tokens: law (in semimajor axis): as the semimajor axis increases, the number of massive planets increases beyond the limit in which they can dynamically coexist. In the case of RV1 and RV2, the choice of “optimistic,” “nominal,” and “pessimistic” does not directly affect the Jovian planets; it changes the distribution of the Neptune and Terran planets which are drawn from SAG13. However, there may be some differences even in the RV1 or RV2 Jovian population between the “optimistic,” “nominal,” and “pessimistic,” due to random chance or due to secondary effects imposed by the implementation of a “trusted” region, which we discuss further in Section 3.4 . Imposing Hill-stability criteria by iteratively injecting planets and assessing their resulting orbital architectures based on mass and spacing regulates the number of planets per star. The SAG13 distribution (black lines in Figure 4 ) is suppressed much more strongly than the RV1 (blue lines) and RV2 (orange lines) distributions. As an example, the “optimistic” SAG13 distribution results in 71% of the predicted Jupiters to be unstable. Table 2 quantifies the percentage of predicted planets that are stable for each of the various models. Table 2 Percentage of Jupiters Predicted by Each Power-law Set which are Found to be Dynamically Stable Both the RV1 and RV2 models include power-law breaks that effectively reduce the number density of Jovian planets at larger orbital radii. As a result of a lower frequency and strength of dynamic interactions, the relative suppression of the RV1 and RV2 distributions is more modest. For RV1 and RV2, respectively 79% and 93% of Jupiters over the parameter space are found to be dynamically stable. Table 3 Percentage of Neptunes Predicted by Each Power-law Set which are Found to be Dynamically Stable Table 4 Percentage of Terrans Predicted by Each Power-law Set which are Found to be Dynamically Stable Because we assume that the largest planet in each system is stable and retain the larger planet in any unstable pair, the distribution of Jovians has an impact on the stability of all other planet types as we explore in Sections 3.1.2 and 3.1.3 . 3.1.2. Neptune Planets (2.04 ≤ <italic>M</italic><sub><italic>p</italic></sub>/<italic>M</italic><sub>⊕</sub> ≤ 75.51) Interestingly, the influence on the semimajor axis distribution of the imposing stability criteria becomes even more pronounced for lower-mass planets. Cold Neptunes, which are concentrated near the SAG13 radius critical point of R = 3.4 R Earth , have an unrealistically high occurrence rate. These cold Neptunes are unstable. Of all planet types, cold Neptunes are being removed in the greatest number (although not in the largest percentage). Table 3 quantifies the percentage of predicted Neptunes that are stable for each of the various models. All three demographics sets we implement—SAG13, RV1, and RV2—use SAG13 power-law indices for Neptune- and Terran-mass planets. Each Neptune population begins the same,
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