The G-dwarf problem: A tentative analytical approach, relaxing instantaneous recycling

Abstract

Starting from a general solution for the birth functionB(m, t) of stars described in detail in Casusoet al. (1989), we have obtained a first-order analytical approximation to this function as a function of metallicityZ. Using this, we obtained a fit to the observational curve compiled by Tinsley (1980) for the cumulative function of stars with metallicity lower than a given value in the solar neighbourhood. In addition, using the same expression, with its numerical fit to previous data, we obtain a good fit to the differential distributions of stars at low metallicity given in the review by Pagel (1987), given a bifurcation in the birth function at low values ofZ, which would correspond to two distinct epochs of onset of star formation. The analysis gives an infall of gas towards the solar neighbourhood up to the epoch of metallicityZ=6.7×10−3 with a correspondingly increased star formation rate, which subsequently stabilized, and another similar inflow up toZ=1.2×10−3, followed again by a steady star formation rate for largerZ. Although the assumptions made are still relatively crude, and the numbers should be considered tentative, the flexibility of the model in handling the problem is that we wish to show here.