etection of the Permanent Strain Offset Component of Gravitational-Wave Memory in Black Hole Mergers

We propose a novel approach to detecting the elusive gravitational-wavememory predicted by general relativity to accompany black hole mergers: directmeasurement of the permanent space-time strain offset. Compared to previoustechniques modeling and disentangling both the "chirp" and memory signals, thisapproach has several advantages: it targets the feature of the signal carryingnearly all its Shannon information, has great simplicity, circumvents the needfor precise modeling of the time evolution of all components of thegravitational wave signal, and uses only data largely free of the morecomplicated chirp signal. The frequency spectrum of the predicted memory signalis roughly similar to that of the chirp signal. However its inclusion of lowerfrequencies, where noise and data calibration are problematic, makes detectiondifficult but not impossible. We applied this novel analysis, implemented witha template-like algorithm, to a selection of 67 observations of 41 black holemergers in the LIGO/Virgo Gravitational Wave Transient Catalog. Statisticalsignificance was assessed by analyzing many time-shifted intervals. The result:a few possible detections ($2\sigma-4\sigma$) and many upper limits. Theprobability that a random ensemble of 67 strain time series, with the samenoise but no memory signals, will yield a particular figure-of-merit computedfor the actual data is approximately 0.1. Several validation checks proveduseless, partly due to large measurement and theoretical uncertainties, sothese results should be viewed with reservation. Appendices contain MatLab codefor various operations, including an algorithm for the complex Fouriertransform of arbitrarily spaced data.