On the use of polarized thermal emission to constrain cloud grain size and temperature structure of sub-stellar objects

Emission spectroscopy is an invaluable tool for probing the atmospheres of brown dwarfs and exoplanets, but interpretations based on flux spectra alone often suffer from degeneracies among temperature structure, chemical composition, and cloud properties. Thermal emission spectropolarimetry offers complementary sensitivity to these atmospheric characteristics. Previous studies have shown that linear polarization in fixed bandpasses depends on emission angle, temperature profile, and cloud scattering. In this study, we revisit these dependencies, emphasizing the wavelength-dependent effects that shape polarized spectra. We show that thermal polarization spectrum is primarily governed by: (1) a combination of temperature, temperature gradient, and wavelength; (2) cloud particle size; and (3) cloud optical thickness. Using the 3D Monte Carlo radiative transfer code ARTES, we simulate polarization spectra from a modeled 1D atmosphere. We find that, for a fixed cloud optical thickness, the polarization exhibits peaks at size parameters near 0.2 and 1. However, the dependence on cloud optical thickness is more pronounced and tends to dominate the broadband polarization. We further show that much narrower polarization features in molecular absorption band, can in principle trace the local temperature gradient at the photosphere of each wavelength. Future low-resolution (resolving power around 100) spectropolarimeter operating at 1-2 micron with sensitivities of 1e-5 would be able to capture these polarization features, and may provide a new diagnostic for breaking degeneracies that commonly affect flux-only retrievals. This work represents an incremental step toward the challenging goal of jointly interpreting atmosphere from both intensity and polarization spectra.