Seismic probing of the first dredge-up event through the eccentric red-giant and red-giant spectroscopic binary KIC 9163796

Context. Binaries in double-lined spectroscopic systems (SB2) 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. Aim. In this work, we aim to study the eccentric binary system KIC 9163796, whose two components are very close in mass and both are low-luminosity red-giant stars. Methods. We analysed four years of Kepler space photometry and we obtained high-resolution spectroscopy with the Hermes instrument. The orbital elements and the spectra of both components were determined using spectral disentangling methods. The effective temperatures, and metallicities were extracted from disentangled spectra of the two stars. Mass and radius of the primary were determined through asteroseismology. The surface rotation period of the primary is determined from the Kepler light curve. From representative theoretical models of the star, we derived the internal rotational gradient, while for a grid of models, the measured lithium abundance is compared with theoretical predictions. Results. From seismology the primary of KIC 9163796 is a star of 1.39 ± 0.06M⊙, while the spectroscopic mass ratio between both components can be determined with much higher precision by spectral disentangling to be 1.015 ± 0.005. With such mass and a difference in effective temperature of 600 K from spectroscopy, the secondary and primary are, respectively, in the early and advanced stage of the first dredge-up event on the red-giant branch. The period of the primary’s surface rotation resembles the orbital period within ten days. The radial rotational gradient between the surface and core in KIC 9163796 is found to be $6.9^{+2.0}_{-1.0}$ 6.9−1.0+2.0 6.9−1.0+2.0 . This is a low value but not exceptional if compared to the sample of typical single field stars. The seismic average of the envelope’s rotation agrees with the surface rotation rate. The lithium’abundance is in agreement with quasi rigidly rotating models. Conclusions. 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 se