How do wavelength correlations affect transmission spectra? Application of a new fast and flexible 2D Gaussian process framework to transiting exoplanet spectroscopy

Abstract

The use of Gaussian processes (GPs) is a common approach to account for correlated noise in exoplanet time series, particularly for transmission and emission spectroscopy. This analysis has typically been performed for each wavelength channel separately, with the retrieved uncertainties in the transmission spectrum assumed to be independent. However, the presence of noise correlated in wavelength could cause these uncertainties to be correlated, which could significantly affect the results of atmospheric retrievals. We present a method that uses a GP to model noise correlated in both wavelength and time simultaneously for the full spectroscopic dataset. To make this analysis computationally tractable, we introduce a new fast and flexible GP method that can analyse 2D datasets when the input points lie on a (potentially non-uniform) 2D grid - in our case a time by wavelength grid - and the kernel function has a Kronecker product structure. This simultaneously fits all light curves and enables the retrieval of the full covariance matrix of the transmission spectrum. Our new method can avoid the use of a `common-mode' correction, which is known to produce an offset to the transmission spectrum. Through testing on synthetic datasets, we demonstrate that our new approach can reliably recover atmospheric features contaminated by noise correlated in time and wavelength. In contrast, fitting each spectroscopic light curve separately performed poorly when wavelength-correlated noise was present. It frequently underestimated the uncertainty of the scattering slope and overestimated the uncertainty in the strength of sharp absorption peaks in transmission spectra. Two archival VLT/FORS2 transit observations of WASP-31b were used to compare these approaches on real observations. Our method strongly constrained the presence of wavelength-correlated noise in both datasets, and significantly different constraints on atmospheric features such as the scattering slope and strength of sodium and potassium features were recovered.