The ζ Herculis binary system revisited

Calibration and seismology

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

Corresponding author: P. Morel, Pierre.Morel@obs-nice.fr

Received: 9 July 2001
Accepted: 14 September 2001

Abstract

We have revisited the calibration of the visual binary system ζ Herculis with the goal to give the seismological properties of the G0 IV sub-giant ζ 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 minimization is performed to approach the most reliable modeling parameters which reproduce the observations within their error bars. For the age of the ζ Her binary system we have obtained Myr, for the masses and , for the initial helium mass fraction , for the initial mass ratio of heavy elements to hydrogen and for the mixing-length parameters and using the Canuto & Mazitelli ([CITE], [CITE]) convection theory. Our results do not exclude that ζ 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 , a value significantly smaller than previous determinations. A calibration made with an overshoot of the convective core of ζ Her A leads to similar results but with a slight increase of ≈ +250 Myr for the age. The adiabatic oscillation spectrum of ζ 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 the modes all have both energy in the core and in the envelope; they are mixed modes. For 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 . The large difference is found to be of the order of Hz, in agreement with the Martić et al. ([CITE]) seismic observations.