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Exoplanetary observations reveal that the occurrence rate of hot Jupiters iscorrelated with star clustering. In star clusters, interactions betweenplanetary systems and close fly-by stars can significantly change thearchitecture of primordially coplanar, circular planetary systems. Flybys indense clusters have a significant impact on hot Jupiter formation viaactivation of high eccentricity excitation mechanisms such as theZeipel-Lidov-Kozai (ZLK) effect and planet-planet scattering. Previous studieshave shown that if there are two giant planets in the planetary system, closeflybys can efficiently activate the ZLK mechanism, thus triggering higheccentricity tidal migration and ultimately form hot Jupiters in star clusters.Here we extend our previous study with a multi-planet (triple) system. Weperform high precision, high-accuracy few-body simulations of stellar flybysand subsequent planetary migration within the perturbed planetary systems usingthe code {\tt SpaceHub}. Our simulations demonstrate that a single close flybyon a multi-planet system in a cluster can activate secular chaos and ultimatelylead to hot Jupiter formation via high eccentricity migration. We find that thehot Jupiter formation rate per system increases with both the size of theplanetary system as well as with the mass of the outer planet, and we quantifythe relative formation fractions for a range of parameters. Hot Jupiters formedvia secular chaos are expected to be accompanied by massive companions withvery long periods. Our study further shows that this flyby-induced secularchaos is preferred in low-density clusters where multi-planet systems are morelikely to survive, and that it contributes a significant fraction of the hotJupiter formation in star clusters compared to the flyby-induced ZLK mechanism.

Hot Jupiter formation in dense clusters: secular chaos in multi-planetary systems