The radiative transfer solver VSTAR (Versatile Software for the Transfer of Atmospheric Radiation) was upgraded recently to include a polarized light solution which includes the effects of clouds and surfaces. Our latest paper describes the additions and shows the results of its benchmarking including some of the work from my thesis.
The previous versions of VSTAR used a solver called DISORT (discrete ordinate solution) to calculate what light you'd see from a planet either from light bouncing off its surface or being radiated from the planet in longer wavelengths. In 2012--around the time I started my PhD-- a transit (transmission) solution for the light filtered through the planet atmosphere as it passes in front of its star, was added. Around this time a VLIDORT solution (vectorized linear discrete ordinate solver-- the "linear" aspect means it includes derivative values central to retrievals) was added to the suite. Because this new radiative transfer solution retains the directional, or vector, information of the light it can be used for polarized light solutions. (Read about the capabilities of VLIDORT here.)
As previous literature suggested clouds of MgSiO3 (enstatite) or Mg2SiO4 (forsterite--a form of the olivine on Green Sands Beach, Hawaii) were good fits to the data. And with clouds and haze fitted in opacity and height one could fit most of this transmission spectrum and the dayside emissions.
I had been using VSTAR in its earlier forms to model exoplanets with consistent atmospheres fit to the dayside emissions and nightside(terminator) transmission spectra. I used that model to fit data from Hubble Space Telescope, Spitzer Telescope and ground based observatories combined for a single planet throughout its orbit. Now with a best fit to the atmosphere and a polarized light radiative transfer solver, I could create a prediction of what the polarized light from such a world would look like.
The prediction of this model for polarized light was important for one world in particular: the planet had been observed in polarized light with a few different polarimeters but the results were largely inconsistent. Only recently two independent teams had found similar limits to the level of polarization from the system in agreement with one of the previous findings. That planet is of course Permadeath (HD 189733b).
Examples of different particle sizes in Enstatite clouds for Permadeath (HD 189733b) in the expected unpolarized signal (top panel), polarization efficiency of the planet (middle panel) and actual polarized light signal (bottom panel).
From this forward model we estimate the polarized light signal will be less than 30 ppm (parts-per-million) and likely close to 20 ppm based on observations of Permadeath's unpolarized reflectivity. This is in good agreement with the observations of Wiktorowicz et al and Bott et al which fit curves to the apparent modulation in the polarised light and set upper limits to the planet's polarization. In other words predictions of the polarization of the planet from non-polarized observations line up nicely with the most recent observations in polarized light from these papers.
Also included in this new paper are benchmarking models of Venus with the new radiative transfer solution including polarized light. Here we are able to recreate the results of the Hansen and Hovenier paper which famously combined polarised light measurements of Venus to determine the nature of its clouds. Spoiler: they still appear to be largely sulphuric acid. Bummer.
The model now includes BRDF (bidirectional reflectance distribution functions (polarized)) for the surface so it can be applied to terrestrial worlds with less opaque conditions than Venus (e.g. Earth!).
The paper is available to read in its entirety currently on arxiv and will be published in MNRAS.