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Register a new userHow eccentric orbital solutions can hide planetary systems in 2:1 resonant orbits
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Added by
Mercedes Lopez-Morales
Publication date
2009
fields
Physics
and research's language is
English
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The Doppler technique measures the reflex radial motion of a star induced by the presence of companions and is the most successful method to detect exoplanets. If several planets are present, their signals will appear combined in the radial motion of the star, leading to potential misinterpretations of the data. Specifically, two planets in 2:1 resonant orbits can mimic the signal of a single planet in an eccentric orbit. We quantify the implications of this statistical degeneracy for a representative sample of the reported single exoplanets with available datasets, finding that 1) around 35 percent of the published eccentric one-planet solutions are statistically indistinguishable from planetary systems in 2:1 orbital resonance, 2) another 40 percent cannot be statistically distinguished from a circular orbital solution and 3) planets with masses comparable to Earth could be hidden in known orbital solutions of eccentric super-Earths and Neptune mass planets.
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The results of an extensive numerical study of the periodic orbits of planar, elliptic restricted three-body planetary systems consisting of a star, an inner massive planet and an outer mass-less body in the external 1:2 mean-motion resonance are presented. Using the method of differential continuation, the locations of the resonant periodic orbits of such systems are identified and through an extensive study of their phase-parameter space, it is found that the majority of the resonant periodic orbits are unstable. For certain values of the mass and the orbital eccentricity of the inner planet, however, stable periodic orbits can be found. The applicability of such studies to the 1:2 resonance of the extrasolar planetary system GJ876 is also discussed.
We present refined parameters for the extrasolar planetary system HAT-P-2 (also known as HD 147506), based on new radial velocity and photometric data. HAT-P-2b is a transiting extrasolar planet that exhibits an eccentric orbit. We present a detailed analysis of the planetary and stellar parameters, yielding consistent results for the mass and radius of the star, better constraints on the orbital eccentricity, and refined planetary parameters. The improved parameters for the host star are M_star = 1.36 +/- 0.04 M_sun and R_star = 1.64 +/- 0.08 R_sun, while the planet has a mass of M_p = 9.09 +/- 0.24 M_Jup and radius of R_p = 1.16 +/- 0.08 R_Jup. The refined transit epoch and period for the planet are E = 2,454,387.49375 +/- 0.00074 (BJD) and P = 5.6334729 +/- 0.0000061 (days), and the orbital eccentricity and argument of periastron are e = 0.5171 +/- 0.0033 and omega = 185.22 +/- 0.95 degrees. These orbital elements allow us to predict the timings of secondary eclipses with a reasonable accuracy of ~15 minutes. We also discuss the effects of this significant eccentricity including the characterization of the asymmetry in the transit light curve. Simple formulae are presented for the above, and these, in turn, can be used to constrain the orbital eccentricity using purely photometric data. These will be particularly useful for very high precision, space-borne observations of transiting planets.
We investigate the resonant rotation of co-orbital bodies in eccentric and planar orbits. We develop a simple analytical model to study the impact of the eccentricity and orbital perturbations on the spin dynamics. This model is relevant in the entire domain of horseshoe and tadpole orbit, for moderate eccentricities. We show that there are three different families of spin-orbit resonances, one depending on the eccentricity, one depending on the orbital libration frequency, and another depending on the pericenters dynamics. We can estimate the width and the location of the different resonant islands in the phase space, predicting which are the more likely to capture the spin of the rotating body. In some regions of the phase space the resonant islands may overlap, giving rise to chaotic rotation.
We have numerically explored the stable planetary geometry for the multiple systems involved in a 2:1 mean motion resonance, and herein we mainly study the HD 82943 system by employing two sets of the orbital parameters (Mayor et al. 2004; Ji et al. 2004). In the simulations, we find that all stable orbits are related to the 2:1 resonance that can help to remain the semi-major axes for two companions almost unaltered over the secular evolution for $10^{8}$ yr. In addition, we also show that there exist three possible stable configurations:(1) Type I, only $theta_{1} approx 0^{circ}$, (2) Type II, $theta_{1}approxtheta_{2}approxtheta_{3}approx 0^{circ}$ (aligned case), and (3) Type III, $theta_{1}approx 180^{circ}$, $theta_{2}approx0^{circ}$, $theta_{3}approx180^{circ}$ (antialigned case), where two resonant arguments are $theta_{1} = lambda_{1} - 2lambda _{2} + varpi_{1}$ and $theta_{2} = lambda_{1} - 2lambda_{2} + varpi_{2}$, the relative apsidal longitudes $theta_{3} = varpi_{1}-varpi_{2}=Deltavarpi$. And we find that other 2:1 resonant systems (e.g., GJ 876) may possess one of three stable orbits in their realistic motions. Moreover, we also study the existence of the assumed terrestrial bodies at $sim 1$ AU for HD 82943 and GJ 876 systems (see main texts).
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 planets orbit. The fit with the minimum chi_{nu}^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 chi_{nu}^2. For an assumed coplanar inclination i = 30 deg. (sin i = 0.5), only good fits with both of the lowest order, eccentricity-type mean-motion resonance variables at the 2:1 commensurability, theta_1 and theta_2, librating about 0 deg. are stable. For sin i = 1, there are also some good fits with only theta_1 (involving the inner planets periapse longitude) librating that are stable for at least 10^8 years. The libration semiamplitudes are about 6 deg. for theta_1 and 10 deg. for theta_2 for the stable good fit with the smallest libration amplitudes of both theta_1 and theta_2. We do not find any good fits that are non-resonant and stable. Thus the two planets in the HD 82943 system are almost certainly in 2:1 mean-motion resonance, with at least theta_1 librating, and the observations may even be consistent with small-amplitude librations of both theta_1 and theta_2.
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