Flux and polarization signals of Earth-like exoplanets covered by sub-solar clouds

Abstract

We investigate the flux and polarization signals of Earth-like exoplanets covered by sub-solar clouds. These clouds occur at the region where solar zenith angle is smaller than a specific angle \(\sigma\). We calculate the flux and polarization of the light reflected by the planetary disk, and we include multiple scattering. For a given \(\sigma\), the sub-solar cloud coverage will change with the phase angle, corresponding to the various viewing geometries. We study the influences of cloud optical thicknesses, surface albedos, cloud particle sizes and wavelengths. Then we investigate how these parameters together with the variation of cloud coverage caused by viewing geometries leave traces on flux and polarization signals. The larger values of \(\sigma\) corresponding to larger cloud coverage before the cloud totally disappears, which increases flux and reduces polarization. For a given value of \(\sigma\), while considering the influences of parameters such as cloud optical thickness, surface albedo, cloud particle size and wavelength, the cloud coverage variation also should be taken into account. The location of a rainbow is not affected by \(\sigma\), cloud optical thickness and surface albedo. However, both the larger values of sub-solar cloud optical thicknesses and the larger surface albedos would reduce the polarization of the rainbow peaks. The location of a rainbow may be affected by cloud particle effective radius (\(r_{\mathrm{eff}}\)) and wavelength. As \(r_{\mathrm{eff}}\) and/or wavelength increases, the polarization signal shows a stronger primary rainbow feature. The location of the maximum polarization can be affected by \(\sigma\), cloud optical thickness, surface albedo and wavelength. But the \(r_{\mathrm{eff}}\) seems not to affect the location of maximum polarization. The longer wavelength (such as 865 nm) is suitable to derive sub-solar cloud coverage, and the rainbow feature can help to characterize cloud particles. All these results emphasize the importance of polarimetry for the characterization of exoplanets.