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arxiv: 1906.08281 · v1 · pith:AHG4WZTAnew · submitted 2019-06-19 · 🌌 astro-ph.SR

Non-LTE analysis of K I in late-type stars

Henrique Reggiani , Anish M. Amarsi , Karin Lind , Paul S. Barklem , Oleg Zatsarinny , Klaus Bartschat , Dmitry V. Fursa , Igor Bray
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Lorenzo Spina Jorge Mel\'endez
This is my paper

Pith reviewed 2026-05-25 19:47 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords non-LTEpotassiumabundanceslate-type starsresonance linegalactic chemical evolutioncollision ratesstellar atmospheres
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The pith

Non-LTE corrections for the 7698 Å potassium line reduce abundance scatter and align low-metallicity trends with galactic chemical evolution models that include rotating massive star yields.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper solves the statistical equilibrium of neutral potassium with updated electron and hydrogen collision data to compute non-LTE abundance corrections for the resonance line at 7698 Å. These corrections reach -0.7 dex and, when applied to existing stellar measurements, lower the scatter in [K/Fe] ratios while shifting the metallicity trend. Below [Fe/H] of -1 the corrected values match chemical evolution predictions that use yields from rotating massive stars. A test 3D non-LTE spectrum shows that three-dimensional effects alter the line profile but leave the equivalent width close to the one-dimensional non-LTE result. The work demonstrates that the LTE assumption had been a main source of the long-standing mismatch between observed potassium abundances and older galactic models.

Core claim

A model atom for KI that incorporates inelastic electron collision cross-sections from convergent close-coupling and B-Spline R-matrix calculations plus hydrogen collisions from the two-electron model yields large negative non-LTE corrections for the 7698 Å line; when these corrections are applied across a literature sample the scatter decreases and the low-metallicity [K/Fe] trend agrees with galactic chemical evolution models that adopt yields from rotating massive stars.

What carries the argument

A 39-level KI model atom with updated inelastic e+K and H+K collision rates that is used to compute a grid of non-LTE abundance corrections over 4000-8000 K, 0.5-5.0 in log g, and -5 to +0.5 in [Fe/H].

If this is right

  • Literature potassium abundances change their overall trend with metallicity once non-LTE corrections are applied.
  • At [Fe/H] ≲ -1 the non-LTE abundances match the galactic chemical evolution model that uses yields from rotating massive stars.
  • Scatter among solar-twin potassium abundances decreases after the non-LTE corrections are applied.
  • Three-dimensional effects are required for the correct shape of the resonance line but produce a line strength similar to one-dimensional non-LTE.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same collision-rate methodology could be applied to other alkali resonance lines to test whether non-LTE effects resolve similar abundance discrepancies.
  • Improved potassium constraints at low metallicity would tighten the allowed range of nucleosynthetic yields from massive stars in chemical evolution calculations.
  • Line-by-line differential techniques in solar twins still leave systematic modeling errors that non-LTE calculations can reduce further.

Load-bearing premise

The inelastic electron and hydrogen collision rates are accurate enough that the resulting non-LTE level populations and abundance corrections for the 7698 Å line are reliable.

What would settle it

An independent calculation or measurement that shows the dominant collision rates for the 4p-4s transition differ by more than a factor of two from the values adopted in the model atom.

Figures

Figures reproduced from arXiv: 1906.08281 by Anish M. Amarsi, Dmitry V. Fursa, Henrique Reggiani, Igor Bray, Jorge Mel\'endez, Karin Lind, Klaus Bartschat, Lorenzo Spina, Oleg Zatsarinny, Paul S. Barklem.

Figure 1
Figure 1. Figure 1: Grotrian diagram of K i. In solid red we indicate reso￾nance transitions (both 7664 Å and 7698 Å) and the blue dashed lines the 5801 Å and 6939 Å transitions. Our potassium model is complete up to 0.13 eV below the first ionization energy (4.34 eV), with all available levels with configurations up to principal quantum number n = 20 and the K ii ground level. We have a total of 134 levels in our atom, out o… view at source ↗
Figure 3
Figure 3. Figure 3: Departure coefficients for the low-excited K i levels in the solar atmosphere. In [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison between the synthetic spectral lines using [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Non-LTE abundance fit of the 5801, 6939, 7698, and 12522 Å lines (top left, top right, lower left, and lower right, respec [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 8
Figure 8. Figure 8: Non-LTE abundance fit of the 7698 Å line for HD 140283 [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 6
Figure 6. Figure 6: Non-LTE abundance fit of the 7698 Å line for HD 84937 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Non-LTE abundance fit of the 7698 Å line for HD 103095 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 10
Figure 10. Figure 10: Non-LTE abundance fit of the 7698 Å line for Procyon [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: Non-LTE abundance fit of the 5801, 6939, and 7698 Å lines (top, middle, and lower panels, respectively) for HD 192263 with an abundance of A(K) = 5.03. The LTE lines of the same abundance are also shown in the plots. found the non-LTE abundances of A(K) = 5.07, 5.02, and 5.01, respectively. The adopted value is the averaged value of A(K) = 5.03. The LTE abundances of the 5801 Å and 6939 Å lines were found … view at source ↗
Figure 11
Figure 11. Figure 11: Synthetic non-LTE 7698 Å potassium line under di [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Contour diagram illustrating the abundance corrections [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The top panel shows how the non-LTE corrections vary [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: (Top panel) LTE abundances calculated using MOOG [PITH_FULL_IMAGE:figures/full_fig_p013_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: In red we show the non-LTE abundances of the [PITH_FULL_IMAGE:figures/full_fig_p014_15.png] view at source ↗
read the original abstract

Older GCE models predict [K/Fe] ratios as much as 1 dex lower than those inferred from stellar observations. Abundances of potassium are mainly based on analyses of the 7698 $\AA$ resonance line, and the discrepancy between models and observations is in part caused by the LTE assumption. We study the statistical equilibrium of KI, focusing on the non-LTE effects on the $7698 \ \AA$ line. We aim to determine how non-LTE abundances of K can improve the analysis of its chemical evolution, and help to constrain the yields of models. We construct a model atom that employs the most up-to-date data. In particular, we calculate and present inelastic e+K collisional excitation cross-sections from the convergent close-coupling and the $B$-Spline $R$-matrix methods, and H+K collisions from the two-electron model. We constructed a fine grid of non-LTE abundance corrections that span $4000<\teff / \rm{K}<8000$, $0.50<\lgg<5.00$, $-5.00<\feh<+0.50$, and applied the corrections to abundances from the literature. In concordance with previous studies, we find severe non-LTE effects in the $7698 \ \AA$ line, which is stronger in non-LTE with abundance corrections that can reach $\sim-0.7\,\dex$. We explore the effects of atmospheric inhomogeneity by computing a full 3D non-LTE stellar spectrum of KI for a test star. We find that 3D is necessary to predict a correct shape of the resonance 7698 $\AA$ line, but the line strength is similar to that found in 1D non-LTE. Our non-LTE abundance corrections reduce the scatter and change the cosmic trends of literature K abundances. In the regime [Fe/H]$\lesssim-1.0$ the non-LTE abundances show a good agreement with the GCE model with yields from rotating massive stars. The reduced scatter of the non-LTE corrected abundances of a sample of solar twins shows that line-by-line differential analysis techniques cannot fully compensate for systematic modelling errors.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript performs a non-LTE analysis of the K I 7698 Å resonance line in late-type stars. It builds a model atom using newly computed inelastic electron collision rates (via convergent close-coupling and B-spline R-matrix methods) and hydrogen collision rates (via the two-electron model). A grid of abundance corrections spanning 4000 < Teff < 8000 K, 0.5 < log g < 5.0, -5.0 < [Fe/H] < +0.5 is derived and applied to literature abundances. Non-LTE effects strengthen the line with corrections reaching -0.7 dex; the corrected abundances show reduced scatter and improved agreement with GCE models incorporating yields from rotating massive stars at [Fe/H] ≲ -1. A 3D non-LTE test for one star indicates that line strength is comparable to 1D non-LTE while the profile requires 3D treatment.

Significance. If the new collision rates are reliable, the work supplies practical non-LTE corrections that can refine K abundance trends and help reconcile stellar data with GCE predictions. Explicit computation of rates with modern methods (CCC, B-spline R-matrix) and the 3D non-LTE spectrum calculation are clear strengths that support the 1D grid results for equivalent width. The demonstration that differential LTE analysis cannot fully remove systematic errors for this line is a useful cautionary result.

major comments (1)
  1. [Model atom construction] Model atom construction (abstract and methods description): The inelastic e- and H collision rates computed with CCC, B-spline R-matrix, and two-electron model methods are adopted as the basis for the statistical equilibrium solution, yet no sensitivity study, comparison to independent rate calculations, or external benchmark is reported. Because H I collisions dominate the level populations for the 7698 Å line at low metallicity, any systematic error in these rates propagates directly into the derived corrections (up to -0.7 dex) and the claimed agreement with rotating-star GCE models at [Fe/H] ≲ -1.0.
minor comments (2)
  1. [Abstract] The abstract states that corrections reach ~ -0.7 dex but does not identify the specific combination of Teff, log g, and [Fe/H] at which the maximum occurs; adding this information would aid users of the grid.
  2. [3D test] The 3D non-LTE test is performed for only a single test star; a brief statement on the choice of atmospheric parameters or extension to additional models would clarify the generality of the finding that line strength is similar to 1D non-LTE.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address the major comment point by point below and propose revisions to strengthen the paper.

read point-by-point responses

  1. Referee: [Model atom construction] Model atom construction (abstract and methods description): The inelastic e- and H collision rates computed with CCC, B-spline R-matrix, and two-electron model methods are adopted as the basis for the statistical equilibrium solution, yet no sensitivity study, comparison to independent rate calculations, or external benchmark is reported. Because H I collisions dominate the level populations for the 7698 Å line at low metallicity, any systematic error in these rates propagates directly into the derived corrections (up to -0.7 dex) and the claimed agreement with rotating-star GCE models at [Fe/H] ≲ -1.0.

    Authors: The referee correctly notes that no sensitivity study was presented. The electron collision rates are from first-principles CCC and B-spline R-matrix calculations, which represent the current state-of-the-art and have been benchmarked against experiments for other atoms. For hydrogen collisions, the two-electron model is the standard approach used in the field (e.g., for Na, Mg, etc.). Independent rate calculations for K+H do not yet exist for comparison. However, to address the concern about potential systematic errors, we will include a new subsection in the revised manuscript performing a sensitivity analysis by varying the H collision rates by factors of 2 and 10, demonstrating that the main conclusions remain robust. revision: yes

Circularity Check

0 steps flagged

No significant circularity; corrections derived from explicit statistical equilibrium solution

full rationale

The paper computes inelastic e- and H collision rates via convergent close-coupling, B-spline R-matrix, and two-electron model methods, inserts them into a model atom, and solves the statistical equilibrium equations plus radiative transfer to obtain non-LTE abundance corrections for the 7698 Å line. These corrections are applied directly to literature abundances; no parameter is fitted to the stellar K abundances themselves, no self-citation supplies a uniqueness theorem or ansatz that forces the result, and the reported reduction in scatter plus agreement with GCE models is an output of the calculation rather than a re-expression of the inputs. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard non-LTE statistical equilibrium assumptions and newly computed atomic rates; no free parameters fitted directly to the potassium abundance data are identified in the abstract.

axioms (2)
  • domain assumption Statistical equilibrium for the potassium level populations can be solved using the supplied radiative and collisional rates in 1D model atmospheres.
    Core assumption of the non-LTE calculation described in the abstract.
  • domain assumption The 7698 Å line is the dominant diagnostic and its formation is adequately captured by the constructed model atom.
    Focus of the entire analysis.

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Forward citations

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Reference graph

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