The effects of a magnetic field on planetary migration in laminar and turbulent discs

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We investigate the migration of low-mass planets (5 M⊕ and 20 M⊕) in accretion discs threaded with a magnetic field using 2D MHD code in polar coordinates. We observed that, in the case of a strong azimuthal magnetic field where the plasma parameter is β 1-2, density waves at the magnetic resonances exert a positive torque on the planet and may slow down or reverse its migration. However, when the magnetic field is weaker (i.e., the plasma parameter β is relatively large), then non-axisymmetric density waves excited by the planet lead to growth of the radial component of the field and, subsequently, to development of the magneto-rotational instability, such that the disc becomes turbulent. Migration in a turbulent disc is stochastic, and the migration direction may change as such. To understand migration in a turbulent disc, both the interaction between a planet and individual turbulent cells, as well as the interaction between a planet and ordered density waves, have been investigated.