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 \(\omega=284.1\pm 0.5^\circ\). 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.