On the 9:7 Mean Motion Resonance Capture in a System of Two Equal-mass Super-Earths

Cui, Zijia; Papaloizou, J. C. B.; Szuszkiewicz, Ewa

doi:10.3847/1538-4357/aafeda

Cited by 3 publications

(2 citation statements)

References 33 publications

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“…On the other hand, the trapping of multiple planets in studies that performed hydrodynamical simulations has not been vigorously investigated. Papaloizou & Szuszkiewicz (2005) and Cui et al (2019) inspected the convergent migration of low-mass two-planet systems in a disc with a surface density profile that resembled the disc inner edge. The surface density in the inner part of their disc rose linearly from the inner boundary up to a given distance and then became constant.…”

Section: Introductionmentioning

confidence: 99%

Pushing planets into an inner cavity by a resonant chain

Ataiee

Kley

2021

A&A

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Context. The orbital distribution of exoplanets indicates an accumulation of super-Earth sized planets close to their host stars in compact systems. When an inward disc-driven migration scenario is assumed for their formation, these planets could have been stopped and might have been parked at an inner edge of the disc, or be pushed through the inner disc cavity by a resonant chain. This topic has not been properly and extensively studied. Aims. Using numerical simulations, we investigate the possibility that the inner planets in a resonant chain can be pushed into the disc inner cavity by outer planets. Methods. We performed hydrodynamical and N-body simulations of planetary systems embedded in their nascent disc. The inner edge of the disc was represented in two different ways, resembling either a dead zone inner edge (DZ) or a disc inner boundary (IB). The main difference lies in the steepness of the surface density profile. The innermost planet always has a mass of 10 MEarth, with additional outer planets of equal or higher mass. Results. A steeper profile is able to stop a chain of planets more efficiently than a shallower profile. The final configurations in our DZ models are usually tighter than in their IB counterparts, and therefore more prone to instability. We derive analytical expressions for the stopping conditions based on power equilibrium, and show that the final eccentricities result from torque equilibrium. For planets in thinner discs, we found, for the first time, clear signs for over-stable librations in the hydrodynamical simulations, leading to very compact systems. We also found that the popular N-body simulations may overestimate the number of planets in the disc inner cavity.

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Section: Introductionmentioning

confidence: 99%

Pushing planets into an inner cavity by a resonant chain

Ataiee

Kley

2021

A&A

View full text Add to dashboard Cite

show abstract

“…On the other hand, the trapping of multi planets in studies that performed hydrodynamical simulations has not been vigorously investigated. Papaloizou & Szuszkiewicz (2005) and Cui et al (2019) inspected the convergent migration of low-mass two-planet systems in a disc with a surface density profile that resembles the disc inner edge. The surface density in the inner part of their disc rises linearly from the inner boundary up to a A&A proofs: manuscript no.…”

Section: Introductionmentioning

confidence: 99%

Pushing planets into an inner cavity by a resonant chain

Ataiee,

Kley

2021

Preprint

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Context. The orbital distribution of exoplanets indicates an accumulation of compact Super-Earth sized planetary systems close to their host stars. Assuming an inward disc-driven migration scenario for their formation, these planets could have been stopped and eventually parked at an inner edge of the disc, or be pushed through the inner disc cavity by a resonant chain. This topic has not been properly and extensively studied. Aims. Using numerical simulations we investigate how much the inner planets in a resonant chain can be pushed into the disc inner cavity by outer planets. Methods. We perform hydrodynamical and N-body simulations of planetary systems embedded in their nascent disc. The inner edge of the disc is represented in two different ways, resembling either a dead zone (DZ) inner edge or a disc inner boundary (IB), where the main difference lies in the steepness of the surface density profile. The innermost planet has always a mass of 10 M Earth , with equal or higher mass additional outer planets. Results. A steeper profile is able to stop a chain of planets more efficiently than a shallower profile. The final configurations in our DZ models are usually tighter than in their IB counterparts, and therefore more prone to instability. We derive analytical expressions for the stopping conditions based on power equilibrium, and show that the final eccentricities result from torque equilibrium. For planets in thinner discs, we found, for the first time, clear signs for overstable librations in the hydrodynamical simulations, leading to very compact systems. We also found that the popular N-body simulations may overestimate the number of planets in the disc inner cavity.

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The role of disc torques in forming resonant planetary systems

Ataiee

Kley

2020

A&A

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Context. The most accurate method for modelling planetary migration and hence the formation of resonant systems is using hydrodynamical simulations. Usually, the force (torque) acting on a planet is calculated using the forces from the gas disc and the star, while the gas accelerations are computed using the pressure gradient, the star, and the planet's gravity, ignoring its own gravity. For the non-migrating the neglect of the disc gravity results in a consistent torque calculation while for the migrating case it is inconsistent. Aims. We aim to study how much this inconsistent torque calculation can affect the final configuration of a two-planet system. Our focus will be on low-mass planets because most of the multi-planetary systems, discovered by the Kepler survey, have masses around 10 Earth masses. Methods. Performing hydrodynamical simulations of planet-disc interaction, we measure the torques on non-migrating and migrating planets for various disc masses as well as density and temperature slopes with and without considering the disc self-gravity. Using this data, we find a relation that quantifies the inconsistency, use it in an N-body code, and perform an extended parameter study modelling the migration of a planetary system with different planet mass ratios and disc surface densities, in order to investigate the impact of the torque inconsistency on the architecture of the planetary system. Results. Not considering disc self-gravity produces an artificially larger torque on the migrating planet that can result in tighter planetary systems. The deviation of this torque from the correct value is larger in discs with steeper surface density profiles. Conclusions. In hydrodynamical modelling of multi-planetary systems, it is crucial to account for the torque correction, otherwise the results favour more packed systems. We examine two simple correction methods existing in the literature and show that they properly correct this problem.

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On the 9:7 Mean Motion Resonance Capture in a System of Two Equal-mass Super-Earths

Cited by 3 publications

References 33 publications

Pushing planets into an inner cavity by a resonant chain

Pushing planets into an inner cavity by a resonant chain

Pushing planets into an inner cavity by a resonant chain

The role of disc torques in forming resonant planetary systems

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