Solar-like Oscillations In The Red Giant Star ε Ophiuchi

εOphiuchi is a peculiarly red giant star, because solar-like oscillation has been observed inεOphiuchi. Its frequency is about 25-80μHz, and large separation is about 4.8μHz. The oscillation mode is p-mode. Based on the position ofεOphiuchi in the Hertzsprung-Russell diagram,εOphiuchi is regarded as one of the red giant stars. The effective temperature and luminosity of the star are 4888±100K and L/L_⊙= 59±5.It is important to observe the stellar oscillations and to study the stellar theory, because it can be used to probe the interior structure and constrain the important parameters of star. The method is that when stellar oscillation frequencies, mode and the position in the HR diagram are determined, one can utilize the stellar structure and evolution theory and select some important parameters, such as mass, initial chemical abundance, convective parameter to construct the stellar models which can pass through the error box and then calculate the oscillation frequencies. If the frequencies and the mode of theory model can suit the observed, we can use the theory model to explore the stellar interior structure and the important parameters, such as mass, chemical abundance, age and convective parameter and so on.Astrophysical observation has observed a set of frequencies and the position ofεOphiuchi, so we can make use of the stellar structure and evolution theory to probe the interior structure and constrain the important parameters of star. Our aim is according to the observed oscillation frequencies ofεOphiuchi and the position in the HR diagram to research the interior structure and the important parameters ofεOphiuchi.The stellar structure and evolution models are determined by the initial mass and the component of the chemical abundance and are affected by some condition such as how to do with the convection, the stellar wind, rotation, magnetic field and so on. Because the mass ofεOphiuchi is small and the velocity is low, the effect of two factors can be neglected in the theory models. Furthermore, the effect of magnetic field on the stellar structure and evolution is one of the unresolved problem. In our paper we only consider that how to select the suitable initial mass and chemical abundance, especially metallicity and the mixing length to let the model from the zero age main sequence to reach the observed position ofεOphiuchi in the HR diagram and use the data of the model to calculate the oscillation information. Finally, we check the theory frequencies whether or not suit the observed frequencies. If the theory frequencies can suit the observed well, we can get the information of the interior structure and the important parameters ofεOphiuchi, such as mass, chemical abundance, age and convective parameter and so on. But in most case, there is difference between the theory frequencies and the observed frequencies. It is necessary to analyze the reason. In our paper, we think that the difference between the theory frequencies and the observed frequencies is caused by the effect of g-mode modulating p-mode and the limitation of our own stellar models.