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Steady-state planet migration by the Kozai-Lidov mechanism in stellar binaries

We study the steady-state orbital distributions of giant planets migrating through the combination of the Kozai-Lidov (KL) mechanism due to a stellar companion and friction due to tides raised on the planet by the host star. We run a large set of Monte Carlo simulations that describe the secular evolution of a star-planet-star triple system including the effects from general relativistic precession, stellar and planetary spin evolution, and tides. Our simulations show that KL migration produces Hot Jupiters (HJs) with semi-major axes that are generally smaller than in the observations and they can only explain the observations if the following are both true: (i) tidal dissipation at high eccentricities is at least $\sim 150$ times more efficient than the upper limit inferred from the Jupiter-Io interaction; (ii) highly eccentric planets get tidally disrupted at distances $\gtrsim 0.015$ AU. Based on the occurrence rate and semi-major axis distribution of HJs, we find that KL migration in stellar binaries can produce at most $\sim 20\%$ of the observed HJs. Almost no intermediate-period (semi-major axis $\sim0.1-2$ AU) planets are formed by this mechanism - migrating planets spend most of their lifetimes undergoing KL oscillations at large orbital separations ($>2$ AU) or as Hot Jupiters.