In any science it is often prudent to conduct simplified tests early on to get a sense of what can be learned. In polarimetry (see: Wiki or Video) we’ve certainly done this on many counts but as we’re now capable of building fairly robust polarimeters it seems we need to start examining the details.
My doctoral thesis included a comparison of spectral and photometric (non polarized) measurements of light from the exoplanet HD 189733b and compared them to polarimetric observations of the system. The atmospheric model retrieved with non-polarized photometry and spectroscopy was then used to create a forward model of the polarized light from the system. This allowed us to compare the light we expect to see for a given atmosphere in polarized light to the light we measured for it (see Bailey, Kedziora-Chudczer & Bott 2018) in a way that has never been done before: normally measurements are only fit to a simplified model.
When we took measurements with our polarimeter of yet another hot Jupiter system, WASP 18, we saw what to the naked eye might look like a signal. If confirmed this would have been the first detection of polarized light from an exoplanet. Further analysis revealed that this was not the case: this was a non-detection, although we were able to produce an upper limit for the signal from the planet.
Our unbinned polarimetric measurements of the combined WASP 18 system (star and planet). At 0 and 1 the planet is between you and the star (new phase); at 0.5 on the x-axis the planet is on the far side (in this case behind the star, full phase). The red lines are the best fit for a hot Jupiter that produced Rayleigh scattering in optimised conditions. The top panel and bottom panel are just Stokes vectors— that tells us about the particular direction of the polarization (so comparing them we could tell what the orbit of an unknown planet was… if it fit a red line…).
Because we were able to compare this to atmosphere models based on recent observations of WASP 18 in non-polarized light (see: Kedziora-Chudczer et al 2018, in review) we were able to rule out certain scenarios in the atmosphere (namely an optically thick Rayleigh scattering cloud). This shows the utility of polarimetry as a method to detect planets and constrain their orbits but also as a complementary observational approach: without combining these observations we would not be able to rule out certain types of clouds!
One thing we examine is whether we have evidence of the transit measured around new phase. Here the planet occults the limb of the star where the polarized light vectors are strongest, the directions of the vectors then don’t cancel out (aren’t symmetric) so you get a net polarization from the star. You’ll notice the data points in the last image are noisy around new phase, that’s because they’re much shorter (in duration). We don’t see evidence of the transit in the data, but through modelling find we are unlikely to.
To do this with any confidence though, we needed to consider the details. This was initially driven by a desire to be certain of a detection if there was one, but in the end we also hoped it would provide a roadmap for exoplanet polarimetric measurements. We examined effects of transit, where the planet upsets the apparent symmetry of the stellar disk so there is a polarization from the star; tides, where the planet or star can become asymmetric (as was measured for the first time through rotational distortions by Cotton et al 2017), circumstellar dust which can impart noise and produce an offset to the signal on top of the ISM; and provided a confidence test for different levels of signal to determine whether we were fitting to noise.
We caution the community in selecting targets too near their stars for the decreased likelihood of reflective cloud formation, relying on estimates for signals for much cooler planets, and, of course, against ignoring the sources of noise.
However the message of this paper is, overall, encouraging! We find that, as suggested by photometric studies of the past (e.g. Nymeyer et al 2011), the planet may be quite dark on the dayside. So while this system may not be capable of producing a strong signal in visible wavelength reflected polarized light, other planets with more reflective clouds may be. With only a couple high precision polarimeters on Earth currently operating on 4 meter class telescopes we should not be discouraged: there are likely better candidates out there for polarimetry. We just need to be careful to consider their atmospheric chemistry and the many sources of noise which might affect our measurements.
The paper will be published in AJ and is available as preprint here: https://arxiv.org/abs/1811.06527
Using non-polarized observations of the system that were fit to atmospheric retrieval models, we create forward polarized light models for different cloud scenarios which might be present on the planet. The top panel is the relative flux, telling you in part how good each planet cloud scenario is at reflecting light; the middle panel is the polarization, telling you how good each cloud scenario is at polarizing light; the bottom panel is the main event: the polarized light signal for the system, or how much polarized light you could measure compared to how much light you get from the system (in parts-per-million, the best polarimeters can measure down to a couple ppm). The optically thick Rayleigh cloud is the strongest signal, and since we don’t see that strong a signal (60 ppm) in our measurements, we can probably rule out this scenario for the planet.