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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 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. 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 dependency 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. 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. Our analysis sets further constraints on the semi-analytical models and, at large, on possible metal enrichment scenarios for the Sculptor dwarf spheroidal galaxy.