\Delta Y/ \Delta Z from the analysis of local K dwarfs
  The stellar helium-to-metal enrichment ratio, \Delta Y/\Delta Z, is a widely
studied astrophysical quantity. However, its value is still not precisely
constrained. This paper is focused on the study of the main sources of
uncertainty which affect the \Delta Y/\Delta Z derived from the analysis of the
low-main sequence (MS) stars in the solar neighborhood. The possibility to
infer the value of \Delta Y/\Delta Z from the study of low-MS stars relies on
the dependence of the stellar luminosity and effective temperature on the
initial Y and Z. 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 on the result of different sources of
uncertainty, i.e. observational errors, evolutionary effects, systematic
uncertainties of the models. As a check of the procedure, the method has been
applied to a different data set, namely the low-MS of the Hyades. Once a set of
ZAMS and atmosphere models have 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 an underestimate of the inferred
\Delta Y/\Delta Z of ~2 units. On the contrary the method firmly recovers the
\Delta Y/\Delta Z value for not evolved samples of stars such as the Hyades
low-MS. Adopting a solar calibrated mixing-length parameter and the PHOENIX
GAIA v2.6.1 atmospheric models, we found \Delta Y/\Delta Z = 5.3 +/- 1.4 once
the age correction has been applied. The Hyades sample provided a perfectly
consistent value.
