Example of the time evolution on 1 Gyr of the disk offset coordinates (X (solid line) and Y (dashed line)) for outer perturbers. Top left: one of the best candidates (Case D). Because of the orientation of the perturber orbit, where its semi-major axis is along the X-axis with positive periastron, this corresponds to a negative X-offset ΔX ~  − 30 AU and a zero Y-offset for a disk located at a_c ~ 100 AU. Top right: the oscillations of the offset coordinates reveal the spiral-winding regime (Case E). Bottom: the offset seems to relax; left: case F; right: case G.