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$^{+ 0.01}_{- 0.02}$ $M_{\odot}$, 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$^{+ 0.01}_{- 0.005}$ and metal abundance $Z_{i}$ = 0.0275$^{+ 0.002}_{- 0.001}$. 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.