The formation efficiency of close-in planets via Lidov-Kozai migration: analytic calculations

TL;DR

This paper develops an analytical approach to estimate the likelihood of close-in planet formation via Lidov-Kozai oscillations, considering various physical effects, and compares it with population synthesis results.

Contribution

It introduces a new analytical method to calculate hot Jupiter formation and migration fractions, including octupole and short-range forces effects, matching numerical simulations.

Findings

Analytical method accurately reproduces population synthesis results.

Migration fraction weakly depends on system parameters.

Conditions for super-Earth survival during Lidov-Kozai migration are discussed.

Abstract

Lidov-Kozai oscillations of planets in stellar binaries, combined with tidal dissipation, can lead to the formation of hot Jupiters (HJs) or tidal disruption of planets. Recent population synthesis studies have found that the fraction of systems resulting in HJs (F_HJ) depends strongly on the planet mass, host stellar type and tidal dissipation strength, while the total migration fraction F_mig = F_ HJ + F_dis (including both HJ formation and tidal disruption) exhibits much weaker dependence. We present an analytical method for calculating F_HJ and F_mig in the Lidov-Kozai migration scenario. The key ingredient of our method is to determine the critical initial planet-binary inclination angle that drives the planet to reach sufficiently large eccentricity for efficient tidal dissipation or disruption. This calculation includes the effects of the octupole potential and short-range forces on the planet. Our analytical method reproduces the resulting planet migration/disruption fractions from population synthesis, and can be easily implemented for various planet, stellar/companion types, and for different distributions of initial planetary semi-major axes, binary separations and eccentricities. We extend our calculations to planets in the super-Earth mass range and discuss the conditions for such planets to survive Lidov-Kozai migration and form close-in rocky planets.