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

Self Cite

In dealing with the G-dwarf problem in the solar neighbourhood, simple comoving models of chemical evolution are generalized on two respects, assuming that star formation occurs: (i) within discrete regions instead of a continuous interstellar medium, and (ii) via stochastic processes instead of a uniform generation, with the additional hypotheses: (iii) mass conservation, (iv) instantaneous recycling, and (v) instantaneous mixing within the system at the end of a fixed time step, in connection with identical regions. In the special case of the expected evolution, when the number of star-forming regions equals the expected value of the related, binomial distribution, the gas mass fraction shows an exponential time dependence, the oxygen mass fraction a linear time dependence, and the star formation rate (related to the system) a linear dependence on the gas mass fraction, i.e. the gas density, whatever the star formation rate (related to a region) may be, provided the corresponding parameters are independent of evolution. In addition, it is shown that the dependence of oxygen gas mass fraction on gas mass fraction remains unchanged with respect to a simple model. Two main classes of theoretical age-metallicity relation (TAMR) are analysed and discussed, according if the contribution to an assigned metallicity bin comes from long-lived stars which are born during all the, or only a fraction of, time steps. It is found that, under some simplifying assumptions, the theoretical, differential, G-dwarf metallicity distribution (TGD) has the same expression as in simple models, in connection with the main body of the TAMR. An application is made for the solar neighbourhood, and the input parameters are constrained to both the empirical age-metallicity relation (EAMR) and the empirical, differential, G-dwarf metallicity distribution (EGD). A different, power-law, initial mass function (IMF) is allowed during and after disk formation. A power-law steeper than the Salpeter IMF, which fits the Scalo IMF, is necessary to ensure a lower stellar mass limit above the stellar Jeans mass. An acceptable fit to the EAMR is provided by models where the ratio of oxygen yield, and lower stellar mass limit, during and after disk formation, range from about one half to about three halves. On the other hand, a fit to the EGD allows models where the IMF changes only slightly, or remains unchanged, during and after disk formation. Then a solution to the G-dwarf problem demands, in the light of the current model, nothing but an initial, substructured disk made of pre-enriched material, with same metallicity as the lower limit detected in G dwarfs belonging to the sample under consideration. Several runs are made in different situations, related to either constant number of regions or constant mass of a region, separately during and after disk formation. Significant statistical fluctuations are found when the number of regions is low enough, i.e. of the order of ten. A sharp peak exhibited by the EGD cannot be interpreted in terms of statist...

Section: Theoretical Age-metallicity Relation and G-dwarf Metallicitymentioning

confidence: 93%

Section: Main Assumptionsmentioning

confidence: 99%

Section: Main Assumptionsmentioning

confidence: 99%

Section: Special Casesmentioning

confidence: 99%

See 2 more Smart Citations

The G-dwarf problem in the solar neighbourhood: a statistical approach within a inhomogeneous, simple model

Caimmi¹

2000

Self Cite

“…Accordingly, the oxygen abundance within stars is monotonically increasing with time in the range ´Ø µ ´Ø µ ,in ½ ¾ , is (Caimmi 1998): …”

Section: 2 Inhomogeneous Modelsmentioning

confidence: 99%

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

Caimmi

2001

Self Cite

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⊙, 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⊙, 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, Δt = 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.

The G-dwarf problem in the solar neighbourhood: a statistical approach within a inhomogeneous, simple model

Caimmi

2000

In dealing with the G‐dwarf problem in the solar neighbourhood, simple comoving models of chemical evolution are generalized on two respects, assuming that star formation occurs: (i) within discrete regions instead of a continuous interstellar medium, and (ii) via stochastic processes instead of a uniform generation, with the additional hypotheses: (iii) mass conservation, (iv) instantaneous recycling, and (v) instantaneous mixing within the system at the end of a fixed time step, in connection with identical regions. In the special case of the expected evolution, when the number of star‐forming regions equals the expected value of the related, binomial distribution, the gas mass fraction shows an exponential time dependence, the oxygen mass fraction a linear time dependence, and the star formation rate (related to the system) a linear dependence on the gas mass fraction, i.e. the gas density, whatever the star formation rate (related to a region) may be, provided the corresponding parameters are independent of evolution. In addition, it is shown that the dependence of oxygen gas mass fraction on gas mass fraction remains unchanged with respect to a simple model. Two main classes of theoretical age‐metallicity relation (TAMR) are analysed and discussed, according if the contribution to an assigned metallicity bin comes from long‐lived stars which are born during all the, or only a fraction of, time steps. It is found that, under some simplifying assumptions, the theoretical, differential, G‐dwarf metallicity distribution (TGD) has the same expression as in simple models, in connection with the main body of the TAMR. An application is made for the solar neighbourhood, and the input parameters are constrained to both the empirical age‐metallicity relation (EAMR) and the empirical, differential, G‐dwarf metallicity distribution (EGD). A different, power‐law, initial mass function (IMF) is allowed during and after disk formation. A power‐law steeper than the Salpeter IMF, which fits the Scalo IMF, is necessary to ensure a lower stellar mass limit above the stellar Jeans mass. An acceptable fit to the EAMR is provided by models where the ratio of oxygen yield, and lower stellar mass limit, during and after disk formation, range from about one half to about three halves. On the other hand, a fit to the EGD allows models where the IMF changes only slightly, or remains unchanged, during and after disk formation. Then a solution to the G‐dwarf problem demands, in the light of the current model, nothing but an initial, substructured disk made of pre‐enriched material, with same metallicity as the lower limit detected in G dwarfs belonging to the sample under consideration. Several runs are made in different situations, related to either constant number of regions or constant mass of a region, separately during and after disk formation. Significant statistical fluctuations are found when the number of regions is low enough, i.e. of the order of ten. A sharp peak exhibited by the EGD cannot be interpreted in terms o...