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Issue A&A
Volume 379, Number 1, November III 2001
Page(s) 245 - 256
Section Formation, structure and evolution of stars
DOI http://dx.doi.org/10.1051/0004-6361:20011336



A&A 379, 245-256 (2001)
DOI: 10.1051/0004-6361:20011336

The $\zeta$ Herculis binary system revisited

Calibration and seismology
P. Morel, G. Berthomieu, J. Provost and F. Thévenin

Département Cassini, UMR CNRS 6529, Observatoire de la Côte d'Azur, BP 4229, 06304 Nice Cedex 4, France

(Received 9 July 2001 / Accepted 14 September 2001 )

Abstract
We have revisited the calibration of the visual binary system $\zeta$ Herculis with the goal to give the seismological properties of the G0 IV sub-giant $\zeta$ Her A. The sum of masses and the mass fraction are derived from the most recent astrometric data mostly based on the HIPPARCOS ones. We have derived the effective temperatures, the luminosities and the metallicities from available spectroscopic data and TYCHO photometric data and calibrations. For the calculations of evolutionary models we have used updated physics and the most recent physical data. A $\chi^2$ minimization is performed to approach the most reliable modeling parameters which reproduce the observations within their error bars. For the age of the $\zeta$ Her binary system we have obtained $t_{\zeta\rm Her}=3387$ Myr, for the masses $m_{\zeta\rm Her A}=1.45 M_\odot$ and $m_{\zeta\rm Her B}=0.98 M_\odot$, for the initial helium mass fraction $Y_{\rm i}=0.243$, for the initial mass ratio of heavy elements to hydrogen $(\frac ZX)_{\rm i}=0.0269$ and for the mixing-length parameters $\Lambda_{\zeta\rm Her A}=0.92$ and $\Lambda_{\zeta\rm Her B}=0.90$ using the Canuto & Mazitelli (1991, 1992) convection theory. Our results do not exclude that $\zeta$ Her A is itself a binary sub-system as has been suspected many times in the past century; the mass of the hypothetical unseen companion would be $m_{\zeta\rm Her A}\loa 0.05 M_\odot$, a value significantly smaller than previous determinations. A calibration made with an overshoot of the convective core of $\zeta$ Her A leads to similar results but with a slight increase of $\approx$ +250 Myr for the age. The adiabatic oscillation spectrum of $\zeta$ Her A is found to be a complicated superposition of acoustic and gravity modes. Some of these waves have a dual character. This greatly complicates the classification of the non-radial modes. For $\ell=1$ the modes all have both energy in the core and in the envelope; they are mixed modes. For $\ell=2,3$ there is a succession of modes with energy either in the core or in the envelope with a few mixed modes. The echelle diagram used by the observers to extract the frequencies will work for $\ell=0, 2, 3$. The large difference is found to be of the order of $\overline{\Delta\nu_0}\approx 42 \mu$Hz, in agreement with the Martic et al. (2001) seismic observations.


Key words: stars: binaries: visual -- stars: evolution -- stars: fundamental parameters -- stars: individual: $\zeta$ Her

Offprint request: P. Morel, Pierre.Morel@obs-nice.fr

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© ESO 2001


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