Asteroseismic modelling of the solar-type subgiant star beta Hydri

Context. Comparing models and data of pulsating stars is a powerful way to understand the stellar structure better. Moreover, such comparisons are necessary to make improvements to the physics of the stellar models, since they do not yet perfectly represent either the interior or especially the surface layers of stars. Because β Hydri is an evolved solar-type pulsator with mixed modes in its frequency spectrum, it is very interesting for asteroseismic studies. Aims. The goal of the present work is to search for a representative model of the solar-type star β Hydri, based on up-to-date non-seismic and seismic data. Methods. We present a revised list of frequencies for 33 modes, which we produced by analysing the power spectrum of the published observations again using a new weighting scheme that minimises the daily sidelobes. We ran several grids of evolutionary models with different input parameters and different physics, using the stellar evolutionary code ASTEC. For the models that are inside the observed error box of β Hydri, we computed their frequencies with the pulsation code ADIPLS. We used two approaches to find the model that oscillates with the frequencies that are closest to the observed frequencies of β Hydri: (i) we assume that the best model is the one that reproduces the star's interior based on the radial oscillation frequencies alone, to which we have applied the correction for the near-surface effects; (ii) we assume that the best model is the one that produces the lowest value of the chi-square (χ²), i.e. that minimises the difference between the observed frequencies of all available modes and the model predictions, after all model frequencies are corrected for near-surface effects. Results. We show that after applying a correction for near-surface effects to the frequencies of the best models, we can reproduce the observed modes well, including those that have mixed mode character. The model that gives the lowest value of the χ² is a post-main-sequence model with a mass of 1.04 M⊙ and a metallicity slightly lower than that of the Sun. Our results underscore the importance of having individual frequencies to constrain the properties of the stellar model.