  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.

Earth and Planetary Astrophysics