An illustration of the influence of the disk’s quadrupole. The solid blue line represents the outer planet’s nodal regression in the case with no disk, whereas the three dashed lines represent the case where the disk’s quadrupole moment is included. When the outer planet is forced to regress faster than the giant (red line) throughout the entire disk lifetime, the secular resonant encounter described in the text is prevented. The left panel considers a hot Jupiter, at 0.04 au interior to a test particle at 0.12 au. The right panel depicts the case for a warm Jupiter at 0.1 au with an exterior test particle at 0.3 au. The closer, hot Jupiter system encounters the secular resonance later (black circle) and so the disk is more likely to have dispersed, whereas the warm Jupiter system entirely bypasses the secular resonance even for very short disk lifetimes (e.g., 1 Myr).