On the divergence of first-order resonance widths at low eccentricities

Malhotra, Renu; Zhang, Nan

doi:10.1093/mnras/staa1751

Cited by 16 publications

(62 citation statements)

References 15 publications

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“…We also notice that a Polenov does not reach the values of a of the two neighbouring MMRs (24J:11A and 13J:6A). However, the resonant locations are not strictly fixed to one value of a but are capable for small local migrations along the semi-major axis (Malhotra and Zhang 2020).…”

Section: The Stability Propertiesmentioning

confidence: 99%

The physical and dynamical characteristics of the asteroid 4940 Polenov

et al. 2021

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The asteroid (1986 QY4) 4940 Polenov is the first Solar system object whose 3D shape is determined using the observations from the newly built Astronomical Station Vidojevica (ASV). Here we present the results of photometric observations for Polenov, gathered from the ASV, and from the Bulgarian National Astronomical Observatory (BNAO) Rozhen, during 2014, 2019 and 2020 apparitions. Polenov is a 17.8km object located in the outer part of the main belt and belongs to the asteroid family Themis. We have determined the lightcurves, the synodic period of 4.161?0.001 h, as well as the solution for the shape and spin axis. Using the lightcurve inversion method, the combination of our lightcurves and the sparse data from ATLAS{HKO and ATLAS-MLO, we also found the sidereal period, indicating a retrograde rotation of the asteroid, with two possible mirrored pole solutions. The ratio of the largest to smallest reecting surface is about 1.4. In addition, we studied the dynamical properties of the asteroid and obtained a long stability time that exceeds 0.4 Gyrs.

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Section: The Stability Propertiesmentioning

confidence: 99%

The physical and dynamical characteristics of the asteroid 4940 Polenov

et al. 2021

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“…10). As we adopt a more efficient eccentricity damping for the planet at the truncation radius, we find that the 2:1 MMR of planet b & c is weaker due to a smaller libration width and longer libration timescale (Murray & Dermott 1999;Malhotra & Zhang 2020;Lei & Li 2020). Hence, while planet g must still be formed within the 3:2 MMR of planet f in order to convergently migrate to get trapped in the 4:3 MMR, such a requirement is no longer necessary for planet b and c. At the end of Stage I, all adjacent planet pairs are trapped in 3:2 MMR except planet f & g, which are in 4:3.…”

Section: Simulationsmentioning

confidence: 99%

The dynamics of the TRAPPIST-1 system in the context of its formation

Huang,

Ormel

2021

Preprint

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TRAPPIST-1 is an 0.09 𝑀 star, which harbours a system of seven Earth-sized planets. Two main features stand out: (i) all planets have similar radii, masses, and compositions; and (ii) all planets are in resonance. Previous works have outlined a pebble-driven formation scenario where planets of similar composition form sequentially at the H 2 O snowline (∼0.1 au for this low-mass star). It was hypothesized that the subsequent formation and migration led to the current resonant configuration. Here, we investigate whether the sequential planet formation model is indeed capable to produce the present-day resonant configuration, characterized by its two-body and three-body mean motion resonances structure. We carry out N-body simulations, accounting for type-I migration, stellar tidal damping, disc eccentricity damping, and featuring a migration barrier located at the disc's inner edge. We demonstrate that the present-day dynamical configuration of the TRAPPIST-1 system is in line with the sequential formation/migration model. First, a chain of first-order resonances was formed at the disc inner edge by convergent migration. We argue that TRAPPIST-1b and c marched across the migration barrier, into the gas-free cavity, during the dispersal of the gas disc. The dispersing disc then pushed planets b and c inward until they settled in a configuration close to the observed resonances. Thereafter, the stellar tidal torque also attributed towards a modest separation of the inner system. We argue that our scenario is also applicable to other compact resonant planet systems.

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“…for producing Poincaré sections in comparison to the traditional versions used by Malhotra (1996); Winter & Murray (1997a,b); Morais & Giuppone (2012); Morais & Namouni (2013b); Wang & Malhotra (2017); Malhotra et al (2018) and Malhotra & Zhang (2020) in terms of the following two points.…”

Section: Poincaré Surfaces Of Sectionmentioning

confidence: 99%

“…According to the traditional notations (Malhotra & Zhang 2020), the resonant centres with the usual critical argument at ϕ = 0 belong to the pericentric branch and the ones at ϕ = π belong to the apocentric branch. From equation (11), we have ϕ = kθ1 − kpθ2.…”

Section: Numerical Widths Over the Full Range Of Eccentricitymentioning

confidence: 99%

“…The technique of Poincaré sections has been widely used in studying MMRs, e.g. Malhotra (1996); Winter & Murray (1997a,b); Morais & Giuppone (2012); Morais & Namouni (2013b); Wang & Malhotra (2017); Malhotra et al (2018) and Malhotra & Zhang (2020). About the choice of Poincaré sections, Wang & Malhotra (2017) made an important improvement: recording the states of test particles at every successive perihelion passage.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical structures of retrograde resonances: analytical and numerical studies

Lei

2021

Monthly Notices of the Royal Astronomical Society

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In this work, retrograde mean motion resonances (MMRs) are investigated by means of analytical and numerical approaches. Initially, we define a new resonant angle to describe the retrograde MMRs and then perform a series of canonical transformations to formulate the resonant model, in which the phase portrait, resonant centre and resonant width can be analytically determined. To validate the analytical developments, the non-perturbative analysis is made by taking advantage of Poincaré surfaces of section. Some modifications are introduced in the production of Poincaré sections and, in particular, it becomes possible to make direct comparisons between the analytical and numerical results. It is found that there exists an excellent correspondence between the phase portraits and the associated Poincaré sections, and the analytical results agree well with the numerical results in terms of the resonant width and the location of resonant centre. Finally, the numerical approach is utilized to determine the resonant widths and resonant centres over the full range of eccentricity. In particular, seven known examples of retrograde asteroids including 2015 BZ509, 2008 SO218, 1999 LE31, 2000 DG8, 2014 AT28, 2016 LS and 2016 JK24 are found inside the libration zones of retrograde MMRs with Jupiter. The results obtained in this work may be helpful for understanding the dynamical evolution for asteroids inside retrograde MMRs.

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On the divergence of first-order resonance widths at low eccentricities

Cited by 16 publications

References 15 publications

The physical and dynamical characteristics of the asteroid 4940 Polenov

The physical and dynamical characteristics of the asteroid 4940 Polenov

The dynamics of the TRAPPIST-1 system in the context of its formation

Dynamical structures of retrograde resonances: analytical and numerical studies

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