Formation and stellar spin-orbit misalignment of hot Jupiters from Lidov–Kozai oscillations in stellar binaries

Observed hot Jupiter (HJ) systems exhibit a wide range of stellar spin-orbit misalignment angles. This paper investigates the inward migration of giant planets due to Lidov–Kozai (LK) oscillations induced by a distant stellar companion. We conduct a large population synthesis study, including the octupole gravitational potential from the stellar companion, mutual precession of the host stellar spin axis and planet orbital axis, tidal dissipation in the planet and stellar spin-down in the host star due to magnetic braking. We consider a range of planet masses (0.3–5MJ) and initial semimajor axes (1–5 au), different properties for the host star, and varying tidal dissipation strengths. The fraction of systems that result in HJs depends on planet mass and stellar type, with fHJ = 1–4 per cent (depending on tidal dissipation strength) for Mp = 1MJ, and larger (up to 8 per cent) for more massive planets. The production efficiency of ‘hot Saturns’ (Mp = 0.3MJ) is much lower, because most migrating planets are tidally disrupted. We find that the fraction of systems that result in either HJ formation or tidal disruption, fmig 11–14 per cent is roughly constant, having little variation with planet mass, stellar type and tidal dissipation strength. The distribution of final HJ stellar obliquities exhibits a complex dependence on the planet mass and stellar type. For Mp = (1–3)MJ, the distribution is always bimodal, with peaks around 30◦ and 130◦. The distribution for 5MJ planets depends on host stellar type, with a preference for low obliquities for solar-type stars, and higher obliquities for more massive (1.4M ) stars.