Super lithium-rich K giant with low $^{12}\rm{C}$ to $^{13}\rm{C}$ ratio

Abstract: The lithium abundances in a few percent of giants exceed the value predicted by the standard stellar evolution models, and the mechanisms of Li enhancement are still under debate. The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) survey has obtained over six million spectra in the past five years, and thus provides a great opportunity to search these rare objects and to more clearly understand the mechanisms of Li enhancement. Based on the high-resolution spectrum we obtained the stellar parameters ($T_\mathrm{eff}$, $\log g$, [Fe/H]), and determined the elemental abundances of Li, C, N, $\alpha$, Fe-peak, r-process, s-process elements, and the projected rotational velocity. For a better understanding of the effect of mixing processes, we also derived the $^{12}\rm{C}$ to $^{13}\rm{C}$ ratio, and constrained the evolutionary status of TYC\,3251-581-1 based on the BaSTI stellar isochrones. The super Li-rich giant TYC\,3251-581-1 has $\rm{A(Li)} = 3.51$, the average abundance of two lithium lines at $\lambda = 6708$ \AA\ and 6104 \AA\ based on the non-local thermodynamic equilibrium (NLTE) analysis. The atmospheric parameters show that our target locates on the luminosity function bump. The low carbon isotopic ratio ($^{12}\rm{C}/^{13}\rm{C} = 9.0 $), a slow rotational velocity $v\sin i = 2.2\ \rm{km\,s}^{-1}$, and no sign of IR excess suggest that additional mixing after first dredge up (FDU) should occur to bring internal synthesized Li to the surface. The low carbon ($[\rm{C}/\rm{Fe}] \sim -0.34$ ) and enhanced nitrogen ($[\rm{N}/\rm{Fe}] \sim 0.33$) are also consistent with the sign of mixing. Given the evolutionary stage of TYC\,3251-581-1 with the relatively low $^{12}\rm{C}/^{13}\rm{C}$, the internal production which replenishes Li in the outer layer is the most likely origin of Li enhancement for this star.