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Phosphorus in cool stars of various metallicities: The non-local thermodynamic equilibrium consideration

S. M. Andrievsky, S. A. Korotin

Abstract

The phosphorus abundance distribution in field stars as a function of metallicity reveals a complex pattern. The LTE data for [P/Fe] in the low-metallicity range are sparse and scattered around [P/Fe]~ 0 dex. Near [Fe/H]~ -2 dex, the relative abundance [P/Fe] increases and reaches a maximum value of around [Fe/H]~ -1 dex. In this domain, P-rich stars and (super)phosphorus-rich stars are observed; the [P/Fe] value can exceed 1 dex. Until now, no attempts have been made to study the NLTE effects on the ultraviolet and infrared phosphorus lines in spectra of cool stars to test the robustness of the observed LTE phosphorus abundance distribution. We developed an atomic model of P I that can be used to analyze phosphorus lines in the spectra of cool dwarfs and giants in the NLTE approximation. The model was tested using the solar flux and intensity spectra, as well as the spectra of Procyon and sigma Boo. Profiles of 14 phosphorus lines in the infrared regions and equivalent widths were analyzed. Our NLTE phosphorus abundance in the Sun is (P/H)=5.35+/-0.04 dex. Using our NLTE model, we selected 12 ultraviolet and infrared phosphorus lines and calculated a grid of NLTE corrections for the following parameter ranges: Teff from 4000 to 6750 K, step 250 K; log g from 1 to 5 dex, step 1 dex; and Vt = 2 km/s, [Fe/H] from -3 to +0.5 dex, step 0.5 dex. The NLTE corrections were calculated for phosphorus abundance ratios of [P/Fe]=-0.4, 0.0, +0.4 dex. For the Sun, the NLTE correction is -0.08 dex. The grid of the NLTE corrections, as well as the direct line profile synthesis, were used to refine the literature data on the phosphorus abundance in metal-poor, intermediate-deficient, and solar-metallicity stars. NLTE corrections do not qualitatively alter the overall phosphorus abundance distribution over a wide metallicity range, and do not change the characteristic pattern of phosphorus-rich stars.

Phosphorus in cool stars of various metallicities: The non-local thermodynamic equilibrium consideration

Abstract

The phosphorus abundance distribution in field stars as a function of metallicity reveals a complex pattern. The LTE data for [P/Fe] in the low-metallicity range are sparse and scattered around [P/Fe]~ 0 dex. Near [Fe/H]~ -2 dex, the relative abundance [P/Fe] increases and reaches a maximum value of around [Fe/H]~ -1 dex. In this domain, P-rich stars and (super)phosphorus-rich stars are observed; the [P/Fe] value can exceed 1 dex. Until now, no attempts have been made to study the NLTE effects on the ultraviolet and infrared phosphorus lines in spectra of cool stars to test the robustness of the observed LTE phosphorus abundance distribution. We developed an atomic model of P I that can be used to analyze phosphorus lines in the spectra of cool dwarfs and giants in the NLTE approximation. The model was tested using the solar flux and intensity spectra, as well as the spectra of Procyon and sigma Boo. Profiles of 14 phosphorus lines in the infrared regions and equivalent widths were analyzed. Our NLTE phosphorus abundance in the Sun is (P/H)=5.35+/-0.04 dex. Using our NLTE model, we selected 12 ultraviolet and infrared phosphorus lines and calculated a grid of NLTE corrections for the following parameter ranges: Teff from 4000 to 6750 K, step 250 K; log g from 1 to 5 dex, step 1 dex; and Vt = 2 km/s, [Fe/H] from -3 to +0.5 dex, step 0.5 dex. The NLTE corrections were calculated for phosphorus abundance ratios of [P/Fe]=-0.4, 0.0, +0.4 dex. For the Sun, the NLTE correction is -0.08 dex. The grid of the NLTE corrections, as well as the direct line profile synthesis, were used to refine the literature data on the phosphorus abundance in metal-poor, intermediate-deficient, and solar-metallicity stars. NLTE corrections do not qualitatively alter the overall phosphorus abundance distribution over a wide metallicity range, and do not change the characteristic pattern of phosphorus-rich stars.
Paper Structure (11 sections, 15 figures, 2 tables)

This paper contains 11 sections, 15 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Phosphorus abundance in the Sun
  3. Phosphorus atomic model
  4. Spectral line synthesis
  5. Phosphorus abundance in the solar atmosphere. Our non-LTE result
  6. Testing the P i model using spectra of the stars
  7. Grid of the non-LTE corrections
  8. Discussion
  9. Conclusion
  10. Data availability
  11. Grid of the non-LTE corrections.

Figures (15)

  • Figure 1: Compiled LTE data on phosphorus abundance in the stars of various metallicities. Caffau2011 -- filled black circles, Roederer2014 -- open triangles, Caffau2016 -- filled black asterisks, Maas2019 -- filled blue asterisks, Maas2022 -- open circles, SadakaneNishimura2022 -- open asterisks, Nandakumar2022 -- filled blue circles, Brauner2023 -- filled red triangles, Barbuy2025a -- filled green asterisks, Barbuy2025b -- filled green circles.
  • Figure 2: Electronic level and transition diagram for the phosphorus atomic model.
  • Figure 3: Left panel: $b$ factors in the solar atmosphere. Right panel: Change with optical depth in the ratio, $S/B$, between the source function and Planck function for IR lines. The arrows mark the depth of formation of the cores of some phosphorus lines.
  • Figure 4: Same as Fig. \ref{['b_sun']} but for Procyon. The locations of the UV line formation are also indicated.
  • Figure 5: Observed (Kurucz1984, open circles) and synthetic profiles of the phosphorus lines for the Sun (non-LTE profiles -- solid line, LTE profiles calculated with the same phosphorus abundance -- dashed line).
  • ...and 10 more figures