Flux and polarisation spectra of water clouds on exoplanets

Context. A crucial factor for a planet's habitability is its climate. Clouds play an important role in planetary climates. Detecting and characterising clouds on an exoplanet is therefore crucial when addressing this planet's habitability. Aims. We present calculated flux and polarisation spectra of starlight that is reflected by planets covered by liquid water clouds with different optical thicknesses, altitudes, and particle sizes, as functions of the phase angle alpha. We discuss the retrieval of these cloud properties from observed flux and polarisation spectra. Methods. Our model planets have black surfaces and atmospheres with Earth-like temperature and pressure profiles. We calculate the spectra from 0.3 to 1.0 mu m, using an adding-doubling radiative transfer code with integration over the planetary disk. The cloud particles' scattering properties are calculated using a Mie-algorithm. Results. Both flux and polarisation spectra are sensitive to the cloud optical thickness, altitude and particle sizes, depending on the wavelength and phase angle alpha. Conclusions. Reflected fluxes are sensitive to cloud optical thicknesses up to similar to 40, and the polarisation to thicknesses up to similar to 20. The shapes of polarisation features as functions of a are relatively independent of the cloud optical thickness. Instead, they depend strongly on the cloud particles' size and shape, and can thus be used for particle characterisation. In particular, a rainbow strongly indicates the presence of liquid water droplets. Single scattering features such as rainbows, which can be observed in polarisation, are virtually unobservable in reflected fluxes, and fluxes are thus less useful for cloud particle characterisation. Fluxes are sensitive to cloud top altitudes mostly for alpha < 60 degrees and wavelengths <0.4 mu m, and the polarisation for a around 90 degrees and wavelengths between 0.4 and 0.6 mu m.