Parametrized multipolar gravitational waveforms for testing general relativity: Amplitude corrections up to 2PN order

TL;DR

This paper derives a parametrized multipolar gravitational wave amplitude at 2PN order, enabling model-agnostic tests of the multipolar structure of compact binaries with gravitational wave observations.

Contribution

It provides a closed-form expression for the amplitude including multiple radiative moments, enhancing the ability to test general relativity's multipolar predictions.

Findings

Derived a 2PN order multipolar amplitude expression

Includes contributions from five mass-type and four current-type moments

Framework allows for improved multipole structure testing in gravitational wave data

Abstract

A parametrized multipolar gravitational wave phasing within multipolar post-Minkowskian and post-Newtonian formalism was developed in earlier works [S. Kastha et al., PRD 98, 124033 (2018) and PRD 100, 044007 (2019)]. This facilitates the model-agnostic tests for the multipolar structure of compact binaries using gravitational wave observations. In this paper, we derive a parametrized multipolar amplitude of the gravitational wave signal in terms of mass and current-type radiative multipole moments within the post-Newtonian approximation to general relativity. We assume the compact binary to be moving in quasicircular orbits, with component spins (anti-) aligned with respect to the binary's orbital angular momentum. We report a closed-form expression for the parametrized multipolar amplitude of the waveform at second post-Newtonian order both in time and frequency domains. This includes the contribution from the leading five mass-type and the leading four current-type radiative moments. This framework of constructing a parametrized waveform accomplishes a generic parametrization of both gravitational wave phase and amplitude with the same set of phenomenological parameters. Hence, it should significantly enhance the precision of the multipole tests in the context of present and future gravitational wave detectors.