Mapping and dynamical systems

Sidlichovsky, M.

doi:10.1007/bf00048439

Cited by 10 publications

(15 citation statements)

References 33 publications

(33 reference statements)

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“…Then we integrated the N -body equations of motion without dissipation for additional 32768 steps of 400 days (∼ 1/40 of the innermost period), in order to determine the proper mean motions for all planets. The proper mean motions are the fundamental frequencies f i resolved with the refined Fourier frequency analysis (Laskar 1993;Šidlichovský & Nesvorný 1996) of the time series {a i (t) exp(iλ i (t))}, where a i (t) and λ i (t) are the canonical osculating semimajor axis and the mean longitude, respectively, as inferred in the Jacobi or Poincaré frame. Then we computed the linear combinations of the fundamental frequencies,…”

Section: A Set Of Mmr Captured Systemsmentioning

confidence: 99%

The Orbital Architecture and Debris Disks of the HR 8799 Planetary System

Goździewski

Migaszewski

2018

ApJS

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The HR 8799 planetary system with four 10 m Jup planets in wide orbits up to 70 au, and orbital periods up to 500 yrs has been detected with the direct imaging. Its intriguing orbital architecture is not yet fully resolved due to time-limited astrometry covering only 20 years. Earlier, we constructed a heuristic model of the system based on rapid, convergent migration of the planets. Here we developed a better structured and CPU-efficient variant of this model. With the updated approach, we reanalyzed the self-consistent, homogeneous astrometric dataset in (Konopacky et al. 2016). The bestfitting configuration agrees with our earlier findings. The HR 8799 planets are likely involved in dynamically robust Laplace 8e:4d:2c:1b resonance chain. Hypothetical planets with masses below the current detection limit of 0.1-3 Jupiter masses, within the observed inner, or beyond the outer orbit, respectively, do not influence the long term stability of the system. We predict positions of such nondetected objects. The long-term stable orbital model of the observed planets helps to simulate the dynamical structure of debris disks in the system. A CPU-efficient fast indicator technique makes it possible to reveal their complex, resonant shape in 10 6 particles scale. We examine the inner edge of the outer disk detected between 90 and 145 au. We also reconstruct the outer disk assuming that it has been influenced by convergent migration of the planets. A complex shape of the disk strongly depends on various dynamical factors, like orbits and masses of non-detected planets. It may be highly non-circular and its models are yet non-unique, regarding both observational constraints, as well as its origin.

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Section: A Set Of Mmr Captured Systemsmentioning

confidence: 99%

The Orbital Architecture and Debris Disks of the HR 8799 Planetary System

Goździewski

Migaszewski

2018

ApJS

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“…8 we report the amplitude scan (∆φ 1 ) for a selected critical angle φ 2:1 = λ 1 − 2λ 2 + ϖ 1 for 10 4 points to resolve a fine structure of the resonance. The fundamental frequencies are determined via the Frequency Modified Fourier Transform (FMFT, Sidlichovský & Nesvorný 1996) of the time series defined through {a i (t) exp[iλ i (t)]}, where a i (t) and λ i (t) are the osculating, canonical semi-major axis and the true longitude of the i-th planet, respectively. The total integration time is equal to 2 18 time steps of 1.0 days ( 2 × 10 3 P 3 ).…”

Section: Dynamical Setup Of the Kepler-30 Systemmentioning

confidence: 99%

The architecture and formation of the Kepler-30 planetary system

Panichi

Goździewski

Migaszewski

et al. 2018

Monthly Notices of the Royal Astronomical Society

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We study the orbital architecture, physical characteristics of planets, formation and long-term evolution of the Kepler-30 planetary system, detected and announced in 2012 by the KEPLER team. We show that the Kepler-30 system belongs to a particular class of very compact and quasi-resonant, yet long-term stable planetary systems. We re-analyse the light curves of the host star spanning Q1-Q17 quarters of the KEPLER mission. A huge variability of the Transit Timing Variations (TTV) exceeding 2 days is induced by a massive Jovian planet located between two Neptune-like companions. The innermost pair is near to the 2:1 mean motion resonance (MMR), and the outermost pair is close to higher order MMRs, such as 17:7 and 7:3. Our re-analysis of photometric data allows us to constrain, better than before, the orbital elements, planets' radii and masses, which are 9.2 ± 0.1, 536 ± 5, and 23.7 ± 1.3 Earth masses for Kepler-30b, Kepler-30c and Kepler-30d, respectively. The masses of the inner planets are determined within ∼ 1% uncertainty. We infer the internal structures of the Kepler-30 planets and their bulk densities in a wide range from (0.19 ± 0.01) g·cm −3 for Kepler-30d, (0.96 ± 0.15) g·cm −3 for Kepler-30b, to (1.71 ± 0.13) g·cm −3 for the Jovian planet Kepler-30c. We attempt to explain the origin of this unique planetary system and a deviation of the orbits from exact MMRs through the planetary migration scenario. We anticipate that the Jupiter-like planet plays an important role in determining the present dynamical state of this system. tems make it possible to further refine their orbital parameters and masses (e.g., Borsato et al. 2014;Barros et al. 2014).In this paper, we report on a new and up-to-date characterization of the Kepler-30 system composed of three planets. These planets have been validated by Fabrycky et al. (2012) on the basis of the very initial Q1-Q6 KEPLER data quarters ( 600 days) as well as by Tingley et al. (2011) on the basis of the first Q0-Q2 quarters.The early studies on this system were focused on the orbital-spin alignment and star-spots detection (Sanchis-Ojeda et al. 2012) or on differential rotation of the parent star (Lanza et al. 2014). Here, we take full advantage of the available light curves of Kepler-30, spanning Q1-Q17 quarters ( 1600 days) to constrain better the masses and orbital elements of the planets.We find the Kepler-30 system particularly interesting and unique in the KEPLER sample for several reasons. One of them is the huge TTV full-amplitude of the innermost planet of 2 days (48 hours), which is two times larger than the TTV fullamplitude of 1 day for the innermost planet in the Kepler-88 system (Nesvorný et al. 2013) dubbed as "the king of the transit c 2017 RAS

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“…In order to determine the value of e 55 , we perform an integration for 10 Myr using the final giant planet configurations and discard any remaining disk bodies. This secondary integration is analyzed using the Frequency Modified Fourier Transform 1 byŠidlichovský & Nesvorný (1996). The secular mode of Jupiter has been used to broadly describe the long-term evolution of the solar system as it affects the observed structure found in populations of small bodies.…”

Section: Criteria For Successmentioning

confidence: 99%

Instabilities in the Early Solar System Due to a Self-gravitating Disk

Quarles

Kaib

2019

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Modern studies of the early solar system routinely invoke the possibility of an orbital instability among the giant planets triggered by gravitational interactions between the planets and a massive exterior disk of planetesimals. Previous works have suggested that this instability can be substantially delayed (∼100s Myr) after the formation of the giant planets. Bodies in the disk are typically treated in a semi-active manner, wherein their gravitational force on the planets is included, but interactions between the planetesimals are ignored. We perform N -body numerical simulations using GENGA, which makes use of GPUs to allow for the inclusion of all gravitational interactions between bodies. Although our simulated Kuiper belt particles are more massive than the probable masses of real primordial Kuiper belt objects, our simulations indicate that the self-stirring of the primordial Kuiper belt is very important to the dynamics of the giant planet instability. We find that interactions between planetesimals dynamically heat the disk and typically prevent the outer solar system instability from being delayed by more than a few tens of million years after giant planet formation. Longer delays occur in a small fraction of systems that have at least 3.5 AU gaps between the planets and planetesimal disk. Our final planetary configurations match the solar system at a rate consistent with other previous works in most regards. Pre-instability heating of the disk typically yields final Jovian eccentricities comparable to the modern solar system value, which has been a difficult constraint to match in past works.

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Mapping and dynamical systems

Cited by 10 publications

References 33 publications

The Orbital Architecture and Debris Disks of the HR 8799 Planetary System

The Orbital Architecture and Debris Disks of the HR 8799 Planetary System

The architecture and formation of the Kepler-30 planetary system

Instabilities in the Early Solar System Due to a Self-gravitating Disk

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