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 commonplacein 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 planetaryembryos, while the second explores planetary migration. After applying observational biases to thesimulations, we compare them to 250+ observed multi-planetary systems, including 13 systems withplanets in the habitable zone. For all of the systems, we calculate two of the so-called statisticalmeasures: the mass concentration (Sc) and orbital spacing (Ss). After analytic and empirical analyses,we find that the measures are related to first-order with a power law: Sc ∼ Sβs. The in-situ systemsexhibit steeper power-law relations relative to the migration systems. We show that different formationscenarios cover different regions in the Ss − Sc diagram with some overlap. Furthermore, we discoverthat observed systems with Ss < 30 are likely dominated by the migration scenario, while those withSs ≥ 30 are likely dominated by the in-situ scenario. We apply these criteria to determine thata majority (62%) of observed multi-planetary systems formed via migration, whereas most systemswith currently observed habitable planets formed via in-situ assembly. This work provides methodsof leveraging the statistical measures (Ss and Sc) to disentangle the formation history of observedmulti-planetary systems based on their present-day architectures.