Fundamental properties of nearby stars and the consequences on DeltaY/DeltaZ

One of the greatest difficulties in astrophysics is the determination of the fundamental stellar parameters (FSPs), one of which is the initial mass fraction of helium (Y). However, given that Y can be measured spectroscopically in only a small percentage of stars, a linear relationship is assumed between Y and the mass fraction of metals (Z). This Y-Z relation is generally represented as Y=Yp+DY/DZxZ, with the value of the helium-to-metal enrichment ratio (DY/DZ) assumed as a constant. However, there is no fundamental reason for every star to have a Y value on a linear scale with Z. In this paper a method for determining the FSPs of nearby stars is presented that uses at the same time Mbol, Teff, and log g. One of these parameters is Y, which is used to determine the validity of the Y-Z relation. A new set of evolutionary tracks is created using the PGPUC stellar evolution code, which includes 7 masses (0.5parallaxes, and spectroscopic measurements of [Fe/H], Teff and g. The proposed method is compared to other techniques used to determine the FSPs, where one assumes an age of 5 Gyr for all nearby stars. This comparison demonstrates that the hypothesis regarding constant age leads to an underestimation of the Y value, especially for low metallicities. In addition, the suggested method is limited to masses above 0.60 Msun and requires high-precision measurements of spectroscopic surface gravities in order to obtain reliable results. Finally, estimating masses and ages assuming a Y-Z relation rather than a free Y value may induce average errors of approximately 0.02 Msun and 2 Gyr, respectively.