Energy losses by gravitational radiation in inspiralling compact binaries to five halves post-Newtonian order

TL;DR

This paper calculates the energy loss due to gravitational waves in inspiralling compact binaries up to 2.5 post-Newtonian order, highlighting the significance of tail effects and their impact on gravitational wave phase evolution.

Contribution

It extends the gravitational-wave generation formalism to 2.5PN order, including tail effects, and derives the resulting energy loss and phase evolution for inspiralling binaries.

Findings

2.5PN energy loss is dominated by tail effects.

The 2.5PN phase correction is comparable to 2PN but opposite in sign.

Finite mass effects at 2.5PN are small.

Abstract

This paper derives the total power or energy loss rate generated in the form of gravitational waves by an inspiralling compact binary system to the five halves post-Newtonian (2.5PN) approximation of general relativity. Extending a recently developed gravitational-wave generation formalism valid for arbitrary (slowly-moving) systems, we compute the mass multipole moments of the system and the relevant tails present in the wave zone to 2.5PN order. In the case of two point-masses moving on a quasi-circular orbit, we find that the 2.5PN contribution in the energy loss rate is entirely due to tails. Relying on an energy balance argument we derive the laws of variation of the instantaneous frequency and phase of the binary. The 2.5PN order in the accumulated phase is significantly large, being grossly of the same order of magnitude as the previous 2PN order, but opposite in sign. However finite mass effects at 2.5PN order are small. The results of this paper should be useful when analyzing the data from inspiralling compact binaries in future gravitational-wave detectors like VIRGO and LIGO.