Are lithium-rich giants binaries? A radial velocity variability analysis of 1400 giants

Context. The existence of low-mass giants with large amounts of lithium (Li) in their surfaces has challenged stellar evolution for decades. One of the possibilities usually discussed in the literature to explain these Li-rich giants involves the interaction with a close binary companion, a scenario that predicts that, when compared against their non-enriched counterparts, Li-rich giants should preferentially be found as part of binary systems. Aims. We aim to assemble the largest possible sample of low-mass giants with well-measured Li abundances, to determine with high statistical significance the close binary fractions of Li-rich and Li-normal giants, and thus test the binary interaction scenario for the emergence of Li-rich giants. Methods. We developed a method that uses radial velocities (RVs) at three different epochs to quantify the degree of RV variability, which we used as a proxy for the presence of a close binary companion. The method was tested and calibrated against samples of known RV standard stars and known spectroscopic binaries. We then assembled a sample of 1418 giants with available RVs from RAVE, GALAH, and Gaia, as well as stellar parameters and Li abundances from GALAH, to which we applied our variability classification. We could determine an evolutionary state for 1030 of these giants. We also compared the results of our RV variability analysis with binarity indicators from the Gaia mission. Results. When applying our methodology to the control samples, we found that the accuracy of the classification is controlled by the precision of the RVs used in the analysis. For the set of RVs available for the giants, this accuracy is 80–85%. Consistent with seismic studies, the resulting sample of giants contains a fraction of Li-rich objects in the red clump (RC) that is twice as large as that in the first ascent red giant branch (RGB). Among RC giants, the fractions of Li-rich objects with a high RV variability and with no RV variability are the same as those for Li-normal objects, but we find some evidence that these fractions may be different for giants in the first-ascent RGB. Analysis of binary indicators in Gaia DR3 shows a smaller fraction of binary giants than our criteria, but no relation can be seen between Li enrichment and binarity either. Conclusions. Our RV variability analysis indicates that there is no preference for Li-rich giants in the RC to be part of binary systems, thus arguing against a binary interaction scenario for the genesis of the bulk of Li-rich giants at that evolutionary stage. On the other hand, Li-rich giants in the RGB appear to have a small but measurable preference for having close companions, something that deserves further scrutiny with more and better data. Additional measurements of the RVs of these giants at a higher RV precision would greatly help in confirming and more robustly quantifying these results.