Quadrupolar bremsstrahlung waveform at the third-and-a-half post-Newtonian accuracy

TL;DR

This paper computes the quadrupolar gravitational waveform during scattering at 3.5PN accuracy, including nonlinear memory effects, using the MPM formalism and compares results with EFT approaches.

Contribution

It provides the first explicit 3.5PN order frequency-domain waveform for hyperbolic scattering, including nonlinear memory, within the MPM formalism.

Findings

Waveform computed at 3.5PN accuracy in time domain.

Frequency-domain waveform evaluated up to 2-loop level, O(G^4).

Nonlinear memory contribution checked against soft-limit.

Abstract

We study the quadrupolar part of the gravitational waveform $h_{ij}$ (encoded in the helicity-($-2)$ radiative quadrupole moment $U_2 = \frac{1}{2!} \bar m^{i} \bar m^{j } U_{i j} \in\frac{R}{4G} \bar m^{i} \bar m^{j } h_{i j}\equiv W $) emitted during the scattering of two masses. Working within the Multipolar Post-Minkowskian (MPM) formalism, we compute the time-domain value of $U_2$ at the third-and-a-half post-Newtonian (3.5PN) accuracy by using the 3.5PN radiation-reacted quasi-Keplerian representation of the hyperbolic motion. We then explicitly evaluate the {\it frequency-domain} value of $U_2$ up to the 2-loop level, i.e. $ O(G^4)$ contributions to $h_{ij}(\omega, \theta,\phi)$, corresponding to $O(G^3)$ contributions to $\hat U_2(\omega, \theta,\phi)$. The nonlinear memory contribution to the waveform in the center-of-mass frame is computed too, and checked against the soft-limit of the waveform. The 1-loop truncation of our 3.5PN frequency-domain MPM waveform is found to agree with corresponding existing Effective Field Theory (EFT) results when subtracting the dipolar part of the Veneziano-Vilkovisky supertranslation connecting the MPM and EFT Bondi-Metzner-Sachs (BMS) frames.