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Spot and Facula Activity Variations of the Eccentric Detached Eclipsing Binary KIC 8098300 Based on the Time-series Orbital Solutions

The LAMOST spectra and $\it{Kepler}$ light curves are combined to investigate the detached eclipsing binary KIC 8098300, which shows the O'Connell effect caused by spot/facula modulation. The radial velocity (RV) measurements are derived by using the tomographic spectra disentangling technology. The mass ratio $q = K_1/K_2 = 0.812 \pm 0.007$, and the orbital semi-major axis $a\mathrm{\sin}i = 14.984 \pm 0.048\ R_\odot$ are obtained by fitting the RV curves. We optimize the binary model concerning the spot/facula activity with the code PHOEBE and obtain precise parameters of the orbit including the eccentricity $e=0.0217 \pm 0.0008$, the inclination $i=87.71\pm 0.04^\circ$, and the angle of periastron $ω=284.1\pm 0.5^\circ$. The masses and radii of the primary and secondary star are determined as $M_1=1.3467 \pm 0.0001\ M_\odot$, $R_1=1.569 \pm 0.003\ R_\odot$, and $M_2=1.0940 \pm 0.0001\ M_\odot$, $R_2=1.078 \pm 0.002\ R_\odot$, respectively. The ratio of temperatures of the two component stars is $r_{teff}=0.924 \pm 0.001$. We also obtain the periastron precession speed of $0.000024\pm 0.000001\ \mathrm{d}\ cycle^{-1}$. The residuals of out-of-eclipse are analyzed using the Auto-Correlation Function (ACF) and the Discrete Fourier Transform (DFT). The spot/facula activity is relatively weaker, but the lifetime is longer than that of most single main sequence stars in the same temperature range. The average rotation period of the spots $P_{rot}=4.32\ d$ is slightly longer than the orbital period, which may be caused by either the migration of spots/faculae along the longitude or the latitudinal differential rotation. The activity may be spot-dominated for the secondary star and facula-dominated for the primary star.