The gravitational-wave memory effect

TL;DR

Favata surveys gravitational‑wave memory, focusing on both linear and nonlinear (Christodoulou) memory. He highlights that nonlinear memory contributes at leading Newtonian order for quasi‑circular binaries and is sourced by the GW energy flux, making it a distinct, slowly growing feature in the waveform. The work synthesizes 3PN memory corrections to the inspiral, analytic modeling of memory through merger and ringdown, and forecasts memory detectability with LISA (and ground detectors to a lesser extent), underscoring memory as a fundamental nonlinear GW effect with practical observational prospects.

Abstract

The nonlinear memory effect is a slowly-growing, non-oscillatory contribution to the gravitational-wave amplitude. It originates from gravitational waves that are sourced by the previously emitted waves. In an ideal gravitational-wave interferometer a gravitational-wave with memory causes a permanent displacement of the test masses that persists after the wave has passed. Surprisingly, the nonlinear memory affects the signal amplitude starting at leading (Newtonian-quadrupole) order. Despite this fact, the nonlinear memory is not easily extracted from current numerical relativity simulations. After reviewing the linear and nonlinear memory I summarize some recent work, including: (1) computations of the memory contribution to the inspiral waveform amplitude (thus completing the waveform to third post-Newtonian order); (2) the first calculations of the nonlinear memory that include all phases of binary black hole coalescence (inspiral, merger, ringdown); and (3) realistic estimates of the detectability of the memory with LISA.

Figures (2)

• Figure 1: Examples of gravitational-wave signals with memory. The left plot shows the waveform modes $\ddot{I}_{2m}$ for a hyperbolic orbit with eccentricity $e_0=2$ as a function of time [see (\ref{['eq:Ilmhyperbolic']}) and surrounding text]. Note the linear memory present in the imaginary part of $\ddot{I}_{22}$. The right plot shows the $h_{+}$ polarization for an equal-mass binary black hole coalescence with (blue/solid) and without (red/dashed) the nonlinear memory. The oscillatory piece of $h_+$ was computed using an effective-one-body (EOB) model for the $h_{22}$ mode. The memory piece was computed by substituting this mode into (\ref{['eq:memhplus']}). See favata-memory-saturation for details.
• Figure 2: Detectability of the memory with LISA. The left plot shows the LISA noise amplitude $h_n$ (solid/black) and the characteristic amplitudes $h_c$ for the inspiral waves (solid/orange) and the nonlinear memory for a black hole binary with the indicated parameters. The short-dashed/blue curve uses the MWM (\ref{['eq:FThmem']}) to compute the memory; the long-dashed/red curve uses a truncated-inspiral model based on kennefick-memory (see favata-memory-saturation for details). The right plot shows the angle-averaged SNR of the nonlinear memory signal for equal-mass LISA binaries as a function of the total binary (source-frame) mass $M$ and redshift $z$.