Addressing wavelength-correlated systematics in exoplanet transmission spectroscopy: a 2D Gaussian Process approach

TL;DR

This work addresses wavelength-correlated systematics in ground-based exoplanet transmission spectroscopy by adopting a two-dimensional Gaussian Process (2D GP) that models correlations in both time and wavelength using a LuasKernel. Applied to TOI-4153b observations from the 2 m Himalayan Chandra Telescope, the authors construct a 2D input grid from spectroscopic bins and fit a 2D transit mean function $T(cphi,clambda,t)$ with shared hyperparameters across wavelengths, performing MAP optimization followed by four MCMC chains with the NUTS sampler. The analysis yields consistent posterior estimates for $r_p/r_\ast$ and a detrended, flatter transmission spectrum compared to 1D, independently-fitted approaches, with a Transmission Spectroscopic Metric around $4$ indicative of a non-detectable atmospheric feature given the data. This demonstrates the 2D GP method's capacity to mitigate complex systematics and improve atmospheric retrievals, particularly for smaller or cooler planets, and paves the way for incorporating additional auxiliary inputs to further refine measurements.

Abstract

Ground-based transmission spectroscopy is often dominated by systematics, which obstructs our ability to leverage the advantages of larger aperture sizes compared to space-based observations. These systematics could be time-correlated, uniform across all spectroscopic light curves, or wavelength-correlated, which could significantly affect the characterization of exoplanet atmospheres. Gaussian Processes were introduced in transmission spectroscopy by Gibson et al. (2012) to model correlated systematics in a non-parametric way. The technique uses auxiliary information about the observation and independently fits each spectroscopic light curve to provide robust atmospheric retrievals. However, this method assumes that the uncertainties in the transmission spectrum are uncorrelated in wavelength, which can cause discrepancies and degrade the precision of atmospheric retrievals. To address this limitation, we explore a 2D GP framework formulated by Fortune et al. (2024) to simultaneously model time- and wavelength-correlated systematics. We present its application to ground-based observations of TOI-4153b obtained using the 2-m Himalayan Chandra Telescope (HCT). As we move towards detecting smaller and cooler planets, developing new methods to address complex systematics becomes increasingly essential.

Figures (5)

• Figure 1: White light curve analysis of TOI-4153b using 1D GP
• Figure 2: Posterior distributions for $r_p/r_\ast$ (rho) from 4 independent MCMC chains. The consistent overlapping contours and quantiles across chains indicate convergence of the sampling process.
• Figure 3: 2D input data with predicted 2D transit model and residual noises. In each plot, the actual data is scaled and over-plotted in white for the first spectroscopic light curve.
• Figure 4: Spectroscopic light curve analysis of TOI-4153b using 2D GP. The central wavelength of each spectroscopic bin is annotated above its corresponding light curve.
• Figure 5: Comparison between transmission spectra of TOI-4153b obtained by 2D GP analysis using luas (left) and by independently modeling each spectroscopic light curve using PyLightcurve (right)