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.
An Enhanced Formation Channel for Galactic Dual-Line Gravitational-Wave Sources: von Zeipel-Lidov-Kozai Effect in Triples Involving Sgr A*
Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学科维理天文与天体物理研究所）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础物理与数学学院）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Institute of Fundamental Physics and Quantum Technology, Ningbo University（宁波大学基础物理与量子技术研究所）；School of Physical Science and Technology, Ningbo University（宁波大学物理科学与技术学院）；Department of Astronomy, School of Physics, Peking University（北京大学物理学院天文学系）；Institute for Astronomy, School of Physics, Zhejiang University（浙江大学物理学院天体物理研究所）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）
