Abstract
Full, non-linear general relativity predicts a memory effect for gravitational waves. For compact binary coalescence, the total gravitational memory serves as an inferred observable, conceptually on the same footing as the mass and the spin of the final black hole. Given candidate waveforms for any LIGO event, then, one can calculate the posterior probability distribution functions for the total gravitational memory, and use them to compare and contrast the waveforms. In this paper we present these posterior distributions for the binary black hole merger events reported in the first Gravitational Wave Transient Catalog (GWTC-1), using the Phenomenological and Effective-One-Body waveforms. On the whole, the two sets of posterior distributions agree with each other quite well though we find larger discrepancies for the $\ell=2, m=1$ mode of the memory. This signals a possible source of systematic errors that was not captured by the posterior distributions of other inferred observables. Thus, the posterior distributions of various angular modes of total memory can serve as diagnostic tools to further improve the waveforms. Analyses such as this would be valuable especially for future events as the sensitivity of ground based detectors improves, and for LISA which could measure the total gravitational memory directly.
Highlights
The detection of gravitational waves enables tests of general relativity that were not possible using the electromagnetic window
Given candidate waveforms for any LIGO-Virgo event, one can calculate the posterior probability distribution functions for the total gravitational memory and use them to compare and contrast the waveforms. We present these posterior distributions for the binary black hole merger events reported in the first Gravitational Wave Transient Catalog, using the phenomenological and effective-one-body waveforms
Precisely for the same reason, the merger provides a promising place to look for potential deviations from general relativity
Summary
The detection of gravitational waves enables tests of general relativity that were not possible using the electromagnetic window. There is no generally accepted framework to test the accuracy of theoretical predictions describing the merger itself, several tests have been proposed in the literature to probe different aspects of these predictions These include, for example, various consistency checks between the inspiral and the merger [4,5], extending the idea of black hole spectroscopy [6,7,8,9,10,11] toward the merger [12,13], and tests of phenomenological waveform models for the merger [1]. The total gravitational wave memory is on a similar footing as these: given the waveform parameters and a particular waveform model, values of various modes in the angular decomposition of the memory can be uniquely inferred assuming general relativity. IV concludes with a discussion of the results and possible future applications of the memory
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