Optimal Strategies for Gravitational Wave Memory Detection in Pulsar Timing Arrays

TL;DR

This paper develops two efficient detection statistics for gravitational-wave memory signals in pulsar timing data, enabling improved identification and parameter estimation of such signals in different SNR regimes.

Contribution

It introduces coherent and incoherent detection statistics analogous to existing methods, with a detailed analysis of their distribution and estimation accuracy across SNR levels.

Findings

Both statistics follow a chi-squared distribution with non-centrality parameters related to SNR.

Estimators are inaccurate at low SNR but become reliable at higher SNR.

The methods facilitate maximum likelihood estimation of gravitational-wave memory parameters.

Abstract

In this work we derive two computationally efficient frequentist detection statistics that can be used in searches for gravitational-wave bursts with memory in pulsar timing data. By maximizing the likelihood ratio in two different ways we construct a coherent statistic and an incoherent statistic, which are analogs of the $\pazocal{F}_e$ and $\pazocal{F}_p$ statistics commonly used for continuous-wave searches in pulsar timing data. We show that both statistics are $\chi^2$-distributed with varying degrees of freedom and non-centrality parameters given by the signal-to-noise (SNR) ratio of the signal present in our data. The statistics can also be used to compute the maximum likelihood estimators of amplitude parameters of a possible gravitational-wave memory signal in pulsar timing data. We find that in the low-signal regime ($\mathrm{SNR} \lesssim 5$), the estimators are inaccurate. However, in intermediate- to high-signal regimes, we show that these estimators can accurately determine the correct signal parameters.