Determining the initial helium abundance of the Sun

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.