تقرير
Higher-order effects in the dynamics of hierarchical triple systems. Quadrupole-squared terms
| العنوان: | Higher-order effects in the dynamics of hierarchical triple systems. Quadrupole-squared terms |
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| المؤلفون: | Will, Clifford M. |
| المصدر: | Phys. Rev. D 103, 063003 (2021) |
| سنة النشر: | 2020 |
| المجموعة: | Astrophysics General Relativity and Quantum Cosmology |
| مصطلحات موضوعية: | Astrophysics - Earth and Planetary Astrophysics, Astrophysics - Astrophysics of Galaxies, Astrophysics - Solar and Stellar Astrophysics, General Relativity and Quantum Cosmology |
| الوصف: | We analyze the secular evolution of hierarchical triple systems to second-order in the quadrupolar perturbation induced on the inner binary by the distant third body. The Newtonian three-body equations of motion, expanded in powers of the ratio of semimajor axes $a/A$, become a pair of effective one-body Keplerian equations of motion, perturbed by a sequence of multipolar perturbations, denoted quadrupole, $O[(a/A)^3]$, octupole, $O[(a/A)^4]$, and so on. In the Lagrange planetary equations for the evolution of the instantaneous orbital elements, second-order effects arise from obtaining the first-order solution for each element, consisting of a constant (or slowly varying) piece and an oscillatory perturbative piece, and reinserting it back into the equations to obtain a second-order solution. After an average over the two orbital timescales to obtain long-term evolutions, these second-order quadrupole ($Q^2$) terms would be expected to produce effects of order $(a/A)^6$. However we find that the orbital average actually enhances the second-order terms by a factor of the ratio of the outer to the inner orbital periods, $ \sim (A/a)^{3/2}$. For systems with a low-mass third body, the $Q^2$ effects are small, but for systems with a comparable-mass or very massive third body, such as a Sun-Jupiter system orbiting a solar-mass star, or a $100 \, M_\odot$ binary system orbiting a $10^6 \, M_\odot$ massive black hole, the $Q^2$ effects can completely suppress flips of the inner orbit from prograde to retrograde and back that occur in the first-order solutions. These results are in complete agreement with those of Luo, Katz and Dong, derived using a "Corrected Double-Averaging" method. Comment: 16 pages, 7 figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevD.103.063003 |
| URL الوصول: | http://arxiv.org/abs/2011.13286 |
| رقم الأكسشن: | edsarx.2011.13286 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevD.103.063003 |
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