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The 2.5PN gravitational wave polarisations from inspiralling compact binaries in circular orbits

K G Arun, Luc Blanchet, Bala R Iyer, Moh'd S S Qusailah

TL;DR

The paper delivers a complete 2.5PN gravitational waveform for inspiralling compact binaries in quasi-circular orbits using the multipolar post-Minkowskian framework, including both instantaneous and hereditary contributions (tails and memory). It extends prior 2PN results to 2.5PN, providing ready-to-use expressions for the plus and cross polarizations and detailing the source multipole moments required, while discussing regularization issues and the role of past history in memory terms. The authors model the past binary evolution with an adiabatic Newtonian inspiral to evaluate memory and tail integrals, and they reformulate the waveform in terms of a phase variable that absorbs logarithmic frequency terms to simplify templates. These results enhance gravitational-wave data analysis for both ground-based detectors (LIGO/VIRGO) and space-based detectors (LISA) by delivering higher-accuracy templates and clarifying the structure of non-linear effects such as memory and tails at this order.

Abstract

Using the multipolar post-Minkowskian and matching formalism we compute the gravitational waveform of inspiralling compact binaries moving in quasi-circular orbits at the second and a half post-Newtonian (2.5PN) approximation to general relativity. The inputs we use include notably the mass-type quadrupole at the 2.5PN order, the mass octupole and current quadrupole at the 2PN order, the mass $2^5$-pole and current $2^4$-pole at 1PN. The non-linear hereditary terms come from the monopole-quadrupole multipole interactions or tails, present at the 1.5PN, 2PN and 2.5PN orders, and the quadrupole-quadrupole interaction arising at the 2.5PN level. In particular, the specific effect of non-linear memory is computed using a simplified model of binary evolution in the past. The ``plus'' and ``cross'' wave polarisations at the 2.5PN order are obtained in ready-to-use form, extending the 2PN results calculated earlier by Blanchet, Iyer, Will and Wiseman.

The 2.5PN gravitational wave polarisations from inspiralling compact binaries in circular orbits

TL;DR

The paper delivers a complete 2.5PN gravitational waveform for inspiralling compact binaries in quasi-circular orbits using the multipolar post-Minkowskian framework, including both instantaneous and hereditary contributions (tails and memory). It extends prior 2PN results to 2.5PN, providing ready-to-use expressions for the plus and cross polarizations and detailing the source multipole moments required, while discussing regularization issues and the role of past history in memory terms. The authors model the past binary evolution with an adiabatic Newtonian inspiral to evaluate memory and tail integrals, and they reformulate the waveform in terms of a phase variable that absorbs logarithmic frequency terms to simplify templates. These results enhance gravitational-wave data analysis for both ground-based detectors (LIGO/VIRGO) and space-based detectors (LISA) by delivering higher-accuracy templates and clarifying the structure of non-linear effects such as memory and tails at this order.

Abstract

Using the multipolar post-Minkowskian and matching formalism we compute the gravitational waveform of inspiralling compact binaries moving in quasi-circular orbits at the second and a half post-Newtonian (2.5PN) approximation to general relativity. The inputs we use include notably the mass-type quadrupole at the 2.5PN order, the mass octupole and current quadrupole at the 2PN order, the mass -pole and current -pole at 1PN. The non-linear hereditary terms come from the monopole-quadrupole multipole interactions or tails, present at the 1.5PN, 2PN and 2.5PN orders, and the quadrupole-quadrupole interaction arising at the 2.5PN level. In particular, the specific effect of non-linear memory is computed using a simplified model of binary evolution in the past. The ``plus'' and ``cross'' wave polarisations at the 2.5PN order are obtained in ready-to-use form, extending the 2PN results calculated earlier by Blanchet, Iyer, Will and Wiseman.

Paper Structure

This paper contains 18 sections, 71 equations.

Table of Contents

  1. Introduction
  2. On gravitational-wave astronomy
  3. An overview of current calculations of radiation from ICBs
  4. The post-Newtonian wave generation formalism
  5. The MPM expansion and matching to a post-Newtonian source
  6. Application to compact binary systems
  7. The 2.5PN gravitational waveform
  8. Waveform as a functional of multipole moments
  9. Instantaneous versus hereditary contributions
  10. Source multipole moments required at the 2.5PN order
  11. Hereditary terms at the 2.5PN order
  12. Model for adiabatic inspiral in the remote past
  13. The nonlinear memory integral
  14. Gravitational-wave tails
  15. Results for the 2.5PN polarisation waveforms
  16. ...and 3 more sections