Mean motion resonance capture in the context of type I migration

Abstract

Capture into mean motion resonance (MMR) is an important dynamical mechanism because it shapes the final architecture of a planetary system. We simulate systems of two or three planets undergoing migration with varied initial parameters such as planetary mass and disk surface density and analyse the resulting resonant chains. In contrast to previous studies, our results show that the disk properties are the dominant impact on capture into MMR, while the total planetary mass barely affects the final system configuration as long as the planet does not open a gap in the disk. We confirm that adiabatic resonant capture is the correct framework for understanding the conditions leading to MMR formation because its predictions are qualitatively similar to the numerical results. However, we find that eccentricity damping can facilitate the capture in a given resonance. We find that under typical disk conditions, planets tend to be captured into 2:1 or 3:2 MMRs, which agrees well with the observed exoplanet MMRs. Our results predict two categories of systems: those that have uniform chains of wide resonances (2:1 or 3:2 MMRs), and those whose inner pair is more compact than the outer pair, such as 4:3:2 chains. Both categories of resonant chains are present in observed exoplanet systems. On the other hand, chains whose inner pair is wider than the outer pair are very rare and emerge from stochastic capture. Our work here can be used to link the current configuration of exoplanetary systems to the formation conditions within protoplanetary disks.