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

We investigate the migration of low-mass planets (1, 5 and 20 M⊕) in accretion discs threaded with a magnetic field using 2D magnetohydrodynamic code in polar coordinates. We observed that, in the case of a strong azimuthal magnetic field where the plasma parameter is β ∼ 2–4, 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 magnetorotational 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.