Making hot Jupiters in stellar clusters: the importance of binary exchange

It has been suggested that the occurrence rate of hot Jupiters (HJs) in open clusters might reach several per cent, significantly higher than that of the field ($\sim$ a per cent). In a stellar cluster, when a planetary system scatters with a stellar binary, it may acquire a companion star which may excite large amplitude von Zeipel-Lidov-Kozai oscillations in the planet's orbital eccentricity, triggering high-eccentricity migration and the formation of an HJ. We quantify the efficiency of this mechanism by modelling the evolution of a gas giant around a solar mass star under the influence of successive scatterings with binary and single stars. We show that the chance that a planet $\in(1,10)$ au becomes an HJ in a Gyr in a cluster of stellar density $n_*=50$ pc$^{-3}$ and binary fraction $f_\mathrm{bin}=0.5$ is about 2\% and an additional 4\% are forced by the companion star into collision with or tidal disruption by the central host. An empirical fit shows that the total percentage of those outcomes asymptotically reaches an upper limit determined solely by $f_\mathrm{bin}$ (e.g., $10\%$ at $f_\mathrm{bin}=0.3$ and 18\% at $f_\mathrm{bin}=1$) on a timescale inversely proportional to $n_*$ ($\sim$ Gyr for $n_*\sim100$ pc$^{-3}$). The ratio of collisions to tidal disruptions is roughly a few, and depends on the tidal model. Therefore, if the giant planet occurrence rate is 10~\%, our mechanism implies an HJ occurrence rate of a few times 0.1~\% in a Gyr and can thus explain a substantial fraction of the observed rate.