Hydrodynamical turbulence in eccentric circumbinary discs and its impact on the in situ formation of circumbinary planets

Eccentric gaseous discs are unstable to a parametric instability involving the resonant interaction between inertial-gravity waves and the eccentric mode in the disc. We present three-dimensional global hydrodynamical simulations of inviscid circumbinary discs that form an inner cavity and become eccentric through interaction with the central binary. The parametric instability grows and generates turbulence that transports angular momentum with stress parameter alpha similar to 5 x 10(-3) at distances less than or similar to 7 a(bin), where a(bin) is the binary semimajor axis. Vertical turbulent diffusion occurs at a rate corresponding to alpha(diff) similar to 1-2 x 10(-3). We examine the impact of turbulent diffusion on the vertical settling of pebbles, and on the rate of pebble accretion by embedded planets. In steady state, dust particles with Stokes numbers St less than or similar to 0.1 form a layer of finite thickness H-d greater than or similar to 0.1H, where H is the gas scale height. Pebble accretion efficiency is then reduced by a factor r(acc)/H-d, where r(acc) is the accretion radius, compared to the rate in a laminar disc. For accreting core masses with m(p) less than or similar to 0.1 M-circle plus, pebble accretion for particles with St greater than or similar to 0.5 is also reduced because of velocity kicks induced by the turbulence. These effects combine to make the time needed by a Ceres mass object to grow to the pebble isolation mass, when significant gas accretion can occur, longer than typical disc lifetimes. Hence, the origins of circumbinary planets orbiting close to their central binary systems, as discovered by the Kepler mission, are difficult to explain using an in situ model that invokes a combination of the streaming instability and pebble accretion.