# Kozai-Lidov-GW project

Cartoon of a hierarchical triple consisting of inner binary and distant third body. Angular momentum vectors of the inner and outer orbits are shown in the cartoon. The ration a/R must be small for us to treat this under perturbation theory.

The plus mode of the gravitational wave emitted from the inner binary. The plot is over the first year of observation in the LISA band. The KL oscillations leave an imprint on the waveform that can be seen in the form of amplitude modulations that peak when the eccentricity peaks. The amplitude also "chirps" slowly over the radiation reaction timescale.

Gravitational waves emitted by inner binaries in hierarchical triples are interesting astrophysical candidates for space-based detectors like LISA.

In the presence of a third body, the inner binary undergoes oscillations in eccentricity and inclination angle due to the Kozai-Lidov (KL) mechanism. This happens due to conservation of angular momentum. We work in the quadrupolar approximation of the third body's perturbation and are interested in looking at the gravitational waves emitted by the inner binary. These GWs will be modulated by the oscillations in eccentricity and inclination angle.

Our goal is to construct analytic gravitational waveforms in the Fourier domain, with this effect included. Using multiple-scale analysis, we make use of the separability of timescales in the system to combine the effects of KL oscillations and radiation reaction. The imprint on the waveform, due to this combined evolution, can then be analytically computed in the stationary phase approximation. We also explore the parameters of the hierarchical triple which can produce a detectable (by LISA) imprint of KL oscillations on the waveform and outline potential implications for gravitational wave data analysis and tests of GR.