Elemental Abundances in Milky Way-like Galaxies from a Hierarchical Galaxy Formation Model

We develop a new method to account for the finite lifetimes of stars and trace individual abundances within a semi-analytic model of galaxy formation. At variance with previous methods, based on the storage of the (binned) past star formation history of model galaxies, our method projects the information about the metals produced by each simple stellar population (SSP) in the future. Using this approach, an accurate accounting of the timings and properties of the individual SSPs composing model galaxies is possible. We analyse the dependence of our chemical model on various ingredients, and apply it to six simulated haloes of roughly Milky Way mass and with no massive close neighbour at z=0. For all models considered, the [Fe/H] distributions of the stars in the disc component are in good agreement with Milky Way data, while for the spheroid component (whose formation we model only through mergers) these are offset low with respect to observational measurements for the Milky Way bulge. This is a consequence of narrow star formation histories, with relatively low rates of star formation. The slow recycling of gas and energy from supernovae in our chemical model has important consequences on the predicted star formation rates, which are systematically lower than the corresponding rates in the same physical model but with an instantaneous recycling approximation. The halo that resembles most our Galaxy in terms of its global properties also reproduces the observed relation between the average metallicity and luminosity of the Milky Way satellites, albeit with a slightly steeper slope.