Abstract
Context. Planet formation remains an open field of research, and many fundamental physical processes regarding planetary formation in protoplanetary disks are still imperfectly understood. It remains to be investigated how different conditions in these protoplanetary disks affect the emergence of different types of observed systems. An elusive phenomenon is the turbulence in these disks. Observations are available of planetary systems and of some protoplanetary disks, which can serve as a starting point for these investigations. The 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. This implies a certain migration history. Aims. We aim to use the orbital configuration of the Kepler-223 planets to constrain the parameters of the protoplanetary disk that allow the formation of a chain of mean-motion resonances that resembles the resonances of Kepler-223. We primarily investigate the disk viscosity and surface density. Methods. We used the swift_symba N-body integrator with additional dissipative forces to mimic planet-disk interactions. Results. We constrained 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 surface densities and disk viscosity parameters α of a few × 10−3 up to × 10−2 are most successful at reproducing the architecture of this particular planetary system. We describe the connection of these two quantities with each other, considering the success of reproducing the chain. We find that higher disk surface densities in turn require lower viscosities to build the chain. Conclusions. 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. This helps to constrain planet formation.
Highlights
The study of exoplanetary systems is a key element for understanding the formation and evolution of planets, as well as the assembly of planetary systems and their dynamical evolution
After finding initial conditions that are favorable for the formation of the resonance chain, we investigated the effects of turbulence on the formation of the chain to determine constraints for the turbulence strength in the protoplanetary disk during the formation of the chain
To apply the concept of inferring disk parameters from a planetary system after the disk itself has already dissipated, we adopted the prescription by Cresswell & Nelson (2008) for the additional dissipative forces added to the N-body integrator
Summary
The study of exoplanetary systems is a key element for understanding the formation and evolution of planets, as well as the assembly of planetary systems and their dynamical evolution. The exoplanet sample is largely dominated by data from the Kepler mission, which provided well-constrained planetary radii and orbital periods using the transit detection method. Out of all detected planets, small and close-in planets, the so-called super-Earths and mini-Neptunes, are thought to be orbiting up to 50% of Sun-like stars (Howard et al 2012; Mayor et al 2011; Mulders et al 2018), and they often occur in multiplanetary configurations, in which the planets within each system mostly have similar masses and radii (e.g., Millholland et al 2017; Weiss et al 2018). In addition to orbital periods and radii, Mills et al (2016) used transit-timing variations (TTVs) to obtain masses, eccentricities, and inclinations of the planets. The masses are and 4.8+−11..42 given MEarth by for
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