Conditions of Dynamical Stability for the HD 160691 Planetary System (original) (raw)
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On the 2 : 1 Orbital Resonance in the HD 82943 Planetary System
The Astrophysical Journal, 2006
We present an analysis of the HD 82943 planetary system based on a radial velocity data set that combines new measurements obtained with the Keck telescope and the CORALIE measurements published in graphical form. We examine simultaneously the goodness of fit and the dynamical properties of the best-fit double-Keplerian model as a function of the poorly constrained eccentricity and argument of periapse of the outer planet's orbit. The fit with the minimum 2 is dynamically unstable if the orbits are assumed to be coplanar. However, the minimum is relatively shallow, and there is a wide range of fits outside the minimum with reasonable 2 . For an assumed coplanar inclination i ¼ 30 ( sin i ¼ 0:5), only good fits with both of the lowest order, eccentricity-type mean-motion resonance variables at the 2:1 commensurability, 1 and 2 , librating about 0 are stable. For sin i ¼ 1, there are also some good fits with only 1 (involving the inner planet's periapse longitude) librating that are stable for at least 10 8 yr. The libration semiamplitudes are about 6 for 1 and 10 for 2 for the stable good fit with the smallest libration amplitudes of both 1 and 2 . We do not find any good fits that are nonresonant and stable. Thus, the two planets in the HD 82943 system are almost certainly in 2:1 mean-motion resonance, with at least 1 librating, and the observations may even be consistent with small-amplitude librations of both 1 and 2 .
Stability and 2:1 resonance in the planetary system HD 829431
Chinese Astronomy and Astrophysics, 2006
We have explored the secular dynamical evolution of the HD 82943 system with two resonant giant planets, by simulating various planetary configurations via direct numerical integration. We also studied their orbital motions in phase space. In the numerical integrations over 107 yr, we found that all the stable orbits are connected with the 2:1 resonance. Typically, there exists the libration of the two resonant arguments 01 and (or) 02 on the same timescale. Hence, both of the semi-major axes are strongly constrained to behave in a regular way, due to the confinement of the libration of the related angles. Using the analytical model we considered the motion of the inner planet in phase space for different values of the outer planet's eccentricity c2 and of the relative apsidal longitude 0. We found that the 2:1 orbital resonance is easily preserved when 0 = 0 ° and when e2 is not too large. A moderate e2 can lock the two planets into deep resonance. The results by the analytical method agree well with those by the numerical simulation, both revealing the 2:1 resonance architecture.
The HD 181433 Planetary System: Dynamics and a New Orbital Solution
The Astronomical Journal, 2019
We present a detailed analysis of the orbital stability of the HD 181433 planetary system, finding it to exhibit strong dynamical instability across a wide range of orbital eccentricities, semi-major axes, and mutual inclinations. We also analyse the behaviour of an alternative system architecture, proposed by Campanella (2011), and find that it offers greater stability than the original solution, as a result of the planets being trapped in strong mutual resonance. We take advantage of more recent observations to perform a full refit of the system, producing a new planetary solution. The best-fit orbit for HD 181433 d now places the planet at a semi-major axis of 6.60±0.22 au, with an eccentricity of 0.469±0.013. Extensive simulations of this new system architecture reveal it to be dynamically stable across a broad range of potential orbital parameter space, increasing our confidence that the new solution represents the ground truth of the system. Our work highlights the advantage of performing dynamical simulations of candidate planetary systems in concert with the orbital fitting process, as well as supporting the continuing monitoring of radial velocity planet search targets.
The dynamics of the HD 12661 extrasolar planetary system
The Astrophysical Journal, 2005
The main goal of this work is to analyze the possible dynamical mechanisms that dominate the motion of the HD 12661 extrasolar planetary system. By an analytical approach using the expansion of the disturbing function given by Ellis & Murray we solve the equation of motion working in a Hamiltonian formulation with the corresponding canonical variables and by means of appropriate canonical transformations. Comparing this results with a direct numerical integration we can conclude that the system is dominated by a pure secular evolution very well reproduced with a disturbing function including at least sixth order terms in the eccentricities. Because of the uncertainties in the orbital elements of the planets, we also contemplate the occurrence of mean-motion resonances in the system and analyze possible contribution from these resonant terms to the total motion.
Analysis of the dynamics of the resonant planetary system HD 45364
The aim of this work is to analyse the orbital dynamics and stability of exoplanetary system in which two planets are in nearly 3:2 MMR. We have taken HD 45364 system for our study in which two planets are most likely in a 3:2 MMR. We have plotted two resonant angles and the relative apsidal longitudes and it is observed that they are librating around a constant value. From this observation our opinion is that there exist nearly 3:2 MMR between HD 45364b and HD 45364c. The perturbative solution is obtained for the time variation of the semi-major axes. The short and long term variations of semimajor axes are studied. For the validation of our analytical results we have compared our analytical solutions with the numerical solutions. The effect of planetary perturbations on eccentricity is studied with the help of secular resonance dynamics theory. The short and long term variations of eccentricities of HD 45364b and HD 45364c are shown graphically. Moreover, using the latest stabilit...
2022
HD 158259 (or HIP 85268) is one of the members of the main sequence in G0 group stars located approximately at 88 lightyears away in the constellation Draco, discussed with respect to the solar system. HD 158259 was discovered by the SOPHIE échelle spectrograph using the radial velocity method. This system includes five confirmed planets orbiting HD 158259, together with one unconfirmed planet. The planets orbit in a near 2/3 (or 3:2) orbital resonance. Starting from the innermost pairing, the period ratios are with the period ratios 1.5757, 1.5146, 1.5296, 1.5128, and 1.4482, respectively, starting from the innermost pairing. Here we theoretically investigate the HD 158259 system for the Semi-major axis, planet's mass, star luminosity, inner, center, outer, and ∆(HZ) habitable zone. We account for radial velocity amplitude, planet density, and Laplace's resonance, theoretically. The existing possibility of the sixth and undetected planet (HD 158259 g) was also investigated. The orbital period and semi-major axis of this planet, computed with 0.047726 years (17.420 days) and 0.135 AU respectively, with 2 = 0.9964. The radial velocity amplitude of this new and undetected planet was computed to be about 1.625 km/s. The mass of planets in terms of Solar, Jupiter, and Earth have shown direct direct proportional relation with an approximate increase in their semi-major axis. The lowest mass is closest to the star and the highest mass is farthest from the star. We compare the habitability zone to that of NASA, Kopparapu et.al, and the original Kopparapu estimate. The application of the relative mean motion ration (RMMR) for resonance in the triads of successive planets showed that the mode of RMMR is approximately 2/3 (or 3:2) orbital resonance, with the calculated period ratios shown above. we have also calculated the planetary equilibrium temperature (PET) in terms of the size, temperature, Albedo and distance planet to its parent star.
The dynamical origin of the multi-planetary system HD 45364
Astronomy and Astrophysics, 2010
The recently discovered planetary system HD45364 which consists of a Jupiter and Saturn mass planet is very likely in a 3:2 mean motion resonance. The standard scenario to form planetary commensurabilities is convergent migration of two planets embedded in a protoplanetary disc. When the planets are initially separated by a period ratio larger than two, convergent migration will most likely lead to a very stable 2:1 resonance for moderate migration rates. To avoid this fate, formation of the planets close enough to prevent this resonance may be proposed. However, such a simultaneous formation of the planets within a small annulus, seems to be very unlikely. Rapid type III migration of the outer planet crossing the 2:1 resonance is one possible way around this problem. In this paper, we investigate this idea in detail. We present an estimate for the required convergent migration rate and confirm this with N-body and hydrodynamical simulations. If the dynamical history of the planetary system had a phase of rapid inward migration that forms a resonant configuration, we predict that the orbital parameters of the two planets are always very similar and hence should show evidence of that. We use the orbital parameters from our simulation to calculate a radial velocity curve and compare it to observations. Our model can explain the observational data as good as the previously reported fit. The eccentricities of both planets are considerably smaller and the libration pattern is different. Within a few years, it will be possible to observe the planet-planet interaction directly and thus distinguish between these different dynamical states.
A Detailed Analysis of the HD 73526 2:1 Resonant Planetary System
The Astrophysical Journal, 2014
We present six years of new radial-velocity data from the Anglo-Australian and Magellan Telescopes on the HD 73526 2:1 resonant planetary system. We investigate both Keplerian and dynamical (interacting) fits to these data, yielding four possible configurations for the system. The new data now show that both resonance angles are librating, with amplitudes of 40 o and 60 o , respectively. We then perform long-term dynamical stability tests to differentiate these solutions, which only differ significantly in the masses of the planets. We show that while there is -2no clearly preferred system inclination, the dynamical fit with i = 90 o provides the best combination of goodness-of-fit and long-term dynamical stability.
The Astrophysical Journal, 2012
We report the detection of three new exoplanets from Keck Observatory. HD 163607 is a metal-rich G5IV star with two planets. The inner planet has an observed orbital period of 75.29 ± 0.02 days, a semi-amplitude of 51.1 ± 1.4 m s −1 , an eccentricity of 0.73 ± 0.02 and a derived minimum mass of M P sin i= 0.77 ± 0.02 M Jup . This is the largest eccentricity of any known planet in a multi-planet system. The argument of periastron passage is 78.7 ± 2.0 • ; consequently, the planet's closest approach to its parent star is very near the line of sight, leading to a relatively high transit probability of 8%. The outer planet has an orbital period of 3.60 ± 0.02 years, an orbital eccentricity of 0.12 ± 0.06 and a semi-amplitude of 40.4 ± 1.3 m s −1 . The minimum mass is M P sin i= 2.29 ± 0.16 M Jup . HD 164509 is a metal-rich G5V star with a planet in an orbital period of 282.4 ± 3.8 days and an eccentricity of 0.26 ± 0.14. The semi-amplitude of 14.2 ± 2.7 m s −1 implies a minimum mass of 0.48 ± 0.09 M Jup . The radial velocities of HD 164509 also exhibit a residual linear trend of -5.1 ± 0.7 m s −1 per year, indicating the presence of an additional longer period companion in the system. Photometric observations demonstrate that HD 163607 and HD 164509 are constant in brightness to sub-millimag levels on their radial velocity periods. This provides strong support for planetary reflex motion as the cause of the radial velocity variations.
Monthly Notices of the Royal Astronomical …, 2011
The three-planet extrasolar system of HD 181433 has been detected with HARPS. The best-fit solution, announced by the discovery team, describes a highly unstable, self-disrupting configuration. In fact, a narrow observational window, only partially covering the longest orbital period, can lead to solutions representing unrealistic scenarios. Taking into account the dynamical stability as an additional observable while interpreting the RV data, we can analyse the phase space in a neighbourhood of the statistically best-fit and derive dynamically stable configurations that reproduce the observed RV signal. Our Newtonian stable best-fit model is capable of surviving for at least 250 Myrs. The two giant companions are found to be locked in the 5:2 MMR as Jupiter and Saturn in the Solar System. This mechanism does not allow close encounters even in case of highly eccentric orbits. Moreover, planets c and d are located in regions spanned by many other strong low-order MMRs. We study the dynamics of some plausible scenarios and we illustrate the behaviours caused by secular apsidal resonances and mean motion resonances. Furthermore, we find a terrestrial planet in the habitable zone of HD 181433 can retain stability. Apart from filling an empty gap in the system, this body could offer a harbour for life indeed. Additional measurements are necessary in order to investigate this hypothesis and can confirm the predictions outlined in the paper.