In this paper the migration of a 10 Earth-mass planetary core is investigated at the outer boundary of the dead zone of a protoplanetary disc by means of 2D hydrodynamic simulations done with the graphics processor unit version of the FARGO code. In the dead zone, the effective viscosity is greatly reduced due to the disc self-shielding against stellar UV radiation, X-rays from the stellar magnetosphere and interstellar cosmic rays. As a consequence, mass accumulation occurs near the outer dead zone edge, which is assumed to trap planetary cores enhancing the efficiency of the core-accretion scenario to form giant planets. Contrary to the perfect trapping of planetary cores in 1D models, our 2D numerical simulations show that the trapping effect is greatly dependent on the width of the region where viscosity reduction is taking place. Planet trapping happens exclusively if the viscosity reduction is sharp enough to allow the development of large-scale vortices due to the Rossby wave instability. The trapping is only temporarily, and its duration is inversely proportional to the width of the viscosity transition. However, if the Rossby wave instability is not excited, a ring-like axisymmetric density jump forms, which cannot trap the 10 Earth-mass planetary cores. We revealed that the stellar torque exerted on the planet plays an important role in the migration history as the barycentre of the system significantly shifts away from the star due to highly non-axisymmetric density distribution of the disc. Our results still support the idea of planet formation at density/pressure maximum, since the migration of cores is considerably slowed down enabling them further growth and runaway gas accretion in the vicinity of an overdense region.
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