Hot Jupiter and Ultra-cold Saturn Formation in Dense Star Clusters

The discovery of high incidence of hot Jupiters in dense clusters challenges the field-based hot Jupiter formation theory. In dense clusters, interactions between planetary systems and flyby stars are relatively common. This has a significant impact on planetary systems, dominating hot Jupiter formation. In this paper, we perform high precision, few-body simulations of stellar flybys and subsequent planet migration in clusters. A large parameter space exploration demonstrates that close flybys that change the architecture of the planetary system can activate high eccentricity migration mechanisms: LK and planet-planet scattering, leading to high hot Jupiter formation rate in dense clusters. Our simulations predict that many of the hot Jupiters are accompanied by "ultra-cold Saturns," expelled to apastra of thousands of astronomical units. This increase is particularly remarkable for planetary systems originally hosting two giant planets with semimajor axis ratios of ∼4 and the flyby star approaching nearly perpendicular to the planetary orbital plane. The estimated lower limit to the hot Jupiter formation rate of a virialized cluster is $\sim 1.6\times {10}^{-4}{(\sigma /1\mathrm{km}{{\rm{s}}}^{-1})}^{5}{({a}_{{\rm{p}}}/20\mathrm{au})({M}_{{\rm{c}}}/1000{M}_{\odot })}^{-2}$ Gyr^-1 per star, where σ is the cluster velocity dispersion, a_p is the size of the planetary system, and M_c is the mass of the cluster. Our simulations yield a hot Jupiter abundance that is ∼50 times smaller than that observed in the old open cluster M67. We expect that interactions involving binary stars, as well as a third or more giant planets, will close the discrepancy.