A substantial fraction of Hot Jupiters have orbital inclinations misaligned with respect to the spin axis of their host star. The prevalence of this phenomenon posed a challenge to the conventional formation paradigm, wherein Hot Jupiters were expected to reach they close-in orbits early in a system’s evolution via disk driven or ‘Type II’ migration. However, recent work has shown that misalignments fall naturally out of the Type II evolutionary track when a binary companion is invoked. In this formulation, the companion gravitationally torques the protoplanetary disk, exciting a spin orbit misalignment via encounter with a secular resonance between the stellar-precession and disk-torquing frequencies.
Fundamental to the disk-torquing model is the prevalence of stellar binaries, particularly during the early stages of star formation. Indeed, stars are more likely to form in stellar associations than in isolation, and the ubiquity of stellar binaries and higher multiplicities throughout and beyond the pre-main sequence phase has been well established. Given that a significant fraction of binaries have had or have additional companions, understanding the dynamics of stellar associations beyond binaries presents an opportunity to standardize expected outcomes of the disk-torquing model across the entire range of stellar and planetary populations.
In pursuit of this goal, this work extends the theoretical framework of the binary disk-torquing model to include a tertiary companion. In such a system the disk experiences multiple, competing modes of gravitational perturbation. As in the binary disk-torquing model, these harmonics can excite distinct secular spin-orbit resonances. But, unlike the binary model, the addition of the tertiary companion creates the possibility of resonant overlap and the conditions necessary for the chaotic evolution of the stellar spin axis. We begin with the simplest, non-trivial model for stellar spin axis dynamics, based on linear Lagrange-Laplace theory of secular dynamics and derive analytical conditions for chaos. Subsequently, we augment our model using a Kaula-type expansion of the governing Hamiltonian to generalize our model to arbitrary inclination. We characterize the dynamics of the system and define regions of parameter space where the stellar obliquity significantly diverges from that of an otherwise identical binary system.