On the Ordering of Exoplanet Systems

Abstract: We present a comprehensive analysis of planetary radii ordering within multi-planet systems, namely their ordinal position with respect to their size in a given system, utilizing data from the NASA Exoplanet Archive. In addition, we consider not only the ordinal positions but also the specific period ratios and radius ratios of planetary pairs in multi-planet systems. We explore various dependencies on stellar host type and metallicity, as well as planetary types, and explore the differences between planetary systems with different planet multiplicities and different planetary pairs in the same system. Focusing on Kepler systems with two to four planets, we account for observational biases and uncover a robust trend of smaller inner planets. This trend is particularly pronounced in inner pairs of three-planet systems and exhibits variations in stellar metallicity and planet multiplicity. Notably, we find that the distribution of inner-to-outer planet radii ratios depends on the system's metallicity, suggesting a link between initial conditions and the resulting system architecture. Interestingly, planet pairs in resonance do not exhibit significantly different size ratios compared to non-resonant pairs, challenging current theoretical expectations, again, possibly suggesting that initially resonant systems could have been later destabilized. Our findings align with planet formation and migration models where larger planets form farther out and migrate inward. Importantly, we emphasize the significance of planet ordering as a novel and crucial observable for constraining planet formation and evolution models. The observed patterns offer unique insights into the complex interplay of formation, migration, and dynamical interactions shaping planetary systems.