Polarization of Rotationally Oblate Self-luminous Exoplanets with Anisotropic Atmospheres

The young self-luminous giant exoplanets are expected to be oblate in shape, owing to the high rotational speeds observed for some objects. Similar to the case of brown dwarfs, the thermal emission from these planets should be polarized by scatterings of molecules and condensate cloud particles, and the rotation-induced asymmetry of the planet's disk would yield to net nonzero detectable polarization. Considering an anisotropic atmosphere, we present here a three-dimensional approach to estimating the disk-averaged polarization that arises due to the oblateness of the planets. We solve the multiple-scattering vector radiative transfer equations at each location on the planet's disk and calculate the local Stokes vectors, and then calculate the disk-integrated flux and linear polarization. For a cloud-free atmosphere, the polarization signal is observable only in the visible wavelength region. However, the presence of clouds in the planetary atmospheres leads to a detectable amount of polarization in the infrared wavelength region where the planetary thermal emission peaks. Considering the different broadband filters of the SPHERE-IRDIS instrument of the Very Large Telescope, we present generic models for the polarization at different wavelength bands as a function of their rotation period. We also present polarization models for the exoplanets β Pic b and ROXs 42B b, as two representative cases that can guide future observations. Our insights into the polarization of young giant planets presented here would be useful for the upcoming polarimetric observations of the directly imaged planets.