tokens: surface term for stellar models is the method proposed by Kjeldsen et al. ( 2008 ). They note that the offset between observed and best model frequencies turns out to be closely fitted by a power law. However, there are issues with many of the surface-term corrections, even for main-sequence stars; and most models perform very badly in the subgiant and red-giant region. Schmitt Basu ( 2015 ) found that the two-term model proposed by Ball Gizon ( 2014 ) works better than other models across a large portion of the HR diagram, and consequently we adopt that for this work. 4. Results and Discussions We show the evolutionary track of our models in Figure 3 . The figure also shows the two error boxes. T eff = 4766 ± 200 K and have been used for the large error box while T eff = 4974 ± 161 K and for the smaller error box. We find that many models fall into the two error boxes. In order to obtain the best-fit model for KIC 8263801 from among these models, we calculated the likelihood for each model and determined the model with the highest likelihood. The likelihood function is defined aswherewith the quantity indicating the observed T eff , [Fe/H], and frequency ν n , l ; while the corresponds to these values of the model. The quantity σ i represents the observational error of . In the study, we use the function as follows:where In the above expression, are the surface-term corrected frequencies of the models. The values of likelihood function for model of KIC 8263801 as a function of mass, metallicity, age, and radius are shown in Figure 4 . We choose the model that maximizes as a candidate for the best-fit model. The model parameters are shown in Table 5 . To clearly compare all of the theoretical frequencies of the best-fit model with observed frequencies, we show the échelle diagram of the best-fit model in Figure 5 . In the figure, open symbols are the model frequencies corrected for the surface term, the filled symbols refer to the observable frequencies. Circles are used for l = 0 modes and squares for l = 2 modes. Figure 4. Likelihood values for models of KIC 8263801 as a function of mass, metallicity, age, and radius, corresponding to panels (a)–(d) respectively. Figure 5. Échelle diagrams for the best-fit model. Open symbols are the surface-term corrected frequencies of the best-fit model; filled symbols refer to the observed frequencies. Circles are used for l = 0 modes, squares for l = 2 modes. Table 5 The Parameters of the Best-fit Model Finally, we derive the parameters of star as the likelihood weighted mean and standard deviation from the models and obtain a mass of , age of t = 1.48 ±0.21 Gyr, and radius of R / R ⊙ = 10.53 ± 0.28. Our best-fit model has an age of 1.596 Gyr, the age as determined from the likelihood weighted average is not too different, and thus the question arises as to whether this star can be a member of NGC 6866. There are a number of results about the age of NGC 6866. For example, Loktin et al. ( 1994 ) derived
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