scholarly journals The onset of instability in resonant chains

2020 ◽  
Vol 494 (4) ◽  
pp. 4950-4968 ◽  
Author(s):  
Gabriele Pichierri ◽  
Alessandro Morbidelli
Keyword(s):  
Dynamical Mechanism ◽  
Mean Motion Resonances ◽  
Secondary Resonances ◽  
Mean Motion ◽  
Large N ◽  
Excited System ◽  
Resonant Systems ◽  
The Mean ◽  
The Stability ◽  
Mean Motion Resonance

ABSTRACT There is evidence that most chains of mean motion resonances of type k:k − 1 among exoplanets become unstable once the dissipative action from the gas is removed from the system, particularly for large N (the number of planets) and k (indicating how compact the chain is). We present a novel dynamical mechanism that can explain the origin of these instabilities and thus the dearth of resonant systems in the exoplanet sample. It relies on the emergence of secondary resonances between a fraction of the synodic frequency 2π(1/P1 − 1/P2) and the libration frequencies in the mean motion resonance. These secondary resonances excite the amplitudes of libration of the mean motion resonances, thus leading to an instability. We detail the emergence of these secondary resonances by carrying out an explicit perturbative scheme to second order in the planetary masses and isolating the harmonic terms that are associated with them. Focusing on the case of three planets in the 3:2–3:2 mean motion resonance as an example, a simple but general analytical model of one of these resonances is obtained, which describes the initial phase of the activation of one such secondary resonance. The dynamics of the excited system is also briefly described. Finally, a generalization of this dynamical mechanism is obtained for arbitrary N and k. This leads to an explanation of previous numerical experiments on the stability of resonant chains, showing why the critical planetary mass allowed for stability decreases with increasing N and k.

scholarly journals Dynamical interactions in the planetary system GJ4276

2019 ◽  
Vol 490 (2) ◽  
pp. 2732-2739
Author(s):  
Fergus Horrobin ◽  
Hanno Rein
Keyword(s):  
Planetary System ◽  
Stable Region ◽  
Mean Motion Resonances ◽  
Orbital Parameters ◽  
First Order ◽  
Mean Motion ◽  
The Mean ◽  
The Stability ◽  
The One ◽  
Mean Motion Resonance

ABSTRACT GJ4276 is an M4.0 dwarf star with an inferred Neptune mass planet from radial velocity (RV) observations. We re-analyse the RV data for this system and focus on the possibility of a second, super-Earth mass, planet. We compute the time-scale for fast resonant librations in the eccentricity to be $\sim \!2000 \, \mathrm{d}$. Given that the observations were taken over $700\, \mathrm{d}$, we expect to see the effect of these librations in the observations. We perform a fully dynamical fit to test this hypothesis. Similar to previous results, we determine that the data could be fit by two planets in a 2:1 mean motion resonance. However, we also find solutions near the 5:4 mean motion resonance that are not present when planet–planet interactions are ignored. Using the mean exponential growth of nearby orbits indicator, we analyse the stability of the system and find that our solutions lie in a stable region of parameter space. We also find that though out-of-resonance solutions are possible, the system favours a configuration that is in a first-order mean motion resonance. The existence of mean motion resonances has important implications in many planet formation theories. Although we do not attempt to distinguish between the one- and two-planet models in this work, in either case, the predicted orbital parameters are interesting enough to merit further study. Future observations should be able to distinguish between the different scenarios within the next 5 yr.

scholarly journals Impactor Flux on the Pluto-Charon System

2009 ◽  
Vol 5 (S263) ◽  
pp. 98-101 ◽  
Author(s):  
Gonzalo C. de Elía ◽  
Romina P. Di Sisto ◽  
Adrián Brunini
Keyword(s):  
Size Distribution ◽  
Kuiper Belt ◽  
Primary Source ◽  
Mean Motion ◽  
Stability And Instability ◽  
The Stability ◽  
Mean Motion Resonance ◽  
Collisional Evolution

AbstractIn this work, we study the impactor flux on Pluto and Charon due to the collisional evolution of Plutinos.To do this, we develop a statistical code that includes catastrophic collisions and cratering events, and takes into account the stability and instability zones of the 3:2 mean motion resonance with Neptune. Our results suggest that if 1 Pluto-sized object is in this resonance, the flux of D = 2 km Plutinos on Pluto is ~4–24 percent of the flux of D = 2 km Kuiper Belt projectiles on Pluto. However, with 5 Pluto-sized objects in the resonance, the contribution of the Plutino population to the impactor flux on Pluto may be comparable to that of the Kuiper Belt. As for Charon, if 1 Pluto-sized object is in the 3:2 resonance, the flux of D = 2 km Plutinos is ~10–63 percent of the flux of D = 2 km impactors coming from the Kuiper Belt. However, with 5 Pluto-sized objects, the Plutino population may be a primary source of the impactor flux on Charon. We conclude that it is necessary to specify the Plutino size distribution and the number of Pluto-sized objects in the 3:2 Neptune resonance in order to determine if the Plutino population is a primary source of impactors on the Pluto-Charon system.

Regular and Chaotic Dynamics in the Mean-Motion Resonances:

Asteroids III ◽  
2002 ◽  
pp. 379-394
Author(s):  
D. Nesvorný ◽  
S. Ferraz-Mello ◽  
M. Holman ◽  
A. Morbidelli
Keyword(s):  
Chaotic Dynamics ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
The Mean

scholarly journals The Configuration Formation of Planetary Systems Observed by Kepler

2012 ◽  
Vol 8 (S293) ◽  
pp. 106-109
Author(s):  
Su Wang ◽  
Jianghui Ji
Keyword(s):  
Star Formation ◽  
Late Stage ◽  
Early Stage ◽  
Planetary Systems ◽  
High Rate ◽  
Mean Motion ◽  
Star Evolution ◽  
Kepler Mission ◽  
Resonant Systems ◽  
Mean Motion Resonance

AbstractThe Kepler mission has found many planetary systems, among them more than 80 systems host three planet candidates which reveal a configuration of near 4:2:1 mean motion resonance. In this paper, we focus on the configuration formation of resonant systems. As shown from our model and N-body simulations, we find that 3:2 mean motion resonance always forms at the early stage of star evolution and planets undergo high rate of migration, while 2:1 mean motion resonance happens at the late stage of the star formation, more often.

scholarly journals An integrable model for first-order three-planet mean motion resonances

2021 ◽  
Vol 133 (8) ◽  
Author(s):  
Antoine C. Petit
Keyword(s):  
Integrable Model ◽  
Degree Of Freedom ◽  
Mass Ratio ◽  
Zeroth Order ◽  
Mean Motion Resonances ◽  
First Order ◽  
Mean Motion ◽  
Formation And Evolution ◽  
The Stability ◽  
Three Body

AbstractRecent works on three-planet mean motion resonances (MMRs) have highlighted their importance for understanding the details of the dynamics of planet formation and evolution. While the dynamics of two-planet MMRs are well understood and approximately described by a one-degree-of-freedom Hamiltonian, little is known of the exact dynamics of three-body resonances besides the cases of zeroth-order MMRs or when one of the bodies is a test particle. In this work, I propose the first general integrable model for first-order three-planet mean motion resonances. I show that one can generalize the strategy proposed in the two-planet case to obtain a one-degree-of-freedom Hamiltonian. The dynamics of these resonances are governed by the second fundamental model of resonance. The model is valid for any mass ratio between the planets and for every first-order resonance. I show the agreement of the analytical model with numerical simulations. As examples of application, I show how this model could improve our understanding of the capture into MMRs as well as their role in the stability of planetary systems.

scholarly journals Higher Order and Iterative Theories to Compute Asteroid Mean Elements

1999 ◽  
Vol 172 ◽  
pp. 359-360 ◽  
Author(s):  
Z. Knežević ◽  
A. Milani
Keyword(s):  
Asteroid Belt ◽  
Dynamical Structure ◽  
Orbital Elements ◽  
Mean Motion Resonances ◽  
First Order ◽  
Mean Motion ◽  
Long Time ◽  
The Mean ◽  
Mean Elements ◽  
Asteroid Families

Mean orbital elements are obtained from their instantaneous, osculating counterparts by removal of the short periodic perturbations. They can be computed by means of different theories, analytical or numerical, depending on the problem and accuracy required. The most advanced contemporary analytical theory (Knežević 1988) accounts only for the perturbing effects due to Jupiter and Saturn, to the first order in their masses and to degree four in eccentricity and inclination. Nevertheless, the mean elements obtained by means of this theory are of satisfactory accuracy for majority of the asteroids in the main belt (Knežević et al. 1988), for the purpose of producing large catalogues of mean and proper elements, to identify asteroid families, to assess their age, to study the dynamical structure of the asteroid belt and chaotic phenomena of diffusion over very long time spans. In the vicinity of the main mean motion resonances, however, especially 2:1 mean motion resonance with Jupiter, these mean elements are of somewhat degraded accuracy.

scholarly journals Mean Motion Resonances in The Asteroid Belt

1999 ◽  
Vol 172 ◽  
pp. 381-382
Author(s):  
D. Nesvorný ◽  
A. Morbidelli
Keyword(s):  
Asteroid Belt ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Lyapunov Time ◽  
Asteroidal Belt ◽  
Kirkwood Gaps ◽  
The Mean ◽  
Three Body

The Kirkwood gaps in the main asteroidal belt (2 – 3.5 AU) coincide with the mean motion resonances with Jupiter (4/1, 3/1, 5/2, 7/3, 2/1). Similarly, several narrower gaps are observed in the outer asteroid belt (3.5 – 4 AU) at places of 11/6, 9/5, 7/4 and 5/3 Jovian resonances (Holman and Murray 1996). As it is now generally accepted, the formation and preservation of these gaps is due to the chaos of the resonant space and efficient ejection of the primordial and collisionaly injected bodies towards high eccentricities and planet-crossing orbits.The Jovian mean motion resonances are not the most important in what concerns the chaos of the observed (i.e. remaining) asteroid population. It was estimated by Šidlichovský and Nesvorný (1998) that about 40% of known objects have the Lyapunov time less than 105 years. It was later found (Nesvorný and Morbidelli 1998, 1999; Morbidelli and Nesvorný 1999) that the resonances responsible for this chaos are, in decreasing order of importance: 1) three-body resonances with Jupiter and Saturn, 2) exterior resonances with Mars, 3) moderate order Jovian resonances, and 4) three-body resonances with Mars and Jupiter.

scholarly journals Fomalhaut b could be massive and sculpting the narrow, eccentric debris disc, if in mean-motion resonance with it

2021 ◽  
Vol 503 (4) ◽  
pp. 4767-4786
Author(s):  
Tim D Pearce ◽  
Hervé Beust ◽  
Virginie Faramaz ◽  
Mark Booth ◽  
Alexander V Krivov ◽  
...  
Keyword(s):  
Dynamical Interaction ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Resonant Interactions ◽  
Significant Mass ◽  
Mean Motion Resonance

ABSTRACT The star Fomalhaut hosts a narrow, eccentric debris disc, plus a highly eccentric companion Fomalhaut b. It is often argued that Fomalhaut b cannot have significant mass, otherwise it would quickly perturb the disc. We show that material in internal mean-motion resonances with a massive, coplanar Fomalhaut b would actually be long-term stable, and occupy orbits similar to the observed debris. Furthermore, millimetre dust released in collisions between resonant bodies could reproduce the width, shape, and orientation of the observed disc. We first re-examine the possible orbits of Fomalhaut b, assuming that it moves under gravity alone. If Fomalhaut b orbits close to the disc mid-plane then its orbit crosses the disc, and the two are apsidally aligned. This alignment may hint at an ongoing dynamical interaction. Using the observationally allowed orbits, we then model the interaction between a massive Fomalhaut b and debris. While most debris is unstable in such an extreme configuration, we identify several resonant populations that remain stable for the stellar lifetime, despite crossing the orbit of Fomalhaut b. This debris occupies low-eccentricity orbits similar to the observed debris ring. These resonant bodies would have a clumpy distribution, but dust released in collisions between them would form a narrow, relatively smooth ring similar to observations. We show that if Fomalhaut b has a mass between those of Earth and Jupiter then, far from removing the observed debris, it could actually be sculpting it through resonant interactions.

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