Of 'cocktail parties' and exoplanets: data analysis in exoplanetary spectroscopy

The field of transiting extrasolar planets and especially the study of their atmospheres is one of the youngest and most dynamic subjects in current astrophysics. To study the atmospheres of those foreign worlds, we typically require a 10^−4 to 10^−5 level of accuracy in flux. Currently available instruments were not designed with these precisions in mind. Calibrating an instrument without knowing its response function at the required level has become the central challenge of exoplanetary spectroscopy. A variety of parametric correction models are used in the literature. These show high degeneracies between the scientific result and the instrument correction used. Hence, an unbiased analysis of the data at the 10^−4 level of accuracy is difficult and the cause of much controversy in the field. In this thesis, I present three novel ways of de-trending exoplanetary data non-parametrically, i.e. without requiring auxiliary or prior information of the instrument or data. This removes correctional bias. These techniques are based on: 1) unsupervised machine-learning algorithms (Chapter 3) to de-convolve non-Gaussian sig- nals, i.e. the systematic noise, from the desired astrophysical feature. Such a ‘blind’ signal de-mixing is commonly known as the ‘Cocktail Party problem’ in signal-processing. I demon- strate its capabilities using spectroscopic Hubble/NICMOS measurements of the hot-Jupiters HD189733b and XO1b and demonstrate the removal of stellar noise in Kepler photometry (Chapter 4). 2) Fourier/Wavelet based self-filtering algorithms based on the concepts of sparsity of the exoplanetary signal in the frequency domain (Chapter 5). The robustness of this method is demonstrated for very low signal-to-noise conditions using four nights of ground-based observa- tions of the secondary eclipse of HD189733b in Chapter 6. Here I unambiguously confirm the detection of a strong non-LTE methane emission in the L-band and can test for residual telluric contamination using this method. 3) an Independent-component-analysis supported wavelet masking of multivariate data, which extends the non-parametric machine learning to Gaussian noise dominated data applications, Chapter 7. In the light of ever increasing data analysis challenges, as we probe ever smaller signals and fainter targets, techniques such as the ones presented in this thesis are paramount to the success of exoplanetary characterisation in the future