Parking planets in circumbinary discs

Abstract

The Kepler space mission discovered about a dozen planets orbiting around binary stars systems. Most of these circumbinary planets lie near their instability boundaries at about 3 to 5 binary separations. Past attempts to match these final locations through an inward migration process were only successful for the Kepler-16 system. Here, we study 10 circumbinary systems and try to match the final parking locations and orbital parameters of the planets with a disc driven migration scenario. We performed 2D locally isothermal hydrodynamical simulations of circumbinary discs with embedded planets and followed their migration evolution using different values for the disc viscosity and aspect ratio. We found that for the six systems with intermediate binary eccentricities ($0.1 \le e_{bin}\le 0.21$) the final planetary orbits matched the observations closely for a single set of disc parameters, specifically a disc viscosity of $\alpha = 10^{-4}$, and an aspect ratio of $H/r \sim 0.04$. For these systems the planet masses were large enough to open at least a partial gap in their discs as they approach the binary, forcing the discs to become circularized and allowing for further migration towards the binary, leading to good agreement with the observed planetary orbital parameters. For systems with very small or large binary eccentricities the match was not as good because the very eccentric discs and large inner cavities in these cases prevented close-in planet migration. In test simulations with higher than observed planet masses better agreement could be found for those systems. The good agreement for 6 out of the 10 modelled systems, where the relative difference between observed and simulated final planet orbit is $\leq 10\%$, strongly supports the idea that planet migration in the disc brought the planets to their present locations.