Separating Signal from Systematics: Characterising Exoplanet Atmospheres using 2D Gaussian Processes

Abstract

Our capabilities to characterise the atmospheres of exoplanets have undergone a seismic shift over the past few years. The exquisite precision and stability of the James Webb Space Telescope (JWST) has already led to countless ground-breaking discoveries within the field - with many more likely to come throughout its lifetime. This has allowed us to understand extrasolar gas giants in unprecedented detail and has enabled us to push towards ever smaller worlds with the hope of eventually studying true Earth analogues in other Solar Systems. As we push the limits of our observing facilities, our understanding of their instruments must increase in step to ensure we are recovering true exoplanetary signals and not confusing atmospheric properties with instrumental systematics. This thesis presents new statistical techniques which have been developed to robustly account for various sources of correlated noise in both ground- and space-based observations of transiting exoplanets. In the first project, I identify a Gaussian process (GP) optimisation yet to be applied within astronomy, and use it to efficiently scale GPs to two-dimensional dataset sizes typical of exoplanet time-series. Combined with gradient-based MCMC methods, this can be used to joint-fit spectroscopic time-series observations of transiting exoplanets, allowing correlations in the noise of these data to be modelled across both time and wavelength. I use simulated observations to demonstrate the importance of accounting for wavelength-correlated noise, demonstrating that atmospheric constraints can be biased if wavelength correlations are ignored. I show that ground-based observations from the Very Large Telescope of the hot Jupiter WASP-31b display wavelength-correlations which could lead to erroneous detections of atmospheric hazes if not correctly accounted for.

The second project presents the first analysis of three JWST mid-infrared photometric time-series observations of the rocky exoplanet, LHS 1140c, as it passes behind its host star. These observations constrain the dayside brightness temperature of the planet, which is compared to a range of forward models, in order to determine whether atmospheric absorption or heat redistribution is taking place on the planet, searching for the presence of an atmosphere. However, we find the observations are most consistent with a low-albedo, bare rock surface without an atmosphere. In this chapter, I also introduce a new GP-based statistical framework to analyse photometric time-series, which joint-fits the pixel time-series and can weight away from systematics which affect individual pixels. On simulated data, this can outperform standard analysis techniques in the scenario where an individual pixel is contaminated by systematics. On the JWST observations it recovered a similar eclipse depth to a standard approach using aperture extraction, further backing-up the result, but it may help resolve issues in the analysis of similar observations of different targets which were more systematics-contaminated.

The final project introduces a range of novel GP optimisations for two-dimensional datasets, which provide a substantial performance boost to the methods introduced in the previous two chapters, along with having a range of other potential applications. These optimisations largely combine Kronecker product-based linear algebra techniques to kernel functions which can be efficiently optimised for one-dimensional datasets using celerite. This allows them to be scaled to two-dimensional datasets, while retaining flexible kernel functions, significantly outperforming current state-of-the-art GP optimisations in performance without introducing approximations.

The combination of these three projects represents substantial progress in the application and optimisation of two-dimensional Gaussian processes to exoplanet time-series. This thesis presents new, sophisticated tools to robustly account for complex systematics present in real observations. The dramatic reductions in runtime achieved through various optimisations and parameter inference procedures should help to make these methods accessible to the wider astronomical community, and permits the scaling of these techniques to ever more ambitious problems.