Time average of the torque density distribution, obtained with Model 1 (top row, plus signs) and Model 2 (bottom row, plus signs). For comparison, the torque density distribution of the inviscid and viscous non-magnetic disc models are overplotted (diamond and star symbols, respectively). The torque profiles of the turbulent runs have been time-averaged over 100 orbits. In each panel, torque density profiles are divided by the maximum of the (absolute value of the) inviscid, viscous, and turbulent torque profiles. In x-axis, orbital separation is depicted from R = 2 to R = 4, which corresponds to a radial extent  ≃±3H_p about the planet location. In each panel, the dashed lines show the approximate location of the separatrices of the planet’s horseshoe region, and the dotted line that of the planet’s corotation radius.