The researchers used atmospheric and radiative-transfer simulations to show that when light emitted from inside an atmosphere is scattered by clouds, it becomes polarized, and this polarization depends strongly on cloud particle size, cloud thickness, and how temperature changes with altitude.
They found that small and large cloud grains produce distinct polarization signatures, thick clouds reduce polarization, and temperature gradients produce wavelength-dependent polarization because different wavelengths come from layers at different temperatures.
The polarization amplitude and the location of polarization peaks are governed by the scattering regime (Rayleigh vs. Mie), which depends on the ratio of particle size to wavelength.
Rayleigh scattering occurs when the cloud particles (or molecules) are much smaller than the wavelength of light. Scattering is strongly wavelength-dependent (∝ 1/λ⁴) → shorter wavelengths scatter more. high linear polarization is produced, especially at ~90° scattering angles.
Mie scattering occurs when particle size is comparable to or larger than the wavelength. Lower net polarization is produced due to multiple scattering directions. It is applied to larger cloud grains (~1–10 μm) in brown dwarf / exoplanet atmospheres.
Optical depth measures how much light is absorbed or scattered as it travels through the star's atmosphere. At low optical depths, insufficient scattering occurs which limits polarization production, whereas at high optical depths, multiple scattering leads to depolarization. Maximum polarization occurs at intermediate optical depths.
Cloud materials observed here: Silicate clouds (MgSiO₃, Mg₂SiO₄) dominate in near-infrared polarization features. Iron and Al₂O₃ contribute mainly at very hot temperatures and shorter wavelengths.
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