Fundamental properties of nearby stars and the consequences on ΔY/ΔZ

Context. One of the greatest difficulties in astrophysics is the determination of the fundamental stellar parameters, 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) from a canonical perspective of the chemical evolution of the galaxies. This Y–Z relation is generally represented as Y = Yp +Δ Y/ΔZ × Z, with the value of the helium-to-metal enrichment ratio (ΔY/ΔZ) assumed as a constant. However, there is no fundamental reason for every star to have a Y value on a linear scale with Z. Indeed, different ΔY/ΔZ values may be expected in different populations which have undergone different chemical enrichment histories. Aims. In this paper a new method for determining the fundamental stellar parameters of nearby stars is presented that uses at the same time Mbol, Teff ,a nd log. One of these parameters is Y, which is used to determine the validity of the Y–Z relation. Methods. A new set of evolutionary tracks is created using the PGPUC stellar evolution code, which includes 7 masses (0.5 ≤ M/M� ≤ 1.1), 7 helium abundances (0.230 ≤ Y ≤ 0.370), and 12 metallicities (1.6 × 10 −4 ≤ Z ≤ 6.0 × 10 −2 ) for solar-scaled chemical compositions ([α/Fe] = 0.0). The suggested method is tested using two different spectroscopic databases of nearby main sequence stars with precise parallaxes, and spectroscopic measurements of [Fe/H], Teff and . Results. The proposed method is compared to other techniques used to determine the fundamental stellar parameters, 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 M� and requires high-precision measurements of spectroscopic surface gravities in order to obtain reliable results. Finally, estimating