Dynamical Analysis of the Orbital Parameters of the HD 82943 Planetary System

Goździewski, Krzysztof; Maciejewski, Andrzej J.

doi:10.1086/338390

Cited by 80 publications

(44 citation statements)

References 6 publications

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“…The white crosses mark the position of the two planets, and the collision lines are traced with white lines. Correia et al 2010) or HD 82943 (Goździewski & Maciejewski 2001), or in a 3/2 mean motion resonance such as HD 45364 (Correia et al 2009). The second one ( j = 2) introduces the short-term oscillations of frequency l θ , corresponding to a period P θ ≈ 101.49 years.…”

Section: Resonant and Secular Dynamicsmentioning

confidence: 99%

Dynamical stability analysis of the HD 202206 system and constraints to the planetary orbits

Couetdic¹,

Laskar²,

Correia

et al. 2010

A&A

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Context. Long-term, precise Doppler measurements with the CORALIE spectrograph have revealed the presence of two massive companions to the solar-type star HD 202206. Although the three-body fit of the system is unstable, it was shown that a 5:1 mean motion resonance exists close to the best fit, where the system is stable. It was also hinted that stable solutions with a wide range of mutual inclinations and low O−C were possible. Aims. We present here an extensive dynamical study of the HD 202206 system, aiming at constraining the inclinations of the two known companions, from which we derive possible value ranges for the companion masses. Methods. We consider each inclination and one of the longitudes of ascending node as free parameters. For any chosen triplet of these parameters, we compute a new fit. Then we study the long-term stability in a small (in terms of O−C) neighborhood using Laskar's frequency map analysis. We also introduce a numerical method based on frequency analysis to determine the center of libration mode inside a mean motion resonance. Results. We find that acceptable coplanar configurations (with low χ 2 stable orbits) are limited with respect to inclinations to the line of sight between 30• and 90• . This limits the masses of both companions to roughly twice the minimum: m b ∈ [16.6 M Jup ; 33.5 M Jup ] and m c ∈ [2.2 M Jup ; 4.4 M Jup ]. Non-coplanar configurations are possible for a wide range of mutual inclinations from 0• to 90• , although ΔΩ = 0[π] configurations seem to be favored. We also confirm the 5:1 mean motion resonance to be most likely. In the coplanar edge-on case, we provide a very good stable solution in the resonance, whose χ 2 does not differ significantly from the best fit. Using our method for the determination of the center of libration, we further refine this solution to obtain an orbit with a very low amplitude of libration, as we expect that dissipative effects have dampened the libration.

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Section: Resonant and Secular Dynamicsmentioning

confidence: 99%

Dynamical stability analysis of the HD 202206 system and constraints to the planetary orbits

Couetdic¹,

Laskar²,

Correia

et al. 2010

A&A

View full text Add to dashboard Cite

show abstract

“…For instance, the angular elements of such solutions might be systematically displaced from a stable MMR region (e.g. Goździewski & Maciejewski 2001;Goździewski & Migaszewski 2014). Therefore, to understand the observed instability, we carried out extensive Monte Carlo experiments.…”

Section: Stability Analysis Of 2-planet Solutionsmentioning

confidence: 99%

“…Next, at each point of the given grid, we computed the Mean Exponential Growth factor of Nearby Orbits (MEGNO from hereafter) for up to 1 Myr (i.e., up to a few 10 4 outermost orbital periods). MEGNO (Cincotta et al 2003;Goździewski & Maciejewski 2001) is a numerical algorithm making it possible to estimate efficiently the Maximal Lyapunov Exponent and to determine quasi-regular and chaotic solutions of the N-body equations of motion. In the examined ranges of semi-major axes, 2-planet systems may be stable only in the regime of MMR's, and chaotic solutions imply shorttime geometric instability (hence short T E ) (e.g.…”

Section: Stability Analysis Of 2-planet Solutionsmentioning

confidence: 99%

The HU Aqr planetary system hypothesis revisited

Goździewski

Słowikowska

Dimitrov

et al. 2015

Monthly Notices of the Royal Astronomical Society

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We study the mid-egress eclipse timing data gathered for the cataclysmic binary HU Aquarii during the years 1993-2014. The (O-C) residuals were previously attributed to a single ∼ 7 Jupiter mass companion in ∼ 5 au orbit or to a stable 2-planet system with an unconstrained outermost orbit. We present 22 new observations gathered between June, 2011 and July, 2014 with four instruments around the world. They reveal a systematic deviation of ∼ 60-120 seconds from the older ephemeris. We re-analyse the whole set of the timing data available. Our results provide an erratum to the previous HU Aqr planetary models, indicating that the hypothesis for a third and fourth body in this system is uncertain. The dynamical stability criterion and a particular geometry of orbits rule out coplanar 2-planet configurations. A putative HU Aqr planetary system may be more complex, e.g., highly non-coplanar. Indeed, we found examples of 3-planet configurations with the middle planet in a retrograde orbit, which are stable for at least 1 Gyr, and consistent with the observations. The (O-C) may be also driven by oscillations of the gravitational quadrupole moment of the secondary, as predicted by the Lanza et al. modification of the Applegate mechanism. Further systematic, long-term monitoring of HU Aqr is required to interpret the (O-C) residuals.

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“…Stability considerations are sometimes used in these cases to help identify a more likely model. However, such a process involves weighing stability against observational data and there is no straightforward method to incorporate stability in a robust statistical manner (for one such method see [36]). Therefore, modifications to orbital parameters based on stability criteria are sometimes based on judgment and their uncertainties are difficult to quantify.…”

Section: Multiplanet Systemsmentioning

confidence: 99%

Exoplanet Observations

Bean

2010

Formation and Evolution of Exoplanets

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Dynamical Analysis of the Orbital Parameters of the HD 82943 Planetary System

Cited by 80 publications

References 6 publications

Dynamical stability analysis of the HD 202206 system and constraints to the planetary orbits

Dynamical stability analysis of the HD 202206 system and constraints to the planetary orbits

The HU Aqr planetary system hypothesis revisited

Exoplanet Observations

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