Fig. 1.

The boundaries of stable libration zones of Neptune’s exterior mean motion resonances in the semimajor axis–eccentricity plane; the abscissa is in units of Neptune’s semimajor axis. The nearly vertical curves in black and red indicate the stable libration zones of mean motion resonances; the zones bounded in red represent previously unknown phase-shifted libration zones which exist only at higher eccentricities. The shaded zone bounded by curves of constant perihelion distance, q = a(1− e) = 0.9 to q = 1.15 indicates the approximate boundaries of the scattered disk

(Figure adapted from Lan and Malhotra (2019))