Three-dimensional continuum radiative transfer of polarized radiation in exoplanetary atmospheres

Abstract

Context. Polarimetry is about to become a powerful tool for determining the atmospheric properties of exoplanets. For example, recent observations of the WASP-18 system allowed the polarized flux resulting from scattering in the atmosphere of WASP-18b to be constrained. To provide the basis for the interpretation of such observational results and for predictive studies to guide future observations, sophisticated analysis tools are required. Aims. Our goal is to develop a radiative transfer tool that contains all the relevant continuum polarization mechanisms for the comprehensive analysis of the polarized flux resulting from the scattering in the atmosphere of, on the surface of, and in the local planetary environment (e.g., planetary rings, exomoons) of extra-solar planets. Furthermore, our goal is to avoid common simplifications such as locally plane-parallel planetary atmospheres, the missing cross-talk between latitudinal and longitudinal regions, or the assumption of either a point-like star or plane-parallel illumination. Methods. As a platform for the newly developed numerical algorithms, we use the 3D Monte Carlo radiative transfer code POLARIS. The code is extended and optimized for the radiative transfer in exoplanetary atmospheres. We investigate the reflected flux and its degree of polarization for different phase angles for a homogeneous cloud-free atmosphere and an inhomogeneous cloudy atmosphere. Our results are compared with already existing results to verify the implementations. To take advantage of the 3D radiative transfer and to demonstrate the potential of the code, the impact of an additional circumplanetary ring on the reflected polarized flux is studied. Therefore, a simple ring model with water-ice particles is used and various inclination angles, optical depths and viewing angles are investigated. Results. The considered test cases show a good agreement with already existing results. The presence of a circumplanetary ring consisting of small water-ice particles has a noticeable impact on the reflected polarized radiation. In particular, the reflected flux strongly increases at larger phase angles if the planetary orbit is seen edge-on because the considered particles tend to scatter forwards. In contrast, the degree of polarization decreases at these phase angles. Conclusions. We present a polarization radiative transfer tool in which all relevant contributions to the reflected polarized continuum flux are considered. In a case study, we investigated the impact of a planetary ring on the net polarization signal.