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 ( Y ini and Y surf , respectively) on the parameters that are used to construct the models. We do so by using reference standard solar models (SSMs) to compute the power-law coefficients of the dependence of Y ini and Y surf on the input parameters. We use these dependencies to determine the correlation between Y ini and Y surf and use this correlation to eliminate uncertainties in Y ini from all solar model input parameters except the microscopic diffusion rate. We find an expression for Y ini that depends only on Y surf and the diffusion rate. By adopting the helioseismic determination of solar surface helium abundance, Y surf ☉ = 0.2485 ± 0.0035, and an uncertainty of 20% for the diffusion rate, we find that the initial solar helium abundance, Y ini ☉ , is 0.278 ± 0.006 independently of the reference SSMs (and particularly on the adopted solar abundances) used in the derivation of the correlation between Y ini and Y surf . When non-SSMs with extra mixing are used, then we derive Y ini ☉ = 0.273 ± 0.006. In both cases, the derived Y ini ☉ value is higher than that directly derived from solar model calibrations when the low-metallicity solar abundances (e.g., by Asplund et al.) are adopted in the models.