Distribution of a few samples of particles after 4.5 Gyrs in the plane (a, q). As indicated in the titles, the first column is for an evolution with only the galactic tides (Hamiltonian , Eq. (12)), and the second and third columns are for an evolution with both planets and galactic tides (Hamiltonian , Eq. (13)). Six slices of initial conditions are shown, as written in the top and right side of the graphs: the first two columns are for initial perihelion distance q_i in [30, 40] au, and the thirdone in [80, 100] au, while the cosine of the initial ecliptic inclination I_i is distributed in [0.9, 1] for the top row, [0.5, 0.6] for the middle row, and [0, 0.1] for the bottom row. On each graph, the horizontal black line shows the semi-major axis of Neptune (~ 30 au) for reference.