Chaotic dynamics of stellar spin driven by planets undergoing Lidov-Kozai oscillations: resonances and origin of chaos

Abstract

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.

Spin–Orbit Misalignment of Merging Black Hole Binaries with Tertiary Companions

“…These behaviors are qualitatively similar to the chaotic evolution of stellar spin driven by Newtonian spin-orbit coupling with a giant planet undergoing high-eccentricity migration (Storch et al 2014;Storch & Lai 2015;Anderson et al 2016;Storch et al 2017).…”

“…The related precession rate Ω L is of order t −1 LK at e ∼ 0 (Equation 17), but increases with e. Depending on the ratio of Ω dS and Ω L , we expect three possible spin behaviors: (i) For Ω L Ω dS ("nonadiabatic"), the spin axisŜ 1 cannot "keep up" with the rapidly changingL, and thus effectively precesses aroundĴ, keeping θ SJ ≡ cos ("trans-adiabatic"), the spin evolution can be chaotic due to overlapping resonances. Since both Ω dS and Ω L depend on e during the LK cycles, the precise transitions between these regimes can be fuzzy (Storch et al 2014;Storch & Lai 2015;Anderson et al 2016;Storch et al 2017).…”

Formation of hot Jupiters through secular chaos and dynamical tides

“…In addition, tidal disruption of the planet, which severely limits the efficiency of Lidov-Kozai migration of giant planets (Petrovich 2015a;Anderson et al 2016;Muñoz et al 2016), has not been systematically explored in the secular chaos scenario. Furthermore, to predict the final stellar obliquities of HJ systems, one must include the effect of spinorbit coupling, as the variation of the stellar spin during the high-e migration plays an important role in determining the spin-orbit evolution (Storch et al 2014;Storch & Lai 2015;Anderson et al 2016;Storch et al 2017).…”

Eccentricity and spin-orbit misalignment in short-period stellar binaries as a signpost of hidden tertiary companions

“…If the inner binary achieves a sufficiently small pericenter distance, a torque due to the stellar quadrupole (arising from stellar oblateness) may induce a change in the direction of the spin axis, but the degree of spin-orbit misalignment depends on several factors. In previous work (Storch et al 2014;Anderson et al 2016), we have investigated the spin dynamics of a planet-hosting star, as a result of the planet undergoing LK oscillations due to a distant stellar companion (see also Storch & Lai 2015). The evolution of the stellar spin-axis can be complicated, with several qualitatively distinct types of possible behavior, depending on the combination of planet mass, stellar spin period and the orbital geometries of the inner and outer binaries.…”