Frequency identification and asteroseismic analysis of the red giant KIC 9145955: fundamental parameters and helium core size

We have analyzed 18 quarters of long-cadence data of KIC 9145955 provided by \emph{Kepler}, and extracted 61 oscillation frequencies from these high precision photometric data. The oscillation frequencies include 7 $l = 0$ modes, 44 $l = 1$ modes, 7 $l = 2$ modes, and 3 $l = 3$ modes. We identify $l = 0$ modes as p modes and $l = 2$ modes as p-dominated modes. For $l = 1$ modes, all of them are identified as mixed modes. These mixed modes can be used to determine the size of the helium core. We conduct a series of asteroseismic models and the size of the helium core is determined to be $M_{\rm He}$ = 0.210 $\pm$ 0.002 $M_{\odot}$ and $R_{\rm He}$ = 0.0307 $\pm$ 0.0002 $R_{\odot}$. Furthermore, we find that only the acoustic radius $\tau_{0}$ can be precisely determined with the asteroseismic method independently. The value of $\tau_{0}$ is determined to be 0.494 $\pm$ 0.001 days. By combining asteroseismic results and spectroscopic observations, we obtain the best-fitting model. The physical parameters of this model are $M$ = 1.24 $M_{\odot}$, $Z$ = 0.009, $\alpha$ = 2.0, $T_{\rm eff}$ = 5069 K, $\log g$ = 3.029, $R$ = 5.636 $R_{\odot}$, and $L$ = 18.759 $L_{\odot}$. In addition, we think that the observed frequency F39 (96.397 $\mu$Hz) is more appropriate to be identified as a mixed mode of the most p-dominated.