The third post-Newtonian gravitational wave polarizations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits

Abstract

The gravitational waveform (GWF) generated by inspiralling compact binaries moving in quasicircular orbits is computed at the third post-Newtonian (3PN) approximation to general relativity. Our motivation is two-fold: (i) To provide accurate templates for the data analysis of gravitational wave inspiral signals in laser interferometric detectors; (ii) To provide the associated spin-weighted spherical harmonic decomposition to facilitate comparison and match of the high post-Newtonian prediction for the inspiral waveform to the numerically-generated waveforms for the merger and ringdown. This extension of the GWF by half a PN order (with respect to previous work at 2.5PN order) is based on the algorithm of the multipolar post-Minkowskian formalism, and mandates the computation of the relations between the radiative, canonical and source multipole moments for general sources at 3PN order. We also obtain the 3PN extension of the source multipole moments in the case of compact binaries, and compute the contributions of hereditary terms (tails, tails-oftails and memory integrals) up to 3PN order. The end results are given for both the complete plus and cross polarizations and the separate spin-weighted spherical harmonic modes.

2.5PN linear momentum flux from inspiralling compact binaries in quasicircular orbits and associated recoil: Nonspinning case

“…(2.1) that the computation of 2.5PN accurate linear momentum flux requires the knowledge of U ij , V ij and U ijk at 2.5PN order, U ijkl and V ijk at 1.5PN order, and U ijklm and V ijkl at Newtonian order. In a recent work [30], U L and V L have been computed with accuracies sufficient for the present purpose using multipolar post-Minkowskian (MPM) approximation approach [31][32][33][34][35][36]. In the multipolar post-Minkowskian formalism U L and [30]).…”

“…In a recent work [30], U L and V L have been computed with accuracies sufficient for the present purpose using multipolar post-Minkowskian (MPM) approximation approach [31][32][33][34][35][36]. In the multipolar post-Minkowskian formalism U L and [30]). Rewriting the expressions for the radiative moments in terms of the source moments, the linear momentum flux can be decomposed as the sum of two distinct parts: the instantaneous terms and the hereditary terms.…”

“…All the source multipole moments in case of nonspinning inspiralling compact binaries moving in quasicircular orbits are now known with the accuracies sufficient for the present purpose and have been computed and listed in [30] (see Eqs. (5.12)-(5.25) there).…”

Accurate inspiral-merger-ringdown gravitational waveforms for nonspinning black-hole binaries including the effect of subdominant modes

“…Thus, only m > 0 modes are considered in this paper. [43,[47][48][49] while the 3.5PN orbital phase φ orb ðtÞ can be computed in the adiabatic approximation using inputs given in [50] and references therein. In order to improve the accuracy of the inspiral waveforms, we compute the phase evolution of the inspiral part from the 22 modes of the effective-one-body (EOB) waveforms calibrated to NR simulations (SEOBNRv4 [13] The dominant, 22 mode inspiral model that we use here is actually 3.5PN accurate [46].…”

Renormalized second post-Newtonian spin contributions to the accumulated orbital phase for LISA sources

“…We note that the logarithmic terms arising from the latter can be eliminated through a modified definition of the phase [58] The list of contributions known at 3PN and 3.5PN are not exhaustive. At 3PN there are known relativistic and tail contributions [46] …”