Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Timescales of Kozai-Lidov oscillations at quadrupole and octupole order
  in the test particle limit   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.

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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn