The Kepler-223 resonance holds information on turbulence during the gas disk phase

Abstract

Many fundamental physical processes regarding planetary formation in protoplanetary disks are still imperfectly understood, with an elusive phenomenon being turbulence in such disks. Observations are available of planetary systems and of some protoplanetary disks, which can serve as a starting point for these investigations. Detected systems reveal different architectures of planets. One particularly interesting case to consider is the Kepler-223 system, which contains a rare configuration of four planets in a resonance chain, implying a certain migration history. We aim to use the orbital configuration of Kepler-223's planets to constrain the parameters of the protoplanetary disk that allow for the formation of a chain of mean-motion resonances that resembles the one of Kepler-223. The parameters we aim to investigate are primarily the disk viscosity and surface density. We use the swift_symba N-body integrator with additional dissipative forces to mimic planet-disk interactions. We constrain the surface densities and viscosities that allow the formation of a resonant chain like that of Kepler-223. We find that surface densities of up to a few minimum mass solar nebula (MMSN) surface densities and disk viscosity parameters $\alpha$ of a few $10^{-3}$ up to $10^{-2}$ are most successful at reproducing the architecture of this particular planetary system. We describe how these two quantities are linked to each other considering the success of reproducing the chain and find that higher disk surface densities in turn require lower viscosities to build the chain. Our results show that well characterized observed planetary systems hold information about their formation conditions in the protoplanetary disks and that it is possible to extract this information, namely the initial disk surface density and viscosity, helping to constrain planet formation.