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ABSTRACT The predominant formation channel of hot Jupiters remains a puzzle in exoplanet science. One potential way to distinguish the different mechanisms is to study the characteristics of close-in companions to hot Jupiters. In this study, our main focus is to investigate the post-disc evolution of planetary systems initially composed of one Jupiter and several super-Earths through numerical N-body simulations spanning a period of 107 yr. By tracing the evolution of each planetary system, we find that only 5.6 per cent of the systems remain stable. Dynamical instabilities are more prevalent in systems with less massive super-Earths and those containing hot Jupiters. Our findings uncover a positive correlation between the presence of close-in companions and the orbital periods of the giant planets. Specifically, we find that approximately 10.9 ± 1.9 per cent of hot Jupiters and 36.4 ± 1.8 per cent of warm Jupiters have close-in companions after 107 yr. Moreover, extending the integration time to 108 yr reveals that only 1.4 ± 1.0 per cent of hot Jupiters and 20.3 ± 2.2 per cent of warm Jupiters host close-in companions. We also investigate the effects of general relativistic, tidal dissipation, and initial spacing between Jupiters and their neighbouring planets on the frequency of close-in companions for these short-period Jupiters. Our simulations suggest that the general relativity effect plays a crucial role in contributing to the isolation of hot Jupiters. Furthermore, we observe that the more compact the planetary systems are initially, the less likely it is for Jupiters to host close-in companions.
He et al. (Mon,) studied this question.