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Register a new userA fast method to identify mean motion resonances
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Added by
Emese Forgacs-Dajka Dr.
Publication date
2018
fields
Physics
and research's language is
English
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The identification of mean motion resonances in exoplanetary systems or in the Solar System might be cumbersome when several planets and large number of smaller bodies are to be considered. Based on the geometrical meaning of the resonance variable, an efficient method is introduced and described here, by which mean motion resonances can be easily find without any a priori knowledge on them. The efficiency of this method is clearly demonstrated by using known exoplanets engaged in mean motion resonances, and also some members of different families of asteroids and Kuiper-belt objects being in mean motion resonances with Jupiter and Neptune respectively.
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GAIA leads us to step into a new era with a high astrometry precision of 10 uas. Under such a precision, astrometry will play important roles in detecting and characterizing exoplanets. Specially, we can identify planet pairs in mean motion resonances(MMRs) via astrometry, which constrains the formation and evolution of planetary systems. In accordance with observations, we consider two Jupiters or two super-Earths systems in 1:2, 2:3 and 3:4 MMRs. Our simulations show the false alarm probabilities(FAPs) of a third planet are extremely small while the real two planets can be good fitted with signal-to-noise ratio(SNR)> 3. The probability of reconstructing a resonant system is related with the eccentricities and resonance intensity. Generally, when SNR >= 10, if eccentricities of both planets are larger than 0.01 and the resonance is quite strong, the probabilities to reconstruct the planet pair in MMRs >= 80%. Jupiter pairs in MMRs are reconstructed more easily than super-Earth pairs with similar SNR when we consider the dynamical stability. FAPs are also calculated when we detect planet pairs in or near MMRs. FAPs for 1:2 MMR are largest, i.e., FAPs > 15% when SNR <= 10. Extrapolating from the Kepler planet pairs near MMRs and assuming SNR to be 3, we will discover and reconstruct a few tens of Jupiter pairs and hundreds of super-Earth pairs in 2:3 and 1:2 MMRs within 30 pc. We also compare the differences between even and uneven data cadence and find that planets are better measured with more uniform phase coverage.
As the discoveries of more minor bodies in retrograde resonances with giant planets, such as 2015 BZ509 and 2006 RJ2, our curiosity about the Kozai-Lidov dynamics inside the retrograde resonance has been sparked. In this study, we focus on the 3D retrograde resonance problem and investigate how the resonant dynamics of a minor body impacts on its own Kozai-Lidov cycle. Firstly we deduce the action-angle variables and canonical transformations that deal with the retrograde orbit specifically. After obtaining the dominant Hamiltonian of this problem, we then carry out the numerical averaging process in closed form to generate phase-space portraits on a $e-omega$ space. The retrograde 1:1 resonance is particularly scrutinized in detail, and numerical results from a CRTBP model shows a great agreement with the our semi-analytical portraits. On this basis, we inspect two real minor bodies currently trapped in retrograde 1:1 mean motion resonance. It is shown that they have different Kozai-Lidov states, which can be used to analyze the stability of their unique resonances. In the end, we further inspect the Kozai-Lidov dynamics inside the 2:1 and 2:5 retrograde resonance, and find distinct dynamical bifurcations of equilibrium points on phase-space portraits.
In circumstellar discs, collisional grinding of planetesimals produces second-generation dust. While it remains unclear whether this ever becomes a major component of the total dust content, the presence of such dust, and potentially the substructure within, it can be used to explore a discs physical conditions. A perturbing planet produces nonaxisymmetric structures and gaps in the dust, regardless of its origin. The dynamics of planetesimals, however, will be very different than that of small dust grains due to weaker gas interactions. Therefore, planetesimal collisions could create dusty disc structures that would not exist otherwise. In this work, we use N-body simulations to investigate the collision rate profile of planetesimals near mean-motion resonances. We find that a distinct bump or dip feature is produced in the collision profile, the presence of which depends on the libration width of the resonance and the separation between the peri- and apocenter distances of the edges of the resonance. The presence of one of these two features depends on the mass and eccentricity of the planet. Assuming that the radial dust emission traces the planetesimal collision profile, the presence of a bump or dip feature in the dust emission at the 2:1 mean-motion resonance can constrain the orbital properties of the perturbing planet. This assumption is valid, so long as radial drift does not play a significant role during the collisional cascade process. Under this assumption, these features in the dust emission should be marginally observable in nearby protoplanetary disks with ALMA.
We present preliminary though statistically significant evidence that shows that multiplanetary systems that exhibit a 2/1 period commensurability are in general younger than multiplanetary systems without commensurabilities, or even systems with other commensurabilities. An immediate possible conclusion is that the 2/1 mean-motion resonance in planetary systems, tends to be disrupted after typically a few Gyrs.
Mean motion resonances [MMRs] play an important role in the formation and evolution of planetary systems and have significantly influenced the orbital properties and distribution of planets and minor planets in the solar system as well as exo-planetary systems. Most previous theoretical analyses have focused on the low-to-moderate eccentricity regime, but with new discoveries of high eccentricity resonant minor planets and even exoplanets, there is increasing motivation to examine MMRs in the high eccentricity regime. Here we report on a study of the high eccentricity regime of MMRs in the circular planar restricted three-body problem. Non-perturbative numerical analyses of the 2:1 and the 3:2 interior resonances are carried out for a wide range of secondary-to-primary mass ratio, and for a wide range of eccentricity of the test particle. The surface-of-section technique is used to study the phase space structure near resonances. We identify transitions in phase space at certain critical eccentricities related to the geometry of resonant orbits; new stable libration zones appear at high eccentricity at libration centers shifted from those at low eccentricities. We present novel results on the mass and eccentricity dependence of the resonance libration centers and their widths in semi-major axis. Our results show that MMRs have sizable libration zones at high eccentricities, comparable to those at lower eccentricities.
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