Lithium abundance and rotation of seismic solar analogues: solar and stellar connection from Kepler and HERMES observations

Context. Lithium abundance A (Li) and surface rotation are good diagnostic tools to probe the internal mixing and angular momentum transfer in stars. Aims. We explore the relation between surface rotation, A (Li), and age in a sample of seismic solar-analogue stars, and we study their possible binary nature. Methods. We selected a sample of 18 solar-analogue stars observed by the NASA Kepler satellite for an in-depth analysis. Their seismic properties and surface rotation rates are well constrained from previous studies. About 53 h of high-resolution spectroscopy were obtained to derive fundamental parameters from spectroscopy and A (Li). These values were combined and compared with seismic masses, radii, and ages, as well as with surface rotation periods measured from Kepler photometry. Results. Based on radial velocities, we identify and confirm a total of six binary star systems. For each star, a signal-to-noise ratio of 80 ≲ S / N ≲ 210 was typically achieved in the final spectrum around the lithium line. We report fundamental parameters and A (Li). Using the surface rotation period derived from Kepler photometry, we obtained a well-defined relation between A (Li) and rotation. The seismic radius translates the surface rotation period into surface velocity. With models constrained by the characterisation of the individual mode frequencies for single stars, we identify a sequence of three solar analogues with similar mass (~1.1  M ⊙ ) and stellar ages ranging between 1 to 9 Gyr. Within the realistic estimate of ~7% for the mass uncertainty, we find a good agreement between the measured A (Li) and the predicted A (Li) evolution from a grid of models calculated with the Toulouse-Geneva stellar evolution code, which includes rotational internal mixing, calibrated to reproduce solar chemical properties. We found a scatter in ages inferred from the global seismic parameters that is too large when compared with A (Li). Conclusions. We present the Li-abundance for a consistent spectroscopic survey of solar-analogue stars with a mass of 1.00 ± 0.15  M ⊙ that are characterised through asteroseismology and surface rotation rates based on Kepler observations. The correlation between A (Li) and P rot supports the gyrochronological concept for stars younger than the Sun and becomes clearer when the confirmed binaries are excluded. The consensus between measured A (Li) for solar analogues with model grids, calibrated on the Sun’s chemical properties, suggests that these targets share the same internal physics. In this light, the solar Li and rotation rate appear to be normal for a star like the Sun.