The gravitational-wave memory effect (1003.3486v1)

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.

Analyzing the Gravitational-Wave Memory Effect

The paper "The gravitational-wave memory effect" by Marc Favata offers an in-depth exploration of the gravitational-wave (GW) memory effect, focusing primarily on its nonlinear manifestation. This phenomenon, which results in a permanent displacement of test masses in an ideal GW interferometer following the passage of a wave with memory, presents an intriguing aspect of GW physics due to its non-oscillatory nature and the challenges it poses for detection.

The GW memory effect can be categorized into linear and nonlinear components. The linear memory, understood since the 1970s, is found in systems with unbound components—such as hyperbolic orbits, supernovae, and gamma-ray bursts—whereas the nonlinear memory, a more recent discovery by Blanchet and Damour, as well as by Christodoulou, arises from the interaction of previously emitted gravitational waves. This nonlinear effect intriguingly emerges at the leading (Newtonian) order, despite being a high post-Newtonian (PN) order phenomenon, and has strong implications for the waveform amplitude of gravitational waves, particularly from coalescing binary systems.

Favata's work offers significant advancements in the understanding of GW memory, presenting a detailed calculation of the memory's contribution to the inspiral waveform amplitude, completing the GW waveform to third post-Newtonian (3PN) order. Additionally, the paper includes the distinct computation of the nonlinear memory across all phases of binary black hole coalescence: inspiral, merger, and ringdown.

While the theoretical framework for evaluating GW memory has advanced, observational challenges remain. Current numerical relativity (NR) simulations struggle to capture the GW memory due to the effect's subtle and non-oscillatory nature—particularly its manifestation predominantly in the $m=0$ modes of the waveform, rather than the usually computed $l=m=2$ modes. Moreover, the memory effect is mainly detected via the $h_{l0}$ waveform modes, which are not readily apparent in typical NR evaluations.

The implications for GW detection are profound. The detectability of the nonlinear memory is limited for initial and advanced LIGO configurations, primarily due to their insensitivity to such non-oscillatory signals. However, the Laser Interferometer Space Antenna (LISA), with its superior low-frequency sensitivity, shows promise for detecting the memory effect from supermassive black hole mergers at cosmological distances, potentially out to redshifts near $z\approx 2$.

Favata puts forth an analytic model known as the minimal waveform model (MWM), providing a framework for approximating the memory by matching the inspiral waveform with a simplified ringdown waveform. Additionally, the paper investigates the potential for detecting the memory with LISA using detailed signal-to-noise ratio calculations, which suggest that LISA will be adept at observing this effect for sizable cosmological events.

In conclusion, while the nonlinear memory effect is a distinctive aspect of GWs that challenges both theoretical understanding and observational capabilities, progress has been made in its analytical interpretation and potential for detection. The research highlights a need for continued investigation into improving NR simulations and refining detection strategies for space-based interferometers, which could further illuminate this fascinating gravitational phenomenon. Future developments in these areas could enhance our understanding of the universe's dynamic nature, accessed through the unique signature of gravitational-wave memory.