The enigma of Li-rich giants and its relation with temporal variations observed in radial velocity and stellar activity signals

Despite the large number of studies focused on the characterisation of Li-rich stars and understanding the mechanisms leading to such enrichment, their origin remains a mystery. Magnetic activity, particularly the phenomena usually associated with it, and the Li abundance (A(Li)) of stars, are in general thought to be connected. As of today, however, just how they are connected is unclear. In this work, we study a sample of young but evolved intermediate-mass red giants that are inhabitants of open clusters where planets have been searched for. Our aim is to use radial velocity (RV) and stellar activity indicator signals to look for relations between Li abundances and stellar activity or variability. We explored how the standard deviation (STD), peak-to-peak amplitude (PTP), mean, and median of typical stellar activity indicators (BIS, FWHM, $T_\textrm{eff}$, and H$\alpha$ index) change as a function of the Li content of 82 red giants. Furthermore, we computed weighted Pearson correlation coefficients ($\rho_w$) between time series of RV measurements and the stellar activity indicators for the stars in our sample. To aid our results, we also studied generalized Lomb-Scargle periodograms (GLSP) to capture possible significant periodic temporal variations in our data. Our analysis indicates that the STD and PTP of BIS and FWHM, the mean and median of the H$\alpha$ index, and $v\sin(i)$ increase exponentially with A(Li) in our sample of red giants. Significant temporal variations and correlations between RVs and activity indicators also tend to be found preferentially for stars where high A(Li) is observed. Most of the Li-rich stars in our sample either show strong correlations of RV with at least one of the stellar activity indicators or reveal significant periodic temporal variations in their GLSPs of stellar activity indicators that are consistent with those found for RV.