We performed 3D MHD simulations of planet migration in stratified disks using the Godunov code PLUTO , where the disk is turbulent due to the magnetorotational instability .
We study the migration for planets with different planet-star mass ratios q = M _ { p } / M _ { s } .
In agreement with previous studies , for the low-mass planet cases ( q = 5 \times 10 ^ { -6 } and 10 ^ { -5 } ) , migration is dominated by random fluctuations in the torque .
For a Jupiter-mass planet ( q = M _ { p } / M _ { s } = 10 ^ { -3 } for M _ { s } = 1 M _ { \odot } ) , we find a reduction of the magnetic stress inside the orbit of the planet and around the gap region .
After an initial stage where the torque on the planet is positive , it reverses and we recover migration rates similar to those found in disks where the turbulent viscosity is modelled by an \alpha viscosity .
For the intermediate-mass planets ( q = 5 \times 10 ^ { -5 } , 10 ^ { -4 } and 2 \times 10 ^ { -4 } ) we find a new and so far unexpected behavior .
In some cases they experience sustained and systematic outwards migration for the entire duration of the simulation .
For this case , the horseshoe region is resolved and torques coming from the corotation region can remain unsaturated due to the stresses in the disk .
These stresses are generated directly by the magnetic field .
The magnitude of the horseshoe drag can overcome the negative Lindblad contribution when the local surface density profile is flat or increasing outwards , which we see in certain locations in our simulations due to the presence of a zonal flow .
The intermediate-mass planet is migrating radially outwards in locations where there is a positive gradient of a pressure bump ( zonal flow ) .