Models of $\mu$ Her with asteroseismic constraints

Abstract

Using the Yale stellar evolution code, models of mu Her based on asteroseismic measurements are constructed. A ${\chi }^2$ minimization is performed to approach the best modeling parameters which reproduce the observations within their errors. By combining all non-asteroseismic constraints with asteroseismic measurements, we find that the observational constraints favour a model with a mass of 1.00${}_{-0.02}^{+0.01}$ $M_{\odot }$, an age t = 6.433 $\pm$ 0.04 Gyr, a mixing-length parameter $\alpha$ = 1.75 $\pm$ 0.25, an initial hydrogen abundance $X_i$ = 0.605${}_{-0.005}^{+0.01}$ and metal abundance $Z_i$ = 0.0275${}_{-0.001}^{+0.002}$. mu Her is in post-main sequence phase of evolution. The modes of $l$ = 1 show up the characteristics of avoided crossings, which may be applied to test the internal structure of this type stars. Asteroseismic measurements can be used as a complementary constraint on the modeling parameters. The models with mass 1.00 - 1.10 $M_{\odot }$ can reproduce the observational constraints. Existing observed data of mu Her do not rule out these models.

14 pages and 8 figures

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