Enhanced Lidov-Kozai migration and the formation of the transiting giant planet WD1856+534b

TL;DR

This paper explores how high-eccentricity migration driven by Lidov-Kozai effects in a complex quadruple star system can explain the formation of the transiting giant planet WD1856+534b orbiting a white dwarf, highlighting the role of secular resonances and octupole effects.

Contribution

It introduces a detailed model of Lidov-Kozai migration in a 2+2 quadruple system, expanding the understanding of how such dynamics can produce close-in giant planets around white dwarfs.

Findings

Secular inclination resonance broadens the LK window for extreme eccentricity.

Octupole effects further enhance eccentricity excitation.

Estimated initial semi-major axis for migration is between 30 and 60 AU.

Abstract

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 an 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 ($e \gtrsim 0.999$), 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. By requiring that perturbations from the companion stars be able to overcome short-range forces and excite the planet's eccentricity to $e \simeq 1$, we obtain an absolute limit of $a_{1} \gtrsim 8 \, {\rm AU} \, (a_{3} / 1500 \, {\rm AU})^{6/7}$ for the planet's semi-major axis just before migration (where $a_{3}$ is the semi-major axis of the 'outer' orbit). We suggest that, to achieve a wide LK window through the 2+2 resonance, WD1856b likely migrated from $30 \, {\rm AU} \lesssim a_{1} \lesssim 60 \, {\rm AU}$, corresponding to $\sim 10$--$20 \, {\rm AU}$ 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.