SIMBAD references

We conducted a detailed study of the 700 day light curve of KIC 9656397. The target is a long-period detached eclipsing binary, exhibiting short eclipses and out-of-eclipse variations, and is reported to be a member of the open star cluster NGC 6811. We retrieved the light curve and spectra from the Kepler and LAMOST databases. We used PHOEBE to simulate the light curve and employ EMCEE to find the best-fitting physical parameters. The effective temperatures of the primary and secondary components are ${T}_{{\rm{p}}}=627{0}_{-130}^{+140}$ K and ${T}_{{\rm{s}}}=636{0}_{-130}^{+140}$ K, respectively. The mass ratio, orbital inclination, and eccentricity are $1.0{0}_{-0.10}^{+0.10}$, $89.84{0}_{-0.001}^{+0.001}$ deg, and $0.22{3}_{-0.002}^{+0.001}$, respectively. We also derived absolute masses, radii, and luminosities of the two components, which are: ${M}_{{\rm{p}}}\,=\,1.1{5}_{-0.09}^{+0.15}$M_⊙, ${M}_{{\rm{s}}}\,=\,1.1{6}_{-0.14}^{+0.19}$M_⊙, ${R}_{{\rm{p}}}\,=\,1.0{9}_{-0.16}^{+0.16}$R_⊙, ${R}_{{\rm{s}}}\,=\,1.0{9}_{-0.15}^{+0.16}$R_⊙, ${L}_{{\rm{p}}}\,=\,1.6{6}_{-0.49}^{+0.51}$L_⊙, ${L}_{{\rm{s}}}\,=\,1.7{6}_{-0.51}^{+0.54}$L_⊙. We compared these values with previous results, finding a good consistency. We employed the Generalized Lomb-Scargle (GLS) method for frequency analysis and suggested that the out-of-eclipse variability is unlikely to be caused by pulsation but rather by stellar surface spots. We fitted the periodogram with Lorentzian profiles and calculated the rotation periods of two components to be 7.464 days and 6.557 days. Using the empirical formula of gyrochronology and isochrone fitting, we estimated the ages of the individual stars. Combined with LAMOST low-resolution spectra ($\mathrm{log}g$≈4.4, [Fe/H] ≈ -0.1), the well-established age and metallicity of NGC 6811, and unpublished radial-velocity measurements, our analysis indicates that both stars are main-sequence objects with slightly subsolar metallicity and are genuine members of NGC 6811.