The G‐dwarf problem in the solar neighbourhood: a Lagrangian picture

Abstract

Recent data on the empirical metallicity distribution of G dwarfs in the disk solar neighbourhood are fitted in two different ways. We use an extended Poisson distribution in the limit where the probability of star formation is small, and a Gauss distribution in the limit where a large number of physical variables is required to determine stellar metal abundance. Both are found to reproduce the data at the same (acceptable) extent, with a slight preference for the former. The empirical, differential metallicity distribution of G dwarfs in the disk solar neighbourhood is compared with its theoretical counterpart, in the picture of a closed, comoving model of chemical evolution. The limits of the currently used infall models are discussed and a scenario of galactic formation and evolution is presented. The Galactic history is thought as made of two main phases: contraction (which produces the extended component) and equilibrium (which gives the disk). In this view, the stars observed within the solar cylinder did not necessarily arise from the primordial gas which later collapsed into the disk solar neighbourhood. It is found that the G-dwarf problem is strongly alleviated, with the possible exception of the low-metallicity and high-metallicity tail of the distribution. The best choice of parameters implies: (i) a metal yield in the contraction phase which is larger by a factor of about 5 with respect to the equilibrium phase; (ii) a model halo mass fraction of about 0.3; (iii) a model disk mass fraction of about 0.6. I t provides additional support to the idea of a generalized Schmidt star formation law, which is different in different phases of evolution. The model, cumulative, G-dwarf metallicity distribution in the disk solar neighbourhood is found to predict too many low-metallicity stars with respect to its empirical counterpart, related to a Poissonian or Gaussian fit. The main reasons for the occurrence of a G-dwarf problem are discussed. Finally, a stochastic process of star formation, related to a Poisson distribution, is briefly outlined.

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

“…In fact, by "comoving model" we mean the chemical evolution of a volume comoving with the contraction. It has been shown in recent attempts that a generalized Schmidt star formation law, in the light of closed, comoving models, is consistent with observations related to both other galaxies (Caimmi 1995(Caimmi , 1996 and the solar neighbourhood (Caimmi 1997).…”

“…As simple, comoving models assume instantaneous recycling, the comparison with observations must be related to oxygen instead of iron (see e.g., Pagel 1989;Wang & Silk 1993;Caimmi 1997). To this aim, we use the empirical fit (e.g., Pagel 1989;Prantzos & Aubert 1995): according to a currently accepted approximation (e.g., Malinie et al 1993):…”

“…Cornoving models of chemical evolution have been exhaustively treated elsewhere by the author (Caimmi 1978b, hereafter quoted as C78; Caimmi 1982, hereafter quoted as C82; Caimmi 1995Caimmi , 1996Caimmi , 1997. For this reason, only what is relevant for the current attempt will be repeated here.…”

“…In dealing with the EGD and AMR., our attention will be limited to the global metallicity. As in Caimmi (1997) we shall restrict to closed models.…”

“…( l s a ) , following the same procedure outlined in e.g., Page1 (1989);Cairnmi (1997). After some algebra, one finds the expression: (19c) In the light of the instantaneous recycling approximation (e.g., Pagel 1989;Wang & Silk 1993;Caimmi 1997) the metal abundance predicted by the model has to be compared with the observed oxygen abundance, according to:…”