Gravitational waveforms for 2- and 3-body gravitating systems

TL;DR

This paper investigates gravitational waveforms from 2- and 3-body systems, highlighting the difficulty in distinguishing sources using quadrupole signals and proposing higher multipole analysis for better classification.

Contribution

It introduces a method to compare waveforms from different self-gravitating systems and suggests higher multipole moments are essential for source differentiation.

Findings

Quadrupole waveforms cannot distinguish between binary and three-body systems.

A chirp mass for triple systems is defined to track waveform evolution.

Higher multipole moments are important for classifying gravitational wave sources.

Abstract

Different numbers of self-gravitating particles (in different types of periodic motion) are most likely to generate very different shapes of gravitational waves, some of which, however, can be accidentally almost the same. One such example is a binary and a three-body system for Lagrange's solution. To track the evolution of these similar waveforms, we define a chirp mass to the triple system. Thereby, we show that the quadrupole waveforms cannot distinguish the sources. It is suggested that waveforms with higher $\ell$-th multipoles will be important for classification of them (with a conjecture of $\ell \leq N$ for N particles).