Abstract
We investigate physical properties of the nearby (∼ 7.5 pc) astrometric binary μ Cas in the context of standard evolutionary theory. Based on the spectroscopically determined relative abundances ([α/Fe] ≳ +0.4 dex, [Fe/H] ∼ −0.7 dex), all physical inputs such as opacities and equation of state are consistently generated. By combining recent spectroscopic analyses with the astrometric observations from the HIPPARCOS parallaxes and the CHARA array, the evolutionary model grids have been constructed. Through the statistical evaluation of the χ<sup>2</sup>-minimization among alternative models, we find a reliable evolutionary solution (M<sub>A</sub>, M<sub>B</sub>, t<sub>age</sub>) = (0.74 M<sub>⊙</sub>, 0.19 M<sub>⊙</sub>, 11 Gyr) which excellently satisfies observational constraints. In particular, we find that the helium abundance of μ Cas is comparable with the primordial helium contents (Y<sub>p</sub> ∼ 0.245). On the basis of the well-defined stellar parameters of the primary star, the internal structure and the p-mode frequencies have been estimated. From our seismic computation, μ Cas is expected to have a first order spacing ∆ν ∼ 169 μHz. The ultimate goal of this study is to describe physical processes inside a low-mass star through a complete modelling from the spectroscopic observation to the evolutionary computation.
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