Seismic probing of the first dredge-up event through the eccentric red-giant & red-giant spectroscopic binary KIC9163796
Binaries in double-lined spectroscopic systems provide a homogeneous set of stars. Differences of parameters, such as age or initial conditions, which otherwise would have strong impact on the stellar evolution, can be neglected. The observed differences are determined by the difference in stellar mass between the two components. The mass ratio can be determined with much higher accuracy than the actual stellar mass. In this work, we aim to study the eccentric binary system KIC9163796, whose two components are very close in mass and both are low-luminosity red-giant stars from four years of Kepler space photometry and high-resolution spectroscopy with Hermes. Mass and radius of the primary were determined through asteroseismology to be 1.39+/-0.06 Mo and 5.35+/-0.09 Ro, resp. From spectral disentangling the mass ratio was found to be 1.015+/-0.005 and that the secondary is ~600K hotter than the primary. Evolutionary models place both components, in the early and advanced stage of the first dredge-up event on the red-giant branch. From theoretical models of the primary, we derived the internal rotational gradient. From a grid of models, the measured difference in lithium abundance is compared with theoretical predictions. The surface rotation of the primary is determined from the Kepler light curve and resembles the orbital period within 10 days. The radial rotational gradient between the surface and core is found to be 6.9+2.0/-1.0. The agreement between the surface rotation with the seismic result indicates that the full convective envelope is rotating quasi-rigidly. The models of the lithium abundance are compatible with a rigid rotation in the radiative zone during the main sequence. Because of the many constraints offered by oscillating stars in binary systems, such objects are important test beds of stellar evolution.