Frequency of Ω ± κ/2 derived from the background potential as a function of planar radius. The solid cyan line denotes to the bar’s pattern speed used in the constant rotating bar model. The co-rotation radius is defined as the planar radius at the intersection between the frequency curve and the pattern speed curve. The dashed blue lines mark the initial and final pattern speed in the decelerating bar model, which shows the change of co-rotation radius during 6 Gyrs. The stars trapped by the bar thus migrate outwards with time until the pattern speed reaches a stable value and the co-rotation radius stops increasing.