Chemical evolution of Local Group dwarf galaxies in a cosmological context - I. A new modelling approach and its application to the Sculptor dwarf spheroidal galaxy

We present a new approach for chemical evolution modelling, specifically designed to investigate the chemical properties of dwarf galaxies in a full cosmological framework. In particular, we focus on the Sculptor dwarf spheroidal galaxy, for which a wealth of observational data exists, as a test bed for our model. We select four candidate Sculptor-like galaxies from the satellite galaxy catalogue generated by implementation of a version of the Munich semi-analytic model for galaxy formation on the level 2 Aquarius dark matter simulations and use the mass assembly and star formation histories predicted for these four systems as an input for the chemical evolution code. We follow explicitly the evolution of several chemical elements, both in the cold gas out of which the stars form and in the hot medium residing in the halo. We take into account in detail the lifetimes of stars of different initial masses, the distribution of the delay times for Type Ia supernova explosions and the dependence of the stellar yields from the initial metallicity of the stars. We allow large fractions of metals to be deposited into the hot phase, either directly as stars die or through reheated gas flows powered by supernova explosions. We find that, in order to reproduce both the observed metallicity distribution function and the observed abundance ratios of long-lived stars of Sculptor, large fractions of the reheated metals must never re-enter regions of active star formation. With this prescription, all the four analogues to the Sculptor dwarf spheroidal galaxy extracted from the simulated satellites catalogue on the basis of luminosity and stellar population ages are found to reasonably match the detailed chemical properties of real Sculptor stars. However, all model galaxies do severely underestimate the fraction of very metal poor stars observed in Sculptor. Our analysis thus sets further constraints on the semi-analytical models and, at large, on possible metal enrichment scenarios for the Sculptor dwarf spheroidal galaxy.