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Many exoplanetary systems containing hot Jupiters are found to possesssignificant misalignment between the spin axis of the host star and theplanet's orbital angular momentum axis. A possible channel for producing suchmisaligned hot Jupiters involves Lidov-Kozai oscillations of the planet'sorbital eccentricity and inclination driven by a distant binary companion. In arecent work (Storch, Anderson & Lai 2014), we have shown that a proto-hotJupiter undergoing Lidov-Kozai oscillations can induce complex, and oftenchaotic, evolution of the spin axis of its host star. Here we explore theorigin of the chaotic spin behavior and its various features in an idealizednon-dissipative system where the secular oscillations of the planet's orbit arestrictly periodic. Using Hamiltonian perturbation theory, we identify a set ofsecular spin-orbit resonances in the system, and show that overlaps of theseresonances are responsible for the onset of wide-spread chaos in the evolutionof stellar spin axis. The degree of chaos in the system depends on theadiabaticity parameter $\epsilon$, proportional to the ratio of the Lidov-Kozainodal precession rate and the stellar spin precession rate, and thus depends onthe planet mass, semi-major axis and the stellar rotation rate. For systemswith zero initial spin-orbit misalignment, our theory explains the occurrence(as a function of $\epsilon$) of "periodic islands" in the middle of a "chaoticocean" of spin evolution, and the occurrence of restricted chaos in middle ofregular/periodic spin evolution. Finally, we discuss a novel "adiabaticresonance advection" phenomenon, in which the spin-orbit misalignment, trappedin a resonance, gradually evolves as the adiabaticity parameter slowly changes.This phenomenon can occur for certain parameter regimes when tidal decay of theplanetary orbit is included.

Chaotic Dynamics of Stellar Spin Driven by Planets Undergoing Lidov-Kozai Oscillations: Resonances and Origin of Chaos