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

¹ Astronomical Observatory, Odessa National University, Shevchenko Park, 65014 Odessa, Ukraine
² Crimean Astrophysical Observatory, Nauchny 298409, Republic of Crimea

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 3 January 2026
Accepted: 3 March 2026

Abstract

Aims. The phosphorus abundance distribution in field stars as a function of metallicity reveals a complex pattern. The local thermodynamic equilibrium (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, many phosphorus-rich (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 non-local thermodynamic equilibrium (non-LTE) effects on the ultraviolet and infrared phosphorus lines in spectra of cool stars to test the robustness of the observed LTE phosphorus abundance distribution.

Methods. 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 non-LTE approximation. The model consists of 101 energy levels of P i and the ground level of P ii; 1070 transitions between mentioned levels were studied. The model was tested using the solar flux and intensity spectra, as well as the spectra of Procyon and σ Boo. Profiles of 14 phosphorus lines in the infrared regions and equivalent widths were analyzed. Our non-LTE phosphorus abundance in the Sun is (P/H) = 5.35 ±0.04 dex.

Results. Using our non-LTE model, we selected 12 ultraviolet and infrared phosphorus lines and calculated a grid of non-LTE corrections for the following parameter ranges: T_eff from 4000 to 6750 K, step 250 K; log g from 1 to 5 dex, step 1 dex; and V_t = 2 km s⁻¹, [Fe/H] from –3 to +0.5 dex, step 0.5 dex. The non-LTE corrections (Abundance_non−LTE – Abundance_LTE) were calculated for phosphorus abundance ratios of [P/Fe] = –0.4, 0.0, and +0.4 dex. For the Sun, the non-LTE correction is –0.08 dex.

Conclusions. The grid of the non-LTE 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. This sample also includes phosphorus-rich stars. Non-LTE 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. After corrections, the phosphorus abundance distribution became more compact in the low-metallicity range. Overall, the observed phosphorus abundance distribution can be described by the combined effect of phosphorus production in rotating massive stars, Type II supernovae explosions, and oxygen-neon-magnesium novae.