Evolutionary outcomes for pairs of planets undergoing orbital migration and circularization: second-order resonances and observed period ratios in Kepler's planetary systems

Xiang-Gruess, Meng; Papaloizou, J. C. B.

doi:10.1093/mnras/stv482

Cited by 34 publications

(11 citation statements)

References 20 publications

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“…A resonance offset of ∆ 2/1 0.05, such as those observed in close-in systems, would require K i ∼ 10 5 , which at least seems improbable. Xiang-Gruess & Papaloizou (2015) proposed that planetary traps close to the central star could halt planetary migration while not affecting the eccentricity damping timescale, leading to an artificial increase of the corresponding magnitude of K. Even if such an idea seems possible, it would not explain the observed trend of decreasing offset as function of the semimajor axis, nor would it be expected to work for orbital periods on the order of 10 2 days.…”

Section: Offset and The K-factorsmentioning

confidence: 99%

Planetary migration and the origin of the 2:1 and 3:2 (near)-resonant population of close-in exoplanets

Ramos

Charalambous

Benítez-Llambay

et al. 2017

A&A

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We present an analytical and numerical study of the orbital migration and resonance capture of fictitious two-planet systems with masses in the super-Earth range undergoing Type-I migration. We find that, depending on the flare index and proximity to the central star, the average value of the period ratio, P 2 /P 1 , between both planets may show a significant deviation with respect to the nominal value. For planets trapped in the 2:1 commensurability, offsets may reach values on the order of 0.1 for orbital periods on the order of 1 day, while systems in the 3:2 mean-motion resonance (MMR) show much smaller offsets for all values of the semimajor axis. These properties are in good agreement with the observed distribution of near-resonant exoplanets, independent of their detection method. We show that 2:1-resonant systems far from the star, such as HD82943 and HR8799, are characterized by very small resonant offsets, while higher values are typical of systems discovered by Kepler with orbital periods approximately a few days. Conversely, planetary systems in the vicinity of the 3:2 MMR show little offset with no significant dependence on the orbital distance. In conclusion, our results indicate that the distribution of Kepler planetary systems around the 2:1 and 3:2 MMR are consistent with resonant configurations obtained as a consequence of a smooth migration in a laminar flared disk, and no external forces are required to induce the observed offset or its dependence with the commensurability or orbital distance from the star.

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Section: Offset and The K-factorsmentioning

confidence: 99%

Planetary migration and the origin of the 2:1 and 3:2 (near)-resonant population of close-in exoplanets

Ramos

Charalambous

Benítez-Llambay

et al. 2017

A&A

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“…8, 12 and 16). Overstability for planets at the inner edge of a protoplanetary disc was observed in N-body simulations by Xiang-Gruess & Papaloizou (2015), but has not been reported yet convincingly in hydrodynamical simulations 7 .…”

Section: Overstabilitymentioning

confidence: 95%

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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“…A semianalytic solution for two planets in a second-order resonance undergoing migration and orbital circularization is described in Xiang-Gruess & Papaloizou (2015). After the system is locked in the resonance, a relationship between the eccentricities e 1 , e 2 , the circularization time, τ c,i = −e i /ė i , and the migration time, τ mig,i = −2a i /ȧ i , for planet i with i = 1, 2 is obtained, which takes the form…”

Section: The Formation Of the 9:7 Resonancementioning

confidence: 99%

“…The first is that a very low migration rate has to be used since the time to move through the resonance must exceed the inverse libration frequency. The latter frequency can be estimated as (see Xiang-Gruess & Papaloizou 2015) n 1 − (9/7)n 2 ∼ 4.2 × 10 −5 (m 1 /M ⊕ )(M /M )n 2 (1) leading to the constraint on the relative migration rate…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Cui

Papaloizou

Szuszkiewicz

2019

ApJ

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We study the formation of the 9:7 mean motion resonance in a system of two low-mass planets (m 1 = m 2 = 3M ⊕ ) embedded in a gaseous protoplanetary disk employing a full 2D hydrodynamic treatment of the disk-planet interactions. Our aim is to determine the disk properties that favor a capture of two equal-mass super-Earths into this second -order resonance. For this purpose, we have performed a series of numerical hydrodynamic simulations of the system of two super-Earths migrating in disks with a variety of different initial parameters and found conditions for the permanent or temporary locking in the 9:7 resonance. We observe that capture occurs during the convergent migration of planets if their resonance angle at the moment of arrival at the resonance assumes values in a certain range (inside a window of capture). The width of such a window depends on the relative migration and circularization rates that are determined by the disk parameters. The window is wide if the relative migration rate is slow, and it becomes narrower as the relative migration rate increases. The window will be closed if the migration rate is sufficiently high, and the capture will not take place. We illustrate also how the 9:7 resonance window of capture is affected by the initial eccentricities and the initial orbits of the planets.

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Evolutionary outcomes for pairs of planets undergoing orbital migration and circularization: second-order resonances and observed period ratios in Kepler's planetary systems

Cited by 34 publications

References 20 publications

Planetary migration and the origin of the 2:1 and 3:2 (near)-resonant population of close-in exoplanets

Planetary migration and the origin of the 2:1 and 3:2 (near)-resonant population of close-in exoplanets

Pushing planets into an inner cavity by a resonant chain

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

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