3D NLTE Sodium abundances in late-type stars. Abundance corrections and synthetic spectra

Abstract

Neutral sodium is an important tracer of the Galactic chemical evolution, a powerful diagnostic of different stellar populations, and the subject of detailed studies of exoplanet atmospheres via transmission spectroscopy. This work aims to study and quantify the errors in stellar analyses of Na I lines caused by the use of one-dimensional (1D) hydrostatic model atmospheres and the assumption of local thermodynamic equilibrium (LTE). We studied the line formation of nine Na I lines in FGK dwarfs and giants via, for the first time, 3D non-LTE (NLTE) radiative transfer post-processing with the code Balder on 3D radiation hydrodynamic stellar atmospheres from the Stagger grid spanning Teff= 4000 to 6500 K, log g = 1.5 to 5.0, and [Fe/H]=-4 to +0.5. We find that the 3D NLTE abundance corrections relative to 1D LTE tend to be negative, and more positive than the corresponding 1D NLTE corrections. This reflects more efficient overionisation in the steeper temperature gradient of the 3D models. The corrections are typically less severe than -0.1 dex for weak lines, but become much larger for saturated lines in low-gravity giants (log g < 2.0), even reaching -0.7 dex. However, for the D resonance lines, the 3D NLTE corrections relative to 1D LTE become slightly positive at the lowest metallicities in our grid, typically around +0.05 dex at [Fe/H]=-4. We make our 3D NLTE grid, together with interpolation routines based on radial basis functions and fully connected feedforward neural networks, publicly available. This will enable more accurate determination of sodium abundances in present and forthcoming stellar spectroscopic surveys, particularly for metal-poor stars, as well as a better characterisation of the Na I D lines in exoplanet atmospheres.

Figures (15)

• Figure 1: Kiel diagram illustrating the Stagger-grid nodes at which the 3D NLTE computations have been performed, for values of [Fe/H] described by the colorbar. The models at [Fe/H] $=0.0$ and $+0.5$ in the yellow-shaded area were previously published in Canocchi2024b.
• Figure 2: Synthetic line profiles for the Na i line at 5682 Å, computed with Balder in 1D LTE (dashed red line), 1D NLTE (dashed blue line), 3D LTE (solid red line), and 3D NLTE (solid blue line) for a cool metal-poor red giant star (left), a solar metallicity F-dwarf (middle), and a metal-rich lower main-sequence dwarf (right). 1D $v_\mathrm{mic}=1.0$ km s$^{-1}$, and a sodium abundance corresponding to [Na/Fe]$=+0.5$ are adopted. No rotational or macroturbulent broadening has been applied. Note that the y-axis has a different scale in each panel.
• Figure 3: Comparison of interpolation models with verification models (not included in the training set) for the Na i line at 5682 Å. The verification models were tailored to specific stars, indicated by the stellar parameters: $T_\mathrm{eff}, \log g,$ [Fe/H], and $A\mathrm{(Na)}$. Note that the range of the y-axis differs between panels.
• Figure 4: Comparison of the REWs in 1D NLTE and 1D LTE for four selected Na i lines for a turn-off star (top) and a giant (bottom). The REWs are computed assuming [Na/Fe]$=0.0$ and $v_\mathrm{mic}=1.0$ km s$^{-1}$. Black points show the REWs obtained in this work, while the red stars and blue squares denote results from Lind2011 and Lind2022, respectively, as indicated in the legend.
• Figure 5: Spatially resolved difference between the reduced equivalent width in NLTE and LTE at disc centre intensity for different Na i lines in a 3D model with $T_\mathrm{eff} = 4978.17$ K, $\log g=2.0$, [Fe/H]$=-2.0$ and $A$(Na)=4.22.