Post-Newtonian Kozai-Lidov Mechanism and its Effect on Cumulative Shift of Periastron Time of Binary Pulsar

TL;DR

This paper investigates how the Kozai-Lidov mechanism in hierarchical triple systems affects the cumulative shift of a binary pulsar's periastron time, potentially enabling indirect gravitational wave detection.

Contribution

It provides a detailed analysis using direct integration of post-Newtonian equations, highlighting the impact of eccentricity variations on gravitational wave emission evaluation.

Findings

Kozai-Lidov oscillations cause detectable bending in the periastron shift curve.

Small eccentricity deviations significantly influence gravitational wave emission estimates.

The method offers a new way to indirectly observe gravitational waves from triple systems.

Abstract

We study the Kozai-Lidov mechanism in a hierarchical triple system in detail by the direct integration of the first-order post Newtonian equations of motion. We analyse a variety of models with a pulsar to evaluate the cumulative shift of the periastron time of a binary pulsar caused by the gravitational wave emission in a hierarchical triple system with Kozai-Lidov mechanism. We compare our results with those by the double-averaging method. The deviation in the eccentricity, even if small, is important in the evaluation of the emission of the gravitational waves. We also calculate the cumulative shift of the periastron time by using obtained osculating orbital elements. If Kozai-Lidov oscillations occur, the cumulative shift curve will bend differently from that of the isolated binary. If such a bending is detected through the radio observation, it will be the first indirect observation of gravitational waves from a triple system.