Inferring the gravitational wave memory for binary coalescence events

TL;DR

This paper calculates and compares the posterior probability distributions of gravitational wave memory for binary black hole mergers, highlighting potential systematic errors and the utility of memory as a diagnostic tool for waveform accuracy.

Contribution

It presents the first posterior distributions of gravitational wave memory for GWTC-1 events using multiple waveform models, revealing discrepancies and potential sources of systematic errors.

Findings

Good agreement between Phenomenological and EOB waveform posteriors

Discrepancies found in the $ ext{l}=2, ext{m}=1$ mode of memory

Memory distributions can diagnose waveform modeling errors

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.