Constraining Background N₂ Inventories on Directly Imaged Terrestrial Exoplanets to Rule Out O₂ False Positives

Direct imaging spectroscopy with future space-based telescopes will constrain terrestrial planet atmospheric composition and potentially detect biosignature gases. One promising indication of life is abundant atmospheric O-2. However, various non-biological processes could also lead to O-2 accumulation in the atmospheres of potentially habitable planets around Sun-like stars. In particular, the absence of non-condensible background gases such as N-2 could result in appreciable H escape and abiotic O-2 buildup, so identifying background atmosphere composition is crucial for contextualizing any O-2 detections. Here, we perform retrievals on simulated directly imaged terrestrial planets using rfast, a new exoplanet atmospheric retrieval suite with direct imaging analysis capabilities. By simulating Earth-analog retrievals for varied atmospheric compositions, cloud properties, and surface pressures, we determine what wavelength range, spectral resolution, and signal-to-noise ratio (S/N) are necessary to constrain background gases' identity and abundance. We find N-2 backgrounds can be uniquely identified with S/N similar to 20 observations, provided that wavelength coverage extends beyond similar to 1.6 mu m to rule out CO-dominated atmospheres. Additionally, there is a low probability of O-2-dominated atmospheres due to an O-2-N-2 degeneracy that is only totally ruled out at S/N similar to 40. If wavelength coverage is limited to 0.2-1.1 mu m, then although all other cosmochemically plausible backgrounds can be readily excluded, N-2 and CO backgrounds cannot be distinguished. Overall, our simulated retrievals and associated integration time calculations suggest that near-infrared coverage to at least 1.6 mu m and apertures approaching 8 m are needed to confidently rule out O-2 biosignature false positives within feasible integration times.