Making hot Jupiters in stellar clusters: the importance of binary exchange by Daohai Li et al. on Wednesday 30 November

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.

arXiv: http://arxiv.org/abs/http://arxiv.org/abs/2211.16015v1