On Lithium-6 as a Diagnostic of the Lithium-enrichment Mechanism in Red Giants

High lithium-7 ($\mathrm{^7Li}$) abundances in giants are indicative of non-standard physical processes affecting the star. Mechanisms that could produce this signature include contamination from an external source, such as planets, or internal production and subsequent mixing to the stellar surface. However, distinguishing between different families of solutions has proven challenging, and there is no current consensus model that explains all the data. The lithium-6 ($\mathrm{^6Li}$) abundance may be a potentially important discriminant, as the relative $\mathrm{^6Li}$ and $\mathrm{^7Li}$ abundances are expected to be different if the enrichment were to come from internal production or from engulfment. In this work, we model the $\mathrm{^6Li}$ and $\mathrm{^7Li}$ abundances of different giants after the engulfment of a substellar mass companion. Given that $\mathrm{^6Li}$ is more strongly affected by Galactic chemical evolution than $\mathrm{^7Li}$, $\mathrm{^6Li}$ is not a good discriminant at low metallicities, where it is expected to be low in both star and planet. For modeled metallicities ([Fe/H]$>-0.5$), we use a "best case" initial $\mathrm{^6Li/^7Li}$ ratio equal to the solar value. $\mathrm{^6Li}$ increases significantly after the engulfment of a companion. However, at metallicities close to solar and higher, the $\mathrm{^6Li}$ signal does not last long in the stellar surface. As such, detection of surface $\mathrm{^6Li}$ in metal-rich red giants would most likely indicate the action of a mechanism for $\mathrm{^6Li}$-enrichment other than planet engulfment. At the same time, $\mathrm{^6Li}$ should not be used to reject the hypothesis of engulfment in a $\mathrm{^7Li}$-enriched giant or to support a particular $\mathrm{^7Li}$-enhancement mechanism.