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.