Determining the initial helium abundance of the Sun

TL;DR

This paper develops a method to determine the Sun's initial helium abundance by analyzing the dependence of helium content on model parameters, using helioseismic data and accounting for uncertainties, resulting in a robust estimate.

Contribution

It introduces a new approach to estimate the Sun's initial helium abundance that minimizes uncertainties from model parameters and compares results for standard and non-standard solar models.

Findings

Initial helium abundance is estimated as 0.278 ± 0.006 for standard models.

For non-standard models with extra mixing, the initial helium is 0.273 ± 0.006.

The derived initial helium abundance is higher than estimates from low-metallicity solar models.

Abstract

We determine the dependence of the initial helium abundance and the present-day helium abundance in the convective envelope of solar models ($\yim$ and $\ysm$ respectively) on the parameters that are used to construct the models. We do so by using reference standard solar models to compute the power-law coefficients of the dependence of $\yim$ and $\ysm$ on the input parameters. We use these dependencies to determine the correlation between $\yim$ and $\ysm$ and use this correlation to eliminate uncertainties in $\yim$ from all solar model input parameters except the microscopic diffusion rate. We find an expression for $\yim$ that depends only on $\ysm$ and the diffusion rate. By adopting the helioseismic determination of solar surface helium abundance, $\ysms= 0.2485\pm0.0035$, and an uncertainty of 20% for the diffusion rate, we find that the initial solar helium abundance, $\yims$, is $0.278 \pm 0.006$ independently of the reference standard solar models (and particularly on adopted the solar abundances) used in the derivation of the correlation between $\yim$ and $\ysm$. When non-standard solar models with extra mixing are used, then we derive $\yims = 0.273 \pm 0.006$. In both cases, the derived $\yims$ value is higher than that directly derived from solar model calibrations when the low metalicity solar abundances (e.g. by Asplund et al.) are adopted in the models.