Abstract
Throughout a planetary system's formation evolution, some of the planetary material may end up falling into the host star and be engulfed by it, leading to a potential variation of the stellar composition. The present study explores how planet engulfment may impact the chemical composition of the stellar surface and discusses what would be the rate of events with an observable imprint, for Sun-like stars. We use data from the NGPPS calculations by the Generation III Bern model to analyse the conditions under which planet engulfment may occur. Additionally, we use stellar models computed with Cesam2k20 to account for how the stellar internal structure and its processes may affect the dilution of the signal caused by planet engulfment. Our results show that there are three different phases associated to different mechanisms under which engulfment events may happen. Moreover, systems that undergo planet engulfment are more likely to come from protoplanetary disks that are more massive and more metal-rich than non-engulfing systems. Engulfment events leading to an observable signal happen after the dissipation of the protoplanetary disk when the convective envelope of the stars becomes thinner. With the stellar convective layer shrinking as the star evolves in the main sequence, they display a higher variation of chemical composition, which also correlates with the amount of engulfed material. By accounting for the physical processes happening in the stellar interior and in the optimistic case of being able to detect variations above 0.02 dex in the stellar composition, we find an engulfment rate no higher than $20\%$ for Sun-like stars that may reveal detectable traces of planet engulfment. Engulfment events that lead to an observable variation of the stellar composition are rare due to the specific conditions required to result in such signatures.