Flux and polarisation spectra of water clouds on exoplanets

Abstract

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 α. 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 μm, 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 α. Conclusions. Reflected fluxes are sensitive to cloud optical thicknesses up to ∼40, and the polarisation to thicknesses up to ∼20. The shapes of polarisation features as functions of α 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 α < 60 • and wavelengths <0.4 μm, and the polarisation for α around 90 • and wavelengths between 0.4 and 0.6 μm.

Looking for the rainbow on exoplanets covered by liquid and icy water clouds

“…(see Stam 2008;Karalidi et al 2011), and corresponds to the planet's geometric albedo A G when α = 0 • . The corresponding normalized polarized flux is given by…”

“…Terrestrial liquid water clouds are in general composed of droplets with radii ranging from ∼5 μm to ∼30 μm (Han et al 1994). We use either small droplets (type A), with r eff = 2.0 μm and v eff = 0.1, or larger droplets (type B) with r eff = 6.0 μm and v eff = 0.4 (see also Karalidi et al 2011). The latter are similar to those used by van Diedenhoven et al (2007) as average values for terrestrial water clouds.…”

“…The latter are similar to those used by van Diedenhoven et al (2007) as average values for terrestrial water clouds. We use a wavelength independent refractive index of 1.335+0.00001i (see Karalidi et al 2011, and references therein). For a given wavelength, and values of r eff and v eff , we calculate the extinction cross-section, single scattering albedo and the single scattering matrix using Mie-theory (de Rooij & van der Stap 1984) and normalized according to Eq.…”

“…Stam 2003;Stam et al 2004;Saar & Seager 2003;Seager et al 2000;Stam 2008;Karalidi et al 2011). Polarization provides us with a unique tool for the detection of liquid water on a planetary atmosphere and surface.…”

“…Bailey 2007;Karalidi et al 2011). Its angular position depends strongly on the refractive index of the scattering particles and slightly on their effective radius (see Karalidi et al 2011, and references therein).…”