clouds at 12 km altitude) consistent with an averaged Earth cloud model. Aerosol was not included in the calculation. The model has been validated from the visual to the mid-infrared wavelength ranges with observations of Earth (Kaltenegger et al. 2007; Kaltenegger & Traub 2009; Rugheimer et al. 2013). For further details, we refer the reader to Rugheimer & Kaltenegger (2018). For each epoch, we consider both clear sky and cloudy sky spectra, which yields a total of 8 scenarios. We assigned every modeled scenario an identifier and a specific color, as listed in Table 1. We will use these identifiers throughout the remainder of the paper. We simulate observations with LIFE via the LIFEsim tool (see Paper II for a description of the simulator). LIFEsim estimates the wavelength-dependent S/N considering all major astrophysical noise sources (stellar leakage, local zodiacal dust emission, and exo-zodiacal dust emission). We consider an Earth-sized planet on a 1 AU orbit around a Sun-like star at 10 pc distance. For our baseline analyses we assumed the nominal simulation parameters for LIFEsim as summarized in Table 2 (see Paper I and Paper II for details). We consider an exo-zodi level of 3 times the local zodiacal dust density, based on the results from the HOSTS survey (Ertel et al. 2020). 2.2. Updates on the Bayesian retrieval framework We denote the input spectra from Section 2.1 as the "true spectra." To simulate a LIFE-like observation of these targets, we run LIFEsim on the true spectra, thus obtaining simulated "observed spectra." We then perform a retrieval on the observed spectra using petitRADTRANS (Mollière et al. 2019) as "forward model" in the retrieval routine, and the Bayesian sampler model pyMultiNest (Buchner et al. 2014) as "parameter estimation routine" (cf. Paper III). The theoretical 1D atmospheric model petitRADTRANS (Mollière et al. 2019) applies the radiative transfer equation to calculate spectra corresponding to a set of parameters. These parameters describe the bulk parameters (planetary mass and radius), the pressure-temperature (P-T) structure (approximated by a fourth-order polynomial), and the chemical composition of the atmosphere. Our Bayesian retrieval framework recursively draws combinations of parameters from a set of "priors" that describe the "a priori" probability distribution of each parameter (listed in Table 3) and uses the forward model to compute the corresponding spectra. Then, the Bayesian framework tests how well these calculated spectra fit the observed one using a "likelihood" function (see Eq. (3) in Paper III). In order to sample the prior space efficiently, our retrieval relies on the parameter estimation routine pyMultiNest (Buchner et al. 2014), which is based on MultiNest (Feroz et al. 2009). This routine applies the Nested Sampling algorithm (Skilling 2006) to fit the theoretical spectral model to the observed spectrum, and thereby yields estimates and uncertainties for the model parameters. These estimates are the "posterior probability distributions" (or "posteriors"). The posteriors contain the information on which combinations of model parameters best describe the observed spectrum. For more details about the Bayesian retrieval framework, we refer the reader to Paper III. In our previous work, we argued that effects of scattering on simulated mid-infrared spectra are negligible at the considered resolutions and LIFEsim noise patterns. In that study, we had to be particularly mindful of the computing time. The version of petitRADTRANS used in Paper III only allowed to calculate spectra at R = 1000, which were subsequently binned down to the resolution of the input spectrum (R = 35 − 100 in Paper III). Calculating a spectrum at R = 1000 excluding scattering required ≈ 0.5 seconds, whereas including scattering required ≈ 18 seconds. Since millions of spectra have to be calculated for a single Bayesian retrieval, including scattering was prohibitive with respect to the computing time, especially when considering a large grid of retrieval runs. Recent updates to petitRADTRANS have enabled us to compute spectra at any resolution, provided a grid of correlated-k tables at that resolution is available. These tables can be produced with petitRADTRANS by binning down the R = 1000 opacity tables. We compiled a correlated-k opacity database for R = 50 and used it to produce spectra directly at this resolution. This reduces the computation time per spectrum significantly and allows us to compute emission spectra in ≈ 0.04 seconds when excluding scattering, and in ≈ 0.5 seconds when including scattering. This reduction in computing time allows us to include scattering in the theoretical spectral model. Other updates on petitRADTRANS were performed. The treatment of collision-induced absorption (CIA) was modified by updating the interpolation of the CIA tables, originally in FORTRAN, to Python. Minor variations in the interpolation options (log-linear compared to nearest neighbor in Paper III) make the new model not directly comparable with its previous version. However, at Earth-like conditions, the differences in the CIA signature on the spectrum remain negligible. Also, the CIA features impact mostly the short wavelengths (λ < 6 µm), where the LIFEsim noise is large. Furthermore, the treatment of scattering was updated. Originally implemented in petitRADTRANS only for gaseous planets (see Mollière et al. 2019), it was adapted to include the scattering by a rocky surface. More information on the new implementation of scattering can be found in Appendix A, as well as the petitRADTRANS documentation[3] . This new version of petitRADTRANS is available in the main GitLab repository[4] . Using the updated retrieval framework, we run retrievals for the eight different spectra introduced in Section 2.1. We retrieve the same parameters as in Paper III and leave most prior distributions unchanged. An exhaustive list of the parameters and priors used, and the corresponding expected values for the different epochs, are listed in Table 3. Most priors are represented by a boxcar function (hereafter "uniform" priors): every value is equally probable if within a certain range. Two notable exceptions are the priors for the planetary radius Rpl and the logarithm of the planetary mass log10(Mpl), whose priors are Gaussian. The prior we assumed on Rpl is based on the radius estimate expected from observing a terrestrial planet with LIFE during its search phase (see Paper II for details). The log10(Mpl) prior was inferred from Rpl using the statistical mass-radius relation presented in Chen & Kipping (2016) (see Paper III for details). 2.3. Assumptions and discrepancies When performing retrievals, we are limited by the maximum number of parameters retrieved in a reasonable computing time. For this reason, we need to make a few simplifications: 1. As in Paper III, we parameterize the P-T profile in the retrieval by a fourth order polynomial. Table 2: Simulation parameters used in LIFEsim for the baseline analyses. 2. We assume the abundances of the considered species to be independent of altitude. 3. Our retrieval framework does not model clouds for any of the considered scenarios. This is a strong simplification for the cases where we retrieve cloudy input spectra. However, this retrieval approach allows us to investigate the biases on the results obtained when retrieving a cloudy spectrum assuming a cloud-free atmosphere. The addition of a cloud model to our retrieval framework will be tackled in a future study 4. A surface reflectance of 0.1 is assumed for all the wavelength range. This is a common value for water-rich habitable terrestrial planets, dominated by the low IR reflectance of oceans and ice. In contrast, Rugheimer & Kaltenegger (2018) used P-T profiles that were self-consistently calculated by their climatephotochemistry model to generate the input spectra. The chemical abundance profiles were also altitude-dependent and calculated self-consistently by the climate-photochemistry model. In order to compare the results of the retrievals with the input, we approximate the input P-T and abundance profiles to calculate expected values of the parameters considered in the retrievals. Regarding the thermal structure of the atmosphere, we determine the expected values of the polynomial coefficients (a4, a3, a2, a1, a0) listed in Table 3 by fitting a fourth-order polynomial to the self-consistent P-T profiles. As for the abundances, we assume the weighted means over the pressure grid of the altitude-dependent abundance profiles. This is sensible, since the denser layers of the atmosphere (which corresponds to higher pressures) are generally the ones that contribute more to the spectrum. The expected values for the considered species are listed in Table 3 as well. For what concerns the surface reflectance, Rugheimer & Kaltenegger (2018) considered a wavelength-dependent reflectance. However, the reflectance still averaged to 0.1 in the wavelength range of interest. We would therefore not expect large variations due to this parameter. There are also differences between the opacity tables that the two models use. We used the default set of opacities for petitRADTRANS as presented in Mollière et al. (2019). We added the N2O opacity from the ExoMol database (Chubb et al. 2021). The CIA opacities are taken from the HITRAN database. Details and reference papers corresponding to the opacity linelists are shown in Tables 4 and 5. In contrast, the input spectra were calculated using HITRAN 2016 opacities (Rugheimer & Kaltenegger 2018). Differences in line-lists and broadening coefficients are therefore to be expected and may cause biases in the results. Due to these differences in the atmospheric models, we would imagine to find some small discrepancies between the spectra that were published in Rugheimer & Kaltenegger (2018) and the ones that our framework can calculate. We will discuss this particular aspect in Section 4.4. [3] https://petitradtrans.readthedocs.io [4] https://gitlab.com/mauricemolli/petitRADTRANS This paper is available on under CC 4.0 license. arxiv

The Methods in Which We're Researching Exoplanets

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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