Timescales of Kozai-Lidov oscillations at quadrupole and octupole order in the test particle limit
By Joseph M. Antognini. 2015
133 citations recorded by the source corpus.
Kozai-Lidov (KL) oscillations in hierarchical triple systems have found application to many astrophysical contexts, including planet formation, type Ia supernovae, and supermassive black hole dynamics. The period of these oscillations is known at the order-of-magnitude level, but dependences on the initial mutual inclination or inner eccentricity are not typically included. In this work I calculate the period of KL oscillations ($t_{\textrm{KL}}$) exactly in the test particle limit at quadrupole order (TPQ). I explore the parameter space of all hierarchical triples at TPQ and show that except for triples on the boundary between libration and rotation, the period of KL oscillations does not vary by more than a factor of a few. The exact period may be approximated to better than 2 per cent for triples with mutual inclinations between 60$^{\circ}$ and 120$^{\circ}$ and initial eccentricities less than $\sim$0.3. In addition, I derive an analytic expression for the period of octupole-order oscillations due to the `eccentric KL mechanism' (EKM). I show that the timescale for EKM oscillations is proportional to $\epsilon_{\textrm{oct}}^{-1/2}$, where $\epsilon_{\textrm{oct}}$ measures the strength of octupole perturbations relative to quadrupole perturbations.
View Paper: https://www.semanticscholar.org/paper/a1f1c963906476ec114305b5fff7823c6613e772
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Citations in the corpus
- Black hole and neutron star mergers in galactic nuclei (2018, background): “In the case of a CO binary, the large values reached by the eccentricity of the inner binary during the KL excursions make its merger time shorter since it efficiently dissipates energy when e ∼ emax (e.g., see Antonini & Perets 2012; Antognini 2015).”
- The Eccentric Kozai-Lidov Effect and Its Applications (2016, background): “However, an approximate analytical condition, for the regular (none chaotic) mode was achieved recently by Antognini (2015), following Katz et al. (2011) formalism.”
- Black Hole Mergers in Galactic Nuclei Induced by the Eccentric Kozai–Lidov Effect (2017, methodology): “The EKL timescale at the quadrupole level of approximation is estimated as: tquad ∼ 16 30π m1 + m2 + m3 m3 P22 P1 (1 − e22) 3/2 , (5) (e.g., Antognini 2015), where P denotes the orbital period and the GR precession of the inner orbit timescale is: tGR,inner ∼ 2π a5/21 c 2(1 − e21) 3G3/2(m1 + m2)3/2…”