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

Abstract

Observed hot Jupiter (HJ) systems exhibit a wide range of stellar spin-orbit misalignment angles. The origin of these HJs remains unclear. This paper investigates the inward migration of giant planets due to Lidov-Kozai (LK) oscillations of orbital eccentricity/inclination induced by a distant (100-1000 AU) stellar companion and orbital circularization from dissipative tides. We conduct a large population synthesis study, including octupole gravitational potential from the stellar companion, mutual precession of the host stellar spin axis and planet orbital axis, pericenter advances due to short-range-forces, tidal dissipation in the planet, and stellar spin-down in the host star due to magnetic braking. We examine a range of planet masses (0.3 − 5 M J ) and initial semi-major axes (1 − 5 AU), different properties for the host star, and varying tidal dissipation strengths. The fraction (f HJ ) of systems that result in HJs is a function of planet mass and stellar type, with f HJ in the range of 1 − 4% (depending on tidal dissipation strength) for M p = 1 M J , and larger (up to 8%) for more massive planets. The production efficiency of "hot Saturns" (M p = 0.3M J ) is much lower, because most of the inward-migrating planets are tidally disrupted. We find that the fraction of systems that result in either HJ formation or tidal disruption, f mig 11 − 14% is roughly constant, having little variation with planet mass, stellar type and tidal dissipation strength. This "universal" migration fraction can be understood qualitatively from analytical migration criteria based on the properties of octupole LK oscillations. The distribution of final stellar obliquities for the HJ systems formed in our calculations exhibits a complex dependence on the planet mass and stellar type. For M p = (1 − 3)M J , the distribution is always bimodal, with peaks around ∼ 30 • and ∼ 130 • . The obliquity distribution for massive planets (M p = 5M J ) depends on the host stellar type, with a preference for low obliquities for solar-type stars, and higher obliquities for more massive (1.4M ) F-type stars.

On the formation of hot and warm Jupiters via secular high-eccentricity migration in stellar triples

“…Compared to the case of a stellar binary and combining the different t V,1 , the KS D and p values are D ≈ 0.10 and p ≈ 0.29 for the '2+2' configuration and D ≈ 0.08 and p ≈ 0.58 for the '3+1' configuration. These distributions are also similar to those of Anderson et al (2016), although the latter are truncated at a smaller orbital period.…”

“…1). For reference, and in order to investigate the differences, we also carried out simulations of a planet in a stellar binary mimicking previous studies of high-e migration in stellar binaries (Wu & Murray 2003;Fabrycky & Tremaine 2007;Naoz et al 2012;Petrovich 2015a;Anderson et al 2016;Petrovich & Tremaine 2016). With some approximations, high-e migration fractions in stellar binaries can also be calculated analytically (Muñoz et al 2016).…”

“…For reference, we also include with black open circles the distribution from Fig. 23 of Anderson et al (2016) for M p = 1M J and χ = 100, where χ ≡ 10 τ 1 /s and τ 1 is the tidal time lag of the planet (cf. Table 1 of the latter paper).…”

“…(ii) secular Lidov-Kozai (LK) oscillations (Lidov 1962;Kozai 1962) induced by a distant companion star or an additional (massive) planet on an inclined orbit (Wu & Murray 2003;Fabrycky & Tremaine 2007;Naoz et al 2012;Petrovich 2015a;Anderson et al 2016;Petrovich & Tremaine 2016); (iii) secular excitation induced by a close and coplanar, but eccentric planetary companion (Petrovich 2015b;Xue & Suto 2016), and (iv) secular chaos in multiplanet systems with at least three planets in mildly inclined and eccentric orbits Hamers et al 2016a). …”

“…Also, a high efficiency of tidal dissipation in the HJ is required, and the predicted orbital periods are on the short end of the observations unless tidal dissipation is very efficient (e.g. Petrovich 2015a; Anderson et al 2016).…”