The G-dwarf problem in the solar neighbourhood: a Lagrangian picture. II

The current paper investigates how the empirical, G-dwarf metallicity distribution constrains simple, comoving models of chemical evolution. In doing this, the application of the models to a data sample, performed in a previous paper, is refined and extended. The key idea is that (i) different star formation rates with different mass spectra take place in different phases of evolution, i.e. contraction and equilibrium, and (ii) disk formation begins at a time t=T_d and ends at t=T_c, which marks the transition from contraction to equilibrium. In this view, the lowest-metallicity point of the empirical, differential distribution, consistent with a linear fit, is related to the beginning of disk formation, and an apparent discontinuity point to the transition from contraction to equilibrium. In addition, different linear fits hold on the left (early distribution) and on the right (late distribution) of the discontinuity point. Models consistent with the empirical, G-dwarf metallicity distribution are related to linear fits on the early and late side. Homologous solutions during the equilibrium phase are analysed in detail with respect to changes in T_c and T_a, the age of the Galaxy. Then we are left with a single free parameter which is relevant to the chemical evolution, i.e. the mass spectrum exponent during the equilibrium phase. The allowed values for the other parameters, thought as a function of the above mentioned one, are plotted for each case. A Salpeter mass spectrum exponent, p=-2.35, is ruled out by the theoretical, lower stellar mass limit, contrary to a Scalo mass spectrum exponent, p=-2.90, in contrast with previous literature. The reasons for this discrepancy are discussed. Our results are marginally consistent with a same initial mass function during the contraction and equilibrium phase, but in this case the disk mass fraction is of the same order, or less, than the halo mass fraction. It is also investigated how the empirical age-metallicity relation constrains the duration of the contraction phase, for a reasonable upper limit of T_a. Keeping in mind that the empirical, G-dwarf metallicity distribution has not been corrected for the large cosmic scatter shown by the empirical, age-metallicity relation, we find a duration of disk formation, T_c-T_d=1.0-1.5 Gyr, by a factor 3-5 less than it is found by use of simple infall models. The reasons of this difference are explained. The idea of a massive, white dwarf halo, which seems to be indicated by microlensing experiments, is ruled out by the empirical, G-dwarf metallicity distribution, in the light of the current model and provided the solar neighbourhood is a typical region of the Galaxy. More refined models involving e.g., the relax of instantaneous recycling would change our results, but the trend is expected to be only slightly altered.