Determining the initial helium abundance of the Sun

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.Comment: 18 pages, including 3 figures and 2 tables. Accepted for publication in Ap