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

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5. Observations of the visual binary [FORMULA] Cen

The calibration of a binary system is based on the adjustment of the stellar modeling parameters, so that the model of each component at time [FORMULA] reproduces the available observables within their error bars. Among different possibilities, one has to choose the most suited set of variables to be used in the calibration according to the observational and theoretical material available. As aforementioned, because of the assumption of a common origin of both components, five unknowns enter the modeling of their evolution. There are six most currently available constraints: (1) the effective temperatures for [FORMULA] Cen A & B, derived from precise detailed spectroscopic analysis, (2) either the spectroscopic gravities or the luminosities, these latter derived from the photometric data and parallax, using bolometric corrections (3) the surface metallicities. In the following, we discuss all the relevant available observations and we choose the most appropriate and accurate observables to be fitted in the calibration process.

5.1. Astrometric data

For a visual binary, the parallax uncertainty is the largest source of error in the derivation of the sum of masses via the third Kepler law (Couteau 1978, 40, VI). Unfortunately, [FORMULA] Cen was "difficult" for Hipparcos with the secondary at the edge of the sensitivity profile (Söderhjelm 2000). Söderhjelm improved the adjustment of the Hipparcos parallax by taking into account the known orbital motion but, as expected, the orbital curvature covered during the 3.25 yr mission, was not sufficient to derive a reliable mass ratio of the components. Table 2 shows that the new parallax value differs from the former by more than [FORMULA]. With respect to the original Hipparcos value this new one is closer to the long focus photographic determination of Kamper & Wesselink (1978) based on Heintz's (1958) orbital elements.


Table 2. Astrometric properties of the [FORMULA] Centauri A & B binary system. P is the orbital period in yr, a the semi major axis in arc second, [FORMULA] the parallax in mas, [FORMULA] the fractional mass.

After numerous independent investigations during almost 100 years, Pourbaix et al. (1999) derived an orbit based both on visual astrometric and precise radial velocity data, leading to consistent determinations of orbital parameters, orbital parallax, sum of masses, mass ratio and, thus, precise mass values for [FORMULA] Cen A & B. Here, we prefer to use of Pourbaix et al. (1999) mass values because Söderhjelm's (2000) ones are based on disparate sources (i.e., Hipparcos parallax, Heintz's (1958) orbit and the mass ratio of Kamper & Wesselink (1978)). We do not take into account mass errors in the calibrations.

The inclinations of the orbits of Heintz (1958 , 1982) and Pourbaix et al. (1999) agree within less than one tenth of a degree, [FORMULA], [FORMULA] (the Sun lies close to the orbital plane of [FORMULA] Cen). With the reasonable assumption that the orbital and rotational axis are parallel, owing to the high inclination, [FORMULA] Cen A & B are seen about equator on and the observed rotational velocities are close to their equatorial values, [FORMULA].

5.2. Photometric data

Photometric data are available in the V, B (Mermilliod et al. 1997) and K (Thomas et al. 1973) bands. But, as claimed by Flannery & Ayres (1978) and Chmielewski et al. (1992), the dynamical range of commonly used photometers is limited, which does not allow precise photometric measurements of bright stars. This makes the [FORMULA] Cen photometric data rather unsafe (Chmielewski et al. 1992) and we preferred to use the spectroscopic data. However, for comparison, we have used these photometric data to derive bolometric corrections and effective temperatures of the two components from (1) the empirical calibrations of Alonso et al. (1995 , 1996) and (2) the theoretical calibrations of Lejeune et al. (1998). The [FORMULA] empirical calibration of Alonso et al. (1996) leads to [FORMULA] K and [FORMULA] K while the theoretical (based on model atmospheres) calibrations of Lejeune et al. (1998) yield [FORMULA] K and [FORMULA] K, all well compatible with spectroscopic temperatures. The [FORMULA] empirical calibration of the bolometric flux (Alonso et al. 1995) provides bolometric corrections [FORMULA] and [FORMULA] close to the values inferred from the theoretical calibrations of Lejeune et al. (1998) (-0.11 and -0.23 respectively). Let us point out that these bolometric corrections are larger than those adopted by Guenther & Demarque (2000).

5.3. Spectroscopic data and atmospheric parameters

For both stars many spectroscopic data exist in the literature with good signal to noise ratios because of their high magnitudes. As Table 3 exhibits rather scattered results we decided to reestimate the effective temperatures, surface gravities and metallicities. For our analysis we used the spectroscopic data published by Chmielewski et al. (1992) and Neuforge-Verheecke & Magain (1997), the atmosphere models of Bell et al. (1976) grid and the basic technique of the curve of growth.


Table 3. Spectroscopic data of the [FORMULA] Cen system. The effective temperatures are in K, the metallicities and the lithium abundance in dex. For sake of brevity the uncertainties are not recalled.

5.3.1. Effective temperatures

Table 3 presents effective temperatures compiled from the literature. Chmielewski et al. (1992) derived the effective temperatures from the best fit of the wings of the [FORMULA] line. Recently Neuforge-Verheecke & Magain (1997) obtained the [FORMULA] by forcing the abundances derived from FeI lines to be independent of their excitation potential. They not only used the FeI lines to determine the effective temperature of each star but also checked their results using the [FORMULA] line profiles. In [FORMULA] Cen A, the two methods lead to consistent results that are also in good agreement with those of Chmielewski et al. (1992), although the two analyses made use of different model atmospheres. In [FORMULA] Cen B, the two methods lead to marginally discrepant results possibly due to Non-LTE effects and to the sensitivity of [FORMULA] to the treatment of convection.

We have reconsidered the fit of hydrogen lines of Chmielewski et al. (1992). We took into account the overabundance of the [FORMULA] Cen system which strengthens the metallic lines and displaces the pure wings of H lines; we also took into account the relative strength of metallic lines in [FORMULA] Cen B, different from what is found in solar-like profiles, because of the lower temperature. Consequently, the fit proposed by Chmielewski et al. (1992) seems to overestimate the temperature and we displace it toward cooler values, more importantly in the case of [FORMULA] Cen B. Our adopted effective temperatures are respectively [FORMULA] K and [FORMULA] K for [FORMULA] Cen A & B. These new proposed temperatures agree, within the 1 [FORMULA] error bars, with the FeI based temperature determinations of Neuforge-Verheecke and Magain (1997) and, as quoted in Sect. 5.2, they are close to the values based on Lejeune et al. (1998) calibrations.

5.3.2. Surface gravities

Usually [FORMULA], the logarithm of the surface gravity, is determined by the detailed spectroscopic analysis using the ionization equilibrium of iron. Table 3 shows the results obtained by different authors. We remind that the surface gravities from Neuforge-Verheecke & Magain (1997) and from Chmielewski et al. (1992) are very close. Using the published equivalent width (hereafter EW) and the error bars of Neuforge-Verheecke & Magain, we derive by the basic curve of growth procedure [FORMULA] and [FORMULA] for [FORMULA] Cen A & B, respectively.

5.3.3. Chemical composition

Furenlid & Meylan (1990) and Neuforge-Verheecke & Magain (1997) have found an average metal overabundance of around 0.2 dex. As in Sect. 5.3.2, using oscillator strengths, microturbulence parameter, EW, published by Neuforge-Verheecke & Magain and the iron curve of growth derived as aforesaid, we get [FORMULA] dex and [FORMULA] dex for [FORMULA] Cen A & B, respectively; the error bars are from Neuforge-Verheecke & Magain. We note that metallicities agree, within the 1 [FORMULA] error bars, with the values of Neuforge-Verheecke & Magain.

Table 4 shows that C, N, O and Fe, the most abundant "metals" and electron donors, have uniform overabundances of about [FORMULA] dex. In consequence, it is reasonable to construct models having a uniform abundance of all metals enhanced by a factor 1.7, corresponding to 0.2 dex compared to the Sun, and use opacities with solar mixture. On the main-sequence, for stellar masses close to the solar one, the differential segregation between the metals does not significantly modify the models (Turcotte et al. 1998) this permits, for the equation of state and opacity data, to keep the ratios between "metals" to their initial value despite the differential segregation by microscopic diffusion and gravitational settling.


Table 4. Atmospheric abundances of [FORMULA] Cen A & B. The references are: (1) Furenlid & Meylan (1990), (2) Neuforge-Verheecke & Magain (1997), (3) Thévenin (1998).

Table 3 reveals a good agreement between the measurements of the lithium abundance. [FORMULA] Cen A presents a depletion close to the solar one ([FORMULA], Grevesse & Sauval 1998) while, in [FORMULA] Cen B, the lithium is clearly more depleted. The assumption of a common origin of the two stars eliminates the possibility of a different initial lithium abundance in the pre-stellar nebulae. Neither an error on temperatures nor on surface gravities in model atmospheres can explain these differences with the solar depletion.

The situation is similar for [FORMULA]. Observations by Primas et al. (1997) indicate that [FORMULA] is depleted in [FORMULA] Cen B while [FORMULA] Cen A exhibits a quasi-solar abundance.

5.3.4. Rotation

For [FORMULA] Cen A, Boesgaard & Hagen (1974) estimated a rotational period 10% larger than the solar one. More recently Saar & Osten (1997) measured rotational velocities for [FORMULA] Cen A & B of respectively [FORMULA] km s-1 and [FORMULA] km s-1, in good agreement with other determinations. With the estimated radius of [FORMULA] and [FORMULA], the periods of rotation are respectively [FORMULA] d, and [FORMULA] d. They bracket the solar value.

5.4. Seismological observations

Many attempts have been made to detect solar-like p-mode oscillations in [FORMULA] Cen A, from ground-based observations. They lead to controversial results. Gelly et al. (1986) reported a detection, but the claimed mean large separation between the oscillation frequencies [FORMULA]Hz was very large and inconsistent with the theoretical value (Demarque et al. 1986). Despite the use of more sensitive techniques, Brown & Gilliland (1990) failed to detect any oscillation and gave an upper limit for the amplitude of 0.7 m s-1, i.e. 2-3 times the solar one. Pottasch et al. (1992) have detected oscillations in [FORMULA] Cen A. They found a set of regularly spaced peaks, with a mean separation corresponding to [FORMULA]Hz, consistent with the known properties of this star, but with an amplitude of oscillation larger than the upper limit of Brown & Gilliland (1990). Edmonds & Cram (1995) did not detect unambiguously the p-mode oscillations, but they found an evidence for almost the same periodicity as that found by Pottasch et al. (1992) in the power spectrum. More recently, Kjeldsen et al. (1999a) found tentative evidence for p-mode oscillations in [FORMULA] Cen A, from equivalent width measurements of the Balmer hydrogen lines. They proposed four different possible identifications of the eight observed frequency peaks in the power spectrum, which correspond to sets of the large and small frequency spacings [FORMULA] and [FORMULA] of (106.94, 12.30), (106.99, 8.15), (100.77, 11.70) and (100.77, 6.42), in µHz. The frequency resolution of the seismological observations will be much improved in a near future, up to 0.1 µHz, with several ground-based and space projects.

5.5. Adopted observables constraining the models

To constrain the models at present day, contrarily to previous works, we prefer to use the spectroscopic gravities we derived consistently from effective temperature and metallicities instead of the luminosity derived from the photometry, bolometric correction and parallax. Table 5 gives the effective temperatures, gravities and metallicities we selected to constrain the models. The masses are from Pourbaix et al. (1999). We emphasize that the parallax is required to derive the masses but neither the effective temperatures nor the gravities.


Table 5. All symbols have their ordinary meaning. {The brackets indicate values derived from basic formula.}
Top, left panel: adopted observational data to be reached by the calibration.
Top, right panel: Observational constraints of the "best" model of Guenther & Demarque (2000).
Bottom panel: Characteristics of [FORMULA] Cen A & B and Sun models computed with the same input physics. The [FORMULA] Cen A ([FORMULA] [FORMULA] Cen B) models are named "A.." ([FORMULA] "B.."). The first four rows recall some items of Table 1: the ages (Myr), the initial helium mass fractions, the initial heavy element to hydrogen mass ratios, and the mixing-length parameters. The next three rows give the effective temperatures in K, the surface gravities and the metallicities. The six next rows present respectively the luminosities, the total radii in solar units, the surface mass fractions of hydrogen and helium, the ratios of heavy element to hydrogen and the lithium abundances. In the next rows [FORMULA] and [FORMULA] are respectively the radius and the temperature (in M K) at the base of the external convection zone, [FORMULA] is the radius of the convective core (including overshoot for model [FORMULA] & [FORMULA]). At center, [FORMULA], [FORMULA], [FORMULA], [FORMULA] are respectively the temperature (in M K), the density (in g cm-3), the hydrogen and the helium mass fractions.

While this work was under investigation, Guenther & Demarque (2000) published new calibrations of the [FORMULA] Cen binary system. As a matter of comparison we have calibrated the [FORMULA] Cen binary system with their constraints. Table 5 presents the observable constraints of the "best" model of Guenther & Demarque (2000). They significantly differ from ours, though correspondingly to almost the same mass ratios. The trigonometrical parallax of Söderhjelm (2000) is larger than the orbital parallax of Pourbaix et al. (1999) and leads to smaller masses and larger ([FORMULA] smaller) luminosity for [FORMULA] Cen A ([FORMULA] [FORMULA] Cen B).

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Online publication: December 11, 2000