About gravitational-wave generation by a three-body system

Abstract

Abstract. We highlight some subtleties that affect naive implementations of quadrupolar and octupolar gravitational waveforms from numerically-integrated trajectories of three-body systems. Some of those subtleties arise from the requirement that the source be contained in its "coordinate near zone" when applying the standard PN formulae for gravitational-wave emission, and from the need to use the non-linear Einstein equations to correctly derive the quadrupole emission formula. We show that some of these subtleties were occasionally overlooked in the literature, with consequences for published results. We also provide prescriptions that lead to correct and robust predictions for the waveforms computed from numerically-integrated orbits.

Gravitational waves from hierarchical triple systems with Kozai-Lidov oscillation

“…In the derivation of the quadrupole formula, a system must be contained in its NCZ, i.e., in order to use the quadrupole formula, a system should be inside a region (centered on the origin of the coordinates) of radius comparable to (or smaller than) the GW wavelength λ (see some good example of what not to do given in [72]). Therefore, we must keep a check that a hierarchical triple system is in its NCZ when the formalism is applied to the center of mass of the triple system for the model in consideration.…”

An Analytical Portrait of Binary Mergers in Hierarchical Triple Systems

“…This is no longer valid in systems such as globular clusters when octupole interactions play an essential role [36]. An N -body code of the triple system with PN corrections were presented in [37] and further subtleties in the calculation of GW radiation from a hierarchical triple were discussed in [38].…”

Gravitational Waves from Hierarchical Triple Systems with Kozai-Lidov Oscillation

“…In the derivation of the quadrupole formula, a system must be contained in its NCZ , i.e., in order to use the quadrupole formula, a system should be inside a region (centered on the origin of the coordinates) of radius comparable to (or smaller than) the GW wavelength λ (see some good example of what not to do given in [62]). Therefore, we must keep a check that a hierarchical triple system is in its NCZ when the formalism is applied to the center of mass of the triple system for the model in consideration.…”