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

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-toleading 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. [Class. Quantum Grav. 25, 165003 (2008)], this completes the waveform polarizations to 3PN order. This paper also discusses: (i) the difficulties in extracting the memory from numerical relativity simulations, (ii) other nonoscillatory effects that enter the waveform polarizations at high PN orders, and (iii) issues concerning the observability of the memory in gravitational-wave detectors.

Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order

“…[22,[26][27][28][29][30] in the mass quadrupole moment at the lowest order, which is 2.5PN. More recently, the 3.5PN corrections beyond leading order have been obtained for both circular [31] and eccentric orbits [32]. Note that the non-linear memory effect does not enter the current-type multipole moments V L , but only the mass-type multipole moments U L , hence V mem L = 0.…”

Expected properties of the first gravitational wave signal detected with pulsar timing arrays

“…The incoherent superposition of many signals will possibly result in a stochastic GWB (Rajagopal & Romani 1995), but particularly massive and/or nearby SBHBs might dominate the signal budget and show up as resolvable continuous waves (Sesana et al 2009) in the data. Moreover, bursts from particularly eccentric binaries (Amaro-Seoane et al 2010;Finn & Lommen 2010) or from the GW memory effect (Favata 2009;Pshirkov et al 2010;van Haasteren & Levin 2010) are also possible. Consequently, several IPTA projects have been established, targeting different types of signals.…”

Gravitational wave astronomy: the current status

“…A GW memory is a permanent distortion in the spacetime metric [247,248]. Such effects can be produced during mergers of supermassive binary black holes and cause instantaneous jumps of pulse frequency.…”