Gravitational-wave memory and pulsar timing arrays

TL;DR

Pulsar timing arrays can detect gravitational-wave memory effects from supermassive black hole mergers, offering a new method to observe these cosmic events over vast distances.

Contribution

This paper develops the theory for detecting gravitational-wave memory from black hole mergers using PTAs and estimates their sensitivity and detection prospects.

Findings

PTAs are sensitive to gravitational-wave memory from black hole mergers.

Mergers of $10^8M_{ ext{sun}}$ black holes are detectable up to 1 billion light years.

Current PTAs have a marginal chance of detecting individual memory jumps.

Abstract

Pulsar timing arrays (PTAs) are designed to detect gravitational waves with periods from several months to several years, e.g. those produced by by wide supermassive black-hole binaries in the centers of distant galaxies. Here we show that PTAs are also sensitive to mergers of supermassive black holes. While these mergers occur on a timescale too short to be resolvable by a PTA, they generate a change of metric due to non-linear gravitational-wave memory which persists for the duration of the experiment and could be detected. We develop the theory of the single-source detection by PTAs, and derive the sensitivity of PTAs to the gravitational-wave memory jumps. We show that mergers of $10^8M_{\odot}$ black holes are $2-\sigma$-detectable (in a direction, polarization, and time-dependent way) out to co-moving distances of $\sim 1$ billion light years. Modern prediction for black-hole merger rates imply marginal to modest chance of an individual jump detection by currently developed PTAs. The sensitivity is expected to be somewhat higher for futuristic PTA experiments with SKA.