Making hot Jupiters in stellar clusters - II. Efficient formation in binary systems

Observations suggested that the occurrence rate of hot Jupiters (HJs) in open clusters is largely consistent with the field (similar to 1percent) but in the binary-rich cluster M67, the rate is similar to 5 percent . How does the cluster environment boost HJ formation via the high-eccentricity tidal migration initiated by the extreme-amplitude von Zeipel-Lidov-Kozai (XZKL) mechanism forced by a companion star? Our analytical treatment shows that the cluster's collective gravitational potential alters the companion's orbit slowly, which may render the star-planet-companion configuration XZKL-favourable. We have also performed direct Gyr N-body simulations of the star cluster evolution and XZKL of planets' orbit around member stars. We find that an initially single star may acquire a companion star via stellar scattering and the companion may enable XZKL in the planets' orbit. Planets around an initially binary star may also be XZKL-activated by the companion. In both scenarios, the companion's orbit has likely been significantly changed by stellar scattering and the cluster potential before XZKL occurs. Across different cluster models, 0.8-3 per cent of the planets orbiting initially single stars have experienced XZKL while the fraction is 2-26 per cent for initially binary stars. Around a star that is binary at 1 Gyr, 13-32 per cent of its planets have undergone XZKL, and combined with single stars, the overall XZKL fraction is 3-21 per cent, most affected by the cluster binarity. If 10 per cent of the stars in M67 host a giant planet, our model predicts an HJ occurrence rate of similar to 1 percent. We suggest that HJ surveys target old, high-binarity, not-too-dense open clusters and prioritize wide binaries to maximize HJ yield.