[Paper Review] Kinetic equilibrium of iron in the atmospheres of cool stars III. The ionization equilibrium of selected reference stars

A. J. Korn, Jianrong Shi+1 more|ArXiv.org|Jun 17, 2003

Stellar, planetary, and galactic studiesPhysics and Astronomy32 references76 citations

TL;DR

This study determines the hydrogen collision scaling factor (S_H) for iron in cool stars using non-LTE line formation calculations and Hipparcos parallaxes to achieve ionization equilibrium between Fe I and Fe II. The optimal S_H = 3 minimizes discrepancies between spectroscopic and astrometric surface gravities, significantly improving metal-poor star abundance analyses and reducing systematic biases in stellar parameter determination.

ABSTRACT

Non-LTE line formation calculations of Fe I are performed for a small number of reference stars to investigate and quantify the efficiency of neutral hydrogen collisions. Using the atomic model that was described in previous publications, the final discrimination with respect to hydrogen collisions is based on the condition that the surface gravities as determined by the Fe I/Fe II ionization equilibria are in agreement with their astrometric counterparts obtained from HIPPARCOS parallaxes. Depending on the choice of the hydrogen collision scaling factor S_H, we find deviations from LTE in Fe I ranging from 0.00 (S_H = infinity) to 0.46 dex (S_H = 0 for HD140283) in the logarithmic abundances while Fe II follows LTE. With the exception of Procyon, for which a mild temperature correction is needed to fulfil the ionization balance, excellent consistency is obtained for the metal-poor reference stars if Balmer profile temperatures are combined with S_H = 3. The correct choice of collisional damping parameters ("van-der-Waals" constants) is found to be generally more important for these little evolved metal-poor stars than considering departures from LTE. For the Sun the calibrated value for S_H leads to average Fe I non-LTE corrections of 0.02 dex and a mean abundance from Fe I lines of log epsilon(Fe) = 7.49 \pm 0.08. We confront the deduced stellar parameters with comparable spectroscopic analyses by other authors which also rely on the iron ionization equilibrium as a gravity indicator. On the basis of the HIPPARCOS astrometry our results are shown to be an order of magnitude more precise than published data sets, both in terms of offset and star-to-star scatter.

Motivation & Objective

• To resolve uncertainties in hydrogen collision efficiency for iron in cool star atmospheres, particularly in metal-poor stars where photoionization dominates.
• To improve the accuracy of spectroscopic stellar parameters by minimizing biases from assuming LTE in iron ionization equilibrium.
• To calibrate the hydrogen collision scaling factor S_H using astrometric constraints from Hipparcos parallaxes.
• To assess the relative importance of non-LTE effects versus atomic damping parameters in determining iron abundances in metal-poor stars.
• To validate the method across a range of reference stars, including the Sun and extreme halo objects like HE 0107–5240.

Proposed method

• Performs non-LTE line formation calculations for Fe I using an atomic model incorporating collisional rates with neutral hydrogen.
• Employs high signal-to-noise, high-resolution échelle spectra to derive individual line profile fits and differential iron abundances.
• Uses Hipparcos parallaxes to determine astrometric surface gravities, which are then compared with gravities derived from Fe I/Fe II ionization equilibrium.
• Varies the hydrogen collision scaling factor S_H to find the value that minimizes the offset between spectroscopic and astrometric log g values.
• Applies Balmer profile temperatures as a temperature indicator and combines them with non-LTE iron ionization equilibrium to derive consistent stellar parameters.
• Validates results against published spectroscopic analyses and uses extreme halo stars (e.g., HE 0107–5240) to test the robustness of the S_H = 3 calibration.

Experimental results

Research questions

• RQ1 What is the optimal value of the hydrogen collision scaling factor S_H that achieves ionization equilibrium between Fe I and Fe II in metal-poor stars?
• RQ2 How does non-LTE affect the derived surface gravity and iron abundance when compared to LTE assumptions?
• RQ3 To what extent do atomic damping parameters (van der Waals constants) influence iron abundance determinations in metal-poor stars compared to non-LTE effects?
• RQ4 Can the combination of Balmer profile temperatures and non-LTE iron ionization equilibrium produce surface gravities consistent with Hipparcos parallaxes?
• RQ5 How does the S_H calibration perform across different metallicity regimes, including the most metal-poor stars?

Key findings

• The hydrogen collision scaling factor S_H is calibrated to 3, which minimizes the discrepancy between spectroscopic and astrometric surface gravities across the reference stars.
• For HD 140283, non-LTE corrections to Fe I abundances range from 0.00 dex (S_H = ∞) to 0.46 dex (S_H = 0), indicating strong non-LTE effects when hydrogen collisions are neglected.
• With S_H = 3, excellent ionization balance is achieved for metal-poor stars, except for Procyon, which requires a 90 K temperature correction (to 6600 K) to reconcile spectroscopic and astrometric constraints.
• The calibrated S_H = 3 value leads to a mean non-LTE correction of 0.02 dex for the Sun, yielding log ε(Fe) = 7.49 ± 0.08.
• The method reduces uncertainties in surface gravity and metallicity by an order of magnitude compared to previous LTE-based analyses, with lower scatter and offset.
• Non-LTE effects in Fe I reach a plateau below the metallicity of typical globular cluster giants, suggesting that the S_H = 3 calibration is robust across most of the Galactic metallicity range.