Predicting the Dominant Formation Mechanism of Multi-Planetary Systems

Most, if not all, sun-like stars host one or more planets, making multi-planetary systems commonplace in our galaxy. We utilize hundreds of multi-planet simulations to explore the origin of such systems, focusing on their orbital architecture. The first set of simulations assumes in-situ assembly of planetary embryos, while the second explores planetary migration. After applying observational biases to the simulations, we compare them to 250+ observed multi-planetary systems, including 13 systems with planets in the habitable zone. For all of the systems, we calculate two of the so-called statistical measures: the mass concentration ($S_{c}$) and orbital spacing ($S_{s}$). After analytic and empirical analyses, we find that the measures are related to first-order with a power law: $S_{c} \sim S_{s}^\beta$. The in-situ systems exhibit steeper power-law relations relative to the migration systems. We show that different formation scenarios cover different regions in the $S_{s} - S_{c}$ diagram with some overlap. Furthermore, we discover that observed systems with $S_{s} < 30$ are likely dominated by the migration scenario, while those with $S_{s} \geq 30$ are likely dominated by the in-situ scenario. We apply these criteria to determine that a majority (62%) of observed multi-planetary systems formed via migration, whereas most systems with currently observed habitable planets formed via in-situ assembly. This work provides methods of leveraging the statistical measures ($S_{s}$ and $S_{c}$) to disentangle the formation history of observed multi-planetary systems based on their present-day architectures.