Simple MCBR Models of Chemical Evolution: An Application to the Thin and the Thick Disk

Simple multistage closed-(box+reservoir) (MCBR) models of chemical evolution, formulated in an earlier attempt, are extended to the limit of dominant gas inflow or outflow with respect to gas locked up into long-lived stars and remnants. For an assigned empirical differential oxygen abundance distribution (EDOD), which can be linearly fitted, a family of theoretical differential oxygen abundance distribution (TDOD) curves is built up with the following prescriptions: (i) the initial and the ending points of the linear fit are common to all curves; (ii) the flow parameter κ ranges from an extremum point to infinity, where negative and positive κ correspond to inflow and outflow, respectively; (iii) the cut parameter ζ ranges from an extremum point (which cannot be negative) to the limit of infinity related to |κ| →+∞. For curves with increasing ζ, the gas mass fraction locked up into long-lived stars and remnants is found to attain a maximum and then decrease towards zero as |κ|→ +∞ while the remaining parameters show a monotonic trend. The theoretical integral oxygen abundance distribution (TIOD) is also expressed. An application is made to the EDOD deduced from two different samples of disk stars, for both the thin and the thick disk. The constraints on formation and evolution are discussed in the light of the model. The evolution is tentatively subdivided into four stages, namely: assembling (A), formation (F), contraction (C), equilibrium (E). The EDOD related to any stage is fitted by all curves where 0≤ζ≤ (ζ)_∞ for inflowing gas and (ζ)_∞≤ ζ≤1.2 for outflowing gas, with a single exception related to the thin disk (A stage), where the range of fitting curves is restricted to 0.35≤ζ≤(ζ)_∞. The F stage may safely be described by a steady inflow regime (κ=-1), implying a flat TDOD, in agreement with the results of hydrodynamical simulations. Finally, (1) the change of fractional mass due to the extension of the linear fit to the EDOD, towards both the (undetected) low-metallicity and high-metallicity tail, is evaluated and (2) the idea of a thick disk - thin disk collapse is discussed, in the light of the model.