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.

scholarly journals Long-term evolution of asteroids in the 2:1 Mean Motion Resonance

2014 ◽  
Vol 9 (S310) ◽  
pp. 178-179
Author(s):  
Despoina K. Skoulidou ◽  
Kleomenis Tsiganis ◽  
Harry Varvoglis
Keyword(s):  
Giant Planets ◽  
Dynamical Models ◽  
Mean Motion Resonances ◽  
First Order ◽  
Mean Motion ◽  
System A ◽  
Term Evolution ◽  
Approximate Treatment ◽  
Mean Motion Resonance

AbstractThe problem of the origin of asteroids residing in the Jovian first-order mean motion resonances is still open. Is the observed population survivors of a much larger population formed in the resonance in primordial times? Here, we study the evolution of 182 long-lived asteroids in the 2:1 Mean Motion Resonance, identified in Brož & Vokrouhlické (2008). We numerically integrate their trajectories in two different dynamical models of the solar system: (a) accounting for the gravitational effects of the four giant planets (i.e. 4-pl) and (b) adding the terrestrial planets from Venus to Mars (i.e. 7-pl). We also include an approximate treatment of the Yarkovksy effect (as in Tsiganis et al.2003), assuming appropriate values for the asteroid diameters.

scholarly journals Four-billion year stability of the Earth–Mars belt

2020 ◽  
Vol 500 (1) ◽  
pp. 1151-1157
Author(s):  
Yukun Huang (黄宇坤) ◽  
Brett Gladman
Keyword(s):  
Semimajor Axis ◽  
Orbital Stability ◽  
Terrestrial Planet ◽  
Small Bodies ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
The Earth ◽  
Steady State Model ◽  
Near Earth Objects

ABSTRACT Previous work has demonstrated orbital stability for 100 Myr of initially near-circular and coplanar small bodies in a region termed the ‘Earth–Mars belt’ from 1.08 < a < 1.28 au. Via numerical integration of 3000 particles, we studied orbits from 1.04–1.30 au for the age of the Solar system. We show that on this time-scale, except for a few locations where mean-motion resonances with Earth affect stability, only a narrower ‘Earth–Mars belt’ covering a ∼ (1.09, 1.17) au, e < 0.04, and I < 1° has over half of the initial orbits survive for 4.5 Gyr. In addition to mean-motion resonances, we are able to see how the ν3, ν4, and ν6 secular resonances contribute to long-term instability in the outer (1.17–1.30 au) region on Gyr time-scales. We show that all of the (rather small) near-Earth objects (NEOs) in or close to the Earth–Mars belt appear to be consistent with recently arrived transient objects by comparing to a NEO steady-state model. Given the <200 m scale of these NEOs, we estimated the Yarkovsky drift rates in semimajor axis and use these to estimate that a diameter of ∼100 km or larger would allow primordial asteroids in the Earth–Mars belt to likely survive. We conclude that only a few 100-km sized asteroids could have been present in the belt’s region at the end of the terrestrial planet formation.

scholarly journals Survey of asteroids in retrograde mean motion resonances with planets

2019 ◽  
Vol 630 ◽  
pp. A60 ◽  
Author(s):  
Miao Li ◽  
Yukun Huang ◽  
Shengping Gong
Keyword(s):  
Solar System ◽  
Integration Time ◽  
Potential Candidate ◽  
Resonant Condition ◽  
Mean Motion Resonances ◽  
Orbital Resonance ◽  
Mean Motion ◽  
Resonant Dynamics ◽  
Orbital Resonances

Aims. Asteroids in mean motion resonances (MMRs) with planets are common in the solar system. In recent years, increasingly more retrograde asteroids are discovered, several of which are identified to be in resonances with planets. We here systematically present the retrograde resonant configurations where all the asteroids are trapped with any of the eight planets and evaluate their resonant condition. We also discuss a possible production mechanism of retrograde centaurs and dynamical lifetimes of all the retrograde asteroids. Methods. We numerically integrated a swarm of clones (ten clones for each object) of all the retrograde asteroids (condition code U < 7) from −10 000 to 100 000 yr, using the MERCURY package in the model of solar system. We considered all of the p/−q resonances with eight planets where the positive integers p and q were both smaller than 16. In total, 143 retrograde resonant configurations were taken into consideration. The integration time was further extended to analyze their dynamical lifetimes and evolutions. Results. We present all the meaningful retrograde resonant configurations where p and q are both smaller than 16 are presented. Thirty-eight asteroids are found to be trapped in 50 retrograde mean motion resonances (RMMRs) with planets. Our results confirm that RMMRs with giant planets are common in retrograde asteroids. Of these, 15 asteroids are currently in retrograde resonances with planets, and 30 asteroids will be captured in 35 retrograde resonant configurations. Some particular resonant configurations such as polar resonances and co-orbital resonances are also identified. For example, Centaur 2005 TJ50 may be the first potential candidate to be currently in polar retrograde co-orbital resonance with Saturn. Moreover, 2016 FH13 is likely the first identified asteroid that will be captured in polar retrograde resonance with Uranus. Our results provide many candidates for the research of retrograde resonant dynamics and resonance capture. Dynamical lifetimes of retrograde asteroids are investigated by long-term integrations, and only ten objects survived longer than 10 Myr. We confirmed that the near-polar trans-Neptunian objects 2011 KT19 and 2008 KV42 have the longest dynamical lifetimes of the discovered retrograde asteroids. In our long-term simulations, the orbits of 12 centaurs can flip from retrograde to prograde state and back again. This flipping mechanism might be a possible explanation of the origins of retrograde centaurs. Generally, our results are also helpful for understanding the dynamical evolutions of small bodies in the solar system.

scholarly journals Exploiting periodic orbits as dynamical clues for Kepler and K2 systems

2020 ◽  
Vol 640 ◽  
pp. A55
Author(s):  
Kyriaki I. Antoniadou ◽  
Anne-Sophie Libert
Keyword(s):  
Periodic Orbits ◽  
Intrinsic Property ◽  
Orbital Elements ◽  
Orbital Parameters ◽  
Mean Motion ◽  
Extrasolar Systems ◽  
Resonant Systems ◽  
Three Body ◽  
Mean Motion Resonance

Aims. Many extrasolar systems possessing planets in mean-motion resonance or resonant chain have been discovered to date. The transit method coupled with transit timing variation analysis provides an insight into the physical and orbital parameters of the systems, but suffers from observational limitations. When a (near-)resonant planetary system resides in the dynamical neighbourhood of a stable periodic orbit, its long-term stability, and thus survival, can be guaranteed. We use the intrinsic property of the periodic orbits, namely their linear horizontal and vertical stability, to validate or further constrain the orbital elements of detected two-planet systems. Methods. We computed the families of periodic orbits in the general three-body problem for several two-planet Kepler and K2 systems. The dynamical neighbourhood of the systems is unveiled with maps of dynamical stability. Results. Additional validations or constraints on the orbital elements of K2-21, K2-24, Kepler-9, and (non-coplanar) Kepler-108 near-resonant systems were achieved. While a mean-motion resonance locking protects the long-term evolution of the systems K2-21 and K2-24, such a resonant evolution is not possible for the Kepler-9 system, whose stability is maintained through an apsidal anti-alignment. For the Kepler-108 system, we find that the stability of its mutually inclined planets could be justified either solely by a mean-motion resonance, or in tandem with an inclination-type resonance. Going forward, dynamical analyses based on periodic orbits could yield better constrained orbital elements of near-resonant extrasolar systems when performed in parallel to the fitting of the observational data.

scholarly journals The relationship between the `limiting' Yarkovsky drift speed and asteroid families' Yarkovsky V-shape

2020 ◽  
pp. 25-41
Author(s):  
I. Milic-Zitnik
Keyword(s):  
Interesting Property ◽  
Parent Body ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Drift Speed ◽  
Yarkovsky Effect ◽  
The Mean ◽  
The Relationship ◽  
Asteroid Families

The Yarkovsky effect is an important force to consider in order to understand the long-term dynamics of asteroids. This non-gravitational force affects the orbital elements of objects revolving around a source of heat, especially their semi-major axes. Following the recently defined `limiting' value of the Yarkovsky drift speed at 7x10-5 au/Myr in Milic Zitnik (2019) (below this value of speed asteroids typically jump quickly across the mean motion resonances), we decided to investigate the relation between the asteroid family Yarkovsky V-shape and the `limiting' Yarkovsky drift speed of asteroid's semi-major axes. We have used the known scaling formula to calculate the Yarkovsky drift speed (Spoto et al. 2015) in order to determine the inner and outer `limiting' diameters (for the inner and outer V-shape borders) from the `limiting' Yarkovsky drift speed. The method was applied to 11 asteroid families of different taxonomic classes, origin type and age, located throughout the Main Belt. Here, we present the results of our calculation on relationship between asteroid families' V-shapes (crossed by strong and/or weak mean motion resonances) and the `limiting' diameters in the (a, 1=D) plane. Our main conclusion is that the `breakpoints' in changing V-shape of the very old asteroid families, crossed by relatively strong mean motion resonances on both sides very close to the parent body, are exactly the inverse of `limiting' diameters in the a versus 1=D plane. This result uncovers a novel interesting property of asteroid families' Yarkovsky V-shapes.

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.

Primordial Stability of the Earth–Mars Belt

2020 ◽  
Author(s):  
Yukun Huang ◽  
Brett Gladman
Keyword(s):  
Semimajor Axis ◽  
Orbital Stability ◽  
Terrestrial Planet ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Yarkovsky Effect ◽  
The Earth ◽  
Steady State Model ◽  
Near Earth Objects

&lt;p&gt;Previous work has demonstrated orbital stability for 100 Myr of initially near-circular and coplanar small bodies in a region termed the 'Earth&amp;#8211;Mars belt' from 1.08 au&lt;a&lt;1.28 au. Via numerical integration of 3000 particles, we studied orbits from 1.04&amp;#8211;1.30 au for the age of the Solar system. We show that on this time scale, except for a few locations where mean-motion resonances with Earth affect stability, only a narrower 'Earth&amp;#8211;Mars belt' covering a&amp;#8764;(1.09,1.17) au, e&lt;0.04, and I&lt;1&amp;#9702; has over half of the initial orbits survive for 4.5 Gyr. In addition to mean-motion resonances, we are able to see how the &amp;#957;3, &amp;#957;4, and &amp;#957;6 secular resonances contribute to long-term instability in the outer (1.17&amp;#8211;1.30 au) region on Gyr time scales. We show that all of the (rather small) near-Earth objects (NEOs) in or close to the Earth&amp;#8211;Mars belt appear to be consistent with recently arrived transient objects by comparing to a NEO steady-state model. Given the &lt;200m scale of these NEOs, we estimated the Yarkovsky effect drift rates in semimajor axis, and use these to estimate that a diameter of &amp;#8764;100km or larger would allow primordial asteroids in the Earth&amp;#8211;Mars belt to likely survive. We conclude that only a few 100 km scale asteroids could have been present in the belt&amp;#8217;s region at the end of the terrestrial planet formation.&lt;/p&gt;

scholarly journals Element history of the Laplace resonance: a dynamical approach

2018 ◽  
Vol 617 ◽  
pp. A35 ◽  
Author(s):  
F. Paita ◽  
A. Celletti ◽  
G. Pucacco
Keyword(s):  
Initial Conditions ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Resonant Interactions ◽  
Extrasolar Systems ◽  
Starting Point ◽  
Mutual Gravitational Interactions ◽  
Three Body

Context. We consider the three-body mean motion resonance defined by the Jovian moons Io, Europa, and Ganymede, which is commonly known as the Laplace resonance. In terms of the moons’ mean longitudes λ1 (Io), λ2 (Europa), and λ3 (Ganymede), this resonance is described by the librating argument φL ≡ λ1 − 3λ2 + 2λ3 ≈ 180°, which is the sum of φ12 ≡ λ1 − 2λ2 + ϖ2 ≈ 180° and φ23 ≡ λ2 − 2λ3 + ϖ2 ≈ 0°, where ϖ2 denotes Europa’s longitude of perijove. Aims. In particular, we construct approximate models for the evolution of the librating argument φL over the period of 100 yr, focusing on its principal amplitude and frequency, and on the observed mean motion combinations n1 − 2n2 and n2 − 2n3 associated with the quasi-resonant interactions above. Methods. First, we numerically propagated the Cartesian equations of motion of the Jovian system for the period under examination, and by comparing the results with a suitable set of ephemerides, we derived the main dynamical effects on the target quantities. Using these effects, we built an alternative Hamiltonian formulation and used the normal forms theory to precisely locate the resonance and to semi-analytically compute its main amplitude and frequency. Results. From the Cartesian model we observe that on the timescale considered and with ephemerides as initial conditions, both φL and the diagnostics n1 − 2n2 and n2 − 2n3 are well approximated by considering the mutual gravitational interactions of Jupiter and the Galilean moons (including Callisto), and the effect of Jupiter’s J2 harmonic. Under the same initial conditions, the Hamiltonian formulation in which Callisto and J2 are reduced to their secular contributions achieves larger errors for the quantities above, particularly for φL. By introducing appropriate resonant variables, we show that these errors can be reduced by moving in a certain action-angle phase plane, which in turn implies the necessity of a tradeoff in the selection of the initial conditions. Conclusions. In addition to being a good starting point for a deeper understanding of the Laplace resonance, the models and methods described are easily generalizable to different types of multi-body mean motion resonances. Thus, they are also prime tools for studying the dynamics of extrasolar systems.

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