Survey of Li-rich giants among Kepler and LAMOST fields: Determination of Li-rich giants Evolutionary Phase

In this letter, we report the discovery of 24 new super Li-rich (A(Li) $\ge$ 3.2) giants of He-core burning phase at red clump region. Results are based on systematic search of a large sample of about 12,500 giants common to the LAMOST spectroscopic and Kepler time resolved photometric surveys. The two key parameters derived from Kepler data; average period spacing ($\Delta p$) between $l=1$ mixed gravity dominated g-modes and average large frequency separation ($\Delta \nu$) $l=0$ acoustic p-modes, suggest all the Li-rich giants are in He-core burning phase. This is the first unbiased survey subjected to a robust technique of asteroseismic analysis to unambiguously determine evolutionary phase of Li-rich giants. The results provide a strong evidence that Li enhancement phenomenon is associated with giants of He-core burning phase, post He-flash, rather than any other phase on RGB with inert He-core surrounded by H-burning shell.