Hierarchical Three-Body Problem at High Eccentricities = Simple PendulumIV: Octupole for Librating Kozai-Lidov Cycles

Clicks: 25
ID: 326445
2026
Free PDF
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This article has not been analysed, so there is no overall score — reader engagement is measured and shown alongside.
AI Quality Assessment
Not analyzed
Readership in this journal
Steady

Ranked #122 of 1,339 articles by views in monthly notices of the royal astronomical society

Most read Least read

Bar heights use a square-root scale. Only the 120 most-read articles are drawn; the journal has 1,339 in total.

Mint this article as an NFT
Not yet minted

Create a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.

5 SUSD one-off · no wallet required
Sign in to mint
Abstract
Abstract We solve analytically the long-term octupole evolution of librating Kozai-Lidov cycles - those with a negative Kozai constant, in which the argument of pericenter librates - in the double-averaged restricted hierarchical three-body problem. Librating cycles reach extreme eccentricities when the normal component of the orbital angular momentum vanishes, as rotating cycles do, but their slow dynamics was left unsolved: the azimuth of the eccentricity vector jumps by half a turn every cycle, so the leading-order octupole kick alternates in sign and cancels pairwise. We show that the surviving dynamics, at second order in the octupole strength, is a simple pendulum with explicit coefficients. The pendulum predicts slow oscillations of the normal angular momentum with amplitude linear in the octupole strength, evolving on a timescale of order the secular timescale divided by the octupole strength, together with an explicit criterion for orbital flips. At octupole strengths typical of hierarchical triples, these amplitudes are comparable to - and in part of the librating window can exceed - those of rotating cycles, provided one waits the longer timescale. The analytic model agrees with numerical integrations of the double-averaged equations across the librating window, for systems ranging from hot-Jupiter formation to gravitational-wave sources.
Reference Key
openalex_W7169561944 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Ygal Y. Klein
Are you one of these authors? Claim your profile
Journal monthly notices of the royal astronomical society
Year 2026
DOI
10.1093/mnras/stag1612
URL
https://doi.org/10.1093/mnras/stag1612
Keywords Keywords not found

Citations

No citations found. To add a citation, contact the admin at info@scimatic.org

Comments

No comments yet. Be the first to comment on this article.