The O₂ A-Band in the Fluxes and Polarization of Starlight Reflected by Earth-Like Exoplanets

Earth-like, potentially habitable exoplanets are prime targets in the search for extraterrestrial life. Information about their atmospheres and surfaces can be derived by analyzing the light of the parent star reflected by the planet. We investigate the influence of the surface albedo A _s, the optical thickness b _cloud, the altitude of water clouds, and the mixing ratio of biosignature O₂ on the strength of the O₂ A-band (around 760 nm) in the flux and polarization spectra of starlight reflected by Earth-like exoplanets. Our computations for horizontally homogeneous planets show that small mixing ratios (η < 0.4) will yield moderately deep bands in flux and moderate-to-small band strengths in polarization, and that clouds will usually decrease the band depth in flux and the band strength in polarization. However, cloud influence will be strongly dependent on properties such as optical thickness, top altitude, particle phase, coverage fraction, and horizontal distribution. Depending on the surface albedo and cloud properties, different O₂ mixing ratios η can give similar absorption-band depths in flux and band strengths in polarization, especially if the clouds have moderate-to-high optical thicknesses. Measuring both the flux and the polarization is essential to reduce the degeneracies, although it will not solve them, especially not for horizontally inhomogeneous planets. Observations at a wide range of phase angles and with a high temporal resolution could help to derive cloud properties and, once those are known, the mixing ratio of O₂ or any other absorbing gas.