Context. Asteroseismology is an effcient tool not only for testing stellar structure and evolutionary theory but also constraining the parameters of stars for which solar-like oscillations are detected, presently. As an important southern asteroseism
ic target, Tau Ceti, is a metal-poor star. The main features of the oscillations and some frequencies of ? 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 Tau 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 Guenthers stellar pulsation code. The chi2c 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 ? Ceti, because our optimal models are in the error boxes B and C, which are derived from spectroscopy results.
Asteroseismology, as a tool to use the indirect information contained in stellar oscillations to probe the stellar interiors, is an active field of research presently. Stellar age, as a fundamental property of star apart from its mass, is most diffic
ult to estimate. In addition, the estimating of stellar age can provide the chance to study the time evolution of astronomical phenomena. In our poster, we summarize our previous work and further present a method to determine age of low-mass main-sequence star.
The basic intent of this paper is to model 70 Ophiuchi A using the latest asteroseismic observations as complementary constraints and to determine the fundamental parameters of the star. Additionally, we propose a new quantity to lift the degeneracy
between the initial chemical composition and stellar age. Using the Yale stellar evolution code (YREC7), we construct a series of stellar evolutionary tracks for the mass range $M$ = 0.85 -- 0.93 $M_{odot}$ with different composition $Y_{i}$ (0.26 -- 0.30) and $Z_{i}$ (0.017 -- 0.023). Along these tracks, we select a grid of stellar model candidates that fall within the error box in the HR diagram to calculate the theoretical frequencies, the large- and small- frequency separations using the Guenthers stellar pulsation code. Following the asymptotic formula of stellar $p$-modes, we define a quantity $r_{01}$ which is correlated with stellar age. Also, we test it by theoretical adiabatic frequencies of many models. Many detailed models of 70 Ophiuchi A have been listed in Table 3. By combining all non-asteroseismic observations available for 70 Ophiuchi A with these seismological data, we think that Model 60, Model 125 and Model 126, listed in Table 3, are the optimum models presently. Meanwhile, we predict that the radius of this star is about 0.860 -- 0.865 $R_{odot}$ and the age is about 6.8 -- 7.0 Gyr with mass 0.89 -- 0.90 $M_{odot}$. Additionally, we prove that the new quantity $r_{01}$ can be a useful indicator of stellar age.
