Journal articles: 'Kozai resonance'

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Libert, A. S., and K. Tsiganis. "Kozai resonance in extrasolar systems." Astronomy & Astrophysics 493, no. 2 (November 20, 2008): 677–86. http://dx.doi.org/10.1051/0004-6361:200810843.

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Qi, Yi, and Anton de Ruiter. "Kozai mechanism inside mean motion resonances in the three-dimensional phase space." Monthly Notices of the Royal Astronomical Society 493, no. 4 (March 13, 2020): 5816–24. http://dx.doi.org/10.1093/mnras/staa684.

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ABSTRACT In this paper, we investigate the Kozai mechanism inside the inclined mean motion resonance (MMR) through a three-dimensional (3D) phase space. The Hamiltonian approximation for both prograde and retrograde MMRs is established by a semi-analytical method. We pick Jupiter as the disturber and study the Kozai mechanism in the Sun–Jupiter circular restricted three-body problem. Kozai islands of the prograde and retrograde MMRs are found in the 3D phase space. Numerical integration demonstrates that the locus of the orbit on the Kozai island is bounded by the Kozai island in the 3D phase space, so the orbit is locked in the Kozai+MMR state. The study of the Kozai dynamics inside a retrograde 1:1 MMR indicates that Kozai islands in the 3D phase space are just a sufficient condition for the Kozai+MMR mechanism rather than a necessary condition. There is no Kozai island in the 3D space for the retrograde 1:1 MMR, but the resonant coupling of Kozai with the retrograde 1:1 MMR appears in the phase space. Finally, dynamical behaviours of the two test particles located on Kozai islands are demonstrated in the ephemeris model.

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Mikkola, Seppo, and Kiyotaka Tanikawa. "Does Kozai Resonance Drive CH Cygni?" Astronomical Journal 116, no. 1 (July 1998): 444–50. http://dx.doi.org/10.1086/300404.

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Lawler, S. M., and B. Gladman. "PLUTINO DETECTION BIASES, INCLUDING THE KOZAI RESONANCE." Astronomical Journal 146, no. 1 (June 5, 2013): 6. http://dx.doi.org/10.1088/0004-6256/146/1/6.

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Šubr, Ladislav, Vladimír Karas, and Jaroslav Haas. "Kozai resonance model for Sagittarius A* stellar orbits." Proceedings of the International Astronomical Union 2, S238 (August 2006): 201–6. http://dx.doi.org/10.1017/s1743921307004978.

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AbstractWe study a possibility of tidal disruptions of stars orbiting a supermassive black hole due to eccentricity oscillations driven by Kozai's mechanism. We apply the model to conditions relevant for the Galactic Centre where we consider two different sources of the perturbation to the central potential, which trigger the resonance mechanism. Firstly, it is a disc of young massive stars orbiting Sgr A* atr≳ 0.08 pc, and, secondly, a molecular circumnuclear disc. Each of the two possibilities appears to be capable of exciting eccentricities to values sufficient for the tidal disruption of ∼100 stars from the nuclear stellar cluster on a time-scale of 0.1–10 Myrs. Tidally disrupted stars may cause periods of increased accretion activity of Sgr A*.

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Migaszewski, C., and K. Goździewski. "Relativistic model of the Lidov-Kozai resonance in binaries." EAS Publications Series 42 (2010): 385–91. http://dx.doi.org/10.1051/eas/1042041.

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Volpi, Mara, Arnaud Roisin, and Anne-Sophie Libert. "The 3D secular dynamics of radial-velocity-detected planetary systems." Astronomy & Astrophysics 626 (June 2019): A74. http://dx.doi.org/10.1051/0004-6361/201834896.

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Aims. To date, more than 600 multi-planetary systems have been discovered. Due to the limitations of the detection methods, our knowledge of the systems is usually far from complete. In particular, for planetary systems discovered with the radial velocity (RV) technique, the inclinations of the orbital planes, and thus the mutual inclinations and planetary masses, are unknown. Our work aims to constrain the spatial configuration of several RV-detected extrasolar systems that are not in a mean-motion resonance. Methods. Through an analytical study based on a first-order secular Hamiltonian expansion and numerical explorations performed with a chaos detector, we identified ranges of values for the orbital inclinations and the mutual inclinations, which ensure the long-term stability of the system. Our results were validated by comparison with n-body simulations, showing the accuracy of our analytical approach up to high mutual inclinations (∼70 ° −80°). Results. We find that, given the current estimations for the parameters of the selected systems, long-term regular evolution of the spatial configurations is observed, for all the systems, (i) at low mutual inclinations (typically less than 35°) and (ii) at higher mutual inclinations, preferentially if the system is in a Lidov-Kozai resonance. Indeed, a rapid destabilisation of highly mutually inclined orbits is commonly observed, due to the significant chaos that develops around the stability islands of the Lidov-Kozai resonance. The extent of the Lidov-Kozai resonant region is discussed for ten planetary systems (HD 11506, HD 12661, HD 134987, HD 142, HD 154857, HD 164922, HD 169830, HD 207832, HD 4732, and HD 74156).

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Wan, X. S., and T. Y. Huang. "An exploration of the Kozai resonance in the Kuiper Belt." Monthly Notices of the Royal Astronomical Society 377, no. 1 (May 1, 2007): 133–41. http://dx.doi.org/10.1111/j.1365-2966.2007.11541.x.

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Britt, Dylan, Ben Johanson, Logan Wood, M. Coleman Miller, and Erez Michaely. "Binary black hole mergers from hierarchical triples in open clusters." Monthly Notices of the Royal Astronomical Society 505, no. 3 (June 9, 2021): 3844–52. http://dx.doi.org/10.1093/mnras/stab1570.

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ABSTRACT A promising channel for producing binary black hole mergers is the Lidov–Kozai orbital resonance in hierarchical triple systems. While this mechanism has been studied in isolation, the distribution of such mergers in time and across star-forming environments is not well characterized. In this work, we explore Lidov–Kozai-induced black hole mergers in open clusters, combining semi-analytical and Monte Carlo methods to calculate merger rates and delay times for nine different population models. We predict a merger rate density of ∼1–10 Gpc−3 yr−1 for the Lidov–Kozai channel in the local Universe, and all models yield delay-time distributions in which a significant fraction of binary black hole mergers (e.g. ∼20–50 per cent in our baseline model) occur during the open cluster phase. Our findings suggest that a substantial fraction of mergers from hierarchical triples occur within star-forming regions in spiral galaxies.

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Giuppone, C. A., and A. M. Leiva. "Secular models and Kozai resonance for planets in coorbital non-coplanar motion." Monthly Notices of the Royal Astronomical Society 460, no. 1 (April 22, 2016): 966–79. http://dx.doi.org/10.1093/mnras/stw938.

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Roisin, Arnaud, Jean Teyssandier, and Anne-Sophie Libert. "Planetary migration in precessing discs for S-type wide binaries." Monthly Notices of the Royal Astronomical Society 506, no. 4 (July 29, 2021): 5005–14. http://dx.doi.org/10.1093/mnras/stab2059.

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ABSTRACT The discovery of numerous circumprimary planets in the last few years has brought to the fore the question of planet formation in binary systems. The significant dynamical influence, during the protoplanetary disc phase, of a binary companion on a giant planet has previously been highlighted for wide binary stars. In particular, highly inclined binary companion can induce perturbations on the disc and the planets through the Lidov–Kozai resonance, which could inhibit the formation process. In this work, we aim to study how the disc gravitational potential acting on the planet and the nodal precession induced by the wide binary companion with separation of 1000 au on the disc act to suppress the Lidov–Kozai perturbations on a migrating giant planet. We derive new approximate formulas for the evolution of the disc’s inclination and longitude of the ascending node in case of a rigidly precessing disc with a decreasing mass and perturbed by a wide binary companion, which are suitable for N-body simulations. We carry out 3200 simulations with several eccentricity and inclination values for the binary companion. The gravitational and damping forces exerted by the disc on the planet tend to keep the latter in the mid-plane of the former, and suppress the effect of the binary companion by preventing the planet from getting locked in the Lidov–Kozai resonance during the disc phase. We also confirm that because of nodal precession induced by the binary, a primordial spin–orbit misalignment could be generated for circumprimary planets with an inclined binary companion.

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de Elía, G. C., M. Zanardi, A. Dugaro, and S. Naoz. "Inverse Lidov-Kozai resonance for an outer test particle due to an eccentric perturber." Astronomy & Astrophysics 627 (June 25, 2019): A17. http://dx.doi.org/10.1051/0004-6361/201935220.

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Aims. We analyze the behavior of the argument of pericenter ω2 of an outer particle in the elliptical restricted three-body problem, focusing on the ω2 resonance or inverse Lidov-Kozai resonance. Methods. First, we calculated the contribution of the terms of quadrupole, octupole, and hexadecapolar order of the secular approximation of the potential to the outer particle’s ω2 precession rate (dω2∕dτ). Then, we derived analytical criteria that determine the vanishing of the ω2 quadrupole precession rate (dω2/dτ)quad for different values of the inner perturber’s eccentricity e1. Finally, we used such analytical considerations and described the behavior of ω2 of outer particles extracted from N-body simulations developed in a previous work. Results. Our analytical study indicates that the values of the inclination i2 and the ascending node longitude Ω2 associated with the outer particle that vanish (dω2/dτ)quad strongly depend on the eccentricity e1 of the inner perturber. In fact, if e1 < 0.25 (>0.40825), (dω2/dτ)quad is only vanished for particles whose Ω2 circulates (librates). For e1 between 0.25 and 0.40825, (dω2/dτ)quad can be vanished for any particle for a suitable selection of pairs (Ω2, i2). Our analysis of the N-body simulations shows that the inverse Lidov-Kozai resonance is possible for small, moderate, and high values of e1. Moreover, such a resonance produces distinctive features in the evolution of a particle in the (Ω2, i2) plane. In fact, if ω2 librates and Ω2 circulates, the extremes of i2 at Ω2 = 90° and 270° do not reach the same value, while if ω2 and Ω2 librate, the evolutionary trajectory of the particle in the (Ω2, i2) plane shows evidence of an asymmetry with respect to i2 = 90°. The evolution of ω2 associated with the outer particles of the N-body simulations can be very well explained by the analytical criteria derived in our investigation.

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Gopakumar, Achamveedu, Manjari Bagchi, and Alak Ray. "Ruling out Kozai resonance in highly eccentric galactic binary millisecond pulsar PSR J1903+0327." Monthly Notices of the Royal Astronomical Society: Letters 399, no. 1 (October 11, 2009): L123—L127. http://dx.doi.org/10.1111/j.1745-3933.2009.00736.x.

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Kimpson, Thomas O., Mario Spera, Michela Mapelli, and Brunetto M. Ziosi. "Hierarchical black hole triples in young star clusters: impact of Kozai–Lidov resonance on mergers." Monthly Notices of the Royal Astronomical Society 463, no. 3 (August 19, 2016): 2443–52. http://dx.doi.org/10.1093/mnras/stw2085.

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Thomas, Fabrice, and Alessandro Morbidelli. "The Kozai resonance in the outer solar system and the dynamics of long-period comets." Celestial Mechanics & Dynamical Astronomy 64, no. 3 (1996): 209–29. http://dx.doi.org/10.1007/bf00728348.

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O’Connor, Christopher E., Bin Liu, and Dong Lai. "Enhanced Lidov–Kozai migration and the formation of the transiting giant planet WD 1856+534 b." Monthly Notices of the Royal Astronomical Society 501, no. 1 (November 30, 2020): 507–14. http://dx.doi.org/10.1093/mnras/staa3723.

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ABSTRACT We investigate the possible origin of the transiting giant planet WD 1856+534 b, the first strong exoplanet candidate orbiting a white dwarf, through high-eccentricity migration (HEM) driven by the Lidov–Kozai (LK) effect. The host system’s overall architecture is a hierarchical quadruple in the ‘2 + 2’ configuration, owing to the presence of a tertiary companion system of two M-dwarfs. We show that a secular inclination resonance in 2 + 2 systems can significantly broaden the LK window for extreme eccentricity excitation (e ≳ 0.999), allowing the giant planet to migrate for a wide range of initial orbital inclinations. Octupole effects can also contribute to the broadening of this ‘extreme’ LK window. By requiring that perturbations from the companion stars be able to overcome short-range forces and excite the planet’s eccentricity to e ≃ 1, we obtain an absolute limit of $a_{1} \gtrsim 8 \, \mathrm{au}\, (a_{3} / 1500 \, \mathrm{au})^{6/7}$ for the planet’s semimajor axis just before migration (where a3 is the semimajor axis of the ‘outer’ orbit). We suggest that, to achieve a wide LK window through the 2 + 2 resonance, WD 1856 b likely migrated from $30 \, \mathrm{au}\lesssim a_{1} \lesssim 60 \, \mathrm{au}$, corresponding to ∼10–$20 \, \mathrm{au}$ during the host’s main-sequence phase. We discuss possible difficulties of all flavours of HEM affecting the occurrence rate of short-period giant planets around white dwarfs.

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Attia, O., V. Bourrier, P. Eggenberger, C. Mordasini, H. Beust, and D. Ehrenreich. "The JADE code: Coupling secular exoplanetary dynamics and photo-evaporation." Astronomy & Astrophysics 647 (March 2021): A40. http://dx.doi.org/10.1051/0004-6361/202039452.

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Close-in planets evolve under extreme conditions, which raises questions about their origins and current nature. Two evolutionary mechanisms thought to play a predominant role are orbital migration, which brings them close to their star, and atmospheric escape under the resulting increased irradiation. Yet their relative roles remain poorly understood, in part because we lack numerical models that couple the two mechanisms with high precision and on secular timescales. To address this need, we developed the Joining Atmosphere and Dynamics for Exoplanets (JADE) code, which simulates the secular atmospheric and dynamical evolution of a specific planet around its star, and can include the perturbation induced by a distant third body. On the dynamical side, the three dimensional evolution of the orbit is modeled under stellar and planetary tidal forces, a relativistic correction, and the action of the distant perturber. On the atmospheric side, the vertical structure of the atmosphere is integrated over time based on its thermodynamical properties, inner heating, and the evolving stellar irradiation, which results, in particular, in extreme ultraviolet induced photo-evaporation. The JADE code is benchmarked on GJ436 b, which is a prototype of the evaporating giants on eccentric, misaligned orbits at the edge of the hot Neptunes desert. We confirm previous results that the orbital architecture of GJ436 b is well explained by Kozai migration and bring to light a strong interplay between its atmospheric and orbital evolution. During the resonance phase, the atmosphere pulsates in tune with the Kozai cycles, which leads to stronger tides and an earlier migration. This triggers a strong atmospheric evaporation several billion years after the planet formed, refining the paradigm that mass loss is dominant in the early age of close-in planets. These results suggest that the edge of the desert could be formed of warm Neptunes whose evaporation was delayed by Kozai migration. They strengthen the importance of coupling atmospheric and dynamical evolution over secular timescales, which the JADE code will allow for one to simulate for a wide range of systems.

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Marzari, Francesco. "Ring dynamics around an oblate body with an inclined satellite: the case of Haumea." Astronomy & Astrophysics 643 (November 2020): A67. http://dx.doi.org/10.1051/0004-6361/202038812.

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Context. The recent discovery of rings and massive satellites around minor bodies and dwarf planets suggests that they may often coexist, as for example around Haumea. Aims. A ring perturbed by an oblate central body and by an inclined satellite may disperse on a short timescale. The conditions under which a ring may survive are explored both analytically and numerically. Methods. The trajectories of ring particles are integrated under the influence of the gravitational field of a triaxial ellipsoid and (a) massive satellite(s), including the effects of collisions. Results. A ring initially formed in the equatorial plane of the central body will be disrupted if the satellite has an inclination in the Kozai–Lidov regime (39.2° < i < 144.8). For lower inclinations, the ring may relax to the satellite orbital plane thanks to an intense collisional damping. On the other hand, a significant J2 term easily suppresses the perturbations of an inclined satellite within a critical semi-major axis, even in the case of Kozai–Lidov cycles. However, if the ring is initially inclined with respect to the equatorial plane, the same J2 perturbations are not a protective factor but instead disrupt the ring on a short timescale. The ring found around Haumea is stable despite the rise in the impact velocities that is due to the asymmetric shape of the body and the presence of a 3:1 resonance with the rotation of the central body. Conclusions. A ring close to an oblate central body should be searched for in the proximity of the equatorial plane, where the J2 perturbations protect it against the perturbations of an external inclined satellites. In an inclined configuration, the J2 term is itself disruptive.

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Speedie, Jessica, and J. J. Zanazzi. "The structure and stability of extended, inclined circumplanetary disc or ring systems." Monthly Notices of the Royal Astronomical Society 497, no. 2 (July 20, 2020): 1870–83. http://dx.doi.org/10.1093/mnras/staa2068.

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ABSTRACT Large dips in the brightness for a number of stars have been observed, for which the tentative explanation is occultation of the star by a transiting circumplanetary disc or ring system. In order for the circumplanetary disc/rings to block the host star’s light, the disc must be tilted out of the planet’s orbital plane, which poses stability problems due to the radial extent of the disc required to explain the brightness dip durations. This work uses N-body integrations to study the structure and stability of circumplanetary disc/ring systems tilted out of the planet’s orbital plane by the spinning planet’s mass quadrupole. Simulating the disc as a collection of test particles with orbits initialized near the Laplace surface (equilibrium between tidal force from host star and force from planet’s mass quadrupole), we find that many extended, inclined circumplanetary discs remain stable over the duration of the integrations ($\sim 3\!-\!16 \, {\rm Myr}$). Two dynamical resonances/instabilities excite the particle eccentricities and inclinations: the Lidov-Kozai effect which occurs in the disc’s outer regions, and ivection resonance which occurs in the disc’s inner regions. Our work places constraints on the maximum radial extent of inclined circumplanetary disc/ring systems, and shows that gaps present in circumplanetary discs do not necessarily imply the presence of exomoons.

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Libert, A. S., Ch Hubaux, and T. Carletti. "The Global Symplectic Integrator: an efficient tool for stability studies of dynamical systems. Application to the Kozai resonance in the restricted three-body problem." Monthly Notices of the Royal Astronomical Society 414, no. 1 (March 16, 2011): 659–67. http://dx.doi.org/10.1111/j.1365-2966.2011.18431.x.

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Thompson, Todd A. "ACCELERATING COMPACT OBJECT MERGERS IN TRIPLE SYSTEMS WITH THE KOZAI RESONANCE: A MECHANISM FOR “PROMPT” TYPE Ia SUPERNOVAE, GAMMA-RAY BURSTS, AND OTHER EXOTICA." Astrophysical Journal 741, no. 2 (October 20, 2011): 82. http://dx.doi.org/10.1088/0004-637x/741/2/82.

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Sotiriadis, Sotiris, Anne-Sophie Libert, and Sean N. Raymond. "Formation of terrestrial planets in eccentric and inclined giant planet systems." Astronomy & Astrophysics 613 (May 2018): A59. http://dx.doi.org/10.1051/0004-6361/201731260.

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Aims. Evidence of mutually inclined planetary orbits has been reported for giant planets in recent years. Here we aim to study the impact of eccentric and inclined massive giant planets on the terrestrial planet formation process, and investigate whether it can possibly lead to the formation of inclined terrestrial planets. Methods. We performed 126 simulations of the late-stage planetary accretion in eccentric and inclined giant planet systems. The physical and orbital parameters of the giant planet systems result from n-body simulations of three giant planets in the late stage of the gas disc, under the combined action of Type II migration and planet-planet scattering. Fourteen two- and three-planet configurations were selected, with diversified masses, semi-major axes (resonant configurations or not), eccentricities, and inclinations (including coplanar systems) at the dispersal of the gas disc. We then followed the gravitational interactions of these systems with an inner disc of planetesimals and embryos (nine runs per system), studying in detail the final configurations of the formed terrestrial planets. Results. In addition to the well-known secular and resonant interactions between the giant planets and the outer part of the disc, giant planets on inclined orbits also strongly excite the planetesimals and embryos in the inner part of the disc through the combined action of nodal resonance and the Lidov–Kozai mechanism. This has deep consequences on the formation of terrestrial planets. While coplanar giant systems harbour several terrestrial planets, generally as massive as the Earth and mainly on low-eccentric and low-inclined orbits, terrestrial planets formed in systems with mutually inclined giant planets are usually fewer, less massive (<0.5 M⊕), and with higher eccentricities and inclinations. This work shows that terrestrial planets can form on stable inclined orbits through the classical accretion theory, even in coplanar giant planet systems emerging from the disc phase.

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Hao, Wei, Rainer Spurzem, Thorsten Naab, Long Wang, M. B. N. Kouwenhoven, Pau Amaro-Seoane, and Rosemary A. Mardling. "Resonant motions of supermassive black hole triples." Proceedings of the International Astronomical Union 10, S312 (August 2014): 101–4. http://dx.doi.org/10.1017/s1743921315007619.

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AbstractTriple supermassive black holes (SMBH) can form during the hierarchical mergers of massive galaxies with an existing binary. Perturbations by a third black hole may accelerate the merging process of an inner binary, for example through the Kozai mechanism. We analyze the evolution of simulated hierarchical triple SMBHs in galactic centers, and find resonances in the evolution of the semi-major axis, the eccentricity and the inclination, for both the inner and the outer orbits of the triple system, which are not only Kozai like. Through resonant oscillations, SMBH can trigger a significant increase of the inner SMBH binary eccentricity shortening the merger timescale expected from gravitational wave (GW) emission. As hierarchical triple SMBHs may be frequent in massive galaxies, the influence of orbital resonances is of great importance to our understanding of black hole coalescence and gravitational wave detection. Although Kozai mechanism is believed to play an important role in this process, detailed studies on the pattern of these resonances is necessary.

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Lei, Hanlun. "A semi-analytical model for secular dynamics of test particles in hierarchical triple systems." Monthly Notices of the Royal Astronomical Society 490, no. 4 (October 18, 2019): 4756–69. http://dx.doi.org/10.1093/mnras/stz2917.

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ABSTRACT In this work, a semi-analytical model is formulated up to an arbitrary order in the semimajor axis ratio of the inner and outer binaries to describe the long-term (secular) dynamics of test particles in hierarchical triple systems. The third-body disturbing function is expressed as a Fourier series, where the harmonic arguments are linear combinations of the perturber’s mean anomaly, and the test particle’s mean anomaly, longitude of the ascending node, and argument of pericentre. Based on the series expansion, it is straightforward to arrive at the secular equations of motion by directly eliminating those terms that are irrelevant to the long-term dynamics. When the perturbations are so strong that the system’s hierarchy is no longer high, the conventional double-averaged model fails to predict the long-term behaviours of test particles. To overcome the difficulty, we develop a corrected double-averaged model by taking into account the short-term effects within the orbital periods of the inner and outer binaries. The resulting averaged model is applied to Jupiter’s irregular satellites, and simulation results show that the corrected model can reproduce the behaviours on time-scales much longer than the orbital periods. Moreover, we retrieve a triple-averaged model and discuss the associated dynamics in the phase space. It is found that the Kozai resonance in the corrected model occurs at a higher inclination than that in the conventional model.

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Li, Daohai, Alexander J. Mustill, and Melvyn B. Davies. "Flyby encounters between two planetary systems II: exploring the interactions of diverse planetary system architectures." Monthly Notices of the Royal Astronomical Society 496, no. 2 (June 9, 2020): 1149–65. http://dx.doi.org/10.1093/mnras/staa1622.

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ABSTRACT Planetary systems formed in clusters may be subject to stellar encounter flybys. Here, we create a diverse range of representative planetary systems with different orbital scales and planets’ masses and examine encounters between them in a typical open cluster. We first explore the close-in multisuper Earth systems ≲0.1 au. They are resistant to flybys in that only ones inside a few au can destabilize a planet or break the resonance between such planets. But these systems may capture giant planets on to wide orbits from the intruding star during distant flybys. If so, the original close-in small planets’ orbits may be tilted together through Kozai–Lidov mechanism, forming a ‘cold’ system that is significantly inclined against the equator of the central host. Moving to the intermediately placed planets around solar-like stars, we find that the planets’ mass gradient governs the systems’ long-term evolution post-encounter: more massive planets have better chances to survive. Also, a system’s angular momentum deficit, a quantity describing how eccentric/inclined the orbits are, measured immediately after the encounter, closely relates to the longevity of the systems – whether or not and when the systems turn unstable in the ensuing evolution millions of years post-encounter. We compare the orbits of the surviving planets in the unstable systems through (1) the immediate consequence of the stellar fly or (2) internal interplanetary scattering long post-encounter and find that those for the former are systematically colder. Finally, we show that massive wide-orbit multiplanet systems like that of HR 8799 can be easily disrupted and encounters at a few hundreds of au suffice.

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Winter, O. C., D. C. Mourão, C. F. de Melo, E. N. Macau, J. L. Ferreira, and J. P. S. Carvalho. "Controlling the Eccentricity of Polar Lunar Orbits with Low-Thrust Propulsion." Mathematical Problems in Engineering 2009 (2009): 1–10. http://dx.doi.org/10.1155/2009/159287.

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It is well known that lunar satellites in polar orbits suffer a high increase on the eccentricity due to the gravitational perturbation of the Earth. That effect is a natural consequence of the Lidov-Kozai resonance. The final fate of such satellites is the collision with the Moon. Therefore, the control of the orbital eccentricity leads to the control of the satellite's lifetime. In the present work we study this problem and introduce an approach in order to keep the orbital eccentricity of the satellite at low values. The whole work was made considering two systems: the 3-body problem, Moon-Earth-satellite, and the 4-body problem, Moon-Earth-Sun-satellite. First, we simulated the systems considering a satellite with initial eccentricity equals to 0.0001 and a range of initial altitudes between 100 km and 5000 km. In such simulations we followed the evolution of the satellite's eccentricity. We also obtained an empirical expression for the length of time needed to occur the collision with the Moon as a function of the initial altitude. The results found for the 3-body model were not significantly different from those found for the 4-body model. Secondly, using low-thrust propulsion, we introduced a correction of the eccentricity every time it reached the value 0.05. These simulations were made considering a set of different thrust values, from 0.1 N up to 0.4 N which can be obtained by using Hall Plasma Thrusters. In each run we measured the length of time, needed to correct the eccentricity value (frome=0.04toe=0.05). From these results we obtained empirical expressions of this time as a function of the initial altitude and as a function of the thrust value.

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Huang, Yukun, Miao Li, Junfeng Li, and Shengping Gong. "Kozai-Lidov mechanism inside retrograde mean motion resonances." Monthly Notices of the Royal Astronomical Society 481, no. 4 (September 20, 2018): 5401–10. http://dx.doi.org/10.1093/mnras/sty2562.

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Efimov, S. S., and V. V. Sidorenko. "On Asymmetric Zeipel–Lidov–Kozai Cycles in Mean Motion Resonances." Cosmic Research 58, no. 4 (July 2020): 249–55. http://dx.doi.org/10.1134/s0010952520040097.

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Qi, Yi, and Anton de Ruiter. "Erratum: Kozai mechanism inside mean motion resonances in the 3-dimensional phase space." Monthly Notices of the Royal Astronomical Society 496, no. 4 (July 16, 2020): 4646. http://dx.doi.org/10.1093/mnras/staa1830.

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GALLARDO, T. "The occurrence of high-order resonances and Kozai mechanism in the scattered disk." Icarus 181, no. 1 (March 2006): 205–17. http://dx.doi.org/10.1016/j.icarus.2005.11.011.

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Vinson, Benjamin R., and Eugene Chiang. "Secular dynamics of an exterior test particle: the inverse Kozai and other eccentricity–inclination resonances." Monthly Notices of the Royal Astronomical Society 474, no. 4 (December 1, 2017): 4855–69. http://dx.doi.org/10.1093/mnras/stx3091.

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Storch, N. I., and D. Lai. "Chaotic dynamics of stellar spin driven by planets undergoing Lidov-Kozai oscillations: resonances and origin of chaos." Monthly Notices of the Royal Astronomical Society 448, no. 2 (February 21, 2015): 1821–34. http://dx.doi.org/10.1093/mnras/stv119.

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Gomes, Rodney S., Tabaré Gallardo, Julio A. Fernández, and Adrián Brunini. "On The Origin of The High-Perihelion Scattered Disk: The Role of The Kozai Mechanism And Mean Motion Resonances." Celestial Mechanics and Dynamical Astronomy 91, no. 1-2 (January 2005): 109–29. http://dx.doi.org/10.1007/s10569-004-4623-y.

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Mańko, Rafał. "Artur Kozak’s Juriscentrist Concept of Law: a Central European Innovation in Legal Theory." Review of Central and East European Law 45, no. 2-3 (June 23, 2020): 334–75. http://dx.doi.org/10.1163/15730352-bja04502003.

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Artur Kozak (1960–2009) was one of the most original and innovative philosophers of law to emerge from the so-called ‘middle generation’ of Polish post-War jurisprudence. Kozak’s principal achievement was to break away from the analytical paradigm of legal theory, dominant in the in Poland at the time, and engage legal theory in a fruitful dialogue with contemporary sociology and philosophy, including such currents as social constructionism or postmodernism. To name his original theoretical project, Kozak coined a new term – ‘juriscentrism’ (juryscentryzm), consciously evoking Richard Rorty’s concept of ethnocentrism. Juriscentrist legal theory was mainly focused on providing legitimacy for the newly gained power of the legal community in a post-socialist society, but its theoretical resonance is universal. Kozak’s premature death made it impossible to complete the theoretical project of juriscentrism, nonetheless he managed to elaborate its main tenets, including the concept of juristic discretional power and a juriscentrist concept of law. Kozak’s legacy in contemporary Polish legal theory is particularly visible in Wrocław, where not only the post-analytical paradigm in Poland is the strongest, but also the first Polish school of critical legal theory has recently emerged.

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de la Fuente Marcos, C., and R. de la Fuente Marcos. "On the orbital evolution of 2020 AV2, the first asteroid ever observed to go around the Sun inside the orbit of Venus." Monthly Notices of the Royal Astronomical Society: Letters 494, no. 1 (February 19, 2020): L6—L10. http://dx.doi.org/10.1093/mnrasl/slaa027.

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ABSTRACT The innermost section of the Solar system has not been extensively studied because minor bodies moving inside Earth’s orbit tend to spend most of their sidereal orbital periods at very low solar elongation, well away from the areas more frequently observed by programs searching for near-Earth objects. The survey carried out from the Zwicky Transient Facility (ZTF) is the first one that has been able to detect multiple asteroids well detached from the direct gravitational perturbation of the Earth–Moon system. ZTF discoveries include 2019 AQ3 and 2019 LF6, two Atiras with the shortest periods among known asteroids. Here, we perform an assessment of the orbital evolution of 2020 AV2, an Atira found by ZTF with a similarly short period but following a path contained entirely within the orbit of Venus. This property makes it the first known member of the elusive Vatira population. Genuine Vatiras, those long-term dynamically stable, are thought to be subjected to the so-called von Zeipel–Lidov–Kozai oscillation that protects them against close encounters with both Mercury and Venus. However, 2020 AV2 appears to be a former Atira that entered the Vatira orbital domain relatively recently. It displays an anticoupled oscillation of the values of eccentricity and inclination, but the value of the argument of perihelion may circulate. Simulations show that 2020 AV2 might reach a 3:2 resonant orbit with Venus in the future, activating the von Zeipel–Lidov–Kozai mechanism, which in turn opens the possibility to the existence of a long-term stable population of Vatiras trapped in this configuration.

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Póti, Zsuzsa, Csilla Katona, Tibor Szalai, and Árpád Mayer. "Változások a korai stádiumú operált méhtestcarcinoma sugárkezelésének indikációjában. Újabb stádiumbeosztás, prediktív tényezők. Tanulságok saját eredményeink alapján." Orvosi Hetilap 157, no. 27 (July 2016): 1059–64. http://dx.doi.org/10.1556/650.2016.30484.

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Optimal postoperative radiotherapy indications for early-stage operated endometrial cancers have drastically changed with the new imaging generation (magnetic resonance imaging, positron emission tomography/computed tomography) and more detailed pathomorphology. The depth and growth of tumor invasion, presence or absence of the lymph node metastases, grading and lymphovascular invasion are the most important factors to predict the progression and to influence the prognosis. In 2016, on the basis of these, the European Gynecologist Oncology and Radiotherapy Society published a report in which they proposed unanimously indications for postoperative radio- and/or radiochemotherapy. The basis of their work was prospective multilevel randomized investigations which could avoid over- or undertreatment hazards. The results obtained by the authors of this article from 164 operated patients in early-stage endometrium carcinoma seem to be acceptable, in spite of the fact that their earlier radiotherapy indication was different and in the pathological description lymphovascular invasion was not included and the grading was not always applied. Orv. Hetil., 2016, 157(27),1059–1064.

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Lawler, Samantha M. "The Debiased Kuiper Belt: Our Solar System as a Debris Disk." Proceedings of the International Astronomical Union 8, S299 (June 2013): 232–36. http://dx.doi.org/10.1017/s1743921313008466.

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AbstractThe dust measured in debris disks traces the position of planetesimal belts. In our Solar System, we are also able to measure the largest planetesimals directly and can extrapolate down to make an estimate of the dust. The zodiacal dust from the asteroid belt is better constrained than the only rudimentary measurements of Kuiper belt dust. Dust models will thus be based on the current orbital distribution of the larger bodies which provide the collisional source. The orbital distribution of many Kuiper belt objects is strongly affected by dynamical interactions with Neptune, and the structure cannot be understood without taking this into account. We present the debiased Kuiper belt as measured by the Canada-France Ecliptic Plane Survey (CFEPS). This model includes the absolute populations for objects with diameters >100 km, measured orbital distributions, and size distributions of the components of the Kuiper belt: the classical belt (hot, stirred, and kernel components), the scattering disk, the detached objects, and the resonant objects (1:1, 5:4, 4:3, 3:2 including Kozai subcomponent, 5:3, 7:4, 2:1, 7:3, 5:2, 3:1, and 5:1). Because a large fraction of known debris disks are consistent with dust at Kuiper belt distances from the host stars, the CFEPS Kuiper belt model provides an excellent starting point for a debris disk model, as the dynamical interactions with planets interior to the disk are well-understood and can be precisely modelled using orbital integrations.

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de la Fuente Marcos, C., and R. de la Fuente Marcos. "Understanding the evolution of Atira-class asteroid 2019 AQ3, a major step towards the future discovery of the Vatira population." Monthly Notices of the Royal Astronomical Society 487, no. 2 (May 24, 2019): 2742–52. http://dx.doi.org/10.1093/mnras/stz1437.

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ABSTRACT Orbiting the Sun at an average distance of 0.59 au and with the shortest aphelion of any known minor body, at 0.77 au, the Atira-class asteroid 2019 AQ3 may be an orbital outlier or perhaps an early indication of the presence of a new population of objects: those following orbits entirely encompassed within that of Venus, the so-called Vatiras. Here, we explore the orbital evolution of 2019 AQ3 within the context of the known Atiras to show that, like many of them, it displays a present-day conspicuous coupled oscillation of the values of eccentricity and inclination, but no libration of the value of the argument of perihelion with respect to the invariable plane of the Solar system. The observed dynamics is consistent with being the result of the combined action of two dominant perturbers, the Earth–Moon system and Jupiter, and a secondary one, Venus. Such a multiperturber-induced secular dynamics translates into a chaotic evolution that can eventually lead to a resonant behaviour of the Lidov–Kozai type. Asteroid 2019 AQ3 may have experienced brief stints as a Vatira in the relatively recent past and it may become a true Vatira in the future, outlining possible dynamical pathways that may transform Atiras into Vatiras and vice versa. Our results strongly suggest that 2019 AQ3 is only the tip of the iceberg: a likely numerous population of similar bodies may remain hidden in plain sight, permanently confined inside the Sun’s glare.

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Sidorenko, Vladislav V. "The eccentric Kozai–Lidov effect as a resonance phenomenon." Celestial Mechanics and Dynamical Astronomy 130, no. 1 (December 28, 2017). http://dx.doi.org/10.1007/s10569-017-9799-z.

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Journal articles on the topic 'Kozai resonance'

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