Disc dichotomy signature in the vertical distribution of [Mg/Fe] and the
  delayed gas infall scenario
  The analysis of the APOGEE data suggests the existence of a clear distinction
between two sequences of disc stars in the [$\alpha$/Fe] vs. [Fe/H] abundance
ratio space. We aim to test if the two-infall chemical evolution models
designed to reproduce these two sequences in the solar neighbourhood are also
capable to predict the disc bimodality observed in the vertical distribution of
[Mg/Fe] in APOGEE DR16 data. Along with the predicted chemical composition of
SSPs born at different Galactic times in the solar vicinity, we provide their
maximum vertical height |zmax| above the Galactic plane computed assuming the
relation between the vertical action and stellar age in thin disc stars. The
predicted vertical distribution of the [Mg/Fe] abundance ratio is in agreement
with the one observed combining the APOGEE DR16 data and the astroNN catalogue
(stellar ages, orbital parameters) for stars younger than 8 Gyr (only
low-$\alpha$ sequence stars). Including the high-$\alpha$ disc component, the
dichotomy in the vertical [Mg/Fe] abundance distribution is reproduced
considering the observational cut in the Galactic height of |z| < 2 kpc.
However, our model predicts a too flat growth of the |zmax| as a function of
[Mg/Fe] for high-$\alpha$ objects in contrast with the median values from
APOGEE data. Possible explanations for such a tension are: i) the data sample
with |z| < 2 kpc is more likely contaminated by halo stars, causing the median
values to be kinematically hotter, ii) external perturbations such as minor
mergers could have heated up the disc, and the heating of the orbits cannot be
modelled by only scattering processes. Assuming for the data a disc dissection
based on chemistry, the observed |zmax| distributions for high-$\alpha$ and
low-$\alpha$ sequences are in good agreement with our model predictions if we
consider in the calculation the errors in the vertical action estimates.
