The helium abundance and ΔY/ΔZ in lower main-sequence stars

We use nearby K dwarf stars to measure the helium-to-metal enrichment ratio  Δ Y /Δ Z   , a diagnostic of the chemical history of the solar neighbourhood. Our sample of K dwarfs has homogeneously determined effective temperatures, bolometric luminosities and metallicities, allowing us to fit each star to the appropriate stellar isochrone and determine its helium content indirectly. We use a newly computed set of Padova isochrones which cover a wide range of helium and metal content.
Our theoretical isochrones have been checked against a congruous set of main-sequence binaries with accurately measured masses, to discuss and validate their range of applicability. We find that the stellar masses deduced from the isochrones are usually in excellent agreement with empirical measurements. Good agreement is also found with empirical mass-luminosity relations.
Despite fitting the masses of the stars very well, we find that anomalously low helium content (lower than primordial helium) is required to fit the luminosities and temperatures of the metal-poor K dwarfs, while more conventional values of the helium content are derived for the stars around solar metallicity.
We have investigated the effect of diffusion in stellar models and the assumption of local thermodynamic equilibrium (LTE) in deriving metallicities. Neither of these is able to resolve the low-helium problem alone and only marginally if the cumulated effects are included, unless we assume a mixing-length which is strongly decreasing with metallicity. Further work in stellar models is urgently needed.
The helium-to-metal enrichment ratio is found to be  Δ Y /Δ Z = 2.1 ± 0.9  around and above solar metallicity, consistent with previous studies, whereas open problems still remain at the lowest metallicities. Finally, we determine the helium content for a set of planetary host stars.