The interaction of a giant planet with a disc with MHD turbulence — II. The interaction of the planet with the disc

Abstract

We present a global magnetohydrodynamics (MHD) simulation of a turbulent accretion disc interacting with a giant protoplanet of 5 Jupiter masses in a fixed circular orbit. The disc model had an aspect ratio H/r= 0.1, and in the absence of the protoplanet a typical value of the Shakura–Sunyaev stress parameter α= 5 × 10−3. As expected from previous work, the protoplanet was found to open and maintain a significant gap in the disc, with the interaction leading to inward migration of the protoplanet orbit on the expected time-scale. No evidence for a persistent net mass flow through the gap was found. However, this may be because an extensive inner cavity could not be formed for the model adopted. Spiral waves were launched by the protoplanet and, although these appeared to be diffused and dissipated through interaction with the turbulence, they produced an outward angular momentum flow which compensated for a reduced flux associated with the MHD turbulence near the planet, so maintaining the gap. When compared with laminar disc models, with the same estimated α in the absence of the planet, the gap was found to be deeper and wider, indicating that the turbulent disc behaved as if it in fact possessed a smaller α, even though analysis of the turbulent stress indicated that it was not significantly affected by the planet in the region away from the gap. This may arise for two reasons. First, unlike a Navier–Stokes viscosity with anomalous viscosity coefficient, the turbulence does not provide a source of constantly acting friction in the near vicinity of the planet that leads to steady mass flow into the gap region. Instead, the turbulence is characterized by large fluctuations in the radial velocity, and time averaging of these fluctuations over significant time-scales is required to recover the underlying mass flow through the disc. In the vicinity of the planet, the disc material experiences high amplitude periodic perturbations on time-scales that are short relative to the time-scale required for averaging. Consequently the disc response is likely to be significantly altered relative to that expected from a Navier–Stokes model. Secondly, the simulation indicates that an ordered magnetic connection between the inner and outer disc can occur enabling angular momentum to flow out across the gap, helping to maintain it independently of the protoplanet's tide. This type of effect may assist gap formation for smaller mass protoplanets which otherwise would not be able to maintain them. There is also some evidence that magnetic connection between the circumstellar disc and material that flows into the protoplanet's Hill sphere may lead to significant magnetic braking of the resulting circumplanetary disc, thereby modifying the expected gas accretion rate on to forming gas giant planets.