The interaction of giant planets with a disc with MHD turbulence – III. Flow morphology and conditions for gap formation in local and global simulations

We present the results of both global cylindrical disc simulations and local shearing box simulations of protoplanets interacting with a disc undergoing magnetohydrodynamic (MHD) turbulence with zero net flux magnetic fields. We investigate the nature of the disc response and conditions for gap formation. This issue is an important one for determining the type and nature of the migration of the protoplanet, with the presence of a deep gap being believed to enable slower migration. For both types of simulation we find a common pattern of behaviour for which the main parameter determining the nature of the response is M p R 3 /(M*H 3 ), with M p , M*, R and H being the protoplanet mass, the central mass, the orbital radius and the local disc semi-thickness respectively. We find that as M p R 3 /(M*H 3 ) is increased to ∼ 0.1 the presence of the protoplanet is first indicated by the appearance of the well-known trailing wake which, although it may appear to be erratic on account of the turbulence, appears to be well-defined. Once M p R 3 /(M*H 3 ) exceeds a number around unity, a gap starts to develop inside which the magnetic energy density tends to be concentrated in the high-density wakes. This condition for gap formation can be understood from simple dimensional considerations of the conditions for non-linearity and the balance of angular momentum transport due to Maxwell and Reynolds' stresses with that due to tidal torques applied to the parameters of our simulations. An important result is that the basic flow morphology in the vicinity of the protoplanet is very similar in both the local and global simulations. This indicates that, regardless of potentially unwanted effects arising from the periodic boundary conditions, local shearing box simulations, which are computationally less demanding, capture much of the physics of disc-planet interactions. Thus they may provide a useful tool for studying the local interaction between forming protoplanets and turbulent, protostellar discs.

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