The polarization state of starlight reflected by a planetary atmosphere uniquely reveals coverage, particle size, and composition of aerosols as well as changing cloud patterns. It is not possible to obtain a comparable level of detail from flux-only observations. It is therefore a powerful tool to better understand the crucial role played by clouds and aerosols in the chemistry, dynamics, and radiative balance of a planet. Furthermore, polarization observations can probe the atmosphere of planets independently of the orbital geometry (hence it applies to both transiting and non-transiting exoplanets). A high-resolution spectropolarimeter with a broad wavelength coverage, particularly if attached to a large space telescope, would enable simultaneous study of the polarimetric planetary properties of the continuum and to look for and characterize the polarimetric signal due to scattering from single molecules, providing detailed information about the composition and vertical structure of the atmosphere.

Context. Detecting moons around exoplanets is a major goal of current and future observatories. Moons are suspected to influence rocky exoplanet habitability, and gaseous exoplanets in stellar habitable zones could harbor abundant and diverse moons to target in the search for extraterrestrial habitats. Exomoons contribute to exoplanetary signals but are virtually undetectable with current methods. Aims. We identify and analyze traces of exomoons in the temporal variation of total and polarized fluxes of starlight reflected by an Earth-like exoplanet and its spatially unresolved moon across all phase angles, with both orbits viewed in an edge-on geometry. Methods. We compute the total and linearly polarized fluxes, and the degree of linear polarization P of starlight that is reflected by the exoplanet with its moon along their orbits, accounting for the temporal variation of the visibility of the planetary and lunar disks, and including the effects of mutual transits and mutual eclipses. Our computations pertain to a wavelength of 450 nm. Results. Total flux F shows regular dips due to planetary and lunar transits and eclipses. Polarization P shows regular peaks due to planetary transits and lunar eclipses, and P can increase and/or slightly decrease during lunar transits and planetary eclipses. Changes in F and P will depend on the radii of the planet and moon, on their reflective properties, and their orbits, and are about one magnitude smaller than the smooth background signals. The typical duration of a transit or an eclipse is a few hours. Conclusions. Traces of an exomoon due to planetary and lunar transits and eclipses show up in the F and P of sunlight reflected by planet-moon systems and could be searched for in exoplanet flux and/or polarization phase functions.