Post-Newtonian corrections to the gravitational-wave memory for quasicircular, inspiralling compact binaries

TL;DR

This paper extends the calculation of the nonlinear gravitational-wave memory effect for inspiralling binaries to 3PN order, providing explicit formulas and discussing implications for detection and waveform modeling.

Contribution

It presents the first 3PN order calculation of the memory contribution for quasicircular inspiralling binaries, improving waveform accuracy.

Findings

PN corrections tend to reduce the memory magnitude

Explicit expressions for memory contributions are provided

Completes the waveform to 3PN order with implications for detection

Abstract

The Christodoulou memory is a nonlinear contribution to the gravitational-wave field that is sourced by the gravitational-wave stress-energy tensor. For quasicircular, inspiralling binaries, the Christodoulou memory produces a growing, nonoscillatory change in the gravitational-wave "plus" polarization, resulting in the permanent displacement of a pair of freely-falling test masses after the wave has passed. In addition to its nonoscillatory behavior, the Christodoulou memory is interesting because even though it originates from 2.5 post-Newtonian (PN) order multipole interactions, it affects the waveform at leading (Newtonian/quadrupole) order. The memory is also potentially detectable in binary black-hole mergers. While the oscillatory pieces of the gravitational-wave polarizations for quasicircular, inspiralling compact binaries have been computed to 3PN order, the memory contribution to the polarizations has only been calculated to leading order (the next-to-leading order 0.5PN term has previously been shown to vanish). Here the calculation of the memory for quasicircular, inspiralling binaries is extended to 3PN order. While the angular dependence of the memory remains qualitatively unchanged, the PN correction terms tend to reduce the memory's magnitude. Explicit expressions are given for the memory contributions to the plus polarization and the spin-weighted spherical-harmonic modes of the metric and curvature perturbations. Combined with the recent results of Blanchet et al.(2008), this completes the waveform to 3PN order. This paper also discusses: (i) the difficulties in extracting the memory from numerical simulations, (ii) other nonoscillatory effects that enter the waveform at high PN orders, and (iii) issues concerning the observability of the memory.