In a study published in Monthly Notices of the Royal Astronomical Society, ZHANG Xinyi, LI Yan, WU Tao, and SU Jie from Yunnan Observatories of the Chinese Academy of Sciences reported a theoretical study on the red giant KIC 9970396. They determined the size of the helium core of red giant KIC 9970396 by asteroseismology.

In the Hertzsprung-Russel diagram, red giants are referred to as solar-like oscillations. The p-mode and g-mode have different propagation regions inside the star and carry information in different regions. There are mixed modes in the red giant stage, which behave as a p-mode signature in the stellar envelope and a g-mode signature in the stellar core. The mixed modes can propagate deeper into the star compared to the p modes and are easier to observe than the g modes. But the nature of the mixed mode makes its spectrum deviate from the pure g-mode and pure p-mode spectrum, which will cause difficulty in frequency fitting.

KIC 9970396 is a pulsating red giant star located in a binary system. The existence of mixed modes in this giant’s observational frequencies have been confirmed. Previous work showed that its evolutionary state is very close to the red giant star cluster (RGB bump).

A "mode identification" method was proposed in this study to fit the observational and calculated values of mixed modes very accurately. This method is that mixed modes should be divided into the p-dominated mixed modes and g-dominated modes before the fitting process. The basic parameters and the evolution stage of KIC 9970396 as well as its helium core parameters can be determined from the best-fitting model.

Asteroseismic model was then used to investigate stellar internal structure. The researchers found that two best-fitting models are obtained by fitting the observational mixed modes and the calculated mixed modes. The stellar parameters of these two models are consistent with the results obtained by the eclipse modelling.

In addition, effective temperature, surface gravity and metallicity of these two models are within the observation errors of LAMOST. These two models have the similar evolution stages with different input parameters. Since the size of the helium core is directly related to the propagation region of the g-mode, the mass and radius of the helium core of KIC9970396 can be more accurately determined by the asteroseismic model, which are 0.229±0.001M⊙ and 0.03055±0.00015R⊙, respectively.

The best-fitting model showed that KIC 9970396 is undergoing a stage that is between the first dredge-up event and the red giant bump. This is the first time that a giant red star whose evolutionary state is located near RGB bumps can obtain accurate helium core size as well as its internal structure through asteroseismology.