Probing Binary Architectures of Lithium-Rich Giants in GALAH with COSMIC and Stellar Models

Surface lithium is depleted when a star goes through the first dredge-up phase, yet $1\%$ of red giants are found to be Li-rich. The formation mechanism for these remains uncertain. We combine observational constraints from GALAH Li-rich giants, with the binary population synthesis code COSMIC to investigate system properties of these objects assuming binary mass transfer. By evolving 9 million binary systems, we find that binary histories most consistent with observational constraints are mass transfer from an intermediate-mass AGB donor to a main-sequence star now observed as a Li-rich red giant. In GALAH, $9\%$ of main-sequence stars have $\rm A(Li)=2.5-3.2$ dex making it plausible to create red giants with $\rm A(Li)=1.5-2.2 \; dex$ via main-sequence mass transfer, but cannot explain the more enriched giants $\rm A(Li) \gtrsim 2.2 \; dex$. Nucleosynthetic yields from stellar models show that AGB stars with initial masses of $4.25-5 \; \rm M_\odot$ and $8 \; \rm M_\odot$ contain the most Li in their ejecta. Intermediate-mass AGB stars comprise $29\%$ of COSMIC results, with present-day separations $s=3.3\pm0.5 \rm \; AU$ and mass ratios $q=0.5-1.6$. We achieve $95\%$ agreement in mean enhancements in $\rm (Ba, Y)$ between GALAH observations and stellar models of 6 and $8 \rm \; M_\odot$ AGB, assuming $1\%$ mass transfer efficiency. We find a low mass transfer efficiency best reproduces GALAH observations suggesting that the preferred mass transfer mechanism for Li-enrichment is via wind Roche Lobe Overflow. While we constrain the most plausible binary parameters assuming AGB mass transfer creates Li-rich giants, discrepancies in nucleosynthesis comparisons, and the small fraction of Li-enhanced main-sequence stars suggests additional enrichment mechanisms are likely.