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Astron. Astrophys. 363, 675-691 (2000)

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2. Previous theoretical works

On the basis of rotational velocity measurements, observed [FORMULA] abundances and [FORMULA] emission intensity, Boesgaard & Hagen (1974) attributed to the system an age of [FORMULA] Gyr. Then, several groups calculated stellar evolution models to calibrate the system and draw information on the two components as well as on the physics governing their structure. Table 1 gives the values of the calibration parameters derived in all those studies which we now briefly summarize.


Table 1. Modeling parameters and main characteristics of the oscillation spectrum of [FORMULA] Cen A & B derived in this study and taken from the literature. The symbols have their usual meaning (see text). The references are: (1) this paper, models [FORMULA] & [FORMULA], (2) this paper, models [FORMULA] & [FORMULA], (3) this paper, models [FORMULA] & [FORMULA], (4) this paper, models [FORMULA] & [FORMULA], (5) Flannery & Ayres (1978), (6) Demarque et al. (1986), (7) Noels et al. (1991), (8) Edmonds et al. (1992), (9) Neuforge (1993), (10) Lydon et al. (1993), (11) Pourbaix et al. (1999), (12) Guenther & Demarque (2000).

Initially, Flannery & Ayres (1978) and Demarque et al. (1986) could only use the luminosities of [FORMULA] Cen A & B as observational constraints. Flannery & Ayres models support the fact that the system is metal rich with respect to the Sun with [FORMULA]. Demarque et al. (1986) derived the age of the system as a function of metallicity; they also computed the p-mode oscillation spectrum of [FORMULA] Cen A. Noels et al. (1991) introduced a general procedure for fitting models to the binary system. They derived the age, the helium content and the metallicity of the system and the value of the MLTBV parameter assuming that it is the same for the two stars. Neuforge (1993) revisited that work using OPAL opacities (Iglesias et al. 1992) complemented by her own low-temperature opacities. Fernandes & Neuforge (1995) showed that the mixing-length parameter [FORMULA] obtained through calibration is different for the two stars and that their values become very similar if the mass fraction of heavy elements increases above [FORMULA]. They also performed model calibrations with the MLTCM convection treatment with a mixing-length equal to the distance to the top of the convective envelope, thus avoiding the calibration of a convection parameter. In parallel, Edmonds et al. (1992) were the first to add the observed metallicity as a constraint (releasing in turn the hypothesis that [FORMULA] is unique) and to include the effect of microscopic diffusion. More recently, Pourbaix et al. (1999) revisited the calibration of the [FORMULA] Cen system. They calculated a new visual orbit on the basis of available separations, position angles and precise radial velocities measurements and derive new consistent values of the orbital parallax, sum of masses, mass ratio and individual masses. The main result is that the masses of the components are 5% higher and that the helium abundance and age are significantly smaller than previous estimates. Guenther & Demarque (2000) performed several calibrations of the system using different values of the parallax including the Hipparcos value and models calculated with updated physics including helium and heavy elements diffusion. They estimated the uncertainties on the calibrated parameters resulting from the error bars on mass, luminosity, effective temperature and chemical composition.

The differences between these calibrations reflect the great improvements in the description of the stellar micro-physics achieved during the last two decades and the progress of the analysis of the observational data. However, uncertainties remain on the transport processes (e.g. convection, microscopic and turbulent diffusion). Apparently none of the previous calibrations has attempted to reproduce the observed surface metallicities (except Guenther & Demarque 2000) and lithium abundances which are fundamental data for the understanding of the transport processes beneath the convection zone of solar-like stars.

As asteroseismology will in a near future strongly constrain the stellar models, some of the above described theoretical works give the main characteristics of the oscillation spectrum of the components ([FORMULA] and [FORMULA] - see definitions Sect. 8.3.1). The "mean" large separation [FORMULA] between the frequencies of modes of a given degree and of consecutive radial order depends on the stellar radius and mass. The "mean" small separation [FORMULA] between the frequencies of modes with degree [FORMULA] and 2 and consecutive radial order, measured by [FORMULA], is sensitive to the structure of the stellar core. Table 1 gives estimates of these quantities from the literature and from this work.

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© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000