Modeling $\epsilon$ Eridani and asteroseismic tests of element diffusion

Taking into account the helium and metal diffusion, we explore the possible evolutionary status and perform seismic analysis of MOST target: the star $\epsilon$ Eridani. We adopt the different input parameters to construct the models by fitting the available observational constraints: e.g., $T_{eff}$, $L$, $R$, $[Fe/H]$. From computation, we obtain the average large spacings of $\epsilon$ Eridani about $194\pm 1 \mu$Hz. The age of the diffused models has been found to be about 1 Gyr, which is younger than one determined previously by models without diffusion. We found that the effect of pure helium diffusion on the internal structure of the young low-mass star is slight, but the metal diffusion influence is obvious. The metal diffusion leads the models to have much higher temperature in the radiation interior, correspondingly the higher sound speed in the interior of the model, thereby the larger frequency and spacings.