Stochastic gravitational wave background due to gravitational wave memory

TL;DR

This paper models the stochastic gravitational wave memory background as Brownian motion, deriving a power-law spectrum dependent on binary black hole merger rates, and discusses its potential for detection and insights into gravity and black hole mergers.

Contribution

It introduces the first investigation of the gravitational wave memory background from binary black hole coalescences, modeling it as Brownian motion and deriving its spectral properties.

Findings

Memory background spectrum follows a power law with index -2.

Amplitude depends solely on binary black hole merger rate.

Space-based detectors are suitable for detecting this background.

Abstract

Gravitational wave memory is an important prediction of general relativity, which has not been detected yet. Amounts of memory events can form a stochastic gravitational wave memory background. Here we find that memory background can be described as a Brownian motion in the condition that the observation time is longer than the averaged time interval between two successive memory events. We investigate, for the first time, the memory background of binary black hole coalescences. We only consider the spectrum of the memory background for a relatively low frequency range. So we can use the step function to approximate the waveform for each memory event. Then we find that the spectrum is a power law with index -2. And the amplitude of the power law spectrum depends on and only on the merger rate of the binary black holes. Consequently, the memory background not only provides a brand new means to detect gravitational wave memory but also opens a new window to explore the event rate of binary black hole mergers and the gravity theory. Space-based detectors are ideal to detect the gravitational wave memory background which corresponds to supermassive binary black holes. Since gravitational wave memory is only sensitive to the merger stage of binary black hole coalescence, the memory background will be an ideal probe of the famous final parsec problem.