Hints for hidden planetary companions to hot Jupiters in stellar binaries

Searches for stellar companions to hot Jupiters (HJs) have revealed that planetary systems hosting a HJ are approximately three times more likely to have a stellar companion with a semimajor axis between 50 and 2000 AU, compared to field stars. This correlation suggests that HJ formation is affected by the stellar binary companion. A potential model is high-eccentricity migration, in which the binary companion induces high-eccentricity Lidov-Kozai (LK) oscillations in the proto-HJ orbit, triggering orbital migration driven by tides. A pitfall of this `binary-LK' model is that the observed stellar binaries hosting HJs are typically too wide to produce HJs in sufficient numbers, because of suppression by short-range forces. We propose a modification to the binary-LK model in which there is a second giant planet orbiting the proto-HJ at a semimajor axis of several tens of AU. Such companions are currently hidden to observations, but their presence could be manifested by a propagation of the perturbation of the stellar binary companion inwards to the proto-HJ, thereby overcoming the barrier imposed by short-range forces. Our model does not require the planetary companion orbit to be eccentric and/or inclined with respect to the proto-HJ, but its semimajor axis should lie in a specific range given the planetary mass and binary semimajor axis, and the inclination with respect to the binary should be near $40^\circ$ or $140^\circ$. Our prediction for planetary companions to HJs in stellar binaries should be testable by future observations.