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

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 planet migration/disruption fractions obtained from population synthesis, and can be easily implemented for various planet and stellar/companion types, and for different distributions of initial planetary semimajor 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.