Ultra-short-period (USP) planet formation by high-eccentricity Kozai-Lidov migration

Описание: An example of the Kozai-Lidov high-eccentricity migration scenario.
Some kind of migration process is required to form an USP planet. Two main migration scenarios have been proposed: high-ecentricity migration (e.g. Petrovich 2015) and low-eccentricity (Pu & Lai 2019). In both scenarios, the eccentricity of the inner planet is excited by some kind of mechanism, triggering tidal circularization with subsequent shrinking of the semi-major axis.
One process that can excite the eccentricity of the inner planet is the so-called Kozai-Lidov mechanism. This is a secular exchange of angular momentum between two mutually inclined orbits which results in periodic oscillations in eccentricity and inclination.
This animation shows the evolution of two orbits with Kozai-Lidov oscillations. The inner planet has an orbital period of 4 days, and is inclined by 89 degrees with respect to the outer planet's orbital plane. This configuration leads to rapid Kozai-Lidov oscillations, during which the inner planet becomes highly eccentric. The eccentricity is then damped by tidal forces, and the planet stabilizes in a circular orbit with period 0.7 days, which quenches Kozai-Lidov oscillations.