Dynamics of Stellar Spin Driven by Planets Undergoing Lidov-Kozai Migration: Paths to Spin-Orbit Misalignment

TL;DR

This paper develops an analytic theory for the evolution of stellar spin-orbit misalignment caused by Lidov-Kozai migration of planets in binary systems, revealing distinct evolutionary paths influenced by secular resonances, short-range forces, and tidal effects.

Contribution

It introduces a comprehensive analytic framework that categorizes the paths to spin-orbit misalignment during high-eccentricity planetary migration, highlighting the role of secular resonances and key parameters.

Findings

Identified five distinct spin-orbit evolution paths.

Only two paths can produce retrograde orbits.

Evolution depends on two key dimensionless parameters.

Abstract

Many exoplanetary systems containing hot Jupiters (HJs) exhibit significant misalignment between the spin axes of the host stars and the orbital angular momentum axes of the planets ("spin-orbit misalignment"). High-eccentricity migration involving Lidov-Kozai oscillations of the planet's orbit induced by a distant perturber is a possible channel for producing such misaligned HJ systems. Previous works have shown that the dynamical evolution of the stellar spin axis during the high-$e$ migration plays a dominant role in generating the observed spin-orbit misalignment. Numerical studies have also revealed various patterns of the evolution of the stellar spin axis leading to the final misalignment. Here we develop an analytic theory to elucidate the evolution of spin-orbit misalignment during the Lidov-Kozai migration of planets in stellar binaries. Secular spin-orbit resonances play a key role in the misalignment evolution. We include the effects of short-range forces and tidal dissipation, and categorize the different possible paths to spin-orbit misalignment as a function of various physical parameters (e.g. planet mass and stellar rotation period). We identify five distinct spin-orbit evolution paths and outcomes, only two of which are capable of producing retrograde orbits. We show that these paths to misalignment and the outcomes depend only on two dimensionless parameters, which compare the stellar spin precession frequency with the rate of change of the planet's orbital axis, and the Lidov-Kozai oscillation frequency. Our analysis reveals a number of novel phenomena for the stellar spin evolution, ranging from bifurcation, adiabatic advection, to fully chaotic evolution of spin-orbit angles.