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

TL;DR

This work addresses degeneracies in brown-dwarf and self-luminous exoplanet atmospheres that plague flux-only retrievals by exploring polarized thermal emission as a diagnostic across wavelengths. Using the 3D Monte Carlo radiative transfer code ARTES with a parameterized 1D atmosphere and a MgSiO$_3$ cloud layer, the study shows broadband polarization is mainly governed by cloud particle size and optical depth, while narrow-band features trace the local temperature gradient at the photosphere. It predicts a characteristic two-peak polarization signature arising from cloud scattering, and demonstrates that molecular bands can enhance polarization by probing higher-altitude layers with different gradients, thereby offering a potential route to break degeneracies between temperature structure and gas abundances. The work also discusses observational prospects for low-resolution spectropolarimetry with future instruments, highlighting challenges and outlining how joint intensity-polarization retrievals could yield tighter constraints on cloud microphysics and thermal structure in sub-stellar atmospheres.

Abstract

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.

Figures (16)

• Figure 1: Schematic diagram of the thermal radiation process. Photons emitted by thermal radiation from the lower atmosphere are scattered by cloud particle in the high atmosphere. The dark area represents regions of higher temperature and thus larger thermal radiation flux. Photons traveling perpendicular to the atmospheric layering (illustrated by the black arrow) originate from a lower altitude compared to photons traveling at other angles (illustrated by the red arrow). Upper panel gives the single scattering polarization of different scattering angles.
• Figure 2: Polarization at $\lambda = 1.5 \, \mu \mathrm{m}$ is shown for atmospheres with a high-altitude cloud, illustrating the effects of (left) varying cloud grain size parameters and (right) different cloud optical thicknesses. Dashed lines correspond to emission angles of $80^\circ$, while dotted lines indicate $30^\circ$. In the left panel, two cloud optical thickness values are tested to examine their impact on the location of the polarization peak. Right panel suggests clouds with higher absorption (lower scattering albedo, $\omega$) can sustain significant polarization even at higher optical thicknesses ($\tau \ge 10$).
• Figure 3: Left: spectral dependence of the single scattering polarization and single scattering albedo of $\rm MgSiO_{3}$ cloud in a gamma distribution of effective particle size of 0.1, 0.5 and 1 $\rm \mu m$ Right: spectral dependence of cloud extinction cross section ($\rm \kappa_{ext}$) and cloud scattering cross section ($\rm \kappa_{sca}$) for different grain sizes.
• Figure 4: Schematic figure illustrates how cloud size parameter and cloud optical thickness influence the thermal polarization spectrum. The cloud size parameter determines the single scattering polarization and scattering albedo. Left panel shows the response of polarization to the changes to single scattering polarization and scattering albedo. Right panel: response of polarization to the changes to the cloud optical thickness. The artificially constant $\rm \tau_{cld}$ and more realistic wavelength dependent $\rm \tau_{cld}$ determined by the cloud cross section and column density of the cloud particle are shown with gray and blue curve respectively. For a non-gray cloud with a fixed column density, the wavelength dependence of $\tau_{\rm cld}$ is governed by the cloud’s refractive index and particle size distribution. Consequently, the polarization varies with wavelength, and the peak occurs at wavelengths where $\tau_{\rm cld}(\lambda)$ is in the regime that favors efficient single-scattering while suppressing multiple-scattering events.
• Figure 5: Linear polarization for atmospheres with a high-altitude cloud is shown as a function of wavelength-dependent scaling ($\frac{1}{\lambda} \frac{1}{T^{2}}$) and temperature gradient ($\frac{dT}{d\log P}$). Note the x axis is not a linear scale, only the grid points list in the x and y axis are considered in this plot. The color-coded circles represent the the product of $\frac{1}{\lambda} \frac{1}{T^{2}}$ and $\frac{dT}{d\log P}$. When circle value remains is the same, the polarization is similar. These two factors jointly determine the $I_{\rm ratio}$, which governs the single scattering polarization. A larger product of $\frac{1}{\lambda} \frac{1}{T^{2}}$ and $\frac{dT}{d\log P}$ leads to stronger single scattering polarization.