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.

12 pages, 7 figues, accepted for publication in A&A

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• TOI-1136 is a Young, Coplanar, Aligned Planetary System in a Pristine Resonant Chain
• TOI-1130: A photodynamical analysis of a hot Jupiter in resonance with an inner low-mass planet
• Mean motion resonance capture in the context of type-I migration
• Proximity of exoplanets to first-order mean-motion resonances
• Confirming the 3:2 Resonance Chain of K2-138
• A recipe for orbital eccentricity damping in the type-I regime for low viscosity 2D-discs
• Sculpting the circumbinary planet size distribution through resonant interactions with companion planets
• Resonance Capture and Stability Analysis for Planet Pairs under Type I Disk Migration
• Inferred Properties of Planets in Mean-Motion Resonances are Biased by Measurement Noise
• Emerging population of gap-opening planets around type-A stars -- Long-term evolution of the forming planets around HD 163296
• Diversity of disc viscosities can explain the period ratios of resonant and non-resonant systems of hot super-Earths and mini-Neptunes
• Timescales diagnostics for saving viscous and MHD-driven dusty discs from external photoevaporation
• The Dynamical Environment of Kepler-223 Planetary System