# Cumulative Shift of Periastron Time of Binary Pulsar with Kozai-Lidov Oscillation

## TL;DR

This paper investigates how the Kozai-Lidov mechanism affects the cumulative shift of periastron time in binary pulsars, considering gravitational wave emission and orbital dynamics, revealing conditions for observable deviations within a century.

## Contribution

It introduces a detailed analysis of the cumulative periastron shift in hierarchical triple systems influenced by Kozai-Lidov oscillations, incorporating post-Newtonian effects.

## Key findings

- Kozai-Lidov oscillations cause notable bending in the cumulative shift curve.
- The parameter space for third companion mass and semi-major axis is identified for observable effects within 100 years.
- The study provides insights into gravitational wave emission impacts on pulsar timing in triple systems.

## Abstract

We study a hierarchical triple system with the Kozai-Lidov mechanism, and analyse the cumulative shift of periastron time of a binary pulsar by the emission of gravitational waves. Time evolution of the osculating orbital elements of the triple system is calculated by directly integrating the first-order post-Newtonian equations of motion. The Kozai-Lidov mechanism will bend the evolution curve of the cumulative shift when the eccentricity becomes large. We also investigate the parameter range of mass and semi-major axis of the third companion with which the bending of the cumulative-shift curve could occur within 100 years.