[Paper Review] The elemental composition of the Sun I. The intermediate mass elements Na to Ca

Pat Scott, N. Grevesse+7 more|Queensland's institutional digital repository (The University of Queensland)|May 1, 2014

Astro and Planetary SciencePhysics and Astronomy93 references116 citations

TL;DR

This paper presents a comprehensive re-evaluation of the solar abundances of intermediate-mass elements (Na to Ca) using a state-of-the-art 3D hydrodynamic solar atmosphere model, non-LTE line formation calculations, and the most up-to-date atomic data. The authors report revised 3D+NLTE solar abundances with improved accuracy, showing systematic reductions compared to previous 1D models, particularly the Holweger & Müller (1974) model, and provide a homogeneous, reliable reference for astrophysical abundance studies.

ABSTRACT

The composition of the Sun is an essential piece of reference data for astronomy, cosmology, astroparticle, space and geo-physics. This article, dealing with the intermediate-mass elements Na to Ca, is the first in a series describing the comprehensive re-determination of the solar composition. In this series we severely scrutinise all ingredients of the analysis across all elements, to obtain the most accurate, homogeneous and reliable results possible. We employ a highly realistic 3D hydrodynamic solar photospheric model, which has successfully passed an arsenal of observational diagnostics. To quantify systematic errors, we repeat the analysis with three 1D hydrostatic model atmospheres (MARCS, MISS and Holweger & Müller 1974) and a horizontally and temporally-averaged version of the 3D model ($\langle$3D$ angle$). We account for departures from LTE wherever possible. We have scoured the literature for the best transition probabilities, partition functions, hyperfine and other data, and stringently checked all observed profiles for blends. Our final 3D+NLTE abundances are: $\logε_{\mathrm{Na}}=6.21\pm0.04$, $\logε_{\mathrm{Mg}}=7.59\pm0.04$, $\logε_{\mathrm{Al}}=6.43\pm0.04$, $\logε_{\mathrm{Si}}=7.51\pm0.03$, $\logε_{\mathrm{P}}=5.41\pm0.03$, $\log ε_{\mathrm{S}}=7.13\pm0.03$, $\logε_{\mathrm{K}}=5.04\pm0.05$ and $\logε_{\mathrm{Ca}}=6.32\pm0.03$. The uncertainties include both statistical and systematic errors. Our results are systematically smaller than most previous ones with the 1D semi-empirical Holweger & Müller model. The $\langle$3D$ angle$ model returns abundances very similar to the full 3D calculations. This analysis provides a complete description and a slight update of the Na to Ca results presented in Asplund, Grevesse, Sauval & Scott (arXiv:0909.0948), with full details of all lines and input data.

Motivation & Objective

• To provide a more accurate and homogeneous determination of the solar abundances of intermediate-mass elements (Na to Ca) by re-evaluating all analysis ingredients.
• To reduce systematic uncertainties in solar abundance determinations by employing a realistic 3D hydrodynamic solar atmosphere model that accounts for granulation and convective motions.
• To quantify the impact of non-LTE effects and 3D atmospheric structure on elemental abundance calculations, improving consistency with observational diagnostics.
• To establish a benchmark dataset with rigorous line selection, atomic data, and uncertainty quantification for use across astrophysics, cosmology, and planetary science.

Proposed method

• Utilizes a highly realistic 3D hydrodynamic solar atmosphere model (based on radiation-hydrodynamics simulations) that successfully passes multiple observational diagnostics.
• Performs spectral line formation calculations using non-LTE (NLTE) corrections wherever possible, accounting for departures from local thermodynamic equilibrium in atomic level populations.
• Employs a stringent line selection process, rejecting blended or poorly characterized lines based on observed profile quality and atomic data reliability.
• Incorporates the most up-to-date and carefully vetted input data, including transition probabilities, hyperfine splitting parameters, and partition functions.
• Compares results across multiple models: full 3D, three 1D hydrostatic models (MARCS, MIST, Holweger & Müller 1974), and a 3D-averaged 1D model (⟨3D⟩) to assess systematic differences.
• Applies a comprehensive uncertainty budget that includes both statistical and systematic errors, derived from line-by-line analysis and model comparisons.

Experimental results

Research questions

• RQ1 How do 3D hydrodynamic models of the solar photosphere affect the derived abundances of intermediate-mass elements (Na to Ca) compared to traditional 1D models?
• RQ2 To what extent do non-LTE effects alter the inferred solar abundances for these elements, and how can they be accurately modeled?
• RQ3 What is the impact of improved atomic data—particularly hyperfine splitting and transition probabilities—on the final abundance determinations?
• RQ4 How do the abundances derived from a 3D model compare to those from a 1D-averaged version of the same 3D model, and what does this reveal about systematic model biases?
• RQ5 What is the most accurate, homogeneous, and reliable set of solar abundances for Na to Ca, given the latest observational and theoretical constraints?

Key findings

• The final recommended 3D+NLTE solar abundances are: log ε(Na) = 6.21 ± 0.04, log ε(Mg) = 7.59 ± 0.04, log ε(Al) = 6.43 ± 0.04, log ε(Si) = 7.51 ± 0.03, log ε(P) = 5.41 ± 0.03, log ε(S) = 7.13 ± 0.03, log ε(K) = 5.04 ± 0.05, and log ε(Ca) = 6.32 ± 0.03.
• The 3D+NLTE abundances are systematically lower than those derived from the 1D semi-empirical Holweger & Müller (1974) model, indicating that 1D models overestimate abundances due to incorrect treatment of atmospheric structure and non-LTE effects.
• The abundances derived from the horizontally and temporally averaged 3D model (⟨3D⟩) are very similar to those from the full 3D model, suggesting that the 3D effects are well-captured in the average and that 3D effects are not dominated by transient features.
• The study identifies and discards lines suspected of blending, based on profile quality and atomic data, leading to a more robust and reliable line list.
• The uncertainty estimates include both statistical and systematic components, providing a comprehensive error budget for each element.
• The results represent a significant refinement and update of the solar abundances for Na to Ca, building on but improving upon the Asplund et al. (2009) analysis with more advanced modeling and data.