  We investigated the theoretical biases affecting the asteroseismic grid-based
estimates of stellar parameters in the presence of a mismatch between the heavy
element mixture of observed stars and stellar models. We performed a controlled
simulation adopting effective temperature, [Fe/H], average large frequency
spacing, and frequency of maximum oscillation power as observational
constraints. Synthetic stars were sampled from grids of stellar models computed
with different [alpha/Fe] values from 0.0 to 0.4. The mass, radius, and age of
these objects were then estimated by adopting a grid of models with a fixed
[alpha/Fe] value of 0.0. The experiment was repeated assuming different sets of
observational uncertainties. In the reference scenario, we adopted an
uncertainty of 1.5% in seismic parameters, 50 K in effective temperature, and
0.05 dex in [Fe/H]. A higher uncertainty in the atmospheric constraints was
also adopted in order to explore the impact on the precision of the
observations of the estimated stellar parameters. Our simulations showed that
estimated parameters are biased up to 3% in mass, 1.5% in radius, and 4% in age
when the reference uncertainty scenario was adopted. These values correspond to
45%, 48%, and 16% of the estimated uncertainty in the stellar parameters. These
biases in mass and radius disappear when adopting larger observational
uncertainties because of the possibility of the fitting algorithm exploring a
wider range of possible solutions. However, in this scenario, the age is
significantly biased by -8%. Finally, we verified that the stellar mass,
radius, and age can be estimated with a high accuracy by adopting a grid with
the incorrect value of [alpha/Fe] if the metallicity [Fe/H] of the target is
adjusted to match the Z in the fitting grid. In this scenario, the maximum bias
in the age was reduced to 1.5%.
