The model we are adopting is described by Ballero et al. (2007) and belongs to the category of fast dissipational collapse prior to the settling of the disc. It follows the trend of previous models by Matteucci & Brocato (1990) and Matteucci et al. (1999). The star-formation rate is proportional to the gas surface mass density of the disc:
where v is the star-formation efficiency, i.e. the inverse of the star-formation timescale. The stellar initial mass function (IMF) is parametrised as a power law of logarithmic index x:
which may differ among the various mass ranges. Finally, the bulge forms via infall of gas shed from the Galactic halo on a timescale t :
We updated the stellar lifetimes by adopting those of Kodama (1997) and we introduced the stellar yields published by Francois et al. (2004), which were calibrated in order to fit the chemical properties of the Solar neighbourhood. Following the photometric measurements of Zoccali et al. (2000) the IMF index for below MQ was set to x = 0.33. The Type-Ia supernova rate was computed following the singledegenerate scenario, according to Matteucci & Recchi (2001). Finally, we considered primary production of nitrogen from massive stars, as computed by Matteucci (1986), as opposed to purely secondary production, which is usually adopted in chemical-evolution models. We also introduced a supernova-driven wind in analogy with elliptical galaxies. To develop it, we supposed that the bulge lies at the bottom of the potential well of the Galactic halo, whose mass is M = 1012M© and whose effective radius is ~100 times the effective radius of the bulge's mass distribution. The binding energy of the bulge is then calculated following Bertin et al. (1992), who split the potential energy into two parts, one due to the interaction between the bulge gas and the bulge potential and the other to the interaction of the bulge gas with the potential well of the dark-matter halo of the Milky Way, which depends on the relative mass distribution. The thermal energy of the interstellar medium due to supernova explosions is given by
Eth,SNI + Eth,SNII = i e(t - t')RsNI/II(t')dt', (48.4)
where R is the rate of Type-Ia and Type-II supernovae, t' is the explosion time and e is the energy content of a supernova remnant, whose evolution is calculated following Cox (1972) and Cioffi & Shull (1998). When Eh.SNI/n = Eb.gas a
Figure 48.1. Left panel: the predicted metallicity distribution in our bulge reference model (x = 0.95 for M > M0, v = 20 Gyr-1, t = 0.1 Gyr) compared with the observed distributions (Zoccali et al. 2003; Fulbright et al. 2006). Right panel: the evolution of [O/Fe] and [Mg/Fe] versus [Fe/H] in the bulge for the reference model (solid line). A Solar-neighbourhood fiducial line (dotted line) is plotted for comparison. Data are taken from the infrared-spectroscopic database (Origlia et al, 2002; Origlia & Rich 2004; Origlia et al. 2005; Rich & Origlia 2005).
wind develops and deprives the bulge of all its gas, and the evolution is passive thereafter.
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