KIC 10417986: Spectroscopic Confirmation of the Nature of the Binary System with a δ Scuti Component

KIC 10417986 is a short orbital period (0.0737 day) ellipsoidal variable star with a delta Sct and gamma Dor hybrid pulsation component discovered by Kepler. The ground-based spectroscopic observations were carried out in the winters of 2020 and 2021 to investigate the binary nature of this star. We derive the orbital parameters using the rvfit code with a result of K-1 = 29.7 +/- 1.5 km s(-1), gamma = -18.7 +/- 1.7 km s(-1), and confirm an orbital period of 0.84495 day instead of the result given by Kepler. The atmospheric parameters of the primary are determined by the synthetic spectral fitting technique with the estimated values of T-eff = 7411 +/- 187 K, log g = 4.2 +/- 0.3 dex, [M/H] = 0.08 +/- 0.09 dex and vsini = 52 +/- 11 km s(-1). KIC 10417986 is a circular orbit binary system. From the single-lined nature and mass function of the star, the derived orbital inclination is 26 degrees +/- 6 degrees, and the mass of the secondary is 0.52(-0.09)(+0.18) M-circle dot, which should be a late-K to early-M type star. Fourteen frequencies are extracted from Kepler light curves, of which six independent frequencies in the high-frequency region are identified as the p-mode pulsations of delta Sct star, and one independent frequency in the low-frequency region (f(2) = 1.3033 cd(-1)) is probably the rotational frequency due to the starspots rather than the ellipsoidal effect.