Fig. D.3
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Histograms of the semi-major axes, eccentricities, and inclinations of the PDS 70 systems, separated by planet. Panel (a): Isolated resonant systems. Orbital evolution oscillates around the initial conditions and the MMR chain is maintained. Panel (b): Perturbed resonant systems. The MMR is rarely broken and any systems with a broken MMR are rapidly destroyed. The inclinations do not diverge far from planar. Panel (c): Isolated non-resonant systems. Some of the systems diverge from the broken MMR. A semi-major axis valley appears for PDS 70 b around the initial semi-major axis of PDS 70 c. The eccentricities are not as sharply bound as the resonant systems. Some of the systems get perturbed violently enough that the direction of PDS 70 b reverses. Despite the issues with random orientations in Fig. D.1c, all systems remain planar here. We believe these systems can manage to stay planar due to a weaker chaotic growth of numerical errors because they contain fewer bodies. Panel (d): Perturbed non-resonant systems. The semi-major axes and the eccentricities are nearly identical to the semi-major axes and the eccentricities in panel c. In contrast to panels (b) and (c), the inclinations are more strongly perturbed and now cover all of the possible parameter space for PDS 70 b. The dataset of each of the histograms contains all states of all its relevant simulations. These are 10000 states per simulation, with one simulation for panel (a) and 50 simulations for panels (b), (c), and (d). By including all states instead of just the final state, longer-lived states become more prominent even if these states are not the final state.
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