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

Abstract

We present the results of both global cylindrical disc simulations and local shearing box simulations of protoplanets interacting with a disc undergoing 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 disc semi-thickness respectively. We find that as this parameter is increased towards 0.1, the presence of the protoplanet is first indicated by the appearance of the well known trailing wake which, although it may appear erratic on account of the turbulence, appears to be well defined. Once the above parameter 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 gap formation condition can be understood from simple dimensional considerations of the conditions for nonlinearity, and the balance of angular momentum transport due to Maxwell and Reynolds' stresses with that due to tidal torques. 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 local shearing box simulations, which are computationally less demanding, capture much of the physics of disc-planet interaction. Thus they may provide a useful tool for studying the local interaction between forming protoplanets and turbulent, protostellar discs.