Large Interferometer For Exoplanets (LIFE) III. Spectral resolution, wavelength range, and sensitivity requirements based on atmospheric retrieval analyses of an exo-Earth

Context. Temperate terrestrial exoplanets are likely to be common objects, but their discovery and characterization is very challenging because of the small intrinsic signal compared to that of their host star. Various concepts for optimized space missions to overcome these challenges are currently being studied. The Large Interferometer For Exoplanets (LIFE) initiative focuses on the development of a spacebased mid-infrared (MIR) nulling interferometer probing the thermal emission of a large sample of exoplanets. Aims. This study derives the minimum requirements for the signal-to-noise ratio (S/N), the spectral resolution (R), and the wavelength coverage for the LIFE mission concept. Using an Earth-twin exoplanet as a reference case, we quantify how well planetary and atmospheric properties can be derived from its MIR thermal emission spectrum as a function of the wavelength range, S/N, and R. Methods. We combined a cloud-free 1D atmospheric radiative transfer model, a noise model for observations with the LIFE interferometer, and the nested sampling algorithm for Bayesian parameter inference to retrieve planetary and atmospheric properties. We simulated observations of an Earth-twin exoplanet orbiting a G2V star at 10 pc from the Sun with different levels of exozodiacal dust emissions. We investigated a grid of wavelength ranges (3-20 mu m, 4-18.5 mu m, and 6-17 mu m), S/Ns (5, 10, 15, and 20 determined at a wavelength of 11.2 mu m), and Rs (20, 35, 50, and 100). Results. We find that H2O, CO2, and O-3 are detectable if S/N >= 10 (uncertainty <= +/- 1.0 dex). We find upper limits for N2O (abundance less than or similar to 10(-3)). In conrtrast, CO, N-2, and O-2 are unconstrained. The lower limits for a CH4 detection are R = 50 and S/N = 10. Our retrieval framework correctly determines the exoplanet's radius (uncertainty <= +/- 10%), surface temperature (uncertainty <= +/- 20 K), and surface pressure (uncertainty <= +/- 0.5 dex) in all cloud-free retrieval analyses. Based on our current assumptions, the observation time required to reach the specified S/N for an Earth-twin at 10 pc when conservatively assuming a total instrument throughput of 5% amounts to approximate to 6-7 weeks with four 2m apertures. Conclusions. We provide first order estimates for the minimum technical requirements for LIFE via the retrieval study of an Earth-twin exoplanet. We conclude that a minimum wavelength coverage of 4-18.5 mu m, an R of 50, and an S/N of at least 10 is required. With the current assumptions, the atmospheric characterization of several Earth-like exoplanets at a distance of 10 pc and within a reasonable amount of observing time will require apertures >= 2m.