Are WASP-107-like Systems Consistent with High-eccentricity Migration?

WASP-107 b seems to be a poster child of the long-suspected high-eccentricity migration scenario. It is on a 5.7-day, polar orbit. The planet is Jupiter-like in radius but Neptune-like in mass with exceptionally low density. WASP-107 c is on a 1100-day, $e=0.28$ orbit with at least Saturn mass. Planet b may still have a residual eccentricity of $0.06\pm 0.04$: the ongoing tidal dissipation leads to the observed internally heated atmosphere and hydrodynamic atmospheric erosion. We present a population synthesis study coupling octopole Lidov-Kozai oscillations with various short-range forces, while simultaneously accounting for the radius inflation and tidal disruption of the planet. We find that a high-eccentricity migration scenario can successfully explain nearly all observed system properties. Our simulations further suggest that the initial location of WASP-107 b at the onset of migration is likely within the snowline ($<0.5\,{\rm AU}$). More distant initial orbits usually lead to tidal disruption or orbit crossing. WASP-107 b most likely lost no more than 20% of its mass during the high-eccentricity migration, i.e. it did not form as a Jupiter-mass object. More vigorous tidally-induced mass loss leads to disruption of the planet during migration. We predict that the current-day mutual inclination between the planets b and c is substantial: at least 25-55$^\circ$ which may be tested with future Gaia astrometric observations. Knowing the current-day mutual inclination may further constrain the initial orbit of planet b. We suggest that the proposed high-eccentricity migration scenario of WASP-107 may be applicable to HAT-P-11, GJ-3470, HAT-P-18, and GJ-436 which have similar orbital architectures.