Asteroseismic modelling of the metal-poor star τ Ceti

¹ Department of Physics, Dezhou University, Dezhou 253023, PR China
e-mail: tyk450@163.com
² Key Lab of Biophysics in Universities of Shandong, Dezhou 253023, PR China
³ Department of Astronomy, Beijing Normal University, Beijing 100875, PR China
e-mail: gaining@mail.bnu.edu.cn
⁴ Department of Astronomy, Yale University, PO Box 208101, New Haven, CT 06520-8101, USA

Received: 29 April 2010
Accepted: 6 October 2010

Abstract

Context. Asteroseismology is an efficient tool not only for testing stellar structure and evolutionary theory but also constraining the parameters of stars for which solar-like oscillations are presently detected. As an important southern asteroseismic target τ Ceti, is a metal-poor star. The main features of the oscillations and some frequencies of τ Ceti have been identified. Many scientists propose to comprehensively observe this star as part of the Stellar Observations Network Group.

Aims. Our goal is to obtain the optimal model and reliable fundamental parameters for the metal-poor star τ Ceti by combining all non-asteroseismic observations with these seismological data.

Methods. Using the Yale stellar evolution code (YREC), a grid of stellar model candidates that fall within all the error boxes in the HR diagram have been constructed, and both the model frequencies and large- and small- frequency separations are calculated using the Guenther’s stellar pulsation code. The ${\mathit{\chi }}_{\mathit{\nu }\mathrm{c}}^{\mathrm{2}}$ minimization is performed to identify the optimal modelling parameters that reproduce the observations within their errors. The frequency corrections of near-surface effects to the calculated frequencies using the empirical law, as proposed by Kjeldsen and coworkers, are applied to the models.

Results. We derive optimal models, corresponding to masses of about 0.775–0.785 M_⊙ and ages of about 8–10 Gyr. Furthermore, we find that the quantities derived from the non-asteroseismic observations (effective temperature and luminosity) acquired spectroscopically are more accurate than those inferred from interferometry for τ Ceti, because our optimal models are in the error boxes B and C, which are derived from spectroscopy results.