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Planetary engulfment events have long been proposed as a lithium (Li) enrichment mechanism contributing to the population of Li-rich giants $(A(mathrm{Li}) geq 1.5$ dex). Using $GALAH$ survey data and MESA stellar models, we calculate the strength and duration of the Li enrichment signature produced in the convective envelope of a host star that has engulfed a hot Jupiter (HJ) companion. We consider solar-metallicity stars in the mass range of $1.0-2.0~mathrm{M_{odot}}$ and the Li supplied by a HJ of $1.0~mathrm{M_{J}}$. We explore engulfment events that occur near the main sequence turn-off (MSTO) and out to orbital separations of $R_{star}{sim}~0.1~mathrm{AU}= 22~mathrm{R_{odot}}$. We map our results onto the Hertzsprung-Russell (H-R) Diagram, revealing the parameter space where planetary engulfment events produce significant Li enrichment signatures. We also map the associated survival times of these signatures, which range across 9 orders of magnitude. Our calculations indicate that if the HJ engulfment event occurs near the MSTO or on the subgiant branch, Li enrichment can be measured at a $5sigma$ confidence level and with strengths that exceed meteoritic abundance measurements. Moreover, for stars of $1.4~mathrm{M_{odot}}$, these signatures are predicted to survive for up to 1 Gyr. We determine that Li enrichment beyond the subgiant branch must be produced by other mechanisms, such as the Cameron-Fowler process or accretion of material from an AGB companion.
The method of gyrochronology relates the age of its star to its rotation period. However, recent evidence of deviations from gyrochronology relations was reported in the literature. Here, we study the influence of tidal interaction between a star and
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