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.

Many exoplanetary systems containing hot Jupiters are observed to have highly misaligned orbital axes relative to the stellar spin axes. Kozai-Lidov oscillations of orbital eccentricity and inclination induced by a binary companion, in conjunction with tidal dissipation, constitute a major channel for the production of hot Jupiters. We demonstrate that gravitational interaction between the planet and its oblate host star can lead to chaotic evolution of the stellar spin axis during Kozai cycles. As parameters such as the planet mass and stellar rotation period are varied, periodic islands can appear in an ocean of chaos, in a manner reminiscent of other dynamical systems. In the presence of tidal dissipation, the complex spin evolution can leave an imprint on the final spin-orbit misalignment angles.

Eclipsing binaries are observed to have a range of eccentricities and spin-orbit misalignments (stellar obliquities). Whether such properties are primordial, or arise from post-formation dynamical interactions remains uncertain. This paper considers the scenario in which the binary is the inner component of a hierarchical triple stellar system, and derives the requirements that the tertiary companion must satisfy in order to raise the eccentricity and obliquity of the inner binary. Through numerical integrations of the secular octupole-order equations of motion of stellar triples, coupled with the spin precession of the oblate primary star due to the torque from the secondary, we obtain a simple, robust condition for producing spin-orbit misalignment in the inner binary: In order to excite appreciable obliquity, the precession rate of the stellar spin axis must be smaller than the orbital precession rate due to the tertiary companion. This yields quantitative requirements on the mass and orbit of the tertiary. We also present new analytic expressions for the maximum eccentricity and range of inclinations allowing eccentricity excitation (Lidov-Kozai window), for stellar triples with arbitrary masses and including the non-Keplerian potentials introduced by general relativity, stellar tides and rotational bulges. The results of this paper can be used to place constraints on unobserved tertiary companions in binaries that exhibit high eccentricity and/or spin-orbit misalignment, and will be helpful in guiding efforts to detect external companions around stellar binaries. As an application, we consider the eclipsing binary DI Herculis, and identify the requirements that a tertiary companion must satisfy to produce the observed spin-orbit misalignment.

Many exoplanetary systems containing hot Jupiters are found to possess significant misalignment between the spin axis of the host star and the planet's orbital angular momentum axis. A possible channel for producing such misaligned hot Jupiters involves Lidov-Kozai oscillations of the planet's orbital eccentricity and inclination driven by a distant binary companion. In a recent work (Storch, Anderson & Lai 2014), we have shown that a proto-hot Jupiter undergoing Lidov-Kozai oscillations can induce complex, and often chaotic, evolution of the spin axis of its host star. Here we explore the origin of the chaotic spin behavior and its various features in an idealized non-dissipative system where the secular oscillations of the planet's orbit are strictly periodic. Using Hamiltonian perturbation theory, we identify a set of secular spin-orbit resonances in the system, and show that overlaps of these resonances are responsible for the onset of wide-spread chaos in the evolution of stellar spin axis. The degree of chaos in the system depends on the adiabaticity parameter ǫ, proportional to the ratio of the Lidov-Kozai nodal precession rate and the stellar spin precession rate, and thus depends on the planet mass, semi-major axis and the stellar rotation rate. For systems with zero initial spin-orbit misalignment, our theory explains the occurrence (as a function of ǫ) of "periodic islands" in the middle of a "chaotic ocean" of spin evolution, and the occurrence of restricted chaos in middle of regular/periodic spin evolution. Finally, we discuss a novel "adiabatic resonance advection" phenomenon, in which the spin-orbit misalignment, trapped in a resonance, gradually evolves as the adiabaticity parameter slowly changes. This phenomenon can occur for certain parameter regimes when tidal decay of the planetary orbit is included.

We study the possibility of tidal dissipation in the solid cores of giant planets and its implication for the formation of hot Jupiters through high-eccentricity migration. We present a general framework by which the tidal evolution of planetary systems can be computed for any form of tidal dissipation, characterized by the imaginary part of the complex tidal Love number, Im[k 2 (ω)], as a function of the forcing frequency ω. Using the simplest viscoelastic dissipation model (the Maxwell model) for the rocky core and including the effect of a nondissipative fluid envelope, we show that with reasonable (but uncertain) physical parameters for the core (size, viscosity and shear modulus), tidal dissipation in the core can accommodate the tidal-Q constraint of the Solar system gas giants and at the same time allows exoplanetary hot Jupiters to form via tidal circularization in the high-e migration scenario. By contrast, the often-used weak friction theory of equilibrium tide would lead to a discrepancy between the Solar system constraint and the amount of dissipation necessary for high-e migration. We also show that tidal heating in the rocky core can lead to modest radius inflation of the planets, particularly when the planets are in the high-eccentricity phase (e ∼ 0.6) during their high-e migration. Finally, as an interesting by-product of our study, we note that for a generic tidal response function Im[k 2 (ω)], it is possible that spin equilibrium (zero torque) can be achieved for multiple spin frequencies (at a given e), and the actual pseudosynchronized spin rate depends on the evolutionary history of the system.