Waveform models for the gravitational-wave memory effect: Extreme mass-ratio limit and final memory offset

The gravitational-wave (GW) memory effect is a strong-field relativistic phenomenon that is associated with a persistent change in the GW strain after the passage of a GW. The nonlinear effect arises from interactions of GWs themselves in the wave zone and is an observable effect connected to the infrared properties of general relativity. The detection of the GW memory effect is possible with LIGO and Virgo in a population of binary-black-hole (BBH) mergers or from individual events with next-generation ground- and space-based GW detectors or pulsar timing arrays. Matched-filtering-based searches for the GW memory require accurate, and preferably rapid-to-evaluate waveform models of the memory effect's GW signal. One important element of such a waveform model is a model for the final memory offset---namely, the net change in strain between early and late times. In this paper, we construct a model for the final memory offset from the merger of nonspinning BBH systems in quasicircular orbits. A novel ingredient of this model is that we first compute the memory signal for extreme mass-ratio inspirals using a high post-Newtonian-order analytic calculation, and we use this analytical result to fix the coefficient in the fit which is linear in the mass-ratio. The resulting memory-offset fit could be used for detecting the GW memory for binaries that merge on a timescale that is short relative to the inverse of the low-frequency cutoff of a GW detector. Additionally, this fit will be useful for analytic waveform models of the GW memory signals in the time and frequency domains.