Asteroseismic modelling of the solar-like star $\beta$ Hydri

We present the results of modelling the subgiant star $\beta$ Hydri using the seismic observational constraints. We have computed several grids of stellar evolutionary tracks using Aarhus STellar Evolution Code (ASTEC, Christensen-Dalsgaard, 2008a), with and without helium diffusion and settling. For those models on each track that are located at the observationally determined position of $\beta$ Hydri in the HR diagram, we have calculated the oscillation frequencies using Aarhus adiabatic pulsation package (ADIPLS, Christensen-Dalsgaard, 2008b). Applying the near-surface corrections to the calculated frequencies using the empirical law presented by Kjeldsen et al. (2008), we have compared the corrected model frequencies with the observed frequencies of the star. We show that after correcting the frequencies for the near-surface effects, we have a fairly good fit for both $l$=0 and $l$=2 frequencies. We also have good agreement between the observed and calculated $l$=1 mode frequencies although there is room for improvement in order to fit all the observed mixed modes simultaneously.