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

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6. The method of calibration

The calibration of a binary system is based on the adjustment of stellar modeling parameters to observational data at the age of the system. For a given mass, fixing the physics, the effective temperature, surface gravity and metallicity of a model have the formal dependences with respect to modeling parameters:

[EQUATION]

The basic idea of the [FORMULA] fitting has been developed by Lastennet et al. (1999). To find a set of modeling parameters:

[EQUATION]

leading to observables as close as possible to the observations [FORMULA], [FORMULA] and [FORMULA], we minimize the [FORMULA] functional defined as:

[EQUATION]

where [FORMULA], [FORMULA] and [FORMULA] are the uncertainties associated to each star. For a grid of modeling parameters [FORMULA], we have computed main-sequence evolution of models with [FORMULA] Cen A & B masses. Then the [FORMULA] was computed using Eq. (1) in a refined grid obtained by interpolations. We kept for the solution the "best" [FORMULA] which corresponds to the [FORMULA]. These best modeling parameters are used to compute models of [FORMULA] Cen A & B including pre main-sequence and their frequencies. We do not further attempt neither to improve nor to investigate the stability of the solution via the steepest descent method (Noels et al. 1991; Morel et al. 2000b). Table 1 shows the confidence limits of modeling parameters of models computed in this paper. The confidence limits of each modeling parameter, the other being fixed, correspond to the maximum/minimum values it can reach, in order that the generated models fit the observable targets within their error bars.

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© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000
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