Delta Y/Delta Z from the analysis of local K dwarfs

Context. The stellar helium-to-metal enrichment ratio, Delta Y/Delta Z, is a widely studied astrophysical quantity. However, its value has still not been precisely constrained. Aims. This paper is focused on studying the main sources of uncertainty that affect the Delta Y/Delta Z ratio derived from the analysis of the low-main sequence (MS) stars in the solar neighborhood. Methods. The possibility of inferring the value of the helium-to-metal enrichment ratio from the study of low-MS stars relies on the dependence of the stellar luminosity and effective temperature on the initial helium and metal abundances. The Delta Y/Delta Z ratio is obtained by comparing the magnitude difference between the observed stars and a reference, theoretical zero age main sequence (ZAMS) with the related theoretical magnitude differences computed from a new set of stellar models with up-to-date input physics and a fine grid of chemical compositions. A Monte Carlo approach has been used to evaluate the impact of different sources of uncertainty, i.e. observational errors, evolutionary effects, systematic uncertainties of the models. As a check of the procedure, the method was applied to a different data set, namely the low-MS of the Hyades. Results. Once a set of ZAMS and atmosphere models had been chosen, we found that the inferred value of Delta Y/Delta Z is sensitive to the age of the stellar sample, even if we restricted the data set to low-luminosity stars. The lack of an accurate age estimate of low-mass field stars leads to underestimating the inferred Delta Y/Delta Z of similar to 2 units. On the contrary, the method firmly recovers the Delta Y/Delta Z value for unevolved samples of stars like the Hyades low-MS. Adopting a solar-calibrated mixing-length parameter and the PHOENIX GAIA v2.6.1 atmospheric models, we find Delta Y/Delta Z = 5.3 +/- 1.4 once the age correction has been applied. The Hyades sample provided a perfectly consistent value. Conclusions. We have demonstrated that assuming that low-mass stars in the solar neighborhood can be considered as unevolved does not necessarily hold, and it may indeed lead to a bias in the inferred Delta Y/Delta Z. The effect of the still poorly constrained efficiency of the superadiabatic convection and of different atmosphere models adopted to transform luminosities and effective temperature into colors and magnitudes are also discussed.