Chemical evolution of the Galactic bulge: different stellar populations and possible gradients

Context. The recent although controversial discovery of two main stellar populations in the Galactic bulge, one metal-poor with a spheroid kinematics and the other metal-rich with a bar-like kinematics, suggests a revision of the classical model for bulge formation. Aims. We aim at computing in detail the chemical evolution of the Galactic bulge in order to explain the existence of the two main stellar populations. We also plan to explore the possible existence of spatial abundance gradients inside the bulge. Methods. To do that, we adopt a chemical evolution model that follows the evolution of several chemical species (from H to Ba) and takes into account both infall and outflow of gas. We assume that the metal-poor population formed first and on a short timescale, in agreement with previous models, while the metal-rich population formed later and out of the enriched gas either left from the formation of the previous one or originating from the inner disk. We predict the stellar distribution functions for Fe and Mg, the mean <[Fe/H]> and <[Mg/H]> as well as the [Mg/Fe] vs. [Fe/H] relations in the two stellar populations. Then, we consider the case in which the metal-poor population could be the result of sub-populations formed with different chemical enrichment rates. In particular, the population close to the Galactic center could have evolved very fast, while the more external population could have evolved more slowly, in agreement with the dissipational gravitational collapse scenario. Results. When compared with observations, our results confirm that the old more metal-poor stellar population formed very fast (on a timescale of 0.1-0.3 Gyr) by means of an intense burst of star formation coupled with an initial mass function flatter than in the solar vicinity, but not as flat as suggested in previous works. The metal-rich population, instead, should have formed on a longer timescale (similar to 3 Gyr). We predict differences in the mean abundances of the two populations: in particular, we find a difference of similar to 0.52 dex for <[Fe/H]>. These differences can be interpreted as a metallicity gradient. We also predict possible gradients for Fe, O, Mg, Si, S, and Ba between sub-populations inside the metal-poor population itself (e. g., -0.145 dex for <[Fe/H]>). Finally, by means of a chemo-dynamical model following a dissipational collapse, we predict a gradient inside 500 pc from the Galactic center of -0.26 dex kpc(-1) in Fe. Conclusions. We conclude that the chemical evolution of the Galactic bulge, as suggested by its stellar populations, has been quite complex. A stellar population forming by means of a classical gravitational gas collapse is probably mixed with a younger stellar population created perhaps by the bar evolution. The differences among their mean abundances can be interpreted as a gradient. On the basis of both chemical and chemo-dynamical models, we also conclude that it is possible that the metal-poor population itself contains abundance gradients and thus different stellar populations.