Galactic Archaeology with asteroseismic ages: evidence for delayed gas
  infall in the formation of the Milky Way disc
  Precise stellar ages from asteroseismology have become available and can help
setting stronger constraints on the evolution of the Galactic disc components.
Recently, asteroseismology has confirmed a clear age difference in the solar
annulus between two distinct sequences in the [$\alpha$/Fe] versus [Fe/H]
abundance ratios relation: the high-$\alpha$ and low-$\alpha$ stellar
populations. We aim at reproducing these new data with chemical evolution
models including different assumptions for the history and number of accretion
events. We tested two different approaches: a revised version of the
`two-infall' model where the high-$\alpha$ phase forms by a fast gas accretion
episode and the low-$\alpha$ sequence follows later from a slower gas infall
rate, and the parallel formation scenario where the two disc sequences form
coevally and independently. The revised `two-infall' model including
uncertainties in age and metallicity is capable of reproducing: i) the
[$\alpha$/Fe] vs. [Fe/H] abundance relation at different Galactic epochs, ii)
the age$-$metallicity relation and the time evolution [$\alpha$/Fe]; iii) the
age distribution of the high-$\alpha$ and low-$\alpha$ stellar populations, iv)
the metallicity distribution function. The parallel approach is not capable of
properly reproduce the stellar age distribution, in particular at old ages. In
conclusion, the best chemical evolution model is the revised `two-infall' one,
where a consistent delay of $\sim$4.3 Gyr in the beginning of the second gas
accretion episode is a crucial assumption to reproduce stellar abundances and
ages.
