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Observable Metal Pollution in Main-Sequence Stars: Simulations of Rocky Planets Engulfed by Stars in the $0.5$ to $1.4$ M$_\odot$ Range

The engulfment of planets by their host stars is an expected outcome of various dynamical processes and has been invoked to explain a variety of observed stellar properties, such as rapid rotation, chemical abundance abnormalities, and other transient phenomena. Recent observations support engulfment as the cause of such signatures; however, many engulfment process details remain uncertain. Here, we present a model for determining the chemical signatures produced due to the pollution of main sequence stars by rocky planets, a common engulfment scenario due to the high frequency of observed short-period rocky exoplanets. A key novel element of our model is that we calculate the gradual evaporation of the planet due to drag interactions with the stellar envelope, which can lead to observable pollution on the stellar surface even if the bulk of the planet is only destroyed below the star's outer convective zone. Our results indicate that rocky planet pollution is most easily measurable for stars in the $1.0$ to $1.4$ M$_\odot$ range and that elements such as aluminium, calcium, and vanadium, in addition to lithium, are most suited to detect pollution. We predict that it is also possible to differentiate between the engulfment of one large planet versus several small planets, for the same total pollution mass, for some stellar hosts. We find that rocky planet engulfment events generally take years to decades for most stars. Our results can guide future observational campaigns that may search for sites of past or current engulfment events.