Planet Engulfment Signatures in Twin Stars

Planet engulfment can be inferred from enhancement of refractory elements in the photosphere of the engulfing star following accretion of rocky planetary material. Such refractory enrichments are subject to stellar interior mixing processes, namely thermohaline mixing induced by an inverse mean-molecular-weight gradient between the convective envelope and radiative core. Using MESA stellar models, we quantified the strength and duration of engulfment signatures following planet engulfment. We found that thermohaline mixing dominates during the first $\sim$5$-$45 Myr post-engulfment, weakening signatures by a factor of $\sim$2 before giving way to depletion via gravitational settling on longer timescales. Solar metallicity stars in the 0.5-1.2 $M_{\odot}$ mass range have observable signature timescales of $\sim$1 Myr$-$8 Gyr, depending on the engulfing star mass and amount of material engulfed. Early type stars exhibit larger initial refractory enhancements but more rapid depletion. Solar-like stars ($M$ = 0.9$-$1.1 $M_{\odot}$) maintain observable signatures ($>$0.05 dex) over timescales of $\sim$20 Myr$-$1.7 Gyr for nominal 10 $M_{\oplus}$ engulfment events, with longer-lived signatures occurring for low-metallicity and/or hotter stars (1 $M_{\odot}$, $\sim$2$-$3 Gyr). Engulfment events occurring well after the zero-age main sequence produce larger signals due to suppression of thermohaline mixing by gravitational settling of helium (1 $M_{\odot}$, $\sim$1.5 Gyr). These results indicate that it may be difficult to observe engulfment signatures in solar-like stars that are several Gyr old.