Theoretical investigation of transition data of astrophysical importance in neutral sulphur

TL;DR

This work addresses the need for accurate atomic data for neutral sulphur (S I) to support stellar spectroscopy and non-LTE analyses by providing a large, relativistic dataset of $E1$ transition rates and oscillator strengths for $1730$ transitions among $107$ levels. The authors apply fully relativistic multi-configuration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) methods to generate two data sets: ab initio results and fine-tuned results anchored to experimental energies from the NIST ASD, with a gauge-based accuracy framework using the gauge difference $d\tilde{T}$ and the cancellation factor CF. Key findings include that roughly 16% of ab initio and 24% of fine-tuned transitions achieve the high-accuracy class A–B, energy levels are significantly improved via fine-tuning (RMS errors dropping from $\sim188$ cm$^{-1}$ to $\sim20$ cm$^{-1}$), and that fine-tuning enhances consistency between Babushkin and Coulomb gauges, particularly for weaker transitions. The data, benchmarked against prior theory and measurements (e.g., ZB2006, DH2008, NIST ASD), have important implications for non-LTE modelling and solar sulphur abundance studies, and are disseminated via CDS for broad astrophysical use.

Abstract

Accurate and comprehensive atomic data are essential for the modelling of stellar spectra. Uncertainties in the oscillator strengths of specific lines used for abundance analyses directly translate into uncertainties in the derived elemental abundances; incomplete or biased atomic data sets can impart significant errors in non-local thermodynamic equilibrium (non-LTE) modelling. Theoretical calculations of atomic data are therefore crucial to supplement the limited experimental results. In this work, we present extensive atomic data, including oscillator strengths, transition rates, and lifetimes for 1730 electric-dipole (E1) transitions among 107 levels in neutral sulphur (S I) using the multi-configuration Dirac-Hartree-Fock (MCDHF) and relativistic-configuration-interaction (RCI) methods. These levels belong to the configurations $\mathrm{3p^3np (n=3-7)}$, $\mathrm{3p^3nf (n=4,5)}$, $\mathrm{3s3p^5}$, $\mathrm{3p^3ns (n=4-7)}$, and $\mathrm{3p^3nd (n=3-6)}$. The accuracy of the computed transition rates is assessed by combining the comparison of the differences in transition rates between the Babushkin and Coulomb gauges with a cancellation-factor (CF) analysis. Approximately 16% of the ab initio results achieved an accuracy classification of A-B, corresponding to uncertainties within 10%, as defined by the Atomic Spectra Database of the National Institute of Standards and Technology (NIST ASD). Applying a fine-tuning technique was found to significantly improve the accuracy of the results in the Coulomb gauge, thereby improving the consistency between the Babushkin and Coulomb gauges; about 24% of the fine-tuned transition data are assigned to the accuracy classes A-B.

Figures (5)

• Figure 1: Energy differences as a function of excitation energies provided by NIST ASD. The dashed black and red lines are the linear fit to the data from ab initio (black plus) and fine-tuning (red plus) calculations, respectively. The inset in the upper right shows an enlarged view for $E_\mathrm{NIST} > 5 \times 10^{4}~\mathrm{cm}^{-1}$.
• Figure 2: Left: Comparison of log($gf$) between Babushkin and Coulomb gauges for ab initio (black plus) and fine-tuned (red plus) results, respectively. Insets (a1) and (a2) show the histograms of the log($gf$) differences for transitions with log($gf$) $\geq -2$ and log($gf$) < $-2$, respectively. Right: Comparison of log($gf$) between ab initio and fine-tuned calculations for Babushkin (black diamond) and Coulomb gauges (red hexagon), respectively. Insets (b1) and (b2) show the histograms of the log($gf$) differences for transitions with log($gf$) $\geq -3$ and log($gf$) < $-3$, respectively.
• Figure 3: Comparison of log($gf$) from the current study with those from previous works. Left: ZB2006 2006JPhB...39.2861Z. Middle: DH2008 2008ADNDT..94..561D. Right: NIST ASD NIST_ASD. The data in NIST ASD were compiled from various sources, including 1968ZNatA..23.1707M1994ApJ...428..393B1996AA...309..991B1998ApJ...502.1010BRZerne_1997FROESEFISCHER2006607 and 2006JPhB...39.2861Z. Babushkin results from present ab initio (black plus) and fine-tuned (red plus) RCI calculations are used in the comparison. The inset figures show the histograms of the distribution of the number of transitions for the differences in log($gf$). Note that the y-axis range is consistent across all plots in Figures \ref{['fig:gf']} and \ref{['fig:tr']}.
• Figure 4: Upper panel: Comparison of theoretical log($gf$) values for transitions with log($gf$)$\mathrm{_{RCI}}$ > $-$3.0 and $\Delta$log($gf$) > 1.0 dex shown in the left and middle panels of Figure \ref{['fig:tr']}. Middle panel: Scatter plot of d$T$ values. Lower panel: Scatter plot of CF values. The dashed lines in the middle panel and the lower panel represent d$T$ = 0.1 and CF = 0.05, respectively. ZB2006: 2006JPhB...39.2861Z; DH2008: 2008ADNDT..94..561D.
• Figure 5: Upper: Comparison of fine-tuned lifetimes (ft) between Babushkin (B) and Coulomb (C) gauges. Lower: Comparison of fine-tuned lifetimes with other theoretical results. ZB2006: 2006JPhB...39.2861Z; DH2008 2008ADNDT..94..561D. ZB2006/ft, B/B: the Babushkin gauge of ZB2006 divided by the Babushkin gauge of fine-tuned lifetimes. The three dashed grey lines represent $\tau/\tau_\mathrm{ft}$ = 0.9, 1.0, and 1.1, respectively.