The role of a top-heavy integrated galactic IMF on the chemical evolution of high-redshift starbursts
We apply a top-heavy integrated galactic initial mass function (IGIMF) to the chemical evolution of spheroids and compare our results with high redshift starburst galaxies. These objects are, in fact, very likely to be elliptical galaxies suffering their main burst of star formation. These bursts are very intense and more massive objects suffer more intense star formation than less massive ones (downsizing in star formation). The high star formation rate produces a galactic wind, due to stellar feedback, and devoids the galaxy of the gas residual from star formation. This happens sooner for more massive galaxies (inverse wind model), ensuring the reproduction of the mass-Z relation and the [$\alpha$/Fe]-mass relation in local ellipticals. We compute the chemical evolution, including also a detailed dust treatment, of $\alpha$-elements, Fe, C and N, and we compare our results with the available data for high redshift starburst galaxies. Our main conclusions are: i) the top-heavy IGIMF enhances the rate of star formation; in particular, different $\beta$ (parameter related to the slope of the embedded cluster mass function) determine different times for the occurrence of the galactic wind. The $\beta=1$ value is rejected since it produces models which do not satisfy the condition of the inverse wind model, whereas for $\beta>1$ the inverse wind is preserved. ii) Abundance data are in general better reproduced by models adopting the top-heavy IGIMF than a classical Salpeter IMF. iii) The abundance ratios of refractory elements relative to Fe can be explained only by assuming the presence of dust.