Neptune’s migration versus the mass loss of the planetesimal disk. The upper panel illustrates the connection between the total mass loss of the planetesimal disk (horizontal axis) and the total migration distance of Neptune (vertical axis). Different colors represent differen α, while different line styles indicate different M_disk. In the lower panel, we calculated the time interval takes for Neptune to migrate per 1 au (from 18 au). The horizontal axis displays the average migration rate during each interval (logarithmic scale), and the vertical axis represents the ratio of consumed planetesimal mass to the angular momentum gained by Neptune within this interval.