Enhanced Lidov–Kozai migration and the formation of the transiting giant planet WD 1856+534 b

We investigate the possible origin of the transiting giant planet WD1856+534b, the first strong exoplanet candidate orbiting a white dwarf, through high-eccentricity migration (HEM) driven by the Lidov-Kozai (LK) effect. The host system's overall architecture is a hierarchical quadruple in the '2+2' configuration, owing to the presence of a tertiary companion system of two M-dwarfs. We show that a secular inclination resonance in 2+2 systems can significantly broaden the LK window for extreme eccentricity excitation (e > 0.999), allowing the giant planet to migrate for a wide range of initial orbital inclinations. Octupole effects can also contribute to the broadening of this 'extreme' LK window. We suggest that WD1856+534b likely migrated from a distance of ~30-60 AU, corresponding to a semi-major axis ~10-20 AU during the host's main-sequence phase. We discuss possible difficulties of all flavours of HEM affecting the occurrence rate of short-period giant planets around white dwarfs.