| The secular evolution of hierarchical triple systems plays an important role in many astrophysical contexts, from irregular satellites of giant planets to high-eccentricity mi-gration of hot Jupiters and the formation of compact stellar binaries. When the mutual inclination angle between the inner and outer orbits is sufficiently high, the inner pair can experience large-amplitude Lidov-Kozai oscillations in eccentricity and inclination. Recent work has shown that when the octupole terms are included in the interaction potential, the inner binary can undergo extreme eccentricity excitation as well as incli-nation flips with respect to the outer orbit.Based on the consideration of the short-range forces, we carry out two projects, which focuses on the suppression and resonance, respectively. We also study another project, which is about the evolution of the stellar binary surrounding super massive black hole binary.In the first study, we consider that pericenter precession due to various short-range effects, such as General Relativity, tidal and rotational distortions, can limit the growth of eccentricity and even suppress standard (quadrupolar) Lidov-Kozai oscillations. We systematically study how these short-range forces affect the extreme orbital behaviour found in octupole Lidov-Kozai cycles. In general, the influence of the octupole poten-tial is confined to a range of initial mutual inclinations itot (the inclination angle between the inner and outer orbits) centered around 90° (in the test-mass approximation, when the inner binary mass ratio is<< 1), with the range expanding with increasing octupole strength. We find that, while the short-range forces do not change the width and loca-tion of this "window of influence", they impose a strict upper limit on the maximum achievable eccentricity within this window. This limiting eccentricity can be calculated analytically, and its value holds even for very strong octupole pontential and for the general case of three comparable masses. Short-range forces also affect orbital flips, progressively reducing the range of rtot around 90°within which flips are possible as the intensity of these forces is increased.In the second study, we consider the merging of compact binaries play an impor-tant role in astrophysical context. The gravitational waves takes the angular momentum off the merging binary, which makes the orbit of the inner binary shrink. We study the secular dynamics of merging binary with a small perturber in hierarchical triple systems. From our numerical calculations, we find that the triple system goes through a resonant state between the apsidal precession rates of two orbits during the orbital decay, and the eccentricity of the inner orbit is excited, as well as the corresponding gravitational wave frequency. Our numerical results could be understood under the linear approxima-tion of small orbital eccentricities and coplanar configuration. Especially, the resonant condition and the excited eccentricity can be estimated analytically.In the third study, we consider the merger and the tidal disruption event (TDE) of the stellar binaries in the merging galaxies that host two supermassive black holes (SMBH). We study a stellar binary moving around a SMBH, while the second SMBH orbits the center mass of this "inner triple" on a wider orbit. Particularly, this four-body system can be decomposed into two three-body systems. The "inner triple" is the SMBH-stellar binary triple system. The stellar binary (test particle) and SMBH binary consists of the "outer triple". As expected, the Lidov-Kozai oscillations occur in the inner triple, the stellar binary is likely to merge. Inversely, the Lidov-Kozai oscillations occur in the outer triple, it is possible for the stellar binary to be tidal disrupted. We run a series of N-body simulations to study the evolution of the stellar binary in the four body system, and find that during the SMBH binary shrinking, the merger rate of the stellar binary decreases instead of the TDE rate increasing. |
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