New Insights for High-precision Asteroseismology: Acoustic Radius of KIC 6225718

Abstract

Asteroseismology is a powerful tool for probing stellar interiors and determining stellar fundamental parameters. In previous works, $\chi^2$-minimization method is usually used to find the best matching model to characterize observations. In this letter, we adopt the $\chi^2$-minimization method but only using the observed high-precision oscillation to constrain theoretical models for solar-like oscillating star KIC 6225718, which is observed by \kepler\ satellite. We also take into account the influence of model precision. Finally, we find that the time resolution of stellar evolution can not be ignored in high-precision asteroseismic analysis. Based on this, we find the acoustic radius $\tau_{0}$ is the only global parameter that can be accurately measured by $\chi^2_{\nu}$ matching method between observed frequencies and theoretical model calculations. We obtain $\tau_{0}=4601.5^{+4.4}_{-8.3}$ seconds. In addition, we analyze the distribution of $\chi^2_{\nu}$-minimization models (CMMs), and find that the distribution range of CMMs is slightly enlarged by some extreme cases, which possess both of larger mass and higher (or lower) heavy element abundance, at lower acoustic radius end.