The Origin of Universality in the Inner Edges of Planetary Systems

The characteristic orbital period of the innermost objects within the galactic census of planetary and satellite systems appears to be nearly universal, with P on the order of a few days. Here, we present a theoretical framework that provides a simple explanation for this phenomenon. By considering the interplay between disk accretion, magnetic field generation by young stars, and Kelvin-Helmholtz contraction, we show that orbital frequency corresponding to the magnetospheric truncation of astrophysical disks is independent of the mass of the host body. Our analysis demonstrates that this characteristic frequency corresponds to a period of P ~ 3 days although intrinsic variations in system parameters are expected to introduce a factor of a ~2-3 spread in this result. Standard theory of orbital migration further suggests that planets should stabilize at an orbital period that exceeds disk truncation by a small margin. Cumulatively, our findings predict that the periods of close-in bodies should span P ~ 2-12 days - a range that is consistent with observations.