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Spin memory effect for compact binaries in the post-Newtonian approximation

David A. Nichols

TL;DR

The paper derives the spin memory effect for compact binaries within a Bondi-PN framework by expressing it in terms of radiative multipole moments and relating these to source moments in the PN regime. It reveals that the spin memory grows secularly as $x^{-1/2}$ during inspiral, in contrast to the displacement memory, and identifies the spin-memory mode as a nonlinear, nonhereditary, nonoscillatory contribution at 2.5PN that could be probed by stacking hundreds of detections with next-generation detectors. The authors provide explicit PN leading-order results, connect the spin-memory rate to known waveform terms, and evaluate detectability for ground-based detectors, finding that individual events are unlikely to yield a direct detection but coherent stacking could reveal the effect. They also discuss broader observational avenues, including pulsar timing arrays and LISA, and suggest future refinements in higher-order PN corrections and numerical-relativity validations. Overall, the work links asymptotic symmetries to observable gravitational-wave memory and outlines a practical pathway to measuring a novel relativistic memory effect.

Abstract

The spin memory effect is a recently predicted relativistic phenomenon in asymptotically flat spacetimes that become nonradiative infinitely far in the past and future. Between these early and late times, the magnetic-parity part of the time integral of the gravitational-wave strain can undergo a nonzero change; this difference is the spin memory effect. Families of freely falling observers around an isolated source can measure this effect, in principle, and fluxes of angular momentum per unit solid angle (or changes in superspin charges) generate the effect. The spin memory effect had not been computed explicitly for astrophysical sources of gravitational waves, such as compact binaries. In this paper, we compute the spin memory in terms of a set of radiative multipole moments of the gravitational-wave strain. The result of this calculation allows us to establish the following results about the spin memory: (i) We find that the accumulation of the spin memory behaves in a qualitatively different way from that of the displacement memory effect for nonspinning, quasicircular compact binaries in the post-Newtonian approximation: the spin memory undergoes a large secular growth over the duration of the inspiral, whereas for the displacement effect this increase is small. (ii) The rate at which the spin memory grows is equivalent to a nonlinear, but nonoscillatory and nonhereditary effect in the gravitational waveform that had been previously calculated for nonspinning, quasicircular compact binaries. (iii) This rate of build-up of the spin memory could potentially be detected by future gravitational-wave detectors by carefully combining the measured waveforms from hundreds of gravitational-wave detections of compact binaries.

Spin memory effect for compact binaries in the post-Newtonian approximation

TL;DR

The paper derives the spin memory effect for compact binaries within a Bondi-PN framework by expressing it in terms of radiative multipole moments and relating these to source moments in the PN regime. It reveals that the spin memory grows secularly as during inspiral, in contrast to the displacement memory, and identifies the spin-memory mode as a nonlinear, nonhereditary, nonoscillatory contribution at 2.5PN that could be probed by stacking hundreds of detections with next-generation detectors. The authors provide explicit PN leading-order results, connect the spin-memory rate to known waveform terms, and evaluate detectability for ground-based detectors, finding that individual events are unlikely to yield a direct detection but coherent stacking could reveal the effect. They also discuss broader observational avenues, including pulsar timing arrays and LISA, and suggest future refinements in higher-order PN corrections and numerical-relativity validations. Overall, the work links asymptotic symmetries to observable gravitational-wave memory and outlines a practical pathway to measuring a novel relativistic memory effect.

Abstract

The spin memory effect is a recently predicted relativistic phenomenon in asymptotically flat spacetimes that become nonradiative infinitely far in the past and future. Between these early and late times, the magnetic-parity part of the time integral of the gravitational-wave strain can undergo a nonzero change; this difference is the spin memory effect. Families of freely falling observers around an isolated source can measure this effect, in principle, and fluxes of angular momentum per unit solid angle (or changes in superspin charges) generate the effect. The spin memory effect had not been computed explicitly for astrophysical sources of gravitational waves, such as compact binaries. In this paper, we compute the spin memory in terms of a set of radiative multipole moments of the gravitational-wave strain. The result of this calculation allows us to establish the following results about the spin memory: (i) We find that the accumulation of the spin memory behaves in a qualitatively different way from that of the displacement memory effect for nonspinning, quasicircular compact binaries in the post-Newtonian approximation: the spin memory undergoes a large secular growth over the duration of the inspiral, whereas for the displacement effect this increase is small. (ii) The rate at which the spin memory grows is equivalent to a nonlinear, but nonoscillatory and nonhereditary effect in the gravitational waveform that had been previously calculated for nonspinning, quasicircular compact binaries. (iii) This rate of build-up of the spin memory could potentially be detected by future gravitational-wave detectors by carefully combining the measured waveforms from hundreds of gravitational-wave detections of compact binaries.

Paper Structure

This paper contains 29 sections, 73 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Overview of the displacement memory effect
  3. Summary of the spin memory
  4. Methodology for computing memory effects
  5. Summary of results
  6. Outline of this paper
  7. Elements of the Bondi and PN frameworks
  8. PN approximation
  9. General aspects of PN theory
  10. PN theory for compact binaries in quasicircular orbits
  11. Bondi framework
  12. Multipolar expansion of the displacement memory within the Bondi framework
  13. Displacement memory in terms of radiative multipole moments
  14. Displacement memory for compact binaries in the PN approximation
  15. Multipolar expansion of the spin memory within the Bondi framework
  16. ...and 14 more sections

Figures (2)

  • Figure 1: Spin memory mode in a numerical relativity simulation (solid red curve) and that computed from the analytical expression involving the $l=2$, $m=\pm 2$ modes (black dashed curve). The waveform is scaled to have parameters like that of the GW150914 event, which are described in greater detail in the text.
  • Figure 2: The spin memory effect computed directly from a numerical relativity simulation and the analytical expression containing the $l=2$, $m=\pm 2$ by integrating the curves in Fig. \ref{['fig:SpinMemMode']} numerically.