The gravitational-wave memory from eccentric binaries

TL;DR

This paper extends the understanding of nonlinear gravitational-wave memory to eccentric binaries, deriving waveform corrections for various orbital types and discussing their observability and implications for gravitational-wave detection.

Contribution

It provides the first comprehensive derivation of nonlinear memory effects for arbitrary eccentric orbits, including hyperbolic, parabolic, and radial cases, and analyzes their impact on waveform modeling.

Findings

Nonlinear memory introduces a 2.5PN correction in hyperbolic, parabolic, and radial orbits.

Memory effects differ in PN order between elliptical and hyperbolic cases due to different build-up times.

Estimates of signal-to-noise ratios suggest potential observability of memory jumps in gravitational-wave detectors.

Abstract

The nonlinear gravitational-wave memory causes a time-varying but nonoscillatory correction to the gravitational-wave polarizations. It arises from gravitational waves that are sourced by gravitational waves. Previous considerations of the nonlinear memory effect have focused on quasicircular binaries. Here, I consider the nonlinear memory from Newtonian orbits with arbitrary eccentricity. Expressions for the waveform polarizations and spin-weighted spherical-harmonic modes are derived for elliptic, hyperbolic, parabolic, and radial orbits. In the hyperbolic, parabolic, and radial cases the nonlinear memory provides a 2.5 post-Newtonian (PN) correction to the leading-order waveforms. This is in contrast to the elliptical and quasicircular cases, where the nonlinear memory corrects the waveform at leading (0PN) order. This difference in PN order arises from the fact that the memory builds up over a short "scattering" time scale in the hyperbolic case, as opposed to a much longer radiation-reaction time scale in the elliptical case. The nonlinear memory corrections presented here complete our knowledge of the leading-order (Peters-Mathews) waveforms for elliptical orbits. These calculations are also relevant for binaries with quasicircular orbits in the present epoch which had, in the past, large eccentricities. Because the nonlinear memory depends sensitively on the past evolution of a binary, I discuss the effect of this early-time eccentricity on the value of the late-time memory in nearly circularized binaries. I also discuss the observability of large "memory jumps" in a binary's past that could arise from its formation in a capture process. Lastly, I provide estimates of the signal-to-noise ratio of the linear and nonlinear memories from hyperbolic and parabolic binaries.