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

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1. Introduction

As the Sun's nearest stellar neighbors, the two members of the visual binary [FORMULA] Centauri A & B (G2V + K1V) provide the most accurate potentiality of testing stellar physics in conditions slightly different from the solar ones and then deserve undivided attention for internal structure modeling and oscillation frequency calculations. By coincidence, the masses and the spectral types of components A/B (HD 128620/1, IDS 14328-6025 A/B, Hipparcos 71 683/1) bracket those of the Sun. The high apparent brightness and the large parallax imply that surface abundances and astrometric parameters are known better than for any star (except the Sun. The basic intent of this paper is to model [FORMULA] Cen A & B using updated physics. This allows to predict the p-mode oscillation frequencies, which will be useful to exploit future asteroseismological observations as expected, for instance, from the project Concordiastro at the South Pole (Fossat et al. 2000). Also, as "solar like stars", the two components are primary targets for the MONS (Kjeldsen et al. 1999b) spatial mission and their oscillations are expected to be well separated in the frequency spectrum.

Based on the reasonable hypothesis of a common origin for both components, i.e. same initial chemical composition and age, the calibration of a binary system consists in determining a consistent evolutionary history for the double star, given (1) the positions of the two components in a H-R diagram, (2) the stellar masses and, (3) the present day surface chemical composition. The goal is to compute evolutionary models that reproduce the observations. This procedure yields estimates for the age [FORMULA], the initial helium mass fraction [FORMULA] and initial metallicity [FORMULA] (logarithm of the number abundances of iron to hydrogen relative to the solar value), which are fundamental quantities for our understanding of the galactic chemical evolution. We also derive values of the "mixing-length parameter" or "convection parameter" [FORMULA], ratio of the mixing-length to the pressure scale height. Once the initial masses and the physics are fixed, the modeling of the two components A & B of a binary system requires a set [FORMULA] of five so-called modeling parameters:


In most cases there are only four reliable observables namely, the effective temperatures [FORMULA] and the luminosities [FORMULA] or the gravity [FORMULA] of each component. Therefore, one of the unknowns has to be fixed. Very often the mixing-length parameters are assumed to be the same for both components, even if the mass ratio differs significantly from unity. Once detailed spectroscopic analyses have been performed on the system, the precise present day surface metallicities of stars come as additional observational constraints.

In this paper we attempt to reproduce the observed metallicities and, if possible, the lithium depletion by means of models including microscopic diffusion. We calibrate the binary system using both Böhm-Vitense's (1958, hereafter MLTBV) and Canuto & Mazitelli (1991, 1992, hereafter MLTCM) mixing-length convection theories.

The paper is divided as follows: in Sect. 2, we recall the main results obtained in previous theoretical works and, in Sect. 3, we emphasize the difficulties related to the choice of mixing-length parameters. In Sect. 4, we discuss the modeling of the transport processes acting beneath the convection zone. The observational material, relevant to the evolutionary status of [FORMULA] Cen and available in the literature, is collected in Sect. 5. The method of calibration is described in Sect. 6. In Sect. 7, we present the stellar modeling procedure. In Sect. 8, we give the results with emphasis on the seismological analysis. We summarize our results and conclude in Sect. 9.

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© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000