The G-dwarf problem in the Galactic spheroid

This paper has two parts: one about observational constraints, and the other about chemical evolution models. In the first part, the empirical differential metallicity distribution (EDMD) is deduced from two different samples involving (i) 268 K-giant bulge stars [Sadler, E.M., Rich, R.M., Terndrup, D.M., 1996. AJ 112, 171], and (ii) 149 globular clusters [Mackey, A.D., van den Bergh, S., 2005. MNRAS 360, 631], in addition to previous results (Caimmi, R., 2001b, AN 322, 241 (C01)) related to (iii) 372 solar neighbourhood halo subdwarfs [Ryan, S.G., Norris, J.E., 1991. AJ 101, 1865]. Under the assumption that each distribution is typical for the corresponding subsystem, the EDMD of the Galactic spheroid is determined by weighting the mass. The empirical age-metallicity relation (EAMR) involving absolute ages is deduced from recent results related to a homogeneous sample of globular clusters [De Angeli, F., Piotto, G., Cassisi, S., et al., 2005. AJ 130, 116]. In the second part, models of chemical evolution for the Galactic halo and bulge are computed, assuming the instantaneous recycling approximation. The EDMD data are fitted, to an acceptable extent, by simple models of chemical evolution implying both homogeneous and inhomogeneous star formation, provided that star formation is inhibited during halo formation and enhanced during bulge formation, with respect to the disk solar neighbourhood, taken to be representative of the whole disk. The initial mass function (IMF) is assumed to be a universal power law, which implies the same value of the true yield in different subsystems. The theoretical differential metallicity distribution (TDMD) is first determined for the halo and the bulge separately, and then for the Galactic spheroid by weighting the mass. The EAMR cannot be fitted into the Simple model that implies homogeneous star formation, but shows a non-monotonic trend characterized by large dispersion. On the other hand, simple models involving inhomogeneous star formation yield a theoretical age-metallicity relation (TAMR) which reproduces the data to an acceptable extent. For gas ouflow from the proto-halo, acceptable models give rise to different predictions in different alternatives. If the Galactic spheroid and disk underwent decoupled chemical evolution, i.e. no gas exchange between the related reservoirs, less than one third of the bulge mass outflowed from the proto-halo. If the Galactic spheroid and disk underwent coupled chemical evolution, i.e. some gas exchange between the related reservoirs, the existence of an unseen baryonic halo (or equivalent amount of gas lost by the Galaxy) with mass comparable to bulge mass, is necessarily needed. In this view, the outflowing proto-halo gas which remains bound to the Galaxy, produces both the bulge and the disk.