# How Much Information Does the Sodium Doublet Encode? Retrieval Analysis of Non-LTE Sodium Lines at Low and High Spectral Resolutions

## TL;DR

This study investigates how much atmospheric information the sodium doublet lines encode in exoplanet transmission spectra, revealing limitations in current retrieval methods at different spectral resolutions and the challenges in distinguishing LTE from NLTE conditions.

## Contribution

The paper provides a comprehensive analysis of sodium line retrievals in exoplanet atmospheres, highlighting the limitations of current low- and high-resolution spectra in constraining atmospheric parameters and LTE/NLTE states.

## Key findings

- High-resolution spectra alone cannot precisely determine atmospheric pressure levels.
- Low-resolution retrievals face degeneracies due to Rayleigh scattering and normalization issues.
- Current data cannot reliably distinguish LTE from NLTE sodium line interpretations.

## Abstract

Motivated by both ground- and space-based detections of the sodium doublet in the transmission spectra of exoplanetary atmospheres, we revisit the theory and interpretation of sodium lines in non-local thermodynamic equilibrium (NLTE), where collisions are not efficient enough to maintain a Boltzmann distribution for the excited and ground states of the sodium atom. We consider non-Boltzmann distributions that account for the ineffectiveness of collisions. We analyze the sodium doublet in transmission spectra measured at low (HAT-P-1b, HAT-P-12b, HD 189733b, WASP-6b, WASP-17b and WASP-39b) and high (WASP-49b) spectral resolutions. Nested-sampling retrievals performed on low-resolution optical/visible transmission spectra are unable to break the normalization degeneracy if the spectral continuum is associated with Rayleigh scattering by small cloud particles. Using mock retrievals, we demonstrate that un-normalized ground-based, high-resolution spectra centered on the sodium doublet alone are unable to precisely inform us about the pressure levels probed by the transit chord and hence to identify the region (i.e., thermosphere, exosphere) of the atmosphere being probed. Retrievals performed on the HARPS transmission spectrum of WASP-49b support this conclusion. Generally, we are unable to distinguish between LTE versus NLTE interpretations of the sodium doublet based on the computed Bayesian evidence with the implication that LTE interpretations tend to under-estimate the temperature probed by the transit chord. With the current low-resolution data, the sodium line shapes are consistent with Voigt profiles without the need for sub-Lorentzian wings. The retrieved sodium abundances are consistent with being sub-solar to solar.