The G-dwarf problem in the solar neighbourhood: II. Halo subdwarfs

The oxygen abundance distribution in solar neighbourhood halo subdwarfs is deduced, using two alternative, known empirical relationships, involving the presence or the absence of [O/Fe] plateau for low [Fe/H] values, from a sample of 372 kinematically selected halo stars, for which the iron abundance distribution has been determined by Ryan & Norris (1991). The data are interpreted by a simple, either homogeneous or inhomogeneous model of chemical evolution, using an updated value of the solar oxygen abundance. The effect of changing the solar oxygen abundance, the power-law exponent in the initial mass function, and the rate of oxygen nucleosyntesis, keeping the remaining input parameters unchanged, is investigated, and a theorem is stated. In all cases, part of the gas must necessarily be inhibited from forming stars, and no disk contamination has to be advocated for fitting the empirical oxygen abundance distribution in halo subdwarfs of the solar neighbourhood (EGD). Then a theorem is stated, which allows a one-to-one correspondence between simple, homogeneous models with and without inhibited gas, related to same independent parameters of chemical evolution, except lower stellar mass limit, real yield, and inhibition parameter. The mutual correlations between the latter parameters are also specified. In addition the starting point, and the point related to the first step, of the theoretical distribution of oxygen abundance (TGD) predicted by simple, inhomogeneous models, is calculated analytically. The mean oxygen abundance of the total and only inhibited gas, respectively, are also determined. Following the idea of a universal, initial mass function (IMF), a power-law with both an exponent p = 2.9, which is acceptably close to Scalo IMF for m >~ m(sun), and an exponent p = 2.35, i.e. Salpeter IMF, have been considered. In general, both the age-metallicity relationship and the empirical distribution of oxygen abundance in G dwarfs of the disk solar neighbourhood, are fitted by power-law IMF exponents in the range 2.35 <= p <= 2.9. Acceptable models predict about 15% of the total mass in form of long-lived stars and remnants, at the end of halo evolution, with a mean gas oxygen abundance which is substantially lower than the mean bulge and initial disk oxygen abundance. To avoid this discrepancy, either the existence of a still undetected, baryonic dark halo with about 15% of the total mass, or an equal amount of gas loss during bulge and disk formation, is necessary. The latter alternative implies a lower stellar mass limit close to 0.2 m(sun), which is related to a power-law IMF exponent close to 2.77. Acceptable models also imply a rapid halo formation, mainly during the first step, delta(t) = 0.5 Gyr, followed by a period (three steps) where small changes occur. Accordingly, statistical fluctuations are found to produce only minor effects on the evolution.