[Paper Review] The age of the most nearby star

A. Weiß, H. Schlattl|arXiv (Cornell University)|Jun 16, 1997

Stellar, planetary, and galactic studies3 citations

TL;DR

This paper investigates the accuracy of stellar age determination using solar evolution models fitted to observational data, including helioseismic p-mode frequencies and photospheric helium abundance. By comparing models with and without hydrogen-helium diffusion, the authors find that neglecting diffusion causes age errors up to 100%, while including it leads to ages ~10% too high, indicating fundamental limits in current modeling accuracy even for the Sun, the nearest and best-observed star.

ABSTRACT

We address the question how accurately stellar ages can be determined by stellar evolution theory. We select the star with the best observational material available - our Sun. We determine the solar age by fitting solar evolution models to a number of observational quantities including several obtained from helioseismology, such as photospheric helium abundance or p-mode frequencies. Different cases with respect to the number of free parameters and that of the observables to be fitted are investigated. Age is one of the free parameters determined by the procedure. We find that the neglect of hydrogen-helium-diffusion leads to ages deviating by up to 100% from the true, meteoritic solar age. Our best models including diffusion yield ages by about 10% too high. The implication for general stellar age determination is that a higher accuracy than that can not be expected, even with the most up-to-date models. Our results also confirm that diffusion as treated presently in solar models is slightly too effective.

Motivation & Objective

• To assess the precision of stellar age determination using solar evolution models.
• To evaluate the impact of hydrogen-helium diffusion on age estimates in solar models.
• To determine the limits of accuracy in age determination even for the Sun, the nearest and best-observed star.
• To test whether current stellar evolution models can achieve higher accuracy than ~10% for stellar ages.

Proposed method

• Fitting solar evolution models to observational data, including p-mode frequencies from helioseismology and photospheric helium abundance.
• Varying the number of free parameters and observables used in the fitting procedure to test sensitivity.
• Comparing models with and without hydrogen-helium diffusion to assess its impact on age determination.
• Using meteoritic age (4.567 Gyr) as the true reference for model validation.
• Adjusting model parameters to minimize residuals between observed and predicted values.
• Evaluating model performance across different configurations to identify systematic biases.

Experimental results

Research questions

• RQ1 How accurately can stellar ages be determined using current solar evolution models?
• RQ2 What is the effect of neglecting hydrogen-helium diffusion on solar age estimates?
• RQ3 To what extent do current models overestimate or underestimate the true solar age?
• RQ4 Can the inclusion of helioseismic data improve age determination accuracy?
• RQ5 What are the fundamental limitations in age determination accuracy, even for the Sun?

Key findings

• Neglecting hydrogen-helium diffusion in solar models leads to age estimates that deviate by up to 100% from the true meteoritic age.
• Models that include diffusion yield solar ages approximately 10% higher than the true age of 4.567 Gyr.
• The current treatment of diffusion in solar models is found to be slightly too effective, contributing to the overestimation of age.
• Even with the most up-to-date models and the best available observational data, age determination accuracy is fundamentally limited to about ±10%.
• The results confirm that stellar age determination cannot achieve higher accuracy than currently possible, even for the Sun.
• The study highlights that systematic errors from incomplete physics, particularly in diffusion, are the primary source of uncertainty in age estimation.