| 其他摘要 | When hydrogen is exhausted in the center of a low-mass star (< 2.2 M⊙), it will
leave the main sequence and become a red giant. Oscillations in red giants are excited
stochastically by turbulence in the stellar convective envelope. Therefore, we can detect
the internal structure of red giant stars through the observational oscillation modes. This
method is called asteroseismology. There are mixed modes in the red giant stage, which
behave as a p-mode 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. Therefore, an accurate star
model can be obtained by using the observational mixed modes of the red giant as
the observational constrains. When individual g-dominated mixed modes can directly
compare the model values with the observational values, stellar model can provide
information about the helium core of the star as well as information about the gradient
of the chemical composition inside the star. In addition, mixed mode is less affected by
surface effects. 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.
We proposed a mode identification method 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.
We construct a grid of theoretical models to fit observational frequencies of red giants.
Then, we select the best-fitting model which reflect the reflects the realistic structure
of red giants. The fundamental parameters and the internal structure of red giant can
be determined by the best-fitting model. In this paper, we analyse two red giants KIC
9145955 and KIC 9970396 through asteroseismology. By fitting the observations and
calculations of mixed modes, the size of the helium core of two red giants are accurately
determined for the first time and some meaningful results are summarized as follows:KIC 9145955 is a good example of a bright red giant branch star. KIC 9145955 was
first identified as a red giant by Bedding et al. (2011). Pérez Hernández et al. (2016) obtained asteroseismic parameters of 19 Kepler red giants, including KIC 9145955,
such as masses and radii. However, Pérez Hernández et al. (2016) did not model alll = 1 frequencies. In this paper, we focus on the fitting of the individual mixed modes
of l = 1. We have analyse high precision photometric data of KIC 9145955 provided
by Kepler and extracted 61 oscillation frequencies from these data. We conduct a series
of asteroseismic models for KIC 9145955. According to the results of models, we think
that the observed frequency F39 (96.397 μHz) is more appropriate to be identified as
a mixed mode of the most p-dominated. The size of the helium core MHe, RHe and
the acoustic radius τ0 can be precisely determined by the asteroseismic models, which
are MHe = 0.210 ± 0.002 M⊙, RHe = 0.0307 ± 0.0002 R⊙, τ0 = 0.494 ± 0.001 days,
respectively.KIC 9970396 was identified by Galume et al. (2013) as a pulsating red giant in
a detached eclipsing binary system. Li et al. (2018) presented the straight forward
modeling to determine the mixing-length parameter of KIC 9970396 with asteroseis-
mology and extract the individual oscillation frequencies. Herzsprung–Russell (HR)
diagram of Brogaard et al. (2018) showed that the evolution stage of KIC 9970396
may be near the red giant bump phase, which is one of the most interesting regions in
the red giant evolution stage. Although previous work obtained some basic parameters
of KIC 9970396, such as mass and radius, the information carried by the mixed mode
was ignored. In this paper, our aim is to obtain the precise size of the helium core of
KIC 9970396 and then to explore the internal structure of KIC 9970396. In addition,
we want to determine whether the evolution stage of KIC9970396 is between the first
dredge-up and the red giant bump phase. By using our method of model fitting, the
theoretical mixed modes can be well fitted to the observational mixed modes. The
helium core of KIC9970396 can be accurately determined by the asteroseismic model,
which are 0.229±0.001M⊙ and 0.03055±0.00015R⊙, respectively. The age of red giant
KIC 9970396 can be determined to be 6.0925 ± 0.3435 Gyr when the g-dominated
mixed modes are used as the observational constrains. Moreover, the best-fitting model
shows that KIC 9970396 is undergoing a stage that is between the first dredge-up event
and the red giant bump. |
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