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Register a new userMeasuring the Orbital Parameters of Radial Velocity Systems in Mean Motion Resonance---a Case Study of HD 200964
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The presence of mean motion resonances (MMRs) complicates analysis and fitting of planetary systems observed through the radial velocity (RV) technique. MMR can allow planets to remain stable in regions of phase space where strong planet-planet interactions would otherwise destabilize the system. These stable orbits can occupy small phase space volumes, allowing MMRs to strongly constrain system parameters, but making searches for stable orbital parameters challenging. Furthermore, libration of the resonant angle and dynamical interaction between the planets introduces another, long period variation into the observed RV signal, complicating analysis of the periods of the planets in the system. We discuss this phenomenon using the example of HD 200964. By searching through parameter space and numerically integrating each proposed set of planetary parameters to test for long term stability, we find stable solutions in the 7:5 and 3:2 MMRs in addition to the originally identified 4:3 MMR. The 7:5 configuration provides the best match to the data, while the 3:2 configuration provides the most easily understood formation scenario. In reanalysis of the originally published shorter-baseline data, we find fits in both the 4:3 and 3:2 resonances, but not the 7:5. Because the time baseline of the data is less than the resonant libration period, the current best fit to the data may not reflect the actual resonant configuration. In the absence of a full sample of the longer libration period, we find that it is of paramount importance to incorporate long term stability when fitting for the systems orbital configuration.
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We present an updated analysis of radial velocity data of the HD 82943 planetary system based on 10 years of measurements obtained with the Keck telescope. Previous studies have shown that the HD 82943 system has two planets that are likely in 2:1 mean-motion resonance (MMR), with the orbital periods about 220 and 440 days (Lee et al. 2006). However, alternative fits that are qualitatively different have also been suggested, with two planets in a 1:1 resonance (Gozdziewski & Konacki 2006) or three planets in a Laplace 4:2:1 resonance (Beauge et al. 2008). Here we use c{hi}2 minimization combined with parameter grid search to investigate the orbital parameters and dynamical states of the qualitatively different types of fits, and we compare the results to those obtained with the differential evolution Markov chain Monte Carlo method. Our results support the coplanar 2:1 MMR configuration for the HD 82943 system, and show no evidence for either the 1:1 or 3-planet Laplace resonance fits. The inclination of the system with respect to the sky plane is well constrained at about 20(+4.9 -5.5) degree, and the system contains two planets with masses of about 4.78 MJ and 4.80 MJ (where MJ is the mass of Jupiter) and orbital periods of about 219 and 442 days for the inner and outer planet, respectively. The best fit is dynamically stable with both eccentricity-type resonant angles {theta}1 and {theta}2 librating around 0 degree.
Extrasolar systems with planets on eccentric orbits close to or in mean-motion resonances are common. The classical low-order resonant Hamiltonian expansion is unfit to describe the long-term evolution of these systems. We extend the Laplace-Lagrange secular approximation for coplanar systems with two planets by including (near-)resonant harmonics, and realize an expansion at high order in the eccentricities of the resonant Hamiltonian both at orders one and two in the masses. We show that the expansion at first order in the masses gives a qualitative good approximation of the dynamics of resonant extrasolar systems with moderate eccentricities, while the second order is needed to reproduce more accurately their orbital evolutions. The resonant approach is also required to correct the secular frequencies of the motion given by the Laplace-Lagrange secular theory in the vicinity of a mean-motion resonance. The dynamical evolutions of four (near-)resonant extrasolar systems are discussed, namely GJ 876 (2:1 resonance), HD 60532 (3:1), HD 108874 and GJ 3293 (close to 4:1).
The hot Jupiter HD 217107 b was one of the first exoplanets detected using the radial velocity (RV) method, originally reported in the literature in 1999. Today, precise RV measurements of this system span more than 20 years, and there is clear evidence for a longer-period companion, HD 217107 c. Interestingly, both the short-period planet ($P_mathrm{b}sim7.13$ d) and long-period planet ($P_mathrm{c}sim5059$ d) have significantly eccentric orbits ($e_mathrm{b}sim0.13$ and $e_mathrm{c}sim0.40$). We present 42 additional RV measurements of this system obtained with the MINERVA telescope array and carry out a joint analysis with previously published RV measurements from four different facilities. We confirm and refine the previously reported orbit of the long-period companion. HD 217107 b is one of a relatively small number of hot Jupiters with an eccentric orbit, opening up the possibility of detecting precession of the planetary orbit due to General Relativistic effects and perturbations from other planets in the system. In this case, the argument of periastron, $omega$, is predicted to change at the level of $sim$0.8$^circ$ century$^{-1}$. Despite the long time baseline of our observations and the high quality of the RV measurements, we are only able to constrain the precession to be $dot{omega}<65.9^circ$ century$^{-1}$. We discuss the limitations of detecting the subtle effects of precession in exoplanet orbits using RV data.
Asteroids in mean motion resonances with giant planets are common in the solar system, but it was not until recently that several asteroids in retrograde mean motion resonances with Jupiter and Saturn were discovered. A retrograde co-orbital asteroid of Jupiter, 2015 BZ509 is confirmed to be in a long-term stable retrograde 1:1 mean motion resonance with Jupiter, which gives rise to our interests in its unique resonant dynamics. In this paper, we investigate the phase-space structure of the retrograde 1:1 resonance in detail within the framework of the circular restricted three-body problem. We construct a simple integrable approximation for the planar retrograde resonance using canonical contact transformation and numerically employ the averaging procedure in closed form. The phase portrait of the retrograde 1:1 resonance is depicted with the level curves of the averaged Hamiltonian. We thoroughly analyze all possible librations in the co-orbital region and uncover a new apocentric libration for the retrograde 1:1 resonance inside the planets orbit. We also observe the significant jumps in orbital elements for outer and inner apocentric librations, which are caused by close encounters with the perturber.
We conducted speckle imaging observations of 53 stellar systems that were members of long-term radial velocity (RV) monitoring campaigns and exhibited substantial accelerations indicative of planetary or stellar companions in wide orbits. Our observations were made with blue and red filters using the Differential Speckle Survey Instrument at Gemini-South and the NN-Explore Exoplanet Stellar Speckle Imager at the WIYN telescope. The speckle imaging identifies eight luminous companions within two arcseconds of the primary stars. In three of these systems (HD 1388, HD 87359, and HD 104304), the properties of the imaged companion are consistent with the RV measurements, suggesting that these companions may be associated with the primary and the cause of the RV variation. For all 53 stellar systems, we derive differential magnitude limits (i.e., contrast curves) from the imaging. We extend this analysis to include upper limits on companion mass in systems without imaging detections. In 25 systems, we rule out companions with mass greater than 0.2 $M_{odot}$, suggesting that the observed RV signals are caused by late M dwarfs or substellar (potentially planetary) objects. On the other hand, the joint RV and imaging analysis almost entirely rules out planetary explanations of the RV signal for HD 19522 and suggests that the companion must have an angular separation below a few tenths of an arcsecond. This work highlights the importance of combined RV and imaging observations for characterizing the outer regions of nearby planetary systems.
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