Polarimetric Modeling and Observations for the Jovian satellites

Photometric phase curves of airless Solar System objects exhibit a distinctive opposition effect, characterized by nonlinear brightening as phase angles approach backscattering. At phase angles less than approximately 20 degrees, polarimetric phase curves predominantly display a negative degree of linear polarization

These phenomena arise from electromagnetic wave scattering by discrete media of small particles, due to the interference of reciprocal rays, which travel along the same optical path, but in opposite directions. As such, the coherent backscattering makes the opposition phenomena depend on the medium properties, specifically on the size, refractive index, shape, and packing density of the scatterers in the medium. Incorporating coherent backscattering (CB) into radiative transfer (RT)  models provides a comprehensive modeling solution. In addition to coherent backscattering, nonspherical particles contribute to the negative degree of linear polarization.

In our research, we model photometric and polarimetric phase curves for two Jupiter’s satellites. We employ radiative-transfer coherent-backscattering (RT-CB, [1][2]) modeling with an ensembleaveraged scattering matrix. With this approach, parameterized phase matrix elements are utilized to replicate the observed low-phase-angle polarimetric phase curves for Io and the icy moon Ganymede [3]. Similar analyses have been earlier carried out for Europa [4]. We adjust the scattering matrix until the computations closely match the observed data, resulting in an ensemble-averaged scattering matrix for modeling polarimetric phase curves for these satellites. The scattering matrix can be further used to study the target’s surface regolith, and as such it will give new insight into the structure and composition of these objects.

We find a clear and distinctive difference in the polarimetric and photometric phase curves of the RT-CB models of Jupiter’s icy satellites. Europa and Ganymede exhibit similar linear polarimetric behavior, while Io’s results are much different. Despite Io and Europa sharing similar geometric albedos (A_g) of 0.63 and 0.67, respectively, their negative polarization branch (NPB) shape differ. The NPB of Ganymede (A_g = 0.43) resembles that of Europa morphologically, albeit being described by different parameters for the single-scattering properties. This discrepancy likely stems from the compositions of their surfaces, Europa primarily composed of H₂O ice, Ganymede containing H₂O ice and silicates, and Io composed of sulfuric/silicate materials. Polarimetric observations  indicated only slight or no dependence on wavelength, suggesting wide particle size distributions with different real parts of the refractive index Re(m). For Europa and Ganymede, Re(m) was approximately 1.3, while for Io, Re(m) exceeded 1.4. Numerical computations using the RT-CB method successfully demonstrate a match to the polarimetric observations and to the geometric albedos. Specifically, for Ganymede, the single-scattering albedo (ω) and mean free path length (kl = 2πl/λ_eff) are approximately 0.943 and 150, respectively, where λ_eff is the wavelength. For Io’s regolith, ω ≈ 0.979 and kl ≈ 40.

As future work, simulating light scattering from regolith that is modeled with specified physical properties and comparing the results with an ensemble-averaged scattering matrix can offer more valuable insights into various characteristics of the regoliths of icy satellites, including their scattering particle size distribution, packing factor, and potentially their mineral composition. The decomposition of ensemble-averaged scattering matrices into pure Mueller matrices [2] enables RT-CB computations for discrete random media of nonspherical particles. This decomposition will enable making conclusions about the structure and nature of regolith by comparing the RT-CB model results with observations

The RT-CB model, with photometric and polarimetric measurements of small phase angles, can be effectively utilized to model icy satellites and other airless objects based on ground-based observations. This is particularly useful as it enables modeling without expensive in-situ measurements as Solar System geometry often limits ground-based observations to small phase angles. 

 

[1] K. Muinonen et. al., ApJ 760, 118 (2012)

[2] K. Muinonen et al., present meeting

[3] N. Kiselev et al., Planet. Sci. J. 5, 10 (2024)

[4] N. Kiselev et al., Planet. Sci. J. 3, 134 (2022)