Distribution of orbits recaptured as UTs at the end of the simulations. The blue crosses indicate fast migration (τ = 1 Myr); the orange squares indicate slow migration (τ = 10 Myr). The critical eccentricity for stable UTs (e = 0.1) is depicted by a vertical line. The horizontal lines indicate the critical inclinations for the long-life UTs, which are 7.5°, 42°, and 48° (see Fig. 8). The shaded areas indicate the stable regions.