Mechanic: The MPI/HDF code framework for dynamical astronomy

Słonina, Mariusz; Goździewski, Krzysztof; Migaszewski, Cezary

doi:10.1016/j.newast.2014.05.006

Cited by 11 publications

(7 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We utilized the MECHANIC software 7 Słonina, Goździewski and Migaszewski 2014) to calculate MEGNO maps for Kepler-413 , applying the latest MEGNO implementation (Goździewski et al 2001;Goździewski 2003;Goździewski et al 2008). The maps have a resolution of 350 x 500 initial conditions in planetary semi-major axis (a p ) and eccentricity (e p ) space, each integrated for 200,000 days (corresponding to ∼ 20, 000 binary periods).…”

Section: Orbital Stabilitymentioning

confidence: 99%

Kepler-413b: A Slightly Misaligned, Neptune-Size Transiting Circumbinary Planet

Kostov¹,

McCullough²,

Carter³

et al. 2014

ApJ

184

135

View full text Add to dashboard Cite

We report the discovery of a transiting, R p = 4.347 ± 0.099R ⊕ , circumbinary planet (CBP) orbiting the Kepler K + M Eclipsing Binary (EB) system KIC 12351927 (Kepler-413) every ∼ 66 days on an eccentric orbit with a p = 0.355 ± 0.002AU, e p = 0.118 ± 0.002. The two stars, with M A = 0.820 ± 0.015M , R A = 0.776 ± 0.009R and M B = 0.542 ± 0.008M , R B = 0.484 ± 0.024R respectively revolve around each -2other every 10.11615 ± 0.00001 days on a nearly circular (e EB = 0.037 ± 0.002) orbit. The orbital plane of the EB is slightly inclined to the line of sight (i EB = 87.33±0.06 • ) while that of the planet is inclined by ∼ 2.5 • to the binary plane at the reference epoch. Orbital precession with a period of ∼ 11 years causes the inclination of the latter to the sky plane to continuously change. As a result, the planet often fails to transit the primary star at inferior conjunction, causing stretches of hundreds of days with no transits (corresponding to multiple planetary orbital periods). We predict that the next transit will not occur until 2020. The orbital configuration of the system places the planet slightly closer to its host stars than the inner edge of the extended habitable zone. Additionally, the orbital configuration of the system is such that the CBP may experience Cassini-States dynamics under the influence of the EB, in which the planet's obliquity precesses with a rate comparable to its orbital precession. Depending on the angular precession frequency of the CBP, it could potentially undergo obliquity fluctuations of dozens of degrees (and complex seasonal cycles) on precession timescales.

show abstract

Section: Orbital Stabilitymentioning

confidence: 99%

Kepler-413b: A Slightly Misaligned, Neptune-Size Transiting Circumbinary Planet

Kostov¹,

McCullough²,

Carter³

et al. 2014

ApJ

184

135

View full text Add to dashboard Cite

show abstract

“…Orbits with quasi-periodic time evolution usually assume values of | Y − 2| < 0.001 at the end of the numerical integration. We used the MEGNO implementation within the MECHANIC package (Słonina et al 2015), and considered the integration time for each orbit to be 4.7 × 10 4 binary periods.…”

Section: Methodology and Numerical Techniquesmentioning

confidence: 99%

Predicting a Third Planet in the Kepler-47 Circumbinary System

Hinse

Haghighipour

Kostov

et al. 2015

ApJ

Self Cite

View full text Add to dashboard Cite

We have studied the possibility that a third circumbinary planet in the Kepler-47 planetary system be the source of the single unexplained transiting event reported during the discovery of these planets. We applied the MEGNO technique to identify regions in the phase space where a third planet can maintain quasi-periodic orbits, and assessed the long-term stability of the three-planet system by integrating the entire 5 bodies (binary + planets) for 10 Myr. We identified several stable regions between the two known planets as well as a region beyond the orbit of Kepler-47c where the orbit of the third planet could be stable. To constrain the orbit of this planet, we used the measured duration of the unexplained transit event (∼ 4.15 hours) and compared that with the transit duration of the third planet in an ensemble of stable orbits. To remove the degeneracy among the orbits with similar transit durations, we considered the planet to be in a circular orbit and calculated its period analytically. The latter places an upper limit of 424 days on the orbital period of the third planet. Our analysis suggests that if the unexplained transit event detected during the discovery of the Kepler-47 circumbinary system is due to a planetary object, this planet will be in a low eccentricity orbit with a semimajor axis smaller than 1.24 AU. Further constraining of the mass and orbital elements of this planet requires a re-analysis of the entire currently available data including those obtained post-announcement of the discovery of this system. We present details of our methodology and discuss the implication of the results.

show abstract

“…The Hamiltonian defined by Eq. 9 and the corresponding symplectic map version were studied for resonances and chaotic diffusion phenomena (Froeschlé et al 2000;Lega et al 2003;Froeschlé et al 2005), with the help of fast indicators FLI and MEGNO (Słonina et al 2015). The REM algorithm has been already tested for this Hamiltonian system by Faranda et al (2012) with the canonical map technique for a relatively small time-span of 10 3 iterations.…”

Section: System 1: Fgl Hamiltonian Systemmentioning

confidence: 99%

“…We also note that in order to investigate the global diffusion, motion intervals as long as 10 8 and 10 9 characteristic periods must be considered, see (Lega et al 2003, their Fig. 2) or (Słonina et al 2015).…”

Section: System 1: Fgl Hamiltonian Systemmentioning

confidence: 99%

The reversibility error method (REM): a new, dynamical fast indicator for planetary dynamics

Panichi

Goździewski

Turchetti

2017

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

We describe the Reversibility Error Method (REM) and its applications to planetary dynamics. REM is based on the time-reversibility analysis of the phase-space trajectories of conservative Hamiltonian systems. The round-off errors break the time reversibility and the displacement from the initial condition, occurring when we integrate it forward and backward for the same time interval, is related to the dynamical character of the trajectory. If the motion is chaotic, in the sense of non-zero maximal Characteristic Lyapunov Exponent (mLCE), then REM increases exponentially with time, as exp λt, while when the motion is regular (quasi-periodic) then REM increases as a power law in time, as t α , where α and λ are real coefficients. We compare the REM with a variant of mLCE, the Mean Exponential Growth factor of Nearby Orbits (MEGNO). The test set includes the restricted three body problem and five resonant planetary systems: HD 37124, Kepler-60, Kepler-36, Kepler-29 and Kepler-26. We found a very good agreement between the outcomes of these algorithms. Moreover, the numerical implementation of REM is astonishing simple, and is based on solid theoretical background. The REM requires only a symplectic and time-reversible (symmetric) integrator of the equations of motion. This method is also CPU efficient. It may be particularly useful for the dynamical analysis of multiple planetary systems in the KEPLER sample, characterized by loweccentricity orbits and relatively weak mutual interactions. As an interesting side-result, we found a possible stable chaos occurrence in the Kepler-29 planetary system.

show abstract

Mechanic: The MPI/HDF code framework for dynamical astronomy

Cited by 11 publications

References 38 publications

Kepler-413b: A Slightly Misaligned, Neptune-Size Transiting Circumbinary Planet

Kepler-413b: A Slightly Misaligned, Neptune-Size Transiting Circumbinary Planet

Predicting a Third Planet in the Kepler-47 Circumbinary System

The reversibility error method (REM): a new, dynamical fast indicator for planetary dynamics

Contact Info

Product

Resources

About