Retrieving Temperatures and Abundances of Exoplanet Atmospheres with High-resolution Cross-correlation Spectroscopy

Abstract

High-resolution spectroscopy (R ≥ 25, 000) has recently emerged as one of the leading methods for detecting atomic and molecular species in the atmospheres of exoplanets. However, it has so far been lacking a robust method to extract quantitative constraints on the temperature structure and molecular/atomic abundances. In this work, we present a novel Bayesian atmospheric retrieval framework applicable to high-resolution cross-correlation spectroscopy (HRCCS) that relies on the cross-correlation between data and models for extracting the planetary spectral signal. We successfully test the framework on simulated data and show that it can correctly determine Bayesian credibility intervals on atmospheric temperatures and abundances, allowing for a quantitative exploration of the inherent degeneracies. Furthermore, our new framework permits us to trivially combine and explore the synergies between HRCCS and low-resolution spectroscopy (LRS) to maximally leverage the information contained within each. This framework also allows us to quantitatively assess the impact of molecular line opacities at high resolution. We apply the framework to VLT CRIRES K-band spectra of HD 209458 b and HD 189733 b and retrieve abundant carbon monoxide but subsolar abundances for water, which are largely invariant under different model assumptions. This confirms previous analysis of these datasets, but is possibly at odds with detections of H 2 O at different wavelengths and spectral resolutions. The framework presented here is the first step toward a true synergy between space observatories and ground-based high-resolution observations.

Detection of Fe i in the atmosphere of the ultra-hot Jupiter WASP-121b, and a new likelihood-based approach for Doppler-resolved spectroscopy

“…In addition to applying the standard cross-correlation methods to our data, we also directly compute a full likelihood function inspired by the approach of Brogi & Line (2019). This enables us to explore and compare different model templates using principled statistical techniques.…”

“…Here, we show that we can compute a likelihood map directly from the cross-correlation map, as well as quickly compute the log likelihood for use in model fitting. We also provide a generalised version of the likelihood mapping derived in Brogi & Line (2019), which has the added advantage of explicitly accounting for time-and wavelength-dependent uncertainties. We start with a standard Gaussian likelihood function, with uncertainties that vary in time and wavelength:…”

“…Nonetheless, in practice setting α = 1 assumes one knows the scale height of the atmosphere, or that it is incorporated into the parameterisation of the model. This is of course the standard approach taken for general model fitting, and the one adopted by Brogi & Line (2019). We note that recent work by Gandhi et al (2019) has explored fitting for an α-like term using the Brogi & Line (2019) framework.…”

“…This is of course the standard approach taken for general model fitting, and the one adopted by Brogi & Line (2019). We note that recent work by Gandhi et al (2019) has explored fitting for an α-like term using the Brogi & Line (2019) framework. We choose to fit for α as a free parameter, in part because we are searching for features that are potentially in the exosphere of the planet, where we cannot assume a hydrostatic atmosphere.…”

A weak spectral signature of water vapour in the atmosphere of HD 179949 b at high spectral resolution in the L band

“…The first method used was to remove the linear relationship with the exponential of the airmass, directly following the de-trending method implemented by BR14. The second de-trending algorithm used here follows directly steps 3 -7 from that used in Brogi & Line (2019) as shown in Fig. 1.…”