The effect of poloidal magnetic field on type I planetary migration

We study the effect of poloidal magnetic field on type I planetary migration by linear perturbation analysis with the shearing-sheet approximation and the analytic results are compared with numerical calculation. We investigate the cases where magneto-rotational instability (MRI) does not occur: either the disk is two-dimensional, or a very strong field is exerted. We derive formulae for torque exerted on the planet for both cases. We find that two-dimensional torque is suppressed when plasma beta is less than 1 and three-dimensional modes dominate, in contrast to unmagnetized case.